Comparison of molecular simulation of adsorption with experiment

Experimental measurements of adsorption yield the surface excess. The Gibbs surface excess is the actual or absolute amount of gas contained in the pores less the amount of gas that would be present in the pores in the absence of gas-solid intermolecular forces. Molecular simulation of adsorption yields the absolute amount adsorbed. Comparison of simulated adsorption isotherms and heats of adsorption with experiment requires a conversion from absolute to excess variables. Molecular simulations of adsorption of methane in slit pores at room temperature show large differences between absolute and excess adsorption. The difference between absolute and excess adsorption may be ignored when the pore volume of the adsorbent is negligible compared to the adsorption second virial coefficient (V?B _1s ).     

Interpretation of water isotherm hysteresis for an activated charcoal using stochastic pore networks

Water vapor adsorption equilibria on activated carbons typically exhibit hysteresis. The size and shape of the hysteresis loop which separates the adsorption and desorption branches is a strong function of the pore size and interconnectivity of the pores. Neither conventional pore filling models nor statistical thermodynamics approaches provide a means for predicting the extent of hysteresis from only adsorption measurements. This work uses the Kelvin Equation in conjunction with the structural concept of a stochastic pore network to describe measured water isotherms on BPL carbon. Using a pore segment distribution function determined from the adsorption branch, it is shown that totally random assemblies underestimate the extent of hysteresis. It is possible, however, to closely fit the measured BPL-water hysteresis loop using a patchy heterogeneity in which a proportion of the larger pores are preferentially located on the exterior, mid-range pores are concentrated in a sub-surface layer and some large pores form shielded voids behind much smaller pores.Nomenclature p vapor phase partial pressure of sorbate - p _sat saturation vapor pressure of sorbate - R gas constant - r pore radius - T absolute temperature - t adsorbed layer thickness - V _L molar volume of adsorbed phase - surface tension - contact angle     

High Pressure Adsorption Data of Methane, Nitrogen, Carbon Dioxide and their Binary and Ternary Mixtures on Activated Carbon

Adsorption equilibria of the gases CH₄, N₂, and CO₂ and their binary and ternary mixtures on activated carbon Norit R1 Extra have been measured in the pressure range 0 P 6 MPa at T = 298 K. Pure gas adsorption equilibria were measured gravimetrically. Coadsorption data of the three binary mixtures CH₄/N₂, CH₄/CO₂, and CO₂/N₂ were obtained by the volume-gravimetric method. Isotherms of five ternary mixtures CH₄/CO₂/N₂ were measured using the volumetric-chromatographic method. First, we present in a short overview the method and procedure of measurement. In a second part, the measured data of pressures, surface excess amounts adsorbed and absolute amounts adsorbed are presented and analyzed. In the last part of the paper the resulting pure gas adsorption data are correlated using a generalized dual-site Langmuir isotherm. Mixture adsorption can be predicted by this model using only pure component parameters with fair accuracy. Results are presented and discussed in several tables and figures.     

On the Jovanovic model of adsorption

Summary The effect of the hydrostatic pressure exerted by bulk phases on adsorbed phases depends on the mobility of adsorbed phase and on the topographical distribution of adsorption energy. It is shown in this paper that the Langmuir's equation applies also to adsorption of fully mobile hard discs, on heterogeneous surfaces having fully random topographical distribution of adsorption energy. The effects of the hydrostatic pressure are discussed also in the case of heterogeneous surfaces exhibiting patchwise topographical distribution of adsorption energy.

