UNITED STATES PATENT AND TRADEMARK OFFICE
`_______________
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`_____________
`
`Wavelock Advanced Technology Co., Ltd.,
`Petitioner
`
`v.
`
`Textron Innovations Inc.
`Patent Owner
`
`
`Patent No. 6,455,138
`Issue Date: September 24, 2002
`Title: METALLIZED SHEETING, COMPOSITES,
`AND METHODS FOR THEIR FORMATION
`_______________
`
`Inter Partes Review No. IPR2013-00149 (SCM)
`____________________________________________________________
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`SECOND DECLARATION OF ROBERT IEZZI, Ph.D.
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`I.
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`1.
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`INTRODUCTION
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`I have been retained by Morrison & Foerster LLP in this case as an
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`expert in the relevant art.
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`2.
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`I am the same Robert Iezzi who previously provided a first declaration
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`in support of the Petition For Inter Partes Review for U.S. Patent No. 6,455,138
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`dated February 14, 2013.
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`3.
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`I submit this Second Declaration in support of Petitioner Wavelock
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`Advanced Technology Co., LTD’s Reply to Patent Owner’s Response.
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`4.
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`In addition to the materials I reviewed when preparing my first
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`declaration, I have reviewed Patent Owner’s Corrected Response dated October 9,
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`2013 (Paper 16) (“Response”).
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`5.
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`As discussed in my first declaration, a person of ordinary skill in the
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`art relevant to the '138 patent would have had at least a bachelor’s degree in
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`chemical engineering, material science, or chemistry, and at least five years of
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`experience working with or researching thermoplastic films and composites. The
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`statements in this declaration of what one of ordinary skill in the art would have
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`known or understood are based on the filing date of the '138 patent, i.e., December
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`31, 1997.
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`6.
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`I have been informed and understand the description of a claim
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`element in a prior art reference can be express or inherent. For a prior art reference
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`to describe a claim element inherently, the claim element must be necessarily
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`present. Probabilities are not sufficient to establish inherency. 
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`7.
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`In its Response, Patent Owner challenges my finding that the discrete
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`islands of Kuwahara are in adhesive. My finding was based on numerous facts in
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`Kuwahara as understood by one of ordinary skill in the art. Patent Owner seeks to
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`cast doubt on some of these facts. After reviewing the Response, I disagree with
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`Patent Owner’s arguments. My opinions and underlying reasoning for the
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`opinions in response to Patent Owner are set forth below. To the extent that I refer
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`to printed publications in the accompanying appendices, I have no reason to doubt
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`that the printed publications were published on the dates indicated on the printed
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`publications.
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`II. THE ADHESIVE OF KUWAHARA IS A LIQUID
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`8.
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`In the Response, Patent Owner contends that I erroneously understood
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`the adhesive to be a liquid based on Kuwahara’s disclosure that the adhesive was
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`applied by roll coating. (Response at pp. 22-23.) In my opinion, a person of
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`ordinary skill in the art would have understood Kuwahara’s express disclosure of
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`the roll coated adhesive to refer to a liquid adhesive. This opinion is consistent
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`with how Patent Owner’s Ex. 2002 describes roll coating. For example, the first
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`two sentences of Ex. 2002 provide: “Roll coating machines are commonly used
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`for the application of a liquid to the surface of a part. Rollcoaters can be used to
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`apply liquid adhesives, paints, oils, and coatings such as varnish or clear finish
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`coats.” (Ex. 2002 at p. 1 (emphasis added).) Ex. 2002 further states: “The type of
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`adhesive or coating will influence the way the liquids are brought to the metering
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`point.” (Id. at p. 10 (emphasis added).) There is no mention at all in Ex. 2002 of
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`non-liquids being applied by roll coaters.
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`9.
