#### MINERALS TECHNOLOGIES INC. and Specialty Minerals Inc. Plaintiffs, v. OMYA AG, Omya Industries Inc., and Omya, Inc. Defendants.

No. 04 Civ. 4484(VM).

United States District Court, S.D. New York.

May 8, 2006.

*196Anthony J. Costantini, Duane Morris, LLP (NYC), New York, NY, Laura Danielle, Patricia Bayer Cunningham, Sutherland Asbill & Brennan LLP, Atlanta, GA, for Minerals Technologies Inc., Specialty Minerals Inc.

Jeffrey T. Golenbock, Golenbock Eise-man Assor Bell *&*Peskoe LLP, New York, NY, for Omya AG, Omya Industries Inc., Omya, Inc.

*DECISION AND ORDER*

MARRERO, District Judge.

Plaintiffs Minerals Technologies Inc. (“MTI”) and Specialty Minerals Inc. (“SMI”) (collectively, “MTI”) brought the underlying action against defendants Omya AG, Omya Industries, Inc., and Omya, Inc. (collectively, “Omya”) alleging infringement and inducing infringement of two United States patents, No. 5,043,017, (the “ ’017 Patent”) and No. 5,156,719 (collectively the “Patents”), that are owned by MTI and based on essentially the same *197papermaking technology.1 By a Settlement Agreement (the “Agreement”) dated November 22, 2005, the parties settled a related action,2 resolved a number of other issues in dispute in the instant case, and thus narrowed the scope of this litigation. The Agreement calls upon the Court to provide interpretations of certain important terms used in the Patents and, on the basis of that construction, to resolve the remaining matters about which the parties still disagree. Set forth below are the Court’s findings, conclusions and reasoning in this regard.

I. *FACTUAL BACKGROUND*

The Patents relate to a chemical process for manufacturing paper. The technology uses calcium carbonate as a filler and coating substance that does not affect the acidity of paper when it is mixed with wood pulp during the process and that improves the quality of the product’s color, gloss and opacity.3 Normally, calcium carbonate, an alkaline substance, when mixed with wood pulp decreases the acidity of the mixture, which is referred to as a paper “furnish” or “slurry,” causing the filler to decompose. This change in acidity can be harmful for certain types of neutral or weakly acidic paper.4

The ’017 Patent was issued in 1991 to June Passaretti (“Passaretti”) for a paper-making system based on the use of a calcium carbonate that is “acid-stabilized” in a neutral to mildly acidic environment of a mixture composed of a calcium-chelating agent5 and/or a conjugate base, combined with a requisite amount of “weak acid.”6 In this system the calcium carbonate does not affect the acidity of the slurry because the weak acid works to control the pH of the mixture and maintain it in equilibrium. Claim 1 of the patent asserts protection for:

> An acid-stabilized finely divided calcium carbonate comprising a mixture of at least about 0.1 weight percent of a compound selected from the group consisting of a calcium-chelating agent and a conjugate base, together with at least *198about 0.1 weight percent of weak acid, with the balance to give 100 weight percent being finely divided calcium carbonate, such that the calcium carbonate is coated by and is in equilibrum [sic] with the calcium-chelating agent or conjugate base and the weak acid.

*Id.*

In the underlying action as filed, MTI sought relief against Omya, its primary competitor in the relevant market, on the grounds that Omya had infringed and induced paper manufacturers to infringe the Patents by conducting tests in which calcium carbonate and a calcium-chelating agent were combined with a weak acid used to reduce the alkalinity of the slurry and resulting paper product, and by evidencing Omya’s intentions to expand its papermaking business by means of this process. Specifically, MTI points to pa-permaking tests Omya conducted at a mill owned by a company named Stora Enso North America (“SENA” or “Stora Enso”) in December 2003 (the “2003 SENA Trial”) and August 2004 (the “2004 SENA Trial”) as instances in which Omya induced infringement of MTI’s patents by providing supplies and instructions for paper-making that used the same components in the requisite amounts to satisfy the “weak acid” requirement described in the Patents (the “Weak Acid Requirement”).7 The parties agree that at the 2004 SENA Trial, which was conducted over a seven-day period, Omya injected 36.5 tons of carbon dioxide (C02) into an aqueous paper furnish consisting of a calcium-chelating agent and 1034 tons of calcium carbonate filler.

It is also undisputed that some amount of the carbon dioxide reacted with the water in the furnish to produce some amount of carbonic acid (a weak acid). The quantity of carbonic acid thus formed at the trial was not measured. MTI argues that Omya’s use of carbon dioxide in this test met the Weak Acid Requirement in three ways: (1) by itself, on the ground that carbon dioxide is classified in the chemical literature and recognized by those skilled in the chemical arts as a “Lewis” acid8 that exhibits the properties of a weak acid and that was present in the requisite amount in the system; (2) through its formation of a requisite amount of carbonic acid; and (3) by the production of bicarbonate in a sufficient quantity from the further reaction and disassociation of carbonic acid in the slurry. According to MTI’s computations, the 36.5 tons of carbon dioxide used at the 2004 SENA Trial, in combination with 1034 tons of calcium carbonate, would have exceeded the 0.1 weight percent relationship of these substances in the mixture as claimed by the Patents. Similarly, MTI contends that the amount of carbonic acid and bicarbonate produced at the 2004 SENA Tidal each totaled 50.6 tons, or about 4.9 weight percent, thus exceeding the 0.1 limitation the Weak Acid Requirement specifies. MTI also maintains that Omya’s use of any of these three claimed weak acids at the 2004 SENA Trial infringed the Patents under the doctrine of equivalents.

*199Omya admits that it conducted the Stora Enso trials, but claims that for several reasons the tests did not infringe or induce infringement of the Patents, either literally or under the doctrine of equivalents. First, Omya asserts that carbon dioxide is a gas, not a “weak acid” within the meaning of the literal terms of the Patents, and that indeed by this standard it cannot be classified as an acid at all, whether under the Lewis acid definition claimed by MTI, or according to the “Bronsted” acid9 definition. Omya contends that the latter definition is more commonly known by those skilled in the chemical arts and is thus the understanding of “weak acid” that comports with the ordinary and customary meaning of the terms and teaching of the Patents. Second, Omya argues that at the 2004 SENA Trial it was not the carbon dioxide itself that performed the weak acid function to lower the alkalinity of the paper furnish, but the carbonic acid produced by the carbon dioxide, some portion of which reacted with the water when injected into the slurry. According to Omya’s analysis, the amount of carbonic acid produced totaled approximately 0.0129 weight percent of the calcium carbonate mixture, well below the 0.1 percent measure the Patents claim as a minimum. And third, Omya claims that the 2004 SENA Trial did not infringe because the calcium carbonate in the system was not “acid-stabilized.” Rather, the furnish was maintained at all times at a pH level of 7.2, thus in the alkaline range, rather than neutral or acidic, as the product would have to be if the Passaretti technology had been employed according to its literal terms.

II. *ISSUES BEFORE THE COURT UNDER THE AGREEMENT*

The issues remaining in dispute that the parties have asked the Court to resolve are set forth in Paragraph 4 of the Agreement.10 The first section of Paragraph 4 reads as follows:

> Although the parties have agreed to settle the Antitrust and Patent Actions as set forth above, they continue to disagree as to the requirement in U.S. Patent No. 5,4043,017 (the “’017 Patent”) and U.S. Patent No. 5,516719 (the “ ’719 Patent”) that at least about 0.1 weight percent of weak acid be used (the “Weak Acid Requirement”); specifically, the parties disagree whether the Weak Acid Requirement was met in connection with the papermaking trial that took place at Stora Enso North America, in Duluth, Minnesota, in August 2004 (the “August SENA Trial”).

*(Id.)*

In an earlier ruling addressing a dispute concerning the scope of what the Agreement called upon the Court to resolve, the Court determined that this provision describes the parties’ continuing disagreement as to whether the Weak Acid Requirement was met by any means during the 2004 SENA Trial. *See Minerals Tech. II,*406 F.Supp.2d at 335.

However, because Omya used carbon dioxide at the 2004 SENA Trial, the Agreement describes several additional aspects of the underlying dispute the parties asked the Court to review in connection with its determination of whether the Weak Acid Requirement was met during that experiment. There was no disagreement that *200Paragraph 4 placed before the Court the narrow question of whether the amount of carbonic acid formed at the 2004 SENA Trial satisfied the Weak Acid Requirement. *(See id.*at 335.) This section of the Agreement reads:

> MTI contends that the amount of carbonic acid formed by the use of the C02 satisfied the Weak Acid Requirement. Omya denies that. The parties have agreed ... to resolve this issue before [the District Court].

(Agreement, at ¶ 4.)

The Court also concluded, however, that the remainder of Paragraph 4 enlarges the scope of what the parties request the Court to address. In particular, in addition to rendering a “definitive ruling” on the issue of whether the Weak Acid Requirement was satisfied at the 2004 SENA Trial, the Agreement calls for the Court to provide a detailed explanation concerning the chemical reaction of carbon dioxide in a paper furnish. Specifically, that second task requests that the Court “also” explain “the basis for its decision,” including three distinct components: (1) a “detailed statement” of “its claim construction of the term ‘weak acid’ as it relates to the formation of carbonic acid through the addition of C02 to a paper furnish,” “as well as” (2) an explanation regarding “the circumstances under which the addition of C02 to a paper furnish will meet the Weak Acid Requirement,” “as well as” (3) “the circumstances when carbonic acid, alone or in combination with other weak acids, meets the Weak Acid Requirement.” *(Id.; see also, Minerals Tech. II,*406 F.Supp.2d at 338.)

The last sentence of Paragraph 4 spells out a third task for the Court that also arises as a component of the underlying question. It records that the parties continue to disagree with regard to “the proper application of the Doctrine of Equivalents, Prosecution Estoppel, and other legal issues as they relate to the Weak Acid Requirement,” and asks the Court to “address these issues as well,” to the extent they are raised by the parties. (Agreement ¶ 4.)

