Effects Of Thermodynamic Nonideality Research Articles

Leveraging De Donder relations for a thermodynamically rigorous analysis of reaction kinetics in liquid media

This Mini-review considers the use of De Donder relations to facilitate a thermodynamically rigorous discussion of liquid-phase reaction kinetics through the analysis of elementary steps. In quantifying “solvent effects,” pure species reference states are convenient. Rate expressions developed with this convention capture all effects of thermodynamic non-ideality in solvent-specific activity coefficients or excess free energies, whereas commonly applied infinite dilution reference states lead to solvent- and composition-dependent standard-state rate and equilibrium constants. Two solvent effects are described: a “kinetic” effect, which comprises solvation of a transition state relative to reactants in an elementary step, and a “thermodynamic” effect, which comprises solvation of products relative to reactants in an elementary step. The former impacts the forward rate constant, and the latter impacts the reversibility. These effects are formally encoded in De Donder rate expressions; thus, they inherently account for solvation while maintaining thermodynamic consistency with respect to elementary rate and equilibrium constants. A series of case studies are presented. These demonstrate that solvent effects can lead to substantial deviations from anticipated behavior during routine analysis of liquid-phase reactions. Additionally, we find that surface reactions and degree of rate control in multi-reaction sequences can be impacted by bulk solvation, but such effects are difficult to predict a priori.

Using Molecular Simulations for Elucidation of Thermodynamic Nonidealities in Adsorption of CO2-Containing Mixtures in NaX Zeolite.

Cation-exchanged zeolites are of potential use in pressure swing adsorption (PSA) technologies for CO2 capture applications. Published experimental data for CO2/CH4, CO2/N2, and CO2/C3H8 mixture adsorption in NaX zeolite, also commonly referred to by its trade name 13X, have demonstrated that the ideal adsorbed solution theory (IAST) fails to provide adequately accurate estimates of mixture adsorption equilibrium. In particular, the IAST estimates of CO2/CH4 and CO2/N2 selectivities are significantly higher than those realized in experiments. For CO2/C3H8 mixtures, the IAST fails to anticipate the selectivity reversal phenomena observed in experiments. In this article, configurational-bias Monte Carlo (CBMC) simulations are employed to provide confirmation of the observed thermodynamic nonidealities in adsorption of CO2/CH4, CO2/N2, and CO2/C3H8 mixtures in NaX zeolite. The CBMC simulations provide valuable insights into the root cause of the failure of the IAST, whose applicability mandates a homogeneous distribution of adsorbates within the pore landscape. By sampling 105 equilibrated spatial locations of individual guest molecules within the cages of NaX zeolite, the radial distribution functions (RDFs) of each of the pairs of guest molecules are determined. Examination of the RDFs clearly reveals congregation effects, wherein the CO2 guests occupy positions in close proximity to the Na+ cations. The positioning of the partner molecules (CH4, N2, or C3H8) is further removed from the CO2 guest molecules; consequently, the competition in mixture adsorption faced by the partner molecules is less severe than that anticipated by the IAST. The important message to emerge from this article is the need for quantification of thermodynamic nonideality effects in mixture adsorption.

The Glucagon-Like Peptide 2 Analog Teduglutide Reversibly Associates to Form Pentamers

Glucagon-like peptide 1 and 2 and their analog peptide therapeutics are known to reversibly associate to form oligomers. Here we report the association properties of the glucagon-like peptide 2 analog teduglutide at concentrations up to ∼15 mg/mL. Both sedimentation equilibrium (SE-AUC) and sedimentation velocity (SV-AUC) show that teduglutide dissociates completely to monomers below 0.1 mg/mL. SE-AUC shows that the apparent weight-average molar mass increases substantially between 0.1 and 1 mg/mL, reaching a maximum of ∼14.5 kDa (∼3.9-mer) near 2 mg/mL, and then falling at higher concentrations because of strong solution nonideality effects (highly positive second virial coefficient). Circular dichroism spectra over the range from 0.1 to 2 mg/mL show that self-association is accompanied by significant increases in alpha-helix content, and that the associated state has a distinct tertiary structure. The SV-AUC data up to 2.2 mg/mL are fitted fairly well by an ideal rapidly reversible monomer-pentamer association. The SE-AUC modeling included thermodynamic nonideality effects. SE-AUC data up to ∼15 mg/mL imply a monomer-pentamer association at lower concentrations, but the pentamers also appear to weakly associate to form decamers. These results illustrate the importance of directly modeling the solution nonideality effects, which if neglected would lead to an incorrect preferred stoichiometry.

