Wriggled Lamellar Solutions and Their Stability in the Diblock Copolymer Problem
Wriggled Lamellar Solutions and Their Stability in the Diblock Copolymer Problem
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DOI：
10.1137/s0036141003433589
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Xiaofeng Ren;Juncheng Wei
中科院分区：
文献类型：
--
作者：
Xiaofeng Ren;Juncheng Wei
在二嵌段共聚物体系中，自由能场非局部地依赖于单体密度场。此外，本构关系中还有两个正参数。其中一个是小的，我们对此进行奇异摄动分析。第二个是一阶的，我们对它做了分歧分析。结合这两种技术，我们发现蠕动层状解决方案的欧拉-拉格朗日方程的总自由能的假设下，关于简单的主要特征值，这是一般满足。蠕动层片解从理想层片解分支出来。蠕动层片解的稳定性被简化为一个相对简单的有限维问题，可以用数值方法精确求解。我们的测试表明它们大多数都很稳定。这种稳定的蠕动层状溶液的存在解释了为什么在现实中的层状相是脆弱的，往往存在于扭曲的形式。
In a diblock copolymer system the free energy field depends nonlocally on the monomer density field. In addition there are two positive parameters in the constitutive relation. One of them is small, with respect to which we do singular perturbation analysis. The second one is of order 1, with respect to which we do bifurcation analysis. Combining the two techniques we find wriggled lamellar solutions of the Euler--Lagrange equation of the total free energy under a hypothesis regarding the simplicity of the principal eigenvalue, which is generically satisfied. The wriggled lamellar solutions bifurcate from the perfect lamellar solutions. The stability of the wriggled lamellar solutions is reduced to a relatively simple finite dimensional problem, which may be solved accurately by a numerical method. Our tests show that most of them are stable. The existence of such stable wriggled lamellar solutions explains why in reality the lamellar phase is fragile and often exists in distorted forms.