Solvent bead interactional potential

Usually, MD methods are applied to polymer systems in order to obtain short-time properties corresponding to problems where the influence of solvent molecules has to be explicitly included. Then the models are usually atomic representations of both chain and solvent molecules. Realistic potentials for non-bonded interactions between non-bonded atoms should be incorporated. Appropriate methods can be employed to maintain constraints corresponding to fixed bond lengths, bond angles and restricted torsional barriers in the molecules [117]. For atomic models, the simulation time steps are typically of the order of femtoseconds (10 s). However, some simulations have been performed with idealized polymer representations [118], such as Bead and Spring or Bead and Rod models whose units interact through parametric attractive-repulsive potentials. 

Suppose the bead-solvent interactions are described by either repulsive (r) or attractive (a) LJ potentials in the MD-MPC dynamics. The repulsive interactions are given in Eq. (76) while the attractive LJ interactions take the form cVu(r), where c gauges the strength of the bead-solvent potential, and... 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Here, Pp = mpR is a Cartesian bead momentum, U is the internal potential energy of the system of interest, Xi,.. .,Xk are a set of AT Lagrange multiplier constraint fields, which must be chosen so as to satisfy the K constraints, and is the rapidly fluctuating force exerted on bead p by interactions with surrounding solvent molecules. The corresponding Hamiltonian equation of motion is... 

In the simulation study of fluorescence anisotropy decay, a generic bead-spring model of the polymer was used. It is schematically shown in Fig. 19. Each bead can represent one or several monomer units in a real polymer. The degree of dissociation, a, is defined as the fraction of monomer units carrying electric charges. The interaction between monomer units of the polymer is modeled by the Lennard-Jones potential and the solvent quality is controlled by the depth of this potential, e. As shown by Micka, Holm and Kremer, 0.34 corresponds to the theta state [146]. The simulation study was performed for several values of > 0.33, i.e., under poor solvent conditions. The simulation technique used was MD coupled to a Langevin thermostat, i.e., the polymer was simulated in an implicit solvent. The counterions were simulated explicitly. A more detailed description of the polymer model can be found in the original paper [87]. 

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]). 

EDMD and thermodynamic perturbation theory. Donev et developed a novd stochastic event-driven molecular dynamics (SEDMD) algorithm for simulating polymer chains in a solvent. This hybrid algorithm combines EDMD with the direa simulation Monte Carlo (DSMC) method. The chain beads are hard spheres tethered by square-wells and interact with the surrounding solvent with hard-core potentials. EDMD is used for the simulation of the polymer and solvent, but the solvent-solvent interaction is determined stochastically using DSMC. 

PENE potentials. Nonbonded beads only interact with a single LJ potential. The solvent molecule (CO2 in fee present case) is represented by a point particle (in the case of CO or CgHs, it carries a quadrupole moment in the case of NH3 or H S, it carries a dipole moment). From Yelash etal. [234] ... 

Here Uq is the potential of the "connector force that binds together the two beads of a dumbbell. Uq is the site-site interaction between beads belonging to different dumbbells, Ugg the energy of interaction between a bead and a solvent particle, and Ugg the interaction between two solvent particles. Finally, F is the external force on a solvent molecule and 2 E(R., t) the external force on bead p of dumbbell i. From all of this... 

Fig. 5 Illustration of the interpretation of the coarse grained models for polymers and solvent In the case of short alkanes, typically three C C bonds are taken together in one effective unit (dotted circle). The oligomer C16H34, containing 50 atoms or 16 united atoms, is thus reduced to an effective chain of five beads. Neighboring beads along a chain interact with a combinatirai of LJ and FENE potentials. Nonbonded beads only interact with a single LJ potential. The solvent molecule (CO2 in the present case) is represented by a point particle (in the case of CO2 or C6H6, it carries a quadrupole moment in the case of NH3 or H2S, it carries a dipole moment). From Yelash et al. [234]...

Particle methods (Molecular Dynamics, Dissipative Particle Dynamics, Multi-Particle Collision Dynamics) simulate a system of interacting mass points, and therefore thermal fluctuations are always present. The particles may have size and structure or they may be just point particles. In the former case, the finite solvent size results in an additional potential of mean force between the beads. The solvent structure extends over unphysically large length scales, because the proper separation of scale between solute and solvent is not computationally realizable. In dynamic simulations of systems in thermal equilibrium [43], solvent structure requires that the system be equilibrated with the solvent in place, whereas for a structureless solvent the solute system can be equilibrated by itself, with substantial computational savings [43]. Finally, lattice models have a (rigorously) known solvent viscosity, whereas for particle methods the existing analytical expressions are only approximations (which however usually work quite well). 

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