The SANS data were collected on the W. C. Koehler 30m SANS facility [12] at the Oak Ridge National Laboratory (ORNL) via a 64 x 64 cm2area detector with cell size ~ 1 cm2and aneutronwavelength, X =4.75 A (AX/X=0.006). Thedetectorwasplaced atvarious sample-detector distances and the data were corrected for instrumental backgrounds and detector efficiency on a cell-by-cell basis, prior to radial averaging, to give a Q-range of 0.005< Q =4nX-1 sin 0<0.05 A-1, where 29 is the scattering angle. The net intensities were converted [13] to an absolute (± 3%) differential cross section per unit sample volume [dE (Q)/dQ in units of cm-1]. The experiments were conducted in the same cell that has been usedextensivelyforpolymer synthesis andprevious SANS experiments [2,3,5] andthebeam passed through two 1 cm sapphire windows, with virtually no attenuation or parasitic scattering. The cross section of the cell filled only with CO2 amounted to a virtually flat background [5] due to critical scattering (~ 0.04 cm-1), which formed only a minor correction to the scattering from the solutions. SAXS experiments were performed on the ORNL 10m SAXS instrument [14,15], with using Cuk 1 radiation (k= 1.54,A) and a 20x20cm2 area detector with cell (element) size ~ 3mm. Corrections for instrumental backgrounds and detector efficiency have been described previously [7,14,15] and the net intensities were radially averaged in the Q-range 0.009 c Q < 0.055 A-1 before conversion to an absolute differential cross section [16]. The SAXS cell was similar to that described earlier [11], with single crystal diamond windows (1 mm total thickness) and path length ~ 0.5 mm.


For a homogenous polymer solution the methodology to extract the Rg, the radius of gyration (i.e. the r.m.s. distance of scattering elements from the center of gravity) and the second virial coefficient (A2), which indicates whether a polymer chain swells or contracts in the presence of a solvent is well established [2,9,17]. These parameters are related to the cross section via where A2 is the second virial coefficient, MWis the (weight-averaged) molecular weight, c is the concentration (g cm-3). Ao is Avogadro's number, and K- [ A(SLD)]2/pp2 A„ is the contrast factor. Experiments were performed on poly(1,1 -dihydroperfluorooctylacrylate) [PFOA] in solution in CO2. pp is the polymer density and we have assumed that the volume from which CO2 is excluded by a PFOA chain in the supercritical fluid is the same as the molecular volume in the solid state. [A(SLD)] is the neutron scattering length density (SLD) difference between PFOA and CO2. This gives K = 7.5 x 10-5 mol cm2g-2 at T = 65 OCand P = 340 bar. SANS has previously been used [2] to measure A2andM, in the ranges 0.6 < 104A2 < 0.25 and 114 < 10-3 Mw < 1000. Small angle scattering is the most direct method currently available to provide such information in supercritical fluids.

The molecular structure of PFOA is indicated in fig. (1) and polymer chain dimensions were derived using both Zimm plots [fig. (1a)] and also by fitting the data to a Debye random coil model [9], with good agreement between the two approaches. As the pressure is reduced, the solubility decreases and the PFOA falls out of solution at the critical, "neutron cloud point" (T = 65 OC,P ~ 300 bar), as indicated [fig. (1b)] by a zero intercept [dS/d0(0)-\ .8 ]. The values of Rg are a function of molecular weight (Mw) and may be summarized as Rg = (0.10 ± 0.02)Mw05. The second virial coefficient decreases with molecular weight, as generally observed for polymer solutions, where A2(Mw) is empirically described by A2 ~Mw-s, with 5 ~ 0.3 in various systems [18]. From the two SANS data

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