Sorption Hysteresis Research Articles

Theory of sorption hysteresis in nanoporous solids: Part I: Snap-through instabilities

The sorption–desorption hysteresis observed in many nanoporous solids, at vapor pressures low enough for the liquid (capillary) phase of the adsorbate to be absent, has long been vaguely attributed to some sort of ‘pore collapse’. However, the pore collapse has never been documented experimentally and explained mathematically. The present work takes an analytical approach to account for discrete molecular forces in the nanopore fluid and proposes two related mechanisms that can explain the hysteresis at low vapor pressure without assuming any pore collapse nor partial damage to the nanopore structure. The first mechanism, presented in Part I, consists of a series of snap-through instabilities during the filling or emptying of non-uniform nanopores or nanoscale asperities. The instabilities are caused by non-uniqueness in the misfit disjoining pressures engendered by a difference between the nanopore width and an integer multiple of the thickness of a monomolecular adsorption layer. The wider the pore, the weaker the mechanism, and it ceases to operate for pores wider than about 3nm. The second mechanism, presented in Part II, consists of molecular coalescence, or capillary condensation, within a partially filled surface, nanopore or nanopore network. This general thermodynamic instability is driven by attractive intermolecular forces within the adsorbate and forms the basis for developing a unified theory of both mechanisms. The ultimate goals of the theory are to predict the fluid transport in nanoporous solids from microscopic first principles, determine the pore size distribution and internal surface area from sorption tests, and provide a way to calculate the disjoining pressures in filled nanopores, which play an important role in the theory of creep and shrinkage.

Theory of sorption hysteresis in nanoporous solids: Part II Molecular condensation

Motivated by the puzzle of sorption hysteresis in Portland cement concrete or cement paste, we develop in Part II of this study a general theory of vapor sorption and desorption from nanoporous solids, which attributes hysteresis to hindered molecular condensation with attractive lateral interactions. The classical mean-field theory of van der Waals is applied to predict the dependence of hysteresis on temperature and pore size, using the regular solution model and gradient energy of Cahn and Hilliard. A simple “hierarchical wetting” model for thin nanopores is developed to describe the case of strong wetting by the first monolayer, followed by condensation of nanodroplets and nanobubbles in the bulk. The model predicts a larger hysteresis critical temperature and enhanced hysteresis for molecular condensation across nanopores at high vapor pressure than within monolayers at low vapor pressure. For heterogeneous pores, the theory predicts sorption/desorption sequences similar to those seen in molecular dynamics simulations, where the interfacial energy (or gradient penalty) at nanopore junctions acts as a free energy barrier for snap-through instabilities. The model helps to quantitatively understand recent experimental data for concrete or cement paste wetting and drying cycles and suggests new experiments at different temperatures and humidity sweep rates.

Time-Dependent CO2 Sorption Hysteresis in a One-Dimensional Microporous Octahedral Molecular Sieve

The development of sorbents for next-generation CO(2) mitigation technologies will require better understanding of CO(2)/sorbent interactions. Among the sorbents under consideration are shape-selective microporous molecular sieves with hierarchical pore morphologies of reduced dimensionality. We have characterized the non-equilibrium CO(2) sorption of OMS-2, a well-known one-dimensional microporous octahedral molecular sieve with manganese oxide framework. Remarkably, we find that the degree of CO(2) sorption hysteresis increases when the gas/sorbent system is allowed to equilibrate for longer times at each pressure step. Density functional theory calculations indicate a "gate-keeping" role of the cation in the tunnel, only allowing CO(2) molecules to enter fully into the tunnel via a highly unstable transient state when CO(2) loadings exceed 0.75 mmol/g. The energy barrier associated with the gate-keeping effect suggests an adsorption mechanism in which kinetic trapping of CO(2) is responsible for the observed hysteretic behavior.

