Time-dependent Structure Factor Research Articles

Crystallization with Nodular Aggregation near the Glass Transition Temperature for Syndiotactic Polypropylene

The isothermal crystallization from the melt state of syndiotactic polypropylene (sPP) has been studied by wide-angle X-ray diffraction (WAXD), small-angle X-ray scattering (SAXS), and optical microscopy. The WAXD and SAXS results show the crystallization mechanism near the glass transition temperature in which the crystalline and mesomorphic nodules cover the entire sample with the formation of aggregation regions. For the SAXS analysis, the scattering function for the three-component system has been suggested. Furthermore, to analyze the growth kinetics of the aggregation region for sPP, the time-dependent structure factor combined with the homogeneous and inhomogeneous nucleation-and-growth kinetics has been suggested. The analysis shows that the growth kinetics of the aggregation region for sPP is the homogeneous nucleation-and-growth. The growth velocity of the aggregation region is a natural extrapolation of that of spherulite to the high supercooling region. These results might indicate that the crystallization with the nodular aggregation is a fundamental crystallization process near the glass transition temperature for polymers.

Structure factor of a phase separating binary mixture with natural and forceful interconversion of species

Using a modified Cahn-Hilliard-Cook theory for spinodal decomposition in a binary mixture that exhibits both diffusion and interconversion dynamics, we derive the time-dependent structure factor for concentration fluctuations. We compare the theory and obtain a qualitative agreement with simulations of the temporal evolution of the order parameter and structure factor in a nonequilibrium Ising/lattice-gas hybrid model in the presence of an external source of forceful interconversion. In particular, the characteristic size of the steady-state phase domain is predicted from the lower cut-off wavenumber of the amplification factor in the generalized spinodal-decomposition theory. • A source of forceful interconversion may produce microphase separation. • The time evolution of the phase formation is characterized through two wavenumbers. • Steady-state domain size scales with square root of forceful interconversion rate • Results match with Monte Carlo simulations of a nonequilibrium hybrid model. • Source of forceful interconversion may be connected to an external energy source.

Nonequilibrium dynamics in pumped Mott insulators

We use time-evolution techniques for (infinite) matrix-product-states to calculate, directly in the thermodynamic limit, the time-dependent photoemission spectra and dynamic structure factors of the half-filled Hubbard chain after pulse irradiation. These quantities exhibit clear signatures of the photoinduced phase transition from insulator to metal that occurs because of the formation of so-called $\eta$ pairs. In addition, the spin dynamic structure factor loses spectral weight in the whole momentum space, reflecting the suppression of antiferromagnetic correlations due to the buildup of $\eta$-pairing states. The numerical method demonstrated in this work can be readily applied to other one-dimensional models driven out of equilibrium by optical pumping.

On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems.

The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (TF) of the glassy structure. We solve for the kinetics of TF(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of TF(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.

Kinetics of fluid demixing in complex plasmas: Domain growth analysis using Minkowski tensors.

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power-spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures, qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long-range interaction) are revealed. After proper scaling the graphs for the two length scale scenarios coincide, pointing toward universal behavior. The qualitative difference in demixing scenarios is evidenced by distinct demixing behavior: in the long-range dominated cases demixing occurs in two stages. At first, neighboring particles agglomerate, then domains start to merge in cascades. However, in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski tensor analysis is likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power-spectrum analysis, however, still providing easily interpretable results founded on a solid mathematical framework.

Spinodal decomposition of a binary magnetic fluid confined to a surface

In our previous work [J. Chem. Phys. 136, 024502 (2012)], we reported a demixing phase transition of a quasi-two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we present a theoretical study for the time-dependent coarsening occurring within the two-phase region in the density-concentration plane, also known as spinodal decomposition. Our investigations are based on dynamical density functional theory (DDFT). The particles in the mixture are modeled as Gaussian soft spheres on a two-dimensional surface, where one component carries a classical spin of Heisenberg type. To investigate the two-phase region, we first present a linear stability analysis with respect to small, harmonic density perturbations. Second, to capture nonlinear effects, we calculate time-dependent structure factors by combining DDFT with Percus' test particle method. For the growth of the average domain size l during spinodal decomposition with time t, we observe a power-law behavior l∝t^{δ_{α}} with δ_{m}≃0.333 for the magnetic species and δ_{n}≃0.323 for the nonmagnetic species.

Ripples and dots generated by lattice gases

We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata. Using this efficient approach difficult, unanswered questions of surface growth and its scaling can be studied. The mapping onto binary variables facilitates effective simulations and enables one to consider very large system sizes. We have confirmed that the fundamental Kardar–Parisi–Zhang (KPZ) universality class is stable against a competing roughening diffusion, while a strong smoothing diffusion leads to logarithmic growth, a mean-field type behavior in two dimensions. The model can also describe anisotropic surface diffusion processes effectively. By analyzing the time-dependent structure factor we give numerical estimates for the wavelength coarsening behavior.

