
    COHESIVE TECHNOLOGIES, INC., Plaintiff, v. WATERS CORPORATION, Defendant.
    Civil Action Nos. 98-12308-DPW, 99-11528-DPW, 01-12307-DPW.
    United States District Court, D. Massachusetts.
    Aug. 31, 2007.
    
      Lee C. Bromberg, Bromberg & Sunstein LLP, Erik Paul Belt, Boston, MA, Robert H. Stier, Jr., Pierce Atwood, Portland, ME, for Plaintiff.
    Ralph A. Loren, Palmer & Dodge LLP, Sibley P. Reppert, William A. Scofield, Jr., Lahive & Cockfield, LLP, Boston, MA, for Defendant.
   MEMORANDUM AND ORDER

DOUGLAS P. WOODLOCK, District Judge.

Plaintiff Cohesive Technologies produces equipment for high-performance liquid chromatography (“HPLC”), a process scientists use to separate a mixture of chemical compounds into its various components. Cohesive has patented an apparatus and method for increasing the efficiency of HPLC separations by increasing the rate of flow of solvent (the liquid in which the mixture of compounds is dissolved) through the HPLC column, which is filled with solid particles. These cases stem from allegations by Cohesive Technologies that the Oasis HPLC columns manufactured by Waters Corporation infringe Cohesive’s 5,772,874 ('874) and 5,919,368 ('368) patents.

After a sixteen day trial, a jury in Civil Action No. 98-12308 returned a verdict for Cohesive finding infringement and upholding the validity of the '874 patent. Waters has moved for a judgment as a matter of law notwithstanding the verdict. Waters further alleges that the '874 patent is unenforceable because it was procured by inequitable conduct on the part of Cohesive. Cohesive claims that Waters’ infringement was willful and thus that the court should award enhanced damages and attorneys fees on that ground. After the jury verdict, I held a bench trial on the issues of inequitable conduct, willful infringement, and damages.

Cohesive filed two separate civil cases related to Civil Action No. 98-12308. Civil Action No. 99-11528 alleges that the same columns that infringed the '874 patent infringe Cohesive’s '368 patent, a divisional patent of the '874 patent. In the second related case, Civil Action No. 01-12307, Cohesive seeks to enjoin Waters from making, selling, or using columns with 25-micron-sized particles, as opposed to the 30-micron-sized particles used in the accused columns in the other two cases.

To provide a general context for discussion, a brief description of the technology at issue might be helpful. High-performance liquid chromatography is a form of column chromatography used frequently in biochemistry and analytical chemistry. HPLC is used to separate components of a mixture by using a variety of chemical interactions between the substance being analyzed and the chromatography column. An HPLC column generally consists of a “stationary phase” of solid particles, such as silica. Silica is a sand-like material to which other compounds adsorb with different affinities. Performing HPLC generally involves the elution of a mixture of compounds dissolved in a appropriate solvent, called the “mobile phase,” over the stationary phase. As the mobile phase elutes along the column, the compounds dissolved in the solvent react with and adsorb to the solid particles. Because of the variation in adsorption rates to the stationary phase, the components of the compounds elute at different times from the column, allowing the scientist to collect and analyze the separated components.

The '874 patent, issued on June 30, 1998 to Cohesive’s Hubert Quinn and Joseph Takarewski, claims an apparatus for what Cohesive calls “turbulent flow” HPLC. The '368 patent issued on July 9, 1999 and claims the method for using the '874 apparatus. The invention purports to provide a means for efficient HPLC separations within shorter total elution or run times. Cohesive and Waters both sell hardware for liquid chromatography systems as well as the disposable or consumable columns that the systems require.

In Part I of this memorandum, I will address the question of infringement and validity of the '874 patent raised by Waters’ renewed motion for judgment as a matter of law in Civil Action No. 98-12308. In Part II, I will address my factual findings and conclusions of law on the issues of inequitable conduct and willful infringement in that case. In Part III, I will address the questions of infringement and validity of the '368 patent raised by cross motions for summary judgment submitted by the parties in Civil Action No. 99-11528. In Part IV, I will address the question of summary judgment in Civil Action No. 01-12307, and, in Part V, I address the issue of damages.

I. Post-Jury Trial Motions in Civil Action No. 98-12308 Regarding the '874 Patent

In Civil Action No. 98-12308, Cohesive alleged that Waters infringed the '874 patent by its manufacture and sale of 1 x 50 mm Oasis HLB Extraction Columns containing Oasis 30 micron particles, and Waters counterclaimed that the '874 patent was invalid by reasons of anticipation and obviousness under 35 U.S.C. §§ 102 and 103. The issues of infringement and invalidity on the grounds of obviousness were tried to a jury, which returned a verdict in favor of Cohesive after I granted a directed verdict for Cohesive on the issue of anticipation under 35 U.S.C. § 102. Waters filed a motion for a judgment as a matter of law on the issue of infringement at the close of the evidence, which I denied. Waters has renewed its motion for judgment as a matter of law, adding a motion for a judgment as a matter of law on the issue of obviousness.

A. Infringement

1. “Rigid” particles

Waters first argues that Cohesive has failed to provide sufficient evidence to support a jury verdict that the particles in Waters’ columns are rigid. Every claim of the '874 patent requires that the accused device contain a chromatographic column with a bed of “rigid” particles. Thus, Waters’ OASIS HLB solid particles must be rigid in order for Waters to be liable for infringement.

The jury found that Waters’ device did contain rigid particles. In the Markman hearing in this case, I construed “rigid” to mean “an object’s capacity to maintain substantially zero changes in density and volume under packing pressure of at least about 5000 psi and as a consequence substantially to resist plastic deformation under such pressure.” I further defined “plastic deformation” as “a change in the dimensions of an object under load that is not recovered when the load is removed.” I explicitly did not construe the term “rigid” to exclude polymeric particles (as opposed to the monomeric particles referred to in the preferred embodiment of the '874 patent).

Quinn’s trial testimony provides sufficient evidence that the particles used in the accused Waters columns are rigid. He testified on direct examination that the Waters’ particles met the claim construction above:

Q: If rigid means an object’s capacity to maintain substantially zero changes in density and volume, under packing pressure of at least about 5,000 psi, and as a consequence, substantially to resist plastic deformation under such pressure, do the Waters’ particles qualify as rigid?
A: Yes, they do.
Q: How do you know?
A: Because one of the things that I did was to take the Waters particles and pack them at 5,000 psi, and the particles passed that test because they didn’t plug up or they didn’t crush or they didn’t collapse.

Tr. Day 4 at 38. Cohesive’s attorney continued to examine Quinn on his observation that the particles did not collapse at 5,000 psi or greater:

Q: Now, when you packed the particles at 5,000 psi, the Oasis particles, did they maintain substantially zero changes in density and volume under the packing pressure?
A: Yes, they did.
Q: And did they crush or deform or exhibit any plastic deformation under that packing pressure?
A: No, they did not.
Q: And when you packed them at 10,-000 psi, did they exhibit any crushing or collapsing or plastic deformation then?
A: No, they did not ... There was no trace of the particles crushing or compressing or plugging up. There was no — I saw no evidence of that.

Id. at 39-41. Quinn further testified that, “if the particles collapse, they will shut off all the flow channels, and you won’t be able to get any flow through the column.” Id. In other words, Quinn testified he was able to determine whether the particles collapsed under pressure by simply observing the flow of the packed column. I determined in a three-day Daubert hearing before trial that Quinn was a qualified expert and used scientifically reliable methods to generate his expert opinion. After post-trial review, I similarly conclude that Quinn’s testimony provides sufficient evidence for a reasonable fact finder to determine that the Waters particles are rigid within the meaning of the '874 patent.

Waters does not dispute that Quinn’s method of observing the particles to determine rigidity is scientifically reliable. Waters argues instead that Cohesive provided no evidence of the first part of a two part definition of “rigid.” More particularly, Waters asserts that in order for Cohesive to prove that Waters infringed any claim of the '874 patent it must provide evidence that the particles (1) maintain substantially zero changes in density and volume under pressure of at least about 5000 psi, and (2) substantially resist plastic deformation at that pressure. It argues that Cohesive has provided evidence of (2) but not (1). A particle can compress under pressure, Waters asserts, but still seem as though it resists plastic deformation if it quickly regains its structure when pressure is released. Waters likens a particle that satisfies only element (2) of the definition to a Nerf ball, which would collapse under high pressure but immediately spring back to its original shape when normal pressure resumes.

Although I agree with Waters that Cohesive must provide evidence of both factors in order to meet the claim construction of “rigid,” I find that Cohesive has done so. As stated above, Quinn testified that he observed no compression while applying 5,000 psi and 10,000 psi of pressure. Waters argues that the testimony is conclusory and thus not sufficient evidence of rigidity. But Quinn’s testimony was not merely conclusory. He stated that the proper test for detecting compression was to observe the particles for plugging or interruption in flow rate. He testified that he saw no evidence of compression during his experiment.

Waters argues that its own expert’s testimony that the Waters particles collapse under pressure (Tr. Day 11 at 48-68) combined with testimony from expert Savaria that polymeric particles are generally more compressible than monomeric particles (Tr. Day 8 at 53) militate in favor of overturning the jury’s verdict on infringement. Regardless of any evidence that rebuts Quinn’s conclusion, however, Quinn’s testimony was sufficient to create a material dispute of fact for the jury to resolve. Thus, there is no basis for a judgment as a matter of law with respect to whether the particles in Waters’ accused device are rigid.

2. “Interstitial Volume Fraction of at least 45%”

Waters claims that Cohesive’s calculation of interstitial volume fraction of 45% or more, which is a limitation of claims 1, 3, 7, 9, and 20 of the '874 patent, was not supported by reliable data. Effectively, Waters renews its Daubert challenge to Quinn’s testimony regarding his calculation of the interstitial volume of Waters particles.

Interstitial volume fraction is the volume of the space between the particles in the column divided by the total volume of the column. The definition of interstitial volume does not include the volume of the space in the pores in the solid particles, but only the volume between each particle. Thus, the interstitial volume fraction is equal to the volume of the column minus the volume of the particle pores minus the volume of the skeletons of the particles, expressed as a percentage of the total volume of the column. In order to support a claim of infringement of the '874 patent, Cohesive must provide sufficient evidence that Waters’ column contains an interstitial volume of 45% or more.

Cohesive has produced sufficient and reliable evidence that Waters’ column has an interstitial volume of 45% or greater. Cohesive’s Quinn measured the interstitial fraction of the Waters column by a method called size exclusion chromatography (“SEC”). See Tr. Day 4 at 87-88. (“I knew the interstitial fraction because I determined it by size exclusion.”) (“I wanted to use an independent method [to calculate the interstitial fraction] which was size exclusion chromatography.”)

Size exclusion chromatography allows one to calculate interstitial volume directly by flowing variously sized molecules, dissolved in solvent, through the column and measuring the volume it takes to elute them (“elution volume”). The larger the molecule, the less likely it will fit into the pores of the particles and the more quickly the molecule will pass through the column. The smaller the molecule, the more likely it will adhere to the pores in the particles and the more volume it will take to elute it from the column. By determining the various elution volumes for different sized molecules in a class, one can deduce the pore volume, the interstitial volume, and thus the interstitial fraction as a percentage of the entire column.

Quinn testified that he could not run the size exclusion chromatography on Waters’ accused column — a 50 x 1 mm column— because his equipment was not precise enough to measure the volume changes accurately in such a small column. See Tr. Day 4 at 66. Instead of using Waters’ 50 x 1 mm column, Quinn packed a larger 2.1 x 100 mm column himself with Waters’ Oasis 30 micron particles. He then used size exclusion chromatography to determine the interstitial volume fraction of the larger column. He determined, using this method, that the interstitial volume was about .46, or 46%.

Waters claims that (1) Quinn failed to use the correct value for the density of Waters particles to determine the interstitial volume fraction, and (2) Quinn’s 2.1 x 100 mm column that he packed with Waters particles failed catastrophically and thus any resulting calculations were unreliable. Waters points to Quinn’s testimony under cross-examination regarding the density of Waters’ particles:

Q: And if your measurements are correct, then according to your calculations, the density of the OASIS particles should be about 1.8?
A: Yes, according to these measurements.
Q: Do you know what the density of OASIS 30 micron HLB particles is?
A: Yes.
Q: What is it?
A: It’s around 1.2.
Q: 1.2. But your measurements — your SEC measurement that you’re relying on in this case show a density of 1.8, don’t they?
A: Yes, they do.
Q: So there’s something wrong with your numbers?
A: Yes, there is.
Q: And these are the numbers you are relying on in this suit?
A: Mr. Scofield, I’m not relying on those numbers for the interstitial fraction.

Tr. Day 5 at 100-01. Waters also refers to the cross-examination testimony regarding “a void” in the 2.1 x 100 mm column that Quinn packed:

Q: So the column that you are relying upon for the SEC measurements and the empirical derivation of the Kozeny constant of 270 that you wish to apply in this case, that column, that one single column that you used, is a column that experiences a catastrophic problem and a void?
A: Yes, after the SEC measurements were made, correct.

Tr. Day 6 at 86 In 16-21.

Neither of Waters’ arguments are persuasive. Quinn did not rely upon his (admittedly inaccurate) particle density calculation to determine the interstitial volume of the Waters column. He used an “independent” method of size exclusion chromatography which involved measuring only the various elution volumes of different sized molecules passed over the Waters particles.

It is true that, in order to check his work, Quinn attempted to use his calculation for interstitial volume to calculate a constant in the Ergun equation. Quinn testified that one way to measure interstitial volume indirectly is by utilizing a relationship expressed in the Kozeny-Carman equation. The “pressure drop” of a column is related to the interstitial volume of the column by a set of equations, expressed first in Darcy’s law, Tr. Day 4 at 77-78, and then further refined by scientists Kozeny, Carman, and Blake. Id. at 78. The resulting equation that applies to “turbulent flow,” as opposed to laminar flow, chromatography is called the Ergun equation. Tr. Day 4 at 81-83.

Quinn stated that the Ergun equation contains several parameters that one needs to determine empirically: the length of the column, the particle size, and the flow rate, for example. Tr. Day 4 at 80 In 3-7. In addition, one must also determine the value of a numerical constant, which Quinn called the Kozeny constant. Id. at 80 In 8-15.

