Willem J. Briels

Time and length scales of polymer melts studied by coarse-grained molecular dynamics simulations

We present coarse-grained molecular dynamics simulations of linear polyethylene (PE) melts, ranging in chain length from C80 to C1000. The employed effective potentials, frictions, and random forces are all derived from detailed molecular dynamics simulations, leaving no adjustable parameters. Uncrossability constraints are introduced in the coarse-grained model to prevent unphysical bond crossings. The dynamic and zero-shear rate rheological properties are investigated and compared with experiment and other simulation work. In the analysis of the internal relaxations we identify a new length scale, called the slowing down length Ns, which is smaller than the entanglement length Ne. The effective segmental friction rapidly increases around Ns leading, at constant density, to a transition in the scaling of the diffusion coefficient from D~N–1 to D~N–2, a transition in the scaling of the viscosity from ~N to ~N1.8, and conspicuous nonexponential relaxation behavior. These effects are attributed to strong local kinetic constraints caused by both chain stiffness and interchain interactions. The onset of nonlocal (entanglement) effects occurs at a chain length of C120. Full entanglement effects are observed only above C400, where the shear relaxation modulus displays a plateau and the single chain coherent dynamic structure factor agrees with the reptation model.

The calculation of free-energy differences by constrained molecular-dynamics simulations

In this paper we set out to derive a relation between the constraint force and the derivative of the free energy for a system in which only the reaction coordinate is constrained. Our result differs from the expression by Mulders et al. [J. Chem. Phys. 104, 4869 (1996)] because we take into account the effect of the constraint on the sampled phase-space distribution. The method is illustrated with two prototypical numerical examples.

Uncrossability constraints in mesoscopic polymer melt simulations: Non-Rouse behavior of C120H242

An important feature of a melt of long polymers is that the bonds of the chains cannot cross each other. This seemingly simple fact has a great impact on the long time dynamics and rheology of the material. In this paper an algorithm is described that explicitly detects and prevents bond crossings in mesoscopic simulations of polymers. The central idea is to view the bonds as slippery elastic bands which can become entangled. The method is applied to a simulation of a coarse-grained melt of C120H242, in which each chain is represented by six blobs. The long time dynamics and zero-shear rate rheology are investigated and the relative importance of uncrossability and chain stiffness is established. As a result of the uncrossability of the chains, we observe a subdiffusive exponent in the mean square displacement of the chains, a stretching of the exponential decay of the Rouse mode relaxations, an increase of relaxation times associated with large scales, and a slowing down of the relaxation of the dynamic structure factor. These results are in agreement with results from previous microscopic molecular dynamics simulations. Finally, an increased viscosity as compared to the Rouse model is observed, which is attributed to slowly decaying interchain stress components.

Simulations of stable pores in membranes: System size dependence and line tension

Amphiphilic bilayers with a pore were simulated using a coarse grained model. By stretching the bilayer to 70% beyond its equilibrium surface area, we established the phase diagram of pores, identifying regions where pores are stable, metastable, or unstable. A simple theoretical model is proposed to explain the phase diagram, and to calculate the critical and equilibrium relative stretches. Interestingly, these are found to scale with the inverse cubic root of the number of amphiphiles in the bilayer, thus explaining the order of magnitude difference between the simulated and the measured values. Three different methods are used to calculate a line tension coefficient of (3.5-4.0) x 10(-11) J/m, in good agreement with experimental data.

Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.

MOLECULAR DYNAMICS SIMULATIONS OF YTTRIA-STABILIZED ZIRCONIA

Oxygen diffusion in the oxygen ionic conductor yttria-stabilized zirconia is investigated by means of the molecular dynamics simulation technique. Oxygen ions migrate by means of a discrete hopping process, mainly between neighbouring tetrahedral sites. Diffusion appears to occur in a short time and a long time regime. Only when the oxygen ions have moved over distances much larger than the characteristic distances of the underlying crystal structure, a linear relation is found between the mean square displacement and time. The oxygen tracer diffusion coefficient, obtained from this long time regime, is 1.86 x 10−6 and 3.23 x 10−6 cm2/s at 1759 and 2057 K, respectively. The ionic conductivity, calculated from the tracer diffusion coefficient, agrees well with experimental values.

