In a lattice model

G. I. Menon, R. Pandit. Glass formation in a lattice model for living polymers. Phys Rev Lett 75 4638-4641, 1995. 

Salvi G, De Los Rios P. Effective interactions cannot replace solvent effects in a lattice model of proteins. Phys Rev Lett 2003 91. 

In a lattice model, molecules are assumed to be arranged regularly on an array of sites or cells as shown in Figures 1 and 2, each polymer chain... 

Barkema, G. T., Marko.J. F., and Widom, B. (1994). Electrophoresis of charged polymers Simulation and scaling in a lattice model of reptation. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 49(6), 5303—5309. 

The major simplifications involved in Equation (2D-4) are that it does not account for the probability of overlapping chains and the volume change upon mixing of the polymer and solvent. The volume change cannot be accounted for in a lattice model when all of the lattice sites are assumed to be filled. The probability that a lattice site is filled, however, can be calculated. Huggins (1941,1942a,b,c) included in his calculations probabilities thata polymer molecule would encounter a filled lattice site. This led to a slightly different form for Equation (2D-4), but Flory (1970) states that the refinement probably is beyond the limits of reliability of the lattice model. 

Lattice model of solutions. In a lattice model of mixtures (Guggenheim 1952) the size of particles are assumed to be nearly the same. Hence A and B can occupy the same lattice sites. It is well known that in this case the deviations from SI solutions are expressed in the form (see Appendix M)... 

Figure 8.7 Coexistence of the killer (red), sensitive (blue) and resistant (green) strains in a lattice model with first-neighbor interaction (from Kerr et al. (2002)).

Care C M, Dalby T and Desplat J-C 1997 Micelle formation in a lattice model of an amphiphile and solvent mixture Prog. Colloid Polym. Scl. 103 130-37... 

Koga et al. (2002) found a linear correlation between the PMF and the solvation Gibbs energy in a lattice model of aqueous solutions. As we have demonstrated above, such a correlation does not exist in general. 

G. THE CHEMICAL AND THE PSEUDO-CHEMICAL POTENTIAL IN A LATTICE MODEL... 

S. Sastry, F. Sciortino, and H. E. Stanley, Limits of stability of the liquid phase in a lattice model with water like properties, J. Chem. Phys. 98, 9863 (1993). 

Therefore, the construction of appropriate equilibrium configurations of polymer chains in a lattice model is always a problem. For a dilute solution under good solvent conditions the excluded volume interaction between all monomers of the chain can no longer be ignored. It leads to a swelling of the chain with respect to its size in the melt or in theta solution. Thus, Eq. (5) does not hold, but has to be replaced by... 

Pretti, M. Buzano, C. (2004). Thermodynamic anomalies in a lattice model of water, J. Chem. Phys 121 11856. 

The simultaneous calculation of the amount adsorbed and the distribution of adsorbate within the pores of a reconstructed solid can be impl ented afier the i lication of a Draisity Functional Theory (DFT) mean field model, which is particularly suited for on-lattice simulations on di tised structures [31]. In a lattice model the spatial distribution of adsorbate can be described at each site by the local density fimction. The equilibrium density profile for a given matrix realization and chemical potential ft (xin then be determined by minimising the grand potential 0 p with respect to the fluid density on each lattice site, / (x), leading to ... 

In a lattice model, particles do not deviate from their fixed lattice positions. Consequently, the total entropy in the lattice model is purely communal in nature. 

The above discussion then allows us to conclude that (10.10) or (10.21) determines the ideal glass transition. In a lattice model, which will be considered later in this chapter, we bypass the comphcation due to Sre ( T) and Sb (T) all together. Hence, the total entropy in the lattice model is purely configurational, and the condition for an ideal GT reduces to... 

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