in the united states patent and trademark office...application no.: 11/520,479 1 docket no.:...

Application No.: 11/520,479 1 Docket No.: 638772000109

IN THE UNITED STATES PATENT AND TRADEMARK OFFICE

In re Patent Application of: Neil P. DESAI et al.

Application No.: 11/520,479

Filed: September 12, 2006

For: NOVEL FORMULATIONS OF PHARMACOLOGICAL AGENTS, METHODS FOR THE PREPARATION THEREOF AND METHODS FOR THE USE THEREOF

Confirmation No.: 8972

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

("the Previous Declaration") previously submitted to the Patent Office on January 27, 2012.

2. I have reviewed the Office Action dated May 2, 2013. I understand that claims in the

above-captioned patent application remain rejected as being obvious over one of Abraxis' earlier

patents, U.S. Pat. No. 5,439,686 ("Desai"), for which I am also a named inventor, in view of U.S. Pat.

No. 5,407,683 ("Shively"). In this supplemental declaration, I provide more information about the

data presented in the Previous Declaration as well as the cited reference Desai.

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Actavis - IPR2017-01100, Ex. 1024, p. 1 of 33


3. In the Previous Declaration, I presented, in part, experimental data showing the

advantageous properties of the nanoparticle formulations recited in the claims of the above-captioned

patent application ("the '479 application"). The experiment compared the physical stability of two

pharmaceutical formulations (Composition 1 and Composition 2) containing nanoparticles

comprising a solid core of paclitaxel and an albumin coating at a paclitaxel concentration of 5 mg/ml.

4. 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

Composition 2 indicating instability of Composition 2. Exhibit 1; See also Exhibit 3 of the Previous

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

observed in Composition 1. Exhibit 2; See also Exhibit 4 of the Previous Declaration.

5. Further, as discussed in the Previous Declaration, upon storage at 40°C for 24 hours,

the weight mean diameter of the nanoparticles in Composition 1 remained unchanged. In

Composition 2, by contrast, the weight mean diameter of the nanoparticles increased significantly

upon storage demonstrating instability of Composition 2. Exhibit 3; See also Table 1 of the Previous

Declaration.

6. The table below summarizes and provides additional particle size characteristics of the

two different formulations tested in the experiment.2

Formulation Weight Mean 95% Weight 99% Weight Diameter, nm Distribution (D95), nm Distribution (D99), nm

Composition 1 140 240 282 Composition 2, Lot 1 245 500 633 Composition 2, Lot 2 228 496 638

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

95% and 99% by weight of the particles lie, respectively. For example, in Composition 1, 95% of the

particles in the formulation have a particle size below 240 nm. In Composition 2, 95% of the particles

in the formulation have a particle size below 500 (Lot 1) and 496 nm (Lot 2). In Composition 1, there

was no detectable percentage of nanoparticles that have a size above 400 nm, with 99% of the

particles lying below 282 nm. In Composition 2, by contrast, at least 10% of the nanoparticles in the

formulation had a particle size that was above 400 nm, with 99% of the particles lying below 633 (Lot

1) and 638 nm (Lot 2).

7. The diagram below further illustrates the 99% weight distribution of the two different

formulations.

Composition 1 Composition 2

s 0 2.82.nm 633nm >1000nm

8. Notably, both Composition 1 and Composition 2 are albumin-coated paclitaxel

nanoparticle formulations having a particle size below 1000 nm, yet they behave differently in

stability assays. Composition 1, which contains no detectable percentage of nanoparticles that have a

size above 400 nm, was shown to be stable at paclitaxel concentration of 5 mg/ml. By contrast,

Composition 2, which contains nanoparticles slightly greater than 400 nm, was unstable at the same

paclitaxel concentration under the same conditions. This result was unexpected.

9. As discussed in the Previous Declaration, physical stability is a key consideration for

ensuring safety and efficacy of nanoparticle drug products. The tendency of nanoparticles to

precipitate and/or increase in size (for example by aggregation) increases as the drug concentration

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

particle concentration in tum would increase the frequency of collision of the particles and thus

increase the tendency of the particles to aggregate and become unstable. This is demonstrated in

Bums et al., Langmuir 1997, 13, 6413-6420 (Exhibit 4), for example, which examined particle

aggregation in various formulations having different particle concentrations. The authors concluded

that "[a]s the particle concentration is increased, the aggregate growth is more rapid, most likely due

to the increased collision frequency." See also Kallay et al., J. Colloid and Interface Science 253,

70-76 (2002) (Exhibit 5) at page 75 ("the aggregation rate is proportional to the square of the particle

concentratiOn.... . . ")

10. The estimated particle concentration for Composition 1 discussed above, namely, the

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

mg/ml or higher was unexpected based on the high particle concentration.

11. The stability of albumin-coated paclitaxel nanoparticle formulation having particle

size less than 400 nm is in stark contrast with that of a different non-albumin based paclitaxel

nanoparticle formulation having particle size less than 400 nm. In a study conducted to compare the

physicochemical characteristics and stability of two different commercially-approved nanoparticle

formulations ofpaclitaxel, namely, Abraxane® (an albumin-coated solid paclitaxel nanoparticle

formulation having particle size less than 400 nm, similar to Composition 1 described above) and

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

these conditions. Ron et al., 99th AACR Annual Meeting Abstract, No. 5622 (Exhibit 6). This study

further illustrates the difficulty and challenge in obtaining paclitaxel nanoparticle formulations having

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

unexpected stability of the claimed albumin-coated solid nanoparticle formulation.

12. Thus, albumin-coated paclitaxel nanoparticle formulations having particle size less

than 400 run were stable at 5 mg/ml. This is in stark contrast with an albumin-coated paclitaxel

nanoparticle formulation which contains particles slightly greater than 400 run, and a non-albumin

based paclitaxel nanoparticle formulation having particle size less than 400 run, both shown to be

unstable under the same conditions at paclitaxel concentration of 5 mg/ml. These results demonstrate

the advantageous and unexpected stability of the albumin-coated paclitaxel nanoparticle formulation

recited in the claims of the '479 application, especially in view of the high particle concentration in

such a formulation and the well-known principle that the aggregation rate of nanoparticles is

proportional to the square of the particle concentration.

13. The Examiner cites Desai as allegedly teaching a stable albumin-coated nanoparticle

formulation. As discussed in the Previous Declaration, Example 5 of Desai, which the Examiner

relies on as teaching stability of albumin-coated nanoparticle formulations, refers to the stability of

polymeric shells containing buoyant soybean oil with density less than water. No drug was present

within the polymeric shell. The stability of the "drugless" oil-containing polymeric shells discussed

in Example 5 of Desai thus provides no suggestion that a nanoparticle formulation comprising a solid

core of paclitaxel and an albumin coating would be stable at paclitaxel concentration of between 5-15

mg/ml. Furthermore, as discussed in the Previous Declaration, an increase in loading of paclitaxel

within the polymeric shells as taught in Example 4 of Desai would be expected to increase the particle

size and/or density of the particles, which in tum could increase the tendency of the particles to

precipitate.

14. Although a separate example in Desai, Example 9, teaches preparation of polymeric

shells containing a solid core of pharmaceutically active agent such as paclitaxel, there is no

information about the concentration of the paclitaxel in such polymeric shell formulation. Nor is

there any indication that the particles in such polymeric shell formulation are smaller than 400 run.

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Example 9 teaches that "these polymeric shells are examined under a microscope to reveal opaque

cores .... " The fact that the polymeric shells were viewable under a microscope to reveal opaque cores

indicates that a substantial portion of the particles in the formulation taught in Example 9 were larger

than 400 nm. Thus, these formulations taught in Desai differ from the formulation recited in claims of

the '479 application in at least two aspects: paclitaxel concentration and particle size.

