Multiblock copolymer chains in implicit nonselective solvents are studied by Monte Carlo method which employs a parallel tempering algorithm. Chains consisting of 120 $A$ and 120 $B$ monomers, arranged in three distinct microarchitectures: $(10-10)_{
12}$, $(6-6)_{20}$, and $(3-3)_{40}$, collapse to globular states upon cooling, as expected. By varying both the reduced temperature $T^*$ and compatibility between monomers $omega$, numerous intra-globular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and $n$-clusters with $n>3$ (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the $(T^*, omega)$-space are mapped. The structure factor $S(k)$, for a selected microarchitecture and $omega$, is calculated. Since $S(k)$ can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in term of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.
We present a study of the parallel tempering (replica exchange) Monte Carlo method, with special focus on the feedback-optimized parallel tempering algorithm, used for generating an optimal set of simulation temperatures. This method is applied to a
lattice simulation of a homopolymer chain undergoing a coil-to-globule transition upon cooling. We select the optimal number of replicas for different chain lengths, N = 25, 50 and 75, using replicas round-trip time in temperature space, in order to determine energy, specific heat, and squared end-to-end distance of the hopolymer chain for the selected temperatures. We also evaluate relative merits of this optimization method.
Using the self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d = 5. This is an extension of a previous work for d = 4. The phase diagr
am is parameterized by the chain composition, f, and incompatibility between A and B , quantified by the product c{hi} N. We predict 5 stable nanophases: layers, cylinders, 3 D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large c{hi}N, the order-order transition compositions are determined by the strong segregation theory (SST) in its simplest form. While the predictions of the SST theory are close to the corresponding SCFT extrapolations for d=4, the extrapolations for d=5 significantly differ from them. We find that the S5 nanophase is stable in a narrow strip between the ordered S4 nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected.
