Conductive Polymer Electrolytes: Phase Separation and Ion Transport

Promislow 0708804研究人员分析了聚合物电解质溶液中相分离和离子传输的新型导电聚合物电解质（CPE）模型的数学基础。放热的酸-溶剂反应导致界面能随着表面积的增加而减小，但随着界面曲率的增加而增加。 与界面能相关的梯度流族是Allen-Cahn和Cahn-Hilliard算子的四阶和六阶推广，具有丰富的新结构。 研究人员严格推导出与孔隙形成相关的梯度流动的尖锐界面极限。 排斥势将质子缺陷从阴离子中分离出来，在相分离膜中产生了一种新的平衡电荷分布，从而改变了经典的Gouy-Chapmann扩散双层。 通过对控制电荷分布的椭圆方程的多尺度分析，定量地分析了排斥势对双电层结构的影响，以及静电压力对相分离的影响。 聚合物电解质中的溶剂孔网络是一种新型的高对比度导电复合介质。 对于界面能和静电能引起的相分离的局部极小化，研究者利用介电常数和排斥势提供的高对比度来推导聚合物网络的有效电导率。 这需要渐近分析的鞍点结构的电荷分布在沟道结和发展的变分表征的有效质子电导率。聚合物电解质由长的疏水聚合物（主要是特氟龙）和短的酸性侧链组成，就像一个单极梯子。 它们形成了一个丰富的结构，在水的存在下发生相分离，形成复杂的纳米级几何形状，排列着悬垂的酸基团，充满了带电流体。 这种结构是离子传输的主力，产生细胞膜中离子通道的选择性，脂质膜孔内发生的复杂生化过程，以及这个项目的动机：燃料电池聚合物电解质膜内的电荷传输。 本计画分析了新型导电高分子电解质（CPE）在高分子电解质溶液中相分离与离子传输的数学基础。对这些材料中孔形成和离子传导的基本了解对于燃料电池汽车高温膜的开发至关重要。 高温膜是过渡到氢经济的关键一步，因为更高的燃料电池工作温度将大大降低与铂催化剂装载和发动机辐射冷却相关的成本。

Promislow0708804The investigator analyses the mathematical underpinnings of anovel Conductive Polymer Electrolyte (CPE) model for phaseseparation and ion transport in polymer electrolyte solutions. An exothermic acid-solvent reaction leads to an interfacialenergy that decreases with increasing surface area but grows withthe curvature of the interface. The family of gradient flowsassociated to the interfacial energy are compelling fourth andsixth order extensions of the familiar Allen-Cahn andCahn-Hilliard operators with rich new structure. Theinvestigator rigorously derives sharp interface limits for thegradient flows associated with pore formation. The exclusionpotential that separates the protonic defects from the anionsgenerates a novel equilibrium charge distribution within thephase separated membrane, modifying the classic Gouy-Chapmanndiffusive double layer. A multiscale analysis of the ellipticequations governing the charge distribution quantifies the impactof the exclusion potential on the structure of the electrostaticdouble layer, and the impact of the electrostatic pressure uponthe phase separation. The solvent pore network within thepolymer electrolyte is a novel high-contrast conductive compositemedia. For local minimizers of the phase separation arising frominterfacial and electrostatic energies, the investigator exploitsthe high contrast afforded by the permittivity and exclusionpotential to derive the effective conductivity of polymernetwork. This entails asymptotic analysis of the saddle pointstructure of charge distribution at channel junctions anddevelopment of a variational characterization of the effectiveprotonic conductivity. Polymer electrolytes are comprised of long hydrophobic polymers(essentially Teflon) with short acidic side-chains attached, likea single pole ladder. They form a rich structure that phaseseparates in the presence of water, forming intricate nanoscalegeometries lined with pendant acid groups and filled with chargedfluid. Such structures are the workhorses of ion transport,generating the selectivity of ion channels in cell membranes, thecomplex biochemical processes that occur within the pores oflipid membranes, and the motivation of this project: thetransport of charge within polymer electrolyte membranes of fuelcells. This project analyzes the mathematical underpinnings of anovel Conductive Polymer Electrolyte (CPE) model for phaseseparation and ion transport in polymer electrolyte solutions. The fundamental understanding of pore formation and ionconduction in these materials is essential to the development ofhigh-temperature membranes for fuel cell vehicles. Hightemperature membranes are a key step in the transition to ahydrogen economy, as higher fuel cell operating temperatures willgreatly reduce costs associated with platinum catalyst loadingand radiative cooling of the engine.