Computer simulations of self-avoiding polymerized membranes

Drovetsky, Boris Y.; Chu, J. C.; Mak, C. H.

doi:10.1063/1.476068

Cited by 5 publications

(6 citation statements)

References 24 publications

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“…Long times: for a/L 1 and kt/ζ N/π 2 only the lowest mode contributes to the summation, therefore, expanding the correlation function in equation (32) yields…”

Section: Autocorrelation Function Of a Vector Connecting Two Beadsmentioning

confidence: 99%

“…In contrast to the equilibrium properties, the dynamical properties of membranes have been studied with less intensity. Apart from scaling analyses [27][28][29], the bulk of the research on the dynamics of polymerized membranes are heavily dominated by computer simulations [30][31][32][33], leaving exact analytical results on the dynamics of membranes a relatively open area.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical eigenmodes of a polymerized membrane

Keesman¹,

Barkema²,

Panja³

2013

J. Stat. Mech.

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We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the exact eigenmodes of the membrane dynamics (the "Rouse modes"). This allows us to obtain exact analytical expressions for virtually any equilibrium or dynamical quantity for the membrane.As examples we determine the radius of gyration, the mean square displacement of a tagged bead, and the autocorrelation function of the difference vector between two tagged beads. Interestingly, even in the presence of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes for the membrane. With stronger forces the membrane becomes essentially flat, and does not get the opportunity to intersect itself; in such a situation our analysis provides a useful and exactly soluble approach to the dynamics for a realistic model flat membrane under tension.PACS numbers: 02.50.Ey, 82.35.Lr

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“…Long times: for a/L 1 and kt/ζ N/π 2 only the lowest mode contributes to the summation, therefore, expanding the correlation function in equation (32) yields…”

Section: Autocorrelation Function Of a Vector Connecting Two Beadsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical eigenmodes of a polymerized membrane

Keesman¹,

Barkema²,

Panja³

2013

J. Stat. Mech.

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“…The crumpling transition at high temperatures was in fact observed in Monte Carlo simulations of phantom membranes without self-avoidance [61,62]. However, a number of simulations with purely repulsive self-avoiding interactions find that the flat phase persists for arbitrarily high temperatures [63][64][65][66][67]. We note that a pair potential with an attractive as well as a repulsive part can produce a compact phase (D f ¼ 3) at low temperatures, which transitions to a flat phase with D f ¼ 2 at high temperatures [68,69].…”

Section: Introductionmentioning

confidence: 98%

Statistical Mechanics of Thin Spherical Shells

Košmrlj

Nelson

2017

Phys. Rev. X

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We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the inplane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-ofplane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radiusdependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure." Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

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“…To carry out constant temperature dynamics, either Brownian dynamics [18] or stochastic collision [19] can be used. We have found stochastic collision to be more efficient, because it generally generates a faster relaxation time for the polymer configurations [20]. In our simulations, we assign new velocities to all the particles from a Maxwell-Boltzmann distribution every 100 to 1000 MD time steps.…”

Section: Model and Simulation Methodsmentioning

confidence: 99%

Inter- and intrachain attractions in solutions of flexible polyelectrolytes at nonzero concentration

Chu

Mak

1999

The Journal of Chemical Physics

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Constant temperature molecular dynamics simulations were used to study solutions of flexible polyelectrolyte chains at nonzero concentrations with explicit counterions and unscreened coulombic interactions. Counterion condensation, measured via the self-diffusion coefficient of the counterions, is found to increase with polymer concentration, but contrary to the prediction of Manning theory, the renormalized charge fraction on the chains decreases with increasing Bjerrum length without showing any saturation. Scaling analysis of the radius of gyration shows that the chains are extended at low polymer concentrations and small Bjerrum lengths, while at sufficiently large Bjerrum lengths, the chains shrink to produce compact structures with exponents smaller than a gaussian chain, suggesting the presence of attractive intrachain interactions. A careful study of the radial distribution function of the center-of-mass of the polyelectrolyte chains shows clear evidence that effective interchain attractive interactions also exist in solutions of flexible polyelectrolytes, similar to what has been found for rodlike polyelectrolytes. Our results suggest that the broad maximum observed in scattering experiments is due to clustering of chains.

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Computer simulations of self-avoiding polymerized membranes

Cited by 5 publications

References 24 publications

Dynamical eigenmodes of a polymerized membrane

Dynamical eigenmodes of a polymerized membrane

Statistical Mechanics of Thin Spherical Shells

Inter- and intrachain attractions in solutions of flexible polyelectrolytes at nonzero concentration

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