Pair interaction parameter

Effective pair interaction parameters. In the CVM formalism, effective pair interaction coefficients, defined by the symbol are given in Eq. (7.20)... 

Koningsveld, R. Kleintjens, L.A., "Liquid-liquid Phase Separation in Multicomponent Polymer Systems. X. Concentration Dependence of the Pair-Interaction Parameter in the System Cyclohexane- Polystyrene," Macromolecules, 4, 637 (1971). 

For (sub-) monolayer coverage 9 = adsorbed fraction, w = pair Interaction parameter. 2 coordination number. a , = molecular cross section or site area, a = surface Van der Waals constant, /) = [l - 40(1- 0) l-exp(-io/fcT) ]. ... 

In addition to pure component parameters, mixture calculations require the estimation of the unlike-pair interaction parameters. These were obtained in this study using the Lorenz-Berthelot rules ... 

Effect of Unlike-Pair Interactions on Phase Behavior. No adjustment of the unlike-pair interaction parameter was necessary for this system to obtain agreement between experimental data and simulation results (this is, however, also true of the cubic equation-of-state that reproduces the properties of this system with an interaction parameter interesting question that is ideally suited for study by simulation is the relationship between observed macroscopic phase equilibrium behavior and the intermolecular interactions in a model system. Acetone and carbon dioxide are mutually miscible above a pressure of approximately 80 bar at this temperature. Many systems of interest for supercritical extraction processes are immiscible up to much higher pressures. In order to investigate the transition to an immiscible system as a function of the strength of the intermolecular forces, we performed a series of calculations with lower strengths of the unlike-pair interactions. Values of - 0.90, 0.80, 0.70 were investigated. 

With unlike pair interaction parameter From (16)... 

The unlike pair interaction parameter is determined using binary vapor-liquid equilibrium data as described by Zudkevitch and Joffe (2). The systems used in this study are given in Table I. The interaction... 

The exchange interactions which operate in polynuclear systems are compared in Table 11.23. With increasing number of non-equivalent centres the number of magnetic parameters becomes quite large. In addition to the pair-interaction parameters, triad- and tetrad-interaction parameters can occur. The inclusion of orbital interaction is not well developed for polynuclear systems so far. 

Koningsveld.R., Kteintjens,L.A., Shultz, A. R. Liquid-liquid phase separation in multicomponent polymer solutions. IX. Concentration-depe ent pair interaction parameter from critical miscibility data on the system polystyrene-cyclohexane. J. Polymer Sd. A 2,8,1261 (1970). 

Koningsveld.R., Kleintjens.L.A. Liquid-liquid phase separation in multicomponent polymer systems. X. Concentration dependence of the pair-interaction parameter in the system tyclohexane/polystyrene. Macromole es 4,637(1971). 

As noted in the preceding section, IGC is an excellent tool for measurements of surface properties and of acid base interaction potentials of macromolecular solids (2,10,16). In this section the importance of acid-base interactions relative to the adhesion of PUs is considered in greater detail. IGC has been applied to a series of PU adhesives and to selected polymer substrates, allowing quantitative measurements to be made of the acid/base (electron donor-acceptor) interaction parameters applicable to the surfaces of these materials. Acid base pair-interaction parameters for substrate/PU combinations have been calculated. The bond characteristics of polymer/PU combinations have been measured, in part by conventional lap-shear procedures and in part, by the more recent constrained blister detachment method [11, 12]. Possible relationships between bond properties and acid base interactions have been considered, and a comparison of the two adhesion tests has been made. 

Any attempt to relate acid/base interactions between adhesives and substrates to the bond properties of the relevant pair depend on a quantitative evaluation of a pair interaction parameter. There are no broadly accepted theoretical guidelines to such an evaluation, but a pair interaction parameter, I p, can be defined by... 

Table 7.9 Interaction constants and pair interaction parameters for polyurethane adhesives and substrates ...

Figure 7.10 Initial bond strengths as a function of pair interaction parameter Reproduced with permission from H. P. Schreiber, R. Qin and A. Sengupta, Journal of Adhesion, 1998, 68, 1-2, 31, Figure 2. 1998 Gordon and Breach Science Publishers.

