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We developed in this paper the used methodology to describe the Lennard-Jones potential of two atoms in rare gas. In this treatment we supposed that one atom could be described by a harmonic oscillator. The interaction potential is developed at short and long ranges. The results showed that the obtained physico-chemical parameters such as the oscillator frequency, the atom mass, and the atom charge well reproduce the Lennard-Jones potential. Then the potential well depth and the effective equilibrium diameter are expressed in function of the oscillator frequency, the atom mass and charge. [ABSTRACT FROM AUTHOR]

This research work is a contribution to understand the olfaction mechanism at a molecular level of vanillin, ethyl vanillin, coumarin and quinoline molecules using a modeling of a putative adsorption process by analytical model established by statistical physics formalism. A statistical physics modeling using the monolayer model with identical and independent binding sites of the responses of the two human olfactory receptors OR10G4 and OR2B11 showed that vanillin and quinoline were adsorbed with a mixed non-parallel and parallel orientation on OR10G4 and on OR2B11, respectively. However, ethyl vanillin and coumarin were anchored with a total non-parallel orientation. The adsorption energy values collected from data analysis, which were ranged from 12.51 to 20.91 kJ/mol, confirmed that the adsorption of vanillin and ethyl vanillin on OR10G4 and the adsorption of coumarin and quinoline on OR2B11were exothermic and were based on physical interactions. Furthermore, the dose-olfactory response curves of vanillin, ethyl vanillin, coumarin and quinoline provided access to OR10G4 and OR2B11 steric characterization via the calculation of the studied olfactory receptors site size distributions (RSDs). Indeed, vanillin, ethyl vanillin, coumarin and quinoline RSDs are spread from 0.3 to 12 nm, from 0.5 to 12 nm, from 0.40 to 12 nm and from 0.14 to 12 nm, respectively, with a maximum at 1.55 nm, 2.11 nm, 2.50 and 1.13 nm, respectively. Lastly, the physico-chemical model parameters can be used for the energetic characterization to confirm the physical nature of the vanillin/ethyl vanillin-OR10G4 and the coumarin/quinoline-OR2B11 interactions and to determine an olfactory band of order of 12 kJ/mol [11–23 kJ/mol], 10 kJ/mol [14–24 kJ/mol], 7 kJ/mol [9–16 kJ/mol], 15 kJ/mol [13–28 kJ/mol] for vanillin, ethyl vanillin, coumarin and quinoline, respectively, through the determination of the adsorption energy distributions (AEDs). • Vanillin, ethyl vanillin, coumarin and quinoline dose-response curves were fitted by a statistical physics model. • Steric and energetic interpretations were derived from olfactory response curves. • Calculation with statistical physics model was used to determine the RSDs and the AEDs. [ABSTRACT FROM AUTHOR]

• Advanced adsorption models are derived from grand canonical ensemble in statistical physics. • 2-phenylethanethiol dose–response curves are successfully modeled by a statistical physics monolayer model. • Physico-chemical analysis of 2-phenylethanethiol adsorption on OR1A1 and OR2W1 without and with Cu2+ is provided. • Investigation with statistical physics model was used to determine the receptor site size and the adsorption energy distributions. This paper aims to investigate the effect of metal especially copper ions on the adsorption of a key food odorant (2-phenylethanethiol) on two human olfactory receptors OR1A1 and OR2W1 that was interpreted via a statistical physics monolayer model. To this purpose, four experimental dose-olfactory response curves were used without and with the presence of Cu2+ for each human receptor. In order to reach a theoretical interpretation of the experimental data and understand the effect of the used metal on adsorption process introduced on the olfaction mechanism, a statistical physics monolayer adsorption model with identical and independent sites was applied. The used model showed that the presence of copper ions decreased the efficacy (olfactory response at saturation) of 2-phenylethanethiol key food odorant activating OR1A1, suggesting a negative allosteric action. However, the presence of Cu2+ reduced the potency (concentration at half saturation) of the studied thiol key food odorant in activating OR2W1, suggesting an orthosteric competitive action. Furthermore, the molar adsorption energies retrieved from data analysis varied from 5.568 to 9.886 kJ/mol in studied systems, whose values showed that the process based on a physical adsorption. Lastly, the dose-olfactory response curves of 2-phenylethanethiol on two broadly tuned human olfactory receptors OR1A1 and OR2W1 provided access to the olfactory receptor site size distribution (RSD) and also the adsorption energy distribution (AED). [ABSTRACT FROM AUTHOR]

Steric and energetic characterizations were performed for the adsorption of eugenol (EG), vanillin and ethyl vanillin (EV) onto the mouse eugenol olfactory receptor mOR-EG by using a proposed model expression established by statistical physics methods. We started with a modeling of dose-response curves. The calculated curves fit well the experimental data and the physico-chemical model parameters can be used for the characterization of the interactions between the eugenol, vanillin and ethyl vanillin molecules and the mouse eugenol receptor and the determination of the olfactory band for these three odorant molecules through the determination of the adsorption energy values and the adsorption energy distributions. Furthermore, thermodynamic functions of the odorant adsorption such as the configurational entropy, Gibbs free enthalpy and internal energy were calculated and their negative values indicate that the adsorption process included in the olfaction mechanism was exothermic and spontaneous nature. • Physical interpretations were derived from EG, vanillin and EV response curves modeling by a statistical physics treatment. • Calculation with statistical physics model was used to determine the RSDs and the AEDs. • Determination of olfaction band of eugenol, vanillin and ethyl vanillin molecules. [ABSTRACT FROM AUTHOR]

In the biosensor system, olfactory receptor sites could be activated by odorant molecules and then the biological interactions are converted into electrical signals by a signal transduction cascade that leads the toopening of ion channels, generating a current that leads into the cilia and depolarizes the membrane. The aim of this paper is to present a new investigation that allows determining the olfactory band using a monolayer adsorption with identical sites modeling which may also describe the static and the dynamic sensitivities through the expression of the olfactory response. Moreover, knowing the size of receptor site in olfactory sensory neurons provides valuable information about the relationship between molecular structure and biological activity. The determination of microreceptors and mesoreceptors is mostly carried out via physical adsorption and the radius is calculated using the Kelvin equation. The mean values of radius obtained from the maximum of the receptor size distributions peaks are 4 nm for ℓ-muscone and 6 nm for d-muscone. [ABSTRACT FROM AUTHOR]

Experimental absorption and desorption isotherms of hydrogen in Ti 1-x Zr x Mn 1.4 (x = 0, 0.1, 0.2, 0.3, 0.4) alloys at T = 293 K have been fitted using some theoretical model expressions treated by statistical physics through the grand canonical ensemble. The monolayer model with two types of sites is used to fit and interpret the experimental data. The physicochemical parameters governing the absorption-desorption processes and included into the model expressions could be numerically deduced from the relevant experimental isotherms. Six parameters of the model are fitted, namely the numbers of hydrogen atoms per site n 1 and n 2 , the receptor site densities N 1m and N 2m , and the energetic parameters P 1 and P 2 . The evolution of these parameters as function of composition x is plotted and explained in correlation with absorption-desorption processes. Finally, the thermo-dynamic potential functions which govern the sorption mechanisms such as internal energy E int , free enthalpy of Gibbs G a and entropy S a were derived from statistical physics calculations based on the model adopted. [ABSTRACT FROM AUTHOR]

The hydrogen absorption-desorption isotherms on LaNi 3.8 Al 1.2−x Mn x alloy at temperature T = 433 K is studied through various theoretical models. The analytical expressions of these models were deduced exploiting the grand canonical ensemble in statistical physics by taking some simplifying hypotheses. Among these models an adequate model which presents a good correlation with the experimental curves has been selected. The physicochemical parameters intervening in the absorption-desorption processes and involved in the model expressions could be directly deduced from the experimental isotherms by numerical simulation. Six parameters of the model are adjusted, namely the numbers of hydrogen atoms per site n 1 and n 2 , the receptor site densities N 1m and N 2m , and the energetic parameters P 1 and P 2 . The behaviors of these parameters are discussed in relation with absorption and desorption processes to better understand and compare these phenomena. Thanks to the energetic parameters, we calculated the sorption energies which are typically ranged between 266 and 269.4 KJ/mol for absorption process and between 267 and 269.5 KJ/mol for desorption process comparable to usual chemical bond energies. Using the adopted model expression, the thermodynamic potential functions which govern the absorption/desorption process such as internal energy E int , free enthalpy of Gibbs G and entropy S a are derived. [ABSTRACT FROM AUTHOR]