There is another provision of the Agreement that has some factual bearing on the Court’s resolution of the matters at hand. It is contained in Paragraph 7 and states that “for purposes of this Agreement ... both phosphoric acid and carbonic acid are weak acids,” and that “there is no intent by this Agreement to limit what would *otherwise*constitute ... a weak acid.” *(Id.*¶ 7 (emphasis added).) Therefore, the Agreement does not rule out the prospect that carbon dioxide or bicarbonate could be found to constitute weak acids for purposes of the Weak Acid Requirement.

III. *THE TRIAL*

To address the parties’ remaining disputes as set forth in the Agreement the Court conducted a bench trial on December 19 and 20, 2005 and January 20, 2006. The evidence, issues and arguments at the trial are described below.

A. *MTI’s CLAIMS*

MTI argued at the trial, and in related documents entered into the record of these proceedings, that the Patents allow that various claimed weak acids, alone or in combination, could serve as the weak acid in the system. In particular, it contended that the Weak Acid Requirement was met at the 2004 SENA Trial both literally and under the doctrine of equivalents by the presence of requisite amounts of three different substances MTI claims are weak acids, as summarized above: carbon dioxide, carbonic acid and bicarbonate. According to MTI any one of these weak acids, or a combination of them, functioned during that test to attain the result of *201lowering and maintaining the pH of the slurry at a constant level of about 7.2, thereby achieving what the Patents describe as an acid-stabilized calcium carbonate coated by and in equilibrium with the other compounds in the system.

1. *Carbon Dioxide*

MTI presented the testimony and reports of its expert, Robert Pelton (“Pel-ton”), a chemist whose field of specialty and experience are grounded in the paper-making industry.11

In support of its argument that carbon dioxide qualifies as a “weak acid” as the term is used in the Patents, MTI relied on several sources and forms of evidence. First, it pointed to statements made by Omya representatives during the course of this litigation purportedly acknowledging that carbon dioxide is commonly referred to as a weak acid with an assigned pKa value, a chemical measure by which the weakness of an acid is determined. *(See*Minerals Technologies Inc. and Specialty Minerals Inc.’s Post-Trial Memorandum dated February 3, 2006 (“MTI’s Posh-Trial Mem.”), at 4.)12 Second, MTI cited portions of a number of chemistry texts that refer to or describe carbon dioxide as a weak acid. *(See id.*at 5.) And third, MTI relied on the opinion of Pelton, who testified that carbon dioxide is a Lewis acid that qualifies as a weak acid for the purposes of the Patents. *(See id.)*In this connection, MTI points out that the Patents specifically list boric acid as a weak acid that could satisfy the Weak Acid Requirement and that, as conceded by Omya’s experts at trial, boric acid in an aqueous solution functions as a Lewis acid by bonding with a water molecule and then donating a proton. *(See id.*at 7.)

Alternatively, MTI contended that carbon dioxide may be classified as a weak acid under the doctrine of equivalents. On this point, MTI argued that in a paper furnish, carbon dioxide acts just as boric acid does to perform the same function of lowering pH: it dissolves, reacts with the water to form carbonic acid, a conceded a weak acid, which then donates protons to the furnish, and in turn disassociates to produce bicarbonate, another known weak acid. *(See id.*at 8.) Similarly, MTI maintained that carbon dioxide as used in the 2004 SENA Trial may also be determined the functional equivalent of phosphoric acid, which Omya employed at the 2003 SENA Trial to maintain the pH of the furnish at between 7.1 and 7.3. *(See id.*at 9.) Further, MTI argued that carbon dioxide is also the equivalent of carbonic acid, in that once hydrated it serves as the acid anhydride of carbonic acid, its conjugate acid.

There is no dispute that the 36.5 tons of carbon dioxide injected into the 1034 tons of calcium carbonate in the paper furnish at the 2004 SENA Trial constituted at least 0.1 weight percent of the calcium *202carbonate. Accordingly, were the Court to find that carbon dioxide properly may be termed a weak acid, MTI would have demonstrated that the literal terms of the Weak Acid Requirement were met at the 2004 SENA Trial by this means.

2. *Carbonic Acid*

As stated above, the parties agree that carbonic acid is a weak acid as the term is used in the Patents and that at the 2004 SENA Trial the carbon dioxide injected into the furnish dissolved and reacted with the water. Some or all of the dissolved carbon dioxide — -the precise amount remains in dispute' — converted to form an amount of carbonic acid, which functioned to control alkalinity, maintaining the pH of the slurry at about 7.2. For the purposes of the Agreement, the parties’ principal disagreement in this respect is whether the amount of carbonic acid produced during the test met the Weak Acid Requirement by exceeding the 0.1 weight percent limitation. On this point Pelton testified that at a pH of 7.2 in the slurry most or all of the 36.5 tons of carbon dioxide introduced into the paper furnish converted to form about 50.6 tons of carbonic acid, as a transitional state before further reacting to produce bicarbonate, each of these weak acids yielding a weight percent measure of 4.9 of the calcium carbonate in the system. *(See id.*at 10.)

According to Pelton, the carbon dioxide injected in the slurry dissolved and remained in the system. It continuously recycled and, through a relatively slow reaction by chemical standards, disassociated in the water to generate carbonic acid which, through further consumption of carbon dioxide, formed bicarbonate. Under this analysis of the system, because the carbon dioxide was constantly consumed by the paper furnish, carbonic acid was being produced continuously to generate bicarbonate, and thus, more of the carbon dioxide that was dissolved and recycling in the water was disassociating and converting to produce carbonic acid. *(See id.*at 14; Trial Tr. at 73.)

3. *Bicarbonate*

Citing Pelton’s calculations, MTI argued that the 36.5 tons of carbon dioxide used at the SENA August Trial, at a slurry pH of 7.2, formed 50.6 tons of bicarbonate, which translates into 4.9 weight percent of the calcium carbonate in the paper furnish, thus meeting the Weak Acid Requirement. Moreover, MTI maintained that the formation of bicarbonate satisfied the Weak Acid Requirement under the doctrine of equivalents, insofar as it is a weak acid and functioned as such at the 2004 SENA Trial, lowering the pH of the paper furnish by disassociating and generating hydronium ions and donating protons to the slurry.

B. *OMYA’S RESPONSES*

Omya counters that the evidence produced at the trial and related record of this proceeding was not sufficient to satisfy MTI’s burden to prove its claims by a preponderance of the evidence. In support of its defense, Omya relied on the testimony and reports of two experts, Michael Waller (“Waller”)13 and Christopher Cummins (“Cummins”).14 Omya contend*203ed that the well-established ordinary and customary meaning of the term “weak acid” to a person skilled in the chemical arts at the time the Patents were issued was what is known as a Bronsted-Lowry acid. *(See*Defendants’ Posh-Trial Memorandum of Law in CCyCarbonic Acid Mini-Trial, dated February 3, 2006 (“Def.’s Post-Trial Mem.”), at 4-5.) According to both Waller and Cummins, a person of ordinary skill in the chemical arts at that time would not have classified a Lewis acid within the definition of a weak acid. *(See id.)*

Omya then argued that carbon dioxide is not an acid under any definition of the term, and thus cannot be considered either a weak acid or a Bronsted acid because carbon dioxide (1) does not possess a proton to donate; (2) does not disassociate and release a hydronium ion when reacting in an aqueous solution; and (3) does not have an assigned value on the pKa scale, which is used to measure the strength of Bronsted acids, because it has no protons to donate in reacting with water. *(See id.*at 6.)

Omya dismissed MTI’s argument that carbon dioxide is a Lewis acid as irrelevant because: (1) by definition, a weak acid encompasses only Bronsted acids; (2) there are many Lewis acids that cannot be considered weak acids; (3) Lewis acids are characterized as “hard” or “soft,” unlike Bronsted acids that are termed “weak” or “strong”; and (4) in any event, carbon dioxide is not electron-deficient and thus cannot properly be considered a Lewis acid under the accepted Lewis acid definition as “an electron-deficient molecule that can act as an electron pair acceptor.” *(Id.*at 6-8.) For this reason, Omya asserts that the classification of carbon dioxide as a Lewis acid in the chemistry textbooks cited by MTI is incorrect.

Omya next rejected MTI’s claim that the Patents were also infringed by application of the doctrine of equivalents. First, it argued that MTI’s invocation of the doctrine of equivalents is vitiated under the related doctrine of prosecution history es-toppel because in processing its application to obtain the Patents, MTI made statements asserting that the word “weak” with regard to “weak acid” was well known to those skilled in the chemical acts and that the terms have a well-established meaning in that context. Omya thus contended that because at the time the Patents were issued the recognized meaning of the term “weak acid” to persons skilled in the chemical arts was a weak Bronsted acid, or proton donator, MTI should be estopped from now claiming that a “weak acid” means anything else, in particular a Lewis acid. *(See id.*at 11.)

Moreover, Omya maintained that the carbon dioxide used at the 2004 SENA Trial was not the equivalent of a weak acid because when injected into the paper furnish most of It did not disassociate to convert into carbonic acid, and therefore the unconverted carbon dioxide gas itself (1) did not function as an acid, (2) had no effect on the acid stability of the calcium carbonate, and (3) did not otherwise operate to lower the pH of the slurry to the alkaline pH of 7.2, contrary to the function of the weak acid as described in the Patents, which teach that the calcium carbonate is stabilized in a mildly *acidic*environment. *(See id.*at 12-14.)