Cadmium Sorption and Desorption in Soils: A Review

Cadmium (Cd) is an environmental pollutant that can be readily taken up by plants and may enter the food chain, causing risk to human health. It can also affect soil quality and, if easily leached, has the potential to pollute surface and ground waters. Sorption and desorption are critical processes controlling the phytoavailability and mobility of Cd in soils. The authors present the present knowledge on the mechanisms and hysteresis of Cd sorption and desorption in soils and factors such as pH, ionic strength, index cation, other heavy metal cations, inorganic anions, organic ligands, Cd loading rate, and the type and amounts of organic matter and inorganic colloids influencing these processes. The methods used to determine the nature and magnitude of Cd sorption and desorption are also critically reviewed.

Role of Confinement and Surface Affinity on Filling Mechanisms and Sorption Hysteresis of Water in Nanopores

The liquid–vapor transition in cylindrical pores is studied as a function of pore size and hydrophilicity through molecular dynamics simulations with the mW coarse-grained model of water. We identify two distinct filling mechanisms, depending on whether the water–pore interaction is smaller or larger than the water–water interaction. In the former case (that we term hydrophobic pore), the formation of the condensed phase proceeds gradually with filling, through the nucleation of a water cluster which grows toward the center of the cavity. In hydrophilic pores, instead, the condensed phase develops in conditions of supersaturation, which in principle become more extreme with increasing pore radius and surface affinity. For highly hydrophilic interfaces (those with adsorption energy for water above 10 kcal/mol), the equilibrium and dynamical properties of water in confinement turn out to be practically independent of water affinity.

The water vapour sorption properties of thermally modified and densified wood

The water vapour sorption behaviour of Scots pine (Pinus sylvestris L.) and Scots pine that was densified, thermally-modified, or subjected to a combination of thermal modification and densification has been investigated. It was found that all modifications resulted in a decrease in the equilibrium moisture content of the wood samples throughout the hygroscopic range. The water vapour sorption isotherms were reproducible for the unmodified wood samples, but changed between the first and subsequent sorption cycles for the densified, thermally-modified and for wood subjected to a combination of the two treatments. This is the first time that changes in the sorption isotherm between the first and subsequent cycles have been reported for thermally-modified wood. Irrespective of the wood treatment the difference between the adsorption and desorption isotherm loops (sorption hysteresis) was the same and greater than that observed for the unmodified wood sample. After the first sorption cycle, the hysteresis decreased to the values observed for the unmodified wood, even though the isotherms were different. The sorption kinetic behaviour was also investigated and found to be accurately described using the parallel exponential kinetics (PEK) model. The PEK model describes the dynamic sorption behaviour in terms of a fast and slow kinetic process and this has been interpreted in terms of two Kelvin-Voigt elements coupled in series (i.e. relaxation-limited kinetics).

Retention and Mobility of Copper and Lead in Soils as Influenced by Soil Horizon Properties

The mobility and bioavailability of heavy metals in soils is largely governed by sorption and desorption phenomena. Cu 2+ and Pb 2+ are among the most potentially toxic heavy metals and they are present, often concomitantly, in many polluting spills and in agrochemicals. The objective was to assess and compare the competitive sorption and desorption capacities and sorption hysteresis of Cu 2+ and Pb 2+, as well as their migration through the profiles of four natural soils: a Humic Umbrisol, an Umbric Cambisol, an Endoleptic Luvisol and a Humic Cambisol. In all horizons Pb 2+ was invariably sorbed and retained to a greater extent than Cu 2+. The sorption and retention of Cu 2+ were most influenced by pH, effective cation exchange capacity (CECe) and Mn oxide content. On the other hand, the fixation capacity of Pb 2+ was most influenced by pH, CECe, and Mn oxide and organic matter contents. pH and CECe were the individual soil properties most markedly influencing Cu 2+ and Pb 2+ sorption and retention. In all the horizons Pb 2+ exhibited greater hysteresis than Cu 2+. In each soil the hysteresis in the A horizon was greater than that in the B horizon, except in the Bt horizon of the Endoleptic Luvisol, due to its high pH and vermiculite content. Based on migration indices, Pb 2+ was less mobile than Cu 2+ in the studied soils.

