Partial Molar Surface Area Research Articles

Partial molar surface areas in liquid mixtures. Theory and evaluation in aqueous ethanol

Different definitions for the partial molar surface area (PMSA) of a mixture component are found in the literature. The advanced definition states that it is the change of surface area resultant from the addition of 1 mol of that component to the surface region at constant temperature, T, pressure, p, surface tension and surface amounts of the other components. Estimating this quantity has long been hampered by the fact that a change of composition while holding constant the mixture surface tension cannot be attained in the laboratory. Using formal thermodynamics, a rigorous procedure for the calculation of PMSAs is worked out. As input, it only requires experimentally measurable properties of liquid mixtures and their pure constituents. This PMSA is shown to be comparable to the PMSA defined in terms of Gibbs surface excesses of the components, though not equivalent to the PMSA for changes in composition at fixed T and p only. From their relationship it is argued that the advanced PMSA is made up of two contributions, namely the area alteration at constant T and p, which leads to a change in the mixture surface tension, and an additional area variation for restoring the initial surface tension value. In a binary liquid mixture, the restoring area is necessarily positive for the surface active component and negative for the solvent. A new, robust thermodynamic derivative is used for the calculation of relative adsorptions and molar surface areas. Expressions are obtained for the analytic calculation of different PMSAs in thermodynamically ideal liquid mixtures. Standard molar surface areas are defined, and expressions are given for their calculation from model or experimental quantities. Real and ideal PMSAs of water and ethanol are estimated in their mixtures at 298 K, using literature data. Thermodynamic consistency tests were developed and used to reject some PMSA values in water-rich and ethanol-rich solutions. This unfortunate situation is ascribed to calculation procedures that impose much stress on the experimental data. It is concluded that Rusanov's interpretation of a PMSA as a restoring area only accounts for a small part of this quantity, at least in aqueous ethanol solutions. The surface structure of water + ethanol mixtures is re-examined at the light of PMSA values.

Influence of particle size on electrochemical thermodynamics of Nano-Au electrodes: Mechanism, factors, range and degree

There is a significant effect of particle size on electrochemical thermodynamics of nano-metal electrodes, it is still unclear, however, the mechanism, factors, range and degree of the effect. Herein, in theory, we derived the relations of the electrochemical thermodynamic quantities and the size of nanoparticles which constituted the nano-metal electrodes, discussed the mechanism and the influencing factors. Experimentally, nano-Au with different radii (0.9–37.4 nm) made as nano electrodes to research the size dependence of electrochemical thermodynamic quantities. Combining the results of theory and experiments, discussed the influencing regularities, range and degree. The regularities obtained from these experiments are consistent with the theoretical relations. The research results show that particle size has pronounced effect on electrochemical thermodynamic quantities. Both the Eo and the lnKo decrease with the particle size decreasing, while other electrochemical thermodynamic quantities increase. These effects should be attributed to partial molar surface area, surface tension and its temperature coefficient. Thereinto, partial molar surface area and surface tension are the major influencing factors for Eo, Ko, ΔrGm and ΔrHm, partial molar surface area and temperature coefficient of surface tension are for (∂E/∂T)p, ΔrSm and Qr,m. For Au nanoparticles, as the radius exceeds 10 nm, the major factor is partial molar surface area, there exist linear relationships between the electrochemical thermodynamic quantities and reciprocal of radius. However, as the radius is less than 10 nm, the effects of surface tension and its temperature coefficient gradually hold the main positon with the radii decreasing, respectively; as well as there are no linear relationships. Our research offer significant fundamental insight on the size-dependent electrochemical thermodynamics, and can greatly impact future exploration and application of nano-metal electrodes.

Prediction of surface tension of highly nonideal aqueous-organic mixtures as a function of composition by a partitioning model between surface and bulk phases and use of partial molar surface areas

The composition dependence of the surface tension of highly nonideal aqueous-organic nonelectrolyte solutions is described in detail. The Wilson, NRTL, UNIFAC and ideal solution models are used for activity coefficients of surface and bulk phases and compared with one another and with experimental data. Paquette and Rasmussen molar surface areas are employed for prediction of the surface tension of the mixtures and results compared. A new procedure consisting of a partitioning model between surface and bulk phases combined with determination of partial molar surface areas is evolved and tested with experimental data taken on the surface tension of aqueous-organic systems. Comparisons of the calculated surface tensions with experimental data yield mean absolute errors of only 2.8% for the systems studied, all of which exhibit highly nonideal behavior, with excess surface tensions as high as 35 mN m−1. The surface tension predictions are found to be extremely sensitive to the values of the molar surface areas used in the computation. Use of the partitioning model with partial molar surface areas improves surface tension predictions of highly nonideal aqueous-organic mixtures by 30% over use of pure component molar surface areas. Moreover, this improvement in predictions is found to occur for every value of composition without exception for each aqueous-organic system studied. Analysis of the data suggests the attractive hypothesis that the extent of nonideality of aqueous-organic mixtures is characterized by and is directly proportional not only to the difference in pure component surface tension of the binary constituents but also to the ratio of pure component molar (or partial molar) surface areas of the organic to that of water. It is proposed that this physical area parameter is correlated to the value of the partition constant between the surface and the bulk. It therefore constitutes an important determinant of the surface chemical properties of the organic species in the aqueous-organic mixture, in addition to the intrinsic chemical nature of the organic compound, although further research is needed to find out the exact relationship between them and to arrive at a quantitative theory.