15. To arrive at the claimed formulation from Desai's nanoparticle formulations, one

would at least need to: 1) substantially decrease the size of the particles in the formulation to less than

400 nm; and 2) substantially increase the paclitaxel concentration to 5-15 mg/ml. Desai provides no

teaching on how to obtain a nanoparticle formulation having a particle size of less than 400 nm. Nor

would one expect that an albumin-coated solid nanoparticle formulation having a particle size of less

than 400 nm and paclitaxel concentration of 5-15 mg/ml would have been stable. Specifically,

according to Example 5 of Desai, the particle concentrations of the formulations reported therein is

about 7-9 x1010 per ml. See Table 1 at Column 13 of Desai. The estimated particle concentration of

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

than those reported in Desai. Since the aggregation rate of nanoparticles is proportional to the square

of the particle concentration, one would not have expected that the albumin-coated paclitaxel

nanoparticle formulation having a particle size less than 400 nm at paclitaxel concentration of 5

mg/ml, whose particle concentration is at least 1000 fold higher than those reported in Desai, would

be stable.

16. I hereby declare that all statements made herein of my own knowledge are true and

that all statements made on information and belief are believed to be true; and further that these

statements were made with the knowledge that willful false statements and the like so made are

punishable by fine or imprisonment, or both, under Section 1001 of Title 18 of the United States Code,

and that such willful false statements may jeopardize the validity of the application, any patent issuing

thereon, or any patent to which this verified statement is directed.

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Applic.atiGn No.: 11:'520,479 7 Docket No.: 638772000109

11/1/2013

Date

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Exhibit 1


1


Exhibit 2


Composition 2, Lot 1, 24 hrs at 40°C, 400x Composition 2, Lot 2, 24 hrs at 40°C, 400x

Composition 1, 24 hrs at 40°C, 400x

2


Exhibit 3


Sample Storage Condition Weight Mean Diameter, nm1

0 time 136.9

Composition 1

24 hours at 40°C 135.2

0 time 244.5

Composition 2, Lot 1

24 hours at 40°C 1159.5

0 time 228.0

Composition 2, Lot 2

24 hours at 40°C 561.5

1 Size determined by disc centrifugation method.


Exhibit 4


Langmuir 1997, 13, 6413-64

6414 Langmuir, Vol. 13. No. 24, 1997

F arrest and Wtten. 6 In these experiments metallic oxide smd-2.2 hema-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, a23shear 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 763

(18) Asnaghi, D.; Carpineti, M; Giglio. M; Sazzi, M Phys. Rev. A 199a 45. 1018

(19) Asnaghi, D.; Carpineti, M; Giglio, M; Sazzi, M Frog. Colloid Polym. Sd. 199a 8Q En

(aJ) V\eitz, D. A.; Huang, J. S.; Lin, MY.; Sung, J. Phys. Rev. Lett. 1~ 54. 1416

(21) V\.ilcaxm. J.P.; Martin, J. E.; Schaefer. D. W Phys. Rev. A 19'119, $. a>75 (~ Liu, J.; Shih, W Y.; Sarikaya, M; Aksay,l. A. Phys. Rev. A 1m)

41, 3a:X3. (23) Arnal, R.; Raper, ]. A.; \Mlite, T. D. f Colloid Interface Sd.

lml 14Q 158 (24) Arnal, R.; Gazeau. D.; \Mlite, T. D. Part. Part. Syst. Charact.

1994, 11, 315 (25) Herringtm, T. M; Midmcre, B. R. Colloids Surf. A 1~ 7Q

1ffi (26) Axfcrd, S.D. T.; Herringtm, T. M J. Chem. Soc .. FaradayTrans.

21994, fa ::m5. (27) Bezcr. P.; Hesse-Bezct, C.; Roosset, B.; Diraism, C. Colloids

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 (29) Lin, MY.; Lindsay, H. M; V\eitz, D. A; Ball, R. C.; Klein, R.;

Meakin, P. Proc. R. Soc .. London, Ser. A 1!H}. 423 71. (3)) Lin. MY.; Lindsay, H. M; V\eitz. D. A.; Klein, R.; Ball. R. C.;

lvleakin, P. J. Phys.: Condens. Matter 1m) 2. 3::m (31) Lin, MY.; Lindsay, H. M; V\eitz, D. A.; Ball, R. C.; Klein, R.;

Meakin, P. Phys. Rev. A 19!1), 41, aD5. (~ Tcrres, F. E.; Russel, W B.; Schowalter, W R. J. Colloid Interface

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-limited (i.e., RLCA) colloid aggregatim, fer three ccm-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

Light Scattering Study of a Model Colloidal System

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 ([ 1), and small electric dwble-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:)

Langmuir, Vol. 13 No. 24. J[£)7 6415

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-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 functim cfthe distance between the particles with a range cfthe erder of the thickness cfthe druble layer (l.k). and the van der \1\aals attractive energy decreases as an inverse power cf the distance cf the particles. Cmse-quently, van der \1\aals attractim will predaninate at small and at large distances. At intermediate distances dwble-layer repulsim usually predaninates. However, this largely depends m the actual values of the two ferces and hence en the electrolyte cmcentratim in solutim. 38

Experimental Section Materials. Styrene mmcmer (Aldrich) was first washed with

lCY/o NaOH (3 x 3J cm3) follo..ved by Millipere water (3 x 2&l cm3) and then vacuum distilled at &l "C. The ammooium persulfate initiater (Aldrich) and all other reagents emplcy-ed were cr analytical grade and were used withoot further purifica-tim. Millipcrewaterwas used in all preparatims. Afoor-necked, 2L reactim vessel was used and an overhead stirrer with variable speed cmtrol used to maintain cmstant stirring. The thermo-stated water bath was able tocmtrol the temperature to within ±05 ac. and the dialysis tubing was well bdled in Millipcre water three times befcre use.

Latex Preparation. The polystyrene latices were prepared by the surfactant-free emulsim pdymerizatim methcd cr Gcxxiwin et al. ~using ammooium persulfate as the initiatcr. A typical emulsifier-free preparatim was carried rut in the follo.ving way. The required amoont cr water (aD cm3) was added to the reactim vessel and the stirrer fitted to me ootlet. Typically, the stirrer was adjusted to a distance cr aboot 1-2cm from the bottom cr the flask. A water-rooled reflux cmdenser was added to a secmd ootlet and the flask immersed in the thermcstated bath. Nitrq;:en was bubbled throogh the water in the reactioo vessel to remove o.xygen frcrn the system using a third inlet to the flask. The gas flo..v was cmtinued throoghoot the reactim, but the flo..v rate was kept lo..v to minimize evaporation. The stirrer was adjusted to the required speed (aD rpm) and after stirring for at least 3Jmin with nitrq;:en passing throogh the system, styrene ( lffi g) was added via the foorth ootlet. The system was then left to equilibrate fer another 3J min to allo..v the temperature (8J "C) to attain equilibrium and to saturate the aqueoos phase with styrene.

The initiatcr (Q 565 g) was dissolved in &l cm3 cf water, and the solution was preheated to the reactim temperature and then added to the reactim vessel. A typical reactim time cf 24h was used. At the end cr the reaction time, the vessel was removed

(37) Hamaker, H. C. Physica 1937, 4, 1058. (38) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th

ed.; Butterwcrth-Heinemann: Oxfcrd, U.K .. I~ Chapter 8 (3=)) Gcxxlwin. J. W.; Hearn, J.; Ho. C. C.; Ottewill, R. H. Colloid

Polym. Sci. 197.ol ~ 461.


6416 Langmuir, Vol. 13, No. 24. JW7 -••

••••••••• . ••• : ••••• ••• • • • ••• ••• -~-·

•• •

Figure 1. Electrm micrcwaph of the pdystyrene latex particles used in this study.

frcm the bath and allowed to cool fcr a boot ::0 min. The latex was then decanted throogh a filter packed with glass wad to remove any unreacted mmcmer and any a:agulum fcrmed. The latexwasthendialy.redagainstMillipcrewaterincrdertoremove residual mencmer, ammcnium persulfate, and any ether icnic species left in the reactien mixture. The dialysis was ccnsidered ccmplete when the ccnductance r::f the dialysate became cl05e to that r::f the Millipcre water after 24 h.

