Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains

We use molecular dynamics simulations to investigate centipede-like polymers with stiff charged side chains, end-grafted to a planar wall. The effect of the grafting density and the Bjerrum length on the conformational behaviour of the brush is examined in detail. In addition, we make a comparison of centipede-like polyelectrolyte (CPE) brushes with neutral centipede-like polymer (NCP) and linear polyelectrolyte (LPE) brushes. At weak electrostatic interaction, the main chains of the CPE chains adopt a strongly stretched conformation, and the monomer density profiles of side chains exhibit a clear oscillatory behaviour. With increasing Bjerrum length, the CPE brush undergoes a collapse transition. Compared to the CPE brushes, the counterion condensation effect is stronger for the LPE brushes, regardless of whether the electrostatic interaction is weak or strong and of whether the grafting density is low or high. Additionally, it is shown that the architecture of the grafted chains makes a weak contribution to the counterion condensation at strong electrostatic interaction. We also find that the electrostatic repulsion between charged side chains can enhance the stiffness of the main chains and thus limit the range of movement of the free-end monomers.     

Scaling Theory of Strongly Charged Cylindrical Polyelectrolyte Brushes

Scaling theory of charged cylindrical polyelectrolyte brushes is developed. The dependence of brush thickness on the grafting density, charge fraction, and chain length is analyzed. A full phase diagram is established. Characteristics and boundaries between different regimes of cylindrical polyelectrolyte brushes are summarized. Special attentions are paid to electrostatic interaction induced stiffening and counterion condensation effects. If the Bjerrum length of the solution is larger than the Kuhn length of the polyelectrolyte chains, counterion condensation occurs in the strongly charged polyelectrolyte brushes. On the contrary, the electrostatic interaction stretches the strongly charged grafted polyelectrolyte chains to their contour length.     

Strong-coupling electrostatics in the presence of dielectric inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.     

Simulations of counterions at charged plates

Using Monte Carlo simulations, we study the counterion distribution close to planar charged walls in two geometries: i) when only one charged wall is present and the counterions are confined to one half-space, and ii) when the counterions are confined between two equally charged walls. In both cases the surface charge is smeared out and the dielectric constant is the same everywhere. We obtain the counterion density profile and compare it with both the Poisson-Boltzmann theory (asymptotically exact in the limit of weak coupling, i.e. low surface charge, high temperature and low counterion valence) and the strong-coupling theory (valid in the opposite limit of high surface charge, low temperature and high counterion valence) and with previously calculated correction terms to both theories for different values of the coupling parameter, thereby establishing the domain of validity of the asymptotic limits. Gaussian corrections to the leading Poisson-Boltzmann behavior (obtained via a systematic loop expansion) in general perform quite poorly: At coupling strengths low enough so that the Gaussian (or one-loop) correction does describe the numerical deviations from the Poisson-Boltzmann result correctly, the leading Poisson-Boltzmann term by itself matches the data within high accuracy. This reflects the slow convergence of the loop expansion. For a single charged plane, the counterion pair correlation function indicates a behavioral change from a three-dimensional, weakly correlated counterion distribution (at low coupling) to a two-dimensional, strongly correlated counterion distribution (at high coupling), which is paralleled by the specific-heat capacity which displays a rounded hump at intermediate coupling strengths. For the case of counterions confined between two equally charged walls, we analyze the inter-wall pressure and establish the complete phase diagram, featuring attraction between the walls for large enough coupling strength and at intermediate wall separation. Depending on the thermodynamic ensemble, the phase diagram exhibits a discontinuous transition where the inter-wall distance jumps to infinity (in the absence of a chemical potential coupling to the inter-wall distance, as for charged lamellae in excess solvent) or a critical point where two coexisting states with different inter-wall distance become indistinguishable (in the presence of a chemical potential, as for charged lamellae with a finite fixed solvent fraction). The attractive pressure decays with the inter-wall distance as an inverse cube, similar to analytic predictions, although the amplitude differs by an order of magnitude from previous theoretical results. Finally, we discuss in detail our simulation methods and compare the finite-size scaling behavior of different boundary conditions (periodic, minimal image and open). Received 6 November 2001     

Reentrant behavior of divalent-counterion-mediated DNA-DNA electrostatic interaction

The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetravalent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions.     

Interaction between solute molecules in medium density solvents

Solvation properties of solutes in supercritical, medium density solvents have been analysed using hypernetted-chain theory with the emphasis on the solvent-mediated interaction between solute molecules. The solvent and solute molecules are Lennard-Jones particles, and the solute is present at infinite dilution. Also a pair of solute molecules separated by different distances has been considered using reference interaction site model theory. Mainly, solvents at two typical densities (1.09_pc and 2.91_pc; pc is the critical density) that are in medium and high density regions, respectively, are treated. The temperature is set at 1.04T_C (T_c is the critical temperature). When the solute size is larger than the solvent size and the strength of the solute-solvent attractive interaction is greater than that of the solvent-solvent in the medium density region, the solvent structure confined between a pair of solute molecules is largely different from that near a single solute molecule. The confined solvent becomes denser and more stabilized as the distance between the solute molecules decreases, and an attractive interaction is induced between them. The interaction becomes even more attractive as the strength of the solute-solvent attractive interaction increases. The observations are qualitatively different from those in the high density region. Another high density region, which is well below the critical temperature, has been considered, but the behaviour observed is similar to that in the high density region above the critical temperature.     

