Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s.Comment: 22 pages, 5 figure

Weak 3He\text{}^{3}He Pairing in 3He−He(II)\text{}^{3}He-He(II) Mixtures

In this paper a theoretical study of a possible phase transition in dilute $\text{}^3He-He(II)$ mixtures is presented using the Galitskii-Migdal-Feynman formalism. The effective scattering length is calculated from the Galitskii-Migdal-Feynman T-matrix, which is essentially the effective scattering amplitude dependent on the medium. It is found that at very low $\text{}^3He$ concentrations the s-wave effective scattering length for ^3He-He(II) varies discontinuously from positive to negative values at some critical concentration. This indicates a crossover from a regime with dimers to another with the Cooper pairs. The binding energy of the weakly-bound dimers $\text{}^3He_2$ is computed. The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations. It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%. Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell

Synthesis of Nanosilica for the Removal of Multicomponent Cd2+ and Cu2+ from Synthetic Water: An Experimental and Theoretical Study

Copper and cadmium ions are among the top 120 hazardous chemicals listed by the Agency for Toxic Substances and Disease Registry (ATSDR) that can bind to organic and inorganic chemicals. Silica is one of the most abundant oxides that can limit the transport of these chemicals into water resources. Limited work has focused on assessing the applicability of nanosilica for the removal of multicomponent metal ions and studying their interaction on the surface of this adsorbent. Therefore, this study focuses on utilizing a nanosilica for the adsorption of Cd2+ and Cu2+ from water. Experimental work on the single- and multi-component adsorption of these ions was conducted and supported with theoretical interpretations. The nanosilica was characterized by its surface area, morphology, crystallinity, and functional groups. The BET surface area was 307.64 m2/g with a total pore volume of (Formula presented.) cm3/g. The SEM showed an irregular amorphous shape with slits and cavities. Several Si-O-Si and hydroxyl groups were noticed on the surface of the silica. The single isotherm experiment showed that Cd2+ has a higher uptake (72.13 mg/g) than Cu2+ (29.28 mg/g). The multicomponent adsorption equilibrium shows an affinity for Cd2+ on the surface. This affinity decreases with increasing Cu2+ equilibrium concentration due to the higher isosteric heat from the interaction between Cd and the surface. The experimental data were modeled using isotherms for the single adsorption, with the Freundlich and the non-modified competitive Langmuir models showing the best fit. The molecular dynamics simulations support the experimental data where Cd2+ shows a multilayer surface coverage. This study provides insight into utilizing nanosilica for removing heavy metals from water. 2022 by the authors.The authors would like to acknowledge the University of Jordan, Deanship of Scientific research, and the Department of Chemical Engineering for providing the facility to conduct this research; the Gas Processing Center at Qatar University for performing the characterization techniques for the samples; and Hassan Asiri from King Fahd University of Petroleum and Minerals for providing access to the dynamic molecular simulator.Scopu

Scattering properties of argon gas in the temperature range 87.3-120 K

A theoretical model, based on the Galitskii-Migdal-Feynman formalism, is introduced for determining the scattering properties of argon gas, especially the "effective" total, viscosity and average cross-sections. The effective phase shifts are used to compute the quantum second virial coefficient in the temperature range 87.3-120 K. The sole input is the Hartree-Fock dispersion (HFD-B3) potential. The thermophysical properties of the gas are then calculated. The results are in good agreement with experimental data

Synthesis of Nanosilica for the Removal of Multicomponent Cd2+ and Cu2+ from Synthetic Water: An Experimental and Theoretical Study

Copper and cadmium ions are among the top 120 hazardous chemicals listed by the Agency for Toxic Substances and Disease Registry (ATSDR) that can bind to organic and inorganic chemicals. Silica is one of the most abundant oxides that can limit the transport of these chemicals into water resources. Limited work has focused on assessing the applicability of nanosilica for the removal of multicomponent metal ions and studying their interaction on the surface of this adsorbent. Therefore, this study focuses on utilizing a nanosilica for the adsorption of Cd2+ and Cu2+ from water. Experimental work on the single- and multi-component adsorption of these ions was conducted and supported with theoretical interpretations. The nanosilica was characterized by its surface area, morphology, crystallinity, and functional groups. The BET surface area was 307.64 m2/g with a total pore volume of 4.95×10−3 cm3/g. The SEM showed an irregular amorphous shape with slits and cavities. Several Si–O–Si and hydroxyl groups were noticed on the surface of the silica. The single isotherm experiment showed that Cd2+ has a higher uptake (72.13 mg/g) than Cu2+ (29.28 mg/g). The multicomponent adsorption equilibrium shows an affinity for Cd2+ on the surface. This affinity decreases with increasing Cu2+ equilibrium concentration due to the higher isosteric heat from the interaction between Cd and the surface. The experimental data were modeled using isotherms for the single adsorption, with the Freundlich and the non-modified competitive Langmuir models showing the best fit. The molecular dynamics simulations support the experimental data where Cd2+ shows a multilayer surface coverage. This study provides insight into utilizing nanosilica for removing heavy metals from water