Mathematical Aspects of Frontal Polymerization

DMS Award AbstractAward #： 0103856 PI： Volpert，弗拉基米尔 西北大学课程： 应用数学项目经理：Catherine Mavriplis职务：前沿聚合的数学方面该研究项目致力于前沿聚合（FP）过程的理论研究，其中局部反应区传播到单体中，将其转化为聚合物。该项目解决了特定FP过程的建模和由这些建模工作激发的更一般的数学问题的研究。具体的建模主题包括FP波的初始化研究，其线性和非线性稳定性以及流体动力学行为。渐近方法被用来确定聚合波的结构和产品的组成，以及这种实验测量的波作为其传播速度的函数的动力学和热物理参数的问题和初始条件的特性。更一般的数学性质的主题涉及反应扩散系统中的阈值现象，单调抛物系统的时间周期行波的存在性，描述聚合动力学的新型积分微分方程，以及反应扩散系统的新形式的解，所谓的准行波解，其特征，包括传播速度，在时间上变化缓慢。所提出的前沿聚合研究的重要性是双重的。首先，它是一种生产聚合物的方法，这些聚合物已成为人类生活的一个组成部分。它与发生在前沿区域的另一种技术过程有很强的相似性，即使用燃烧波合成所需无机材料的自传播高温合成。与正面聚合方法不同，自蔓延高温合成方法被充分研究，并且已知其具有优于将混合物置于炉中的常规技术的某些优点。这些包括（i）较短的合成时间，（ii）较低的费用，因为使用的是反应物的内部化学能而不是炉子的外部能量，（iii）使用较简单的设备，和（iv）较纯的产品，因为高温波烧掉挥发性杂质。在聚合物合成中可以预期类似的益处。具体地，可以减少能量成本和废溶剂产生，并且获得独特的材料。然而，在可以实现任何优势和前沿聚合工艺成为一种有竞争力的技术之前，更好地理解影响前沿聚合的因素是必要的。其次，前沿聚合的具体模型的研究提出了更一般的数学性质的问题，这些问题与一般反应/扩散/对流系统的解的行为有关。对这些更普遍的问题的研究有助于理解特定的前沿聚合问题。

DMS Award AbstractAward #: 0103856PI: Volpert, Vladimir Institution: Northwestern UniversityProgram: Applied MathematicsProgram Manager: Catherine MavriplisTitle: Mathematical Aspects of Frontal PolymerizationThe research project is devoted to theoretical investigations of frontal polymerization (FP) processes, in which a localized reaction zone propagates into a monomer converting it into a polymer. The project addresses both modeling of specific FP processes and the study of more general mathematical problems motivated by these modeling efforts. Specific modeling topics include the study of initiation of FP waves, their linear and nonlinear stability and fluid dynamical behavior. Asymptotic approaches are used to determine the structure of the polymerization wave and the composition of the product, as well as such experimentally measurable characteristics of the wave as its propagation velocity as a function of the kinetic and thermophysical parameters of the problem and the initial conditions. Topics of a more general mathematical nature are concerned with threshold phenomena in reaction diffusion systems, existence of time-periodic traveling waves of monotone parabolic systems, new kinds of integro-differential equations describing polymerization kinetics, and new forms of solutions of reaction diffusion systems, the so-called quasi-traveling wave solutions, the characteristics of which, including the propagation speed, vary slowly in time.The importance of the proposed studies of frontal polymerization is twofold. First, it is a method to produce polymers which have become an integral part of human life. It bears strong similarities with another technological process occurring in a frontal regime, namely, self-propagating high-temperature synthesis which uses combustion waves to synthesize desired inorganic materials. Unlike the frontal polymerization process, the self-propagating high-temperature synthesis process is well-studied and is known to enjoy certain advantages over conventional technology, in which the mixture is placed in a furnace. These include (i) shorter synthesis times, (ii) less expense, since the internal chemical energy of the reactants is used rather than the external energy of the furnace, (iii) the use of simpler equipment, and (iv) purer products, since the high-temperature wave burns off volatile impurities. Similar benefits can be expected in polymer synthesis. Specifically, energy costs and waste solvent production can be reduced and unique materials obtained. However, before any advantages can be achieved and the frontal polymerization process becomes a competitive technology, a better understanding of the factors that affect frontal polymerization is necessary. Second, studies of specific models of frontal polymerization pose questions of a more general mathematical nature that are related to the behavior of solutions of general reaction/diffusion/convection systems. The study of these more general problems contributes to the understanding of specific frontal polymerization problems.Date: June 18, 2001