In this paper, an adsorption modeling has been presented to describe the interactions of a binary mixture of ℓ-muscone and d-muscone with the mouse muscone receptor MOR215-1. The formulation of the 2-dimensional monolayer models with identical and two types of sites for the perceived response of odor binary mixture odor are based on statistical physics and some theoretical hypothesis, in order to model pure and binary mixture dose-response curves. Thanks to the grand canonical ensemble of statistical physics, some pertinent physico-chemical parameters describing the adsorption process were introduced in the analytical model expressions. The results showed a high correlation of the 2-dimensional monolayer model using two types of sites with binary mixture of ℓ-muscone and d-muscone response curve. In this model, six physico-chemical parameters derived from the fitting of the experimental data by a numerical simulation were discussed. Furthermore, these statistical physics models include physico-chemical parameters specific to the respective effects of each compound in the binary mixture, which may help to clarify the inhibitory effects that are often seen in ℓ-muscone and d-muscone mixture through the determination of the involved new steric parameters. In addition, the calculation of the molar adsorption energies showed that the two muscone enantiomers and their racemic were physisorbed onto cell surface neurons. [ABSTRACT FROM AUTHOR]

In this work, two experimental dose-response curves of lyral molecules on the OR10J5 and the Olfr16 were employed in order to examine the evolution of physico-chemical parameters involved in the selected statistical physics model(s) to investigate the human and the mouse smelling of a floral scent. Indeed, one layer adsorption model on one type of sites with one energy (1LAM1T1E) and one layer adsorption model on two types of sites with two energies (1LAM2T2E), considered as appropriate models for the adsorption of lyral molecules on the OR10J5 and Olfr16, respectively, have been applied to fit the experimental data. Stereographic and energetic physico-chemical parameters, namely: the maximum response(s) at saturation, the number of docked molecules per olfactory receptor binding site and the concentration(s) at half saturation, were investigated to retrieve helpful information to describe the adsorption process putatively introduced in the olfaction perception. Thus, the advanced modeling results indicated that the studied molecules were docked with a non-parallel orientation (n > 1). Furthermore, for the two olfactory systems, the molar adsorption energies estimated from curves modeling were inferior to 11 kJ/mol, which showed the physisorption process of the adsorption of lyral molecules on OR10J5 and Olfr16. The 1LAM2T2E and the 1LAM1T1E were applied to estimate the OR10J5 and the Olfr175 RSDs, respectively. Hence, lyral RSDs were spread out from 0.7 to 20 nm with maximums at about 4 nm for OR10J5 and at about 3.65 nm for Olfr16. In addition, by using the two advanced models, the olfactory responses of lyral on OR10J5 and Olfr16 can be used for the energetic characterization of the lyral-OR10J5/Olfr16 binding sites interactions and allowed access to the adsorption energy distributions (AEDs). Then, two approximate olfactory bands can be determined for lyral molecules docked on OR10J5 and Olfr16, which are defined between 3 and 15.5 kJ/mol and between 3.5 and 13.5 kJ/mol, respectively. Lastly, thanks to the proposed models the adsorption entropy of the studied systems can be calculated to describe the disorder and the order on OR10J5 and Olfr16 surfaces (disorder peak of the two olfactory systems was attained when the equilibrium concentration was equal to the concentration at half saturation). Furthermore, the Gibbs free enthalpy and the internal energy were estimated and their negative values indicated that the adsorption phenomenon involved in the olfactory perception was spontaneous and exothermic nature. • Theoretical analysis was derived from lyral responses on OR10J5 and Olfr16 modeling by a statistical physics approach. • Stereographic and energetic characterizations were determined through RSDs and AEDs. • Three thermodynamic functions were investigated [ABSTRACT FROM AUTHOR]

The investigation of the adsorption process putatively involved in the olfactory perception of apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules on the mouse eugenol olfactory receptor mOR-EG was a very useful tool for comprising olfaction process at a molecular level. Indeed, the experimental data were correlated by using an advanced monolayer adsorption model with identical and independent binding sites. Thanks to the grand canonical ensemble in statistical physics formalism, the physico-chemical interpretations of modeling results indicated that the five odorants were adsorbed via a multi-molecular mechanism. Hence, the calculation of adsorption energies, that described the interaction between the odorant molecules and the olfactory receptor binding cavities, indicated that weak bonds were made between apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules and mOR-EG binding pockets amino acid residues. In addition, theoretical stereographic and energetic characterizations of mOR-EG were made via the determination of the olfactory receptor site size distributions (RSDs) and the adsorption energy distributions (AEDs) relative to apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol, homoguaiacol molecules. The RSD provided the size of different binding cavities of mOR-EG. Indeed, the five RSDs spectrums situated between 0.5 and 10 nm were spread out around an average size each one. The mean values obtained from the peaks of the distributions were 2.14 nm, 2.20 nm, 2 nm, 2.10 nm and 1.83 nm for apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol molecules, respectively. The AED gave a whole spectrum of adsorption energies that was activated by the odorant molecule. Thus, the apocynin, guaiacylacetone, homovanillyl alcohol, 4-ethylguaiacol and homoguaiacol AEDs were spread out from 5 to 27.5 kJ/mol, from 5 to 30 kJ/mol, from 5 to 35 kJ/mol, from 0 to 22.5 kJ/mol, 5 to 25 kJ/mol, respectively. The thermodynamic study, via the establishment of the adsorption entropy, indicated that the peak of the disorder was obtained when half of the binding sites were occupied. In addition, the Gibbs free enthalpy and the internal energy were determined and their negative values indicated that the adsorption phenomenon involved in the olfactory perception was spontaneous and exothermic physisorption phenomenon. • Modeling of concentration-olfactory response curves by an advanced monolayer adsorption model with identical sites. • Physico-chemical interpretations of the studied systems. • Quantitative characterizations of the five olfactory systems through the determination of the RSDs and the AEDs. • Determination of olfactory bands of the studied molecules. [ABSTRACT FROM AUTHOR]

In order to monitor the greenhouse gases, there is a new focus on substances that can distinguish between no harmful gases rejected to the atmosphere and capture those that must be decreased. The physico-chemical parameters involved in the expression of analytical model are obtained from the adjustments of the experimental data. We observed that this model can be used to characterize the complicated process by the steric parameters. Samples of these parameters are as follows: The number of CO2 molecules captured per binding site of the adsorbent (nCO2). The density of receptor sites of the adsorbent (FM) through the adsorption energies (ΔEa) associated for the adsorption of CO2 on the molecular sieves, which are related to Ps1 parameters. The modulus of the obtained adsorption energies from fitting data ranged between 3.99 and 4.38 kJ/mol, confirming that the adsorption in this system is exothermic and it is founded on physisorption process. Furthermore, a meticulous study of the main intrinsic characteristics of the adsorbent to the temperature impact application and ensuring the compatibility between practical and theoretical statistical physics to find the pore size was carried out. [ABSTRACT FROM AUTHOR]

• Physico-chemical parameters are involved through the grand canonical ensemble. • The internal energy of the WPT-AC/ethanol and M-AC/ethanol systems are calculated. • The enthalpy and entropy functions of the adsorption cooling cycles are derived. • The COP is calculated by means of statistical physics treatment • Discussion of the obtained COP for different two cycles was showed. Thermodynamic analysis of two different adsorption cooling cycles was presented; the first cycle is based on an isobaric adsorption process and the second one projects an isothermal adsorption instead of an isobaric adsorption. These cooling cycles are carried out by employing the grand canonical ensemble of the statistical physics formalism. This investigation is done for two different adsorbate/adsorbent pairs i.e. Ethanol/Waste Palm Trunk (WPT-AC) and Ethanol/Mangrove wood (M-AC). The corresponding adsorption isotherms have been fitted by statistical physics models to give a description of the adsorption process through interpretations of the evolution of the involved physico-chemical parameters, specific for this process. The results showed that the ethanol molecules have been mainly adsorbed with a multimolecular process and non-parallel to the adsorbent surface involving an aggregation process before molecules adsorption. Their adsorption energies are varying from 1.40 to 3.64 kJ/mol for WPT-AC and from 3.2 to 3.81 kJ/mol for the M-AC. These values reflected a physisorption process. The calculated internal energy values suggested the exothermicity and the spontaneity of the ethanol adsorption process. The investigation aims providing a methodology of calculation of the COP for an adsorption cooling cycle by using the statistical physics treatment. The entropy and the enthalpy functions are calculated and used to perform the thermodynamic evaluation and to calculate the coefficient of performance (COP). This parameter was found to be in the interval [0.12–0.69] for ethanol/WPT-AC and [0.11-0.6] for ethanol/M-AC for the first cycle and for the second cycle [0.15-0.81] and [0.15-0.74] respectively. [ABSTRACT FROM AUTHOR]