Symbols

Roman Letters a parameter in the Jovanovic isotherm - A fraction of total surface covered - A ₁ fraction covered of sites having a given adsorption energy - A _j fraction of surface covered as evaluated from the Jovanovic adsorption isotherm - b,b _t parameters in various versions of the Langmuir isotherm - B number of adsorption sites on an adsorbent surface - H enthalpy of adsorption - F free energy of adsorption - k Boltzmann's constant - K, K _j ,K _L parameters in various versions of adsorption isotherms - m mass of the adsorbate molecule - N number of adsorbed molecules - N ₀ monolayer capacity in mobile adsorption - N ₁ local adsorption isotherm - N _t overall adsorption isotherm - p pressure of gas phase adsorbate - q canonical molecular partition function for mobile admolecules - q _st isosteric heat of adsorption - R gas constant - S surface area of adsorbent - S ₁ surface area of sites having a given adsorption energy - S ^* minimum change in the external variable S - T absolute tempetature - T _t frozen temperature Greek Letters Greek Letters parameter of the adsorption isotherm - isothermal-isobaric partition function - adsorption energy - area occupied by one adsorbate molecule - area of box of uniform adsorption energy - chemical potential - v frequency of vibrations of admolecules - range of variation of - () distribution of adsorption energy With 2 figures and 1 table     

Adsorption phenomena at high pressures and temperatures 4. Isotherms of excess and absolute adsorption of Kr on NaA zeolite

The problem of conversion of an isotherm of excess adsorption measured experimentally into values of the total amount of the adsorbate (absolute adsorption) has been formulated. Five isotherms of excess adsorption of krypton on NaA zeolite were measured (at 334–500 K) at equilibrium pressures of -160 MPa. The corresponding isotherms of the total amount were calculated and the temperature dependences of the parameters of an equation describing the isotherms of excess adsorption were identified. It was shown that at high temperatures and pressures, krypton atoms diffuse into the -cavities of the NaA zeolite.For Part 3, seeRuss. Chem. Bull., 1996, 45, 534 (Engl. Transl.).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1138–1142, May, 1996.     

Simulation study of two-dimensional phase transitions of argon on graphite surface and in slit micropores

Molecular simulation has been increasingly used in the analysis and modeling of gas adsorption on open surfaces and in porous materials because greater insight could be gained from such a study. In case of homogeneous surfaces or pore walls the adsorption behavior is often complicated by the order–disorder transition. It is shown in our previous publications (Ustinov and Do, Langmuir 28:9543–9553, 2012a; Ustinov and Do, Adsorption 19:291–304, 2013) that once an ordered molecular layer has been formed on the surface, the lattice constant depends on the simulation box size, which requires adjusting the box dimensions parallel to the surface for each value of loading. It was shown that this can be accomplished with the Gibbs–Duhem equation, which results in decreasing lattice constant with an increase of the amount adsorbed. The same feature is expected to be valid for gas adsorption in narrow pores, but this has not been analyzed in the literature. This study aims at an extension of our approach to adsorption in slit graphitic pores using kinetic Monte Carlo method (Ustinov and Do, J Colloid Interface Sci 366:216–223, 2012b). The emphasis rests on the thermodynamic analysis of the two-dimensional (2D) ordering transition and state of the ordered phase; if the ordered phase exists in narrow slit pores, simulation with constant volume box always leads to erroneous results, for example, seemingly incompressible adsorbed phase. We proposed a new approach that allows for modeling thermodynamically consistent adsorption isotherms, which can be used as a basis for further refinement of the pore size distribution analysis of nanoporous materials.     

Adsorption kinetics of nonionic surfactants using the drop volume method

The kinetic results obtained for the nonionic surfactantsn-octyl,n-decyl, andn-dodecyl dimethyl andn-octyl, andn-decyl diethyl phosphine oxide show purely diffusion controlled adsorption. The drop volume technique applied in a static and dynamic version proves to be useful to measure the adsorption kinetics in the form of surface tensions in function of time. Comparisons of the results obtained from both the static and the dynamic measuring procedure confirm the validity of a theory applied to interpret the kinetic data.Nomenclature a Langmuir parameter - c ₀ surfactant bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - ¯ (t)/ ₀ reduced surface concentration - maximum value of - R gas law constant - surface tension - ₀ surface tension of pure water - t time - T absolute temperature     

Two-dimensional auto-organized nanostructure of sodium hyaluronate and its frictional properties

The two-dimensional auto-organized nanostructure of sodium hyaluronate NaHA on bovine serum albumin BSA monolayer was studied by a layer-by-layer method. The surface properties were studied by a quartz crystal microbalance QCM method and by using an atomic force microscope AFM. NaHA showed a Langmuir-type adsorption and was found to form honeycomb-like networks. With increasing adsorption amount of NaHA, their mesh size decreased and their strand size increased in width. The surface nanomechanical properties, such as adhesion force F_ad and frictional forces F_f between the surfaces of the NaHA layers and the AFM tip, were studied in air and in NaHA solutions using a contact mode and a lateral force modulation LFM of AFM. The values of F_ad and F_f obtained in air were found to be higher than those obtained in the solutions because of the effect of moisture film on the NaHA layers. The values of F_ad and frictional coefficients in the solutions increased with increasing .     