Quinn did not use the Ergun equations to calculate the interstitial volume. Rather, he used the interstitial volume that he measured empirically to derive the Kozeny constant. The purpose of doing this, he testified, was to double check his work. He used size-exclusion chromatography to calculate the interstitial volume fraction, plugged the interstitial volume fraction into the equation with the other parameters, such as pressure drop, and determined that the Kozeny constant was 270. This matched, according to Quinn, the well-known value of the Kozeny constant for his particular experiment. See Tr. Day 4 at 88-89. Quinn testified on cross-examination that he did not rely upon the density of the particles or the Kozeny constant to determine the interstitial volume fraction:

The density measurements that you’re referring to does not have anything to do with the determination for interstitial fraction that I made in this size exclusion. Because the interstitial fraction was made directly by me. Okay. And it doesn’t depend on any value for the density. It is independent. It was determined directly. I simply included those numbers there for additional information, but those numbers had no bearing whatsoever on my determination of the interstitial volume.

Tr. Day 5 at 101 In 20. See also Tr. at 88 In 19-23. (“I did a ratio and calculated the interstitial fraction without the use of any Kozeny constant because they drop out in this analysis.”).

Waters contends that in back-calculating the Kozeny constant, Quinn used an erroneous measurement for the density of the particles. Whether Quinn used an erroneous measurement in calculating the constant is unclear from the testimony. But even if the Kozeny constant he calculated was inaccurate, Cohesive has still provided enough evidence that Waters’ interstitial fraction volume is greater than 45%. Quinn stated several times during cross-examination that he used an independent method of size-exclusion chromatography to achieve that result. Waters does not contend that size exclusion chromatography is an unreliable way of determining interstitial volume fraction. Thus, Quinn’s testimony is sufficient evidence that the interstitial volume fraction of the Waters column is greater than 45%.

Waters’ second argument — that Quinn’s measurement of the interstitial volume is unreliable because the size-exclusion chromatography column failed — is also unavailing. Quinn testified that the failure of the 2.1 x 100 column occurred after he measured the interstitial fraction. Furthermore, the fact that the column was a different size than Waters’ accused column is likely immaterial. Interstitial volume is a percentage of total volume of the particles. There is no reason based upon this record to assume that the percentage volume of the space between particles depends upon the size of the column. Waters provides no evidence that the size-exclusion chromatography experiment conducted by Quinn was based upon unreliable experimentation or principles. The possibly erroneous calculation of the Kozeny constant notwithstanding, Cohesive has provided sufficient evidence to support a jury verdict that Waters’ accused device infringes the interstitial volume fraction limitation.

3. Interstitial channels with mean cross-section dimensions not less than 5 microns.

Waters argues that Cohesive failed to prove infringement of claims 3, 16, 20 that require interstitial channels with mean cross-section dimensions not less than 5 microns. On direct examination, Quinn testified that “if you have particles that are greater than 30-micron and you have an interstitial fraction that is greater than 45%, then the spacing between the particles will not be less than 5-micron.” Tr. Day 4 at 101. Waters argues that because Cohesive did not provide adequate evidence of the interstitial fraction being greater than 45%, there is no evidence of cross-section dimensions of less than 5 microns. As detailed above in Section 1.A.2, because Cohesive produced enough evidence to support a jury verdict that Waters’ columns have an interstitial volume fraction of greater than 45%, Quinn’s testimony on direct is sufficient evidence to support a verdict of infringement regarding the size of the cross-section dimensions as well.

B. Validity

The jury found that Waters had not established by clear and convincing evidence that the '874 patent is invalid because the claimed invention was obvious. Waters asserts that the verdict should be overturned because it is not supported by substantial evidence.

This contention stumbles at the threshold of the protocol for post-verdict review. Waters waived this argument by failing to move for a judgment as a matter of law with respect to obviousness of the '874 patent at the close of all the evidence before the case was submitted to the jury.

Although Waters did move for judgment as a matter of law at the close of the evidence, it moved with regard only to the issue of infringement. As is well-established, “a motion for judgment as a matter of law made at the close of all the evidence preserves for review only those grounds specified at the time, and no others.” See Correa v. Hospital San Francisco, 69 F.3d 1184, 1196 (1st Cir.1995). In Correa, the defendant made a post-trial motion for a judgment notwithstanding the verdict on a legal theory it had failed to preserve at the close of the evidence. The court stated that:

[A] renewed motion for judgment as a matter of law under Fed.R.Civ.P. 50(b) is bounded by the movants’ earlier Rule 50(a) motion. The movant cannot use such a motion as a vehicle to introduce a legal theory not distinctly articulated in its close-of-evidence motion for a directed verdict.

Id. Waters failed to move for judgment on the question of obviousness at the close of all the evidence. Thus, it cannot pursue that theory on a renewed motion.

Waters contends that because “[o]bvi-ousness is a question of law, and is thus freely reviewable on appeal,” Stiftung v. Renishaw PLC, 945 F.2d 1173, 1182 (Fed. Cir.1991), I should review their motion for judgment as a matter of law regarding obviousness even though they failed properly to preserve it. Waters cites Sjolund v. Musland for a similar proposition. See 847 F.2d 1573, 1576 (Fed.Cir.1988) (“[Wjhere a jury is asked to decide a question of law which depends on underlying factual determinations, the jury’s legal conclusion is subject to independent review by the court on appeal.”). These cases discuss the substantive standard for reviewing an obviousness determination on appeal. They are inapposite to whether Waters preserved its argument as is required by procedural law in this circuit. See Correa, 69 F.3d at 1196. Waters cites no case in which a district court judge independently reviewed a jury verdict of non-obviousness after the alleged infringer had waived the argument earlier in the proceedings. And Waters does not dispute that it failed to move for a judgment at the close of the evidence regarding obviousness. Waters is foreclosed from presenting its obviousness contention in a “renewed” motion to overturn the jury verdict.

C. Conclusion

Because Cohesive has provided sufficient evidence to support the jury verdict in Civil Action No. 98-12308, I will deny Waters’ renewed motion for judgment as a matter of law notwithstanding the jury verdict.

II. Bench Trial: Findings and Conclusions Regarding Inequitable Conduct and Willful Infringement

A. Inequitable Conduct

Waters contends that Cohesive’s patent is unenforceable due to inequitable conduct because the applicants for the '874 patent omitted and misrepresented material facts in their application to the Patent and Trademark Office (PTO). In order to prevail, Waters must show by clear and convincing evidence that one of Cohesive’s applicants made a misrepresentation, that the misrepresentation was material, and that it was made with intent to deceive. See Honeywell Intern. Inc. v. Universal Avionics Systems Corp., 488 F.3d 982, 999 (Fed.Cir.2007). After a bench trial on this issue, I find and conclude that Waters has failed to produce clear and convincing evidence that Cohesive intended to deceive the patent examiners. The following constitutes my findings of fact and conclusions of law on this issue pursuant to Fed. R.Civ.P. 52.

1. Facts

The following findings of fact are based upon the live testimony of Hubert Quinn and Robert Schiller, and further affidavit testimony of Hubert Quinn.

a. Patent Prosecution History Summary

Hubert Quinn and Joseph Takarewski are the named inventors on '874 and '368 patents, both of which are assigned to Cohesive. The application for both patents (the Quinn application) was based on one specification, and was filed originally on November 2, 1995. Claims 1-15 of the '874 invention include a limitation that requires “loading ... solute through [the column] ... at a reduced velocity greater than about 5,000.” Another limitation contained in Claim 1 of the '874 patent requires “an interstitial volume between particles of not less than about 45% of the total volume of said column.” ('874 patent Col. 20).

Although none of the claims mention the term “turbulent flow,” Cohesive distinguished the claimed invention from the prior art in the patent application on the basis that the invention provided for turbulent, as opposed to laminar, flow. Cohesive described its invention as, “[a] method and apparatus for liquid chromatography at improved analytical and preparative speeds and quantities that involves flow of fluids through the column at flow rates sufficient to induce turbulent flow in those fluids.” Cohesive also referred to its invention in the patent application and specification as “turbulent flow chromatography.” By utilizing higher flow rates and pressure, the invention was designed to allow chromatographic separations to be performed with greater accuracy and speed than would laminar flow technology.

In its application, Cohesive cited the Af-eyan '270 patent (U.S. Patent No. 5,019,-270) as an instance of prior art. That art describes a method of chromatography that provides higher speed chromatographic separations through the use of higher velocity flow. Cohesive also cited an article by Pretorius and Smuts entitled “Turbulent Flow Chromatography: a New Approach to Faster Analysis,” Analytical Chemistry, vol. 2, pp. 274-80 (1966) (“Pretorius reference”). In the original application, Cohesive stated that, “[t]he use of turbulent flow liquid chromatography would appear to be contraindicated by the teachings of Pretorius, et al., who cites at page 280, col. 2, that a separation in a tube with a diameter of 0.1 cm and a length of 2000 cm ... would apparently take 24 days.” Waters asserts that Cohesive’s statement misquoted the Pretorius reference, page 280 col. 2, which actually states that analysis time can be as short as 100 seconds under turbulent flow conditions, and says in the next sentence that a separation would take up to 24 days under laminar flow conditions. Cohesive does not deny that it misquoted the reference, but claims the misrepresentation was unintentional.

The PTO rejected that original application as anticipated or rendered obvious by the Afeyan patent, but stated it was non-obvious with respect to the Pretorius reference. On June 11, 1996, Cohesive filed a continuation-in-part application (Quinn CIP application), which was ultimately approved. The Examiner initially rejected the CIP application on May 1, 1997, as anticipated by or rendered obvious by the Afeyan patent. In response to this action, Cohesive filed an Amendment B and Remarks dated July 24, 1997, arguing that the Afeyan patent did not anticipate or render obvious the Quinn invention. The examiner rejected all claims in this continuation-in-part of the original application on September 10, 1997, citing the Afeyan patent. Cohesive then filed another Amendment on December 31, 1997 (Amendment After Final), along with a declaration from Professor Georges Guiochon, an expert in chromatography. It is from the Amendment in Final that the Quinn patents were ultimately issued.

b. The Guiochon Declaration

The Guiochon declaration, which was included in the Amendment After Final, stated that the Quinn invention was novel and non-obvious:

The apparatus and method were certainly not obvious to me at the time. I concluded then and am still of the same conclusion ... that the invention described in the '367 application was and is an extremely important, ingenious, and unobvious advance in the art of chromatography. ... I am not aware of any prior art that possesses the combination of elements of the present invention including the interstitial volume in excess of 45% combined with rigid, solid, porous particles.

See Guiochon Deck, Def. Exhibit 9 at 4.

Guiochon avoided the term “turbulent flow” when describing Quinn’s invention. His declaration stated that the “essence of the invention described in the '367 application as I view it is that the flow through the interstitial channels between the particles in the chromatographic column is at an abnormally high rate for such a column,” see Guiochon Decl. page 4, and that “a reduced velocity greater than about 5,000 for the liquid flow is believed to be sufficient to trigger the observed phenomenon.” Schiller admitted that in previous drafts of the Guiochon declaration, these two statements read “between the particles in the chromatographic column necessarily turbulent as opposed to laminar” and “... sufficient to induce turbulent flow," respectively (emphasis supplied). Schiller testified that he changed the sentences to omit any reference to the term “turbulent” because Guiochon “had reservations as to whether the flow was definable within the meaning of the word turbulence, which was up for a great many different interpretations.” See Bench Trial Tr. Day 5 at 57 In 7-9.

In addition, Cohesive argued in the Amendment After Final, citing Guiochon, that the Afeyan patent taught methods using laminar flow, and distinguished the Quinn invention as teaching non-laminar, or turbulent flow. Cohesive relied on statements in the Guiochon declaration that, for example: “the intraparticle and interparticle flow described in Afeyan can only be considered laminar.” (Guiochon Decl. pg 5.); “Ramsay confirms the use of laminar flow ...” (Guiochon Decl. pg 6); “the [Nilsson] patent never teaches or suggests the use of any high value of reduced velocity nor of any turbulent flow characteristics of the particles.” (Guiochon Decl. pg 7). Guiochon’s submitted declaration, of course, never refers to the Quinn invention as turbulent flow chromatography, though he stated that the '367 method has “turbulent flow characteristics.”. See Guio-chon Decl. at 7.

Although Cohesive’s patent application calls the Quinn invention “turbulent flow” technology, Cohesive failed to disclose that Guiochon had reservations about using the term “turbulent” to describe the flow Quinn created. Indeed, Guiochon told Cohesive’s patent attorney, Schiller, via letter prior to submitting his declaration that he did not think that the flow used in the Quinn invention was technically turbulent flow:

It does not bother me to say that X or Y ‘does not teach the use of turbulence’ as long as it is true that they do not (that would be something else if Pretorius was a reference but he is not). Still, I do not believe that the flow is turbulent under the conditions stated in the patent. I still do not understand what is happening, but, as I understand it, you can patent something that you have done and can reproduce, whether you understand it or not, right?

(Guiochon faxed letter to Schiller, 12/15/97, Def. Ex. 19.) Moreover, in his Declaration, Guiochon stated that he had previously been of the opinion that “turbulent flow in liquid chromatography would not work,” and that he was “very surprised” by the data that Quinn gave him regarding the invention. (Guiochon Decl. pg 3-4.) Guio-chon then edited his declaration to omit any reference to the Quinn invention as turbulent flow, preferring to call it “the Quinn effect.” Cohesive did not inform the patent examiner that Guiochon had made these edits.

The Guiochon Declaration also included a calculation of “maximum reduced velocity” of 1,390 for the Afeyan patent — less than half the minimum value of the velocity claimed in the Quinn invention. In the calculation, Guiochon used what he stated was a “reasonable value of about 1 x 10 " for the diffusion coefficient.” Waters argues that if Guiochon had used the accurate diffusion coefficient, he would have calculated a maximum reduced velocity in the Afeyan patent of 139,000 to 1,390,000, a number well above the minimum 5,000 claimed in the Quinn invention.

Guiochon’s declaration also included a statement that “[ajnother characteristic of the present invention that appears to me to be unique is the provision of an interstitial volume of 45%.” Guiochon Decl. at 5. Waters alleges that both Guiochon and Quinn knew that the Pretorius Patent Nos. 3,493,497 (the '497 patent) and 4,208,284 (the '284 patent) each disclosed chromatography columns with an interstitial volume greater than 45%, and thus that Guio-chon’s statement was a misrepresentation.