Characterizing Reversible Protein Association at Moderately High Concentration Via Composition-Gradient Static Light Scattering

Analysis of weakly self-associating macromolecules at concentrations beyond a few g/L is challenging on account of the confounding effect of thermodynamic nonideality on the association signal. When the reversible association comprises only 1 or 2 oligomeric species in equilibrium with the monomer, the nonideality may be accounted for in a relatively rigorous manner, but if more association states are involved, the analysis becomes quite complex. We show that under reasonable assumptions, the nonideality in a composition-gradient static light scattering measurement may be accounted for in a simple fashion. The correction is applied to determining the stoichiometry and binding affinity of a protein previously characterized via sedimentation equilibrium and dynamic light scattering. The results of the new analysis are remarkably self-consistent and in line with the expectations for the form of self-association predicted previously from analysis of the surface residuals, establishing composition-gradient multi-angle static light scattering with nonideality corrections as a critical technology for characterizing associative interactions in concentrated solutions.

OSN Designer, a tool for predicting organic solvent nanofiltration technology performance using Aspen One, MATLAB and CAPE OPEN

The development of OSN Designer is presented: a software tool, which enables commercially available and open source suites of chemical process simulation software for organic solvent nanofiltration (OSN) process modelling and simulation. A modelling framework, comprising state of the art membrane transport models, membrane module flow dynamics, and material balance equations over entire units, was embedded in custom unit operations (UOs) for batch concentration (BC), constant volume semi-batch (CVS), and steady-state (SS) filtration. The numerical solutions of the resulting systems of equations were programmed in MATLAB and implemented in several process simulation environments such as Aspen Plus, HYSYS and COFE. The computer aided process engineering open (CAPE OPEN) standards for communication between chemical engineering software components were used to ensure interoperability amongst MATLAB UOs, process simulation environments and different thermophysical properties servers. Three example simulations using OSN Designer were carried out in the environment of Aspen Plus with dual aims. Firstly, OSN Designer was validated through comparison to available experimental data. Secondly, the example simulations addressed important topics such as energy efficiency of OSN compared to evaporation, use of pore flow or solution diffusion membrane transport models, and effect of thermodynamic non-ideality on the overall process performance.

Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg systems

We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D0 exp{–[Q1bar + (P–1)ΔV+]/RT} for DMg* and DFe*: Mg: Q1bar = 228.3 ± 20.3 kJ/mol, D0 = 2.72 (±4.52) × 10−10 m2/s, Fe: Q1bar = 226.9 ± 18.6 kJ/mol, D0 = 1.64 (±2.54) × 10−10 m2/s. ΔV+ values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization

This reexamination of a high-speed sedimentation equilibrium distribution for α-chymotrypsin under slightly acidic conditions (pH 4.1, IM 0.05) has provided experimental support for the adequacy of nearest-neighbor considerations in the allowance for effects of thermodynamic nonideality in the characterization of protein self-association over a moderate concentration range (up to 8mg/mL). A widely held but previously untested notion about allowance for thermodynamic nonideality effects is thereby verified experimentally. However, it has also been shown that a greater obstacle to better characterization of protein self-association is likely to be the lack of a reliable estimate of monomer net charge, a parameter that has a far more profound effect on the magnitude of the measured equilibrium constant than any deficiency in current procedures for incorporating the effects of thermodynamic nonideality into the analysis of sedimentation equilibrium distributions reflecting reversible protein self-association.

Allowance for the effect of protein charge in the characterization of nonideal solute self-association by sedimentation equilibrium

