Impact of Solvent Quality on Nanoparticle Dispersion in Semidilute

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Impact of Solvent Quality on Nanoparticle Dispersion in Semidilute and Concentrated Polymer Solutions Nupur Dutta and David Green* Department of Chemical Engineering, University of Virginia, 102 Engineers Way, Charlottesville, Virginia 22904, United States Received June 12, 2010. Revised Manuscript Received October 4, 2010 We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/ bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of TΘ =19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.

1. Introduction Colloidal dispersions are of fundamental importance in various biological, environmental, and industrial applications. These systems are routinely encountered in paints, coatings, inks, agrochemicals, pharmaceuticals, and personal care products. Polymers are often adsorbed or grafted on the surface of the colloids in an effort to attain particle stability by primarily screening van der Waals attractions. This phenomenon is referred to as polymeric stabilization, and the mechanisms leading to particle stability in simple solvents and dilute polymer solutions have been elucidated by researchers such as Napper, Vincent, Alexander, and de Gennes.1-4 In contrast, the uniform dispersion of colloids in semidilute and concentrated polymer solutions with good solvents has been recently studied by us, where we have shown that the interfacial wetting of the graft polymer on the colloid with the free polymer in solution controls particle stability.5 Particle stability occurs within the complete wetting region (P/N < 1.0) of the phase diagram shown in Figure 1, where σ is the dimension less graft density, N is the molecular weight of the graft polymer, P is the molecular weight of the free polymer in the solution, and φp is the volume fraction of free polymer in the solution. Over the past 30 years researchers have investigated a wide range of particle-polymer systems in pure and mixed solvents as *To whom correspondence should be addressed. E-mail: dlgreen@virginia. edu. (1) Napper, D. H. Polymer Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (2) Li-In-On, F. K. R.; Vincent, B.; Waite, F. A. ACS Symp. Ser. 1975, 9, 165– 172. (3) Alexander, S. J. Phys. (Paris) 1977, 38(8), 983–987. (4) Gennes, P. G. Macromolecules 1980, 13, 1069–1075. (5) Dutta, N.; Green, D. Langmuir 2008, 24, 5260–5269.

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well as dilute polymer solutions, and excellent monographs include discussions on the effects of solvent quality on the conformation of graft polymers.1 Discussion ensue from investigations conducted by Vincent,2,7-16 Zukoski,17-21 Vrij,22-25 Napper,26 Russel,27,28 (6) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, 3rd ed.; Marcel Dekker, Inc.: New York, 1997. (7) Clarke, J.; Vincent, B. J. Chem. Soc., Faraday Trans. 1981, 77, 1831–1843. (8) Clarke, J.; Vincent, B. J. Colloid Interface Sci. 1981, 82, 208–216. (9) Crowell, C.; Li-On-In, F. K. R.; Vincent, B. J. Chem. Soc., Faraday Trans. 1978, 74, 337–347. (10) Cowell, C.; Vincent, B. J. Colloid Interface Sci. 1982, 87, 518–526. (11) Jones, A.; Vincent, B. Colloids Surf. 1989, 42, 113–138. (12) Milling, A.; Vincent, B.; Emmett, S.; Jones., A. Colloids Surf. 1991, 57, 185– 195. (13) Vincent, B.; Clarke, J.; Barnett, K. G. Colloids Surf. 1986, 17, 51–65. (14) Vincent, B.; Edwards, J.; Emmett, S.; Croot, R. Colloids Surf. 1988, 31, 267–298. (15) Vincent, B.; Edwards, J.; Emmett, S.; Jones, A. Colloids Surf. 1986, 18, 261– 281. (16) Vincent, B.; Luckham, P. F.; Waite, F. A. J. Colloid Interface Sci. 1980, 73, 508–521. (17) Ramakrishnan, S.; Zukoski, C. F. J. Chem. Phys. 2000, 113(3), 1237–1248. (18) Ramakrishnan, S.; Fuchs, M.; Schweizer, K. S.; Zukoski, C. F. Langmuir 2002, 18, 1082–1090. (19) Ramakrishnan, S.; Fuchs, M.; Schweizer, K. S.; Zukoski, C. F. J. Chem. Phys. 2002, 112, 2201–2212. (20) Shah, S. A.; Chen, Y.-L.; Ramakrishnan, S.; Schweizer, K. S.; Zukoski, C. F. J. Chem. Phys. 2003, 118, 3350–3361. (21) Shah, S. A.; Chen, Y.-L.; Ramakrishnan, S.; Schweizer, K. S.; Zukoski, C. F. Langmuir 2003, 19, 5128–5136. (22) Jansen, J. W.; Kruif, C. G. D.; Vrij, A. J. Colloid Interface Sci. 1986, 114(2), 471–480. (23) Jansen, J. W.; Kruif, C. G. D.; Vrij, A. J. Colloid Interface Sci. 1986, 114(2), 481–491. (24) Jansen, J. W.; Kruif, C. G. D.; Vrij, A. J. Colloid Interface Sci. 1986, 114(2), 492–500. (25) Jansen, J. W.; Kruif, C. G. D.; Vrij, A. J. Colloid Interface Sci. 1986, 114 (52), 501–504. (26) Zhu, P. W.; Napper, D. H. Phys. Rev. E 1994, 50(2), 1360–1366.

Published on Web 10/25/2010

DOI: 10.1021/la102401w

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Figure 1. Theoretical wetting phase diagram for a homopolymer brush immersed in a homopolymer solution (adapted from ref 51).

