Low Wave Vector Research Articles

Vibrational Collective Dynamics of Dry Proteins in the Terahertz Region

The coherent density fluctuations of a perdeuterated dry protein have been studied by Brillouin neutron spectroscopy. Besides a nearly wavevector-independent branch located around 5 meV, a propagating mode with a linear trend at low wavevector Q is revealed. The corresponding speed of 3780 ± 130 m/s is definitely higher than that of hydrated proteins. Above Q = 0.8 Å(-1), this mode becomes overdamped, with lifetimes shorter than 0.1 ps, in fashion similar to glassy materials. The present results indicate that dry proteins sustain coherent density fluctuations in the THz frequency regime. The trend of the longitudinal modulus indicates that in this frequency range dry biomolecules are more rigid than hydrated proteins.

Two-dimensional Fermi liquids sustain surprising roton-like plasmons beyond the particle-hole band

Using inelastic neutron scattering, we have investigated the elementary excitations of an isotropic two-dimensional Fermi liquid, 3He adsorbed on graphite. We provide in this article a detailed account of the principles and methods which allowed measuring for the first time inelastic spectra on a liquid monolayer of 3He, a strong neutron absorber. We also summarise the results presented at this Conference, and review our recent experimental and theoretical work on this this interacting many-body system. At low wave-vectors, near the edge of the particle-hole band, a mode identified as the zero-sound excitation by comparison to our theoretical calculations, is found as predicted at energies much lower than in bulk 3He. The mode enters the particle-hole band, where it undergoes Landau damping. Surprisingly, however, intensity is observed in the neutron spectra at wave-vectors larger than twice the Fermi wave-vector. This new branch is interpreted as the high wave-vector continuation of the zero-sound mode, in agreement with the theory. The results open new perspectives in the understanding of the dynamics of correlated fermions.

Ionic Aggregate Structure in Ionomer Melts: Effect of Molecular Architecture on Aggregates and the Ionomer Peak

We perform a comprehensive set of coarse-grained molecular dynamics simulations of ionomer melts with varying polymer architectures and compare the results to experiments in order to understand ionic aggregation on a molecular level. The model ionomers contain periodically or randomly spaced charged beads, placed either within or pendant to the polymer backbone, with the counterions treated explicitly. The ionic aggregate structure was determined as a function of the spacing of charged beads and also depends on whether the charged beads are in the polymer backbone or pendant to the backbone. The low wavevector ionomer peak in the counterion scattering is observed for all systems, and it is sharpest for ionomers with periodically spaced pendant charged beads with a large spacing between charged beads. Changing to a random or a shorter spacing moves the peak to lower wavevector. We present new experimental X-ray scattering data on Na(+)-neutralized poly(ethylene-co-acrylic acid) ionomers that show the same two trends in the ionomer peak, for similarly structured ionomers. The order within and between aggregates, and how this relates to various models used to fit the ionomer peak, is quantified and discussed.

Non-equilibrium fluctuations on earth and in micro-gravity. The GRADFLEX experiment

We present the results of measurements of giant nonequilibrium fluctuations in a single component fluid (density fluctuations) and a mixture (concentration fluctuations) driven by applied temperature gradients, both on Earth and in space. Flight data were obtained during the September 2007 FOTON M3 mission. Spatial power spectra obtained using the shadowgraph method, during flight, confirm that the asymptotic behaviour extends to such low wave vector q, as to be limited by the sample thickness. Quantitative comparison with theory is provided, and is generally quite good. Temporal sequences of shadowgraph images for the mixture, both on Earth and during flight will be presented to emphasize the dramatic differences. Fluctuation lifetimes of thousands of seconds were observed during flight. The rugged but sensitive shadowgraph scattering method (phase fluctuations below 10 milliradians measured to within a few percent absolute accuracy) will be described briefly.

