Thermal Density Fluctuations Research Articles

The overdamped van Hove function of atomic liquids

Using the generalized Langevin equation formalism and the process of contraction of the description we derive a general memory function equation for the thermal fluctuations of the local density of a simple atomic liquid. From the analysis of the long-time limit of this equation, a striking equivalence is suggested between the long-time dynamics of the atomic liquid and the dynamics of the corresponding Brownian liquid. This dynamic equivalence is confirmed here by comparing molecular and Brownian dynamics simulations of the self-intermediate scattering function and the long-time self-diffusion coefficient for the hard-sphere liquid.

Van der Waals supercritical fluid: Exact formulas for special lines

In the framework of the van der Waals model, analytical expressions for the locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, density fluctuation, and sound velocity in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into single Widom line only at T < 1.07T(c), P < 1.25P(c) and become smeared at T < 2T(c), P < 5P(c), where T(c) and P(c) are the critical temperature and pressure. The behavior of the Batschinski lines and the pseudo-Gruneisen parameter γ of a van der Waals fluid were analyzed. In the critical point, the van der Waals fluid has γ = 8/3, corresponding to a soft sphere particle system with exponent n = 14.

Widom Line for the Liquid–Gas Transition in Lennard-Jones System

The locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, and density fluctuations for model particle systems with Lennard-Jones (LJ) potential in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into a single Widom line at T < 1.1T(c) and P < 1.5P(c) and become practically completely smeared at T < 2.5T(c) and P < 10P(c), where T(c) and P(c) are the critical temperature and pressure. The ridge for heat capacity approaches close to critical isochore, whereas the lines of extrema for other values correspond to density decrease. The lines corresponding to the supercritical maxima for argon and neon are in good agreement with the computer simulation data for LJ fluid. The behavior of the ridges for LJ fluid, in turn, is close to that for the supercritical van der Waals fluid, which is indicative of a fairly universal behavior of the Widom line for a liquid-gas transition.

Coherent and spontaneous Rayleigh-Brillouin scattering in atomic and molecular gases and gas mixtures

We study Rayleigh-Brillouin scattering in gases of ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and ${\mathrm{SF}}_{6}$ molecules, Kr atoms, and He-Xe and $\mathrm{He}\ensuremath{-}{\mathrm{CO}}_{2}$ mixtures at pressures ranging from 1 to 3 bar and using two different experimental setups. In one setup, we measure spectra of light scattered by thermal density fluctuations (spontaneous Rayleigh-Brillouin scattering); in the second setup density waves are induced in the overlap region of two counterpropagating laser beams (coherent Rayleigh-Brillouin scattering). We compare measured spectra to the Tenti models and to a recent model for mixtures. We find new values of the bulk viscosity, which is a parameter in line-shape models that allows for internal degrees of freedom. Both experiments agree on the value of the bulk viscosity. Our results indicate a need for new line-shape models for mixtures of molecules with internal degrees of freedom.

On the structure of glasses in the BaO-B2O3-SiO2 system

The structure of single-phase glasses in the BaO-B2O3-SiO2 system has been studied by the large- and small-angle X-ray scattering techniques. The glasses containing 40 mol % BaO upon equimolar replacement of B2O3 by SiO2 have been investigated. It has been demonstrated that the incorporation of barium ions into structural groupings fixes their position and provides ordering in the distribution of barium ions at interatomic distances up to at least 5 A. The glasses under investigation are homogeneous, and their inhomogeneity is determined by thermal density fluctuations and fluctuations of the concentration of a part of barium ions distributed in a statistically random manner in the volume of the glass. The observed ordering in the distribution of barium ions is not reduced to the formation of local clusters with an increased concentration of barium ions but is most likely a characteristic feature of the bulk glass structure. The glass structure is consistent with the model of ideal associated solutions.

Fluctuation interactions of colloidal particles

For like-charged colloidal particles, two mechanisms of attraction between them survive when the interparticle distance is larger than the Debye screening length. One of them is the conventional van der Waals attraction and the second is the attraction mechanism mediated by thermal fluctuations of particle position. The latter is related to the effective variable mass (Euler mass) of the particles produced by the fluid motion. The strongest attraction potential (up to the value of the temperature T) corresponds to the case of uncharged particles and a relatively large Debye screening length. In this case, the third attraction mechanism is involved. It is mediated by thermal fluctuations of the fluid density.