Ageing and collapse in gels with long-range attractions

We report measurements on the ageing dynamics of a colloid–polymer mixture with a large polymer–colloid size ratio of 0.62. Quenched into a two-phase region the system gels and forms a network with a characteristic radius Rc. We find three distinct regimes in the time evolution of Rc(t), reminiscent of the linear, late and gravity-dominated regimes of coarsening seen in classical spinodal decomposition kinetics of binary fluids. In the early stages of gelation, we observe a peak in the time-dependent structure factor S(q, t) which is stationary in q and grows in intensity characteristic of a linear-Cahn regime. The domain size then coarsens continuously with the age t of the sample. In the late stages the domain size follows the approximate algebraic law, Rc ∼ tθ. The growth exponent θ is a strong function of the quench depth: for small polymer concentrations θ is significantly larger than for large polymer concentrations. The gel networks formed are transient, and in the final stages of phase separation, collapse under gravity when the correlation length of the gel becomes ∼ 2π times the capillary length.

Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Exponential vs. slower decay of time dependent structure factors

This article deals with the possible forms of decay of time dependent structure factors in rather generic systems. It concentrates on the distinction between exponential and slower forms of decay. The common form of decay is assumed traditionally to be exponential or approximately so. Slow decay on the other hand, is characteristic of systems such as glasses that may be viewed as being very special. The purpose of the present article is to show, that slow decay is not related necessarily to the system under consideration but rather to the structure factor we prefer to measure. We may think of the decay of structure factors in certain systems as being exponential or slow but this may just reflect experimental practical preference to measure certain correlations and not others.

Atomistic simulation study of the structure and dynamics of a faceted crystal-melt interface

A detailed analysis of the structure and dynamics of the crystal-melt interface region in silicon, modeled with the Stillinger-Weber potential, is performed via molecular dynamics simulations. The focus is on the faceted (111) crystal-melt interface, but properties of the rough (100) interface are also determined. We find an intrinsic 10-90 interface width of 0.681+/-0.001 nm for the coarse-grained density profile at the (111) interface and a 0.570+/-0.005 nm width at the (100) interface. Coarse-grained profiles of a suitably defined local order parameter are found to show a smaller width anisotropy between (111) and (100) interfaces while the order profiles exhibit a 0.20-0.25 nm shift in position toward the crystal phase relative to the corresponding density profiles. The structural analysis of the layer of melt adjacent to the (111) facet of the crystal finds ordered clusters with average lifetimes of 16 ps , as determined from autocorrelations of time-dependent layer structure factors, and cluster radii of gyration from 0.2 nm for the smallest cells to as large as 1.5 nm .

Numerical evidence for stretched exponential relaxations in the Kardar-Parisi-Zhang equation.

We present results from extensive numerical integration of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure factor we confirm scaling and stretched exponential decay. We also give an analytic expression that yields a very good approximation to the numerical data. Our result clearly favors stretched exponential decay over recent results claiming to yield the exact time dependent structure factor of the 1+1 -dimensional KPZ system. We suggest a possible solution to that contradiction.

Translational rotational coupled motions in molten lithium nitrate

Abstract The translational rotational coupled motions will be studied by molecular dynamics simulations in the case of molten lithium nitrate. Calculating separately the time dependent structure factor F(t, q) for the translation and for the rotation of oxygen atoms in nitrate ions we give an evaluation of the characteristic time of each phenomenum. We find that our results are in good agreement with experiments made in aqueous solutions. Then the coupling between these two kinds of motions is analyzed for several values of the space variable “q” in the Fourier space. We show that the coupling presents a maximum for q=2 A −1 which corresponds to the “q” value where the static structure factor S(q) is maximum.

Space time observation of the -process in polymers by quasielastic neutron scattering

We report quasielastic neutron scattering experiments on the momentum (Q) and time (t) dependent dynamic structure factor on the glass-forming polymers polyisobutylene (PIB) and polybutadiene (PB). After outlining the information content of , we exemplify the concept for the case of PB. Thereafter we present data obtained on the self- and pair correlation functions of PIB encompassing a large Q range . Thereby we cover the entire motional regime from translational diffusion, the Rouse modes, the -relaxation regime up to the local relaxation processes. We investigate the limitations of the Rouse model, we present first results on the relation between the intrachain Rouse process and the -relaxation, we show that the -process may be understood in terms of backwards correlated sublinear diffusion and we finally obtain information on a local relaxation process in PIB which appears to connect a main chain relaxation with a methyl-group rotation.

Finite-size scaling of the time-dependent structure factor in the one-dimensional Glauber model

We study the time-dependent structure factor of the one-dimensional Glauber model upon instantaneous cooling. Results obtained earlier by Reiss, Mazenko and Widom, and Bray, are linked together. Next, finite-size scaling in the limit of zero temperature, long times, small wave vectors, and large systems, is established. The scaling function is compared with numerical simulation results obtained by Viñals and Jasnow in the case of a two-dimensional Glauber model quenched into the region of phase separation.

Phase-separation kinetics in a model with order-parameter-dependent mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.

