Thermodynamics of krypton adsorption on microporous carbon adsorbent at high pressures

The behavior of the thermodynamic functions for the adsorption system krypton—microporous carbon sorbent ACC is described. The dependences of the differential molar isosteric heat of adsorption, entropy, enthalpy, heat capacity, and differential molar energy of the adsorption system on the adsorption equilibrium parameters were studied over the temperature range from 178 to 393 K and at pressures ranging from 1 to 6?106 Pa. Consideration of the non-ideality of gas phase and non-inertness of the adsorbent leads to a temperature dependence of the thermodynamic functions of the studied adsorption system, especially in the range of high pressures of the adsorptive. The non-ideality of the gas phase and the energetics of the adsorbent—adsorbate system exert the most significant effect on the thermodynamic functions. The non-inertness of the adsorbent in the investigated range of parameters of the adsorption system has a weak effect on the thermodynamic functions of adsorption. In the region of high filling of ACC micropores, the entropy increases, indicating the existence of processes, which change the structure of the adsorbate in the micropores, in particular, to form associates.     

Carbon dioxide adsorption on the microporous ACC carbon adsorbent

Adsorption isotherms of carbon dioxide on the microporous ACC carbon adsorbent and the adsorption deformation of the adsorbent were measured. The heats of adsorption at temperatures raising from 243 to 393 K and pressures from 1 to 5⋅10⁶ Pa were measured. In the low-temperature region (243 K), an increase in the amount adsorbed is accompanied by adsorbent contraction, and at high micropore fillings (a > 10 mmol g⁻¹) the ACC carbon adsorbent expands. At high temperatures, adsorbent expansion is observed in the whole region of micropore filling. At 243 K in the low filling region (a < 1 mmol g⁻¹), the heat of adsorption decreases smoothly from 27 to 24 kJ mol⁻¹. The heat of adsorption remains virtually unchanged in the interval 2 mmol g⁻¹ < a < 11 mmol g⁻¹ and then decreases to 8 kJ mol⁻¹ at a = 12 mmol g⁻¹. Taking into account the nonideal character of the gas phase and adsorbent deformation the heats of adsorption are strongly temperature-dependent in a region of high pressures. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1331–1335, June, 2005.     

Thermodynamics of CO<Subscript>2</Subscript> adsorption on zeolite NaX in wide intervals of pressures and temperatures

The dependences of the differential molar isosteric heat of adsorption and entropy of adsorption of CO₂ on zeolite NaX were determined in wide temperature (196–423 K) and pressure (0.1 Pa to 5.4 MPa) intervals. In the initial region of adsorption (a < 1 mmol g^–1), the differential molar heat of adsorption increases from 40 to 43 kJ mol^–1 and then decreases to 33 kJ mol^–1. The heat of adsorption remains virtually unchanged at 3 mmol g^–1< a < 6.5 mmol g^–1 and decreases sharply at high fillings of zeolite micropores (a > 7 mmol g^–1). The heat of adsorption was found to be temperature-dependent. The region with the constant heats shrinks with the temperature increase, and the heats begin to decrease at lower fillings of micro pores. The dependences of the change in the differential entropy of the adsorption system on the amount adsorbed were calculated at different temperatures. The specific features of the behavior of the thermodynamic functions of this adsorption system in the initial and medium region of fillings kre associated with interactions of adsorbate molecules with Na⁺ cations and walls of large cavities. For high fillings, an increase in repulsion forces between adsorbed molecules results in a sharp expansion of the adsorbent and a decrease in the heat of adsorption.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1570–1573, August, 2004.     