Modeling of DNA in Nanochannels using Linear Elasticity Theory

We model the dynamics of a single, fluorescence-dyed DNA molecule in a nanochannel. When a single dsDNA molecule is placed in a nanochannel, its extension along the channel is up to 50% of its contour length, depending on the dimensions of the channel. This linear extension offers the possibility to study, e.g., the binding of site-specific proteins or the sequence-dependent melting of DNA, with the latter giving a coarse-grained representation of the sequence [W. Reisner et al., “Single Molecule Denaturation Mapping of DNA in Nanofluidic Channels.” Resubmitted to Nature Nanotechnology (2009)]. The resolution achieved with this approach has two limiting factors: The diffraction limit, which for isolated probes can be circumvented with FIONA, and thermal density fluctuations of the DNA in the channel. Density fluctuations make distances measured along the channel correspond to distances measured along the molecule in an unknown non-linear and random, time-dependent manner. This last problem can be circumvented if the non-linear correspondence between coordinates can be extracted from images at any point in time. To this end, we model the thermal motion of the molecule using linear elasticity theory combined with Boltzmann statistics. The thermal dynamics of the resulting model is consistent with movies of DNA displaying thermal density fluctuations.

On the fluctuation structure of single-phase glasses in the SrO-B2O3-SiO2 system

The structure of single-phase glasses in the SrO-B2O3-SiO2 system has been studied by the small-and large-angle X-ray scattering technique. The glasses containing 35, 40, and 45 mol % SrO upon equimolar replacement of B2O3 by SiO2 have been investigated. It has been demonstrated that the glasses do not contain chemical inhomogeneity regions. The inhomogeneity of the glasses is determined only by thermal density fluctuations. The isothermal compressibility varies insignificantly upon replacement of B2O3 by SiO2 and decreases with an increase in the SrO content. The glass structure is consistent with the model of ideal associated solutions.

Phase coexistence between the (√3 × √3)R30° – β and (1 × 1) phases on Pb/Ge(1 1 1)

We have characterized the phase transition between the (1 × 1) and ( √3 × √ 3)R30 ° – β phases on Pb/Ge(1 1 1) using low energy electron microscopy (LEEM). We show that the transition is first-order and that, in the coexistence region of the two phases, the dominant mechanism for phase separation changes critically with Pb coverage, from nucleation and growth at 1.33 ML (saturation coverage of the β phase) to spontaneous domain switching due to thermal fluctuations of the local Pb density for slightly smaller coverage. As the Pb coverage decreases, the concentration of vacancies in the β phase increases, making additional possible Pb adsorption sites available. The larger resulting local density fluctuation of Pb becomes comparable to the density difference of the two phases, manifesting itself in the observed domain switching.

Quantum Density Fluctuations in Classical Liquids

We discuss the density fluctuations of a fluid due to zero point motion, assuming a linear dispersion relation. We argue that density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We calculate the differential cross section for light scattering by the zero point density fluctuations, and find a result proportional to the fifth power of the light frequency. We give some estimates of the relative magnitude of this effect compared to the scattering by thermal density fluctuations, and find that it can be of the order 13% for liquid neon at optical frequencies. This relative magnitude is proportional to frequency and inversely proportional to temperature. Although the scattering by zero point density fluctuation is small, it may be observable.

Near-field radiative heat transfer and noncontact friction

All material bodies are surrounded by a fluctuating electromagnetic field because of the thermal and quantum fluctuations of the current density inside them. Close to the surface of planar sources (when the distance $d⪡{\ensuremath{\lambda}}_{T}=c\ensuremath{\hbar}∕{k}_{B}T$), thermal radiation can be spatially and temporally coherent if the surface can support surface modes like surface plasmon polaritons, surface phonon polaritons, or adsorbate vibrational modes. The fluctuating field is responsible for important phenomena such as radiative heat transfer, the van der Waals interaction, and the van der Waals friction between bodies. A general formalism for the calculation of the power spectral density for the fluctuating electromagnetic field is presented and applied to the radiative heat transfer and the van der Waals friction using both the semiclassical theory of the fluctuating electromagnetic field and quantum field theory. The radiative heat transfer and the van der Waals friction are greatly enhanced at short separations $(d⪡{\ensuremath{\lambda}}_{T})$ between the bodies due to the evanescent electromagnetic waves. Particularly strong enhancement occurs if the surface of the body can support localized surface modes like surface plasmons, surface polaritons, or adsorbate vibrational modes. An electromagnetic field outside a moving body can also be created by static charges which are always present on the surface of the body due to inhomogeneities, or due to a bias voltage. This electromagnetic field produces electrostatic friction which can be greatly enhanced if on the surface of the body there is a two-dimensional electron or hole system, or an incommensurate adsorbed layer of ions exhibiting acoustic vibrations. Applications of radiative heat transfer and noncontact friction to scanning probe spectroscopy are discussed. The theory gives a tentative explanation for the experimental noncontact friction data.

