Monte Carlo Simulations Of Self-Assembly Of Block Copolymers And Conformation Of A Single Polyelectrolyte Chain

The self-assembly of block copolymers has attracted lots of scientific interests dueto their formation of rich nanostructures and useful applications of these structures. Ithas been demonstrated that confinement is a powerful tool to break the symmetry of astructure, thus allowing materials to form new phases which are not available in bulksystems. Besides block copolymers, many important synthetic and biological macro-molecules are charged polymers or polyelectrolytes. The conformational properties ofpolyelectrolytes differ significantly from that of the corresponding uncharged polymer-s. The ability of polyelectrolytes to change their sizes significantly upon change ofionic conditions and temperature makes them very useful in many technological ap-plications. It is well understood that electrostatic interactions play a very importantrole in the behavior of polyelectrolytes, and the intrachain electrostatic interactions of apolyelectrolyte chain can be regulated by the amount of condensed counterions. Studyof the self-assembly of block copolymers and the conformation of polyelectrolytes isimportant both from fundamental and applied points of view.In this thesis, block copolymer multi-chain system and single polyelectrolyte chainsystem are studied using simulated annealing and parallel tempering Monte Carlo simu-lation under lattice model. Means to choose optimal parameters for the implementationof parallel tempering method are also suggested, which are verified by simulation testsboth in a two-dimensional Ising model system and a one-dimensional function system.In the chapter one, firstly, the research topics of the thesis are introduced. Next, theprinciples of simulating and statistical methods used in the thesis are summarized, in-cluding Monte Carlo method, simulated annealing method, parallel tempering method,error estimating method and histogram analysis method. Then, molecular simulationfor polymer system are introduced, including molecular simulation methods, latticechain model and relative statistics. Finally, the structural arrangement of the thesis issummarized.In the chapter two, under chain length fluctuation lattice chain model, two differnt confinement problems are investigated by using simulated annealing method, includingthe soft confinement-induced morphologies of diblock copolymers and the substrateadsorption of diblock copolymers (one-dimensional confinement). The novel mor-phologies are respectively found in both problems. Especially, for the problem of softconfinement, we present a novel system for studying the self-assembly of block copoly-mers under soft confinement via simulations. The soft confinement is realized by theformation of polymer droplets in a poor solvent environment. For diblock copolymerswith various bulk phases, multiple sequences of soft confinement-induced copolymeraggregates with different shapes and self-assembled internal morphologies are predict-ed as functions of solvent-polymer interaction and the monomer concentration, suchas these with a prolate ellipsoid shape and an internal morphology of stacked lamel-lae, with an oblate ellipsoid shape and an internal morphology of hexagonally packedcylinders, or with a slightly elongated spherical shape and an internal morphology ofstacked toroids or helices. It is discovered that the self-assembled internal morphologyof the aggregates is largely controlled by a competition between the bulk morphologyof the copolymer and the solvent-polymer interaction, and the shape of the aggregatescan deviate from spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copoly-mers formed in poor solvents can be used as a model system to study the self-assemblyof copolymers under soft confinement.In the chapter three, we do not focus on the specific simulation system but on theoptimization problem of parallel tempering method itself. First, by performing sim-ulation tests, we compare between the simulated annealing method and the paralleltempering method. The result suggests that the latter one provides more higher statisti-cal sampling efficiency. Next, our new views about the statistical sampling efficiency ofthe parallel tempering method are raised. We suggest that the replica exchange in paral-lel tempering method causes two kind of accelerating effects. One is local acceleratingeffect and the other is tempering accelerating effect. These two kinds of acceleratingeffects accelerate the statistical sampling in two different ways. Then, we propose ourmeans to choose parameters for implementation of parallel tempering method, includ-ing range of temperature, matching strategy for replica exchange, arrangement of tem- peratures for different replicas, interval between replica exchange and replica number.Finally, we simply introduce the features and implement of multithreaded implementa-tion of parallel tempering method.In the chapter four, we study the problem related to conformational transitions ofpolyelectrolyte chain by using optimized parallel tempering Monte Carlo simulation.In the simulations, the optimized Ewald summation method are used for calculatinglong distance interaction of charges. We show our simulation results in three subsec-tions, including conformation transitions of single polyelectrolyte chain, coil-globulephase transition of single polyelectrolyte in salt-free solvent and the scaling betweenchain size and chain length, and effect of salt for changing the conformation of thepolyelectrolyte chain. The main results are as follows. The strongly charged poly-electrolyte chain can assume a variety of conformations and it undergoes two phasetransitions upon cooling. The first transition is identified as a continuous counterioncondensation transition while the second one as a first-order coil-globule transition. Inthe globular state, the counterions and the charged chain segments are densely packedinto three-dimensional Wigner crystals. The coil-globule transition temperatures in theamalgamated thermodynamic limit for different densities of counterions are determinedby finite-size extrapolation, and finite-size effect for different chain size is investigat-ed. The scaling between chain size and chain length around the coil-globule transitionpoint is also discussed. For salt solution, we found that the monovalent salt can re-duce the strength of coil-globule transition, and change the transition point to highertemperature, but the high valent salt can induce the collapse of the swell chain.