Interfacial Energy of Strained Coherent Interfaces and a New Design Rule To Select Phase Combinations for In Situ Coherent Nanocomposites

Nanocomposites show the best performance when their reinforcing phase precipitates in situ from a matrix upon heat treatment and when coherency between the matrix and the reinforcing phase is preserved even upon coarsening the precipitated particles. In this paper, first a new equation is derived for the interfacial energy of strained coherent interfaces. From here, a new design rule is derived in a form of a new dimensionless number to select phase combinations for in situ coherent nanocomposites (ISCNCs). This is calculated from the molar volume mismatch between the two phases, their elastic constants, and the modeled interfacial energy between them. When this dimensionless number is smaller than a critical value, ISCNCs are formed. The critical value of this dimensionless number is found here using experimental data for the Ni-Al/Ni₃Al superalloy. The validity of the new design rule was confirmed on the Al-Li/Al₃Li system. An algorithm is suggested to apply the new design rule. Our new design rule can be simplified to more easily available initial parameters: if the matrix and the precipitate have the same cubic crystal structure the precipitate is expected to form ISCNCs with that matrix if their standard molar volumes differ less than by about 2%.

Adsorption of Cetylpyridinium Chloride at Silica Nanoparticle/Water Interfaces (II): Dependence of Surface Aggregation on Particle Size

Herein, we report a thermodynamic model that relates the adsorption (aggregation) parameters of surfactants at solid/liquid interfaces to particle radius (r). The adsorption (aggregation) parameters include adsorption amounts, equilibrium constants (or the standard Gibbs free energy changes), the critical surface micelle concentration (csmc), and the average aggregation number of surface micelles (n). The model predicts the size dependence of the surface aggregation of surfactants, which is determined by the changes in the interfacial tension and the molar volume of surface components caused by adsorption. In addition, the adsorption of cetylpyridinium chloride (CPyCl), a cationic surfactant, on silica nanoparticles with different r values (ca. 6-61 nm) was determined at 298 K and pH 4, showing an obvious size dependence, consistent with the prediction of the model. With an increase in r, the adsorption isotherm changes from the double-plateau type to the Langmuir type, accompanied by obvious changes in the adsorption parameters. The size-dependent adsorption data can be well described using the model equations, indicating that the model presented here is acceptable. In addition, the model can extract information on the interfacial tensions from adsorption data. We think that the model deepens the understanding of the aggregation phenomena of surfactants at solid/liquid interfaces.

Adsorption of Cetylpyridinium Chloride at Silica Nanoparticle/Water Interfaces (I): Dependence of Adsorption Equilibrium on Particle Size

In the current work, a size-effect model was developed to describe the particle size-dependence of adsorption at solid/liquid interfaces. A parameter, ΔQ_ad, was introduced, defined as the change of the product of the solid/liquid interfacial tension and the molar volume of solid surface components caused by adsorption. The model predicts that with a decrease in particle radius (r), the saturation adsorption amount per unit area (Γ_m, mol/m²) decreases, while the change of the adsorption equilibrium constant (K_ad) is determined by the ΔQ_ad, namely, it decreases if ΔQ_ad > 0 but increases if ΔQ_ad < 0. There exists a critical r at which the saturation adsorption amount per unit mass (Γ_m^g, mol/g) attains a maximum. In addition, the adsorption of cetylpyridinium chloride (CPyCl), a cationic surfactant, on silica nanoparticles with different r (ca. 6-61 nm) values was determined at 298 K and pH 9, showing an obvious size-dependence. With a decrease in r, K_ad and Γ_m decrease, indicating a decrease in the affinity of silica particles toward CPyCl. The size-dependent adsorption data can be well described using our model. Adsorption can affect the molar volume of the solid surface phase, which plays an important role in the size-dependence of adsorption. This work provides a better understanding of the size-dependent adsorption phenomenon at solid/liquid interfaces.

A coherent set of model equations for various surface and interface energies in systems with liquid and solid metals and alloys

In this paper first a generally valid model is derived from the two fundamental equations of Gibbs for temperature and composition dependences of all types of interfacial energies. This general model is applied here to develop a coherent set of particular model equations for surface tension of liquid metals and alloys, for surface energy of solid metals and alloys, for high-angle grain boundary energy in metals and alloys, for solid/liquid interfacial energy in metals and alloys, for liquid/liquid interfacial energy in alloys and for solid/solid interfacial energy in metals and alloys. The latter case is sub-divided into models on coherent, incoherent and semi-coherent interfaces with the same phases and with different phases on the two sides of the interface. Model parameters are given here as an example for the 111 plane of fcc metals and alloys. For other crystal planes or other crystal structures the model parameters should be adjusted, while the model equations remain the same. The method is demonstrated on various surface and interfacial energies of pure Au, on solid/liquid interfacial energy in the AlCu system, on different types of solid/solid interfacial energies in the AuNi system, on solid/solid, solid/liquid and liquid/liquid interfacial energies in the AlPb system and on the coherent, incoherent and semi-coherent interfacial energies between ordered and disordered fcc phases in the Ni-rich part of the NiAl system. The ability of this method is demonstrated to predict surface and interface transition along free surfaces and grain boundaries and also negative interfacial energies in nano-systems.

