Thermodynamics of water–biopolymer interactions: Irreversible sorption by a single,uniform sorbent phase

Sorption isotherms of water vapor by solid biopolymers are necessary for the determination of thermodynamic quantities for water–biopolymer interactions. Such isotherms are generally irreversible, so equilibrium thermodynamics may not be applicable. General relationships are derived for thermodynamic quantities of sorption when the sorbent is a single uniform phase. In general, use of the Clausius–Clapeyron equation allows correct determination of differential entropies of sorption. However, calorimetric data are also necessary for the correct determination of other thermodynamic quantities. The single uniform phase model appears more useful than a domain model in explaining the hysteresis seen in water–biopolymer sorption isotherms.     

The thermodynamics of water-protein interactions

Information about the effects of water on protein structure and function can be obtained from studies on freeze dried protein powders of varying water content. Sorption isotherms of water on proteins can be used to obtain thermodynamic quantities for water-protein interactions. Since such isotherms show hysteresis, there is doubt in regard to their interpretation.General expressions for the thermodynamic quantities of sorption are derived. If isotherms represent data at equilibrium, it is possible to calculate these thermodynamic quantities.There are two types of hysteresis, non-equilibrium hysteresis and equilibrium hysteresis. Absorption and desorption isotherms can show equilibrium hysteresis if different protein conformations, which are only slowly interconvertible, can be present. In this case valid thermodynamic quantities can be obtained. Experimental tests for equilibrium hysteresis are presented. More experiments are needed before definite conclusions can be drawn in regard to isotherms in the literature.If the protein conformation in a protein powder is similar to the protein conformation in aqueous solution, equilibrium data obtained from sorption isotherms can be used to approximate thermodynamic quantities for the interaction of water with proteins in aqueous solution. Examination of what experimental evidence is available indicates that the protein in powders prepared by desorption of water should have a conformation similar to that in solution. Further study of such samples will help to clarify the thermodynamics of water-protein interactions in aqueous solution.     

Thermodynamic functions of biopolymer hydration. I. Their determination by vapor pressure studies,discussed in an analysis of the primary hydration process

The primary hydration process of native biopolymers is analyzed in a brief review of the literature, pertaining to various aspects of biopolymer–water systems. Based on this analysis, a hydration model is proposed that implies that the solution conformation of native biopolymers is stable at and above a critical degree of hydration (h_p′ = 0.06–0.1 g H₂O/g polymer). This water content corresponds to the fraction of strongly bound water, and amounts to ～20% of the primary hydration sphere. In order to test this model, detailed sorption–desorption scanning experiments were performed on a globular protein (α-chymotrypsin). The results obtained are consistent with the proposed hydration model. They show that under certain experimental conditions, sorption isotherms can be obtained that do not exhibit hysteresis. These data represent equilibrium conditions and are thus accessible to thermodynamic treatment. Valid thermodynamic functions, pertinent to the interaction of water with biopolymers in their solution state, can be obtained from these sorption experiments.     

Effect of water content on the structural reorganization and elastic properties of biopolymer films: a comparative study

In this work, the effect of water uptake on the structural reorganization and elastic properties of three types of biopolymer films was studied. The water-biopolymer interaction for hydroxypropyl cellulose (HPC), gelatin, and cassava starch films prepared from aqueous solutions was studied and compared using Fourier-transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), X-ray diffraction, dynamic vapor sorption (DVS), and dynamic mechanical thermal analysis with humidity generator and controller (DMTA) techniques. The FTIR spectral variations due to the water sorption were generalized into two-dimensional (2D) correlation graphs for each biopolymer, and the effect of water on the molecular conformation was compared. The water sorption isotherms were fitted with Guggenheim-Anderson-De Boer (GAB) and D'Arcy and Watt models. The water content in the mono- and multilayers predicted by both models for each biopolymer was discussed and compared. The correlation of the fitted data obtained from the sorption isotherms to the DMTA data allowed us to conclude that the elastic properties of the HPC films depended on the total water content in contrast to the elastic properties of the gelatin and cassava starch films, which decrease only with the appearance of multilayer water.     