Stable and metastable states in iron–manganese pnictides of the system Fea−xMnxAs

The first-order magnetic phase transitions of the order–order type induced by magnetic field in the layered antiferromagnetic alloys of the system Fea−xMnxAs are analyzed in the model of itinerant magnetism with allowance for the possible coexistence of ferromagnetic and antiferromagnetic deformations of the electronic band structure. In the abstraction to a model description of Fea−xMnxAs a single-band energy spectrum is used in which the filling of the band and the electronic density of states are chosen on the basis of first-principles calculations of the nonmagnetic and ferrimagnetic states. It follows from the results of the this analysis that the order–order transitions might be caused by a slight transformation of the electronic density of states and a change of the degree of filling of the magnetically active band. Such changes may be a consequence of thermal fluctuations of the spin density and pressure. The role of pressure and of the magnetostrictive contribution to the order–order transitions is discussed.

Finding polymorphic structures during vicinal surface growth

A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.

Light intensity fluctuations on a semiconductor microsphere calculated by boundary element method

Abstract For a semiconductor microsphere irradiated by monochromatic unpolarized plane light wave, the governing Maxwell equations, which are transformed into Schrodinger equations through Debye potentials, are solved by the boundary element method, one of the integral formulations. The resultant light intensities on the particle surface show noise-like fluctuations depending on various parameters such as the light wavelength, the particle size, the numerical surface element size, etc. The more the numerical surface elements used, the greater the noise extent of the intensities. We think that this noise is related to the fluctuations happening in the real world and that they are somehow made into shape numerically by Green’s function and surface integration. One can consider a numerical surface element as a crystalline or amorphous unit cell. Actually a few experiments with photon energy conversion devices give the consistent results with ours that the energy conversion efficiency is on the increase with the decreasing size of unit cells. It is thus proposed here that this noise from numerical computation may be modeled to be the real thermal fluctuations of photon density on particle surface for photovoltaic cells, photocatalysts, photoluminescence devices, etc.

Giant enhancement of noncontact friction between closely spaced bodies by dielectric films and two-dimensional systems

The effect of an external bias voltage and spatial variations of the surface potential on the damping of cantilever vibrations in an atomic force microscope (AFM) is considered. The damping is due to an electrostatic friction that arises due to dissipation of the energy of an electromagnetic field generated in the sample by oscillating static charges induced on the surface of the AFM probe tip by the bias voltage or spatial variations of the surface potential. A similar effect appears when the tip is oscillating in an electrostatic field created by charged defects present in the dielectric sample. The electrostatic friction is compared to the van der Waals (vdW) friction between closely spaced bodies, which is caused by a fluctuating electromagnetic field related to the quantum and thermal fluctuations of current density inside the bodies. It is shown that the electrostatic friction and the vdW friction can be strongly enhanced in the presence of dielectric films or two-dimensional (2D) structures—such as a 2D electron system or an incommensurate layer of adsorbed ions exhibiting acoustic oscillations—on the probe tip and sample surfaces. It is also shown that the damping of cantilever oscillations caused by the electrostatic friction in the presence of such 2D structures can have the same order of magnitude and the same dependence on the distance as observed in experiment by Stipe et al. [Phys. Rev. Lett. 87, 096801 (2001)]. At small distances, the vdW friction can be large enough to be measured in experiment. In interpreting the experimental data that obey a quadratic dependence on the bias voltage, one can reject a phonon mechanism according to which the friction depends on the fourth power of the voltage.

