Media polydispersity effect

Theories based on the uniformly effective medium have the practical advantage that they can be extended quite easily to polydisperse systems (227). Viscosity master curves can be predicted from the molecular weight distribution, for example. The only new assumption is that the entanglement time at equilibrium for a chain of molecular weight M in a polydisperse system has the form suggested by the Rouse theory (15) ... 

Equations (16) and (18) discriminate between intraparticle and interparticle interference effects embodied in bj(q. t) and exp rq- ry(/)—r/(/) ), respectively. The amplitude function bj(q.t) contains information on the internal structure, shape, orientation, and composition of individual particles. Variations of bj(q.t) across the particle population reflect the polydispersity of particle size, shape, orientation, and composition. The phase function expjrq (ry (r) — r/(/)]( carries information on the random motion of individual particles, the collective motion of many particles, and the equilibrium arrangement of particles in the suspension medium. 

The formation and size of the colloidal spheres depend on the molecular structures and preparation conditions such as the initial concentration of the polymer in THF, the water content in the medium, and the water-dropping rate. As the polymers studied are of different types and have polydispersity in the molecular weight and DF, it is difficult to give a quantitative relationship to correlate the polymer structures with the colloid size and formation details. As a general tendency, CWC decreases as the molecular weight and hydrophobicity increase, and the colloid size increases as the hydrophobicity increases. The influence of the polymer structure can be better understood after discussing the colloid formation mechanism in Section 5.3.3. The effect of the preparation conditions on the colloid formation and size is discussed herein by using PEAPE (DF = 49.9%) as a typical example. 

While generally less accurate than SEC/MALS measurements, SEC/VISC measurements are usually both more precise and extend to lower molar masses. The increased precision stems from the relatively higher signal-to-noise ratio in viscometric measurements than in dissymmetry experiments. The lack of sufficient angular dissymmetry for medium- to small-size polymers means that it is extremely difficult to determine their rms radius precisely, especially for the low molar mass species of a broad polydispersity sample employing high concentrations is out of the question for these types of sample due to column overloading effects as well as to the possibility of... 

One of the presented structures is a monodispersion of subwavelength inclusions i (spheres) in dielectric host h. Fig. 2.22a. The other is polydispersion. Fig. 2.22b. The first situation can be described by the well-known MaxweU-Gamett model [171], the oldest effective medium model, obtained by the use of Clausius-Mossotti/ Lorenz-Lorentz equation. The other case is polydispersion, described by the implicit Bruggeman expression [172, 173]. 

F. 2.22 Effective medium apinuach. a Sphtaical subwavelength inclusions as monodispta ion in homogeneous host (MaxweU-Gamett model) b polydispersion (Biuggeman model)... 

In the bidisperse case. Figure 4.4(b), fi ctionation does occur. The large droplets cream faster than the small ones and two sharp boundaries form at the base and rise to die top at two discrete rates. The two creaming rates allow two hydrodynamic sizes to be inferred fiom eqn. (4.1). The rates at which die boundary rises at two volume fiacdons (ordinates yi and 2) are sufficient to define completely the cumulative size distribution of a bidisperse dispersion. Polydisperse dispersions are treated as an extension of the bidisperse case, the number of ordinates examined being increased as required until die size distribution is sufficiendy well defined. However, this simplistic analysis is only applicable to very dilute emulsions, where Stokes law is valid (i.e at infinite dilution in an infinite medium). In closed concentrated emulsions, droplets will interfere with one another and the effect of back-flow by the continuous phase becomes significant. 

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