• Advanced modeling of experimental data by a monolayer model of ideal gas was studied. • Stereographic and energetic analyses of the four KFO olfactory systems were determined. • Molecular docking simulation was realized. In this paper, the putative phenomenon of adsorption involved in the insect olfactory perception of four fruity odorants on Machilis hrabei olfactory receptor MhOR5 was studied at a molecular scale. Thus, the experimental concentration–response curves of propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate on MhOR5 were adjusted using the monolayer model of ideal gas established using the powerful statistical physics approach, which was selected as the most appropriate model among the others. The fitted model parameters were applied to stereographic and energetic analyze the four olfactory systems. Indeed, the modeling results indicated that the tested fruity key food odorants (KFOs) were docked as 2- or 3-aggregated molecules on one MhOR5 binding site via a nonparallel position (i.e., multi-molecular adsorption mechanism). Energetic parameters were used to characterize the adsorption process involved in the studied systems via the determination of the molar adsorption energies (ranging from 12.91 to 17.52 kJ/mol). Hence, the values of the molar adsorption energies are positive and inferior to 40 kJ/mol; this means that the putative adsorption mechanism presented an exothermic character and a physical type. The docking simulation results proved that the adsorption of propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate on MhOR5 may occur via physical interactions (weak interactions) like alkyl, pi-alkyl, van der Waals, carbon hydrogen bond, and conventional hydrogen bond. The statistical physics theory may also be utilized to quantitatively characterize Machilis hrabei MhOR5 activated by propyl acetate, butyl acetate, isobutyl acetate, and prenyl acetate odorants via the estimation of the different site size distributions (SSDs) and site energy distributions (SEDs). [ABSTRACT FROM AUTHOR]

[Display omitted] • Recovery of biomass waste and its functionalization with H 2 SO 4 and HNO 3 in order to use it as an adsorbent to remove the reactive red dye 141 from an aqueous solution. • A theoretical physicochemical investigation of the adsorption of red reactive dye 141 on biomass treated with sulfuric acid and nitric acid was performed with statistical physics fundaments. • Physicochemical parameters were utilized to explain the dye adsorption at the molecular scale. The preparation and adsorption properties of avocado peels treated with H 2 SO 4 and HNO 3 for the removal of reactive red 141 dye are reported in this manuscript. Equilibrium adsorption of this organic dye on the two adsorbents was experimentally quantified at pH 6.5 and 298.15–328.15 K. An advanced physical model that assumed the formation of a finite number of layers of the adsorbed pollutant molecules on the adsorption sites was used to estimate the steric and energetic parameters of the dye adsorption mechanism. The modeling results showed dye molecular aggregation, in which each adsorption site of avocado peels treated with H 2 SO 4 and HNO 3 adsorbed several dye molecules simultaneously at different temperatures. The results also demonstrated that dye adsorption on avocado peels treated with these acids was exothermic. The estimated adsorption energies for the dye-treated biomass and dye-dye interactions indicated a physisorption associated with van der Waals forces and hydrogen bonding. The outcomes of this study contribute with insights into the adsorption mechanisms of dye molecules using treated avocado peels with the aim of developing sustainable water treatment methods according with a circular economy approach. [ABSTRACT FROM AUTHOR]

A synthesized MIL-101-NH2 has been used as an adsorbent to analyze Congo red (CR), methyl orange (MO), and acid chrome blue K (AC) dye adsorption phenomena. This investigation, based on statistical physics treatment, applied the double layer model with two energies to understand dye adsorption on three samples, namely, MIL-101-NH2-1, MIL-101-NH2-2, and MIL-101-NH2-3, at T = 298 K. Modeling results indicated that dye adsorption occurred via a mixed adsorption orientation for CR and MO dyes and a non-parallel orientation for AC dye on the MIL-101-NH2 surface. Dye uptake quantities varied from 2534.4 to 3440 mg/g for CR dye, 240.4 to 490.8 mg/g for MO dye, and 277 to 293 mg/g for AC dye. Thus, the highest adsorption amount appeared in the case of CR dye. Interpretation of the calculated energies showed that adsorption of the dyes on MIL-101-NH2 is a physisorption phenomenon, which could be controlled through energetic parameters obtained via numerical findings using the statistical double layer model. Moreover, the expression of the model is exploited to investigate the thermodynamic functions, such as internal energy. [ABSTRACT FROM AUTHOR]

• Microscopic analysis is provided from AP olfactory responses modeling by the one layer statistical physics model. • Energetic characterization is estimated via the discussion of AEDs. • Macroscopic analysis is determined via the investigation of three thermodynamic potentials. In this work, the one layer statistical physics model (M1) was applied to more deeply comprehend the phenomenon of adsorption, which is putatively involved in the olfactory sensation of acetophenone (AP) on mouse and human olfactory receptors. On one hand, the proposed model was utilized to microscopically characterize the studied olfactory systems in order to obtain advanced stereographic and energetic information concerning the studied olfactory systems in terms of a molecular view point. Based on the values of the number of acetophenone molecules docked on mouse and human binding sites n , it was found that the studied sweet odorant was linked with a mixed orientation. Energetically speaking, the values of the molar adsorption energy ΔE 1 , which ranged from 11.81 to 17.67 kJ/mol for mouse olfactory receptors (Olfr62, Olfr1093, Olfr1094, Olfr895, and Olfr876) and from 14.66 to 20.58 kJ/mol for human olfactory receptors (OR2C1, OR1A1, and OR2J2), indicated that acetophenone molecules were exothermically physisorbed. The adsorption energy distributions relative to AP may also be estimated to understand the olfactory sense in the investigated olfactory systems via the calculation of olfactory bands (i. e., AED bands), which may be defined between 4.80 and 27 kJ/mol and between 5.50 and 27 kJ/mol for mouse and human olfactory receptors, respectively. On the other hand, M2 was used to determine three thermodynamic potentials (i.e., the internal energy, the Gibbs free energy, and the adsorption entropy), which macroscopically characterized the investigated olfactory systems via a detailed thermodynamic analysis of the different olfactory systems. [ABSTRACT FROM AUTHOR]

In the present paper, a double layer advanced model was used to investigate the adsorption process putatively involved in the olfactory perception of sotolone and abhexone molecules on the human olfactory receptor OR8D1. The number of adsorbed molecules or the fraction of adsorbed molecule per site, n, informed that the two odorants molecules are docked on OR8D1 binding sites with mixed parallel and nonparallel anchorages. Furthermore, the estimated molar adsorption energy (−ΔE 1 and −ΔE 2) were inferior to 40 kJ/mol for the two adsorption systems, which confirmed the physical nature and the exothermic character of the adsorption process. In addition, stereographic characterizations of the receptor sites surface were carried out through the determination of the receptor site size distribution (RSDs) via Kelvin equation, which spread out from 0.05 to 1.5 nm. The adsorption energy distributions (AEDs) via Polayni equation show an adsorption band spectrum localized between 17 kJ/mol and 22.5 kJ/mol for sotolone and abhexone molecules respectively. A molecular docking calculation was performed. The results indicate that the binding affinities are belonging to the spectrum of the energy band of the molecules sotolone and abhexone, with values 19.66 kJ/mol and 19.24 kJ/mol. [Display omitted] • Description of olfactory perception of sotolone and abhexone molecules on OR8D1 • Statistical physics and molecular docking studies have been applied. • The adsorption energy and the receptor site size distributions are showed. • The best docked positions and the type of interactions are determined. [ABSTRACT FROM AUTHOR]

In this work, an adsorption phenomenon putatively involved in the olfactory sense of phenylacetic acid, 4-chlorophenylacetic acid, and 4-methoxyphenylacetic acid pheromones in the Zebrafish olfactory receptor ORA1 was a helpful mechanism in interpreting and characterizing the olfaction process at a molecular level. Hence, the experimental dose-olfactory response curves were fitted by applying the one-layer adsorption model with a single energy (1LM1E). On one hand, the different parameters introduced in the selected model were used to microscopically study the three olfactory systems. Indeed, the fitting results showed that phenylacetic acid displayed the greatest maximum olfactory response at saturation, due to the effect of functional groups at the R 4 position. The three pheromones were docked via a non-parallel orientation and the adsorption process was a multi-molecular mechanism. The sizes of different binding pockets of ORA1 were determined through the estimation of the olfactory receptor site size distributions (stereographic characterization). The estimated adsorption energies, ranging from 17.340 to 21.332 kJ/mol, can be used to describe the energetic interactions between the studied pheromones and the Zebrafish ORA1 binding pockets. The spectrums of the adsorption energy distributions of phenylacetic acid, 4-chlorophenylacetic acid, and 4-methoxyphenylacetic acid, which were spread out from 10 to 32.5 kJ/mol, 5 to 30 kJ/mol, and 10 to 32.5 kJ/mol, respectively, was determined to estimate the corresponding olfactory bands (energetic characterization). On the other hand, three thermodynamic functions were estimated in order to macroscopically study the three olfactory systems. • Modeling of three dose-olfactory response curves by an advanced model • Quantitative characterizations of the Zebrafish olfactory systems were studied. • Determination of an olfactory band of the investigated pheromones [ABSTRACT FROM AUTHOR]

