Molecular dynamics simulations mean-field theories

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

Most of the theories were based on the self-consistent mean field approximation.12-32 The other ones include the scaling analysis, - molecular dynamics simulations and Monte Carlo simulations.40,41 The self-consistent mean field theories12-32 were developed along the following three lines (1) on the basis of a lattice model,12-22 (2) on the basis of a diffusion type equation,23-28 and (3) analytical approaches.29-32... 

To study the range of possibilities the first molecular dynamics simulations of a DNA duplex tethered to a surface was performed [35,36] The technical aspects of simulations near surfaces are nontrivial, especially as concerns reliable boundary conditions [37], Molecular dynamics provides a more quantitative picture of the salt gradients and DNA structures near the surface responsible for changes in hybridization affinities and specificities than approximate (PB level mean field) theory and so may be used as a check on the simple analytical picture derived above. In addition simulation provides mechanistic clues which can form additional hypotheses for testing. 

Gas transport in nano-confinements can significantly deviate from the kinetic theory predictions due to surface force effects. Kinetic theory-based approaches based on the assumption of dynamic similarity between nanoscale confined and rarefied flows in low-pressure environments by simply matching the Knudsen and Mach numbers are incomplete. Molecular dynamics simulations of nanoscale gas flows in the early transition and free-molecular flow regimes reveal that the wall force field penetration depth should be considered as an important length scale in nano-confined gas flows, in addition to the channel dimensions and gas mean free path. 

Jia R, Hentschke R (2009) Dipolar particles in an external field molecular dynamics simulation and mean field theory. Phys Rev E 80(5) 051502... 

The influence of interfacial interaction is usually neglected. This is because in classical mean-field theories or molecular dynamic simulations it is assumed that interfacial interactions are conq)letely screened within a distance corresponding to the persistence length of the polymer (38). Thus, confinement effects induced during film preparation are not taken into account. However, it has been shown that interfacial interactions can effect the polymer films up to a distance of 200 nm from the interface even after annealing of the polymer films (29, 39,40). 

Both vibrational and rotovibrational relaxation can be described analyti-caDy as multiplicative stochastic processes. For these processes, RMT is equivalent to the stochastic Liouville equation of Kubo, with the added feature that RMT takes into account the back-reaction from the molecule imder consideration on the thermal bath. The stochastic Liouville equation has been used successfully to describe decoupling in the transient field-on condition and the effect of preparation on decay. When dealing with liquid-state molecular dynamics, RMT provides a rigorous justification for itinerant oscillator theory, widely applied to experimental data by Evans and coworkers. This implies analytically that decoupling effects should be exhibited in molecular liquids treated with strong fields. In the absence of experimental data, the computer runs described earlier amount to an independent means of verifying Grigolini s predictions. In this context note that the simulation of Oxtoby and coworkers are semistochastic and serve a similar purpose. 

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