Steric Stabilization of Silica Colloids in Supercritical Carbon Dioxide

and Department of Photographic Science and Engineering, Pukyong National University,. Pusan 608-739, South Korea. Silica colloids were sterically stab...
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Ind. Eng. Chem. Res. 2004, 43, 525-534

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Steric Stabilization of Silica Colloids in Supercritical Carbon Dioxide Stephen M. Sirard,† Hector J. Castellanos,† Ha S. Hwang,‡ Kwon-Taek Lim,‡ and Keith P. Johnston*,† Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712, and Department of Photographic Science and Engineering, Pukyong National University, Pusan 608-739, South Korea

Silica colloids were sterically stabilized in supercritical CO2 by end-grafting poly(1H,1Hdihydroperfluorooctyl methacrylate) (PFOMA) onto the particle surfaces. Turbidity versus time measurements were used to determine the CO2 density below which the colloids flocculated, that is, the critical flocculation density (CFD). The CFD was determined as a function of stabilizer molecular weight and temperature as the solvent density was lowered. All of the CFDs occurred above the upper critical solution density for the corresponding finite-molecular-weight stabilizer in bulk CO2 and corresponded more closely with the estimated Θ density. The CFDs decreased (reflecting greater stability) when temperature was increased or the PFOMA molecular weight was decreased. The latter result suggests that, at lower solvent densities, the shorter chains experience better solvation and, hence, provide greater steric repulsion than the longer chains. For the stabilizers of highest molecular weight, the colloids become unstable slightly above the Θ density, possibly as a result of chain contraction from long-range van der Waals forces with the particle surface. Introduction Compressed carbon dioxide (CO2) has emerged as a leading alternative to toxic organic solvents as it is abundant, nontoxic, and nonflammable and its critical points are relatively mild: Tc ) 31 °C, Pc ) 73.8 bar.1-3 Furthermore, because of the compressible nature of supercritical CO2, large variations in its solvent strength can be achieved with small changes in pressure and/or temperature. Many novel colloidal phenomena have been observed using CO2 as the solvent, including the formation and stabilization of water-in-CO2 emulsions and microemulsions,4,5 nanoparticles,6-8 silica suspensions,9,10 and latexes formed by dispersion polymerization.11,12 Furthermore, several applications using CO2 in semiconductor device fabrication are being developed.13 For example, Bessel et al. recently demonstrated the feasibility of a CO2-based chemical mechanical planarization (CMP) process by using a CO2-etchant solution to etch and remove copper metal.14 The “mechanical” aspects of a CO2-based CMP process will require the dispersion and stabilization of inorganic slurries in CO2.9,10 A great challenge in forming dispersed phases in CO2 is obtaining sufficient solvation of steric stabilizers to overcome attractive van der Waals forces between surfaces. Carbon dioxide has no permanent dipole moment and has a low polarizability per volume (i.e., weak van der Waals interactions), causing many nonvolatile compounds to be insoluble. To use CO2 effectively in environmentally responsible processes, sur* To whom correspondence should be addressed. Address: Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712. Tel.: (512) 471-4617. Fax: (512) 471-7824. E-mail: [email protected]. † The University of Texas at Austin. ‡ Pukyong National University.

factants and polymers have to be developed to transport and stabilize insoluble dispersions. It has been found that polymers with low surface tensions, and hence low cohesive energy densities, such as fluorocarbons, fluoroethers, and siloxanes are most effective as CO2 stabilizers at low to moderate pressures.15,16 Recently, several hydrocarbon-based stabilizers have been explored, including polypropylene oxides, branched methylated hydrocarbons, polycarbonate copolymers, and acetylated sugars.17-21 Previous experimental colloidal studies in liquid and supercritical CO2 detected critical flocculation densities (CFDs) where small changes in pressure resulted in sharp decreases in the colloid stability.9,10,22 To theoretically probe colloid stability in compressible solvents, Peck and Johnston combined lattice fluid theory, accounting for compressibility effects, with self-consistent field theory (LF-SCF) to model the structure and interactions between short end-grafted chains in a supercritical solvent.23 Meredith and Johnston extended the LF-SCF24,25 approach to consider homopolymers and copolymers of higher number-average molecular weight (Mn) and also used Monte Carlo simulations26 to examine the effects of solvent quality on the interaction energy between surfaces containing end-grafted polymers in a compressible solvent. These simulations were performed on symmetric systems where the chain segments and solvent molecules had equal volume and energy parameters. Both theory and simulation concluded that the interaction energy between surfaces coated with grafted polymer chains became attractive at solvent densities corresponding to the upper critical solution density (UCSD) for the finite-Mn stabilizersolvent system.24-26 At solvent densities above the UCSD, the chains were well-solvated, and the interaction energy between surfaces containing the end-grafted stabilizers was repulsive. At densities below the UCSD,

10.1021/ie030543s CCC: $27.50 © 2004 American Chemical Society Published on Web 12/18/2003

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Figure 1. Proposed relationship between bulk-phase behavior for the finite-Mn stabilizer and the colloidal CFD for (a) FCO2 > UCSD, FΘ and (b) FCO2 < UCSD, FΘ. I, Phase diagram; II, bulk-phase behavior; III, colloidal stability/flocculation.