Latex CharacterizatiaL The size and pdydispersity cfthe latex particles were determined using transmissien electrm micr05ccpy (JOEL JEM lax> EXII electrm micr05ccpe). Mi-crcwaphs cf a number r::f representative regicns r::f the sample were taken to obtain images cf at least 3:X) particles. A ccmmerdal sizing sdtware package (Optimas 5. la) was then used to calculate the average particle diameter, and the relative standard deviatien was used toindicate the pdydispersitycfthe particles. A TEM image eft he pdystyrene latex spheres is given in Figure 1. clearly indicating the particle size regularity. The average diameter cfthe pdystyrene latex particles was foond to be 3:D ± 10 nm.

Electrcphcreticmobilitiescfthelatexparticlesweremeasured using a Brcx:khaven Zetaplus apparatus. The effect cf pH and KN(hccncentratien en the particle mobility was examined. The analysis was perfcrmed at 25 oc. using a particle cencentratien cf Io-336 wIN. Determinatim cf the stability regien r::f the pdystyrene latex particles in KN(h was carried oot using an optical methcxl that relies en the sedimentatim rate cf the aggregated dispersien. This invdved measurement cfthe percent transmittance cfthe supernatant fcr latex dispersicns ccntrdled tovarioos salt ccncentraticns. The transmittance was measured at 540nm using a Hitachi spectrcphctcmeter after the dispersicns were left undisturbed fcr 24 h. The results were then plctted against the ccncentratim cf KN(h and the critical a:agulatien ccncentratien (ccc) was determined as the inflectim pdnt r:fthe curve.

Fractal Studies. Small-angle static light scattering was used here to study the structure cfthe latex particle aggregates. The instrument used was a Malvern Mastersizer S, which has a 633 run He-Ne laser as the light soorce. The Mastersizer simul-taneoosly measures scattered intensities at a range cf scattering angles. It also provides a direct measure cf the average size distributien cf the material in the scattering cell. Aggr.egatien was achieved by adding the required amoont cfthe pdystyrene latex particles to a sdutim r::f KN(h cf known ccncentratien at pH 6and at rcx:m temperature. Directly after mixing. the sample was gravity fed into the light scattering cell. The 1~ I(QJ vs 1~ Q plct was then used to determine the scattering expenent (d. eq ~- Typical experimental data fran which the scattering expcnents were calculated are illustrated in Figure 2 The change in thescatteringexpcnents and the average cfthesize distributien cf the scattering material were reccrded with time. Fractal dimensien values fcr the aggregates were determined by taking the absdute value of the limiting scattering expcnent in the plateau regien (vide infra Figure 8).

...... () ._.

scattering exponent =slope

-4

log1o Q

Burns et al.

2.5

1.5

-3

Figure 2 Typical experimental data frcm which thescatterin~ exponents were estimated. Note that Q and I(QJ are in nm-and arbitrary units, respectively.

0+-----:=---1------+-----j • • 4 8 t12 -I e • (,) -2 • ~ • .!I! • • E -3 • • • • :I. • ._. ~ -4 ••• :c • • • • 0 -5 • • ::e • • -6~-------------~

pH Figure 3 Effect of pH and icnicstrength en the electrophcretic mobility of the pdystyrene latex particles. The ccrresponding electrdyte cencentratims are (•) Io-4 M, (+) 1o-3 M, and (II) Io- 1 MKNOs.

Results and Discussic:n

The electrophcretic mobility ci the polystyrene latex particles was measured at three different KN03 cmcen-tratiens and acrcss a bread range cf pH values. The resultantdataareillustratedinFigure3 Thesemobility curves indicate that as the pH was increased. there was a significant increase in the ienizatien ci the surface functienalgroops. AbovepH6 therurvesbegintoflatten rut, suggesting that the surface ienizatien is canplete in this regien. As expected, there was a reductien in electrcphcreticmobility of the particles en increasing the electrolyte ccncentratien.

Generally, the measurement cf sedimentatien rate is a useful means fer aggregatien studies in colloid science.


100 -r------------------. ...... !!! 80 :::J 0 .c

~ 60

e c 40

i ~ 20 ::.e 0

0

0 0.2 0.4 0.6 0.8 1.2 [KNO:J (M)

Figure 4. Percent transmittance of light (at 540 run) as a function of the ccncentratim of electrolyte in the pdystyrene latex dispersion (at pH 6). The onset of aggregation (028 M KNQV and the critical cmgulation ccncentratim (O 70MKNQV are indicated.

Table 1. Fractal Dimensioos ofPdystyrene Latex Aggregates Fcrmed in Various Ccncentratioos ofKN03

at Different Initial Particle Ccncentratioosa

[KN031 (M)

040 OtD 06J 070 085 l.CD 1.25 ltD

initial particle cmcentratim (w ;W)

2m 2m 2m 2ill 2ffi 2ffi 217 211 2CE 28 2ffi 2ffi 2ffi l.ffi l.ffi l.ffi 1.85 1.~ 1~ 1.~ l.ffi 100 1m 1m

• Ncte that since the primary latex particles have a density cla;e to unity, the weight fractims reptained in this way fer oor polystyrene latex particles at pH 6is 028M KN03. However, Hunter43 describes the critical coagula-tim a:ncentraticn as the "electrolyte a:ncentraticn at which slow ccagulaticn gives way to rapid ccagulaticn". This is determined experimentally as the ccncentraticn where the settling material leaves behind it an essentially clear supernatant. On the basis cf this definiticn, the ccc cf oor latex particles is expected to be closer to Q 7 M KN03. ltseemsmerelikelythattheccncentraticnof028 M KN0:3 defines the regicn of stability cf the latex dispersicn; i.e., below028Mthedispersicnisstable, while above this ccncentraticn the dispersicn will be essentially unstable, althoogh the ccagulaticn kinetics may net be rapid. In ccntrast, 0 7 M KN0:3 ccrrespcnds to the ccncentration at which rapid ccagulation begins.

Thefractaldimensicnscfthepolystyrenelatexparticle aggregates fermed in the presence ciKN03 and measured by small-angle static light scattering are summarized in Table 1. The upper limit c:i the initial particle ccncentra-ticn was chcsen to avoid the effects cfmultiple scattering, while the lower limit was selected such that backgroond

(41) Kotera,A.; Furusawa, K.; Takeda, Y. Kolloid-Z Z Polym. 1970, 2%l 017. ~~otera, A.; Furusawa, K.; Kudo. K. Kolloid-Z Z Polym. 1973,

(~Hunter, R. J. Foundations of Colloid Science, Oxfcrd Science Publicatims: Oxfcrd. U.K., 1937; Vd. 1.

Langmuir, Vol. 13 No. 24. HE7 6417

2.50

2.25

• t • • • • • • • 2.00 • • • .... "C • • a • • 1.75

1.50 +-----+-----1-----+------i 0.2 0.6 1.0 1.4 1.8

[KNO:J (M) Figure 5 Dependence of the fractal dimension of aggregates of polystyrene latex spheres with electrolyte ccncentratim and initial particle cmcentration: (.&.) Q 0 (JJT(J'!O wIN. noise woold not have a significant effect. The electrolyte ccncentraticns used in the experiments ranged from 04 to 1. 5M, which allowed beth regimes cf aggregaticn QJLCA and RLCA) to be c.bserved. This also allowed c.bservation c:i the behavicc cf the fractal dimensicn at intermediate salt ccncentraticns. The fractal dimensicns were foond torangefran 1. 78to22Q whichccrrespcndwell toknawn literature values cf 1.8 and 2 I fer diffusicn-limited cluster-cluster aggregaticn and reacticn-limited cluster-cluster aggregaticn, respectively. To illustrate mere clearly the c.bserved trends with particle a:ncentraticn and icnic strength, the fractal dimensicns are plctted in Figure 5

Clearly, the structure c:i aggregates fermed frcrn the colloidal particles differs acccrding to the prevailing a:nditicns within the aggregating system. At any given particle ccncentraticn, mere tightly packed ccrnpact structures were fcrmed at low salt ccncentraticns, while mere q:>en structures were fcrmed at higher salt a:ncen-traticns. At intermediate salt ccncentraticns, the fractal dimensicns were foond to be intermediate to the theereti-cal values predicted by the DLCA and RLCA models. As explained later in this section, strictly speaking, these intermediate values shoold be referred to as "effective" fractal dimensicns.