Berg,29 and Lewis,30 have studied a variety of systems including particle types (polystyrene, polyacrlyonitrile, silica, aluminum oxide), graft polymers and oligomers (poly(ethylene oxide), polystyrene, polyisoprene, polydimethylsiloxane, poly(propylene oxide), poly(methyl methacrylate), stearyl alcohol), free polymers (poly(ethylene oxide), poly(vinyl alcohol), polystyrene, polyisoprene, polydimethylsiloxane, poly(butyl sulfonate), poly(methyl methacrylate), hydroxyethyl cellulose), and solvents (water, ethylbenzene, cyclohexane, nitromethane, n-hexane, toluene, n-octane). To quantify particle stability, the investigators employed a variety of techniques including static light scattering (SLS), dynamic light scattering (DLS), optical microscopy, zeta potential, small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), mechanical rheology, microrheology, and visual observations. On the basis of much of this research, it is well-known in the colloids field that the strength of particle interactions can be finetuned based on solvent quality, free polymer molecular weight, and particle size in pure solvents and dilute polymer solutions. As such, these suspensions have been used as model systems to elucidate phenomena such as the formation of colloidal glasses, which undergo a series of equilibrium and metastable states including fluid-fluid and fluid-crystal phase separation as well as gelation and vitrification.31,32 Under certain conditions, these suspensions can behave like amorphous glassy solids which are routinely encountered in ceramics processing, protein crystallization, electronic fabrication, and food formulation.33,34 Detailed studies have also been carried out on thermoreversible gels,32,35-37 and several review articles have been published on the dynamics of colloidal glasses.34,38-40 (27) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1999. (28) Gast, A. P.; Russel, W. B.; Hall, C. K. J. Colloid Interface Sci. 1986, 109, 161–171. (29) Huang, A. Y.; Berg, J. C. J. Colloid Interface Sci. 2004, 279, 440–446. (30) Ogden, A. L.; Lewis, J. A. Langmuir 1996, 12, 3413–3424. (31) Shah, S. A.; Ramakrishnan, S.; Chen, Y.-L.; Schweizer, K. S.; Zukoski, C. F. Langmuir 2003, 19, 5128–5136. (32) He, G.; Tan, R. B. H.; Kenis, P. J. A.; Zukoski, C. F. J. Phys. Chem. B 2007, 111, 14121–14129. (33) Magid, L.; Penfold, J.; Schurtenberger, P.; Wagner, N. J. Curr. Opin. Colloid Interface Sci. 2004, 8, 491–493. (34) Dawson, K. A. Curr Opin. Colloid Interface Sci.. 2002, 7, 218–227. (35) Rueb, C. J.; Zukoski, C. F. J. Rheol. 1997, 41(2), 197–217. (36) Shah, S. A.; Chen, Y.-L.; Ramakrishnan, S.; Schweizer, K. S.; Zukoski, C. F. J. Phys.: Condens. Matter 2003, 15, 4751–4778. (37) Ramakrishnan, S.; Gopalakrishnan, V.; Zucoski, C. F. Langmuir 2005, 21, 9917–9925. (38) Cates, M. E. Ann. Inst. Henri Poincare 2003, 4(2), S647–S661. (39) Poon, W. C. K. MRS Bull. 2004, No.February, 96–99. (40) Yethiraj, A. Soft Matter 2007, 3, 1099–1115.

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However, little attention has been paid to investigating the effects of solvent quality on nanoparticle dispersions in semidilute and concentrated polymer solutions. Thus, using polydimethylsiloxane (PDMS)-grafted silica nanoparticles, or PDMS-g-silica, we discuss these effects in semidilute and concentrated PDMS solutions. To this end, we have developed a new model system by adding PDMS-g-silica nanoparticles to bromocyclohexane, a theta solvent for PDMS, which permits us to investigate the thermoreversible aggregation of the nanoparticles as the solution temperature is varied around the upper critical solution temperature (UCST). This also enables us to relate the impact of solution temperature on dispersions of PDMS-g-silica nanoparticles in concentrated PDMS/bromocyclohexane solutions. Moreover, we used visual observations to investigate how various solvents affect the stability of the PDMS-g-silica nanoparticles in the PDMS solutions. To our knowledge, our work is the first of its kind. To elucidate the impact of solvent quality on nanoparticle stability, this paper is structured as follows. In section 2 the experimental methodology and theory behind self-consistent mean-field calculations are covered. Section 3 presents our experimental and theoretical results in which we make connection between the wetting of the PDMS brush and the dispersion PDMS-g-silica nanoparticles in semidilute and concentrated PDMS/bromocyclohexane solutions as a function of solvent quality. We also provide a stability ratio analysis in section 3 for the nanoparticle dispersions. The paper concludes in section 4 with a summary of the SCF and DLS results.

