Application No.: 11/520,479
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`1
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`Docket No.: 638772000109
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`IN THE UNITED STATES PATENT AND TRADEMARK OFFICE
`
`In re Patent Application of:
`Neil P. DESAI et al.
`
`Application No.: 11/520,479
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`Confirmation No.: 8972
`
`Filed: September 12, 2006
`
`For: NOVEL FORMULATIONS OF
`PHARMACOLOGICAL AGENTS, METHODS
`FOR THE PREPARATION THEREOF AND
`METHODS FOR THE USE THEREOF
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`Art Unit: 1611
`
`Examiner: T. Love
`
`SUPPLEMENTAL DECLARATION OF NEIL P. DESAI PURSUANT TO 37 C.F.R § 1.132
`
`Commissioner for Patents
`P.O. Box 1450
`Alexandria, VA 22313-1450
`
`Dear Madam:
`
`I, Neil P. Desai, declare as follows:
`
`1.
`
`This declaration is in addition and supplemental to the 37 C.F.R. §1.132 declaration
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`("the Previous Declaration") previously submitted to the Patent Office on January 27, 2012.
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`2.
`
`I have reviewed the Office Action dated May 2, 2013. I understand that claims in the
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`above-captioned patent application remain rejected as being obvious over one of Abraxis' earlier
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`patents, U.S. Pat. No. 5,439,686 ("Desai"), for which I am also a named inventor, in view of U.S. Pat.
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`No. 5,407,683 ("Shively"). In this supplemental declaration, I provide more information about the
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`data presented in the Previous Declaration as well as the cited reference Desai.
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`3.
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`In the Previous Declaration, I presented, in part, experimental data showing the
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`advantageous properties of the nanoparticle formulations recited in the claims of the above-captioned
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`patent application ("the '479 application"). The experiment compared the physical stability of two
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`pharmaceutical formulations (Composition 1 and Composition 2) containing nanoparticles
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`comprising a solid core of paclitaxel and an albumin coating at a paclitaxel concentration of 5 mg/ml.
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`4.
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`As discussed in the Previous Declaration, upon storage at 40 oc for 24 hours, 1 there
`was a distinctly visible sediment layer at the bottom of the vials containing Lot 1 and Lot 2 of
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`Composition 2 indicating instability of Composition 2. Exhibit 1; See also Exhibit 3 of the Previous
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`Declaration. Such sedimentation was not observed in the vial containing Composition 1.
`Microscopic observation of the formulations stored at 40 oc for 24 hours at 400x magnification
`revealed large particles in Composition 2 indicating particle growth and aggregation, which were not
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`observed in Composition 1. Exhibit 2; See also Exhibit 4 of the Previous Declaration.
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`5.
`
`Further, as discussed in the Previous Declaration, upon storage at 40°C for 24 hours,
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`the weight mean diameter of the nanoparticles in Composition 1 remained unchanged. In
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`Composition 2, by contrast, the weight mean diameter of the nanoparticles increased significantly
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`upon storage demonstrating instability of Composition 2. Exhibit 3; See also Table 1 of the Previous
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`Declaration.
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`The table below summarizes and provides additional particle size characteristics of the
`6.
`two different formulations tested in the experiment.2
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`Formulation
`
`Weight Mean
`Diameter, nm
`Composition 1
`140
`Composition 2, Lot 1 245
`Composition 2, Lot 2
`228
`
`99% Weight
`95% Weight
`Distribution (D95), nm Distribution (D99), nm
`240
`282
`500
`633
`496
`638
`
`1
`Storage at 40 °C for 24 hours is equivalent to storage at room temperature for at least three days.
`2 Particle size was determined by disc centrifugation method immediately after reconstitution of the formulations at about 5 mg/ml.
`Size may differ slightly when using a different measurement method such as dynamic light scattering.