This theoretical investigation explores the use of statistical–mechanical approaches to characterize the reversible tetramerization of a protein monomer with the size and charge characteristics of serum albumin under conditions where consideration of nearest-neighbor interactions suffices to describe effects of thermodynamic non-ideality. Such analysis of simulated sedimentation equilibrium distributions points to the adequacy of both the scaled particle theory and potential-of-mean-force methods for determining the self-association constant. Although the latter method usually entails the assignment of a magnitude to monomer net charge, this requirement can be obviated to some extent by repeating the analysis for a range of monomer charges and identifying the most appropriate value as that associated with a minimum in the sum-of-squares-of-residuals (SSR) of the best-fit descriptions of the sedimentation equilibrium distribution. Reasonable estimates of the association constant are usually obtained from corresponding analyses of the same sedimentation equilibrium distributions with activity coefficients obtained by scaled particle theory, an approach which also involves the identification of parameters on the basis of a minimum in SSR. However, the value of monomer charge determined must be regarded as a curve-fitting parameter rather than a true measure of monomer charge. Similar qualifications are shown to prevail in the scaled particle theory approach, which also involves the identification of parameters (the effective monomer volume and the polymer/monomer volume ratio) on the basis of a minimum in SSR. We therefore recommend discontinuation of the practice whereby quite precise distinction between modes of self-association has been attempted on the grounds of the physical credibility of the magnitudes of these additional curve-fitting parameters.

A Study on the Effects of Thermodynamic Nonideality and Mass Transfer on Multi-phase Hydrodynamics Using CFD Methods

A Study on the Effects of Thermodynamic Nonideality and Mass Transfer on Multi-phase Hydrodynamics Using CFD Methods

Direct allowance for the effects of thermodynamic nonideality in the quantitative characterization of protein self-association by osmometry

A procedure is described for the direct analysis of osmotic pressure data for reversibly dimerizing proteins that makes allowance for effects of thermodynamic nonideality on the statistical–mechanical basis of the potential-of-mean-force between molecules. Detailed consideration is also given to calculation of the magnitudes of the required virial coefficients. After illustration of the approach with analysis of simulated osmotic pressure data, the method is used to obtain dimerization constants from published osmotic pressure data for soybean proteinase inhibitor, hemoglobin and α-chymotrypsin.

Modeling of equilibration times at high pressure for multicomponent vapor–liquid diffusional processes

Isothermal multicomponent diffusion in a vapor–liquid system at high pressure is analyzed. It is assumed that there are no composition gradients in the bulk vapor due to mixing; diffusion takes place only in the liquid phase and in a thin film near the interface on the vapor side. This model is of value in the analysis of the supercritical drying of porous media and approach to phase equilibrium in a closed system at high pressure. The principle model used is the Fick's Law in one-dimensional form, which is a second order partial differential equation with respect to time and a spatial dimension. The change in the position of the interface is taken into account as an ordinary differential equation. The Fick diffusivities are estimated through the Maxwell–Stefan approach, which decouples the drag effects from the thermodynamic non-ideality effects. The model equations are solved using a fixed grid finite difference formulation. The effects of temperature, pressure, diameter to height ratio of the autoclave, mixing in the vapor phase, the starting mole fraction of the liquid and the initial liquid composition on the equilibration times and equilibrium compositions are analyzed. It is found that for uniform bulk vapor compositions, equilibration times are in the order of hours, while they increase at least one order of magnitude when there is no mixing in the vapor phase. Also, when the starting mole fraction of liquid increases, the equilibration times and the equilibrium position of the interface change significantly.

A potential role for isothermal calorimetry in studies of the effects of thermodynamic non-ideality in enzyme-catalyzed reactions.

Attention is drawn to the feasibility of using isothermal calorimetry for the characterization of enzyme reactions under conditions bearing greater relevance to the crowded biological environment, where kinetic parameters are likely to differ significantly from those obtained by classical enzyme kinetic studies in dilute solution. An outline of the application of isothermal calorimetry to the determination of enzyme kinetic parameters is followed by considerations of the nature and consequences of crowding effects in enzyme catalysis. Some of those effects of thermodynamic non-ideality are then illustrated by means of experimental results from calorimetric studies of the effect of molecular crowding on the kinetics of catalysis by rabbit muscle pyruvate kinase. This review concludes with a discussion of the potential of isothermal calorimetry for the experimental determination of kinetic parameters for enzymes either in biological environments or at least in media that should provide reasonable approximations of the crowded conditions encountered in vivo.

Multicomponent interphase diffusion of carbon dioxide–methanol–water under near-critical conditions

Multicomponent diffusion between liquid and vapor phases is analyzed for a closed system at high pressure. The movement of the interface during the diffusion is taken into account. The principle model used is the Fick's law in one-dimensional form, which is a second-order partial differential equation with respect to time and a spatial dimension. The model is solved using fixed grid explicit finite difference method. The Fick diffusivities are estimated at each iteration using the Maxwell–Stefan approach, which decouples the drag effects from the thermodynamic nonideality effects. It is found that the thermodynamic correction factor, due to nonideality effects, enhances the off-diagonal Fick diffusivities for gases at high pressure, particularly near critical conditions. The off-diagonal diffusivities in turn make a significant change on the composition-time trajectories.