Bubble Solution Description by Non-Extensive Thermodynamics: Pressure Effect

We showed in this study that nanobubble solutions should not be considered as the simple juxtaposition of autonomous phases (a solution and bubbles) but as particular entities, that is, "supersaturated solutions" where gas is simultaneously in two forms in permanent exchange. Gibbs' extensive thermodynamics cannot claim to describe legitimately their behavior. In this work, we showed how the use of the non-extensive thermodynamics allows describing the physicochemical properties of such media, some of which are counter-intuitive. Thus, an increase in pressure can result in an increase in the bubble size, contrary to what is provided by Boyle-Mariotte's law. The theoretical relationships proposed in this work constitute another approach to bubble solutions, which considers the non-autonomous nature of the components of supersaturated gas solutions and their "non-extensive" nature.

Improved Derivation of the Butler Equations for Surface Tension of Solutions

The Butler equation was published in 1932 to describe the equilibrium surface composition and equilibrium surface tension of solutions. Unfortunately, it used the so-called "partial surface tension of a component", which was not properly defined by Butler, leading to a reluctant acceptance of this equation. Although the present author defined the partial surface tension recently in this journal, it is considered an advantage to derive the same key equations of Butler without the need to employ the concept of partial surface tension. This derivation is offered in the present paper, starting from the two fundamental equations of Gibbs. No assumptions are made on the thickness and structure of the surface region, it is only supposed that the surface region has an average composition with a negligible concentration gradient. In this way, the Butler equations are obtained, which have more general validity compared to the original Butler equations derived by supposing a surface monolayer.

Impact of Delivery System Type on Curcumin Bioaccessibility: Comparison of Curcumin-Loaded Nanoemulsions with Commercial Curcumin Supplements

In this study, nanoemulsion-based delivery systems fabricated using three different methods were compared with three commercially available curcumin supplements. Powdered curcumin was dispersed into the oil-in-water nanoemulsions using three methods: the conventional oil-loading method, the heat-driven method, and the pH-driven method. The conventional method involved dissolving powdered curcumin in the oil phase (60 °C, 2 h) and then forming a nanoemulsion. The heat-driven method involved forming a nanoemulsion and then adding powdered curcumin and incubating at an elevated temperature (100 °C, 15 min). The pH-driven method involved dissolving curcumin in an alkaline solution (pH 12.5) and then adding this solution to an acidified nanoemulsion (pH 6.0). The three commercial curcumin products were capsules or tablets purchased from an online supplier: Nature Made, Full Spectrum, and CurcuWin. Initially, the encapsulation efficiency of the curcumin in the three nanoemulsions was determined and decreased in the following order: pH-driven (93%) > heat-driven (76%) > conventional (56%) method. The different curcumin formulations were then subjected to a simulated gastrointestinal tract (GIT) model consisting of mouth, stomach, and small intestine phases. All three nanoemulsions had fairly similar curcumin bioaccessibility values (74-79%) but the absolute amount of curcumin in the mixed micelle phase was highest for the pH-driven method. A comparison of these nanoemulsions and commercial products indicated that the curcumin concentration in the mixed micelles decreased in the following order: CurcuWin ≈ pH-driven method > heat-driven method > conventional method ≫ Full spectrum > Nature Made. This study provides valuable information about the impact of the delivery system type on curcumin bioavailability. It suggests that encapsulating curcumin within small lipid particles may be advantageous for improving its absorption form the GIT.

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science.

The nano heat effect of replacing macro-particles by nano-particles in drop calorimetry: the case of core/shell metal/oxide nano-particles

Difference in the enthalpy effect by replacing micro- by nano-sized particles in drop calorimetry.

On the Negative Surface Tension of Solutions and on Spontaneous Emulsification

The condition of negative surface tension of a binary regular solution is discussed in this paper using the recently reconfirmed Butler equation (Langmuir 2015, 31, 5796-5804). It is shown that the surface tension becomes negative only for solutions with strong repulsion between the components. This repulsion for negative surface tension should be so strong that this phenomenon appears only within a miscibility gap, that is, in a two-phase region of macroscopic liquid solutions. Thus, for a macroscopic solution, the negative surface tension is possible only in a nonequilibrium state. However, for a nano-solution, negative surface tension is also possible in equilibrium state. It is also shown that nano- and microemulsions can be thermodynamically stable against both coalescence and phase separation. Further, the thermodynamic theory of emulsion stability is developed for a three-component (A-B-C) system with A-rich droplets dispersed in a C-rich matrix, separated by the segregated B-rich layer (the solubility of B is limited in both A and C while the mutual solubility of A and C is neglected). It is shown that when a critical droplet size is achieved by forced emulsification, it is replaced by spontaneous emulsification and the droplet size is reduced further to its equilibrium value. The existence of maximum temperature of emulsion stability is shown. Using low-energy emulsification below this maximum temperature, spontaneous emulsification can appear, which is enhanced with further decrease of temperature. This finding can be applied to interpret the experimental observations on spontaneous emulsification or for the design of stable micro- and nanoemulsions.