Effect of frequency on acoustic parameters in a binary mixture of polar liquids

The densities (α) and ultrasonic velocities (C) of binary mixtures of a polar liquid like acetone and toluene have been measured at different frequencies (lMHz, 3MHz and 5MHz) over the entire range of mole fraction of acetone at temperature 303.16k. The intermolecular free length (L _f ), isentropic compressibility (β), acoustic impedance (Z), excess values of isentropic compressibility (β ^E ) and acoustic impedance (Z ^E ) have been computed using values of ultrasonic velocity (C) and density (α). The ultrasonic velocity (C), intermolecular free length (L _f ) and excess values of isentropic compressibility are positive whereas excess values of acoustic impedance is negative for the entire composition range which indicates the specific interaction between unlike molecules. The results are discussed in the light of intermolecular interactions occurring in the solutions.     

Excess isentropic compressibility and speed of sound of the ternary mixture 2-propanol + diethyl ether + n-hexane and the constituent binary mixtures at 298.15 K

Speed of sound and densities of the ternary mixture 2-propanol + diethyl ether + n-hexane and also the binary mixtures 2-propanol + diethyl ether and 2-propanol + n-hexane have been measured at the entire composition range at 298.15 K. The excess isentropic compressibilities and the excess speed of the sound have been calculated from experimental densities and speed of sound. These excess properties of the binary mixtures were fitted to Redlich-Kister equation, while the Cibulka’s equation was used to fit the values related to the values to the ternary system. These excess properties have been used to discuss the presence of significant interactions between the component molecules in the binary mixtures and also the ternary mixtures. Speed of sound of the binary mixtures and the ternary mixture have been compared with calculated values from free length theory (FLT), collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR) and Junjie’s relation (JR). The results are used to compare the relative merits of these theories and relations in terms of the root mean square deviation relative (RMSD_r).     

Ultrasonic study of binary mixtures of acetone with chlorobenzene at different frequencies

The ultrasonic velocity (C) and density (ρ) have been measured at different frequencies (1MHz, 3MHz and 5 MHz) in the binary mixtures of acetone with chlorobenzene over the entire range of mole fraction at temperature 303.16K. The data of C and ρ have been used to evaluate the isentropic compressibility (β), intermolecular free length (L_f) and acoustic impedance (Z) and their excess values to elucidate the molecular association in the mixture. The variation of these parameters with solute (acetone) indicates the nature of interaction present in the binary mixture.     

Study of acoustic parameters of binary mixtures of a nonpolar liquid with polar liquid at different frequencies

The densities (ρ) and ultrasonic velocities (C) of binary mixture of diisopropyl ether (DIPE) and bromobenzene (BB) have been measured at different frequencies (1 MHz, 3 MHz and 5 MHz) over the entire range of mole fraction of diisopropyl ether (DIPE) at temperature 303 K. The intermolecular free length (L _f ), isentropic compressibility (β), acoustic impedance (Z) and excess values of isentropic compressibility (β ^E ) and acoustic impedance (Z^E) have been computed using values of ultrasonic velocity (C) and density (ρ). The ultrasonic velocity, intermolecular free length are positive whereas the excess values of isentropic compressibility and acoustic impedance are negative over the entire composition range of DIPE which indicates presence of specific interactions between unlike molecules. The results are discussed in the light of intermolecular interactions occurring in the mixtures.      

Continuum percolation of the four-bonding-site associating fluids

Wertheim’s integral equation theory for associating fluids is reformulated for the study of the connectedness properties of associating hard spheres with four bonding sites. The association interaction is described as a square-well saturable attraction between these sites. The connectedness version of the Ornstein-Zernike (OZ) integral equation is supplemented by the PY-like closure relation and solved analytically within an ideal network approximation in which the network is represented as resulting from the crossing of ideal polymer chains. The pair connectedness functions and the mean cluster size are calculated and discussed. The condition for the percolation transition and the analytical form of the percolation threshold are derived. The connection of the percolation with the gas-liquid phase transition is discussed.     

Thermal expansion coefficient of ternary liquid mixture using hard sphere models and Flory’s statistical theory

The coefficients of thermal expansion (α) of ternary liquid mixtures of heterocyclic compounds viz., pyridine/quinoline with phenol in benzene have been evaluated at 308.15, 318.15 and 328.15 K, respectively. A comparative study of thermal expansivity using different models for hard sphere equation of state and Flory’s statistical theory has been made. The computed values of thermal expansivity are compared with the experimental results. The excess values of thermal expansivity have also been computed and utilized to discuss the existence and strength of intermolecular interactions in the ternary liquid system under investigation.     

