Temperature dependence of the interaction

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

This relationship, which is most widely used to take into account the temperature dependence of the interaction parameter, was first confirmed experimentally by Huggins [58]. 

For use below we now explicitly write out the assumed linear temperature dependence of the interaction parameters as... 

It also seems natural to reject the traditional assumption in the kinetics of surface processes that all the parameters of particle interaction in the system adsorbed particles-atoms of the solid do not depend on their internal degrees of freedom. Account of the indicated relation leads to a temperature dependence of the interaction parameters [308], which corresponds to a real situation. 

Due to the complexity of the temperature dependency of the interaction parameters, a three parameter expression is generally necessary to adequately correlate LLE data. The form of the temperature-dependent term proposed by Koningsveld (1975) is... 

Since the initial work of Smidsrod and Guillet numerous investigators have used I.G.C. to determine physicochemical parameters characterising the interaction of small amounts of volatile solutes with polymers Baranyi has shown that infinite dilution weight fraction activity coefficients, interaction parameters and excess partial molar heats of mixing can be readily determined with this technique. Partial molar heats and free energies of mixing, and solubility parameters of a wide variety of hydrocarbons in polystyrene and poly(methyl methacrylete) have been determined The temperature dependence of the interaction parameter between two polymers has also been studied... 

Using the phenomenological temperature dependence of the interaction parameter [Eq. (4.31)], this relation can be transformed to the binodal of the phase diagram in the space of temperature and composition ... 

Knez and Skerget (40) reported good agreement with two interaction constants in the P-R EOS for modeling the S-L-V line for vitamin K3, but agreement for vitamins D2 and D3 was not as good. The significant deviation in the latter systems was attributed to the temperature dependency of the interaction constants. It is however important to employ the most appropriate approach for evaluation of the interaction constants. 

The direct approach to the study of polymer properties and interactions by gas chromatography was initiated by the work of Smidsr d and Guillet (i) on poly(N-isopropyl acrylamide). The polymer was used as the stationary phase and its interaction with known, volatile solutes was recorded. The name inverse gas chromatography is customarily given to this technique. From the magnitude and temperature dependence of the interaction, properties of the polymer-solute solution as well as those of the pure polymer can be measured. The facility of the gas chromatographic route to study highly concentrated polymer solutions has represented a major incentive to the rapid development of this method. 

Croucher and Hair (1978) have presented a plot of temperature dependence of the interaction parameter y(7) as a function of temperature for poly(a-methyl styrene) in -butyl chloride. This is shown in Fig. 12.7. The curve was computed from equation (12.88) using the following numerical values for the parameters 0i )=O-12 (Cowie and McEwen, 1975), 0ya LCFT=254 K and 9l UCFT=403 K (Croucher and Hair, 1978). These results allowed the value of I to be calculated from equation (12.88) since [i—z(T)] =0 at T= ( =-0-483). 

Fig. 12.7. The temperature dependence of the interaction parameter x for poly(a-methylstyiene) in n-butyl chloride I, microscopic theory 2, macroscopic theory (after Croucher and Hair, 1980b).

It should be noted that when the polymer sample employed is not strictly monodisperse, the A values evaluated from cloud point meaurements could entail some error. It has been shown that the error is more likely to affect the concentration dependence and temperature dependence of the interaction energy density. However, in this work, the pdydispersities of the copolymers used are moderate, ranging from 1.2 to 1.5, and also comparable among the several copolymers studied. In comparing the relative compatibility of various styrenic derivative copolymers with PVME, the conclusions drawn should be unaffected by any minor erros due to the differences in the molecular weight distributions. 

When the forces between a particle and another condensed species are treated, thermodynamics and statistical mechanics of the aerosol (particles plus gas) enter through temperature dependence of the interaction forces. However, actual aerosol particle interaction forces may be altered in a fundamental way if one or both of the particles or surfaces absorb molecules from the suspending gas. ASH et al. [5.4] considered nonionic systems in which the relative velocity of the particle and surface or other particle is "sufficiently small, in relation to the rates of absorption and desorption, that absorption equilibrium is maintained as the particles move together, collide and then either adhere or separate." They, therefore, assume constant temperature for the entire aerosol system implying at least several nonabsorbing gas molecular collisions with the sorbent species between each sorbate interaction that is to say, the sorbate must be a minority (< 10 percent) species in the gas. By use of conventional equilibrium thermodynamics they derive the expression for the excess force (beyond van der Waals and electrostatic) between two bodies due to sorption as... 

Thus, the temperature dependence of the interaction parameter g (or x) (Elquation 10 which has the form... 

Figure 3.81. Arrangement of phase separation regions for the temperature dependence of the interaction parameter g (or x) of the type g =, 901 + ff02/ J + gtaT at different values of the parameters in this equation (schematic) (Koningsveld, 1975) [Reprinted from R.Koningsveld, Bril, Polym. J- 7 (1975) 4.35-458. Copyright 1975 by Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

Hashimoto, in comparing a tapered styrene-isoprene copolymer (47% styrene, 50K Mol weight) to the same composition and molecular weight of pure styrene-b-isoprene polymer with equal block sizes, found a value of Tc of 150 C for the tapered polymer and 250 C for the pure polymer.One could expect the Tc to be even lower in the case where the end-blocks were uniform random copolymer and the center block was isoprene of much higher molecular weight. The equation for the temperature dependence of the interaction parameter is ... 

M = 1900 and 2650, respectively) with added S/B copolymer (M = 16300,25000, and 270000). The linear relationship predicted by this equation was found to be obeyed on addition of either of the two lower molecular weight copolymers (see Fig. 9). The temperature dependence of the interaction energy density was deter-... 

Russell TP, Hjebn RP Jr, Seeger PA (1990) Temperature-dependence of the interaction parameter of polystyrene and poly(methyl methacrylate). Macromolecules 23 890... 

Figure 8.3 Temperature dependence of the interaction parameter (U/V ) for mixtures of methoxylated poly(ethylene glycol) and methoxylated poly(propylene glycol) of two different compositions. Reproduced with permission from ref. 18.

The temperature dependence of the interaction parameter for PS/PMMA and PS/styrene-acrylonitrile copolymer mixtures was measured by elHpsometry and evaluated from experimentally-found thickness of the interphase layer using Eq 6.18. It was found that the interfacial thickness increases with temperature. 

Regarding the temperature dependence of the interaction parameter x (or B), in the original Flory-Huggins model the unfavorable enthalpic term is constant with temperature, but the favorable entropic term increases with temperature (see Eq. (2.14) or (2.17)). The model predicts phase diagrams with an Upper Critical Solution Temperature (UCST), or misdbilization upon heating. However, systems... 

This decrease in D derives from the temperature dependence of the interaction parameter x Using Eq. 4 and the measured values of D(T) and D (T), the values of the interaction parameter at various temperatures were calculated and are plotted in Fig. 4 for a (J> = 0.55 blend. The open triangles correspond to X s computed from the diffusion coefficients in Fig. 3 while the closed circle represents the average X calculated from... 

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