arXiv subjects

Roland R. Netz

Publications and source records attributed to Roland R. Netz.

118 records · Page 7Linked to original sources

arXiv2001

Polyelectrolytes in Solution and at Surfaces

This chapter deals with charged polymers (polyelectrolytes) in solution and at surfaces. The behavior of polyelectrolytes is markedly different from that of neutral polymers. In bulk solutions, i.e. disregarding the surface effect, there are two unique features to charged polymers: first, due to the presence of long-ranged electrostatic repulsion between charged monomers, the polymer conformations are much more extended, giving rise to a very small overlap concentration and high solution viscosity. Second, the presence of a large number of counter-ions increases the osmotic pressure of polyelectrolyte solutions, making such polymers water soluble as is of great importance to many applications. At surfaces, the same interplay between monomer-monomer repulsion and counter-ion degrees of freedom leads to a number of special properties. In particular, the adsorption behavior depends on both the concentration of polymers and added salt in the bulk. We first describe the adsorption behavior of single polyelectrolyte molecules, and discuss the necessary conditions to obtain an adsorbed layer and characterize its width. Depending on the stiffness of the polyelectrolyte, the layer can be flat and compressed or coiled and extended. We then proceed and discuss the adsorption of polyelectrolytes from semi-dilute solutions. Mean-field theory profiles of polyelectrolyte adsorption are calculated as function of surface charge density (or surface potential), the amount of salt in the system and the charge fraction on the chains. The phenomenon of charge inversion is reviewed and its relevance to the formation of multilayers is explained. The review ends with a short overview of the behavior of grafted polyelectrolytes.

cond-mat.soft↗

arXiv2000

Binding of Similarly Charged Plates: A Global Analysis

Similarly and highly charged plates in the presence of multivalent counter ions attract each other, leading to electrostatically bound states. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space. The equilibrium plate separation, where the pressure changes from attractive to repulsive, exhibits a novel unbinding transition. A systematic and asymptotically exact strong-coupling field-theory yields the bound state from a competition between counter-ion entropy and electrostatic attraction, in agreement with simple scaling arguments.

cond-mat.soft↗

arXiv2000

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 inverse powers of the coupling parameter. For a planar charged wall, our analytical results compare quantitatively with extensive Monte-Carlo simulations.

cond-mat.soft↗

arXiv2000

Phase behavior of three-component ionic fluids

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-Hueckel theory, we analyze the phase behavior of such systems for different values of the ratio Z/z. We find, for Z/z>1.934, a three-phase coexistence region and, for Z/z>2, 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 Z/z=2 and Z/z=3, corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.

cond-mat.soft↗

arXiv2000

Adsorbed and Grafted Polymers at Equilibrium

This chapter deals with various aspects related to the adsorption of long chain-like macromolecules (polymers) onto solid surfaces. Physical aspects of the adsorption mechanism are elaborated mainly at thermodynamical equilibrium. The basic features needed in modeling of this adsorption are discussed. We first discuss the adsorption of a single and long polymer chain to the surface. The surface interaction is modeled by a potential well with a long-ranged attractive tail. A simple mean-field theory description is presented and the concept of polymer "blobs" is used to describe the conformation of the chain at the surface. The thickness of the adsorbed layer depends on several polymer and surface parameters. Fluctuation corrections to mean-field theory are also discussed. We then review adsorption as well as depletion processes in the many-chain case. Profiles, changes in the surface tension and polymer surface excess are calculated within mean-field theory. Corrections due to fluctuations in good solvent are taken into account using scaling concepts. The proximal exponent is introduced in analogy to surface critical phenomena. The interaction between two surfaces with adsorbed polymer layers is discussed, and various cases leading to attractive and repulsive interactions are mentioned. Polyelectrolytes are of practical importance due to their water solubility; we give a short summary of recent progress in this rapidly evolving field. The behavior of grafted polymers, i.e., polymers which are anchored with one end to a solid substrate is also reviewed.

cond-mat.soft↗

arXiv1999

One-Component Plasma: Going Beyond Debye-Hueckel

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, pg. 489 (1998) / cond-mat/9805358] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter Gamma, 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.

cond-mat.stat-mech↗

arXiv1999

One and two-component hard core plasmas

A field theory is presented for particles which interact via Coulomb and hard-core potentials. We apply the method to the one-component plasma (OCP) with hard cores, consisting of identical particles of fixed charge and diameter in a neutralizing background, and the symmetric two-component plasma (TCP) with hard cores, consisting of equal numbers of positively and negatively charged particles of identical size. We obtain exactly the first few coefficients of a systematic low-density expansion of the free energy for both models. The OCP coefficients go over to the classical Abe result in the high-charge (or small hard-core diameter) limit. The TCP, on the other hand, exhibits diverging coefficients in the high-charge limit, which is due to the formation of strongly bound ion-pairs.

cond-mat.soft↗

arXiv1999

Beyond Poisson-Boltzmann: Fluctuations and Correlations

We formulate the non-linear field theory for a fluctuating counter-ion distribution in the presence of a fixed, arbitrary charge distribution. The Poisson-Boltzmann equation is obtained as the saddle-point, and the effects of fluctuations and correlations are included by a loop-wise expansion around this saddle point. We show that the Poisson equation is obeyed at each order in the loop expansion and explicitly give the expansion of the Gibbs potential up to two loops. We then apply our formalism to the case of an impenetrable, charged wall, and obtain the fluctuation corrections to the electrostatic potential and counter-ion density to one-loop order without further approximations. The relative importance of fluctuation corrections is controlled by a single parameter, which is proportional to the cube of the counter-ion valency and to the surface charge density. We also calculate effective interactions between charged particles, which reflect counter-ion correlation effects.

cond-mat.soft↗

arXiv1998

Field theory fo charged fluids and colloids

A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-Hückel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions given by the screened DH potential. Higher-loop corrections can lead to attractive pair interactions between colloids in asymmetric ionic environments. The free energy follows as a loop-wise expansion in half-integer powers of the density; the resulting two-phase demixing region shows pronounced deviations from DH theory for strongly charged colloids.

cond-mat.stat-mech↗

arXiv1998

Interfaces and Grain Boundaries of Lamellar Phases

Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment.

cond-mat.soft↗