Mathematical Modeling and Experimental Characterization of Polymer Dissolution

Abstract

A new polymer dissolution model was developed by incorporating the polymer chain disentanglement mechanism into the relevant transport equations. The disentanglement time was used as a dissolution characteristic time controlling the moving position of the solvent-polymer boundary. A dimensionless dissolution number was defined as the ratio of the characteristic polymer disentanglement time to the characteristic solvent diffusion time. The dissolution number was shown to be proportional to the square of the gel layer thickness. Scaling law expressions for the dependence of the gel layer thickness and the polymer dissolution rate on polymer molecular weight were also derived. Solution of the model for one-dimensional dissolution showed three distinct dissolution stages and confirmed the proposed scaling law relations for the gel layer thickness and the dissolution rate. Experimental studies of dissolution of polystyrene and poly(methyl methacrylate) in methyl ethyl ketone were used to verify the model, and two types of polymer dissolution behavior were observed. For dissolution of polystyrene in MEK, the solvent diffusion behavior was Fickian and a constant gel layer thickness was observed during the stationary dissolution stage. The effect of polymer molecular weight on the gel layer thickness was investigated for nine monodisperse samples, with Mn ranging from 28 000 to 2 830 000. The experimental results showed that the dependence of the gel layer thickness on molecular weight is more prominent in the high molecular weight region. The polystyrene data verified the new dissolution model. The dissolution of PMMA in MEK was controlled by crack propagation as no significant gel layer was observed.

A review of polymer dissolution

“…Peppas et al [99] proposed a dissolution model based on chain disentanglement and introduced the idea of a dissolution clock. An expression for the reptation time is derived from the reptation theory and the resultant scaling laws [98,100,101] and it scales as follows [102] …”

“…The appropriate boundary condition for the gelliquid interfaces, S; take into account the disentanglement time as defined by Peppas et al [99]. Thermodynamics of swollen networks are used to estimate the concentration at this interface.…”

“…Spin echo NMR has also been applied [32,99]. As the T 1 values decrease when the molecular motion becomes faster or when the correlation time decreases.…”

Understanding isothermal semicrystalline polymer drying: Mathematical models and experimental characterization

“…36 It has been shown by Harland and Peppas 37 that the value of is equal to 3.0 for the diffusion of small molecules through semicrystalline polymers, unless the volume fraction of the crystals is very low. In our studies, we have assumed ϭ1.0 when 2c Յ 0.05 and ϭ 3.0 when 2c Ͼ 0.05.…”

Theoretical and Experimental Analysis of Polymer Molecular Weight and Temperature Effects on the Dissolution Process of Polystyrene in Ethylbenzene

“…In their report, however, the analysis of temperature effect on the dissolution process was omitted. Peppas et al 2 analyzed the dissolution process of polystyrene in MEK using the polymer chain disentanglement mechanism with the concept of dissolution clock. They simulated the change of gel layer thickness during the dissolution process, and observed its existence by experiments.…”