André G. Moreira

Electrostatic Interactions in Strongly-Coupled Soft Matter

Charged soft-matter systems—such as colloidal dispersions and charged polymers—are dominated by attractive forces between constituent like-charged particles when neutralizing counterions of high charge valency are introduced. Such counter-intuitive effects indicate strong electrostatic coupling between like-charged particles, which essentially results from electrostatic correlations among counterions residing near particle surfaces. In this paper, the attraction mechanism and the structure of counterionic correlations are discussed in the limit of strong coupling based on recent numerical and analytical investigations and for various geometries (planar, spherical and cylindrical) of charged objects.

Strong-coupling theory for counter-ion distributions.

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in powers of the fugacity. For a planar charged wall, our analytical results compare quantitatively with extensive Monte Carlo simulations.

Field-theoretic simulations of confined polymer solutions

We used field-theoretic simulations to study the equilibrium behavior of a polymer solution under good solvent conditions confined to a slit of width L. In particular, we obtained the chemical potential and the density profiles across the slit for different values of the monomer excluded volume over a wide range of concentrations C. We also obtained mean field results for the chemical potential and the density profiles. The effective correlation length ξeff was calculated from the density profiles and compared to the mean field result (valid in the limit of high concentrations). For small excluded volume parameters we found that ξeff is well described by the mean field result for all concentrations. For larger excluded volume parameters the correlation length exhibits a C−3/4 scaling behavior for intermediate concentrations, which is compatible with the behavior expected for this system in the semidilute regime.

Field-theoretic simulations of polymer solutions: Finite-size and discretization effects

In this work we analyze the finite-size and discretization effects that occur in field-theoretic polymer simulations. Following our previous work, we study these effects for a polymer solution in the canonical ensemble confined to a slit (with nonadsorbing walls) of width L, and focus on the behavior of two quantities: the chemical potential mu, and the correlation length xi. Our results show that the finite-size effects disappear for both quantities once the lateral size of the system L is larger than approximately 2xi. On the other hand, the chemical potential is dominated by the lattice discretization Deltax. The origins of this dependence are discussed in detail, and a scheme is proposed in which this effect is avoided. Our results also show that the density profiles do not depend on the lattice discretization if Deltax < approximately xi/4. This implies that the correlation length xi, extracted from the density profiles, is free of lattice size and lattice discretization artifacts once L is > approximately 2xi and Deltax < approximately xi/4.

Crossover scales at the critical points of fluids with electrostatic interactions

Criticality in a fluid of dielectric constant D that exhibits Ising-type behavior is studied as additional electrostatic (i.e., ionic) interactions are turned on. An exploratory perturbative calculation is performed for small ionicity as measured by the ratio of the electrostatic energy e2/Da (of two univalent charges, ±e, separated by the atomic/ionic diameter a) to kBTc0 which represents the strength of the short-range nonionic (i.e., van der Waals) interactions in the uncharged fluid. With the aid of distinct transformations for the short-range and for the Coulombic interactions, an effective Hamiltonian with coefficients depending on the ionicity is derived at the Debye-Huckel limiting-law level for a fully symmetric model. The crossover between classical (mean-field) and Ising behavior is then estimated using a Ginzburg criterion. This indicates that the reduced crossover temperature depends only weakly on the ionicity (and on the range of the nonionic potentials); however, the trends do correlate wi...

The role of polymer spacers in specific adhesion

We study the role of flexible spacers in specific adhesion from the point of view of polymer reaction--diffusion theory. By assuming that the interactions between complementary adhesion moieties occur on a length scale much smaller than the size of the polymer spacer, we describe in detail binding and rupture between two opposing surfaces. Predictions are given for the physical properties of interest such as the time evolution of bond density and the ranges of attraction and unbinding. We also discuss the dynamic crossover between reversible and irreversible bridging.

Global stationary phase and the sign problem

We present a computational strategy for reducing the sign problem in the evaluation of high dimensional integrals with nonpositive definite weights whose logarithms are analytic. The method involves stochastic sampling with a positive semidefinite weight that is adaptively and optimally determined during the course of a simulation. The optimal criterion, which follows from a variational principle for analytic actions S(z), is a global stationary phase condition that the average gradient of the phase ImS along the sampling path vanishes. Numerical results are presented from simulations of a model adapted from statistical field theories of classical fluids.

One-component-plasma: Going beyond Debye-Hückel

Using field-theoretic methods, we calculate the internal energy for the One-Component Plasma (OCP). We go beyond the recent calculation by Brilliantov [N. Brilliantov, Contrib. Plasma Phys. 38, 489 (1998)] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter Γ, the effect of the higher-order terms is small and that the final result is not improved relative to the Gaussian theory when compared to simulations.

Virial expansion for charged colloids and electrolytes

Abstract:Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d+ and d- and charge valences q+ and q- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d+∼d- and q+∼q-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient.

Phase behavior of three-component ionic fluids

Abstract:We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hückel theory, we analyze the phase behavior of such systems for different values of the ratio . We find, for , a three-phase coexistence region and, for , a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of and , corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.