2. Experimental and Theoretical Methodology To shed light on the impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions, we synthesized monodipserse silica particles, grafted PDMS polymers to the particle surfaces, formulated well-controlled polymer/ particle suspensions, and characterized the stability of the suspensions with visual assays and dynamic light scattering. Moreover, we corroborated our results with self-consistent mean-field modeling. Our experimental and theoretical methods are discussed in this section. 2.1. Materials. Reagent grade chemicals (purity g99%) were used as purchased from the manufacturer without further purification unless specified. TEOS, absolute ethanol, ammonium hydroxide (30% NH3), 1-pentanol, bromocyclohexane, 1-propanol, and 1-butanol were all obtained from Acros Organics. Cyclohexane, methyl ethyl ketone, tert-butanol, and decalin were obtained from Fisher Scientific. Tetrahydrofuran was obtained from Sigma-Aldrich. All industrial grade PDMS polymers were obtained from Gelest. The 18 MΩ deionized water was produced with a Barnstead E-pure water purification system. 2.2. Nanoparticle Synthesis. The silica nanoparticles were produced using St€ ober synthesis.41,42 The spherical particles were 200 ( 5 nm in diameter (40 particles, 95% confidence interval) as verified by SEM (JEOL 6700 F) in Figure 2. Reagent concentrations of [NH3] = 0.50 M, [H2O] = 4.00 M, and [TEOS] = 0.25 M in ethanol were used to make the 200 nm nanoparticles as derived from an empirical relation that relates the concentrations of the initial reactants to the size of the final particles.42 The particles were subsequently washed five times with absolute ethanol to remove any unreacted chemicals. To facilitate the grafting of the particles in cyclohexane, the surface hydroxyl and ethoxy groups were removed by combining purified ethanol/silica solutions with an equal volume of 1-pentanol and then removing the ethanol through distillation. Subsequently, the esterification of the silica (41) St€ober, W.; Fink, A. J. Colloid Interface Sci. 1968, 26, 62–69. (42) Bogush, G. H.; Tracy, M. A.; Z., C. F., IV J. Non-Cryst. Solids 1988, 104, 95–106.

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Article Table 1. Dynamic Viscosity (η) as a Function of Temperature (T ) for PDMS/Bromocyclohexane Solutions with a PDMS Volume Fraction (Op) of Op = 0.6 η (cP)

Figure 2. SEM micrograph of silica nanoparticles formulated from 0.25 M [TEOS], 0.5 M [NH3], and 4.0 M [H2O]. surface with 1-pentanol was performed to prevent strong adsorption of PDMS, whose siloxane chains are known to form hydrogen bonds with hydroxyl groups on the silica surface.43,44 This reaction was carried out for 24 h at 140 °C. Subsequently, the particles were washed five times into cyclohexane. To graft PDMS to the silica spheres, the experimental procedures of Edwards et al.45 and Auroy et al.46 were adapted. First, the required amounts of PDMS, end-capped with -OH groups at both ends (N=4 and 18 kg/mol as specified by the manufacturer), were weighed into separate Erlenmeyer flasks. Subsequently, the required volumes of esterified silica/cyclohexane solution were added to each flask, and the mixture was capped and homogenized overnight on a shaker. After homogenization, cyclohexane was removed from each flask under vacuum. To initiate the grafting reaction, an Erlenmeyer flask containing the silica particles in PDMS melt were placed in an oil bath, and the grafting reaction was carried out over a period of 72 h continuously at 150 °C. Upon completion of the grafting reaction, the contents of the vessel were allowed to cool to room temperature under stirring. Subsequently cyclohexane was added, and the flasks were tightly sealed, gently swirled, and vigorously sonicated to redisperse their contents. The dispersions were then poured into centrifuge tubes and washed four times with cyclohexane to remove any unreacted polymer. The graft density of PDMS on silica surface was calculated by elemental analysis described in our previous publication.5 The graft density (Σ) was computed to be Σ = 0.17 ( 0.01 chains/nm2. Five separate measurements were performed to ensure statistical accuracy. Subsequently, the PDMS-g-silica nanoparticles were washed four times into a range of solvents, including methyl ethyl ketone, bromocyclohexane, ethanol, 1-propanol, 1-butanol, and tert-butanol, to make a series of purified stock solutions that were used to formulate nanoparticles suspensions as discussed in the next subsection.

2.3. Formulation of Nanoparticle Suspensions in Simple Solvents and Polymer Solutions. The nanoparticles were then added to bromocyclohexane as well as semidilute and concentrated PDMS solutions with bromocyclohexane in addition to methyl ethyl ketone, ethanol, 1-propanol, 1-butanol, and tertbutanol. Two free PDMS polymers were used, permitting us to quantify particle stability within semidilute and concentrated polymer solutions. The molecular weights of the free PDMS polymers at P=2.05 and 11.3 kg/mol were determined with an Agilent Technologies Series 1100 HPLC. The eluent was THF (43) Addad, J.-P. C.; Ebengou, R. Polymer 1992, 33(2), 379–383. (44) Addad, J.-P. C.; Touzet, S. Polymer 1993, 34(16), 3490–3498. (45) Edwards, J.; Everett, D. H.; O’Sullivan, T.; Pangalou, I.; Vincent., B. J. Chem. Soc., Faraday Trans. 1984, 80, 2599–2607. (46) Auroy, P.; Auvray, L.; Leger, L. Macromolecules 1991, 24, 5158–5166.

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T (°C)

P = 2.05 kg/mol

P = 11.3 kg/mol

10 20 30 40

5.00 ( 0.01 4.24 ( 0.03 3.62 ( 0.01 3.10 ( 0.02

52.20 ( 0.10 43.76 ( 0.09 36.67 ( 0.13 31.37 ( 0.29

and samples were eluded through a Polymer Laboratories 5 μm mixed-C guard column and two GPC columns (30 cm in length) at 25 °C and 1.0 mL/min. The polymer molecular weights were calibrated against polystyrene standards from Polymer Laboratories. The free PDMS polymers were then weighed into clean borosilicate vials to adjust the volume fraction of PDMS in solution, φp, between φp = 0.60-0.96. Subsequently the requisite amount of solvent was added to the respective vials, followed by the addition of the PDMS-g-silica nanospheres, whose amount was adjusted to hold the volume fraction of silica cores, φn, constant in all samples at φn = 1.25  10-3.

