Relaxation Of Fluctuations Research Articles

Strain dependence of the nematic fluctuation relaxation in liquid-crystal elastomers

Dynamic light scattering on a nematic liquid-crystal elastomer was performed as a function of deformation perpendicular to the director and along the director. We show that the relaxation rate of the nematic director fluctuations increases with strain along the director, as expected from the theory of semisoft elasticity. Deformation applied perpendicular to the director, on the other hand, decreases the relaxation rate to a very small value at the onset of the soft elastic response, revealing the existence of a dynamic soft mode. The results are in complete agreement with the theory of semisoft elasticity and allow us to determine all the constants of the model.

Concentration fluctuations in a binary glass former investigated by x-ray photon correlation spectroscopy

We investigate structure and dynamics of concentration fluctuations in the binary glass former methyl-tetrahydrofuran and oligomeric methyl metacrylate by photon correlation spectroscopy with partially coherent x-rays from a synchrotron source. Although the system is macroscopically well miscible and optically clear in the full temperature range, calorimetric and dielectric measurements reveal two distinct glass transition temperatures. The relaxation of long range concentration fluctuations turns out to be diffusive and exponential only well above the upper glass transition temperature. As the characteristic time tau(cf) for concentration fluctuations shows a much weaker temperature dependence than the alpha-relaxation both traces finally intersect upon lowering the temperature. Thus, close to T(g), the concentration fluctuations show pronounced features of out-of-equilibrium dynamics such as compressed relaxation functions and a crossover to a ballistic wave vector dependence of tau(cf), like previously observed in various soft matter systems. Moreover, the analysis of time-resolved correlation functions reveals that the relaxation of concentration fluctuations around T(g) involves pronounced dynamic heterogeneities.

Shape fluctuations of nearly spherical lipid vesicles and emulsion droplets

It is known that the relaxation of the shape fluctuations of nearly spherical lipid vesicles is accompanied by a lateral displacement of the monolayers, comprising their bilayers. In this work a dissipation mechanism of the mechanical energy stored in the fluctuation is revealed that concerns the viscous friction of the flow in the liquid around the vesicle caused by this displacement. The time correlation functions of each of the vesicle's fluctuation modes are calculated as a function of the mechanical and rheological properties of the system which are the tension of the vesicle bilayer, its bending elasticities at free and blocked flip-flop, the viscosities of the liquids bathing the bilayer, the friction coefficient between the two monolayers, as well as the vesicle's dimensions: its bilayer thickness and radius. The correlations of the shape fluctuations of nearly spherical emulsion droplets are also calculated for different viscosities of the liquid inside and outside the droplet.

Dynamic Signatures of Microphase Separation in a Block Copolymer Melt Determined by X-ray Photon Correlation Spectroscopy and Rheology

The relationship between structure and dynamics in a polystyrene-polyisoprene block copolymer melt in the vicinity of the order−disorder transition was studied by small-angle X-ray scattering (SAXS), X-ray photon correlation spectroscopy (XPCS), and rheology. Rheological measurements on the disordered state indicate the presence of a fast process arising from the relaxation of polyisoprene chains and a slow process resulting predominantly from the relaxation of concentration fluctuations. In contrast, XPCS measurements of the disordered phase are dominated by diffusion of micelles. Time-resolved SAXS, XPCS, and rheology experiments on samples quenched from disorder-to-order reveal the existence of two regimes. While the microscopic relaxation time, measured by XPCS, increases after all of the quenches, SAXS and rheological signatures of ordering are only seen when the quench depth exceeds a critical value of 10 °C. For quenches 5 °C below the order-to-disorder transition temperature, no changes in the SAXS profiles and rheological properties are observed on experimental time scales. It is evident that nucleation barriers preclude the formation of the ordered phase during shallow quenches. The time-resolved rheology measurements enable estimation of the nucleation barriers that are responsible for the observations in the shallow quench regime.