Finally, though it acknowledged that carbonic acid constitutes a weak acid within the meaning of the Patents, and that at the 2004 SENA Trial it was the carbonic acid, and not the carbon dioxide, that func*204tioned as a weak acid to lower the pH of the paper furnish, Omya nonetheless contended that the amount of carbonic acid formed during the test was less than 0.1 weight percent of the calcium carbonate in the slurry. *(See id.*at 14-15.) Specifically, Waller testified that according to his computation, the 36.5 tons of carbon dioxide injected into the furnish containing 1034 tons of calcium carbonate yielded carbonic acid in an amount of approximately .0129 weight percent in relation to the calcium carbonate present, thus less than the Patents’ 0.1 weight percent limitation. *(See id.*at 16-17.) Relying on Waller’s testimony, Omya asserted that all of the carbon dioxide injected into the furnish dissolved and was then pumped to a decu-lator which, according to Omya, operated to remove all dissolved gases from the furnish to prevent holes and other defects in the paper product. *(See id.*at 16.) By Omya’s theory, the small portion of dissolved carbon dioxide not removed by the deculator reacted with the water in the furnish to form some carbonic acid, and thus, because of the rapid speed at which the slurry moved through the Stora Enso papermaking machine, was not available to form any more carbonic acid. *(See id.)*

In response to Pelton’s analysis calculating the amount of carbonic acid yielded by the 2004 SENA Trial as 4.9 weight percent, Omya challenged the conclusion that all of the carbon dioxide used at the trial remained in the system and was consumed while producing carbonic acid and bicarbonate. On this point Omya asserted that Pelton did not consider the “rate constant” of carbon dioxide nor the time the furnish took to travel from the point of injection of the carbon dioxide to the deculator, where the dissolved unconverted carbon dioxide, according to Omya’s argument, was all removed from the slurry. *(See id.*at 18.) Omya rejected Pelton’s analysis on the ground that it posited a “closed system” that assumed the presence of an infinite amount of carbon dioxide for an infinite time. *(See id.*at 19.)

Finally, Omya contended that Pelton’s theory that the carbon dioxide used in the paper furnish at the 2004 SENA Trial continuously produced carbonic acid until it was all consumed by the bicarbonate, despite the presence of a calcium-chelating agent, is inconsistent with the premise of the Patents, which teach that when the calcium-chelating agent is applied to the surface of the calcium carbonate, it acts to reduce the solubility of the calcium carbonate’s surface and thus to prevent the acid from reacting with the surface of the filler. *(See id.*at 21.)

III. *DISCUSSION*

A. *TESTIMONY OF EXPERTS*

Resolution of a complex dispute laden with disagreements over highly technical and scientific issues, as are the questions the parties have placed before the Court, necessarily rests in substantial part on which of the experts the Court considers more persuasive overall and better qualified to address the specific matters in contention, as well as what arguments, analysis and authority offered in support of their opinions the Court finds more compelling. Here, each of the experts who appeared at trial and submitted reports had impressive professional credentials. The Court found each of them sufficiently learned and distinguished as regards the technical issues they were asked to address. Yet, their explanations of the chemistry of the slurry, the understanding they conveyed of the papermaking process that occurred during the Stora Enso trials, and their professional opinions concerning the scientific issues in contention differed fundamentally. As a matter of scientific fact relevant to the resolution of the in*205stant disputes, those conflicting views cannot all be right, nor can the divergences be fully reconciled. Consequently, insofar as the Court relies upon the opinions and analyses of the experts for this purpose, on balance it gives an edge to Pelton, whose testimony and report the Court credits as more compelling.

Given the large contrast among the experts’ testimony, the Court found several considerations as persuasive. First, the Court takes note that Pelton’s doctorate education, work, professional expertise and writings more closely derive from and relate to the chemistry of the papermaking industry that is at issue here. As MTI points out, Waller’s professional training and specialty, whatever his experience in this field, is as a mechanical engineer, not a chemist, and Cummins admitted at trial that the range of his professional specialty and experience did not extend to the pa-permaking industry. Second, as regards some material issues elaborated below where the analysis and opinions of the experts disagreed sharply, the Court found Pelton’s views of the chemistry and technology both more plausible and more convincing, not only in itself, but in part as well by reason of some material gaps or inconsistencies in the testimony of Omya’s experts. And third, having reviewed the experts’ reports, observed their respective presentations at trial during the parties’ direct case presentations and under cross-examination, and after gauging their overall professional reliability and demeanor in this context, the Court found Pelton’s testimony the more creditable on these grounds as well.

B. *MATERIAL DIFFERENCES*

Among the material issues over which the parties and their experts strongly disagreed, the Court found two .that are particularly central to the questions the Court must address: the function of the deculator in the Stora Enso papermaking machine and, somewhat related, the length of time that the carbon dioxide used in the trial remained dissolved and unconverted in the paper furnish, a duration that consequently determined the amount of carbon dioxide which remained available to form carbonic acid and bicarbonate. How these disputes are resolved substantially guides the adjudication of the issues before the Court.

1. *Function of the Deculator*

As summarized above, MTI, relying on Pelton’s testimony, asserts that the deculator in the Stora Enso papermaking machine operated to remove undissolved air or gas bubbles, *not*dissolved gas, from the paper furnish, and that the carbon dioxide used in the test remained dissolved and recycling in the slurry long enough for all of it to convert to carbonic acid, which in turn formed bicarbonate, each compound in the requisite amount to meet the Weak Acid Requirement. *(See*Trial Tr. 119, 11. 15-21; MTI Post-Trial Mem. at 14.) By contrast, Omya, citing Waller’s testimony, contends that a deculator removes dissolved gas from the slurry and that therefore, at the 2004 SENA Trial, all of the dissolved carbon dioxide injected into the furnish that did not convert to carbonic acid in the relatively small reaction time available was removed. Omya states that the unconverted carbon dioxide removed comprised the bulk of the amount used.

Clearly these two claims regarding the role performed by a significant component of a large machine employed in the paper-making industry are at odds. Absent some technical principle not presented to the Court on this record, one or the other view must be incorrect. Thus, in part for the reasons stated above regarding the respective experts’ credentials, relevant *206knowledge of and experience in the paper-making industry, and their overall persuasiveness, the Court credits Pelton’s testimony on this point.

Pelton’s view comports with a more technically sensible and practical understanding of the chemistry and operation of the papermaking system the parties described. The Court finds it doubtful that carbon dioxide injected into the system at a point located a relatively short distance from the deculator, while the slurry was moving at a speed of approximately 50 miles per hour, would all promptly dissolve, only to be pumped immediately thereafter into the deculator, where the bulk of the gas would then be removed from the furnish, leaving only a minimal amount of it enough time to convert to carbonic acid.

2. *Reaction Time and Amounts of Converted Carbon Dioxide in the System*

The proper function that the deculator performed at the SENA August Trial significantly shapes the determination of the other major issue about which the parties and their experts acutely differ: the time during which the carbon dioxide used in the test remained dissolved in the paper furnish and available to react with the water in the system and, as a result, the amount of carbonic acid formed during that period. For the reasons described above, even if Omya’s view of the function of the deculator were correct, the Court remains more persuaded by Pelton’s explanation and does not find Omya’s analysis regarding the central issues compelling. Omya posits that all of the carbon dioxide injected immediately dissolved in the paper furnish and was then removed by the deculator, and that the carbon dioxide was thus present in the slurry for only a very limited period of time, not long enough to convert to carbonic acid in an amount sufficient to meet the limitation of the Weak Acid Requirement. This theory leaves open to question how the carbon dioxide could have performed its chemical purpose of reacting with water to produce enough carbonic acid to regulate the pH of the slurry. In this regard, the Court notes, as also pointed out by MTI, that Waller’s presentation was not consistent.

At trial Waller repeatedly and unequivocally stated that *all*of the carbon dioxide added to the slurry dissolved. *(See*Trial Tr. at 238,11. 21-22; 239, 11. 9-10.) In his report, however, Waller stated that “only a small percentage of carbon dioxide dissolves in water....”15*(See id.*at 4 (“Only some of the C02 that is injected into the furnish will dissolve.”).) In another part of the report Waller states: “Assuming that 25% of the C02 used dissolved in the furnish (in fact, far less than that), closer to 1% would have dissolved.” *(Id.*at 5.) Omya does not address this large discrepancy in its expert’s testimony. But the inconsistency is important because it touches upon another major point which bears on the calculation of the amount of carbonic acid formed and on which the experts’ presentations clashed.

The amount of carbon dioxide dissolved in the furnish, the time it takes for it to react with the water, and the duration of the dissolved carbon dioxide in the system should be major factors determining how much carbonic acid was formed. In this regard, Waller testified that the reaction time is approximately one minute. *(See*Trial Tr. at 250, 11. 7-9). This assumption *207is not consistent with other aspects of his analysis. There is evidence from Stora Enso officials who conducted the test that it took the furnish under one minute, and most likely between 15 and 45 seconds, to travel to the headbox from the point where the carbon dioxide was injected into the system. *(See*Deposition of Jesse A. De-Witte, dated November 20, 2005, at 29, 11. 1-13.) Waller’s testimony that the conversion reaction takes approximately one minute suggests that the carbon dioxide would not have had sufficient time to fully dissolve before it reached the headbox. However, Waller testified at trial that all of the carbon dioxide injected into the slurry dissolved *(see*Trial Tr. at 239) and that the carbon dioxide conversion reached a state of equilibrium. *(See*Trial Tr. at 214, 11. 19-21; 243, 11. 5-9). This apparent inconsistency raises substantial questions about Waller’s assumptions and analysis.

Pelton, supported by references to other chemistry literature, stated that the reaction time for carbon dioxide to dissolve and react with water takes only a matter of seconds, thus allowing longer opportunity for more of the dissolved carbon dioxide to convert into carbonic acid. *(See*Trial Tr. at 80, 11. 3-17.) Thus, the analysis contained in Waller’s report effectively assumed a static system, and his computation of the amount of carbonic acid formed seems based on a snapshot of any single moment, rather than the aggregate over the course of the entire test. At trial, however, Waller appeared to have modified this position by stating the carbonic acid amount he calculated extended over the duration of the entire experiment. *(See*Trial Tr. at 222.) In fact, the paper furnish had water recycling and carbon dioxide continually being injected into it. As noted above, it took the furnish under one minute and more like 15 to 45 seconds to travel to the headbox from the point where the carbon dioxide was injected into the system. *(See*Trial Tr. at 118.) These discrepancies again raise questions about whether under Waller’s theory there was sufficient reaction time for all of the carbon dioxide to dissolve before the portion of it that remained unconverted was removed, even if the Court accepted his version of how the deculator functioned.