2.4. Determination of Physical Properties of Polymer Solutions. The viscosities (η) and the refractive indices (nD) of the PDMS/bromocyclohexane solutions were required to determine the diffusion coefficients (De) and hydrodynamic radii (Rh) of the PDMS-g-silica nanoparticles from measurements with dynamic light scattering. The viscosities of the PDMS/bromocyclohexane solutions were measured as a function of temperature using Ubbelohde capillary viscometers immersed in a constant temperature bath, which was connected to a Neslab RTE-10 refrigerated bath for temperature control. The capillaries and the constant temperature viscometer bath were purchased from Cannon Instrument Co. Disposable pipettes were used to introduce about 1 mL of sample into the capillary viscometer, and prior to all measurements, the viscometer and sample were equilibrated for 30 min at each temperature between T = 10-40 °C in a Neslab RTE-10 refrigerated bath. Subsequently, viscosity measurements ensued, noting the efflux time, or that required for the meniscus of the sample to fall between the demarcations on the capillary. Each sample was repeated three times for statistical accuracy. The kinematic viscosity was calculated by taking the product of the efflux time and the capillary constant specified by the manufacturer. The dynamic viscosity (η) was calculated by multiplying the kinematic viscosity by the density of the solution that was obtained from a weighted average. Table 1 shows the dynamic viscosities for PDMS/bromocyclohexane solutions with PDMS molecular weights P = 2.0 and 11.3 kg/ mol for T = 10-40 °C. All errors are calculated for a 95% confidence interval. The refractive indices (nD) of the PDMS/bromocyclohexane solutions were measured using an Abbe Mark III refractometer from Reichert Analytical Instruments. A Neslab RTE-10 refrigerated bath was connected to the refractometer to control the sample temperature. Prior to each measurement, the measuring prism was cleaned with ethanol and deionized water and then wiped with lens tissue. A few drops of the sample were pipetted on the measuring prism, and the nD was measured as a function of temperature at least three times for statistical accuracy. Table 2 displays the refractive indices for PDMS/bromocyclohexane solutions with PDMS molecular weights P=2.05 and 11.3 kg/mol at T=10-40 °C. 2.5. Particle Stability Measurements. Visual observations and dynamic light scattering measurements were carried out to detect the impact of solvent quality on nanoparticle dispersion in a theta solvent as well as in semidilute and concentrated polymer solutions. The visual studies were used initially to characterize how theta solvents affect the stability of PDMS-g-silica nanoparticles in bromocyclohexane and in PDMS/bromocyclohexane DOI: 10.1021/la102401w

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Table 2. Refractive Index (nD) as a Function of Temperature (T ) for PDMS/Bromocyclohexane Solutions with a PDMS Volume Fraction (Op) of Op = 0.6

ln g1 ðτÞ ¼ - De q2 τ þ σ SD q4

nD T (°C)

P = 2.05 kg/mol

P = 11.3 kg/mol

12 20 30 40

1.4416 ( 0.0001 1.4379 ( 0.0001 1.4335 ( 0.0001 1.4293 ( 0.0001

1.4442 ( 0.0001 1.4397 ( 0.0001 1.4357 ( 0.0001 1.4319 ( 0.0001

solutions as a function of temperature. To examine the effect of solvents that are marginally soluble with PDMS, additional visual stability studies were carried out in semidilute and concentrated PDMS solutions with ethanol, 1-propanol, 1-butanol, and tertbutanol. Subsequently, DLS measurements were used to pinpoint the theta temperature for the PDMS-g-silica nanoparticles in bromocyclohexane as well as quantify the effect of temperature, and thus solvent quality, on nanoparticle dispersion in PDMS/bromocyclohexane solutions. Visual studies were conducted by adding nanoparticle suspensions to sealed test tubes and observing whether the nanoparticles dispersed or aggregated. In particular, theta temperature of the PDMS-g-silica/bromocyclohexane solutions and the stability of the nanoparticles in the PDMS/bromocyclohexane solutions were roughly quantified by placing the test tubes in water within a clear acrylic container. The temperature of the water in the container was controlled by connecting it to a circulating Neslab RTE-10 refrigerating bath to vary T = 10-60 °C. Observations were carried out over a period of at least 5 h at each temperature. Results of the visual studies were further investigated with DLS to quantify the stability of PDMS-g-silica nanoparticles with respect to temperature in bromocyclohexane and PDMS/bromocyclohexane. The DLS experiments were carried out by tracking the normalized autocorrelation function, g1(τ), which yields information about the diffusion of the nanoparticles, where τ is the correlation time. The DLS apparatus from PhotoCor Instruments consists of an autocorrelator and a goniometer with a temperature-controlled sample chamber together with a 35 mW JDS Uniphase He-Ne laser operating at a wavelength of 633 nm. The temperature of the experiment was controlled by connecting a refrigerated bath to the sample chamber. The sample chamber consists of a sample holder that sits inside of a borosilicate glass vat that holds an index matching fluid, decalin, from which dust was previously removed using a 0.2 μm Millipore filter. DLS measurements were carried out by first sonicating the nanoparticle suspensions within borosilicate glass vials at the temperature of interest and then placing the suspensions within the sample holder of the DLS, where the index matching fluid not only helps to maintain a consistent sample temperature but also mitigates the scattering of light from the borosilicate glass. The intensity autocorrelation functions, G2(τ), of the suspensions were captured using the multiple tau method, characterized by measuring the intensity of the scattered light from the sample with an initial sampling time of t = 2  10-8 s, which was increased logarithmically over the 255 channels of the autocorrelator. The quantity of interest is the normalized autocorrelation function, g1(τ), which is computed from the intensity autocorrelation function, G2(τ), using the Siegert relation:47 G2 ðτÞ ¼ 1 þ βjg1 ðτÞj2

ð1Þ

where β is an instrumental constant. The stability of the PDMSg-nanoparticles in bromocyclohexane and PDMS/bromocyclohexane solutions was quantified using several parameters obtained from the analysis of g1(τ), including the diffusion coefficient (De) (47) Johnson, C. S., Jr.; Gabriel, D. A. Laser Light Scattering; Dover Publications: New York, 1994.

