Modelling of Gels

2 Adsorption-Induced Deformation Model of Electroantive Polymer Gel 

It has been proposed numerous models to describe actively deformable materials, especially electroactive polymers. Novel model is proposed because of the characteristics of the previous one. 

The purpose of most model is to design and optimize the material. 

They are not perspective for the purpose of design and control of machines. 

Chemists and material scientists proposed most of the models. They tend to describe the mechanisms of deformation in detail, since purpose of their models is different from this study. The papers introducing developed materials focus on differentiation from existing materials, which is apparent from the nature of research. Therefore, most of the models depend on the kinds of material. 

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In a further study, Rill et al. [325] developed a model of gel permeation chromatography that included a bimodal pore stracture. The smallest mode in the pore-size distribution represents the basic background polyacrylamide pore structure of about 1-mn mean radius, and the second mode was around 5 nm, i.e., in the range of size of the molecular templates. The introduction of this second pore structure was found to substantially improve the peak resolution for molecules with molecular sizes in the range of the pore size. 

Classical models of gel formation (or sol-gel transitions [4]) by Flory [394], Gordon, Ma-cosko and Miller [228,245], and others (see Ref. 4 for a more complete review) considered... 

In this article we review our experience with hydrophobic polyelectrolyte gel systems. In Sect. 2 we summarize the essentials of the synthesis procedure. In Sect. 3 swelling equilibrium measurements are summarized, and in Sect. 4 these measurements are used to evaluate a simple theoretical model of gel swelling. Significant quantitative discrepancies are found, the putative sources of which are discussed. Swelling and deswelling kinetics results are discussed in Sects. 5 and 6. Section 7 summarizes the article, and suggests some implications of the reported results. 

Numerous models of gels are based on the widespread polymeric model considering gels as mixtures of multicomponent branched polymers of different weight. Then, the main problem consists in the evaluation of the weight distribution of polymers. 

The statistical polymer method, based on the study of averaged structures (statistical polymers) is recommended for modeling of gels and other materials prepared from branched cross-linked macromolecules. Most of real gel systems can be fairly described by the statistical polymer method without any problems related to engineering computer calculations. 

To illustrate the behavior of the ultrafiltration flux, we here adopt Michaels model of gel layer formation. As was done for reverse osmosis, let us again consider the geometry of a two-dimensional parallel plate channel with fully developed flow. Moreover, to simplify the presentation, we examine only the limiting-flux problem. 

Interestingly, the three-dimensional (3D) network of interconnected cavities described in Reference 22 is a perfeet practical reahzation of the lakes-straits model proposed by Zimm [39] as an early model of gel electrophoresis. To be in this regime, a molecule must span several pores, so DNA molecules significantly larger than those used in the experiments described above would be necessary to reach this regime. It would be interesting to check the validity of the lakes-straits model with such molecules. 

Slater GW, Guo HE (1996) An exactly solvable Ogston model of gel electrophoresis I. The role of symmetry and randtunuess of the gel structure. Electrophoresis 17 977-988... 

Figure 3.58. Problem of bond and node percolation a model of gel formation during polymerization of a polyfunctional monomer in solution (Stanley et al., 1980 Efros, 1982 ) [Reprinted with permis.sion from Dynamics of Synergetic Systems Proc. Int. Symp. on Synergetics, Butlfeld, Germany, September 2f-29, 1979 Ed. M.Haken. Copyright by Springer-VerlagJ...

First, we pay attention to models of gels rather than electroactive polymers. This is because most of the models on electroactive polymers are particular to driving mechanism and dependent on kinds of material while models of gels... 

Lee, W. Polymer Gel Based Actuator Dynamic model of gel for real-time control. Ph.D. Thesis, MIT (1996)... 

The quantitative data and observations discussed above appear to be consistent with the qualitative concepts put forward by Mosbach and others to explain the behavior of multistep enzyme systems. Mathematical modelling of gel entrapped, multistep, immobilized enzyme systems, using the collocation technique, is quite straightforward and provides the opportunity not only to compare experiment with theory but also to explore the effect of parameters of the system which are experimentally inaccessible. 

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