solvent was expelled from the chains, resulting in chain collapse and subsequent flocculation of the surfaces. Experimental confirmation of the relationship between the CFD and the stabilizer UCSD for compressible solvents has been mixed. In prior experimental studies, extraneous variables interfered and made a direct comparison to theory and simulation difficult. Often, these systems were physisorbed and dynamic in nature,9,22 and the presence of free polymer often led to unusual stability behavior.9 In other studies, the CFD was found to correspond closely to the UCSD, but it was difficult to determine whether the stabilizers were in the infinite-molecular-weight limit.22 In this limit, the UCSD corresponds to the Θ density (FΘ). One study that investigated a model system was that performed by Yates et al.,10 in which poly(dimethyl siloxane) (PDMS) homopolymers were end-grafted onto silica particles. The silica particles could not be dispersed in pure CO2, even at CO2 densities well above the UCSD for PDMS of finite Mn. Several explanations were given for the discrepancy between experiment and predictions from theory and simulation, such as weak tail-solvent interactions and/or strong chain-substrate interactions. It was also suggested that the stability of these dispersions might correlate with FΘ rather than the UCSD. A Θ-point correlation has been demonstrated in other stabilization studies in conventional liquid solvents using stabilizers with both upper critical solution temperature (UCST) and lower critical solution temperature (LCST) behavior.27,28 Interestingly, recent neutron reflectivity results showed that the CO2-induced extension of PDMS chains end-grafted on silica substrates is limited by strong short- and long-range attractive interactions between the chains and the substrate.29 Thus, these stability issues remain unresolved for compressible solvents. The ability to relate colloidal stability to the bulk-phase behavior of a polymeric stabilizer would be useful for predicting a priori which polymers/surfactants will be effective stabilizers and at what conditions flocculation will occur, as highlighted in Figure 1. Furthermore, these correlations will aid in the design of stabilizers for supercritical solvents.

The main objective of this work is to understand the relationship between CFDs for a model polymerstabilized colloidal dispersion in supercritical CO2 and the bulk-phase behavior of the stabilizing polymer (i.e., UCSD and FΘ). Poly(1H,1H-dihydroperfluorooctyl methacrylate) (PFOMA) was end-grafted onto silica particles, and the stability and dynamics of these model polymergrafted colloids were measured as a function of temperature, CO2 density, and stabilizer Mn. The PFOMAgrafted silica particles offer several advantages over previous colloidal systems9,22 used to probe steric stabilization in CO2 as these particles are hard, relatively monodisperse, and well-defined, given that the stabilizers are covalently attached and unable to migrate along the surface. Furthermore, the molecular weight was varied over a much wider range. The CFDs of the silica/ CO2 dispersions are compared with the UCSDs for the finite-Mn PFOMA homopolymers in CO2, as well as with the estimated FΘ values. PFOMA stabilizers with Mn’s spanning several orders of magnitude were grafted in order to achieve significant variations in the bulk-phase behavior. Correlations between the CFDs and the bulkphase behavior (UCSD and FΘ) are analyzed in terms of previous studies of stabilizer conformation by neutron reflectivity29 and second virial coefficients by SANS,30,31 as well as with previous simulations and theory23,25,26 on the stabilization of colloidal dispersions in compressible solvents. Experimental Section Epoxy-Terminated PFOMA Synthesis. 2-Bromopropionyl bromide (BPB) (Aldrich) and glycidol (Aldrich) were distilled under vacuum. 1H,1H-Dihydroperfluorooctyl methacrylate (FOMA) (SynQuest) was passed through a neutral alumina column, stored over CaH2, and then vacuum distilled before use. Chloroform, pyridine (Junsei), and trifluorotoluene (TFT; Aldrich) were distilled over CaH2 before use. Copper(I) bromide (>99.999%, Aldrich), 2,2′-bipyridine (BIPY; Aldrich), 1,1,2-trichlorotrifluoroethane (Freon-113; Aldrich), and methanol were used as received. 1,2-Epoxypropyl 2-bromopropionate was prepared by reacting glycidol with BPB in the presence of pyridine

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Figure 2. Epoxy-terminated PFOMA.

