Coherent Dynamic Structure Factor Research Articles

Understanding the coherent dynamic structure factor of liquid water measured by neutron spectroscopy with polarization analysis: a Molecular Dynamics simulations study

This work is focused on atomistic molecular dynamics (MD) simulations of water carried out at 300 K. The main goal is to better understand the experimental results of the coherent dynamic structure factor S(Q,ν) of D2O that were obtained by means of neutron scattering with polarization analysis and previously reported by us [A. Arbe et al. Phys. Rev. Res. 2, 022015 (2020)]. From the simulations, we have calculated the coherent dynamic structure factor in the time domain S(Q,t) as well as its selfand distinctcontributions. We have also calculated S(Q,t) corresponding to a H2O sample. The main results obtained are: (i) The Q-independent relaxation process identified in S(Q,ν) in the mesoscopic range (Q0-mode) is the responsible of the restructuring of the hydrogen bond (HB) network at times shorter than that corresponding to the molecular diffusion; (ii) the vibrational contribution identified at high frequency in S(Q,ν) corresponds to a hydrodynamic-like mode propagating in an elastic medium (fixed HB bonding pattern); (iii) in the crossover range from mesoscopic to intermolecular scales, diffusion also progressively contributes to the decay of density fluctuations; (iv) MD-simulations suggest that it would be basically impossible to measure S(Q,ν,) of H2O in the mesoscopic range with the current neutron scattering capabilities.

Unraveling the coherent dynamic structure factor of liquid water at the mesoscale by molecular dynamics simulations.

We present an investigation by molecular dynamics (MD)-simulations of the coherent dynamic structure factor, S(Q, t) (Q: momentum transfer), of liquid water at the mesoscale (0.1 Å-1 ≤ Q ≤ Qmax) [Qmax ≈ 2 Å-1: Q-value of the first maximum of the static structure factor, S(Q), of water]. The simulation cell-large enough to address the collective properties at the mesoscale-is validated by direct comparison with recent results on the dynamic structure factor in the frequency domain obtained by neutron spectroscopy with polarization analysis [Arbe et al., Phys. Rev. Res. 2, 022015 (2020)]. We have not only focused on the acoustic excitations but also on the relaxational contributions to S(Q, t). The analysis of the MD-simulation results-including the self- and distinct contributions to the diffusive part of S(Q, t)-nicely explains why the relaxation process hardly depends on Q in the low Q-range (Q ≤ 0.4 Å-1) and how it crosses over to a diffusion-driven process at Q ≈ Qmax. Our simulations also give support to the main assumptions of the model used to fit the experimental data in the above mentioned paper. The application of such a model to the simulation S(Q, t) data delivers (i) results for the relaxation component of S(Q, t) in agreement with those obtained from neutron experiments and (ii) longitudinal and transverse hydrodynamic-like components with similar features than those identified in previous simulations of the longitudinal and transverse current spectra directly. On the other hand, in general, our MD-simulations results of S(Q, t) qualitatively agree with the viscoelastic transition framework habitually used to describe inelastic x-ray scattering results.

De Gennes Narrowing and Hard-Sphere Approach

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.

Dynamics of Polydots: Soft Luminescent Polymeric Nanoparticles

The conformation and dynamics of luminescent polymers collapsed into nanoparticles or polydots were studied using fully atomistic molecular dynamics (MD) simulations, providing a first insight into their internal dynamics. Controlling the conformation and dynamics of confined polymers is essential for realization of the full potential of polydots in nanomedicine and biotechnology. Specifically, the shape and internal dynamics of polydots that consist of highly rigid dialkyl p-phenylene ethynylene (PPE) are probed as a function of temperature. At room temperature, the polydots are spherical without any correlations between the aromatic rings on the PPE backbone. With increasing temperature, they expand and become slightly aspherical; however, the polymers remain confined. The coherent dynamic structure factor reveals that the internal motion of the polymer backbone is arrested, and the side chains dominate the internal dynamics of the polydots. These new soft nanoparticles retain their overall shape and dy...

Molecular Dynamics Force-Field Refinement against Quasi-Elastic Neutron Scattering Data.

Quasi-elastic neutron scattering (QENS) is one of the experimental techniques of choice for probing the dynamics at length and time scales that are also in the realm of full-atom molecular dynamics (MD) simulations. This overlap enables extension of current fitting methods that use time-independent equilibrium measurements to new methods fitting against dynamics data. We present an algorithm that fits simulation-derived incoherent dynamical structure factors against QENS data probing the diffusive dynamics of the system. We showcase the difficulties inherent to this type of fitting problem, namely, the disparity between simulation and experiment environment, as well as limitations in the simulation due to incomplete sampling of phase space. We discuss a methodology to overcome these difficulties and apply it to a set of full-atom MD simulations for the purpose of refining the force-field parameter governing the activation energy of methyl rotation in the octa-methyl polyhedral oligomeric silsesquioxane molecule. Our optimal simulated activation energy agrees with the experimentally derived value up to a 5% difference, well within experimental error. We believe the method will find applicability to other types of diffusive motions and other representation of the systems such as coarse-grain models where empirical fitting is essential. Also, the refinement method can be extended to the coherent dynamic structure factor with no additional effort.

