Thermodynamic Nonideality Research Articles

(Invited) Bridging the Gap between the Physics and Chemistry of Electric Double Layer

Classical models of electric double layer (EDL) are mostly concerned with ion distributions and their responses to the surface potential that can be regulated by changing either the voltage or the extent of surface ionization. With the help of adjustable parameters, classical EDL models are able to describe diverse physical phenomena including EDL capacitance and ion transport in good agreement with experimental measurements. However, major challenges remain in understanding chemical reactions within EDL important for the rational design and optimization of electrochemical processes such as energy storage and electrocatalysis. In this talk, I will present a molecular-thermodynamic model to predict the charging behavior of ionizable surfaces under various solution conditions. If a solid is non-conductive, the surface reactions can be reliably described with a Langmuir-type model coupled with liquid-state methods to account for the local thermodynamic non-ideality. When a solid is conductive, however, the electronic properties of different surface sites are intrinsically coupled with each other leading to highly correlated surface reactions. While the brute-force prediction of chemical equilibrium at an electrified surface is computationally prohibitive, a combination of the first-principles calculations and coarse-grained modeling provides complemental information that may be useful for diverse electrochemical applications.

Simulation of Gilbert theory for self-association in sedimentation velocity experiments: a guide to evaluate best fitting models.

There is a long tradition in the Biophysics community of using simulations as a means to understand macromolecular behavior in various physicochemical methods. This allows a rigorous means to interpret observations in terms of fundamental principles, including chemical equilibrium, reaction kinetics, transport processes and thermodynamics. Here we simulate data for the Gilbert Theory for self-association, a fundamental analytical ultracentrifuge (AUC) technique to understand the shape of sedimentation velocity reaction boundaries that involve reversible monomer-Nmer interactions. Simulating monomer-dimer through monomer-hexamer systems as a function of concentration about the equilibrium constant allows a visual means to differentiate reaction stoichiometry by determining end points and inflection positions. Including intermediates (eg A1-A2-A3-A4-A5-A6) in the simulations reveals the smoothing of the reaction boundary and the removal of sharp inflections between monomers and polymers. The addition of cooperativity restores sharp boundaries or peaks to the observation and allows more discrimination in the selection of possible fitting models. Thermodynamic nonideality adds additional features when applied across wide ranges of concentration that might be appropriate for high-concentration therapeutic monoclonal antibody (mAb) solutions. This presentation serves as a tutorial for using modern AUC analysis software like SEDANAL for selecting potential fitting models.

Comparative Thermodynamics of the Reversible Self-Association of Therapeutic mAbs Reveal Opposing Roles for Linked Proton- and Ion-Binding Events.

Reversible self-association (RSA) has long been a concern in therapeutic monoclonal antibody (mAb) development. Because RSA typically occurs at high mAb concentrations, accurate assessment of the underlying interaction parameters requires explicitly addressing hydrodynamic and thermodynamic nonideality. We previously examined the thermodynamics of RSA for two mAbs, C and E, in phosphate buffered saline (PBS). Here we continue to explore the mechanistic aspects of RSA by examining the thermodynamics of both mAbs under reduced pH and salt conditions. Dynamic light scattering and sedimentation velocity (SV) studies were conducted for both mAbs at multiple protein concentrations and temperatures, with the SV data analyzed via global fitting to determine best-fit models, interaction energetics, and nonideality contributions. We find that mAb C self-associates isodesmically irrespective of temperature, and that association is enthalpically driven but entropically penalized. Conversely, mAb E self-associates cooperatively and via a monomer-dimer-tetramer-hexamer reaction pathway. Moreover, all mAb E reactions are entropically driven and enthalpically modest or minimal. The thermodynamics for mAb C self-association are classically seen as originating from van der Waals interactions and hydrogen bonding. However, relative to the energetics we determined in PBS, self-association must also be linked to proton release and/or ion uptake events. For mAb E, the thermodynamics implicate electrostatic interactions. Furthermore, self-association is instead linked to proton uptake and/or ion release, and primarily by tetramers and hexamers. Finally, although the origins of mAb E cooperativity remain unclear, ring formation remains a possibility whereas linear polymerization reactions can be eliminated.