as a base. In a 250-mL round-bottom flask, 10 g (0.135 mol) of glycidol, 11 g (0.139 mol) of pyridine, and 15 mL of chloroform were chilled to 0 °C. Then, 28 g (0.13 mol) of BPB in 30 mL of chloroform was added dropwise over 1 h under a nitrogen atmosphere. The reaction solution was stirred at room temperature for 15 h and then washed three times with water. The organic phase was dried over magnesium sulfate, and chloroform was removed by evaporation. The resulting liquid was distilled under reduced pressure at 68 °C. Epoxy-terminated PFOMA was synthesized by atomic transfer radical polymerization of FOMA in TFT using 1,2-epoxypropyl 2-bromopropionate as an initiator. In a typical polymerization, 0.035 g (0.244 mmol) of CuBr and 0.115 g (0.736 mmol) of BIPY were charged to a 50-mL round-bottom flask equipped with a stirring bar. The flask was sealed with a rubber septum, and the contents of the flask were placed under vacuum for 2 h. The flask was then back-filled with nitrogen. Seven milliliters of TFT, 0.05 g (0.24 mmol) of 1,2-epoxypropyl 2-bromopropionate, and 9.5 g (20.3 mmol) of FOMA were degassed and added to the flask via a syringe. A previously degassed reflux condenser was attached to the flask, and the system was purged with nitrogen. The reaction proceeded at 110 °C for 5 h under a nitrogen atmosphere. After the reaction mixture had been cooled to room temperature, the product was diluted with Freon-113 and passed through an activated alumina column to remove the catalyst. The polymer was precipitated into methanol, collected, and dried under vacuum. The structure of epoxy-terminated PFOMA is given in Figure 2. The molecular weight was determined with 1H NMR spectroscopy by taking the ratio of the 1,1-dihydro protons (2H at 4.5 ppm) in the fluoroalkyl group to the methylene proton (1H at 2.6 ppm) in the epoxy group. Phase Behavior. Initially, the epoxy-terminated PFOMA was purified by being dissolved in Freon-113 and stirred with activated carbon overnight. The PFOMA/Freon-113/activated carbon mixture was filtered three times to remove the carbon. The Freon-113 was then evaporated, and the resultant PFOMA was dried overnight under vacuum. Phase behavior was determined by first dissolving PFOMA, at the desired concentration, in CO2 with constant stirring in a variable-volume view cell. The temperature was controlled by immersing the cell in a water bath. The pressure was lowered at a constant rate, -6.8 atm/min, and the cloud-point pressure at a given temperature and concentration was determined as the pressure at which the piston was no longer visible. The range in pressure from the observation of slight turbidity to the cloud-point pressure was typically less than 1 atm. Silica Particle Synthesis. Silica particles were synthesized using the Stober method.32,33 Deionized water (Barnstead; Nanopure), ethanol (Aaper), am-

monium hydroxide (EM Science), and tetraethoxysilane (Fluka) were added in predetermined amounts to control the particle size.32 The solution was stirred for 24 h and then centrifuged, and the particles were dried overnight under vacuum. PFOMA Grafting. Ethanol and deionized water were added to make a 95/5 (w/w) solution. The ethanol/ water solution was added to the silica particles, and the mixture was sonicated until all of the particles were dispersed. 3-Aminopropyldimethylethoxysilane (Gelest) was added to the suspension to make a final solution that was 4.5 wt % with respect to the silane. The mixture was sonicated for 15 min, gently stirred for 15 min, and centrifuged, and then the particles were annealed at 110 °C for 20 min. The silica particles were then twice redispersed in ethanol and centrifuged. The clean silane-coupled particles were dried overnight under vacuum. The silica particles were resuspended in ethanol by sonication. PFOMA in 2 times excess (based on the number of reactive sites on the silica surface, ∼4.6 OH-/ nm2)34 was dissolved in Freon-113. The silica/ethanol mixture was added to the PFOMA/Freon-113 solution. The mixture was sonicated for 20 min, and then the ethanol and Freon were evaporated. The PFOMA/silica was heated to ∼120 °C for 24 h under vacuum to react the epoxy end groups on the PFOMA with the amine groups on the silica surface. The silica particles were then twice redispersed in Freon-113 and centrifuged. The grafted particles were again dried overnight under vacuum. A similar procedure was used to graft PFOMA onto the native oxides of silicon(100) wafers. The wafers were initially cleaned using a procedure described elsewhere.29 Isobaric Turbidity Measurements. The PFOMAgrafted silica particles were placed in a high-pressure variable-volume view cell equipped with sapphire windows for turbidity measurements, as described elsewhere.9 Carbon dioxide (>99.99%; Matheson) was charged to the cell using an automated syringe pump (ISCO) to make a 0.04-0.06 wt % silica mixture. The silica was dispersed in the cell by stirring with a Tefloncoated stir bar. The temperature was controlled using heating tape and a PID temperature controller (Omega). When operating at 35 °C, the cell was pressurized to ∼340 atm, and the silica dispersion was stirred for 1 h prior to any measurements. At 50 °C, the cell was pressurized to ∼367 atm, and the dispersion was again stirred for 1 h prior to any measurements. At a given pressure, turbidity vs time scans were collected at a wavelength of 640 nm for 15 min. The turbidity of a dispersion, τ, is a measure of light attenuation caused by scattering35

τ)

()

I0 1 ln L I

(1)

where L is the path length and I and I0 are the measured intensity and the initial intensity, respectively. The stability of the dispersion was determined by taking the initial slope of the τ vs time plot at a given pressure, as described elsewhere.9,10,22 At each condition, the silica/CO2 mixture was stirred for 5-10 min prior to the recording of any measurements; the τ vs time scans were then performed in duplicate, and the slopes were averaged. Dynamic-Pressure Turbidity Measurements. For the dynamic-pressure τ stability measurements, the

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Figure 3. TEM image of bare (ungrafted) silica particles synthesized by the Stober method. Table 1. Characterization of End-Grafted PFOMA on Silicon Wafers Mn (g/mol)

dry thickness (nm)

