STUDY ON PATTERN FORMATION AND MORHOLOGICAL TRANSITION

我们研究了非均匀时空外界条件下的相分离机制，以考察相分离系统对外界条件的响应。特别是，相分离初期外部条件的变化对后期的花样形成有很大的影响。与目前的理论研究相对应的一个例子是从熔化的材料中拉出一块晶体来形成大的完美晶体的情况。对于聚合物和聚合物与溶剂的混合物，我们也提出了同样的实验。这些实验具有重要的现实意义，提供了一种产生完美体系的有效方法，从学术角度提供了需要解决的非平衡状态下的形态转变。在这个项目中，我们的目标不仅是固体的相分离，而且是液体的相分离。因此，我们研究了液体调幅分解的长度尺度的增长规律。由于相分离的标度性质，L(T)的长度标度随时间t与t^a成正比增长。这里的a称为增长指数，对于固体为a=1/3，对于流体为a=1。另一方面，流体的指数a=1在长时间限制(t**)下与流体动力学演化规律相矛盾，在长时间限制下，a被认为是2/3。我们通过模拟确定了增长指数a=2/3，重要的是a=1*2/3的交叉导致长度尺度增长的减慢。例如，对于水+水蒸气体系，用a=1预测的流体速度(7000 cm/s)比用a=2/3(L(T)=1 cm)预测的10 cm/s大3个数量级。在没有重力场的情况下(如在空间实验室中)，这种显著的减速对材料的组成有重要影响。

We examined the mechanism of the phase separation under the inhomogeneous spatio-temporal external conditions, in order to examine the response of the phase separating system to the external conditions. In particular the change in the external condition in the initial stage of the phase separation drastically affects the pattern formation in later stages. An example corresponding to the present theoretical investigation is the case of the formation of large perfect crystal by drawing up a piece of crystal from molten material. We also propose the same experiment for the polymer and the polymer blend with solvent. These experiments are significant from practical purpose offering an efficient method of producing perfect crystem, and from academic point of view offering morphological transition in nonequilibrium state which should be solved. In this project we aim the phase separation not only of solid but also of liquid. We therefore examined the growth law of the length scale for the spinodal decomposition of liquid. Due to the scaling properties of the phase separation the length scale L(t) grows in proportion to t^a as a function of time t. Here a is called the growth exponent and is given as a = 1/3 for solid and a = 1 for fluid. On the other hand, the exponent a = 1 for fluid is known to contradict with the hydrodynamic evolution law in the long time limit ( t * *), and a is considered to become 2/3 in the long time limit. We confirmed the growth exponent a = 2/3 by the simulation The importance is that the cross-over from a = 1 * 2/3 gives rise to the slowing down of the growth of the length scale. For instance, for water + vapor system, the fluid velocity (7000 cm/sec) predicted with a = 1 is large by three degree than 10 cm/sec predicted with a = 2/3 (at L(t) = 1 cm). Such a remarkable slowing down has an important effect to the composition of material in the absence of the gravitational field (such as in the space laboratory).