Self-correlation Function Research Articles

Quasielastic Neutron Scattering Study on the Effect of Blending on the Dynamics of Head-to-Head Poly(propylene) and Poly(ethylene−propylene)

By means of quasielastic neutron scattering, we have investigated the dynamics of two polymers, head-to-head poly(propylene) (HHPP) and poly(ethylene-propylene) (PEP), through the incoherent scattering function of hydrogens, i.e., the H self-correlation function. Backscattering techniques have allowed us to cover mesoscopic time scales in the momentum transfer region 0.2 e Q e 1.8 A -1 . For both polymers, the glassy dynamics below the glass-transition temperature Tg (HHPP: Tg ) 248 K; PEP: Tg ) 213 K) is dominated by the methyl group rotations. In the temperature region investigated in the supercooled liquid state swell above the glass transitionswe have observed a qualitatively similar behavior for both systems: anomalous sublinear diffusion with deviations from Gaussian behavior in the high-Q range. Because of the differences in Tg, the time scales associated with HHPP are slower than those observed for PEP in this regime. These results have been taken as reference to address the question of the dynamic miscibility in the blend system composed by a mixture of 50% HHPP/50% PEP. Exploiting isotopic labeling, we could experimentally isolate the HHPP-component dynamics in the blend by using a mixture of protonated HHPP and deuterated PEP. In the glassy state, we found that the methyl group dynamics of HHPP is not affected by blending. On the other hand, well above the average glass transition of the blend, the hydrogen motions in HHPP become faster in the presence of PEP. The combined analysis of these results and measurements on the fully protonated blend allowed us finally to deduce also the PEP-component dynamics in the blend in the supercooled liquid state. This dynamics is slowed down by blending but remains faster than that shown by the HHPP component in the blend. These results are discussed in the light of a recent model for blend dynamics proposed by Lodge and McLeish based on the concept of self-concentration. The experimentally observed behavior is well predicted by such a model in the Q and temperature range investigated well above the glass transitions of the polymers.

Effect of Interfacial Structure on Permeation Properties of Glassy Polymers

Gas permeation has been studied in two fully atomistic molecular models of a glassy polyimide, which differ by their chain configurations and packing. The first polyimide system is an isotropic 56 025-atom bulk model of the amorphous phase while the second is a 141 100-atom model of an actual membrane. The preparation procedure of the membrane was based loosely on the experimental solvent-casting process. The membrane model exhibits density oscillations at the interfaces with chains being aligned and flattened parallel to it. The structuration persists throughout the membrane, and this leads to the gas diffusing in a slightly anisotropic way in the center of the membrane model. However, the diffusion coefficient obtained using either approximate analytical solutions or numerical solutions to the one-dimensional diffusion equation as well as a time-lag approach was found to be very similar to that in the bulk, which was evaluated from mean-square displacements, probability density distributions of displacement vector components, and the van Hove self-correlation function. Solubilities obtained from Widom's insertion technique and from the equilibrium density of gas within the matrix were in very good agreement for the membrane model. Despite a small drop in solubility in the region corresponding to the density peak of the polymer at the interface, the solubility coefficient also remained similar to that of the bulk. The changes in configurations and the high-density interface have thus little effect on the permeability of the gas used in this case.

Fast rotational matching of single-particle images

The presence of noise and absence of contrast in electron micrographs lead to a reduced resolution of the final 3D reconstruction, due to the inherent limitations of single-particle image alignment. The fast rotational matching (FRM) algorithm was introduced recently for an accurate alignment of 2D images under such challenging conditions. Here, we implemented this algorithm for the first time in a standard 3D reconstruction package used in electron microscopy. This allowed us to carry out exhaustive tests of the robustness and reliability in iterative orientation determination, classification, and 3D reconstruction on simulated and experimental image data. A classification test on GroEL chaperonin images demonstrates that FRM assigns up to 13% more images to their correct reference orientation, compared to the classical self-correlation function method. Moreover, at sub-nanometer resolution, GroEL and rice dwarf virus reconstructions exhibit a remarkable resolution gain of 10–20% that is attributed to the novel image alignment kernel.