A Molecular Theory of Polypeptide Adsorption at Inorganic Surfaces

A faithful description of polypeptide adsorption at ionizable surfaces remains a theoretical challenge from a molecular perspective due to the strong coupling of local thermodynamic nonideality and ionizations of both the adsorbate and substrate that are sensitive to the solution condition such as pH, ion valence, and salt concentration. Building upon a recently developed coarse-grained model for natural amino acids in bulk electrolyte solutions, here we report a molecular theory applicable to polypeptide adsorption on ionizable inorganic surfaces over a broad range of inhomogeneous conditions. Our thermodynamic model is able to account for diverse solution effects as well as the amino-acid sequence on polypeptide adsorption and surface association such as hydrogen bonding or bidentate coordination. The theoretical predictions have been validated by extensive comparison with experimental data for the adsorption isotherms of three representative polypeptides at a titanium surface.

Computational Modeling of Electrochemomechanics of High-Capacity Composite Electrodes in Li-Ion Batteries

Abstract Mechanical failure and its interference with electrochemistry are a roadblock in deploying high-capacity electrodes for Li-ion batteries. Computational prediction of the electrochemomechanical behavior of high-capacity composite electrodes is a significant challenge because of (i) complex interplay between mechanics and electrochemistry in the form of stress-regulated Li transport and interfacial charge transfer, (ii) thermodynamic solution non-ideality, (iii) nonlinear deformation kinematics and material inelasticity, and (iv) evolving material properties over the state of charge. We develop a computational framework that integrates the electrochemical response of batteries modulated by large deformation, mechanical stresses, and dynamic material properties. We use silicon as a model system and construct a microstructurally resolved porous composite electrode model. The model concerns the effect of large deformation of silicon on charge conduction and electrochemical response of the composite electrode, impact of mechanical stress on Li transport and interfacial charge transfer, and asymmetric charging/discharging kinetics. The study captures the rate-dependent, coupled electrochemomechanical behavior of high-capacity composite electrodes that agrees well with experimental results.

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.

Molecular thermodynamics for amino‐acid adsorption at inorganic surfaces

AbstractThe interaction of polypeptides and proteins with an inorganic surface is intrinsically dependent on the interfacial behavior of amino acids and sensitive to solution conditions such as pH, ion type, and salt concentration. A faithful description of amino‐acid adsorption remains a theoretical challenge from a molecular perspective due to the strong coupling of local thermodynamic nonideality and inhomogeneous ionization of both the adsorbate and substrate. Building upon a recently developed coarse‐grained model for natural amino acids in bulk electrolyte solutions, here we report a molecular theory to predict amino‐acid adsorption on ionizable inorganic surfaces over a broad range of solution conditions. In addition to describing the coupled ionization of amino acids and the underlying surface, the thermodynamic model is able to account for both physical binding and surface associations such as hydrogen bonding or bidentate coordination. It is applicable to all types of natural amino acids regardless of the solution pH, salt type and concentration. The theoretical predictions have been validated by extensive comparison with experimental data for the adsorption of acidic, basic, and neutral amino acids at rutile (α‐TiO2) surfaces.

Dense-vapor effects in compressible internal flows

Paradigmatic compressible one-dimensional flows provide insights regarding the loss mechanisms of fluid machinery components typical of power and propulsion systems, like turbomachines and heat exchangers. Their performance also depends on the working fluid, thus, on both molecular complexity and thermodynamic state. Four typical flow configurations have been investigated, namely, Rayleigh and Fanno flows, mixing of two co-flowing streams, and flow injection into a mainstream. It was found that the Grüneisen parameter allows the quantitative characterization of the influence of molecular complexity on losses. Moreover, the influence of dense vapor effects has been evaluated and assessed in terms of other fluid parameters. The analysis allowed the quantification of how, in Rayleigh flows, the energy transferred as heat is converted into kinetic and internal energy of the fluid, and, in Fanno flows, entropy is generated due to friction. In Rayleigh flow, the fluid at the inlet of the channel must have more energy for the flow to choke, depending on the molecular complexity. Similarly, in Fanno flows and for a given value of the compressibility factor, molecular complexity determines the choking point in the channel, and the higher its value the further downstream is the location. Moreover, for both Fanno and Rayleigh flows, if the flow is subsonic and dense vapor effects are relevant, the Mach number varies non-monotonically along the channel. Finally, it was proven that the amount of entropy generated in mixing flows increases with both the fluid molecular complexity and with the thermodynamic non-ideality of the fluid states.

