Equilibrium MD simulations

Figure 1 A Snapshot of a DOPC bilayer during an equilibrium MD simulation. Water is denoted by small spheres, DOPC phosphorus and nitrogen are large spheres, and DOPC tails are gray lines. B Partial density profile for a DOPC bilayer. C A water defect present in a DOPC bi layer. D A water pore across a DMPC bi layer. Both (C) and (D) have the same representations as (A).

Our experimental set-up (described in ref. 7), allows us to record steady state absorption and emission spectra over a wide range of densities (10 5 to 20 at/nm3) in the Ar supercritical domain (Tc = 150.8 K, Pc = 49 bar). Representative absorption and emission spectra are shown in figure 1. These spectra could be reproduced with a good accuracy by means of equilibrium MD simulations performed with a standard procedure [8], In these simulations, the NO X-Ar and Ar-Ar interaction potentials were taken from the literature [9], We extracted an analytical NO A-Ar pair potential by an iterative fit of the experimental spectra, valid for the whole supercritical domain. 

Figure 3.15 Results of simulation of solvation dynamics of chromophore C153 in room-temperature acetonitrile via nonequilibrium and equilibrium MD simulation methods. SRF stands for solvation response function. In the notation used here neq is the nonequilibrium response S(t), ground is the equilibrium TCF C0(t) and excited is the equilibrium TCF C, (f). (Reprinted from F. Ingrosso, B. M. Ladanyi, B. Mennucci, M. D. Elola, and J. Tomasi, I. Phys. Chem. B, 109, 3553-3564. Copyright (2005), with permission from American Chemical Society).

Methodology. Equilibrium MD simulations were carried out at six different temperatures (550-800 K, at 50 K intervals) and atmospheric pressure. 

Using the imposed heat flux method, we carried out NEMD simulations for the HMX melt at six temperatures (550 K - 800 K, in 50 K intervals) and atmospheric pressure. The simulation methodology was similar to the one described above for equilibrium MD simulations with a few exceptions. Each system contained 100 HMX molecules. The orthorhombic simulation box, extended in the z direction, was subdivided into 10 equal slabs with width of about 5.0 A and cross-sectional area of about 625.0 A2. The molecular center-of-mass velocities were exchanged every 500 fs (W=0.002 fs 1) for pairs of molecules belonging to the cold and hot slabs. This choice of the W was based on our previous experience with simulations of liquid n-butane and water [52],... 

The classical dynamics simulation was initialized from a distribution of all variables in the equilibrium MD simulation of liquid N2O4,1 except the NN distance of a selected N2O4 was compressed to some value R so as to give the NN mode enough energy to dissociate. After replacing the harmonic intramolecular potential of the N2O4 by a sum of an intermolecular potential between NO2 molecules and harmonic intramolecular potential for N02, the dynamics were calculated both forward and backward in time, for a time period of 20 ps with a... 

Equilibrium MD simulations of self-diffusion coefficients, shear viscosity, and electrical conductivity for C mim][Cl] at different temperatures were carried out [82] The Green-Kubo relations were employed to evaluate the transport coefficients. Compared to experiment, the model underestimated the conductivity and self-diffusion, whereas the viscosity was over-predicted. These discrepancies were explained on the basis of the rigidity and lack of polarizability of the model [82], Despite this, the experimental trends with temperature were remarkably well reproduced. The simulations reproduced remarkably well the slope of the Walden plots obtained from experimental data and confirmed that temperature does not alter appreciably the extent of ion pairing [82],... 

Reverse nonequilibrium MD (NEMD) and equilibrium MD simulations were carried out by Zhao et al. to compute the shear viscosity of the pure IL system [C4mim] [PF6] at 300 K [83], The two methods (NEMD and MD) yielded consistent results comparable to experiments. The calculated viscosity was below the experimental value by 25—40Cf depending on which experiment was used as reference. This result was a vast improvement over some previous force fields, which typically overestimated the viscosities of ILs by more than one order of magnitude [83],... 

In contrast with the AB system described above, RDX and most other energetic materials have long reaction times—fractions of a microsecond—and extended reaction zone lengths, on the order of a millimeter. Due to the size of the reaction zone and the complexity of the interatomic potentials necessary to describe real nitramines, steady-state NEMD simulations of detonation are beyond current and near-fixture capabilities, both in computation time and computer memory requirements. Keeping these limitations in mind, we use NEMD to study the initial chemical events in RDX under shock loading. In Section 5 we will describe equilibrium MD simulations to study phenomena at longer time-scales. 

Equilibrium MD simulations can provide valuable information about the thermal decomposition of energetic materials and can also enable the exploration of phenomena with time-scales much longer than in shockwaves. As an example, we studied the decomposition and subsequent reactions of RDX under various temperatmes (between T = 1200 K and T = 3000 K) and densities (at low density, 0.21 g/cm near normal density, 1.68 g/cm and under compression, 2.11 g/cm ), using MD with RDX interactions given by the reactive potential ReaxFF. 

