Correlation Length Of Density Fluctuations Research Articles

Critical point for membrane bilayer formation

Unilamellar liposomes often are employed in investigations of lipid-protein interactions and the delivery of drugs in therapies for disease. Also, related lipid-containing nanoparticles have been developed as elements of a new class of mRNA vaccines. We show that only unilamellar films form in equilibrium lipid dispersions, at temperature values {T*} that depend on the identities of the lipids (e.g., T* ≈ 29 °C for DMPC). Thermodynamic analysis confirms that films at air-water surfaces can be used to monitor the properties of the lipid vesicles that form in the dispersion. When T > T*, critical exponents describing film properties as T approaches T* are μ ≈ 1.4 and ν ≈ 0.7, which are close to values for the interfacial tension and the correlation length of density fluctuations at fluid interfaces. These results, and observations that within the bilayer the lateral diffusion of fluorescent lipid probes demonstrates increases at T*, suggest that unilamellar vesicles at T* are a transition state between two different multilamellar structures. We generalize the thermodynamic arguments to explain the linkage between lipid structures in the surface and bulk dispersion within more complex samples, showing that dispersions containing total lipid extracts of cell membranes have properties similar to those in dispersions containing single lipids. Information from various independent studies indicates that T* noted for bilayer membranes of a population of cells is identical to the temperature at which the growth or gestation of the cells occurs in vivo. Examples include whole-cell lipid extracts obtained from bacteria, and poikilothermic and homeothermic animals.

Statistical properties and correlation length in star-forming molecular clouds

Observations of molecular clouds (MCs) show that their properties exhibit large fluctuations. The proper characterization of the general statistical behavior of these fluctuations, from a limited sample of observations or simulations, is of prime importance to understand the process of star formation. In this article, we use the ergodic theory for any random field of fluctuations, as commonly used in statistical physics, to derive rigorous statistical results. We outline how to evaluate the autocovariance function (ACF) and the characteristic correlation length of these fluctuations. We then apply this statistical approach to astrophysical systems characterized by a field of density fluctuations, notably star-forming clouds. When it is difficult to determine the correlation length from the empirical ACF, we show alternative ways to estimate the correlation length. Notably, we give a way to determine the correlation length of density fluctuations from the estimation of the variance of the volume and column-density fields. We show that the statistics of the column-density field is hampered by biases introduced by integration effects along the line of sight and we explain how to reduce these biases. The statistics of the probability density function (PDF) ergodic estimator also yields the derivation of the proper statistical error bars. We provide a method that can be used by observers and numerical simulation specialists to determine the latter. We show that they (i) cannot be derived from simple Poisson statistics and (ii) become increasingly large for increasing density contrasts, severely hampering the accuracy of the high end part of the PDF because of a sample size that is too small. As templates of various stages of star formation in MCs, we then examine the case of the Polaris and Orion B clouds in detail. We calculate, from the observations, the ACF and the correlation length in these clouds and show that the latter is on the order of ~1% of the size of the cloud. This justifies the assumption of statistical homogeneity when studying the PDF of star-forming clouds. These calculations provide a rigorous framework for the analysis of the global properties of star-forming clouds from limited statistical observations of their density and surface properties.

On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover

The problem of large-density variations in supercooled and ambient water has been widely discussed in the past years. Recent studies have indicated the possibility of nanometer-sized density variations on the subpicosecond and picosecond time scales. The nature of fluctuating density heterogeneities remains a highly debated issue. In the present work, we address the problem of possible association of such density variations with the dynamics of terahertz longitudinal acoustic-like modes in liquid water. Our study is based on the fact that the subpicosecond dynamics of liquid water are essentially governed by the structural relaxation. Using a mode coupling theory approach, we found that for typical values of parameters of liquid water, the dynamic mechanism coming from the combination of the structural relaxation process and the finiteness of the amplitude of terahertz longitudinal acoustic-like mode gives rise to a soliton-like collective mode on a temperature-dependent nanometer length scale. The characteristics of this mode are consistent with the estimates of the amplitudes and temperature-dependent correlation lengths of density fluctuations in liquid water obtained in experiments and simulations. Thus, the fully dynamic mechanism could contribute to the formation and dynamics of fluctuating density heterogeneities. The soliton-like collective excitations suggested by our analysis may be relevant to different phenomena connected with supercooled water and can be expected to be associated with some ultrafast biological processes.

