Gaussian approximation liquids

At this time the only experimental method available for determining to what extent the Gaussian approximation is realistic is molecular dynamics studies of polyatomic liquids such as the ones we have been discussing. We have therefore tested this approximation by... 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

The single relaxation time approximation corresponds to a stochastic model in which the fluctuating force on a molecule has a Lorentzian spectrum. Thus if the fluctuating force is a Gaussian-Markov process, it follows that the memory function must have this simple form.64 Of course it would be naive to assume that this exponential memory will accurately account for the dynamical behavior on liquids. It should be regarded as a simple model which has certain qualitative features that we expect real memory functions to have. It decays to zero and, moreover, is of a sufficiently simple mathematical form that the velocity autocorrelation function,... 

The xi, X2,... are displacements of the atoms, and this is a gaussian convolution of the mechanical potential energy I/(TV) with the variances depending on the masses of the atoms, on the temperature, and on h. If /(TV) is weakly dependent on the displacements xi,X2,..., then this FH model reduces to the QFH model, Eq. (3.67). Near minima of I/(TV) this gaussian convolution means that /(TV) > /(TV) this is an approximate description of zero point motion. Near maxima of /(TV) this gaussian convolution means that /(TV) < /(TV) this is an approximate description of barrier tunneling. Simulations of liquid water have been conducted... 

In analog to the approach used by Odijk when dealing with elastic constants, Lee (1988) took the orientation distribution function approximately as Gaussian. When the system is highly ordered, the asymptotic expression can be deduced for viscosities of liquid crystalline polymers, e.g., the Miesowicz viscosities (in the unit of fj) are expressed by... 

Fig. 9.13 Schematic shapes of saturation curves for homogeneous, inhomogeneous and Voigt ESR-lines. A homogeneous line has the Lorentz shape usually occurring in liquids. An inhomogeneous line is an envelope of narrow homogeneous lines, with the envelope usutilly approximated by a Gaussian, wWle the Voigt line is an envelope of homogeneous lines with an appreciable line-width...

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