Derivative Of Chemical Potential Research Articles

Statistical Mechanic and Phenomenological Approaches to Isomeric Effects in Thermodiffusion.

We present a model that explains variance in the thermodiffusion of hydrocarbon isomers in binary liquid mixtures. The model relies on material transport equations for binary nonisothermal liquid systems that were derived through a nonequilibrium thermodynamic approach in a previous work, coupled with one of two methods: (i) use of equilibrium chemical potentials for each component under conditions of constant pressure, derived using statistical mechanics or (ii) use of the temperature derivative of chemical potential expressed phenomenologically as molecular entropy. The model is evaluated using Soret coefficients (ST) measured in binary solutions of heptane isomers in benzene. The statistical mechanic approach yields moderately acceptable agreement with experimental data. The phenomenological approach, which relies on both measured and calculated values of molecular entropy from the literature, yields values of ST centered around the experimental data, with the scatter likely due to poor precision in the measured or calculated values of entropy. For the latter case, we identify several methods for calculating entropy that yield good agreement with experimental data.

Isochoric heat capacity, phase transition and derived key thermodynamic properties of methyl decanoate

In the present work single – and two–phase isochoric heat capacity (CV) and liquids-gas phase transition temperature (TS) and density (ρS) of methyl decanoate as component of biodiesel derived from coconut oil or babassu oil have been studied. The 15 liquid and vapor isochores between (152 and 834) kg·m−3 at temperatures from (300 to 463) K and at pressures up to 16 MPa were determined using high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. For each experimental isochores the measurements were conducted in the two-phase region in the immediate vicinity of the phase-transition temperatures (TS) to precisely determine the phase boundary density, one-phase and two-phase isochoric heat capacities (ρS,CV1, and CV2) using isochoric heat -capacity discontinuity behavior technique. For ten liquid isochores, the TSwas experimentally determined usingCVdiscontinuity method (irregular behaviour of CV). For vapor (152.09 and 204.55) kg·m−3 and near-critical (235.13 and 300.83) kg·m−3 isochores we have never reached isochoric heat-capacity discontinuity temperatures TSdue to thermal decomposition of the methyl decanoate at high temperatures (above 473 K). The measured CV2 as a function of specific volume (V) along the various isotherms (below 473 K) were used to accurately estimate the values of the second temperature derivatives of chemical potential and vapour-pressure using theoretically based Yang-Yang relation. The contributions of the vapour-pressure and the chemical potential to the measured total two-phase CV2 of methyl decanoate were estimated. The measured CV2ρS, and TS were used for determination many key thermodynamic properties of methyl decanoate along the saturation curve as well as the critical property data (TC=669.5 ± 5 K andρC = 287 ± 5 kg·m−3).

Thermodynamic factor of quaternary mixtures from Kirkwood–Buff integration

Expressions for the thermodynamic factor matrix Γ of quaternary mixtures are derived in terms of Kirkwood–Buff integrals and implemented into the massively parallel simulation tool ms2. To assess these expressions, a liquid-like supercritical quaternary Lennard–Jones mixture is sampled throughout its entire composition range, employing molecular dynamics in the canonical ensemble. Good agreement is found between numerical chemical potential derivatives and the results from the present Kirkwood–Buff integral expressions. Moreover, the limits of the thermodynamic factor matrix for pure, binary and ternary subsystems are discussed.

Nonlinear chiral plasma transport in rotating coordinates

The nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms arising from the Coriolis and fictitious centrifugal forces. Then in the short relaxation time regime the angular velocity and electromagnetic fields are treated as perturbations. The current densities are obtained by retaining the terms up to second order in perturbations. The time evolution equations of the inhomogeneous chemical potentials are derived by demanding that collisions conserve the particle number densities.

Temperature derivative of the chemical potential and its magneto-oscillations in a two-dimensional system

We report first thermodynamic measurements of the temperature derivative of chemical potential (d{\mu}/dT) in two-dimensional (2D) electron systems. In order to test the technique we have chosen Schottky gated GaAs/AlGaAs heterojunctions and detected experimentally in this 2D system quantum magnetooscillations of d{\mu}/dT. We also present a Lifshits-Kosevitch type theory for the d{\mu}/dT magnetooscillations in 2D systems and compare the theory with experimental data. The magnetic field dependence of the d{\mu}/dT value appears to be sensitive to the density of states shape of Landau levels. The data in low magnetic field domain demonstrate brilliant agreement with theory for non-interacting Fermi gas with Lorentzian Landau level shape.