Microphase Separation in Poly(Imide Siloxane) Copolymer

The comparative analysis of microheterogeneous structure of the surface of films of amorphous aromatic polyetherimide: poly[4, 4'-bis(4''-N-phenoxy)diphenylsulfon]imide of 1,3-bis(3', 4-dicarboxyphenoxy)benzene (PEI) and poly(imide siloxane) block copolymer (PSI) containing PEI blocks and blocks of dimethylsiloxane units was performed according to electron microscopy. It was shown that anisotropy, long-range order, and the correlation length of density fluctuations increase in PSI film as compared to PEI. PSI samples are characterized by asymmetrical biaxial surface texture, as opposed to PEI, which exhibits axial texture. Periodic density oscillations are observed along the directions of axes of PSI structure at the micron scale. The obtained results evidence microphase separation in PSI film caused by spatially oriented contact interactions between the blocks of dimethylsiloxane units.

Molecular weight dependence of the physical aging of polycarbonate

In our previous paper, we reported that the impact value of polycarbonate (PC) increases with increasing molecular weight and decreases upon annealing [Polymer 2012, 53, 895–896]. To clarify these phenomena, the effects of molecular weight and heat treatment on the fracture of PC are investigated in this study. The results show that the stress for craze nucleation increased as the molecular weight increased but was not affected by annealing. The shear modulus and bulk modulus do not exhibit molecular weight dependence, but annealing resulted in a slightly increased shear modulus and a decreased bulk modulus. Furthermore, the amplitude and correlation length of density fluctuations of the Debye–Buche mode in small-angle X-ray scattering profiles were shown to increase upon annealing. On the basis of these results, it is suggested that, as the molecular weight increases, the toughness of PC is enhanced because the increase in molecular weight increases the stress of slippage for entangled molecular chains. In addition, it is proposed that the change in the fraction of fine voids resulting from density fluctuations may affect the toughness, resulting in the reduced toughness observed for annealed PC.

Superlattices of lamellae in microporous oriented polyolefine films

The structure and mechanism of the formation of superlattices lamellae in microporous polyolefine (polyethylene and polypropylene) films obtained by polymer melt extrusion followed by annealing, uniaxial extension, and thermal fixation stages have been studied by scanning electron and atomic-force microscopy. It has been shown that oriented anisometric particles, i.e., lamellae aggregates, are formed in films as the spin draw ratio λf increases. At the stage of uniaxial extension (pore formation) of annealed films, a particle ensemble transforms to spatial superlattices of lamellae. Numerical processing of electron microscopy images of the film surface show that the nonmonotonic dependences of the correlation length of density fluctuations and the ratios of the alternation period of particles along extension to their thickness on the parameter λf correspond to a unified mechanism of lamellae ordering.

Universal Shape of the Fluid Density Profiles Near a Solid Boundary: LJ Vapor Near Weakly Attractive and Hard Walls

The universality class of the fluid critical behavior near surfaces with vanishing fluid-wall attraction is studied by the analysis of the density profiles of the saturated Lennard-Jones (LJ) vapor near hard and weakly attractive walls. The depletion of the fluid density ρ(z) toward such surfaces can be described in a universal way by the exponential law ρ(z) = ρ0 (1 − 0.5 exp(−z/ξ)) at z/ξ > 1, where z is the distance to the surface, ξ is the correlation length and ρ0 is the density of the saturated bulk vapor. The surface critical behavior of fluids exhibiting density depletion at the critical point agrees with the universality class of the ordinary transition in Ising magnet at zero or vanishing surface field. In the narrow pore with hard walls, the perturbation of a vapor by a surface is enhanced, as the density of the saturated vapor in the pore approaches the density of the bulk vapor spinodal and the correlation length of density fluctuations increases.