Acccrding to the DL VO thecry cf call ad stability, the aggregaticn behavicc of aqueoos colldds is determined by the energy barrier en the interacticn potential energy curve between two collddal particles, which in turn is a:ntrolled by the salt ccncentraticn in the medium. The primary effect cf salt en a charge-stabilized aqueoos dispersicn is to suppress the extent of the electricdooble layer (eq 8). This leads to a reducticn in the repulsive potential energy (eq -n. Since VA is largely unaffected and is typically attractive, the system becanes mere unstable. The estimated pctential energy curves fer the polystyrene latex particles in water at 25 •c are plctted in Figure 6 A value cf 1 x 1o-;;o J was taken fer the Hamaker ccnstant. 43 The surface pctentials used in the calculations ranged frcrn -:n to -35 mV, which were estimated frcrn the experimental mobility data (Figure 3).

Observation of these pctential energy diagrams indi-cates two regimes cibehavier. At salt ccncentrations less than aboot 0 7M, sane fcrm cf a pctential energy barrier exists, even when the curve is essentially negative over all particle separaticns. Hence, fcc salt levels between 0 3 and 0 7 M the pctential energy curves indicate that


6418 Langmuir, Vol. 13 No. 24, lrE7

80 ....,,.,.,.,..0.1 M

60 f" -o.3M ;~ \ l 1-. -O.SM 40 1\ -0.7M ··········l.OM 20

--l.SM

~ 0 ;; -20 H(nm)

-40

-60

-80

-100

Figure 6. Influence cf the electrolyte concentratim m the total potential energy of interactim using a Hamaker anstant cf 1 x IQ-aJ J and surface potentials cf - ::D to -35 m V.

the particles can initially cane to rest in a weak secoodary minimum fran which deflocculati01 is relatively easy. If the oolliding particles have suffident thermal energy, they can surmoont the barrier and enter the deep primary minimum fran which particle escape is virtually impa;-sible. At greater than aboot Q 7 M salt, no barrier is present and all oollisi01s must result in an irreversible aggregati01. Such potential energy curves shoold be canpared with the dJserved transiti01 fran dense toloa:;e aggregates over a range of coocentrati01s fran 0 7to 1.0 M salt. Thus, the absence of any barrier to a:Bgulati01 in a potential energy curve woold indicate the DLCA regime, while the presence of a significant barrier leads to a higher fractal dimensioo and the RLCA regime.

The fractal results repated here are coosistent with those by Zhoo and Chu, 16whoused a canbinati01 c:i static and dynamic light scattering measurements to study the fractal aggregates c:i polystyrene spheres induced by the additi01 c:isalt (Q2-1.5MNaCl) at a coostant pH cf92 Fractal dimensi01s ranging fran 1. 72 (DLCA) to 2 15 (RLCA) were foond. Intermediate values fer dF were also cbtained at intermediate salt coocentrati01s. They at-tributed this to the restructuring cfthe ramified collcidal aggregates, which they suggest may occur in the presence c:i a finite interpartideattracti01 energy. Hence, althoogh a different univalent salt was used at a much higher pH, the trends dJserved fer the fractal dimensioo c:ithe latex aggregates are similar to curs.

In cootrast, some c:i the reperted dJservati01s cf the aggregati01 behavior of pdystyrene latex particles do not agree with the above findings. Bolle et al. 11 investigated the aggregati01 c:i pdystyrene particles in a univalent salt (NaCI) over a wide coocentrati01 range. They foond a value of 1. 75 fer the fractal dimensioo c:i aggregates in the fast aggregati01 regime when the salt coocentratioo was high. In low salt cooditi01s a different kinetic regime was dJserved, hence a different fractal dimensi01 was expected. However, the growth of the aggregates was foond to proceed with a fractal dimensi01 (dF = 1. 75) equal to that fcund fer the DLCA regime. Asnaghi et al. 17- 19 also fcund for low salt coocentratioos that dF was at first larger than 2 and therefore dose to the typical RLCA fractal dimensioo but then gradually reverted to lower values not far fran those typical cfDLCA They suggested

Burns et al.

that the aggregati01 crossed fran reactim-limited to diffusi01-limited because as the average duster mass grows, diffusi01 becanes the rate-limiting process. How-ever, they did note that decreasing the coocentrati01 c:i salt resulted in higher fractal dimensi01s that were more stable in time.

In this study, aggregate structures were also fcund to becane less canpact as the latex particle coocentrati01 was increased (cf. FigureS). Verylittlehasbeenrepated 01 the effects of particle coocentrati01 01 the aggregate structure of collcidal systems. Carpineti et al. 14. 15 have studied the aggregati01 of polystyrene spheres at a fixed salt coocentrati01 (3)mM MgC12) in the fast aggregati01 regime and varying particle coocentrati01 fran 1 x 10'1 to 5 x 1010partides.6n3• The data showed that at larger coocentratiOOS they COOSistently foond dF = 1.61 ± 0(£, but as the coocentratioo was decreased, dF grew to 1.83 ± 002. In cootrast, Martin et al. 10 have provided experimental evidence fer an increase in the fractal dimensi01 with an increase in the coocentratioo of aggregating silica particles, in the rapid aggregati01 regime.

In cur study, three particle coocentrati01s were examined: l.C:Ox 10'1, 185x 10'1, and 3 70x 10lpartides/ an3, with each being investigated over a wide range of salt c01centratioos. Our results exhibited trends similar to those c:i Carpineti et al. 01 increasing the particle coocentratioo at a fixed level of electrolyte; that is, the fractal dimensi01 was dJserved to increase with a decrease inthenumberc:iinitialpartidesintheaggregatingsystem. However, the particle coocentratioo had its most pro-ncunced effect oo the aggregate structure at low i01ic strengths, i.e., in the slow aggregatioo regime.

Our werk reveals that there is a noticeably larger variatioo in the fractal dimensi01 with particle coocen-tration at lower salt coocentrati01s. At high levels cfsalt, where there is nopctential energy barrier toaggregati01, the fractal dimensioo does net vary significantly with changes in the particle coocentrati01. This can be attributed to the fact that all duster (cr particle) collisi01s wculd result in permanent coo tact; hence recoofigurati01 c:i dusters wculd be effectively prevented. In cootrast, under slow growth cooditi01s, dusters (cr particles) cwld undergo a number of collisi01s befere they became permanently locked intopositi01, since they may initially 01ly be in a weak secoodary minimum. Thus, particles attached to the edge of an aggregate will have the ability to "roll aroond" as the structure develcps as they attempt to find their minimum energy state. The ability c:i such a particle to sample a number of possible coofcrmati01s within an aggregate will depend oo the prcbability of ancther particle colliding with it in a given time, which may effectively lock it in positi01. This will, c:i ccurse, be influenced by the frequency c:i particle cdlisioos within the aggregating system. This suggests that if the primary particle coocentratioo is reduced, the frequency of cdli-sioos is also reduced and hence there will be mere time fer the particles to restructure and form a denser ag-gregate. C01sequently, the fractal dimensioo will be higher at lower particle coocentratioos, as cur results indicate.

