You may want to look at the following article published by NA Peppas back in 1976 where he tried to estimate the interaction parameter for PVA and water in cross-linked gels.

All The Best!

A polymer, with cross-linked network structure, will have inter-molecular primary bonds of the covalent type. In order for a polymer to dissolve in a solvent, the polymeric molecules must be separated & the solvent molecules will surround the macro molecules forming many polymer-solvent interactions of the secondary type of bonding.

Since primary bonds are much stronger than secondary bonds, then there is no dissolution of a cross-linked polymer in a solvent. Therefore, we do not look for polymer-solvent parameter for this particular case.

I suggest seeking polymer-solvent interaction parameters for linear or branched polymers.

Rashid,

try using the Hansen-Flory theory for interaction parameter between solvent and polymers. You may have to think of boundary conditions for the cross-linked network. Start with the uncrosslinked systems and compare the parameters with crosslinked systems. Look into Hansen Solubility Parameter book.

Consult some articles by Dr. Nazar Muhammad Ranjha.

I found the paper by Peppas et al., recommended by A. Patil rather intractable, mainly because of the insufficient explanation of the meaning of symbols. Rather I propose to apply the simplified relationship between swelling power q and number of monomers per cross-link Nc as derived by Flory (P.J. Flory, Principles of Polymer Chemistry, 1953, Chapter XIII).

q5/3 = (1/2 - chi). (vm/vs). Nc

Here, 'chi' is the polmer-solvent interaction parameter and vm and vs are the molar volumes of monomer and solvent, respectively. The latter are defined as molar mass/density. Nc can be estimated from the applied ratio of monomer to cross-linker in solution, corrected for unreacted cross-linker remaining in solution after completion of the reaction.

By measuring the swelling power of gels (volume/volume) with different degrees of cross-linking (= different Nc) and plotting q5/3 vs Nc one finds (1/2 - chi).(vm/vs) as the intercept. A linear relationship points to an independence of chi with polymer concentration. Please note that this relationship is a first approximation and may only apply to low degrees of cross-linking. It also assumes that chi can only vary between 0 (good solvent) and 0.5 (marginal solvent) as negative q values are physically impossible.

I found the paper by Peppas et al., recommended by A. Patil rather intractable, mainly because of the insufficient explanation of the meaning of symbols. Rather I propose to apply the simplified relationship between swelling power q and number of monomers per cross-link Nc as derived by Flory (P.J. Flory, Principles of Polymer Chemistry, 1953, Chapter XIII).

q5/3 = (1/2 - chi). (vm/vs). Nc

Here, 'chi' is the polmer-solvent interaction parameter and vm and vs are the molar volumes of monomer and solvent, respectively. The latter are defined as molar mass/density. Nc can be estimated from the applied ratio of monomer to cross-linker in solution, corrected for unreacted cross-linker remaining in solution after completion of the reaction.

By measuring the swelling power of gels (volume/volume) with different degrees of cross-linking (= different Nc) and plotting q5/3 vs Nc one finds (1/2 - chi).(vm/vs) as the intercept. A linear relationship points to an independence of chi with polymer concentration.

Please note that this relationship is a first approximation and may only apply to low degrees of cross-linking. It also assumes that chi can only vary between 0 (good solvent) and 0.5 (marginal solvent) as negative q values are physically impossible.

Please see the attached file on the Flory swelling method.

I am sorry! Repetitions are due to site operator's messages pointing at the impossibility to forward my answers.

Dear Haroon,

Swelling experiments are utilized to get an estimate of the crosslinked density not the otherway around since the theoretical value of the crosslinked density may be quite different from the actual one. Further, the variability on these experiments is quite large.

I also recommend the suggestions to estimate the chi parameter used in these equations through the computation of the Hansen parameters. Hansen's group has also develop a software that may help you have a theoretical estimate of the parameters. There is a relationship between Hansen parameters and chi parameter.

Alternatively, if you'd rather want to find the crosslinked density you can also find it utilizing a viscoelastic characterization of the gels. There is a relationship between the elastic modulus, crosslinked density, temperature, and specific gravity that do not depend on the chi parameter variable.

Kind regards