## O

points, the exponent is 8 = 0.4 ± 0.1 for PFOA in supercritical CO2.Thus, within the experimental error PFOA in CO2 in this range of temperature and pressure behaves similarly to polymers in "good" organic solvents (e.g. polymethyl methacrylate in acetone [18]).

### Block Copolymer Micelles

Fig. 2 shows a plot ofKc[d Z /dQ(0)]-1 vs c for poly(hexafluoropropylene oxide) (PHFPO or KrytoxTM). The SANS-Mw is in good agreement with the nominal Mw given by the manufacturer (16k/mol) and A2is zero within the experimental error, indicating that the polymer coil adopts the unperturbed chain dimensions. In general, Rg ~ Mw0 5 and for c < 0.093 g cm-2, Rg is in the range 26-33A, giving Rg/Mw0.5 ~ 0.24 A(g mo1)-0.5 compared to 0.45 for polyethylene, 0.35 for polypropylene, 0.27 for polystyrene and 0.1 A (g mo1)-05 for PFOA. Thus, polyethylene molecules have the largest size for a givenMw,because all the CH2groups are in the backbone. As the size of the pendant group increases, the fraction of the chain in the backbone decreases. As the radius of gyration depends predominantly on the length and stiffness of the backbone, the overall size of the coil for a given (total) molecular weight becomes smaller.

The SANS data were modelled as a system in which core-shell micelles interact in a solvent medium and, assuming no orientational correlations, the differential scattering cross section is given by

where Np is the number density of particles, S(Q) is the structure function arising from interparticle scattering and B is the coherent background (~ 0.04 cm-1) from CO2.For the dilute solutions considered here, interparticle interactions may be neglected, and the interparticle structure function is similar to that of a dilute gas (S(Q) = 1). For a core/shell micelle the intraparticle term in Equation (2) may be obtained by integrating over a distribution of core radii with a normalized frequency of f(Ri) and the structure function of a particle with (inner) core radius R1and (outer) shell radius R2is given by [3]

Pi, p2 are the core/shell SLDs and several particle shapes were used to calculate P(Q). The best fits were given by a spherical core-shell model with a Schultz distribution [3] ofparticle sizes and the aggregation number (i.e. the number of molecules per micelle, Nagg), the shell-SLD (p2) and the breadth parameter in the Schultz distribution (Z) were adjusted to fit the data. Ri and R2 were calculated from the fitted parameters.

Styrene has been polymerized in CO2 using polystyrene-b-PFOA (PS-b-PFOA) surfactants, which give rise to quantitative yields (>90%). Samples are designated by the number averaged molecular weights of the blocks (in k Daltons) and figure 3 illustrates the ghenomenon of micelle formation for the 3.7k/16.6k PS-b-PFOA copolymer [(4% w/v, 65 OC, 343 bar (5Kpsi)], caused by the aggregation of the block copolymers in solution. The cross section is much higher than for single molecules, indicating that the particle has a larger molecular mass than the unimer. The subsidiary maximum at Q = 0.04 A-1 is related to the spherical shape and the core-shell morphology of the particle. When the PS-block size was kept constant, and the PFOA-block size was increased by a factor of ~ 4, the aggregation

Figure 3.d X/d H(Q) for 3.7k/16.6k polystyrene-PFOA block copolymer and fit to core-shell model (4% w/v, 65 OC,344 bar).

Figure 3.d X/d H(Q) for 3.7k/16.6k polystyrene-PFOA block copolymer and fit to core-shell model (4% w/v, 65 OC,344 bar).

number ( Nagg) was shown to be relatively independent of the PFOA (corona) block length (MW), as predicted by Halperin and coworkers [ 19]. Figure 4 shows a comparison of the independently calibrated SAXS and SANS data taken from 3.7k/40k block copolymer solutions at similar experimental conditions and the values of Ri and Nagg, resulting from model fits (Figure 4) are virtually identical. This forms a useful cross check on the methodology, as the contrast factors are quite different for SANS and SAXS. However, SANS has the additional advantage of using isotopic substitution to vary the contrast (see below) and the results [6] indicate that the adjustable parameters are insensitive to changes in concentration, as expected in the "dilute solution" limit. The core radius (Ri) increases with PS-block length and similarly, R2 appears to increase with the corona block length [6], although the dependence is not strong.

Polystyrene oligomer (Mn = 0.5K g mole-1) was added to the block copolymer solutions to study the solubilization of homopolymers within the micelles. Separate concentration series were run for normal (PSH) and deuterated (PSD) oligomers and the isotopic difference between the oligomers should have a major effect on the scattered

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