Structure and dynamics of confined flexible and unentangled polymer melts in highly adsorbing cylindrical pores.

Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0). In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨R(g)(2)⟩ and the average relative shape anisotropy ⟨κ(2)⟩ of the conformation of the polymer chains indicate a pancake-like conformation near the surface and a bulk-like conformation near the center of the confining cylinder. This was confirmed by direct visualization of the polymer chains. Despite the presence of these different conformations, the average form factor of the confined chains still follows the Debye function which describes linear ideal chains, which is in agreement with small angle neutron scattering experiments (SANS). The experimentally inaccessible mean-square displacement (MSD) of the confined monomers, calculated as a function of radial distance from the pore surface, was obtained in the simulations. The simulations show a gradual increase of the MSD from the adsorbed, but mobile layer, to that similar to the bulk far away from the surface.

Coherent Dynamic Structure Factor of a Polymer Chain Confined Into a Harmonic Radial Potential

The coherent dynamic structure factor of a single polymer chain is calculated based on the model of a Rouse polymer chain constrained (confined) by a harmonic radial potential and its behavior in different limiting cases is analyzed. The strength of confinement is characterized using an effective diameter of the harmonic radial potential as a model parameter. The method provides a reliable model to study the crossover between unconstrained (Rouse) and constrained dynamics.

Molecular dynamics simulation of temperature and pressure effects on the intermediate length scale dynamics and zero shear rate viscosity of cis-1,4-polybutadiene: Rouse mode analysis and dynamic structure factor spectra

A well-relaxed atomistic configuration of a 32-chain C 128 cis-1,4-polybutadiene ( cis-1,4-PB) system has been subjected to long (on the order of a few microseconds) molecular dynamics (MD) simulations in the NPT ensemble using the united-atom forcefield introduced by Smith et al. [G. Smith, D. Bedrov, W. Paul, A molecular dynamics simulation study of the alpha-relaxation in a 1,4-polybutadiene melt as probed by the coherent dynamic structure factor, J. Chem. Phys. 121 (2004) 4961–4967] on the basis of quantum chemistry calculations. This allowed us to study the temperature and pressure dependences of the Rouse-mode relaxation spectrum of cis-1,4-PB over a wide range of temperature (ranging from T = 430 K down to 165 K) and pressure (from P = 1 atm up to 3.5 kbar) conditions. Results are presented for: (a) the time decay of the autocorrelation function of the normal coordinates (Rouse modes), (b) the single chain intermediate coherent dynamic structure factor, S coh( q, t), and (c) the intermediate incoherent dynamic structure factor, S inc( q, t), for different values of the wavevector q. By mapping our MD simulation results onto the Rouse model, we have been able to extract a prediction for the zero shear rate viscosity of the simulated cis-1,4-PB system as a function of temperature and analyze its fragile character. In agreement with our previous MD simulation studies on the same system [G. Tsolou, V.A. Harmandaris, V.G. Mavrantzas, Atomistic molecular dynamics simulation of the temperature and pressure dependences of local and terminal relaxations in cis-1,4-polybutadiene, J. Chem. Phys. 124 (2006) 084906-1-11] and in contrast to what is experimentally observed [see, e.g., G. Floudas, T. Reisinger, Pressure dependence of the local and global dynamics of polyisoprene, J. Chem. Phys. 111 (1999) 5201–5204; C.M. Roland, R. Casalini, T. Psurek, S. Pawlus, M. Paluch, Segmental- and normal-mode dielectric relaxation of poly(propylene glycol) under pressure, J. Polym. Sci. Part B: Polym. Phys. 41 (2003) 3047–3052], we predict that pressure and temperature influence practically similarly all normal mode relaxation times along the simulated C 128 cis-1,4-PB chain. Furthermore, our MD simulation results predict a transition from a homogeneous to a heterogeneous dynamical behavior in the region of wavevectors near the first (intermolecular) peak in the static structure factor, consistently with recent neutron scattering (NS) measurements [see, e.g., B. Frick, G. Dosseh, A. Cailliaux, C. Alba-Simionesco, Pressure dependence of the segmental relaxation of polybutadiene and polyisobutylene and influence of molecular weight, Chem. Phys. 292 (2003) 311–323; A. Arbe, J. Colmenero, B. Farago, M. Monkenbusch, U. Buchenau, D. Richter, Intermediate length scale dynamics in glass forming polymers: coherent and incoherent quasielastic neutron scattering results on polyisobutylene, Chem. Phys. 292 (2003) 295–309] and previous simulation studies [see, e.g., J. Colmenero, F. Alvarez, A. Arbe, Self-motion and the alpha relaxation in a simulated glass-forming polymer: Crossover from Gaussian to non-Gaussian dynamic behavior, Phys. Rev. E 65 (2002) 041804-1-12].

