Note: Percolation in two-dimensional flexible chains systems

Pawłowska, Monika; Żerko, Szymon; Sikorski, Andrzej

doi:10.1063/1.3679168

Cited by 16 publications

(21 citation statements)

References 22 publications

(17 reference statements)

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“…being A 1 = θ j (∞) = 0.4045 (19) the result for the limit coverage of a simple cubic lattice by infinitely long k-mers. In addition, A 2 = 2.63(5) and A 3 = −5.2 (2).…”

Section: Simulation Results: Random Sequential Adsorption Of Straightmentioning

confidence: 99%

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Random sequential adsorption of straight rigid rods on a simple cubic lattice

García

Sánchez-Varretti

Centres

et al. 2015

Physica A: Statistical Mechanics and its Applications

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“…being A 1 = θ j (∞) = 0.4045 (19) the result for the limit coverage of a simple cubic lattice by infinitely long k-mers. In addition, A 2 = 2.63(5) and A 3 = −5.2 (2).…”

Section: Simulation Results: Random Sequential Adsorption Of Straightmentioning

confidence: 99%

“…On the basis of the behavior of θ j vs. k in the range 2 ≤ k ≤ 64, and the best fit to this curve, the expression θ j (k) = A 1 + A 2 /k + A 3 /k 2 was found, being A 1 = θ j (∞) = 0.4045 (19) the result for the limit coverage of a simple cubic lattice by infinitely long k-mers. In addition, A 2 = 2.63(5) and A 3 = −5.2(2).…”

Section: Discussionmentioning

confidence: 99%

Random sequential adsorption of straight rigid rods on a simple cubic lattice

García

Sánchez-Varretti

Centres

et al. 2015

Physica A: Statistical Mechanics and its Applications

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“…It was shown that the percolation threshold depends on the local chain density N /〈 S 2 〉 ( N is the chain length and S the radius of gyration) and therefore, the percolation threshold depends on the chains' fractal dimension. It was also shown that the RSA method gives quite different results for longer chains and that it was rather ineffective for studies of larger and irregular objects 16, 31…”

Section: Introductionmentioning

confidence: 99%

Percolation in Two‐Dimensional Copolymer Systems

Polanowski

Wawrzyńska

Sikorski

2013

Macro Theory & Simulations

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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.

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“…[50][51][52][53] It has recently been shown that the RSA is not a suitable method for studies of the percolation process in systems containing long fl exible chains (and other large and irregular objects) because it becomes ineffi cient for longer macromolecules and percolation thresholds obtained via this method are rather underestimated. [ 28,54 ] Therefore, we have developed and employed the cooperative motion algorithm (CMA) for studies of 2D lattice models containing macromolecules and explicit solvent molecules. [ 47,48 ] Contrary to above-mentioned works, we focus on coarse-grained models of heterpolymer chains consisting of two types of beads.…”

Section: Macromolecular Theory and Simulationsmentioning

confidence: 99%

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

Kuriata

Polanowski²,

Sikorski

2016

Macro Theory & Simulations

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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.

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Note: Percolation in two-dimensional flexible chains systems

Abstract: A simple model of stiff and flexible polymer chain adsorption: The influence of the internal chain architecture

Cited by 16 publications

References 22 publications

Random sequential adsorption of straight rigid rods on a simple cubic lattice

Random sequential adsorption of straight rigid rods on a simple cubic lattice

Percolation in Two‐Dimensional Copolymer Systems

Percolation in Two‐Dimensional Copolymer‐Solvent Systems

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