Alternative theory of hydrodynamic interactions in polymer solutions

The model is presented for coarse grained dynamics of macromolecules in dilute solutions. The coarse graining is achieved by dividing the polymer chain into subchains, consisting of many monomers, and spatial averaging over lengths that are large compared to the mean-square end-to-end distance of subchains and small compared to macromolecule size. Kinetic equations of the model are derived from first principles of statistical mechanics under the assumption that subchain center of mass positions and solvent flow velocity field are the only slow variables of the system. In this approach hydrodynamic interactions result from the intercomponent friction forces between polymer and solvent instead of boundary conditions on the bead surfaces as in traditional theories. The integrodifferential diffusion equation is obtained for steady flows with the kernel involving the Oseen tensor multiplied by equilibrium distribution in the space of the subchain center of mass positions.     

Free energy of solvation of a small Lennard–Jones particle

In molecular dynamics (MD) and Monte Carlo (MC) free energy calculations, the choices of the thermodynamic paths from state a to state b affect the accuracy of the result and the efficiency of the programs. Most of the problems occur at the initial stages of growing in a new particle into a solvent. Based on statistical mechanical perturbation theory, an accurate and efficient direct calculation of inserting a small Lennard–Jones particle into solvent is derived. This eliminates the need for calculation of the initial stages of growing in a new particle by MD or MC simulation. Examples are given to show the utility of direct calculation. The recommended procedure is to use direct calculation for a small Lennard–Jones particle and then use MD or MC simulations to calculate the ΔG of changing the small Lennard–Jones particle into the target molecule. © 1994 by John Wiley & Sons, Inc.     

Dissipative Particle Dynamics Simulations of Polymer Brushes: Comparison with Molecular Dynamics Simulations

Summary: The structure of polymer brushes is investigated by dissipative particle dynamics (DPD) simulations that include explicit solvent particles. With an appropriate choice of the DPD interaction parameters , we obtain good agreement with previous molecular dynamics (MD) results where the good solvent behavior has been modeled by an effective Lennard–Jones potential. The present results confirm that DPD simulation techniques can be applied for large length scale simulations of polymer brushes. A relation between the different length scales and is established.

Polymer brush at a solid–liquid interface.     

Molecular dynamics simulation study of friction and diffusion of a tracer in a Lennard–Jones solvent

The friction and diffusion coefficients of a tracer in a Lennard–Jones (LJ) solvent are evaluated by equilibrium molecular dynamics simulations in a microcanonical ensemble. The solvent molecules interact through a repulsive LJ force each other and the tracer of diameter σ₂ interacts with the solvent molecules through the same repulsive LJ force with a different LJ parameter σ. Positive deviation of the diffusion coefficient D of the tracer from a Stokes–Einstein behavior is observed and the plot of 1/D versus σ₂ shows a linear behavior. It is also observed that the friction coefficient ζ of the tracer varies linearly with σ₂ in accord with the prediction of the Stokes formula but shows a smaller slope than the Stokes prediction. When the values of ratios of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation D = k _B T/ζ, from which the tracer is considered as a Brownian particle.     

Single polyelectrolyte macromolecule in the salt solution: Effect of escaped counter ions

We developed simplest theory of swelling of polyelectrolyte macromolecules in the solution of low‐molecular salts. The novel feature taken into account is the electrostatic interaction between the macro‐ion and counter ions which escaped from the interior of the macromolecular coil and distributed in the whole volume of solution. The phase diagram in the variables solvent quality vs. salt concentrationis derived. One of the unexpected findings is that the total charge within the sphere surrounding the macro‐ion changes in a non‐monotonical manner with the increase of the salt concentration. In particular, our calculations predict that the electrophoretic mobility of a polyelectrolyte macromolecule can demonstrate non‐monotonic behavior with an increase of salt concentration. The results of the calculations are compared with those obtained under the assumption of electroneutrality of the macromolecule when all of the counter ions are kept within the effective volume of macromolecule.     

