Correlation functions collective orientational

Figure 7.8 log-log plot (solid lines) of the collective orientational correlation functions Qoii for water confined in pores of different diameters (inserted number) and power-law fits (dashed lines). Lower and upper traces are for hydrophilic and hydrophobic pores, respectively [16],... 

Despite extensive investigation of phase behavior of liquid crystals in computer simulation studies [97-99], the literature on computational studies of their dynamics is somewhat limited. The focal point of the latter studies has often been the single-particle and collective orientational correlation functions. The Zth rank single-particle orientational time correlation function (OTCF) is defined by... 

The first term on the right hand side of equation (18) contains the collective orientational correlation function <0 2(0) weighted by the (generally un-... 

According to Keyes and Kivelson 22 the collective orientational correlation function in the diffusion limit is given by equations (21) and (22). It has been argued 22 and to a certain extent verified experimentally 131, that the angular velocity correlation factor j2 is close to unity for ordinary liquids. 

Figure 7 Single-molecule orientational correlation times (circles) from NMR data (57) and collective orientational correlation times (triangles) from OHD-RIKES data (56) as a function of rj/T and estimated static orientational correlation parameter (squares) as a function of temperature for acetonitrile-d3.

Figure 3.5. The plot of temperature dependenee of the experimentally measured orientational correlation function at t = 100 fs as a function of O-D stretching fiequency. Note the near dependence of the fiequency of the O-D stretch at low temperature, which is an indication of the collective nature of die dynamics. Adapted from Proc. Natl. Acad. Sci. USA, 105 (2008), 5295. Copyright (2008) Proc. Natl. Acad. Sci. USA.

The first evaluation method, mainly applied to analyse scattering data from larger prganic molecules, starts with the assumption that reorientational dynamics can be described by a collective diffusion law 122, 1. For molecules with a threefold and higher symmetry axis the orientational correlation function... 

Figure 10, The collective orientational correlation at 244K calculated from (47), The functions are averaged over five values of m. The number indicates the index of +++ i = 1, i = 2, i = 3.

Gottke et al. [5] offered a theoretical treatment of collective motions of mesogens in the isotropic phase at short to intermediate time scales within the framework of the Mode coupling theory (MCT). The wavenumber-dependent collective orientational time correlation function C/m(, t) is defined as... 

The growth of orientational correlations and the slow down of collective orientational dynamics were subsequently investigated using a soft potential [106]. Allen and Warren (AW) studied a system consisting of N = 8000 particles of ellipsoids of revolution, interacting with a version of the Gay-Beme potential, GB (3, 5, 1, 3), originally proposed by Berardi et al. [107]. AW computed the direct correlation function, c( 1, 2), in the isotropic phase near the I-N transition. The direct correlation function is defined through the Omstein-Zemike equation [108]... 

Figure 9. Orientational relaxation in the model liquid crystalline system GB(3, 5, 2, 1) (N = 576) at several densities across the I-N transition along the isotherm at T = 1. (a) Time dependence of the single-particle second-rank orientational time correlation function in a log-log plot. From left to right, the density increases from p = 0.285 to p = 0.315 in steps of 0.005. The continuous line is a fit to the power law regime, (b) Time dependence of the OKE signal, measured by the negative of the time derivative of the collective second-rank orientational time correlation function C t) in a log-log plot at two densities. The dashed line corresponds to p = 0.31 and the continuous line to p = 0.315. (Reproduced from Ref. 112.)...

The far infra-red and Rayleigh spectra are related to the correlation function of the collective orientation density fluctuations... 

The anisotropic ( -2) light scattering spectrum is slightly more complicated. The underlying correlation function contains a purely collective orientational part, a collision induced part, and a cross term. 

---