Understanding olfaction process at a microscopic or molecular level needs more elucidation of the multiple stages involved in the olfaction mechanism. A worth full elucidation and a better understanding of this molecular mechanism, a necessary preamble should be achieved. The content of this work is a preamble for that. A study of the mouse and human olfactory receptors activation in response to two nitro musks stimuli, which are the musk xylol and the musk ketone, are considered here, first, for their wide expanded use in perfumery, but also to show some particular aspects of this process in the case of these two stimuli, which could help to deduce more details and more general aspects in the global olfactory mechanism. A statistical physics modeling using the monolayer model with two independent types of receptor binding sites of the response of the mouse olfactory receptor MOR215-1 and the human olfactory receptor OR5AN1, which are identified as specifically responding to musk compounds, is used to characterize the interaction between the two nitro musk molecules, the mouse and the human olfactory receptors and to determine the olfactory band of these two odorants through the determination of the molar adsorption energies and the adsorption energy distributions. The physico-chemical model parameters can be used for the steric characterization via the calculation of the receptor site size distributions. The docking computation between these two nitro musks and the human olfactory receptor OR5AN1 is performed demonstrating a large similarity in receptor-ligand detection process. Thus, docking finding results prove that the calculated binding affinities were belonging to the spectrum of adsorption energies. • Physico-chemical interpretations were derived from two nitro musks olfactory response curves. • Determination of the receptor site size and the adsorption energy distributions. • Determination of olfaction band of musk odorants. • Various interactions were discovered by molecular docking analysis. [ABSTRACT FROM AUTHOR]

Thermodynamic, energetic, and stereographic parameters controlling the acetylene adsorption on (0001) exfoliated graphite were determined. The results showed that statistical physics model 2 (monolayer with two energies) has the best correlation with the experimental data. The adsorption of acetylene molecules on exfoliated graphite surface is multimolecular adsorption. The adsorption entropies and the Gibbs free enthalpies were determined for temperature ranging from 147.72 K to 161.50 K. The obtained adsorption energy distributions show the same maximum value of 5.6 kJ.mol−1. The stereographic parameters evolution with temperature is related to the two-dimensional (2D) critical temperature, and their values suggest the formation of polyacetylene. [ABSTRACT FROM AUTHOR]

To obtain good economic and environmental benefits, LaMgNi 3.6 M 0.4 (M = Al, Mn, Ni, Co, Cu) alloys are investigated for the hydrogen storage. The absorption data of hydrogen in the tested alloys are measured experimentally at 373 K. The hydrogen absorption isotherms are analyzed using three models derived from statistical physics formalism. The adequate model permits to discover significant details about the absorption phenomenon via determining the density of the interstitial sites (D m), the number of hydrogen atoms per site (n) and the energetic parameter ΔE. The results indicate that multi-atomic (n > 1) and multi-linking (n < 1) phenomena are feasible for hydrogen absorption in LaMgNi 3.6 M 0.4 (M = Al, Mn, Ni, Cu, Co) metals. The effects of the substitutions of Ni with Mn, Co, Cu and Al on the hydrogen absorption capacity are investigated. The interaction hydrogen/metal is analyzed by the calculation of the absorption energies. The chemical interaction is the responsible for the hydrogen absorption phenomenon. The contribution of this work is to provide advanced investigations of the hydrogen absorption mechanism in LaMgNi 3.6 M 0.4 (M = Al, Mn, Ni, Co, Cu) metals, which are promising alloys for the hydrogen storage. • Advanced absorption models are derived from statistical physics formalism. • Hydrogen absorption isotherms are modelled by monolayer model with three energies. • Steric and energetic analysis of hydrogen absorption mechanism is provided. [ABSTRACT FROM AUTHOR]

The statistical physics approach has been well studied by our research team for liquid and gaseous adsorption systems. This treatment is based on the grand canonical partition function to give new interpretations of the adsorption process at molecular level for chemical senses: olfaction and taste. This work represents a contribution to understand the olfaction mechanism of four of enantiomeric terpenes by applying a statistical physics treatment that allows giving a physico-chemical meaning to parameters involved in the analytical model. It is possible to estimate the number of adsorbed molecules per site, the anchorage number, the receptor density, the concentration at half saturation and the molar adsorption energy. Through this selection of the best fitting model and through fitted values of these parameters, we showed that the adsorption of carvone and limonene enantiomers is not a multilayer process but a monolayer monosite process (monolayer adsorption model with identical and independent sites (n ≠ 1)). The physico-chemical model parameters can be used for the energetic characterization of the interactions between the carvone and the limonene enantiomers and the human olfactory receptor OR1A1 and the determination of an olfactory band of order of 14 kJ/mol, 7 kJ/mol, 9 kJ/mol, 8 kJ/mol for (R)-(−)-carvone, (S)-(+)-carvone, (R)-(+)-limonene and (S)-(−)-limonene, respectively, through the determination of the adsorption energy values and the adsorption energy distributions (AEDs). Thanks to the grand canonical formalism in statistical physics, the negative values of the Gibbs free enthalpy indicate that the adsorption process of the four enantiomeric terpenes onto the human olfactory receptor OR1A1 was spontaneous. The exothermic adsorption mechanism involved in the olfactory perception was explained via the negative values of the internal energy. [ABSTRACT FROM AUTHOR]

[Display omitted] • The adsorption of two dyes on HKUST-1 was examined in single and binary solutions. • A competitive effect was observed during the binary adsorption. • An advanced theoretical approach was applied to analyze the single and binary adsorption data. • Dye adsorption orientation on HKUST-1 was discussed. The paper analyzes the single and binary adsorption of textile water pollutants, namely Direct Blue 1 (DB-1) and Direct Yellow-4 (DY-4) dyes, on HKUST-1 at 30 – 50 °C and pH 6.8. Experimental adsorption data indicated that the DB-1 and DY-4 adsorption capacities using this MOF decreased from single to binary systems confirming the presence of a competition effect between these dye molecules on the HKUST-1 adsorbent site. This antagonistic adsorption effect was exothermic. A theoretical approach based on the application of two enhanced adsorption models was utilized to understand the mechanisms for the adsorption of both dye molecules. This approach allowed the calculation of the saturation adsorption capacities for these pollutants in single and binary systems, which followed the next sequence: Q m (DB-1/HKUST-1) > Q m (DY-4/HKUST-1) and Q mb (DB-1 (DB-1 + DY-4)/HKUST-1) > Q mb (DY-4 (DB-1 + DY-4)/HKUST-1). The binary adsorption of these dyes occurred via the presence of an antagonistic effect that reduced the MOF removal performance. HKUST-1 showed better adsorption performance to remove DB-1 dye. The adsorption orientations of DB-1 and DY-4 on HKUST-1 surface were discussed at different temperatures. The models determined the adsorption energies describing the interactions between both dyes and HKUST-1 surface, with range values from 17 to 21 kJ/mol, 12 to 16.5 kJ/mol in single and binary systems respectively. These calculations indicated that physical interactions may trigger the removal of these water pollutants. Overall, this work reports a cutting-edge application of HKUST-1 as adsorbent to remove toxic pollutants such as dye molecules from water. [ABSTRACT FROM AUTHOR]

In this work, four carbon xerogels (XCs) adsorbents, which were prepared by the polymerization of formaldehyde (F) and resorcinol (R) using cesium carbonate (Cs) as catalyst at 4 M ratios R/Cs = XCs-100, XCs-500, XCs-1000 and XCs-2000, were utilized to interpret and understand the adsorption mechanism at a molecular level of non steroidal anti inflammatory drug (NSAID), namely diclofenac sodium (DCF). Hence, Four adsorption isotherms were utilized to present the evolution of the adsorbed quantity (Q a) as a function of drug concentration describing the DCF adsorption on the four carbons xerogels at T = 298 K and at pH = 7. In addition, two other adsorption systems, describing the adsorption of DCF on XCs-500, were plotted by varying two experimental conditions: temperature and solution pH. All these experimental data were adjusted and analyzed via the advanced two layers model with two adsorption energies (A2LM2E), which was chosen as the most adequate statistical physics model. Furthermore, stereographic and energetic parameters of A2LM2E namely: the number of DCF molecules per XCs sites (n), the adsorbed quantity at saturation (Q as) and the concentrations at half saturation (C 1 and C 2) were estimated by a multi-variable non-linear regression. The fitting results indicated that the DCF drug molecules were docked with mixed and non-parallel orientations on the different XCs adsorbents. The investigation of the adsorbed quantity at saturation indicated that Q as increased as follows: Q as (XCs-2000) < Q as (XCs-100) < Q as (XCs-1000) < Q as (XCs-500), showing that the XCs-500 was more efficient for the adsorption of DCF drug than the other adsorbents. The calculated molar adsorption energies ΔE 1 and ΔE 2 for the studied adsorption systems affirmed the exothermic and the physical characters of the adsorption mechanism since ΔE 1 and ΔE 2 values were positive and inferior to 40 kJ/mol. Lastly, the XCs-100, XCs-500, XCs-1000 and XCs-2000 adsorbents presented unimodal pore size distributions (PSDs) centered at a pore radius of 8.38 nm, 7.17 nm, 6.05 nm and 5 nm, respectively. Finally, the estimated thermodynamic parameters such as the adsorption entropy (S a), the Gibbs free enthalpy (G) and the internal energy (E int) indicated that DCF adsorption on XCs-500 was spontaneous and exothermic process. • Adsorption mechanism of DCF from aqueous solution on carbon xerogels adsorbents was investigated. • DCF adsorption isotherms were fitted by an advanced two layers model with two energies. • Stereographic and energetic analysis was provided from adsorption isotherms. • XCs can be performed for industrial applications to obtain adsorbents for good and low costs adsorption of drug. [ABSTRACT FROM AUTHOR]