Integrated and dispersed photon echo studies of nitrile stretching vibration of 4-cyanophenol in methanol

By means of integrated and dispersed IR photon echo measurement methods, the vibrational dynamics of C-N stretch modes in 4-cyanophenol and 4-cyanophenoxide in methanol is investigated. The vibrational frequency-frequency correlation function (FFCF) is retrieved from the integrated photon echo signals by assuming that the FFCF is described by two exponential functions with about 400 fs and a few picosecond components. The excited state lifetimes of the C-N stretch modes of neutral and anionic 4-cyanophenols are 1.45 and 0.91 ps, respectively, and the overtone anharmonic frequency shifts are 25 and 28 cm(-1). At short waiting times, a notable underdamped oscillation, which is attributed to a low-frequency intramolecular vibration coupled to the CN stretch, in the integrated and dispersed vibrational echo as well as transient grating signals was observed. The spectral bandwidths of IR absorption and dispersed vibrational echo spectra of the 4-cyanophenoxide are significantly larger than those of its neutral form, indicating that the strong interaction between phenoxide and methanol causes large frequency fluctuation and rapid population relaxation. The resonance effects in a paradisubstituted aromatic compound would be of interest in understanding the conjugation effects and their influences on chemical reactivity of various aromatic compounds in organic solvents.

Multiscale dynamics of pretransitional fluctuations in the isotropic phase of a lyotropic liquid crystal

Using an improved static and dynamic light-scattering technique, we have observed multiscale relaxation of the pretransitional fluctuations in the isotropic phase of a cromolyn aqueous solution, a lyotropic liquid crystal where rods are formed by aggregates of disklike molecules. We have detected the onset of cromolyn aggregation about 12 degrees C above the transition temperature. The onset is manifested by the emergence of strong scattering due to the fluctuations of local anisotropy and by the split of the diffusion dynamics into two distinctly different modes, one associated with the relatively fast diffusion of monomer-size particles and the other one with the much slower diffusion of the cromolyn aggregates. A third observed dynamic mode is associated with the pretransitional slowing down of fluctuations of the local anisotropy. This mode behaves differently in polarized and depolarized light scattering, due to a coupling between fluctuations of the local-anisotropy and velocity fluctuations.

A fluctuation–relaxation relation for homogeneous, isotropic turbulence

A Liouville-type equation is solved perturbatively for the exact pdf of fluctuating velocities by expansion about an invariant Gaussian measure, which is an approximation to the symmetric part of the pdf and is constrained to give the correct covariance. The antisymmetric part of the pdf is calculated to the lowest nontrivial order and leads to closed equations for the covariance in terms of a response function which arises from the Liouville operator averaged against the ground-state distribution. As the latter is a stationary Gaussian pdf, we obtain an expression for the system response which is linear in the covariance.

Critical phenomena at electrosorption of organic compounds on electrodes

Problems associated with the effect of surfactants on polarization characteristics of a liquid metal electrode-electrolyte interface, as well as the fluctuations of its adsorption coverage, are considered. For the effective adsorption potential, the analytical dependence of which on the state parameters is determined by a nonequilibrium surface pressure, an expression derived earlier in terms of a quasichemical approximation is proposed. It is shown that the excessive differential capacitance of the interface, associated with the specific adsorption of surfactants, turns to infinity on the spinodal. The relaxation and correlation of equilibrium fluctuations of the adsorption process completeness in the interface plane at different electrode potentials are studied. Expressions for the correlation length of fluctuation are obtained. Their fundamental importance as the natural scale for the size and the duration of a nanochemical process is discussed. It is shown that the relaxation time and the correlation radius of fluctuations turn to infinity at the adsorption phase stability limit.

