Search results for "Structure factor"

Intra- and Interchain Correlations in Semidilute Polymer Solutions:  Monte Carlo Simulations and Renormalization Group Results

2000

We investigate the intra- and intermolecular correlations in semidilute polymer solutions by large-scale computer simulations and renormalization group calculations. In the framework of the bond fluctuation model we study polymers with chain lengths up to N = 2048 monomers and determine the intermolecular pair correlation function, the coherent scattering intensity, and its distinct part at all length scales. The simulations are compared quantitatively to renormalization group calculations of the universal crossover scaling function. Special attention is paid to length scales smaller than the density screening length ξ, where the distinct part of the scattering function in the simulations i…

The neutron electric form factor and quasi-elastic electron-deuteron scattering

2008

Neutron scattering and molecular correlations in a supercooled liquid

1999

We show that the intermediate scattering function $S_n(q,t)$ for neutron scattering (ns) can be expanded naturely with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the $q$-dependence and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor $S_n(q)$ is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic m…

Scattering from concentration fluctuations in polymer blends: A monte carlo investigation

1989

The collective scattering function Scoll( $$\vec q$$ ), which describes light (neutron-, x-ray) scattering under wavevector $$\vec q$$ , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN A=NB=N steps on a simple cubic lattice, where a fractionφ V of sites is left vacant, and an attractive energye occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S coll −1 (0) vs.e/k B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, str…

The structural relaxation of molten sodium disilicate

2002

We use molecular dynamics computer simulations to study the relaxation dynamics of Na2O-2(SiO2) in its molten, highly viscous state. We find that at low temperatures the incoherent intermediate scattering function for Na relaxes about 100 times faster than the one of the Si and O atoms. In contrast to this all coherent functions relax on the same time scale if the wave-vector is around 1AA^-1. This anomalous relaxation dynamics is traced back to the channel-like structure for the Na atoms that have been found for this system. We find that the relaxation dynamics for Si and O as well as the time dependence of the coherent functions for Na can be rationalized well by means of mode-coupling th…

The dynamics of sodium in sodium disilicate: Channel relaxation and sodium diffusion

2001

We use molecular dynamics computer simulations to study the dynamics of amorphous (Na_2O)2(SiO_2). We find that the Na ions move in channels embedded in a SiO_2 matrix. The characteristic distance between these channels gives rise to a prepeak in the structure factor at around q=0.95 A^-1. The dynamics of sodium is given by a fast process which can be seen in the incoherent scattering function and a slow process which is seen in the coherent function. The relaxation time of the latter coincides with the alpha-relaxation time of the matrix. The Kohlrausch exponent of the fast process for q>1.6 A^1 is the same as the von Schweidler exponent for the slow one, demonstrating that the two proc…

Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom

1997

A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T_c, where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c agrees with that found earlier for the orientational dynamics within the error bars. In the beta- regime of MCT the factorization of space- and time dependence is satisf…

Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics

1997

Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited …

Dynamic coarse-graining of polymer systems using mobility functions.

2021

We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To enable the mapping over a range of relevant wave vectors, we propose to modify the CG dynamics by …

Asymptotic structure factor for the two-component Ginzburg-Landau equation

1992

We derive an analytic form for the asymptotic time-dependent structure factor for the two-component Ginzburg-Landau equation in arbitrary dimensions. This form is in reasonable agreement with results from numerical simulations in two dimensions. A striking feature of our analytic form is the absence of Porod's law in the tail. This is a consequence of the continuous symmetry of the Hamiltonian, which inhibits the formation of sharp domain walls.