5000 50 000 100 000

4 10 17

sample loading and initial pressurization and stirring were the same as described for the isobaric stability measurements. At 35 °C, τ was measured as a function of time as the pressure was decreased from 272 to 68 atm at a constant rate of -6.8 atm/min. At 50 °C, τ vs time scans were performed by decreasing the pressure from from 299 to 95 atm at the same rate. Results Silica Synthesis and PFOMA Grafting. The silica particles were characterized by transmission electron microscopy (TEM), as shown in Figure 3, and dynamic light scattering (DLS). The PFOMA was end-grafted onto both silicon wafers and silica particles. Table 1 shows the dry thickness, as measured by ellipsometry, for PFOMA samples of three different Mn’s that were end-grafted onto the silicon wafers. After the grafting reaction is performed, the wafers that were initially hydrophilic (water contact angle < 10°) become hydrophobic (water contact angle > 90°). In addition, ellipsometry and XPS clearly show the presence of a film that is stable to prolonged exposure to a good solvent. The dry brush thickness determined by ellipsometry clearly increases with increasing PFOMA Mn, ranging from 4 to 17 nm. After the PFOMA grafting reaction is performed on the silica particles, the particles can be dispersed and stabilized in a fluorinated solvent, Freon113, for days. DLS on silica particles dispersed in Freon113 containing grafted 5k, 50k, and 100k PFOMA gave average particle diameters of 175, 207, and 201 ( 20 nm, respectively. Phase Behavior. The cloud-point pressures for epoxy-terminated PFOMA at 35 and 50 °C are shown in Figure 4 for various polymer concentrations and Mn’s. The PFOMA Mn’s differ by a couple of orders of magnitude. For both temperatures, the phase boundaries are shifted to higher pressures for larger Mn’s. Furthermore, the pressures required to dissolve the

Figure 4. Pressure-concentration phase diagrams for epoxyterminated PFOMA in CO2 at (a) 35 and (b) 50 °C.

PFOMA at 35 °C are lower than those required at 50 °C. However, when cloud-point densities are plotted instead of pressures, it is observed that lower densities are required to dissolve a given PFOMA Mn at the higher temperature. Others have observed similar temperature trends for polymer phase behavior in CO2.36,37 The UCSP or UCSD corresponds to the maximum in the pressure- or density-concentration phase diagram. The UCSD phase boundary is analogous to the entropically driven lower critical solution temperature (LCST) type of phase separation. As seen in Figure 4, the phase boundary is relatively flat. Table 2 lists the UCSDs for each temperature and PFOMA Mn. For a given Mn, the UCSD decreases as the temperature increases. Furthermore, at a given temperature, the UCSD increases as the PFOMA Mn increases. The UCSD for the 5k PFOMA is noticeably lower than the UCSDs for the polymers with higher Mn’s, whereas the difference between the UCSDs for 50k and 100k PFOMA is much smaller. This indicates that the PFOMA might be approaching the infinite-molecular-weight limit at these higher Mn’s. In this limit, the UCSD corresponds to FΘ. Thus, FΘ can be estimated by extrapolating the UCSDs

Ind. Eng. Chem. Res., Vol. 43, No. 2, 2004 529 Table 2. CFD, UCSD, and GΘ for PFOMA-Grafted Silica Particles and PFOMA Homopolymers Mn (g/mol)

T (°C)

CFDa (g/mL)

UCSD (g/mL)

FΘ (g/mL)

5000 50 000 100 000 5000 50 000 100 000

35 35 35 50 50 50

0.80 0.83 0.83 0.77 0.80 0.80

0.787 0.804 0.812 0.755 0.773 0.780

0.82 0.82 0.82 0.78 0.78 0.78

a

Dynamic-pressure turbidity.

Figure 6. log(|dτ/dt|) versus CO2 density: (9) 50k PFOMA endgrafted silica particles at 35 °C and (b) 100k PFOMA end-grafted silica particles at 50 °C. The CFD is determined as the density at the intersection of the best-fit lines between stable and unstable regimes.

Figure 5. PFOMA/CO2 UCSD versus 1/Mn0.5. Lines are best fits used to extrapolate FΘ.

to infinite molecular weight as shown in Figure 5. The FΘ value determined by this method is 0.82 g/mL at 35 °C and 0.78 g/mL at 50 °C. Similarly to the trend in the UCSD, FΘ decreases as the temperature is increased. The FΘ values agree well with measurements reported by others for the FΘ of a non-epoxy-terminated PFOMA homopolymer, using a sensitive laser technique,37 where FΘ was determined to be ∼0.80 and ∼0.77 g/mL at 35 and 50 °C, respectively.37 Critical Flocculation Densities. Previous studies involving latexes,38 emulsions,37 and inorganic particles9,10 dispersed in CO2 have reported a sharp decrease in the stability of the dispersions upon lowering of the solvent density at a certain CO2 density. This density is known as the CFD and is similar to the critical flocculation temperature (CFT) observed in conventional liquid solvent/colloidal systems. Typically, the CFD is determined by suspending the colloidal particles in CO2 at a given temperature and pressure and measuring τ as a function of time. The stability of the dispersion is related to the initial slope of the τ vs time plot, i.e.

stability ∝

| |

dτ -1 dt tf0

(2)

