Viscosity coefficients order parameter dependence

The above equation provides a basis for correlating the temperature dependence of a transport coefficient such as mass diffusivity in the supercritical region. The effects of composition, solute, and solvent characteristics can also be introduced into the correlations via and A which are system-dependent amplitudes. However, a rigorous ftest of the applicability of equation 5 requires independent measurements of the decay rate of the order-parameter fluctuations, the correlation length, and the viscosity. 

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

The order parameter S is a very important quantity in a partially ordered system. It is the measure of the extent of the anisotropy of the liquid crystal physical properties, e.g., elastic constants, viscosity coefficients, dielectric anisotropy, birefringence, and so on. S is temperature dependent and decreases as the temperature increases. The typical temperature dependence of S is shown in Figure 1.16. 

The coefficient y is rotational viscosity of the director similar to coefficient yi for nematics. In fact, it does not include a factor of sin cp and, in the same temperature range, can be considerably larger than the viscosity ytp for the Gold-stone mode. This may be illustrated by Fig. 13.10 the temperature dependence of viscosities y and have been measured for a chiral mixture that shows the nematic, smectic A and smectic C phases [15]. The pyroelectric and electrooptic techniques were the most appropriate, respectively, for the measurements of ya and ytp describing the viscous relaxation of the amplitude and phase of the SmC order parameter. The result of measurements clearly shows that y is much larger than y and, in fact, corresponds to nematic viscosity yj. 

Figure 2.22 shows the temperature dependences of In ry (Fig. 2.21) on the inverse temperature 1/T, which are very close to linear functions [68]. As seen from Fig. 2.22 the isotropic viscosity rjs = a4/2 does not undergo considerable change near the phase transition region, while Vi and rj2 vanish in the isotropic phase. Several approaches have been proposed to describe the temperature dependences of the anisotropic liquid crystal viscosity coefiicients [75, 76]. In [75] phenomenological viscosity coefficients in the equations of nematodynamics were found in terms of the order parameter S — S T)... 

Recently Tao et al. extended the MS theory by adding to Eq. (3) the isotropic, density-dependent component of the molecular interactions (/o(r) in the form of the Lennard-Jones potential (/o(r) = 4e [(o-/r) -(o-/r) ]. As a result they obtained a better agreement of the calculated and experimental quantities characterizing the nematic-isotropic transition, for example, volume change at and the values of dT ldp. Chrzanowska and Sokalski considered the case when the parameter Lennard-Jones potential is dependent on the orientation of molecules that allows one to predict properly for MBBA such properties as order parameters, elastic constants, and rotational viscosity coefficients. 

The shear viscosity coefficients t], 1)2, V3 and 77i2 and the rotational viscosity coefficient 7i form a complete set of independent coefficients from which the Leslie coefficients can be determined with the help of the Parodi equation. The corresponding equations are given in Chap. VII, Sec. 8.1 of Vol. 1. Figure 24 [74] shows the Leslie coefficients for MBBA as a function of temperature. Due to the different dependence on the order parameter (see Chap. VII, Sec. 8.1 of Vol. 1 of this Handbook), the coefficients exhibit different bending above the clearing point. The temperature dependence of differs greatly from that of the other coefficients, as it is not a real viscosity. 

Rafler et al. showed in an early work [102] that the diffusion coefficient of EG varies with the overall effective polycondensation rate and they proposed a dependency of the diffusion coefficient on the degree of polycondensation. This dependency is obvious, because the diffusion coefficient is proportional to the reciprocal of the viscosity which increases by four orders of magnitude during polycondensation from approximately 0.001 Pas (for Pn = 3) to 67Pas (for Pn = 100) at 280 °C. In later work, Rafler et al. [103, 104, 106] abandoned the varying diffusion coefficient and instead added a convective mass-transport term to the material balance of EG and water. The additional model parameter for convection in the polymer melt and the constant diffusion coefficient were evaluated by data fitting. 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Pulsed-Field Gradient Spin-Echo NMR Diffusion NMR experiments resolve different compounds in a mixture based on their diffusion coefficients, depending on physical parameters such as size and shape of the molecules, temperature, and viscosity. The diffusion NMR technique is often referred to as diffusion-ordered spectroscopy (DOSY) or pulsed-field gradient spin-echo (PGSE) NMR. A series of NMR diffusion spectra are acquired as a function of the gradient strength G (Fig. 2.19) [56], and the slope of the peak decay is used to obtain the diffusion coefficient D. Furthermore, the hydrodynamic radius can be obtained from the Stokes-Einstein equation (Eq. 2.3). 

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