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`The 95% and 99% weight distribution in the table above provides the size in nanometers below which
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`95% and 99% by weight of the particles lie, respectively. For example, in Composition 1, 95% of the
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`particles in the formulation have a particle size below 240 nm. In Composition 2, 95% of the particles
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`in the formulation have a particle size below 500 (Lot 1) and 496 nm (Lot 2). In Composition 1, there
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`was no detectable percentage of nanoparticles that have a size above 400 nm, with 99% of the
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`particles lying below 282 nm. In Composition 2, by contrast, at least 10% of the nanoparticles in the
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`formulation had a particle size that was above 400 nm, with 99% of the particles lying below 633 (Lot
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`1) and 638 nm (Lot 2).
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`7.
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`The diagram below further illustrates the 99% weight distribution of the two different
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`formulations.
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`Composition 1
`
`Composition 2
`
`0
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`2.82.nm
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`633nm
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`s
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`>1000nm
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`8.
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`Notably, both Composition 1 and Composition 2 are albumin-coated paclitaxel
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`nanoparticle formulations having a particle size below 1000 nm, yet they behave differently in
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`stability assays. Composition 1, which contains no detectable percentage of nanoparticles that have a
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`size above 400 nm, was shown to be stable at paclitaxel concentration of 5 mg/ml. By contrast,
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`Composition 2, which contains nanoparticles slightly greater than 400 nm, was unstable at the same
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`paclitaxel concentration under the same conditions. This result was unexpected.
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`9.
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`As discussed in the Previous Declaration, physical stability is a key consideration for
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`ensuring safety and efficacy of nanoparticle drug products. The tendency of nanoparticles to
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`precipitate and/or increase in size (for example by aggregation) increases as the drug concentration
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`increases. For example, an increase in drug concentration in a nanoparticle formulation can result in
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`an increase in particle concentration, namely, the number of particles per unit volume. An increase in
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`particle concentration in tum would increase the frequency of collision of the particles and thus
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`increase the tendency of the particles to aggregate and become unstable. This is demonstrated in
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`Bums et al., Langmuir 1997, 13, 6413-6420 (Exhibit 4), for example, which examined particle
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`aggregation in various formulations having different particle concentrations. The authors concluded
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`that "[a]s the particle concentration is increased, the aggregate growth is more rapid, most likely due
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`to the increased collision frequency." See also Kallay et al., J. Colloid and Interface Science 253,
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`70-76 (2002) (Exhibit 5) at page 75 ("the aggregation rate is proportional to the square of the particle
`.
`")
`concentratiOn....
`.
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`10.
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`The estimated particle concentration for Composition 1 discussed above, namely, the
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`albumin-coated solid paclitaxel nanoparticle formulation having a particle size less than 400 nm at
`paclitaxel concentration of 5 mg/ml, is about 8.0 x 1013 /m1.3 The stability of such a formulation at 5
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`mg/ml or higher was unexpected based on the high particle concentration.
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`11.
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`The stability of albumin-coated paclitaxel nanoparticle formulation having particle
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`size less than 400 nm is in stark contrast with that of a different non-albumin based paclitaxel
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`nanoparticle formulation having particle size less than 400 nm. In a study conducted to compare the
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`physicochemical characteristics and stability of two different commercially-approved nanoparticle
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`formulations ofpaclitaxel, namely, Abraxane® (an albumin-coated solid paclitaxel nanoparticle
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`formulation having particle size less than 400 nm, similar to Composition 1 described above) and
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`Genexol-PM ®(a non-albumin polymeric-micelle formulation ofpaclitaxel having particle size less
`than 400 nm), only Abraxane® was shown to be stable at 40 oc over 24 hours at paclitaxel
`concentration of5 mg/ml while the Genexol-PM ®formulation showed excessive precipitation under
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`these conditions. Ron et al., 99th AACR Annual Meeting Abstract, No. 5622 (Exhibit 6). This study
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`further illustrates the difficulty and challenge in obtaining paclitaxel nanoparticle formulations having
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`3
`The particle concentration is estimated with the assumption that the average particle size of the particles in the formulation is about
`140 nm and the particle density is about 1165 kg/m3
`.
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`particle size less than 400 run that are stable at paclitaxel concentration of 5 mg/ml or higher, and the
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`unexpected stability of the claimed albumin-coated solid nanoparticle formulation.
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`12.
