Ensemble In Statistical Physics Research Articles

Horizon thermodynamics and cosmological equations: a holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk

Horizon thermodynamics is expected to be related to the effective energy based on the energy density calculated from the Friedmann equation for a Friedmann–Robertson–Walker (FRW) universe. In the present study, the effective energy and thermostatistical quantities on a cosmological horizon are examined to clarify the holographic-like connection between them, with a focus on a de Sitter universe. To this end, the Helmholtz free energy on the horizon is derived from horizon thermodynamics. The free energy is found to be equivalent to the effective energy calculated from the Friedmann equation. This consistency is interpreted as a kind of holographic-like connection. To examine this connection, Padmanabhan’s holographic equipartition law, which is related to the origin of spacetime dynamics, is applied to a de Sitter universe. It is found that the law should lead to a holographic-like connection. The holographic-like connection is considered to be a bridge between thermostatistical quantities on the horizon and in the bulk. For example, cosmological equations for a flat FRW universe can be derived from horizon thermodynamics by accepting the connection as a viable scenario. In addition, a thermal entropy equivalent to the Bekenstein–Hawking entropy is obtained from the Friedmann equation using the concept of a canonical ensemble in statistical physics. The present study should provide new insight into the discussion of horizon thermodynamics and cosmological equations.

Advanced investigation of the olfactory perception of semiochemical TMT on OR5K1 and Olfr175 by statistical physics approach

The adsorption of the trimethylthiazoline (TMT) on the human olfactory receptor OR5K1 and the mouse olfactory receptor Olfr175 was the object of the present paper. The main contribution of this work was to characterize stereographically and energetically OR5K1 and Olfr175 activated by trimethylthiazoline molecules docked on the human and the mouse olfactory binding pockets using the grand canonical ensemble in statistical physics. The experimental data and the advanced statistical physics models revealed that the adsorption of the trimethylthiazoline on the human olfactory receptor OR5K1 can be interpreted using the monolayer model with single energy, while the monolayer model with two energies described the interaction between the trimethylthiazoline molecules and the mouse olfactory receptor Olfr175. In fact, the investigated odorant was shown to be docked by a multi-docking process and non parallel orientation on OR5K1 and Olfr175 since the values of the number of TMT molecules per binding site n were superior to 1. The proposed models were applied to calculate the human and the mouse olfactory receptor binding site size distributions relative to TMT, which were spread out from 0.30 to 20 nm with a maximum at about 1.75 nm for OR5K1 and from 1 to 25 nm with a peak at about 4.25 nm for Olfr175. Furthermore, it was found from the calculated molar adsorption energies, which were lower than 11 kJ/mol, that physical adsorption process was occurred in the two olfactory systems. The adsorption energy distributions relative to TMT can be also calculated in order to understand of olfaction process in general through the determination of olfactory bands (i. e., adsorption energy distribution bands), which were situated between 0 and 10.50 kJ/mol and between 3 and 12.50 kJ/mol for OR5K1 and Olfr175, respectively. Referring to the investigation of thermodynamic functions governing the adsorption process such as the adsorption entropy, the Gibbs free enthalpy and the internal energy, it may be noted that the disorder peak of the two olfactory systems was reached when the equilibrium concentration was equal to the concentration at half saturation. In addition, the Gibbs free enthalpy and the internal energy were calculated and their negative values indicated that the adsorption process involved in the olfactory mechanism was exothermic and spontaneous nature.

Interpretation the olfactory perception of musk tibetene, muscone and dihydrocivetone on the human musk olfactory receptor OR5AN1 via an advanced statistical physics modeling

