Model lattice-fluid

IC Sanchez, AC Balazs. Generalization of the lattice-fluid model for specific interactions. Macromolecules 22 2325-2331, 1989. 

One usually distinguishes two types of lattice models. The first type may be called lattice-gas models. In this case, the number of molecules in the system is less than the number of available sites. In other words, there are vacant sites. The second type of lattice models may be called lattice fluids. In this case, all lattice sites are filled exactly by the molecular components in the system the system is considered to be incompressible. It is easily shown that a two-component incompressible lattice fluid model can be mapped on a one-component lattice gas one. In other words, it is possible to interpret vacant sites to be occupied by a ghost ... 

Equation of state for polymer systems based on lattice fluid model... 

To extend a close-packed lattice model Equation (15) to a lattice fluid model, we adopt a two-step process as shown in Figure 15 to establish an EOS (Hu et al., 1992). In the first step, pure chain molecules at close-packed lattice are mixed to form a close-packed mixture. In the second step, the close-packed mixture is mixed with N0 holes to form an expanded realistic system with volume V at temperature T and pressure p. According the two-step process, the Helmholtz energy of mixing can be expressed as... 

The EOS based on the lattice fluid model has also be used to describe thermodynamic properties such as pVT behaviors, vapor pressures and liquid volumes, VLE and LLE of pure normal fluids, polymers and ionic... 

For polymer liquids, the gradient approximation in conjunction with the lattice fluid model has been used to calculate surface tensions [24,25]. The Cahn-Hilliard relation for surface tension o, in terms of reduced variables, can be expressed as... 

The theoretical treatment accounting for nonrandom mixing which may be induced by the specific interactions was first carried out by Guggenheim [38]. Sanchez and Balazs [39] have generalized the lattice fluid model by introducing the idea of specific interaction in an incompressible binary blend into the origi-... 

Moreover, we introduce a temperatiue oflfset, 7J,ir, because this lattice fluid model is less suitable at low temperatures. Because this model is based on a mean-field treatment and does not account for the difference in molecular size... 

Wang, W., Tree, D.A., and High, M.S., A comparison of lattice-fluid models for the calculation of the liquid-liquid equilibria of polymer solutions. Fluid Phase Equilibria, 114, 47-62, 1996. a) Novenario, C.R., Caruthers, J.M., and Chao, K.-C., VLE of polymer+solvent mixtures by the chain-of-rotators EoS, Ind. Eng. Chem. Res., 21, 1033, 1998. b) Saraiva, A., Bogdanic, G., and Fredenslund, Aa., Revision of the GC-Flory EoS for phase equilibria calculations in mixtures with polymers. 2. Prediction of LLE for polymer solutions, Ind. Eng. Chem. Res., 34, 1835, 1995. 

While so far we have considered the volume fraction computer simulations [84-99,101-103,107], it also is useful to consider the melt as compressible and then the pressure controls the vacancy concentration. This interpretation is the starting point of the lattice fluid model [108-110] of polymer mixtures and related models [111, 112], but will not be pursued further here. 

DEA DeAngelis, M.G., Meikel, T.C., Bondar, V.I., Freeman, B.D., Doghieri, F., and Sard, G.C., Gas sorption and dilation in poly(2,2-bistrifluorometltyl-4,5-difluoro-l,3-dioxole-co-tetra-fluoroethylene) comparison of experimental data with predictions of the nonequilibrium lattice fluid model, Macromolecules, 35, 1276, 2002. 

From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added in this paper because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. 

Figure 2.14. (a) A realistic intermolecular pair potential in a liquid, with a hard repulsive core and a more long-ranged intermolecular interaction, (b) The simple potential implicit in the lattice fluid model, with an infinitely steep repulsion defining the size of the lattice cell and an attraction confined to nearest neighbours. 

Figure 2.23. The reduced surface tension as a function of the reduced temperature for a number of polymers (A, poly(vinyl acetate) , polystyrene , polyisobutylene A, poly(dimethyl siloxane) , linear polyethylene o, branched polyethylene), compared with the prediction of a gradient theory using the Poser and Sanchez lattice fluid model and a square gradient term modified to account for loss of polymer configurational entropy near a surface (full line). After Sanchez (1992).

Sanchez IC (1978) Statistical thermodynamics of polymer blends. Chapter 3. In Paul DR, Newman S (eds) Polymer blends. Academic, New York Sanchez IC, Balazs AC (1989) Generalization of the lattice-fluid model for specific interactions. Macromolecules 22 2325-2331... 

M. Giacinti Baschetti, F. Doghieri, G. C. Sarti, Solubility in glassy polymers correlations through the non-equilibrium lattice fluid model, Ind. Eng. Chem. Res., 40, 3027-3037 (2001). 

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