Figure 6 shows a plot of log(|dτ/dt|) vs CO2 density for the silica particles stabilized with 50k end-grafted PFOMA at 35 °C and with 100k end-grafted PFOMA at 50 °C. For both the 50k and 100k PFOMA-grafted particles, there is a CO2 density at which small decreases in the density result in an increase in the value

of |dτ/dt| by ∼1.5-2 orders of magnitude. Thus, the CFD can be extracted from Figure 6 by the intersection of the best-fit lines through these “stable” and “unstable” regimes. The isobaric τ measurements are challenging in the poor-solvent regime where it often becomes difficult to resuspend the particles and accurately measure the value of dτ/dt because of very rapid particle flocculation and settling. An alternative method for measuring the CFDs of the particles is to measure τ as a function of time while slowly decreasing the pressure and, hence, the CO2 density. In the good-solvent regime, τ will decrease slightly with time as the pressure is slowly decreased as a result of particle settling because the silica particles are denser than the CO2 solvent. At the CFD, an increase in τ is observed because of the dependence of τ on particle concentration and particle size, i.e.27,39

τ ∼ Vp2Np

(3)

where Np is the particle number concentration and Vp is the particle volume. Thus, if two particles flocculate to essentially form a single, larger particle, then Np decreases by a factor of 2, and Vp increases by a factor of 2. According to eq 3, the particle flocculation should cause a net increase in τ. This dynamic approach for determining the CFD is advantageous because it is a continuous measurement, it is much more rapid than the above isobaric method, and it avoids the difficulties associated with redispersing particles in the poorsolvent regions. The results of dynamic-pressure τ measurements at 35 and 50 °C are shown in Figure 7 for the silica particles end-grafted with 5k, 50k, and 100k PFOMA. In Figure 7, τ is multiplied by (FSiO2 - FCO2) to correct for particle settling from the increasing density difference as the CO2 pressure is lowered. The CFD is determined by the intersection of tangent lines through the settling and flocculation regimes as in Figure 6. Table 2 lists the CFDs determined from Figure 7.

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grafted particles corresponds closely to but is slightly below FΘ. Discussion Silica particles dispersed in CO2 without stabilizers will coagulate as a result of the attractive core-core van der Waals interactions. However, the particles might be kinetically stabilized in CO2 when a stabilizer is either physically or covalently attached to the particles and the solvent quality is sufficiently good. Thus, for silica particles containing covalently end-grafted homopolymers dispersed in CO2, the total interaction energy, Φtotal, comprises the attractive core-core van der Waals interactions, ΦvdW, an osmotic term, and an elastic term40,41

Φtotal ) ΦvdW + Φosm + Φels

(4)

The osmotic term, Φosm, accounts for the balance between chain-chain and chain-solvent interactions. The repulsive elastic term, Φels, accounts for the entropy loss upon compression of the stabilizers. The potential energy of attraction for two spheres of equal radius is given by eq 5 as a function of the distance between the particle surfaces42

ΦvdW ) -

[

2r2 2r2 A + 2 + 2 6 d + 4rd d + 4rd + 4r2 d2 + 4rd ln 2 d + 4rd + 4r2

(

)]

(5)

where r is the particle radius, d is the centerline distance of separation between particle surfaces, and A is the Hamaker constant. The Hamaker constant for two identical silica particles interacting across a solvent medium can be estimated using a simplification of Lifshitz theory43

(

)

silica - solvent 3 A ) kT 4 silica + solvent

Figure 7. Dynamic-pressure τ stability measurements for silica particles in CO2 at (a) 35 and (b) 50 °C: ()) particles end-grafted with 100k PFOMA, (0) particles end-grafted with 50k PFOMA, and (O) particles end-grafted with 5k PFOMA. From left to right, the vertical lines correspond to the CO2/PFOMA UCSDs for 100k, 50k, and 5k PFOMA, respectively.

Excellent agreement within 1-2% is observed between the CFDs determined from Figures 6 and 7. As seen in Table 2, the CFDs decrease with decreasing PFOMA Mn. As with the trends in the PFOMA homopolymer UCSDs, the CFDs for the 50k and 100k grafted particles are similar, whereas the CFD for the 5k grafted silica is noticeably lower. In addition, for a given PFOMA Mn, the CFD is reduced when the temperature is increased. Others have also reported a similar temperature dependence on the CFD for other dispersions in CO2.9,22,37 For all of the PFOMA-grafted particles, the CFD occurs at a larger density than the corresponding UCSD. Furthermore, the CFDs for the 50k and 100k PFOMA-grafted silica particles are larger than the estimated FΘ. However, the CFD for the 5k

2

+

3hνe(nsilica2 - nsolvent2)2 16x2(nsilica2 + nsolvent2)3/2 (6)

where  is the dielectric constant, h is Plank’s constant, and νe is the maximum electronic ultraviolet adsorption frequency (typically assumed to be 3 × 1015 s-1).43 Figure 8 shows the attractive ΦvdW potential for three different silica particle sizes at two different CO2 densities. (The pure-component properties used in the calculations can be found elsewhere10,44). To prevent flocculation, Φtotal should be greater than -3/2kT (the energy associated with Brownian motion). In general, Φosm should be greater than ΦvdW to prevent flocculation of the silica particles. In good solvents, Φosm is repulsive and counteracts the attractive ΦvdW. In contrast, Φosm is attractive in poor solvents, aiding particle flocculation. It is important to note that particles can aggregate even though Φosm is repulsive if the repulsive contribution is too weak or too short-range to screen the attractive core-core interactions (i.e., coagulation occurs).27 Therefore, to achieve kinetically stable dispersions with polymeric stabilizers, several criteria have to be satisfied, including (i) the solvent quality must be good enough to screen inter- and intrachain interactions, (ii) the interaction between the stabilizing moiety and the particle surface must not be too strong, and (iii) the stabilizers should have sufficient coverage

