Statistical interpretation of the Dubinin-Radushkevich equation

A statistical approach was applied to describe the model of a homogeneous microporous adsorbent and obtain the dependences of the thermodynamic functions on the number of molecules and the temperature for molecular aggregates in discrete micropores over a wide region of fillings that lead to the Dubinin—Radushkevich equation. The energy nonuniformity of the adsorption space is the fundamental property of carbon adsorbents. In the region of small fillings, the statistical approach leads to Henry's law and the finite value of the initial differential energy of adsorption. The value of sorption corresponding to the saturated vapor pressure decreases with increasing temperature, but the decrease is considerably less than for the density of the corresponding liquid. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 261–265, February, 1999.     

Adsorption deformation of a microporous AR-V carbon adsorbent during the adsorption of <Emphasis Type="Italic">n</Emphasis>-hexane

Adsorption isotherms of n-hexane and adsorption deformation isotherms of an AR-V carbon adsorbent are measured in a pressure range of 1 Pa to 20 kPa at temperatures of 254.8–353 K. It is found that, except for the initial pressure range (p < 800 Pa), the relative linear deformation increases with increasing pressure and decreases with increasing temperature. At temperatures of 254.8, 273.2, and 293 K, the curves of adsorption and adsorption deformation exhibit hysteresis in the region close to the saturated vapor pressure. It is noted that, at pressures below 800 Pa, microporous AR-V carbon adsorbent undergoes contraction in the range of high temperatures. It is revealed that the contraction range of the adsorbent with respect to pressure gradually narrows with decreasing temperature and degenerates at 254.8 K.     

Evaluation of adsorbent materials for heat pump and thermal energy storage applications in open systems

The evaluation of solid adsorbents in open sorption systems for heating, cooling and thermal energy storage (TES) applications is crucial for the ecological and economical performance of these systems. An appropriate adsorbent has to reach the temperature limit given by the heating/cooling system of the consumer. It has to provide high energy efficiency and a high energy density for storage applications. A method for an easy evaluation of different adsorbents for a specific application has been developed. The method is based on the adsorption equilibrium of the adsorbent and water vapor. The crucial property for the discussed field of applications is the differential heat of adsorption. Criteria for the evaluation of the adsorbent are the breakthrough curves (responsible for the dynamics of the process), the possible temperature lift (or the dehumidification) of the air, the thermal COP and the storage capacity.     

Adsorption–desorption phenomena of water vapor on a superabsorbent polymer partially crosslinked with potassium

The objective of this article is to study an amorphous superabsorbent polymer, which is able to absorb up to 300 times its weight of water. Adsorption–desorption phenomena of water vapor on the polymer as a function of temperature showed a reversibility of the adsorption–desorption phenomena. The thermal stability of the polymer at atmospheric pressure was also studied. The kinetic study of the desorption phenomena of water vapor on the polymer according to certain physicochemical parameters was discussed. The results showed that the kinetic regime governing the desorption phenomena of water vapor on the polymer is a process limited by a mono-dimensional diffusion for low masses and by a three-dimensional diffusion for high masses.     

Low-temperature Data for Carbon Dioxide

Summary. We investigated empirical data for the vapor pressure (154≤T≤196 K) and the heat capacity (12.52≤T≤189.78 K) of solid carbon dioxide. A computer algebra system (CAS) was used for all calculations. From the numerical point of view, we have adopted a cubic piecewise polynomial representation for the heat capacity and reached an excellent agreement between the available empirical data and the calculated ones. Furthermore, we have obtained values for the vapor pressure and heat of sublimation at temperatures below 195 right down to 0 K. The theoretical key prerequisites are: 1) Determination of the heat of sublimation of 26250 J · mol⁻¹ at vanishing temperature and 2) Elaboration of a ‘linearized’ vapor pressure equation that includes all the relevant properties of the gaseous and solid phases. It is shown that: 1) The empirical vapor pressure equation derived by Giauque & Egan remains valid below the assumed lower limit of 154 K (a similar argument holds for Antoine’s equation), 2) The heat of sublimation reaches its maximum value of 27211 J · mol⁻¹ at 58.829 K and 3) The vapor behaves as a (polyatomic) ideal gas even for temperatures below 150 K.     

Low-temperature Data for Carbon Dioxide

We investigated empirical data for the vapor pressure (154≤T≤196 K) and the heat capacity (12.52≤T≤189.78 K) of solid carbon dioxide. A computer algebra system (CAS) was used for all calculations. From the numerical point of view, we have adopted a cubic piecewise polynomial representation for the heat capacity and reached an excellent agreement between the available empirical data and the calculated ones. Furthermore, we have obtained values for the vapor pressure and heat of sublimation at temperatures below 195 right down to 0 K. The theoretical key prerequisites are: 1) Determination of the heat of sublimation of 26250 J · mol⁻¹ at vanishing temperature and 2) Elaboration of a ‘linearized’ vapor pressure equation that includes all the relevant properties of the gaseous and solid phases. It is shown that: 1) The empirical vapor pressure equation derived by Giauque & Egan remains valid below the assumed lower limit of 154 K (a similar argument holds for Antoine’s equation), 2) The heat of sublimation reaches its maximum value of 27211 J · mol⁻¹ at 58.829 K and 3) The vapor behaves as a (polyatomic) ideal gas even for temperatures below 150 K.     