Dynamics of liquid benzene: A cage analysis

Dynamics of single molecules in liquids, inspected in the picosecond time scale by means of spectroscopic measurements or molecular-dynamics (MD) simulations, reveals a complex behavior which can be addressed as due to local confinement (cage). This work is devoted to the analysis of cage structures in liquid benzene, obtained from MD simulations. According to a paradigm proposed for previous analysis of atomic and molecular liquids [see, for example, A. Polimeno, G. J. Moro, and J. H. Freed, J. Chem. Phys. 102, 8094 (1995)], the istantaneous cage structure is specified by the frame of axes which identifies the molecular configuration at the closest minimum on the potential-energy landscape. In addition, the modeling of the interaction potential between probe molecule and molecular environment, based on symmetry considerations, and its parametrization from the MD trajectories, allows the estimation of the structural parameters which quantify the strength of molecular confinement. Roto-translational dynamics of probe and related cage with respect to a laboratory frame, dynamics of the probe within the cage (vibrations, librations, re-orientational motions), and the restructuring processes of the cage itself are analyzed in terms of selected time self-correlation functions. A time-scale separation between the processes is established. Moreover, by exploiting the evidence of fast vibrational motions of the probe with respect to the cage center, an orientational effective potential is derived to describe the caging in the time scale longer than approximately 0.2 ps.

A planar functional processor of complex signals based on the effect of domain-acoustic echo

The paper presents results of investigation of a domain-acoustic correlation processor, equipped with a long-term memory, for processing complex radio pulses. The basic functional materials of the processor represented a set of specimens of polycrystalline yttrium iron garnet, and epitaxial films in the shape of plates and rings. The specimens were excited by piezoelectric transducers with different polarization of ultrasonic oscillations, and the largest amplitude of the self-correlation function was recorded for shear waves with longitudinal polarization and in specimens with ring-shaped geometry.

Crystal Water Dynamics of Guanosine Dihydrate: Analysis of Atomic Displacement Parameters, Time Profile of Hydrogen-Bonding Probability, and Translocation of Water by MD Simulation

The dynamics of crystal water molecules of guanosine dihydrate are investigated in detail by molecular dynamics (MD) simulation. A 2 ns simulation is performed using a periodic boundary box composed of 4 x 5 x 8 crystallographic unit cells and using the particle-mesh Ewald method for calculation of electrostatic energy. The simulated average atomic positions and atomic displacement parameters are remarkably coincident with the experimental values determined by X-ray analysis, confirming the high accuracy of this simulation. The dynamics of crystal water are analyzed in terms of atomic displacement parameters, orientation vectors, order parameters, self-correlation functions of the orientation vectors, time profiles of hydrogen-bonding probability, and translocations. The simulation clarifies that the average structure is composed of various stable and transient structures of the molecules. The simulated guanosine crystal forms a layered structure, with four water sites per asymmetric unit, classified as either interlayer water or intralayer water. From a detailed analysis of the translocations of water molecules in the simulation, columns of intralayer water molecules along the c axis appear to represent a pathway for hydration and dehydration by a kind of molecular valve mechanism.

Diagrammatic kinetic theory for a lattice model of a liquid. I. Theory.

We present a diagrammatic formalism for the time correlation functions of density fluctuations for an excluded volume lattice gas on a simple d-dimensional hypercubic lattice. We consider a multicomponent system in which particles of different species can have different transition rates. Our theoretical approach uses a Hilbert space formalism for the time dependent dynamical variables of a stochastic process that satisfies the detailed balance condition. We construct a Liouville matrix consistent with the dynamics of the model to calculate both the equation of motion for multipoint densities in configuration space and the interactions in the diagrammatic theory. A Boley basis of fluctuation vectors for the Hilbert space is used to develop two formally exact diagrammatic series for the time correlation functions. These theoretical techniques are generalizations of methods previously used for spin systems and atomic liquids, and they are generalizable to more complex lattice models of liquids such as a lattice gas with attractive interactions or polymer models. We use our formalism to construct approximate kinetic theories for the van Hove correlation and self-correlation function. The most simple approximation is the mean field approximation, which is exact for the van Hove correlation function of a one component system but an approximation for the self-correlation function. We use our first diagrammatic series to derive a two site multiple scattering approximation that gives a simple analytic expression for the spatial Fourier transform of the self-correlation function. We employ our second diagrammatic series to derive a simple mode coupling type approximation that provides a system of equations that can be solved for the self-correlation function.

COLLECTIVE DYNAMICS OF LIQUID Al

The recently suggested modified microscopic theory of liquids has been used successfully to explain the collective dynamics of liquid Al near its melting point. Considering the frequency-dependent self-diffusion coefficient occurring in the intermediate self-correlation function, which is inextricably linked with the collective dynamics of the system, the observed variation in dynamical structure factor of Al can be quantitatively reproduced for wave vector range 0.42 Å-1 to 1.38 Å-1 taking into account single relaxation time.