Homogeneous nucleation and growth in the critical three-dimensional Ising regime of a binary polymer blend

Phase separation in a binary blend of deutero-polystyrene and polyphenylmethylsiloxane was studied with time-resolved light scattering (small-angle light scattering) for a nearly critical concentration at temperatures between 0.2 and 2.6 K below the binodal. It was shown by additional neutron small-angle scattering experiments that all quenches end in the metastable region, i.e., in the gap between binodal and spinodal of ${\mathrm{T}}_{\mathrm{B}}$-${\mathrm{T}}_{\mathrm{S}}$\ensuremath{\cong}4 K. A Ginzburg number of 0.48\ifmmode\pm\else\textpm\fi{}0.14 was found much larger than in simple binary mixtures, indicating that thermal concentration fluctuations are very strong and that the three-dimensional (3D) Ising model is valid. It was shown that strong thermal concentration fluctuations determine the phase separation, leading to homogeneous nucleation and growth in the metastable region as proposed by Binder [Phys. Rev. A 29, 341 (1984)]. Scattering patterns similar to those of spinodally decomposed structures were observed in a time region of the intermediate and the late stage. Power laws were obtained for the time dependence of position ${\mathrm{Q}}_{\mathrm{m}}$(t) and intensity ${\mathrm{I}}_{\mathrm{m}}$(t) of the scattering maximum in the late stage. Furthermore, the data were analyzed with scaling concepts based on the evolution of self-similar structures. The time-dependent structure factor scales in the range of x=Q/${\mathrm{Q}}_{\mathrm{m}}$\ensuremath{\leqslant}2 for all times in the late stage and all temperatures studied, following the relation S(Q,t)=${\mathrm{Q}}_{\mathrm{m}}$(t${)}^{\mathrm{\ensuremath{-}}\mathrm{d}}$F(x). But instead of the Euclidean dimension d=3, an exponent of ${\mathrm{d}}_{\mathrm{f}}$=2.43\ifmmode\pm\else\textpm\fi{}0.05 was found. This is tentatively explained by a precipitation process where the compactness of the domains decreases with time. In the range x>2 a second characteristic length was observed, namely, an apparent interface thickness ${\mathrm{l}}_{\mathrm{I}}$=7000\ifmmode\pm\else\textpm\fi{}200 \AA{} independent of time and quench depth. This was interpreted by a waviness of the interface separating the coarsening domains. Furthermore, scaling was also observed for the position ${\mathrm{Q}}_{\mathrm{m}}$(t) and intensity ${\mathrm{I}}_{\mathrm{m}}$(t) of the scattering maximum with the appropriate values for the collective diffusion coefficient and the correlation length in the two-phase region. Their values were determined by photon correlation spectroscopy (PCS) and small-angle neutron scattering in the one-phase region by an extrapolation into the two-phase region. Finally, by the PCS measurements an extra relaxation process with a characteristic time from 0.1 to 1 sec was discovered, which was related to density fluctuations.

Dynamic structure factor scaling in dense gelling silica suspensions

Small-angle neutron scattering data from dense (30% by mass) gelling 7 nm colloidal silica spheres are presented. The coarsening process that occurs during gelation exhibits temporal self-similarity, and the time-dependent structure factor obeys the dynamic scaling relation . Here, q is the scattered wavevector, is the location of the low-angle peak in is a time-independent characteristic structure function which has a maximum at x = 1, and is the fractal dimension. Connections between the silica gelation and spinodal decomposition in a simple fluid are reviewed.

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S( q, t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T I and characterized by the structure factor S( q,0)= x( q, T I, upon a sudden increase in temperature T I→ T F at constant coverage, such that the adsorbates equilibrate at T F in a disordered phase. The initial decay of a peak in x( q, T I) proceeds exponentially in time, exp(− t τ q ) , where τ q is a wavevector-dependent lifetime, before it crosses over to a power-law, t −1 decay. When x( q, T I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S( q, t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T F, x( q, T F), in that the ratio S(q,t) x(q,T F ) is independent of q, is dependent on time, approaching unity as t −1 for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ q strongly depends on q, diverging as q −2 for q→0. For these systems too, away from the center of the BZ, S (q,t) x(q,T F ) rapidly evolves to a slowly decaying function of t t w , independent of q. In this case, however, the characteristic time scale, t w , is anomalously long, proportional to ξ 2, where ξ is the correlation length associated with the initial state. This behavior of t w can be related to the random walk of domain boundaries.

Fractal growth during early-stage spinodal decomposition in a hydrogen-bonded polymer blend.

Small-angle neutron scattering has been used to study phase separation in a polymer blend made miscible by a dilute, random distribution of hydrogen bonds between the two components. In the one-phase region, scattering below a well-defined wave vector ${\mathit{q}}_{\mathit{c}}$ remains weak as the critical point is approached. During the early stages of spinodal decomposition, the formation of domains of a characteristic size R(t)\ensuremath{\ge}1/${\mathit{q}}_{\mathit{c}}$ is apparent as a peak in the time-dependent structure factor, which scales as ${\mathit{q}}^{\mathrm{\ensuremath{-}}2.40}$ independent of quench depth, raising interesting questions about the morphology of early-stage spinodal decomposition in these mixtures.