Energy matrices conformational distributions

As the water uptake proceeds, the increased sidechain-counterion dissociation allows for more complete ionic hydration. The deformation of the polymer chain network upon further incorporation of water molecules also proceeds by a shift in the distribution of rotational isomers to higher energy conformations and changes in other intramolecular, as well as intermolecular interactions. Consequently, the increased overall energy state, for a given membrane water content of n moles, per equivalent of resin, is manifested by polymer chain retractive forces that resist expansion of the network. Accordingly, the configurational entropy decreases as less conformations become available within the matrix. Eventually, an equilibrium water content, nQ, is... 

As a check, we calculated the transition rate matrix for solvated tetra-alanine at r = 300 K, and we also solved the Master equation starting with the extended conformation at f = 0 sec. We plotted the time evolution of the occupation probabilities of the 300 lowest free energy states. That plot is given in Fig. 47. The equihbrium probability distribution is achieved in about 10 ° sec. 

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