Adsorption of Gases, Vapors and Liquids by Microporous Adsorbents

Adsorption of Xe, Kr, Ar, N₂, O₂, H₂ CH₄, CO₂, He, and freons by PAU-10 and ACC microporous carbon adsorbents as well as by A and X zeolites was investigated over a wide range of pressures (0.1 Pa – 20 MPa) and temperatures (77, 120–600 K). The amount of gases, vapors and liquids adsorbed by microporous adsorbents increases steadily with increasing pressure and does not change dramatically if phase transitions occur in the adsorptive. Isosteres of adsorption constructed as a curve of ln P against f(1/T)_a retain a linear form over a wide range of pressures and temperatures. The slope of isosteres does not vary on going through the critical temperature of the gaseous phase. At high pressures, due to non-ideality of the gaseous phase and non-inert behavior of the adsorbent the differential molar heat of adsorption is dependent on temperature. At high fillings of micropores the differential molar isosteric heat capacities of adsorption systems show maxima that indicate the occurrence of structural rearrangements in the adsorbate.     

Determination of the Kinetic and Thermodynamic Parameters of Adsorption Processes by a Volume Step Thermal Method

A volume step method measuring the pressure and the adsorbent temperature of an adsorbent-adsorbate system has been developped. It is shown that this method allows the determination of all the relevant parameters of an adsorption process, kinetic as well as thermodynamic in case of Linear Driving Force mass transfer. The method for determining the parameters can be extended to the case of diffusive mass transfer if the mass transfer kinetics is faster than the heat transfer kinetics. An example is given, showing the determination of the diffusion coefficient of carbon dioxide in NaX zeolite pellets and the change of the diffusion coefficient and of the isosteric heat of adsorption when the adsorbent is not fully dehydrated.     

Adsorption of carbon dioxide on microporous carbon adsorbent PAU-10

Carbon dioxide adsorption on the microporous carbon adsorbent PAU-10 within the 177.8—423 K temperature and 0.1—5.13·10⁶ Pa pressure intervals was studied. The isosteres of absolute adsorption are well approximated by straight lines, which do not change their slope on going to temperatures higher than the critical temperature of CO₂. An increase in the differential molar isosteric heat of adsorption (q _st) at 0 < a < 1 mmol g^–1 is explained by the influence of the endothermic effect of adsorption expansion of the adsorbent. In the region of high pressures and nonideal gas phase, q _st is temperature-dependent.     

Two methods of describing adsorption equilibrium

The thermodynamics of adsorption equilibrium with a single-component gas phase have been analyzed for two different models of adsorption. It has been shown that with a cell model of adsorption, the differential energy of the adsorbent/adsorbate system is expressed by the same formula as in the other model, in terms of quantities characterizing the equilibrium gas. An expression is derived for the differential energy, with deformation of the adsorbent taken into account. The two methods of calculating the isosteric heat of adsorption are compared.Institute of Physical Chemistry, Russian Academy of Sciences, Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 19–23, January, 1992.     

甲烷在石墨化热解碳黑和活性炭上的吸附

为研究影响碳基吸附剂吸附超临界温度气体的主要因素,选择石墨化热解碳黑BP280和Ajax活性炭,分析超临界温度高压甲烷在其上的吸附平衡。应用容积法,在压力0~20.5 MPa、温度253 K~313 K测定甲烷的吸附平衡数据,并由等量吸附线标绘和亨利定律常数确定等量吸附热。引入通用吸附等温方程,再由方程的Langmuir标绘确定最大吸附容量,进而通过方程的线性化计算吸附平衡态中甲烷分子的作用能。结果表明,甲烷在两种吸附剂上的最大吸附容量均随温度而变化,并都小于液态甲烷的密度;甲烷在碳黑和活性炭上的等量吸附热分别为11.9 kJ/mol~12.5 kJ/mol和17.5 kJ/mol~22.5 kJ/mol,体现了两种吸附剂不同的表面能量分布;甲烷分子间作用能随吸附量的变化特点反映了超临界温度甲烷以类似于压缩气体状态聚集的特点和吸附剂结构上的差异。碳基吸附剂的比表面积和微孔容积是影响其储存甲烷容量的重要因素。     

Gas adsorption process in activated carbon over a wide temperature range above the critical point. Part 2: conservation of mass and energy