Quantifying Additive Interactions of the Osmolyte Proline with Individual Functional Groups of Proteins: Comparisons with Urea and Glycine Betaine, Interpretation of m-Values

To quantify interactions of the osmolyte l-proline with protein functional groups and predict their effects on protein processes, we use vapor pressure osmometry to determine chemical potential derivatives dμ2/dm3 = μ23, quantifying the preferential interactions of proline (component 3) with 21 solutes (component 2) selected to display different combinations of aliphatic or aromatic C, amide, carboxylate, phosphate or hydroxyl O, and amide or cationic N surface. Solubility data yield μ23 values for four less-soluble solutes. Values of μ23 are dissected using an ASA-based analysis to test the hypothesis of additivity and obtain α-values (proline interaction potentials) for these eight surface types and three inorganic ions. Values of μ23 predicted from these α-values agree with the experiment, demonstrating additivity. Molecular interpretation of α-values using the solute partitioning model yields partition coefficients (Kp) quantifying the local accumulation or exclusion of proline in the hydration water of each functional group. Interactions of proline with native protein surfaces and effects of proline on protein unfolding are predicted from α-values and ASA information and compared with experimental data, with results for glycine betaine and urea, and with predictions from transfer free energy analysis. We conclude that proline stabilizes proteins because of its unfavorable interactions with (exclusion from) amide oxygens and aliphatic hydrocarbon surfaces exposed in unfolding and that proline is an effective in vivo osmolyte because of the osmolality increase resulting from its unfavorable interactions with anionic (carboxylate and phosphate) and amide oxygens and aliphatic hydrocarbon groups on the surface of cytoplasmic proteins and nucleic acids.

Quantifying functional group interactions that determine urea effects on nucleic acid helix formation.

Urea destabilizes helical and folded conformations of nucleic acids and proteins, as well as protein-nucleic acid complexes. To understand these effects, extend previous characterizations of interactions of urea with protein functional groups, and thereby develop urea as a probe of conformational changes in protein and nucleic acid processes, we obtain chemical potential derivatives (μ23 = dμ2/dm3) quantifying interactions of urea (component 3) with nucleic acid bases, base analogues, nucleosides, and nucleotide monophosphates (component 2) using osmometry and hexanol-water distribution assays. Dissection of these μ23 values yields interaction potentials quantifying interactions of urea with unit surface areas of nucleic acid functional groups (heterocyclic aromatic ring, ring methyl, carbonyl and phosphate O, amino N, sugar (C and O); urea interacts favorably with all these groups, relative to interactions with water. Interactions of urea with heterocyclic aromatic rings and attached methyl groups (as on thymine) are particularly favorable, as previously observed for urea-homocyclic aromatic ring interactions. Urea m-values determined for double helix formation by DNA dodecamers near 25 °C are in the range of 0.72-0.85 kcal mol(-1)m(-1) and exhibit little systematic dependence on nucleobase composition (17-42% GC). Interpretation of these results using the urea interaction potentials indicates that extensive (60-90%) stacking of nucleobases in the separated strands in the transition region is required to explain the m-value. Results for RNA and DNA dodecamers obtained at higher temperatures, and literature data, are consistent with this conclusion. This demonstrates the utility of urea as a quantitative probe of changes in surface area (ΔASA) in nucleic acid processes.

Introductory lecture: interpreting and predicting Hofmeister salt ion and solute effects on biopolymer and model processes using the solute partitioning model.

Understanding how Hofmeister salt ions and other solutes interact with proteins, nucleic acids, other biopolymers and water and thereby affect protein and nucleic acid processes as well as model processes (e.g. solubility of model compounds) in aqueous solution is a longstanding goal of biophysical research. Empirical Hofmeister salt and solute "m-values" (derivatives of the observed standard free energy change for a model or biopolymer process with respect to solute or salt concentration m3) are equal to differences in chemical potential derivatives: m-value = delta(dmu2/dm3) = delta mu23, which quantify the preferential interactions of the solute or salt with the surface of the biopolymer or model system (component 2) exposed or buried in the process. Using the solute partitioning model (SPM), we dissect mu23 values for interactions of a solute or Hofmeister salt with a set of model compounds displaying the key functional groups of biopolymers to obtain interaction potentials (called alpha-values) that quantify the interaction of the solute or salt per unit area of each functional group or type of surface. Interpreted using the SPM, these alpha-values provide quantitative information about both the hydration of functional groups and the competitive interaction of water and the solute or salt with functional groups. The analysis corroborates and quantifies previous proposals that the Hofmeister anion and cation series for biopolymer processes are determined by ion-specific, mostly unfavorable interactions with hydrocarbon surfaces; the balance between these unfavorable nonpolar interactions and often-favorable interactions of ions with polar functional groups determine the series null points. The placement of urea and glycine betaine (GB) at opposite ends of the corresponding series of nonelectrolytes results from the favorable interactions of urea, and unfavorable interactions of GB, with many (but not all) biopolymer functional groups. Interaction potentials and local-bulk partition coefficients quantifying the distribution of solutes (e.g. urea, glycine betaine) and Hofmeister salt ions in the vicinity of each functional group make good chemical sense when interpreted in terms of competitive noncovalent interactions. These interaction potentials allow solute and Hofmeister (noncoulombic) salt effects on protein and nucleic acid processes to be interpreted or predicted, and allow the use of solutes and salts as probes of