An adsorption mechanism of three odorants, namely musk tibetene, muscone and dihydrocivetone, on the human musk olfactory receptor OR5AN1 has been investigated using the grand canonical ensemble in statistical physics. Experimental concentration-olfactory response curves have been fitted using two advanced models derived from statistical physics approach by numerical simulation that showed a good correlation between the advanced adsorption models and the experimental data. The adequate model, that was the monolayer adsorption model with identical and independent binding sites (MM), allowed recovering important information about the adsorption process putatively introduced in the olfactory perception by determining the maximum response at saturation (RM), the fraction or the number of captured musk molecule(s) per binding site (n) and the adsorption energy (ΔEa) by referring to the concentration at half saturation (C1), which could correspond mainly to the odorant-human olfactory receptor binding cavity interaction energy.For the three studied olfactory systems, the adsorption energies from dissolved state in module calculated from experimental data modeling were ranged from 5.98 to 9.93 kJ/mol, which could be associated to a physisorption mechanism. The monolayer model (MM) was additionally applied to determine the human musk olfactory receptor binding site (cavity) size distribution (RSD). Indeed, musk tibetene, muscone and dihydrocivetone RSDs were spread out from 0.3 to 16 nm, from 1 nm to 16 nm and from 1 nm to 16 nm, respectively, with a maximum of order of 2.3 nm, 3.4 nm and 3 nm, respectively. In addition, the adsorption energy distribution (AED) can be also estimated for the energetic characterization to confirm the heterogeneity of the OR5AN1 surface, the physical nature of the musk tibetene/muscone/dihydrocivetone-OR5AN1 interactions and the binding of the human musk olfactory receptor OR5AN1 with the three musk odorants for a better understanding of the olfaction process in general through the determination of an olfactory band (AED band) of order of 16 kJ/mol [2–18 kJ/mol], 8 kJ/mol [2–10 kJ/mol] and 9.5 kJ/mol [3–12.5 kJ/mol] for musk tibetene, muscone and dihydrocivetone, respectively.

A study of single and quaternary adsorption of Cu2+, Co2+, Ni2+ and Ag+ on sludge modified by alkaline fusion

• Quaternary adsorption of Cu 2+ , Co 2+ , Ni 2+ and Ag + ions was investigated. • Development of a new quaternary adsorption model. • Adsorption of Cu 2+ , Co 2+ and Ni 2+ ions was endothermic, while the Ag + adsorption was exothermic. • Ag + adsorption was reduced from single-compound to quaternary system. Quaternary adsorption of Cu 2+ , Co 2+ , Ni 2+ and Ag + ions on an adsorbent obtained from the alkaline fusion of wastewater treatment sludge was investigated. Adsorption tests in both single-compound and quaternary systems were carried out and the analysis of adsorption mechanism was done by the application of a new quaternary model. This model was developed from a general methodology based on the application of grand canonical ensemble in statistical physics. This adsorbent was characterized by different analytical techniques. Experimental data showed that the adsorption of Cu 2+ , Co 2+ and Ni 2+ ions was endothermic, while the Ag + adsorption was exothermic. Ag + adsorption was significantly reduced from single-compound to quaternary system due to the competitive effect caused by the other divalent ions, while the adsorption capacities of Cu 2+ , Co 2+ and Ni 2+ were not significantly affected in the multicomponent solution. A significant competitive effect of Cu 2+ , Co 2+ and Ni 2+ ions on the adsorption of Ag + ions occurred. Modelling analysis showed that the adsorption of Cu 2+ , Co 2+ and Ni 2+ ions was a multi-ionic process at all tested temperatures, while the adsorption of Ag + was a multi-ionic process only at low temperatures (298 and 308 K). Finally, the statistical physics model confirmed that the adsorption energies corresponded to physical interactions forces and the water molecule adsorption played a relevant role during the removal of these trace metals.

Adsorption isotherms of N3 dye on TiO2 mesoporous for dye sensitized solar cells: Their realization, their modeling and consequent interpretations using a statistical physics treatment

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 TiO2 (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 Nm, the two energetic parameters: the concentrations at half saturation C1 and C2 and the number of layers NL. 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 TiO2 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 TiO2.