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`Thus, albumin-coated paclitaxel nanoparticle formulations having particle size less
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`than 400 run were stable at 5 mg/ml. This is in stark contrast with an albumin-coated paclitaxel
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`nanoparticle formulation which contains particles slightly greater than 400 run, and a non-albumin
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`based paclitaxel nanoparticle formulation having particle size less than 400 run, both shown to be
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`unstable under the same conditions at paclitaxel concentration of 5 mg/ml. These results demonstrate
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`the advantageous and unexpected stability of the albumin-coated paclitaxel nanoparticle formulation
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`recited in the claims of the '479 application, especially in view of the high particle concentration in
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`such a formulation and the well-known principle that the aggregation rate of nanoparticles is
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`proportional to the square of the particle concentration.
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`13.
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`The Examiner cites Desai as allegedly teaching a stable albumin-coated nanoparticle
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`formulation. As discussed in the Previous Declaration, Example 5 of Desai, which the Examiner
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`relies on as teaching stability of albumin-coated nanoparticle formulations, refers to the stability of
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`polymeric shells containing buoyant soybean oil with density less than water. No drug was present
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`within the polymeric shell. The stability of the "drugless" oil-containing polymeric shells discussed
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`in Example 5 of Desai thus provides no suggestion that a nanoparticle formulation comprising a solid
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`core of paclitaxel and an albumin coating would be stable at paclitaxel concentration of between 5-15
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`mg/ml. Furthermore, as discussed in the Previous Declaration, an increase in loading of paclitaxel
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`within the polymeric shells as taught in Example 4 of Desai would be expected to increase the particle
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`size and/or density of the particles, which in tum could increase the tendency of the particles to
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`precipitate.
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`14.
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`Although a separate example in Desai, Example 9, teaches preparation of polymeric
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`shells containing a solid core of pharmaceutically active agent such as paclitaxel, there is no
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`information about the concentration of the paclitaxel in such polymeric shell formulation. Nor is
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`there any indication that the particles in such polymeric shell formulation are smaller than 400 run.
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`Application No.: 11/520,479
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`Example 9 teaches that "these polymeric shells are examined under a microscope to reveal opaque
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`cores .... " The fact that the polymeric shells were viewable under a microscope to reveal opaque cores
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`indicates that a substantial portion of the particles in the formulation taught in Example 9 were larger
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`than 400 nm. Thus, these formulations taught in Desai differ from the formulation recited in claims of
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`the '479 application in at least two aspects: paclitaxel concentration and particle size.
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`15.
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`To arrive at the claimed formulation from Desai's nanoparticle formulations, one
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`would at least need to: 1) substantially decrease the size of the particles in the formulation to less than
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`400 nm; and 2) substantially increase the paclitaxel concentration to 5-15 mg/ml. Desai provides no
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`teaching on how to obtain a nanoparticle formulation having a particle size of less than 400 nm. Nor
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`would one expect that an albumin-coated solid nanoparticle formulation having a particle size of less
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`than 400 nm and paclitaxel concentration of 5-15 mg/ml would have been stable. Specifically,
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`according to Example 5 of Desai, the particle concentrations of the formulations reported therein is
`about 7-9 x10 10 per ml. See Table 1 at Column 13 of Desai. The estimated particle concentration of
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`the albumin-coated paclitaxel nanoparticle formulation having a particle size less than 400 nm at
`paclitaxel concentration of 5 mg/ml, on the other hand, is about 8 x 1013 /ml. This is 1000 fold higher
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`than those reported in Desai. Since the aggregation rate of nanoparticles is proportional to the square
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`of the particle concentration, one would not have expected that the albumin-coated paclitaxel
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`nanoparticle formulation having a particle size less than 400 nm at paclitaxel concentration of 5
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`mg/ml, whose particle concentration is at least 1000 fold higher than those reported in Desai, would
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`be stable.
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`16.
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`I hereby declare that all statements made herein of my own knowledge are true and
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`that all statements made on information and belief are believed to be true; and further that these
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`statements were made with the knowledge that willful false statements and the like so made are
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`punishable by fine or imprisonment, or both, under Section 1001 of Title 18 of the United States Code,
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`and that such willful false statements may jeopardize the validity of the application, any patent issuing
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`thereon, or any patent to which this verified statement is directed.