液态RbCl的态密度

给出了在分子动力学模拟基础上Fumi-Tosi势离子液体的正则模式分析方法,用Fumi-Tosi势(包括长程势)代替Lennard-Jones势,并且用等效Coulomb势处理长程Coulomb作用.讨论了Hessian矩阵元的计算方法和Hessian矩阵特征值的计算方法.计算实践表明，取用余误差函数形式的等效库仑势,可以合理地得到Hessian矩阵和态密度.液态RbCl中构型平均态密度的数值结果表明，液态RbCl的态密度表现出与Lennard-Jones液体的态密度相仿的特点.     

Orientation of Polymer Chains in Dilute Solution under Shear: Effect of Chain Model and Excluded Volume

Summary: Polymer orientation in dilute solutions undergoing shear flow is investigated computationally by means of the Brownian dynamics simulation technique applied to the bead‐spring chain model. The dependence of the degree of orientation on the shear intensity is evaluated through a quantity called orientation resistance. All simulations were performed using non‐preaveraged hydrodynamic interaction (HI). The spring type (Gaussian or FENE) is shown to strongly determine the shear flow behavior of the chain orientation. Solvent quality (Θ, good or bad), represented by a suitable Lennard‐Jones intramolecular potential, does not affect the flow behavior but influences the values of the orientation resistance. Hence, the orientability of the polymer molecule is, in a way, related to the flow intensity.

Evolution of m_G (orientational resistance parameter, open circles are simulation, dashed line is Gaussian approximation) and m_τ (filled circles are simulation, dotted line is Gaussian approximation) with β for ideal Gaussian chains with N = 15.     

Two-particle friction in a mesoscopic solvent

The effects of hydrodynamic interactions on the friction tensors for two particles in solution are studied. The particles have linear dimensions on nanometer scales and are either simple spherical particles interacting with the solvent through repulsive Lennard-Jones forces or are composite cluster particles whose atomic components interact with the solvent through repulsive Lennard-Jones forces. The solvent dynamics is modeled at a mesoscopic level through multiparticle collisions that conserve mass, momentum, and energy. The dependence of the two-particle relative friction tensors on the interparticle separation indicates the importance of hydrodynamic interactions for these nanoparticles.     

Collinear collision of an atom with a homonuclear diatomic molecule

The problem of collinear scattering of an atom from a homonuclear diatomic molecule is formulated in terms of a first-order nonlinear matrix differential equation for the variable coefficient of reflection. For a homonuclear molecule when the target Hamiltonian is invariant under the parity transformation, only transitions between even states or odd states are possible. This selection rule reduces the number of open or closed channels that contribute to the reflection and transmission coefficients. But for numerical calculation, under the conditions of the problem, one can approximate the target Hamiltonian by the Hamiltonian of a displaced harmonic oscillator. In this approximation, the reflectional symmetry of the Hamiltonian is not preserved and transitions between any two levels of the target are possible. To simplify the problem further, the interaction between the projectile and the target is assumed to be a sum of two Gaussian terms. For this combination of the potentials the many-channel interaction can be expressed analytically. By fitting the Lennard–Jones potential with a sum of two Gaussian potentials and solving the matrix differential equation, transition probabilities are obtained for the He? H₂ collision. The numerical results are compared with the results found by Secrest and Johnson, and by Clark and Dickinson.     

Studies on the dynamics of poly(carboxylic acids) with covalently bound thionine and phenosafranine in dilute aqueous solutions

The poly(carboxylic acid) bound phenosafranine and thionine dyes show that, the fluorescence intensity and lifetime increases first and starts to decrease after reaching a maximum at pH 4.0. The fluorescence decay curve of the fluorophore bound polymers follow the biexponential decay fit independent of pH, while poly(MAA-Th) follows single exponential function above pH 4.0. At low pH, a more compact environment of the fluorophore exerts a more hydrophobic environment. In the subnanosecond time domain the solvation process is found to be incomplete while in the nanosecond time scale the solvation of the macromolecular chains is found to be over. The time resolved fluorescence spectra of the polymer bound fluorophores at different pH indicate distinct hydrophobic and hydrophilic environments due to the dynamics of the macromolecules in dilute aqueous solutions. For the first time structural transitions involving solvent are observed in the nanosecond and picosecond time domains for the same macromolecule.     