Microscopic dynamics in molten Ni: Experimental scrutiny of embedded-atom-potential simulations

The stochastic dynamics in molten nickel is studied by neutron scattering. The quasielastic spectrum shows two distinct components having disparate linewidths. The wave-vector dependence of the narrow component is shown to arise from incoherent scattering at low momentum transfers. In turn, the spectral half-width of the wider component shows a modulation with wave vector characteristic of coherent quasielastic scattering. The analysis of both components provides direct experimental estimates for the self-diffusion coefficient, as well as the effective particle diameter. The experimental data are then used to validate computer simulation results which are derived using an embedded-atom potential. Such results are also employed to explore regions in frequency-wave-vector space not easily amenable to experiment. In addition, simulation results are also compared with data pertaining to the collective motions. Such an exercise reveals the need to develop a further level in the memory function expansion of the coherent dynamic structure factor. The implications of such findings for our current understanding of the dynamics of liquid metals are finally assessed.

A molecular dynamics simulation study of the alpha-relaxation in a 1,4-polybutadiene melt as probed by the coherent dynamic structure factor.

The dynamic coherent structure factor Scoh(q,t) for a 1,4-polybutadiene (PBD) melt has been investigated using atomistic molecular dynamics simulations. The relaxation of Scoh(q,t) at q = 1.44 angstroms(-1) and q = 2.72 angstroms(-1), corresponding to the first and second peaks in the static structure factor for PBD, was studied in detail over a wide range of temperature. It was found that time-temperature superposition holds for the alpha-relaxation for both q values over a wide temperature range and that the alpha-relaxation can be well described by a stretched (Kohlrauch-William-Watts) exponential with temperature independent but q dependent amplitude and stretching exponent. The alpha-relaxation times for both q values were found to exhibit the same non-Arrhenius temperature dependence, indicating that the same physical processes are responsible for relaxation on both length scales. The alpha-relaxation time was found to depend strongly upon the dynamical range of data utilized in determining the relaxation time, accounting for qualitative discrepancies between alpha-relaxation times reported here and those extracted for PBD from experimentally measured Scoh(q,t).

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 η∼N to η∼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. In this region the viscosity scales as η∼N3.6, the tube diameter is d≈5.4 nm, the entanglement molecular weight is Me≈1700 g/mol, and the plateau modulus is GN0≈2.4 MPa, all in good agreement with experimental data.

The stretched-exponential approximation to the dynamic structure factor in non-entangled polymer melts

The coherent and incoherent dynamic structure factor S(Q,t) measured in neutron scattering experiments (Q being the momentum transfer) provides invaluable information about the intramolecular dynamics of polymer chains. Here we report an analysis of the calculated S(Q,t) for low-molar-mass chains in the molten state with no entanglements. The theoretical results from coarse-grained and realistic models are empirically fitted with the Kohlrausch–Williams–Watts (KWW) stretched-exponential function exp[−(t/τ)β]. Both the characteristic time τ and the β exponent (β < 1) are allowed to depend on Q. The KWW function fit is shown to be adequate down to S(Q,t)/S(Q,0) ≈ 0.05, but to become increasingly poorer at longer times, much earlier than the diffusive regime sets in, due to the breadth of the spectrum of relaxation times. Results are discussed in terms of τ and β, which are tentatively correlated with the stiffness of the model chains, and compared both with recent experimental results and with theoretical approaches.

Understanding the anomalous 1/t3 time dependence of velocity correlation function in one dimensional Lennard-Jones systems

One dimensional Lennard-Jones fluids are known to exhibit an interesting 1/t3 time (t) dependence of the velocity correlation function. The origin of this decay is apparently not well understood. We have studied this problem both by molecular dynamic simulations and by mode coupling theory. We find that this t−3 decay of the velocity autocorrelation function (VACF) arises from the coupling of the tagged particle’s motion to the longitudinal current mode of the fluid. Interestingly such a decay is intern rendered possible by the Gaussian time dependence of the coherent dynamic structure factor at the relevant times. This is confirmed by the simulations of Lennard-Jones rods. The t−3 dependence is found to be dominant at low and intermediate densities. We show that the mode coupling theory provides an accurate description of the VACF both at short and long time limits.

