Dynamic structure factor of crosslinked polymer blends

The ionic dynamic structure factor is examined to assess the relative roles of dissipation and the effective ionic interaction. Two disparate physically based models of dissipation, which can differ numerically by orders of magnitude, are used in molecular dynamics. We find a negligible impact on the amplitudes of the dynamic structure factors for physically realistic parameter values. We then examine the effective ionic interaction by varying its strength, the size of the atomic core (through a pseudopotential), and the screening model. We find that "diffusive" peaks in the dynamic structure factor are very sensitive to the form of the ionic interaction, and this sensitivity arises primarily from atomic physics through the pseudopotential. This suggests that it would be useful to employ the measured zero-frequency dynamic structure factor S_{ii}(k,0) as a constraint on the effective interaction, which in turn can be used to compute physical properties.

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of RbMnF$_3$, treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent $z$ between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\pm 0.03$, in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at $T_c$, seen in experiments and previous simulations, but absent in the renomalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.

The internal dynamics of semiflexible fibrin gels has been investigated by means of dynamic light scattering (DLS). Fibrin gels, grown at room temperature from fibrinogen solutions at different NaCl concentrations, exhibit rather different structural features. High salt concentrations produce “fine” gels characterized by thin fibers and small mesh sizes, while low salt concentrations give rise to “coarse” gels with thick fibers and much larger mesh sizes. The observed dynamics of these two kinds of gels are quite different as well. “Fine” gels behave as typical semiflexible polymer gels, in which the dynamic structure factor f(q,t) shows an initial monoexponential decay followed by a stretched exponential decay, f(q,t) ∼ exp -(Γqt)β. Conversely, “coarse” gels exhibit a highly arrested dynamics, in which the dynamic structure factor does not relax to zero, but decays to a plateau whose value depends on the scattering wavevector q. Moreover, only the stretched exponential decay is observed at the fastest decay times, with the exponent β = 0.63±0.07 being independently of q. This behaviour can be interpreted as given by the contributions of the internal elastic modes of many different length scales.

We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose—Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that: the effects of three-body interactions on the static structure factor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.

The dynamic structure factor (DSF) for single (labeled) chains well entangled in polymer melts has been developed based on the Rouse-Mooney picture; the DSF functions derived from the Langevin equations of the model in both discrete and continuous forms are given. It is shown that for all practical purposes, it is sufficient to use the continuous form to analyze experimental results in the "safe" q region (q being the magnitude of the scattering wave vector q) where the Rouse-segment-based theories are applicable. The DSF form reduces to the same limiting form as that of the free Rouse chain as q(2)a(2) or q(2)R(2)-->infinity (a and R being the entanglement distance and the root mean square end-to-end distance, respectively), confirming what has been expected physically. The natural reduction to the limiting form allows the full range of DSF curves to be displayed in terms of the reduced Rouse variable q(2)(Z(d)t)(0.5) in a unified way. The displayed full range represents a framework or "map," with respect to which effects occurring in different regions of the DSF may be located and studied in a consistent manner. One effect is the significant or noticeable deviations of the theoretical DSF curves from the limiting curve in the region approximately 4>q(2)(Z(d)t)(0.5)> approximately 0.1 (a time region where t<tau(1) (e)) to the faster side as qa is in the range 1-5. This is supported by the comparison of the experimental results of an entangled poly(vinylethylene) sample with the theoretical curves. The DSF functional forms predict plateaus with heights depending on the value of q-q-split plateaus-as can be experimentally observed in the time region greater than the relaxation time tau(1) (e) of the lowest Rouse-Mooney mode, when qa falls between approximately 1 and approximately 7. High sensitivity of the distribution of the q-split plateaus to a enables its value to be extracted from matching the calculated with the experimental results. The thus obtained a value for a well-entangled poly(ethylene-co-butene) polymer is in close agreement with the rheological result. It is shown that the fixed-end boundary conditions in the Rouse-Mooney model are responsible for the correct prediction of the distribution of the q-split plateaus.

We provide a description of the dynamic structure factor of a homogeneous unitary Fermi gas at low momentum and low frequency, based on the dissipative two-fluid hydrodynamic theory. The viscous relaxation time is estimated and is used to determine the regime where the hydrodynamic theory is applicable and to understand the nature of sound waves in the density response near the superfluid phase transition. By collecting the best knowledge on the shear viscosity and thermal conductivity known so far, we calculate the various diffusion coefficients and obtain the damping width of the (first and second) sounds. We find that the damping width of the first sound is greatly enhanced across the superfluid transition and very close to the transition the second sound might be resolved in the density response for the transferred momentum up to the half of Fermi momentum. Our work is motivated by the recent measurement of the local dynamic structure factor at low momentum at Swinburne University of Technology and the on-going experiment on sound attenuation of a homogeneous unitary Fermi gas at Massachusetts Institute of Technology. We discuss how the measurement of the velocity and damping width of the sound modes in low-momentum dynamic structure factor may lead to an improved determination of the universal superfluid density, shear viscosity and thermal conductivity of a unitary Fermi gas.

We investigate the short-time universal behavior of the two-dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power-law decay of the magnetization. Thus, the dynamic critical exponents θ_{m} and θ_{p}, related to the magnetic and electric order parameters, as well as the persistence exponent θ_{g}, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent z and the static critical exponents β and ν for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another, which is taken over temporal variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio β/ν exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

Using an analytic method involving continued fractions, we calculate the site-site, two-time Green's functions for a general one-dimensional crystal. These Green's functions give the electron correlations for a tight-binding model in the noninteracting-electron approximation, or the displacement correlations of a vibrating system with harmonic interatomic forces. The Green's functions can be summed in closed form to give the density of states for either model. The resulting expression depends only on the trace of a ``transfer matrix,'' and on its derivative with respect to energy. We use this formula to determine the densities of states of a large class of quasiperiodic models, and we check our results against perturbation-theory calculations of the band structure of our models. From the Green's functions, we also derive an expression for the dynamic structure factor of our vibrating-lattice model, and we derive a class of iteration relations which allow us to evaluate it very rapidly for quasiperiodic chains. We give results for two different quasicrystals, and compare them against known general restrictions on the form of the dynamic structure factor.