Correlation reflectometry at TEXTOR

In high temperature fusion plasmas the transport of energy and particles is commonly believed to be driven by turbulence. Turbulence quantities as correlation length and decorrelation time are important for the confinement properties of a plasma. Besides other diagnostics, correlation reflectometry has proven to be a suitable tool for the measurement of turbulence properties. At the medium sized Toroidal EXperiment for Technical Oriented Research (TEXTOR) the existing correlation reflectometry has been recently upgraded. A new reflectometer based on a microwave synthesizer has been developed and installed for the investigation of turbulence properties in a fusion plasma. Together with the existing reflectometer the measurement of radial correlation length and decorrelation time becomes available. Both reflectometers are computer controlled and allow to program individual frequency sequences and the duration of each frequency step. With the existing poloidal antenna array at θ=0° and on top of the vacuum vessel, the system allows the measurement of radial correlation and poloidal correlations at the same time. First experiments have been performed and the results on the radial correlation length of density fluctuations in a fusion plasma are presented.

Polyamorphism and the universal liquid–liquid critical point in the supercooled state

The physics of critical phenomena is well established in systems as diverse as molecular fluids, crystalline alloys and magnetic materials. As the critical point is approached, the susceptibility increases anomalously and fluctuations give rise to dramatic opalescence. Evidence has recently emerged for the existence of a second critical point in the liquid state at supercooled temperatures, below which polyamorphic phases coexist differing in density but sharing the same composition. Whilst much attention has been paid to supercooled water, polyamorphic phases have been observed in many elemental and oxide liquids potentially offering routes to low-entropy glasses. Our recent direct observation of a polyamorphic phase transition in levitated molten yttria–alumina offers the first opportunity to study the associated critical point in a real supercooled system.In situsmall-angle X-ray scattering records sharp rises in the average correlation length of density fluctuations and in the compressibility as the transition is approached. Both increases approximate to the universal power-law relations predicted by the three-dimensional Ising model in common with all critical point phenomena. The observation brings the second critical point predicted in liquids into line with other critical phenomena.

Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide

A recently introduced coarse-grained pair potential for carbon dioxide molecules is used to compute structural properties in the supercritical region near the critical point, applying Monte Carlo simulations. In this model, molecules are described as point particles, interacting with Lennard-Jones (LJ) forces and a (isotropically averaged) quadrupole–quadrupole potential, the LJ parameters being chosen such that gratifying agreement with the experimental phase diagram near the critical point is obtained. It is shown that the model gives also a reasonable account of the pair correlation function, although in the nearest neighbour shell some systematic discrepancies between the model predictions and results from simulations of fully atomistic models and experiments are found. By comparison with results from an equivalent model but with the full angle-dependent quadrupolar interaction these discrepancies are traced back to the effect of orientational correlations and of the insufficient representation of molecular packing. Furthermore, the correlation length of density fluctuations is obtained from Ornstein–Zernike plots of the inverse structure factor, and shown to be in rough agreement with corresponding experimental results. Finally possible refinements of this coarse-grained model are briefly discussed.

