From a physical point of view, interfaces are not simply borders between two contacting continuous phases, but material objects with specific properties [...]

There are various thermodynamic models to quantitatively describe the adsorption of surfactant molecules at the surface of their aqueous solutions. The Frumkin adsorption model is one of the most successful ones as it provides essential parameters, such as the surface activity of the studied surfactant, the minimal required molecular area at the interface, and the intermolecular interaction in the adsorption layer. Since it was published 100 years ago, the model has served as the starting point for various refinements, such as for molecular reorientations or two-dimensional aggregations at fluid interfaces or as generalized model for the adsorption of surfactant mixtures. Also, the recently developed approach for understanding the cooperativity in the formation of surfactant adsorption layers at water/oil interfaces is based on Frumkin's model. Due to its clear physical idea, it was successfully applied to quantitatively describe various types of surfactant systems. The values of the three model parameters allow for a categorization of surfactants with respect to their efficient application in numerous technological fields.

Dynamic dilational viscoelasticity is an important physical characteristic of interfacial layers because it influences dynamics and stability of multiphase systems, such as thin liquid films, foams and emulsions. Dilational viscoelasticity depends on many factors. Less studied, but very important, factors are the solubility of the solution components in two contacting liquids, simultaneous presence of two solution components within a mixed adsorption layer and curvature of the interface. In this review we considered several new developments of previously proposed models, which can be used for the analysis of new experimental data. In the presence of such effects, the behaviour of the dilational viscoelasticity becomes more complicated and requires more parameters for its description. An alternative way is to use phenomenological models, which do not identify the particular relaxation processes but propose a description of the dilational viscoelasticity in general terms.

Profile analysis tensiometry (PAT) with drops and bubbles is a successful methodology to characterize liquid-fluid interfaces. Questions about the most suitable size of drops and bubbles have been solved now on the basis of dimensionless numbers. The consideration of the standard deviation between measured and calculated liquid profiles as sensitive measure for the applicability of PAT provides a tool for its correct use. For solutions of highly surface-active compounds, bulk depletion effects can cause systematic errors in the analysis of adsorption kinetics, equations of state, and the visco-elastic interfacial behavior of liquid adsorption layers. Great progress has been made in measurements of interfacial dilational rheology with large amplitude perturbations providing additional information about structure and dynamics of complex adsorption layers. Also, first attempts are successfully made to use artificial intelligence (AI) to enhance the efficiency of PAT applications. Thus, PAT has established a solid position in surface science.

During recent years, great progress has been made in understanding the adsorption of surfactants at liquid interfaces. In addition to tensiometry, new efficient methodologies have been developed, in particular interfacial selective optical methods which allow direct access to the adsorbed amounts and interfacial layer compositions. In addition to these new experimental tools, the thermodynamic description by equations of state now allows one to provide a quantitative picture of surfactant interfacial layers. This is most notable for surfactant layers at water/oil interfaces. Additional knowledge about the structure of interfacial layers was gained through different types of molecular modeling. Improved interrelationships between these three aspects are the challenges for current and future work. Particular attention must be paid to dilational interfacial rheology studies, as these mechanical quantities are much more sensitive to small changes in the interfacial composition and structure.

Experimental data for tridecyl dimethyl phosphine oxide (C13DMPO) adsorption layers at the water/air interface, including equilibrium surface tension and surface dilational viscoelasticity, are measured by bubble and drop profile analysis tensiometry at different solution concentrations and surface area oscillation frequencies. The results are used to assess the applicability of a multistate model with more than two possible adsorption states. For the experiments with single drops, the depletion of surfactant molecules due to adsorption at the drop surface is taken into account. For the assessment, the same set of model parameters is used for the description of all obtained experimental dependencies. The agreement between the proposed model and the experimental data shows that for the nonionic surfactant C13DMPO, the description of the adsorption layer behavior by three adsorption states is superior to that with only two adsorption states.

