Values Of Σeff Research Articles

The dependence of the size of confined water fluid molecules on the radius of carbon nanotube

A recently-derived perturbation-theory-based equation of state (EoS) has been used for describing the p-v-T behavior of water confined inside a carbon nanotube (CNT). The one-center united atom model (OCUA) was employed for modeling of water molecules inside the CNT with temperature-dependent effective diameter, σeff. The interaction between two nearest-neighbor molecules was taken into account as an effective pair potential (EPP) which is an average effective extended Lennard-Jones (12, 6, 3) (AEELJ) pair interactions in the framework of thermodynamic perturbation theory (TPT). A new concept as effective molecular diameter tensor (EMDT) was introduced to consider the anisotropic character of compression factor in the EoS. The values of σeff,zz, and σeff,xy of the EMDT for the axial and radial directions, respectively, in both filled and unfilled states of the CNT, were estimated by using the simulated p-v-T data in the EoS. The results mirror the fact that the σeff,zz, and σeff,xy values of water molecule increase with the radius of CNT (R). Moreover, the values of σeff,zz for the different radii of CNT are nearly close to those of σeff,xy. Also, the results show that the layers of water molecule formed in the filled state are of less space with respect to those of the unfilled state. Our results showed that the EMDT is of the importance to follow the changes of molecular shape of the nanoconfined fluid with the CNT's size.

Modeling of the n–alkane homologous series in the range of C6 to C20 using linear Yukawa isotherm regularity (LYIR)

The linear Yukawa isotherm regularity (LYIR) equation of state (EoS) was used to model the p–v–T behavior of n–alkane homologous series CnH2n+2 (6≤n≤20) in the dense fluid region. A molecular model was proposed and the LYIR EoS was modified based on this model to take the effects of segments of the chain molecule into account. In the proposed model, each n–alkane molecule was assumed as an n–fold tangentially one–center spherical segments. In the other word, the n–alkane fluid was considered as a hypothetical mixture of methyl and methylene groups. The average effective pair potential (AEPP) between two segments was modeled by the hard–core Yukawa (HCY) potential in the framework of liquid's thermodynamic perturbation theory (TPT). The experimental p–v–T data of the selected n–alkanes were used to evaluate the validity of the modified LYIR EoS (MLYIR). Four important conclusions were obtained in this work: (a) The average coordination number (z) in the hypothetical mixture depends on n as well as temperature (T) and molar density (ρ) so that its value increases and decreases for the odd and even values of n, respectively. (b) the effective HS diameter (σeff) of segment increases and decreases with the chain length for the n–alkanes with odd and even value of n, respectively, and become independent of the chain length for n>20. (c) The σeff of the n–alkanes with the even number of carbon atoms is greater than that of the molecules with the odd value of n for n<18. (d) The MLYIR EoS showed that the εeff and λeff of Yukawa AEPP for the segment–segment interaction are independent of the chain length. Moreover, the results demonstrated the relationship between the symmetry of chain structure and the value of σeff.

Modeling the p–v–T behavior of furfural compounds using perturbed linear Yukawa isotherm regularity

The p–v–T behavior of furfural compounds (FCs) such as 5–methylfurfural (5–MF) and tetrahydrofurfuryl alcohol (THF–A) by using the perturbation-based linear Yukawa isotherm regularity (LYIR) were modeled. The LYIR is a perturbation–based equation of state (EoS) which was recently derived by making use of the attraction part of hard–core Yukawa (HCY) potential as perturbation average effective pair potential (AEPP) in the framework of liquid's thermodynamic perturbation theory. To use the LYIR EoS for modeling FCs, each molecule of the FC was considered as an one–center spherical united atom with temperature–dependent effective diameter. The results showed that the LYIR model can predict the p–v–T behavior of the selected FCs very well and the reproduced densities obtained by the LYIR EoS are in very good agreements with the available experimental densities. The range of the relative deviations percentage between the experimental and calculated density are from −0.006% to 0.02% for 5–MF and 0.009% to −0.01% for THF–A. In addition, the parameters of the HCY potential (σeff, λeff), as AEPP, were obtained for the selected FCs using the LYIR model and provided valuable information on the structure, intermolecular interactions, and the role of substitution groups on the p–v–T behavior of this class of green fluids. Moreover, the results of the study mirror the effect of the hydrogenation and the dehydrogenation processes on the value of σeff. Additionally, the contribution of internal pressure in compression factor and also the effect of both pressure and temperature on the internal compression factor were investigated.