Simulations of the thermal effects during adsorption cycles are a valuable tool for the design of efficient adsorption-based systems such as gas storage, gas separation and adsorption-based heat pumps. In this paper, we present simulations of the thermal phenomena associated with hydrogen, nitrogen and methane adsorption on activated carbon for supercritical temperatures and high pressures. The analytical expressions of adsorption and of the internal energy of the adsorbed phase are calculated from a Dubinin-Astakhov adsorption model using solution thermodynamics. A constant adsorption volume is assumed. The isosteric heat is also calculated and discussed. Finally, the mass and energy rate balance equations for an adsorbate/adsorbent pair are presented and are shown to be in agreement with desorption experiments.     

Analysis of Adsorbate–Adsorbate and Adsorbate–Adsorbent Interactions to Decode Isosteric Heats of Gas Adsorption

A qualitative interpretation is proposed to interpret isosteric heats of adsorption by considering contributions from three general classes of interaction energy: fluid–fluid heat, fluid–solid heat, and fluid—high‐energy site (HES) heat. Multiple temperature adsorption isotherms are defined for nitrogen, T=(75, 77, 79) K, argon at T=(85, 87, 89) K, and for water and methanol at T=(278, 288, 298) K on a well‐characterized polymer‐based, activated carbon. Nitrogen and argon are subjected to isosteric heat analyses; their zero filling isosteric heats of adsorption are consistent with slit‐pore, adsorption energy enhancement modelling. Water adsorbs entirely via specific interactions, offering decreasing isosteric heat at low pore filling followed by a constant heat slightly in excess of water condensation enthalpy, demonstrating the effects of micropores. Methanol offers both specific adsorption via the alcohol group and non‐specific interactions via its methyl group; the isosteric heat increases at low pore filling, indicating the predominance of non‐specific interactions.     

Isosteric heat of adsorption in liquid–solid equilibria: Theoretical determination and measurement by liquid chromatography/mass spectrometry

The isosteric heat of adsorption of a pure compound dissolved in a solution in equilibrium with a solid adsorbent was determined, based on the Gibbs surface excess model. The exact isosteric heat of adsorption differs from the usual value derived from the variation of the Henry’s constant with the reciprocal temperature because this procedure assumes ideal behavior of the bulk liquid solution, which, in most cases, is only approximately so. An experimental protocol, based on the determination of the excess adsorption isotherms by combining frontal analysis (for strongly adsorbed components) and spectrometric tracer pulse chromatography (for weakly adsorbed compounds) is proposed. It allows the determination of the exact isosteric heat of adsorption provided that the activity coefficient of the compound in the bulk solution can be explicitly expressed as a function of the bulk liquid composition.     

Adsorption-stimulated deformation of microporous carbon adsorbent

Deformation of the ACC microporous carbon adsorbent during adsorption of carbon dioxide, nitrogen, and argon in the temperature interval from 243 to 393 K and at pressures of 1—5·10⁶ Pa was studied. The effect of adsorbent contraction was found in the initial temperature interval at relatively low pressures. However, the negative value of relative linear deformation L/L smoothly transforms into positive values with the pressure increase. Only the effect of adsorbent expansion is observed at high temperatures in the whole pressure interval. The dependence of the deformation effects for different systems on the adsorbent nature was revealed.     

Analysis of adsorption isosteres of gas and vapor on microporous adsorbents

The adsorption isosteres and isotherms of methane on the microporous carbon adsorbent PAU-10 were calculated using the Dubinin—Radushkevich equation taking into account nonideality of the gas phase. The conditions under which the adsorption isosteres are linear were outlined. The calculated and experimentally found adsorption isosteres were compared for the methane—PAU-10 system. The slope of the isosteres remains unchanged on going to the region of strong nonideality of the gas phase. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 382–385, March, 2007.     