Collapse of polyelectrolyte brushes: Scaling theory and simulations

We investigate polyelectrolyte brushes using both scaling arguments and molecular dynamics simulations. As a main result, we find a novel collapsed brush phase. In this phase, the height of the brush results from a competition between steric repulsion between ions and monomers and an attractive force due to electrostatic correlations. As a result, the monomer density inside the brush is independent of the grafting density and the polymerization index. For small ionic and monomer radii (or for large Bjerrum length) the brush undergoes a first-order phase transition from the osmotic into the collapsed state. Received 26 September 2000     

Attraction of like-charged macroions in the strong-coupling limit

Like-charged macroions attract each other as a result of strong electrostatic correlations in the presence of multivalent counterions or at low temperatures. We investigate the effective electrostatic interaction between i) two like-charged rods and ii) two like-charged spheres using the recently introduced strong-coupling theory, which becomes asymptotically exact in the limit of large coupling parameter (i.e. for large counterion valency, low temperature, or high surface charge density on macroions). In contrast to previous applications of the strong-coupling theory, we deal with curved surfaces and an additional parameter, referred to as Manning parameter, is introduced, which measures the ratio between the radius of curvature of macroions to the Gouy-Chapman length. This parameter, together with the size of the confining box enclosing the two macroions and their neutralizing counterions, controls the counterion-condensation process that directly affects the effective interactions. For sufficiently large Manning parameters (weakly-curved surfaces), we find a strong long-ranged attraction between two macroions that form a closely-packed bound state with small surface-to-surface separation of the order of the counterion diameter in agreement with recent simulations results. For small Manning parameters (highly-curved surfaces), on the other hand, the equilibrium separation increases and the macroions unbind from each other as the confinement volume increases to infinity. This occurs via a continuous universal unbinding transition for two charged rods at a threshold Manning parameter of , while the transition is strongly discontinuous for spheres because of a pronounced potential barrier at intermediate distances. Unlike the cylindrical case, the attractive forces between spheres disappear slowly for increasing confinement volume due to the complete de-condensation of counterions. Scaling arguments suggest that for moderate values of coupling parameter, strong-coupling predictions remain valid for sufficiently small surface-to-surface separations.Received: 20 August 2003, Published online: 2 March 2004PACS: 87.15.-v Biomolecules: structure and physical properties - 82.70.Dd Colloids - 87.15.Nn Properties of solutions; aggregation and crystallization of macromolecules     

Measuring inter-DNA potentials in solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, approximately 16 mM Mg2+. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.     

Small-angle neutron scattering study of temperature vs. salt dependence of clouding in charged micellar system

Clouding is studied by small-angle neutron scattering (SANS) on a charged micellar system of sodium dodecyl sulphate (SDS) and tetrabutylammonium bromide (TBAB) with varying temperature and salt NaCl. We show that the clouding occurs as a result of increase in the attractive potential between the micelles mediated by the dehydrated TBA(+) counterions on increasing temperature and in the presence of salt. Both micelles and clusters coexist at cloud point temperature (CP) and beyond CP. The addition of salt can be used to obtain CP at room temperature (30° C). The relative effect of different salts on clouding has been found in the order CaCl(2) > MgSO(4) > Na(2)SO(4) > NaF > NaCl > KCl > CsCl > NaBr > NaNO(3). This order is explained on the basis of two important roles played by salt ions: i) counterion condensation that increases the size of the micelles and ii) dehydration of TBA(+) counterions by salt ions for bridging the micelles.     

Structure and switching of single-stranded DNA tethered to a charged nanoparticle surface

Using a molecular theory, we investigate the temperature-dependent self-assembly of single-stranded DNA(ss DNA)tethered to a charged nanoparticle surface. Here the size, conformations, and charge properties of ss DNA are taken into account. The main results are as follows: i) when the temperature is lower than the critical switching temperature, the ss DNA will collapse due to the existence of electrostatic interaction between ss DNA and charged nanoparticle surface; ii)for the short ss DNA chains with the number of bases less than 10, the switching of ss DNA cannot happen, and the critical temperature does not exist; iii) when the temperature increases, the electrostatic attractive interaction between ss DNA and charged nanoparticle surface becomes weak dramatically, and ss DNA chains will stretch if the electrostatic attractive interaction is insufficient to overcome the elastic energy of ss DNA and the electrostatic repulsion energy. These findings accord well with the experimental observations. It is predicted that the switching of ss DNA will not happen if the grafting densities are too high.     

The Influence of Surfactant Self-Association on 23Na Relaxation in Aqueous Solutions and Silica Aqueous Dispersions

Nuclear magnetic resonance ²³Na studies were carried out for sodium octanoate in aqueous solution and in silica aqueous dispersion. The concentration and temperature dependencies of spin–lattice and spin–spin relaxation times of sodium were investigated for ternary systems and binary solutions. The results indicate that the specific chemical association between counterion and ion rather than electrostatic interaction takes place in all systems. The existence of premicellar aggregates in octanoate solution was found.     