The theoretical description of the adsorption of proteins at liquid/fluid interfaces suffers from the inapplicability of classical formalisms, which soundly calls for the development of more complicated adsorption models. A Frumkin-type thermodynamic 2-d solution model that accounts for nonidealities of interface enthalpy and entropy was proposed about two decades ago and has been continuously developed in the course of comparisons with experimental data. In a previous paper we investigated the adsorption of the globular protein β-lactoglobulin at the water/air interface and used such a model to analyze the experimental isotherms of the surface pressure, Π(c), and the frequency-, f-, dependent surface dilational viscoelasticity modulus, E(c)f, in a wide range of protein concentrations, c, and at pH 7. However, the best fit between theory and experiment proposed in that paper appeared incompatible with new data on the surface excess, Γ, obtained from direct measurements with neutron reflectometry. Therefore, in this work, the same model is simultaneously applied to a larger set of experimental dependences, e.g., Π(c), Γ(c), E(Π)f, etc., with E-values measured strictly in the linear viscoelasticity regime. Despite this ambitious complication, a best global fit was elaborated using a single set of parameter values, which well describes all experimental dependencies, thus corroborating the validity of the chosen thermodynamic model. Furthermore, we applied the model in the same manner to experimental results obtained at pH 3 and pH 5 in order to explain the well-pronounced effect of pH on the interfacial behavior of β-lactoglobulin. The results revealed that the propensity of β-lactoglobulin globules to unfold upon adsorption and stretch at the interface decreases in the order pH 3 > pH 7 > pH 5, i.e., with decreasing protein net charge. Finally, we discuss advantages and limitations in the current state of the model.

The adsorption behaviour of linear poly(oxyethylene) alkyl ether (CnEOm) is best described by a reorientation model. Based on a complete set of experimental data, including the adsorption kinetics, the equilibrium surface tension isotherm and the surface dilational visco-elasticity, the thermodynamic and kinetic adsorption parameters for some CnEOm at the water/air interface were determined. For the study, six CnEOm surfactants were selected (n = 10, 12 and 14 and m = 4, 5 and 8) and were studied by bubble profile analysis and maximum bubble pressure tensiometry. A refined theoretical model based on a reorientation-adsorption model combined with a diffusion-controlled adsorption kinetics and exchange of matter allowed us to calculate the surface layer composition by adsorbing molecules in different orientations. It turns out that at larger surface coverage, the adsorption rate decreases, i.e., the apparent diffusion coefficients are smaller. This deceleration can be explained by the transition of molecules adsorbed in a state of larger molar surface area into a state with smaller molar surface area.

The dynamic and equilibrium properties of adsorption layers of poly (oxyethylene) alkyl ether (CnEOm) can be well described by the reorientation model. In its classical version, it assumes two adsorption states; however, there are obviously surfactants that can adsorb in more than two possible conformations. The experimental data for C14EO4 and C14EO8 (dynamic and equilibrium surface tensions and surface dilational visco-elasticity as measured by bubble profile analysis tensiometry) are used to verify if a reorientation model with more than two possible adsorption states can better describe the complete set data of CnEOm adsorption layers at the water/air interface. The proposed refined theoretical model allows s different states of the adsorbing molecules at the interface. The comparison between the model and experiment demonstrates that, for C14EO4, the assumption of s = 5 adsorption states provides a much better agreement than for s = 2, while for C14EO8, a number of s = 10 adsorption states allows an optimum data description.

In mixed solutions of anionic and cationic surfactants, called catanionics, ion pairs are formed which behave like non-ionic surfactants with a much higher surface activity than the single components. In equimolar mixtures of NaCnSO4 and CmTAB, all surface-active ions are paired. For mixtures with n + m = const, the interfacial properties are rather similar. Catanionics containing one long-chain surfactant and one surfactant with medium chain length exhibit a strong increase in surface activity as compared with the single compounds. In contrast, catanionics of one medium- and one short chain surfactant have a surface activity similar to that of the medium-chain surfactant alone. Both the Frumkin model and the reorientation model describe the experimental equilibrium data equally well, while the adsorption kinetics of the mixed medium- and short-chain surfactants can be well described only with the reorientation model.