Efficient lookup table using a linear function of inverse distance squared

The major bottleneck in molecular dynamics (MD) simulations of biomolecules exist in the calculation of pairwise nonbonded interactions like Lennard‐Jones and long‐range electrostatic interactions. Particle‐mesh Ewald (PME) method is able to evaluate long‐range electrostatic interactions accurately and quickly during MD simulation. However, the evaluation of energy and gradient includes time‐consuming inverse square roots and complementary error functions. To avoid such time‐consuming operations while keeping accuracy, we propose a new lookup table for short‐range interaction in PME by defining energy and gradient as a linear function of inverse distance squared. In our lookup table approach, densities of table points are inversely proportional to squared pair distances, enabling accurate evaluation of energy and gradient at small pair distances. Regardless of the inverse operation here, the new lookup table scheme allows fast pairwise nonbonded calculations owing to efficient usage of cache memory. © 2013 Wiley Periodicals, Inc.     

Theoretical study of tetrahydrofuran: Comparative investigation of spectroscopic and structural properties between gas and liquid phases

Rovibrational spectroscopic constant of tetrahydrofuran (THF) dimer have been calculated starting from three potential energy curves, each one obtained in a different way: (i) by ab initio calculations at MP2/aug‐cc‐pVDZ level; (ii) using Lennard‐Jones liquid parameters available in the literature, and (iii) from the pair obtained through Monte Carlo Simulation of liquid THF. The comparison among these results allowed the characterization of many solvent effect contributions. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Second quantization for composite particles,reactive collisions,and unstable particles

The salient features of generalized second-quantization representations for nonrelativistic systems of composite particles are reviewed and their application to a reformulation of the quantum theory of reactive collisions is discussed. Such representations allow the properties of the bound composite states to be built explicitly into the algebra of states and observables. A single unperturbed Hamiltonian simultaneously describes the free propagation of the various species of bound composites as well as of their unbound constituents, while the interaction Hamiltonian describes only true scattering and reaction processes. The inclusion of the binding of all composites in the unperturbed Hamiltonian cures the divergences in the Born series arising from bound-state poles. Unstable composites can be included in a natural way, leading to an explicit representation for the kinematics and dynamics of their decay and their contribution to collision phenomena.     

Multiple‐Replica Exchange with Information Retrieval

The parallel tempering simulation method was recently extended to allow for possible exchanges between non‐adjacent replicas. We introduce a multiple‐exchange variant which naturally incorporates the information from all replicas when calculating statistical averages, building on the related virtual‐move method of Coluzza and Frenkel (ChemPhysChem 2005 , 6, 1779). The method is extensively tested on three model systems, namely, a Lennard‐Jones cluster exhibiting a finite size phase transition, the Lennard‐Jones fluid, and the 2D ferromagnetic Ising model. In all cases, the present method performs significantly better and converges faster than conventional parallel tempering Monte Carlo simulations. The standard deviations are also systematically decreased with respect to virtual moves.     

Properties of Apolar Solutes in Alkyl Imidazolium‐Based Ionic Liquids: The Importance of Local Interactions

The solvation and the dynamic properties of apolar model solutes in alkyl imidazolium‐based ionic liquids (IL) are studied by using all‐atom molecular dynamics simulations. In regards to specific IL effects, we focused on the often used 1‐ethyl‐3‐methyl imidazolium cation in combination with the anions tetrafluoroborate, acetate, and bis(trifluoromethanesulfonyl)imide. Our findings reveal that the size of the anion crucially influences the accumulation behavior of the cations, which results in modified IL solvation properties. Deviations between the different alkyl imidazolium‐based IL combinations can be also observed with regard to the results for the radial distribution functions, the number of surrounding molecules, and the molecular orientation. The analysis of the van Hove function further shows pronounced differences in the dynamic behavior of the solutes. The simulations verify that the solute mobilities are mainly influenced by the composition of the local solvent shell and the properties of the underlying Lennard–Jones interactions. Additional simulations with regard to modified short‐range dispersion energies for alkyl imidazolium‐based ILs validate our conclusions.