arXiv subjects

J. Stecki

Publications and source records attributed to J. Stecki.

6 recordsLinked to original sources

arXiv2012

On the power spectrum of undulations of simulated bilayers

The best finite Fourier Series for a smooth surface $h(x,y)$ closest to the positions of heads of amphiphiles in the least-square sense, agrees fully with the Fourier coefficients obtained by a direct summation over raw data points. Both metods produce structure factors $S(q)$ containing all necessary features: small-q divergence, a minimum, the raise to the ubiquitous nearest neighbor peak near $q=2π/$(coll.diameter) and further peaks. The Laurent series is also discussed.

cond-mat.soft↗

arXiv2012

Simulations of Liquid Bilayer and the Hunt for Protrusions

New simulations are reported of a single bilayer immersed in a liquid solvent, using a simple extension of the model of the Max-Plack group and of model used in earlier work. Fluctuation spectrum vel structure factor is dissected in detail and the role of bulk fluctuations is revealed.We propose to search for protrusions direcdtly where they are, i.e. at the solvent-heads boundary. In this context new single-point quantities and new two-point correlations are introduced and determined for the solvent-head pairs. Most unusual shapes are obtained.

cond-mat.soft↗

arXiv2008

Exact Calculations of Membrane Areas with Simple Models

The distinction between the true total area and the projected area is elucidated with soluble models which represent the membrane as a self-avoiding string on a plane. Constraining the total area to a predetermined value changes the averages very significantly. The latter are calculated exactly from the generating functions of self-avoiding walks and are shown as functions of activities $q$ and $r$ related to temperature $T=\pm 1/\log (q)$ and lateral force $f=-\log (r)$. The constraint makes the partition functions and averages valid for all $q,r >0$ and reduces the ratio of $A_{tot}$ to the projected area $L$. High temperature divergences are supressed. Possible applications to simulated bilayers/membranes are discussed.

cond-mat.soft↗

arXiv2008

Balance of forces in simulated bilayers

Two kinds of simulated bilayers are described and the results are reported for lateral tension and for partial contributions of intermolecular forces to it.Data for a widest possible range of areas per surfactant head, from tunnel formation through tensionless state, transition to floppy bilayer,to its disintegration, are reported and discussed. The significance of the tensionless state, is discussed. Conclusions: (1) the tensionless state is a coincidence;(2) the transition from extended to floppy bilayer occurs nearby and has hallmarks of a phase transition (3) there is no theory of that transition.(4)The lateral tension of the floppy bilayer scales with size; that of the extended bilayer does not depend on size. (4) The drumhead model not appropriate for interfaces as these fluctuate via diffusion.(5) The radius of gyration also! shows a discontinuity.

cond-mat.soft↗

arXiv2006

Size dependence, stability, and a transition to buckling in model reverse bilayers

Molecular Dynamics simulations of a model bilayer made of surfactant dimers in a Lennard-Jones solvent are reported for three sizes of the systems up to an area of $100σ\times 100σ$ and for a large interval of specific areas:from hole formation under tension to the floppy state of a compressed bilayer. The transition to the floppy state appears quite abrupt and discontinuous; in the floppy state the lateral tension is negative. Lateral tension and the structure factor were determined for all 3 sizes and all areas; the apparent rigidity constant and apparent surface tension are determined and correlated with the specific area and the finite size. The replacement of the $1/q^2$ capillary-wave divergence by a pole is accounted for and explained. The derivative of the lateral tension jumps from a high value in a flat bilayer to a low value in the floppy, rough, and buckling state, where the tension itself is negative.

cond-mat.soft↗

arXiv2006

Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model

The solid-on-solid (SOS) model of an interface separating two phases is exactly soluble in two dimensions (d=2) when the interface becomes a one-dimensional string. The exact solution in terms of the transfer matrix is recalled and the density-density correlation function $H(z_1,z_2;Δx)$ together with its projections, is computed. It is demonstrated that the shape fluctuations follow the (extended) capillary-wave theory expression $S(q)=kT/(D+γq^2 +κq^4) $ for sufficiently small wave vectors $q$. We find $κ$ {\it negative}, $κ<0$ . At $q=2π$ there is a strong nearest-neighbor peak. Both these results confirm the earlier findings as established in simulations in d=3 and in continuous space, but now in an exactly soluble lattice model.

cond-mat.soft↗