聚合物系反常扩散现象及扩散过程可视化研究

【作者】 雷华；

【导师】 潘勤敏； 鲁阳；

【作者基本信息】 浙江大学 ， 化学工程， 2002， 博士

【摘要】 非费克扩散是化工过程，尤其是涉及高聚物的过程常见的现象之一，其特征、产生机理和本构描述是近年来扩散领域和非线性领域共同关心的问题。要准确地理解和精确地控制这些工业过程，过程中间变量的可探知或可视化(摆脱“黑箱”技术)是非常重要的一环。鉴于此，本论文对非费克扩散现象在理论分析和扩散过程基础场量的测定技术方面进行了新的探索。 非费克扩散现象模型和仿真研究 分析了高聚物/小分子扩散体系的各种非费克现象，讨论了各种可能的影响因素，指出小分子物质对高聚物的溶胀以及高分子链结构的有限松弛是导致非费克扩散的关键。文献上，为了对这些反常现象的进行抽象描述，已提出多种解释非费克扩散现象的理论，虽然这些理论都不能完全解释所有的非费克扩散行为，但在某些层面或特定的范围可有满意的效果。其中EIT理论在处理这些非线性问题上具有明显的理论基础，已成功地应用在一些非线性问题上，因此本论文选择建立在EIT理论基础上的D. Jou模型来研究非费克扩散现象，经过简化处理，导得如下扩散动力学方程：通过仿真分析表明，该模型能够成功描述长时间吸附中发现的“超调”现象，从理论上说明了引起“超调”现象的原因。通过对模型中三个组合参数的分析，研究了参数的变化可能导致的不同的扩散行为： 参数τ′(扩散的瞬态过程引起的滞后时间与松弛时间之比)的存在与否决定了方程是双曲型还是抛物型。如果该参数趋近于零，则模型所预测的扩散行为始终不会出现“超调”现象；如果该参数很大，则一定出现“超调”现象。这里说明扩散的瞬态过程引起的滞后是引起“超调”的必要条件。τ′从大到小的变化过程描述了这样一种行为：扩散滞后在减小，超调的幅度也在减小。这可能是在扩散的初期，由于小分子的进入，改变了聚合物体系的结构，积累了能量，从而阻碍扩散过程，随着扩散的进行，由于聚合物的松弛，把这部分能量释放出来，成为 浙 江 大 学 博 士 学位 论 文扩散的推动力，出现了超调，初期积累的能量越大，阻碍越厉害，很明显释放的能量也越多，所以超调的幅度也越大。 参数De（定义为松弛时间与扩散时间之比），在适当，’下，De类似于扩散系数，这体现在吸收过程达到平衡的时间随＊e的增大而减小。通过对＊e的分析，可以得出产生“超调”现象的机理的另一种解释：小分于渗透物质的扩散时间相对于聚合物的松弛时间要短（相当于有个更快的扩散速度），所以小分子迅速扩散进聚合物中达到一个极值，由于小分子物质对聚合物的溶胀，使得聚合物链结构产生松弛，由于聚合物链结构的变化，小分子物质占有的自由体积会减小，这样会挤出小分子物质，使得小分于物质在聚合物中的浓度减小，如果高聚物粘弹性明显，甚至可能出现多个浓度的衰减振荡（这在实验中没有发现）并达到平衡值。De越大，“超调”越明显。这说明松弛时间大于扩散时间是引起“超调”的充分条件。 参数D”，作为积分项的系数，其大小代表了聚合物“记忆”的能力。积分项使得浓度的变化趋于缓和，回此在吸收曲线中，浓度振荡的趋势不如 De和，’变化的影响剧烈。当D”小于1以后，它对吸收曲线的影响很小。扩散过程基础场量的测定技术研究 要对非费克扩散产生的机理进行深入的研究，必须解决一些基础场量的测定，摆脱“黑箱”研究方法，把黑箱测量透明，或称之为测量过程的可视化。本文的目的是测得高聚物／小分子扩散体系的三维浓度场分布。为此，在总结各种实现三维场量测量的实验手段的基础上，本文提出了“微分干涉分析”的概念，井结合光学相干层析（OCT ）技术，建立了全息相干层析（HCT）的三维场量测试原理：将双曝光全息干涉计量同层析探测相结合，通过对双曝光全息再现象的层析探测，实现三维折射率测量。作为该原理的实现，构建了一个全息相干层析 （HCT）的测试系统：利用一个共焦检测系统对被测对象的像面全息干涉图进行三维扫描，并记录干涉强度，通过对强度数据的处理，重构出三维折射率场。还给出了初步的试验验证（一维的），证明该方法是可行的。它相对于传统的工业CT，没有复杂的传感器设备，也不需要复杂的重构算法以及漫长的重构过程（对计算机设备的要求很高）。而且它不破坏测量场，是一种无损检测。 11 摘 要 作为实现HCT的基础，本文还研究了全息干涉技术在高聚物测试体系的应用和高粘体系折射率测量方法的研究。它们分别对应一维浓度分布的测量和均相体系浓度的测量。 通过对激光全息干涉术的研究，本文认为激光全息干涉技术在高聚物扩散体系这种应用背景下具有明显的优势，它避免了高粘体系的非均匀性给测量带来的误差。把它应用于小分子在聚合物中的扩散过程的研究，记录下了PMMA／MMA扩散体系扩散过程，通过对所得全息图的处理，得到了浓度场分布，由于全息干涉在成像方面的优势，它还能?更多还原

【Abstract】 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更多还原