Modeling of essential oils adsorption onto clays towards a better understanding of their interactions

A large number of aromatic plants have been used against diverse insect pests. Unlike conventional pesticides, usually these natural products present less risk to human health and the environment. To enhance the insecticidal activity, essential oils (Eos) can be adsorbed on a solid support such as clay since it is abundant in nature. Clays were characterized by several physicochemical techniques such as X-ray diffraction (XRD), thermal gravimetric and differential analysis (TGA, TDA), Fourier transformed infrared spectroscopy (FTIR) and nitrogen adsorption-desorption isotherms. The measured adsorption isotherms of essential oil component (sabinene) onto Cameroonian clays (montmorillonite and kaolinite) were modeled using empirical and theoretical models. The analytical expressions of this theoretical model(so-called finite multilayer with multisite occupancy model (FMM)) have been established from an application of the grand canonical ensemble in statistical physics. The finite multilayer with multisite occupancy model was identified to be the most appropriate option for modeling the adsorption isotherms in terms of physical significance, goodness of model fit and error analysis. The results of the theoretical investigations lead us to point out that a number of agglomerated sabinene molecules are oriented perpendicular to the surface. The main mechanisms interaction for adsorption of sabinene onto clays were electrostatic, hydrophobic, π-π interactions and hydrogen bonds. Furthermore, the chemical modification of clays by basic solution has to reduce the number of adsorbed layers at the surface. However, the treatment of montmorillonite with low concentration of acid solution promotes the formation of several layers. The highest adsorption capacity of sabinene was observed in the case of montmorillonite activated with acid solution. The evolution of the calculated of some thermodynamic functions such as the configurational entropy, Helmholtz and Gibbs free enthalpies indicate that the sabinene adsorption is exothermic and spontaneous in nature.

Theoretical study of hydrogen absorption-desorption on LaNi3.8Al1.2−xMnx using statistical physics treatment

The hydrogen absorption-desorption isotherms on LaNi3.8Al1.2−xMnx alloy at temperature T = 433K 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 n1 and n2, the receptor site densities N1m and N2m, and the energetic parameters P1 and P2. 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 269.4KJ/mol for absorption process and between 267 and 269.5KJ/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 Eint, free enthalpy of Gibbs G and entropy Sa are derived.

Physicochemical and thermodynamic study of malachite green adsorption on raw and modified corn straw

AbstractPhysicochemical and thermodynamic interpretations of malachite green (MG) adsorption on raw (RCS) and modified corn straw (MCS) are detailed in this work. Experimental isotherms were constructed at different temperatures (from 298 to 328 K). To interpret these curves, three models named multilayer model with saturation, double layer model with two energies, and monolayer model with one energy were developed based on the principle of grand canonical ensemble in statistical physics. The double layer model with two energies was the more adequate to represent the adsorption process. Thermodynamic functions such as configurational entropy (Sa), free adsorption enthalpy (G), and internal energy (Eint) were studied. The number of MG molecules per site (n) ranged from 0.33 to 2.33 and the adsorbed quantity at saturation (Qasat) ranged from 164.15 to 528.19 mg g−1 and both increased with the temperature. The density of the receptor sites (NM) ranged from 248.71 to 104.88 and decreased with the temperature. For RCS and MCS, the first and second energies, ϵ1 and ϵ2, increased with the temperature, with ϵ1 being higher than ϵ2. The adsorption energies of MCS (7.77–11.19 kJ mol−1) were higher than the adsorption energies of RCS (6.17–10.88 kJ mol−1). The adsorption process occurred by physisorption and the disorder increased at low equilibrium concentrations, but decreased at high concentrations. The free enthalpy and internal energy described with care the spontaneity of the studied system.

Investigation of adsorption process of benzene and toluene on activated carbon by means of grand canonical ensemble

In this work, the performances of a commercial activated carbon (Filtrasorb 400, provided by Calgon) were experimentally tested for the adsorption of different aromatic compounds, i.e., toluene and benzene from synthetic groundwater. Batch adsorption tests were carried out at constant pH (8) and four different temperatures (10–50°C). The experimental equilibrium adsorption data were fitted with a new statistical physics model named as ‘multilayer model with saturation’ and established through the grand canonical ensemble in statistical physics. The characteristic model parameters of the adsorption isotherm such as the number of benzene or toluene molecule(s) per site, n, the receptor site densities, NM, the number of adsorbed layers (NL) and the energetic parameter, (-ε1) and (-ε2), were estimated for the studied systems by a non-linear least square regression. These parameters were discussed and interpreted for their temperature dependence. The calculated thermodynamic parameters such as entropy, Gibbs free energy and internal energy from experimental data showed that the adsorption of benzene and toluene onto activated carbon Filtrasorb 400 was feasible, spontaneous and exothermic in nature.