On these points as well the Court finds Pelton’s report and testimony explaining the chemistry of the system more persuasive. If all of the carbon dioxide did dissolve in the slurry but, contrary to Waller’s testimony, it was *not*removed by the deculator, but rather, as Pelton argued, the carbon dioxide remained in the system through fresh injections and by continuous recirculating in the furnish, it would have been available for reaction long enough to create in the aggregate greater quantities of carbonic acid, which in turn promptly disassociated to generate bicarbonate. The process would continue recycling until all of the dissolved carbon dioxide would have been consumed by the chemical reactions. By this means, the amount of carbonic acid created would have been greater than that resulting from Waller’s assumptions and analysis, and more consistent with Pelton’s calculation.

The Court’s acceptance of Pelton’s theory and analysis of the chemistry and operation of the paper furnish at the 2004 SENA Trial serves as the technical foundation for the Court’s own determinations of the questions it is asked to resolve. With this scientific support as framework for its determination, and upon consideration of the entire record before it, the Court concludes that the Weak Acid Requirement was met at the 2004 Stora Enso Trial, both literally and under the doctrine of equivalents. The Court addresses these findings and explains its reasoning below.

*208IV. *FINDINGS*

A. *CARBON DIOXIDE AND THE WEAK ACID REQUIREMENT*

The Court finds the evidence mixed, perhaps at best evenly divided and thus inconclusive, on the issue of whether the carbon dioxide used at the 2004 SENA Trial by itself literally met the Weak Acid Requirement. MTI produced evidence, through Pelton’s testimony and scientific literature, supporting the proposition that carbon dioxide may be considered a Lewis acid. The issue before the Court, however, entails a broader inquiry: whether, giving the terms of MTI’s patent claims their ordinary and customary meaning, the phrase “weak acid” would have been regarded by a person of ordinary skill in the chemical arts in 1991 as encompassing the classification of carbon dioxide as a weak acid, and whether “weak acid” referred to a Lewis acid, rather than only a Bronsted acid.

A preliminary step of the analysis is whether the skilled person the standard refers to is one possessing sufficient technical knowledge and ordinary skill relating to the general art in question, here the “chemical arts,” or whether the inquiry may be further confined to a narrower sub-specialty within a particular technical field or industry. MTI’s argument suggests this more limited standard: that persons such as Pelton and Passaretti skilled in the specialized chemistry of papermak-ing would understand that carbon dioxide is a Lewis acid within the literal meaning of the weak acid element of the Patents and would function as such in a paper furnish. *{See*Trial Tr. at 91,11. 1-14; 302, 11. 12-25; 303, 11. 1-7.) However, MTI’s argument is somewhat undercut in that, in its application to the Patent and Trademark Office (“PTO”) for the Patents, MTI noted that the term “weak” in the reference to “weak acid” is well known to those “skilled in the chemical arts” and has a well-established meaning in that context. There is no indication that MTI sought to narrow the relevant technical field to the chemical arts specifically associated with the papermaking industry.

Omya, on the other hand, implicitly suggests the application of a more general standard, enlarging the field more broadly to encompass persons skilled in the chemical arts, not necessarily those involved in papermaking. By this measure, Omya, citing the testimony of Waller and Cum-mins, contends that the reference to weak acids means only a Bronsted *acid*— a proton donator that partially ionizes in water — and points out that only Bronsted acids are chemically classified as “weak” or “strong” in accordance with the scale of pKa values, as opposed to the “soft” and “hard” terminology applied to Lewis acids.

The Court concludes that the skilled person the standard refers to is appropriately defined here as a person with skill in the specialized art of papermaking. A “person of ordinary skill in the art” is defined as “a hypothetical person who is presumed to be aware of all the pertinent prior art.” *Custom Accessories, Inc. v. Jeffrey-Allan Indus., Inc.,*807 F.2d 955, 962 (Fed.Cir.1986). “Prior art” is elsewhere defined as that which is “reasonably pertinent to the particular problem with which the inventor was involved.” *Stratoflex, Inc. v. Aeroquip Corp.,*713 F.2d 1530, 1535 (Fed.Cir.1983). These definitions, together with case law applying the “person of ordinary skill in the art” standard, suggest that the more restrictive formulation of the standard is appropriate. *See, e.g., Cargill, Inc. v. Sears Petroleum & Transp. Corp.,*334 F.Supp.2d 197, 215-16 (N.D.N.Y.2004). In *Cargill,*which involved a patent for a chemical composition used in road de-icing, the court weighed the parties’ competing definitions of “one *209with ordinary skill in the art” and concluded that the skilled person possessed specialized experience in road de-icing and training in chemistry, rather than chemistry training alone. *See id.*

If, as this authority suggests, the more restrictive field were the applicable test, MTI’s position would be somewhat undercut by evidence emanating from its own sources. As Omya points out, at his deposition in an earlier phase of this litigation, apparently before the question of whether carbon dioxide may qualify as a Lewis acid arose, Pelton, a person with skill in the specialized art of papermaking, offered a definition of an acid that reflected the Bronsted definition; he made no mention then of a Lewis acid. Likewise, Bruce Evans, another MTI representative, testified at a deposition that an acid is a compound that in an aqueous solution donates protons.

The Court concludes that the record does not contain sufficient evidence to support a compelling determination with regard to whether, in the context of the Patents, carbon dioxide alone would have been classified as a weak acid within the ordinary and customary meaning of the term to a person of ordinary skill in the papermaking arts at the time of issuance. To this extent, MTI did not meet its burden to establish by a preponderance of the evidence its claim that the Weak Acid Requirement was literally met at the 2004 SENA Trial by the use of carbon dioxide alone.

B. *CARBONIC ACID IN COMBINATION WITH OTHER WEAK ACIDS*

The Agreement calls for the Court to determine whether the Weak Acid Requirement was satisfied at the 2004 SENA Trial by the use of carbonic acid alone *or*in combination with other weak acids. The parties agree that carbonic acid falls within the chemical definition of a weak acid. It seems undisputed as well, since Waller testified to this effect *(see*Trial Tr. at 253), that bicarbonate may also be classified as a weak acid. MTI contends that all of the carbon dioxide infused into the paper furnish during the 2004 SENA Trial remained dissolved and that during the time it was present in the system the requisite amount of carbonic acid formed, which then disassociated and converted to bicarbonate. According to MTI, the entire amount of carbon dioxide was consumed, in the process forming enough carbonic acid, and an equivalent amount of bicarbonate, to meet the Weak Acid Requirement, alone or in combination. Pelton calculated the amounts of carbonic acid and bicarbonate yielded to be 4.9 weight percent of the calcium carbonate in the furnish.

The Court credits the testimony of Pel-ton on this point. Accepting Pelton’s theory of the chemistry of the reaction of carbon dioxide in the paper furnish during the 2004 SENA Trial, as supported by other evidence in the record, the entire amount of carbon dioxide used in the test dissolved in the water circulating in the system and, through continuous recycling and fresh injections during the course of the seven-day trial, had sufficient reaction time in the furnish to disassociate and to be fully consumed in converting to carbonic acid, which in turn formed bicarbonate, in amounts that in the aggregate exceeded 0.1 weight percent of the calcium carbonate in the slurry. Accordingly, the Court finds that the carbonic acid generated by the reaction of carbon dioxide and water, alone or in combination with the bicarbonate that the carbonic acid in turn produced, satisfied the literal terms of the Weak Acid Requirement.

C. *THE DOCTRINE OF EQUIVALENTS AND PROSECUTION HISTORY ESTOPPEL*

The Agreement asks the Court to address the proper application of the doc*210trine of equivalents and prosecution history estoppel as they relate to the Weak Acid Requirement, to the extent raised by the parties. MTI claims that under the doctrine of equivalents, by means of the carbon dioxide used at the 2004 SENA Trial, Omya infringed the Patents, insofar as the carbon dioxide or the bicarbonate to which it ultimately converted, through an intermediate state as carbonic acid, performed substantially the same function of the weak acid substantially the same way to achieve substantially the same result that the Patents teach. Omya counters that in statements MTI made to the PTO to obtain issuance of the Patents, MTI asserted that the terms “weak” and “weak acid” were well established in the chemical arts and were to be read in accordance with their ordinary and customary meaning in that context. On this basis Omya contends that because at that time the recognized definition of a weak acid to persons skilled in the chemical arts was a Bronsted acid, MTI is therefore bound by those representations and should now be estopped from claiming that carbon dioxide may be classified as a Lewis acid and a weak acid. To address this dispute the Court reviews the standards that govern the application of these doctrines.

1. *Doctrine of Equivalents*

The judicial doctrine of equivalents emerged as a means to recognize patent infringement in the case of a product or process that “does not literally infringe upon the express terms of a patent claim [but] may nonetheless be found to infringe if there is ‘equivalence’ between the elements of the accused product or process and the claimed elements of the patented invention.” *Warner-Jenkinson Co., Inc. v. Hilton Davis Chem. Co.,*520 U.S. 17, 21, 117 S.Ct. 1040, 137 L.Ed.2d 146 (1997) (citing *Graver Tank & Mfg. Co. v. Linde Air Prods. Co.,*339 U.S. 605, 70 S.Ct. 854, 94 L.Ed. 1097 (1950)). Thus, the doctrine recognizes that if a patent were interpreted unremittingly by the express language of its claims alone, the value to the inventor would be diminished. The rule thus serves to acknowledge and mitigate the limitations of literalism, and to enlarge the scope of patent protection the inventor can claim. As the Supreme Court noted in *Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki, Co., Ltd.:*“[T]he nature of language makes it impossible to capture the essence of a thing in a patent application.” 535 U.S. 722, 731, 122 S.Ct. 1831, 152 L.Ed.2d 944 (2002).

