In the following sections, the bond graph based lumped parameter models of both non-electrolyte and electrolyte gel are described. Control volume for non-electrolyte gel model.
Since the amount of polymer inside the c. As the solvent fluid enters the c. Lettingrepresent the changes in dimensions resulting from the combination of swelling and elongation, is therefore constant during the elongation.
Illustration of entropy generating mixing process. The polymer-solvent contact effect involves enthalpy change, and its effect on Gibbs free energy is where is the Flory-Huggins polymer-solvent interaction parameter.
The second term on RHS represented the chemical energy brought in by the incoming surrounding solvent, and the last term represented the effect of mechanical work on the gel.
Subsequently, kinetic models of gel swelling developed so far were mainly based on the macroscopic continuum description.
The modeling assumptions were: Similarly, change in entropy of control volume due to mixing,may be defined as where Scv1 is the entropy of c.
The combinatorial effects on entropy and Gibbs free energy are where R is the universal gas constant, ns is the molar quantity of solvent, np is the molar quantity of polymer, is the volume fraction of solvent, is the volume fraction of polymer, and s is the number of chain segments of a polymer molecule such that the volume of a polymer molecule is equal to s time the volume of a solvent molecule, i.
The gel is represented as a multiport capacitance with three energy ports corresponding to thermal, chemical and mechanical interactions.
According to Flory, the Gibbs free energy change due to mixing of polymer and solvent is considered to be of two effects; combinatorial effect and polymer-solvent contact effect. Assuming that the gel solution is sufficiently diluted, Flory treated these three contributions to be additive.
The above expression then simplifies to. In state 1, pure polymer network and pure solvent inside the control volume are completely separated whereas in state 2, they mix and form a homogeneous solution, while maintaining constant volume.
Dividing the gel structure into many fine subunits should yield results equivalent to the finite difference method, and thus may be used for checking validity. Here we will briefly describe his model, and investigate how his model can fit into a lumped parameter frame work.
With the assumption of a quasistatic process, the system inside the control volume was treated as a lumped parameter multiport capacitance field with the relation. In the subsequent deformation due to stretching, the volume is assumed to stay constant.In presenting this thesis in partial fulfillment of the requirements for a master’s degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection.
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