Osmolyte-Induced Effects on the Hydration Behavior and the Osmotic Second Virial Coefficients of Alkyl-Substituted Urea Derivatives: Critical Assessment of Their Structure-Making/Breaking Behavior.

We analyzed the hydration behavior of alkyl-substituted urea osmolytes in terms of their deviation from Lewis-Randall solution ideality and characterized their structure-making/breaking tendency according to a proposed solvation formalism that provides a rigorous cause-effect connection between the system microstructure and its solution thermodynamic nonidealities. After a brief introduction of the rationale behind the use of Lewis-Randall over alternative solution ideality references, we (i) assessed the effect of the nature and type of alkyl substitution on the osmolyte-induced perturbation of the solution microstructure as a function of composition, (ii) analyzed their microstructural responses to changes in temperature and pressure, and (iii) demonstrated the structure-breaking nature of urea and the magnifying behavior of its alkyl-substituted osmolytes, whose trend follows the increasingly positive deviation of the osmolyte solutions from Lewis-Randall ideality. Then, we discussed the falsifiability of a pair of frequently used conjectured structure-making/breaking criteria, supported by the derived exact relationships between the structure-making/breaking parameter, the solution thermodynamic nonideality, and the osmotic second virial coefficient of the aqueous osmolytes. Finally, we provided an outlook on how the proposed approach could guide the quest for a truly (microstructural to free energy) causative explanation for the denaturation mechanism of proteins.

Thermodynamics of real polymer solutions in the new Rényi and Tsallis formalism

The generalized non-ideality factor of systems (GNF) was introduced into the Renyi and Tsallis information entropy equations, and new expressions were obtained for information and thermodynamic entropies with a fractional moment of the order entropy gS and thermodynamic gth nonideality factors. Equations in formalism of Renyi and Tsallis: The equations describe self-organized structures of essentially non-equilibrium systems and can be used in studying the topological and conformational properties of solutions of high-molecular compounds. GNF: where is are relative average characteristics (pi are statistical probabilities) of opposite processes. Factor g varies in the range 0 ≤ g ≤ 2 and depends on which of the competitive processes prevails. An algorithm for calculating the thermodynamic functions of the state of the system under study is presented. The equations are intended for calculating the thermodynamic functions of objects of fractal nature, including real solutions of synthetic and natural highmolecular compounds of plant and animal origin (hyper branched structures, dendrimers, lignins, biological systems, dendrites, systems of internal organs, blood vessels, etc.).

Energetic Dissection of Mab-Specific Reversible Self-Association Reveals Unique Thermodynamic Signatures.

Reversible self-association (RSA) remains a challenge in the development of therapeutic monoclonal antibodies (mAbs). We recently analyzed the energetics of RSA for five IgG mAbs (designated as A-E) under matched conditions and using orthogonal methods. Here we examine the thermodynamics of RSA for two of the mAbs that showed the strongest evidence of RSA (mAbs C and E) to identify underlying mechanisms. Concentration-dependent dynamic light scattering and sedimentation velocity (SV) studies were carried out for each mAb over a range of temperatures. Because self-association was weak, the SV data were globally analyzed via direct boundary fitting to identify best-fit models, accurately determine interaction energetics, and account for the confounding effects of thermodynamic and hydrodynamic nonideality. mAb C undergoes isodesmic self-association at all temperatures examined, with the energetics indicative of an enthalpically-driven reaction offset by a significant entropic penalty. By contrast, mAb E undergoes monomer-dimer self-association, with the reaction being entropically-driven and comprised of only a small enthalpic contribution. Classical interpretations implicate van der Waals interactions and H-bond formation for mAb C RSA, and electrostatic interactions for mAb E. However, noting that RSA is likely coupled to additional equilibria, we also discuss the limitations of such interpretations.