• Experimental dose-olfactory response curves of OR1A1 activated by two nitro musk odorants were fitted using two statistical physics models. • Stereographic and energetic analyses of the two olfactory systems were realized. • Three thermodynamic functions were studied at a macroscopic level. The experimental dose-olfactory response curves of the two nitro musk odorants, such as musk tibetene and musk ambrette, on the broadly human olfactory receptor OR1A1 have been analyzed using four statistical physics models by means of the grand canonical formalism. For such a purpose, the monolayer model with one energy level and the monolayer model with two energy levels were selected to describe the adsorption mechanism of musk tibetene and musk ambrette, respectively. Indeed, three main physicochemical parameters introduced in the selected models affecting the putative adsorption phenomenon involved in the sense of smell, namely, the olfactory response at saturation, the number of nitro musk odorants per OR1A1 binding site, and the half saturation concentration related to the molar adsorption energy. Actually, the investigation of the number of nitro musk fragrances per binding site showed that musk tibetene and musk ambrette odorants were docked on OR1A1 binding sites by a non-parallel orientation and a multi-docking mechanism since the values of this stereographic parameter were higher than unity. Moreover, the selected adsorption models were used to estimate the broadly tuned human olfactory receptor site size distributions relative to musk tibetene and musk ambrette, which were spread out from 1 to 30 nm with a maximum at 4.10 nm for musk tibetene and at 3.55 nm for musk ambrette. Energetically speaking, the magnitudes of the molar adsorption energies, which were inferior to 5 kJ/mol, indicated that the two nitro musk fragrances were physisorbed on OR1A1 binding sites. Furthermore, the adsorption energy distributions, relative to the two olfactory systems, may be estimated to deeply comprehend human olfactory perception, at a molecular level, via the determination of two approximate olfactory bands through the estimation of two adsorption energy distribution bands, which were spread out from 0 to 8.50 kJ/mol for musk tibetene and from 0 to 8 kJ/mol for musk ambrette. Lastly, macroscopically speaking, three thermodynamic potentials governing the adsorption mechanism were studied. Hence, the disorder during the putative adsorption mechanism was followed via the study of the adsorption entropy. Lastly, the adsorption process introduced in the two olfactory systems was spontaneous and exothermic as it was suggested by the Gibbs free energy and the internal energy. [ABSTRACT FROM AUTHOR]

[Display omitted] • Three compounds of Sr-La-phosphosilicates apatites were synthesized. • Mechanochemical synthesis and solid-state reaction techniques were applied. • The compounds were composed of a single pure apatitic phase. • Solid 31P and 29Si NMR data displayed a single crystallographic site for phosphor. • Statistical physics suggested that the adsorption of methylene blue was physical with energies lower than 30 kJ/mol. In this work, three compounds of Sr-La-phosphosilicates apatites, with the chemical formula Sr 10 -xZn 0.66 Ndx(PO 4) 6-x (SiO 4) x O (where x = 0, 2 and 4), were synthesized using mechanochemical synthesis and solid-state reaction techniques. The prepared compounds were characterized using powder X-ray diffraction (XRD), Infrared spectroscopy (FT-IR), 31P and 29Si MAS NMR, Scanning Electron Microscopy (SEM), Thermogravimetric analysis (TGA), and Brunauer-Emmett-Teller (BET). The compounds were composed of a single pure apatitic phase crystallizing in a hexagonal system with the space group P6 3 /m. The calcined compounds showed an increase of the crystallinity degree and the size of the crystals. Solid 31P and 29Si NMR data displayed a single crystallographic site for phosphor element. The single resonance peak at −76.21 ppm, in the 29Si specruim, confirmed to Q0 type silicon specie. The compounds were further applied for the adsorption of Methylene Blue from water. The highest adsorption capacity was reached using Milled-4 sample (515 mg/g). It was 363 mg/g for the calcined-4 one. The statistical physics (AMSP) investigation suggested that the adsorption of methylene blue was physical with energies lower than 30 kJ/mol. [ABSTRACT FROM AUTHOR]

A monolayer model extended to two energy levels (monolayer model 2) has been developed to fit the adsorption isotherms of acid blue 9 on Spirulina platensis (Sp LEB-52). These isotherms were obtained at different values of pH and different temperatures. The adsorption isotherm modeling was based on a statistical physics approach. The evolutions of stereographic and energetic parameters involved in the model equation were presented in this work. The obtained values of nd1 and nd2 are always higher than unity, indicating that the adsorption of acid blue 9 molecules on Sp LEB-52 is a multimolecular adsorption. The highest adsorption capacity (Qs = 1251.8 mg g−1) is signaled at pH = 4 and T = 298.15 K. Furthermore, we have used the monolayer model 2 as local isotherm to determine the adsorption energy distribution (AED) and the pore size distribution (PSD). The adsorption energy values corresponding to active sites of type 1 and type 2 are, respectively, in the intervals [10.5 − 27.5 kJ mol−1] and [15 − 25 kJ mol−1]. Obtained PSDs indicate that acid blue 9 molecules are adsorbed on macro-pores of Sp LEB-52. [ABSTRACT FROM AUTHOR]

Experimental adsorption isotherms of hydrogen in CNT samples (CNT-A, activated CNT-A CNT-B and activated CNT-B) at T = 77, 87 and 90 K have been fitted using some theoretical model expressions treated by statistical physics through the grand canonical ensemble. The monolayer model with single energy is selected to fit and interpret the experimental data obtained with CNTs. The physico-chemical parameters, interfering in the adsorption process and implicated in the model expressions, could be directly determined from the experimental data through numerical simulation. Three parameters of the model are fitted, namely the number of hydrogen molecule per site n, the interstitial site density Nm and the energetic parameter P1/2. The evolution of these parameters as function of temperature is plotted and interpreted in relation to adsorption process. Finally, the thermo-dynamic potential functions, which involve in the adsorption mechanism like free enthalpy of Gibbs Ga, internal energy Eint and entropy Sa, are derived by statistical physics calculations from the selected model. [ABSTRACT FROM AUTHOR]

This work is a contribution to understand the taste mechanism of caffeine molecule using a modeling of a putative adsorption process by model expressions established by a statistical physics treatment. A physicochemical and a gustative parts are the main constituents of this work. We start with a physicochemical investigation of the adsorption process of caffeine molecule, as adsorbate in liquid phase, onto β-cyclodextrin as adsorbent. Experimental adsorption isotherm curves of caffeine onto β-cyclodextrin coated onto Quartz crystal are carried out at three different temperatures. The Hill model expression with three parameters n, N M and C 1/2 , established by statistical physics formalism investigated in part I, is the best fitting model of the experimental data. Thermodynamic potential functions that govern the adsorption process, such as entropy, internal energy and Gibbs free enthalpy are investigated. PSD and AED are derived by a steric and energetic derivatives of the Hill model. In part II the same method of fitting is applied to the taste electrophysiological dose-response curve by a caffeine putative adsorption on gustative nerve in caterpillar. All the physicochemical parameters introduced in the fitting Hill model expression, serve first, to analyze the taste mechanism of the bitter caffeine taste. Secondly, all these stereographic and energetic parameters will be considered henceforward for an objective characterization of caffeine molecule taste in both its two aspects, intensive and qualitative aspects of caffeine taste. • Modeling of adsorption process isotherms of caffeine on β-cyclodextrin. • Modeling of electrophysiological dose-taste response curve of caffeine in caterpillar by a putative adsorption process. • Comparison of physicochemical proprieties of caffeine deduced from its adsorption on β-cyclodextrin receptor sites and of caterpillar nerve receptor sites. • Quantitative characterization of caffeine taste by means of fitting model parameters of its taste dose-response curve. [ABSTRACT FROM AUTHOR]

