Single particle dynamics

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Finally, we note that a different type of exponential scaling that links single-particle dynamics to entropy has now been found to hold for atomistic super-cooled liquids.122 In particular, the relationship,... 

Quantitative Link Between Single-Particle Dynamics and Static Structure of Supercooled Liquids. 

Eq. (20) can also be used to identify the contributions of single-particle dynamics to G(t). They are obtained by constructing autocorrelations of... 

Thus, the real time steps, At, are unequal in Nosd s formulation. As in constant-pressure calculations, the value of Q, in units of energy (time)2, determines the dynamical quantities, although the equilibrium quantities are independent of the value of Q. The procedure for the selection of the optimum value for Q has been discussed by Nose 11). It is believed that single-particle dynamics are less sensitive to the value of Q. 

Chen SH, Liao C, Sciortino F, Gallo P, Tartaglia P. Model 94. for single-particle dynamics in supercooled water. Phys. Rev. 

The results presented here are still prdiminary in quantitative sense. The problem which can be easily reco iized is the miKh faster initial dmy in every case than what is observed in die experiments (or simulations). Two remedies for the problem are under investigation (1) rqdacing the translational diffusion constant by more elaborated model for the single particle dynamics which explicitly includes the rigid body rotation, and (2) inclusion of the nonlinearity in the density fidd in the SSSV equation. 

It appears that the short time dynamics of water molecules at or near the hydrophilic model surface and at a soluble protein surface is much slower than that of the bulk water. It is important to note that the more significant slow dynamics of interfacial water is reflected in the long residence time for jump diffusion. This suggests that there may be a common underlying mechanism for the slowing down of the single-particle dynamics of interfacial water. 

In order to understand the effect of temperature on the water dynamics and how it leads to the glass transition of the protein, we have performed a study of a model protein-water system. The model is quite similar to the DEM, which deals with the collective dynamics within and outside the hydration layer. However, since we want to calculate the mean square displacement and diffusion coefficients, we are primarily interested in the single particle properties. The single particle dynamics is essentially the motion of a particle in an effective potential described by its neighbors and thus coupled to the collective dynamics. A schematic representation of the d)mamics of a water molecule within the hydration layer can be given by ... 

The potential surface on which the hydrogen atom vibrates can be probed in some detail for two different cases single particle dynamics where dispersion is absent and collective dynamics where dispersion is important. 

Single particle dynamics occurs where there are no interactions between hydrogen atoms in the metal so the oscillator mass, p, is close to unity and the INS spectra extend over several harmonics ( 5.2.1.2). 

C. Andreani, E. Degiorgi, R. Senesi, F. Cilloco, D. Colognesi, J. Mayers, M. Nardone E. Pace (2001). J. Chem. Phys., 114, 387-398. Single particle dynamics in fluid and solid hydrogen sulphide An inelastic neutron scattering study. 

Figures 16a and 16b show the time evolution of the single-particle second-rank OTCF and the OKE signal derived from the system in log-log plots at several temperatures down to TC. The slowdown in the single-particle dynamics is evident on approaching Tc upon cooling. The single-particle second-rank OTCF shows a shoulder at intermediate timescales below a certain temperature. The shoulder develops into a plateau as the temperature is further lowered. It is evident in Figure 16b that a rather long power law decay regime with a...

In summary, the strategy of these calculations is to explicitly consider products of phase-space density fields in the theory. These product fields describe the correlated motion of the solute and solvent molecules. An examination of the coupling of these higher order fields to the solute fields should then lead to a precise description of the effects on single-particle dynamics of correlated motion of many particles. 

Magnetic resonance experiments probe of single-particle dynamics... 

The interpolation of the experimental data was carried out by a least-squares fitting procedure of the DCF values. The most appropriate number of elementary Debye processes involved is determined by the minimum of the standard deviation x - The dielectric response obtained reflects some properties inherent in single particle dynamics. The best-fit curves of the experimental data are reported in Figure 19 Time dependence of the macroscopic dipole correlation... 

The primary aim of molecular dynamics is to numerically solve the N-body problem of classical mechanics. Molecular dynamics methods are used for used for simulating molecular-scale models of matter in order to relate collective dynamics to single-particle dynamics. Typical situations for its application are self-assembly of structures, such as micelles and vesicles. 

The volume of neutron data on biopolymer-water systems is small [60,82,83]. In fact, the case of water close to different residues of a biological material is certainly more interesting for future applications. However, the situation is also more complex due to contributions such as the hydrogen atoms of the protein itself, the possibility of their exchange with water molecules, and the presence of hydrophilic and hydrophobic regions. Studies of the single-particle dynamics of hydration water in proteins have been hampered by the fact that about 40% of the constituent... 

Mittal, J., Errington, J. R. Truskett, T. M. (2006). Quantitative link between single-particle dynamics and static structure of supercooled liquids, /. Phys. Chem. B 110 18147. 

One should not conclude from this discussion that we are somehow limited to single-particle dynamics and ordinary, though stochastic, differential equations. One can also deal rather easily with many-body dynamics in some subset of phase space, where a portion of the time evolution operator is itself stochastic, provided everything remains linear with respect to the distribution. Consider the following random operator equation ... 

---