Experimental studies on the applicability of the Kelvin equation to highly curved concave menisci

The thermodynamic properties of liquids trapped in microscopic pores are described in theory by the Kelvin equation, which relates the equilibrium meniscus curvature to the relative vapor pressure. We report here two series of experiments designed to test the validity of the Kelvin equation by direct measurement of the mean radius of curvature of the surface of cyclohexane condensed between crossed mica cylinders. In one series of experiments, the relative vapor pressure of the volatile cyclohexane was controlled by mixing it with a relatively involatile solute (n-dodecane or n-hexadecane). We found that the mean radius of curvature rapidly reached that predicted by the Kelvin equation at each relative vapor pressure of the volatile liquid, but that there was also a slow, but continuous, accumulation of the “involatile” solute at the point of condensation as the system approached true equilibrium. Such accumulation of very low vapor pressure materials may be one factor responsible for the discordant results reported by earlier workers. We find that the process of impurity buildup is complex, and suggest that studies of real porous systems may be affected by accumulation of “involatile” impurities through the vapor phase and by surface diffusion. The other series of experiments was designed to eliminate the impurity problem by maintaining the vapor pressure by temperature control of the pure liquid. The results from this series of experiments were not time dependent, and no evidence of contamination was found. The measured radii were within ±6% of those predicted by the Kelvin equation, for radii in the range 4–20 nm. We conclude that the thermodynamic basis of the Kelvin equation is valid in principle for menisci with radii as low as 4 nm.     

A model of the two-stage condensation mechanism of water adsorption on nonporous carbon adsorbents

The mechanism of adsorption of water molecules on nonporous carbon adsorbents has been suggested in terms of two different states of adsorbed water; stretched liquid water and water that occupies an intermediate state between the liquid and vapor. Two stages of adsorption were distinguished: condensation and pre-condensation that assumes the formation of molecular associates. The BET model was used to describe the pre-condensation stage. The equations of the adsorption isotherm for water vapor in the region of condensation process and the expression for the determination of the specific hydrophilic surface of adsorbents were found. Examination of the experimental data on adsorption of water vapor on nongraphitized samples of carbon adsorbents shows that in the region of polymolecular adsorption, all isotherms fall into a common curve determined by the equation of the stretched liquid film and can be calculated regardless of the properties of individual liquid water. The equation for adsorption of water vapor on the hydrophobic surface was obtained. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1933–1939, October, 1998.     

State and structure of water in vicinity of hydrophobic surfaces

Criterial values of the specific heat of water wetting, surface pressure, and contact angle classifying surfaces into hydrophilic and hydrophobic are proposed based on the analysis of own and published data. The most characteristic properties of hydrophobic surfaces, i.e., large surface area per water molecule in the conventional adsorption monolayer and the absence of continuous two-layer water film on the adsorbent surface at vapor pressure close to saturation, are discussed using nonporous carbon-based materials as example. The presence of residual hydrophilic groups that act as sites of the clusterization of polar molecules on the surface of graphitized carbon black is confirmed by gas chromatography and the concentration of these sites is calculated. The amount of water molecules in the surface cluster is determined at different stages of adsorption. Procedures for preparing organically modified layered silicates and silica as basic objects of the study of the interaction between water molecules and hydrophobic surfaces are considered. It is proven that the boundary water layer in the vicinity of hydrophobic surface consists of a thin (∼0.5 nm) depletion layer with a density of 0.4 g/cm³ and a considerable amount (25–30%) of water molecules with free OH groups and thicker (∼35 nm) layer, which is characterized by a more ordered network of hydrogen bonds compared to liquid water. Data obtained by X-ray scattering and neutron and reflection methods, and sum-frequency vibrational spectroscopy are compared with the results of calorimetric study of the interaction between water and hydrophobic surface, as well as with the data of molecular-statistical calculations of the state of water molecules in the surface layer.     