Correlation of isothermal compressibility coefficient and reduced bulk modulus of dense fluids using perturbed linear Yukawa isotherm regularity

ABSTRACTA new simple analytical expression has been derived for predicting the reduced bulk modulus () and isothermal compressibility coefficient () of dense fluids using a new proposed equation of state (EoS) known as the linear Yukawa isotherm regularity (LYIR). The advantage of the derived expressions is that the variation of Br and with the changes of the parameters of Yukawa effective pair potentials (εeff, σeff and λeff) can be investigated. The calculated isotherms of Br and obtained from the derived expression show a good agreement with the literature data for some selected dense fluids. The variation of Br with σeff of effective pair Yukawa potential was studied and it was observed that the increase in the value of σeff accompanied by the increase of Br. The ability of the derived expressions for predicting Br and was compared with the corresponding expressions obtained from the linear isotherm regularity (LIR) and Goharshadi–Morsali–Abbaspour (GMA) EoSs, which are based on an average effective near neighbour pair interaction. It was found that the ability of LYIR EoS in predicting Br is comparable with LIR and GMA EoSs. This comparison also showed that the LYIR EoS can be successfully used to predict and correlate the Br and of dense fluids and the hard-core Yukawa potential can be adequately used in the modelling of the thermodynamical and thermo-physical properties of the dense systems. Finally, the derived expression for Br predicted the common bulk modulus region at which the different isotherms of Br vs. density intersect each other in a density region.

Characteristics of amplification of high-power laser pulses in neodymium silicate and phosphate glasses

An investigation was made of the amplification of microsecond radiation pulses in neodymium-activated glasses. The effective cross sections σeff of stimulated transitions were determined before and after the passage of a high-power pulse. The cross section σeff, representing the active medium at the maximum of a luminescence pulse, was found to depend on the degree of excitation N0 of the active element in the amplifier. When the energy density E0 of the radiation at the amplifier input was increased, the value of σeff (measured after the passage of the pulse being amplified) decreased in the case of silicate glasses, but increased for phosphate glasses. A hypothesis was put forward that the equilibrium profile of the luminescence line of neodymium glasses could become deformed under the action of superluminescence during an optical pump pulse, which would lead to the dependence of σeff on N0. This hypothesis was confirmed by computer calculations carried out on the basis of an approximate model of an active medium with a single inhomogeneously broadened laser transition line and with parameters typical of neodymium glasses. The dependence of the efficiency η of energy extraction on E0 almost reached its maximum value at E0 ≈ 30 J cm-2. A further increase in E0 for the purpose of increasing η would be pointless. The maximum experimental efficiency of extraction of the energy of excited particles was ~95% for phosphate glasses.

The inelastic mean free path of electrons in some semiconductor compounds and metals

AbstractThe elastic backscattering probability Pe of electrons is proportional to the product of the inelastic mean free path (IMFP), effective backscattering cross section (σeff), and atomic density (N). Thus, experimental evaluation of Pe, e.g. from the elastic peak intensity measurements, enables the determination of the IMFP. σeff can be calculated by integrating the differential elastic scattering cross sections using a simplified model based on the first Born approximation and the Thomas–Fermi–Dirac atomic potential. No significant difference in the values of σeff was found using the Thomas–Fermi, the Thomas–Fermi–Dirac and the Hartree–Fock atomic potentials or integrating the scattering cross sections tabulated by Fink et al. From the experimental values of Pe reported by Schmid et al. and by Gergely the IMFP was determined for a number of elements. A good agreement was found with the data on the IMFP published in the literature. Comparing the elastic peak of two samples and using the data of Ashley and Tung as reference values, the IMFP has been determined for GaP, GaSb, InP, InSb and Si3N4 samples. Good agreement with the data of Ashley and Tung was obtained for Si, Ge, SiO2 and GaAs.

Determination of the effective stimulated emission cross section of neodymium ions in various matrices using the luminescence dumping method

An improved method for direct measurement of the effective stimulated emission cross section σeff for neodymium ions in various matrices is proposed. The relationship between the cross sections measured using the luminescence dumping and traditional spectroscopic techniques is determined. Values of σeff are obtained for various crystals and it is shown that σeff can be measured in samples of poor optical quality, including powders.