The effect of hydration on molecular chain mobility and the viscoelastic behavior of resilin-mimetic protein-based hydrogels

The outstanding rubber-like elasticity of resilin and resilin-mimetic proteins depends critically on the level of hydration. In this investigation, water vapor sorption and the role of hydration on the molecular chain dynamics and viscoelastic properties of resilin-mimetic protein, rec1-resilin is investigated in detail. The dynamic and equilibrium swelling behavior of the crosslinked protein hydrogels with different crosslink density are reported under various controlled environments. We propose three different stages of hydration; involving non-crystallizable water, followed by condensation or clustering of water around the already hydrated sites, and finally crystallizable water. The kinetics of water sorption for this engineering protein is observed to be comparable to hydrophilic polymers with a diffusion coefficient in the range of 10 −7 cm 2 s −1. From the comparison between the absorption and desorption isotherms at a constant water activity, it has been observed that rec1-resilin exhibits sorption hysteresis only for the tightly bound water. Investigation of molecular mobility using differential scanning calorimetry, indicates that dehydrated crosslinked rec1-resilin is brittle with a glass transition temperature ( T g ) of >180 °C, which dramatically decreases with increasing hydration; and above a critical level of hydration rec1-resilin exhibits rubber-like elasticity. Nanoindentation studies show that even with little hydration (<10%), the mechanical properties of rec1-resilin gels change dramatically. Rheological investigations confirm that the equilibrium-swollen crosslinked rec1-resilin hydrogel exhibits outstanding elasticity and resilience of ∼92%, which exceeds that of any other synthetic polymer and biopolymer hydrogels.

A rheological description of the water vapour sorption kinetics behaviour of wood invoking a model using a canonical assembly of Kelvin-Voigt elements and a possible link with sorption hysteresis

AbstractThe dynamic vapour sorption behaviour of two Malaysian hardwoods, acacia (Acacia mangiumWild) and sesendok (Endospermum malaccenseBentexMüll. Arg.) was studied over a narrow temperature range (20–40°C). The rate of sorption or desorption of water into or out of the wood cell wall was considered to be limited by the viscoelastic behaviour of the material and the sorption kinetics was accordingly analysed in terms of a canonical series of Kelvin-Voigt elements. A two series and three series model have been applied to the kinetic data and the results are compared. Characteristic times and moisture contents were obtained from the models. The Arrhenius equation was used in conjunction with the reciprocals of the characteristic times to calculate the activation energy and activation entropy of sorption, and the Gibbs free energy of activation for the sorption process was also determined. This is the first time that entropy of activation and Gibbs free energy of activation for sorption processes with wood have been reported. Interpretation of these data invokes a model describing the polymeric relaxation processes occurring within the cell wall during adsorption or desorption. A possible link between sorption kinetics, polymeric relaxation processes, and sorption hysteresis is discussed.

Predicting moisture state of timber members in a continuously varying climate

A prerequisite for a sensible estimate of moisture induced stresses in timber members is an accurate prediction of the members’ moisture states during their service life. There are, however, an infinite number of possible moisture states for an arbitrary timber member in a natural varying climate. The naturally varying humidity is possible to describe as harmonic cycles, with different periods, superimposed. This work presents realizations of envelop curves over the possible moisture states in a timber member for some carefully chosen harmonic humidity variations. The calculations, on which the realizations were made, are based on a fully coupled transport model including a model for the influential sorption hysteresis of wood. A format containing required information suitable for assessing the “moisture” action on timber members is proposed. In addition it is illustrated how a model of high complexity and nonlinearity renders results with large degree of consistency. Large moisture gradients in a timber member are detected when variations of the humidity are frequent (daily period) and with large amplitude at high humidity levels. Overall and complete moisture changes of structural timber members with normal dimensions are found for members subjected to varying humidity with long (annual) periods. A timber member’s initial moisture state in relation to the ambient humidity can have a significant influence on both moisture gradients and overall moisture change of the member.