Removal of zinc metal ion (Zn) from its aqueous solution by kaolin clay mineral: A kinetic and equilibrium study

A laboratory batch study has been performed to study the effect of various physic-chemical factors such as initial metal ion concentration, solution pH, and amount of adsorbent, contact time and temperature on the adsorption characteristics of zinc (Zn²⁺) metal ions onto kaolin. It has been found that the amount of adsorption of zinc metal ion increases with initial metal ion concentration, contact time, solution pH but decreases with the amount of adsorbent and temperature of the system. Kinetic experiments clearly indicate that adsorption of zinc metal ion (Zn²⁺) on kaolin is a two steps process: a very rapid adsorption of zinc metal ion to the external surface is followed by possible slow decreasing intra-particle diffusion in the interior of the adsorbent which has also been confirmed by intra-particle diffusion model. The equilibrium time is found to be in the order of 60 min. Overall the kinetic studies showed that the zinc adsorption process followed pseudo-second-order kinetics among pseudo-first-order and intra-particle diffusion model. The different kinetic parameters including rate constant are determined at different initial metal ion concentration, solution pH, amount of adsorbent and temperature respectively. The equilibrium adsorption results are analyzed by both Langmuir and Freundlich models to determine the mechanistic parameters associated with the adsorption process. The value of separation factor, R_L from Langmuir equation also gives an indication of favorable adsorption. Finally thermodynamic parameters are determined at three different temperatures and it has been found that the adsorption process is exothermic due to negative ΔH° accompanied by decrease in entropy change and Gibbs free energy change (ΔG°).     

碳纳米管内N2吸附行为及等量吸附热的GCMC分子模拟研究

碳纳米管及石墨烯具有高比表面积、高化学稳定性以及高耐蚀性等优点,被认为是一种理想的吸附材料。分子模拟技术的发展和应用丰富了人们对吸附机理研究的方式,而简单气体吸附体系的吸附机理研究对吸附理论的发展有着重要的推动作用。本文以单壁碳纳米管（SWCNT）-N₂吸附体系为研究对象,首先通过透射扫描电镜和氮气吸/脱附测试对所选用碳纳米管的微观孔形貌及吸/脱附等温线进行了表征,然后根据对应孔径参数采用巨正则蒙特卡罗方法对该体系的吸附过程进行了分子模拟,并详细研究了碳纳米管孔径和温度对该体系吸附行为的影响。结果显示,SWCNT孔径越小,吸附能力则越强;孔半径为0.746nm的SWCNT的吸附体系发生凝聚相变的临界温度为66K。通过对等量吸附热进行计算发现,孔半径0.746、1.15、1.56和1.83 nm的SWCNT-N₂吸附体系对应的初始固-液等量吸附热分别为10.9、9.2、8.6和8.4 kJ/mol。67.5K时,孔半径1.56和1.83 nm的吸附体系的等量吸附热有热峰出现。     

Effect of pore expansion and amine functionalization of mesoporous silica on CO2 adsorption over a wide range of conditions

Adsorption of CO₂ was investigated over a wide range of conditions on a series of mesoporous silica adsorbents comprised of conventional MCM-41, pore-expanded MCM-41 silica (PE-MCM-41) and triamine surface-modified PE-MCM-41 (TRI-PE-MCM-41). The isosteric heat of adsorption, calculated from adsorption isotherms at different temperatures (298–328 K), showed a significant increase in CO₂–adsorbent interaction after amine functionnalization of PE-MCM-41, consistent with the high CO₂ uptake in the very low range of CO₂ concentration. The CO₂ adsorption isotherm and kinetics data showed the high potential of TRI-PE-MCM-41 material for CO₂ removal in gas purification and separation applications. With TRI-PE-MCM-41, the CO₂ selectivity over N₂ was drastically improved over a wide range of conditions compared to pure mesoporous silica. Moreover, the adsorption was reversible and fast, and the adsorbent was thermally stable and tolerant to moisture.     