The rate at which a dispersien will a:Bgulate depends en the frequency with which particles encwnter me ancther and the prcbability that the energy barrier to a:Bgulatioo can be overcane when collisiens take place. Figure 7illustrates cur findings 01 the dependence of the relative rate of aggregate growth en the electrdyte coocentratioo and hence the pctential energy barrier to aggregati01. In excess electrdyte, the aggregate grows rapidly and to a canparatively large size. This growth



14~--------------------------·

12 (a)

10

8

6

4

2

0

14 ... ! 12 (b) E 10 ca :g

.;'E 8 m::::&. 6 e-m m 4 ca c

2 : :E

0

14

12 (c)

10

8

6

4

2

0 0 so 100 150 200

Time (min)

Figure 7. Variatirn of the mean ag&regate size with time at different particle crnrentratirns: (a) a aJ70'!6; (b) a CXB'J'J6; (c) QCXBJ'J6 wIN. The ccrrespcnding crncentratirns ci electrdyte are (0) a4M, ¢:1) a5M, () a6M, (LI.) a7M, (e) a85M, •> 1.0 M, (+) 1.25 M. and (•) 1.5 M KNOs. Fer the particle crncentratirn ci Q CXBJ'A. wIN, a 4 M KNOs. has been excluded fer clarity.

shows a power-law behavier and is, therefere, assodated with diffusirn-limited cluster-cluster aggregatim. Fur-thermere, since every particle callisirn results in a permanent em tact, the number ci single particles present becanes rapidly reduced. This, in canbinatim with the decreasing probability of cluster-cluster aggregatirn due to the reduced mcbility of these clusters, results in an eventual plateau of the aggregate size. The intrcx:luctim cfarepulsiveenergybarrierbyredudngthecrncentratirn of electrolyte reduces the size of the aggregates and causes the aggregatirn kinetics to be slowed. The reductirn in the sticking probability of the particles also prcx:luces a linear growth in the size of the aggregates over the time scale examined, where singlets are still readily available to attach to the existing aggregates. The canmm exprnential growth behavier ci reactirn-limited cluster-cluster aggregatim cannot readily be identified in this

Langmuir, Vol. 13 No. 24, JW7 6419

study due to the relatively shert time scale ci the cbservatirn.

An interestingsituatirn arises when the latex dispersirn is aggregated at intermediate electrolyte crncentratirns. The aggregate size appears to grow in mere of a stepwise fashirn, which suggests a transitim fran slaw aggregatirn to rapid aggregatirn at this level ci electroJ.yte. This stepwise growth, althoogh not clearly visible at Q CXBJ'J6 wIN particles, appears to begin aroond Q 7 M KNO:> Therefere, at the intermediate salt levels oor data indicate that there was a crcssover behavier fran RLCA to DLCA as the aggregatim progressed. Acccrding to the scale-invariant definitirn of fractal aggregates, the previoosly reperted fractal dimensirns at these intermediate salt crncentratims shoold, in a strict sense, be termed "effective" fractal dimensirns, as already suggested in the literature. 18

In all, these results indicate that due to the law sticking prcbability of the particles at law levels of electrolyte the growth cfthe aggregates is slaw but results in crnsistently higher fractal dimensirns. In crntrast, fast aggregatirn ch>erved under high salt crnditirns gives larger aggregate sizes but less dense structures, ch>ervatims crnsistent with a high prcbability of particle sticking. Furthermere, the growth of the aggregates is dependent m the number of particles present in the aggregating system. As the particle crncentratirn is increased, the aggregate growth is more rapid, mcst likely due to the increased col.lisim frequency. The fractal dimensirn ci the aggregates is ch>erved to decrease under such crnditirns, with this effect being mere prmoonced at the law salt cmcentratirns.

In this study the change in the slcpe ci the scattering curves (i.e., the scattering exprnent) was alsommitered with time and the results are illustrated in Figure 8 The results indicate that in excess electrdyte the scattering expment is cmstant over time, while at law electrolyte levels a growth in the scattering expment was ch>erved. The absolute value of the scattering exprnent will represent the mass fractal dimensim of the aggregated particles, provided that the aggregate size is much larger than that of the primary particles. In these experiments it was noted that the limiting scattering exprnents ccrresprnded to sufficiently large aggregates, and thus, a fractal dimensirn coold be assigned at this pdnt. As a result, the scattering exprnents cbtained in the initial stages of the aggregatim, with particular cmcem to the law salt crnditirns, do net ccrresprnd to a fractal dimen-sirn fer the aggregating system. Nevertheless, the change in the scattering exprnent with time does provide a measure ci the relative rate ci aggregate growth and reactim kinetics fer varioos aggregating cmditirns. It was foond that the lower the salt cmcentratirn used in the aggregatim, the lmger the time required to achieve a constant scattering expment, hence slower reactirn kinetics. Similarly, lmger times were required fer the aggregates to becane scale invariant when the particle crncentratim was lowered.

On the basis of the results given in Figure 8 it appears that the transitim fran slaw to fast aggregatim can be readily ch>erved. If rapid aggregatirn is assumed to be the regim in which the scattering exprnent is cmstant over time, then the critical coagula tim cmcentraticn can be readily determined. It appears that this change occurs between Q70and Q85MKNO:> This is cmsistent with the results in Figure 7, where the above crncentraticns ci electrolyte ccrrespcnd to a stepwise growth in aggregate size. These results also canpare faverably with experi-mental data cbtained fran turbidity measurements (Figure 4) using the definitim provided by Hunter. 43 Hence, fractal measurements appear to also provide a


642D Langmuir, Vol. 13, No. 24, lfE7

2.20 -..----------------..,

2.05

1.90

(a)

1.75

2.20

-c CD c 2.05 0 C1. )( CD m c

"i: 1.90 ! cu ()

(b) (/)

1.75

2.20

2.05

1.90

(c)

1.75 ......... .___--+-------+------1 0 50 100 150 200

Time (min) Figure 8 Variatirn of the scattering exponent with time at different particlecrncentratirns: (a) OCXJ7CY;6; (b) OCXJ3EP;6; (c) OCXBY;6 w ;W. The ccrresponding ccncentrations of electrdyte are (O) 04M, ¢:1) 05M, (0) 06M, (e.) 07M, (e) 085M, •> 1.0 M, (+) 1.25 M. and (•) 1.5 M KN0:3. Fcc the particle ccncentraticn of 0 CXB:J';6 w ;W, 0 4 M KNOs has been excluded fcc clarity.

sensitive methcx:l fcr the estimatirn of the critical coogu-latirn ancentratioo. Based oo these observatioos, the "effective" fractal dimensirn e

Exhibit 5


Journal of Colloid and Interface Science 253, 70-76 (2002) doi: 10.1 006/jcis.2002.8476

Stability of Nanodispersions: A Model for Kinetics of Aggregation of Nanoparticles

Nikola Kallay1 and Suzana Zalac2

Depanment of Chemistry, Faculty of Science, University of Zagreb, Marulicev trg 19, P. 0. Box 163, HR I 0000 Zagreb, Croatia

Received October 29, 2001; accepted May 9, 2002

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically com-plete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent ofthe diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Br0nsted concept based on the Transition State The-ory was applied. The charge of interacting nanoparticles was calcu-lated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentra-tion on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is char-acterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the speci-ficity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Addition-ally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number COncentration. © 2002 Elsevier Science (USA)

Key Words: stability of nanodispersions.

INTRODUCTION

It is commonly accepted that the stability of colloidal systems is, in most cases, the result of an extremely slow aggregation pro-cess. The main reason for such a slow aggregation process is a high electrostatic energy barrier, and in some cases a protective layer of adsorbed chains. The theory of Colloid Stability consid-ers collision frequency and efficiency (1, 2). Collision frequency was theoretically solved by Smoluchowski (3), while the basis for evaluation of the collision efficiency was given by Fuchs ( 4 ). In order to use the Fuchs theory one should know the interaction energy as a function of the distance between interacting parti-

1 To whom correspondence should be addressed. Fax: +385-1-4829958. E-mail: nkallay@ prelog.chem.pmf.hr.

2 Present address: PLIVA d. d., R&D-Research, Prilaz baruna Filipovica 25, HR 10000 Zagreb, Croatia.

0021-9797/02$35.00 © 2002 Elsevier Science (USA) Alt" rights reserved.