Overscreening in colloidal systems: the attractive branch of pair macroion interaction

The effective pair macroion interaction for colloidal systems, obtained in general form by Trigger, Podloubny and Schram (TPS potential) is considered for the case of a strong Coulomb interaction between the macroion and counterion subsystems of a colloid. For this potential a good agreement with the experiments on the shear modules as function of the volume fraction is found.     

Dipolar interaction in a colloidal plasma

The dipole-dipole interaction between macroscopic grains in a plasma is calculated. The presence of a plasma medium shields the Coulomb grain interactions as well as necessitates that nonzero temperature effects be accounted for. The resulting electrostatic but not so much the Helmholtz free energy shows overshooting when equal strength parallel dipoles align with or are perpendicular to the line joining their centers. More striking is the appearance of a short range attractive well interaction for angles near pi/3. The contribution of the dipole-dipole to the total interaction in so-called plasma crystals has become increasingly recognized.     

Temperature-Induced Coil-Globule Transition of Alkali Metal Polyacrylates in Aqueous Organic Solvent Mixtures

A counterion-specific coil-globule transition (CGT) has been observed for alkali metal poly(acrylate)s (PAAM, M; Li, Na, K, Cs) in aqueous organic solvent (ethanol, dimethyl sulfoxide, acetone, acetonitrile) mixtures. In the present study we found that the reduced viscosity of PAAM, except for PAALi, in the relevant mixed solvents, except for those containing acetonitrile, significantly increased with increasing temperature. The observed temperature-induced CGT was interpreted as being caused by disintegration of the ion-clusters, i.e., the associated state of contact ion-pairs formed between the polymer charge and the counterion. In fact, the NMR line width of ²³Na and ¹³³Cs, which were used as a measure of the counterion mobility, indicated that the counterion binding was significantly weakened with increasing temperature, while the temperature effects for the PAALi and acetonitrile systems were only marginal. All these results suggested that the temperature-induced CGT behavior occurs only for systems where the ion-cluster formation promotes the CGT in the relevant solvent systems, which is also consistent with the known similar behavior of some betaine polymers.     

Influence of the volume fraction on the electrokinetic properties of maghemite nanoparticles in suspension

We used several complementary experimental and theoretical tools to characterise the charge properties of well-defined maghemite nanoparticles in solution as a function of the volume fraction. The radius of the nanoparticles is equal to 6 nm. The structural charge was measured from chemical titration and was found high enough to expect some counterions to be electrostatically attracted to the surface, decreasing the apparent charge of the nanoparticle. Direct-current conductivity measurements were interpreted by an analytical transport theory to deduce the value of this apparent charge, denoted here by ‘dynamic effective charge’. This dynamic effective charge is found to decrease strongly with the volume fraction. In contrast, the ‘static’ effective charge, defined thanks to the Bjerrum criterion and computed from Monte Carlo simulations turns out to be almost independent of the volume fraction. In the range of Debye screening length and volume fraction investigated here, double layers around nanoparticles actually interact with each other. This strong interaction between nanocolloidal maghemite particles is probably responsible for the experimental dependence of the electrokinetic properties with the volume fraction.     

Statistical mechanics of bilayer membranes in troubled aqueous media

We consider a bilayer membrane surrounded by small impurities, assumed to be attractive or repulsive. The purpose is a quantitative study of the effects of these impurities on the statistical properties of the supported membrane. Using the replica trick combined with a variational method, we compute the membrane mean-roughness and the height correlation function for almost-flat membranes, as functions of the primitive elastic constants of the membrane and some parameter that is proportional to the volume fraction of impurities and their interaction strength. As results, the attractive impurities increase the shape fluctuations due to the membrane undulations, while repulsive ones suppress these fluctuations. Second, we compute the equilibrium diameter of (spherical) vesicles surrounded by small random particles starting from the curvature equation. Third, the study is extended to a lamellar phase composed of two parallel fluid membranes, which are separated by a finite distance. This lamellar phase undergoes an unbinding transition. We demonstrate that the attractive impurities increase the unbinding critical temperature, while repulsive ones decrease this temperature. Finally, we say that the presence of small impurities in an aqueous medium may be a mechanism to suppress or to produce an unbinding transition, even the temperature and polarizability of the aqueous medium are fixed, in lamellar phases formed by parallel lipid bilayers.     

Counterion distribution and many-body interaction in charged dendrimer solutions

Coarse-grained molecular dynamics simulations are performed to study the structural formation, counterion distribution and effective interaction on charged dendrimers in an aqueous solution. In particular, the many-body effects in triplet systems are clarified. The conformation of a dendrimer molecule depends on the size of counterions, and the counterion distribution can be scaled by the gyration radius of a dendrimer molecule. Two-body and three-body interactions have been numerically investigated, and the results indicate both similarities and differences between dendrimer solutions and other soft colloidal systems, such as star polymer solutions.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms

We consider the BCS-BEC (Bose-Einstein-condensate) crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.