Cohesive and Waters do not dispute the general facts of the prosecution history. The sole dispute is over whether Cohesive’s omissions and alleged misrepresentations were material, and, if so, whether there is clear and convincing evidence that Cohesive intended to deceive the patent examiner.

2. Discussion

Waters asserts that Cohesive engaged in inequitable conduct by (1) stating that “turbulent flow” was contraindicated in the Pretorius and Smuts article, and then, in support, misquoting page 280, col. 2 of that reference by stating that a chromatographic separation would take 24 days rather than 100 seconds, (2) failing to disclose the opinion of Guiochon that the Quinn invention did not teach turbulent flow and that turbulent flow was not novel and had been shown in the prior art by Pretorius, (3) falsely stating that an interstitial volume of 45% was “unique” in the art, knowing that the Pretorius patents disclosed that element, and (4) inaccurately representing that the Afeyan patent taught a maximum reduced velocity of 1,390, a calculation which relied upon an erroneous particle diffusion coefficient.

Patent applicants have a duty to act with good faith, honesty, and candor when submitting their applications to the Patent and Trademark Office. See Honeywell Intern. Inc. v. Universal Avionics Systems Corp., 488 F.3d 982, 999 (Fed.Cir.2007). If a patent applicant breaches this duty, an otherwise valid patent becomes unenforceable. See id.; J.P. Stevens & Co., Inc. v. Lex Tex Ltd., Inc., 747 F.2d 1553, 1559 (Fed.Cir.1984) (stating that inequitable conduct is broader than common law fraud and “includes failure to disclose material information, or submission of false material information, with an intent to mislead.”).

The standard of proof for finding inequitable conduct is a high one; there must be clear and convincing evidence that Cohesive (1) failed to disclose material information or submitted false information in its dealings with the PTO, and (2) that it did so with the intent to deceive the patent examiner. J.P. Stevens & Co., Inc., 747 F.2d at 1559. Gross negligence does not suffice as intent to deceive, Kingsdown Med. Consultants, Ltd. v. Hollister, Inc., 863 F.2d 867, 876 (Fed.Cir.1988), and materiality for purposes of this determination means that there is a substantial likelihood that a patent examiner would have considered the omitted information important in deciding whether to allow the application to issue as a patent. See Molins PLC v. Textron, Inc., 48 F.3d 1172, 1179 (Fed.Cir.1995).

The nondisclosure or misrepresentation to the patent examiner must meet threshold levels of both materiality and intent. Id. at 1178. Once the threshold levels of materiality and intent have been established, the trial court must weigh materiality and intent to determine whether the equities warrant a conclusion that inequitable conduct occurred. Id. The more material the information misrepresented or withheld by the applicant, the less evidence of intent will be required in order to find inequitable conduct. Honeywell Intern., Inc., 488 F.3d at 999 (citing N.V. Akzo v. E.I. DuPont de Nemours, 810 F.2d 1148, 1153 (Fed.Cir.1987)). If the court finds inequitable conduct, it must hold that the patent claims at issue are unenforceable.

a. Misrepresentations regarding the Pretorius and Smuts references

Cohesive stated in its patent application that the Pretorius, et al., reference “contraindicated turbulent flow in liquid chromatography.” Waters asserts that in support of this conclusion, Cohesive intentionally misquoted the Pretorius reference as concluding that a separation using turbulent flow in liquid chromatography would take 24 days, when the article actually says 100 seconds.

Cohesive admittedly did misquote the reference. And the Pretorius reference does, indeed, state that high rates of turbulent flow in liquid chromatography could reduce separation time to 100 seconds (as opposed to 24 days for laminar flow.) The patent examiner would likely have relied on this fact in order to determine whether the Quinn invention, which touts high-speed separations, was anticipated by the Pretorius patent or otherwise rendered obvious by it. Thus, I find the misquote would have been relevant to the patent examiner. Notwithstanding the Pretorius results, however, I found as a matter of law in Civil Action No. 98-12308 that the reference did not anticipate the '874 patent. For its part, the jury supportedly found that the Pretorius reference did not render the Quinn invention obvious. Therefore I conclude the Pretorius misquote is not so material as clearly to render Cohesive’s patent anticipated or obvious as a matter of law.

Even though the misstatement regarding the Pretorius result was relevant and arguably material, I find no evidence of Cohesive’s intent to deceive the patent examiner. The patent application included an extended discussion of the details of the prior art. The misstatement came from one paragraph in a long article that included both the timed separation results for laminar and turbulent flow in liquid chromatography, one right after another. The two results could reasonably have been transposed unintentionally. Without more evidence that Cohesive misrepresented the Pretorius results intentionally, I conclude that the misquote was a negligent error.

b. Omission of Guiochon’s Opinion that the Quinn Invention Did Not Teach “Turbulent Flow”

Waters asserts that Cohesive intentionally failed to disclose Guiochon’s opinion that the Quinn invention did not teach what he would call “turbulent” flow in order to deceive the patent examiner. Because I credit Cohesive’s testimony that it did not believe Guiochon’s definitional distinction was material to the ultimate conclusion of his declaration, I do not find clear and convincing evidence of Cohesive’s intent to deceive the patent examiner.

Guiochon stated in the declaration that the Quinn invention was non-obvious, not anticipated by prior art, and “ingenious.” He stated that he was surprised by the efficiency of the separations that Quinn achieved with abnormally high-flow conditions, and described how the prior art had only appeared to teach “laminar flow” rather than flow with “turbulent characteristics.”

It is true that Cohesive never disclosed to the patent examiner Guiochon’s opinion that the flow in Quinn’s invention was not truly “turbulent.” Cohesive does not dispute this fact. “Turbulent flow,” however, is not defined in the specification, nor is it mentioned in any of the actual claims of either the '864 or '368 patents. Schiller testified that it “never crossed his mind” that the patent examiner might reject the application based upon Guiochon’s reluctance to call the Quinn invention “turbulent flow.” Indeed, the patent examiner issued the patent despite the fact that Guiochon’s declaration does not characterize the Quinn invention as using turbulent rather than laminar flow.

The essential conclusion of the Guiochon declaration was that he found the Quinn invention to be novel and non-obvious compared to laminar flow chromatography and the prior art, regardless of whether he would employ the technical label of “turbulent.” He stated in his deposition testimony:

There are two things. There’s the Quinn effect and the interpretation of the Quinn effect. I consider the Quinn effect as real. I don’t agree with Mr. Quinn in the interpretation of the Quinn effect and I have a good one for myself. What I understand — it’s irrelevant to the existence of the Quinn effect.

Guiochon Dep. at 46-47.

Guiochon’s opinion that the flow was not definitionally “turbulent” was arguably relevant, in that a patent examiner could have considered it in determining whether the Quinn invention was anticipated by prior art. On the other hand, the patent specification makes it clear that the inventors merely theorized that turbulent flow was the cause of the increased efficiency and speed of chromatographic separations. See '874 Patent at 8 (“It is believed that under such conditions, turbulent flow of the mixture is induced ... ”). The essence of the invention was the enhanced performance of the chromatographic separation, and not the theory behind it. Thus, although I find Guiochon’s definitional reservations arguably relevant to a full discussion of invention, I do not find the patent examiner’s overall determination that the invention was novel would have changed had the drafting history of Guio-chon’s declaration on this point been disclosed.

No doubt in hindsight it is apparent that it would have been better practice to have informed the patent examiner of Guio-chon’s opinion. Nonetheless, I cannot find by clear and convincing evidence that Cohesive’s omission constituted intentional deceit. There is a competing explanation for Cohesive’s omission, which is that it believed the Guiochon’s reluctance to label something as technically “turbulent” was a matter of mere semantics. While this competing explanation, is self-serving, it vitiates the effort to show intentional misrepresentation to the demanding clear and convincing standard. As a result, I find no inequitable conduct with regard to the material omission.

For similar reasons, Cohesive’s failure to disclose Guiochon’s opinion that the Pre-torius reference taught turbulent flow has likewise not been shown to be intentional. Guiochon’s declaration stated that the Quinn invention was not anticipated or rendered obvious by prior art. Guiochon clearly knew of the Pretorius reference; he identified it in his faxed letter to Schiller. Waters claims that this faxed letter is evidence that Guiochon thought the Preto-rius reference taught turbulent flow in liquid chromatography. But it is at most unclear from the Guiochon fax whether he believed that the Pretorius reference taught turbulent flow in liquid chromatography. And even if Guiochon considered the Pretorius reference to teach so-called “turbulent flow,” in liquid chromatography, it is far short of establishing clear and convincing evidence of Cohesive’s deceptive intent. Cohesive reasonably believed that Guiochon did not consider turbulent flow definitionally the same as the flow created in the Quinn invention. If Guio-ehon did believe that the Pretorius reference taught turbulent flow, it is consistent with his conclusions that (1) the Quinn effect is not technically turbulent flow, and (2) the prior art does not anticipate or render obvious the Quinn invention. Moreover, the patent examiner had determined well before Cohesive filed its Amendment that the Pretorius reference, the title of which included the term “turbulent flow,” did not render the Quinn invention obvious. Thus, I find that (1) there is no showing by clear and convincing evidence of deceptive intent on the part of Cohesive by failing to disclose Guioehon’s opinion that the Pretorius reference taught turbulent flow, and (2) it is unlikely the disclosure would have had a material effect on the patent examiner’s disposition of the patent application.

c. Alleged misstatement that 45% interstitial volume is “unique”

Guiochon also stated in his declaration that an interstitial volume of 45% “appears to me to be unique.” Waters contends that this statement was false, and that both Quinn and Guiochon were aware that several prior art references, specifically the Pretorius patents, disclosed an interstitial volume of greater than 45%. Waters also claims that this information was highly material.

Guiochon did state in his declaration that a 45% interstitial volume fraction was unique to the Quinn invention, but he made the statement to distinguish it from the Afeyan technology:

Another characteristic of the present invention that appears to me to be unique is the provision of an interstitial column of 45% claimed in claims 1 and 36 of the '367 application, and which appears to contribute to the capability of the invention to provide the requisite high reduced velocity of 5000 or more. Afeyan et. al. teach using a column with a ‘void fraction of 0.35" (Col. 15, lines 31-32) which is far below the claimed interstitial volume of 45%.

Guiochon Decl. at 5. That paragraph is the final paragraph of a section which discusses only the Afeyan references. There is no evidence that Guiochon was trying to distinguish the Pretorius references on this ground. Defendant does not claim that Afeyan teaches an interstitial volume of greater than 45%. Furthermore, the patent examiner had already determined that the Quinn invention was novel over the Pretorius patents in an earlier application; the Amendment with which Guio-chon’s declaration was filed was a response to, among other things, the novelty of the Quinn invention over the Afeyan patent. Thus, I do not find clear and convincing evidence that Guiochon, and through him Cohesive, made a material representation in this paragraph, or, if he did, that he did so intentionally.

d. Misrepresentations Relating to the Maximum Reduced Velocity Disclosed in the Afeyan Patent

Waters claims that Guiochon also miscalculated the “maximum reduced velocity” disclosed in the Afeyan '270 patent to be 1,390, using what his declaration called a “reasonable value of about 1 x 10 ~ for the diffusion coefficient.” Guiochon Decl. at 5. Waters contends that this diffusion coefficient was not a proper coefficient to use given the large biomolecules disclosed in the Afeyan patent, which have diffusion coefficients orders of magnitude smaller, in the range of 1 x 10 “ or 1 x 10 ~. Guiochon stated in his declaration that the Afeyan patent characterized a “bed velocity” of 5,000 cm/hr to be “very high.” He then stated that bed velocity, which is a linear velocity, must be scaled by the diffusion coefficient and particle size to determine what the corresponding reduced velocity is. According to Waters, his resulting calculation of the corresponding reduced velocity was understated by a factor of 100 to 1,000.

There is no clear and convincing evidence that the Guiochon declaration contained a miscalculation of the reduced velocity that corresponds to a bed velocity of 5,000 cm/hr. Guiochon did indeed cite a diffusion coefficient of 1 x 10 ~ in his declaration. See Guiochon Decl. at 5. There is no evidence, however, of what the units of his coefficient were or which mathematical formula Guiochon used to determine the reduced velocity. The only evidence of the precise formula by which to translate linear bed velocity into reduced velocity is provided by the Defendant in demonstrative exhibit, a worksheet with hand-written calculations hypothesizing Guiochon’s purported reduced velocity determination. Def. Ex. 10. Although the exhibit provided by Defendant supports the hypothesis that Guiochon used the same equation in his calculations, I do not find this unauthenticated scratch sheet to be clear evidence that Guiochon in fact relied upon that equation.

The testimonial evidence offered by Defendant also does not provide clear and convincing evidence that Guiochon made a mistake. Quinn testified in his deposition that, although he believed large biomolec-ules to have a diffusion coefficient of 10 ~7 to 10 ~8 cm2/sec (Quinn Dep. at 159), he could not confirm whether Guiochon’s calculation was inaccurate. He stated:

I am not going to correct Professor Gui-ochon’s calculation, and I’m going to tell you why. In his calculation, I don’t know what assumption that he used for, A, the bed velocity, for the porosity of the column, et cetera. There are a number of other factors that go into the estimation of linear velocity, so therefore I’m not even going to — I’m not going to recalculate these numbers, because I may not use the same assumptions he did.

Quinn Dep. at 162. I find no demonstration by clear and convincing evidence that Guiochon’s declaration contained a misrepresentation as to the reduced velocity associated with a linear velocity of 5,000 cm/hr.

Even if Guiochon’s declaration did contain an inaccurate calculation of the reduced velocity that corresponds to a linear velocity of 5,000 cm/hr, it is not likely that this calculation would have been material to the examiner’s novelty determination. Guiochon stated independently of his calculation of the reduced velocity that, “I have found no teaching or suggestion whatever in Afeyan et. al., of the term ‘turbulence’ or a variant thereof, and liquid flow rates that would result in a reduced flow rate greater than 5,000, and/or means for producing the same.” Guiochon Decl. at 5.

