Motion Of Molecules In Liquids Research Articles

Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study

Rotational motion of molecules in liquids plays an important role in determining the liquids' Nuclear Magnetic Resonance (NMR) spin-relaxation properties. The traditional theory of NMR spin relaxation assumes that the reorientational dynamics of molecules in liquids can be described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that the simple rotational-diffusion model does not fully capture the rotational dynamics of molecules in liquids: for example, the reorientation of molecules in liquid water occurs through a combination of continuous-time rotational diffusion and discrete, large angular jumps resulting from collective rearrangements of the hydrogen-bond network of water.In order to obtain further insights into the origin of large angular jumps in the rotational motion of liquid water, we studied the rotational dynamics of methane - an apolar, non‑hydrogen-bonding liquid with a spherically symmetric molecule. The reorientational propagator and the ensemble-averaged Legendre polynomial reorientational functions of liquid methane were analysed using molecular dynamics simulations. On the femtosecond timescale, the reorientational motion of methane molecules was found to be characterised by free-rotation gas-like Gaussian decay of the reorientational Legendre polynomials, a result consistent with the available experimental data for liquid methane. On the long timescale (picoseconds) the decay of the reorientational Legendre polynomials was exponential, suggestive of a Debye-like continuous-time rotational diffusion behaviour. However, the ratios of the exponential time constants for different orders of the Legendre polynomials failed to match the rotational-diffusion model. We discuss the implications of these findings for the understanding of rotational motion of molecules in hydrogen-bonding and non‑hydrogen-bonding liquids.

Relaxation Resonance Properties of the Dielectric Response of Water

Broadband terahertz infrared absorption spectra of liquid water are described using the nonstandard Frenkel gas–solid model for water, supplemented by the interconversion of molecules and ions due presumably to the mixed translational–vibrational motion of molecules in liquids. The periods of water molecule retention by hydration and ionic shells are calculated.

Nature of the kinematic shear viscosity of low-molecular liquids with averaged potential of Lennard-Jones type

The main attention is focused on the kinematic shear viscosity of argon, nitrogen, benzene and nitrobenzene which have different molecular shapes and sizes and intermolecular interactions, as well. We show that all these liquids demonstrate the argon-like behavior of their kinematic shear viscosities and belong to the same similarity class. Additionally, we show that the kinematic shear viscosity of argon is mainly determined by the packing factor which is characteristic for the van der Waals equation of state. We suggest the explicit formula for the shear viscosity. We found out that the similarity in the behavior of the shear viscosities of low-molecular liquids is connected with the identical structure of their averaged interparticle potentials for enumerated and other low-molecular liquids. This circumstance is a consequence of rotational motion of molecules in liquids.

Ulteriori esperienze geofisiche sul lago di Caldouazzo. Morfologia ed origine delle sesse. Dati microtermologici. Progressivo insabbiamento elei piccoli lagbi*.

The limnographic, barographic and tliermological recordings, taken in a week of October of the years 1906, 1967 and 1971 on the Lake of Caldonazzo, are reviewed. The properties of free uninodal, binodal etc. oscillations of the Lake have been examined, once again with the result that they coincide with the values previously elaborated theoretically: the amplitudes of uninodals in the North (Lido di San Cristoforo) are about twice as large as those measured in the extreme South (Lido di Caldonazzo); the behaviour of uninodals in the Northern part of the Lake (besides the uninode) in conformity with the theory, etc. The simultaneous function of a microbarograph, mounted near the Lido of San Cristoforo, proved that the main, if not exclusive, reason of the seiches lies in the interaction between the atmosphere and the hydrosphere. The passage of even the slightest pressure variations above the Lake, with rhythms of 10m, 5m, . . . cause an immediate response of the Lake by free uninodal, binodal. . . oscillations, and the amplitude of water oscillations is all the larger the more the period of perturbing causes approaches the period of the corresponding free oscillation, in other words, the more it approaches resonance. Observations on microvariations of temperature have been made as well which may occur on very short periods (in the order of 1 -2 sec) and give evidence of a swift brownian motion of liquid molecules. This must have a considerable influence on the Lake's microbiology. The increase of the period of uninodals, against the period of batliymetric mea-

The special theory of Brownian relativity: Equivalence principle for dynamic and static random paths and uncertainty relation for diffusion

The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the “diffusive horizon” as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a “universal” law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz–Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.