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Figure 8. ΦvdW versus particle separation distance calculated with eqs 5 and 6: (- - -) silica particles with 175-nm diameters, (- -) 210-nm particles, and (s) 300-nm particles. For each pair of curves at a given particle size, the potential on the left is for a CO2 density of 0.83 g/mL, and the potential on the right is for a CO2 density of 0.77 g/mL. The horizontal line is the threshold potential for flocculation.

and be long enough to screen the long-range attractive van der Waals interactions between the particle cores.10,45 Previous LF-SCF theory,23,25 Monte Carlo simulations,26 and experiments29 have examined the effect of solvent quality on the structure of end-grafted chains exposed to a compressible solvent. All of these studies showed that the structure and extension of the chains are strong functions of solvent density. For compressible solvents, there is an entropy gain when the solvent expands away from the chains and into the bulk solvent. At high solvent densities above the stabilizer UCSD and FΘ, this entropic driving force is small, and the chains are well solvated and extend into the solvent.46 As the solvent density is lowered, the entropic driving force increases and eventually offsets the enthalpic penalties due to lost solvent-chain interactions. Thus, the solvent expands away from the stabilizers, and the chains collapse as a result of insufficient solvation and screening of inter- and intrachain interactions. This situation is analogous to an entropically driven lower critical solution temperature (LCST) type of phase separation (see Figure 1). Monte Carlo simulations of surfaces with end-grafted stabilizers in a compressible solvent predicted that flocculation of the surfaces would occur at the UCSD for a finite-molecular-weight stabilizer.26 These simulations were performed in the absence of van der Waals forces between the surfaces and on symmetric systems where the solvent and chains had equal energy and volume parameters.

We are interested in how the stability of a polymerstabilized colloidal dispersion is related to the bulkphase behavior of the stabilizer. From Table 2, we observe that, at higher temperatures, the colloids are stable to lower CO2 densities. Previous studies of the stabilization of latexes,22 emulsions,37 and inorganic colloids9 in liquid and supercritical CO2 using adsorbed homopolymer and block copolymer stabilizers also found that higher temperatures lowered the CFDs. Increased temperatures, and hence higher thermal energies, decrease the relative importance of attractive inter- and intrachain interactions. Luna-Barcenas et al. highlighted this effect using Monte Carlo simulations, where they found that the mean-square end-to-end distance of a single polymer chain in a supercritical fluid increased at constant solvent density with increasing temperature.47 Furthermore, temperature effects on the solvent quality of supercritical CO2/polymer solutions have been shown. Neutron reflectivity showed that the extension of end-grafted PDMS chains in CO2 was greater at higher temperatures for a given solvent density.29 SANS experiments by Melnichenko et al. found that FΘ for PDMS in CO2 decreased from 0.97 to 0.87 g/mL when the temperature was increased from 50 to 80 °C.48,49 We find a similar trend for the bulkphase behavior of PFOMA in CO2, where the UCSDs and FΘ decrease as temperature is increased, as shown in Table 2. Similar trends have been observed for the effects of temperature on the CO2 phase behavior of a structurally similar stabilizer, poly(1,1-dihydroperfluorooctyl acrylate) (PFOA).22 Thus, the lower CFDs result from the improved CO2 solvent quality for PFOMA at the higher temperature, which leads to greater chain extension and repulsive osmotic interactions at lower densities. The data in Table 2 indicate that the CFDs for the dispersions occur at densities above the corresponding UCSD. Θ-point correlations for flocculation have been demonstrated for various colloidal systems stabilized with polymers in solvents with both UCST and LCST behavior.27 Table 3 provides a sampling of results from other colloid stability studies in liquid and supercritical CO2. In these previous studies, the CFD always occurs at densities higher than the UCSD. Furthermore, the CFDs typically occur nearer to FΘ. Our CFDs for the model polymer-grafted particles also correspond more closely to FΘ. As seen in Table 3, attempts to stabilize silica particles using end-grafted PDMS stabilizers were unsuccessful, even at densities well above the UCSD for the finite-molecular-weight polymer. Furthermore, neutron reflectivity results showed that the segment density profiles of PDMS brushes end-grafted to a silica surface and exposed to CO2 contained a concentrated regime near the substrate as a result of strong attractive interactions between the PDMS and the substrate.29

Table 3. CFD, UCSD, and GΘ for Various Stabilizer/Colloidal Systems in CO2 stabilizer

T (°C)

Mn × 10-3 (g/mol)

PDMSa

25

10

PDMSa

65

10

PS-b-PFOAb PS-b-PFOAc PFOAc

45 45 65

4.5-b-24.5 4.5-b-24.5 1200

a

Reference 10. b Reference 9. c Reference 22.

