Size-Scale Sensitivity in Multiphase Systems with a Liquid Crystalline Phase

摘要/ CTS-0112358 / Denn， Morton M / CUNY City CollegeSize -Scale在具有液晶的多相系统中的灵敏度。液晶系统包含一个固有长度尺度，即保持液晶顺序的相关长度；在向列液晶聚合物（lcp）中，这个尺度约为几微米。在多相体系中，液晶顺序会影响相间结构，而相间结构又会影响宏观性能。因此，体系行为取决于不同长度尺度之间的相互作用：表征界面区域的分子纳米尺度，表征相关长度和相尺寸的中尺度，以及决定性质的宏观尺度。在柔性热塑性塑料基体中含有少量LCP的共混物具有相当大的技术价值。通过在LCP分散相中形成纤维状形态，可以开发出利用LCP纤维优异拉伸性能的“自增强”复合材料。此外，lcp可以作为传统热塑性塑料的“流动调节剂”，在低浓度下降低挤出压力。我们之前的研究表明，LCP共混物的线性粘弹性对小于向列相关长度的液滴不敏感，并且LCP液滴的动力学不遵循与柔性聚合物液滴相同的缩放。此外，我们已经在初步的蒙特卡罗计算中表明，LCP和柔性聚合物之间的界面张力取决于液滴中的远场向列取向。提出的研究包括三种互补的方法来阐明多长度尺度对含lcp共混物力学的影响：连续统理论、蒙特卡罗计算和实验。连续介质理论。液滴中的LCP取向分布将是影响变形力学的主要因素，随着液滴变形，径向取向和双极取向之间的转变将影响界面张力。首席研究员计划首先使用具有相等Frank弹性常数的Leslie-Ericksen （LE）材料的微扰分析来分析液滴变形的一阶效应。LE流体是最基本的向列模型，它是Doi理论扩展的更完备的lcp模型的渐近极限。然后，首席研究员将对具有不等Frank系数的LE材料在变形球体中的平衡分布进行完整的三维有限元求解。本计算的目的是了解剪切后液滴中可能的取向分布。液滴响应的时间尺度决定了在共混流变中可以观察到界面效应的频率范围。首席研究员将首先确定LE流体的响应，使用球面谐波的膨胀。这是根据混合线性粘弹性和液滴动力学的实验观察得出的一个重要计算。当一个“域”内的弹性应力与拉普拉斯压力相当时，研究人员期望液滴在线性状态下的瞬态响应依赖于弗兰克弹性。现有的数据并没有显示出这种依赖性，但它们确实显示了对初始应变的依赖性，而这对于柔性聚合物的液滴来说是不存在的。这种行为需要通过对这里提出的类型的分析来合理化。首席研究员将重复单畴液晶液滴粘弹性混合物的帕里恩分析，首先使用LE理论进行简化。计算的流变特性可能取决于边界处施加在向列相上的锚定条件，这将定义区域内部的向列顺序。主要研究者期望响应在奇异点附近对LE方程中的Frank弹性项敏感。LE理论在结构上类似于lcp的多域理论，因此这些计算应该为解释实验观察到的多域和单域液滴之间的差异提供一个框架。研究人员预计，存储模量G'依赖于一个涉及相关长度的新的无量纲群。然后，首席研究员将对Doi理论和相关扩展进行可比计算。蒙特卡罗计算。键波动模型（BFM）将用于研究向列顺序对LCP液滴与非晶基体之间界面张力的影响，探索链长、能量参数和多分散性。为了解决LCP和柔性链单体之间的较大尺寸差异，需要通过开发一种合理的方法在界面附近的晶格上放置插值点来修改BFM。剪切流动对界面附近链取向和界面张力的影响将使用自回避晶格链的伪势模型进行探讨。实验。线性粘弹性测量旨在将界面和弗兰克取向弹性的影响从大分子效应中分离出来，将对含有低摩尔质量液晶（lmmlc）的共混物进行测量。主要研究人员的初步测量表明，lmmlc的线性粘弹性行为可能是不寻常的（负G'），并且依赖于剪切历史。因此，第一步将是阐明线性粘弹性行为，并在LE和Doi理论预测的背景下分析结果。然后，首席研究员将研究共混物的流变学，使用表现出相变的lmmlc来获得具有相同粘度和相同化学成分的向列相和各向同性分散相。

Abstract/ CTS-0112358 / Denn, Morton M / CUNY City CollegeSize -Scale Sensitivity in Mutliphase Systems with a Liquid Crystalline PhaseLiquid crystalline systems contain an intrinsic length scale, the correlation length over which the liquidcrystalline order is preserved; this scale is of the order of a few micrometers in nematic liquid crystalline polymers (LCPs). The liquid crystalline order can affect the interphase structure in a multiphase system, which in turn can affect macroscopic properties. Thus, the system behavior depends on the interaction between the different length scales: the molecular nanoscale characterizing the interfacial region, the mesoscales characterizing the correlation length and the phase dimensions, and the macroscopic scale on which properties are determined. Blends containing small amounts of a LCP in a matrix of a flexible thermoplastic are of considerable technological interest. It is possible to develop "self-reinforced" composites that exploit the outstanding tensile properties of fibers made from LCPs by creating a fibrillar morphology in the LCP dispersed phase. In addition, LCPs can act as "flow modifiers" for conventional thermoplastics, effecting a reduction in extrusion pressure at low concentrations. Our prior research has shown that the linear viscoelasticity of LCP blends is insensitive to droplets smaller than the nematic correlation length, and that the dynamics of LCP droplets do not follow the same scaling as droplets of flexible polymers. Furthermore, we have shown in preliminary Monte Carlo calculations that the interfacial tension between a LCP and a flexible polymer depends on the far-field nematic orientation in the droplet.The proposed research comprises three complementary approaches to elucidate the effect of multiple length scales on the mechanics of blends containing LCPs: continuum theory, Monte Carlo calculations, and experiments.Continuum theory. The LCP orientation distribution in the droplet will be a major factor in the deformation mechanics, and transitions between radial and bipolar orientations, which will affect the interfacial tension, are expected with droplet deformation. The Principal Investigator plans initially