THE SOLITARY WAVE MODEL OF SUPERFLUIDITY

We propose the solitary wave model of superfluidity. According to harmonic oscillator model of quasi-lattice of liquid, it is proven that superfluid domains (SD) exist in He liquid, in which the resistanceless motion of liquid molecules (LM) can be carry out. At temperature lower than T c, all SD connect with each other and superflow in whole liquid takes place. Applying Toda's potential, under continuous conditions, we obtain the motion equation of LM, and its exact solution. Substituting these results into Schrödinger equation of LM, we can prove the existence of solitary waves of LM and the non-linear Schrödinger equation of LM. The motion of solitons of LM leads to a superflow. On the basis of coherent condition of wave of LM, we derive the formula of transition temperature Tc of superfluidity. From the formula, the relation of the onset temperature Tc of superflow on inert layers is explained.

Translational-orientational coupling motion of molecules in liquids and solutions

Theoretical framework of the transnational and orientational coupling motion of molecules is described based on the de Gennes' phenomenological treatment. The coupling of the transverse and longitudinal modes with the orientational mode is treated by a unified approach. Comparison with irreversible statistical mechanical treatments is discussed. Furthermore, the expressions of the ultrasonically induced birefringence for polymer solutions are derived from the recent theoretical treatments of polymer dynamics.

Manifestation of the collective effects in the rotational motion of molecules in liquids

The Lagrange approach to the theory of thermal hydrodynamic fluctuations is developed. The rotational motion of a Lagrange particle is studied in detail. The apparent expression for the angular velocity autocorrelation function (AVACF) at arbitrary times is derived. The obtained results are used to explain the specificity of the behaviour of the AVACF for a molecule. The collective contribution to the rotational self-diffusion coefficient as well as the manifestation of collective effects in the frequency dispersion of the dielectric permittivity are discussed. The peculiarities of the AVACF for two-dimensional liquids are considered.

Phase-coherent light scattering spectroscopy. II. Depolarized dynamic light scattering

In our preceding paper, we demonstrate the basic principle of the phase-coherent light scattering (COLS) method, focusing on polarized light scattering. In this paper we describe the principle of depolarized COLS. We explain how to excite coherent orientational motion of molecules in liquids and transverse sound waves in amorphous solids by using the electric-field grating, which is generated by crossing two cw laser beams in the media. We also explain how to observe complex spectra of depolarized light scattering from these anisotropic modes. The advantage of COLS over the conventional method is also discussed.

Rotational Brownian motion of solute fluorescent molecules in liquids: Theory and experiment

The theories for the rotational Brownian motion of molecules in liquids were experimentally verified on the example of selected fluorescent probe molecules dissolved in various solvents. Agreement between theories and experimental results as well as some disagreements between them were found. The model of a “coloured noise” random torque has been employed to diminish the discrepancy between the Hubbard-Morita model of rotational Brownian motion of molecules in liquids and the experimental data. A “mass drag” effect due to the existence of viscosity shear waves is taken into account in the explanation of inertial effects in molecular motion in liquids. The hypothesis of microviscosity has been confirmed in some experimental situations.

Time-resolved anisotropic coherent anti-Stokes Raman scattering: A new probe of reorientational dynamics

A formalism for the time-dependent anisotropic third-order susceptibility induced by a linearly polarized excitation pulse has been derived to describe the time dependence of coherent anti-Stokes Raman scattered (CARS) and Raman time-resolved experiments. The third-order susceptibility induced in a randomly oriented molecular system contains nine independent molecular parameters—three isotropic and six anisotropic—as compared to three independent parameters in an isotropic system. Methods of time-resolved anisotropic anti-Stokes Raman scattering (TRA CARS) are discussed as an approach to reorientational measurements. The dependence of the TRA CARS or TRA Raman signal on vibration and polarization component can in principle provide more rotational information than fluorescence depolarization or linear dichroism measurements and may allow more complete characterization of rotational dynamics. Results are reported for three types of TRA CARS experiments to demonstrate the capabilities of TRA CARS to study the rotational motion of molecules in liquids.

Incoherent inelastic neutron scattering from liquid water: A theoretical investigation.

A theory of incoherent inelastic neutron scattering from liquid water is presented, and recent experimental data obtained by employing the spallation sources are interpreted. This theory is a statistical theory, similar to those describing optical spectra of liquids. The experimental spectra of liquid ${\mathrm{H}}_{2}$O and ${\mathrm{D}}_{2}$O are reproduced theoretically. The incoherent neutron- and light-scattering spectra of water are compared. The suitability of this type of experiment to study high-frequency modes of translational-rotational motion of molecules in liquids is emphasized.

Investigation of Complex Intramolecular Motion in Supercooled Liquids

AbstractAfter a brief résumé of the Woessner theory which treats nuclear magnetic relaxation effects caused by internal and anisotropic motion of molecules in liquids we present proton magnetic relaxation rates of specifically deuterated molecules possessing an interacting group (–OH or –COOH) and a hydrocarbon chain of increasing length, namely methanol and acetic acid, ethanol and propionic acid, n‐propanol. Measurements were done in the range from room temperature to ∼ 15 K. Various interacting substances were added to slow down the movement of the interacting group relative to the internal molecular motions, yielding respective experimental manifestations. Some brief hints are given to show the shortcomings of the Woessner theory.