Viscoelasticity of suspensions of long, rigid rods

A microscopic theory for the viscoelastic behaviour of suspensions of rigid rods with excluded volume interactions is presented, which is valid in the asymptotic limit of very long and thin rods. Stresses arising from translational and rotational Brownian motion and direct interactions are calculated for concentrations up to (L/D) (with L the length; D, the thickness of the rods; and their volume fraction). It is argued that for very long and thin rods, contributions to the stress arising from hydrodynamic interactions vanish asymptotically with increasing aspect ratio relative to the single particle contribution. As will be discussed, this is supported by calculations of Shaqfeh and Fredrickson (Phys. Fluids A2 (1990) 7), although convergence to negligible hydrodynamics interactions with increasing aspect ratio is very slow (for aspect ratios larger than ≈50, the contribution of hydrodynamic interactions to the stress is at most ≈20%). It is argued that the pair-correlation function is in good approximation given by the Boltzmann exponential of the pair-interaction potential. The neglect of hydrodynamic interactions and the use of the Boltzmann exponential approximation for the pair-correlation function allows the microscopic evaluation of stresses in terms of concentration and the orientation order parameter tensor to within a Ginzburg–Landau expansion up to third order, without having to resort to thermodynamic arguments. The orientational order parameter tensor in turn is obtained from an equation of motion that is derived from the N-particle Smoluchowski equation. The resulting expression for the stress tensor and the equation of motion are similar to, but also in some respects significantly differing from, the well known theory due to Doi, Edward and Kuzuu. Analytic expressions are derived for linear and leading order non-linear, viscoelastic response functions. It is found that the zero shear viscosity varies linearly in concentration. The Huggins coefficient vanishes like the square of the shear-rate. Such a linear concentration dependence of the zero shear viscosity for very long and thin rods is also found in simulations by Claeys and Brady (J. Fluid Mech. 251 (1993) 443) and Yamane et al. (J. Non-Newtonian Fluid Mech. 54 (1994) 405) for the long rods, but is in contradiction with the Berry–Russel theory (J. Fluid Mech. 180 (1987) 475), where interactions are treated in an approximate, orientationally pre-averaged fashion. In addition, we find a Maxwellian frequency dependence of response functions at zero shear-rate. Highly non-linear viscoelastic response functions at higher shear-rates are computed numerically. Among other things, we find normal stress differences that do not change sign as a function of shear-rate and higher order harmonic response functions that are qualitatively different for the paranematic and nematic states.

A single particle model to simulate the dynamics of entangled polymer melts

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter n(ij) for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C(800)H(1602) chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties.

The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics

Helfrichs theory predicts that the bending free energy of a tensionless amphiphilic bilayer is proportional to the square of the Fourier coefficients of the undulation modes. Equilibrium molecular dynamics simulations with coarse-grained amphiphiles confirm the correctness of this prediction for thermally excited undulations. The proportionality constant then provides the bending rigidity of the layer. Non-equilibrium methods, in particular umbrella sampling, potential of mean constraint force, and thermodynamic integration in Cartesian coordinates, have been used to extend the range of sampled amplitudes. For small amplitudes there is a good agreement with the equilibrium simulations, while beyond the thermally accessible amplitudes a clear deviation from theory is observed. Calculations of the elastic modulus showed a pronounced system size dependence.

From wave function to crystal morphology: application to urea and alpha-glycine

In this paper the relation between the molecular electron density distribution and the crystal growth morphology is investigated. Accurate charge densities derived from ab initio quantum chemical calculations were partitioned into multipole moments, to calculate the electrostatic contribution to the intermolecular interaction energy. For urea and alpha-glycine the F-faces or connected nets were determined according to the Hartman-Perdok PBC theory. From attachment energy and critical Ising temperature calculations, theoretical growth forms were constructed using different atom-atom potential models. These were compared to the Donnay-Harker model, equilibrium form and experimental growth forms. In the case of alpha-glycine, the theoretical growth forms are in good agreement with crystals grown from aqueous solution. Crystals obtained by sublimation seem to show some faces which are not F-faces sensu stricto.