Mathematical Aspects of Frontal Polymerization

DMS奖项摘要获奖编号：0103856PI: Volpert， Vladimir机构：Northwestern university项目：应用数学项目经理：Catherine mavriplis标题：正面聚合的数学方面该研究项目致力于正面聚合（FP）过程的理论研究，在该过程中，局部反应区繁殖成单体，将其转化为聚合物。该项目涉及特定FP过程的建模和由这些建模工作所激发的更一般的数学问题的研究。具体的建模主题包括研究FP波的起始，它们的线性和非线性稳定性以及流体动力学行为。使用渐近方法来确定聚合波的结构和产物的组成，以及实验可测量的波的特征，如其传播速度作为问题的动力学和热物理参数的函数和初始条件。更一般的数学性质的主题涉及反应扩散系统的阈值现象，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类型的积分微分方程，以及反应扩散系统的新形式的解，即所谓的准行波解，其特征，包括传播速度，随时间变化缓慢。提出的正面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，聚合物已成为人类生活中不可或缺的一部分。它与另一种发生在前沿的工艺过程有很强的相似之处，即利用燃烧波合成所需无机材料的自传播高温合成。与正面聚合工艺不同，自传播高温合成工艺得到了充分的研究，并且已知与传统技术相比具有某些优势，在传统技术中，混合物被放置在炉中。这些包括(i)更短的合成时间，（ii）更少的费用，因为使用反应物的内部化学能而不是炉子的外部能量，（iii）使用更简单的设备，（iv）更纯净的产品，因为高温波燃烧掉挥发性杂质。在聚合物合成中也可以预期类似的效益。具体来说，可以减少能源成本和废溶剂的产生，并获得独特的材料。然而，在取得任何优势并使正面聚合工艺成为一项有竞争力的技术之前，有必要更好地了解影响正面聚合的因素。其次，对正面聚合的特定模型的研究提出了与一般反应/扩散/对流系统的解的行为有关的更一般的数学性质的问题。这些更普遍的问题的研究有助于理解具体的正面聚合问题。日期：2001年6月18日

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