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and the hydrodynamic radius (Rh). To this end, a third-order cumulant expansion was used:6 τ2 τ3 -K 2! 3!

ð2Þ

where q = (4πnD/λ) sin(θ/2) is the magnitude of the scattering vector and θ is the scattering angle. The first two terms are of interest where the first term on the right of eq 3 yields the average particle diffusion coefficient (De), the second term yields the standard deviation of the distribution of the diffusion coefficients (σSD), and the third term K is related to the skew of the distribution. Subsequently, the Stokes-Einstein relation was used to calculate the hydrodynamic radius (Rh) of the particles from their diffusion coefficients.6 Rh ¼

kB T 6πηDe

ð3Þ

where kB is the Boltzmann constant and η is the viscosity of the solution. 2.6. Self-Consistent Mean-Field Calculations. The free energies of interaction between polymer-grafted interfaces were calculated using the Schuetjens-Fleer self-consistent field (SCF) theory. The details of this method have been discussed in our previous work.5 We determined the interaction potential (Aint/ LkT ) as a function of separation distance (H ) between two approaching surfaces with graft polymers immersed in a solution of variable solvency. For these calculations the graft PDMS molecular weight (N) was varied from 4 to 18 kg/mol while the volume fraction of PDMS in solution was held constant at fp = 0.6. The solvent quality was varied from good ( χ = 0) to theta ( χ = 0.5) to poor ( χ = 1.0). Two separate calculations were run, first within the complete wetting region, i.e., P/N < 1.0 where P = 2.05 kg/mol, and the second outside the complete wetting region of dewetting region, i.e., P/N > 1.0 where P = 11.3 kg/mol. These calculations support the experimental results obtained from DLS on the impact of solvent quality on the stability of PDMSg-silica in semidilute and concentrated PDMS/bromocyclohexane solutions.

3. Results and Discussion As discussed previously, nanoparticle dispersions in semidilute and concentrated polymer solutions are ubiquitous to various industrial applications; however, the conditions that control nanoparticle stability have not been clearly elucidated. To this end, SCF calculations were used as a guide to formulate suspensions for visual observations and DLS experiments over a wide range of conditions. DLS measurements were analyzed to quantify particle stability, and the aggregation rates from unstable particles were compared to predictions from theory to determine whether the particles experienced diffusion-limited or reactionlimited aggregation. 3.1. Impact of Solvent Quality on Nanoparticle Dispersion in Polymers Solutions. SCF calculations were carried out to gain insight into how solvent quality would impact the stability of polymer-grafted nanoparticles in pure solvents and in semidilute and concentrated polymer solutions. The first step was to calculate the interparticle interaction potential (Aint/LkT) as a function of separation distance (H) and Flory interaction parameter ( χ), which is used to simulate solvent quality. Figure 3 shows the interaction potential between surfaces grafted with a polymer whose polymerization index is equivalent to a PDMS molecular weight of N = 18 kg/mol5 in a monomeric solvent in which χ is varied to simulate good ( χ = 0), theta ( χ = 0.5), and poor ( χ = 1.0) solvent conditions. As expected in good and theta solvents ( χ e 0.5) with no free polymer (φp = 0), Aint/LkT is Langmuir 2010, 26(22), 16737–16744

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Figure 3. Interaction potential as a function of separation distance H for surfaces with graft PDMS of molecular weight N = 18 kg/ mol in a monomeric solvent. Interaction potentials are repulsive for good (χ = 0.0) and theta (χ = 0.5) solvents and attractive for poor solvent (χ = 1.0).

always repulsive, increasing dramatically at closer separation distances and indicating that polymer-grafted nanoparticles should remain stable under these conditions. In contrast, an attractive well in Aint/LkT develops in poor solvents ( χ > 0.5), indicating particle instability and aggregation. These calculations have been detailed in the literature over the past 30 years and have been shown to correspond to the experimentally determined transitions of stability and instability in theta solvents where, as a function of temperature, polymer-grafted nanoparticles are stable in good-to-theta conditions and unstable in thetato-poor conditions.48,49 However, the impact of solvent quality on particle stability in semidilute and concentrated polymer solutions has not been thoroughly investigated. To this end, SCF calculations were performed to simulate the effect of increasing the free polymer molecular weight, P, with respect to that of graft polymer, N, the ratio of which yields the dimensionless swelling parameter, P/N. For a system of polymer-grafted nanoparticles of constant graft density and graft polymer molecular weight, increasing P/N is equivalent to moving horizontally in Figure 1 across the regions of wet and dry brushes or where P/N < 1.0 to P/N > 1.0, respectively. Figure 4 shows that within the wet brush region for P/N < 1.0 soft, repulsive interparticle interactions are predicted, indicating that based on χ the particles should remain stable in good, theta, and marginally poor solvents. Figure 5, in contrast, shows that for P/N > 1.0 or in the dry brush region the interaction potentials have attractive minima, indicating that the nanoparticles should aggregate and become unstable irrespective of solvent quality. On the basis of the predictions in Figures 4 and 5, solvent quality, i.e., good, theta, and sparingly soluble or marginally poor solvents, should not affect the stability of polymer-grafted particles in semidilute and concentrated polymer solutions. To investigate this prediction, three sets of experiments were used. First, the stability of PDMS-g-silica nanoparticles was quantified in bromocyclohexane, a theta solvent for PDMS, to determine the theta (48) Scheutjens, J. M. H. M.; Fleer, G. J. Adv. Colloid Interface Sci. 1982, 16, 361–380. (49) Fleer, G. J.; Scheutjens, J. H. M. H. Croat. Chem. Acta 1987, 60(3), 477– 494.

