Ground state structure and interactions between dimeric 2D Wigner crystals

We study the ground state ordering and interactions between two two-dimensional Wigner crystals on neutralizing charged plates by means of computer simulation. We consider crystals formed by (i) point-like charges and (ii) charged dimers, which mimic the screening of charged surfaces by elongated multivalent ions such as aspherical globular proteins, charged dendrimers or short stiff polyelectrolytes. Both systems, with point-like and dimeric ions, display five distinct crystalline phases on increasing the interlayer distance. In addition to alteration of translational ordering within the bilayer, the phase transitions in the dimeric system are characterized by alteration of orientational ordering of the ions.Comment: Revised versio

Statics and Dynamics of Strongly Charged Soft Matter

Soft matter materials, such as polymers, membranes, proteins, are often electrically charged. This makes them water soluble, which is of great importance in technological application and a prerequisite for biological function. We discuss a few static and dynamic systems that are dominated by charge effects. One class comprises complexation between oppositely charged objects, for example the adsorption of charged ions or charged polymers (such as DNA) on oppositely charged substrates of different geometry. The second class comprises effective interactions between similarly charged objects. Here the main theme is to understand the experimental finding that similarly and highly charged bodies attract each other in the presence of multi-valent counterions. This is demonstrated using field-theoretic arguments as well as Monte-Carlo simulations for the case of two homogeneously charged bodies. Realistic surfaces, on the other hand, are corrugated and also exhibit modulated charge distributions, which is important for static properties such as the counterion-density distribution, but has even more pronounced consequences for dynamic properties such as the counterion mobility. More pronounced dynamic effects are obtained with highly condensed charged systems in strong electric fields. Likewise, an electrostatically collapsed highly charged polymer is unfolded and oriented in strong electric fields. At the end of this review, we give a very brief account of the behavior of water at planar surfaces and demonstrate using ab-initio methods that specific interactions between oppositely charged groups cause ion-specific effects that have recently moved into the focus of interest.Comment: 61 pages, 31 figures, Physics Reports (2005)-in press (high quality figures available from authors

Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances

Electrostatic colloid-membrane complexation

We investigate numerically and on the scaling level the adsorption of a charged colloid on an oppositely charged flexible membrane. We show that the long ranged character of the electrostatic interaction leads to a wrapping reentrance of the complex as the salt concentration is varied. The membrane wrapping depends on the size of the colloid and on the salt concentration and only for intermediate salt concentration and colloid sizes we find full wrapping. From the scaling model we derive simple relations for the phase boundaries between the different states of the complex, which agree well with the numerical minimization of the free energy.Comment: 7 page, 11 figure

Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders

We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical temperature, which is also found to be universal and in accordance with the mean-field prediction.Comment: 31 pages, 16 figure

Surface states in nearly modulated systems

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

Which mechanism underlies the water-like anomalies in core-softened potentials?

Using molecular dynamics simulations we investigate the thermodynamic of particles interacting with a continuous and a discrete versions of a core-softened (CS) intermolecular potential composed by a repulsive shoulder. Dynamic and structural properties are also analyzed by the simulations. We show that in the continuous version of the CS potential the density at constant pressure has a maximum for a certain temperature. Similarly the diffusion constant, $D$, at a constant temperature has a maximum at a density $\rho_{\mathrm{max}}$ and a minimum at a density $\rho_{\mathrm{min}}<\rho_{\mathrm{max}}$, and structural properties are also anomalous. For the discrete CS potential none of these anomalies are observed. The absence of anomalies in the discrete case and its presence in the continuous CS potential are discussed in the framework of the excess entropy.Comment: 8 page

Markov state modeling reveals competing collective hydrogen bond rearrangements in liquid water

We construct a Markov state model for the dynamic rearrangement of the local hydrogen bond network in liquid water. The model is based on trajectories from classical molecular dynamics simulations and accounts for the dynamics of relative angular and separation coordinates of water molecules. We analyze first the conformational subspace of three water molecules and find five well separated dynamic modes with reaction times in the 2 - 5 ps range, which correspond to different interchanges of hydrogen bond donor and acceptors, followed by an entire continuum spectrum of modes. We then analyze the switching of one hydrogen bond between two water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along different intermediate states that involve alternative hydrogen bonds or unbound states

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure