Equilibrium swelling theory

The equilibrium swelling theory of Flory and Rehner [64] assumes that the degree of swelling of an uncharged gel results from the effects of just two opposing forces the thermodynamic effects of mixing tending to dilute the polymer component and the elastic constraints imposed by the force required to stretch the polymer chains. At equilibrium, these two forces are equal. 

Theories have been advanced which account for the equilibrium amount of water absorbed and for the diffusion of water in natural rubber. The equilibrium swelling theory is an Improved version of that of Briggs et al. (2) in that a more reallsltic calculation of the rubber pressure is used. The diffusion theory accounts for the experimental observations both in predicting the correct order of magnitude of the diffusion coefficient of water in rubber and also its concentration dependence. 

As already mentioned earlier, the stracture of a polymer network can be elucidated from its macroscopic network properties, like swelling or mechanical characteristics. The most prominent methods used are the equilibrium swelling theory and the mbber elasticity theory (RET). 

The equilibrium swelling theory of Flory and Rehner (76) treats simple polymer networks in the presence of small molecules. The theory considers forces arising from three sources ... 

A further test of the validity of ideal network theory can be obtained through studies of the equilibrium swelling of polymer networks (Eq. 11-22). The maximum amount of information can be extracted by inducing changes in the equilibrium swelling preferably combined with unidirectional stress-strain data (Eqs. III-21, 26 and 27). 

Such networks have been widely used to establish whether the theories of rubber elasticity and of equilibrium swelling are valid. But these theories are based on a number of hypotheses which are obviously far from being fulfilled by the above networks. The so-called ideal networks should obey the following requirements ... 

The question now arises whether the so-called model networks are really close to ideality, and whether they may be used to check the validity of the existing theories of equilibrium swelling and of rubber elasticity. This question deserves some discussion. 

There is only an alternative way of determining crosslink density by a non empirical method, using the theory of equilibrium swelling of a network in a solvent (Flory and Rehner, 1943). This method, usual in the domain of rubbers, needs the knowledge of a polymer solvent interaction coefficient proportional to (8p — 8S)2, which is not very easy to determine accurately. Furthermore, damaging by swelling stresses and the need to work at elevated temperatures complicate the analysis seriously for the usual thermosets... 

Important theoretical and experimental considerations of the use of macromolecular theories for the description of coal network structures have been recently analyzed (1). Relevant equations describing the equilibrium swelling behavior of networks using theories of modified Gaussian distribution of macromolecular chains have been developed by Kovac (2 ) and by Peppas and Lucht (3) and applied to various coal systems in an effort to model the relatively compact coal network structures (1 4). As reported before (1), Gaussian-chain macromolecular models usually employed in the description of polymer networks (such as the Flory... 

If the objective of the experiment is to estimate the network chain density by the statistical theory, and if swelling is resorted to as a means for alleviating the above experimental difficulties, then the measurement of stresses becomes redundant the theory of equilibrium swelling of Flory and Rehner (127,128) makes an estimate of the desired network chain density possible with only the knowledge of the equilibrium swelling volume. The usual procedure is to calculate the volume fraction of polymer in the swollen rubber (ar) under the assumption that the filler does not swell. The Flory-Rehner theory then yields, for a network containing no sol fraction ... 

The theory proposed for equilibrium swelling and diffusion is based on the assun tlon that the hydrophilic impurities are present in particulate form and are dispersed throughout the rubber. The precise nature of this impurity in natural rubber is not known so it was decided to make a model rubber by adding 0.17. of a hydrophilic Impurity (sodium chloride) to a solution polymerised synthetic rubber (cis-polyisoprene) Ich is chemically the same as natural rubber. Using this model rubber it is possible to check the theory more precisely since both the nature and concentration of the hydrophilic lgq>urlty in the model rubber are known. It is proposed that the water diffuses through the rubber and forms droplets of solution inside the rubber where there are particles of the hydrophilic impurity thereby causing a non-uniform distribution of water in the rubber. The... 

---