Molecular dynamics simulations of liquid gallium at 320 and 970 K

We performed large scale molecular dynamics simulations of liquid gallium at 320 and 970 K, exploiting a phenomenological model of the ion-pair potential depending only on the electron density. The simulations provided a description of the structure and of several dynamic properties of the system, in quantitative agreement with the experimental findings. The analysis of the intermediate self-correlation function indicated the presence of a second process, other than the diffusive process, driving the dynamics of liquid gallium at short times. This fast process, having a characterizing decay time of the order of a fraction of a picosecond, is here identified with a cage motion.

A path integral influence functional for excess electron in fluids: Density-functional formulation.

In this paper, we propose a path integral influence functional from a solvent to determine a self-correlation function of a quantum particle in classical simple fluid. It is shown that the influence functional is related to a grand potential functional of the pure solvent under a three-dimensional external field arising from a classical isomorphic polymer, on which the quantum particle is mapped. The influence functional can be calculated from the self-correlation function, the solute-solvent and the solvent-solvent pair correlation function. The obtained equation of the self-correlation function is applied to an excess electron problem in fluid helium. The Fourier path-integral Monte Carlo method is employed to perform the path integral of the electron. The solute-solvent pair correlation function is estimated from a reference interaction site model integral equation. These results obtained form our proposed influence functional and from that proposed by Chandler, Singh, and Richardson are compared with those provided by a path integral Monte Carlo simulation with the explicit helium solvent.

Efficient calculation of digital convolution based on fast Hartley transform

The paper describes an economic (from the computation cost viewpoint) algorithm for calculation of the cyclic digital convolution, and of the cross- and self-correlation functions of signals based on the fast Hartley transform. Application of the new algorithm makes it possible to diminish the computational complexity and the memory resource by one third as compared with the known version of the algorithm.

Model for the translation–rotation coupling of molecular motion in water

Using molecular dynamic simulations of an extended-simple-point-charge model of water, we investigated the effect of translation–rotation coupling on the motion of the hydrogen atom in a water molecule in low temperature water. We introduce a translation–rotation probability distribution PCM,Ω(r,θR,t), where r(t) is the scalar displacement of the center of mass from origin at time t starting from the origin at t=0; and θR(t)=arccos[b(t)⋅b(0)/b2] is the angle of rotation of the vector, b, connecting the center of mass of the water molecule to the hydrogen atom position. We developed a procedure to determine PCM,Ω(r,θR,t) starting from the van Hove self-correlation function of the center of mass, GsCM(r,t), taking into account the translation–rotation coupling effect. In the long time region, we use a translation–rotation coupling parameter, Q*, to determine the angular dependence of PCM,Ω(r,θR,t) from GsCM(r,t). Thus, the dynamics of the hydrogen atoms in a water molecule is fully determined by the van Hove self-correlation function of the center of mass and by the value of the translation–rotation coupling parameter. In particular, we show that the self intermediate scattering function of the hydrogen atom can be calculated with a better accuracy than using the traditional decoupling approximation. The model can be used to analyze incoherent quasielastic neutron scattering spectra of water in the future.

Tagged particle motion in a dense liquid: feedback effects from the collective dynamics.

The nature of the tagged particle motion in the strongly correlated state of a dense liquid is studied with the self-consistent mode-coupling model. The tagged particle time correlation function psi(s)(q,t) is computed by taking into account the nonlinear feedback effects on its dynamics from the coupling with density fluctuations. We consider the two cases where (a) the short-time dynamics is diffusive resembling colloidal system and (b) the short-time dynamics is Newtonian as in an atomic system. The non-Gaussian parameter alpha(2)(t) is evaluated using the fourth- and second-order spatial moments of the van Hove self-correlation function G(s)(r,t). We observe a two-peaked structure of alpha(2)(t) for both (a) and (b) types of dynamics. We also compare other characteristic aspects of tagged particle dynamics such as the mean square displacement, non-Gaussian nature of G(s)(r,t), and fraction of mobile particles. A qualitative comparison is drawn between the theoretical results with the experimental and computer simulation results on colloids.

Experimental evidence by neutron scattering of a crossover from Gaussian to non-Gaussian behavior in the alpha relaxation of polyisoprene.

