Polymer Department Of Anomalous Diffusion Phenomena And Diffusion Process Visualization

Non-Fickian diffusion is one of the important phenomena often observed in chemical processes, especially in polymer-related operations. The characterization, mechanism, and constitutive description of non-Fickian phenomena have recently become a research focus in the field of diffusion and nonlinear science. In order to understand well the non-Fickian phenomenon as well as the related processes, it is necessary to acquire/visualize the details between input and output of the processes involved and get rid of the conventional "black-box" method. . The purpose of this paper is to reveal the mechanism of non-Fickian diffusion phenomenon by theoretical analysis and by technical establishment of novel measurement methods capable of visualizing the details of diffusion processes.Modeling and simulation of non-Fickian phenomenaVarious non-Fickian phenomena observed in polymer/small molecule diffusion systems were analyzed, and the possible influences on them are discussed. The key origins which non-Fickian diffusion in a polymer/small molecules system results from were pointed out, i.e. the swelling of the polymer by the small molecules and the limited relaxation process of the polymer to respond to the diffusion or swelling of the small molecules. In the literatures, there have been many theories to interpret non-Fickian diffusion. Although no any one of them can cover all phenomena, some of them can provide satisfactory description in some special scope or within a certain extent. BIT (Extended Irreversible Thermodynamics), one of the methods/theories in the literature, shows reasonable fundamental aspects to describe nonlinear problems like non-Fickian diffusion and has been successfully applied to a certain fields. In this paper, the D. Jou model based on EIT was selected to study non-Fickian diffusion. After simplification, the following dynamic equation for diffusion can be resulted:Simulation analysis indicates that this equation can describe "overshoot" phenomenon observed in a long-term sorption process, so that the cause of generating "overshoot" can be interpreted theoretically/mathematically. The analysis of the model parameters indicates that there are various diffusion behaviors, depending on the model parameters.Parameter r' (ratio of lag time of diffusion process to relaxation time of polymer) can define the form of the differential equation: hyperbolic or parabolic. When it approaches to zero, there must not exist the "overshoot" behavior according to the model; when it is large enough, there must have the "overshoot" behavior. Here it is indicated that the retardance of diffusion process is the cause of "overshoot". When r' is changed from large to small, both the diffusion retardance and the amplitude of "overshoot" decrease. It is most possibly caused by the change in the assembling structure of the polymer during diffusion. In the initial period, the small molecules which has entered the polymer changes the assembling structure of the polymer and then some energy is accumulated in the polymer, and the diffusion process was slowed down. With the sorption developing, due to the relaxation of polymer, the accumulated energy then is released, which can be an additional driving force for diffusion, and therefore "overshoot" behavior is possibly initiated. The more energy were accumulated in the initial period, more significant the retardance would be, obviously, the more energy would be released and the larger amplitude of "overshoot" could be expected.De (defined as the ratio of relaxation time to diffusing time), with proper r', behaves like diffusivity, which was embodied in that the time for approaching sorption equilibrium decreases with De increasing. Through the analysis of De, an alternative mechanism interpreting of the "overshoot" phenomena can be obtained: when the diffusing time of small molecular penetrants is shorter than relaxation time of the involved polymer, small molecular substance penetrates into the polymer quickly and its concentration reached a maximum, then the sw...