Scattering concentration fluctuations

In the next section we shall pursue the scattering by fluctuations in density. In the case of solutions of small molecules, it is the fluctuations in the solute concentration that plays the equivalent role, so we shall eventually replace 6p by 6c2. First, however, we must describe the polarizability of a density fluctuation and evaluate 6p itself. 

In the next section, we consider the application of Eq. (10.49) to scattering from fluctuations in concentration. 

For a more complete discussion of critical phenomena, we consider the scattering intensity S(q) from concentration fluctuations (q is the wavenumber of the scattering) which can be derived when one supplements Eq. (1) by a gradient-square term " ... 

This effective Q,t-range overlaps with that of DLS. DLS measures the dynamics of density or concentration fluctuations by autocorrelation of the scattered laser light intensity in time. The intensity fluctuations result from a change of the random interference pattern (speckle) from a small observation volume. The size of the observation volume and the width of the detector opening determine the contrast factor C of the fluctuations (coherence factor). The normalized intensity autocorrelation function g Q,t) relates to the field amplitude correlation function g (Q,t) in a simple way g t)=l+C g t) if Gaussian statistics holds [30]. g Q,t) represents the correlation function of the fluctuat-... 

Rosenweig, R. E., Hottel, H. C., and Williams, G. C., Smoke-scattered light measurement of turbulent concentration fluctuation. Chem. Eng. Sd. 15, 111 (1961). 

There are other types of fluctuations. For example, if sugar is dissolved in water, after thorough stirring the sugar concentration will be statistically homogeneous, but concentration fluctuations will give rise to scattering. If the molecules are nonspherical, there will be orientation fluctuations. 

In the case of solutions, concentration fluctuations only contribute to the central elastic part of the scattering spectrum. However, the Brownian movement of solute molecules creates weak frequency displacements that broaden the central peak. This phenomenon is called Rayleigh line broadening or quasielastic scattering [26-28]. This section deals with elastic scattering only. 

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... 

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

See for example R. G. Rubio, M. Caceres, R. M. Masegosa, L. Andreolli-Ball, M. Costas, and D. Patterson, Mixtures with W-Shape Curves. A Light Scattering Study , Ber. Bunsenges. Phys. Chem., 93, 48-56 (1989) and A. Lainez, M. R. Lopez, M. Caceres, J. Nunez, and R. G. Rubio, Heat Capacities and Concentration Fluctuations in Mixtures of... 

Dynamic processes at thermodynamic equilibrium that occur within a time range from sub-microseconds to seconds can be probed without the imposition of a transient disturbance by optical intensity fluctuation spectroscopy. As such, dynamic light scattering (DLS) [155] measures the fluctuation of quasielastic scattering intensity and fluorescence correlation spectroscopy (FCS) [156-158] measures concentration fluctuations of specific fluorescent molecules... 

This simple model predicts that the structure factor will develop a butterfly pattern and grow along an axis that is at 45° with respect to the flow direction, which is parallel to the principal axis of strain in this flow. Since the structure factor is the Fourier transform of the pattern of concentration fluctuations causing the scattering, the model predicts an enhancement of fluctuations perpendicular to the principal axis of strain. 

An alternative explanation of the observed turbidity in PS/DOP solutions has recently been suggested simultaneously by Helfand and Fredrickson [92] and Onuki [93] and argues that the application of flow actually induces enhanced concentration fluctuations, as derived in section 7.1.7. This approach leads to an explicit prediction of the structure factor, once the constitutive equation for the liquid is selected. Complex, butterfly-shaped scattering patterns are predicted, with the wings of the butterfly oriented parallel to the principal strain axes in the flow. Since the structure factor is the Fourier transform of the autocorrelation function of concentration fluctuations, this suggests that the fluctuations grow along directions perpendicular to these axes. 

---