GraphsfromLecture4

# GraphsfromLecture4 - the square of the at is the physical...

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Unformatted text preview: the square of the at is the physical Jerature TS as a (4.105) e three different E for this blend. observed cloud g the scattering in SANS) which er, in practice concentration nee volume v0 Polymer solutions In this chapter, our understanding of ideal chain conformations (Chapter 2), real chain conformations (Chapter 3), and thermodynamics (Chapter 4) will be combined to describe the conformations of polymer solutions at all concentrations and temperatures. In this chapter, the focus is on semidilute and concentrated solutions that span the large range of concentrations between dilute solutions and melts. 5.1 Theta solvent The phase diagram for a polymer solution is shown in Fig. 5.1. Here the attention is focused on the case where A = 0 and B > 0 in Eq. (4.31), which is the most common case for polymer solutions. The B—temperature sep- arates the poor solvent” (bottom) half of the diagram from the good solvent (top) half. At this special temperature (T =0) the interaction parameter X = 1/2 and the excluded volume is zero [see Eq (4.72)]: T—B v= (1—2X)b3=Tb3 =0. (5.1) ll‘l TV Dilute \ it ’ good “(1" ,z’ (swollen) 'U D T E g .............................................................. .35: ..... "+9 .... ..1/2 Dilute poor globules) Two-phase (is! 1‘ Fig. 5.1 Phase diagram for polymer solutions with a UCST. The solid curve denotes the bimodal and phase separation occurs for polymer solutions with T and p below the binodal. The dashed curve is the low temperature boundary of the semidilute good solvent regime. Ion, AND DIFFUSION of vitrification. ——— lines riZontal lines are classical ler, Palym. Comm, 29, binodal line, may 6 solvent at high eVer, if the polymer polymer solution tlon (see Section "ation binodal line When the vitri— rdinary tie lines far slower than diffuse into the integrates, the 4.2 REGIONS OF THE POLYMER—SOLVENT PHASE DIAGRAM 151 «90, = (DV)‘3/5N'4/5 semidilute (psm = p'av marginal Figure 4.5 illustration of the positions of the ﬁve stable solution regimes: ideal, dilute, semi- dilute, marginal, and concentrated, and the phase separated region, hatched, for polymer solu— tions. The dependencies of the various crossovers on N, p, and v and the dependence of the correlation lengths on the concentration (p are indicated. (G. J. Fleer, M. A. Cohen Stuart, J. M. H. M. Scheutjens, T. Cosgrove, and B. Vincent, Polymers at Interfaces, Chapman and Hall, London, 1993). ' Notation: (p = volume fraction, 5: correlation length, p = C_/6, v = excluded volume parame- ‘ ter, 1 - 2x, N= number of bonds per chain, 75: Flory—Huggins polymer-solvent interaction para meter, vc = cross-over from swollen to ideal. Subscripts: cr = critical, i = ideal, d = dilute, s = semi-dilute, m = marginal regime, c = concentrated regime, 0v: cross-over from dilute to semi-dilute, cp = cross-over from concentrated to phase separated, sm = cross-over from semi-dilute to marginal, mc: cross-over from marginal to concentrated. The concentration of the ﬁnal solution, of course, depends on the relative proportions of polymer and solvent. In Chapter 3 the solutions were assumed to be dilute, generally below 1% concentration, because this is required to obtain molecular weights. However, many solutions are used in the 10% to 50% concentration range. More concentrated systems are better described as plasticized polymers. Daoud and Jannink (11) and others divided polymer—solvent space into several regions, plotting the volume fraction of polymer, go, vs the excluded volume parameter, v (see Figure 4.5). Each of these ...
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## This note was uploaded on 11/29/2010 for the course BME 104 taught by Professor Kasko during the Fall '10 term at UCLA.

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GraphsfromLecture4 - the square of the at is the physical...

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