Hydration of stratum corneum

A model for the hydration behavior of human stratum corneum has been developed from measurements on in vitro samples isolated in a manner which minimized tissue treatment and trauma. Water sorption/desorption rate measurements as a function of water activity, temperature, and tissue integrity are reported. These data, together with thermodynamic data (infrared and nmr results reported earlier) are consistent with a model in which rapidly sorbed/desorbed water (ca. 0.5 mg water/mg stratum corneum) is associated with (“bound” by) the tissue, while slowly sorbed/desorbed “free” water (up to 12 mg water/mg stratum corneum) is kinetically restricted and probably intracellular in location. Both equilibrium water binding and desorption kinetic data suggest structural changes of this cellular water barrier upon hydration. Evidence for hysteresis in water sorption isotherms (reported by others) could not be reproduced.     

Thermodynamic of Water Sorption of Grape Seed: Temperature Effect of Sorption Isotherms and Thermodynamic Characteristics

After determination of sorption isotherms of grape seeds using gravimetric method, five models with temperature effect were used to fit water sorption isotherms of grape seeds to investigate temperature effect on sorption isotherms and its thermodynamic characteristics. Halsey model had minimum mean relative percentage error (M _e ) and all other models used were good in fitting experimental data (with M _e of less than 10 %). Differential parameters such as net isosteric heat, isosteric heat, differential entropy and integral function such as equilibrium heat, net equilibrium heat, integral entropy and surface potential have been calculated. The net isosteric heat, isosteric heat and differential entropy decreased with moisture content. The net equilibrium enthalpy, equilibrium enthalpy and integral entropy decreased with moisture content. The surface potential at four temperatures (35, 45, 55 and 65 °C) was estimated, and low temperature effect was reported.     

Adsorption of Five Model Organic Compounds on a Peat at Different Stages of Drying

Acridine orange (AO), dinitrobenzoic acid (DNB), bromocresol green (BCG), bromophenol blue (BPB), and methylene blue (MB) were chosen as model aromatic compounds of different polarity, charge, and solubility in water to examine the effects of solute properties on hydrophobic adsorption. These compounds show strict structural similarities to some herbicides and other potential xenobiotic pollutants and exhibit distinct absorption maxima in the visible region, which allows for their easy determination. A well-decomposed peat (medisaprist) at four different stages of drying was used to determine compound adsorption/desorption influences based on the degree of hydrophobicity and charge density of an organic surface. Adsorption and desorption isotherms were investigated using the batch equilibration method and determining the concentration of free chemicals by UV-Vis spectrophotometry. AO had a high tendency of adsorption and was strongly sorbed on peat samples that had been air-dried for 12 months. The lower Freundlich coefficient values found for MB when compared with AO at all the drying stages of the peat indicated that electrostatic attraction has a secondary contribution to sorption. On the contrary, the higher energy that must be spent to break solute-solvent interactions in the case of charged or polar molecules is one of the main factors in determining the position of the equilibrium. For a given solute, K_f values varied with the degree of hydrophobicity and the charge density of the surface, but again solute-solvent interactions appear to be much more important in the overall energy balance of hydrophobic pollutants than the electrostatic sorbate-sorbent interactions. A change in the solution pH does not improve the adsorption of the relatively polar DNB molecule, but sorption increases strongly for BCG and BPB when these molecules are in non-dissociated forms. The larger increase in BPB sorption observed on H⁺ saturated peat suggests that the degree of interaction increases with the suppression of the negative charge, but charge repulsion has a small effect in preventing adsorption of molecules bearing hydrophobic groups such as BCG. Desorption results differed depending on the chemical structure of the compound examined. For example, with AO there was no desorption from the more hydrophobic peat surfaces. A negative hysteresis was observed for DNB; the magnitude of hysteresis, evaluated using the ratio of Freundlich coefficients for adsorption and desorption, increased with the drying stage of the sorbent and was larger on oven-dried samples.     

The hydration of proteins in nearly anhydrous organic solvent suspensions

Water sorption isotherms at 27°C have been measured for lysozyme and chymotrypsin in suspensions of toluene, di(n-butyl) ether, n-propanol, and a solution of 1M n-propanol in benzene. Sorption isotherms for the different suspensions are compared by converting solvent water content to the thermodynamic activity of water in each solvent. The sorption behavior is also compared to that for the two proteins hydrated from the vapor phase. At low water activities, all sorption isotherms are similar when compared on the basis of water activity. However, at higher activities, water sorption by the proteins in the organic suspensions is suppressed relative to the sorption of water vapor. The greatest suppression is observed for n -propanol, which suggests that the suppression may be due to a competition for water-binding sites on the protein by the organic solvent. Sorption isotherms at low water activities have also been predicted using a thermodynamic model in which it is assumed that water binds selectively to the ionizable residues on the surface of the protein. A comparison of predicted and measured sorption isotherms shows that the model can provide reasonable estimates of water sorption in nonpolar or moderately polar organic solvent suspensions at low levels of hydration. © 1993 John Wiley & Sons, Inc.     

