Static light scattering theory

Philipse (5) also assumed that fast hydrolysis created an active monomer bulk. He studied the growth of silica nuclei, already synthesized, after extra addition of different amounts of TES with static light scattering. To explain his growth curves (radius versus time), he used a diffusion-controlled particle growth in a finite bulk of monomers or subparticles. The model contained equations from classical flocculation theories. It takes into account the exhaustion of the monomer bulk and the retarding influence of an (unscreened) electrostatic repulsion between growing spheres and monomers. 

Figure 18.3. Static light scattering from latex particles. The experimental points are fitted with the exact Mie theory and a size distri tion including polydispersity. The resulting average radius is / = 291 nm and the polydispersity index e = 0.038 (reproduced from ref. (24)), with permission from Academic Press...

Theory and experiments on polyelectrolytes by static light scattering, together with the viscosity results, were reviewed by Nagasawa and Takahashi in 1972 [4]. Their conclusions are still vaUd if the following simplifications are accepted. 

Hill developed the thermodynamics of small systems and also applied it to the aggregation of solutes. This theory serves as a bridge between the mass-action and phase-separation models. Further development has been done by Hall. " Recently, Tanaka applied the theory to static light scattering data for aqueous solutions of nonionic surfactants, and proved its usefulness. This chapter introduces the fundamental concept of this thermodynamics as a basis for understanding micellar solutions. 

Table 5.1 Comparison of the cross second virial coefficients obtained experimentally by static laser light scattering with those calculated from theory on the basis of the excluded volume contribution only.

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. 

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