Figure 7.12 Dependence of pair interaction parameter on bond strength ratio...

Kambour RP, Bendler JT, Bopp RC (1983) Phase behavior of polystyrene, poly(2,6-dimethyl-l,4-phenylene oxide), and their brominated dtaivatives. Macromolecules 16 753-757 Koningsveld R, Kleijens LA (1971) Liquid-liquid phase separation in multicomponent polymer systems. X. Concentration dependence of the pair-interaction parameter in the system cyclohexane-polystyrene. Macromolecules 4 637-641 Maron SH (1959) A theory of the thermodynamic behavior of non-electrolyte solutions. J Polym Sci 38 329-342... 

I hus, the pair interaction parameter at the tricritical point 0(oo) has a finite value which i.s exclusively dependent on the cut-off Sq. Besides, for finite chains... 

The classic rigid lattice model still proves to be a valuable tool for predictive calculations of phase stability in polymer blends. It depends on the required accuracy whether the simple model needs improvement. Miscibility behaviour of blends containing statistical copolymers do not seem to require such Improvements since values of pair-interaction parameters obtained on one system appear to be transferable to another, fig.6 bears witness of this welcome feature. A similar transferability was observed previously in an analysis of critically demixing poly(styrene) solutions in n-alkanes and n-alcohols varying in number of carbon atoms [31]. The data allowed extraction of the end/middle group interaction function for n-alkanes that correctly predicted the lower critical miscibility behavior of n-alkane /poly(ethylene) systems. 

Other electrolytes featured in studies of cosolvents in aqueous solutions, for example Bu NBr with a number of cosolvents as reported by Korolev, Kustov, and coworkeis [19,20] are also shown in Table 6.3. Enthalpic pair interaction parameters for CaCl with MeOH, EtOH, and n-PrOh were reported in Ref. 24 and for NaNOj, KNO3, CaCNOj), and La(N03>3 with MeOH in Ref. 25 by Taniewska-Osinska and coworkers. Many other studies concerned electrolyte interactions with cosolvents in water without reporting pair interaction parameters. Examples are the enthalpy of solvation of NaNO, KSCN, and NH BF in aqueous methanol reported by Manin and Korolev [26] and of NH Br and NH BF in aqueous HMPT reported by Kustov [27], but such studies are too numerous to be presented here. 

Several studies concerned the pair interaction parameters of systans where the reference solvent was not water, but deal with dilute solutions of water and other cosolvents in solutions of electrolytes in these reference solvents. An example is the report by Piekarski and Kubalczyk [8], in which the reference solvent was acetonitrile and the electrolyte again was Nal see Table 6.3. Pair interaction coefficients of Nal with water in several lower alkanols as reference solvents were reported in Ref. 28 and those of Nal with MeCN in several solvents were reported in Ref. 7 by Piekarski et al. 

The thermodynamic properties of electrolytes in mixed solvents include not only the enthalpic pair interaction parameters at one temperature (25 C) but also at several temperatures according to Korolev et al. and Piekarski et al. [20,28] from which the heat capacity pair interaction parameters, (where (ref) denotes the reference solvent) may be calculated as may also deriv quantities, such as the entropic ones [20]. Several pair interaction parameters for heat capacities of electrolyte interacting with cosolvents in two reference solvents and reported by Piekarski... 

Similar cases of specific interactions have been found also for the partial molar volumes of electrolytes (ions) in mixed solvents. The reports concerning the partial molar volumes of electrolytes in mixed solvents generally do no pertain to dilute solutions of the cosolvent, but on the contrary, most such studies cover the entire composition range. The curves tend to be very asymmetric in the solvent composition and changes in direction are often encountered, as shown, for example, in Figure 6.1 for some electrolytes in aqueous DMSO according to Letellier et al. [30]. In a few cases were very dilute solutions were studied, so that pair-interaction parameters could be... 

PED Pedemonte, E. and Lanzavecchia, L., Pair interaction parameter for compatible polystyrene-poly(a-methylstyrene) mixtures, Thermochim. Acta, 162, 223, 1990. 

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