Ordering in Stretched Bernoullian Copolymers

Abstract

A new approach is suggested to estimate the theoretical maximum capability to order for stretched Bernoullian copolymers AB, provided interchain AB contacts are unfavorable. A simple Monte Carlo procedure simulating the ordering of such copolymers via rotation of ring‐shaped chains reveals the capability to order even for quite long copolymer chains. The analytical probabilistic consideration is elaborated, which enables one to interpret the ordering via rotation in terms of a sliding of periodic Bernoullian chains. Using both the probabilistic analysis and Monte Carlo simulations it is shown that estimations of a capability to order given by the rotation procedure are also good for a sliding of true Bernoullian copolymers. Therefore, the simple Monte Carlo procedure seems suitable for estimating ordering in other classes of copolymers for which an analytical approach is more complicated. Such estimations might be useful for a consideration of various properties of irregular copolymers connected with their tendency to order.

Microphase separation in regular and random сopolymer melts by DPD simulations

“…In the lack of laboratory experiments, computer modeling is a powerful tool for checking theoretical predictions and exploring the behavior of systems beyond the applicability range of existing theories. A few studies on modeling random copolymers using the Monte Carlo method were reported [17][18][19][20]. Litmanovich et al [17] proposed a simple two-dimensional model for estimating the maximum capability to an ordering for stretched copolymers AB with an arbitrary unit distribution.…”

Theory of supramolecular co-polymerization in a two-component system

“…39 The coupling constant J appearing in our model is not unlike the Flory-Huggins interaction parameter χ 35 describing the phase behavior of homopolymer solutions, binary homopolymer melts of copolymer melts. [36][37][38] The difference, of course, is that in Flory-Huggins theory the interaction parameter describes non-bonded interactions, whereas our coupling parameter pertains to bonded interactions. Interestingly, nonbonded interactions have been predicted to lead to similar type of correlations between monomeric species that we find, i.e., random, block, and alternating structure, except that in this case they occur on different, not the same, polymers.…”

Phase Transitions in Melts of Alternating Rodlike Copolymers: Monte Carlo Simulation by the Wang‐Landau Approach

“…[21] In the present article a simple theoretical interpretation of these tasks is proposed, which allows elucidation of some basic principles of molecular recognition in a range of synthetic and biological systems. The model under consideration is an expanded version of a model [22] where the self-organization of stretched statistical copolymers was considered.…”

“…In such a manner, the ring-shaped molecules are discussed, like in the model. [22] However, in the present model a two-dimensional array of such molecules is considered, and alternating copolymers ( Figure 1c) serve as objects of investigation, in contrast to the Bernoullian (random) copolymers of the study. [22] The thermodynamics of the system were studied using the Wang-Landau method.…”

“…[22] However, in the present model a two-dimensional array of such molecules is considered, and alternating copolymers ( Figure 1c) serve as objects of investigation, in contrast to the Bernoullian (random) copolymers of the study. [22] The thermodynamics of the system were studied using the Wang-Landau method. [25] It is a kind of Monte Carlo algorithm that calculates the density of states.…”