• Indium (III) adsorption on raw, supercritical- and ultrasound-modified chitin was studied. • Monolayer and multilayer models were utilized to explain the indium (III) adsorption mechanism. • Indium (III) adsorption on all adsorbents involved multi-ionic and multi-anchorage processes. The adsorption of indium (III) on raw, supercritical- and ultrasound-modified chitin was experimentally and theoretically studied. Experimental adsorption data demonstrated that the profile of all adsorption isotherms was different from a system to another. Indeed, the adsorption behavior of the systems indium (III) – chitin and indium (III) – supercritical-modified chitin tended to a saturation process at high concentration thus suggesting that the adsorption can be occurred by the formation of a fixed number of adsorbate layers. Contrary to this finding, the adsorption of indium (III) on an ultrasound-modified chitin can be associated to a variable number of layers involving two adsorption energies. Statistical physics models were selected to understand the adsorption data and they demonstrated that the adsorption of indium (III) – chitin and indium (III) – supercritical-modified chitin was achieved by the formation of one layer; while the adsorption of this adsorbate on an ultrasound-modified chitin was performed with a variable number of layers. Based on the modeling analysis, it was demonstrated that the ultrasonic treatment improved the properties of chitin to remove this pollutant: Q esat of ultrasound-modified chitin > Q esat of supercritical-modified chitin > Q esat of raw chitin. The interpretation of parameter n , which is defined as a number of bonded ions of indium (III) per responsible site of the adsorbent, was higher than 1 at high temperature. This result suggested that the indium adsorption was a multi-ionic mechanism. All adsorption systems were characterized by an estimation of the adsorption energy reflecting that the removal of this pollutant involved physical interactions. A general analysis of all model parameters indicated that the receptor site density and the adsorption energy controlled the indium adsorption. [ABSTRACT FROM AUTHOR]

• Phenol and 2-nitrophenol on a biopolymer derived biochar adsorbent was analyzed. • Theoretical analysis of phenol and 2-nitrophenol adsorption mechanisms was performed. • The role of adsorbate structure on tested adsorbents was theoretically explained. In this paper, the adsorption of phenol and 2-nitrophenol on a biopolymer-based biochar in single and binary systems was investigated at 298–328 K and pH 5. Experimental results indicated that the adsorption capacities of phenol were significantly reduced from single to binary systems compared to those obtained for 2-nitrophenol. This experimental evidence suggested an antagonistic effect between both adsorbates generating an inhibitive adsorption. In terms of modeling analysis, the single and binary adsorption isotherms were well reproduced by monolayer and competitive monolayer statistical physics models, respectively. These two models showed that phenol and 2-nitrophenol molecules have been mainly docked with an inclined and horizontal positions in single and binary systems, respectively. A detailed analysis of the number of captured phenol (n 1) and 2-nitrophenol (n 2) molecules per site in the binary systems demonstrated that its corresponding evolution varied with a completely inverse way thus corroborating the inhibition effect between phenol and 2-nitrophenol molecules. The monolayer and competitive monolayer models were used to estimate two adsorption energies to characterize the single and binary adsorption mechanisms. The analysis of the energetic parameters suggested that the adsorption process was a physisorption. The interpretation of all monolayer and competitive monolayer model parameters provided new insights that contributed to understand the single and binary adsorption mechanisms of phenol and 2-nitrophenol molecules on tested adsorbent. [ABSTRACT FROM AUTHOR]

• The single and binary adsorption of amoxicillin and doripenem on HKUST-1 was evaluated. • Interpretation of the single and binary adsorption mechanisms at different temperatures. • Description the competitive effect via statistical physics model. • Simulation of the adsorption process via DFT. The adsorption of amoxicillin (AMX) and doripenem (DRPNM) on copper benzene-1,3,5-tricarboxylate (HKUST-1) in single and binary systems is analyzed in this paper. The experimental results showed that the adsorption capacities of this MOF for the removal of these pharmaceuticals reduced from single to binary solutions. A monolayer adsorption model and its extended competitive version were successfully applied to analyze the adsorption data. The modeling results showed that the reduction of AMX and DRPNM adsorption capacities was explained by a competitive effect of these adsorbates generating an antagonistic behavior for both molecules where the same adsorption site was involved during their removal. The statistical physics model was also utilized to estimate the AMX and DRPNM adsorption orientation on the HKUST-1 surface. Adsorption energies were calculated confirming an exothermic removal process for both molecules and DFT simulations allowed to determine the role of hydrogen bonding in the adsorption mechanism. It was concluded that the interactions for the adsorption of DRPNM on this MOF were higher than those for AMX removal. Particularly, the oxygens linked to the cupper ions on MOFs structure played a crucial role during the adsorption mechanisms of these organic compounds. Overall, this paper presents a combination between experiment results and two different theoretical approaches to provide a new explanation of the mechanism of adsorption of two relevant antibiotics on HKUST-1 MOF. [ABSTRACT FROM AUTHOR]

The aim of this work is to facilitate the fight against COVID-19 pandemic using a comparative study of seven drug molecules, in order to select the most efficient drug molecules. This comparision has been achieved by using statistical physics modeling to provide physicochemical interpretations of the adsorption process of remdisivir (GS-5734), lopinavir, chloroquine, niclosamide, ciclesonide, berbamine hydrochloride and Salinomycin sodium drug molecules onto coronavirus SARS-CoV-2. By modelling the dose response curves of these drug molecules with the best fitting model, the monolayer with one energy model, steric and energetic characterizations of the interactions between the drug molecules and the virus receptor sites have been done. This investigation showed that all drug molecules exhibited a multi molecular anchorage to the virus receptor sites. Also, the quantification of the molar adsorption energy showed that the interactions between these drug molecules and the coronavirus receptor sites take place via physical forces and also the antiviral activity of salinomycin, ciclesonide, and niclosamide against SARS-CoV-2 virus was more important than the other competitive molecules. In addition, a thermodynamic analysis was performed by demonstrating that adsorption process is exothermic for the selected drug molecules. Interestingly, niclosamide showed higher spontaneity than other drugs and therefore higher antiviral activity against coronavirus. As a result, we demonstrated that physicochemical modeling could be useful for medicine and pharmacology, through the study of drug efficiency parameter. Salinomycin and niclosamide were found the most efficient drugs against SARS-CoV-2 virus since their optimal doses corresponding to the efficiency saturation were the lowest. [Display omitted] • Statistical physics study of 7 drug molecules adsorption onto the virus SARS-COV-2. • Physicochemical interactions between molecules and virus are physical and exothermic. • Adsorption energy is more important for salinomycin, ciclesonide and niclosamide. • Thermodynamically niclosamide has higher spontaneity to adsorb than other drugs. • Salinomycin and niclosamide are the most efficient drugs against coronavirus. [ABSTRACT FROM AUTHOR]

Abstract In this article, a theoretical study was performed in order to elucidate the adsorption mechanism of methylene blue (MB) on Cortaderia selloana flower spikes (FSs) and on Cortaderia selloana flower spikes derived carbon fibers (CFs). For this objective, the Hill model developed using grand canonical ensemble was successfully applied. This model represents the general case of Langmuir model assuming that the receptor sites of CFs and FSs accepts a variable number of MB molecules and is defined by the number of molecules captured per adsorbent site (n). Based on the model parameters, the MB adsorption geometry was described at different temperatures indicating that the MB molecules were fixed by an angled position on the investigated adsorbents. The elucidation of the adsorption capacity showed that CFs was more effective for removing MB from wastewater than FSs. This behavior was detailed and corroborated by an energetic investigation. Moreover, the adsorption energy varies from 22.187 to 25.378 kJ mol−1 for FSs and from 24.503 to 27.412 kJ mol−1 for the CFs reflecting a physisorption process. Interestingly, and based on this energetic investigation, it was deduced that the adsorption mechanism of MB was endothermic. Excellent correlation between the number of molecules captured by the receptor site, the adsorption capacity, and the adsorption energy was observed. Highlights • Using the statistical physics, we could describe the adsorption of the MB onto CFs and FSs at the microscopic level. • The MB adsorption onto CFs and FSs is monolayer physisorption with one level of energy. • The temperature enhances the adsorption of MB. [ABSTRACT FROM AUTHOR]

Highlights • Dye adsorption followed by photo-Fenton degradation is promising for water treatment. • Iron-modified composite adsorbent coating is a novel material for water treatment. • Several dye adsorption-desorption cycles can be performed via photo-Fenton oxidation. Abstract Adsorption is an extensively used technique in wastewater treatment because this process is low cost, practical in operation and efficient. However, the regeneration of spent adsorbents is usually restricted by the strong interactions between the surface of adsorbents and adsorbates. Costs of water purification can be reduced significantly if the spent adsorbents can be regenerated and reused for several cycles. Hence, one alternative to face this issue is based on the formulation of adsorbent in a form of coating by improving its function so that it will be feasible to perform the regeneration. In this study, we have improved a coating formulation by modifying it with an iron salt to carry out the photo-Fenton process in the presence of H 2 O 2 and light assistance. Results showed that the adsorption of Acid Red 1 on an iron modified composite adsorbent coating was effective and able to achieve up to ten adsorption-regeneration cycles via photo-Fenton process. A statistical physics model was applied to understand the dye adsorption mechanism. This model was utilized to estimate the adsorption geometry of this dye and to calculate the adsorption capacities at different temperatures. This statistical physics model relied on an energetic consideration in order to describe the interaction between the dye molecule and iron-modified composite adsorbent coating surface. [ABSTRACT FROM AUTHOR]