Interpreting the hydrogen adsorption on organic groups functionalized MOF-5s by statistical physics model

The hydrogen adsorption isotherms at equilibrium on four adsorbents (MOF-5 and three modified MOF-5s named, CH3-MOF-5, Br-MOF-5 and Cl-MOF-5) were studied using a monolayer model with four adsorption sites energies. The analytical expression of this model was developed using the grand canonical ensemble in statistical physics by taking some working hypotheses involving some physicochemical parameters which can describe the adsorption process. These parameters are: four numbers of hydrogen adsorbed molecules per site (n1, n2, n3 and n4), four receptor site densities (NM1, NM2, NM3 and NM4), four saturation adsorbed quantities (Q1, Q2, Q3 and Q4) and four adsorption energies (−ɛ1, −ɛ2, −ɛ3 and −ɛ4). The evolutions of these parameters in relation with temperature were discussed to understand and interpret the adsorption process at different temperatures. Fitting results revealed that the adsorption of hydrogen on MOF-5 is an exothermic physisorption process. The adsorption surface is inhomogeneous with many site energies. The fitting of the adsorption site is achieved by an aggregate of hydrogen molecules. The adopted model expression is used to derive the thermodynamic potential functions which govern the sorption mechanism such as entropy Sa, free enthalpy of Gibbs G and internal energy Eint.

A macroscopic investigation to interpret the absorption and desorption of hydrogen in LaNi4.85Al0.15 alloy using the grand canonical ensemble

Using the grand canonical ensemble in statistical physics, a hydrogen absorption and desorption isotherms on LaNi4.85 Al0.15 alloy have been modeled by a monolayer model with two level of energy. The model has six physicochemical parameters which are deduced from the fitting of the isotherms at three temperatures T = 298 K, T = 303 K and T = 313 K. These parameters were used to better understand and compare between the absorption and desorption phenomena. A macroscopic study is achieved through thermodynamic functions as the internal energy, the entropy, the free enthalpy, the chemical potential, the enthalpy, and the free energy. We proved the coexistence of the α and β phases during absorption process.

Modeling of adsorption isotherms of dye N719 on titanium oxide using the grand canonical ensemble in statistical physics for dye sensitized solar cells

In this study we are interested in the modeling of the adsorption phenomenon of dye N719 on titanium oxide. Three adsorption isotherms of dye at three different temperatures: (293.15K, 313.15K and 333.15K) are fitted by using a statistical physics treatment based on the grand canonical ensemble to deduce the adequate model in order to describe the adsorption process.The physio chemical parameters involved in the adsorption process have been deduced directly from experimental adsorption isotherms by numerical simulation. We will introduce six main parameters to describe the adsorption process, namely; two densities of dye receptor sites Nm1 and Nm2, the numbers of absorbed molecules per site n1 and n2, the concentrations at half saturation C1 and C2. In order to investigate the type of interaction between the dye molecule and titanium dioxide, we calculate the adsorption energies of the dye molecule using our statistical physics model and the known Dubinin–Radushkevich model for comparison. The numerical values of adsorption process energy (Ea) indicated a chemical adsorption allowing a strong bound to avoid a dye desorption which is very useful to keep a DSSCs in good working order. We apply then our model to deduce thermodynamic functions which govern the adsorption mechanism such as internal energy, entropy and free enthalpy.

A microscopic study of absorption and desorption of hydrogen in LaNi4.85Al0.15 using the grand canonical ensemble of statistical physics

Modeling of absorption and desorption isotherms of hydrogen on LaNi4.85Al0.15 alloy at 298 K, 303 K and 313 K has been achieved through the use of grand canonical ensemble in statistical physics. In fact, a monolayer model with two levels of energy has been adopted to better fit the experimental data. Besides, six physicochemical parameters have been used to better describe the absorption and desorption processes from the point of view of α and β phases. These parameters are divided into two types. The first type of parameters contains four main parameters, namely the number of atoms per site, nα and nβ, and the densities of hydrogen receptor sites Nmα as well as Nmβ. The second type of parameters are mainly the two energetic parameters Pα and Pβ which respectively refer to the pressures at half saturations for the α phase and the β phase. Thanks to these steric and energetic parameters, we could compare the absorption and desorption processes to highlight the evolution of these parameters during hysteresis encountered in the desorption isotherms.