Modeling of composite sorption isotherm for stratum corneum

Equilibrium water sorption in stratum corneum (SC) is considered by treating it as a biocomposite with two main phases, namely, corneocytes and lipids. To validate the rule of mixtures for the individual phase sorption isotherms, a new flexible fitting model is introduced by accounting for characteristic features observed in the variations of the thermodynamic correction factors corresponding to the individual sorption isotherms. The comparison of the model fitting performance with that of the five-parameter Park's model shows a remarkably good ability to fit experimental data for different types of sorption isotherms. The effect of the lipids content on the variance of the composite sorption isotherm of stratum corneum is highlighted. The sensitivity analysis reveals that for the typical water content 20–30 wt%, which corresponds to the SC in a stable condition, the sensitivity of the composite sorption isotherm to the variation of the lipids content on dry basis is predominantly positive and sufficiently small. The good agreement observed between the experimental sorption isotherm for SC and the composite isotherm, which is based on the rule of mixtures for the individual phase sorption isotherms, yields a plausible conclusion (hypothesis) that the corneocytes–lipids mechanical interaction during unconstrained swelling of the SC membrane in the in vitro laboratory experiment is negligible.     

Chromium (VI) uptake by grape stalks wastes encapsulated in calcium alginate beads: equilibrium and kinetics studies

Abstract

The removal of hexavalent chromium from aqueous solution using grape stalks wastes encapsulated in calcium alginate (GS–CA) beads was investigated. Cr(VI) sorption kinetics were evaluated as a function of chromium initial concentration and grape stalks (GS) content in the calcium alginate (CA) beads. The process follows pseudo second-order kinetics. Transport properties of hexavalent chromium on GS–CA beads was characterised by calculating chromium diffusion coefficient using the Linear Absorption Model (LAM). Langmuir isotherms, at pH 3.0 were used to describe sorption equilibrium data as a function of GS percentage in the CAbeads. Maximum uptake obtained was 86.42 mmol of Cr(VI) per L of wet sorbent volume. Results indicated that both kinetic and equilibrium models describe adequately the adsorption process.     

Removal of selenium and arsenic by animal biopolymers

The animal biopolymers prepared from hen eggshell membrane and broiler chicken feathers, which are byproducts of the poultry-processing industry, were evaluated for the removal of the oxyanions selenium [Se(IV) and Se(VI)] and arsenic [As(III) and As(V)] from aqueous solutions. The biopolymers were found to be effective at removing Se(VI) from solution. Optimal Se(IV) and Se(VI) removal was achieved at pH 2.5–3.5. At an initial Se concentration of 100 mg/L (1.3 m M), the eggshell membrane removed approx 90% Se(VI) from the solution. Arsenic was removed less effectively than Se, but the chemical modification of biopolymer carboxyl groups dramatically enhanced the As(V) sorption capacity. Se(VI) and As(V) sorption isotherms were developed at optimal conditions and sorption equilibrium data fitted the Langmuir isotherm model. The maximum uptakes by the Langmuir model were about 37.0 mg/g and 20.7 mg/g of Se(VI) and 24.2 mg/g and 21.7 mg/g of As(V) for eggshell membrane and chicken feathers, respectively.     

A non-intrusive method for the measurement of water vapour sorption by bacterial spores

Single particle levitation (SPL) is used to measure the sorption and desorption of water vapour from microparticles comprising of Bacillus spores. Water gain is determined from increases in the weight-balancing levitation voltages. Spore water isotherms are compared to values previously reported using bulk gravimetric methods. Two salient differences are found between the SPL and bulk data: (1) greater osmotic swelling is observed in the SPL data; and (2) the SPL data exhibit open loop hysteresis while bulk data exhibit closed loop hysteresis.     