Thermodynamic non-ideality in charge regulation of weak polyelectrolytes

Polymer ionization differs from that for their monomeric counterparts due to intramolecular correlations. Such effects are conventionally described in terms of the site-binding model that accounts for short-range interactions between neighboring sites. With an apparent equilibrium constant for each ionizable group and the nearest-neighbor energy as adjustable parameters, the site-binding method is useful to correlate experimental titration curves when the site-site interactions are insignificant at long ranges. This work aims to describe the electrostatic behavior of weak polyelectrolytes in aqueous solutions on the basis of the intrinsic equilibrium constants of the individual ionizable groups and solution conditions underlying the thermodynamic non-ideality. A molecular thermodynamic model is proposed for the protonation of weak polyelectrolytes by incorporating classical density functional theory into the site-binding model to account for the effects of the local ionic environment on both inter-chain and intra-chain correlations. By an extensive comparison of theoretical predictions with experimental titration curves, we demonstrate that the thermodynamic model is able to quantify the ionization behavior of weak polyelectrolytes over a broad range of molecular architectures and solution conditions.

A unified description of macroion diffusiophoresis, salt osmotic diffusion and collective diffusion coefficient

Diffusiophoresis describes the net migration of a macroion within an aqueous fluid due to a concentration gradient of salt, while salt osmotic diffusion describes the net motion of small ions toward Donnan equilibrium due to a macroion concentration gradient. A new theoretical description of macroion diffusiophoresis, salt osmotic diffusion and the light-scattering collective diffusion coefficient of macromolecules conforming to Onsager Reciprocal Relation (ORR) is developed. Specifically, symmetric transport equations for macroion-salt coupled transport in isothermal conditions are derived. These equations, which can be regarded as a generalization of Nernst–Planck equations, incorporate an electrokinetic factor for diffusiophoresis, salt thermodynamic non-ideality and concentration-dependent ionic transport coefficients. Due to the electrokinetic factor, thermodynamic driving forces must be modified to ensure that ORR is not violated. A mathematical expression for the collective diffusion coefficient compatible with ORR was then extracted. Diffusiophoresis and salt osmotic diffusion equations are discussed in relation to experimental transport data on lysozyme in aqueous NaCl. These transport equations represent a more appropriate theoretical reference model, compared to multicomponent-diffusion limiting laws for describing protein-salt coupled diffusion in aqueous mixtures.

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.

Amplification of Salt-Induced Protein Diffusiophoresis by Varying Salt from Potassium to Sodium to Magnesium Chloride in Water.

Salt-induced diffusiophoresis is the migration of a macromolecule or a colloidal particle induced by a concentration gradient of salt in water. Here, the effect of salt type on salt-induced diffusiophoresis of the protein lysozyme at pH 4.5 and 25 °C was examined as a function of salt concentration for three chloride salts: NaCl, KCl, and MgCl2. Diffusiophoresis coefficients were calculated from experimental ternary diffusion coefficients on lysozyme-salt-water mixtures. In all cases, diffusiophoresis of this positively charged protein occurs from high to low salt concentration. An appropriate mass transfer process was theoretically examined to show that concentration gradients of MgCl2 produce significant lysozyme diffusiophoresis. This is attributed to the relatively low mobility of Mg2+ ions compared to that of Cl- ions at low salt concentration and a strong thermodynamic nonideality of this salt at high salt concentration. These findings indicate that MgCl2 concentration gradients could be exploited for protein manipulation in solution (e.g., using microfluidic technologies) with applications to protein adsorption and purification. The dependence of lysozyme diffusiophoresis on salt type was theoretically examined and linked to protein charge. The effect of salts on hydrogen-ion titration curves was experimentally characterized to understand the role of salt type on protein charge. Our results indicate that binding of Mg2+ ions to lysozyme further enhances protein diffusiophoresis.