We report incoherent quasielastic neutron scattering experiments exploring the alpha-relaxation range in polyisoprene over an unprecedented range in momentum transfer Q. The data corroborate and validate earlier molecular dynamics simulations and reveal the existence of a crossover from Gaussian to non-Gaussian character of the main chain protons self-correlation function in the alpha-relaxation regime. The real challenge of the experiment was to push the neutron techniques to cover a Q range as wide as possible. By combining two neutron spin echo spectrometers and a backscattering instrument, we have been able to study the dynamics in a Q range of 0.1 < or = Q < or = 4.7 A(-1). In the low-Q regime the shape of the relaxation function was found to be related to the dispersion of the relaxation times as predicted by the Gaussian assumption. At short distances or large Q, this relationship is strongly violated indicating a non-Gaussian regime. We have performed a detailed comparison between the experiments and simulations at different temperatures and found, apart from a temperature shift, complete agreement. Combining experiments and simulations led to a consistent interpretation in terms of a distribution of jumps underlying the diffusive motion of protons in the alpha process. This model leads to a time-dependent non-Gaussianity parameter that agrees nearly quantitatively with the simulations and exhibits all features resolved so far from various simulations.

Double dynamical regime of confined water

The Van Hove self-correlation function of water confined in a silica pore is calculatedfrom molecular dynamics trajectories upon supercooling. At long time in the αrelaxation region we found that the behaviour of the real space time dependentcorrelators can be decomposed into a very slow, almost frozen, dynamics due to thebound water close to the substrate and a faster dynamics of the free water whichresides far from the confining surface. For free water we confirm the evidence of anapproach to a cross-over mode coupling transition, previously found inQspace. In the short time region we found that the two dynamical regimes aresuperimposed and cannot be distinguished. This shows that the interplay betweenthe slower and the faster dynamics emerges in going from early times to the αrelaxation region, where a layer analysis of the dynamical properties can beperformed.

Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts.

We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from proportional, variant t(1/2) to proportional, variant t(1/4) is expected and clearly corroborated by the incoherent NSE results.

Rotational Brownian motion of a pair of linear molecules or dipoles with anisotropic interaction

The rotational Smoluchowski equation for the orientational distribution function of two identical linear molecules or dipoles with anisotropic interaction is solved by expansion in terms of a limited set of eigenfunctions of the operator for free rotational diffusion. The equilibrium self-correlation and pair time-correlation functions of the two axial unit vectors or dipole moments are evaluated for the special case of electrostatic or magnetostatic dipole interaction. The interactions appreciably influence the relaxation behavior.

Dynamic structure factor of liquid mercury

The low momentum dynamics of liquid mercury has been investigated by means of inelastic neutron scattering and molecular dynamics (MD) simulations. Due to the rather high incoherent cross-section and the high mass of mercury, the measured dynamic structure factor is dominated by the self-correlation function which has been studied in details. The low momentum collective dynamics are also made accessible by the very good energy resolution of the experiment. Collective modes are clearly visible against the incoherent scattering up to a momentum transfer of 0.6 Å −1. The self-dynamics, as resulting from either the experiment and MD simulations, turn out to be characterized by two time scales.

Self-dynamics and collective dynamics of liquid mercury

Abstract The low-momentum dynamics of liquid mercury has been investigated by means of inelastic neutron scattering and molecular dynamics (MD) simulations. Because of the rather high incoherent cross-section and the high mass of mercury, the measured dynamic structure factor is dominated by the self-correlation function, although the low-momentum collective dynamics are made accessible by the very good energy resolution of the experiment. Collective modes are clearly visible against the incoherent scattering up to a momentum transfer of 0.4A−1 and the associated velocity is found to be 2200 ± 200 m s−1, well in excess of the sound velocity which is equal to 1470 m s−1. The self-dynamics, as resulting from either the experiment or the MD simulations, turn out to be characterized by two time scales.

A generalized Ornstein–Zernike integral equation study of atomic impurities in quantum fluids

In this paper, solvation structure and thermodynamic properties of rare gas and alkali impurities in liquid helium-4 have been studied theoretically. A generalized Ornstein–Zernike integral equation for pure quantum fluids [J. Chem. Phys. 114, 7497 (2001)] was extended to the quantum solutions at infinite dilution. Self-correlation function of the solute atom which appears in the integral equation was determined self-consistently with the solvent density fluctuation. Numerical calculations have been performed for the helium-4 solutions at 4 K, with Boltzmann statistics being assumed. It was found that all the rare gas species investigated in this study have negative partial molar volumes, owing to the well-defined solvation structure around the impurities. In contrast to this, the alkali atoms have large positive partial molar volumes, primarily coming from the excluded volume contribution. Further, while the rare gas atoms have negative excess chemical potentials, the alkali atoms have large positive values. The former may be dominated by the negative interaction energy between the impurity and surrounding solvent atoms, and the latter by the work done by the volume of the solute to exclude the solvent atoms.