The surface tension of C13DMPO aqueous solution drops in hexane vapor is studied using the drop profile method. The hexane was injected into the measuring cell at three different conditions: before the formation of the solution drop, at a certain moment during the adsorption process, and after reaching the equilibrium of surfactant adsorption. The surface tension values for all experiments at the same concentration and different injection situations ultimately coincide with each other after attaining the final equilibration stage. The equilibrium surface tension isotherms of C13DMPO solutions, and the adsorption of both components—surfactant and hexane—were calculated. It was shown that the presence of surfactant leads to an increased hexane adsorption.

Rutile decomposition by sulfuric acid, including the formation of two salts, Ti(SO4)2/TiOSO4, is thermodynamically modelled. It is shown that TiO2 can spontaneously dissolve in H2SO4 solutions. However, titania is considered as an inert (ballast) phase component of titanium-containing raw materials due to the decelerated separate nature of such chemical transformations. It is concluded that the hampered related kinetics of dissolution can be attributed to the lability of Ti(IV) cations/the specific engineered features of the hierarchical crystalline structure. It is suggested that the breaking of Ti–O–Ti bonds without additional mechanical strains in crystal lattice geometry becomes more advantageous when smaller negative anions/fluoride ions can be used. The analysis of sulfate-fluoride extraction leaching of titanium confirmed that a decrease in the Gibbs energy in the presence of F occurs. It is indicated by kinetic research studies that the addition of corrosive sodium reagent (NaF) reduces the activation by 45 kJ/mol, which results in intensification. A mechanism is proposed for the interactions involving the Ti–O–Ti cleavage on the surface/the H2SO4-induced Ti dioxide degradation on the sites of defects. Moreover, F acts as a homogeneous/heterogeneous bifunctional catalyst.

Bubble profile analysis tensiometry was used to study the surface tension and dilational visco-elasticity of individual and mixed solutions of β-casein (BCS) and β-lactoglobulin (BLG) at various mixing ratios of the components. The results for the individual protein solutions were analysed based on a new theory, which is applicable in the pre-critical and post-critical concentration range of the surface tension isotherm. It is shown that these proteins are capable of displacing each other from the adsorption layer, which affects the surface tension and visco-elasticity modulus of the adsorbed layers. The model developed for protein mixtures agrees well with the experimental data and the calculated dependencies of the surface properties on the solution composition confirm the mutual influence of added proteins.

A thermodynamic model is used to analyse the adsorbed layers of CnDMPO (n = 12, 13), CnTAB (n = 10, 12, 14, 16) and SDS at the aqueous solution/hexane and aqueous solution/dodecane interfaces. The combined model assumes that the adsorption of alkane from the oil phase is governed by the Frumkin model, and the adsorption of the surfactant molecules from the solution obeys the reorientation model. We are able to show that at low surfactant concentrations a remarkable decrease of interfacial tension occurs due to a cooperative formation of a mixed adsorption layers by surfactant and alkane molecules. By a quantum chemical semi-empiric (PM3) simulation we analyse the orientation of oil and surfactant molecules in the interfacial layer, and calculate the relative amounts of adsorbed surfactant and alkane. The values obtained from the thermodynamic models agree well with those results calculated via the PM3 simulation. The results show, that at the interface the short-chain hexane molecules can form bi-layers with the long-chain surfactants, while the dodecane and surfactant molecules having commensurable chain lengths are mainly forming mixed monolayer.

The theoretical description of the adsorption of surfactants at interfaces between aqueous solutions and oil was based over a very long time on models derived for the solution/air interface. Thus, most of the experimentally observed peculiarities could not be specifically considered but were merely interpreted in terms of a penetration of oil molecules into the alkyl chain layer of the adsorbed surfactant molecules. These penetrating oil molecules enhance the surfactant adsorption as compared to the water/air interface. Later on, for the special situations at water/oil interfaces a competitive adsorption of surfactant and oil molecules was postulated, allowing a much better description of experimental data. This picture, however, was unable to explain why the interfacial tension of the water/oil interface decreases very quickly when extremely small amounts of surfactants are added to the water. This effect cannot be of competitive nature, but a cooperativity of surfactant and oil molecules forming a mixed adsorption layer is required instead. This cooperative effect means that already few surfactant molecules adsorbed at the interface can induce a significant ordering of oil molecules in the interfacial layer. This new interfacial structure, in turn, attracts further surfactant molecules to adsorb. Improving the theoretical description of experimental data was finally achieved by applying suitable adsorption models for the two adsorbing compounds, i.e. a Frumkin adsorption model for the oil molecules and a Langmuir, Frumkin, or reorientation model for the adsorbing surfactant molecules. Here, the progress in modelling surfactant adsorption at water/oil interfaces is discussed mainly for the homologous series of the cationic surfactants CnTAB, of the anionic surfactant SDS, and members of the homologous series of the non-ionic surfactants CnDMPO at water/alkane interfaces.