(CFD - UCSD) × 102 (g/mL)

(CFD - FΘ) × 102 (g/mL)

>8

-

0.95

>14

-

0.80 0.80 0.75

4 1 1

3 0 0

FΘ (g/mL)

CFD (g/mL)

UCSD (g/mL)

unstable, F < 0.99 unstable, F < 0.93 0.83 0.80 0.75

0.91

-

0.79 0.79 0.79 0.74

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However, the solvated portion of the brush extended sharply into the CO2 in the vicinity of FΘ. Melnichenko et al. have also observed by SANS that free PDMS chains in CO2 expand beyond their unperturbed radius of gyration, Rg, at either a Θ pressure or Θ temperature.48,49 At 65 °C and 340 bar, well below PΘ ≈ 447 bar, Chillura-Martino et al. showed that attractive forces are dominant for PDMS in CO2, as they determined a negative second virial coefficient (A2) using SANS.31 All of these results suggest that better stabilization of PDMS-grafted silica particles can be expected at densities above FΘ. In light of the results in Tables 2 and 3, there is increasing evidence that the limit for steric stabilization of colloidal dispersions in supercritical CO2 will be the Θ point for the free polymer in bulk solution, analogous to what has been found previously for dispersions in conventional liquid solvents.27 One of the novelties of supercritical fluids is that this transition can be induced with changes in pressure and/or temperature. Previous Monte Carlo simulations suggested a correlation between the CFD and the UCSD for a finite-molecularweight polymer.26 However, these simulations were performed only on symmetric systems where the volume and energy parameters were equivalent. Some degree of asymmetry will likely exist in most real polymer/CO2 systems; thus, simulations should be performed in the future on asymmetric systems to relate the CFD to FΘ. The CFDs in Table 2 show an interesting dependence on molecular weight. The CFDs at both temperatures for the highest Mn’s are relatively constant, whereas the CFD for the lowest Mn is significantly lower. According to Napper, for sufficiently high molecular weights, the flocculation condition is independent of the stabilizer molecular weight.27 It is usually assumed that highermolecular-weight polymers are better stabilizers because they can form thicker steric layers and impart a longer-range repulsion to counteract the attractive core-core interactions. Consequently, it is not uncommon to observe coagulation in better-than-Θ solvents when low-molecular-weight stabilizers are used.27 In these cases, the range of steric repulsion is not long enough to screen the attractive van der Waals forces between particles. However, enhanced stabilization with low-molecular-weight stabilizers has been reported in worse-than-Θ solvents.50 From Figure 8, we see that, for 175-nm particles, the attractive potential reaches a value of -3/2kT at a separation distance of ∼10-12 nm. From Table 1, the 5k PFOMA has a dry thickness of ∼4.3 nm, giving a minimum overlap separation of 8.6 nm. As the brush is exposed to increasing CO2 densities, significant chain extension is expected as a result of the improved solvent quality. In fact, spectroscopic ellipsometry shows that the chains have extended to a length of ∼7-9 nm at 35 °C and 68 atm (still well below the UCSP in Figure 4a). Thus, assuming that the thicknesses on the wafers are good estimates of the stabilizer thickness on the particles, the steric layer should have sufficient range to counteract the attractive core-core potential. There are several explanations for the observed Mn dependence on the CFD in Table 2. First, asymmetry between the segment-segment, segment-surface, and segment-solvent interactions could inhibit the chain extension of the high-Mn stabilizers because of longrange van der Waals interactions with the silica surface, similarly to what was observed previously with PDMS,

resulting in flocculation at densities slightly higher than FΘ.29 A second explanation of the Mn dependence could be the variation of A2 with molecular weight. The Θ point for a polymer/solvent mixture corresponds to the condition where A2 vanishes.27 Interestingly, experiments show that A2 is molecular-weight-dependent, i.e, A2 ∼ M-δ, where δ ≈ 0.2-0.3 for high-molecular-weight polymers in good and marginal solvents.51 Furthermore, δ is found to increase as M becomes smaller. Yamakawa et al. reported numerous A2 measurements for polystyrene (PS) and poly(methyl methacrylate) covering a large range of molecular weights and solvent conditions in conventional liquid UCST-type solvents.52,53 They found a strong molecular-weight dependence of A2 for low-molecular-weight (∼103 g/mol) polymers where A2 increased significantly as the molecular weight was decreased. Thus, the temperature at which A2 vanished decreased with decreasing molecular weight. The data were explained quantitatively using the Yamakawa theory, which takes into account the effects of chain ends.52-54 According to this theory, A2 is composed of two contributions, one that does not include the effects of chain ends and vanishes at the Θ condition (i.e., TΘ for infinite molecular weight) and another that includes chain-end effects/interactions and is nonvanishing at the Θ condition and increases with decreasing molecular weight.52,54 Both theory and experiments show that chain-end effects become appreciable for low-molecularweight polymers. Therefore, two cases can be envisioned concerning colloid stabilization in CO2 using low-molecular-weight stabilizers: (i) If the low-Mn stabilizers are too short to screen the attractive van der Waals interactions, then better stabilization will be achieved with longer chains because they win the tradeoff between solvation and screening length; (ii) If the low-Mn stabilizers are thick enough to screen the attractive core-core potential, then according to the molecular weight dependence of A2, the shorter chains might provide stabilization at lower densities than the longer chains because of increased solvation and repulsion. The results in this study would correspond to case (ii). Little work has been done on measuring the molecular-weight dependence of A2 for polymers in supercritical CO2. McClain et al. did show that A2 for PFOA in CO2 (good solvent conditions) increased with decreasing molecular weight, where A2 ∼ M-0.4, for M between 105-106 g/mol.30,31 In light of the results presented in this paper, it would be interesting to determine how A2 varies with M for lower-Mn oligomers in CO2. Conclusions Turbidity versus time measurements were used to determine the stability of silica particles sterically stabilized with end-grafted PFOMA. The particles are stable to flocculation at high solvent densities for all stabilizers, but they exhibit a CFD upon lowering the CO2 density. For all molecular weights, the CFDs decreased with increasing temperature. Higher temperatures decrease the relative importance of attractive intra- and interchain interactions and improve the CO2 solvent strength, leading to greater stabilizer extension and repulsive interactions at lower solvent densities. At a given temperature, the CFD decreased as the PFOMA Mn was decreased for the range of Mn’s studied. This is likely related to the behavior of the second virial coefficient (A2), which is known to increase (become