Moisture Sorption Isotherms of Various Tobaccos

The equilibrium moisture contents of sun-cured (Kroumougrad), flue-cured (Bright Yellow—4) and air-cured (Burley-21 and Matsukawa) tobaccos were measured over a relative humidity range from 5 to 80% at 20°C. The moisture sorption isotherms of tobaccos were of sigmoid type, and classified into two groups. In a lower humidity range below ca. 40% RH, the A group (Kroumougrad and BY-4) had a smaller moisture sorption capacity than B group (Burley-21 and Matsukawa), while in a higher humidity range above ca. 50% RH the former had a larger moisture sorption capacity than the latter. By extracting with water, the moisture content of BY-4 was increased in the lower humidity range, while it decreased in the higher humidity range. However, the moisture content of Matsukawa was scarecely changed by extracting it with water. These results suggest that the differences in equilibrium moisture content with the type of curing were due to the differences in contents of water soluble com- ponents. To control the hygroscopic properties of a tobacco, therefore, the influences of the addition of sucrose and glycerol on the equilibrium moisture content were quantitatively analysed. The moisture sorption capacity of tobacco was greatly different from its nitrogen sorption capacity. The specific surface area of tobacco calculated from moisture sorption isotherm was ca. 110 times larger than the specific surface area calculated from the nitrogen sorption isotherm. Both the nitrogen and moisture sorption data should be necessary for better understanding of the complicated sorption-desorption phenomena in tobaccos.     

Equilibrium sorption isotherm for metal ions on tree fern

A new sorbent system for removing heavy metal ions, such as Zn(II), Cu(II) and Pb(II), from aqueous solutions has been investigated. This new sorbent is tree fern, an agriculture product. Variables of the system include solution temperature and sorbent particle size. The experimental results were fitted to the Langmuir, Freundlich and Redlich–Peterson isotherms to obtain the characteristic parameters of each model. Both the Langmuir and Redlich–Peterson isotherms were found to well represent the measured sorption data. According to the evaluation using the Langmuir equation, the maximum sorption capacities of metal ions onto tree fern were 7.58 mg/g for Zn(II), 10.6 mg/g for Cu(II) and 39.8 mg/g for Pb(II). It was noted that an increase in temperature resulted in a higher metal loading per unit weight of the sorbent. Decreasing the particle sizes of tree fern led in an increase in the metal uptake per unit weight of the sorbent.     

Improvement of the binding capacity of metal cations by sugar-beet pulp. 2. Binding of divalent metal cations by modified sugar-beet pulp

Binding of some divalent cations (Ca²⁺, Cd²⁺, Cu²⁺, Ni²⁺, Pb²⁺ and Zn²⁺) in aqueous solution by saponified and cross-linked sugar-beet pulp was investigated. Saponification doubled the cation-exchange capacity, while cross-linking decreased specific surface area and hydration properties to low and stable values independent of pH and ionic strength conditions. The sorption isotherms indicated a high metal-binding capacity which increased with sorbent concentration, and followed a clear order of selectivity: Cu²⁺˜Pb²⁺ Zn²⁺˜Cd²⁺ > Ni²⁺ > Ca²⁺. The sorption data were better represented by the Langmuir isotherm than by the Freundlich one, suggesting that the monolayer sorption, mainly due to ion-exchange, would not be disturbed by lateral interactions between cations sorbed with similar sorption energies. The same order of selectivity could be drawn from the Langmuir parameters, sorption equilibrium constants (K_L) and maximum binding capacities (Me_Amax). Whatever the cation, K_L decreased with increasing sorbent concentration, while Me_bmax increased. Higher quantities of Cu²⁺ and Pb²⁺ than predicted by the one divalent cation to two carboxyl functions ratio were bound. This was attributed to the partial contribution to the sorption phenomenon of hydroxyl functions close to ionic sites, explaining the higher affinity of such cations for substrates. Cross-linked pulp exhibited higher metalbinding capacity per volume unit than the raw pulp.     

On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature

Monte Carlo simulations in the grand ensemble and meso-canonical ensemble in which the adsorbent is connected to a finite reservoir have been used to study adsorption isotherms for monolayer argon adsorption on graphite at temperatures below the 2D-critical temperature in order to elucidate the microscopic details of the 2D-transitions: vapour–solid, vapour–liquid and liquid–solid. An S-shaped van der Waals (vdW) loop was found when a small square surface was used; however, for large square surfaces and rectangular surfaces the isotherms exhibit a vdW-type loop with a vertical segment which indicates the coexistence of two phases separated by a boundary that changes its shape with the loading. This coexistence occurs at the same chemical potential as determined by the mid-density scheme, developed by Do and co-workers (Z. Liu, L. Herrera, V.T. Nguyen, D.D. Do, and D. Nicholson, A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 37(11):932–939, 2011; Z. Liu, D.D. Do, and D. Nicholson, A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 38(3):189–199, 2011).     

