Constant stress molecular dynamics

Also, the approach provides the potential for constant-stress molecular dynamics [40,45] with realistic retracting forces acting on the atomistic periodic box. This would provide an advantage over the current situation, where constant-stress molecular dynamics is weakened by the fact that the device, which maintains constant stress, (a) acts directly and without time delay on each atom, and (b) requires an arbitrary wall mass. The question of efficiency for atomistic-continuum constant-stress molecular dynamics must be answered first, of course. 

Shinoda, W., Shiga, M., Mikami, M. Rapid estimation of elastic constants by molecular dynamics simulation under constant stress. Phys. Rev. B 69, 134103 (2(K)4)... 

In such molecular dynamic simulations, one starts with an array of atoms or molecules , initially on a lattice, interacting with one another via an interatomic potential. These interacting potentials were taken by Paskin et al (1980, 1981) to be the Lennard-Jones potential (l> rij) = e[(l/rij) — 2(l/rij) ], where e denotes the depth of the potential energy and rij denotes the interatomic separation of the atoms. This potential is assumed to have a sharp cut-off at an arbitrarily chosen value 1.6 (lattice constant) of the interatomic separation. The external stress or force is applied only at the boundary surface atoms. In order to investigate the Griffith fracture phenomena, one can consider for example a two-dimensional lattice of linear size L, remove a few I L) consecutive bonds along a horizontal row in the middle of the network, and apply tensile force on the upper and lower surface atoms in the vertical direction. 

Molecular dynamics simulations have been used in a variety of ways. They can be used to compute mechanical moduli by studying the response of a model of the bulk polymer to a constant stress or strain, and to study the diffusion of molecules in membranes and polymers.There are numerous biomolecular applications. Structural, dynamic, and thermodynamic data from molecular dynamics have provided insights into the structure-function relationships, binding affinities, mobility, and stability of proteins, nucleic acids, and other macromolecules that cannot be obtained from static models. 

In both molecular dynamics and lattice dynamics, the effect of pressure, essential if one is to obtain accurate predictions of phenomena such as phase transitions and anisotropic compression, can be modelled by allowing constant stress, variable geometry cells. 

To date, results have been obtained for minimum-energy type simulations of elastic deformations of a nearest-neighbor face-centered cubic (fee) crystal of argon [20] with different inclusion shapes (cubic, orthorhombic, spherical, and biaxially ellipsoidal). On bisphenol-A-polycarbonate, elastic constant calculations were also performed [20] as finite deformation simulations to plastic unit events (see [21]). The first molecular dynamics results on a nearest-neighbor fee crystal of argon have also become available [42]. The consistency of the method with thermodynamics and statistical mechanics has been tested to a satisfactory extent [20] e.g., the calculations with different inclusion shapes all yield identical results the results are independent of the method employed to calculate the elastic properties of the system and its constituents (constant-strain and constant-stress simulations give practically identical values). 

Molecular dynamics The initial positions for the atoms are chosen at a particular temperature and a particular interaction potential is assumed. The equations of motion are solved to follow ensuing transitions until constant thermodynamic properties are achieved. This allows determination of the atom positions (structure), energies (surface energy) and forces on the atoms (surface stress) observed at any point in the simulation. 

An important point to note is that although Eq. 2.1 is the most commonly used boundary condition for a hydrodynamic slip, it is not widely appreciated that also postulated the more general relation, Au = Mr where r is the local shear stress (normal traction) and M is the constant interfacial mobility (velocity per surface stress). For a Newtonian fluid, r = rjdufdz, this reduces to (2.1) with b = Mrj, where rj is the viscosity. Molecular dynamics (MD) simulations have shown that the equation with constant M is more robust than (2.1)... 

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

This theory was able to account for both the molecular-weight scaling of the dynamic quantities Dg, r, and x as well as for the shape of the relaxation spectrum (see Fig. 5) apart from one important feature - the constant v in the leading exponential behaviour that multiplies the dimensionless arm molecular weight needed to be adjusted. This can be understood as follows. The prediction of the tube model for the plateau modulus from the stress Eq. (7) is... 

The model of a reacting molecular crystal proposed by Luty and Eckhardt [315] is centered on the description of the collective response of the crystal to a local strain expressed by means of an elastic stress tensor. The local strain of mechanical origin is, for our purposes, produced by the pressure or by the chemical transformation of a molecule at site n. The mechanical perturbation field couples to the internal and external (translational and rotational) coordinates Q n) generating a non local response. The dynamical variable Q can include any set of coordinates of interest for the process under consideration. In the model the system Hamiltonian includes a single molecule term, the coupling between the molecular variables at different sites through a force constants matrix W, and a third term that takes into account the coupling to the dynamical variables of the operator of the local stress. In the linear approximation, the response of the system is expressed by a response function X to a local field that can be approximated by a mean field V ... 

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