Order parameters measurement

M. Allain, P. Oswald, J. M. di Meglio. Structural defects and phase transition in a lyotropic system optical birefringence and order parameter measurements. Mol Cry St Liq Cryst 7625 161-169, 1988. 

This order parameter measures the spatial coherence of the dynamics and can be normalized by dividing it with its value corresponding to the spatially uniform oscillatory system Ro = R(6 0), 0 < R/Rq <... 

The lateral pressure concept provides useful insight into the spatial distribution of forces and is a sum over terms corresponding to layers of finite thickness (dz). Quantitative measurements of the LP remain difficult and even the concept has been criticized. Chain order parameters, measured by H-NMR studies on amphiphiles with specifically deuterium-labelled methylene units in the tails, ° gave a similar view of the distribution of the chain attractions/repulsions as a function of position in the tails. Increasing quad-rupole splittings, indicated by an increasing distance between the two peaks in the H-NMR spectrum, are associated with increasing chain order. 

However, order parameter measurements for have been performed... 

R. J. Miller and H. F. Gleeson.Order parameter measurements from the Kossel diagrams of the liquid-crystal blue phases, Phys. Rev. E52, 5011-5016 (1995). 

P.J. CoUings, T.J. McKee, J.R. McCoU, Nuclear magnetic resonance spectroscopy in cholesteric hquid crystals. I. Orientational order parameter measurements, J. Chem. Phys. 65 (1976) 3520. 

Within the limit of experimental errors scaled dynamic order parameters measured from the MQ experiments show a linear dependence on cross-link density (cf Fig. 11). 

Fig. 11. (a) The dependence of d3Tiamic-order parameters measured from DQ (squares) and TQ (circles) buildup curves on the cross-link density for ssmthetic pol5dsoprene. (b) The effective residual dipolar coupling Deff (circles) measured from dipolar encoded longitudinal magnetization decays together with the Z)efr values (squares) computed from d5mamic-order parameters. A linear dependence on the cross-link density is evidenced in all cases (solid lines). Reproduced from Ref 68, with permission from American Institute of Physics. 

In fig. 35 a summary is given of the order parameters measured at the first harmonic of Dy, Ho, Er and Tm (Helgesen et al. 1995). Within error (here 0.05) the derived exponents for Dy and Ho are the same and equal to values reported earUer from neutron... 

The most common way of dealing with non-rigid (macro) molecular systems is the model free analysis proposed by Lipari and Szabo and even earlier, in a slightly different formulation, by Wennerstrom et al. The Lipari-Szabo model assumes uncorrelated internal and global motions. The spectral densities are expressed in terms of a global and a local correlation time and a generalized order parameter, measuring the... 

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