70

cles. The effect of dispersion forces was solved by Hamaker (5), Bradly (6), and de Boer (7), while electrostatic repulsion could be evaluated on the basis of the Derjaguin, Landau, Vervey, Overbeek (DLVO) theory (1, 8). Recently, more sophisticated models were elaborated (9-14). In most of the cases the theory of Colloid Stability explains the experimental data, especially if the correct values of the electrostatic surface potentials, as obtained from the Surface Complexation model (15-19), are used (20-22). However, small particles, with sizes below 10 nm (called nanoparticles), generally do not show electrostatic sta-bilization. According to de Gennes (23), the reason for the in-stability of nanocolloidal systems might be in their low charge (surface charge density times surface area). In some cases sta-ble systems of nanoparticles could be prepared (24, 25) but no kinetic measurements were published.

In this paper we analyze the theoretical aspect of the kinetics of aggregation of nanoparticles based on the Brj1insted theory (26, 27), which was developed for the salt effect on the kinetics of ionic reactions (primary salt effect). The reason for such a choice lies in the fact that the classical DLVO approach cannot be used for nanoparticles: nanoparticles are small with respect to the thickness of the electrical diffuse layer, so that in the course of the collision of two nanoparticles a complete overlap of two diffuse layers takes place. Let us consider extension of the diffuse layer. According to the Gouy-Chapman theory, depending on the ionic strength and surface potential, the latter is reduced to 10% of its original value at a distance of 2 to 2.5 reciprocal K values. This means that at the ionic strength of w-z mol dm-3 the diffuse layer is extended up to 6 nm from the surface. As shown on Fig. 1, in such a case overlap of diffuse layers of two nanoparticles is practically complete. In the case of ordinary colloid particles the overlap is partial so that the DLVO theory is applicable.

A nanoparticle surrounded by a diffuse layer is similar to an ion situated in the center of an ionic cloud. In the course of colli-sion two nanoparticles in contact have a common diffuse layer or "ionic cloud." Therefore, interaction of nanoparticles could be considered in a manner similar to that for two interacting ions, and consequently described by the Br!11nsted theory. This theory considers the "transition state" or "activated complex" which is a pair of two interacting ions with a common ionic cloud. The


STABILITY OF NANODISPERSIONS 71

FIG. 1. Overlap of electrical interfacial layers for two ordinary colloid par-ticles (r = 30 nm) and for two nanoparticles (r = 3 nm).

equilibration of the transition state is fast, while the transforma-tion of the transition state into product(s) is slow, and thus the rate determining step.

THEORY

Introduction of the Brf!lnsted Concept to Kinetics of Aggregation of Nanoparticles

The quantitative interpretation of kinetics of aggregation of nanoparticles will follow the Bnzmsted concept (26, 27). It will be based on the Transition State theory using the activity coef-ficients as given by the Debye-Hiickellimiting law.

Aggregation of two charged nanoparticles A ZA and Bzs could be represented by

[1]

where z denotes the charge number. The rate of aggregation v is proportional to the product of concentrations of interacting particles (AZA](BZB]

[2]

where k is the rate constant (coefficient) of aggregation. According to the Brjlinsted concept, in the course of aggrega-

tion two charged nanoparticles undergo reversible formation of the transition state with charge number being equal to the sum of the charges of interacting species. The transition state ABZA+zs undergoes the next step (binding) which is slow and is therefore the rate determining step

[3]

Note that equilibration of the interface may result in a change of the total charge of the doublet. In such a case ZA + ZB f=. ZAB. Since the equilibration of the first step is fast, and the second process is slow, the overall rate of reaction (v) is proportional to

the concentration of the transition state

[4]

where k' is the rate constant (coefficient) of the second process. Equilibration of the first step is fast so that one calculates the concentration of the transition state [ABzA+zs] from the rele-vant equilibrium constant K=~' taking into account the activity coefficients y of reactants and of the transition state

[5]

The equilibrium constant K =ft is defined in terms of activities, and consequently its value does not depend on the ionic strength; i.e., it corresponds to infinite dilution. Equations [4] and [5] result in

[6]

According to the above equation, the overall rate constant, as defined by Eq. [2], is given by

k = k' K=~' _y_(A_z_A )_y"7'(B_z_s) y(ABZA+Zs) [7]

It is clear that the overall rate constant k depends on the ionic strength of the medium through activity coefficients. Activity coefficients could be obtained from the Debye-Hiickel equation derived for ionic solutions. The same equation is assumed to be applicable for extremely small particles i of charge number z;

2 1/2 Z; AnHic

logy;=- 1/2. 1 +able

[8]

The ionic strength Ic for 1 : 1 electrolytes is equalto their concen-tration. The Debye-Hiickel constant AnH depends on the electric permittivity of the medium e( =eoer)

[9]

where L is .the Avogadro constant and R, T, and F have their usual meaning. (For aqueous solutions at 25°C: AnH = 0.509 mol-112 dm312 .) Coefficient bin Eq. [8] is equal to

b= (2F2)1/2 eRT '

[10]

while parameter a is the distance of closest approach of the interacting charges, which is in the case of nanoparticles related


72 KALLAY AND ZALAC

to their radius. By introducing Eq. [8] into Eq. [7] one obtains electrical interfacial layer

1/2 , # 2ZAZBAoHic

logk = logk +log K + 112

. 1 +able

[11]

Equation [11] suggests that the plot of the experimental log k value as the function of J}/2 j(l + ab/}12 ) should be linear with the slope of 2ZAZBAoH' which is true if charges of interacting species do not depend on the ionic strength. However, as it will be shown later, the charge of a colloidal particle decreases with ionic strength due to association of counterions with surface charged groups.

Estimation of the Equilibrium Constant of the Transition State Formation

To analyze the effect of repulsion between two charged par-ticles on the equilibrium constant Ki' we shall split the Gibbs energy of the transition state formation !), i' G0 into electrostatic term, !), i' G~1 , and the rest, which we shall call the chemical term, !), i' G~h. The latter includes van der Waals dispersion attraction

-RTlnKi' = -RTln(K;K~)=!),.i'G0

= !),i'G~h + !),i'G~I•

where !),.i'G~h = -RT InK; and !),i'G~1 = -RT InK~.

[12]

As noted before, the equilibrium constant Ki' is based on the activities of the interacting species and its definition (Eq. [5]) considers the corrections for the nonideality. It corresponds to the zero-ionic strength so that the value of K~ could be ob-tained considering simple Coluombic interactions between two nanoparticles. Accordingly, the (molar) electrostatic energy be-tween particles A ZA and Bzs of radii r A and rB in the medium of the permittivity e is

[13]

where rA + rB is the center to center distance between inter-acting particles in close contact. In the case of two identical particles (r A= rB = r and ZA = ZB = z)

[14]

This approach, based on the Coulomb law, could be tested by the Hogg-Healy-Fuerstenau (HHF) theory (9). For two equal spheres of the same surface potential cp, separated by surface to surface distance x, the electrostatic interaction energy, expressed on the molar scale, is equal to

where K is the Debye-Hiickel reciprocal thickness of the

K = (2IcF2) 1/2 eRT

[16]

At the zero-ionic strength Uc ---+ 0) the surface potential cp of a sphere of radius r and the charge number z is

ze cp=--.

4xer [17]

(Note that cp potential is in fact the electrostatic potential at the onset of diffuse layer.) Under such a condition the diffuse layer extends to infinity (K ---+ 0), so that for zero separation (x ---+ 0) Eq. [15] reads

[18]

The comparison ofEq. [18] with Eq. [14] shows that HHF theory results in "-'30% lower value of energy than the Coulomb law. This discrepancy is not essential for the purpose of this study, so that in further analysis we shall use the Coulomb expression.

By introducing Eqs. [12] and [13] into Eq. [11] for the rate constant of aggregation of nanoparticles A ZA and B'8 , one ob-tains

2 2 A 1112 lo k= lo k' + lo Ki' _ ZAZBF + ZAZB DH c g g g ch 4xeL(rA+rB) 1+ab!}12

[19]

or in another form

( B !}

12 ) log k = log ko - ZAZB - 2AoH l/2 , [20] rA+rB 1+ablc

where

and

F 2 ln 10 B=---

4xeLRT

ko=k'K~.