Ultrasonic study of molecular interaction in binary liquid mixtures at 30°C

Densities ρ and ultrasonic speeds u of the binary mixtures of tetrahydrofuran (THF) with 1-butanol and tert-butanol, at 30°C, over the entire composition range were measured. From these data isentropic compressibility, K _s, intermolecular free length L _f, relative association R _A, acoustic impedance Z, molar sound speed R _m, deviations in isentropic compressibility ΔK _s, and excess volume V ^E were calculated. The variation of these parameters with composition of the mixture helps us in understanding the nature and extent of interaction between unlike molecules in the mixtures. Further, theoretical values of ultrasonic speed were evaluated using theories and empirical relations. The relative merits of these theories and relations were discussed.     

Molecular interaction and other thermodynamic properties in ternary liquid mixtures

Molecular interaction, adiabatic compressibility, intermolecular free length, molar volume, available volume and free volume have been computed by measuring ultrasonic velocity and density at 23°C in three ternary liquid mixtures with p-xylene as common component. The systems are I p-xylene-acetone-carbon tetrachloride, II p-xylene-acetone-cyclohexane and III p-xylene-benzene-cyclohexane. Molecular interaction is maximum when the mole fraction of acetone is 0.5 in I and 0.6 in II. It remains almost constant in III indicating no interaction in this case. The excess properties have also been given and the interactions explained.     

Relativistic Dynamics of Accelerating Particles Derived from Field Equations

In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein’s celebrated energy-mass relation E=mc ² is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein’s energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements.     

Ultrasonic and IR study of intermolecular association through hydrogen bonding in ternary liquid mixtures

Complex formation in ternary liquid mixtures of dimethylsulfoxide (DMSO) with phenol and o-cresol in carbontetrachloride has been studied by measuring ultrasonic velocity at 2 MHz, in the concentration range of 0.019-0.162 (in mole fraction of DMSO) at varying temperatures of 20, 30 and 40 degrees C. Using measured values of ultrasonic velocity, other parameters such as adiabatic compressibility, intermolecular free length, molar sound velocity, molar compressibility, specific acoustic impedance and molar volume have been evaluated. These parameters have been utilized to study the solute-solute interactions in these systems. The ultrasonic velocity shows a maxima and adiabatic compressibility a corresponding minima as a function of concentration for these mixtures. The results indicate the occurrence of complex formation between unlike molecules through intermolecular hydrogen bonding between oxygen atom of DMSO molecule and hydrogen atom of phenol and o-cresol molecules. The excess values of adiabatic compressibility and intermolecular free length have also been evaluated. The variation of both these parameters with concentration also indicates the possibility of the complex formation in these systems. Further, to investigate the presence of O-HO bond complexes and the strength of molecular association with concentrations, the infrared spectra of both the systems, DMSO-phenol and DMSO-o-cresol, have been recorded for various concentrations at room temperature (20 degrees C). The results obtained using infrared spectroscopy for both the systems also support the occurrence of complex formation through intermolecular hydrogen bonding in these ternary liquid mixtures.     

Saha’s ionization equation for highZ elements

Saha’s ionization equation has been solved for highZ elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bohr’s formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha’s equation solutions has been checked by comparing theP _T andE _T computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV.     

Ultrasonic and infrared study of molecular interactions in ternary mixtures of 1-naphthol and 2-naphthol with 2-propanone in benzene

The measurements of ultrasonic velocity and density were made for the ternary mixtures of l-naphthol/2-naphthol with 2-propanone in benzene at 20, 30 and 40°C in the mole fraction range of 0.00 to 0.05. Adiabatic compressibility and intermolecular free length have been evaluated using ultrasonic velocity data. The non-linear variation of ultrasonic velocity and allied parameters with mole fraction indicates solute-solute interactions through hydrogen bonding between unlike molecules. Results of ultrasonic velocity and density measurements are further supported by FT-IR spectra. The change in transmittance as well as the shift in the frequency of the representative peak of the OH stretching in FT-IR spectra give inferences about the complex formation.     

Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation

We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force. Deceased     

Optodynamic description of a linear momentum transfer from a laser induced ultrasonic wave to a rod

We present a new optodynamic experimental technique to measure the linear momentum obtained by a rod during a nanosecond laser pulse ablation of the rod’s front face on the basis of the displacement due to an ultrasonic wave reflection at its rear end. With the help of a simple theory, we explained the step-like motion of the rod’s free end. This theory conforms well with the general shape of the measured displacement history curve. The acquired momentum can be directly estimated by measuring the height of a step from the step-like motion of the rod’s end. Measurements based on an arm-compensated Michelson interferometer also enabled us to follow the attenuation of an ultrasonic wave and so to determine the characteristic attenuation time. This quantity plays a major role in the transfer of linear momentum from within the initial ultrasonic wave to the final net uniform motion of the specimen. PACS  52.38.Mf; 43.35.Yb; 43.35.Cg     

Methods of investigation of boundary value problems in viscoelasticity theory

The present paper is devoted to some classical and modern methods of solving boundary value problems of viscoelasticity theory, including the Volterra principle, Il’yushin’s approximation method, Pobedrya’s method of numerical realization of an elastic solution, the method of Laplace (Laplace-Carson) transform and Z-transform, the method of time steps, the usage of viscoelastic models with fractional time derivatives (fractal models), and methods using a new representation of constitutive relations of nonlinear viscoelasticity To Boris Efimovich Pobedria on the occasion of his 70th birthday     

Ultrasonic study of binary mixtures of acetylacetone with polar diluents at 303.16 K vis-a-vis molecular interaction

The ultrasonic velocity (C) and density (p) of binary mixture of acetylacetone with polar diluents have been measured at temperature 303.16 K and frequency of 2 MHz. The data of C and p have been used to evaluate, isentropic compressibility (β), acoustic impedence (Z) and intermolecular free length (L _f ) to study the molecular interaction. The study reveals that interaction is maximum in bromo-benzene acetylacetone mixture.      

Speeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory’s statistical theory and hard sphere models

Speeds of sound and densities of three ternary liquid systems namely, toluene + n-heptane + n-hexane (I), cyclohexane + n-heptane + n-hexane (II) and n-hexane + n-heptane + n-decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory’s statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory’s statistical theory has been established quite reasonably over hard sphere models.      

LRS Bianchi Type-I Universe in Barber’s Second Self Creation Theory

We consider Barber’s second self creation theory with perfect fluid source for an LRS Bianchi type-I metric by using deceleration parameter to be time dependent where the metric potentials are taken as function of x and t. The present models are free from singularity and the results are consistent within the observational limit. Some physical properties of the models are also discussed.     

Fifty years of Szigeti’s dielectric theory — A review

During the period 1949–1961 Szigeti published four seminal papers on the dielectric behaviour of crystals. Szigeti’s theory is applicable to isotropic and anisotropic, ionic and covalent crystals with different structures. Szigeti’s theory connects dielectric, spectroscopic and elastic properties. An important outcome of Szigeti’s theory is the concept of the effective ionic charge (s). It is pointed out that s correlates with a number of physical properties and is a measure of ionicity of the interatomic bond. Since Szigeti’s work, several theoretical models have been proposed to account for the fact that s < 1. These models provide an insight into the complex polarization mechanisms in solids. This review summarizes Szigeti’s work and the work that followed; the implications and applications of Szigeti’s theory are discussed. Some new results are also included. Dedicated to the memory of late Prof. P S Narayanan.     

Physical aging in Zr46.75Ti8.25Cu7.5Ni10Be27.5 typical bulk metallic glass manifested as enthalpy relaxation

Enthalpy recovery is not only an important characteristic of physical aging of glass, but also a good tool to investigate the physical aging. Using differential scanning calorimeter (DSC), the enthalpy recovery of Zr_46.75Ti_8.25Cu_7.5Ni₁₀Be_27.5 bulk metallic glass (BMG) was studied. The typical characteristics of enthalpy recovery of glass including the sub-T _g peak and ‘overshot’ were found in BMG. The evolution of the sub-T _g peak and ‘overshot’ were described by the free volume theory and Hodge’s model, respectively. It was found that the former failed to describe the enthalpy recovery in the BMG, while the latter could give a qualitative explanation. In combination with the dynamics in the BMG, the origin of the enthalpy recovery in the BMG was discussed. The results show that BMGs are an ideal material to investigate the physical aging. The further understanding of physical aging of BMGs is useful to clarify the nature of glass and improve the application and device of new types of BMGs. Supported by the National Natural Science Foundation of China (Grant No. 50671118)