Polystyrene Flory-Huggins value

We calculated the microphases of a thin film of neat three-block polystyrene - polybutadiene - polystyrene (SBS) deposited on a solid substrate [33]. The parametrization protocol was somewhat different from the case of L64, now using data on the microphase-separation temperature of a bulk melt to determine the critical Flory-Huggins value, rather than solution data. 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

Fig. 61. Correlation of the Flory-Huggins interaction parameter, %, for polystyrene-liquid systems at 25 °C with the volume fraction (v) of polymer in the system. The filled circles represent experimentally determined data recorded in Table XIX of Ref. 43. The empty circles represent estimations by interpolation or extrapolation of the linear relationships established on the basis of the experimental data shown. The value for x reported for acetone at v = 1 is placed in brackets to indicate that this point seems too high, and therefore it was not included in the data set used to establish by linear regression the equation shown for this linear relationship...

Modifications to the MKA equation have been proposed to take into account the swelling pressure and the dependence of the interfacial tension (y) and the Flory-Huggins interaction parameter (/) on particle size [62, 63] as well as the presence of adsorbed surfactant on particle swelling [64, 65], These modifications have allowed to obtain better agreement between theory and experimental data for the swelling of polystyrene particles using reasonable parameter values. 

Precipitation data for several systems have proved the validity of Equation 8.47. Linear plots are obtained with a positive slope from which the entropy parameter /i can be calculated, as shown in Figure 8.4. Typical values are shown in Table 8.1, but /i values measured for systems such as polystyrene-cyclohexane have been found to be almost ten times larger than those derived from other methods of measurement. This appears to arise from the assumption in the Flory-Huggins theory that is concentration independent and improved values of /i are obtained when this is rectified. 

Figure 4.24. Diffusion coefficients as functions of the composition in the miscible blend polystyrene-poly(xylenyl ether) (PS-PXE) at a temperature 66 °C above the (concentration-dependent) glass transition temperature of the blend, measured by forward recoil spectrometry. Squares represent tracer diffusion coefficients of PXE (VpxE = 292), circles the tracer diffusion coefficients of PS and diamonds the mutual diffusion coefficient. The upper solid line is the prediction of equation (4.4.11) using the smoothed curves through the experimental points for the tracer diffusion coefficients and an experimentally measured value of the Flory-Huggins interaction parameter. The dashed line is the prediction of equation (4.4.11), neglecting the effect of non-ideality of mixing, illustrating the substantial thermodynamic enhancement of the mutual diffusion coefficient in this miscible system. After Composto et al. (1988).

Figure 6.17. The excess of styrene-2-vinyl pyridine block copolymer at a polystyrene/ poly(2-vinyl pyridine) interface, determined by forward recoil spectrometry. The degrees of polymerisation of the styrene and vinyl pyridine blocks were 391 and 68, respectively. The solid line is the prediction of self-consistent field theory, assuming a value for the Flory-Huggins interaction parameter %ps-pvp of 0.11. After Shull et al. (1990).

Figure 6.18. Interfacial tension between polystyrene and poly(vinyl pyridine) in the presence of styrene-2-vinyl pyridine block copolymer, as calculated by self-consistent field theory for the system whose interfacial excess is shown in figure 6.17. The value of the Flory-Huggins interaction parameter Xps-pvp was taken as 0.11, which provides a good fit to the adsorption isotherm below the CMC. After Shull et al. (1990).

Li et al., from a knowledge of the phase diagram for PCL/polystyrene blends, determined a value of the Flory-Huggins interaction parameter x for this polymer pair of 0.061-i-150(RT) J moL [81], while Watanabe et al. quoted a value of x=(-469/32) (1 -2.46x1 O /T) [82 ]. 

All of the fluorescence observations were successfully interpreted in terms of the Flory-Huggins thermodynamics. This indicates that, although the possible existence of kinetic restrictions must be recognized, they may be less significant if the only objective is to explain the occurrence of changes in the photophysical parameters. In a later chapter, we review work on blends of polystyrene with poly(vinyl methyl ether) that permits interpretation of the absolute values of the photophysical parameters. 

Some assumptions were made for the derivation of Equation [4.4.54], especially the partial specific volume, the refractive index, and the derivative dn/dw2 must not depend on the molar mass distribution of the polymer. If one further assumes that the Flory-Huggins X-function depends only on temperature and concentration, but not on molar mass, the partial derivative of the chemical potential can be calculated by Equation [4.4.13a] to obtain values of the x-function. Scholte carried out experiments for solutions of polystyrene in cyclohexane or toluene at different temperatures and in a concentration range of 0 to 80 wt%. 

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