Manuel Laso

Simulation of polyethylene above and below the melting point

Polyethylene at equilibrium is studied by computer simulation. Configuration space is sampled efficiently by a novel Monte Carlo simulation scheme developed for the study of long molecules at high densities. Simulations are carried out in an isobaric‐isothermal statistical‐mechanical ensemble which permits calculation of the density of the polymer matrix at specified conditions of pressure and temperature. A systematic study of the polymer at different temperatures indicates a phase transition; in agreement with experiment, at low temperatures, the polyethylene model studied here crystallizes spontaneously. At temperatures above the melting point, the simulated melt is described accurately by the model.

Calculation of viscoelastic flow using molecular models: the connffessit approach

Abstract A new method for numerical calculation of viscoelastic flow based on simulation of molecular models of polymers is presented. The CONNFFES-SIT ( C alculation o f N on- N ewtonian F low: F inite E lements and S tochastic S imulation T echnique) approach directly combines standard finite element methods as currently used in the calculation of viscoelastic flow with stochastic simulations of polymer dynamics and thus obviates the need for a rheological constitutive equation to describe the fluid. The stresses are obtained from the molecular configurations rather than from constitutive equations. As an illustration of the method, the time development of plane Couette flow is studied for the upper-convected Maxwell, Oldroyd-B, FENE-P and FENE fluids. For the upper-convected Maxwell, Oldroyd-B and FENE-P models comparisons with analytical and existing numerical solutions are presented. Significant deviations between the behavior of the FENE-P and FENE models for the start-up of plane Couette flow are found.

Estimation of the chemical potential of chain molecules by simulation

A novel method is presented for the calculation of the chemical potential of molecules with articulated structure by molecular simulation. The method, based on a biased sampling of phase space, is applied here to systems of linear alkanes represented by methylene pseudoatoms connected by rigid bonds at fixed angles. The results of our biased‐sampling scheme are compared to those of other available methods (when they can provide results) for calculation of the chemical potential of dense systems.

Simulation of phase equilibria for chain molecules

In this Communication we present a configurational bias technique that permits phase equilibrium simulation of long chain. We present phase-equilibrium results for a few linear alkanes at several temperatures, and we compare them to those of conventional simulation methods (where such methods work)

Numerical simulation of 3D viscoelastic flows with free surfaces

A numerical model is presented for the simulation of viscoelastic flows with complex free surfaces in three space dimensions. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different.A splitting method is used for the time discretization. The prediction step consists in solving three advection problems, one for the volume fraction of liquid (which allows the new liquid domain to be obtained), one for the velocity field, one for the extra-stress. The correction step corresponds to solving an Oldroyd-B fluid flow problem without advection in the new liquid domain.Two different grids are used for the space discretization. The three advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristics method. The Oldroyd-B problem without advection is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons.Efficient post-processing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces the memory requirements.Convergence of the numerical method is checked for the pure extensional flow and the filling of a tube. Numerical results are presented for the stretching of a filament. Fingering instabilities are obtained when the aspect ratio is large. Also, results pertaining to jet buckling are reported.

Continuum-configurational-bias Monte Carlo simulations of long-chain alkanes

The recently introduced continuum-configurational-bias method for Monte Carlo simulations is employed for the generation of large samples of many-chain n-alkane systems with chain lengths of 11, 24 and 71 carbon atoms. The simulations are used to investigate the adequacy of representing methylene groups as united-atom Lennard-Jones interaction sites, and to test the configurational-bias approach against traditional random moves and reptation moves with respect to the computational efficiency and numerical stability of the calculated ensemble averages. The results of simulations with constant pressure, temperature, and number of molecules demonstrate that, with an appropriate mixture of different types of Monte Carlo moves, an efficient and stable strategy can be obtained. Adjustment of the Lennard-Jones parameters leads to results that are in good agreement with experimental data for the density of liquid alkanes over a large temperature interval.

Variance reduced Brownian simulation of a bead-spring chain under steady shear flow considering hydrodynamic interaction effects

To obtain numerical estimates for the properties of a model for polymers in dilute theta solutions in its long-chain limit we follow a stochastic approach to polymer kinetic theory. The model takes into account configuration-dependent hydrodynamic interaction (HI) and simplifies to the Zimm bead-spring chain model in the case of preaveraged HI, for which parameter-free “universal ratios” such as the ratio between radius of gyration and hydrodynamic radius are known. The Chebyshev polynomial method and a variance reduction simulation technique are used to implement an efficient Brownian dynamics simulation. We resolve the full dependence of several characteristic ratios versus both chain length and hydrodynamic interaction parameter, we extrapolate their values to determine universal behaviors, and compare with analytical and experimental results.

Calculation of free surface flows using CONNFFESSIT

A calculation method for two-dimensional time-dependent free surface flows is presented. The method extends the capabilities of CONNFFESSIT (calculation of non-Newtonian flows: finite elements and stochastic simulation technique) to transient free surface flows. The macroscopic unknowns are the velocity and the pressure fields together with the shape of the free surface. Particle tracking techniques, one of the main components of CONNFFESSIT, are capitalized upon in order to efficiently track the time evolution of the free surface. The ability of CONNFFESSIT to treat models for which no closed-form constitutive equation can be derived and to yield full molecular information is now enhanced with a technique for the calculation of free surface flows. In order to validate the method, transient, free jet swell calculations for the Oldroyd-B fluid using CONNFFESSIT are compared with continuum-mechanics POLYFLOW calculations

Structure, Dimensions, and Entanglement Statistics of Long Linear Polyethylene Chains

This work elucidates the effect of both temperature and molecular length on the conformational and structural properties as well as on the entanglement statistics of long amorphous, polydisperse, and molten linear polyethylene (PE). A large number of PE samples are modeled in atomistic detail, with average molecular lengths ranging from C24 up to C1,000 over a wide range of temperatures in the interval of 300 <or= T <or= 600 K under constant pressure (P ) 1 atm). By employing enhanced chain-connectivity-altering moves, full-scale equilibration is achieved within modest computational time even for the longest molecules at ambient conditions.At a second stage, direct geometrical analysis is applied on all equilibrated polymer configurations providing the corresponding primitive paths and intermolecular entanglements. Simulation findings on the characteristic ratio, density, and atomic packing are in excellent agreement with available experimental data. The same holds for the calculated plateau modulus; simulation predicts 1.8 ( 0.1 MPa. Regarding the primitive path statistics, the average contour length and the number of entanglements are found to exhibit a simple exponential type dependency on temperature. For the polydisperse samples studied here, a superposition of Poissonians(often represented by a negative binomial) describes best the distribution of entanglements of the primitive paths.

On the reduction of stochastic kinetic theory models of complex fluids

Kinetic theory models involving the Fokker–Planck equation are usually solved in the framework of stochastic approaches, which allows us to circumvent the difficulties related to the multidimensional character of that equation. In fact, the Fokker–Planck equation governs the evolution of the distribution function that defines the molecular configuration at each point of the physical space and at each time. As the molecular conformation is usually defined by several coordinates, the resulting distribution function will depend on the physical and configuration coordinates and the time. Although different numerical strategies have recently been proposed for solving that equation with efficiency and accuracy (Ammar et al 2006 J. Non-Newtonian Fluid Mech. 134 136–47, Ammar et al 2006 J. Non-Newtonian Fluid Mech. 139 153–76) the stochastic approach is today the most common for solving general kinetic theory models. This paper presents some preliminary results that provide evidence for the potential applicability of model reduction techniques based on the Karhunen–Loeve decomposition or on separated representations for reducing the computational efforts related to the solution of such models in the Brownian configuration fields framework.