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`In addition, Kuwahara expressly discloses the adhesive as vinyl
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`chloride-vinyl acetate copolymer adhesive. (Kuwahara at 5:14-27.) Persons of
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`ordinary skill in the art would have understood that this adhesive is applied as a
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`liquid. The Adhesives Technology Handbook at pages 127-128 states: “PVC and
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`copolymers of both vinyl chloride and vinyl acetate with other monomers, such as
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`maleic acid esters, alkyl acrylates, maleic anhydride, and ethylene, are also used to
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`produce solvent-based adhesives.” (Ebnesajjad, S., Adhesives Technology
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`Handbook, 2nd ed., 2008 (emphasis added) (App. AA).) Solvent based adhesives
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`are clearly liquids. Further, Skeist’s Handbook of Adhesives at page 280 teaches:
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`“Vinyl dispersion resins have typically consisted of inert homopolymer or
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`copolymers of vinyl chloride and vinyl acetate.…” (Skeist, I., Handbook of
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`Adhesives, 3rd ed., 1990 (emphasis added) (App. BB).) Persons of ordinary skilled
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`in the art of adhesives would have known that a vinyl chloride-vinyl acetate
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`dispersion is a liquid.
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`10. Based on Kuwahara’s express disclosure of roll coating adhesive and
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`as further confirmed by Patent Owner’s Ex. 2002 and the above references
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`describing a vinyl chloride-vinyl acetate copolymer adhesive as a liquid, one of
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`ordinary skill in the art would have necessarily understood Kuwahara’s adhesive as
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`a liquid.
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`11.
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`In the Response, Patent Owner points to the electrostatic printing
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`process of Xerox machines as an example of roll coating a solid. (Response at p.
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`21.) One of ordinary skill in the art would not have considered electrostatic
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`printing using charged toner particles roll coating, and thus would not have
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`understood Kuwahara’s reference to roll coating in the manner asserted by Patent
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`Owner. This argument is also inconsistent with Patent Owner’s Ex. 2002, which
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`states: “A roll coating machine works by transferring a layer of coating from the
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`surface of a roller to the surface of a part. When this happens, a phenomenon
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`know[n] as ‘film splitting’ occurs. The layer of coating on the surface of the roll
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`splits – part of it stays on the roller, and part sticks to the surface of the part. The
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`percentage of coating that sticks to the part (the substrate) depends on the surface
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`characteristics of both the roller and the substrate.” That is, roll coating relies on a
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`liquid’s adhesive properties to itself, to the surfaces of the roller and to the
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`application surface. In comparison, Xerox machines transfer particles from a
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`charged toner drum to paper using electrostatic charge—there is no film splitting in
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`a Xerox machine.
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`III. THE LIQUID ADHESIVE WOULD FLOW INTO THE VOIDS
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`IN KUWAHARA’S METALLIZED LAYER
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`12.
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`In the Response, Patent Owner states that Kuwahara discloses spaces
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`between islands of 500 Angstroms. (Response at p. 24.) However, Kuwahara
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`explicitly discloses distances between islands of up to 5000 Angstroms.
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`Specifically, Kuwahara at 4:6-7 states: “The distance between the islands is set to
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`between 100 and 5000 Å.” Given this express disclosure of 5000 Angstroms,
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`persons of ordinary skill in the art would not have understood Kuwahara as limited
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`to 500 Angstroms spacings. Instead, persons of ordinary skill in the art would
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`have understood that the vinyl chloride-vinyl acetate adhesive of Examples 1 and 2
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`would have flowed around areas between islands with spacings of 500 Angstroms
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`or up to 5000 Angstroms.
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`1. The viscosity of the adhesive in Kuwahara was low enough
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`to flow between the islands
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`13. Persons of ordinary skill in the art would have understood that the
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`viscosity of the vinyl chloride-vinyl acetate adhesive in Kuwahara was applied
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`with a low enough viscosity to flow between the metal islands in Examples 1 and
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`2.
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`14. Patent Owner contends that the copolymer resin could be so viscous
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`that it would not flow and “fill” any voids. (See, e.g., Response at p. 24.) This
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`argument is inconsistent with Kuwahara’s express disclosure of roll coating an
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`adhesive. Roll coating, as Patent Owner’s Ex. 2002 explains, is a method of
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`applying a liquid film layer. Highly viscous liquids cannot be rolled coated as they
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`would form clumps or bind up the equipment. As Ex. 2002 states: “Certain types
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`of adhesives (such as hotmelts, waxes and certain high viscosity materials) require
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`that the machine or the rollers be heated to melt the material or lower the viscosity
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`to a point where it can be applied.” (Ex. 2002 at p. 10 (emphasis added).)
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`15.