Allowance for thermodynamic non-ideality in the characterization of protein self-association by frontal exclusion chromatography: hemoglobin revisited

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the characterization of protein self-association by frontal exclusion chromatography, and thereby provides methods of analysis with greater thermodynamic rigor than those used previously. Their application is illustrated by reappraisal of published exclusion chromatography data for hemoglobin on the controlled-pore-glass matrix CPG-120. The equilibrium constant of 100/M that is obtained for dimerization of the α 2β 2 species by this means is also deduced from re-examination of published studies of concentrated hemoglobin solutions by osmotic pressure and sedimentation equilibrium methods.

Further evidence for the reliance of catalysis by rabbit muscle pyruvate kinase upon isomerization of the ternary complex between enzyme and products

Isothermal calorimetry has been used to examine the effect of thermodynamic non-ideality on the kinetics of catalysis by rabbit muscle pyruvate kinase as the result of molecular crowding by inert cosolutes. The investigation, designed to detect substrate-mediated isomerization of pyruvate kinase, has revealed a 15% enhancement of maximal velocity by supplementation of reaction mixtures with 0.1 M proline, glycine or sorbitol. This effect of thermodynamic non-ideality implicates the existence of a substrate-induced conformational change that is governed by a minor volume decrease and a very small isomerization constant; and hence, substantiates earlier inferences that the rate-determining step in pyruvate kinase kinetics is isomerization of the ternary enzyme product complex rather than the release of products.

Analysis of thermodynamic non-ideality in terms of protein solvation

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical–mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter δ are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein–protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.

Interpreting the effects of small uncharged solutes on protein-folding equilibria.

Proteins are designed to function in environments crowded by cosolutes, but most studies of protein equilibria are conducted in dilute solution. While there is no doubt that crowding changes protein equilibria, interpretations of the changes remain controversial. This review combines experimental observations on the effect of small uncharged cosolutes (mostly sugars) on protein stability with a discussion of the thermodynamics of cosolute-induced nonideality and critical assessments of the most commonly applied interpretations. Despite the controversy surrounding the most appropriate manner for interpreting these effects of thermodynamic nonideality arising from the presence of small cosolutes, experimental advantage may still be taken of the ability of the cosolute effect to promote not only protein stabilization but also protein self-association and complex formation between dissimilar reactants. This phenomenon clearly has potential ramifications in the cell, where the crowded environment could well induce the same effects.

Ultracentrifugal studies of the effect of molecular crowding by trimethylamine N-oxide on the self-association of muscle glycogen phosphorylase b.

The suitability of sedimentation equilibrium for characterizing the self-association of muscle glycogen phosphorylase b has been reappraised. Whereas sedimentation equilibrium distributions for phosphorylase b in 40 mM Hepes buffer (pH 6.8) supplemented with 1 mM AMP signify a lack of chemical equilibrium attainment, those in buffer supplemented additionally with potassium sulfate conform with the requirements of a dimerizing system in chemical as well as sedimentation equilibrium. Because the rate of attainment of chemical equilibrium under the former conditions is sufficiently slow to allow resolution of the dimeric and tetrameric enzyme species by sedimentation velocity, this procedure has been used to examine the effects of thermodynamic nonideality arising from molecular crowding by trimethylamine N-oxide on the self-association behaviour of phosphorylase b. In those terms the marginally enhanced extent of phosphorylase b self-association observed in the presence of high concentrations of the cosolute is taken to imply that the effects of thermodynamic nonideality on the dimer-tetramer equilibrium are being countered by those displacing the T<==>R isomerization equilibrium for dimer towards the smaller, nonassociating T state. Because the R state is the enzymically active form, an inhibitory effect is the predicted consequence of molecular crowding by high concentrations of unrelated solutes. Thermodynamic nonideality thus provides an alternative explanation for the inhibitory effects of high concentrations of glycerol, sucrose and ethylene glycol on phosphorylase b activity, phenomena that have been attributed to extremely weak interaction of these cryoprotectants with the T state of the enzyme.

Analysis of Sedimentation Equilibrium Distributions Reflecting Nonideal Macromolecular Associations

A rigorous statistical–mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226–2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.