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`Applic.atiGn No.: 11:'520,479
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`Docket No.: 638772000109
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`11/1/2013
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`Date
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`Exhibit 1
`Exhibit 1
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`
`
`
`
`
`
`.
`
`-
`
`v
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`~
`
`v
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`Sedimented
`ié er
`y
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`' Composition 2, Lot 2,
`24 hrs
`40 “E
`
`No
`sediment
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`,
`
`.
`
`'
`
`”
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`.
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`24.5 at 40 °C
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`
`
`1
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`Exhibit 2
`Exhibit 2
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`Composition 2, Lot 1, 24 hrs at 40°C, 400x
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`Composition 2, Lot 2, 24 hrs at 40°C, 400x
`
`Composition 1,
`24 hrs at 40°C, 400x
`
`2
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`Exhibit 3
`Exhibit 3
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`Sample
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`Storage Condition
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`Weight Mean Diameter, nm1
`
`Composition 1
`
`Composition 2, Lot 1
`
`Composition 2, Lot 2
`
`0 time
`
`24 hours at 40°C
`
`0 time
`
`24 hours at 40°C
`
`0 time
`
`24 hours at 40°C
`
`136.9
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`135.2
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`244.5
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`1159.5
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`228.0
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`561.5
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`1 Size determined by disc centrifugation method.
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`Exhibit 4
`Exhibit 4
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`Langmuir 1997, 13, 6413-64<D
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`6413
`
`A Light Scattering Study of the Fractal Aggregation
`Behavior of a Model Colloidal System
`
`Janine L. Burns, t.+ Yao-de Yan, + Graeme J. Jameson,+ and Simon Biggs*·t
`
`Departments of Chemistry and Chemical Engineering, The Unive~sity of Newcastle,
`University Drive, Callaghan, NSW23JS Australia
`
`Received March a:? 1997. In Final Form: August a}, 1991J
`
`The mass fractal dimension of aggregates of colloidal polystyrene l~tex particles ~s measured using
`small-angle static light scattering over a range of electrolyte and parttde c:ncentratt~s. The measured
`fractal dimensioos ranged from 1. 78to 2.:::0 whidl are in gcxxl agreement Wlth the predicted ~alues <;fthe
`diffusioo-limited duster-duster aggregatioo and reactioo-limited duster-duster aggregatloo regtmes,
`respectively. It was found that increasing the salt concentration had the eff~ of redudng the fractal
`dimension, indicating a more c.pen aggregate structure. Two regimes of behaVIor were cbserved for ~he
`fractal dimensioo as a functioo of particle coocentratioo. At high salt levels (> 1 M KN0:3) t_he partic;Je
`coocentratioo was seen to have little or no effect, while at low salt levels (< 1M KN0:3) .an ~ncreas~ m
`coocentration led to a decrease in the fractal dimensioo. This was attributed to a reductioo m the ttme
`available for recoofiguring of particles in the aggregates due to an increased particle ~lision freque~cy.
`The particle aggregatioo rate was also found to increase at higher electrolyte levels and With larger particle
`coocentrations.
`
`Introduction
`Aggregati<n of colloidal particles is of fundamental
`interest to many academic and industrial researchers. A
`typical aquerus colloidal dispersi<n c<nsists of particles
`wha;e stability is cootrolled by the presence of scene
`surface charge. The suppressi<n of this stabilizing effect
`is easily achieved by the additi<n of moderate amrunts of
`an inert electrolyte. Until recently, the structures fccmed
`upm aggregati<n of these oolloidal dispersi<ns were not
`easy to define in a mathematical sense. The advent of
`fractal mathematics has resulted in a renaissance in this
`field of study. The interest is greatly motivated by the
`fact that fractal growth phenccnena are da;ely related to
`many processes of practical impcrtance. For instance,
`the structure of particle aggregates has important im(cid:173)
`plicati<ns for problems relating to air and water polluti<n
`cootrol.I
`.Mandelbrot2 was the first to rec<:Wlize that many
`ccmm<n structures pa;sess a rather spedal kind of
`cccnplexity. He gave them the term fractal to express
`that they can be characterized by a nminteger (fractal)
`dimensi<nality. Wth the develq:>ment of research in this
`directioo, the list of examples of fractals has becane
`extensive and includes structures ranging in size frccn
`micra;ccpic aggregates to clusters of galaxies. Fractal
`morphology has already been demoostrated for a range
`of particle aggregates indudingtha;e of silica, gold, latex,
`clay, polymer, shale, cad, and soot, among others.