Pseudo-isotherms for the sorption of cadmium ion onto tree fern

The kinetics of cadmium sorption on to tree fern has been investigated based on the assumption of a pseudo-second order rate law. The batch sorption model has been applied to predict the rate constant of sorption and the equilibrium capacity with the effect of initial cadmium concentration. The experimental results have been analysed by pseudo-Langmuir, pseudo-Freundlich and pseudo-Redlich–Peterson isotherms based on pseudo-second order kinetic expression constant. Both pseudo-Langmuir and pseudo-Redlich–Peterson isotherms were found to represent the measured sorption data well. According to the evaluation using the pseudo-Langmuir equation, the monolayer sorption capacity was obtained to he 16.3 mg/g. In addition, χ² analysis was also used to determine the most suitable model. Pseudo-Langmuir and pseudo-Redlich–Peterson were also the best models for the experiment data from χ² analysis.     

Thermodynamic functions of biopolymer hydration. II. Enthalpy–entropy compensation in hydrophilic hydration processes

The thermodynamic functions of biopolymer hydration were investigated by multitemperature vapor pressure studies. Desorption measurements were performed that allowed determination of reversible isotherms in the hydration range of 0.1 to 0.3–0.5 g H₂O/g dry polymer. These isotherms are accessible to thermodynamic interpretation and are relevant to the interaction of water with biopolymers in their solution conformation. The results obtained on a series of different biopolymers (lysozyme, α-chymotrypsin, apo-lactoferrin, and desoxyribonucleic acid), show the following common features of interest: (1) The differential excess enthalpies (ΔH^e ) and entropies (ΔS^e ) are negative, and exhibit pronounced anomalies in a well-defined low-humidity range (approx. 0.1 g H₂O/g dry polymer). These initial extrema are interpretable by structural changes, induced in the native biopolymer structures by water removal below a critical degree of hydration. (2) The ΔH^e and ΔS^e terms exhibit statistically significant linear enthalpy–entropy compensation effects in all biopolymer–water systems investigated. The compensation temperatures \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \beta = \overline {\Delta H} ^e /\overline {\Delta S} ^e $\end{document} are approximately identical for all biopolymers, ranging from 360 to 500 K. The compensation effects are attributable to phase transitions of water molecules between the bulk liquid and the inner-sphere hydration shell of native biopolymers. (3) The negative excess free energies (ΔG^e ) decrease monotonically with increasing water content and are close to zero at 0.3 to 0.5 g H₂O/g polymer. This result indicates that only transitions between the bulk liquid and the inner-sphere hydration shell are associated with significant net free energy effects. The outer-sphere hydration water is thermodynamically comparable to bulk water. The importance of the proportionality factor \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \beta $\end{document} in the control of the free energy term is discussed.     

Effect of pH on lead removal from water using tree fern as the sorbent

The sorption of lead from water onto an agricultural by-product, tree fern, was examined as a function of pH. The sorption processes were carried out using an agitated and baffled system. Pseudo-second-order kinetic analyses were performed to determine the rate constant of sorption, the equilibrium sorption capacity, and the initial sorption rate. Application of the pseudo-second-order kinetics model produced very high coefficients of determination. Results showed the efficiency of tree fern as a sorbent for lead. The optimum pH for lead removal was between 4 and 7, with pH 4.9 resulting in better lead removal. Ion exchange occurred in the initial reaction period. In addition, a relation between the change in the solution hydrogen ion concentration and equilibrium capacity was developed and is presented.     

Influence of Soil Components on Sorption of Atrazine under Aerobic and Anoxic Conditions

The adsorption of atrazine onto untreated and soils when oxides and hydroxides of Fe, Mn, and organic matter have been reduced was studied under aerobic and anoxic conditions. The Freundlich model appeared to fit the isotherm data better than the Langmuir model, while second-order reaction rates were best fit for atrazine in the aqueous phase. Simple regression analysis indicated that the Fe content of the geosorbents is the most important primary factor controlling the sorption processes of atrazine (r² = 0.947). Similar sorption capacity of atrazine by geosorbents but different isotherm nonlinearity indicated different sorption domains due to structural modifications and hydrophobicity. The sample treated to significantly remove organic carbon exhibited the greatest organic carbon–normalized sorption capacity. There existed apparent sorption–desorption hysteresis for each sorbent–sorbate system with desorption being more significant under anoxic conditions. The study suggests that, in remediation exercise, in situ redox barriers such as Fe²⁺-enriched zones can be created by stimulation of Fe³⁺ through chemical reduction. This study observed that soil predominated by Fe and with low OC content is probably a more effective sorbent for atrazine, implying that atrazine applied to such soils is less likely to leach into groundwater.