[21]

[22]

At high ionic strength the counterion association is so pro-nounced that the effective charge number of nanoparticles ap-proaches to zero. In such a case the electrostatic repulsion dimin-ishes and the aggregation is controlled by the diffusion (k = kdiff), as described by the Smoluchowski theory. Accordingly,

ko = kdiff· [23]



The stability coefficient (reciprocal of the collision efficiency), commonly defined as W = kctiff/ k, is then equal to

k ( B 1IJ2 ) log W = log ko = ZAZB - 2AnH e l/2 . rA +rB 1 +able

[24]

In the case of aggregation of identical nanoparticles the above equation is reduced to

ko 2 (B 1112 ) log W = log -k = 2z - - AnH 112

• r 1 +able

[25]

Evaluation of the Charge Number

For a given electrolyte concentration, the stability coefficient of the nanodispersion could be obtained by Eq. [24] (or by Eq. [25], in the case of uniform particles), once the charge number of particles is known. The surface potential (as used in the theory of Colloid Stability) and charge number are deter-mined by the ionic equilibrium at the solid/liquid interface which will be considered here for metal oxide particles dispersed in aqueous electrolyte solutions. The Surface Complexation model (2-pK concept) considers (15-22) amphotheric surface =MOH groups, developed by the hydration of metal oxide surfaces, that could be protonated (p) or deprotonated (d)

=MOH+H+--+ =MOHi;

r(MOHi) Kp = exp(F¢0 / RT) a(H+)r(MOH) [26]

=MOH --* =MO- + H+;

r(MO-)a(H+) Kct= exp(-F¢0 /RT) . [27] r(MOH)

Kp and Kct are equilibrium constants of protonation and depro-tonation, respectively, ¢0 is the potential of the 0-plane affecting the state of charged surface groups MOHi and Mo-, r is the surface concentration (amount per surface area), and a is activity in the bulk of solution.

Charged surface groups bind counterions, anions A- (surface equilibrium constant Ka), and cations c+ (surface equilibrium constant Kc)

From the d-plane (onset of diffuse layer, potential ¢ct), ions are distributed according to the Gouy-Chapman theory.

The total concentration of surface sites rtot is equal to

rtot = r(MOH) + r(MOHi) + r(MO-)

+ r(MO- · c+) + r(MOHi · A-).

Surface charge densities in the 0- and f3-planes are

ao = F(r(MOHi) + r(MOHi ·A-)

- r(Mo-)- r(Mo- . c+))

ap = F(r(MO- · c+)- r(MOHi ·A-)).

[30]

[31]

[32]

The net surface charge density a 8 corresponding to the charge fixed to the surface is opposite in sign to that in the diffuse layer act

The relations between surface potentials, within the fixed part of electrical interfacial layer (ElL), are based on the constant capacitance concept

[34]

where C 1 and C2 are capacities of the so-called inner and outer layer, respectively. The general model of ElL could be simplified (19) by introducing rfJtJ =¢ct. which corresponds to C2 --* oo. The equilibrium in the diffuse layer is described by the Gouy-Chapman theory. For planar surfaces (relatively large particles)

2RTeK . as= -ad= --F- smh(-F¢ct/2RT) [35]

and for small spherical particles (nanoparticles)

[36]

Once the system is characterized, the Surface Complexation

=MOHi+A---* =MOHi -A-;

r(MOHi ·A-) K - exp(-FA."fRT)---'---"---.--a- 'f',_, a(A-)r(MOHi)

=Mo- + c+ --* =Mo- . c+;

r(Mo-. c+)

[28] model enables calculation of the colloid particle charge num-ber under given conditions. This means that one should know equilibrium constants of surface reactions, capacitances of in-ner and outer layers, and total density of surface sites. By an

Kc = exp(F¢fl/ RT) a(C+)r(MO ) , [29] iteration procedure one obtains the net surface charge density as (defined by Eq. [33]) from which the particle charge number is

where ¢tJ is the potential of f3-plane affecting the state of asso-ciated counterions. [37]


74 KALLAY AND ZALAC

Numerical Simulation and Discussion 1 o ...-----r--r---------------,

The above theory, developed for kinetics of aggregation of nanoparticles (nanocoagulation), will be demonstrated on a few examples. Two systems (hematite and rutile) under different con-ditions will be examined. The values of equilibrium parameters, used in calculation of the particle charge number, were obtained by interpretation of adsorption and electrokinetic data for ordi-nary colloid particles (21, 22). It was assumed that these param-eters approximately describe the properties of corresponding nanosystems. In the evaluation the Gouy-Chapmen equation for spherical interfacial layer, Eq. [36], was used. Once the charge number was obtained, the stability coefficient was calculated via Eq. [25].

Figure 2 demonstrates the effect of electrolyte concentration on the stability of hematite nanodispersions containing parti-cles of r = 3 nm. It is obvious that the stability of the system decreases rapidly with electrolyte addition. At pH 4, particles are positively charged so that association of anions with the surface charged groups takes place. Nitrate ions were found to aggregate the system more effectively with respect to the chlo-ride ions, which is due to lower values of the surface associa-tion equilibrium constant of the latter counterions. The effect of electrolyte concentration is explicitly included in Eq. [25] through ionic strength. However, particle charge number also depends on the electrolyte concentration due to counterion as-sociation so that both effects result in a decrease of stability at

5

KCI

HEMATITE pH=4 r=3nm

oL---~--~---~----~~--~----~

·3 ·2 -1

lg(lJmol dm-3)

0

FIG. 2. Effect of electrolytes on the stability of hematite aqueous nanodispersion (r = 3 nm) at T = 298 K and pH 4, as obtained by Eq. [25]. The charge number was calculated by the Surface Com-plexation model (Eqs. [26]-[39]) using parameters obtained (21) with hematite colloid dispersion (r =60 nm): f 101 = 1.5 x to-5 mol m-2; Kp = 5xl04; Kd=l.5xl0- 11 ; pHpzc=7.6; K(N03)=1410; K(Cl-)=525; C1(N03") = 1.88 Fm-2; C1(Cl-) = 1.81 F m-2; C2 = oo; Er =sf so =78.54.

5

HEMATITE

KN03 r=3nm

oL-----~--~----~--~~----~----~

-3 -2 -1 0

lg(IJmol dm-3)

FIG. 3. Effect of pH on the stability of hematite aqueous nanodispersion (r = 3 nm) in the presence of potassium nitrate at T = 298 K. The parameters used in calculations are the same as in Fig. 2.

higher electrolyte concentrations. Figure 3 demonstrates the ef-fect of the activity of potential determining H+ ions. At lower pH values particles are more positively charged, the system is more stable, and higher electrolyte concentration is necessary for aggregation. The effect of particle size on the stability of the system is dramatic. As shown in Fig. 4, systems with smaller

10

HEMATITE KN03 pH=4

~

~

5 r=3nm

oL---~-----L---=~==~~----~--~ ·3 -2 0

FIG. 4. Effect particle size on the stability of hematite aqueous nanodisper-sions in the presence of potassium nitrate at pH 4 and T = 298 K. The parameters used in calculations are the same as in Fig. 2.



10~------~------------------------.

