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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 $k$, which are analogous to the first-passage probabilities, are calculated analytically and determined from the computer simulations. 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 $exp(-const , k a^2/d_{as}^2)$ 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 block length 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 das can depend on all of them.
In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the equilibrium c
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood fr
It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that th
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime
Following Florys ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $delta