Flory interaction parameter critical

Flory-Huggins interaction parameter critical degree of polymerization (= 2/X) phase separation not observed... 

K 01 0 4 lhody Tp S, t) X Xb Xc overlap volume iraction. laimensioniessi. d. overlap volume fraction for /9-solvents, [dimensionless], p. 172 semidilute-concentrated crossover volume fraction, [dimensionless], p. 180 crossover volume fraction in mean-field theory, [dimensionless], p. 181 probability for segment s to still be part of the tube at time t, [dimensionless], p. 405 Flory interaction parameter, [dimensionless], p. 142 Flory interaction parameter for a binodal, [dimensionless], p. 150 critical interaction parameter, [dimensionless], p. 152 Florv interaction oarameter for a soinodal. 

We present here a forward recoil spectrometry (FRES) study of thermodynamic slowing down" of mutual diffusion in isotopic polymer mixtures and of the diffusion of homopolymers into symmetric diblock copolymer structures. The measurements of "thermodynamic slowing down" were performed on binary mixtures of normal and deuterated polystyrene (PS). Both the Flory interaction parameter, the upper critical... 

The Flory-Huggins theory of polymer solutions has been documented elsewhere [26, 27]. The basic parameters necessary to predict polymer miscibility are the solubility parameter 6, the interaction parameter %, and the critical interaction parameter ( ) . 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

Calculate the for solutions in chlorobenzene of polystyrenes with molar weights of 2 x 105,5 x 105 and 106 g/mol the intrinsic viscosity, the critical concentration, the swelling factor, the hydrodynamic swollen volume, the second virial coefficient and the Flory-Huggins interaction parameter. 

In the early 1940s, Flory and Huggins proposed, separately, a lattice model to describe polymer solutions and introduced the interaction parameter This parameter increases as solvent power decreases hence, a thermodynamically good solvent is characterized by a low interaction parameter. In practice, most polymer-solvent combinations result in x-values ranging from 0.2 to 0.6. Moreover, the theory predicts that a polymer will dissolve in a solvent only if the interaction parameter is less than a critical value Xc. which, at a given temperature, depends on the degree of polymerization (x) of the dissolved polymer ° ... 

Schultz, A.R. and Flory, P.J., Phase equilibria in polymer-solvent systems. II. Thermodynamic interaction parameters from critical miscibility data, J. Am. Chem. Soc., 75, 496, 1953. 

FIGURE 6.17 Solubility of a homopolymer according to the Flory-Huggins theory. Variables are the excluded volume parameter ft (or the polymer-solvent interaction parameter y), the net volume fraction of polymer q>, and the polymer-to-solvent molecular volume ratio q. Solid lines denote binodal, the broken line spinodal decomposition. Critical points for decomposition (phase separation) are denoted by . See text. 

Block and graft copolymers based on two or more incompatible polymer segments phase separate and self-assemble into spatially periodic structure when the product ixN) of the Flory-Huggins interaction parameter and the total number of statistical segments in the copolymer exceeds a critical value [25,262,263]. Since the incompatible... 

Here ct,2 and XerSre the composition and the interaction parameter at the critical point. Having a number of critical data it is possible to obtain the temperature dependence of Xs/mma because at the critical point Xs/mma = Xc Critical data were also obtained for the blend systems PS-1.39K/PMMA-6.35K and PS-1.39K/PMMA-12K. Figure 11 shows the temperature dependence of Xs/mma obtained by phase diagrams and applying the FH theory. Furthermore, a number of literature data and the temperature dependence of Xs/mma calculated with Flory s EOS theory can be seen and will be discussed below. Using Flory s EOS the interaction parameter X12 is ... 

The critical value for the Flory-Huggins interaction parameter is obtained from the combination of Equations (6-94) and (6-95) ... 

The Flory-Huggins interaction parameter can, however, exceed its critical value above a certain temperature for solutions in poor solvents. In this case, separation into two liquid phases also occurs with crystalline... 

The Flory-Huggins interaction parameter can, however, exceed its critical value above a certain temperature for solutions in poor solvents. In this case, separation into two liquid phases also occurs with crystalline polymers, as is shown, for example, by poly(ethylene) in nitrobenzene at mass fractions W2 < 0.75 (Figure 6-19). On the other hand, separation into one crystalline and one liquid phase is observed at poly(ethylene) concentrations W2 > 0.75. In xylene, separation into one liquid and one crystalline phase always occurs, no matter what the mass fraction is. 

Further improvements of Flory-Huggins theory (the third approximation) were possible. after development of experimental methods to determine the phase separation region, the spinodal, the critical point, and Flory-Huggins interaction parameter. 

To verify the theory of phase sepau ation in the system P+LMWL, it was required to improve the methods for determining the characteristic values and phase separation functions, first of all, of the phase separation boundary, the spinodal, the critical point and the Flory-lluggins interaction parameter. The development of experimental methods ha.s lead, in turn, to new modifications of the theory, in particular, to its second and third approximations. 

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