Polymer concentration fluctuation

The term in equation (5.20) denotes the mean-square polymer concentration fluctuation. It is related directly to the osmotic pressure n = - (Api/Fi) in the polymer solution by the equation ... 

This has a clear physical meaning the large variation in the values of the osmotic pressure in neighbouring solution volumes hinders the development of polymer concentration fluctuations, and consequently it reduces the intensity of the light scattering. 

When crosslinks are introduced to these polymer solutions, the concentration fluctuations are perturbed due to the presence of crosslinks. The exact solution for the scattering function from gels has not been found yet because of the... 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

As long as the concentration of the small molecule is low (<5%), the scattered intensity due to concentration fluctuations will be negligible relative to the density or anisotropy fluctuations. In polystyrene, the HV spectrum will not have any contribution due to concentration fluctuations, but in principle there could be a contribution due to the diluent anisotropy. The average relaxation time will be determined by the longest time processes and thus should reflect only the polymer fluctuations. The data were collected near the end of the thermal polymerization of styrene. Average relaxation times were determined as a function of elapsed time during the final stages of the reaction... 

Although the above work was serendipitous, the study of concentration fluctuations in bulk polymers should be a fruitful area of research. Intentional polymer mixtures could be prepared which would allow the mutual diffusion of polymers in polymers to be obtained. Although the molecular weights might need to be kept low, the measurement of polymer motions in the bulk state would be very valuable. 

Paints, adhesives and lubricants are typically multicomponent polymer systems. The behavior of phase-separated blends in the bulk after quenching into the unstable region of the phase diagram is variable. In the bulk, the concentration fluctuations... 

More recently, the Onuki-Doi theory has been experimentally verified for the problem of flow-induced enhancement of concentration fluctuations in polymer solutions [60]. This problem is explored in greater detail in section 7.1.7. A similar verification has been achieved in the problem of electric field induced enhancement of fluctuations [61]. 

J. van Egmond and G.G. Fuller, Time dependent small angle light scattering of shear-induced concentration fluctuations in polymer solutions, J. of Chem. Physics, 96, 7742 (1992). 

J. van Egmond and G. G. Fuller, Concentration fluctuation enhancement in polymer solutions by extensional flow, Macromolecules, 26,7182 (1993). 

T. Hashimoto and T. Kume, Butterfly light scattering pattern in shear-enhanced concentration fluctuations in polymer solutions and anomaly at higher shear rates, J. Phys. Soc. Japan, 61, 1839 (1992). 

X.-L. Wu, D. J. Pine, and P. K. Dixon, Enhanced concentration fluctuations in polymer solutions under shear flow, Phys. Rev. Lett., 66, 2408 (1991). 

In this section we would like to deal with the kinetics of the liquid-liquid phase separation in polymer mixtures and the reverse phenomenon, the isothermal phase dissolution. Let us consider a blend which exhibits LCST behavior and which is initially in the one-phase region. If the temperature is raised setting the initially homogeneous system into the two-phase region then concentration fluctuations become unstable and phase separation starts. The driving force for this process is provided by the gradient of the chemical potential. The kinetics of phase dissolution, on the other hand, can be studied when phase-separated structures are transferred into the one-phase region below the LCST. 

As mentioned above, the life-time t of concentration fluctuations in polymer systems is very long. On the other hand, the distortion time of the concentration fluctuations by shear is y 1 and one may establish that x > y . As a result, the polymer system is highly sensitive to shear which results in distortion and suppression of concentration fluctuations by shear. 

Several attempts have been made to explain theoretically the effects of flow on the phase behavior of polymer solutions [112,115-118,123,124]. This has been done by modification of the mean-field free energy. The key point is to include properly the elastic energy of deformation produced by flow. A more rigorous approach originates from Helfand et al. [125, 126] and Onuki [127, 128] who proposed hydrodynamic theories for the dynamics of concentration fluctuations in the presence of flow coupled with a linear stability analysis. 

Generally, one may establish that in some cases greatly enhanced concentration fluctuations occur under flow, in others, however, the size of concentration fluctuations is reduced and, obviously, flow promotes mutual miscibility of the polymers. Concentration fluctuations are accompanied by inhomogeneities of transport quantities as shear viscosity and diffusity. In a flow field the molecules are transferred into a non-equilibrium situation of extension. Two polymer molecules in a state of excess extension feel an additional repulsion due to the enhanced normal stress difference. Thus, the rate of dissipation by diffusion is low compared with the shear rate and the concentration fluctuations tend to grow. The opposite is true for a state of lower extension. In that case the dissipation of the concentration fluctuations is enhanced owing to an additional attraction between the chain molecules. 

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