5 RUTILE pH= 9.5 LiN03

r=3nm

oL---~----~~==~~L---~--~ -3 -2 -1 0

lg(lJmol dm-3)

FIG. S. Effect of kind of material on the stability of aqueous nanodisper-sion (r = 3 nm) at T = 298 K. For hematite particles, the parameters used in calculations are the same as in Fig. 2. For rutile rods (length is I 00--240 nm and width is 45 nm) the parameters are (22): r 1o1 = w-5 mol m-2 ; Kp = 6 x 107 ; Kd =6 x w-5; pHpzc =6.0; K(Li+) =380; C1(Li+)= 1.58 F m-2 ; Cz =oo.

particles are markedly less stable. In fact, such a system is un-stable even at low electrolyte concentrations. It is interesting to analyze the particle size effect on the basis of Eq. [25], assum-ing that surface charge density does not depend significantly on the particle size. In such a case the particle charge number is proportional to r 2 so that first term associated with B is pro-portional to r 3• Accordingly, one would expect an increase of stability coefficient with particle size. The second term, associ-ated with ionic strength, acts in the opposite direction. However, this term is not significant at low ionic strength so that the first one prevails. At high ionic strength the second term becomes influential, but also the charge density and charge number are reduced so much that log W approaches zero for any particle size. A similar conclusion would be obtained if one assumes that surface potential does not depend significantly on parti-cle size. However, according to Eq. [36], the size effect on the stability will be less pronounced. The reality is between the above-noted extremes, but the use of the Surface Complexa-tion model enabled us to avoid such speculations. Generaly, one may conclude that smaller particles are less stable. Indeed, as shown for zirconia (24) the nanodispersion coud be stable at very high surface potentials which were achieved 6 pH units below the point of zero charge. The specificity of the material comprising nanoparticles could be seen through the values of the equilibrium parameters. Figure 5 shows the difference between the predicted behavior of hematite and rutile nanosystems. The pH values were chosen to be approximately equally far from the point of zero charge, but in the opposite direction. At pH 9.5 rutile is negatively while at pH 4 hematite is positively charged.

The absolute values of surface potentials are approximately the same. However, due to the different values of the equilibrium parameters, rutile was found to be significantly less stable than hematite.

It may be concluded that application of the Br¢nsted concept to the stability of nanodispersions shows that the presence of electrolytes may completely reduce the stability, and that the electrolytes with counterions exhibiting higher affinity are more effective for association at the interface. Lower surface poten-tial (pH closer to the point of zero charge) slightly reduces the stability. In the above analysis the parameters used for calcula-tions may differ from the reality since they were obtained from measurements with relatively large colloid particles; however, the general behavior of nanosystems may be still explained. The comparison between hematite and rutile showed how sensitive the stability of nanosystems is on the inherent characteristics of the solid. Different equilibrium parameters result in a very pronounced difference in the stability. However, the major char-acteristics of the system are the particle size; smaller particles are significantly less stable. The interpretation based on the Br1

76 KALLAY AND ZALAC

8. Deijaguin, B. V., and Landau, L., Acta Physicochim., USSR 14, 552 (1941).

9. Hogg, R., Healy, T. W., and Fuerstenau, D. W., Trans. Faraday Soc. 62, 1638 (1966).

10. Bhattachaijee, S., Elimelech, M., and Borkovec, M., Croat. Chem. Acta 71, 883 (1998).

11. Semmler, M., Ricka, J., and Borkovec, M., Colloids Surf. 165, 79 (2000).

12. Hsu, J.-P., and Liu, B.-T., J. Colloid Interface Sci. 217,219 (1999). 13. Ohshima, H., J. Colloid Interface Sci. 225, 204 (2000). 14. Sun, N., and Walz, Y., J. Colloid Interface Sci. 234, 90 (2001). 15. Yates, D. E., Levine, S., and Healy, T. W., J. Chem. Soc., Faraday Trans. I

70, 1807 (1974). 16. Davis, J. A., James, R. 0., and Leckie, J. 0., J. Colloid Interface Sci. 63,

480 (1978). 17. Westall, J., and Hohl, H., Adv. Colloid Interface Sci. 12, 265

(1980).

18. Dzombak, D. A., and Morel, F. M. M., "Surface Complexation Modelling." Wiley Interscience, New York, 1990.

19. Kallay, N., Kova~evic, D., and Cop, A., in "Interfacial Dynamics" (N. Kallay, Ed.), Surfactant Science Series, Vol. 8. Dekker, New York, 1999.

20. Kallay, N., and Zalac, S., J. Colloid Interface Sci. 230, 1 (2000). 21. Colic, M., Fuerstenau, D. W., Kallay, N., and Matijevic, E., Colloid Surf.

59, 169 (1991). 22. Kallay, N., Colic, M., Fuerstenau, D. W., Jang, H. M., and Matijevic, E.,

Colloid Polym. Sci. 272,554 (1994). 23. de Gennes, P.-G., Croat. Chem. Acta 71, 833 (1998). 24. Peyre, V., Spalla, 0., Belloni, L., and Nabavi, M., J. Colloid Interface Sci.

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3128 (2001). 26. Br!'lnsted, J. N., Z. Physik. Chem. 102, 169 (1922). 27. Christiansen, J. A., Z. Physik. Chem. 113, 35 (1924 ).


Exhibit 6


Comparison of physicochemical characteristics and stability onhree novel tonnu1at1ons ot paclitaxeJ: ADraxane, Nanoxei, ana uenexo1 rM -... rage 1 v• ~

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99th AACR Annual Meeting-- Apr 12-16, 2008; San Diego, CA

Drug Delivery and Targeting: Poster Presentations -Proffered Abstracts

Abstract #5622

Comparison of physicochemical characteristics and stability of three novel formulations of paclitaxel: Abraxane, Nanoxel, and Genexol PM

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Niles Ron, Jon Cordia, Andrew Yang, Sherry Ci, Phithi Nguyen, Melissa Hughs and Neil Desai

Abraxis Bioscience, Inc., Los Angeles, CA

Background: Abraxane (Abraxis BioScience, Inc., Los Angeles, CA, approved in USA and Canada), Nanoxel (Dabur Pharma, H.P., India, approved in India), and Genexol PM (Samyang Pharmaceuticals, Seoul, Korea, approved in Korea) are 3 commercially approved, novel formulations of paclitaxel. Abraxane consists of albumin-bound injectable nanoparticles of paclitaxel, while Genexol and Nanoxel (utilizing cosolvents) are polymeric-micelle formulations. Abraxane and Genexol are lyophilized products approved for 25°C ± 2°C storage, while Nanoxel is a liquid formulation approved for 2-8°C storage. This study investigated the physicochemical characteristics and short-term stability of the 3 products under recommended clinical use conditions and under accelerated conditions. Methods: The drugs were reconstituted and prepared per the instructions provided in the respective package inserts. Abraxane and Genexol were reconstituted using the recommended saline diluent, while Nanoxel was mixed and diluted in 10% dextrose. Each drug was reconstituted to 0.7 mg/mL and 5 mg/mL. Physical stability was monitored both visually and microscopically; particle size was measured and monitored over time at room temperature (RT, measured to be 23°C) and 40°C using photon correlation spectroscopy (PCS) (Zetasizer 3000, Malvern, UK). Chemical purity was measured by reduced reversed-phase HPLC (Shimadzu Scientific Instruments, MD). Results: Following reconstitution, Abraxane was determined to be stable both physically and chemically


Comparison of physicochemical characteristics and· stability of three novel fonnulations ofpaclitaxel: Abraxane, Nanoxel, and Genexol PM-... Page 2 of2

at RT and 40°C over 24 hrs, with no evidence ofnanoparticle size growth at either 0.7 mg/mL or 5 mg/mL. While reconstituted Genexol was stable at RT over 24 hrs, micelle instability resulting in precipitation of paclitaxel in the form of large needle-like crystals for both 0. 7 mg/mL and 5 mg/mL formulations was seen between 2 to 4 hrs at 40°C. These observations were confirmed using orthogonal techniques, visual assessment from photomicrographs, and PCS particle size measurement. For Nanoxel at 0.7 mg/mL, a minor, but consistent, increase in particle size was observed at RTover 24 hrs. However, significant aggregation, particle-size growth, and crystallization were seen within 4 hrs at 40° C. HPLC data comparing pre- and post-filtration confirmed that the crystal formation for both Nanoxel and Genexol resulted from paclitaxel precipitation and aggregation. In addition, analytical results showed that Nanoxel had slightly lower paclitaxel purity as compared to either Abraxane or Genexol. Conclusions: Nanoparticle albumin-bound paclitaxel, Abraxane, showed excellent physicochemical stability as compared to the micellar formulations, Nanoxel and Genexol. Particle size growth and crystal formation were readily apparent in Nanoxel and Genexol, especially in the short term under accelerated conditions.

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