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`In addition, Kuwahara states that the “vinyl chloride-vinyl acetate
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`copolymer resin was applied to the deposited Sn layer of the examples to a
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`thickness of 2µm with a roller coater, then heated with a 2002 µm thick
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`polyvinylchloride film and laminated under pressure.” (Ex. 1007 at 5:19-22
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`(emphasis added).) Persons of ordinary skill in the art would have understood that
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`the purpose of applying heat and pressure during the lamination process is to get
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`the adhesive to flow in order to obtain intimate contact between the adhesive and
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`surface features of the surfaces being laminated in order to create the laminated
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`article. Accordingly, persons of ordinary skill in the art would have understood
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`that the vinyl chloride-vinyl acetate adhesive in Kuwahara would have further
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`necessarily flowed between the metal islands in Examples 1 and 2 when heat and
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`pressure was applied during the lamination process. Thus, Patent Owner’s
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`argument as to highly viscous liquids fails to take into account how one of ordinary
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`skill in the art would have understood Kuwahara’s express disclosure of roll
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`coating adhesive and then lamination with heat and pressure.
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`2. The diameter of the polymer molecules of the adhesive in
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`Kuwahara would be below 500 Angstroms
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`16.
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`In the Response, Patent Owner argues that the discrete islands could
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`not be in the Kuwahara adhesive because the molecular weight, and hence the
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`length of the polymer chains, of the vinyl chloride-vinyl acetate adhesive are too
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`large to physically fit in the 500 Angstroms spacing between the discrete islands.
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`(Response at p. 25.) I disagree. Persons of ordinary skill in the art would have
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`understood that it is the polymer diameter and mobility, and not the polymer
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`length, that determine whether a polymer would flow between the spacing between
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`the discrete islands. As described below, persons of ordinary skill in the art would
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`have understood that the polymer diameter was well below 500 Angstroms and,
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`therefore, necessarily would have flowed between the metal islands in Examples 1
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`and 2 of Kuwahara.
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`17. Typical polymer molecules are very thin and flexible like cooked
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`spaghetti. In a flowing adhesive, the huge number of polymer chains would be
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`oriented in every conceivable direction. The chains that are aligned width-wise
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`with the openings would necessarily flow between the metal islands.
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`18. This result is confirmed when the calculations are applied specifically
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`to a vinyl chloride-vinyl acetate adhesive as disclosed in Kuwahara. Zang, Y.-H.
`
`et al. at pages 1965-68 provide the cross-sectional area of poly-vinyl-chloride and
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`poly-vinyl-acetate polymers. (Zang, Y.-H and Carreau, P. J., A Correlation
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`Between Critical End-to-End Distance for Entanglements and Molecular Chain
`
`Diameter of Polymers, J. Appl. Polym. Sci. (1991), 42: 1965–1968 (App. CC).)
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`This reference explains that the polymer chain diameter can be estimated by taking
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`the square root of these areas. (Id. at 1965.) The cross-sectional area of poly-
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`vinyl-chloride is 27.2 square Angstroms. (Id. at 1966.) Taking the square root of
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`27.2 square Angstroms gives us an estimated average polymer diameter of 5.2
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`Angstroms for poly-vinyl-chloride. Similarly, the cross-sectional area of poly-
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`vinyl-acetate is 59.3 square Angstroms. (See id.) Taking the square root of 59.3
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`square Angstroms gives us an estimated average polymer diameter of 7.7
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`Angstroms for poly-vinyl-acetate. Even assuming that these polymer chains
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`appear exactly side by side in a vinyl chloride-vinyl acetate adhesive, the total
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`polymer chain diameter would be 12.9 Angstroms, considerably below both the
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`5000 and 500 Angstrom spacing between the discrete islands disclosed in
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`Kuwahara.
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`IV. KUWAHARA’S ROLLER COATS THE LIQUID RESIN ONTO
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`THE METALLIZED LAYER
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`19.
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`In the Response, the Patent Owner states that I am “implying that a
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`liquid is applied to the top of the metallized film as it might be oriented vertically,
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`and consequently, gravity would cause the liquid to seep into the spaces between
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`the islands of metal.” (Response at pp. 27-28.) I disagree with this
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`characterization of my first declaration. The term “top” in my first declaration was
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`used relative to the structure in which metal islands are formed on Kuwahara’s
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`PET layer. This term was not meant to identify any positioning with respect to
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`coordinates external to the structure.