`Computer simulations have played a major role in
`understanding the structure of these aggregates. This is
`because it is difficult to devise real experiments that can
`isolate an aggregatioo mechanism as predsely as do
`cccnputer simulatioos. Hence, mudl of the knowledge
`abrut aggregati<n and fractal growth has been derived
`from computer mcx:leling. Simulatioo studies have shown
`thatthemassfractaldimensi<n, dF. of particle aggregates
`
`• To whan c<rresprndence shwld be addressed
`t Department ci Chemistry.
`* Department ci Chemical Engineering.
`® AbstractpublishedinAdvanceACSAbstracts,OctdJer 15. 1007.
`(1) Wng, K.; Cabane, B.; Duplessix, R.; Sanasundaran, P. Langmuir
`1~ 5 1346
`(~ Mandelbra:, B. B. The Fractal Geometry of Nature; Freeman:
`San Frandsco. CA. 1!E2
`
`is a functi<n of the spatial dimensi<n alme and is
`essentially independent of the details of the simulation.
`And the resulting fractal dimensi<DS are largely dependent
`upoo the particle sticking effi.dency, that is, the potential
`energy barrier to aggregation.
`For a Brownian particle, when it fallows a randccn walk
`between two points, it rovers a large space in between.
`There is a high prdJa.bility that as the particle moves
`from an exterior point to a point deep inside a cluster, it
`will intercept an arm cfthe cluster. Therefere, the growing
`arms will screen the interier of the cluster frcm the
`incoming particles. As a coosequence, a particle is more
`likely to stick near the rutside of the cluster than to
`penetrate near the center, resulting in a very q:>en
`structure. In many real systems involving diffusion(cid:173)
`limited growth, a large number of diffusing cluste~s ~II
`exist at any given time, and these can grow by stickmg
`to each ether as well as frccn single particle addition. It
`became clear that cluster-cluster aggregates have very
`q:>en structures with dF = 1. 75-1.ffi 34 The low fractal
`dimensioos of this diffusion-limited cluster-cluster ag(cid:173)
`gregatioo (.DLCA) mcx:lel reflect the lcx:se, q:>en appearance
`of the aggregates fccmed.
`In this simple mcx:lel <nly aggregatim pr<XESSes in which
`the rate-limiting step is diffusioo have been coosidered.
`It is also pa;sible fer the aggregati<n rate to be limited
`by the probability that particles will stick upm cootact.
`If the sticking prdJa.bility (or collisi<n effi.dency) is very
`small, the clusters will need to collide many times before
`they stick, and this will have the net effect of allowing the
`diffusing clusters to penetrate further into each other
`before sticking. The facter respoosible fer the low sticking
`probability is usually an electric double-layer repulsion.
`This type of aggregatioo is ccmmonly referred to as
`reactioo-limited cluster-cluster aggregation (RLCA).
`Simulations5 show an increase in the fractal dimension
`over the diffusioo-limited case with dF = 2. 1 (i.e .. denser
`aggregates). coofirming that the effect of screening is
`somewhat reduced.
`The first experiments that explidtly investigated the
`fractal nature of aggregates were reported in 1979 by
`
`(3) Meakin, P.; \1\asserman, Z. R. Phys. Lett. 1984. 1034, '331.
`(4) Jullien, R. Phys. Rev. Lett. l{R'). 55. 1ffi7.
`(5) Brown, W D.; Ball, R. C. J. Phys. A 1{BS. 18 L517.