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more repulsive) with decreasing molecular weight, especially for oligomers. Hence, the lower-Mn PFOMA wins the tradeoff between solvation (favoring short chains) and screening length (favoring long chains), allowing the particles to remain stable at lower CO2 densities. All of the CFDs occurred above the UCSD for the corresponding finite-Mn stabilizer in bulk CO2, instead corresponding more closely with FΘ (i.e., the UCSD for infinite Mn). There is increasing experimental evidence9,10,22,29,31,49 that the limit for polymeric stablilization of colloidal dispersions in compressed CO2 will be closer to the Θ condition (FΘ for infinite molecular weight) than the UCSD for finite-Mn stabilizers. However, for high-molecular-weight stabilizers, the observation that the CFD is still slightly higher than FΘ indicates unusual behavior in compressible supercritical fluids. Asymmetry between the segment-segment, segment-surface, and segment-solvent interactions could lead to chain contraction from long-range van der Waals forces with the particle surface.29 These results indicate that widely available bulk-phase diagrams are useful for selecting polymeric stabilizers for supercritical fluids. However, a modest shift in colloid stability (CFD) relative to FΘ might be expected when there is large asymmetry in the intermolecular interactions. Acknowledgment This work was supported by the STC program of the NSF under agreement CHE-9876674 and the Department of Energy. K.-T.L. acknowledges the support of the Korean-United States Cooperative Science Program of the Korea Science and Engineering Foundation (20015-308-01-2). Literature Cited (1) Eckert, C. A.; Knutson, B. L.; Debenedetti, P. G. Supercritical fluids as solvents for chemical and materials processing. Nature 1996, 373, 313. (2) Taylor, D. K.; Carbonell, R.; DeSimone, J. M. Opportunities for Pollution Prevention and Energy Efficiency Enabled by the Carbon Dioxide Technology Platform. Annu. Rev. Energy Environ. 2000, 25, 115. (3) Wells, S. L.; DeSimone, J. CO2 Technology Platform: An Important Tool for Environmental Problem Solving. Angew. Chem. 2001, 40, 518. (4) Lee, C. T.; Psathas, P. A.; Johnston, K. P.; deGrazia, J.; Randolph, T. W. Water-in-carbon dioxide emulsions: Formation and stability. Langmuir 1999, 15, 6781. (5) Lee, C. T.; Psathas, P. A.; Ziegler, K. J.; Johnston, K. P.; Dai, H. J.; Cochran, H. D.; Melnichenko, Y. B.; Wignall, G. D. Formation of water-in-carbon dioxide microemulsions with a cationic surfactant: A small-angle neutron scattering study. J. Phys. Chem. B 2000, 104, 11094. (6) Holmes, J. D.; Bhargava, P. A.; Korgel, B. A.; Johnston, K. P. Synthesis of cadmium sulfide Q-particles in water-in-CO2 microemulsions. Langmuir 1999, 15, 6613. (7) Ji, M.; Chen, X. Y.; Wai, C. M.; Fulton, J. L. Synthesizing and dispersing silver nanoparticles in a water-in-supercritical carbon dioxide microemulsion. J. Am. Chem. Soc. 1999, 121, 2631. (8) McLeod, M. C.; McHenry, R. S.; Beckman, E. J.; Roberts, C. B. Synthesis and Stabilization of Silver Metallic Nanoparticles and Premetallic Intermediates in Perfluoropolyether/CO2 Reverse Micelle Systems. J. Phys. Chem. B 2003, 107, 2693. (9) Calvo, L.; Holmes, J. D.; Yates, M. Z.; Johnston, K. P. Steric stabilization of inorganic suspensions in carbon dioxide. J. Supercrit. Fluids 2000, 16, 247. (10) Yates, M. Z.; Shah, P.; Johnston, K. P.; Lim, K. T.; Webber, S. Steric Stabilization of Colloids by Poly(dimethylsiloxane) in Carbon Dioxide: Effect of Cosolvents. J. Colloid Interface Sci. 2000, 227, 176.

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Received for review June 30, 2003 Revised manuscript received November 3, 2003 Accepted November 4, 2003 IE030543S