Effect of viscous dissipation on acousto-spinodal decomposition of compressible polymer solutions: Early stage analysis

A compressible Newtonian–Cahn–Hilliard fluid mixture in conjunction with the Sanchez–Lacombe equation of state is used to develop a one-dimensional linear model that describes acousto-spinodal decomposition by pressure-induced phase separation in compressible polymer solutions. The integrated model extends previous work (Rasouli and Rey, 2011) on inviscid acousto-spinodal decomposition of compressible polymer solution. Acousto-spinodal decomposition by pressure-induced phase separation couples density wave phenomena with mass transfer driven by spinodal decomposition process. For dissipative acousto-spinodal decomposition the relevant parameters are the ratio of diffusion speed to density wave speed Mach number (Ma) and the Reynolds number (Re). Under diffusion limitation (low Ma) polymer concentration gradients act as a sound source in a wave equation that feeds back into the polymer concentration balance equation, producing oscillatory spinodal decomposition. Phase diagrams in terms of Mach and Reynolds numbers show that under low viscosity, oscillatory growth is independent of viscous dissipation and only arises under low Ma number. On the other hand, under high viscosity effects, oscillatory spinodal decomposition may be generated by increasing Re or by decreasing Ma. The viscous attenuation of spinodal decomposition kinetics and the amplitude of density waves are characterized. Total structure factor calculations are qualitatively consistent with experiments at low wave vectors. Acousto-spinodal decomposition is a novel process that offers new processing and characterization routes for polymer solutions and melts.

Manipulating thermal conductivity through substrate coupling

We report an approach to the thermal conductivity manipulation-substrate coupling. Generally, the phonon scattering with substrates can decrease the thermal conductivity, as observed in recent experiments. However, we find that at certain regions the coupling to substrates can increase the thermal conductivity due to a reduction of anharmonic phonon scattering induced by shift of the phonon band to the low wave vector. In this way, the thermal conductivity can be efficiently manipulated via coupling to different substrates, without changing or destroying the material structures. This idea is demonstrated by calculating the thermal conductivity of modified double-walled carbon nanotubes and also by the ice nanotubes coupled within carbon nanotubes.

Thermal fluctuations of clusters with the long-range interaction

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.

Acousto-spinodal decomposition of compressible polymer solutions: Early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.

Effect of Polymer Architecture and Ionic Aggregation on the Scattering Peak in Model Ionomers

We perform molecular dynamics simulations of coarse-grained ionomer melts with two different architectures. Regularly spaced charged beads are placed either in the polymer backbone (ionenes) or pendant to it. The ionic aggregate structure is quantified as a function of the dielectric constant. The low wave vector ionomer scattering peak is present in all cases, but is significantly more intense for pendant ions, which form compact, discrete aggregates with liquidlike interaggregate order. This is in qualitative contrast to the ionenes, which form extended aggregates.

Direct Fourier Analysis of Lipid Bilayer Fluctuations in Particle-Based Simulations

The particles in the lipid bilayer undergo fluctuations from their equilibrium positions. These motions are best described in terms of correlated monolayer motions (undulations), anticorrelated monolayer motions (thickness fluctuations) and number density correlations, both within and between the monolayers. Particle-based computer simulations, atomistic or coarse-grained, can be used to calculate the spectra of these equilibrium fluctuations. This has conventionally been done by interpolating the particle structure onto a grid to facilitate for the discrete Fourier transform. However, the gridding introduces artifacts and an upper cutoff on the available wave vectors. Here, we instead analyze the simulations directly in Fourier space, circumventing the need for a grid approximation. The fluctuation spectra can then be calculated at high precision up to any wave vector desired, and the low wave vectors are only bounded by the size of the lateral simulation box. From the analysis, a picture emerges which bridges a continuum regime at low wave vectors, and a domain that can be attributed to the in-plane bilayer molecular structure at high wave vectors. We calculate spectra for undulations, thickness fluctuations, and the spectrum of the number density along the undulating surface, and we discuss how the shape of the spectra in the low-wave vector and high-wave vector regimes are related to membrane material constants, and give some predictions from an analytical theory based on equilibrium correlation functions.