The activation energy in the thermal motion of liquid molecules

The activation energy in the thermal motion of liquid molecules

Non-Markoffian excitation-relaxation processes

It is shown that the Mori theory of relaxation provides a suitable theoretical framework for the study of excitation-relaxation processes of a non-Markoffian kind, provided that the point of view of Nordholm and Zwanzig be adopted. According to their interpretation of the generalized Langevin equation, it is indeed possible to describe the back reaction of an excited thermal bath on the time evolution of a subsystem of interest. Since the equilibrium distribution of the thermal bath of a non-Markoffian system is significantly affected in the course of excitation of the subsystem, it is then possible to evaluate the time evolution subsequent excitation processes of such a system by pulses of finite duration. In other words, the limitations of linear-response theory leading to the second fluctuation-dissipation theorem can be avoided. A general approach, valid even in the case of non-Hermitian dynamical operators and which allows us to build up a generalized equation, is developed. This approach shows, furthermore, that it is possible to replace the thermal bath of a non-Markoffian variable with a chain of variables undergoing relaxation processes of a Markoffian nature. Since in the new Markoffian system, considered in its totality, the relaxation process is completely independent of the excitation one, the time evolution of any variable of the chain can be evaluated for any intensity of the excitation field. This means that even the limitations of the linear response involved by the first fluctuation-dissipation theorem can be avoided. Owing to the formal similarity between the Schrodinger equation and the equation of motion for operators, it is possible, once suitable scalar products among operators are defined, to apply the one approach both to the quantum-mechanical time evolution of an isolated molecule system and to the classical Brownian motion of molecules in liquids. In the former case, the theory developed in the present paper allows us to build up in a rigorous way a “reduced” effective Hamiltonian which results in a wide range of free-relaxations behaviours, including the damped oscillatory and biexponential types. It is then possible to describe in a realistic way the whole excitation-relaxation process and evaluate both the effects of pulse duration and intensity on any kind of decay behaviour.

A model for rotational relaxation and resonance

Depolarized Rayleigh and Raman scattering and far infrared absorption has revealed the rotational motion of polar molecules in liquids. The presence of both a Debye relaxation spectrum and a broad resonance indicates that the molecules oscillate and in addition are subject to some sort of relaxation mechanism. A model is proposed in which the molecule oscillates in a potential well until thermal fluctuations cause it to surpass the potential barrier and jump to a neighbouring well. For two-dimensional rotation approximate analytic expressions are obtained for the spectrum, which agree qualitatively with the measurements. The conclusion is that both resonance and relaxation can be obtained from a single mechanism, so that it is not necessary to introduce one mechanism for each of them.

Relaxation of the optical Kerr effect of anisotropic molecules in mixed liquids

The relaxation time of the Kerr effect of nitrobenzene and m-nitrotoluene in various mixtures with carbon tetrachloride and various alcohols was determined by measuring the kinetics of the Kerr effect using picosecond laser techniques. These measurements yield information on the rotational motion of molecules in liquids. The relaxation time data are interpreted in terms of an effective local viscosity effect, pair correlation, and coupling of rotational motion with shear modes.

The comparison of the two friction models for spherical-top molecules reorientation

Steele's and Lewis' et al. methods for description a reorientational motion of molecules in liquids are compared. It is shown by use of the cumulant method that for spherical-top molecules both these methods give the same result.

Rotational Relaxation of Molecules in Fluids for Reorientations of Arbitrary Angle

A theory of rotational motion of molecules in liquids is presented. The traditional Debye diffusion model is generalized so as to include arbitrary reorientation angles by means of a nonlocal master equation. Random walk models are a special case of this generalization. We have obtained the conditional probabilities for the orientation of a body and of a vector fixed in the body for arbitrary body geometry. These results are then specialized to specific symmetries. From these conditional probabilities we calculate correlation functions which describe a large number of spectroscopic experiments such as NMR, ESR, NQR, dielectric relaxation, and infrared and Raman spectroscopy. We find that the form of these results for the correlation functions depend only on medium isotropy and body geometry. The same number of decaying exponentials are found as in the diffusion model regardless of the details of the reorientation mechanism. Only the amplitudes and relaxation times depend on these details.

Vibrational-spectroscopic study of the intermolecular dynamics of condensed states of aggregation

Classical statistical methods are used to analyze the intensity distribution in the intermolecular spectrum due to the modulation of an incident light wave by the thermal motion of liquid molecules. The dependence obtained contains three molecular parameters characterizing the dynamics of the intermolecular motion.