Numerical investigation on fuel injection into a multicomponent gaseous environment under trans/supercritical condition

Large eddy simulation is performed on trans/supercritical fuel injection into a multispecies supercritical environment, where the pressure and temperature exceed the fuel critical point. The real equation of state Peng-Robinson is employed and thermodynamic nonideality and anomalies in transport properties of the fluid mixture are considered. The dissolution of the surrounding gas has an important influence on the thermodynamic and transport properties. Much larger density-gradients are formed in the transcritical case, which has an effect of stabilizing the flow field and inhibiting the development of unstable waves. In contrary, in the supercritical case eddies tend to grow up and roll into a series of circular vortices, and the injected n-heptane tends to mix with the surrounding gas leading to a shorter penetration. In addition, conditional averages performance indicate that the critical parameters of mixture are closer to that those of n-heptane. In the transcritical injection, a dense “liquid core” region still exists, while this phenomenon does not appear in the supercritical case. A mixing layer thickness based on the density gradient is suggested to quantify the mixing characteristics. In the supercritical injection, a significantly larger mixing layer thickness is predicted than the transcritical injection condition.

Characterisation of the molecular properties of scleroglucan as an alternative rigid rod molecule to xanthan gum for oropharyngeal dysphagia

Scleroglucan, a neutral β(1–3) glucan with β(1–6) glucan branches every third residue, is being considered as an alternative rod-like, shear thinning high molecular weight β-glucan based polysaccharide to xanthan gum for the management of patients with oropharyngeal dysphagia. It is therefore important to understand more fully its hydrodynamic properties in solution, in particular heterogeneity, molecular weight distribution and its behaviour in the presence of mucin glycoproteins. A commercially purified scleroglucan preparation produced by fermentation of the filamentous fungus Sclerotium rolfsii was analysed in deionised distilled water with 0.02% added azide. Sedimentation velocity in the analytical ultracentrifuge showed the scleroglucan preparation to be unimodal at concentrations >0.75 mg/ml which resolved into two components at lower concentration and with partial reversibility between the components. Sedimentation coefficient versus concentration plots showed significant hydrodynamic non-ideality. Self-association behaviour was confirmed by sedimentation equilibrium experiments with molecular weights between ~3 × 106 g/mol to ~5 × 106 g/mol after correcting for thermodynamic non-ideality. SEC-MALS-viscosity experiments showed a transition between a rod-shape at lower molar masses to a more flexible structure at higher masses consistent with previous observations. Sedimentation velocity experiments also showed no evidence for potentially problematic interactions with submaxillary mucin.

Investigation of Thermodynamic Nonideality of Solid Li-ion Electrodes Using Concentrated Solution Theory

