Nonreverse random walk

This expression accounts for the configurational entropy of an ideal binary mixture with identical molecular sizes, but not for that of a polymer solution, since polymer chains are large and flexible. For that case, more contributions arise from the chain conformational entropy, first considered by Meyer [19] and then derived by Huggins [20] and Flory [21]. In analogy with a nonreversing random walk on a lattice, the conformational contribution of polymer chains to the partition function is given by... 

If we denote by f the probability of finding a bond in the excited state, we get for the intramolecular part of the partition function, neglecting excluded volume effects but assuming a nonreversal random walk, Eq. [35]... 

G. Zifferer, Macromol. Theory Simulations, 3, 163 (1994). Monte Carlo Simulation of Tetrahedral Chains. 7. The Shape of Linear and Star-Branched Polymers Neat to Theta-Conditions. G. Zifferer, Macromol. Theory Simulations, 4, 137 (1995). The Shape of Linear and Star-Branched Nonreversal Random Walks Embedded in a Tetrahedral Lattice. 

Problem 1.16 Nonreverse random walk (NRRW) is often used in lattice simulations. The random walker can choose any direction except for returning to the preceding site. Otherwise, the walker can return to the site it visited earlier. We can expect that the trajectory is between that of an ideal chain and that of an excluded volume chain. For a cubic lattice of lattice unit b, assume that the random walker chooses one out of the five directions at random and answer the following questions. 

Fig. 6.8 Radius of gyration vs. temperature for the same cooling rates as in Fig. 6.7. The error bars are only included for the fastest cooling rate for the sake of clarity. The dashed-dotted and the dashed lines correspond to the generalized nonreversal random walk (NRRW) approximation. ...

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