Furthermore, the Defendant does not indicate where the Afeyan patent discloses a method for chromatography at a reduced velocity of 5,000. The Afeyan reference does refer to a “very high” bed velocity of 5,000, but only to demonstrate the flaws of the old technology. The Afeyan reference states only that 5,000 cm/hr is a bed velocity that would lead to severe “premature solute breakthrough” in conventional chromatography. See Afeyan Patent at column 15, line 42. This statement does not support the converse conclusion, that is, that the new Afeyan technology teaches a method to solve this issue at a velocity of 5,000 cm/hr. The Defendant has not clearly demonstrated where the Afeyan patent discloses a method for successful chromatography at a bed velocity of 5,000 cm/hr. Thus, even if a bed velocity of 5,000 is associated with a reduced velocity of 139,-000, as the Defendant claims, one cannot conclude as a result that the Afeyan patent anticipates the Quinn invention. Guiochon stated that he found nothing in the Afeyan patent that taught a method for chromatography at a reduced velocity of 5,000. The Defendant does not provide evidence to rebut this conclusion, and thus I do not find that Guiochon’s potentially erroneous estimation of the corresponding reduced velocity to be a material misrepresentation.

Even assuming that Guiochon’s declaration contained a misrepresentation as to the reduced velocity associated with a bed velocity of 5,000 and that the miscalculation would have been material to the patent examiner, there is no evidence that the mistake constituted more than negligent error. Quinn testified that “it is common in the chromatography literature to select 10 “5 cm2/see as a typical value,” citing several scientific references. See Quinn Decl. of 3/6/02 at ¶ 16. Waters claims that Guiochon should have known this diffusion coefficient was an improper value based upon the Afeyan patent’s disclosure of the use of large biomolecules. It provides no evidence, however, that Guiochon intentionally chose the wrong coefficient. In the absence of evidence to the contrary, I find it reasonable that if Guiochon chose a “typical” but ultimately incorrect diffusion coefficient in his analysis, he did so by mistake. Thus, I do not find clear and convincing evidence that Cohesive engaged in inequitable conduct on this ground.

3. Conclusion

Because Waters has failed to meet its burden of establishing inequitable conduct by clear and convincing evidence, judgment will enter for Cohesive on this issue.

B. Willful Infringement

Cohesive alleged that Waters’ infringement was willful and in knowing disregard of the '874 patent, and consequently it should be awarded enhanced damages on that ground. Under 35 U.S.C. § 284, “the court may increase damages up to three times the amount found or assessed.” While the statute is silent as to when enhanced damages are appropriate, the Federal Circuit en banc held earlier this month that “proof of willful infringement permitting enhanced damages requires at least a showing of objective recklessness.” See In re Seagate Technology, LLC, 497 F.3d 1360, 1371 (Fed.Cir.2007) (en banc). Recognizing that “the term [reckless] is not self-defining,” the Federal Circuit has determined that:

to establish willful infringement, a pat-entee must show by clear and convincing evidence that the infringer acted despite an objectively high likelihood that its actions constituted infringement of a valid patent.... The state of mind of the accused infringer is not relevant to this objective inquiry. If this threshold objective standard is satisfied, the patentee must also demonstrate that this objectively-defined risk (determined by the record developed in the infringement proceeding) was either known or so obvious that it should have been known to the accused infringer.

Id. (citation omitted).

The patentee bears the burden of persuasion and must prove willful infringement by clear and convincing evidence. See Comark Comm. Inc. v. Harris Corp., 156 F.3d 1182, 1190 (Fed.Cir.1998). Willful infringement is not established by the simple fact of infringement, even where the accused has knowledge of the patents. Id. In determining whether infringement was willful, a court should consider: (1) whether there was a bona fide disagreement regarding patent invalidity or infringement, (2) whether the infringer solicited or followed the advice of counsel, (3) whether there was continued infringement after notice of probable infringement was received, (4) whether there was a degree of similarity between the patented and accused devices, (5) whether the infringer took efforts to avoid infringement, and (6) whether the infringer was indemnified against infringement costs. Because I find that Waters obtained an opinion of counsel in good faith, and because there was a bona fide dispute over whether the Oasis polymeric particles infringed Cohesive’s patents, Cohesive has not demonstrated that Waters’ infringement was willful.

The following findings are based upon the affidavit testimony of Eduardo Bouvier, Alice Carroll, Michael Early, Anthony Janiuk, Ian King, Patrick McDonald, Uwe Neue, and Robert Plumb, the deposition testimony of Devette Russo, Ian King, and Michael Early, and the live testimony of Anthony Janiuk and Michael Early.

1. Facts

Cohesive published its application for the '874 patent in May 1997. A little more than a week after the patent was filed, Dr. Patrick McDonald, a Water’s employee, forwarded the patent application to Waters’ in-house counsel, Anthony Janiuk. Waters then obtained a copy of the Cohesive prototype column that Cohesive had supplied to Glaxo-Wellcome for testing. Waters began manufacturing and producing its columns in February 1998, four months prior to the issuance date of the Cohesive patent.

Dr. Bouvier, a scientist employed by Waters, compared the Cohesive prototype to the Oasis column in order to determine whether Cohesive’s patents would preclude Waters from selling an HPLC column filled with 30 micron Oasis particles. Bou-vier completed experiments and presented his results in May 1997 focusing on the particle size, interstitial fraction, and reduced velocity of Oasis columns. He used size-exclusion chromatography to determine the interstitial volume and pore-size distribution of the Oasis 30-micron particles.

Bouvier, Janiuk, scientist Uwe Neue, and Ian King, Waters’ marketing manager for the Chromatography Division, held a meeting with scientists and in-house counsel on August 19, 1998 to review the Cohesive patent application and discuss whether Waters’ columns infringed. Bouvier presented the results of his experiments, which demonstrated, among other things, that the Oasis particles collapsed when subjected to a pressure of up to 5,000 psi. Bouvier’s experiments also showed the particles resisted post-compression deformation at pressures of 7,000 psi and above.

After the August 25 meeting, Janiuk drafted an opinion that concluded that the Waters columns were not infringing. In his opinion, Janiuk stated that “Oasis particles are unmistakably in the nature of a polystyrene-type composition” and that therefore the Oasis HLB columns “do not have rigid particles as such term ‘rigid’ is defined in the patent.” Janiuk did not confer with outside counsel. He wrote an opinion memorandum dated September 1, 1998, summarizing the scientific evidence communicated at the August meeting, con-eluding non-infringement, either literally or under the doctrine of equivalents. Cohesive argues that Waters opinion ignored evidence that articles resist plastic deformation at pressures up to 7,000 psi. See Tr. Transcript Day 7 at 33-36.

2. Discussion

I do not find clear and convincing evidence that Waters’ infringement by manufacture and sale of the Oasis HPLC columns was undertaken willfully. First, Waters did not copy the column it obtained from Cohesive through Glaxo-Well-come. Cohesive’s particles are silica particles 50 micron in diameter, while Waters’ particles are polymeric particles of 30-micron size.

Second, Waters engaged in sufficient due diligence in determining whether its product would infringe to convince me that its effort to avoid infringement was in good faith. I find that it manufactured the accused column only after satisfying its obligation to ensure there was not a high likelihood, considered both objectively and subjectively, that its actions would constitute infringement.

Waters obtained a copy of Cohesive’s September 1997 patent application, conducted experiments, and held a meeting among its in-house counsel and scientists on August 25, 1998, prior to the sale and manufacture of the infringing columns. The scientists presented their results and unanimously concluded that the Oasis polymeric particles were not rigid. In particular, Dr. Bouvier conducted tests, the evidence of which was admitted at trial in this case, showing that the Oasis particles were compressible at pressures well below 5,000 psi, that the interstitial volume of the column was 40%, and that the flow in the Waters columns was not “turbulent.” .

Cohesive contends that Waters’ production of the infringing columns after learning of Cohesive’s patented technology in August 1998 was willful and knowing because Dr. Bouvier ignored evidence that the Oasis particles “resist plastic deformation,” as defined in my claim construction relating to the term “rigid.” Waters does not dispute that Oasis particles resist plastic deformation. Waters claims, however, that Bouvier reasonably believed the particles not to be rigid because they demonstrated substantial collapse during compression at pressures 5,000 psi and greater. I adopted a functional definition of rigid from the description of rigid particles during my claim construction of the '874 patent specification: “an object’s capacity to maintain substantially zero changes in density and volume under packing pressure of at least about 5000 psi and as a consequence substantially to resist plastic deformation under such pressure.” Waters argues that there was sufficient evidence to conclude that — despite the particles’ ability to resist plastic deformation- — they did not maintain substantially zero changes in density and volume under a packing pressure of at least 5,000 psi. Thus, Waters argues, Dr. Bouvier reasonably determined that the evidence that the particles resisted plastic deformation was not relevant to the conclusion that the particles were not rigid.

I find Bouvier’s conclusion that the Oasis particles were not rigid to be reasonable despite the evidence available at the time that the particles resisted plastic deformation. The definition of rigid is first and foremost a definition that turns on whether the particles collapse under pressure. Moreover, the '874 patent specification expressly states that polymeric particles are generally not rigid enough to induce turbulent flow. See '874 Patent Specification at Col. 15 (“Such polymeric material cannot be expected to maintain the requisite rigidity to withstand the pressure required to obtain turbulent liquid flow.”). Bouvier’s experiments created, at a minimum, a material dispute of fact in this case as to whether Waters’ particles were rigid, and was countered only by Quinn’s observation that the Oasis particles did not collapse under pressure. Waters continues to maintain that the jury verdict of infringement is not supported by sufficient evidence. Although I denied its motion for judgment as a matter of law, I have nonetheless independently decided that a reasonable jury could find that the Oasis particles were not rigid. The mere fact that the jury found infringement is not sufficient to prove that Waters should have known it had infringed. I do not find clear and convincing evidence that Bouvier willfully erred in coming to the conclusion that the Oasis particles are rigid.

Nor is Cohesive’s argument persuasive that Waters’ infringement was willful because the pre-litigation opinion was generated by in-house counsel, rather than an attorney from outside the corporation. Courts have found lack of willfulness even when a defendant failed to get any attorney opinion before engaged in the infringement. See Pall Corporation v. Micron Separations, Inc., 66 F.3d 1211, 1221 (finding no willful infringement even though the infringer failed to obtain an opinion of counsel because they “made significant efforts to avoid the claims of the patent.”); Insituform Technologies, Inc. v. CAT Contracting, Inc., 385 F.3d 1360, 1377 (Fed. Cir.2004) (“[T]he failure to obtain an exculpatory opinion of counsel shall no longer provide an adverse inference or presumption that such an opinion would have been unfavorable.”) (internal quotes omitted). The fact that Janiuk was in-house counsel is not determinative of the whether his opinion of noninfringement was written other than in good faith. Given the results of Bouvier’s experiments, there is no clear and convincing evidence that Janiuk willfully or recklessly concluded that Waters’ column would not infringe Cohesive’s patents.

3. Conclusion

I find that based on the evidence, Waters reasonably believed that its Oasis columns did not infringe Cohesive’s '874 and '368 patents and consequently did not engage in willful infringement. Thus, I find there to be no ground for awarding enhanced damages or attorneys fees in this case.

III. Cross-Motions for Summary Judgment Regarding the Infringement and Validity of the '368 Patent in Civil Action No. 99-11528

Cohesive filed this related ease alleging that Waters infringed the method claimed in Claims 1, 3, and 8 of the '368 patent by making, using, selling, and offering for sale 1 x 50 mm Oasis HLB extraction columns with 30 micron particles (the “accused Waters Column”).

The '368 patent is a divisional patent of the '874 patent, meaning that it claims a subset of the subject matter claimed in the '874 patent. The specifications of the two patents are identical; the '874 patent claims the apparatus for the chromatography invention and the '368 patent claims the method. The application for the '874 patent was filed on June 11, 1996 and issued June 30, 1998. The application for the '368 patent was filed on December 8, 1997 and the patent issued on July 6,1999.

Cohesive and Waters filed cross-motions for summary judgment regarding whether Waters has directly infringed or actively induced the infringement of Claims 1, 2, and 8 of the '368 patent. Claim 1 of the '368 patent reads:

A method of performing liquid chromatography comprising the steps of:
packing within a tubular container a substantially uniformly distributed multiplicity of rigid, solid, porous particles with chromatographically active surfaces, so as to form a chromatographic column having an interstitial volume between said particles, said particles having average diameters of not less than about 30 microns; and
loading said surfaces with at least one solute that is reactive with said surfaces, by flowing a liquid mixture containing said solute through said column at a velocity sufficient to induce flow of said mixture within at least a substantial portion of said interstitial volume at a reduced velocity greater than about 5,000.

Waters counterclaimed asserting that the '368 patent is invalid as obvious; Cohesive and Waters have filed cross-motions for summary judgment on the issue. For reasons stated below, I will grant the Cohesive motion for summary judgment and deny that of Waters with respect to infringement and validity of the '368 patent.

A. Infringement

Cohesive alleges in this case that Waters not only infringed the '874 patent by making and selling a chromatography apparatus, but also infringed the '368 patent by performing or inducing the performance of the patented method. Waters argues that it does not directly infringe or actively induce the infringement of the claims of the '368 patent because: (1) it does not pack its columns with “rigid” particles, (2) it has not practiced the element of the claim that requires loading solute at a reduced velocity greater than 5,000, (3) its customer, Bristol-Meyers Squibb did not practice the claimed method after the patent issued, and (4) Waters cannot be liable for inducing infringement because neither it nor its customers perform both steps of the patented method. For reasons stated below, I reject Waters’ arguments.

In order to prove direct infringement, Cohesive must show that Waters performed every step of the claimed method. Resolution of issue of patent infringement is two-step process: first, the court must determine the scope of claims of the patent; then, once the scope of claims is ascertained, the court must determine whether defendant’s alleged infringing activity falls within scope of claims. 35 U.S.C.A. § 271(a). I construed the relevant terms in a Markman hearing for Civil Action No. 98-12308 regarding the '874 patent. That construction is applicable here.

1. “Rigid”

Waters is barred by collateral es-toppel from contending that the accused infringing column does not contain rigid particles. The '368 patent and the '874 patent involve the same invention, and in both patents Claim 1 states an independent claim with a limitation for “rigid, solid, porous particles with chromato-graphically active surfaces.” The jury in the '874 case concluded that the accused column does contain rigid particles, issuance of this memorandum and order.