Introducing a hybrid radiative transfer method for smoothed particle hydrodynamics

A new means of incorporating radiative transfer into smoothed particle hydrodynamics (SPH) is introduced, which builds on the success of two previous methods - the polytropic cooling approximation as devised by Stamatellos et al (2007), and flux limited diffusion (e.g. Mayer et al 2007). This hybrid method preserves the strengths of its individual components, while removing the need for atmosphere matching or other boundary conditions to marry optically thick and optically thin regions. The code uses a n on-trivial equation of state to calculate temperatures and opacities of SPH particles, which captures the effects of H2 dissociation, H 0 ionisation, He 0 and He + ionisation, ice evaporation, dust sublimation, molecular absorption, bound-free and free-free transitions and elec tron scattering. The method is tested in several scenarios, including: (1) the evolution of a 0.07 M⊙ protoplanetary disc surrounding a 0.5 M⊙ star; (2) the collapse of a 1 M⊙ protostellar cloud, and (3) the thermal relaxation of temperature fluctuations in a static homogeneous sphere.

Vibrational Spectral Diffusion in Supercritical D2O from First Principles: An Interplay between the Dynamics of Hydrogen Bonds, Dangling OD Groups, and Inertial Rotation

We have presented a first principles theoretical study of vibrational spectral diffusion and underlying molecular dynamics in supercritical heavy water at three different densities ranging from 1.1 to 0.39 g cm(-3). Our calculations are based on ab initio molecular dynamics simulations for trajectory generation and wavelet analysis for frequency calculations, and no empirical potential parameters are involved in the present study. Calculations of OD frequency-distance (D...O) conditional probabilities reveal that the rate of increase of OD frequency with D...O distance gradually decreases with lowering of density. Also, the maximum probability moves to a higher frequency-larger D...O distance region with decreasing density due to weakening of hydrogen bonds and increased number of dangling OD bonds in these systems. The correlations between the stretch frequencies and the electric fields on D atoms (along OD bonds) are also calculated, and the magnitude of such correlations is found to be similar to those of frequency-distance (D...O) correlations for the present supercritical systems. The vibrational spectral diffusion in supercritical water shows two time scales: one around 100 fs or less and the other in the region of 150-600 fs with the shorter time scale carrying the larger weight. It is found that, unlike ambient water, for supercritical water the slower component of the spectral diffusion does not necessarily capture the hydrogen bond dynamics at all densities. Rather, an interplay between the dynamics of hydrogen bonds, dangling OD groups, and the inertial rotation of OD bonds determines the times scales of spectral diffusion in a rather subtle manner. While the slower component of spectral diffusion at high density is determined by the lifetimes of hydrogen bonds, it is the lifetime of dangling OD groups that decides the slower component at low density, and the reverse holds for the faster components. The fast inertial rotation also shows up as the faster component of spectral diffusion. Dynamical correlations between the relaxation of frequency fluctuations and that of electric field fluctuations are also explored. Our calculations of rotational dynamics show, unlike ambient water, no frequency dependence of the rotational relaxation of OD bonds because of faster interconversion of different hydrogen bonding states and a reduced role of the hydrogen bond strength as a significant determinant of rotational motion caused by higher thermal energy of supercritical states.

Diffusion of colloidal fluids in random porous media

The diffusive relaxation of a colloidal fluid adsorbed in a porous medium depends on many factors, including the concentration and composition of the adsorbed colloidal fluid, the average structure of the porous matrix, and the nature of the colloid-colloid and colloid-substrate interactions. A simple manner to describe these effects is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural properties. Within this model one may describe the relaxation of concentration fluctuations of the adsorbed fluid by simply setting to zero the short-time mobility of one species (the porous matrix) in a theory of the dynamics of equilibrium colloidal mixtures, or by extending such dynamic theory to explicitly consider the porous matrix as a random external field, as recently done in the framework of mode coupling theory [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)]. Here we consider the first approach and employ the self-consistent generalized Langevin equation (SCGLE) theory of the dynamics of equilibrium colloidal mixtures, to describe the dynamics of the mobile component. We focus on the short- and intermediate-time regimes, which we compare with Brownian dynamics simulations involving a binary mixture with screened Coulomb interactions for two models of the average static structure of the matrix: a porous matrix constructed by quenching configurations of an equilibrium mixture in which both species were first equilibrated together, and a preexisting matrix with prescribed average structure, in which we later add the mobile species. We conclude that in both cases, if the correct static structure factors are provided as input, the SCGLE theory correctly predicts the main features of the dynamics of the permeating fluid.

