Temperature dependence of interaction parameter

The system PS dissolved in cyclohexane, sketched in Figure 3, displays an UCST. At high temperatures cyclohexane is a good solvent. It turns into a poor solvent for temperatures below 35.4 °C (0 temperature). Expansion factor a was calculated as a function of temperature after Equation (13). Temperature dependence of interaction parameter % might be represented by ... 

Fig. 1. Schematic temperature dependence of interaction parameters resulting from different ts pes of interactions in a pol3aner blend. (1-dispersive interactions, 2-free-volume interactions, 3-specific interactions, A-sum of 1-1-2, B-sum of 1-I-2-I-3).

Figure 8.6 Temperature dependence of interaction parameters for mixtures of deuterated and hydrogenous vinyl butadienes. % =Xab = Xcd.X2 = Xad = Xbc,X = Xac = Xbd Reproduced with...

Two-constant equation of state phase behavior calculations for aqueous mixtures often require the use of temperature dependent binary interaction parameters. The methods used for evaluating these parameters for some of the typical aqueous binary pairs found in coal gasification and related process streams are described. Experimental and predicted phase compositions based on these methods are illustrated for aqueous pairs containing CO2. H2S, NH3, and other gases. 

The activation energy thus found reflects the overall effect of temperature on a few parameters characterising the process of interaction of those phases (see equation (5.19)). Not only is the temperature dependence of each of them characterised by its own activation energy, but it may well happen to be quite different from temperature dependences of other parameters. Therefore, both sets of activation energies prove to be of little practical value, irrespective on whether these were calculated from an ascending or from a descending portion of an experimental kinetic relationship. 

The character of temperature dependence of order parameter r =r (T) is defined to a large extent by the value and sign of the quantity 8. The evaluation showed that >0, oo2<0, oo3=2cn2<0, as is shown later. It should be noted that energetic parameter c i is defined by interaction between d>-Pt pairs and energetic parameter (o2 is determined by interaction between -H pairs. 

For fitting the temperature-dependent group interaction parameters of modified UNIFAC, in contrast to original UNIFAC, besides VLE data the following data are also used ... 

While linear temperature-dependent group interaction parameters are already required to describe the VLE behavior and excess enthalpies simultaneously, quadratic temperature-dependent parameters are used when the system shows a strong temperature dependence of the excess enthalpies. 

In the case of the group contribution equation of state VTPR, instead of temperature-independent group interaction parameters from original UNIFAC, temperature-dependent group interaction parameters as in modified UNIFAC are used. As for modified UNIFAC, the required temperature-dependent group interaction parameters of VTPR are fitted simultaneously to a comprehensive data base. Besides VLE data for systems with sub and supercritical compounds, gas... 

As the Muthukumar equalities (hiquation 5.6-.3G, 28,-.30) enable one to take account of two-body and three-body interactions in different combinations, the comparison of these equations with experimental data will allow one to study the contributi< n of two-body and three-body interactions as well as the temperature dependence of the parameters of the two-body x and three-body w interactions for certain systems. 

The concentration dependence of many physical properties indicates the quality of the polymer-solvent interactions, through the second virial coefficients. Study of the concentration and temperature dependence of these parameters provides information on the theta temperature, radius of gyration, and the mean square end-to-end distance for a polymer coil. The radius of gyration is defined as the root mean square distance from the center of mass of a polymer chain to a given mass element. The characteristic ratio is a measure of the ratio of the square of the average random-flight end-to-end distance to the product of a number of backbone imits times the interactions along the polymer chain. These parameters provide useful information on the validity of a particular theoretical model and its ability to describe the architecture and conformation of a polymer (104). 

Hansen, H.K., Goto, B., and Kuhhnann, B., 1992. UNIFAC with fineary temperature-dependent group-interaction parameters, IVC-SEP Internal Report 9212, Technical University of Denmark. 

In describing the mechanism of adsorption, it is necessary to account for the nature of the solvent. The thermodynamic quality of the solvent is the main factor, determining the chain conformations. All current theories of adsorption from dilute solutions include the parameter of interaction between polymer and solvent. Temperature dependence of this parameter also determines the temperature dependence of adsorption and the characteristics of the adsorption layer (for more details see references 1-13). 

Table 3 Coefficients of temperature and concentration dependence of interaction parameter...

Vector (length 20) of stream composition (I = 1,N). Contribution from temperature dependence of UNIQUAC binary interaction parameters, here taken as 0. 

In many applications the phase stmcture as a function of the temperature is of interest. The discussion of this issue requires the knowledge of the temperature dependence of the Flory-Huggins parameter x (T). If the interactions... 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

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... 

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