Waters incorporates the argument it made in its renewed judgment as a matter of law in Civil Action 98-12308 that Cohesive has failed to adduce sufficient evidence that Waters’ accused columns used rigid particles. I have denied that motion. See Section II above. The standard for summary judgment is effectively identical to the standard for a judgment as a matter of law notwithstanding a jury verdict; consequently, the determination in Civil Action No. 98-12308 that Waters used rigid particles governs the determination in this case.

A party seeking to invoke the doctrine of collateral estoppel must establish that (1) the issue sought to be precluded in the later action is the same as that involved in the earlier action; (2) the issue was actually litigated; (3) the issue was determined by a valid and binding final judgment; and (4) the determination of the issue was essential to the judgment. See Ramallo Bros. Printing, Inc. v. El Dia, Inc., 490 F.3d 86, 90 (1st Cir.2007); Simmons v. Small Business Admin., 475 F.3d 1372, 1374 (Fed.Cir.2007). There can be no dispute that those factors are satisfied here as a result of my determination to enter final judgment for the plaintiff in Civil Action No. 98-12308. The accused columns in both cases are identical, and “rigid” has precisely the same construction in both claims. That the Oasis particles are rigid is consequently res judicata.

2. Loading solute at reduced velocity of greater than 5,000

The jury also determined, by finding that the Waters column infringed the '874 patent, that the Waters column provided a “means for loading said surface ... with a reduced velocity of greater than about 5,000.” Cohesive argues that the jury verdict resolves whether Waters also infringes the method of loading solute at a reduced velocity of greater than 5,000. I do not agree that the issue of whether Waters loads (as distinct from providing for a means to load) solute has been litigated. Whether Cohesive actually loaded columns in the '874 case was not essential to a judgment of infringement. Certainly, however, the issue of whether the column provided a means for loading the solvent at a reduced velocity of 5000 or greater, as opposed to another velocity, is res judica-ta. The reduced velocity limitation was a key issue at the trial because many of the claims asserted in the '874 patent contained the limitation. By finding infringement, the jury found that Waters infringed every element of the claim 1 of the '874 patent, including providing a means for loading solute at a reduced velocity of greater than 5,000.

Although I do not find that Waters is precluded from arguing that it did not “load” the solute onto its infringing device, I find on the summary judgment record in this case that Waters performed the step of the '368 method that requires loading the column with solute during experimentation and demonstrations to its customers. Waters’ Michael Early conducted experiments with the Oasis columns as well as demonstrations for training sales reps with a flow rate of 4 ml/min, resulting in a reduced velocity of over 5,000, as late as the spring of 2000. Early testified that Waters’ sales reps were asked to demonstrate a similar method for them by customers during sales pitches. Insofar as Waters has performed both the steps of packing and loading on site or by demonstration after July 6, 1999 — the date the '386 patent was issued — it is liable for direct infringement.

3. Inducement of Infringement

Waters contends that it cannot be liable for direct infringement or actively inducing infringement because neither Waters nor its customers perform both steps of the '368 method, that is, packing and loading. In Section III.A.2 above, I found Waters to be liable for direct infringement insofar as it has practiced the '368 method for its own experimentation and customer demonstrations after July 6, 1999. For reasons stated below, I also find that Waters engaged in actively inducing the infringement of its customers insofar as Waters sells pre-packed columns to clients who perform the loading step.

To be sure, Waters cannot be found liable for direct infringement when it performs only one step of the patented method and sells it to its customers who then perform the second. Infringement requires that the patentee show that the accused device contains or performs each limitation of the asserted claim, Mas-Hamilton Group v. LaGard, Inc., 156 F.3d 1206, 1211 (Fed.Cir.1998), or an equivalent of each limitation not satisfied literally, Warner-Jenkinson Co. v. Hilton Davis Chemical Co., 520 U.S. 17, 117 S.Ct. 1040, 137 L.Ed.2d 146 (1997). The sale or manufacture of equipment to perform a claimed method is not direct infringement within the meaning of 35 U.S.C. § 271(a). See Moba, B.V. v. Diamond Automation, Inc., 325 F.3d 1306, 1313 (Fed.Cir.2003). (citing Mendenhall v. Cedarapids, Inc., 5 F.3d 1557, 1579 (Fed.Cir.1993)).

Liability for indirect infringement is another matter. Cohesive has asserted inducement of infringement under 35 U.S.C. § 271(b). Under § 271(b), “whoever actively induces infringement of a patent shall be liable as an infringer.” To succeed on this theory, a plaintiff must prove that the defendant’s “actions induced infringing acts and that [it] knew or should have known [its] actions would induce actual infringement.” Manville Sales Corp. v. Paramount Sys., Inc., 917 F.2d 544, 553 (Fed.Cir.1990). “Inducement requires proof that the accused infringer knowingly aided and abetted another’s direct infringement of the patent.” Rodime PLC v. Seagate Tech., Inc., 174 F.3d 1294, 1306 (Fed.Cir.1999). Thus, intent to cause the acts which constitute the infringement is a necessary prerequisite to finding active inducement. Hewlett-Packard Co. v. Bausch & Lomb Inc., 909 F.2d 1464, 1469 (Fed.Cir.1990). As with any proof of intent, direct evidence is not required; circumstantial evidence may suffice. See Warner-Lambert Co. v. Apotex Corp., 316 F.3d 1348, 1363 (Fed.Cir.2003).

a. Presence of Direct Infringement

Waters cannot avoid infringement liability by performing step (a) of the patented method and then intentionally selling it to its customers knowing they will perform step (b). It is true that, as an initial matter, in order for Waters to be liable for actively inducing infringement there must be direct infringement. Waters argues that there is no direct infringement in this case because a single entity does not perform both the packing and loading steps.

Neither party disputes that, in general, Waters will only perform step (a) while its customers Bristol-Myers Squibb and Du-pont Pharmaceutical perform step (b) of the '368 patented method. Chromatography involves flowing solvent (containing a chemical mixture) under pressure over a column filled with solid particles. Waters sells packed columns to its clients, who then use the columns in their scientific analysis and experiments. Loading does not occur until the actual chromatography is performed; the scientist performing the separation generally loads the solvent onto pre-packed columns. Thus, Waters performs the first step of the '368 patent — the packing of the column — while Bristol-Myers and Dupont perform the second step — the loading of the column with solvent.

Even though Waters’ customers have not performed the first step of the '368 method, they are liable for direct infringement because they perform the second step after purchasing a product from an entity that has performed the first. See E.I. DuPont De Nemours and Co. v. Monsanto Co., 903 F.Supp. 680, 735-37 (D.Del. 1995) (stating that where a seller actually practices step (a) of the claimed process and sells the resulting product to a customer, who then practices steps (b) and (c), the customer, but not the seller, would be liable for direct infringement). Interestingly, both Waters and Cohesive cite E.I. DuPont v. Monsanto to support their opposing arguments on this issue — Waters for the proposition that it cannot be held liable for direct infringement, and Cohesive for the proposition that its customers can. From either perspective, E.I. DuPont supports the proposition that Waters’ customers can be held to have engaged in direct infringement even though they do not perform both steps of the '368 method.

Waters also cites Shields v. Halliburton, 493 F.Supp. 1376, 1389 (W.D.La.1980), for the proposition that it cannot be liable for the loading activity of its customers. But Shields stands for the opposite proposition:

When infringement results from the participation and combined action of several parties, they are all joint infringers and jointly liable for patent infringement ... Infringement of a patented process or method cannot be avoided by having another perform one step of the process or method.

Shields, 493 F.Supp. at 1389. Shields parallels the DuPont holding that a customer can be liable for direct infringement by purchasing a product to perform the second step of a patented method knowing that the seller has performed the first. Indeed, Waters’ customers essentially pay Waters by contract to perform the packing step of the '368 method. Waters offers no other legal authority for the proposition that its customers could not be held to have engaged in direct infringement of the '368 patent because they perform only step (b) of the method after Waters performed step (a) and I am aware of none.

Neither party disputes that Waters performs the packing step while its customers perform the loading step. Thus, there is no question, given the authority cited by both parties, that there was direct infringement of the '368 method, performed by Waters’ customers Bristol-Myers Squibb and Dupont.

b. Intent to Induce Infringement

Cohesive has provided sufficient evidence to support judgment as a matter of law that Waters induced the direct infringement of its customers. Cohesive has demonstrated that Waters directs its customers to use a flow rate of 4 ml/min, which, as determined in the '874 trial, is sufficient to induce a reduced velocity of greater than 5,000 in the accused columns. Promoting sales material that instructs customers on how to infringe the patent is sufficient evidence of intent to induce infringement. See Snuba v. Dolphin World, 2000 WL 961363, *7 (Fed.Cir.2000) (“The promotional materials, particularly when combined with sales of elements of the claimed invention, evidence [defendant’s intent to induce infringement by its customers.”).

Waters does not dispute that it promotes and sells infringing columns to its customers with the knowledge that they will load the column in a way that infringes claim 1 of the '368 patent. Waters’ argument, instead, is that it is not liable for what its customers do with the column because it and its customers are not contractually bound. Waters cites no legal authority, however, for the proposition that two parties must be contractually bound in order for one to be liable for actively inducing a patented method. Inducement requires the plaintiff to show only that the alleged infringer’s actions “induced infringing acts and that he knew or should have known his actions would induce actual infringements.” Manville Sales Corp. v. Paramount Systems, Inc., 917 F.2d 544, 553 (Fed.Cir.1990).

Waters cites E.I. DuPont for the proposition that it cannot be held to be a joint direct infringer without performing both steps of the method. The DuPont case, however, did not hold that such a seller cannot be held liable for the inducement of direct infringement. See E.I. DuPont at 736 (finding that the seller could be held liable for inducing infringement after determining that it could not be held liable for joint direct infringement.) Cohesive has shown, in the trial on the '874 case, that Waters distributes a product and teaches a means for eluting solute over a column at a reduced velocity of greater than 5,000. Waters does not dispute that it knew or should have known that its columns would be used to perform the loading step of the '368 method. Thus, Waters cannot escape liability for induced infringement merely because it performs only one of the two steps described in claim 1 of the '368 patent while its customers perform the second. I will deny Waters’ motion for summary judgment on indirect infringement and grant Cohesive’s.

4. Evidence that Bristol-Meyers Squibb directly infringed

Waters initially argued in its opposition to Cohesive’s motion for summary judgment that there was no evidence that Bristol-Meyers Squibb (BMS), its main customer, infringed the '368 patent after the patent was issued, because though they documented their experiments in October 1999, the experiments could have been performed more than a year beforehand. Cohesive has submitted an affidavit by BMS that it performed its infringing experiments within ten days prior to the documentation. This date is plainly after issuance of the '368 patent.

5. Claim 3 and interstitial volume

Claim 3 of the '368 patent requires an interstitial volume of not less than about 45 percent of the total volume of the column. The jury found that the Waters columns did contain an interstitial volume sufficient to infringe this limitation in the '874 patent. Thus, the issue of whether Waters infringes this limitation of Claim 3 is similarly res judicata. Waters has incorporated its arguments for renewed judgment as a matter of law on this issue as well, but, as stated above, I have denied that motion. Consequently, if Waters infringes Claim 1 as a matter of law, it also infringes Claim 3.

6. Claim 8 and pore size

Claim 8 of the '368 patent reads:

A method of performing liquid chromatography as set forth in claim 1 wherein said particles are selected to have pores having average diameters lying within the range of from about 60 angstroms to 5,000 angstroms.

Trial testimony in Civil Action No. 98-12308 was sufficient to establish that the Waters’ Oasis particles have average pore diameters of between 60 and 5000 angstroms. Waters does not dispute that the pore size of its particles is within the claimed limitation of claim 8. Thus, the jury verdict having determined by means of collateral estoppel that Waters infringes claim 1 of the '368 patent, I find that the Waters’ column also infringes claim 8.

7.Conclusion

For these reasons, I will grant Cohesive’s motion in its entirety that Waters has infringed, directly through Early’s demonstrations and indirectly through Bristol-Myers Squibb and Dupont Pharmaceutical, claims 1, 3, and 8 of the '368 patent. Waters’ cross-motion with regard to infringement will therefore be denied.

B. Validity

Waters moved for summary judgment that the '368 Patent is invalid as obvious, citing the same Pretorius and Afeyan references they relied upon in litigating the validity of the '874 patent. Cohesive also filed a motion for summary judgment that the '368 is not invalid on grounds of obviousness. For reasons stated below, I grant Cohesive’s motion for summary judgment and deny that of Waters.

Waters is collaterally estopped from re-litigating the issue of obviousness with respect to the opinions it presented to prove obviousness of the Quinn invention in the '874 case. The jury found that Cohesive’s '874 patent — which claimed the apparatus and means for the '368 method — was not obvious to a person versed in the field of chromatography given the prior art. Waters failed to preserve its motion for judgment as a matter of law with respect to obviousness at the close of evidence, and thus cannot now challenge the jury verdict in the '874 case.

Waters does not deny that a standing jury verdict bars it from relitigating the same obviousness issues it raised in the '874 trial. Instead, Waters offers a new affidavit by Richard Niemi, which I allowed over Cohesive’s motion to strike. Niemi is a Waters technician who worked at a company called Varían between 1995 and 2000. He declares that in June 1996 he was running liquid chromatography on a Varían Prospekt system with rigid, solid silica particles of 40 microns and concluded that using a higher flow rate on the column could increase the speed of the separations. He declares that “based upon [his] own activities and [his] understanding of the practice of liquid chromatography, the method set forth in Claim 1 was obvious to one of ordinary skill in the field of liquid chromatography.” See Niemi Aff. at ¶ 8.

The Niemi affidavit is insufficient evidence of obviousness because it does not demonstrate that the Quinn invention was obvious at the time the invention was made. In order to prove obviousness, Waters must show that “the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having the ordinary skill in the art to which said subject matter pertains.” 35 U.S.C. § 103. See also Ransomes, Inc. v. Great Dane Power Equipment, Inc., 2000 WL 347931, *3 (Fed.Cir.2000) (evidence that an invention was obvious to a person skilled in the art one year after the invention was made was “simply too late” to be probative of obviousness). Even simultaneous development of similar inventions “may or may not be indicative of obviousness,” and thus evidence of “contemporaneous development” that occurs after the date of the patented invention will almost never be probative of the ultimate conclusion of obviousness. See Hybritech Inc. v. Monoclonal Antibodies, Inc., 802 F.2d 1367, 1380 n. 4 (Fed.Cir.1986) (contemporaneous development more than a year after the filing date of patent is “of little probative value”); Environmental Designs, Ltd. v. Union Oil Co. of Cal., 713 F.2d 693, 698 n. 7 (Fed.Cir.1983) (“the virtually simultaneous making of the same invention does not in itself preclude patentability of that invention.”).

