Rao Number Research Articles

The second Feng–Rao number for codes coming from telescopic semigroups

In this manuscript we show that the second Feng–Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first study the behavior of Apery sets under gluings of numerical semigroups. These results provide a bound for the second Hamming weight of one-point Algebraic Geometry codes, which improves upon other estimates such as the Griesmer Order Bound.

Compatibility studies of chitosan/PVA blend in 2% aqueous acetic acid solution at 30 °C

The miscibility of chitosan (CS) and poly(vinyl alcohol) (PVA) blends in aqueous acetic acid solution was studied using viscosity, ultrasonic velocity and refractive index techniques at 30 °C. From the viscosity data by using Sun and Chee et al., approaches, the interaction parameters Δ B, μ and α are also calculated to predict the blend compatibility of the blend solutions. The results of these blends data suggest that CS/PVA blends were completely miscible in all proportions. The results pertaining to variation of ultrasonic velocity ( v ) and their derived parameters such as adiabatic compressibility, acoustic impedance, relaxation strength and Rao number also supports the miscibility nature of these blends. This is further confirmed by refractive index results also. Differential scanning calorimetry (DSC), XRD and FT-IR were also used to confirm the compatibility of the CS/PVA blends in the solid state (thin films). Experimental results showed that the blends of CS and PVA are miscible at all the compositions due to the strong intermolecular hydrogen bonding interactions between CS and PVA.

Thermodynamic and acoustical parameters of some nematic liquid crystals

Ultrasonic and density measurements on solutes in dilute solutions are used to obtain thermodynamic and acoustical parameters and their excess values. The physical parameters that can be obtained such as molar sound velocity or Rao's number ( R), molar compressility or Wada's constant ( B), characteristic acoustic impedance ( Z), intermolecular or free length ( L f), free volume ( V f), available volume ( V a) and adiabatic compressibility ( β) play an important role in the phenomenon of sound transmission. For example, the parameter Z determined by the product of density ( d) and ultrasonic velocity ( c) has a greater significance as a characteristic property than density or velocity. In the case of sound transmission the parameter of more concern is the molar sound volume ( V m) rather than molar sound velocity or Rao's number. Such studies on pure liquid crystals around phase transition temperature yield important information. In view of the above facts, the ultrasonic velocity and density measurements on pure samples of nematics, namely, 4,4′-azoxy anisole and 4,4′-dibutoxy azoxy benzene in dilute solutions were taken up. The results of this work is presented in this paper and discussed.

Characterization of Some Liquid Crystals through Sound and Thermodynamic Parameters

The structural changes arising from transition between the mesophases of liquid crystalline materials can be better understood by ultrasound in conjunction with specific volume properties. In particular, ultrasonic studies are found to give clear information regarding the nature of the phase transition, pretransitional effects, and molecular ordering. For example, temperature corresponding to the maximum value of acoustic impedance, adiabatic compressibility, and temperature corresponding to the minimum value of ultrasonic velocity, Rao's number, order parameter, and molar compressibility, in thermotropic liquid crystals are very useful in understanding their structural behavior. In view of these facts, it was thought worthwhile to study ultrasonic velocity with data available for density measurements on pure samples of nematics, namely, 4,4′-azoxy anisole and 4,4′-dibutoxy azoxy benzene. The results of this work, are presented in this article and discussed.

A study on thermodynamic and sound parameters of some nematics

Measurements of ultrasonic velocity and density of solutes in dilute solutions as a function of concentration and temperature can be used to obtain several thermodynamic and acoustical parameters and their excess adiabatic compressibility. The physical parameters that can be determined through these are: molar sound velocity or Rao's number (R), molar compressibility or Wada's constant (B), characteristic acoustic impedance (Z), intermolecular or free length (L f), free volume (V f), available volume (V a) and adiabatic compressibility (β). These parameters play an important role in the phenomenon associated with intermolecular interaction and hence in sound transmission. For example, the parameter Z that is determined by the product of density (d) and ultrasonic velocity (c) has a greater significance as a characteristic property of the medium than does either the density or velocity individually so also in case of sound transmission the parameter of more concern is the molar sound volume (V m) rather than molar sound velocity or Rao’ number. Such studies on liquid crystals around phase transition temperature in their pure state yield important information and so also in their dilute solutions. In view of above facts, the ultrasonic velocity with density measurement studies on pure samples of nematics, namely, Butyl-p-(p-ethoxy phenoxy carbonyl)phenyl carbonate, p-(p-ethoxy phenyl azo)phenyl undecylenate and p-[N-(p-methoxy benzylidene)amino]phenyl benzoate in dilute solutions was taken up both as a function of mole fraction (in benzene) and temperature. The results of the above work is presented in this article and discussed.