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`20. One of ordinary skill in the art would not have understood Kuwahara
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`as requiring gravity to force the vinyl chloride-vinyl acetate adhesive between the
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`metal islands. Adhesives can be applied “upside down” by roll coating because the
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`driving forces, such as (a) surface tension; (b) capillary action; (c) the adhesive’s
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`polymer chain small molecular diameter, mobility, and orientation; and (d)
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`intrinsic molecular inter-diffusion, cause the adhesive to spread into the crevices of
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`a surface and obtain intimate contact with the surface.
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`21. A liquid adhesive “wets” the solid surface it comes into contact with
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`and spreads across all exposed surfaces (including the exposed surfaces between
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`the islands). Wetting is the ability of a liquid to maintain contact with a contact
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`surface due to intermolecular interactions.
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`22.
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`It is well-known to one skilled in the art of adhesive and coatings
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`technology that for a liquid to wet a solid surface, the surface tension of the liquid
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`must be lower than the surface tension of the solid, and that metals have a high
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`surface tension relative to adhesives and are easily coated by polymer adhesives
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`and coatings. This is reinforced by Wicks at p. 125: “The surface tension of a
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`clean metal surface (usually, metal oxide) is higher than that of any potential
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`coating.” (Wicks, Z.W., Jr., et. al., Organic Coatings Science & Technology, 3rd
`
`ed., 2007 (App. DD).)
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`23. The surface tension of tin metal islands in Kuwahara is 587 dyne/cm
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`calculated as follows.
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`σ (T) = 570.0 – 0.08 (T-Tm)1 where σ is mN/m; T is °K; Tm is tin melt
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`temperature = 505°K
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`σ at room temperature (20°C = 293°K) = 570.0 – 0.08 (293°K - 505°K)
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`σ = 587 mN/m
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`1 mN/m = 1 dyne/cm Footnote 2
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`1 Alchagirov, B.B., et al., Surface Tension of Tin and Its Alloys with Lead, Russian
`
`
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`Journal of Physical Chemistry A, vol. 81, no. 8, 2007 at p. 1281 (App. EE).
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`σ = 587 dyne/cm
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`24. The surface tension of vinyl chloride is 41.9 dyne/cm, and of vinyl
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`acetate is 36.5 dyne/cm. (Baghdachi, J.A., Fundamentals of Adhesion, J. of
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`Coatings Technology, vol. 69, no. 870, July, 1997, at p. 90 (App. FF).) Thus, the
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`vinyl chloride-vinyl acetate adhesive of Kuwahara will readily wet and flow into
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`the metal islands.
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`25. The Response at page 14 also offers a scenario where solvent may be
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`used to dissolve the resin. Typical solvents used for adhesives have much lower
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`surface tension (about half) than the vinyl chloride-vinyl acetate adhesive, as
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`shown in the following table:
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`
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`2 Wicks, Z.W., Jr., et al., Organic Coatings Science & Technology, 3rd ed., 2007, at
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`
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`p. 490 (App. DD).
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`(Baghdachi, J.A., Fundamentals of Adhesion, J. of Coatings Technology, vol. 69,
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`no. 870, July, 1997, at p. 90 (App. FF)). Therefore, if the adhesive of Kuwahara
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`was dissolved in solvent, the surface tension of the adhesive-solvent mixture would
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`be even lower and interact with the metal islands and flow into the spaces between
`
`the metal islands even more.
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`26. Capillary forces will also facilitate the flow of the adhesive into the
`
`small space between the metal islands. The Concise Encyclopedia of Plastics at
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`page 134 defines capillary forces as “[t]he attraction between molecules, similar to
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`surface tension, which results in the rise of a liquid in small tubes or fibers, as can
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`occur in filled compounds or reinforced plastics.” (Rosato, D.V., et. al., Concise
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`Encyclopedia of Plastics, 2000 (App. GG) (emphasis added).) The Response’s
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`depiction of the Kuwahara’s adhesive possibly being applied to the bottom side of
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`the part being coated is irrelevant because the adhesive will flow upwards into the
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`small space between the metal islands due to capillary forces alone, irrespective of
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`other driving forces such as: (a) surface tension; (b) the adhesive’s polymer chain
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`small molecular diameter, mobility, and orientation; (c) intrinsic molecular inter-
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`diffusion; and (d) surface roughness of the metal islands.