Niemi’s affidavit states that the invention was obvious to him as of June 1996. Although the '874 patent was not issued until after that date, the Quinn invention was made in July 1995. Waters does not dispute this fact, and indeed, agreed at the hearing on its motion for summary judgment that the evidence would have to show that Niemi’s invention was made contemporaneously or before Quinn’s in order to be probative of obviousness.

Waters’ additional evidence of obviousness of the Quinn invention could not support a jury verdict of validity with regard to the '368 patent. Consequently, I will deny its motion for summary judgment on the issue of validity and grant Cohesive’s.

IV. Motions for Summary Judgment in Civil Action No. 01-12307 (“25 Micron Case”)

Cohesive filed a separate but related action, Civil Action No. 01-12307, alleging that Waters’ manufacture, sale, and use of a 1 x 50mm chromatography column filled with 25 micron particles (as opposed to the column filled with 30 micron particles at issue in Civil Actions No. 98-12308 and 99-11518) infringes the '874 and '368 patents. All independent claims of'874 patent and '368 patents require particles to have diameters of not less than about 30 microns. See '874 Patent (“rigid, solid, porous particles with ehromatographically active surfaces, said particles having average diameters of greater than about 30 microns” (Claim 1), “not less than about 30 microns” (Claim 15), “in the range between about 30 microns and 500 microns” (Claim 16)); '368 Patent Claim 1 (“not less than about 30 micron”). Thus, in order for Waters to have infringed either patent, the accused column must contain particles with an average diameter of not less than “about 30 microns.” Although Cohesive had earlier pressed its claims through a motion for preliminary injunction, Cohesive has, in response to my suggestion that the parties seek to press their positions to final judgment, filed a motion for summary judgment of infringement of both patents requesting a permanent injunction against Waters to enjoin them from producing, marketing, and selling the 25 micron columns. It became apparent at the final hearing on this matter that if I rejected Cohesive’s contention that the 25 micron Waters particles met the limitations of the '874 and '368 patents, I would necessarily have determined that Waters was entitled to judgment as a matter of law. Consequently, Waters made an oral cross-motion for summary judgment as to infringement at the hearing. For reasons stated below, I will deny Cohesive’s motion and grant the oral motion for summary judgment made by Waters.

A. Facts

Waters began selling the 1 x 50mm 25 micron particle columns in October 2001, shortly before the jury trial in Civil Action No. 98-12308. It sold the 25 micron column for six months before ceasing production in March 2002. During those six months, Waters sold approximately 163 columns. Apart from the size of the particles, the 25 micron column accused in this case is identical to the infringing column in Civil Actions No. 98-12308 and 99-11518.

The parties dispute the actual size of the particles in the accused column. According to Cohesive’s analysis by the “Coulter counter,” the average particle size of the Oasis particles is not 25 microns but 29.01 microns. See Statement of Facts at paragraph 16. According to Waters, the average size of the particles is 25.22 or 25.16 microns, depending on the method of calculation. See Grover Aff. (Ex. 1) at paragraph 22; Grover Second Aff. (Exhibit 2) (contesting the accuracy of Cohesive’s measurements).

B. Discussion

Even assuming that Cohesive’s calculation of the particle diameter is accurate, I conclude that Waters’ 25-micron column does not infringe Cohesive’s patents. Cohesive claims that the sale of the 25-micron column (1) literally infringes the particle diameter limitation in the '368 and '874 patents, and (2) even if it does not literally infringe, it infringes under a theory of doctrine of equivalents. Because the claimed language “about 30 microns” does not include a particle that is 29.01 microns in diameter, which is a factual predicate for Cohesive’s motion, I find there to be no literal infringement in this case.

Furthermore, I find as a matter of law that Waters has not infringed Cohesive’s patents under the doctrine of equivalents. Cohesive cannot now invoke the doctrine of equivalents to broaden a claim that specifically excludes a product with particles less than about 30 microns in size.

1. Literal Infringement

In order for Waters to have infringed Cohesive’s patents literally through the manufacture, use, and sale of the 25 micron column, the column must contain particles of “greater than about 30 microns.” The claim explicitly excludes particles less than about 30 microns in size.

The words in a claim are “generally given their ordinary and customary meaning, which is the meaning that the term would have to a person of ordinary skill in the art in question at the time of ... the effective filing date of the patent application.” Phillips v. AWH Corp., 415 F.3d 1303, 1312 (Fed.Cir.2005) (quoting Vitronics Corp. v. Conceptronic, Inc., 90 F.3d 1576, 1582 (Fed.Cir.1996)). In some cases, the ordinary meaning of claim language as understood by a person of skill in the art “may be readily apparent even to lay judges, and claim construction in such cases involves little more than the application of the widely accepted meaning of commonly understood words.” Phillips, 415 F.3d at 1314. Claim construction is a matter of law, and the Federal Circuit has construed “about” in its ordinary meaning to mean “approximately” when interpreting a patent claim. See Merck & Co., Inc. v. Teva Pharmaceuticals USA, Inc., 395 F.3d 1364, 1372 (Fed.Cir.2005); see also Christiana Industries v. Empire Electronics, Inc., 443 F.Supp.2d 870 (E.D.Mich. 2006) (holding that 111 degrees is not “about”, or approximately, 90 degrees).

I construe the language “greater than about 30 microns” to exclude 29.01 microns. “About” has remained over time an adverb designed to denote “some degree of exactness, in respect to quantity, number, and time.” Compare Webster’s Unabridged Dictionary 2d. ed. (1950) with Webster’s Third New International Dictionary (1986). Cohesive’s argument is that a particle 29 microns (or even 25 microns) in size is “approximately” 30 microns. But a 29 micron particle is not approximately a 30 micron particle with any degree of precision. It does not communicate with any meaningful degree of exactness to say that 29 is approximately 30. One does not ordinarily “round up” a number from 29.01 to 30. Under all ordinary and common sense definitions, 29 is less than 30.

The particle diameters provided by the patent are rendered with some exactness. A difference in size of plus or minus 1 micron is not immaterial. The patent specification for both the '874 and '368 patents states that particles of small diameters such as 5 to 20 microns are too small even to achieve the turbulent flow that is characteristic of the patented technology. See '874 Patent Specification at col. 5-6; cite to '368 patent. The preferred embodiment calls for particles of 50 micron size. Claim 16 calls more broadly for particles “having substantially uniform average diameters in the range between about 30 to 500” microns. The specified dimensions would be meaningless if not interpreted with some rigor.

Cohesive chose the micron as a unit of measurement and to denote the limiting size of its patented particles by whole integers. It could have applied for a patent that included particles of “greater than 29 microns” rather than 30. It did not. Thus, I do not hesitate in construing “about 30 microns” to exclude a magnitude of 29.01 microns. Even reading the disputed evidence regarding particle size in the light most favorable to Cohesive, I find, as a matter of law, no literal infringement by the “25 micron” of Waters columns.

2. Doctrine of Equivalents

For related reasons, I deny Cohesive’s argument that Waters has equivalently infringed its patents by producing a column with 29 micron particles. “A particular structure can be deemed outside the doctrine of equivalents because that structure is clearly excluded from the claims whether the exclusion is express or implied.” See SciMed Life Systems v. Advanced Cardiovascular Systems, 242 F.3d 1337, 1345 (Fed.Cir.2001). Cohesive’s patents expressly exclude particles “less than about 30 microns in size.” In the patent description, Cohesive relies on the large particle size in its technology to distinguish it from the prior art. This is not a case in which particle size is left undefined in the claim or patent specification. Nor is this a case in which Cohesive has claimed a nominal size of “about 30 microns.” Rather, what has been claimed excludes all particles with a diameter “not less than” about 30 microns. Cohesive has carved out a substantial set of diameters for particle structure, and cannot now use the doctrine of equivalents to broaden patent language which specifically limits its property rights to a set of particles sized “not less than” a certain amount.

Cohesive argues that deloying the SciMed analysis in this manner swallows the entirety of the doctrine of equivalents because in a case where a claim defines a structure, a finding that an accused device does not literally infringe would necessarily lead to a finding that structure is explicitly or implicitly excluded from the patent claim. That argument was rejected in Ethicon Endo-Surgery, Inc. v. U.S. Surgical Corp., 149 F.3d 1309, 1317 (Fed.Cir.1998). The Ethicon court stated that although “any analysis of infringement under the doctrine of equivalents necessarily deals with subject matter that is ‘beyond,’ ‘ignored’ by and not included in the literal scope of a claim,” subject matter will be found to be ‘specifically excluded’ from coverage and thus unavailable for accusation under the doctrine “if its inclusion is somehow inconsistent with the language of the claim.” Id. Under this analysis, “literal failure to meet a claim limitation does not necessarily amount to ‘specific exclusion.’ ” Id. Cohesive essentially argues that I should include a 29.01 micron particle in the claimed language of the patent under the doctrine of equivalents. As stated above, however, including a column of 29.01 micron particles as covered by the patent would be inconsistent with the explicit language of the claim. Consequently, I conclude that SciMed and related cases are directly applicable in this case.

3. Conclusion

Because I find that Waters has not infringed, literally or equivalently, the “not less than about 30 micron” limitation, I need not determine whether there is a material dispute of fact concerning the remaining limitations of the relevant claims.

For the reasons stated above, I will deny Cohesive’s motion for summary judgment and grant the oral motion of Waters.

V. Bench Trial: Findings and Conclusions Regarding Damages for Infringement of the '874 and '368 patents

The following findings of fact are based upon testimony submitted by Cohesive’s experts Hubert Quinn and Christopher Bokhart and Waters’ experts Philip Saunders and Michael Early. Those witnesses were cross-examined during the six-day bench trial in Civil Action No. 98-12308 following the jury’s finding of infringement as to the '874 patent. As I have found in Section III.A. above, Waters has also infringed claims of Cohesive’s '368 patent by manufacturing and selling the accused is a 1 x 50mm column packed with 30 micron Oasis particles. Consequently, these findings also govern the issue of damages in Civil Action No. 99-11528.

Under 35 U.S.C. § 284, upon a finding of infringement “the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention of the infringer, together with the interests and costs as fixed by the court.” Thus, Cohesive is entitled to damages in the amount of at least the reasonable royalty rate for making and selling the infringing products.

Courts allow a plaintiff to recover lost profits, rather than reasonable royalties, if the plaintiff can prove that it would have made the profit “but for” the infringement. See Grain Processing Corp. v. American Maize-Products Co., 185 F.3d 1341, 1349 (Fed.Cir.1999) (stating that plaintiffs must prove “causation in fact” to recover lost profits). To obtain damages of lost profits on sales it would have made absent the infringement, a patent owner must prove the four so-called Panduit factors: (1) demand for the patented product, (2) absence of acceptable noninfringing substitutes, (3) its manufacturing and marketing capability to exploit the demand, and (4) the amount of the profit it would have made but for the infringement. Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1157 (6th Cir.1978). When actual damages in the form of lost profits cannot be proven, the patent owner is entitled to a reasonable royalty. 35 U.S.C. § 284. Courts have discretion to award a hybrid of lost profits and royalties. See State Industries Inc. v. Mor-Flo Industries, Inc., 883 F.2d 1573, 1577 (Fed. Cir.1989).

In Section V.A. below, I find that Cohesive has failed to prove that it is entitled to actual damages in the form of lost profits because there is insufficient evidence that Cohesive would have made the sales that Waters made during the infringement period. Having found actual damages are not available, I address in Section V.B. below the question of reasonable royalty.

A. “But-For” Lost Profits

Cohesive has failed to prove that it would have sold the accused columns that Waters sold during the infringing period. Broadly stated, I base this finding on the following: (1) the evidence does not establish that Cohesive and Waters were the only two suppliers of infringing columns during the infringing period, (2) Cohesive has failed to show that there was a lack of an acceptable non-infringing substitute during the infringement period, (3) few customers of Waters switched to purchasing accused columns from Cohesive after Waters took its product off the market, and (4) it appears that certain of Waters’ customers preferred Waters polymeric particles over the silica particles produced by Cohesive.

1. Two-supplier market analysis

Though Cohesive has not formally argued that it is entitled to lost-profits under the two-supplier test (perhaps because a formal two-supplier test was not articulated by the Federal Circuit until 2003), it suggested in argument that the market for its columns is a two-supplier market. Cohesive’s experts Quinn and Bokhart, however, admitted at trial that the market for the infringing column was not limited to two suppliers. See Trial Transcript Day 1 at pp. 10-16 (admitting that Phenomex and Metachem both make 1 x 50mm columns). Bokhart stated that the market is a two-supplier market only if you exclude other potential infringers, like Phenomex and Metachem, from the calculus. Cohesive is not entitled to actual damages if other infringers would have made Waters sales. The two-supplier test is merely a short cut method of proving but-for profits; whether the other suppliers were potentially infringing the '874 patent is not relevant to the issue of causation. Cohesive was admittedly operating in a market with other suppliers of a high-speed, 1 x 50 mm columns. Thus, it has not succeeded in proving lost profits under the two-supplier market analysis.

2. Panduit Factors

Even without the short cut provided by the “two-supplier market analysis,” a patent holder may also prove but-for damages based upon lost profits for sales by proving: (1) demand for the patented product, (2) absence of acceptable noninfringing substitutes, (3) the patent holder’s manufacturing and marketing capability to exploit the demand, and (4) the amount of the profit it would have made but for the infringement. Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1157 (6th Cir.1978). The parties do not dispute that there was demand for the patented product, or that Cohesive would have had the manufacturing and marketing capability to handle the sales that Waters made during the infringing period.

Instead, Waters asserts that Cohesive cannot recover lost profits because the evidence offered by Waters shows that there are suitable noninfringing substitutes, including (1) the Waters’ 2.1 x 20 mm, 2.0 x 15mm, and 1 x 50mm columns filled with 25 micron Oasis particles, (2) the Spark-Holland Prospekt solid-phase extraction column; (3) and the Waters’ 96-well automated plate, also used for solid-phase extraction.

