Diffusion in glassy polymers

Fluid diffusion in glassy polymers proceeds in ways that are not explained by the standard diffusion model. Although the reasons for the anomalous effects are not known, much of the observed behavior is attributed to the long times that polymers below their glass transition temperature take to adjust to changes in their condition. The slow internal relaxations of the polymer chains ensure that the material properties are history-dependent, and also allow both local inhomogeneities and differential swelling to occur. Two models are developed in this thesis with the intent of accounting for these effects in the diffusion process.

In Part I, a model is developed to account for both the history dependence of the glassy polymer, and the dual sorption which occurs when gas molecules are immobilized by the local heterogeneities. A preliminary study of a special case of this model is conducted, showing the existence of travelling wave solutions and using perturbation techniques to investigate the effect of generalized diffusion mechanisms on their form. An integral averaging method is used to estimate the penetrant front position.

In Part II, a model is developed for particle diffusion along with displacements in isotropic viscoelastic materials. The nonlinear dependence of the materials on the fluid concentration is taken into account, while pure displacements are assumed to remain in the range of linear viscoelasticity. A fairly general model is obtained for three-dimensional irrotational movements, with the development of the model being based on the assumptions of irreversible thermodynamics. With the help of some dimensional analysis, this model is simplified to a version which is proposed to be studied for Case II behavior.

Trace metals in fresh water plankton

The uptake of Cu, Zn, and Cd by fresh water plankton was studied by analyzing samples of water and plankton from six lakes in southern California. Co, Pb, Mn, Fe, Na, K, Mg, Ca, Sr, Ba, and Al were also determined in the plankton samples. Special precautions were taken during sampling and analysis to avoid metal contamination.

The relation between aqueous metal concentrations and the concentrations of metals in plankton was studied by plotting aqueous and plankton metal concentrations vs time and comparing the plots. No plankton metal plot showed the same changes as its corresponding aqueous metal plot, though long-term trends were similar. Thus, passive sorption did not completely explain plankton metal uptake.

The fractions of Cu, Zn, and Cd in lake water which were associated with plankton were calculated and these fractions were less than 1% in every case.

To see whether or not plankton metal uptake could deplete aqueous metal concentrations by measurable amounts (e.g. 20%) in short periods (e.g. less than six days), three integrated rate equations were used as models of plankton metal sorption. Parameters for the equations were taken from actual field measurements. Measurable reductions in concentration within short times were predicted by all three equations when the concentration factor was greater than 10^5. All Cu concentration factors were less than 10^5.

The role of plankton was regulating metal concentrations considered in the context of a model of trace metal chemistry in lakes. The model assumes that all particles can be represented by a single solid phase and that the solid phase controls aqueous metal concentrations. A term for the rate of in situ production of particulate matter is included and primary productivity was used for this parameter. In San Vicente Reservoir, the test case, the rate of in situ production of particulate matter was of the same order of magnitude as the rate of introduction of particulate matter by the influent stream.