Abstract By means of the grand canonical ensemble and using statistical physics, experimental adsorption isotherms of hydrogen on three adsorbents (zeolite A, X and Y) at T = 77 K have been best fitted with a developed monolayer model with one type of sites. Exploiting some simplifying hypotheses, the model analytical expression of this model was established involving three physicochemical parameters with which we can describe the adsorption process at a microscopic level. These characteristic parameters are: the number of hydrogen molecules per site n, the receptor site density N m and the energetic parameter P 1/2 which are all deduced from the experimental data by numerical simulation. The evolution of these parameters was investigated of different types of zeolite and different type of exchanged cations. Our fitting results revealed that the hydrogen adsorption surface for each zeolite is homogeneous with physical bond energies. Finally, the thermo-dynamical potential functions which govern the adsorption process such as internal energy E int , free enthalpy of Gibbs G a and entropy S a are derived by statistical physics derivation from the adopted model. Graphical abstract Image 108 Highlights • Application of statistical physics models to desribe the adsorption of hydrogen in zeolites A, X and Y. • Steric and energetic interpretations of hydrogen adsorption process are given. • a thermodynamic study is applied to calculate internal energy, free enthalpy and entropy. [ABSTRACT FROM AUTHOR]

Abstract In this study, the formalism of statistical physics is used to describe and interpret the adsorption mechanism by applying the law of real gas which takes into account the interaction between the reactive red 120 dye (RR-120) molecules due to its very large size (approximately 2.11 nm). Modeling of the RR-120 dye adsorption isotherms on Spirulina platensis sp. is performed. Five models based on statistical physics formalism are developed: Hill model with one adsorbed site energy, Hill model with two energies, Hill model with three energies, double layer model with one energy and double layer model with two energies. These five models are treated alternatively with the ideal gas law (IG) and with the law of Ven Der Waals (VDW) real gas (RG). Fitting of six adsorption isotherms at different temperatures (298K, 303K,308K, 313K, 318K and 328K) is performed with, the pH fixed to 2. According to values of correlation coefficient, the Hill model with one energy and a VDW real gas interaction has been chosen as the adequate model to best fit the experimental data. Highlights • The Reactive red 120 adsorption isotherms were modeled by the Hill model. • The adsorption process was interpreted sterically and energetically. • The adsorption energy, thermodynamic quantities were calculated. [ABSTRACT FROM AUTHOR]

Highlights • Bentonite-chitosan adsorbent was synthetized and applied in heavy metal adsorption. • Single and binary adsorption of Cd2+ and Pb2+ on bentonite-chitosan composite was analyzed. • Statistical physics models were applied to understand the adsorption mechanisms. Abstract In this study, a bentonite-chitosan composite was tested for the single and binary adsorption of Cd2+ and Pb2+ ions at constant pH (6) and different temperatures (30, 40, and 50 °C). For both adsorbates, the adsorption capacities decreased in binary systems due to an antagonistic adsorption effect. Statistical physics models were used to analyze the adsorption isotherms and to attribute microscopic interpretations to the experimental evidences at a molecular level. Specifically, a monolayer model with one energy and an exclusive extended monolayer model were applied to single and binary adsorption data, respectively. The crossing of the experimental and modelling results proved that Cd2+ ion was more adsorbed in the binary system. The modelling analysis allowed determining that the numbers of ions linked per adsorbent site varied significantly in binary system with respect to single-compound ones, thus confirming that an inhibition effect occured. Finally, the adsorption energy was estimated for both adsorption systems indicating the occurrence of an endothermic adsorption. Moreover, adsorption energies showed concordant trends with the corresponding adsorption capacities of both Cd2+ and Pb2+, hence being able to describe the adsorption phenomena. [ABSTRACT FROM AUTHOR]

A new adsorbent (amphoteric adsorbent coating: AAC) based on composite coating with amphoteric functionality was employed to study the adsorption mechanism of Brilliant Green (BG) and Acid Red 1 (AR1) dyes. This adsorbent was prepared as a coating and supported on cotton cloth by application of a facile method, based on the combined use of smectite-based clay powder, acrylic polymer emulsion (APE) and cationic polyelectrolyte. The novel adsorbent coating was characterized by FE-SEM, EDX, zeta potential and FTIR analysis. Subsequently, the equilibrium adsorption isotherms of AR1 and BG dyes were performed and analyzed at different temperatures (from 303 to 343 K) in order to achieve a thorough comprehension of dyes adsorption mechanism. To this aim, a multilayer model with saturation was developed using statistical physics theory and was applied as a sophisticated tool for data interpretation. The correlations of experimental and theoretical results allowed to understand two distinct behaviours for the adsorption of AR1 and of BG dyes, which were related to the formation of two different adsorbed layers and a variable number of layers, respectively. Based on the parameter of the adopted model, the adsorption geometry of dyes has been described at different temperatures. Interestingly, the adsorption process was energetically typified by estimation of the adsorption energies, which indicated that the adsorption of AR1 and BG dyes were exothermic and endothermic, respectively. [ABSTRACT FROM AUTHOR]

In this paper, three adsorption isotherms of natural yellow Gardenia dye, at three different temperatures and at three pH values, were fitted by models established through statistical physics treatment. A double-layer model with two energies is able to give good fitting of these experimental data. Four physicochemical parameters are involved in the fitting of the experimental adsorption isotherms such as the number of adsorbed dye molecules per site n, the density of receptor sites Nm and the two energetic parameters C 1 and C 2 . From the numerical simulation, the number of molecules per site showed that the adsorbate molecules have two anchorage positions parallel and nonparallel respectively when pH and temperature vary. The variation of the adsorbed quantity at saturation with temperature shows the exothermic nature of aggregation process of the natural Gardenia yellow dye. In the case of variation of pH, the acidic conditions are more favorable for the adsorption process. The numerical values of the calculated adsorption energies have revealed that the Gardenia yellow dye is physisorbed onto TiO 2 mesoporous. A new method based on Kelvin equation in liquid phase has been developed to determine the pore size distribution (PSD) of TiO 2 mesoporous in comparison with other experimental measurements. The result of PSD shows a significant effect of the variation with temperature and with pH values on the morphology of pore size structure. Finally, the calculated thermodynamic functions such as entropy, free enthalpy and internal energy exhibited that the system evolved spontaneously. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we have realized three adsorption isotherms of the ruthenium-based dye molecules, cisdi (thiocyanato)bis (2,2′bipyridyl-4,4′-dicarboxylate)ruthenium (II) (N3) into the mesoporous TiO 2 (anatase) at three different temperatures:298.15, 313.15 K and 333.15 K using the UV–vis spectroscopy method. These adsorption isotherms have been simulated using several models established through a statistical physics formalism in order to involve in model expressions some parameters which have physicochemical meaning and to better interpret information about the adsorption process at the molecular level. A multilayer model was determined to best reproduce and simulate the experimental data. In this model, five parameters affecting the adsorption process have been adjusted, namely the number of molecules per adsorption site n, the density of receptor sites N m , the two energetic parameters: the concentrations at half saturation C 1 and C 2 and the number of layers N L. These parameters have been deduced from the fitting of the experimental adsorption isotherms by numerical simulation. Thanks to the grand canonical ensemble in statistical physics, the energetic parameters suggest physical bonding of the N3 dye to the TiO 2 surface in the case of low concentrations through monodentate and bidentate with hydrogen bond configurations. Finally, a new method based on Kelvin equation in the liquid phase is used to determine the pore size distribution (PSD) and the adsorption energy distribution (AED) of the mesoporous TiO 2. Graphical abstract Image 1 Highlights • A statistical physics model has been developed for the considered N3 adsorption. • Three adsorption isotherms of N3 dye on TiO 2 were fitted and interpreted. • Using the energetic parameters to calculate the adsorptions energies. • New method based on Kelvin equation is used to determine the (PSD) and the (AED). [ABSTRACT FROM AUTHOR]

• Four response curves were fitted by an advanced monolayer model of ideal gas. • Physico-chemical interpretations of the studied olfactory systems were determined. • Quantitative characterizations of the olfactory systems were investigated. • Four olfactory bands of the four vanilla-like odorants were determined. An advanced monolayer adsorption model of an ideal gas was successfully employed to investigate the adsorption of vanillin, vanillin methyl ether, vanillin ethyl ether, and vanillin acetate odorants on mouse eugenol olfactory receptor mOR-EG. In order to understand the adsorption process putatively introduced in olfactory perception, model parameters were analyzed. Hence, fitting results showed that the studied vanilla odorants were linked in mOR-EG binding pockets with a non-parallel orientation, and their adsorption was a multi-molecular process (n > 1). The adsorption energy values that ranged from 14.021 to 19.193 kJ/mol suggested that the four vanilla odorants were physisorbed on mOR-EG (ΔEa < 40 kJ/mol) and the adsorption mechanism may be considered as an exothermic mechanism (ΔEa > 0). The estimated parameters may also be utilized for the quantitative characterization of the interactions of the studied odorants with mOR-EG to determine the corresponding olfactory bands ranging from 8 to 24.5 kJ/mol. [ABSTRACT FROM AUTHOR]

