| I will first discuss the effects of quenched, annealed and partially annealed fixed charge disorder on effective electrostatic interactions between charged surfaces in a one-component (counterion-only) Coulomb fluid and between charged surfaces in vacuo. Analytical results can be explicitly derived for two asymptotic and complementary cases: i) mean-field or Poisson-Boltzmann limit (including Gaussian-fluctuations correction), which is valid for small electrostatic coupling, and ii) strong-coupling limit, where electrostatic correlations mediated by counterions become significantly large as, for instance, realized in systems with high-valency counterions. In the particular case of two apposed and ideally polarizable planar surfaces with equal mean surface charge, the effect of the disorder is nil on the mean-field level and thus the plates repel. In the strong-coupling limit, however, the effect of charge disorder turns out to be additive in the free energy and leads to an enhanced long- range attraction between the two surfaces. The equilibrium inter- plate distance between the surfaces decreases for elevated disorder strength (i.e. for increasing mean-square deviation around the mean surface charge), and eventually tends to zero, suggesting a disorder-driven collapse transition. I will then switch to the case of two charged surfaces with disordered charge distribution in vacuo which is simpler and leads to long range Casimir-like effects. In the vacuum case I will discuss the effects of various types of monopolar charge disorder on the interaction between two macroscopic surfaces, delimiting two semi-infinite net-neutral dielectric half-spaces, separated by a layer of vacuum or an arbitrary dielectric material. I will consider different a priori models for the distribution of disorder. I will show that the type and the nature of the disorder has important consequences for the total interaction between apposed bodies and can even dominate or give a contribution comparable to the underlyin g thermal Casimir interaction. Finally I will discuss the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. I will show that the effective interaction at long distances is self averaging and its value is given by a that between non-random media with the effective dielectric tensor of the corresponding random media. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric constants proximal to each other across the homogeneous slab. I will finally extend these considerations to the regime of intermediate slab separations by using perturbation theory for weak disorder and also by extensive numerical simulations for a number of systems where the dielectric function has a log-normal distribution. |
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