Li-Ion batteries (LIBs) is poised to dominate the energy storage market of electric vehicles (EVs) and renewable-energy-integrated grids over the next few decades. To address safety and lifetime concerns of the technology, significant efforts have been devoted to advancing online battery diagnostic tools and evolving charging/discharging protocols to enhance their stability and elongate their lifetime, and both have been found to be highly amenable to physics-based models (PBMs). With the continuous improvements and breakthroughs of computer technology, PBMs in substitute of equivalent circuit models (ECMs) have been employed to produce high-fidelity, low-computational-cost reduced-order-models (ROMs) for battery management system (BMS), despite the fact that simplifications have regularly been made. For example, in a general PBM of LIBs, Li-ion diffusion is governed by Fick’s second law of diffusion in a dilute solution (Fig. 1), which neglected the thermodynamic nonideality of a solid active material which experiences large concentration variation in electrochemical processes. Though the above fact likely indicates that such PBMs contain some battery physics to represent the key electrochemical processes, it does not exclude the possibility that important correlations could be associated with physics that have been neglected. For example, although both ks (solid/liquid interface reaction rate) and D (diffusivity of Li-ion in a solid phase) exhibited correlations with battery State-Of-Charge (SOC), especially at the end of discharge, they have been assumed to be constants over the entire range of SOC. In fact, their values reported from different researchers show variation spanning over 2 to 5 order of magnitude. With this large variation, both battery SOC and State-Of-Health (SOH) will remain unpredictable, which means that ultimately the battery management and diagnosis remains uncertain. Numerous theoretical and experimental studies support the inevitable Li-Li interactions when Li-ion deintercalation/intercalation from/into the active materials, especially with a sufficiently large concentration. This Li-Li interaction introduces thermodynamic nonideality which could not be described by the Fick’s second law of diffusion. Consequently, critical electrochemical kinetic and transport properties such as ks and D will have a strong correlation with the SOC. In this research, we will try to understand the nonideality of a solid Li-ion solution by the concentrated solution theory, as shown in Fig.1. We will use nonequilibrium thermodynamics in a concentrated solution to correlate ks/D with the activity coefficient of the solid solution γ and elaborate new governing equations for D and ks. Then, utilize the new correlations to process experimental data tested by EIS method and to regress the experimental activity coefficient γ. Furthermore, a methodology in determining the most appropriate constants for ks and D with a minimum discrepancy for a full charge/discharge cycle will be provided. Figure 1. (a) Inconsistency in KsS and D values between dilute solution model prediction and experimental results; (b) Ks and D comparison between dilute solution theory and concentrated solution theory; (c) Experimental and model prediction based on concentrated solution theory. Figure 1

A Comprehensive Brownian Dynamics Approach for the Determination of Non-ideality Parameters from Analytical Ultracentrifugation.

Brownian dynamics (BD) has been applied as a comprehensive tool to model sedimentation and diffusion of nanoparticles in analytical ultracentrifugation (AUC) experiments. In this article, we extend the BD algorithm by considering space-dependent diffusion and solvent compressibility. With this, the changes in the sedimentation and diffusion coefficient from altered solvent properties at increased pressures are accurately taken into account. Moreover, it is demonstrated how the concept of space-dependent diffusion is employed to describe concentration-dependent sedimentation and diffusion coefficients, in particular, through the Gralen coefficient and the second virial coefficient. The influence of thermodynamic nonideality on diffusional properties can be accurately simulated and agree with well-known evaluation tools. BD simulations for sedimentation equilibrium and sedimentation velocity (SV) AUC experiments including effects of hydrodynamic and thermodynamic nonideality are validated by global evaluation in SEDANAL. The interplay of solvent compressibility and retrieved nonideality parameters can be studied utilizing BD. Finally, the second virial coefficient is determined for lysozyme from SV AUC experiments and BD simulations and compared to membrane osmometry. These results are in line with DLVO theory. In summary, BD simulations are established for the validation of nonideal sedimentation in AUC providing a sound basis for the evaluation of complex interactions even in polydisperse systems.

Influence of water content on alkali metal chloride transport in cross-linked Poly(ethylene glycol) Diacrylate.1. Ion sorption

The relationship between ion size and sorption properties in water swollen uncharged polymers was investigated as a model system for understanding ion sorption and transport in more complex systems (i.e., charged polymer networks). Alkali metal chloride (e.g., LiCl, NaCl, and KCl) sorption coefficients in a series of cross-linked poly(ethylene glycol) diacrylate (XLPEGDA) polymer membranes were measured as a function of external salt concentrations ranging from 0.01 to 1.0 M. The relative order of salt sorption coefficients was: KCl > LiCl > NaCl. This order does not correspond to the order of ion hydration size (i.e., Li+ > Na+ > K+). The alkali metal chloride sorption behavior in XLPEGDA polymers is influenced by both ion hydration and polymer-ion specific interactions. XLPEGDA polymers having three different equilibrium water uptake values were prepared to investigate the effect of water content on salt sorption in these polymers. Generally, ion sorption coefficients increase as polymer water content increases. Salt activity coefficients in the polymers were quantified to better understand the thermodynamic non-ideality of ions in polymer networks. Flory-Rehner theory was used to predict water volume fraction in the polymers equilibrated with salt solution based on salt sorption measurements.