Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling, the probability distributions of block length k being calculated. The problem is similar to that of gambler’s ruin and first passage time in probability theory but the consideration is generalized to 3D and the domains of different shapes are considered. In any domain, the probability distribution can be described by the asymptote ∼k ^−3/2 at moderate values of k if the spatial size of the block is less than the smallest characteristic size of the domain. For large blocks, the exponential asymptote exp(−const ) is valid, d _as being the asymptotic domain length (a is the monomer unit size). The number average block lengths and their dispersities change linearly with the domain size for lamellae, cylinders, and balls, when the domain is characterized by a single characteristic size. If the domain is described by more than one size, the number average block length can grow nonlinearly with the domain sizes and the length d _as can depend on all of them.

聚合物序列的构象相关设计可被视为控制大分子自组装的工具。我们根据单体单元的空间位置，考虑通过在均匀熔体中对聚合物进行改性而产生的单体单元序列。排列在体心立方晶格中的薄片、六边形圆柱和球的几何图案被认为是嵌段共聚物的典型微相分离形态。聚合物链的随机轨迹由扩散型方程描述，同时在计算机建模中模拟，嵌段长度k的概率分布被计算。该问题类似于概率论中的赌徒破产和第一次通过时间，但将考虑推广到 3D，并考虑了不同形状的域。在任何域，概率分布可以通过渐近〜描述ķ ^-3/2在中度值ķ如果所述块的空间大小小于所述域的最小特征尺寸。对于大块，指数渐近线 exp(−const ) 是有效的，d _作为渐近域长度 ( a是单体单元尺寸）。当域以单一特征尺寸为特征时，数均块长度及其分散性随薄片、圆柱和球的域尺寸线性变化。如果该域是由一个以上的尺寸所述，数均嵌段长度可与域大小和长度非线性增长d _作为可取决于所有这些。