A new statistical physics model to interpret the binary adsorption isotherms of lead and zinc on activated carbon

New statistical physicochemical interpretations of an adsorption process at molecular level were developed to explain the binary adsorption isotherms of lead and zinc ions on activated carbon derived from Styrax officinalis seeds (Balikesir, Turkey) and a commercial activated carbon at different temperatures, 298, 308 and 318K. The extended Hill model was developed to explain heterogeneous model in terms of the grand canonical ensemble in statistical physics. Steric and energetic parameters, like the numbers of ions per site n1 and n2, the densities of receptor sites NM1 and NM2 and the adsorption energies (−ε1) and (−ε2) were directly obtained from the fitting of the experimental adsorption isotherms by numerical simulation to describe the process. The simulation results suggested that two adsorbates per site were anchored on activated carbon surface. The magnitudes of the calculated adsorption energies indicated that Zn2+ and Pb2+ were physically adsorbed by the activated carbon. Thermodynamic potential functions, namely entropy, enthalpy and internal energy were calculated to explain the order and disorder of the adsorbate at the adsorbent surface during the binary adsorption process. The values of the free enthalpy and the internal energy indicated spontaneous adsorption process.

Modeling and Thermodynamic Study of Water Vapor Desorption Isotherms of Orange Peel and Leaves using Statistical Physics Treatment

The shelf life and safety of food products is related to the water content, in particular to the water activity (aw). This is important to predict the physical, chemical and biological processes that take place during food storage. Analytical expression for modeling water desorption isotherms of food is developed using the grand canonical ensemble in statistical physics. The model is further applied to fit and interpret the desorption isotherms of water vapor on the orange peel and leaves at three different temperatures. In the developed model we introduce essentially six parameters such as the number of adsorbed water molecules per site, the number of adsorbed layers, the energy of desorption and receptor sites density. We interpret the results of fitting then we apply the model to calculate thermodynamic functions which govern the desorption mechanism such as internal energy and entropy.

Statistical physics studies of multilayer adsorption isotherm in food materials and pore size distribution

Water sorption isotherms of foodstuffs are very important in different areas of food science engineering such as for design, modeling and optimization of many processes. The equilibrium moisture content is an important parameter in models used to predict changes in the moisture content of a product during storage. A formulation of multilayer model with two energy levels was based on statistical physics and theoretical considerations. Thanks to the grand canonical ensemble in statistical physics. Some physicochemical parameters related to the adsorption process were introduced in the analytical model expression. The data tabulated in literature of water adsorption at different temperatures on: chickpea seeds, lentil seeds, potato and on green peppers were described applying the most popular models applied in food science. We also extend the study to the newest proposed model. It is concluded that among studied models the proposed model seems to be the best for description of data in the whole range of relative humidity. By using our model, we were able to determine the thermodynamic functions. The measurement of desorption isotherms, in particular a gas over a solid porous, allows access to the distribution of pore size PSD.

Study on adsorption of herbicide onto functionalized cellulose extracted from Juncusacutus L. plant: Experimental results and theoretical modeling

Static equilibrium measurements were performed for the study of linuron adsorption on amine functionalized cellulose fiber extracted from Juncusacutus L. plant (Smar) at pH 7. We have noticed that the retention capacities of loaded aminated smar support were 64.8, 51.8, 38.9 and 32.3mg/g at 20, 40, 60 and 80°C, respectively. While for the non saturated support, these capacities were 31, 28.5, 26.4 and 23.5mg/g at 20, 40, 60 and 80°C, respectively. The obtained adsorption isotherms cannot be evaluated by using the Freundlich or Langmuir equations. New equation has been derived by making use of the grand canonical ensemble in statistical physics and some working hypotheses. The characteristic model parameters of the adsorption isotherm such as the number or fraction of adsorbed molecule(s) per site, n, the number of receptor sites per gram of adsorbent, NM, and the energetic parameter, w, were estimated for the studied systems by a non-linear least square regression. The calculated curves fit well to the experimentally obtained isotherms and the parameters of the model can be used for the characterization of the herbicide–adsorbent interactions. Thermodynamic parameters of adsorption process, i.e., entropy, Gibbs free energy and internal energy were computed and their negative values indicate that the adsorption was exothermic and favorable nature.