Transmission characteristics in double and triple non-uniform magnetic barriers based on graphene

We evaluate the transmission and the conductance through double and triple non-uniform magnetic barriers in graphene-based nanostructures. The results indicate that non-uniform magnetic modulation results in rich transport properties. Compared with uniform double barrier magnetic structures, both the transmission and the conductance are drastically reduced through non-uniform ones. In the non-uniform triple magnetic barriers, the transmission and the conductance exhibit complicated oscillations, which vary with the width or the height of magnetic barriers. The non-uniformity introduced by altering the height and width of magnetic barriers have different effects on the transmission. For the magnetic barriers with different heights, the transmission is suppressed greatly in both low and high incident wave vector regions, while for the magnetic barriers with different widths, the obvious suppression occurs in the low incident wave vector region.

The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides

We successfully used the tight binding theory to derive the extended discrete nonlinear Schrödinger equation to describe the soliton propagation and to obtain the soliton propagation criteria (SPC) in the nonlinear photonic-crystal waveguides (PCWs) and coupled resonant optical waveguides (CROWs) containing Kerr media. From these criteria, we obtain the soliton-propagating region of CROWs in different numbers of separated rods and strengths of self-phase modulation (SPM). The defined soliton-propagating regions coincide with the regions of modulation instability in the CROWs. In the PCWs, the positive Kerr coefficient medium needs to be added to support the pulse propagation in low frequency or low wave vector region of the dispersion curve; while negative Kerr effect is for high frequency case. Due to the linear combination of various cosine harmonic functions in the dispersion relations of both CROWs and PCWs, the pulse broadening which is mainly caused by the third-order dispersion at SPC is the lowest at the boundary of dispersion curves. However, due to the different magnitudes of coupling coefficients in CROWs and PCWs, the group velocity, dispersion and strength of SPM in CROWs are all smaller than those in PCWs.

Collective Thermal Diffusion of Silica Colloids Studied by Nonlinear Optics

We investigate the collective thermal diffusion of silica charged spheres in Sulpho-Rhodamine B/water solution at different concentrations by measuring time-dependent thermal and Soret lensings. We show a significant concentration-dependence of the thermal diffusion coefficient D(T), not previously reported. Moreover, the results clearly show that both mass diffusion and Soret coefficient are collective quantities being strongly dependent on the particles' packing fraction. Our Z-scan setup allows us to investigate the dynamics of the system at low wave vector, which addresses the influence of the interparticle interactions on the thermal diffusion of the colloids.

Observation of Zero-Sound at Atomic Wave-Vectors in a Monolayer of Liquid 3He

The elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid 3He adsorbed on graphite preplated by a monolayer of solid 4He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid 3He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk 3He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle-hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid 4He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmon excitations in electronic systems).

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty epsilon. This is done to vary systematically the dimensionless compressibility g of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various static properties at constant overall monomer density. The compressibility is obtained directly from the low-wave vector limit of the static structure factor. We consider, e.g., the intrachain bond-bond correlation function P(s) of two bonds separated by s monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed (s<<g) the chains are swollen according to the classical Fixman expansion where, e.g., P(s) approximately g(-1)s(-1/2). More importantly, the polymers behave on larger distances (s>>g) like swollen chains of incompressible blobs with P(s) approximately g(0)s(-3/2).

