Interaction potential bond angle

Bonded potentials Interactions between two or more specific particles include FENE and harmonic bond potentials, bond angle and dihedral interactions. Again, potentials can also be included as tables. 

The system was studied as a function of external load on the surfaces. As molecules which detached from the droplet were removed from the simulation, the system was not in equilibrium with the vapor phase. The solid substrates were modeled after crystalline solids with both weak attraction (ej = 1) and strong attraction (es = 3) between the surface atoms and the polymer segments, which were treated as UA monomers here es is the well-depth of the surface-monomer potential and is measured in units of the well-depth of the monomer-monomer potential. Bond angles were constrained in the simulation. In Ref. 32, constant pressure simulations of liquid tridecane were performed for a system periodic in the x and y directions. The surface structure was that of the (111) face of an fee crystalline solid. Here, an explicit atom representation of the alkane chains was used. Results are presented for surface atom-polymer atom interactions equal to those of the carbon-carbon and carbon-hydrogen interactions for carbon and hydrogen atoms, respectively (a weakly attractive surface) for films nominally 4nm thick at 450 K. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

The potential energy of a molecular system in a force field is the sum of individual components of the potential, such as bond, angle, and van der Waals potentials (equation 8). The energies of the individual bonding components (bonds, angles, and dihedrals) are functions of the deviation of a molecule from a hypothetical compound that has bonded interactions at minimum values. 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

The radius of the beads and the interactions, Eqs. (8,9), have been chosen such that the chains may not intersect themselves or each other in the course of their movement within the box. Thus entanglement constraints are obeyed automatically and need not be enforced by extra (time consuming ) control. The chains are treated as fully flexible and a potential for bond angles is not considered, although an extension of the model to allow for semi-flexibihty of the chains is straightforward. 

Molecular mechanics calculations use an empirically devised set of equations for the potential energy of molecules. These include terms for vibrational bond stretching, bond angle bending, and other interactions between atoms in a molecule. All of these are summed up as follows ... 

Currently, a wide variety of methods exists for calculating the molecular structure of large liquid crystal molecules which make use of pre-determined functional forms for the interactions in a molecule and semi-empirical information to parametrise the potentials. In general the interaction terms represent the energy cost of distorting bonds and bond angles from equilibrium. These can be expressed as... 

Fig. 1 a Model bead-spring chain interacting through bond potential Dj, bond angle potential Uq, and van der Waals potential C7v(jw> and b the form of the bond angle potential Ug... 

The focus of this chapter is on an intermediate class of models, a picture of which is shown in Fig. 1. The polymer molecule is a string of beads that interact via simple site-site interaction potentials. The simplest model is the freely jointed hard-sphere chain model where each molecule consists of a pearl necklace of tangent hard spheres of diameter a. There are no additional bending or torsional potentials. The next level of complexity is when a stiffness is introduced that is a function of the bond angle. In the semiflexible chain model, each molecule consists of a string of hard spheres with an additional bending potential, EB = kBTe( 1 + cos 0), where kB is Boltzmann s constant, T is... 

---