Lattice chain model

The usual structure of off-lattice chain models is reminiscent of the Larson models the water and oil particles are represented by spheres (beads), and the amphiphiles by chains of spheres which are joined together by harmonic springs... 

Another example is that of lattice chain models. Simple square lattice models were established by Flory as a vehicle for calculating configurational entropies etc., and used later in the simulations of the qualitative behaviour, e.g. of block copolymer phase separation. More sophisticated models such as the bond fluctuation model, and the face centred cubic lattice chain modeP ... 

The question about these empirical schemes is whether they can be generalized or automated in any way. At the moment it seems that for each specific material, the process needs to done from scratch, involving a lot of human interaction and judgement. Also with the diversity of models and empirical schemes, parameterization is strongly model dependent - the bead size and interaction parameters in MesoDyn, the bond-fluctuation or the fee lattice chain model of the same system will all be different. The situation hence seems confusing. Any emerging efforts aimed at some more coherence in this area would be beneficial. 

Dubois-Violette, Monnery, Geny et al. and Taran have developed a theory of PL for the rotational-isomeric tetrahedral lattice chain model A rela-... 

The third part of this article covers computer simulations of polymer chains. Methods of simulation of chains on lattices are presented and the equivalence between lattice chains and off-lattice chain models is discussed. The simulation of excluded volume effect is examined. The polymer chain collapse from random coil to dense globular state, and simulations of dense polymer systems are discussed. 

The Flory-Huggins theory uses the lattice model to arrange the polymer chains and solvents. We have looked at the lattice chain model in Section 1.4 for an excluded-volume chain. Figure 2.1 shows a two-dimensional version of the lattice model. The system consists of si,e sites. Each site can be occupied by either a monomer of the polymer or a solvent molecule (the monomer and the solvent molecule occupies the same volume). Double occupancy and vacancy are not allowed. A hnear polymer chain occupies N sites on a string of N-l bonds. There is no preference in the direction the next bond takes when a polymer chain is laid onto the lattice sites (flexible). Polymer chains consisting of N monomers are laid onto empty sites one by one until there are a total tip chains. Then, the unoccupied sites are filled with solvent molecules. The volume fraction of the polymer is related to rip by... 

Then, with Eq. 2.A.4 (v = Vsjte in the lattice chain model), the osmotic pressure II is given as... 

Problem 2.8 Show that A2M = (5 )dNVs and A3M = in the lattice chain model, where v p is the specific volume of the polymer in solution. 

Problem 4.4 In the lattice chain model, the osmotic pressure is given as (Problem 2.4)... 

The theory of relaxation spectra in polarized luminescence for various dynamic models of a flexible polymer chain has been developed by several groups of workers. Wahl has proposed a theory for the model of Gaussian subchains. The authors and cowork-en used dynamic chain models counting of ri d or deformable elements with continuous visco-elastic mechanism of mobility and rotational-isomeric lattice chain models ... 

We regard these dynamic Monte Carlo lattice chain simulations as computer "experiments" which complement analytical calculations. A lattice chain model has been widely used in both analytical and numerical calculations to describe equilibrivim properties of polymers (l6). Numerical calculations have been paurticularly helpful in treating equilibrium properties which are difficult to handle analytically (3J, 12 ). Similarly, the Monte Carlo... 

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