Anomalous Diffusion of Dextran in Polymer Solutions
Student thesis: Doctoral Thesis
Diffusion processes are used in numerous models to describe phenomena in different areas including natural sciences and even economics. Diffusion describes the mass transportation of substances from their high concentration regions to low concentration regions. Diffusion coefficients, which play a key role in the study of diffusion process, have been analysed by many scientists, some of whose work are widely identified by nowadays scientific workers, by using various methods and models. In a crowded environment, the diffusion coefficients have been found to vary, possibly, with concentrations, solvent states, positions or time. This type of diffusion is generally called "anomalous diffusion". In the past half century, much effort has been made to investigate the mechanisms of anomalous diffusion, such as polymer's diffusion in gels. We designed a method to yield a scaling law of diffusion coefficients by processing the experimental data of diffusants' concentrations to calculate a possible diffusion coefficients for our system. The main idea of this method utilised a functional approaching to find an alternative concentration approximated to the experimentally obtained data, and then used this approximation to calculate the diffusion coefficient from the equation. Indeed, we analysed the experimental data and found that the diffusion coefficients in gels had a form of D ~ αt/c, where D denoted the diffusion coefficient of the diffusant in gels, c was the concentration of the diffusant larger than 0 and t was the diffusing time. In the above relationship, α was a parameter determined by experiments and we guessed that α depended on the concentration of hydrogels although we had not found out the law yet. In this case, we reformed the function of D to
D (chydrogel, cdextran ) = α (chydrogel ) t /cdextran ,
when cdextran was large enough. Our work provided novel insights into a very basic but important molecular process, diffusion, and resolved analytical simulation of the spreading of molecules in complex environments that were much relevant to physiological conditions, including viscous polymeric condition and concentration dependent variations.