`
`S0743-74fi3(97)cx:xn3-X CCC: $14CD
`
`© 1007 American Chemical Society
`
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`6414 Langmuir, Vol. 13. No. 24, 1997
`
`F arrest and Wtten. 6 In these experiments metallic oxide
`smd<e particles weredepcsited mtotransmissim electrm
`micrcscopy (fEM) substrates and their fractal dimensioos
`determined using image analysis tedmiques to ccmpute
`the pair rorrelatim functim and the mean density as a
`functimcfsize. Valuesintherange 1.85-1.00werefound
`fer dF. The primary difficulty in these experiments was
`that the three-dimensimal clusters were simply prqjected
`mtothetwo-dimensimal TEMsubstrates. Nmetheless,
`these experiments were the first to demoostrate the
`essential fractal nature cf particle aggregates.
`Schaefer et al. 7 avoided the inherent limitatims of the
`sample preparatim required by micrcscopy methcds by
`using light and X-ray scattering to measure the fractal
`dimensim cf rolloidal silica aggregates in situ. Since their
`intrcductim, a wide variety cf rolloidal systems have been
`studied using these scattering techniques. These range
`frcm silica&- 10 to polystyrene latex, ll-ls gold, a:>-2.2 hema(cid:173)
`tite, ~2A kaolinite, 25 bent mite clay, ao and even carbm
`black. zr Wthin the published fractal studies nearly all
`have coosidered the aggregatim of rolloidal particles in
`the presence cf electrolyte, thrugh studying a wide range
`cf parameters. Sane include the effect cf varying the
`electrdyte cmcentratim, a 1o- 1~ I&- 1Q2A2B-31 pH, 8IQ2'ia> tem-
`perature, a 23shear rates, 3233and particle cmcentratim 14 15
`m the fractal structure cf the aggregates.
`
`(6) Fcrrest, S. R.; V\.itten, T. A. J. Phys. A 1979, 12. L 1ffi
`(7) Schaefer, D. W; Martin, J. E.; V\.iltzius, P.; Cannell, D. S. Phys.
`Rev. Lett. 1~ 52 2371.
`(8) Cannell. D. S.; Aubert. C. Phys. Rev. Lett. 1~ 56 'rn
`(9) Tang, P.; Cdflesh, D. E.; Chu, B. J. Colloid Interface Sci. 19'la
`126. 3J4.
`(1G Martin, J. E.; V\.ilcaxm, J.P.; Schaefer, D.; O:linek, J. Phys. Rev.
`A 1ml 41, 4379.
`(11) Bdle, G.; Cametti, C.; Ccdastefano. P.; Tartaglia, P. Phys. Rev.
`A 1987, 3:i f!Zl.
`(121 Magazu. S.; Majdino, D.; Mallamace. F.; Micali, N.; Vasi, C.
`Solid State Commun. 1!H}. 7Q 233.
`(13) Majdino, D.; Mallamace, F.; Migliardo, P.; Micali, N.; Vasi, C.
`Phys. Rev. A 1~ 4Q 4665
`(14) Carpineti,M; Ferri, F.; Giglio,M; Paganini, E.; Perini, U.Phys.
`Rev. A 1m) 42. 7?A7.
`(15) Carpineti, M; Giglio. M; Paganini, E.; Perini, U. Frog. Colloid
`Polym. Sci. 1991, 84. 3J5
`(16) lboo, Z; Chu, B. J. Colloid Interface Sd. 1991. 143, 356
`(17) Asnaghi, D.; Carpineti, M; Giglio. M; Sazzi, MIn Structure
`and Dynamics of Strongly Interacting Colloids and Supramolecular
`Aggregates in Solution; Chen, S.-H., Huang, J. S., Tartaglia, P., Eds.;
`Kluwer Academic Publishers: Dcrdrecht, The Netherlands, 1002 p
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`(18) Asnaghi, D.; Carpineti, M; Giglio. M; Sazzi, M Phys. Rev. A
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`(aJ) V\eitz, D. A.; Huang, J. S.; Lin, MY.; Sung, J. Phys. Rev. Lett.