to use a perturbation analysis of a Leslie-Ericksen (LE) material with equal Frank elastic constants to analyze the first-order effect of droplet deformation. The LE fluid is the most elementary nematic model, and it is the asymptotic limit of more complete models for LCPs that are extensions of the Doi theory. Then the Principal Investigator will undertake a full three-dimensional finite-element solution of the equilibrium distribution in a deformed sphere for a LE material with unequal Frank coefficients. The purpose of this computation is to understand the likely orientation distributions in droplets after shearing. The time scale for droplet response defines the frequency range in which interfacial effects can be observed in blend rheology. The Principal Investigator will initially determine the response of a LE fluid, using an expansion in spherical harmonics. This is an important calculation in light of the experimental observations for blend linear viscoelasticity and droplet dynamics. The principal investigator expects the transient response of the droplet in the linear regime to depend on the Frank elasticity when the elastic stresses in a "domain" become comparable to the Laplace pressure. Available data do not show this dependence, but they do show a dependence on initial strain that is absent for droplets of a flexible polymer. This behavior needs to be rationalized by an analysis of the type proposed here. The principal investigator will repeat the Palierne analysis of viscoelastic blends for a monodomain liquid crystalline droplet, first using the LE theory for simplicity. The computed rheological properties are likely to depend on the anchoring conditions imposed on the nematic phase at the boundary, which will define the nematic order in the domain interior. The principal investigator expects the response to be sensitive to the Frank elasticity terms in the LE equation in the neighborhood of singularities. The LE theory is structurally similar to multi-domain theories for LCPs, so these calculations should provide a framework for interpreting experimentally observed differences between multidomain and monodomain droplets. The principal investigator anticipates a dependence of the storage modulus G' on a new dimensionless group involving the correlation length. The principal investigator will then carry out the comparable calculation for the Doi theory and relevant extensions.Monte Carlo Calculations. The Bond Fluctuation Model (BFM) will be used to study the effect of nematic order on the interfacial tension between a LCP droplet and an amorphous matrix, exploring chain length, energy parameters, and polydispersity. Modification of the BFM by developing a rational method for placing interpolated points on the lattice near the interface is required to account for the large size differences between LCP and flexible chain monomers. The effect of shear flow on the chain orientation near the interface and on the interfacial tension will be explored using a pseudopotential model for self-avoiding lattice chains. Experiments. Linear viscoelastic measurements intended to isolate the effect of the interface and Frank orientational elasticity from macromolecular effects will be carried out on blends containing low molar mass liquid crystals (LMMLCs). The principal investigators preliminary measurements suggest that the linear viscoelastic behavior of the LMMLCs may be unusual (negative G') and shear history dependent. Thus, the first step will be to elucidate the linear viscoelastic behavior and to analyze the results in the context of the predictions of LE and Doi theories. The principal investigator will then study the rheology of the blends, employing LMMLCs that exhibit a phase transition to obtain nematic and isotropic dispersed phases with equal viscosities and identical chemical compositions.