Kinetic Theory of Swelling

The kinetic theory of rubber elasticity is so well known and exhaustively discussed (17, 27, 256-257, 267) that the remarks here will be confined to questions which relate only to its application in determining the concentration of elastically effective strands. In principle, both network swelling properties and elasticity measurements can provide information on network characteristics. However, swelling measurements require the evaluation of an additional parameter, the polymer-solvent interaction coefficient. They also involve examining the network in two states, one of which differs from its as-formed state. This raises some theoretical difficulties which will be discussed later. Questions on local non-uniformity in swelling (17) also complicate the interpretation. The results described here will therefore concern elasticity measurements alone. 

The swelling kinetic theory of gels began by simply solving the difiusion equation for the difiusion of solvent into gels. As early as 1965, Dusek had already treated the swelling of ion exchange resins as the... 

The kinetic theory of gel swelling has been explained fi om the viewpoints of theory, experiments and applications, all of which are summarized in... 

It is important to propose molecular and theoretical models to describe the forces, energy, structure and dynamics of water near mineral surfaces. Our understanding of experimental results concerning hydration forces, the hydrophobic effect, swelling, reaction kinetics and adsorption mechanisms in aqueous colloidal systems is rapidly advancing as a result of recent Monte Carlo (MC) and molecular dynamics (MO) models for water properties near model surfaces. This paper reviews the basic MC and MD simulation techniques, compares and contrasts the merits and limitations of various models for water-water interactions and surface-water interactions, and proposes an interaction potential model which would be useful in simulating water near hydrophilic surfaces. In addition, results from selected MC and MD simulations of water near hydrophobic surfaces are discussed in relation to experimental results, to theories of the double layer, and to structural forces in interfacial systems. 

Fig. 9. Plot of normalized approach to equilibrium mass against the square root of time for a temperature-sensitive 10 x 4 PNIPAAm gel sheet swelling and shrinking between 10 and 25 °C-Shown are the curve fits to the kinetic data of theory developed from Fick s law of diffusion in a polymer-fixed reference frame [149]. The equilibrium degree of swelling is 17.0 at 10 °C and 11.1 at 25 °C the diffusion coefficients obtained from the curve fits are 2.3 x 10 7 cm2/s for swelling and 3.6 x 10 7 cm2/s for shrinking [121]...

The kinetics of swelling is successfully described as a collective diffusion process. Tanaka et al. (Tanaka et al. 1973) developed a theory for the dynamics of polymeric gels. They realized that the polymer chains are cormected by chemical bonds and a gel has to be treated as a continuum. In addition, the network behaves as an assembly of springs due to their entropy elasticity. 

The swelling kinetics of stimuli-responsive hydrogels is described by the theory of cooperative diffusion (Sect. 3.2.2 and 3.2.3, (Tanaka and Fillmore 1979)). Besides the cooperative diffusion constant, which is specific for each solvent-polymer network combination (see Eq. (3.2.9)), the time behaviour of active hydrogel components can be as well influenced by further design-dependent aspects (Richter 2006, 2008b). 

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