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`27. Finally, after applying the adhesive to the metal island layer, and
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`stacking a polyvinylchloride film on top of the adhesive, Kuwahara discloses
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`applying heat and pressure to the structure to form a lamination. (Ex. 1007 at 5:21-
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`22.) The heat and pressure applied during the lamination procedure would
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`necessarily further drive the adhesive into any unfilled spaces between the islands.
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`V. KUWAHARA DOES NOT TEACH AWAY
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`28. Patent Owner argues that Kuwahara teaches away from the presence
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`of adhesive between the islands because residual solvent would permit electricity
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`to flow between the metal islands, which is to be avoided in Kuwahara. (Response
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`at pp. 30-31.) This argument is incorrect since if the adhesive was conducting as
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`the Patent Owner states, it would still electrically connect the metal islands even if
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`it was on top of the metal islands, as the Patent Owner argues. In addition, it is
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`known that most of the solvent would have evaporated during the lamination
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`process. One skilled in the art would understand that the small amount of solvent
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`that remained would not have turned a non-conducting polymer adhesive into a
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`conductor as Patent Owner argues.
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`VI. CONCLUSION
`
`29. Patent Owner contends that my finding that the discrete islands of
`
`Kuwahara would have been in adhesive as “unsupported opinion testimony.” I
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`disagree. As discussed in my first declaration, my finding was based on the
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`express disclosure of Kuwahara, including references to roll coating, the spacing
`
`between the islands and the discussion of lamination by heat and pressure as
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`understood by one of ordinary skill in the art.
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`30. Patent Owner’s Response does not compel me to change my finding.
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`In this second declaration, I have sought to respond to Patent Owner by showing
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`that one skilled in the art would have understood that the metal islands in
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`Kuwahara are necessarily in adhesive for the following reasons: 1) the adhesive is
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`roll coated as a liquid and would, therefore, have a viscosity low enough to be a
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`mobile liquid; 2) the diameter of the adhesive polymer molecules is significantly
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`less than the 500 Angstroms voids used in the examples of Kuwahara and even
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`more significantly less than the 5000 Angstroms voids also disclosed in Kuwahara;
`
`3) the “wetting” action of the adhesive and capillary action would pull the adhesive
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`into these relatively large pores; and 4) the heat and pressure applied during the
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`lamination procedure would further drive the adhesive into any unfilled spaces
`
`between the islands. In short, the arguments that Patent Owner has made do not
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`properly reflect how one of ordinary skill in the art would have understood
`
`Kuwahara’s facts.
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`31. This declaration is based on my present assessment of materials and
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`information currently available to me. My investigation and assessment may
`
`continue, which may include reviewing documents and other information that may
`
`yet to be made available to me. Accordingly, I expressly reserve the right to
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`continue my study in connection with this case and to expand or modify my
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`opinions and conclusions as my study continues.
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`32.
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`I declare under penalty of perjury under the laws of the United States
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`IPR2013—00149
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`that the foregoing is true and correct.