Isosteric enthalpies for hydrogen adsorbed on nanoporous materials at high pressures

A sound understanding of any sorption system requires an accurate determination of the enthalpy of adsorption. This is a fundamental thermodynamic quantity that can be determined from experimental sorption data and its correct calculation is extremely important for heat management in adsorptive gas storage applications. It is especially relevant for hydrogen storage, where porous adsorptive storage is regarded as a competing alternative to more mature storage methods such as liquid hydrogen and compressed gas. Among the most common methods to calculate isosteric enthalpies in the literature are the virial equation and the Clausius–Clapeyron equation. Both methods have drawbacks, for example, the arbitrary number of terms in the virial equation and the assumption of ideal gas behaviour in the Clausius–Clapeyron equation. Although some researchers have calculated isosteric enthalpies of adsorption using excess amounts adsorbed, it is arguably more relevant to applications and may also be more thermodynamically consistent to use absolute amounts adsorbed, since the Gibbs excess is a partition, not a thermodynamic phase. In this paper the isosteric enthalpies of adsorption are calculated using the virial, Clausius–Clapeyron and Clapeyron equations from hydrogen sorption data for two materials—activated carbon AX-21 and metal-organic framework MIL-101. It is shown for these two example materials that the Clausius–Clapeyron equation can only be used at low coverage, since hydrogen’s behaviour deviates from ideal at high pressures. The use of the virial equation for isosteric enthalpies is shown to require care, since it is highly dependent on selecting an appropriate number of parameters. A systematic study on the use of different parameters for the virial was performed and it was shown that, for the AX-21 case, the Clausius–Clapeyron seems to give better approximations to the exact isosteric enthalpies calculated using the Clapeyron equation than the virial equation with 10 variable parameters.     

甲烷在层状石墨烯和活性炭上的吸附平衡

以吸附式天然气（ANG）吸附剂的工程应用为目的,以0-10 MPa、283.15-303.15 K甲烷在层状石墨烯（GS（3D）,比表面积2062 m²/g）和活性炭SAC-01（比表面积1507 m²/g）上的吸附平衡数据作分析。首先,在77.15 K下由氮气吸附表征样品的孔径大小及分布（PSD）和比表面积。其次,选择极低压力下的吸附平衡数据标定亨利定律常数,确定甲烷在两吸附剂上的极限吸附热,并由维里方程和10-4-3势能函数计算甲烷与两吸附剂壁面之间的相互作用势。最后,依据测试的甲烷在吸附剂上的高压吸附平衡数据,比较了Langmuir系列方程的关联数据后的拟合精度,并由绝对吸附量计算了甲烷的等量吸附热。结果表明,甲烷在GS（3D）和活性炭SAC-01上的平均极限吸附热为23.07、20.67 kJ/mol;283.15 K下甲烷分子与GS（3D）和活性炭SAC-01之间的交互作用势ε_sf/k为67.19、64.23 K,与洛伦混合法则的计算值64.60 K相近;Toth方程关联甲烷在活性炭SAC-01和GS（3D）上吸附平衡数据的拟合累计相对误差为0.25%和2.29%;甲烷在活性炭SAC-01和GS（3D）上的等量吸附热平均值为16.8和18.3 kJ/mol。相对于活性炭SAC-01,比表面积和微孔容积均较高的GS（3D）对甲烷的吸附更具有优势。     

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.     

Discussion of thermodynamic data obtained by adsorption gas chromatography of hydrocarbons on carbograph 4

Summary A new graphitized carbon black, Carbograph 4, with a specific surface area of 240 m² g⁻¹ was studied in terms of enthalpy, entropy and free energy of adsorption, determined by gas chromatographic method on a series of alkanes (C₂−C₆) and on benzene. The changes in the isosteric heat and entropy of adsorption when a non-polar stationary phase (squalane) was added to the adsorbent were also investigated. The data obtained are discussed and compared to those present in the literature for other graphitized carbon blacks. Some examples of separations obtained with Carbograph 4 are reported.