28 research outputs found
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
Two methods are compared that are used in path integral simulations. Both
methods aim to achieve faster convergence to the quantum limit than the
so-called primitive algorithm (PA). One method, originally proposed by
Takahashi and Imada, is based on a higher-order approximation (HOA) of the
quantum mechanical density operator. The other method is based upon an
effective propagator (EPr). This propagator is constructed such that it
produces correctly one and two-particle imaginary time correlation functions in
the limit of small densities even for finite Trotter numbers P. We discuss the
conceptual differences between both methods and compare the convergence rate of
both approaches. While the HOA method converges faster than the EPr approach,
EPr gives surprisingly good estimates of thermal quantities already for P = 1.
Despite a significant improvement with respect to PA, neither HOA nor EPr
overcomes the need to increase P linearly with inverse temperature. We also
derive the proper estimator for radial distribution functions for HOA based
path integral simulations.Comment: 17 pages, latex, 6 postscript figure
Preparation and Friction Force Microscopy Measurements of Immiscible, Opposing Polymer Brushes
Solvated polymer brushes are well known to lubricate high-pressure contacts, because they can sustain a positive normal load while maintaining low friction at the interface. Nevertheless, these systems can be sensitive to wear due to interdigitation of the opposing brushes. In a recent publication, we have shown via molecular dynamics simulations and atomic force microscopy experiments, that using an immiscible polymer brush system terminating the substrate and the slider surfaces, respectively, can eliminate such interdigitation. As a consequence, wear in
the contacts is reduced. Moreover, the friction force is two orders of magnitude lower compared to traditional miscible polymer brush systems.
This newly proposed system therefore holds great potential for application in industry. Here, the methodology to construct an immiscible polymer brush system of two different brushes each solvated by their own preferred solvent is presented. The procedure how to graft poly(Nisopropylacrylamide) (PNIPAM) from a flat surface and poly(methyl methacrylate) (PMMA) from an atomic force microscopy (AFM) colloidal probe is described. PNIPAM is solvated in water and PMMA in acetophenone. Via friction force AFM measurements, it is shown that the friction
for this system is indeed reduced by two orders of magnitude compared to the miscible system of PMMA on PMMA solvated in acetophenone
Portable implementation of a quantum thermal bath for molecular dynamics simulations
Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M.
Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics
simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum
statistics of vibrations in condensed systems at low temperature could be
simulated by running molecular dynamics simulations in the presence of a
colored noise with an appropriate power spectral density. In the present
contribution, we show how this method can be implemented in a flexible manner
and at a low computational cost by synthesizing the corresponding noise 'on the
fly'. The proposed algorithm is tested for a simple harmonic chain as well as
for a more realistic model of aluminium crystal. The energy and Debye-Waller
factor are shown to be in good agreement with those obtained from harmonic
approximations based on the phonon spectrum of the systems. The limitations of
the method associated with anharmonic effects are also briefly discussed. Some
perspectives for disordered materials and heat transfer are considered.Comment: Accepted for publication in Journal of Statistical Physic
Yield conditions for deformation of amorphous polymer glasses
Shear yielding of glassy polymers is usually described in terms of the
pressure-dependent Tresca or von Mises yield criteria. We test these criteria
against molecular dynamics simulations of deformation in amorphous polymer
glasses under triaxial loading conditions that are difficult to realize in
experiments. Difficulties and ambiguities in extending several standard
definitions of the yield point to triaxial loads are described. Two
definitions, the maximum and offset octahedral stresses, are then used to
evaluate the yield stress for a wide range of model parameters. In all cases,
the onset of shear is consistent with the pressure-modified von Mises
criterion, and the pressure coefficient is nearly independent of many
parameters. Under triaxial tensile loading, the mode of failure changes to
cavitation.Comment: 9 pages, 8 figures, revte
Simulations of the Static Friction Due to Adsorbed Molecules
The static friction between crystalline surfaces separated by a molecularly
thin layer of adsorbed molecules is calculated using molecular dynamics
simulations. These molecules naturally lead to a finite static friction that is
consistent with macroscopic friction laws. Crystalline alignment, sliding
direction, and the number of adsorbed molecules are not controlled in most
experiments and are shown to have little effect on the friction. Temperature,
molecular geometry and interaction potentials can have larger effects on
friction. The observed trends in friction can be understood in terms of a
simple hard sphere model.Comment: 13 pages, 13 figure
Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation
We perform a thorough analysis of the relationship between discrete and
series representation path integral methods, which are the main numerical
techniques used in connection with the Feynman-Kac formula. First, a new
interpretation of the so-called standard discrete path integral methods is
derived by direct discretization of the Feynman-Kac formula. Second, we
consider a particular random series technique based upon the Levy-Ciesielski
representation of the Brownian bridge and analyze its main implementations,
namely the primitive, the partial averaging, and the reweighted versions. It is
shown that the n=2^k-1 subsequence of each of these methods can also be
interpreted as a discrete path integral method with appropriate short-time
approximations. We therefore establish a direct connection between the discrete
and the random series approaches. In the end, we give sharp estimates on the
rates of convergence of the partial averaging and the reweighted
Levy-Ciesielski random series approach for sufficiently smooth potentials. The
asymptotic rates of convergence are found to be O(1/n^2), in agreement with the
rates of convergence of the best standard discrete path integral techniques.Comment: 20 pages, 4 figures; the two equations before Eq. 14 are corrected;
other typos are remove
Velocity dependence of kinetic friction in the Prandtl-Tomlinson model
The Prandtl-Tomlinson model for friction has been used extensively for the interpretation of atomic force microscopy data during the past decade. Up to this point, the kinetic friction F-k has nevertheless not been studied in a range of velocities v that would be sufficiently broad to cover the crossover from the high-velocity logarithmic to the low-velocity linear F-k(v) dependence. This gap will be closed here through a combination of an asymptotic analysis and direct simulations of the relevant Langevin equation. The simulations span three decades in temperature T and up to six decades in v. All numerical data can be fit quite accurately with a F-k = a(T) arsinh[v/v(c)(T)] law, where the prefactor a(T) scales with T-2/3. Correction terms proportional to odd powers of arsinh(v/v(c)), only need to be included at v >> v(c). Reasons are given as to why it is difficult to confirm meticulously the (ln v)(2/3) dependence of kinetic friction predicted by recent rate theories, although they can be easily modified to produce the correct prefactor to the a(T) alpha T-2/3 law