Phase Transitions of Confined Lattice Homopolymers

The effect of confinement on the phase behavior of lattice homopolymers has been studied using grand canonical Monte Carlo simulations in conjunction with multihistogram reweighting. The scaling of critical parameters and chain dimensions with chain length was determined for lattice homopolymers of up to 1024 beads in strictly 2D and quasi-2D (slab) geometries. The inverse critical temperature scales linearly with the Shultz Flory parameter for quasi-2D geometries, as it does for the bulk system. The critical volume fraction scales as a power law for all systems, with exponents 0.110 ( 0.024 and 0.129 ( 0.004 for the strictly 2D and slab geometries, respectively. The influence of confinement on critical behavior persists even in a thick slab due to the diverging correlation length of density fluctuations. The scaling of the radius of gyration with chain length in the quasi-2D system increasingly resembles the scaling in the strictly 2D system as the chain length increases. At the extrapolated infinite chain critical temperature, the radius of gyration of the 2D system scales with chain length with exponent 0.56 ( 0.01 = (4/7), in agreement with theoretical predictions.

A study of density fluctuations near the critical point of fluid Se by small angle X-ray scattering

Small angle X-ray scattering (SAXS) measurements for dense Se vapour have been carried out to investigate the characteristics of the density fluctuations near the critical density region. For this reason the correlation lengths of the density fluctuations and the number-density fluctuations have been measured precisely at different temperatures and pressures near the critical point. In this experiment a new spectrometer with a high brilliance source is used and SAXS spectra are detected using an imaging plate. Less noisy spectra with better fitting conditions to calculate correlation lengths of density fluctuations are found. Larger values of the correlation length of density fluctuations (and also the number-density fluctuations) are obtained near the critical density region, which agrees with the results of our previous experiments [J. Non-Cryst. Solids 250–252 (1999) 531]. The correlation length of the density fluctuations increases as we approach to the critical point of fluid Se along the path of critical density region.

Small angle X-ray scattering measurements for fluid selenium near the liquid–vapour critical point

Small angle X-ray scattering (SAXS) measurements for fluid Se near the liquid–vapour critical point have been carried out to investigate the correlation between the density fluctuation and electronic properties of fluid Se near the isochore of critical density. For this purpose, correlation lengths of density fluctuations of fluid Se have been measured precisely at different temperatures and pressures near the critical point. In this experiment a side-by-side multi-layered mirror for Mo Kα 1 is used for monochromatizing and focusing X-ray beam for the first time. A better fitting condition to calculate the correlation lengths of the density fluctuation is found. Larger values of the correlation length of the density fluctuation are obtained near the critical density region.

Recent progress in high performance and steady-state experiments on the Japan Atomic Energy Research Institute Tokamak-60 Upgrade with W-shaped divertor

In the Japan Atomic Energy Research Institute (JAERI) Tokamak-60 Upgrade [H. Shirai and the JT-60 Team, Phys. Plasmas 5, 1712 (1998)], high performance and steady-state experiments have been conducted in the W-shaped divertor. The equivalent deuterium-tritium (D-T) fusion multiplication factor, QDTeq, was enhanced transiently up to 1.25 in the reversed shear plasma. The reduction in particle diffusivity in the internal transport barriers (ITB) region of the reversed shear plasma was confirmed as well as the thermal diffusivity. It was also confirmed that the correlation length of density fluctuations is reduced inside the ITB of density. The performance with a confinement-enhancement factor (H-factor, H89) of 2.2 and QDTeq of 0.16 was sustained in a quasi-steady-state in the high-poloidal-beta (βp) and high confinement mode (H-mode) regime. The reversed shear configuration with ITBs was sustained by injecting the lower-hybrid waves combined with neutral beam injection and fully noninductive current drive in the reversed shear plasmas was realized for the first time. The driven current by the negative-ion-based neutral beam (NNB) injection increased up to 0.6 MA. The H-mode transition was triggered with the NNB injection and the H-mode with H89∼1.6–1.8 was sustained. The toroidicity-induced Alfvén eigenmode was excited for a volume-averaged fast ion beta, 〈βh〉, as low as ∼0.1%.