Implicitly, the enhanced patent rights that the doctrine of equivalents warrant encompass two basic concepts. First is that at the time of prosecution of the patent the applicant cannot reasonably be expected to foresee and express in anticipatory language every technical advance and interchangeable element by which the invention may later be altered, however insubstantially, to achieve essentially the same product or process. Second, in going beyond the literal terms of the patent to validate claims to equivalents, what the doctrine endeavors to embody within its protection is the “essence” of the concept and the “range of its novelty” to which the inventor seeks to give expression in the wording of the claims, but that the constraints of language and foresight do not allow capturing those qualities with complete precision. *Id.; see also Atlas Powder Co. v. E.I. du Pont De Nemours & Co.,*750 F.2d 1569, 1582 (Fed.Cir.1984) (“Although there is no legally recognized ‘essence’ or ‘heart’ of the invention in determining validity ... it can be applicable in a determination of infringement under the doctrine of equivalents.”) (internal citations omitted) *(citing Medtronic, Inc. v. Cardiac Pacemakers, Inc.,*721 F.2d 1563, 1567 (Fed.Cir.1983)).

*211Accordingly, an accused device or method should be deemed equivalent, and thus not an insubstantial alteration of an element of a patented technology, if in its basic elements it employs the essence of the concept on which the claimed novelty of the original invention is fundamentally grounded, as evidenced by substantial similarities in the role each element plays in the operation of the claimed product, the way it functions and the result obtained. *See id.*(“Unimportant and insubstantial substitutes for certain elements could defeat the patent and its value to investors could be destroyed by simple acts of copying.”).

What constitutes equivalency, the Supreme Court counseled in *Graver Tank,*“is not the prisoner of a formula and is not an absolute to be considered in a vacuum,” nor does it “require complete identity for every purpose and in every respect.” 339 U.S. at 609, 70 S.Ct. 854. Rather:

> In determining equivalents, *things equal to the same thing may not be equal to each other and, by the same token, things for most purposes different may sometimes be equivalents.*Consideration must be given to the purpose for which an ingredient is used in a patent, the qualities it has when combined with the other ingredients, and the function which it is intended to perform. An important factor is whether persons reasonably skilled in the art would have known of the interchangeability of an ingredient not contained in the patent with one that was.

*Id.*(emphasis added).

As it developed in early applications, the doctrine was invoked in patent disputes in which the claimed equivalence pertained to mechanical components employed in the competing devices. Particularly germane to the matter at hand, in later extensions, as the chemical arts advanced, the same principles were also applied to inventions entailing chemical compositions and processes, where the claim of equivalence involved chemical ingredients or processes that embodied the essence of a component of the patented product or method. *Id.*

Two expressions of the doctrine of equivalents are generally articulated by the courts. The earlier version, ordinarily more apt for mechanical devices, enabled the patentee to invoke equivalency if the accused product “ ‘performs substantially the same function in substantially the same way to obtain the same result.’ ” *Graver Tank,*339 U.S. at 608, 70 S.Ct. 854 (quoting *Sanitary Refrig. Co. v. Winters,*280 U.S. 30, 42, 50 S.Ct. 9, 74 L.Ed. 147 (1929)). As refined by *Graver Tank,*a case involving chemical compositions, a second formulation places greater emphasis on the substantiality of the alteration: “whether under the circumstances the change was so insubstantial that ... invocation of the doctrine of equivalents was justified.” *Id.*at 610, 70 S.Ct. 854. In the most recent applications of the doctrine, the Federal Circuit has framed the basic inquiry of equivalency as grounded on the insubstantiality standard, while employing the function-way-result test as one consideration to be weighed. *See Eagle Comtronics, Inc. v. Arrow Communication Labs., Inc.,*305 F.3d 1303, 1315 (Fed.Cir.2002). In either event, the theory recognizes that if two products operate substantially the same way and achieve substantially the same result, “ ‘they are the same, even though they differ in name, form or shape.’ ” *Graver Tank,*339 U.S. at 608, 70 S.Ct. 854*(quoting Union Paper-Bag Mach. Co. v. Murphy,*97 U.S. 120, 125, 24 L.Ed. 935 (1877)).

Recognizing the conflict that broad application of the doctrine of equivalents poses for the definitional and public notice purposes of the patent statute’s claiming *212requirement, the Supreme Court in *Warner-Jenkinson*elaborated a further limitation. It declared that the doctrine “must be applied to individual elements of the claim, not to the invention as a whole.” 520 U.S. at 29, 117 S.Ct. 1040. Accordingly, the Supreme Court instructed that the essential inquiry in applying the test of substantiality is:

> Does the accused product or process contain elements identical or equivalent to each claimed element of the patented invention.... [A]n analysis of the role played by each element in the context of the specific patent claim will thus inform the inquiry as to whether a substitute element plays a role substantially different from the claimed element.

*Id.*at 40,117 S.Ct. 1040.

Unlike the temporal rules that govern literal infringement, which are designed to prevent enlargement of the scope and protection for an invention by construing its language in accordance with the ordinary and customary meaning of the terms of the claims as of the time the patent issued, the doctrine of equivalents focuses on a different point in time: knowledge of the art and interchangeability of elements as of the date of the alleged infringement. *See id.*at 37, 117 S.Ct. 1040 (“Insofar as the question under the doctrine of equivalents is whether an accused element is equivalent to a claimed element, the proper time for' evaluating equivalency ... and thus knowledge of interchangeability between elements — is at the time of infringement, not at the time the patent was issued.”); *Atlas Powder Co.,*750 F.2d at 1581 (“It is not a requirement of equivalence ... that those skilled in the art know of the equivalence when the patent application is filed or the patent issues. That question is determined as of the time infringement takes place.”).

Moreover, knowledge of the interchangeability of elements is determined by objective factors. *See Graver Tank,*339 U.S. at 608, 70 S.Ct. 854 (“An important factor is whether persons reasonably skilled in the art would have known of the interchangeability of an ingredient not contained in the patent with one that was.”); *see also Warner-Jenkinson,*520 U.S. at 36, 117 S.Ct. 1040 (noting that though independent experimentation by an infringer may not always reflect on the objective question of whether a person skilled in the art would have known of the interchangeability between two elements, “in many cases it would likely be probative of such knowledge”). These rules recognize that judging the alleged equivalency of elements of a device or process as of the point of patent issuance would unduly curtail the coverage of patent rights by barring the original inventor from enforcing approved claims against methods or devices later developed with refinements of the technology. Absent application of equivalence, such an adverse result would occur even if fundamentally the accused product incorporates the creative essence and technology embodied in the original invention and is thus not substantially different, insofar as it demonstrably employs substantially the same elements and operates substantially the same way to achieve substantially the same result as the patented product.

2. *Prosecution History Estoppel*

Prosecution history estoppel is a rule of patent construction that works in tandem with the doctrine of equivalents, ensuring that the latter “remains tied to its underlying purpose.” *Festo,*535 U.S. at 734, 122 S.Ct. 1831. While the rule of equivalence extends protection to a patent owner over insubstantial modifications of the invention that may not be literally expressed in the claim as patented, but *213that could be developed by minor alterations, “when ... the patentee originally claimed the subject matter alleged to be infringed but then narrowed the claim in response to a rejection, he may not argue that the surrendered territory comprised unforeseen subject matter that should be deemed equivalent to the literal claims of the issued patent.” *Id.*at 733-34, 122 S.Ct. 1831.

As most recently elaborated by the Supreme Court in *Festo,*application of prosecution history estoppel takes into account several considerations. These standards provide that: (1) the inventor knew of the terms describing both a broader and the narrower claim; (2) the choice to narrow the claim or disavow or surrender claim territory or particular equivalents must be made by the applicant affirmatively; (3) ordinarily the narrowing amendment or statement was made as a condition for obtaining the patent to protect its validity, or to comply with any requirement of the Patent Act, especially in the face of a claim rejection by the PTO that would have rendered the invention unpat-entable; (4) the patentee’s decision to narrow the particular claim raises a presumption that the territory surrendered by the claim amendment is not the equivalent of the territory claimed; and, (5) estoppel should not apply to bar claims of equivalents that the patent application could not reasonably be held to have literally expressed and surrendered in an amendment or representation made during prosecution, in particular where the equivalents may have been unforeseeable at the time of the narrowing statement. *See id.*at 735-40, 122 S.Ct. 1831. “[T]he patentee must show that at the time of the amendment one skilled in the art could not reasonably be expected to have drafted a claim that would have literally encompassed the alleged equivalent.” *Id.*at 741, 122 S.Ct. 1831. Thus, the scope of prosecution history estoppel is limited to claim-narrowing amendments and representations that were foreseeable and that affirmatively surrendered the particular equivalents in contention. “There is no reason why a narrowing amendment should be deemed to relinquish equivalents unforeseeable at the time of the amendment and beyond a fair interpretation of what was surrendered.” *Id.*at 738, 122 S.Ct. 1831.

In synthesis, viewed together, the doctrines of equivalents and prosecution history estoppel encapsulate various central principles that go to the core and mark the contours of patent rights, a body of law which as a whole reflects a great confluence of human energies, ends and limitations. These principles are given expression through several concepts fundamental to the law of patents that are prominent in the issues the instant case presents, and are touched upon here as a helpful backdrop to their application in the discussion that follows. First, patent doctrines are ultimately designed to validate original invention, to this end conferring a bounty on inventors’ creativity and innovation, rewarding their ambition, initiative and diligence, and thereby providing incentive for novel contributions to useful arts. Second, they acknowledge the shortcomings of language, underscoring the limitations of words to capture with precision the full scope, both actual and potential, of the novelty and operation of new technology. Third, they recognize the practical bounds of foresight, in other words, the limited ability of an inventor, prior to prosecuting a patent application, to anticipate advancements of the art and to experimentally test every conceptual variation and mechanical configuration by which a new product or process may also function to achieve a claimed result.

*214Fourth, through claim disclosure, equivalents, estoppel and related principles, patent law also reaffirms the proposition that truly new ideas are a free commodity and that no one should possess an unbounded monopoly on any particular unique concept. In consequence, the creation and advancement of original arts reflect the practical workings of an extensive process akin to a conceptual marketplace. Given enough passage of time, combined with ever-expanding spheres of knowledge, the outer reaches of human imagination, the virtually infinite variety of natural and synthetic ingredients supplied by the world around us, and a large pool of persons similarly animated by ambition and creative forces, new products and processes are bound to develop. Hence, it is not unusual that, by operation of the laws of probability and contingencies, out of this amalgamation of circumstances an inspired mix would evolve from which one or more inventions could emerge independently that operate to attain a result closely similar to that achieved by another known device employing substantially different means and innovative concepts.

