Chi parameter

Polymer simulations can be mapped onto the Flory-Huggins lattice model. For this purpose, DPD can be considered an off-lattice version of the Flory-Huggins simulation. It uses a Flory-Huggins x (chi) parameter. The best way to obtain % is from vapor pressure data. Molecular modeling can be used to determine x, but it is less reliable. In order to run a simulation, a bead size for each bead type and a x parameter for each pair of beads must be known. 

The CHI parameter approximates the percentage of organic modifier in the mobile phase for eluting the compounds and can be used for high-throughput determination of physicochemical properties (50-100 compounds per day). CHI is a system property index, and depends on the nature of the stationary phase and the organic modifier as well as the pH of the mobile phase for ionizable compounds. 

The second approach using gradient mode to assess log P values first proposed by Valko et al. is the use of the chromatographic hydro phobicity index (CHI) obtained from a single fast gradient run (<15 min) [103]. Since CHI is considered as a relevant parameter for QSAR studies, it was demonstrated using LSER that differences occur between CHI parameters and true log P because C HI (and log k) are sensitive to H-bond acidity ability whereas log P is not [104]. Thus, CHIs have to be used with precaution. 

Here F(q) is a function of radius of gyration and composition of the block copolymer. This equation should be compared with eqn 2.11 for block copolymer melts. The effective chi parameter in semidilute solution is X N = %abiV0(1+ )/(,v l), where yAB is the chi parameter for the block copolymer, v is the Flory exponent (v = 0.588 in good solvents) and z = 0.22 (Fredrickson and Leibler 1989 Olvera de la Cruz 1989). The function F q) has a minimum, and hence S(<7)-1 has a maximum, at q = q, which is independent of % and thus temperature. Empirically, is found to be inversely proportional to temperature... 

Consider one of the ternary blend mixtures described in the previous section. Data from sample 3 were taken from room temperature to 160°C and are analyzed [43], using the RPA formalism for a ternary blend. The three components are called A PSD, B PVME, C PSH. Also, temperature dependencies for the two known chi parameters (Xpsd/pvme/vo and Xpsd/psh/vo) were assumed [31, 32] ... 

For the Flory-Huggins model of the activity, Equations (2C-4)-(2C-6), the data are reported in terms of a concentration dependent chi parameter. Data must be taken or extrapolated to the 6 = 0 limit in order to remove solution structure effects. 

This example shows how to calculate a weight fraction activity coefficient from the Flory-Huggins method when the chi parameter is known. 

Figure 9.2 Schematic phase diagram of a polymer/solvent mixture, where y is the Flory chi parameter, and xe = 1/2 is x at the theta temperature. The quantity Xe X along the ordinate is a reduced temperature, and is the polymer volume fraction. CP is the critical point, and BL is the binodal line. SSL and KSL are the static symmetry line and the kinetic symmetry line, respectively. These lines define the phase-inversion boundaries during quenches. In quenches that end at the right of such a line, the polymer-rich phase is the continuous phase, while to the left of the line the solvent-rich phase is the continuous one. SSL applies at long times, after viscoelastic stresses have relaxed, while KSL applies at shorter times before relaxation of viscoelas-...

The tendency of differing blocks to microseparate from each other is quantified by Flory s chi parameter /, introduced in Chapter 2. An increasing, positive value of x implies an increasing tendency for the two chemically dissimilar species to segregate from each other. As discussed in Section 2.3.1.2, for a blend of two different homopolymers (A and B) of equal degree of polymerization Na — Ag at a 50/50 composition, the Flory-Huggins theory predicts that phase separation should occur at a critical value of Xc = For block... 

The absolute magnitude of the CHI parameter depends on the values assigned to the set of standards. The method has the advantage that, once the calibration equation has been established, the retention parameter is obtained from a single fast gradient run, thus saving time and solvents. The CHI parameter has been reported to correlate satisfactorily with log P. 

VAB(r) being the intermolecular potential. Working out Eqs. (129)—(132) with this closure, one finds with some algebra that the effective % parameter becomes strongly renormalized in comparison to the mean field or bare chi parameter xo = pjvAB(r) dr/k T,... 

Qualitatively, a strong reduction of the effective chi-parameter in solutions has indeed been seen in experiments [242], although a quantitative explanation of these data is still lacking. 

Correlation effects in dense blends can also be discussed in terms of a screening effect of the interactions [243] which shows that the coil radii depend on both volume fraction and the chi-parameter of the blend, unlike the simple version of the RPA discussed in Sect. 2.3. We shall return to such effects when we discuss the Monte Carlo simulations (Sect. 4). 

Fig. 22a. Plot of SCO li(q- 0) vs e/kBT for the model of Fig. 19b, N = 128, L = 80 and several choices of m = < M ) as indicated in the figure. For m = 0 the extrapolated curve for L- oo is shown as a full curve, while the linear extrapolations are shown as dash-dotted straight lines. For m = 0.3 and m = 0.S the linear extrapolations ate also shown, the actual temperatures of the coexistence curve being shown by stars in all three cases. Note that in this immediate vicinity of Tc all the curvature seen in the data (which are generated by histogram extrapolation) is due to finite size effects, b Plot of (1 — ()>,) 2/Scoii(q = 0) vs e/kBT for the model of Fig. 3, N = 32, < >v = 0.6, and various choices of the volume fraction <)>a/(1 — v) as indicated. Curves are a guide to the eye only. Since data over a very wide regime of temperatures are shown, curvature is due to an effective renormalization of the effective chi-parameter with temperature. Both the location of Tc and of the spinodal temperatures are shown with arrows. From Sariban and Binder [265]...

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