`
`
`
`Robert Iezzi
`
`Date
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`Wavelock
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`Exhibit 1018
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`IPR2013-00149
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`Appendix List for Second Declaration of Robert Iezzi, Ph.D. (Exhibit 1018)
`
`In Inter Partes Review of U.S. Patent No. 6,455,138
`
`Appendix Description
`
`
`
`Ebnesajjad, S., Adhesives Technology Handbook, 2nd ed., 2008
`
`Skeist, I., Handbook of Adhesives, 3rd ed., 1990
`
`Zang, Y.-H and Carreau, P. J., A Correlation Between Critical End-
`to-End Distance for Entanglements and Molecular Chain Diameter of
`Polymers, J. Appl. Polym. Sci. (1991), 42: 1965–1968
`
`Wicks, Z.W., Jr., et. al., Organic Coatings Science & Technology, 3rd
`ed., 2007
`
`Alchagirov, B.B., et al., Surface Tension of Tin and Its Alloys with
`Lead, Russian Journal of Physical Chemistry A, vol. 81, no. 8, 2007
`
`Baghdachi, J.A., Fundamentals of Adhesion, J. of Coatings
`Technology, vol. 69, no. 870, July, 1997
`
`Rosato, D.V., et. al., Concise Encyclopedia of Plastics, 2000
`
`AA
`
`BB
`
`CC
`
`DD
`
`EE
`
`FF
`
`GG
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`
`
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`Wavelock Exhibit 1018
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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX AA - page 1
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`Wavelock Exhibit 1018
`Page 18
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`

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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX AA - page 2
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`Wavelock Exhibit 1018
`Page 19
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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX AA - page 3
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`Wavelock Exhibit 1018
`Page 20
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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX AA - page 4
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`Wavelock Exhibit 1018
`Page 21
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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX BB - page 1
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`Wavelock Exhibit 1018
`Page 22
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`

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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX BB - page 2
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`Wavelock Exhibit 1018
`Page 23
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`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX BB - page 3
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`Wavelock Exhibit 1018
`Page 24
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`

`

`A Correlation between Critical End-to-End Distance for
`Entanglements and Molecular Chain Diameter of Polymers
`
`YONC-HUA ZANC**' and PIERRE J. CARREAU*
`'Pulp and Paper Research Institute of Canada, 70 St. John's Boulevard, Pointe Claire, Quebec, Canada H9R 3J9, and
`2Department of Chemical Engineering, Ecole Polytechnique de Montreal, Quebec, Canada H3C 3A7
`
`SYNOPSIS
`The critical molecular weight M , of 36 flexible and semirigid polymers has been studied.
`A unique correlation between the critical end-to-end distance (R,) for entanglements and
`the average polymer chain diameter D is found. This correlation is discussed in the light
`of the reptation concept.
`
`INTRODUCTION
`The onset of entanglement behavior with increasing
`molecular weight appears universally in polymer
`melts and concentrated solutions.'S2 An example of
`this is the critical molecular weight M,, which sep-
`arates the dependence of zero-shear viscosity T~ on
`molecular weight M into two regions: qo cc M and
`7.1~ cc M3.4. In order to understand the molecular na-
`ture of entanglements, many attempts have been
`made to correlate Mc (or the critical number of main-
`chain bonds N,) with some structural parameters
`of polymers.3-" A comparison of these different cor-
`relations reveals that the critical molecular weight
`M,, or N,, depends especially on the rigidity and
`cross-sectional area S of polymer chains. On the
`other hand, it has been recently recognized that en-
`tanglements can be modeled as a tube constraint on
`the diffusion of molecules (reptation models) .12,13
`According to the reptation models, the parameter
`controlling the degree of chain entanglement is the
`tube diameter, which is taken to be equal to the end-
`to-end distance between entanglements. However,
`no relationship between the tube diameter and the
`properties of polymer chains has been given. In the
`present work, the critical molecular weight for en-
`tanglements has been studied using the framework
`of the reptation models. Without linking directly
`M, (or N,) with structural parameters of polymers,
`
`* To whom correspondence should be addressed.
`Journal of Applied Polymer Science, Vol. 42,1965-1968 (1991)
`0 1991 John Wiley & Sons, Inc.
`CCC 0021-8995/91/071965-04$04.00
`
`the critical end-to-end distance of a macromolecular
`chain for entanglements, (R,) (corresponding to
`M,) , has been correlated with the average diameter
`D of the polymer chains.
`
`DATA ANALYSIS
`The critical end-to-end distance for entanglements,
`(R,), has been calculated from the critical molecular
`weight Mc through the following relation14:
`
`(R,) = (R:)'/'= M E / 2 ( ( R 2 ) o / M ) 1 / 2 (1)
`where ( R2)o is the mean-square end-to-end distance
`for a polymer of molecular weight M in a theta sol-
`vent, which is approximately identical with that in
`amorphous or molten p01ymers.l~
`The use of eq. ( 1 ) implies the assumption that
`M, is large enough so that the polymer chain is
`Gaussian.
