Total moment correlation

U typically relaxes through molecular reorientation (or dephasing) but % depends upon the relative positions and orientation of molecules in the fluid. The question which arises is - what aspects of the total moment correlation function (or its associated spectrum) reflect on the properties of M, or,to what extent can the spectrum be used to study reorientatTon ... 

In terms of the projected quantities the total moment correlation function becomes... 

The calculation of dielectric properties in computer simulations is complicated by the long-ranged nature of the coulomb interactions and by the fact that the total moment correlation function is a "collective" function which requires long runs to properly average. These issues have been discussed by Tildesley in these lectures and in several reviews. 

Fig 6 Two decompositions of the total moment correlation function for a model of methyl cyanide, from Ref. 55. 

Dielectric Properties. If the linear lattice has a charge of +eon one end and a charge of — e on the other, the polarization per chain is directly proportional to the mean extension (2). This example relates to the special physical case where there exist monomer level dipole components that add up in such a manner that the total chain moment correlates exactly with the end-to-end length. Calculations similar to those of Onishi and Yamamoto (71) lead to the following result for the dielectric constant ... 

If the dipoles are so tightly correlated that all move together, we have essentially one molecule with an enormous dipole moment, as in the low-frequency response of a single ferroelectric domain. The response is likely to be strongly non-linear at moderate field intensities. Another example is a polypeptide molecule coiled into a solid polar bar, and in this case it may be possible to uncoil the molecule and study it in a less corrdated motion. In the most interesting situation of biological material, polar long-chain molecules are dispersed in an ionic fluid, and the total moment associated with one molecule is a sum of more or less correlated permanent dipoles with a certainly-correlated ionic atmosphere. 

Time dependence of the normalized total moment-moment time correlation function [ J M(t)] for the water molecules, both in the CsPFO micellar solution (solid line) and in neat water. Circles are the simulation data and the continuous line is a multiexponential fit. 

A remark applies to the experimental values of deduced from experimental bandshapes. Since we deal with total (multimolecular) correlation functions, their moments might also contain contributions arising from the intercorrelations of different molecules - or multimolecular effects - since cross terms in the statistical averages do not necessarily vanish. On this account it is necessary to estimate the extent of high-frequency collective effects if any, whenever torques are to be computed from the spectral moments. 

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