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`1994, 11, 315
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`Surf. A 1995, 97, 53
`(28) Lin, MY.; Lindsay, H. M; V\eitz, D. A.; Ball, R. C.; Klein, R.;
`lvleakin, P. Nature 19'119, 33Q 3En
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`Meakin, P. Proc. R. Soc .. London, Ser. A 1!H}. 423 71.
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`lvleakin, P. J. Phys.: Condens. Matter 1m) 2. 3::m
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`Meakin, P. Phys. Rev. A 19!1), 41, aD5.
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`Sd. 1991, 142. 554.
`(33) Oles, V. J. Colloid Interface Sci. 199a 154. 351.
`
`Burns et al.
`
`Lin and co-werkers2B-31 have studied the universality
`cf fractal rolloid aggregates using beth static and dynamic
`light scattering. They investigated the two limiting
`regimes, diffusim-limited (i.e., DLCA), and reactim(cid:173)
`limited (i.e., RLCA) colloid aggregatim, fer three ccm(cid:173)
`pletely different rolloids: gdd, silica, and polystyrene.
`They frund the aggregatim behavier to be independent
`of the detailed chemical nature cfthe rolloid system. The
`fractal dimensims of the aggregates were frund to be in
`goal agreement with thcse obtained fran calculatioos
`using ccmputer mcdels. For DLCAall aggregates had dF
`= 1.85± QCEand a power-law kinetic growth behavier,
`while fer RLCA dF = 2 11 ± Q <15and the kinetics cf growth
`were expmential in nature.
`A number cf aggregatim studies cmducted m hema(cid:173)
`tite~2A have resulted in fractal dimensims in the range
`2 3-2 8, much higher than thcse reported fer DLCA and
`RLCA. Higher than usual fractal dimensims have also
`been reported for aggregatim in clay systems where the
`material can have dual charge character, hence the
`pa;;sibili ty cfheterdlocculatim. 2'ia> Shear ferces have also
`been frund to have a significant effect m the aggregate
`structure cf fractal clusters. 33 High fractal dimensims
`(dF ~ 25) fer aggregates fccrned under shear cmditims
`have been propcsed toresult fran selective breakup, which
`removes preferably the weakest and mcst perrus areas cf
`the aggregate until finally leading to a balance between
`growth and breakup. Shearing effects may pcssibly
`provide an explanatim fer the unusually high results
`d:>tained for the hematite systems.
`In this study, an extensive investigatim into the effect
`of particle cmcentratirn, over a wide range of salt
`cmcentratims, m the mass fractal dimensims of ag(cid:173)
`gregates of polystyrene latex particles has been cmducted
`using small-angle static light scattering. The changes in
`average aggregate size distributirn and the scattering
`exprnent were mrnitored over time to gain additimal
`insight into the aggregatim processes.
`
`Thea:etical Background
`Fractals and Static Light Scattering. A fractal
`d:>ject is an d:>ject that is cmsidered to be self-similar,
`meaning that the structure cf the d:>ject is invariant to a
`change of scale. In the general thecry of fractals, the
`fractal dimensim ccrrespmds to the degree cfirregularity
`er the space-filling capacity of an d:>ject. Fer a mass (er
`volume) fractal aggregate its mass, m (R), is propertimal
`to its radius, R, raised to power dF, i.e.,
`
`m(R) oc: ~F
`
`( 1)
`
`Here dF is called the mass fractal dimensim and is not
`limited to integer values, unlike erdinary mass-size
`relatimships. This fractal dimensirn can further be used
`to characterize changes in mass density cf the aggregate,
`p(R), chserved within a sphere of radius R centered at
`sane point in the aggregate:
`
`(2)
`
`where 1 s dF s 3fer an d:>ject in 3-dimensimal Euclidean
`space. An entirely ccmpact aggregate such as a ccalesced
`sphere will have a dF of 3 Aggregates with an open
`cmfiguratim of particles are characterized by smaller
`fractal dimensims.
