Interaction unlike pair

Dispersive Interactions. For pairs of nonpolar polymers, the intermolecular forces are primarily of the dispersive type, and in such cases the energy of interaction between unlike segments is expected to be closely approximated by the geometric mean of the energies of interaction between the two like pairs (98). In this case, the Flory-Huggins interaction energy between this polymer pair can be expressed in terms of the solubiUty parameters 5 of the pure components. 

The justification for using the combining rule for the a-parameter is that this parameter is related to the attractive forces, and from intermolecular potential theory the attractive parameter in the intermolecular potential for the interaction between an unlike pair of molecules is given by a relationship similar to eq. (42). Similarly, the excluded volume or repulsive parameter b for an unlike pair would be given by eq. (43) if molecules were hard spheres. Most of the molecules are non-spherical, and do not have only hard-body interactions. Also there is not a one-to-one relationship between the attractive part of the intermolecular potential and a parameter in an equation of state. Consequently, these combining rules do not have a rigorous basis, and others have been proposed. 

The reason for the experimentally proven lipophobicity, i.e., the tendency of fluorinated and hydrogenated chains to phase separate, is much less clear than the other effects of fluorination and is still under debate. Mostly it is assigned to the disparity of cohesive energy densities between perfluoroalkanes and alkanes. A reduction of ca. 10% in the interactions between unlike pairs of molecules was estimated by several methods [90]. However, there are also simulations suggesting slightly stronger attractive contributions to the interaction between Rf/Rh pairs compared to the like interactions under certain circumstances [94]. 9 However,... 

Water (H20), a highly polar hydrogen donor and acceptor, is the common species for all four systems in all four cases, it experiences strong attractive interactions with the second species. Here, interactions between unlike molecular pairs are stronger than interactions between pairs of molecules of the same kind, and therefore AH is negative. (See the discussion of signs for HE in Sec. 16.7.)... 

Step 13 Calculate the group-group interaction energies, emn, for like and unlike pairs using Equation (3D-11). 

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 ... 

A parameter, appears in the combining rule for the energy parameter. It describes the deviations of the unlike-pair interactions from the geometric-mean rule. Values less than 1 indicate that the unlike pair interactions are less favorable compared to the like-pair interactions. 

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. 

Results from these calculations with varying strength of the unlike-pair interactions are presented in Fig. 2. Clearly, if one artificially varies the strength of the unlike-pair interactions, the systems that result are hypothetical, and no longer represent real mixtures of acetone and CO2. For simplicity, we will still refer to the components of these hypothetical mixtures as acetone and CO2. The results are expressed as mole fractions of CO2 in the acetone-rich (liquid) phase and mole fractions of acetone in the C02-rich (fluid) phase, as functions of pressure. Miscible behavior was observed for - 1 (the base case) and 0.90, while immiscibility that persists for pressures significantly higher than the critical pressure of pure C02... 

The mole fraction of acetone in the liquid phase is not a strong function of intermolecular interactions for pressures less than approximately 80 bar. For the immiscible systems, the shape of the mole fraction versus pressure curve is characteristic of solubility curves of solids in supercritical solvents Q4), with a minimum around the pure solvent critical point. The effect of changing the intermolecular interactions is in the expected direction the solubility of acetone in the fluid phase is lower (by a factor of 5) for the system with - 0.70 relative to the one with - 0.80. Again, a few percent change in the magnitude of the unlike-pair interactions has a greatly amplified effect on the solubility. 

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

The limiting activity coefficient is also of great theoretical interest At infinite dilution each solute molecule is surrounded by only solvent mol ules, and the most nonideal conditions are represented, yi is in fact an excess property, so like-pair interactions are normalized out. Since only unlike-pair interactions are involved, any composition dependence of the solute on the properties of the mixture are removed. 

Equation (1.7) requires fly for unlike pairs. The method of calculating fly from and Ujj is called a combining rule. It is in the combining rule that a binary interaction parameter is typically introduced ... 

In most cases, interactions between unlike molecules are treated with Lorentz-Berthelot combination rules [28]. Non-additive pair interactions have been used for N2 and O2 [18]. The resulting N2 model accurately matches double shock data, but is not accurate at lower temperatures and densities [22]. A combination of experiments on mixtures and theoretical developments is needed to develop reliable unlike-pair interaction potentials. 

The difficulty in the application of Equation 29 is in the assignment of values to tt when i /. While such a parameter is said to represent the effects of unlike-pair interactions, it is often difficult to give this idea a clear physical or mathematical statement. Thus one usually resorts to combination rules, which relate nto the pure-component parameters and (possibly) to an empirical interaction parameter, a number (by optimistic definition) usually either of order zero or of order unity. 

The x terms are mole fractions and is the unlike pair interaction coefficient obtained by Mollerup and Rowlinson (16,17,18) for the VDW one-fluid procedure. The particular form of the unlike pair interactions was developed by Hsu (19) who tested several alternative formulations. 

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... 

However magnetic and EPR studies of 64 indicated that the Fe and Cu centers were essentially non-interacting, unlike the strongly coupled [Cuu /Cytaa ] pair in the natural system. 

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