`The average polymer chain diameter D is esti-
`mated from the cross-sectional area of the polymer
`S using the approximate relation6
`
`where the values of S are generally obtained from
`crystallographic data.17
`Table I summarizes the values (taken from the
`literature) of Mc( ( R 2 ) o / M ) 'I2 and S together with
`the characteristic ratio C , ( C , = (R2)o/N12, with
`N and lo being, respectively, the number and the
`1965
`
`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX CC - page 1
`
`Wavelock Exhibit 1018
`Page 25
`
`

`

`1966
`
`ZANG AND CARREAU
`
`Table I Critical Molecular Weight M, and Characteristic Parameters of Polymers
`
`No.
`
`Polymer
`
`1
`2
`3
`4
`5
`6
`7
`8
`9
`10
`11
`12
`13
`14
`15
`16
`17
`18
`19
`20
`21
`22
`23
`24
`25
`26
`27
`28
`
`29
`30
`31
`32
`33
`34
`35
`
`36
`
`3800'*''
`7000'
`35,000'~''
`62501',''
`24,500'>''
`53001'
`9100"
`40,8005~"
`15,200'
`24, 1001O~a
`31,300''~"
`31,0008~''
`60,40010fa
`91,90010*"
`114,00010~a
`42,800''7'
`24, 5008*''
`44007."
`77001'.''
`2500''
`77001'
`40001'."
`45008s10
`59OO1O
`12,70019.a
`26,700193"
`50001'
`47001'
`
`460010v'8
`440O1"."
`4500''~''
`48001'
`33001'
`49001'
`4800''
`
`7100''
`
`Polyethylene
`Polypropylene
`Polystyrene
`Poly(viny1 chloride)
`Poly(viny1 acetate)
`Poly(viny1 alcohol)
`Pol yacrylamide
`Poly( a-methyl styrene)
`Polyisobutylene
`Poly(methy1 acrylate)
`Poly(ethy1 acrylate)
`Poly(methy1 methacrylate)
`Poly(n-butyl methacrylate)
`Poly( n-hexyl methacrylate)
`Poly(n-octyl methacrylate)
`Poly(2-ethylbutyl methacrylate)
`Poly(dimethy1 siloxane)
`Poly(ethy1ene oxide)
`Poly(propy1ene oxide)
`Poly(tetramethy1ene oxide)
`Cis-polyisoprene
`Hydrogenated polyisoprene
`Cis, trans, vinyl-polybutadiene
`Cis-polybutadiene
`1,2-Polybutadiene
`Hydrogenated 1,2-polybutadiene
`Poly (t-caprolactam) nylon 6
`Poly(hexamethy1ene adipamide)
`nylon 66
`Poly(decamethy1ene succinate)
`Poly(decamethy1ene adipate)
`Poly(decamethy1ene sebacate)
`Poly(diethy1ene adipate)
`Poly(ethy1ene terephthalate)
`Poly(carbonate of bisphenol A)
`Poly(ester carbonate of 1-
`bisphenol A and 2-
`terephthalic acid)
`Poly(ester of bisphenol A and
`diphenyl sulfone)
`Average value
`Standard deviation
`Estimated as M,
`= 2M..
`Calculated from C,.
`' Estimated from 1,2-polybutadiene.
`Calculated from ((R*),,/M).
`Estimated from poly(decamethy1ene adipate) and poly(decamethy1ene sebacate).
`Estimated between poly(ethy1ene terephthalate) and poly(carbonate of bisphenol A).
`
`7.0
`6.2
`10.3
`7.7
`9.0
`8.3
`14.8
`10.5
`6.2
`8.0
`8.8
`8.7
`8.0
`10.3
`10.0
`9.1
`5.2
`4.2
`5.1
`6.1
`5.0
`6.8'
`5.4
`4.9
`6.6'
`5.519
`5.3
`6.1
`
`5.5d
`4Bd
`6.0d
`4.7d
`
`18.311
`34.3'1
`69.8l'
`27.2'l
`59.311
`21.417
`45.211
`100.0"
`41.2'l
`59.311
`73.0"
`63.8l'
`93.611
`114.2"
`135.111
`100.011
`63.811
`21.511
`24.511
`17.617
`28.0"
`28.511
`19.311
`20.711
`49.911
`49.gc
`17.911
`17.611
`
`18.5"
`18.5'
`18.57
`18.117
`20.0"
`30.911
`30.9''
`
`30.9"
`
`15.6
`11.9
`15.1
`12.4
`14.2
`13.6
`14.2
`13.1
`14.2
`13.7
`14.9
`13.7
`13.2
`15.3
`14.5
`10.6
`15.6
`11.6
`13.7
`11.2
`13.9
`11.4
`15.4
`14.9
`13.7
`15.8
`15.7
`15.4
`
`13.7
`12.8
`14.7
`12.9
`12.6
`11.7
`11.8
`
`12.1
`
`13.6
`0.11
`
`average length of main-chain bondsI4) for 36 poly-
`mers.
