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 on oppositely charged substrates of different geometry. Here the main questions are whether adsorption occurs and what the effective charge of the resulting complex is. We explicitly discuss the adsorption behavior of polyelectrolytes on substrates of planar, cylindrical and spherical geometry with specific reference to DNA adsorption on supported charged lipid layers, DNA adsorption on oppositely charged cylindrical dendro-polymers, and DNA binding on globular histone proteins, respectively. In all these systems salt plays an important role, and some of the important features can already be obtained on the linear Debye-Hückel level. 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. All charged systems occur in water, and water by itself is not a very well understood material. At the end of this review, we give a very brief and incomplete account of the behavior of water at planar surfaces. The coupling between water structure and charge effects is largely unexplored, and a few directions for future research are sketched. On an even more nanoscopic level, we demonstrate using ab-initio methods that specific interactions between oppositely charged groups (which occur when their electron orbitals start to overlap) are important and cause ion-specific effects that have recently moved into the focus of interest.

We consider structures formed by one semiflexible polyelectrolyte (PE) and one oppositely charged sphere and calculate the interaction between two such complexes within the ground-state approximation, where the PE assumes its optimal configuration. Using parameters appropriate for DNA-histone systems, we find the second virial coefficient of inter-complex interactions to be negative for intermediate salt concentrations within the range where stable complexes are formed, in agreement with experiments. A simple screened monopole-dipole model reproduces these findings.

We investigate the thermodynamic stability of complexes formed by one semiflexible charged polymer wrapped around an oppositely charged sphere. Choosing parameters for DNA and histones, we determine all conformational eigen-modes and the corresponding eigen-value spectrum of the complexed chain, from which the free energy of complexation and thus the reaction constant is obtained. The resulting complexation diagram exhibits qualitative agreement with experimental results as a function of salt and DNA/histone concentration.

We review the problem of complex formation between a macroion and an oppositely charged polyelectrolyte on the linear level. We study the effect of changing the ionic strength and the valency of the macroion on the complexed polymer configuration. Distinguishing four different configurational symmetry classes, we are able to map out the global configurational phase diagram. We also study the interaction between two complexes of macroion and polyelectrolyte, which gives rise to configurational changes of two complexes as they approach each other. Most of these calculations are performed on the ground-state level and are thus accurate only for very stiff polymers or highly charged and therefore strongly bound systems. We also give a short outlook into the problem of thermal fluctuations around the polymer ground state configuration as it is wrapped around the macroion. This problem is tackled by a normal-mode analysis. All calculations are performed for parameters corresponding to DNA–histone complexes, which are the basic building blocks of the nucleosomal genetic structure.

The structure and stability of strongly charged complex fibers, formed by complexation of a single long semi-flexible polyelectrolyte chain and many oppositely charged spherical macroions, are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal fiber configurations exhibit a variety of helical structures for the arrangement of macroions including zig-zag, solenoidal and beads-on-a-string patterns. These structures result from the competition between attraction between spheres and the polyelectrolyte chain (which favors chain wrapping around the spheres), chain bending rigidity and electrostatic repulsion between chain segments (which favor unwrapping of the chain), and the interactions between neighboring sphere-chain complexes which can be attractive or repulsive depending on the system parameters such as salt concentration, macroion charge and chain length per macroion (linker size). At about physiological salt concentration, dense zig-zag patterns are found to be energetically most stable when parameters appropriate for the DNA-histone system in the chromatin fiber are adopted. In fact, the predicted fiber diameter in this regime is found to be around 30 nanometers, which roughly agrees with the thickness observed in in vitro experiments on chromatin. We also find a macroion (histone) density of 5-6 per 11nm which agrees with results from the zig-zag or cross-linker models of chromatin. Since our study deals primarily with a generic chain-sphere model, these findings suggest that structures similar to those found for chromatin should also be observable for polyelectrolyte-macroion complexes formed in solutions of DNA and synthetic nano-colloids of opposite charge. In the ensemble where the mean linear density of spheres on the chain is fixed, the present model predicts a phase separation at intermediate salt concentrations into a densely packed complex phase and a dilute phase.