Improvement of water vapor adsorption ability of natural mesoporous material by impregnating with chloride salts for development of a new desiccant filter

The aim of this study is the development of a new adsorbent for the desiccant material which can be regenerated by the domestic exhaust heat by using natural mesoporous material, Wakkanai siliceous shale. To improve this shale’s performance to adsorb/desorb the water vapor, lithium chloride, calcium chloride or sodium chloride was supported into the mesopores by impregnating with each chloride solution. Especially sodium chloride was effective to increase the water vapor adsorption amount 5–7 times of that of natural shale in the relative humidity range from 50 to 70%. Moreover, the appropriate impregnating concentrations were determined as 5wt% from the relationship between the maximum water vapor adsorption amount and the mesopore volume. Based on these results, a new desiccant filter has been developed by impregnated original paper with lithium chloride and sodium chloride. This paper contained shale powder in the synthetic fibers. The dehumidification performance of this filter was evaluated under the simulated summer condition in Tokyo. From the cyclic adsorption/regeneration test, this shale and chlorides filter could adsorb and desorb 60 g/h water vapor repeatedly at the regeneration temperature of 40°C. On the other hand, a silica gel filter and a zeolite filter adsorbed and desorbed only 10 g/h and 25 g/h, respectively. These results suggested that the shale impregnated with the chlorides has the best dehumidification ability as a new desiccant material. Further, the desiccant filter made from the shale will achieve the effective use of the low temperature exhaust heat.     

Effect of nonvolatile solute on vapor–liquid equilibrium at fixed liquid composition

The influence of some nonvolatile solutes on boiling points of two azeotropic mixtures (1-propanol–water and methanol–tetrahydrofuran systems) was determined by means of isobaric vapor–liquid equilibrium experiments. A basic thermodynamic equation of nonvolatile solute effect on vapor–liquid equilibrium at fixed liquid composition was derived. Based on the theoretical analysis about the equation, two criterions of universal significance were obtained: (1) when a little nonvolatile solute dissolves in a binary liquid mixture with constant composition, if the vapor composition of less volatile component is increased the boiling point must be elevated at given pressure or the vapor pressure must be depressed at given temperature; (2) when a little nonvolatile solute dissolves in an azeotropic mixture, any kind of nonvolatile solute always causes the elevation of boiling point at given pressure or the depression of vapor pressure at given temperature irrespective of the variation of vapor composition. Verifying through the experiments of this paper and lot of the relevant experimental data in the literature, all of the experimental results were in agreement with both criterions without exception.     

Response of semiconducting metal oxides to water vapor as a result of water molecules chemical transformations on catalytically active surfaces

The sensitivity (response) of six semiconducting metal oxide (SMO) structures on the basis of SnO₂ to water vapor was studied in dry and humid air over the H₂O vapor concentration range 0–2.9 vol % (0–100% RH) as the temperature of the samples changed from 200 to 600°C. The temperature dependence of the conductivity and response of SMOs to H₂O vapor had extrema at 300–400 and 250–400°C, respectively, and the sensitivity to water vapor did not decrease below 1.7–1.9 up to 600°C. Data on changes in the conductivity of SMOs and the number of OH⁻ groups in the oxygen-hydroxyl layer on the surface of SMOs depending on temperature and air humidity were obtained. A sharp change in conductivity as air humidity increased from 0 to 10% RH could be related to either a sharp change in the number of OH⁻ groups in the oxygen-hydroxyl layer because of the high polarity of water molecules or a decrease in the intergrain energy barrier. The phenomena observed and the behavior of SMO conductivity in dry and humid air were interpreted. The experimental data were used to suggest a mechanism of the formation of hydroxyl groups on the surface of SMOs. The paper contains practical recommendations concerning the temperature conditions under which the influence of humidity on changes in the conductivity of SMOs is weakest.     

The adsorption of chlorobenzene on a carbon adsorbent obtained by the pyrolysis of hypercrosslinked polystyrene

The adsorption of chlorobenzene vapor on an experimental D4609 (Purolite Int.) adsorbent prepared by the pyrolysis of hypercrosslinked polystyrene was studied. The adsorbent was characterized by a large specific surface area, a narrow pore size distribution with the predominant fraction of pore diameters 0.9–3.4 nm, and a high absorption ability with respect to chlorobenzene. The adsorption isotherms were measured over the temperature range 100–140°C, and the thermodynamic characteristics of adsorption were determined. In spite of the correspondence to the formal requirements of the theory of volume filling of micropores, the mechanism of adsorption in narrow micropores (<1.2—1.5 nm) was different from filling with a condensed phase.     

Densities and vapor pressures of mixed-solvent desiccant systems containing {glycol (diethylene,or triethylene,or tetraethylene glycol) + salt (magnesium chloride) + water}

In this present work, new experimental data for density and vapor pressure of the mixed-solvent desiccant systems containing {(40.0 wt%) glycol + salt + water} were reported for temperatures up to 343.15 K at normal atmospheric condition. The considered glycols were diethylene, triethylene, and tetraethylene glycol; and the salt is magnesium chloride (wt% = 4.0, 9.0, and 16.0). The density and vapor pressure were presented as functions of temperature and compositions. An empirical equation was used to correlate the temperature and compositional dependence of the present density data and a model based on the mean spherical approximation for aqueous electrolyte solutions incorporating the pseudo-solvent approach was used to represent the measured vapor pressure as functions of temperature and composition. Satisfactory results were obtained for both density and vapor pressure calculations.     