Surface activity and mercury flotation in solutions of n-dodecanoic acid and n-dodecylamine

The flotation and adsorption properties of two ionic collectors (n-dodecylamine andn-dodecanoic acid) are compared on the bases of results of mercury flotation in the model flotation apparatus and electrochemical measurements of the double layer capacity.The flotation recovery and the adsorption parameters (standard free enthalpyG° _A, the interaction coefficient of Frumkin's isotherm, the surface area per molecule) have been determined within the pH range 2.5–12 in solutions of various collector concentrations containing 0.1 N KCl. The maxima of flotation recovery and surface excess have been found at pHs corresponding to pK values for both substances. The influence of the electrolyte on flotation recovery and the gas bubble size distribution dependent upon the pH of the solution is presented forn-dodecanoic acid. The maxima of flotation recovery are involved through the formation of ion-molecule associates (11) as well as an optimum of the bubble size distribution.Publ.-No. 811 from Research Institute of Mineral Processing, Academy of Sciences of the German Democratic-Republic, Freiberg.     

Theory of measurement of gas-adsorption equilibria by rotational oscillations

The gas adsorbed on the inner surface of a highly porous material like activated carbon or zeolite can be measured by slow damped oscillations of a torsional pendulum. The physical principles and the theory of this method are outlined. Formulas are given relating the increase in mass due to adsorption to changes of the frequency and the logarithmic decrement of slow, damped rotational oscillations of the pendulum. Preliminary measurements of gas adsorption equilibria of nitrogen on activated carbon show that the ratio of the mass adsorbedm, to the mass of the adsorbentm ^s , can be determined by this method with mean absolute error |m/m ^s |0.04%.Dedicated to the memory of Joseph Kestin (1913–1993).     

A criterion for judging the purity of surfactant solutions based on diffusion controlled adsorption kinetics

Based on the theory of diffusion controlled adsorption, simple relations are derived for judging the grade of purity of surfactant solutions. The difference of surface tension values between adsorption and desorption under well-defined conditions is used as the experimental measure. Experimental data on surface-chemically puren-alkyl dimethyl phosphine oxides demonstrate the application of the relations derived. It could be demonstrated that it is also possible to use the criterion to evaluate the concentration and surface activity of present impurities in surfactant solutions.Notations a _i surface activity parameter - ratio of the initial to the final area in the case of compression of the adsorption layer (desorption experiments) - c _i bulk concentration - D _i diffusion coefficient - _t8 maximum surface concentration - _i surface concentration - surface tension - t time indices i number of the component (i=2 main component,i= 3,... contaminations) - A adsorption - D desorption     

The influence of the water content on the adsorption properties of γ-Al2O3

Summary One of the most important parameters which decide the peaks resolution in HPLC with the nonmodified adsorbents, is the amount of water which is present on the adsorbent surface. This article tries to show that the change in the adsorption properties of -Al₂O₃ is dependent on the amount of adsorbed water. These changes are shown with the help of adsorption isotherms, isosteric heats of adsorption and adsorption energy distributions. The data is analysed on the bases of Jovanovic equations. It was also found that a relationship exists between the Brockman activity scale and the adsorption isotherm of water on -Al₂O₃.     