Ideal glass transitions, shear modulus, activated dynamics, and yielding in fluids of nonspherical objects

An extension of naive ideal mode coupling theory (MCT) and its generalization to treat activated barrier hopping and glassy dynamics in fluids and suspensions composed of nonspherical hard core objects is proposed. An effective center-of-mass description is adopted. It corresponds to a specific type of pre-averaging of the dynamical consequences of orientational degrees of freedom. The simplest case of particles composed of symmetry-equivalent interaction sites is considered. The theory is implemented for a homonuclear diatomic shape of variable bond length. The naive MCT glass transition boundary is predicted to be a nonmonotonic function of the length-to-width or aspect ratio and occurs at a nearly unique value of the dimensionless compressibility. The latter quantifies the amplitude of long wavelength thermal density fluctuations, thereby (empirically) suggesting a tight connection between the onset of localization and thermodynamics. Localization lengths and elastic shear moduli for different aspect ratio and volume fraction systems approximately collapse onto master curves based on a reduced volume fraction variable that quantifies the distance from the ideal glass transition. Calculations of the entropic barrier height and hopping time, maximum restoring force, and absolute yield stress and strain as a function of diatomic aspect ratio and volume fraction have been performed. Strong correlations of these properties with the dimensionless compressibility are also found, and nearly universal dependences have been numerically identified based on property-specific nondimensionalizations. Generalization of the approach to rigid rods, disks, and variable shaped molecules is possible, including oriented liquid crystalline phases.

Critical issues highlighted by collective Thomson scattering below electron cyclotron resonance in FTU

Strong anomalous spectra were systematically observed in collective Thomson scattering (CTS) at 140 GHz in the high-field tokamak FTU, a proof-of-principle experiment of CTS on thermal density fluctuations performed with propagation below electron cyclotron (EC) resonance with the final aim of demonstrating high-density CTS in the extraordinary mode. Following the results of two experimental campaigns expressly performed to investigate them, these spectra are ascribed to a gyrotron perturbation caused by a back-reflected signal originating in the beam injection port, where the electron cyclotron layer, the upper-hybrid layer and the right-handed cutoff layer unavoidably crossed by the probing beam are activated by a breakdown plasma sustained by the beam itself. The degree of generality ascribable to our results and the constraints they set on present and future CTS experiments with propagation below electron cyclotron resonance are discussed. A viable solution in terms of a transmit antenna robust against the risk of gyrotron perturbation is suggested.

Influence of water on the structure and kinetics of structural relaxation in sodium borate glasses

The influence of the water content on the microinhomogeneous structure of sodium borate glasses containing 2.5 and 5.0 mol % Na2O and on the kinetics of structural relaxation in vitreous boron oxide and sodium borate glasses is studied by the small-angle X-ray scattering (SAXS) technique. It is demonstrated that an increase in the water content brings about an increase in the size of the inhomogeneity regions and a decrease in the mean square of the difference between the electron densities 〈(Δρ)2〉 for the microinhomogeneous structure. The inference is made that water has a catalytic effect on the aggregation of alkali borate structural units. The kinetic dependence of the intensity of small-angle X-ray scattering by thermal density fluctuations is described by the Kohlrausch equation. The exponent β in the Kohlrausch equation is close to 1.0 for “dry” glasses and decreases to 0.5 for glasses containing 0.7–1.0 mol % H2O.

Counterion-Mediated Attraction and Kinks on Loops of Semiflexible Polyelectrolyte Bundles

The formation of kinks in a loop of bundled polyelectrolyte filaments is analyzed in terms of the thermal fluctuations of charge density due to polyvalent counterions adsorbed on the polyelectrolyte filaments. It is found that the counterion-mediated attraction energy of filaments depends on their bending. By consideration of curvature elasticity energy and counterion-mediated attraction between polyelectrolyte filaments, the characteristic width of the kink and the number of kinks per loop is found to be in reasonable agreement with existing experimental data for rings of bundled actin filaments.

Thermal Phonon Resonance in Solid Glass

Thermal phonon resonance was observed in a stiff solid material of fused silica, from which a lower intensity of scattered light is expected than from liquids. The improved detection sensitivity of the optical beating Brillouin spectroscopy technique enabled us to observe the spontaneous elastic resonance of the solid sample attributable to thermal density fluctuation with a frequency resolution of 1 kHz. The accuracy in determining phonon velocity was then increased up to 10-5. The high frequency resolution also revealed the fine structure of the resonance peak train brought about by the lateral mode vibration, and the eigen frequencies of the compound mode are in good agreement with those theoretically estimated. Volume and shear elasticities were uniquely determined from the resonance spectra of longitudinal and shear phonons. Phonon absorption at about 100 MHz was also determined from the resonance peak width of the Brillouin component.