Size-dependent dissolution kinetics of CaCO3 nanoparticles in theory and experiment

In preparation and application of nanomaterials, the dissolution of nanoparticles is usually involved. However, it remains unclear about size dependent the dissolution kinetic parameters of nanoparticles. In this paper, kinetic model for the dissolution of nanoparticles is proposed, and the relations between dissolution kinetic parameters (rate constant, order, apparent activation energy and pre-exponential factor), respectively, and particle sizes were theoretically deduced by applying the transition state theory to the dissolution process, and then the influence regularity and mechanism of particle size on the kinetic parameters were discussed. Experimentally, the dissolution kinetic parameters of nano-CaCO3 with different particle sizes were determined by conductivity meter, and the quantitative influences of particle size on the dissolution kinetics were obtained. The experimental results are consistent with the theoretical relations. The results show that there are significant effects of the particle sizes of CaCO3 nanoparticles on dissolution kinetic parameters; with the particle diameter decreasing, the apparent activation energy and the pre-exponential factor correspondingly decrease, while the rate constant and the dissolution order increase sharply. When the diameter of nanoparticle exceeds 20 nm, the logarithm of the dissolution rate constant, the apparent activation energy, and the logarithm of the pre-exponential factor are all linearly related with the reciprocal of particle diameter. Furthermore, the apparent activation, the dissolution order, the pre-exponential factor, and the dissolution rate constant are influenced by the partial molar surface enthalpy, the partial molar surface area, the partial molar surface entropy, and the partial molar surface Gibbs energy, respectively.

Use of the Law of Corresponding States for the evaluation of surface properties of pure compounds and binary systems

A new methodology for the evaluation of the interfacial energy using the Law of Corresponding States is employed here in order to study the behavior of the surface area of pure fluorocarbons and four binary mixtures (CCl 4 + CS 2, C 6H 6 + C 6H 14, H 2O + 2-methoxyethanol, and H 2O + ethylene glycol) as a function of temperature and composition. The surface tensions of partly halogenated hydrocarbons can be reproduced using a procedure formerly devised for non-polar hydrocarbons. Other polar compounds specially those which contain hydroxyl groups can be evaluated in a similar manner using a slightly different analytical expression. The assumption that a mixture behaves like a pseudo-compound, allows the estimation of the partial molar surface areas of binary mixtures. The dependence of the surface concentration with respect to the partial molar areas is examined for polar and non-polar systems. Arguments are given to estimate the surface concentrations more rigorously than it is usually done. This allows explaining some phenomena that occur in the interface, probably related to the aggregate formation.

Thermodynamics of adsorption of binary aqueous organic liquid mixtures on a RPLC adsorbent

The surface excess adsorption isotherms of organic solvents commonly used in RPLC with water as co-eluent or organic modifiers (methanol, ethanol, 2-propanol, acetonitrile and tetrahydrofuran) were measured on a porous silica surface derivatized with chlorotrimethylsilane (C 1-silica with 3.92 μ mol C 1 groups per m 2 of SiO 2), using the dynamic minor disturbance method. The 5 μ m diameter particles were packed in a 150 mm × 4.6 mm column. The isotherm data were derived from signals resulting from small perturbations of the equilibrium between the aqueous–organic solutions and the adsorbent surface. The partial molar surface area of the adsorbed components were assumed to be the same as those of the pure components. The difference σ − σ i ∗ between the surface tensions of the adsorbed mixtures and that of the pure liquids was measured as a function of the organic modifier molar fraction. A simple and unique convention for the position of the Gibbs dividing surface was proposed to delimit the Gibbs’s adsorbed phase and the bulk liquid phase. The activity coefficients of the organic modifiers and of water and their thermodynamic equilibrium constants between the two phases were measured. The strong non-ideal behavior of the adsorbed phase is mostly accounted for by the surface heterogeneity. Some regions of the surface (bonded –Si(CH 3) 3 moieties) preferentially adsorb the organic compound while the regions close to unreacted silanols preferentially adsorb water.