By the same token, these principles also recognize certain commonplace realities, the real world of expediency borne of human competition and commerce. The same creative energies can also be harnessed to motivate tinkering at the margins of existing technology and impel inventiveness to devise a product ostensibly novel, but that in reality amounts to a minor modification of one already patented. In this instance, creativity is more derivative than original; the inventor is moved less by uncharted novelty than by the known or potential success of a concept engendered by another. Craft and language claiming a technological breakthrough is then employed not to innovate, but to imitate, edging as close to the line, and tapping as much of the creative essence of prior art, as verisimilitude might lawfully allow.

The challenge in patent controversies arising from the operation of these principles, as is the case of the dispute now before the Court, is to ascertain on which side of the line the doctrinal circumstances and the parties’ conduct fall.

3. *Application of Doctrines*

As a backdrop for application of the doctrines of equivalents and prosecution history estoppel, the Court notes some aspects of the parties’ dispute that present novel points. At the 2003 SENA Trial, Omya employed phosphoric acid in the paper furnish as the substance designed to function as the weak acid feature of the system tested. The parties agree that the experiment worked to lower the pH of the slurry and that the Weak Acid Requirement was met on that occasion. During the 2004 test, although carbon dioxide was used for the purpose of controlling the pH of the slurry through the formation of carbonic acid, a supply of phosphoric acid was kept in hand to serve as a backup in the event the carbon dioxide did not perform properly. The parties do not dispute, and the Court finds, that at the time of the Stora Enso trials a person skilled in the chemical arts would know that the injection of carbon dioxide into a paper furnish would cause a chemical reaction in which some carbon dioxide would dissolve in the water and react to convert to some amount of carbonic acid, which in turn would disassociate to produce bicarbonate. There is also no disagreement here that carbonic acid and bicarbonate both satisfy the definition of “weak acid,” and thus that if either of these compounds were found to have been present in the slurry at the 2004 SENA Trial in amounts exceeding the 0.1 weight percent limitation claimed in the *215Patents, the experiment would satisfy the Weak Acid Requirement.

Theoretically, therefore, if either carbonic acid or bicarbonate could have been produced and practically introduced into the paper furnish at the 2004 SENA Trial as a free-standing substance in the requisite amount, the test presumably would have met the literal terms Weak Acid Requirement. In response to a question by the Court on this point the parties indicated that it would be difficult or impossible to maintain pure carbonic acid in an aqueous form suitable for injection into the slurry. *(See*Trial Tr. at 82, 11. 18-25 and 83, 11. 1-3, and 221, 11. 15-22.) Instead, as the parties acknowledged, because the amount of these acids needed for the purposes of lowering the pH of the slurry at the 2004 SENA Trial could more practically and economically be produced in the system through an antecedent step — the conversion of carbon dioxide injected into the paper furnish as a gas- — the process went through a transitional reaction. During that process the admitted weak acid was formed in some amount and used to achieve the claimed pH lowering function not initially, but indirectly; it was introduced into the system in two steps rather than one, in effect, as the byproduct of a prior chemical reaction. In this respect, the carbonic acid, in combination with the carbon dioxide used to produce it, played a role in satisfying the weak acid element of the technology either literally or essentially as an equivalent.

There are thus two ways to frame the issue in dispute for the purposes of an equivalency determination. First is whether the carbon dioxide itself may be objectively considered a weak acid that served at the 2004 SENA Trial as an interchangeable substance to satisfy the weak acid component of the process that operated to lower and maintain the pH of the slurry. A second formulation is whether carbon dioxide, even if not independently considered a weak acid, may reasonably be held to be an equivalent of the claimed ingredient when employed to serve an indirect function — as an agent for the formation of another substance that undisputably qualifies as a weak acid performing the claimed function.

4. *Prosecution History Estoppel*

To respond to these questions the Court first addresses Omya’s invocation of the doctrine of prosecution history estop-pel to bar MTI’s equivalency claims. The Court does not accept Omya’s argument as a proper application of the theory of estop-pel. In asserting during the prosecution of its applications for the Patents that the terms “weak” and “weak acid” were to be understood in accordance with their well-established, ordinary and customary meaning, MTI essentially stated a truism, providing a common reference point for the definition of those words that in fact generally applies to all language employed in patent claims. *See Phillips v. AWH Corp.,*415 F.3d 1303, 1313 (Fed.Cir.2005) (noting that the claims of a patent should be construed in accordance with the ordinary and customary meaning of the terms as understood by a person of ordinary skill in the art). Declaring that particular terms are to be given their ordinary and customary meaning cannot reasonably be construed to encompass every specific example or embodiment that may (or may not) satisfy the accepted general definition- — an indefinite and potentially large number of substances — and thus to affirmatively surrender those particular applications. *See Festo,*535 U.S. at 741, 122 S.Ct. 1831.

It would be peculiar indeed that by representing that the words of a patent are to be read according to the rule of interpreta*216tion the law itself would adopt, an applicant would be later barred by estoppel from claiming the fuller scope of the terms that would encompass particular embodiments which could not be considered insubstantial differences in the technology. What MTI is claiming now is not a different general definition of the term “weak acid” narrower than the one it adopted during patent prosecution, but rather that three particular substances may be so classified within an accepted ordinary and customary definition. Moreover, under the *Festo*standards stated above, there is no compelling evidence on the record before the Court that in making the general definitional statements in question MTI’s representations were made affirmatively to narrow the scope of the Patents’ claims and to surrender a broader scope that would have extended to carbon dioxide or bicarbonate as specific embodiments of weak acids interchangeable with the weak acid requirement of the Patents. *See id.*

5. *Equivalents*

MTI argues that carbon dioxide itself served as a weak acid at the 2004 SENA Trial under the doctrine of equivalents because in a paper furnish it reacts with the water and functions to reduce the pH in the same manner as four other conceded weak acids: (1) boric acid, which is identified in the Patents as a substance that could serve the weak acid component of the system, and which in an aqueous solution operates as a Lewis acid; (2) phosphoric acid, the weak acid that the Patents claim as the preferred embodiment and that was successfully used in the 2003 SENA Trial, at which the parties agree the Weak Acid Requirement was satisfied; (3) carbonic acid, which is generated by the infusion of carbon dioxide and its reaction with water in the paper furnish, and which functions as a Bronsted acid by donating protons to the solution, thereby lowering the pH; and (4) bicarbonate, which forms from the disassociation of carbonic acid and, like carbonic acid, donates protons and also serves the function of lowering the pH of the slurry.

Omya responds that carbon dioxide does not satisfy any of the criteria of the equivalency test in that it is neither a Bronsted or a Lewis acid, a weak acid, or indeed any kind of acid, and that there are substantial differences between carbon dioxide and weak acids. Specifically, Omya argues that references to other weak acids, some of which may represent the preferred embodiments of the claim, are not germane; that there is no evidence that the carbon dioxide used at the 2004 SENA Trial functioned as the claimed “weak acid” term of the Patents properly construed, that the carbon dioxide did not work in combination with a calcium-chelating agent to form an acid-stabilized calcium carbonate in substantially the same way a weak acid would perform that function, or that the carbon dioxide not converted to carbonic acid had any effect on the acid stability of the calcium carbonate or acted to lower the pH of the furnish; and that the 0.0129 weight percent amount of carbonic acid formed at the 2004 SENA Trial that Waller’s computation produced is substantially different from the 0.1 limitation the Patents specify.

The Court is persuaded that MTI’s invocation of equivalency satisfies the prerequisites for application of the doctrine. The conceptual essence of the technology the Patents describe calls for a papermak-ing system that employs a paper furnish consisting of a mixture of calcium carbonate, a calcium-chelating agent and/or conjugate base, and weak acid used to lower the pH of the system, resulting in the calcium carbonate reaching equilibrium. Here, the 2004 SENA Trial undisputably employed the first two elements of the *217technology as claimed. The only dispute relates to whether the claimed weak acid component was satisfied. In this regard the Court returns to the discussion above concerning the formation of carbonic acid at the 2004 SENA Trial. The Court determined that the evidence MTI introduced through the testimony of Pelton and other materials was sufficient to warrant a finding that the carbon dioxide used in the test remained dissolved and recycling in the paper furnish in quantities and duration long enough to generate carbonic acid in an amount that satisfied the Weak Acid Requirement — as much as 4.9 weight percent in relation to the calcium carbonate in the system. By the same token, the Court rejected the analysis of Waller, whose calculation indicated formation of a much lower amount of carbonic acid, 0.0129 weight percent. Because Omya concedes that carbonic acid is a weak acid that functioned as a proton donor to lower the pH of the paper furnish, the use of carbonic acid in amounts approximating the 0.1 weight percent limitation specified in the Patents would perform substantially the same function in substantially the same way as the weak acid component of the claim to achieve substantially the same result. If, as the Court found above, Waller’s explanation of the technology and the chemistry of the Stero Enso paper furnish is materially flawed as regards the operation of the deculator or the reaction time of the carbon dioxide, and Pelton’s comparable analysis and computations are more correct, the amount of carbonic acid present in the slurry would be higher than Waller’s measure, and closer to an amount that would either satisfy the Weak Acid Requirement literally, or operate substantially as an equivalent to perform the same weak acid function called for by the terms of the Patents.