Calculation of the dynamic structure factor from thermal neutron time-of-flight spectra

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. In the contexts of both the single-link coherent potential approximation and a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the usual p(4) law is recovered for small momentum. On the contrary, if the disorder induces a nonvanishing density of states at zero energy, a linear behavior is obtained. The dynamical structure factor is numerically calculated in lattices as large as 96(3) and satisfactorily agrees with the analytical computations.

Reflexion absorbtion and scattering of electromagnetic irradiation by Coulomb sytems are considered. The first two can be analysed provided that transverse dielectric susceptibility of the Coulomb system is known. Practically the latter can be calculated in the limit of long wavelenghs in which case it immediately follows from proper time correlation function. The scattering the power of electromagnetic field scattered by Coulomb system depends on the dynamical structure factor of electrons Direct determination of the transverse dielectric susceptibility and the dynamical structure factor for strongly coupled Coulomb system is hardly possible. For this reason a new technique is proposed to calculate frequency dependence of absorbtion and reflection coefficients and scattering spectra. The technique is based on proper approximations for the transverse dielectric susceptibility and the dynamical structure factor with a number of fitting parameters and the sum rules (frequency moments) being used. The technique enables one to simplify considerably calculation of dynamical characteristics of nonideal Coulomb systems reducing the problem to calculating moments of these characteristics, i.e. coordinate correlation function. Frequency moments are in fact thermodynamical characteristics of Coulomb systems.

We consider cigar-shaped Fermi superfluid in the Bose-Einstein condensation (BEC)-BCS crossover. Using the polytropic form of equation of state, we derive low energy multibranch bosonic excitations and the corresponding density fluctuations in three different regimes along the crossover, namely weak-coupling BCS, unitarity, and molecular BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of the low-energy bosonic excitations by measuring the dynamic structure factor. Therefore we calculate the dynamic structure factor in those three different regimes. In Bragg spectroscopy, an actual observable is momentum imparted to the superfluid due to the Bragg potential. We also present results of the momentum imparted to the superfluid due to the Bragg pulses.

A theory is presented for the dynamic structure factor [S(K,t]) of weakly bending rods. This treatment is based on a discrete bead model for the Brownian dynamics in which all bead motions associated with bending are constrained to occur in a plane perpendicular to the end-to-end vector, thus prohibiting extension or contraction along that axis. Preset hydrodynamic interactions are incorporated in a numerically exact manner. The predicted normalized dynamic structure factor S(K,t)/S(K,0) should be valid for short times t such that the rms rotation of the end-to-end vector around any transverse axis is much less than 1.0 radian. With geometrical parameters appropriate for the M13 virus, the intensity autocorrelation function G(2) (K,t) = 1 + magnitude of S(K,t)/S(K,0)2 is calculated over a range of times and scattering vectors K for selected values of the persistence length P. The calculated G(2) (K,t) are fitted to a single exponential with unit baseline over the same range of times as the experimental photon correlation functions, and the apparent diffusion coefficients Dapp (K) are obtained from the best-fit relaxation times. For the sake of completeness, an exact expression is derived for the apparent diffusion coefficient obtained from the initial slope of the dynamic structure factor. However, this does not reduce to the known correct result in the rigid rod limit. To obtain the correct result, the limit of infinite bending rigidity must be taken before the limit of zero time. For this and other reasons, the initial slope value of Dapp (K) is not useful for weakly bending rods. Photon correlation functions are measured for the M13 virus, which is virtually identical to the often-studied fd virus. The experimental photon correlation functions are fitted over 8 relaxation times to a single-exponential plus baseline, and the Dapp (K) are calculated from the best-fit relaxation times. Theoretical curves of Dapp (K) vs K2 for selected values of P are compared with the experimental data, which are satisfactorily reproduced when P = 22000 +/- 2000 A. This dynamic value is close to the static value, P = 20000 +/- 2000 A, reported for the very similar fd virus. The most recent theories of Maeda and Fujime and their dynamic light scattering studies of fd virus are compared with the present results in some detail. Their optimum value of P is in surprisingly good agreement with the present value.

We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f-sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.

Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-$\frac{1}{2}$ square-lattice ${J}_{1}$-${J}_{2}$ model with ferromagnetic ${J}_{1}$ and competing antiferromagnetic ${J}_{2}$ interactions. To this end, we use a fermion representation, generalizing it to $N$ flavors. We begin with a spin-triplet pairing state of fermion fields, called ${Z}_{2}$ planar state, which is a stable saddle-point solution in the large-$N$ limit in a finite parameter range where the couplings ${J}_{1}$ and ${J}_{2}$ compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-$N$ expansion, we take into account fluctuations around this saddle point up to corrections of order $1/N$. The dynamical spin structure factors thus obtained signify the existence of gapless $q$-linear director-wave (spin-wave) modes at $\mathbit{q}=(0,0)$ and gapped ``gauge-field''-like collective modes at $\mathbit{q}=(\ensuremath{\pi},\ensuremath{\pi})$, whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless $q$-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate $1/{T}_{1}$ in the low-temperature regime as $1/{T}_{1}\ensuremath{\propto}{T}^{2d\ensuremath{-}1}$, where $d$ is the effective spatial dimension.