Surface tension experiments were performed using the drop profile analysis tensiometry method. The hexane was injected into the measuring cell at certain times before the formation of the solution drop. The influence of the capillary diameter and solution drop size on the measured apparent dynamic surface tension was studied. The amount of hexane transferred from the vapor phase to the drop was estimated. For large pure water drops, it was shown that the ageing of the drop in the hexane vapor during a long time resulted in the formation of a liquid hexane phase covering the drop, but the volume of this phase did not exceed 0.5 mm3. On the contrary, for surfactant solution drops the volume of the hexane phase covering the drop was essentially larger. Experiments with solution drops were performed to measure the surface tension within a wide range of surfactant concentration. It was found that the dependencies of dynamic surface tension on the C13DMPO and C14EO8 solutions concentration exhibit maxima at concentrations of about 1–2 μmol/L for C14EO8 and 2–5 μmol/L for C13DMPO at ageing times of 100 to 1000 s; these maxima were shown to exist also at equilibrium. This phenomenon is presumably ascribed to the competitive character of simultaneous adsorption of hexane and surfactant.

A two-component interfacial layer model was employed to describe the experimental results obtained for various surfactants. In contrast to the previous works, here it is shown that the adsorption activity of alkane depends on its interaction with the adsorbed surfactant and is proportional to the surface coverage by this surfactant. Also, it is assumed that this increase of the adsorption activity parameter is limited by some maximum value. This model provides a good description of the influence of hexane and dodecane, which results in the decrease of surface tension by 2-5 mN/m at very low surfactant concentrations. The adsorbed amounts of the surfactant and alkane molecules in this low surfactant concentration range have been calculated. The reorientation model of surfactant adsorption predicts a smaller number of alkane molecules per one surfactant molecule than that which follows from the Frumkin model.

In the present work, the properties of dodecyl dimethyl phosphine oxide (C12DMPO) at the water/decane interface are studied and compared with those obtained earlier at the interface to hexane. To simulate the interfacial behavior, a two-component thermodynamic model is proposed, which combines the equation of state and Frumkin isotherm for decane with the reorientation model involving the intrinsic compressibility for the surfactant. In this approach, the surface activity of decane is governed by its interaction with C12DMPO. The theory predicts the influence of decane on the decrease of the surface tension at a very low surfactant concentration for realistic values of the ratio of the adsorbed amounts of decane and surfactant. The surfactant's distribution coefficient between the aqueous and decane phases is determined. Two types of adsorption systems were used: a decane drop immersed into the C12DMPO aqueous solution, and a water drop immersed into the C12DMPO solution in decane. To determine the distribution coefficient, a method based on the analysis of the transfer of C12DMPO between water and decane is also employed.

Difference in adsorption properties of Fe(III), Mo(VI) oxides and Fe(III) molybdate as a cause of high selectivity of methanol oxidation on iron molybdate catalyst

The surface tension isotherms and dilational visco-elasticity for three nonionic surfactants (C10EO8, C12EO5 and C14EO8) were comparatively studied using the bubble and drop profile analysis tensiometry. The experiments based on drop profiles were analysed assuming the depletion of surfactant molecules from the bulk of the drop due to adsorption. To process the experimental results, two theoretical adsorption layer models (Frumkin and reorientation) were applied, while the reorientation model provides a better description of the experimental results. In addition, the visco-elasticity moduli obtained from drop and bubble profile experiments were compared. It was shown that at higher surfactant concentrations the drop profile method provides visco-elasticities systematically larger than those obtained from bubble profile experiments, even though the adsorption-related depletion has been correctly considered. The proposed correction protocol provides the option for direct comparison between data obtained by the drop profile analysis method with those from other methods.