An Experimental and Theoretical Study of the Performance of a Continuous Counter-Current Adsorber

The performance of a simple counter-current adsorber based on the endless belt concept has been studied for vapor phase operation, using as a model system the adsorption of CO₂ from N₂ on a silicalite adsorbent. For this system the isotherm is essentially linear. The steady-state performance can be represented either by the Kremser equation or on a McCabe-Thiele operating diagram. The system is equivalent to 3–8 theoretical stages, depending on to the flow conditions, and both the steady-state and transient behavior are reasonably well predicted by this model. Under properly selected operating conditions it is possible to obtain a reduction in the CO₂ concentration by a factor of 100.     

Temperature and humidity compensation in the determination of solvent vapors with a microsensor system

Accounting for changes in temperature and ambient humidity is critical to the development of practical field vapor-monitoring instrumentation employing microfabricated sensor arrays. In this study, responses to six organic vapors were collected from two prototype field instruments over a range of ambient temperatures and relative humidities (RH). Each instrument contains an array of three unthermostated polymer-coated surface acoustic wave (SAW) resonators, a thermally desorbed adsorbent preconcentrator bed, a reversible pump and a small scrubber cartridge. Negligible changes in the vapor sensitivities with atmospheric RH were observed owing, in large part, to the temporal separation of co-adsorbed water from the organic vapor analytes upon thermal desorption of preconcentrated air samples. As a result, calibrations performed at one RH level could be used to determine vapors at any other RH without corrections using standard pattern recognition methods. Negative exponential temperature dependences that agreed reasonably well with those predicted from theory were observed for many of the vapor-sensor combinations. It was possible to select a subset of sensors with structurally diverse polymer coatings whose sensitivities to all six test vapors and selected binary vapor mixtures had similar temperature dependences. Thus, vapor recognition could be rendered independent of temperature and vapor quantification could be corrected for temperature with sufficient accuracy for most applications. The results indicate that active temperature control is not necessary and that temperature and RH compensation is achievable with a relatively simple microsensor system.     

On a mathematical description of the isotherm of water vapor sorption on grains of various cereals

A model describing the hygroscopic properties of hydrophilic biological polymers is suggested. The quasi-chemical approach was used to obtain an equation for the sorption of water vapor in them. An analysis of experimental data showed that this equation correctly described the hygroscopic properties of the main biopolymers of cereal grains, starch and protein, over a wide range of humidity values. The equation also well described the hygroscopic properties of many cereal grains. The nonlinear regression method was applied to obtain the main parameters of absorption isotherms for grains of certain crops.     

Stochastic diffusion interactions and coarsening in a system of droplets growing from a supersaturated gas mixture

In this work we study diffusion interactions among liquid droplets growing in stochastic population by condensation from supersaturated binary gas mixture. During the postnucleation transient regime collective growth of liquid droplets competing for the available water vapor decreases local supersaturation leading to the increase of critical radius and the onset of coarsening process. In coarsening regime the growth of larger droplets is prevailing noticeably broadening the droplet size-distribution function when the condensation process becomes more intensive than the supersaturation yield. Modifications in the kinetic equation are discussed and formulated for a stochastic population of liquid droplets when diffusional interactions among droplets become noteworthy. The kinetic equation for the droplet size-distribution function is solved together with field equations for the mass fraction of disperse liquid phase, mass fraction of water vapor component of moist air, and temperature during diffusion-dominated regime of droplet coarsening. The droplet size and mass distributions are found as functions of the liquid volume fraction, showing considerable broadening of droplet spectra. It is demonstrated that the effect of latent heat of condensation considerably changes coarsening process. The coarsening rate constant, the droplet density (number of droplets per unit volume), the screening length, the mean droplet size, and mass are determined as functions of the temperature, pressure, and liquid volume fraction.     

The effect of the water vapor pressure on the kinetics of thermal dehydration of manganese(II) formate dihydrate

The effect of the water vapor pressure on the thermal dehydration of manganese(II) formate dihydrate was studied by means of isothermal gravimetry under various water vapor pressure, ranging from 4.6 to 24.4 torr. The kinetics of dehydration was described by a two-dimensional phase-boundary model,R ₂. The rate of dehydration decreased with increasing atmospheric water vapor pressure, but the Smith-Topley phenomenon was not observed for the present dehydration. The activation energy and the frequency factor for the dehydration were 110–170 kJ·mol⁻¹ and 10¹⁰–10¹⁶ cm·s⁻¹, respectively. These values increased with increasing water vapor pressure, and were much larger than those reported for the dehydration in vacuum.