We present a theoretical description of polymer adsorption from solution which is based on a mean field approximation but which goes beyond the standard ground state dominance approximation. The properties of the adsorbed polymer chains are described by two coupled order parameters. This allows a description of the chains in terms of tails and loops. When the bulk solution is dilute, the adsorbed polymer layer has a double layer structure with an inner layer dominated by loops and an outer layer dominated by tails. Explicit asymptotic forms are found for the monomer concentration profile and for the crossover distance between the loops and tail regions. The precise concentration profile is obtained by a numerical solution of two coupled differential equations. One of the surprising results is that the total polymer adsorbed amount has a nonmonotonic variation with molecular weight and decreases for large values of the molecular weight. The concentration profiles are also determined when the bulk solution is semidilute or concentrated. At any bulk concentration, the monomer concentration has a nonmonotonic variation with the distance to the adsorbing wall and shows a minimum at a finite distance. This depletion effect can be significant in the vicinity of the crossover between dilute and semidilute solutions. All the results are in agreement with the existing numerical solutions of the complete mean field theory of polymer adsorption. Excluded volume correlations are taken into account by constructing scaling laws for polymers in a good solvent both in dilute and in semidilute solutions.

The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the evolution of the probability distribution for the system is deduced together with the corresponding fluctuation-dissipation theorems ensuring that the ab initio chosen equilibrium probability distribution for the relevant variables is a stationary solution. When energy conservation is included, the system can sustain temperature gradients and heat flow can be modeled.

The dynamics of Keggin polyoxoanions in aqueous solution in the presence of monovalent cations is analyzed through molecular dynamics simulations. Together with structural information yielding the radial distribution functions of Li(+), Na(+), and K(+) with three polyoxometalates (POMs) bearing 3-, 4-, and 5- charges, the diffusion coefficient of these POMs is calculated. We found that the effect of the microscopic molecular details of the solvent is a key aspect to interpreting the structural and dynamic data because a competition between electrostatic interactions between the ions and the stability of the solvation shell is established. Furthermore, we show that solvent-shared structures weakly bound to the POM anion play a crucial role in the determination of the dynamic properties of the anion. The nature of these ion pairs, structurally characterized for the first time, is consistent with experimental data available.