Accordingly, whether or not carbon dioxide itself may properly be classified as an acid or a weak acid, and whether any unconverted carbon dioxide in the slurry directly played any role in lowering the pH of the paper furnish, the carbon dioxide served indirectly as the chemical agent that generated carbonic acid, which in turn formed bicarbonate, both conceded weak acids whose presence in the slurry would serve to lower the pH level. Thus, however carbon dioxide may properly be classified in this context, it played a central role at the 2004 Stora Enso Trial as a critical component of performing the weak acid function. Recalling the pragmatic and flexible guidance of *Graver Tank*that the test of equivalency “is not the prisoner of a formula,” that it “does not require complete identity for every purpose and in every respect,” and that “things for most purposes different may sometimes be equivalents,” 339 U.S. at 609, 70 S.Ct. 854, a finding that the Weak Acid Requirement was met at the 2004 Stora Enso Trial by the use of carbon dioxide as a weak acid equivalent to lower the pH of the system indirectly through the formation of carbonic acid would not be unwarranted under these circumstances.

In connection with the amounts of carbonic acid formed Omya makes two points. First, it argues that at both Stora Enso tests the pH of the paper furnish was maintained at approximately 7.2, which falls within the alkaline range and therefore outside of the scope of the Patents’ claim specifying that the calcium carbonate, in combination with the calcium-che-lating agent and weak acid, would be acid-stabilized and used in a mildly *acidic*environment. Second, Omya contends that the order of magnitude between the amount of carbonic acid present in the paper furnish at the 2004 SENA trial and what the Patents describe — 0.0129 weight percent by Waller’s calculation as opposed to the *218claimed 0.1 limitation — cannot be considered an insubstantial difference.

The Court already determined above that it would not accept Waller’s analysis of the amount of carbonic acid formed at the 2004 SENA Trial, and found that the quantity was higher, probably closer to the figure in Pelton’s analysis. As discussed below, the Court need not decide exactly how much less than 0.1 weight percent an amount of weak acid substitute may reach to be deemed sufficient to warrant a finding of equivalence.

Before addressing Omya’s objections to the applicability of the doctrine of equivalents in this case, the Court finds some instructive analogies to the instant dispute in the facts of *Wamer-Jenkinson.*The patented invention in that case entailed a process for the purification of dyes by means of ultrafiltration of an aqueous solution through a membrane of a specified diameter at a specified range of pressures and at a pH varying from approximately 6.0 to 9.0. *See*520 U.S. at 22, 117 S.Ct. 1040. The claim regarding the pH level was added during prosecution of the patent to distinguish the invention from a previous patent for an ultrafiltration process operating at a pH above 9.0. There was disagreement as to why the applicant added the lower pH limit of 6.0.16 The accused system involved an ultrafiltration process for dyes employing a membrane and pressures within the same range of the patent’s specifications, but functioning at a pH of 5.0. The plaintiff conceded that there was no literal infringement and grounded its lawsuit solely on the doctrine of equivalents. The defendant argued that because the plaintiff, during the prosecution of the patent application, had limited the pH element of the claim to levels of 6.0 to 9.0, that range formed limits beyond which claims of equivalents would be barred.

Holding that the doctrine of equivalents applied to individual elements of a claim rather than to the invention as a whole, the Supreme Court noted that the lower 6.0 pH limit the invention claimed did not distinguish it from the earlier patent’s 9.0 limit, which did not address pH levels below 6.0. The Court then added: “thus, while a lower limit of 6.0, by its mere inclusion, became a material *element*of the claim, that did not necessarily preclude the application of the doctrine of equivalents as to that element.” *Id.*at 40, 117 S.Ct. 1040 (emphasis in original). In assessing whether an accused element is equivalent to an element claimed in the patented invention, the Court suggested that “an analysis of the role played by each element in the context of the specific patent claim will thus inform the inquiry as to whether a substitute element matches the function, way, and result of the claimed element, or whether the substitute element plays a role substantially different from the claimed element.” *Id.*

In the matter at hand, although the Patents indicate that the Passaretti technology operates in a “mildly acidic environment,” the claims do not specify any particular pH or range of pH at which the system is to function. Moreover, just as in *Wamer-Jenkinson*the 6.0 lower limit of the pH range the patent described did not preclude a claim of equivalence for a lesser pH level, the limitation of 0.1 weight percent of weak acid to calcium carbonate in the instant case does not function categorically as a bright line barring equivalency at lower relative levels of weak acid. Rather, this element of the claim could be satisfied by some smaller weight percent *219of a weak acid that would operate to satisfy the weak acid element of the claim in a manner not substantially different from the process the Patents claim. Omya appears to acknowledge as much, insofar as it concedes that carbonic acid is a weak acid and that it functioned at the 2004 SENA Trial to lower the pH of the paper furnish by donating protons to the system. Omya’s only challenge to the application of the doctrine of equivalents as it pertains to carbonic acid seems to be based on a quantitative test, a measure of “order of magnitude” between the relative weight of weak acid the Patents claim as a limitation and the amount of the carbonic acid the 2004 SENA Trial produced.

This case thus presents an instance of the shortcomings which the *Wamer-Jen-kinson*Court noted in the application of both formulations of the doctrine of equivalents, and in particular of the insubstan-tiality test as applied to products or processes other than mechanical devices. *See id.*at 40, 117 S.Ct. 1040 (“[T]he insubstantial differences test offers little additional guidance as to what might render any given difference ‘insubstantial.’ ”). If, as Omya contends, 0.01 weight percent weak acid used at the 2004 Stora Enso Trial process cannot be considered sufficiently substantial to qualify as a substitute for the claimed element, would an amount of 0.03 be enough? Or what about 0.05 or 0.075?

The Court does not deem it particularly enlightening or productive in the resolution of the matter at hand to decide at which precise point along the line between 0.01 and 0.1 weight percent an amount of carbonic acid employed as the weak acid element of the Passaretti system would serve as the demarcation of what constitutes a substantial or insubstantial difference in the technology. The Court does not read the test of equivalency to turn on absolute numerical differences or quantitative formulas. *See Graver Tank,*339 U.S. at 609, 70 S.Ct. 854. Instead, the standard is more properly grounded on qualitative differences between the elements of the accused product and those claimed by the patent, in other words, whether, assessed element by element, the two inventions creatively derive from and rely upon the same conceptual “essence.” *See Festo,*535 U.S. at 731, 122 S.Ct. 1831. On this point, as *Wamer-Jenkinson*suggests, the more instructive inquiry is “the role played by each element,” and thus whether the substitute element “matches or plays a role substantially different from the claimed element.” 520 U.S. at 40, 117 S.Ct. 1040.

Applying this formulation, the Court finds that the carbonic acid used at the 2004 SENA Trial, even if in amounts below the weight percent limitation claimed, served as a substitute for the weak acid element of the Patents in that the substance played the role of lowering the pH of the paper furnish by disassociating and donating protons to the mixture and in the process, in combination with the calcium-chelating agent, stabilizing the calcium carbonate in the system. To this extent, the role the amount of carbonic acid present in the paper furnish played in that experiment was not substantially different from the role of the weak acid element the Patents describe. By the same token, crediting Pelton’s analysis, the carbonic acid in the slurry further disassociated to form a corresponding amount of bicarbonate, another undisputed weak acid that in an aqueous solution operates as a proton donor. Thus, the bicarbonate may also be found to satisfy the claims of the Patents as an equivalent of the weak acid component. That the technology would also work successfully at a pH level of 7.2, and thus at a mildly alkaline rather than mildly acidic range, represents an insubstantial difference in operation by an interchangea*220ble weak acid element that may not have been reasonably foreseeable at the time the Patents issued, given the state of the art, but that became known through later technological development. *See Festo,*535 U.S. at 731, 122 S.Ct. 1831.

In support of its conclusion the Court has taken into account several evidentiary and legal considerations. First, the Court considered Omya’s extensive experimentation at the two Stora Enso tests. Second, as a related matter, the Court weighed the interchangeability of elements known at that time to satisfy the Patents’ weak acid component. In response to MTI’s pointing to several other acknowledged weak acids as equivalents of the Patents’ weak acid requirement, Omya dismisses the argument as inapposite to the application of the equivalency doctrine. This reference, however, does have some relevance; it bears on the issue of other substances then known to persons skilled in the chemical arts of papermaking that would satisfy or be interchangeable with the weak acid component. *See Warner-Jenkinson,*520 U.S. at 36, 117 S.Ct. 1040 (“The known interchangeability of substitutes for an element of a patent is one of the express objective factors ... bearing upon whether the accused device is substantially the same as the patented invention.”).

In this regard Omya concedes that at the 2003 SENA Trial phosphoric acid, a known weak acid identified by the Patents as the preferred embodiment of the claim, was used to control the pH of the paper furnish in an alkaline range of 7.2 to 7.4. Omya also admits that at the 2004 test, “in place of phosphoric acid” carbon dioxide was used “to help control the pH of the furnish in the same approximate alkaline pH range.” (Def.’s Pre-Trial Mem. at 4-5.) At the same time, Omya also acknowledged that the Patents teach that “when phosphoric acid (the weak acid) and ... [the chelant] are added to the calcium carbonate slurry, the [chelant] will chelate with the calcium on the surface of the calcium carbonate, and the system will reach an equilibrium ... and the equilibrium pH is acidic.” (Def.’s Post-Trial Mem. at 14.)

The Court regards these statements, together with Omya’s actual experimentation at Stora Enzo, as evidence circumstantially demonstrating Omya’s knowledge of the interchangeability of carbon dioxide with phosphoric acid as an equivalent to the weak acid component, even if the carbon dioxide served that function only indirectly as an agent to produce carbonic acid, a known weak acid. *See Warner-Jenkinson,*520 U.S. at 36, 117 S.Ct. 1040 (noting that “the need for independent experimentation thus could reflect knowledge — or lack thereof — of interchangeability possessed by one presumably skilled in the art,” and that even if such experimentation may not always reflect on the objective interchangeability between two elements, “in many cases it would likely be probative of such knowledge.”).17

*221Thus, the evidence sufficiently demonstrates that at the time of the alleged infringement at issue here, objective knowledge existed regarding the interchangeability of carbon dioxide, as an agent for the production of carbonic acid, and the weak acid described in the terms of the Patents. The Court further concludes that by a preponderance of the evidence before it MTI has demonstrated equivalency, under the circumstances discussed above, between the carbonic acid and the bicarbonate formed by the use of carbon dioxide at the 2004 SENA Trial and the weak acid component of the Patents.

