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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 (such as DNA) on oppositely charged substrates of different geometry. 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. At the end of this review, we give a very brief account of the behavior of water at planar surfaces and demonstrate using ab-initio methods that specific interactions between oppositely charged groups cause ion-specific effects that have recently moved into the focus of interest.
This paper discusses the elastic behavior of a very long crosslinked polyelectrolyte chain (Debye-Huckel chain), which is weakly charged. Therefore the response of the crosslinked chain (network) on an external constant force $f$ acting on the ends o
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An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the
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