Percolation in Two‐Dimensional Copolymer Systems

Abstract

The aim of the study is the investigation of the percolation phenomena in some model copolymer systems. Diblock, triblock, random copolymers, and a blend of homopolymers are studied. For this purpose, we developed an idealized model of polymeric systems. The positions of polymer segments are restricted to vertices of a simple cubic lattice. The chains are at good solvent conditions – the excluded volume is the only interaction between the segments of the chain. The properties of the model chains are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The differences and similarities in the percolation behavior are shown and discussed. The percolation threshold is found to be very weakly dependent on the chain length, however, it appears that the main factor that influenced the percolation threshold is the screening effect of other parts of chains.

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

“…In general, the probability of the percolation increases with the concentration of the components A and forms an S ‐shaped curve. This is a typical behavior, which was also observed for homopolymers within the frame of the same model . The slope of the curves depends on the chain length: the shorter the chain was the steeper the curve (to be more precise the slope depends on the N/L ratio and thus, for an infinite system we have the step function).…”

“…The percolation is detected using a tree‐based union/find efficient algorithm invented by Newman and Ziff . The percolation threshold is studied for chains consisting of N > 16 beads as for shorter chains it is impossible to obtain the sufficient number of points defining the probability on the percolation curve …”

“…The main conclusion is that the split the A block into two pieces (from the sequence AB to the sequence ABA ) is overcoming the screening of the inert B component regardless the amount of solvent molecules. The distance between the random copolymer curves decreases with the increase of the total polymer concentration: in the case of a pure polymer melt one can see one curve only …”

“…Contrary to above‐mentioned works, we focus on coarse‐grained models of heterpolymer chains consisting of two types of beads. Studies of the percolation in heteropolymer systems have recently been carried out in the case of the 3D multiblock amphiphilic chains and in strictly 2D systems . The present work is an extension of the previous studies where we focused on a dense polymer melt containing chains only without any solvent molecules .…”

“…Studies of the percolation in heteropolymer systems have recently been carried out in the case of the 3D multiblock amphiphilic chains and in strictly 2D systems . The present work is an extension of the previous studies where we focused on a dense polymer melt containing chains only without any solvent molecules . In the present work, the chains are represented by linear sequences of lattice points restricted to vertices of a 2D triangular lattice.…”