`Figure 1 shows the critical end-to-end distance
`for entanglements (R,) plotted as a function of D
`
`for all of the polymers listed in Table I. Despite some
`scatter, (R,) is clearly a linear function of polymer
`chain diameter D , given by
`( R , ) = 13.60
`
`( 3 )
`
`Second Declaration of Robert Iezzi, Ph.D.
`APPENDIX CC - page 2
`
`Wavelock Exhibit 1018
`Page 26
`
`

`

`MOLECULAR CHAIN DIAMETER OF POLYMERS
`
`1967
`
`The proposed correlation [ eq. ( 3 ) ] can also be
`reduced to a form which is similar to the Graessley-
`Edwards’ and Fox-Allen3 correlations for N,. These
`authors found’
`
`cm-’
`
`N,p((R2)0/M) = 2.3 X
`where p is the density of the polymer.
`Using the relation proposed by Vincent,24 S = %/
`( Naplo) ( mo is the average molecular weight per
`main-chain bond, and N, Avogadro’s number), one
`obtains, by combining eqs. ( 1 ) , ( 2 ) , and ( 3 ) ,
`
`( 5 )
`
`I
`
`I
`
`,
`
`.
`
`
`
`I
`
`Average molecular diameter, D (A)
`Critical end-to-end distance ( R , ) vs. average
`Figure 1
`molecular diameter D of polymer chains.
`
`DISCUSSION AND CONCLUSION
`Equation ( 3 ) provides a new correlation for en-
`tanglements relating the critical end-to-end dis-
`tance to polymer chain diameter. As already men-
`tioned in the Introduction, many other empirical
`correlations3-” have been developed before. Some
`similarities can be found between the proposed cor-
`relation and the literature ones: Using the relation
`(RE) = C,N,l;,
`the critical number of main-chain
`bonds N, can be calculated from eq. ( 3 ) :
`
`N, = (185/l;)(D/C’,/2)2
`
`( 4 )
`
`Equation (4) is similar to the Privalko-Lipatov
`relation,6 N, = 240 ( D / u ) ’ . ~ , where u is the chain
`stiffness factor. Moreover, Boyer and Miller pointed
`out that the exponent of the Privalko-Lipatov cor-
`relation should be between 2 and 2.2 instead of 2.5,
`thus supporting the proposed correlation.
`Equation ( 4 ) predicts that for polymers with
`similar characteristic ratios C,
`, like polyalkyl
`methacrylates, N, should depend only on the poly-
`mer chain diameter D, or cross-sectional area S, as
`suggested by Boyer and Miller7 earlier. On the other
`hand, for polymers having similar average molecular
`diameters, N, should decrease with increasing rigid-
`ity of the chains. This was indeed observed by Pre-
`vorsek and De Bona, 23 who reported that replacing
`a fraction of the flexible carbonate moiety in poly-
`carbonates with a more rigid group (such as tere-
`phthalate ) reduces the average molecular weight
`between entanglements.
`
`Taking a typical value, lo = 1.5 X lo-’ cm, the
`cm-’,
`value on the right side of eq. ( 6 ) is 2.1 X
`showing a good agreement with eq. ( 5 ) .
`On the other hand, the proposed correlation [ eq.
`( 3 ) ] has the following main advantages compared
`with the literature correlations:
`
`( 1 ) Most of the literature correlations provide a
`purely empirical relation between N, (or M,)
`with some structural parameters of the poly-
`mer chains. As they are not dimensionally
`consistent, the connection between the mo-
`lecular nature of entanglements and the crit-
`ical molecular weight is unclear. In contrast,
`the proposed correlation [ eq. ( 3 ) ] is very
`simple, and is dimensionally consistent. It is
`also clearly related to the