Sorption to Attain Gel-Saturation

Although the kinetics of liquid uptake to attain gel-saturation is history-dependent, the composition at the true end-state (i.e. thermodynamic equilibrium in excess liquid) is not therefore the observed end-state is usually reproducible [19]. Gel-saturation is attained when the restraining force (per unit area) of the polymeric crosslinked network becomes equal and opposite to the osmotic pressure that causes the system to swell [20], In other words saturation is achieved when the chemical potential of swelling liquid, p1 in the swollen network is equal to the chemical potential of the excess pure liquid, p , outside the network. It was logical to anticipate that the volume of liquid sorbed per gram of polymer, at this state of thermodynamic equilibrium with excess liquid, would correlate with the molecular structure of the liquid. In fact two parameters already exist which relate the sorption affinity to the molecular structure, namely the solubility parameter, 8, first proposed by Hildebrand [21], and the interaction parameter, %, introduced by Flory [22] and Huggins [23-26], 

Thermodynamic relationships stated in Eqs. 4 and 5 imply that the more equal the cohesive energy densities of solute and solvent the greater is their mutual compatibility [21] (i.e. like dissolves like). 

Marked differences between observed and predicted results occur, however, when the entropy effects are too great to be ignored. In the derivation of Eqs. 4 and 5, only dispersion forces between molecular components were taken into 

The solubility parameters of many volatile liquids have been calculated directly from their respective heats of vaporization and molar volumes (Eq. 5). Hoy [32] has shown that 8 for relatively non-volatile liquids can be calculated from vapor pressure data using a modification of the Haggenmacher Eq. [33], Large numbers of such data have been reported and these are collected in extensive tables [27, 28, 34], 

Small [36] showed that most of the reported 8 can be estimated by the last of the above three relationships, on the basis of the molecular structure of the solvent. He used this method to calculate the solubility parameter of poly(styrene) to obtain a value, 5pol = 9.12 (cal/mL)1 2, which is within the range of the experimental 8-values [8.6 to 9.7 (cal/mL)1/2] reported for this polymer [34, 37 39], [note that (joule/mL)1/2 = 2.046 (cal/mL)1/2]. 

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