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Figure 4. Interaction potential between surfaces with graft PDMS of molecular weight N = 4 kg/mol in a solution of PDMS of molecular weight P = 2.05 kg/mol and volume fraction of φp = 0.6 as a function of separation distance H. Interaction potentials are predicted to be repulsive for all solvencies within the complete wetting region, P/N < 1.0.

Figure 5. Interaction potentials as a function of separation distance H for surfaces with graft PDMS of molecular weight N = 4 kg/mol in a solution of PDMS with molecular weight of P = 11.3 kg/mol and volume fraction of φp = 0.6. Interaction potentials are predicted to be attractive for all solvencies within the incomplete wetting region, P/N > 1.0.

temperature (TΘ) for the suspension, denoting the transition from good-to-poor solvent quality. Second, the stability of PDMS-gsilica nanoparticles was quantified with respect to the theta temperature to determine the impact of theta solvents on nanoparticle dispersion in semidilute and concentrated PDMS/bromocyclohexane solutions. Third, to further investigate how solvent quality affects nanoparticle stability, visual studies of the PDMS-g-silica nanoparticles were carried out within a variety of different semidilute and concentrated PDMS/solvent solutions. 3.2. Determination of the Theta Temperature of PDMSg-Silica in Bromocyclohexane. DLS measurements and were performed to determine TΘ for the PDMS-g-silica nanoparticles with graft polymers of N = 18 kg/mol in bromocyclohexane. Both sets of experiments were carried out by varying the solution temperature from T = 10.0-60.0 °C with a resolution of 0.1 °C. Figures 6 and 7 show the autocorrelation functions g1(τ) calculated from the DLS measurements that were used to detect the TΘ at which the PDMS-g-silica nanoparticles aggregate in bromocyclohexane. The g1(τ) at T=19.6 °C shown in Figure 6 does not change over time, indicating that the particles were stable. This DOI: 10.1021/la102401w

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Figure 6. Autocorrelation functions with respect to time for 18 kg/ mol PDMS-g-silica nanoparticles in bromocyclohexane at a temperature of T = 19.6 °C. Particle volume fraction φn = 0.001 25; scattering angle θ = 90°. Overlapping autocorrelation functions indicate particles are stable and disperse in solution.

Figure 7. Autocorrelation functions with respect to time for 18 kg/ mol PDMS-g-silica nanoparticles in bromocyclohexane at a temperature of T = 19.5 °C. Particle volume fraction φn = 0.001 25; scattering angle θ = 90°. Autocorrelation functions shift to right with time indicative of particle aggregation.

was confirmed at T = 19.6 °C in Figure 8 by calculating the hydrodynamic radius of the particles, Rh, from the g1(τ) using eqs 3-5, which yields Rh = 125 nm, a little greater than the bare silica obtained from SEM in Figure 2, due to the presence of the PDMS grafts and hydrodynamic solution layer around the particles. Ultimately, we found that all PDMS-g-silica/bromocyclohexane suspensions remained uniformly dispersed from T = 19.6-60.0 °C. However, at T = 19.5 °C, Figure 7 shows that the g1(τ) shift toward increasing correlation time, τ, indicative of increasing particle size, corresponding to the aggregation of the PDMS-gsilica nanoparticles. Particle aggregation is observed in Figure 8 where the rate of the increase in Rh, i.e., the aggregation rate, increases dramatically with decreasing temperature over a 0.2 °C range from 19.5 °C down to 19.3 °C. The elevation in the 16742 DOI: 10.1021/la102401w

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Figure 8. Hydrodynamic radii (Rh) as a function of time (t) and temperature (T ) for the 18 kg/mol PDMS-g-silica nanoparticles in bromocyclohexane. Particle volume fraction φn = 1.25  10-3.