Thus, y (0 s are calculated every Ax interval (or time-segment) with a time resolution determined according to the interval in which the trajectory data are stored [16], In Equation 8.17, is the a-component of the ith atom velocity vector in the case of PMD simulations while )°a is the a-component in the case of reference equilibrium MD simulations without perturbations, i.e., a set of UMD simulations. Therefore, shows the relative correlation strength in comparison to the reference correlation Vj (Equation 8.18), which is the average within the Lth Ax time-segment over the latter UMD simulations numbers of trajectories). The present way to calculate the velocity correlation is to find the fundamental frequencies without combination tones in each Ax time-segment. 

The free-energy profile for the Uthium desolvation (AG(z)) in the range of kfiT could be obtained from equilibrium MD simulations using Eq. 7.5 ... 

Fig. 7.24 The free-energy profile for the lithium cation desolvation from EC DMC(3 7)A iPFg at 1 M electrolyte at 298 K calculated using the Li probability profile from equilibrium MD simulations and the integration of the constrained force method. Z = 0 at the position of hydrogen atoms of graphite...

Box 5 Periodic boundary conditions commoniy used for equilibrium MD simulations... 

A. Study of Polymer Viscoelasticity Through Equilibrium MD Simulations... 

Relaxed configurations thus obtained are subjected to equilibrium MD simulations to monitor their evolution in time and extract dynamic properties. During the atomistic MD simulations, a large number of dynamical trajectories are accumulated. 

Pore volume. The total pore volume is eqiuOl to that of for a fine tessellation i.e. it is independent of d). The pore volume accessible to fluid-i in the absence of pore network ects is equal to that part of the total that is oivered by the fluid molecules in a GCMC simulation at saturation. The pore volume accessible to a fluid-i in the presence of pore network effects is equal to S/59) for a fine trasellation that is covered by fluid molecules in a GCMC simulation at saturation, for all pores-y visited by the fluid in a non-equilibrium MD simulation (see below). 

Mean coordination number. Two measures are used (i) the mean numba of pores emanating fiom junctions in T and (ii) the dynamo mean coordination number, which is the mean coordination numba of the network defined by the pore throats in T crossed by diffusing molecules of a fluid during a non-equilibrium MD simulation (see below). 

Encouragingly, the adsorption-based m n coordination is inline with die mean number of pores that actually emanate from the pore junctions as determined by direct analysis of the pore space. However, analysis of where the SFs molecules diSuse during non-equilibrium MD simulations show that whilst not aU die pore throats are op i to the fluid, they do have access to all the pores this is refl ited in the dynamic coordination number for the pore network defined by SF at 2S6K of 3.6. Thus, the assumpticm that urtoerpms the method of Ldpez-Ramdn et al. [11] - i.e. that the differetice betwerai the PSIHt of die two molecules is due to some pores being inaccessible to the latter because of network - is not met here. 

Consider the simplest dynamic property one can compute, the self-diffusivity, Dj. The standard approach for computing Ds is to conduct an equilibrium MD simulation and accumulate the mean-square displacement as a function of time. The self-diffusivity is then computed using the Einstein equation ... 

Earlier we mentioned that Voth and co-workers conducted equilibrium MD simulations on [C2mim][N03] at 400 K and computed the self-diffusivity and shear viscosity using both a fixed charge and polarizable force field. They computed the viscosity not from integrating the stress-stress autocorrelation function as is normally done, but rather from integrating the so-called transverse current correlation function, details of which are foimd in a work by Hess. ° They used the standard Einstein formula (Eq. [15]) for the self-diffusivity and were careful to ensure that diffusive behavior was achieved when computing the self-diffusivity. Their calculated values of ca. 1 x 10 m /s for the polarizable model and ca. 5 x 10 m /s are reasonable. The finding that the polarizable model yielded faster dynamics than with the nonpolarizable model... 

Experimental diffusion coefficients, as obtained from time-lag measiu ements, report a transport diffusion coefficient which carmot be obtained from equilibrium MD simulation. Comparisons made in the simulation literatme are typically between time-lag diffusion coefficients (even calculated for glassy polymers without correction for dual-mode contributions and self-diffusion coefficients. As discussed above, mutual diffusion coefficients can be obtained directly from equilibrium MD simulation but simulation of transport diffusion coefficients require the use of NEMD methods, that are less commonly available and more computationally expensive [117]. 

As discussed above, mutual diffusion coefficients can be obtained direetly from equilibrium MD simulation but simulation of transport diffusion coeffieients require the use of NEMD methods, that are less commonly available and more computationally expensive [117],... 

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