Correlation Measurements for Fusion Plasma Diagnostics

Fluctuation analysis of various physical parameters, mainly neutron flux or other radiation, has long been used for the diagnostics of both fission and fusion reactors. However, it appears that there has been relatively little exchange of information regarding research in the two fields. Some noise diagnostic methods used in fission reactors that may have some relevance for or resemblance to fusion plasma diagnostics are described, and this may contribute to the exchange between the two areas. An example is given to illustrate the possibility of such a transfer of experience. Namely, a method is described, taken from experience with fission reactor technology, that has been suggested for fusion applications. The method is used in general for nonintrusive determination of the correlation length of density fluctuations by spectral and correlation analysis. It can be applied to the analysis of plasma soft X rays for investigation of turbulence and magnetohydrodynamic effects. The proposed method has been partially tested on data from the Joint European Torus (JET) tokamak.

Noncritical behavior of density fluctuations in supercooled water.

We have measured the absolute structure factor of liquid water over the wave-number range 0.05k0.30 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ and temperature range -34T25 \ifmmode^\circ\else\textdegree\fi{}C with small-angle x-ray scattering. The correlation lengths of density fluctuations are small and change very little with temperature, suggesting that supercooled water may not be approaching a proposed spinodal point. The increasing density fluctuations with supercooling in water appear to be due to an increasing fraction of water molecules participating in clusters, not an increasing range of correlations.

Radial scale length of turbulent fluctuations in the main core of TFTR plasmas.

A new theory of microwave reflectometry is applied to turbulence measurements in the TFTR tokamak. Results indicate that in the main core of neutral beam heated plasmas in the supershot regime, the radial correlation length of density fluctuations is a weak decreasing function of heating power in the range 2--4 cm. Over the same interval of heating powers (0--14 MW), the level of density fluctuations is observed to steadily increase by more than an order of magnitude.

Viscosity of aqueous solutions of monohydric alcohols in the normal and supercooled states

Viscosities of solutions of Met−, Et−, and n-PropOH were measured by quasielastic light scattering of polystyrene lattice spheres of 800 Å diameter, in the low-concentration, low-temperature ranges where effects of alcohols on the structure and properties of liquid water are most pronounced. Raw data already indicate that alcohols promote the formation of clathrate-like structures of H bonds which add to those occurring naturally in the pure solvent. Evaluation of the number of water molecules taking part in longer-lived structures further indicates that this promotion is most effective in the infinite-dilution limit. Available thermodynamic data agree with this evaluation. Mismatches among solute-promoted clathrate-like cages are evidenced. The known disruptive effects of alcohols on the anomalous properties of cold and supercooled water are thus understood in terms of limitations to the correlation length of density fluctuations, set by mismatches. A contribution of OH groups to cage promotion is also evidenced at least at low temperature. Constraints or hindrances to the motion of water molecules, irrespective of their nature, appear to be effective in favoring structures of stabler, longer-lived H bonds, corresponding to water molecules of lower mobility. This offers a unified view of hydrophobic and hydrophilic interactions which agrees with earlier work and with more recent computer experiments. The possibility here evidenced for structures of H bonds promoted in solvent water of being conflictual or synergistic, adds to the microscopic understanding of solvent-mediated interactions, e.g., of biosolutes.

Brownian motion in a critical fluid; A critical long time tail

The frictioncoefficient of a Brownian particle in a critical fluid was evaluated, taking into account the finite correlation length of density fluctuations. A t −3 2 tail of the Brownian particle velocity autocorrelation function exists close to the critical point whose amplitude is 10 2–10 3 times the amplitude of the usual long time tail found far from the critical point.

Correlation Length of Density Fluctuations in Liquids

It is shown that in a liquid whose bulk modulus relaxes with relaxation time ${\ensuremath{\tau}}^{\ensuremath{'}}$, there exist density fluctuations whose correlation length is approximately $\frac{v{\ensuremath{\tau}}^{\ensuremath{'}}}{\ensuremath{\pi}}$, where $v$ is the sound velocity at ${\ensuremath{\Omega}}_{0}={({\ensuremath{\tau}}^{\ensuremath{'}})}^{\ensuremath{-}1}$.