Mathematical Aspects of Frontal Polymerization

前沿聚合的数学方面

• 批准号: 0103856
• 负责人: Vladimir Volpert
• 金额: $ 16.35万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103856&HistoricalAwards=false
• 关键词: Mathematical; Aspects; Frontal; Polymerization

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

DMS奖摘要奖#：0103856PI：Volpert，弗拉基米尔研究所：西北大学项目：应用数学项目经理：Catherine Mavriplis标题：正面聚合的数学方面研究项目致力于正面聚合(FP)过程的理论研究，在FP过程中，局部反应区传播到单体，将其转化为聚合物。该项目既涉及具体FP过程的建模，也涉及由这些建模工作所激励的更一般数学问题的研究。具体的模拟主题包括FP波的起始、其线性和非线性稳定性以及流体动力学行为的研究。用渐近方法确定了聚合波的结构和产物的组成，以及聚合波的传播速度作为问题的动力学参数和热物理参数以及初始条件的函数的可实验测量的特性。更一般的数学问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型积分-微分方程组，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缓慢变化。首先，这是一种生产聚合物的方法，聚合物已经成为人类生活中不可或缺的一部分。它与另一种发生在锋面区域的技术过程有很大的相似之处，即利用燃烧波合成所需无机材料的自蔓延高温合成。与前向聚合过程不同，自蔓延高温合成过程得到了很好的研究，并且众所周知，与将混合物放入炉中的传统技术相比，它具有一定的优势。这包括(I)更短的合成时间，(Ii)更少的费用，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)使用更简单的设备，以及(Iv)更纯净的产品，因为高温波燃烧挥发性杂质。类似的好处也可以在聚合物合成中得到预期。具体地说，可以减少能源成本和废溶剂生产，并获得独特的材料。然而，在实现任何优势并使前向聚合工艺成为一项有竞争力的技术之前，必须更好地了解影响前向聚合的因素。其次，对前锋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/对流系统的溶液的行为有关。对这些更一般问题的研究有助于理解特定的正面聚合问题。日期：2001年6月18日