Characterisation of the surface of a cellulosic multi-purpose office paper by inverse gas chromatography

The surface of multi-purpose cellulosic office paper has been analysed by inverse gas chromatography (IGC). The parameters determined were the dispersive component of the surface free energy, the enthalpy of adsorption and the entropy of adsorption of polar and apolar probes, the Lewis acidity constant, K _a, and the Lewis basicity constant, K _b. It can be concluded that the dispersive component of the surface free energy, _s ^d decreases with temperature, in the range 50–90°C. The temperature coefficient of _s ^d, d_s ^d/dT, is –0.35 mJm ^–2K^–1. The values of K _a and K _b were determined to be 0.11±0.011 and 0.94±0.211, respectively. The predominant surface basicity agrees with expectation, bearing in mind the presence of calcium carbonate, and of a styrene-acrylic copolymer, in the surface sizing formulation. It is thought that during the drying stages following the surface sizing treatment, the starch used as the binder migrates to the interior of the surface sizing layer and then to the paper bulk itself. This migration contributes to a decrease in the hydrophilicity of the surface, and also results in the surface showing only slight Lewis.     

Adsorption characteristics of synthesized mordenite membranes

Nitrogen adsorption at 77 K was measured for a self-supporting mordenite membrane synthesized on and detached from, a polytetrafluoroethylene (PTFE) substrate, and for a simultaneously formed powder. The adsorption by the membrane saturated an amount which was about half that found for adsorption by the powder. To examine this difference in adsorption characteristics, both of powder and membrane were measured for adsorption for water, methanol,n-hexane andtert-butyl alcohol. For methanol,n-hexane andtert-butyl alcohol, the powder and membrane both showed the same adsorption behavior as for nitrogen. When water molecules were adsorbed, however, there was no difference in saturated adsorption amount between powder and membrane, suggesting the presence of deformed pores in the rectangular crystal layer of the mordenite membrane. The deformed pores are assumed to occur as gaps among crystallites which displaced along theab planes of the rectangular crystals, forming the rectangular crystal layer. The channel bonding sites resulting from such displacement were found to serve as pore walls against adsorbable molecules which have a cross-sectional area greater than that of the water molecule. and so to hinder their entrance into the deformed pores. X-ray diffraction analysis revealed that the rectangular crystals have no periodic, continuous structure along thec-axis; they show a slight distortion of the crystallite shift from the plane perpendicular to thec-axis.     

Kinetics of double-layer charging/discharging of the activated carbon fiber cloth electrode: effects of pore length distribution and solution resistance

The effects of pore length distribution (PLD) and solution resistance, R_sol, on the kinetics of double-layer charging/discharging of the activated carbon fiber cloth electrode (ACFCE) were investigated in a 30 wt% H₂SO₄ solution using nitrogen gas adsorption, a.c. impedance spectroscopy, the current transient technique, and cyclic voltammetry. The impedance spectra of the ACFCE were theoretically calculated based upon the transmission line model in consideration of the pore size distribution (PSD) and the PLD. From comparison of both the experimental and theoretical impedance spectra of the ACFCE, it is suggested that the deviation from the ideal impedance behavior of a cylindrical pore in the experimental impedance spectrum of the ACFCE is mainly ascribed to PLD, rather than to PSD. The cathodic current transients and cyclic voltammograms were theoretically calculated based upon the transmission line model as functions of the standard deviation of the PLD and R_sol. From the results, it is concluded that ion penetration into the pores is closely related to both and R_sol during double-layer charging/discharging of the ACFCE, that is, the larger and R_sol, the lower is the rate capability, thus causing higher retardation of ion penetration into the pores.     

Steam-carbon gasification catalyzed by calcium: Assessment of the porous structure of active carbons from plum stones and synthetic active carbons

