Abstract:In this study we investigated the percolation in the system containing long flexible polymer chains. The system also contained explicit solvent molecules. The polymer chains were represented by linear sequences of lattice points restricted to a two-dimensional triangular lattice. The Monte Carlo simulations were performed applying the cooperative motion algorithm. The percolation thresholds and the critical exponents of chains and solvent molecules were determined. The influence of the chain length on the perc… Show more
“…All P ( φ ) curves are typical, i.e., S-shaped and the increase of the chain length shifts the curve toward lower polymer concentrations. Qualitatively the same behavior was found for other two-dimensional polymer chains: for short chains on the square lattice [17], long linear chains with explicit solvent molecules on the triangular lattice [26] and the square lattice [21] and for off-lattice hard ellipsoids [11]. One can also observe that the slope of curves decreases with the chains length which is caused by the finite size of the system.Fig.…”
Section: Resultssupporting
confidence: 73%
“…This hypothesis was already validated for a slightly different model of two-dimensional linear and cyclic chains on triangular lattice with explicit solvent molecules introduced [26, 27]. This suggests that the main factor, which determines the percolation threshold of a complex object, is its structure.…”
Section: Resultsmentioning
confidence: 80%
“…Mixtures of small objects (oligomers) of a different shape were also studied by means of the RSA method [24] while mixtures of stiff rods and flexible chains appeared to be tractable by a theory (a connectedness Ornstein-Zernike formalism) [25]. Long flexible chains were recently studied by means of the RSA [10] and the CMA (the cooperative motion algorithm) [26–29] simulation methods. The influence of the presence of explicit solvent molecules, the analysis of the clusters formed by macromolecules and the confirmation of the universal critical behavior of these systems were the main results discussed in these works.…”
The structure of a two-dimensional film formed by adsorbed polymer chains was studied by means of Monte Carlo simulations. The polymer chains were represented by linear sequences of lattice beads and positions of these beads were restricted to vertices of a two-dimensional square lattice. Two different Monte Carlo methods were employed to determine the properties of the model system. The first was the random sequential adsorption (RSA) and the second one was based on Monte Carlo simulations with a Verdier-Stockmayer sampling algorithm. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length on both thresholds was presented and discussed. It was shown that the RSA method gave considerably lower thresholds for longer chains. This behavior can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.FigureThe percolation cluster (in red) in the system consisting of long flexible chains
“…All P ( φ ) curves are typical, i.e., S-shaped and the increase of the chain length shifts the curve toward lower polymer concentrations. Qualitatively the same behavior was found for other two-dimensional polymer chains: for short chains on the square lattice [17], long linear chains with explicit solvent molecules on the triangular lattice [26] and the square lattice [21] and for off-lattice hard ellipsoids [11]. One can also observe that the slope of curves decreases with the chains length which is caused by the finite size of the system.Fig.…”
Section: Resultssupporting
confidence: 73%
“…This hypothesis was already validated for a slightly different model of two-dimensional linear and cyclic chains on triangular lattice with explicit solvent molecules introduced [26, 27]. This suggests that the main factor, which determines the percolation threshold of a complex object, is its structure.…”
Section: Resultsmentioning
confidence: 80%
“…Mixtures of small objects (oligomers) of a different shape were also studied by means of the RSA method [24] while mixtures of stiff rods and flexible chains appeared to be tractable by a theory (a connectedness Ornstein-Zernike formalism) [25]. Long flexible chains were recently studied by means of the RSA [10] and the CMA (the cooperative motion algorithm) [26–29] simulation methods. The influence of the presence of explicit solvent molecules, the analysis of the clusters formed by macromolecules and the confirmation of the universal critical behavior of these systems were the main results discussed in these works.…”
The structure of a two-dimensional film formed by adsorbed polymer chains was studied by means of Monte Carlo simulations. The polymer chains were represented by linear sequences of lattice beads and positions of these beads were restricted to vertices of a two-dimensional square lattice. Two different Monte Carlo methods were employed to determine the properties of the model system. The first was the random sequential adsorption (RSA) and the second one was based on Monte Carlo simulations with a Verdier-Stockmayer sampling algorithm. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length on both thresholds was presented and discussed. It was shown that the RSA method gave considerably lower thresholds for longer chains. This behavior can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.FigureThe percolation cluster (in red) in the system consisting of long flexible chains
“…One has to remember that in the case of macromolecular chains the deposited objects are large and differ one from another and their size and shapes are widely distributed. When one looks at systems containing short flexible chains the percolation threshold decreases with the increase in the chain's length while for semiflexible chains it exhibits a minimum for considerably long polymers . The influence of the macromolecular architecture (linear chains, star‐branched chains with a different number of branches and cyclic chains) on the percolation and jamming thresholds is found to be surprisingly weak .…”
In this work, the structure of a strictly 2D dense polymer film for some model copolymer systems: diblock, triblock, and random copolymers is studied. An idealized model of these macromolecular systems is developed where positions of polymer beads are restricted to vertices of a simple cubic lattice and chains are under good solvent conditions (the excluded volume is the only interaction between beads of the chain and solvent molecules). The properties of the system are determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local cooperative changes of conformation. Scaling of the chain size is studied and the influence of the polymer concentration on the chain's size and shape is discussed. The differences and similarities in the behavior of the percolation thresholds of one component in chains with different bead sequences are also shown and discussed. The percolation threshold is found to be weakly dependent on the chain length and more sensitive to the total polymer concentration.
“…This hypothesis was already validated for a slightly different model of two-dimensional linear and cyclic chains on triangular lattice with explicit solvent molecules introduced. 21,22 This suggests that the main factor, which determines the percolation threshold for a complex object is its structure. Other RSA results but concerning shorter chains (N ≤ 15) 15 were also included into Figure 1.…”
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