Developing Solutes as Quantitative Probes of Protein and DNA Processes

To develop the use of urea, trifluoroethanol, KGlutamate, proline and other biochemical solutes as probes of interface formation and large scale conformational changes in protein and DNA processes, we are quantifying the thermodynamics of the competition between these solutes and water to interact with different types of biopolymer surface (e.g. aliphatic and aromatic C, polar and charged O and N). Model compounds displaying one or more of these surface types are used to obtain this information. Interactions of solutes with these model compounds are quantified from excess osmolalities (ΔOsm) from vapor pressure osmometry (VPO) or from the solute's effect on model processes like solubility or micelle formation. These experiments yield chemical potential derivatives (μ23) which are dissected in an analysis based on water accessible surface area (ASA) assuming additivity of interactions. From this analysis we determine a set of interaction potentials (μ23/RT(ASA)i) for the interaction of a solute with a unit area of each significant type of biopolymer surface (i). These solute interaction potentials are interpreted using the solute partitioning model (SPM) to obtain Kp, the partition function describing the distribution of the solute between local (hydration) water and bulk water. Effects of these solutes on protein folding, DNA helix formation or other biopolymer processes (m-values = Δμ23) are interpreted or predicted using this quantitative information together with structural information about the change in amount of each type (i) of water accessible biopolymer ΔASAi in the process. Also, the large effects of urea , KGlutamate, trifluoroethanol and glycine betaine on the rate constant for dissociation of RNA polymerase-promoter DNA open complexes are interpreted in terms of folding and assembly of a jaw/clamp on downstream duplex DNA after opening of the initiation bubble in open complex formation.Supported by NIH GM47022

Kirkwood–Buff theory of four and higher component mixtures

Explicit expressions are developed for the chemical potential derivatives, partial molar volumes, and isothermal compressibility of solution mixtures involving four components at finite concentrations using the Kirkwood-Buff theory of solutions. In addition, a general recursion relationship is provided which can be used to generate the chemical potential derivatives for higher component solutions.

Chemical Potential Derivatives and Preferential Interaction Parameters in Biological Systems from Kirkwood-Buff Theory

New expressions for chemical potential derivatives and preferential interaction parameters for ternary mixtures are derived for open, semiopen, and closed ensembles in terms of Kirkwood-Buff integrals, where all three components are present at finite concentrations. This is achieved using a simple approach that avoids the use of the general matrix formulation of Kirkwood-Buff theory. The resulting expressions provide a rigorous foundation for the analysis of experimental and simulation data. Using the results, a simple model is developed and used to investigate the possible effects of finite protein concentrations on the corresponding cosolvent dependent chemical potential and denaturation thermodynamics.

Resolving the Yang-Yang Dilemma in3He Near the Critical Point

A challenging problem is to experimentally resolve the Yang-Yang dilemma for fluids-whether the critical singularity of the isochoric heat capacity is shared between the second temperature derivatives of pressure and chemical potentials. In the lattice-gas model, which serves as a well-established guidance to study fluid criticality, the divergence of the second derivative of pressure is solely responsible for the heat capacity anomaly. If it is proven that the heat capacity singularity is shared between the pressure and chemical potential derivatives, a revision of the conventional scaling theory for fluids based on the analogy between fluids and lattice-gas model will be required. Thus far, experiments on real fluids have been inconclusive, in particular, because of possible impurity effects and the intrinsic vapor-liquid asymmetry. A study of the 3He isotope gives a unique opportunity to resolve the Yang-Yang dilemma. In 3He all other impurities except 4He are frozen out. The almost perfect purity of the available 3He samples (typically less than 1 ppm of 4He in 3He) enables the elimination or quantitative study of impurity effects. Also the well-known symmetry of the 3He coexistence curve implies an absence of confluent singularities caused by liquid-gas asymmetry. In this paper we reanalyze early experimental data of near-critical 3He and show that they are internally not completely consistent. While the second derivative of chemical potential obtained from the density dependence of the two-phase isochoric heat capacity does not show a noticeable anomaly, the analysis of the same property obtained by combining the PVT and heat capacity implies the existence of the Yang-Yang anomaly. An unambiguous test of the Yang-Yang dilemma will require more accurate heat-capacity measurements closer to the critical point. To thoroughly distinguish between these alternatives one may ultimately require a microgravity experiment that will allow measurements very close to the critical point.