Viscosity-Dependent Protein Dynamics

Spectrally resolved stimulated vibrational echo spectroscopy is used to investigate the dependence of fast protein dynamics on bulk solution viscosity at room temperature in four heme proteins: hemoglobin, myoglobin, a myoglobin mutant with the distal histidine replaced by a valine (H64V), and a cytochrome c 552 mutant with the distal methionine replaced by an alanine (M61A). Fructose is added to increase the viscosity of the aqueous protein solutions over many orders of magnitude. The fast dynamics of the four globular proteins were found to be sensitive to solution viscosity and asymptotically approached the dynamical behavior that was previously observed in room temperature sugar glasses. The viscosity-dependent protein dynamics are analyzed in the context of a viscoelastic relaxation model that treats the protein as a deformable breathing sphere. The viscoelastic model is in qualitative agreement with the experimental data but does not capture sufficient system detail to offer a quantitative description of the underlying fluctuation amplitudes and relaxation rates. A calibration method based on the near-infrared spectrum of water overtones was constructed to accurately determine the viscosity of small volumes of protein solutions.

Slow relaxation mode in concentrated oil-in-water microemulsions consisting of repulsive droplets

The present contribution reports on the observation of two diffusive relaxation modes in a concentrated microemulsion made of repulsive droplets. These two modes can be interpreted in the frame of Weissman's and Pusey's theoretical pioneering works. The fast mode is associated to the collective diffusion of droplets whereas the slow one corresponds to the relaxation of droplet concentration fluctuations associated with composition and/or size. We show that (i) repulsive interactions considerably slow down the latter and (ii) a generalized Stokes Einstein relationship between its coefficient of diffusion and the Newtonian viscosity of the solutions, similar to the Walden's rule for electrolytes, holds for concentrated microemulsion systems made of repulsive droplets.

Nonequilibrium Thermodynamic Model of Water-in-Water Emulsions

The dynamic behavior of highly permeable interfaces in phase-separated biopolymer solutions, liposomes, polymersomes, and colloidosomes is investigated. Using nonequilibrium thermodynamics, an expression for the correlation function of the height of a flat interface is derived for a multicomponent system, incorporating the effects of mass transfer across the interface. In addition, an expression is derived for the relaxation time of the height correlation function. This relaxation time is calculated for a phase-separated gelatin−dextran−water system. Comparing our expression with the expression for an impermeable interface shows that mass transfer has a significant impact on the fluctuations of the interface. At small values for the amplitude, the relaxation of fluctuations is completely dominated by the permeability of the interface. At high values for the amplitude, the relaxation is dominated by the viscosities and densities of the bulk phases. In this regime, the long-time limit of the height correlat...

Dynamic scaling and background relaxation in the ultrasonic spectra of the ethanol–dodecane critical mixture

Ultrasonic attenuation spectroscopy of a noncritical ethanol–dodecane mixture revealed a low frequency relaxation term. Considering this term in the spectra for the mixture of critical composition the experimental scaling function agrees well with the predictions of the dynamic scaling theory. Dynamic light scattering and shear viscosity measurements yield the amplitudes ξ 0 = (0.37 ± 0.02) nm and Γ 0 = (6.4 ± 0.3) × 10 9 s −1 for the fluctuation correlation length and relaxation rate of concentration fluctuations, respectively. The adiabatic coupling constant results as small as ∣ g∣ = 0.13 ± 0.03 from the ultrasonic spectra and as g = 0.094 ± 0.01 from the pressure dependence of the critical temperature and the thermal expansion coefficient.