`Static light scattering has been extensively used in the
`study of aggregating and aggregated rolloidal systems. In
`a static light scattering experiment a beam cf light is
`directed mto a sample and the scattered intensity is
`
`Actavis - IPR2017-01100, Ex. 1024, p. 16 of 33
`
`

`

`Light Scattering Study of a Model Colloidal System
`
`Langmuir, Vol. 13 No. 24. J[£)7 6415
`
`measured as a functim of the magnitude of the scattering
`vecter, Q. with
`
`(3)
`
`where n 0 is the refractive index of the dispersim medium,
`(J is the scattering angle, and A.0 is the in va cu owavelength
`of the incident light.
`If the individual particles in a fractal aggregate are
`mmodisperse and within the Rayleigh-Gans-Debye
`regime, the scattered intensity I( OJ fran such an aggregate
`can be written as34
`
`I(Qj = kcf>(Qj S(Q)
`
`(4)
`
`In the above expressim k0 is a scattering cmstant. P(Qj
`isthesingleparticlefcrmfacterandisrelatedtotheshape
`cftheprimaryparticle. S(Qj is the interparticle structure
`facter, which represents the ccrrelatims between different
`primary particles within an aggregate, assuming there
`are no correlatims between the aggregates themselves.
`Thus, it describes the spatial arrangement of the particles
`in an aggregate.
`At large Qs cr Qr0 » 1, where r0 is the radius c:i the
`primary particle, S(Q) is approximately equal to 1. The
`scattered intensity is then daninated by the single particle
`ferm factcr and only the scattering due to individual
`particles is seen. At Qs small canpared to lfo. but large
`canpared to 1R (i.e .. 1R« Q« Lfo). P(Qj ~ 1andS(QJ
`reduces to34
`
`(5)
`
`Hence, provided that R is much larger than ro. eq 4 takes
`the form of the well-known pavver-law scattering, i.e.,
`
`(~
`
`It is eq 6that was used in estimating dp in this work. In
`the remainder cf this paper, any reference to a fractal
`dimensim will necessarily imply a mass fractal dimensim.
`Potential Energy Calculations. The total pair
`interactim energy between particles in a dispersim can
`be ootained by summatim cfthe repulsive and attractive
`interactim energies. Healy et al. 3ti33derivedan expressim
`fer the repulsive interactim energy between twoparticles.
`Assuming low surface potentials, spherical particles of
`equal size, electric dwble layers that are thin canpared
`to the particle size ([<:r0 > 1), and small electric dwble(cid:173)
`layer overlap, the repulsive interactim energy, VR. is given
`by
`
`(7)
`
`where E is the permittivity, 1/Jd is the particle surface
`potential, and H is the separatim distance between
`particles. The inverse Debye length, K, is related to the
`cmcentration of a symmetrical electrolyte, c, by
`
`(8)
`
`where ze is the icn charge, NA is Avcgadro's cmstant, and
`kT is the thermal energy. It is custanary to refer to Lk
`as the thickness of the diffuse druble layer. It is impcrtant
`to note that apart fran fundamental cmstants, K depends
`mly m the temperature, em centra tim of electrolyte, and
`
`(34) Teixeira, J. J. Appl. Crystallogr. 19!& 21, 781
`(35) H~. R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc.
`1900 6Z lim.
`(33) \1\eise, G. R.; Healy, T. W. Trans. Faraday Soc. 1970. ffi 49:)
`
`the im charge. Fer a 1-1 type electrolyte, the value of
`K (in nm- 1) in water at 25 •c is 32&'12• Clearly, any
`change in the imic strength cf a colloidal dispersim will
`significantly influence the energy of interactim c:i the
`particles.
`The fcrces cf attracticn between neutral particles are
`Lmdm-van der \1\aals dispersim fcroes. Hamaker37
`derived the following expressim for the attractive inter(cid:173)
`actim energy, VA. between twospherical particles of radius
`ro. At a small interparticle separatim, i.e., H « ro. VA is
`given by
`
`(9)
`
`where A is the Hamaker cmstant. Hence, the tttal
`potential energy cf interactim between two particles in
`an aquerus dispersim is ootained by summing the electric
`dwble layer and van der \1\aals energies, i.e.,
`
`The repulsive energy is approximately an expmential
`func