Light scattering elastic constants

The results obtained by the present mechanical measurements are also consistent with the previous experimental results of the dynamic light scattering studies of the collective diffusion coefficient of gels and the rheological studies of the shear modulus of gels. The studies published by different researchers indicate that the concentration dependence of the collective diffusion constant of the polymer networks of gel and that of the elastic modulus are well represented by the following power law relationships [2, 3, 5]... 

A recent study has employed the new technique of quasi-elastic light scattering for estimation of diffusion constants (257). The result for the native enzyme at 24° is in close agreement with the data given in the tabulation. The value of D as a function of temperature was measured through the thermal transition. The method was also used to follow the kinetics of the urea-induced transition. 

We investigate here the dynamic behavior of fully charged NaPSS solutions with multivalent salt (LaCl3) measured by quasi-elastic light scattering. The bimodal decay of the correlation function of polyelectrolyte concentration (C) at constant salt concentration (Cs) is studied first. The ratio Cs/C varies from 0.2 to 10 2. Then the dynamics of the solution at constant C as a function of Cs from Cs/C approximately 10 2 to 0.2 are investigated. 

The elastic constants of liquid crystalline polymers can be measured in terms of the Frederiks transitions under the presence of a magnetic or electric field. Raleigh light scattering is also a method for measuring the elastic constants. Those techniques successfully applied to small molecular mass liquid crystals may not be applicable to liquid crystalline polymers. This is why very few experimental data of elastic constants are available for liquid crystalline polymers. 

The Raleigh light scattering, another important approach to measure elastic constants and viscosities simultaneously, is applicable to liquid crystalline polymers as well. 

Here nd are elastic constants. The first, is associated with a splay deformation, K2 is associated with a twist deformation and with bend (figure C2.2.11). These three elastic constants are termed the Frank elastic constants of a nematic phase. Since they control the variation of the director orientation, they influence the scattering of light by a nematic and so can be determined from light-scattering experiments. Other techniques exploit electric or magnetic field-induced transitions in well-defined geometries (Freedericksz transitions, see section (C2.2.4.1I [20, M]. 

Models for the low-frequency motions of a semiflexible linear molecule usually treat the system as an elastic wire with force constants for bending and stretching. The model of Harris and Hearst (1966) has been extensively applied to the light-scattering problem by Fujime (1972). In this model the chain is represented by a space vector r which is a... 

Current theories for the dynamic fluctuations and kinetics of polymeric gel swelling are reviewed. The cooperative diffusion constant can be determined either from quasi-elastic light scattering experiments or from the swelling kinetics of spherical or cylindrical gels. The influence of the structure and ionization degree of the network on the cooperative diffusion constant is discussed. 

An important source of error in these calculations is the neglect of short-range order. In particular, the theory fails for the bend and twist elastic constants when smectic-like short-range order is present in the nematic liquid crystal. Under such circumstances these two constants exhibit a critical divergence as the temperature approaches the smectic-nematic point and the light scattering also shows a marked temperature dependence. The present treatment is then inadequate and more elaborate models have been proposed. The phenomenological theory of this aspect of the problem will be discussed in chapter 5. 

We observe that both modes are purely dissipative (non-propagating) involves the elastic constants while co, does not. The slow mode therefore represents the relaxation of the orientational motion of the director, while the fast mode may be looked upon as the diffusion of a vorticity but one in which there is no torque on the molecules. The light scattering, being dependent primarily on the orientational fluctuations, is controlled entirely by the slow mode, as we shall proceed to show. 

The integrated intensity gives the elastic constants while the half width yields It is therefore possible to measure the viscosity coefficients from an analysis of the scattered light using appropriate geometries. 

---