Soft-sphere microgel model

Fig. 25. Guinier plot of the soft sphere model. The numbers denote the number of branching shells the filled and open circles are lightscattering results from polyvinyl acetate (PVAc) microgels in methanol at 20 °C at A0 = 546 nm and 436 nm, respectively. The dot-dash line corresponds to the Rayleigh-Gans behavior of hard spheres, i.e. no Mie scattering93)...

Fig. 39. Measurement of the apparent diffusion coefficient Dapp = 17q2 for two concentrations of a PVAc microgel in methanol 88 189. The full lines are theoretical curves for a soft sphere model with 7 branching shells93 ...

The polyelectrolyte microgels have been established as model soft spheres as, in addition to the above features, their softness and properties can be tuned by altering the physico-chemical environment (pH, ionic strength, degree of ionization) [152-160], The response varies from that of colloidal (polydisperse hard-sphere) suspensions and that of polymer gels and in this respect such microgels fit within the theme of Fig. 1 [157-160],... 

Polymer colloids are important model systems for investigating fundamental aspects of colloid science. Traditionally rigid particles that have rather simple, for example, hard sphere-like or Yukawa, interaaion potentials have been employed. Such systems have been reviewed in the past, see, for example, a review on hard spheres by Pusey et al In this chapter, we focus on recent developments depletion interaction and soft spheres. Concerning the latter topic, two different types of materials are discussed star polymers and microgels. 

Figure 4 shows die measurement results on a poly(vinyl acetate) microgel and the Kratky plot of die calculated branching number dependence assuming the soft-sphere model [27]. A characteristic of this plot is the appearance of a maximum as die amount of branching increases. 

Fig. 4 A Kratky plot of the calculated results by soft-sphere model (solid line) and hard-sphere model (broken line) and the measurement results of poly-(vinyl acetate) microgel [27].

In reference [73], a comparison similar to that in Figure 1.5 was also performed for a soft-sphere system, namely, a dispersion of microgel particles studied by Bartsch et al. [32], who indicate a value of the soft-sphere diameter of 1.0 [im, and report the glass transition to occur at a volume fraction = 0.644. In reference [73], this system was modeled with the soft potential in Equation 1.29. Unfortunately, the experimental report does not define or quantify the degree of softness of the particles, in a manner that serves to determine the parameter t of the model. In reference [73], however, the glass transition volume fraction was calculated for each v using Equation 1.39. 

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