A need for an elaboration of the methods for synthesis and characterization of activated carbons with a requisite porous structure has existed for a long time. One of the methods giving possibility for creating controlled mesopore and micropore structures deals with the steam gasification of various carbon materials. In this work the effects of calcium catalyst on the catalytic steam gasification of active carbons from plum stones and porous polymers are presented. Determination of micropores capacity and specific adsorption in mesopores have been performed by means of the _s method, but adsorption on the heterogeneous solids was described by the integral equation with various local isotherms. This equation has been solved by the regularization method. Based on this method the changes in structural parameters of active carbons depending on the amount of calcium catalyst were estimated.Nomenclature d width of slit-like micropore - F(x) distribution function of the half-width - p vapor pressure of sorbate - p/p _N relative pressure - PSAC Plum Stone Active Carbon - average pore radius, nm - S ₁ relative limit of the validity of experimental point on the adsorption isotherm in the computations by means of regularization method - SAC Synthetic Active Carbon - S _BET specific surface area calculated by means of BET method, m²/g - S _mes mesopore surface area, m²/g - S _mic micropore surface area, m²/g - T absolute temperature, K - V _mes sorption capacity of mesopores, cm³/g - V _mic sorption capacity of micropores, cm³/g - V _p sorption capacity of pores, cm³/g - w/w weight in weight concentration - x half-width of slit-like micropore, nm - x ₁ maximum of half-width of micropore slit, nm - average half-width of slit-like micropore, nm - X _min-X _max integration limits of thex Greek Letters Greek Letters variance of average half-width of slit-like micropore, nm² - local relative filling of micropores - total relative filling of micropores     

Chemical structure and surface activity

Surface tension measurements on aqueous solutions of 2-alkyl-2-methyl-1,3-dioxolanes, 2-alkyl-4-methyl-1,3-dioxolanes, and 2-alkyl-1,3-dioxanes at a temperature of 293.2 K are presented. The surface tension isotherms obtained were used to calculate some adsorption parameters, i. e. the efficiency of surface tension reduction, pC₂₅, surface excess concentration, , and surface area,A, per molecule in the adsorption layer. The Temkin adsorption isotherm equation was used to calculate standard free energy of adsorption, G ⁰ _=0.5 . The increments for a methylene group in the alkyl chain, G ^o [–CH₂–], and for the residual part of the molecule, G ^o [W], were also determined.The results obtained show that: (i) an increase in alkyl chain length at the C-2 carbon atom of the ring by one methylene unit brings about a marked increase in surface activity; (ii) the introduction of a methyl group into the 1,3-dioxolane ring (i. e., at C-2 or C-4 atom) has a weaker effect on surface activity of alkyl-substituted 1,3-dioxolanes, and (iii) the contribution of the 5- and 6-membered 1,3-dioxacyclane rings to a total surface activity of, respectively, 2-alkyl-1,3-dioxolanes and 2-alkyl-1,3-dioxanes is similar.     

Synthesis and Surface Properties of Novel N-Alkyl Quinoline-Based Cationic Gemini Surfactants

Two series of cationic dimeric (gemini) surfactants are prepared with respect to key surfactants properties, such as surface activity and solubilization. The influence of both the dimerization and the spacer group is examined in order to establish structure-property relationships. The surface tension and critical micelle concentration can be markedly reduced compared to the monomeric surfactants in the pure state. The critical micelle concentration (cmc) of each series has been determined using equilibrium surface tension measurements. Furthermore, air/water interface parameters including effectiveness (π_cmc), efficiency (P_C20), maximum surface excess (Γ _max ), and minimum surface area (A _min ) have been also derived using Gibb's adsorption equation at 25°C. Standard free energies of micellization and adsorption were calculated. Solubilization behaviors of the synthesized surfactants were measured towards paraffin oil as solubilized material using light transmission technique.     

Studies on the Effects of Additional Components on Micellization of CTAB via Surface Tension Measurements

The effects of Tris-HCl buffer solution on the cmc of cetyltrimethylammonium bromide (CTAB) were studied by surface tension measurement. The result shows that the effect of the buffer solution depends on the interaction between CTAB and NaCl and the structure accelerants of water, Tris. A series of parameters, including the critical micelle concentration (cmc), the surface tension at cmc (γ_cmc), the adsorption efficiency (pC₂₀), and the effectiveness of surface tension reduction (∏_cmc) were obtained from the surface tension measurements in the presence of glycine with different concentration in the Tris-HCl buffer solution at 27°C. In addition, maximum surface excess concentration (Γ _max) and minimum surface area per molecule (A_min) at the air-water interface were estimated according to the Gibbs adsorption isotherm. The thermodynamic parameters (Δ C _p,m , Δ H _m,tr , Δ C _p,m,tr ) of micellization for CTAB in the absence and presence of glycine at different temperature were also been obtained.