Temperature dependence of collective modes in liquid sodium

We present results for the purely coherent dynamic structure factor of liquid sodium obtained from inelastic X-ray scattering experiments. Measurements were carried out at four temperatures between 388 and 1173 K. The dispersion relations for longitudinal collective excitations in the liquid could be determined for each temperature. It is found that the adiabatic sound velocity given as the slope of the dispersion at lower Q is increased compared to the bulk value. This `positive dispersion' still exists even at the highest temperatures attained in this experiment. From the data an estimate is given for the shear modulus of the liquid along the temperature range covered by our experiment.

Calculation of the coherent dynamic structure factor of polyisoprene from molecular dynamics simulations

The static structure factor $S(Q)$ and the coherent dynamic structure factor $S(Q,t)$ are calculated from molecular dynamics simulations of polyisoprene melts and compared with neutron scattering results [R. Zorn, D. Richter, B. Farago, B. Frick, F. Kremer, U. Kirst, and L. J. Fetters, Physica B 180&amp;181, 534 (1992)]. Both the shape and the absolute time scale of the calculated $S(Q,t)$ are consistent with experimental results. The decay of $S(Q,t)$ can be almost entirely attributed to intramolecular dynamics throughout the Q range studied $(1.2&lt;~Q&lt;~3.0{\AA{}}^{\ensuremath{-}1}),$ i.e., the full $S(Q,t)$ can be approximated by considering only the self terms and the cross terms localized to within a few repeat units along the chain. It was found that the factor of 5 observed between the dynamics at the first two peaks of $S(Q)$ is part of a general trend largely independent of whether $S(Q)$ is at a minimum or a maximum. A comparison of $S(Q,t)$ in the region of the first peak in $S(Q)$ and the ${P}_{2}\mathrm{C}\mathrm{---}\mathrm{H}$ bond vector orientation autocorrelation function ${F}_{C}(t)$ suggests that the same molecular motions influence both the neutron spin echo and NMR ${T}_{1}$ relaxation experiments.

Studyof the lattice dynamics of hexagonal close-packed 3He and 4Heusing inelastic x-ray scattering

We present the first measurement of the coherent dynamic structure factor S(Q,) of solid 3He. At a density of 13.25(10) cm3 mol-1, we observed longitudinal phonons, using high-resolution inelastic x-ray scattering at momentum transfers 6 nm-1 < |Q| < 23 nm-1. Their dispersion relation was determined along the c-axis in single crystals of hcp 3He, and the spectra were described with a single-phonon model. For comparison, hcp 4He at the same density was studied with the same technique. The comparison, including all available 4He data from neutron scattering experiments, results in a phonon frequency ratio 3/4 of 1.11(5). Special attention is given to the scattering contribution due to multi-phonon excitations.

Distribution functions and dynamical properties of stiff macromolecules

AbstractAn analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky‐Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne‐Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well‐known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q8/3tp1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.

Coherent dynamic structure factor of orthoterphenyl around the mode coupling crossover temperatureTc

The coherent dynamic structure factor of supercooled orthoterphenyl has been measured by time-of-flight neutron scattering. The data extend previous backscattering and spin-echo data towards shorter times. In the $\ensuremath{\beta}$ relaxation regime the two-step decay of density correlations can be described by the same master function as found before for self-correlations. We show that the mode-coupling crossover temperature ${T}_{c}$ can be determined from $\ensuremath{\beta}$ relaxation data alone. The wave-number dependence of the relaxation amplitude follows, to some extent, that of the static structure factor.

Coherent Dynamic Structure Factor of Liquid Lithium by Inelastic X-Ray Scattering

We present high resolution inelastic x-ray scattering measurements of the coherent dynamic structure factor $S(Q,\ensuremath{\omega})$ of liquid lithium at momentum transfers $0.36\ensuremath{\le}Q\ensuremath{\le}5{\AA{}}^{\ensuremath{-}1}$. The determined $S(Q,\ensuremath{\omega})$ agrees much better with molecular dynamic simulations using the neutral pseudo-atom potential rather than the empty core potential. We observe a positive dispersion in the sound velocity confirming that in liquid lithium the longitudinal dynamics reaches a solid-like response at high frequencies.

Influence of stiffness on the dynamics of macromolecules in a melt

Analytical expressions are derived for the incoherent and coherent dynamic structure factor of macromolecules in a melt. In particular, the influence of chain stiffness on these quantities is investigated. For scattering vectors q&amp;lt;πp/2, where 1/2p is the persistence length of the macromolecules, the well known results for the Rouse model are reproduced. However, in the scattering vector range q&amp;gt;πp/2 the incoherent dynamic structure factor is shown to be a universal function of only the combination q8/3tp1/3, reflecting the strong influence of the local chain stiffness on dynamical properties at small length scales. Moreover, the q dependence of both the full width at half maximum of the Fourier transformed incoherent dynamic structure factor and the initial decay rate of the coherent dynamic structure factor are calculated. The comparison of the theoretical results with quasielastic neutron scattering experiments of different polymers exhibits good agreement.