Fast Dynamics of Semiflexible Chain Networks of Self-Assembled Peptides

We present the first neutron spin echo (NSE) measurements of self-assembling peptide hydrogel networks to study the fibril dynamics on the nanometer and nanosecond length and time scales. MAX1 and MAX8 are synthetic beta-hairpin peptides that undergo triggered self-assembly at the nanoscale to form a physically cross-linked network of fibrils with a defined cross-section. When subjected to physiological pH and ionic strength (pH 7.4, 150 mM NaCl), the soluble peptides fold into a beta-hairpin and, subsequently, self-assemble to form a structurally rigid hydrogel stabilized by noncovalent cross-links. The sequence of MAX8 is identical to MAX1 with the exception of one single amino acid substitution that reduces the net charge on the peptide. As a result, faster folding and self-assembly kinetics are observed for MAX8 at the same peptide concentration and identical buffer conditions, and gels with a larger storage modulus are formed. NSE measurements of the peptide hydrogels demonstrate that the self-assembled peptide fibrils can be described as semiflexible chains on nanolength and time scales. Alteration of the peptide sequence affected the nanoscale dynamics of the hydrogels but not to an extent comparable to the large difference observed in the bulk viscoelasticity. Small angle neutron scattering (SANS) of the hydrogels reveals increased scattering for MAX8 at low wavevectors, an indication of a heterogeneous network with a tighter mesh size. Therefore, we conjecture that the difference in elastic modulus arises from differences in assembly kinetics that result in increased fibrillar branching and physical cross-links rather than a change in the fibril nanostructure or persistence length.

Liquid–liquid transitions, crystallization and long range fluctuations in supercooled yttrium oxide–aluminium oxide melts

Employing small angle X-ray scattering (SAXS) and wide angle X-ray scattering (WAXS) combined with laser-heated aerodynamic levitation has enabled different transitions in supercooled yttrium oxide–aluminium oxide to be distinguished. These include liquid–liquid phase transitions as well as high temperature crystallization for different compositions. Prerequisites for avoiding crystallization in order to reveal polyamorphic phase separation in the supercooled state are established. We also show how the rise in SAXS intensity at low wavevectors can be used to identify correlation distances in long range fluctuations in high temperature melts. These distances appear to scale with melt viscosity and to extend temporarily during liquid–liquid transitions.

Dynamic Structure Factors from Lipid Membrane Molecular Dynamics Simulations

Dynamic structure factors for a lipid bilayer have been calculated from molecular dynamics simulations. From trajectories of a system containing 1024 lipids we obtain wave vectors down to 0.34 nm−1, which enables us to directly resolve the Rayleigh and Brillouin lines of the spectrum. The results confirm the validity of a model based on generalized hydrodynamics, but also improves the line widths and the position of the Brillouin lines. The improved resolution shows that the Rayleigh line is narrower than in earlier studies, which corresponds to a smaller thermal diffusivity. From a detailed analysis of the power spectrum, we can, in fact, distinguish two dispersive contributions to the elastic scattering. These translate to two exponential relaxation processes in separate time domains. Further, by including a first correction to the wave-vector-dependent position of the Brillouin lines, the results agree favorably to generalized hydrodynamics even up to intermediate wave vectors, and also yields a 20% higher adiabatic sound velocity. The width of the Brillouin lines shows a linear, not quadratic, dependence to low wave vectors.

Effects of porous confinement on the structural properties of the Gaussian core model

We have investigated the structural properties of a fluid in which particles, interacting via soft potentials, are imbibed into a disordered porous structure built up by soft particles. Using a Gaussian potential for all interactions involved, we determine via Monte Carlo simulations and integral-equation theory the fluid–fluid, fluid–matrix, connected, and blocked structure factors. Within the explored range of state parameters, the fluid–fluid structure factors display a distinct pre-peak, which we identify as a fingerprint of the structure of the matrix. We show that this feature at low wave-vectors arises from contributions of blocked correlations to the fluid–fluid structure factor. We argue that a similar feature may be found also in systems in which particles interact via harshly repulsive potentials. On the other hand, the variation of the main peak of the fluid–fluid structure factor resembles the behaviour of the equilibrium Gaussian core model fluid. In particular, the height of the main peak changes non-monotonically with increasing fluid density at fixed matrix density. Finally, we analyse the effect of a mismatch between the temperature of the fluid and the temperature of the matrix on the structural properties of the system.

Membrane Tension Lowering Induced by Protein Activity

Using videomicroscopy we present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin pumps. When the pumps are activated, we observe a significant increase of the fluctuations in the low wave vector region, which we interpret as due to a lowering of the effective tension of the membrane.