aggregation rate of the PDMS-g-silica nanoparticles is indicative of a worsening solvent quality between PDMS and bromocyclohexane, resulting in stronger interparticle attractions as supported by the SCF calculations in Figure 3 for χ > 0.5. Thus, on the basis of DLS studies, the theta temperature for the PDMS-g-silica nanoparticles in bromocyclohexane is TΘ = 19.6 °C. It should be noted that the particles redispersed upon heating the suspensions above T = 19.5 °C; therefore, the TΘ is an upper critical solution temperature (UCST). Further, the observed UCST for the graft PDMS is lower than the literature value of 28 °C for free PDMS chains in bromocyclohexane because tethering the graft layer at one end reduces its conformational entropy in comparison to the free polymer.50 3.3. Stability of the PDMS-g-silica Nanoparticles in PDMS/Bromocyclohexane Solutions. Subsequently, visual observations and DLS measurements were used to quantify the effect of solvent quality on the stability of PDMS-g-silica nanoparticles in semidilute and concentrated PDMS/bromocyclohexane solutions. Two sets of sample were prepared: one with the graft polymers longer than free polymers (P/N < 1.0) and other with the graft polymers shorter than free polymers (P/N > 1.0). All experiments were repeated in triplicate in which the temperatures of the solutions were varied from T = 10-40 °C to elucidate how good and poor solvent conditions (i.e., above and below TΘ) affect particle dispersion in semidilute and concentrated polymer solutions. For systems with P/N < 1.0, silica nanoparticles with PDMS grafts of N = 4 kg/mol were dispersed in PDMS/bromocyclohexane solution with P = 2.05 kg/mol and φP = 0.6. For systems of P/N > 1.0, the nanoparticles with same PDMS grafts of N = 4 kg/mol were placed in a higher molecular weight PDMS/ bromocyclohexane solution with P = 11.3 kg/mol and φp = 0.6. The particle volume fraction was held constant at dilute concentrations of φn = 1.25  10-3 for all samples. Figure 9 shows the autocorrelation functions g1(τ) with respect to time for N = 4 kg/mol PDMS-g-silica nanoparticles in (P = 2.05 kg/mol) PDMS solutions at T = 10 °C. The g1(τ) did not change with time, indicating that within the complete wetting region (P/N < 1.0) varying the solvent quality (or temperature of a theta solvent) did not affect the dispersion of PDMS-g-silica nanoparticles in semidilute and concentrated polymer solutions. (50) Rasmusson, M.; Vincent, B. React. Funct. Polym. 2003, 58, 203–211. (51) Maas, J. H.; Fleer, G. J.; Leermakers, F. A. M.; Cohen Stuart, M. A. Langmuir 2002, 18, 8871.

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Figure 9. Autocorrelation functions with respect to time for the 4 kg/mol PDMS-g-silica nanoparticles in 2.05 kg/mol PDMS/bromocyclohexane solutions at T = 10 °C. Particle volume fraction φn = 0.001 25; PDMS free polymer volume fraction φp = 0.6; scattering angle θ = 45°. Overlapping autocorrelation functions indicate that particles are stable within complete wetting region, P/N < 1.0.

The results in this figure are representative of those obtained across T = 10-40 °C for P/N < 1.0. Figure 10 shows the g1(τ) as a function of time for N = 4 kg/mol PDMS-g-silica nanoparticles in P = 11.3 kg/mol solutions at T = 10 °C. The g1(τ) shift to the right with increasing time, indicating that the PDMS-g-silica nanoparticles aggregated in the incomplete wetting region (P/N > 1.0) of the semidilute and concentrated PDMS/bromocyclohexane solutions. This trend is representative of the experiments from T = 10-40 °C for P/N > 1.0. We did not quantify the nonmonotonic behavior observed in the autocorrelation functions at later time (e.g., t = 15 min) as we were interested in the initial aggregation of primary particles, whereas the change in the decay of the autocorrelation function toward higher correlation time is indicative of the formation and diffusion of particle flocs. Figure 11 shows the particle size (Rh) as a function of time at different temperatures for PDMS-g-silica nanoparticles in PDMS/ bromocyclohexane solutions. Rh was constant over time for particles within the complete wetting region (P/N < 1.0); thus, these particles were stable above and below TΘ or, alternatively, in good, theta, and marginally poor solvent conditions. In contrast, Rh increased with time for particles outside the complete wetting (P/N > 1.0), indicating that particles were unstable under similar conditions. The variations in particle size in Figure 11 at and beyond time t = 2.5 min are most like due to the formation of flocs caused by rapid particle aggregation as discussed in the next section. We observed similar trends in visual studies, that is, particle stability for P/N < 1.0 and instability for P/N > 1.0 for the PDMSg-silica nanoparticles in semidilute and concentrated PDMS solutions in the following marginally poor solvents for PDMS: ethanol, 1-propanol, 1-butanol, and tert-butanol. The Flory parameters for the solvents range from χ = 0.8-2.0. These results along with those in bromocyclohexane for nanoparticles in PDMS solutions with N > P or N < P are in accord with the SCF predictions in Figures 4 and 5 as well as with our previous findings for PDMS-g-silica in semidilute and concentrated PDMS solutions with a good solvent,5 indicating that interfacial wetting controls particle stability in good, theta, and sparingly soluble or marginally poor solvents. 3.4. Kinetic Stability: A Stability Ratio Analysis. The kinetic stability of the PDMS-g-silica nanoparticles in semidilute and concentrated PDMS/bromocyclohexane solutions was Langmuir 2010, 26(22), 16737–16744

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Figure 10. Autocorrelation functions with respect to time for the 4 kg/mol PDMS-g-silica nanoparticles in 11.3 kg/mol PDMS/bromocyclohexane solutions (φp = 0.6) at T = 10 °C. Particle volume fraction φn = 0.001 25; PDMS free polymer volume fraction φp = 0.6; scattering angle θ = 45°. Autocorrelation functions shift to right with time indicative of particle aggregation within the incomplete wetting region, P/N > 1.0.