V. *CONCLUSION*

To summarize, in response to the specific tasks the Agreement requests the Court to address, the Court concludes as follows. The ordinary and customary meaning of “weak acid,” as used in the Passaretti technology described in the Patents and as the term would have been understood by a person of ordinary skill in the chemical arts relating to papermaking in 1991, at minimum18 would encompass Bronsted acids: compounds that in an aqueous solution partially disassociate and donate protons to the mix.

The record before the Court is not sufficient to support by preponderance of the evidence a determination that carbon dioxide by itself when used in the context of the Patents objectively would have been classified as a weak acid by a person of ordinary skill in the chemical arts relating to papermaking in 1991. However, when injected into a paper furnish, some amount of carbon dioxide dissolves relatively quickly, reacts with the water in the mixture and forms carbonic acid. The latter compound then does function as a weak acid in the technology of the Patents in that it ionizes in the water and donates protons to the solution, thereby lowering and maintaining the pH of the system at a given level. Thus, the addition of carbon dioxide to a paper furnish consisting of calcium carbonate and a calcium-chelating agent and/or conjugate base would meet the Weak Acid Requirement by application of the doctrine of equivalents. This conclusion follows insofar as the injection of carbon dioxide into the slurry to perform the role of the claimed weak acid constitutes an insubstantial difference in the technology, even though the carbon dioxide would achieve the weak acid function indirectly. In reacting with the water in the furnish it would serve as an agent for the production of carbonic acid, which in turn operates as a weak acid. In that role, the carbonic acid donates protons to the solution, and lowers the pH of the paper furnish, thereby accomplishing substantially the same desired result of stabilizing the calcium carbonate filler.

Carbonic acid produced in the requisite amount described in the Patents could meet the Weak Acid Requirement by it*222self, or in combination with bicarbonate, which forms through the consumption of the carbon dioxide dissolved in the paper furnish and its conversion to carbonic acid, followed by the further disassociation of carbonic acid. This result occurs through the continuous injection, dissolving and recycling of carbon dioxide in the paper furnish. Under these circumstances the carbon dioxide, given sufficient reaction time through continuous injection and recirculation in the system, would produce an amount of carbonic acid and/or bicarbonate sufficient to satisfy the Weak Acid Requirement, as the Court has determined occurred at the 2004 Stora Enso Trial.

Finally, even if the amount of carbonic acid and/or bicarbonate formed in a paper furnish by the addition of carbon dioxide were not sufficient to satisfy the requisite 0.1 weight percent limitation claimed by the Patents, the presence of those substances in the system nonetheless would meet the Weak Acid Requirement by application of the doctrine of equivalents. This conclusion follows to the extent that the use of carbonic acid and/or bicarbonate to perform the weak acid function of lowering the pH of the slurry constitutes an insubstantial alteration of that element of the Passaretti technology. Those substances, even in relative weight amounts below the 0.1 limitation claimed by the Patents, perform substantially the same role of lowering the pH of the system, the function the Patents claim as the role of the weak acid, in substantially the same way by donating protons to the mixture, thereby achieving substantially the same result of stabilizing the calcium carbonate in the system.

VI. *ORDER*

For the reasons discussed above it is hereby

ORDERED that the Court’s determinations and explanations set forth herein respond to the requests contained in the Agreement dated November 22, 2005 between the parties to this action; and it is further

ORDERED that within twenty (20) days of the date of this Order the parties submit to the Court for approval a stipulated Order necessary to give effect to the parties’ Agreement in the light of the Court’s determinations herein.

SO ORDERED.

1

. Facts describing the issues involved in the underlying action as originally filed are discussed in the Court's Decision and Order dated October 8, 2004, reported as *Minerals Technologies Inc. v. Omya AG,*339 F.Supp.2d 528 (S.D.N.Y.2004) *("Minerals Tech. I”).*Insofar as relevant to the Court's determinations of the remaining issues, those facts are summarized below.

2

. The related action, involving alleged antitrust violations, was filed as *Specialty Minerals, Inc. v. Pluess-Staufer AG, Pluess-Staufer Industries, Inc., and Omya Inc.,*Docket No. 98 Civ. 7775(VM). The matters the parties presented to the Court for adjudication in the proceeding at hand pursuant to the Agreement are described in the Court’s Decision dated December 19, 2005, reported as *Minerals Technologies, Inc. v. Omya AG,*406 F.Supp.2d 335 (S.D.N.Y.2005) *("Minerals Tech. II”).*

3

. According to the parties’ briefs, calcium carbonate has a number of important uses as a filler in the papermaking industry. Among other things, it brightens and improves the optical quality of the paper and, as a less expensive material than wood pulp, when mixed with pulp, reduces paper production costs.

4

. At higher pH levels in the alkaline range the paper product begins to undergo an undesirable effect referred to as "alkaline darkening” that adversely affects the color of the paper.

5

. A calcium-chelating agent, or “chelant” is a compound that "when applied to the surface of the calcium carbonate, acts to reduce the solubility of the surface of the calcium carbonate.” '017 Patent, attached as Exhibit A to Minerals Technologies Inc. and Specialty Minerals Inc.'s Pre-Trial Memorandum for Weak Acid Mini-Trial, dated December 9, 2005 ("MTI Mini-Trial Mem.”), at col. 4, 11. 1-4.

6

. *Id.*at col. 7,11. 65 — col. 8,11. 6.

7

. The Weak Acid Requirement as defined by the parties refers to the weight percent of the amount of weak acid in relation to the amount of calcium carbonate in the paper furnish at the 2004 SENA Trial. The weight percent is determined by a fractional formula in which the numerator is the weight of the weak acid used and the denominator that of the calcium carbonate. *(See*MTI Mini-Trail Mem. at 7.) To meet the literal terms of the Patents the relationship of the components to which this formula is applied must exceed 0.1.

8

. A Lewis acid is a compound that can act as an electron pair acceptor. *(See*MTI Mini-Trial Mem. at 14.)

9

. A Bronsted-Lowiy acid is a compound that in an aqueous solution donates a proton in a reversible manner. *(See*MTI Mini-Trial Mem. at 10; Trial Tr. at 128, 11. 21-25; 129, 11. 14-16.)

10

. The Agreement is attached as Exhibit A to Minerals Technologies Inc. and Specialty Minerals Inc.'s Pre-Trial Memorandum Regarding Scope of Issues at and Timing of Mini-Trial, dated December 16, 2005.

11

. Pelton has a Ph.D. in Colloid Chemistry from Bristol University and has heldiresearch scientist positions at the Pulp and í’hper Research Institute of Canada (PAPRICÁN) and Union Carbide. Pelton is currently a full professor of Chemical Engineering at McMaster University, where he is the founder and director of the McMaster Centre for Pulp and Paper Research. *(See*Rebuttal Expert Report of Dr. Robert H. Pelton Concerning Conversion of Carbon Dioxide to Carbonic Acid during August 2004 Store Enso Trial, dated December 7, 2005, attached as Exhibit C to MTI’s Mini-Trial Mem.)

12

. For convenience and judicial economy the Court, having reviewed the citations to factual materials on record for accuracy, rather than citing the source directly, except as otherwise appropriate, relies on the parties' references to the Trial Transcript ("Trial Tr.") and other evidence as set forth in their post-trial submissions.

13

. Waller's professional credentials include a masters of science and a masters of professional mechanical engineering degree from the Massachusetts Institute of Technology. He is a professor in the Paper and Chemical Engineering Department of Miami University. He is the author of over 50 journal articles and a book. *(See*Curriculum Vitae of Michael H. Waller, attached as Attachment 1 to Proposed Joint Pre-Trial Order, filed December 12, 2005, at 1.)

14

. Cummins holds a Ph.D. in inorganic chemistry from the Massachusetts Institute of Technology. He is a full professor of chemistry at *203MIT. He was awarded the National Science Foundation Alan T. Waterman Award for scientists or engineers age 35 or younger. *(See*Trial Tr. at 277-8.)

15

. Supplemental Expert Report of Michael H. Waller Concerning Carbonic Acid Amounts During August 2004 Stora Enso Trial, dated November 11, 2005, attached as Exhibit 1 to Def.’s Pre-Trial Mem., at 3.

16

. The patentee asserted that the process had been successfully tested at a pH level of 2.2, but did not explain its choice to place a lower limit of 6.0. See *id.*at 22 n. 2.

17

. MTI cites to certain third-party patents relating to the use of carbon dioxide in paper-making issued in September 2003, after the Patents and prior to Omya's Stora Enzo trials, that make reference to the effect carbon dioxide in an aqueous solution produces in lowering the pH of a pulp suspension. *See*MTI Mini-Trial Mem. at 14-5. One such patent provides:

> Thus, *decreasing the pH with carbon dioxide does not have the same negative effects on calcium carbonate as decreasing the pH With other acid*.... As mentioned above, carbon dioxide has an inherent capacity of decreasing the pH and this capacity may be utilized in the present invention in order to provide a desired decrease in the pH of a pulp suspension. Thus, carbon dioxide may be introduced in an amount sufficient for lowering the pH of said pulp suspension below the critical level of pH 8, or *when another acid has been used for decreasing**221*the pH, carbon dioxide may preferably be used to decrease the pH further.*The pH of the pulp suspension may, for instance, be adjusted with carbon dioxide to a pH of 5.5 to 7.6, preferably, 6.5 to 7.5.

*Id. (quoting*U.S. Patent No. 6, 623, 599, col. 4, 11. 24-30 and col. 5, 11. 6-14 (emphasis added by MTI)).

18

. The Court uses this qualifier in recognition of the parties’ unresolved dispute as to whether a Lewis acid may also be properly classified as a weak acid. In support of that proposition MTI points out that the Patents themselves list boric acid, known to react in an aqueous solution as a Lewis acid, as an example of a substance that would satisfy the weak acid component of the claimed system. Omya responds, through Cummins's testimony, that in fact boric acid is scientifically classified as both a Bronsted acid and a Lewis acid. *(See*Trial Tr. at 287, 11. 3-25.)