Comparison of nonideal sorption formulations in modeling the transport of phthalate esters through packed soil columns

Sorption of dimethyl phthalate (DMP), diethyl phthalate (DEP) and dipropyl phthalate (DPP) to two soil materials that vary in organic matter content was investigated using miscible displacement experiments under saturated flow conditions. Generated breakthrough curves (BTCs) were inversely simulated using linear, equilibrium sorption (LE), nonlinear, equilibrium sorption (NL), linear, first-order nonequilibrium sorption (LFO), linear, radial diffusion (LRD), and nonlinear, first-order nonequilibrium sorption (NFO) models. The Akaike information criterion was utilized to determine the preferred model. The LE model could not adequately describe phthalate ester (PE) BTCs in higher organic matter soil or for more hydrophobic PEs. The LFO and LRD models adequately described the BTCs but a slight improvement in curve-fitting was gained in some cases when the NFO model was used. However, none of the models could properly describe the desorptive tail of DPP for the high organic matter soil. Transport of DPP through this soil was adequately predicted when degradation or sorption hysteresis was considered. Using the optimized parameter values along with values reported by others it was shown that the organic carbon distribution coefficient ( K oc ) of PEs correlates well with the octanol/water partition coefficient ( K ow ). Also, a strong relationship was found between the first-order sorption rate coefficient normalized to injection pulse size and compound residence time. A similar trend of timescale dependence was found for the rate parameter in the radial diffusion model. Results also revealed that the fraction of instantaneous sorption sites is dependent on K ow and appears to decrease with the increase in the sorption rate parameter.

Assessing surface chemistry and pore structure of active carbons by a combination of physisorption (H2O, Ar, N2, CO2), XPS and TPD-MS

In order to address open questions concerning the surface chemistry and pore structure characterization of nanoporous carbons, we performed extensive experiments by combining various experimental techniques on a series of commercially available activated carbons which exhibit diverse surface chemistry characteristics. Pore size analysis was performed on Ar (87 K), N2 (77 K) and CO2 (273 K) adsorption isotherms using state-of-the art methods based on density functional theory, including the recently developed quenched solid density functional theory (QSDFT). A detailed study of the surface chemistry was obtained by applying temperature programmed desorption coupled with mass spectrometry (TPD-MS) as well as XPS (X-Ray-Photoelectron Scattering). This information together with the pore structure information leads to a reliable interpretation of systematic water adsorption measurements obtained on these materials. Our results clearly suggest that water adsorption is indeed a sensitive tool for detecting differences in surface chemistry between chemically and physically activated active carbon materials with comparable ultramicropore structure. The occurrence of sorption hysteresis associated with the filling of micro- and narrow mesopores (in a range where nitrogen and argon isotherms are reversible) provides additional structural information, complementary to the insights from argon/nitrogen/carbon dioxide adsorption.

Analysis of moisture sorption hysteresis in hard gelatin capsules, maize starch, and maize starch: drug powder mixtures.

Moisture sorption and desorption isotherms at 25 degrees C for hard gelatin capsules, maize starch and 50:50 mixes of maize starch: barbitone and maize starch: sodium barbitone have been measured. The sorption hysteresis observed in all four systems studied has been analysed according to the hypothesis of Young & Nelson (1967a) which distinguishes three locations for moisture--monolayer adsorbed moisture, normally condensed moisture and absorbed moisture. Hysteresis is explained by a separation of absorption and desorption isotherms for absorbed moisture and different patterns of moisture distribution are demonstrated in the four systems examined.