Figure 11. Hydrodynamic radii (Rh) as a function of time (t) and temperature (T ) for the 4 kg/mol PDMS-g-silica nanoparticles in PDMS/bromocyclohexane solutions. Particle volume fraction φn = 0.001 25; PDMS free polymer volume fraction φp = 0.6; scattering angle θ = 45°. The particle radius remains constant with time, indicating particle stability for samples with P/N < 1.0, in contrast to samples with P/N > 1.0 where radius increases with time noting particle aggregation.

evaluated from the stability ratio, W, at different temperatures. W is defined as follows:27 W ¼ kd =ks ð4Þ where kd is the rate constant for rapid coagulation based on the Smoluchowski theory 4kB T ð5Þ kd ¼ 3η and ks is the experimental aggregation rate constant determined from the initial slope of the mean apparent hydrodynamic radius vs time in Figure 11 from the equation   1 dRh ð6Þ ks ¼ RN0 dt t ¼ 0 DOI: 10.1021/la102401w

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Table 3. Stability Ratio (W) for 18 kg/mol PDMS-g-Silica Nanoparticles in Bromocyclohexane as a Function of Temperature (T ) T (°C)

W

19.3 19.4 19.5 19.6 19.7 19.8

(2.20 ( 0.04)  103 (2.20 ( 0.04)  103 (1.50 ( 0.03)  104 (3.00 ( 0.06)  104 (5.80 ( 0.01)  104 (1.40 ( 0.03)  105

Table 4. Stability Ratio (W) for 4 kg/mol PDMS-g-Silica Nanoparticles in PDMS/Bromocyclohexane Solutions as a Function of Temperature (T )a W T (°C)

P/N < 1.0

10 (1.51 ( 0.04)  105 20 (5.62 ( 0.01)  105 30 (7.61 ( 0.03)  105 40 (1.10 ( 0.06)  105 a PDMS volume fraction held constant at φp = 0.6.

P/N > 1.0 96 ( 4 108 ( 40 88 ( 15 124 ( 24

where R is the initial radius and N0 is the number density and (dRh/dt)t=0 is the initial slope. For diffusion-limited aggregation (DLA), W ≈ 1, corresponding to particle aggregation rate that is only limited by particle diffusion as every particle collision results in an aggregation event. The crossover from DLA to slow or reaction-limited aggregation (RLA) occurs around W ≈ 104, where energetic barriers between particles reduce the probability of aggregation.6,29 When W . 104, the particles are stable and disperse in solution due to strong, repulsive interactions.27 On the basis of the DLS data, we calculated the stability ratios for PDMS-g-silica nanoparticles in pure bromocyclohexane as well as the PDMS/bromocyclohexane solutions as a function of temperature. Table 3 shows the values of W for the nanoparticles in pure bromocyclohexane, where W is large (W > 104) at and above the theta temperature (T g 19.6 °C) and just below the theta temperature (T = 19.5 °C). The magnitudes of the stability ratios indicate that the particles are largely stabile in solutions above and just below the theta temperature. In contrast, at poor solvent conditions between T = 19.3-19.4 °C the stability ratio at W = 2.2  103 is within an order of magnitude of W ≈ 104, suggesting that particle aggregation is reaction-limited. In line with our findings are those of Huang and Berg29 as well as Zhu and Napper26 in their respective investigations of solvency effects on the stability of silica grafted with polystyrene in cyclohexane29 and polystyrene colloids grafted with poly(N-isopropylacrylamide) in water.26 On the basis of the results of both studies, reduced rate aggregation led to the formation of compact structures,29 which is consistent with reaction-limited aggregation.6 The stability ratios for PDMS-g-silica in PDMS/bromocyclohexane solutions are shown in Table 4 for the particles in the

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complete wetting region (P/N < 1.0) as well as the incomplete wetting region (P/N > 1.0) between T = 10-40 °C. For P/N < 1.0, W is essentially infinite, as the dispersions are stable. For P/N > 1.0 or outside the complete wetting region, the values for the stability ratio range from W = 88-124, but on the basis of associated errors, the ratios are essentially the same at W ≈ 100. Thus, we observed the process of aggregation in concentrated PDMS solutions is an order of magnitude faster than in pure bromocyclohexane; however, both processes are still slower than diffusion-limited aggregation (DLA), characterized by W ≈ 1.

4. Conclusions The aim of this study was to elucidate the effect of solvent quality on the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions. To this end, we used monodisperse silica particles (radius, R = 100 nm) grafted with PDMS chains with molecular weights N = 4-18 kg/mol at a graft density of Σ = 0.17 chains/nm2. The molecular weights of the free PDMS polymers ranged from P = 2.05-11.3 kg/mol with PDMS volume fractions between φp = 0.60-0.96. Bromocyclohexane, a theta solvent for PDMS, was used along with ethanol, 1-propanol, 1-butanol, and tert-butanol, which are all marginally poor solvents for PDMS. The theta temperature for the PDMS-g-silica nanoparticles in bromocyclohexane was established at TΘ = 19.6 °C with visual studies and dynamic light scattering. Below TΘ, the nanoparticles aggregated in bromocyclohexane. In contrast, in semidilute and concentrated PDMS/ bromocyclohexane solutions, we found that the PDMS-g-silica nanoparticles were stable when the graft polymer was longer than the free polymer (P/N < 1.0) with decreasing temperature (or solvent quality) below TΘ. However, the aggregation of the PDMS-g-silica nanoparticles was independent of temperature and solvent quality when the free polymer was longer than the graft polymers (P/N > 1.0). The same correspondence between graft and free polymer molecular weights were found across a range of solvents including ethanol, 1-propanol, 1-butanol, and tert-butanol in semidilute and concentrated PDMS solutions. Overall, our results imply that changing solvent quality from good through marginally poor solvents has minimal impact on particle dispersion in semidilute and concentrated polymer solutions. Thus, we conclude that interfacial wetting, i.e., the penetration of graft polymers by free polymers, still controls the stability of polymer grafted particles in semidilute and concentrated polymer solutions irrespective of solvent quality for good, theta, and marginally poor solvents. Acknowledgment. This work was supported by the National Science Foundation (NSF) in the division of Chemical, Bioengineering, Environment and Transport Systems (CBET-0649081, Small Grant for Exploratory Research, and CBET 0644890, NSF Career Award).

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