Molecular association of aliphatic ketones and phenol in a nonpolar solvent-ultrasonic and IR study

Density and ultrasonic velocity at 2 MHz have been measured for the two ternary liquid mixtures of acetone and ethyl methyl ketone with phenol in the nonpolar solvent carbon tetrachloride for different concentrations at varying temperatures of 30°C, 40°C and 50°C. The measured values of ultrasonic velocities have been compared with the theoretically calculated velocities using Nomoto and Ideal mixing relation. Adiabatic compressibility, intermolecular free length, Rao's number and degree of intermolecular attraction parameters were also computed. Excess values of adiabatic compressibility, intermolecular free length and volume were calculated to study the molecular association occurring between solute-solute molecules in a nonpolar solvent. Ultrasonic velocity for each mixture shows a maximum at certain concentration for specific temperatures; adiabatic compressibility, intermolecular free length and their excess values in mixtures show minima at the same concentrations and temperatures. The corresponding maxima position of velocity and minima positions of other parameters show that maximum complexation due to the interaction between solute molecules through hydrogen bonding occurs at this concentration. On further increasing or decreasing the concentration, the molecular association occurring in the mixture decreases. These results are further supported by the observed infrared spectrum for these mixtures, which provide for the evidence of complex formation as observed through ultrasonic data.

Acoustical Parameters of CuCl-KCl System in Acetonitrile-Water Solvent Mixture

Ultrasonic velocity (U) and density (d) have been measured for CuCl-KCl in. acetonitrile water co-solvent at various temperatures from 298.15 to 318.15K. The adiabatic compressibility (βad), molar compressibility (β) specific acoustical impedance (Z), Rao Number (R) and Van der Waals Constant (b) have been computed. The variation of d, βad, β, Z, R and b with molarity of CuCl have been studied. The association between the components and the formation of complexes are treated.

Acoustical parameters of polyethylene glycol/water mixtures

Ultrasonic velocity (v) and density (d) have been measured for polyethylene glycol/water mixtures at 30°C. The adiabatic compressibility (β ad), molar compressibility (β), specific acoustic impendance (Z), Rao number (R) and van der Waals constant (b) have been computed. The variations ofv, d, β ad,β, Z, R andb with mole ratio of water/ether group oxygen have been studied. The association between the components and the formation of tetrahydrate have been reported.

Acoustical Study and Thermodynamics of Dissociation and Micellization of Lanthanum and Cerium Linoleates in A Mixture of Benzene and Methanol

Abstract Ultrasonic measurements on lanthanum and cerium linoleates were made in a mixture of 60% benzene and 40% methanol (V/V), to determine the CMC, soap-solvent interaction and various acoustic and thermodynamic parameters. The values of the CMC increase with the increase in temperature. The ultrasonic velocity, specific acoustic impedance, apparent molar compressibility, relative association and Rao's number increase while the adiabatic compressibility, intermolecular free length, apparent molar volume, solvation number and available volume decrease with increasing soap concentration. The dissociation constant and thermodynamic parameters for dissociation and micellization processes of lanthanum and cerium linoleates were evaluated from conductivity measurements. The results showed that these soaps behave as weak electrolytes in dilute solutions and the micellization process is dominant over the dissociation process.

Acoustical parameters of poly(vinyl pyrrolidone) in N, N-dimethyl formamide solutions

Ultrasonic velocity, viscosity, density and refractive index measurements have been made for solutions for poly(vinyl pyrrolidone) (PVP; viscosity average molecular weight ≅40,000) in N, N-dimethyl formamide (DMF) at various concentrations and temperatures. The molar compressibility (β), specific acoustic impedance ( Z), Rao number ( R), Van der Waals constant ( b) and the relaxation strength ( r) have been computed. The variations of β, Z, R and b with concentration at several temperatures have been studied; the solute-solvent interaction for PVP in DMF is confirmed.

Acoustical parameters of poly(vinyl pyrrolidone) solutions

AbstractUltrasonic velocity, viscosity, density, and refractive index measurements have been made with aqueous solutions of poly(vinyl pyrrolidone) at various concentrations and temperatures. The molar compressibility β, specific acoustic impedance Z, Rao number R, and VAN DER WAALS constant b have been calculated. From the variation of β, Z, R, and b with concentration at different temperatures the formation of a hydrogen bonded complex for this polymer at definite concentrations has been confirmed.

Phase transition studies in 50CB and 80CB

AbstractInvestigations on the temperature variation of specific volume and ultrasonic velocity are carried out to study the phase transitions in the liquid crystals 4′‐n‐Pentyloxy‐4‐Cyanobiphenyl (50CB) and 4′‐n‐Octyloxy‐4‐Cyanobiphenyl (80CB). From these studies various parameters like the adiabatic compressibility (βad), molar sound velocity or Rao number (Rn), molar compressibility (B), Van der Waals constant (b) and the intermolecular free lengths (L) are estimated as a function of temperature in the isotropic as well as in the mesophases. Finally the variation of the order parameter with temperature in the nematic phase is studied and the results are discussed.

