Sedimentation profiles of systems with reentrant melting behavior

We examine sedimentation density profiles of star polymer solutions as an example of colloidal systems in sedimentation equilibrium which exhibit reentrant melting in their bulk phase diagram. Phase transitions between a fluid and a fluid with an intercalated solid are observed below a critical gravitational strength $\alpha^{*}$. Characteristics of the two fluid-solid interfaces in the density profiles occurring in Monte Carlo simulations for $\alpha < \alpha^{*}$ are in agreement with scaling laws put forth in the framework of a phenomenological theory. Furthermore we detect density oscillations at the fluid-gas interface at high altitudes for high gravitational fields, which are verified with density functional theory and should be observable in surface scattering experiments.Comment: 10 pages, 6 figure

Monte Carlo simulation of melting transition on DNA nanocompartment

DNA nanocompartment is a typical DNA-based machine whose function is dependent of molecular collective effect. Fundamental properties of the device have been addressed via electrochemical analysis, fluorescent microscopy, and atomic force microscopy. Interesting and novel phenomena emerged during the switching of the device. We have found that DNAs in this system exhibit a much steep melting transition compared to ones in bulk solution or conventional DNA array. To achieve an understanding to this discrepancy, we introduced DNA-DNA interaction potential to the conventional Ising-like Zimm-Bragg theory and Peyrard-Bishop model of DNA melting. To avoid unrealistic numerical calculation caused by modification of the Peyrard-Bishop nonlinear Hamiltonian with the DNA-DNA interaction, we established coarse-gained Monte Carlo recursion relations by elucidation of five components of energy change during melting transition. The result suggests that DNA-DNA interaction potential accounts for the observed steep transition.Comment: 12 pages, 5 figure

Counterion-mediated Electrostatic Interactions between Helical Molecules

We study the interaction of two cylinders with helical charge distribution mediated by neutralizing counterions, by analyzing the separation as well as the azimuthal angle dependence of the interaction force in the weak and strong coupling limit. While the azimuthal dependence of the interaction in the weak coupling limit is overall small and mostly negligible, the strong coupling limit leads to qualitatively new features of the interaction, among others also to an orientationally dependent optimal configuration that is driven by angular dependence of the correlation attraction. We investigate the properties of this azimuthal ordering in detail and compare it to existing results.Comment: 11 pages, 12 figure

Rare isotope production in statistical multifragmentation

Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble. Both the initial fragmentation and the the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments. The importance of sequential decay, exact particle-number conservation and the sensitivities to parameters such as density and temperature are explored. Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture.Comment: 10 eps figure

Torsional fluctuations in columnar DNA assemblies

In columnar assemblies of helical bio-molecules the azimuthal degrees of freedom, i.e. rotations about the long axes of molecules, may be important in determining the structure of the assemblies especially when the interaction energy between neighbouring molecules explicitly depends on their relative azimuthal orientations. For DNA this leads to a rich variety of mesophases for columnar assemblies, each categorized by a specific azimuthal ordering. In a preceding paper [A. Wynveen, D. J. Lee, and A. A. Kornyshev, Eur. Phys. J. E, 16, 303 (2005)] a statistical mechanical theory was developed for the assemblies of torsionally rigid molecues in order to determine how thermal fluctuations influence the structure of these mesophases. Here we extend this theory by including torsional fluctuations of the molecules, where a DNA molecule may twist about its long axis at the cost of torsional elastic energy. Comparing this with the previous study, we find that inclusion of torsional fluctuations further increases the density at which the transition between the hexagonal structure and the predicted rhombic phase occurs and reduces the level of distortion in the rhombic phase. As X-ray diffraction may probe the 2-D lattice structure of such assemblies and provide information concerning the underlying interaction between molecules, we have also calculated correlation functions for the azimuthal ordering which are manifest in an x-ray scattering intensity profiles.Comment: 33 pages, 8 figure

Statistical mechanics of columnar DNA assemblies

Many physical systems can be mapped onto solved or "solvable" models of magnetism. In this work, we have mapped the statistical mechanics of columnar phases of ideally helical rigid DNA -- subject to the earlier found unusual, frustrated pair potential [A. A. Kornyshev and S. Leikin, J. Chem. Phys. 107, 3656 (1997)] -- onto an exotic, unknown variant of the XY model on a fixed or restructurable lattice. Here the role of the 'spin' is played by the azimuthal orientation of the molecules. We have solved this model using a Hartree-Fock approximation, ground state calculations, and finite temperature Monte Carlo simulations. We have found peculiar spin order transitions, which may also be accompanied by positional restructuring, from hexagonal to rhombohedric lattices. Some of these have been experimentally observed in dense columnar aggregates. Note that DNA columnar phases are of great interest in biophysical research, not only because they are a useful in vitro tool for the study of DNA condensation, but also since these structures have been detected in living matter. Within the approximations made, our study provides insight into the statistical mechanics of these systems.Comment: 19 pages, 18 figure

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure

Phase Behavior of Columnar DNA Assemblies

The pair interaction between two stiff parallel linear DNA molecules depends not only on the distance between their axes but on their azimuthal orientation. The positional and orientational order in columnar B-DNA assemblies in solution is investigated, based on the DNA-DNA electrostatic pair potential that takes into account DNA helical symmetry and the amount and distribution of adsorbed counterions. A phase diagram obtained by lattice sum calculations predicts a variety of positionally and azimuthally ordered phases and bundling transitions strongly depending on the counterion adsorption patterns.Comment: 4 pages, 3 figures, submitted to PR

Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure

Star polymers: From conformations to interactions to phase diagrams

We review recent progress achieved in the theoretical description of the interactions, correlations, and phase behavior of concentrated solutions of star polymers, sterically stabilized colloids, and micelles. We show that the theoretical prediction of an ultrasoft, logarithmically diverging effective interaction between the star centers, which has been confirmed by SANSexperiments and computer simulations, lies in the core of a host of unusual phenomena encountered in such systems. These include anomalous structure factors, reentrant melting behavior, as well as a variety of exotic crystal phases. Extensions to polydisperse stars and the role of many-body forces are also discussed. A particular ‘mean-field’ character of star polymer fluids is presented and it is shown that it manifests itself in the shape and structure of sedimentation profiles of these systems.Здійснено огляд недавніх досягнень у теоретичному описі взаємодій, кореляцій і фазової поведінки концентрованих розчинів зіркових полімерів, просторово стійких колоїдів і міцел. Ми покажемо, що теоретично передбачена надм’яка логарифмічно розбіжна ефективна взаємодія між центрами зірок, що була підтверджена SANS-експериментами і комп’ютерними симуляціями, потрапляє в множину незвичних явищ, які спостерігаються в таких системах. Сюди відносяться аномальні структурні фактори, поведінка зворотнього плавлення, множини екзотичних кристалічних фаз. Також обговорено узагальнення на випадок полідисперсних зірок і роль сил багатьох тіл. Представлено особливу поведінку типу “cереднього поля” плинів зіркових полімерів і показано, що вона проявляється у формі і структурі профілів осаджування цих систем