Impact of coal structural heterogeneity on the nonideal sorption of organic contaminants

Carbonaceous geosorbents (black carbon, coal, and humin/kerogen) play a primary role in the nonideal sorption (isotherm nonlinearity, hysteresis, and multiphasic kinetics) of hydrophobic organic chemicals by soils and sediments. The present study investigated the impact of coal structural heterogeneity on sorption/desorption of two model monoaromatic compounds (1,3-dichlorobenzene and 1,3-dinitrobenzene). Due to the higher degree of aromaticity and condensation, anthracite showed stronger sorption affinity and nonlinearity and slower sorption kinetics than lignite. Removal of humic substances by alkali extraction and/or mineral fraction by acidification did not much affect organic carbon-normalized sorption coefficient to the coal, suggesting nearly complete accessibility of adsorption sites on the condensed organic carbon. However, the treatments greatly increased sorption kinetics and meanwhile alleviated hysteresis of 1,3-dinitrobenzene, as compared with the original lignite. These observations were attributed to the enhanced exposure of high-energy adsorption sites on the condensed organic carbon after exfoliating the surface coverage by humic substances and minerals. An empirical biphasic pseudo-second-order model consisting of a fast sorption phase and a slow sorption phase adequately quantified the overall sorption kinetics for the coal sorbents. The results indicated that the condensed organic carbon, in combination with other structural components, controls the nonideal sorption of unburned coal.

The water vapour sorption behaviour of three celluloses: analysis using parallel exponential kinetics and interpretation using the Kelvin-Voigt viscoelastic model

The objective of this study was to examine the water vapour sorption behaviour of three celluloses, which were originally derived from cotton fibers, using a dynamic vapour sorption apparatus, including analyses of the sorption rate and hysteresis occurring in the isotherm run. Cotton linter, α-cellulose, and microcrystalline cellulose (MCC), respectively attained equilibrium moisture contents of 14.2, 20.6, and 16.9% at a relative humidity (RH) of 95%. All three cellulosic materials exhibited sorption hysteresis to varying degrees throughout the full RH range; the MCC and α-cellulose displayed the lowest and highest total hysteresis, respectively. The sorption kinetics were analysed in terms of the parallel exponential kinetics (PEK) model, with excellent fits to the data being obtained. The PEK data is further interpreted on the basis of two Kelvin-Voigt elements operating in series. Clear differences in behaviour were seen between the α–cellulose and the other two celluloses in this study. The relative importance of capillary condensation and matrix viscoelasticity with respect to sorption hysteresis is discussed.

The influence of soil properties on the individual and competitive sorption and desorption of Cu and Cd

The sorption and retention of mixtures of heavy metals by soil are complex processes that depend on both soil properties and competition between metals for sorption sites. Cu 2+ and Cd 2+ are among the most potentially toxic heavy metals, they are present –often together – in numerous polluting spills and in agrochemicals. The objective was to evaluate and compare the competitive and individual sorption and desorption capacity and sorption hysteresis of Cu 2+ and Cd 2+ on four natural soils: a Humic Umbrisol, an Umbric Cambisol, an Endoleptic Luvisol and a Humic Cambisol. To evaluate the sorption and retention capacity, we used the parameter K r proposed and determined in a previous work. In all the horizons Cu 2+ is sorbed and retained to a greater extent than Cd 2+. The individual sorption and retention of Cu 2+ are most influenced by pH, CECe, and vermiculite, chlorite, and total clay content; however, Cu 2+ competitive sorption and retention do not depend on chlorite content. On the other hand, the individual and competitive sorption and retention of Cd 2+ are most influenced by pH, CECe and Mn oxides, vermiculite, chlorite, and total clay content. In all the horizons the greatest hysteresis corresponds to Cu 2+, and in each soil the hysteresis in the A-horizon is greater than in B, except in the Bt of Endoleptic Luvisol, due to its high pH and vermiculite content. The sorption irreversibility is higher in soils of lower acidity, high levels of oxides and the presence of vermiculite and chlorite in the clay fraction. By multiple linear regression analysis, individual and competitive explanatory models of fixation capacity were obtained. In all equations the most important characteristics that explain the metal fixation are included.

