Lennard-Jones potential truncated

As already mentioned above, the extent of tail correetions strongly depends on the property under study. In the case of pressure, this correction can be very large for example, in the case of a Lennard-Jones potential truncated at rc=2.5a, at conditions close to the triple point, E/Ne=-6.12, to which the tail correction contributes -0.48, but pP/p=0.22, of which -1.24 comes to the tail. The neglecting of the tail correction would lead to a strongly positive value for pressure. ... 

An efficient method of solving the Percus-Yevick and related equations is described. The method is applied to a Lennard-Jones fluid, and the solutions obtained are discussed. It is shown that the Percus-Yevick equation predicts a phase change with critical density close to 0.27 and with a critical temperature which is dependent upon the range at which the Lennard-Jones potential is truncated. At the phase change the compressibility becomes infinite although the virial equation of state (foes not show this behavior. Outside the critical region the PY equation is at least two-valued for all densities in the range (0, 0.6). 

The equation will be solved under the assumption that the particles in the fluid are interacting through a truncated Lennard-Jones 12-6 potential. The Lennard-Jones potential has been used by several workers, including Khan and Broyles,5 Throop and Bearman,6 and Levesque.7 These workers studied the PY equation above the reduced critical temperature T c in considerable detail. Their results in that region provided a good check on the accuracy of the method described here. 

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

Fig. 6. Grand-canonical simulation of a Lennard-Jones monomer system. Particles interact via a shifted and truncated Lennard-Jones potential of the form Elj =...

Fig. 12. Equation of state (a) and phase diagram (b) of a bead-spring polymer model. Monomers interact via a truncated and shifted Lennard-Jones potential as in Fig. 6 and neighboring monomers along a molecule are bonded together via a finitely extensible non-linear elastic potential of the form iJpENE(r) = — 15e(iJo/

Fig. 8. Density variation of the inherent structure pressure for a fluid with a smoothly truncated Lennard-Jones potential (Sastry etal., 1997b). Regions A, B, and C identify distinguishing density intervals for the inherent structures discussed in the text.

This section discusses simulations in which the parameters are explicitly mapped to experimental systems. In particular, this mapping affects ion diameter cr, rod radius r0, Bjerrum length B, and line charge density A. In order to have a rod radius different from cr this requires the introduction of a new potential for ion-rod interactions, for which a modified truncated and shifted Lennard-Jones potential has been used ... 

In order to limit the total number of interactions exp>erienced by each molecule in a computer simulation, the potential energy is usually truncated so that a molecule s interaction range is finite. For example, the ordinary (spherical) Lennard-Jones potential is truncated at about 2.5cr the interactions between all molecules separated by more than this distance are weak enough to be neglected. In order to maintain conservation of energy, an anisotropic potential function should be truncated at an equipotential surface. However, if the potential is not too anisotropic, truncation at a fixed distance leads to only minor effects on energy conservation. ... 

When we consider molecules of substantial anisotropy, the interaction range r, for the orientation-dependent Lennard-Jones potential is quite large. For example, if the truncation equipotential surface corresponds to an energy of —0.01eo then for a = 3.5 we find r, IOo-q. As a result, a very large number of pairs of molecules must be examined for possible interaction. 

Like the Cooke model, the Lenz model [77] is a generic model for membranes, but it has been designed for studying internal phase transitions. Therefore, it puts a slightly higher emphasis on conformational degrees of freedom than the Cooke model. Lipids are represented by semiflexible linear chains of seven beads (one for the head group, six for the tail), which interact with truncated Lennard-Jones potentials. Model parameters such as the chain stiffness are inspired by the properties of hydrocarbon tails [78]. The model includes an explicit solvent, which is, however, modeled such that it is simulated very efficiently it interacts only with lipid beads and not with itself ( phantom solvent [79]). 

The two species of particles in the simulation interact with truncated Lennard-Jones potentials with energy parameter e, distance parameter Cy, and cutoff radius... 

The FENE model with short chains of ten beads interacting with a truncated Lennard-Jones potential has been used for an MD investigation (381,382) of mode coupling theory just above the predicted critical temperatiue, which in turn is above the Tg. It is too early to say whether this theory will prove to be of practical use for polymer science, but simulations of this kind are probing deeply into the natiue of the glass transition, which can only help to illiuninate the physics of this important transition. 

Street et al. " originally presented the MTS method in the context of a distance truncated Lennard-Jones potential, so that the total number of computed interactions was somewhat less that N. For biological MD applications there is evidence that cutoffs can cause undesirable artifacts. ... 

Fig. 7.11 Phase diagrams for a symmetrical off-lattice mixture with Na = Ng = N = 20, where both components are modeled as bead-rod chains, and all nonbonded beads interact with standard Lennard-Jones potentials which are truncated at 2.5b), and data are shown for a bulk system (full dots) and thin films with repulsive walls for thickness IO.Sct (squares) and 5cr (triangles). Lines represent a fit according to xi - xic oc (T- (From Kumar et...

The bead-spring model of polymer chains utilized for molecular dynamics calculations in Ref. 19 consists of beads interacting through a truncated and shifted 12-6 Lennard-Jones potential... 

Fig. 9.8 Distribution function P(R) for the center-to-end distances versus R for (a) a star with /= 10, 20 and 50 arms in good solvent and (b) a/ = 20-arm star for T = 2.0, 3.0 and 4.0i/ks (from left to right).The results for (a) are for a purely repulsive Lennard-Jones potential at r= lle/ks, while the results shown in (b) are for the potential, eq. (9.3), truncated at rc = 2.5

For the good solvent condition, there is a modification of the LJ potential, which does not present attractive interactions at any distance between the particles. This is possible by a little modification of the potential of Eq. 8. First the interaction range of the potential is cut at its minimum. Second this potential is traslated along the ordinates such that the minimum value reaches to zero, this is achieved by the addition of Eu to the potential. The resulting LJ modification is called truncated or purely repulsive Lennard-Jones potential, and has the following form ... 

To complete the definition of our coarse-grained model, we also use a truncated Lennard-Jones potential between segments of different species. For the size parameter, we use a simple mixing rule... 

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