I do not find that the Spark-Holland Prospekt system or the Waters’ 96-well plate to be fully-suitable substitutes for the 1 x 50mm direct injection column that Cohesive patented. I do, however, find that Waters’ columns filled with 25 micron particles are reasonably acceptable nonin-fringing substitutes for the patented technology.

I find neither the Prospekt system nor the 96 well automated plate to be an acceptable substitute for Cohesive’s technology. Both the Prospekt column and the 96-well plate are solid-phase extraction technologies. Though a solid phase extraction cartridge uses the same stationary phase (i.e. packing material) as an HPLC column, solid phase extraction is a sample preparation technique used in conjunction with HPLC and thus is not equivalent to HPLC, as Quinn testified.

Furthermore, the 96-well plate and arguably the Prospekt cartridge precludes the customer from performing high-speed separations with direct injection, which was a primary benefit of the patented technology. See Panduit, 575 F.2d at 1162 (“A product lacking the advantages of that patented can hardly be termed a substitute ‘acceptable’ to the customer who wants those advantages.”). Finally, the 96-well automated plate is an automated technology useful for companies which are separating many samples at a time. Thus, a scientist running smaller projects with only one or two separations at a time would not find the 96-well plate a useful substitute.

The Waters 1 x 50mm and 2.1 x 20mm columns, by contrast, are both direct-injection HPLC columns, rather than solid phase extraction columns. The main difference between these columns and the columns produced by Cohesive is that the particle size of the polymeric particles are 25 micron instead of 30 micron. The 2.1 x 20mm, of course, is also a differently-sized column than the accused column. Although it is only slightly larger, it would likely not be a fully-acceptable substitute for those customers would rather elute their compounds over a smaller 1 x 50mm column. Nevertheless, I find it a reasonably acceptable substitute.

The 25 micron 1 x 50mm column, which differs only from the accused column in particle size, also does not infringe the '874 patent, as I have found in Section IV above. There is evidence that the 25 micron particles have both advantages and disadvantages over the 30 micron particles — e.g. more efficient separations and higher backflow pressure, respectively. Thus, the 25 micron column is not a perfect substitute for the accused column. The 25 micron column does, however, contain Oasis polymeric particles rather than the Cohesive silica particles. It is likely that some customers would find that the benefits of having polymeric rather than silica particles outweigh whatever detriment they would suffer by using 25 micron rather than 30 micron particles. The 25 micron and 30 micron columns are used for identical purposes with similar systems. The time for running assays on the columns are essentially the same, and the prices of the columns are comparable. Thus, I find it more likely than not that the availability of the 25 micron particle columns in approximately the same size as the accused column would have constituted an acceptable yet noninfringing substitute.

During the period between 2002 and 2006, Waters sales of parallel Oasis products, which include the 96 well plates, the 2.1 x 20mm and 2.0 x 15mm columns, and the Prospekt 2 cartridges, rose from approximately $3 million per quarter to $8 million per quarter. During the brief period in which Waters was selling the 25 micron column in the 1 x 50mm size, it sold 103 of those columns. Although the sales data is not conclusive evidence that these products are substitutes for the Oasis 1 x 50 mm column, (because the increase in sales could be due to factors other than the lack of availability of the patented technology), it is probative of the capacity of the other Oasis products’ ability to serve as substitutes.

3. Other evidence that But-for Lost Profits are not available

There is further corroboration that acceptable noninfringing substitutes to Waters’ accused column existed in the market; (1) Waters’ customers did not begin buying Cohesive’s columns after Waters ceased producing the patented technology, and (2) Waters’ Oasis particles could provide an benefit to Waters’ customers which would have prevented Cohesive from capturing all of Water’s sales.

In the two to fifteen months after Waters ceased selling the accused column, only two out of fourteen of Waters’ regular customers — Cephlon and GlaxoSmithK-line-purchased Cohesive’s 1x50mm 30 micron columns. These customers accounted for 1400 of the 1669 column sales that Waters made during the infringing period. The amount of data that Waters produced varies by customer; for some customers, notably Bristol-Myers and Pharmacia, Waters has only two months of records from Cohesive. Nonetheless, Cohesive has not provided any evidence countering Waters contention that these customers have not begun purchasing columns from Cohesive.

The record demonstrates, in short, that there exist acceptable substitutes in the market and that the demand for Cohesive’s patented technology is fairly elastic. I do not find compelling the competing inference that the large pharmaceutical clients of Waters coincidentally stopped using HPLC columns as soon as Waters ceased selling them, having purchased columns monthly from Waters for years. Another competing inference, Cohesive points out, is that those companies were still using leftover Waters’ columns during the months after Waters stopped selling the infringing product and thus had no need to purchase from Cohesive. But Cohesive’s hypothesis does not account for why the companies would have suddenly stopped purchasing columns for future use.

Furthermore, Cohesive’s expert Quinn conceded that the Waters’ polymeric Oasis particles differ from Cohesive’s silica particles, arguably providing more desirable separations for certain customers. In particular, there is evidence I credit that Oasis particles can better handle the separation of acidic or polar compounds.

I find the evidence of lack of customer switching, although limited in this record to only the few months after Waters stopped selling its columns, substantial support for the proposition that the demand for Cohesive’s patented technology was not inelastic. The lack of customer switching is evidence that Cohesive would not necessarily have made the same sales that Waters made to customers during the infringement period. Customers appear to have chosen not to purchase the patented technology from Cohesive for several reasons, (1) there were indeed available ae-ceptable substitutes, (2) Waters is a larger organization than Cohesive and offered various advantages to clients through more substantial customer service or reliability, and (3) Waters’ customers found the Oasis particles to have benefits that Cohesive’s particles could not provide. I cannot conclude that Cohesive would have made sales to those customers “but for” Waters’ infringement. See SmithKline Diagnostics, Inc. v. Helena Laboratories Corp., 926 F.2d 1161, 1166 (Fed.Cir.1991) (“If the realities of the market are that others would likely have captured sales made by the infringer, despite a difference in products, it follows that the ‘but-for’ test is not met.”). The evidence in the record does not support a finding that Cohesive is entitled to actual damages in this case.

B. Reasonable Royalty Rate

Because Cohesive has failed to prove lost profits, i.e., actual damages, it is entitled to reasonable royalties on sales made by Waters’ from August 1998, the date of first infringement, until December 2001, when Waters ceased producing the infringing columns. A reasonable royalty is an amount “which a person, desiring to manufacture and sell a patented article, as a business proposition, would be willing to pay as a royalty and yet be able to make and sell the patented article, in the market, at a reasonable profit.” See Panduit, 575 F.2d at 1157-58. A court may calculate a reasonable royalty by relying upon an established royalty rate within the relevant market, if there is one, or by projecting a hypothetical negotiation between a willing licensor and licensee at the time infringement commenced. See Mineo, 95 F.3d at 1119. The hypothetical negotiation requires the court to envision the terms of a licensing agreement reached as a result of a supposed meeting of minds between the patent holder and infringer at the time infringement began. See Rite-Hite, 56 F.3d at 1554. In this case, there is no evidence of an established royalty rate in the market for HPLC direct-injection columns. Thus, I must determine a hypothetical royalty rate based upon the evidence provided by the parties.

In determining a proper hypothetical royalty rate, courts tend to rely upon the multiple evidentiary factors catalogued in the trial court opinion Georgia-Pacific v. United States Plywood, 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), aff'd 446 F.2d 295 (2d. Cir.1971) (“Georgia Pacific factors”). Because there is no evidence of an established royalty rate in this market beyond one license that is newly submitted by Cohesive, I rely mainly upon the experts’ opinions to determine the royalty rate to which Cohesive is entitled.

1. The Experts’ Opinions

Waters’ expert Saunders testified that the reasonable royalty rate on sales of the patented columns would have been 4-5%. He based his royalty rate upon three licensing agreements entered into by Waters in the past: (1) A 1983 license from Millipore Corporation, of which Waters was a division, for the coating technology for packing materials, under which Milli-pore received 5% of the first 20 million dollars of net sales per year and 3% of net sales in a year over that amount; (2) A 1988 license from Rohm and Haas for the rights to use an adsorption process in media or columns for analytical and preparative chromatography, under which Rohm and Haas would get 3% to 12% of net sales, (3) a 1997 license from World Precision Instruments for an optical wave guide technology that directs light in certain fluids in HPLC, for which the royalty rate was 7% of net sales. Although these licenses are all for products that are used in chromatography, none of them involve the license of a chromatographic column. Moreover, the first license cannot be said to have been an arms length transaction, because Waters was a part of Millipore Corporation at the time. I find these three agreements not particularly useful in determining what royalty Waters would agree upon with Cohesive.

Cohesive’s expert Bokhart testified that a reasonable royalty rate was 15%. It is unclear precisely how he arrived at this estimate given that under his main analy-ses (the “25% rule”, and the book-of-wisdom analysis), the royalty rate ranged from 2 to 17.1%. See Bokhart Report 3/6/2002 Ex. 12, 13, 14, 15, 16 (11.4%, 16.5%, 2%, 3.9%, 8.5% based upon the “25% rule”); Ex. 17, 18, 19, 20 (12.6%, 17.1%, 6%, 4.6% based upon book-of-wisdom analysis).

Since trial, Cohesive has supplemented the evidence at trial with a licensing agreement between Cohesive and Quest Diagnostics Incorporated (Quest) entered into in 2003. The license is for two columns (50 x 1.0mm and 50 x 2.0mm) and implicates six of Cohesive’s patents — not only the '874 and '368 patents but also Patent Nos. 5,795,469, 5,968,367, 6,110,362, and 6,149,816. Under the license agreement, Quest would pay $100 per column to Cohesive for each column it had manufactured by a third party for its use. The Quest license does not allow Quest to resell a column to a third party, so the royalty rate cannot be calculated based upon Quest’s “revenues” for sales of the columns. The additional evidence provided in the Supplemental reports in August 2007, however, show that the average price of a column sold by Cohesive since trial has been $350. Consequently, the effective royalty rate under the Quest license can be calculated as approximately 29%.

Waters argues that the Quest license is wholly irrelevant because the purpose of the license was not to resell the manufactured columns. The scope of the agreement was to license the making of the proprietary columns only for use in Quest’s laboratories. Thus, Quest would not need to market or distribute the columns it made, and consequently its costs would be less than the cost Waters would have incurred in manufacturing a column for sale.

I do not find the Quest license a particularly helpful measure of a reasonable royalty rate in this market. It is not, however, wholly irrelevant. It is more relevant than the license agreements that Waters entered into during the infringement period because the license is for the manufacturing of the patented product, rather than other non-column HPLC products. On the other hand, the Quest license is likely an overestimate of the royalty rate to which Cohesive and Waters would have agreed to because it did not involve royalties for sales at all. Quest merely paid $100 per column for the license to manufacture the patented technology for its own use, and its license implicated patents other than the two patents at issue in this case.

Recognizing, as I must on this record, that the judgment is a less than fully informed estimate, I note that a license from Cohesive to Waters would have increased Cohesive’s sales base, involved marketing and support from the larger Waters organization, and placed the risk of manufacture on Waters. Under the circumstances, I find that 10% is a reasonable royalty rate in the relevant market.

2. The Number of Infringing Sales

The parties dispute the number of sales of the infringing columns for which Waters can be held liable. Waters asserts that, according to the jury verdict, it can be held liable only for (1) direct infringement of the '874 patent through the experiments of Dr. Ding in the fall of 1998, (2) contributory infringement of the '874 patent through sales to Bristol-Myers Squibb and DuPont Pharmaceutical, and (3) the inducement of infringement of the '874 patent through sales to Bristol-Myers Squibb and DuPont Pharmaceutical. See Jury Verdict at Infringement B.

I find that Waters can be held liable for infringement for any sale of the infringing column it made in the United States regardless of the identity of the customer. The jury instructions and jury verdict support — and using my authority under Fed. R.Civ.P. 49(a) — I find that Waters infringed all claims 1, 3, 7, 9, 15, 16, and 20. Claim 16 is an independent claim regarding a chromatographic column. Claims 1, 13, and 15, on the other hand, of course, claim an apparatus as well as a “means for loading said surfaces ... by flowing a liquid mixture ... at a reduced velocity greater than about 5,000.” Waters’ argument that Cohesive has provided evidence only that with respect to Bristol-Myers Squibb and Dupont Pharmaceutical used Waters’ columns at the claimed reduced velocity ignores the fact that Cohesive has also proven that the sale of Waters’ columns infringe Claim 16. Claim 16 claims:

A chromatographic column comprising, in combination,

a container packed with a substantially uniformly distributed multiplicity of rigid, solid, porous particles with ehromato-graphically active surfaces, said particle having substantially uniform average diameters in the range between about 30 to about 500 pm, the interstitial volume between said particles being greater than about 45% of the total volume of said body, said volume being formed of a multiplicity of interstitial channels between said particles, at least a majority of said channels having mean cross-section dimensions substantially not less than about 5 pm.

See Patent '874 Claim 16.

The jury verdict supports and I find as well under Fed.R.Civ.P. 49(a) that Waters infringed all the disputed claim limitations of Claim 16, that is, that Waters’ column contains rigid particles, that it has an interstitial volume fraction of 45% or more, and that a majority of the interstitial channels of the accused Waters column have mean cross section dimensions of not less than 5 (xm. This determination is independent of whether Waters customers employed the claimed means for loading. Thus, there is no dispute that Waters directly infringed independent Claim 16 of the '874 patent by manufacturing and selling the infringing columns, regardless of whether the customer engages in “loading said columns” by flowing a liquid containing said solute “at a reduced velocity of about 5,000.”

The evidence initially submitted by the parties differed as to how many columns Waters sold within the United States during the infringing period from July 1998 to December 2001. According to Waters, it sold 1,612 columns, with sales to Bristol-Myers Squibb and Dupont make up approximately half, at 850 columns sold. See Saunders 3/6/2002 Aff. (Saunders’ 2nd Supplemental Report) at Attachment 2. Indeed, it was unclear how many columns Cohesive claims, as the evidence submitted by Bokhart is conflicting.

Consequently, at the final hearing on damages in this case, I asked the parties to see if they could stipulate as to the number of infringing columns. They have now jointly stipulated that a total of 2,112 Waters infringing columns were sold during the infringing period. I find that this stipulation governs the universe of infringing columns for which Cohesive is entitled to damages.