Transition Temperatures of Bose–Einstein Condensation in Traps

A careful study is made of the definitions of the transition temperature T c of an ideal Bose system in traps. We review several physical quantities that are used to define the transition temperature, which corresponds to different kinds of T c. The different definitions give different values for T c and the differences are quite large for finite systems. This makes the comparisons of theoretical predictions of the transition temperature shift with experimental results quite difficult. We also find that the derivative of chemical potential with respect to temperature is nearly discontinuous. This implies that in the thermodynamic limit the system might undergo a first-order phase transition.

Thermodynamical Cross-Relations for Superconductors at the Critical Point

We investigate superconducting systems with the use of the phenomenological Landau's theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

Extraction of Thermodynamic Data from Ternary Diffusion Coefficients. Use of Precision Diffusion Measurements for Aqueous Lysozyme Chloride−NaCl at 25 °C To Determine the Change of Lysozyme Chloride Chemical Potential with Increasing NaCl Concentration Well into the Supersaturated Region

For ternary systems, we present a method for using measured values of the four ternary diffusion coefficients and the Onsager reciprocal relations to extract derivatives of solute chemical potentials with respect to solute molar concentrations. The method is applicable to systems in which the molar concentration of one solute is very small compared to that of the other, and also small enough that an inverse concentration dependence dominates certain activity coefficient derivatives. These conditions apply to a large number of aqueous systems involving macromolecules of biological interest. Unlike other techniques, the present method can be used to study undersaturated and supersaturated solutions. The approach is illustrated for the lysozyme chloride−NaCl−H2O system at 25 °C, using data reported here for pH 6.0 at 0.60 mM (8.6 mg/mL) lysozyme chloride and 0.25, 0.50, 0.65, 0.90, and 1.30 M (1.4, 2.8, 3.7, 5.1, and 7.2 wt %) NaCl concentrations, and our earlier data for pH 4.5 at the same concentrations. We use these solute chemical potential derivatives to compute the protein cation charge approximately, and to construct a function approximating the derivative of the lysozyme chloride chemical potential with respect to NaCl concentration, which we integrate over a range of NaCl concentrations. This provides the change of the lysozyme chloride chemical potential with NaCl concentration well into the supersaturated region, and hence provides the driving force for nucleation and crystal growth of lysozyme chloride as a function of the extent of supersaturation. We also compute the diffusion Onsager coefficients (Lij)0 for each composition at pH 4.5 and 6.0. Binary diffusion coefficients of aqueous lysozyme chloride at 0.89 mM (12.7 mg/mL) for pH values from 4.0 to 6.0, and at pH 6.0 for concentrations from 0.25 to 1.95 mM (3.6−27.9 mg/mL) are also reported.