Prediction of liquid–vapour surface tension in multi-component systems

It is shown, using the lattice theory and regular solution assumption, that the activity coefficient of each component at a liquid–vapour interface is equal to the second root of that component's activity coefficient in the bulk liquid phase. Making use of this important finding, an equation for prediction of liquid–vapour surface tension in multi-component systems has been developed. The new equation needs the temperature, composition of the liquid phase, activity coefficient and partial molar surface area of each compound as input data. The equation does not include any empirical parameter and has no limitation with the number of components. Comparing the predicted results with the experimental data of various systems revealed the reliability of the new model.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: high-pressure and cosolute studies on recombinant human IFN-gamma.

The equilibrium dissociation of recombinant human IFN-gamma was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was -209 +/- 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 +/- 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-gamma in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were -41 +/- 9 ml/mol of dimer and 3.5 +/- 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values approximately 4-fold larger for both transitions.

Surface Tension of Nonideal Binary Liquid Mixtures as a Function of Composition

The composition dependence of the surface tension of highly nonideal organic–organic and aqueous–organic nonelectrolyte solutions is described, based on the assumption that the surface layer can be treated as a separate phase located between vapor and bulk liquid phases. The Wilson, NRTL, and UNIFAC methods are used for activity coefficients of surface and bulk phases and three techniques for calculation of molar surface areas, based on Paquette areas, Rasmussen areas, and a Langmuir-type approach are tested. Comparisons of the calculated surface tensions with experimental data yield mean absolute errors, in the best case, of less than 2.5% for the systems studied, all of which exhibit highly nonideal behavior. The surface tension predictions are found to be extremely sensitive to the values of the molar surface areas used in the computation. A Langmuir-type adsorption model is formulated to determine the surface mole fractions from a knowledge of the mixture surface tension as a function of bulk composition. A novel procedure is developed to obtain the partial molar surface area of the larger organic component as a function of composition in binary aqueous–organic systems, assuming that the two components are very dissimilar in size, and that deviations in the partial molar surface area of the smaller component (water) from its pure component molar surface area contribute negligibly to the total molar surface area of the mixture. This removes the approximation of equality of partial and pure component molar surface area for the larger organic component. Use of the Langmuir-type approach with partial molar surface areas improves surface tension predictions of highly nonideal aqueous–organic mixtures by 20% over use of pure component molar surface areas. It is an important first step in the development of a thermodynamically consistent theory of surfaces for liquid mixtures based on an accurate determination of the composition dependence of partial molar surface areas for all components.

Adsorption of alkyl dimethyl phosphine oxides at the solution/air interface

The surface tension isotherms were measured for homologous series of alkyl dimethyl phosphine oxides using different experimental techniques: maximum bubble pressure technique, drop volume technique and ring tensiometry. The adsorption data obtained for the surfactants with hydrocarbon chains from 8 to 16 alkyl groups are interpreted by a reorientation isotherm assuming two possible partial molar surface areas of surfactant molecules, i.e. states with maximum ( ω 1) and minimum ( ω 2) surface area. The lower homologues ( n⩽13) of C n DMPO do not adsorb in the state with the large molar area, while the molecules with long alkyl chains ( n⩾14) adsorb in both states. The area values determined from the experimental isotherms agree well with those calculated from the molecular geometry.

Adsorption Isotherm and Surface Tension Equation for a Surfactant with Changing Partial Molar Area. 2. Nonideal Surface Layer

An adsorption model is proposed that assumes different partial molar surface areas ω for adsorbed molecules depending on the degree of saturation of the adsorption layer. Equations for an adsorption isotherm and a surface tension isotherm are derived for the adsorption of one single surfactant or of a mixture of surfactants. The model assumes that the molecules may adsorb in two different states, i.e., large at smaller surface pressures Π, and smaller at large surface pressures Π. Adsorption data of N-n-hexadecyl-N,N-dimethylammonio acetic acid bromide at the solution/air interface are used to demonstrate the application of the theory. Experimental results are in very good agreement with the model.

Anomalous Dynamic Surface Tension of Mixtures of Nonionic Surfactants with Different Partial Molar Areas at the Water−Air Interface

On the basis of a thermodynamic model, the adsorption isotherm and a surface tension equation are derived for mixtures of nonionic surfactants with different partial molar surface area. The ratio o...

Application of an improved thermodynamic description of multilayer surface compositions of binary alloys

The previous developed new thermodynamic theory, the “modern thermodynamic calculation of interface properties” (MTCIP), in its first calculational approximation to a successful description of the surface composition of dilute binary alloys, has been improved in a multilayer description (using several surface atomic sublayers) by allowing for any bulk composition, accounting for farther than first neighbour effects, describing component partial molar surface areas as functions of the mixture surface composition, and including a treatment of surface reconstructions. The calculations for the {100}, {100} and {111} surfaces of Pt50Ni50 single crystal alloys at≈1000 K are presented, which are in good agreement with experimental results [1–3] for all surface atomic sublayers and all surface orientations.