Orientational partition function

The possibility to calculate the anomalous properties of water quantitatively with a simple two step function of the orientations partition function of water molecules gives the possibility to estimate the size of the network of H-bonded molecules in liquid water too. We have to take into account the cooperative mechanism of H-bonds and the preference of C2v symmetry of intermolecular arrangements in... 

The fact that the orientational partition function Zorient increases as y increases can be understood. Suppose the next neighbor of each cell in a lattice is six. If the orientation is random each basic unit of a particle has five ways and hence the particle of x units has 5a ways to enter into the lattice and thus the contribution to the entropy of the system is ksx In 5. In the perfectly ordered state, after the first unit is put into the lattice the remaining units enter the lattice via the same direction. The contribution to the system entropy is about zero, and thus is not favored, taking only the orientational entropy into account. Therefore, the fundamental reason... 

This differs from pn in an isotropic phase by the presence of the orientational partition function. The probability of the nth conformer in a mesophase is governed by the integral in Eq. (4.11). 

By taking the ratio xj/x we can see that the nematic phase will favor the conformer with the largest orientational partition function which in this model is the linear conformer. The N-I transition is located by finding when the molar Helmholtz free energy in the isotropic phase... 

In these expressions the conformational-orientational partition functions are given by... 

We see that the anisotropic environment of the nematic is predicted to modify the conformational probability according to the orientational partition function of the conformer. 

The orientational partition functions cause the statistical weights p to differ from their values in the isotropic phase. Thus for well-ordered conformations oj) will be large and negative which means that Q ... 

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