Ultrasonic Study on 2-Aminopyridine in Solution in Benzene at 309 K

Abstract The ultrasonic velocity at 2 MHz, density, viscosity and refractive-index are measured at various concentrations in the solution of 2-aminopyridine in benzene at 309 K. Using the measured data, various useful parameters like adiabatic compressibility, Rao number, Wada's constant, Van der Waals constant, specific acoustic impedance, molar refraction, classical absorption, dielectric relaxation time, intermolecular free length and collision factor are computed. 2-Aminopyridine is found to be associative, showing strong molecular interactions with benzene.

Multifrequency ultrasonic investigations in the liquid crystal 80CB

AbstractInvestigations on the temperature variation of the specific volume and ultrasonic velocity (at four different fixed frequencies) in the liquid crystal 4′‐n‐octyloxy‐4‐cyanobiphenyl (80CB) are carried out both in the nematic and isotropic phases. From these studies various physical parameters like adiabatic compressibility (ßad), molar sound velocity or Rao number (Rn), molar compressibility (B), Van der Waal's constant (b) and the intermolecular free lengths (L) as a function of temperature are estimated. The variation of all these parameters with the ultrasonic frequency is also studied. The variation of the order parameter with temperature is also studied at the four frequencies and the results are discussed.

Phase Transition Studies of the Liquid Crystal Pentyloxybenzylidene Phenylazoaniline

AbstractPhase transition studies of the liquid crystal pentyloxybenzylidene phenylazoaniline are investigated with density and ultrasonic velocity measurements. The density variation with temperature confirms that the isotropic liquid‐nematic, nematic‐smectic A and smectic A‐smectic B transitions are of first order. The temperature variation of ultrasonic velocity confirms all the phase transitions. The adiabatic compressibility (βad), Rao number (Rn) and Molar compressibility (B) are estimated from density and ultrasonic velocity.

Phase transition studies inN(p-n-pentyloxy benzylidene)p-n-decyl aniline

Abstract The temperature dependences of the molar volume, the ultrasonic velocity and the refractive index in N(p-n-pentyloxy benzylidene) p-n-decyl aniline, which exhibits nematic, smectic-A and smectic-B, phases, are presented. The isotropic-nematic and smectic-A-smectic-B phase transitions are found to be of first order while the nematic-smectic-A transition is of second order. The thermal expansion coefficient (a) computed from the molar volume data agrees with a second-order N-SA transition. The computed adiabatic compressibility βad, molar sound velocity (or Rao number Rn ) and molar compressibility (or Wada constant A) are presented.

Ultrasonic investigations ofN-(p-n-pentyloxybenzylidene)p-n-butylaniline

Abstract The ultrasonic velocity in N-(p-n-pentyloxybenzylidene) p-n-butylaniline is measured as a function of temperature from the isotropic liquid phase to the smectic G phase. A mixed smectic phase (SAG) for a temperature interval of 2°C is reported. The derived parameters such as adiabatic compressibility (βad). Rao number (Rn) and molar compressibility (B) are also reported.

Dielectric and Ultrasonic Relaxation of P-Azoxy Anisole in Benzene and Carbon Tetrachloride at Room Temperature

The dielectric, conductivity, and ultrasonic measurements for p-azoxy anisole are done in its solution in benzene and carbon tetrachloride at room temperature and various concentrations. The density and viscosity are also measured for these solutions. The dipole moment and relaxation time are computed using a new alternative method as suggested by Johri and compared with the Gopala Krishna microwave method, and the Higasi and Guggenheim static methods. Adiabatic compressibility, Rao number, van der Waal's constant, specific acoustic impedance, and free volume are obtained using density and ultrasonic velocity. Both the solutions show 99% solid-like behavior. The measured and evaluated dielectric and ultrasonic parameters provide information about the structure of p-azoxy liquid crystals and about the solute-solvent interactions.

Phase transition studies inp-n-nonyloxybenzoic acid

Abstract Phase transitions of the liquid crystal p-n-nonyloxybenzoic acid have been investigated with density and ultrasonic velocity measurements. The variation of density with temperature confirms that the isotropic-nematic and nematic-smectic C transitions are of first order. All the phase transitions are confirmed by the variation of ultrasonic velocity with temperature. The adiabatic compressibility (βad), and Rao number (Rn) are also estimated.

Properties and structures of some butoxysiloxanes

AbstractTetrabutoxysilane and polybutoxysiloxanes were prepared by reacting SiCl4 with I‐butanol and I‐butanol‐water mixtures in liquid phase. The effect of water content on some of the physical properties, such as viscosity, density, surface tension, refractive index, specific heat, thermal expansion and ultrasonic sound velocity, was determined. Also, the molecular weights and the percentages of silica and butoxy group were estimated. Using these experimentally determined physical properties, other properties such as Rao's number, molecular radius, Van der Waal's constant, isothermal and adiabatic compressibilities, the ratio of specific heats, thermal conductivity and the activation energies for vaporisation and viscosity were calculated theoretically. Based on the experimental values and theoretical calculations, the cyclic structure of some of the compounds was established.