Statistical thermodynamics of adsorption of dye DR75 onto natural materials and its modifications: double-layer model with two adsorption energies

In this article, adsorption modelling was presented to describe the sorption of textile dye, Direct Red 75 (DR75), from coloured wastewater onto the natural and modified adsorbent, Posidonia oceanica. The formulation of the double-layer model with two energy levels was based on statistical physics and theoretical considerations. Thanks to the grand canonical ensemble in statistical physics some physico-chemical parameters related to the adsorption process were introduced in the analytical model expression. Fitting results show that the dye molecules are adsorbed in parallel position to the adsorbent surface. The magnitudes of the calculated adsorption energies show that the DR75 dye is physisorbed onto Posidonia. Both Van der Waals and hydrogen interactions are implicated in the adsorption process. Despite its simplicity, the model fits a wide range of experimental data, thereby supporting the underlying data that the grafted groups facilitate the parallel anchorage of the anionic dye molecule. Thermodynamic parameters, such as adsorption energy, entropy, Gibbs free adsorption energy and internal energy were calculated according to the double-layer model. Results suggested that the DR75 adsorption onto Posidonia was a spontaneous and exothermic process.

A new biophysical metric for interrogating the information content in human genome sequence variation: Proof of concept

The 21st century emergence of genomic medicine is shifting the paradigm in biomedical science from the population phenotype to the individual genotype. In characterizing the biology of disease and health disparities in population genetics, human populations are often defined by the most common alleles in the group. This definition poses difficulties when categorizing individuals in the population who do not have the most common allele(s). Various epidemiological studies have shown an association between common genomic variation, such as single nucleotide polymorphisms (SNPs), and common diseases. We hypothesize that information encoded in the structure of SNP haploblock variation in the human leukocyte antigen-disease related (HLA-DR) region of the genome illumines molecular pathways and cellular mechanisms involved in the regulation of host adaptation to the environment. In this paper we describe the development and application of the normalized information content (NIC) as a novel metric based on SNP haploblock variation. The NIC facilitates translation of biochemical DNA sequence variation into a biophysical quantity derived from Boltzmann's canonical ensemble in statistical physics and used widely in information theory. Our normalization of this information metric allows for comparisons of unlike, or even unrelated, regions of the genome. We report here NIC values calculated for HLA-DR SNP haploblocks constructed by Haploview, a product of the International Haplotype Map Project. These haploblocks were scanned for potential regulatory elements using ConSite and miRBase, publicly available bioinformatics tools. We found that all of the haploblocks with statistically low NIC values contained putative transcription factor binding sites and microRNA motifs, suggesting correlation with genomic regulation. Thus, we were able to relate a mathematical measure of information content in HLA-DR SNP haploblocks to biologically relevant functional knowledge embedded in the structure of DNA sequence variation. We submit that NIC may be useful in analyzing the regulation of molecular pathways involved in host adaptation to environmental pathogens and in decoding the functional significance of common variation in the human genome.

Modelling of water vapour adsorption on foods products by a statistical physics treatment using the grand canonical ensemble

Knowledge of water adsorption isotherms is very important with regard to concentration, dehydration and drying of food products as well as determining the quality, stability and the shelf life of foods. A new analytical isotherm equation that can be applicable to water vapour–food systems similar to BET equation but modified is developed using the grand canonical ensemble in statistical physics. The establishment of the expression model is based on a statistical physics treatment and some working hypothesises.We mainly introduce four parameters affecting the adsorption process, namely, the density of water receptor sites NM, the number of water molecules per site and the water adsorption energies. The proposed model is applied to experimental water adsorption isotherms taken from the literature. The fitting of the experimental curves with this model showed an improvement of the coefficient of determination R2 in comparison with the BET model and other equations.