3. Calculation

The reasonable royalty to which Cohesive is entitled for Waters sales of infringing column is determined by multiplying the royalty base (revenues = sales x price) times the royalty rate,100. The average sales price for the waters accused column was $250.

Total sales: 2,112
Price per column: $250
Revenues: $528,000
Royalty Rate: 10%
Damages = Revenues * Royalty Rate: $52,800

C. Prejudgment Interest

Prejudgment interest is left to the discretion of the court. Viewing the royalty rate to be essentially a contract measure of damages, I will look to the Massachusetts state law of prejudgment interest for contract damages. The Massachusetts state law analog is Mass. Gen. Laws ch. 231 § 6B, which directs prejudgment interest at 12% from the date of the commencement of the lawsuit (Civil Action No. 98-12308) and comprehends the damages necessary to afford the patentee full compensation for infringement. See General Motors Corp. v. Devex Corp., 461 U.S. 648, 654, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983).

VII. Conclusion

For reasons set forth above,

(A) In Civil Action No. 98-12308, I DENY Waters’ renewed motion for judgment as a matter of law notwithstanding the jury verdict and I find the '874 patent enforceable notwithstanding Waters’ claim of inequitable conduct. Accordingly, I direct the clerk to enter judgment for the Plaintiff against the Defendant in the amount of $52,800 in royalty damages together with prejudgment interest at the rate of 12% per annum to run from November 12, 1998 to the date of judgment. Post-judgment interest shall be in accordance with 28 U.S.C. § 1961;

(B) In Civil Action No. 99-11528, I DENY Waters’ and GRANT Cohesive’s motion for summary judgment, finding both infringement and validity of the '368 Patent. Accordingly, I direct the clerk to enter judgment for the Plaintiff declaring that the Defendant has infringed Patent No. 5,919,368, that the '368 patent is valid, and that Plaintiffs damages are subsumed in the damages award entered in Civil Action No. 98-12308;

(C) In Civil Action No. 01-12307, I DENY Cohesive’s motion for summary judgment of infringement and GRANT that of Waters as to noninfringement. Accordingly, I direct the clerk to enter judgment declaring that the Defendant’s 25 micron column does not infringe either Patent No. 5,772,874 or Patent No. 5,919,-368. 
      
      . On the basis of a three-day pre-trial eviden-tiary hearing, I determined that certain of Quinn's testimony was admissible as expertise under the Daubert standard. Waters incorporates its arguments from that hearing in its motion for judgment as a matter of law. In response to Waters’ motion, I have reconsidered my ruling that Quinn’s testimony is admissible as part of my evaluation the impact of the trial testimony on the scientific reliability of the evidence. I remain of the view that Quinn's expert testimony is admissible.
     
      
      . There appears no dispute that laminar flow is the opposite of turbulent flow; laminar is smooth flow, turbulent is rough flow.
     
      
      . A finding of willful or deliberate infringement would also support a finding that the patent case is an exceptional case for purposes of awarding attorneys fees to the prevailing party. nCube Corp. v. Seachange Intern., Inc., 436 F.3d 1317, 1319 (Fed.Cir. 2006).
     
      
      . Waters later retained outside non-trial counsel to provide an opinion on the issue of infringement in 1999, after Cohesive filed the complaint in this case. On the basis of additional testing by Dr. Bouvier and a review of the patent file and history, Alice O. Carroll rendered a written opinion to Waters on March 17, 1999 that the accused Waters coi-umn did not infringe the Cohesive patent either literally or under the doctrine of equivalents. Because this opinion was not written at the time that Waters decided to produce its product, however, it was not timely attorney advice for the purposes of determining whether Waters actions prior to 1999 were willful.
     
      
      . Cohesive alleges that Bouvier later corrected his measurement of interstitial volume to 48%. Because I find below that Waters reasonably believed the Oasis columns particles’ did not infringe based upon the lack of evidence of rigidity, Bouvier's determination of interstitial volume does not alter my finding that Waters’ infringement was not willful.
      Cohesive also maintains that Waters attempted to "cover up” its infringement by avoiding the use of the term "turbulent flow” in marketing the Oasis columns. I do not find Waters' avoidance of the term "turbulent” to constitute anything more than an attempt to avoid litigation. Waters’ behavior is consistent with a finding that it believed in good faith that it had successfully avoided infringement by manufacturing the accused column.
     
      
      . For reasons stated in my Markman Order, the fact that Waters’ particles are polymeric does not exclude the possibility that their particles are rigid within the definition of the patent claim. Nonetheless, the fact that the preferred embodiment of the patent used silica rather than polymeric particles militates in favor of a finding of good-faith in Waters’ opinion that the manufacture of polymeric particles would not infringe Cohesive's patents.
     
      
      . Cohesive also suggests that the fact that Janiuk wrote his opinion after a meeting between himself and the Waters scientists is somehow evidence of bad faith. But it was certainly reasonable for Janiuk to wait to compose his opinion of noninfringement until he had heard and discussed the results of the scientists' experiments.
     
      
      . Claim 1 of the '874 patent, on the other hand, claims:
      Chromatography apparatus comprising, in combination, a chromatographic body formed as a substantially uniformly distributed multiplicity of rigid, solid, porous particles with chromatographically active surfaces, said particles having average diameters of greater than about 30 microns, the interstitial volume between said parti-des being not less than about 45% of the total volume of said column; and
      a means for loading said surfaces with at least one solute that is reactive with said surfaces, by flowing a liquid mixture containing said solute through said body at a velocity sufficient to induce flow of said mixture within at least a substantial portion of said interstitial column at a reduced velocity greater than about 5,000.
     
      
      . The jury verdict found contributory and induced infringement specifically as to two of Waters' customers, Bristol-Myers Squibb and Dupont Pharmaceutical.
     
      
      . Cohesive has also provided evidence that Dr. Ding of Waters conducted experiments using 4 ml/min flow rates in August 1998 and February 1999. Neither of these instances, however, constitutes direct infringement because the '386 patent had not yet been issued.
     
      
      . Waters does assert that it cannot “know” that its customers will load the solvent with a particular flow rate. The argument is meretricious. Waters does not dispute that its promotional materials and demonstrations teach its customers to infringe the '368 patent.
     
      
      . I do not find that there is prosecution history estoppel in this case. "[Prosecution history estoppel limits the range of equivalents available to a patentee by preventing recapture of subject matter surrendered during prosecution of the patent.” See Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., Ltd., 493 F.3d 1368, 1377 (Fed.Cir.2007) (internal quotation omitted). Cohesive did not attempt to claim a limitation for a particle size of less than 30 microns in its patent application, and thus it was never required to "surrender” that subject matter in order to achieve patentability. Nevertheless, I note, as a cross check against my construction of the word “about”, that the prosecution history in this case supports the proposition that Cohesive understood it was excluding particle sizes of less than 30 microns from the patent claim. Cohesive in its patent application Cohesive cited 30 microns as the "minimum” particle size that would be required to achieve the desired flow. See SciMed Life Systems, 242 F.3d at 1345 ("Having specifically identified, criticized, and disclaimed the dual lumen configuration, the patentee cannot now invoke the doctrine of equivalents to 'embrace a structure that was specifically excluded from the claims.’ ”) (quoting Dolly, Inc. v. Spalding & Evenflo Cos., 16 F.3d 394, 400 (Fed.Cir. 1994)).
     
      
      . The scope of infringement of the '368 patent is not identical to the scope of infringement of the '874 patent. The '874 patent is an apparatus patent (particularly Claim 16, as discussed below, which claims a column) whereas '368 is a method patent. With regard to the '874 patent, Cohesive is entitled to damages, as stated below, for all sales of infringing columns during the infringing period because the jury verdict permits a finding of infringement of Claim 16 as to all the accused columns sold. With regard to the '368 patent, however, Cohesive would be entitled to damages only for sales to Bristol-Myers Squibb and Dupont.
     
      
      . The Federal Circuit has also recognized that where the patent holder and the infringer are the only two producers in the relevant market, the plaintiff can prove but-for profits by proving a lack of any other suppliers. See State Industries, Inc. v. Mor-Flo Industries, Inc., 883 F.2d 1573, 1578 (Fed.Cir.1989) ("In the two-supplier market, it is reasonable to assume, provided the patent owner has the manufacturing and marketing capabilities, that it would have made the infringer’s sales. In these instances, the Panduit test is usually straightforward and dispositive.”). Thus, under the two-supplier test, “a patentee must show: 1) the relevant market contains only two suppliers, 2) its own manufacturing and marketing capability to make the sales that were diverted to the infringer, and 3) the amount of profit it would have made from these diverted sales.” Micro Chemical, Inc. v. Lextron, Inc., 318 F.3d 1119, 1124 (Fed.Cir.2003).
     
      
      . Although Waters is not currently selling its 25 micron 1 x 50 mm column, the column can still be considered a substitute based upon the fact that Waters began manufacturing the column in place of the 30 micron column soon after this litigation commenced. See Grain Processing v. American Maize-Products Co., 185 F.3d 1341, 1351-52 (Fed.Cir. 1999) (holding that an alleged substitute need not be on the market during the infringement period in order to constitute an acceptable substitute). In any event, the 2.1 x 20mm column was introduced in October 1999, and thus was available during the infringement period.
     
      
      . Waters argues that Cohesive could not have made Waters sales because the customers purchasing Waters columns would have had to purchase a Cohesive's HPLC system in order to use its columns. The entire system is a capital purchase of approximately $80,000. Waters ignores the fact that these customers would necessarily have spent approximately the same amount to purchase Waters' system in order to use Waters' columns. Thus, I find the capital expenditure would likely amount to a wash; I do not find it to be a barrier to Cohesive's proof of lost profits.
     
      
      . A stronger argument is that I should award lost profits based upon those two customers, if Cohesive could show that those customers were not purchasing Cohesive’s columns during the infringing period. The evidence, however, shows that Cephlon and GlaxoSmithKline purchased 20 and 69 columns from Cohesive from 1998-2001, respectively. It appears unlikely that Waters' sales to these two customers were sales that Cohesive could have captured, given the diversified buying practices of those customers during the relevant period.
     
      
      .Cohesive's supplemental report filed in August 2007 makes no mention of whether Waters customers eventually began buying the patented technology from Cohesive. Thus, Cohesive has not provided any additional further basis since trial upon which I can conclude that it would have made Waters' sales during the infringing period.
     
      
      . As a result, Cohesive is also not entitled to price erosion damages, that is, damages for the higher price that Cohesive might have been able to charge for the columns it would have sold had Waters not sold the infringing product. See Minco Inc. v. Combustion Engineering, 95 F.3d 1109, 1119 (Fed.Cir.1996) (stating that to prove price erosion damages, plaintiff must show that but for the infringement it would have been able to charge higher prices).
     
      
      . Those factors are:
      1. The royalties received by the patentee for the licensing of the patent in suit, proving or tending to prove an established royalty.
      2. The rates paid by the licensee for the use of other patents comparable to the patent in suit.
      3. The nature and scope of the license, as exclusive or non-exclusive; or as restricted or non-restricted in terms of territory or with respect to whom the manufactured product may be sold.
      4. The licensor's established policy and marketing program to maintain his patent monopoly by not licensing others to use the invention or by granting licenses under special conditions designed to preserve that monopoly.
      5. The commercial relationship between the licensor and licensee, such as, whether they are competitors in the same territory in the same line of business; or whether they are inventor and promoter.
      6. The effect of selling the patented specialty in promoting sales of other products of the licensee; that existing value of the invention to the licensor as a generator of sales of his non-patented items; and the extent of such derivative or convoyed sales.
      7. The duration of the patent and the term of the license.
      8. The established profitability of the product made under the patent; its commercial success; and its current popularity.
      9. The utility and advantages of the patent property over the old modes or devices, if any, that had been used for working out similar results.
      10. The nature of the patented invention; the character of the commercial embodiment of it as owned and produced by the licensor; and the benefits to those who have used the invention.
      11. The extent to which the infringer has made use of the invention; and any evidence probative of the value of that use.
      12. The portion of the profit or of the selling price that may be customary in the particular business or in comparable businesses to allow for the use of the invention or analogous inventions.
      13. The portion of the realizable profit that should be credited to the invention as distinguished from non-patented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer.
      14. The opinion testimony of qualified experts.
      15. The amount that a licensor (such as the patentee) and a licensee (such as the infringer) would have agreed upon (at the time the infringement began) if both had been reasonably and voluntarily trying to reach an agreement; that is, the amount which a prudent licensee — who desired, as a business proposition, to obtain a license to manufacture and sell a particular article embodying the patented invention — would have been willing to pay as a royalty and yet be able to make a reasonable profit and which amount would have been acceptable by a prudent patentee who was willing to grant a license.
      
        See Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y. 1970).
     
      
      . The "25% rule” is a rule of thumb for calculating a hypothetical royalty rate, determined by taking 25% of Cohesive's gross profit margin (revenues minus marginal costs divided by revenues) for the year of the infringement. The rule assumes that the Waters gross profit margin would be similar. Bokhart states that Cohesive’s gross profit margin for fiscal year 1998 was 45%.
     
      
      . The book-of-wisdom analysis calculates a royalty rate based upon a 25% rule of the profits as hypothesized by but-for lost profits during the infringement period. Thus, Bok-hart assumes that the relevant royalty revenues should be $572,722, the amount he previously calculated as Cohesive’s lost sales as a result of Waters infringement.
     
      
      . To summarize, parties claimed at various times that the relevant infringing sales are of:
      1,915 columns (Bokhart Report 3/6/02, Ex. 5)
      2,070 columns (Bokhart Report 3/6/02, Ex. 6)
      2,112 columns (Bokhart Report Aug. 2007)
      2,290 columns (Bokhart Report 3/6/02, at 19)
      1,612 columns (Saunders Report 3/6/02, Attachment 2)
     
      
      . The parties also stipulate that of those sales, 850 were made to Bristol-Myers Squibb and Dupont Pharmaceutical.
     
      
      . Cohesive requests that I treble damages because the infringement in this case was willful, and asserts that I should award Cohesive attorney’s fees because due to willfulness this is an exceptional case within the meaning of fee shifting statute 35 U.S.C. § 285. Having found in Section II.B. above that Waters’ infringement was in good faith, I decline to award treble damages or attorney’s fees.
     
      
      . Cohesive’s list price, by contrast, was $495 for single columns and $3950 for a 10-pack.
     