Miao Bing, Yan Dadong, Han Charles C, Shi An-Chang
Beijing National Laboratory for Molecular Sciences (BNLMS), Joint Laboratory of Polymer Science and Materials, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, China.
J Chem Phys. 2006 Apr 14;124(14):144902. doi: 10.1063/1.2187492.
The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.
从理论上研究了受限对二嵌段共聚物熔体有序-无序转变的影响。通过将二嵌段共聚物限制在具有不同几何形状（平板、圆柱和球体）的有限空间中来实现受限。在随机相位近似下，利用拉普拉斯算子∇²在适当几何形状中的本征值和本征函数来计算相关函数。这导致了一个与尺寸有关的散射函数，并且反向散射函数的最小值决定了均相的旋节线点。对于限制在平板或圆柱形纳米孔中的二嵌段共聚物，发现均相的旋节线点(χN)s与受限无关。另一方面，对于限制在球形纳米孔中的二嵌段共聚物，(χN)s取决于受限情况，并且它作为球体半径的函数而振荡。通过使用朗道-布拉佐夫斯基模型研究涨落模式，进一步理解了有限尺寸效应。