In the present paper, a putative adsorption process of two odorants thiols (3-mercapto-2-methylbutan-1-ol and 3-mercapto-2-methylpentan-1-ol) on the human olfactory receptor OR2M3 has been investigated via advanced models developed by a grand canonical formalism of statistical physics. For the two olfactory systems, a monolayer model with two types of energy (ML2E) has been selected to correlate with the experimental data. The physicochemical analysis of the statistical physics modeling results showed that the adsorption system of the two odorants was multimolecular. Furthermore, the molar adsorption energies were inferior to 22.7 kJ/mol, which confirmed the physisorption process of the adsorption of the two odorant thiols on OR2M3. In addition, quantitative characterizations of both odorants were determined via the olfactory receptor pore size distribution (RPSD) and the adsorption energy distribution (AED), which were spread out from 0.25 to 1.25 nm and from 5 to 35 kJ/mol, respectively. For thermodynamic characterization of the olfactory process, the adsorption entropy indicated the disorder of the adsorption systems of 3-mercapto-2-methylbutan-1-ol and 3-mercapto-2-methylpentan-1-ol on the human olfactory receptor OR2M3. Besides, the used model showed that the presence of copper ions increases the efficacy (olfactory response at saturation) of 3-mercapt-2-methylpentan-1-ol odorant activating OR2M3. The docking molecular simulation indicated that the 3-mercapto-2-methylpentan-1-ol molecule presented more binding affinities (17.15 kJ/mol) with olfactory receptor OR2M3 than 3-mercapto-2-methylbutan-1-ol (14.64 kJ/mol). On the other hand, the two estimated binding affinities of the two odorants belonged to the adsorption energies spectrum (AED) to confirm the physisorption nature of the olfactory adsorption process. • Statistical physics was used to study the dose-olfactory response curve of odorous thiols. • Thermodynamic investigation has been carried out with statistical physics models. • The olfactory receptor pore size distributions (RPSD) and the adsorption energy distributions (AED) are determined. • Effect of metal transition ion Cu2+ on 3-mercapto-2-methylpentan-1-ol complex is studied. • Molecular docking simulation have been applied to investigate the ligand/receptor complex interactions. [ABSTRACT FROM AUTHOR]

Apis cerana cerana counted on its sensitive olfactory system to make survival activities in the surrounding environment and the olfactory receptors can be considered as a primary requirement of odorant detection, recognition and coding. Indeed, the exploitation of the olfactory system of insects in particular the Asian honeybee " Apis cerana cerana " can be the best experimental model to investigate the essentials of the chemosensitivity and may help to better understand the olfactory perception in insects. Hence, an advanced statistical physics modeling via the monolayer model with single energy (n ≠ 1) of the three dose-olfactory responses curves indicated that undecanoic acid, 1-octyl alcohol and 1-nonanol were docked with a mixed parallel and non-parallel orientation on AcerOr1. Furthermore, in the present work, the Apis cerana cerana olfactory receptor AcerOr1 showed high sensitivity and discrimination power to detect undecanoic acid, 1-octyl alcohol and 1-nonanol with concentrations at half saturations values of 10−7 mol/L and the molar adsorption energy values obtained from data fitting results, which were ranged from 17.91 to 24.00 kJ/mol, confirmed the exothermic and the physisorption nature of the adsorption of the studied floral odorants on AcerOr1. The studied experimental dose-response curves of undecanoic acid, 1-octyl alcohol and 1-nonanol provided access to quantitative (i.e., stereographic and energetic) characterizations of AcerOr1 via the determination of the olfactory receptor site size distributions (RSDs) and the adsorption energy distributions (AEDs). The stereographic characterization showed RSDs spread out from 0.20 to 8 nm presenting average values corresponding to the maximum of the peaks at 1.50 nm, at 1.10 nm and at 1.04 nm for undecanoic acid, 1-octyl alcohol and 1-nonanol, respectively. The energetic characterization presented AEDs ranged from 0 to 40 kJ/mol showing an approximate adsorption energy bands defined between 7.50 and 27.50 kJ/mol, between 15 and 33 kJ/mol and between 13.50 and 34.50 kJ/mol for undecanoic acid, 1-octyl alcohol and 1-nonanol, respectively. The utilization of the analytical expression of the olfactory threshold allowed giving important and helpful informations about the occupation rate of AcerOr1 binding sites that fired a minimal olfactory response at a honeybee olfactory receptor. Hence, the olfactory response can be detected only when 1.97 %, 1.13 % and 2.00 % of AcerOr1 binding sites were occupied by undecanoic acid, 1-octyl alcohol and 1-nonanol, respectively. Lastly, by means of the selected model, the thermodynamic potentials, such as the adsorption entropy, the Gibbs free enthalpy and the internal energy could be calculated and interpreted. • Modeling of three dose-olfactory response curves by an advanced monolayer model with single energy (n ≠ 1). • Physical interpretations of the olfactory systems. • Quantitative characterizations of the three olfactory systems. [ABSTRACT FROM AUTHOR]

A new statistical physics model is developed to elucidate the ternary adsorption of some heavy metal ions, i.e. copper (Cu 2+ ), cadmium (Cd 2+ ) and zinc (Zn 2+ ) on bone char. The model is derived by the partition function describing the statistical properties in thermodynamic equilibrium of the investigated adsorption system. Ternary equilibrium adsorption isotherms of these heavy metals on bone char are determined and analyzed at different temperatures (30, 40 and 50 °C). The study of the adsorption capacity shows that the bone char is more effective to remove Cu 2+ ions, in both single-compound and ternary systems, while Cd 2+ and Zn 2+ are adsorbed at lower but similar extent. Moreover, in ternary system, all the adsorption capacities are reduced and Cd 2+ and Zn 2+ experienced the highest competition effects, as their adsorption capacity significantly decreased with respect to single-compound counterparts. On the other hand, the ternary statistical physics model includes several physicochemical parameters that can attribute microscopic insights to the investigated system. The application of this model indicates that all heavy metal ions are mainly bonded by a horizontal position on bone char. By analyzing and comparing the evolution of the number of ions bonded per adsorbent receptor site (RS), an inhibition effect is observed. The new model is also adopted to characterize the energy of the system, in terms of the interactions between heavy metal ions and adsorbent surface. In particular, both single-compound and ternary adsorption on bone char are endothermic and mainly characterized by physisorption, with a tendency to chemisorption, as confirmed by model outcomes. [ABSTRACT FROM AUTHOR]

The adsorption isotherms achieved at four temperatures of the Iron nitrate and Iron chloride to a biosensor (Porphyrin TPP coated onto Quartz crystal) were simulated using models established through statistical physics formalism. Modeling of experimental isotherms using statistical physics has to offer microscopic interpretations for the mechanism of adsorption. The results showed that the adsorption was exothermic and took place with physisorption. The Iron nitrate adsorption occurred by the formation of multilayer adsorption whereas for Iron chloride the adsorption was monolayer. The parameters deduced from fitting of the experimental data were discussed and interpreted. The statistical models were also used to investigate thermodynamics functions that govern adsorption mechanism, such as entropy, internal energy, and Gibbs free enthalpy. It is shown that the two systems release energy which confirms that the adsorption is exothermic process. [ABSTRACT FROM AUTHOR]

Based on statistical physics elements, the equilibrium adsorption of diclofenac (DFC) and nimesulide (NM) on activated carbon was analyzed by a multilayer model with saturation. The paper aimed to describe experimentally and theoretically the adsorption process and study the effect of adsorbate size using the model parameters. From numerical simulation, the number of molecules per site showed that the adsorbate molecules (DFC and NM) were mostly anchored in both sides of the pore walls. The receptor sites density increase suggested that additional sites appeared during the process, to participate in DFC and NM adsorption. The description of the adsorption energy behavior indicated that the process was physisorption. Finally, by a model parameters correlation, the size effect of the adsorbate was deduced indicating that the molecule dimension has a negligible effect on the DFC and NM adsorption. [ABSTRACT FROM AUTHOR]

A modeling study has been effectuated on the adsorption kinetics of ethanol onto parent Maxsorb III and the two chemically modified activated carbons (H 2 –Maxsorb III and KOH–H 2 –Maxsorb III). In this work, a mathematical model of diffusion-adsorption is used to describe a nonlinear sorption equilibrium coupled with the diffusion of adsorbate in porous media. The new model equation is deduced from kinetic Boltzmann equation by using a term of diffusion and a term of trapping or adsorption of ethanol at the surface of activated carbon. The term of trapping is expressed by means of Henry model of adsorption, which is in turn deduced from the Hill model developed by using statistics physics treatment. In this study, we propose a new simulation model of a gas kinetic adsorption in a microporous solid in order to find a better correlation with the experimental data. Then, we determine the effect of diffusion term and source term or more exactly trapping term, which is depending on the physicochemical parameters like the number n of molecules per site, the density of receptor sites N m per unit mass, the half-saturation concentration N 1/2 , and the residence time τ ν on the dynamic development of ethanol adsorption on the three types of activated carbon. [ABSTRACT FROM AUTHOR]