Dynamic structure factor slow modes

When the solvent molecules are explicitly included, one needs to treat a ternary system (two ions and the dipolar solvent molecules). The additional slow variables to be included in the mode coupling theory are the products of the ion charge and solvent densities. This will explicitly introduce terms like Fis(k,t), which is the partial dynamic structure factor involving the ion and the solvent molecules. The calculation of the microscocpic terms of the friction, containing the density terms, does not appears to be difficult, but calculation of the current terms now appears to be formidable. 

Fig. 11 The dynamic structure factor C(, r) of polybutadiene star 12880 (nominally f = 128, Ma = 80kgmol ) in cyclohexane at ci = 0.016gmL and q = 0.035nm , along with the fit (solid line) from the ILT analysis. The corresponding relaxation distribution function L(ln(T)) (shown here for f i and q = 0.023gmL ) embraces the cooperative diffusion (1), the collective apparent diffusion (2), and the self-diffusion (3). The slowing-down of the middle structural mode (2) and the increase of its intensity with q are shown in the upper inset whereas the lower cartoon illustrates the liquid-like ordering [43,189]. The core regions are drawn out of scale (larger) for clarity...

Such a dramatic change is also reflected in the time-dependence of the dynamical structure factor. The line shape, non-exponential in the gel regime at the 0-temperature, becomes more and more exponential as we increase the temperature from 35°C to 65 C. A single exponential line is observed in polystyrene-benzene system.This is due to the fact that the relative intensity I /Ig of the slow mode (x ) to the fast mode (x ) is proportional to the ratio of the elastic modulus to the osmotic bulk modulus... 

Finally the book reaches properties that are determined by the collective properties of the dissolved polymers, including the dynamic structure factor, the polymer slow mode, the zero-shear viscosity, and linear and nonlinear viscoelasticity. Chapter 11 treats the dynamic structure factor S(q,t) of polymer solutions as... 

This chapter has considered measurements of the dynamic structure factor S q, t) of polymer solutions. Here behaviors of the first cumulant, the polymer slow mode, and the high-frequency Rayleigh-Brillouin spectrum have been considered. Neutron spin-echo methods as supplements to light scattering spectroscopy were noted. Results on Ki and the Rayleigh-Brillouin spectrum are readily summarized. The discussion of the slow mode is considerably more extended, but leads to a comparison with modem models for glass formation. 

Fifth, there are hints in measurements of the dynamic structure factor of a transition for polymer concentrations near 800 g/1. Konak and Brown(8) examined the slow mode of polystyrene toluene at volume fractions 0.9 and 0.8. The slow mode scaled as (diffusive) or (structural), depending on concentration and temperature, q being found at larger c and smaller T, but with a transition to diffusive behavior (melting) at larger T, especially at the smaller concentration. Koch, et al.(9), measuring VV and VH spectra of 700 and 810 g/1 polystyrene in dioxane, similarly found that (tvv) depends on q at higher temperature but not at lower temperature. 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of the monomers determines the interaction strength between the chains, the interactions of the polymer with host molecules or with interfaces. The monomer structure also determines the possible local conformations of the polymer chain. This relationship between the molecular structure and any interaction with surrounding molecules is similar to that found for low-molecular-weight compounds. The second important parameter that controls polymer properties is the molecular weight. Contraiy to the situation for low-molecular-weight compounds, it plays a fundamental role in polymer behaviour. It determines the slow-mode dynamics and the viscosity of polymers in solutions and in the melt. These properties are of utmost importance in polymer rheology and condition their processability. The mechanical properties, solubility and miscibility of different polymers also depend on their molecular weights. 

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