Diffusion in silicate melts: III. Empirical models for multicomponent diffusion

Empirical models for multicomponent diffusion in an isotropic fluid were derived by splitting the component's dispersion velocity into two parts: (a) an intrinsic velocity which is proportional to each component's electrochemical potential gradient and independent of reference frame and (b) a net interaction velocity which is both model and reference frame dependent. Simple molecules (e.g., M pO q) were chosen as endmember components. The interaction velocity is assumed to be either the same for each component (leading to a common relaxation velocity U) or proportional to a common interaction force (F). U or F is constrained by requiring no local buildup in either volume or charge. The most general form of the model-derived diffusion matrix [D] can be written as a product of a model-dependent kinetic matrix [L] and a model independent thermodynamic matrix [ G], [D] = [L] · [ G]. The elements of [ G] are functions of derivatives of chemical potential with respect to concentration. The elements of [L] are functions of concentration and partial molar volume of the endmember components, C io and V io, and self diffusivity D i, and charge number z i of individual diffusing species. When component n is taken as the dependent variable they can be written in a common form L ij = D jδ ij + C io[V noD n − V joD j)A i + (p nz nD n − p jz jD j)B i] where the functional forms of the scaling factors A i and B i depend on the model considered. The off-diagonal elementL ij (i ≠ j) is directly proportional to the concentration of component i, and thus negligible when i is a dilute component. The salient feature of kinetic interaction or relaxation is to slow down larger (volume or charge) and faster diffusing components and to speed up smaller (volume or charge) and slower moving species, in order to prevent local volume or charge buildup.Empirical models for multicomponent diffusion were tested in the ternary system CaOAl 2O 3SiO 2 at 1500°C and 1 GPa over a large range of melt compositions. Model-derived diffusion matrices calculated using measured self diffusivities (Ca, Al, Si, and O), partial molar volumes, and activities were compared with experimentally derived diffusion matrices at two melt compositions. Chemical diffusion profiles computed using the model-derived diffusion matrices, accounting for the compositional dependency of self diffusivities and activity coefficients, were also compared with the experimentally measured ones. Good agreement was found between the ionic common-force model derived diffusion profiles and the experimentally measured ones. Secondary misfits could result from either inadequacies of the model or inaccuracies in activity-composition relationship. The results show that both kinetic interactions and thermodynamic nonideality contribute significantly to the observed diffusive coupling in the molten CaOAl 2O 3SiO 2.

Calculation of multicomponent ionic diffusion from zero to high concentration: II. Inclusion of associated ion species

This paper presents a theoretical model of multicomponent ionic diffusion which is valid to high concentration for systems which show ion association. The development is completely general for species which do not react with the solvent. It is demonstrated that the Onsager phenomenological coefficients for associated ion species can be unambiguously determined only in solutions where the concentration of these species can be independently measured. In all other instances, only combinations of the Onsager coefficients for the bare ions and the ion pairs can be experimentally determined. The results of our formulations are contrasted with those of more simplified models for systems containing Na 2SO 4 and MgSO 4, as well as for multicomponent natural seawater. The differences between our model and simplified models are significant, especially at high concentration. Inconsistencies which may develop with the use of the simplified approaches are demonstrated. Our approach requires considerable data which are not available at temperatures other than 25°C. Therefore, other approaches which are based only on data at infinite dilution are of great interest. We show here that, if chemical potential derivatives are included in the infinite dilution model of Nernst and Hartley which uses only infinite dilution mobilities, the model can be extended to slightly concentrated solutions. This extended Nernst-Hartley model gives good agreement with all of the existing experimental mutual diffusion coefficient data at concentrations below about 0.2 M in the six component system Na-K-Ca-Mg-Cl-SO 4-H 2O. This may be the most reliable way to extend infinite dilution data into more concentrated regions. In the systems we have studied, the inclusion of ion-association species for weakly interacting species does not appear to provide significant improvement over our generalized Nernst-Hartley model.

ChemInform Abstract: Isopiestic Determination of the Osmotic and Activity Coefficients of ZnCl2(aq) at 298.15 K

Abstract Isopiestic vapor-pressure measurements were performed at 83 molalities of ZnCl 2 (aq) from 0.31358 to 13.134 mol · kg −1 at 298.15 K. Measurements were made by using high-purity ZnCl 2 adjusted to its stoichiometric pH value. Our results are critically compared with previous isopiestic, direct vapor-pressure, and e.m.f. measurements, and recommended values are reported for osmotic coefficients, water activities, solute activity coefficients, and chemical-potential derivatives. Published isopiestic values for ZnCl 2 (aq) up to 10 mol · kg −1 and most e.m.f. values up to about 6 mol · kg −1 generally agree well with our experimental results, but some e.m.f. results and direct vapor-pressure measurements appear to have been inaccurate.

Isopiestic determination of the osmotic and activity coefficients of ZnCl 2(aq) at 298.15 K

Isopiestic vapor-pressure measurements were performed at 83 molalities of ZnCl 2(aq) from 0.31358 to 13.134 mol · kg −1 at 298.15 K. Measurements were made by using high-purity ZnCl 2 adjusted to its stoichiometric pH value. Our results are critically compared with previous isopiestic, direct vapor-pressure, and e.m.f. measurements, and recommended values are reported for osmotic coefficients, water activities, solute activity coefficients, and chemical-potential derivatives. Published isopiestic values for ZnCl 2(aq) up to 10 mol · kg −1 and most e.m.f. values up to about 6 mol · kg −1 generally agree well with our experimental results, but some e.m.f. results and direct vapor-pressure measurements appear to have been inaccurate.