The dynamic water vapour sorption properties of natural fibres and viscoelastic behaviour of the cell wall: is there a link between sorption kinetics and hysteresis?

In a previous article, the sorption kinetics’ properties of a range of natural fibres were reported. Analysis of the sorption kinetics was made using the parallel exponential kinetics (PEK) model, and it was argued that the rate limiting step of the sorption process was determined by substrate swelling rather than being diffusion limited. The PEK model divides the sorption kinetics curve into two first-order kinetics processes (fast and slow) but there is as yet no generally accepted explanation of what these two processes represent. In this article, the PEK parameters for sorption have been further evaluated in terms of two Kelvin–Voigt elements arranged in series. The force constant in the spring of each Kelvin–Voigt elements determines the equilibrium moisture content for each of the processes, whereas the viscosity of the dashpot is represented by the time constant for each process. Determination of interfibrillar matrix modulus using the Kelvin–Voigt model gives values that are in line with what would be predicted, giving credence to this interpretation of the sorption kinetics. Possible interpretations of the fast and slow kinetics processes are discussed.

Nanotubular Metal−Organic Frameworks with High Porosity Based on T-Shaped Pyridyl Dicarboxylate Ligands

Two nanotubular metal-organic frameworks (MOFs), {Cu(L1)·2H(2)O·1.5DMF}(∞) (1) and {Cu(2)(L2)(2)(H(2)O)(2)·7H(2)O·3DMF}(∞) (2), with novel topologies have been constructed based on Cu(2+), 5-(pyridin-4-yl)isophthalic acid (L1) and 5-(pyridin-3-yl)isophthalic acid (L2), respectively. Two MOFs were characterized by IR spectroscopy, thermogravimetry, single-crystal, and powder X-ray diffraction methods. Network analysis reveals a two-nodal (3,6)-connected (4·6(2))(2)(4(2)·6(10)·8(3)) net and a three-nodal (3,4)-connected (4·8(2))(4)(4(2)·8(2)·10(2))(2)(8(4)·12(2)) net. Interpenetration is inherently prevented by both of the topologies of the frameworks. The porosity of MOF 1 was confirmed by N(2) and CO(2) gas adsorption investigations. MOF 1 exhibits remarkable hydrogen sorption hysteresis at low pressure and a H(2) uptake capacity of 1.05 wt% at 77 K and 1 atm.

Inclusion of the sorption hysteresis phenomenon in future drying models. Some basic considerations

The sorption hysteresis effect, i.e. different wood equilibrium moisture contents (EMCs) in desorptionand adsorption for the same relative humidity, is well known. However, quantitative sorption isotherms,in the form of tables or analytical correlations, are almost always given as the average of the desorptionand adsorption curves. Consequently most drying simulation models use these average curves, and doesnot take into account the sorption hysteresis phenomenon.The equilibrium state of a wood sample is thus not a function of the relative humidity only, butdepends on the moisture history also. This means that Fick�s equations - with moisture content as asingle driving force - are not valid any more. For a pure desorption process the state of the samplefollows the desorption isotherm, but a problem arises when desorption is followed by adsorption - asfor instance in the timber conditioning phase. It seems reasonable to assume that for each EMC point,on or between the desorption/adsorption isotherms, the moisture content change follows a unique pathwhen the surrounding climate changes. This path - the so called scanning curve - does not need to be thesame in desorption and adsorption. Some selected results and corresponding scanning curve suggestionsare presented and discussed.Drying models with the sorption hysteresis phenomenon included should be developed for the analysisof experimental data and more generally for use as an improved tool in practical applications.

A three-dimensional microporous metal–organic framework with large hydrogen sorption hysteresis

A three-dimensional microporous metal-organic framework [Cd(2)(Tzc)(2)](n), which is dehydrated from [Cd(2)(Tzc)(2)(H(2)O)(2)](n), exhibits selective gas adsorption and large hydrogen sorption hysteresis.