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.

Asymmetric fluctuation–relaxation paths in FPU models

A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim predicts a temporal asymmetry in the fluctuation–relaxation paths of certain observables of nonequilibrium systems in local thermodynamic equilibrium. We find temporal asymmetries in the fluctuation–relaxation paths of a form of local heat flow, in the nonequilibrium FPU- β model of Lepri, Livi and Politi.

Diffusion behavior of pharmaceutical O/W microemulsions studied by dynamic light scattering

Dynamic light scattering experiments have been performed at various concentrations, of pharmaceutical oil-in-water microemulsions consisting of Eutanol G as oil, a blend of a high (Tagat O2) and a low (Poloxamer 331) hydrophilic–lipophilic balance surfactant, and a hydrophilic phase (propylene glycol/water). We probe the dynamics of these microemulsions by dynamic light scattering. In the measured concentration range, two modes of relaxation were observed. The faster decaying mode is ascribed classically to the collective diffusion D c (total droplet number density fluctuation). We show that the slow mode is also diffusive and suggest that its possible origin is the relaxation of polydispersity fluctuations. The diffusion coefficient associated with this mode is then the self-diffusion D s of the droplets. It was found that D c and D s had opposite volume fractions of oil plus surfactants (ϕ) dependence and a common limiting value D 0 for ϕ=0. Average hydrodynamic radius (R h=10.5 nm) of droplets was calculated from D 0. R h is supposed to compose the inner core, a surfactant film including possible solvent molecules, which migrate with the droplet. The concentration dependence of diffusion coefficients reflects the effect of hard sphere and the supplementary repulsive interactions which arises due to loss of entropy, when absorbed chains of surfactant intermingle on the close approach of the two droplets. This mechanism could also explain the observed stability of our systems. The estimated extent of polydispersity is 0.22 from the amplitude of slower decaying mode. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least three orders of magnitude longer than the estimated time between droplet collisions.

A modified tube dilatation theory for the relaxation of entangled linear polymer melts

In this paper, the “tube dilatation” or “tube Enlargement” concept introduced by Marrucci, is revisited in the case of broad entangled linear polymer melts. Using the tube fluctuation relaxation function of Doi and a linear mixing rule, the model implicitly contains both the features of double reptation and time modification by tube renewal. It has been shown that theoretical arguments of both double reptation with tube renewal and tube dilatation can be used to take into account the effect of polydispersity on the distribution of relaxation times. The model has been tested for some polymers with various N/Ne values. However, experiments indicate that the loss of only one entanglement does not systematically induce a change of the relaxation times through a constraint release and tube renewal process. The freeing of a critical volume, larger than the volume of a tube segment, is required to induce an efficient dilution effect on relaxation times.

Self-Diffusion and Collective Diffusion of Charged Colloids Studied by Dynamic Light Scattering

A microemulsion of decane droplets stabilized by a nonionic surfactant film is progressively charged by substitution of a nonionic surfactant molecule by a cationic surfactant. We check that the microemulsion droplets remain identical within the explored range of volume fraction (0.02-0.18) and of the number of charges per droplet (0-40). We probe the dynamics of these microemulsions by dynamic light scattering. Despite the similar structures of the uncharged and charged microemulsions, the dynamics are very different. In the neutral microemulsion, the fluctuations of polarization relax, as is well-known, via the collective diffusion of the droplets. In the charged microemulsions, two modes of relaxation are observed. The fast one is ascribed classically to the collective diffusion of the charged droplets coupled to the diffusion of the counterions. The slow one has, to our knowledge, not been observed previously neither in similar microemulsions nor in charged spherical colloids. We show that the slow mode is also diffusive and suggest that its possible origin is the relaxation of local charge fluctuations via the local exchange of droplets bearing different numbers of charges. The diffusion coefficient associated with this mode is then the self-diffusion coefficient of the droplets.