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Experimental data for tridecyl dimethyl phosphine oxide (C 13 DMPO) 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 C 13 DMPO, the description of the adsorption layer behavior by three adsorption states is superior to that with only two adsorption states.

To assess the surface basicity constant (p K b ) of aliphatic amine films, the use of a theoretical approach recently developed to evaluate the p K a of carboxylic acid monolayers on the water surface is tested. The present paper gives a new full picture of the change of acid-base properties of surfactants during their aggregation at the air/water interface. The exploited approach is simple because it does not involve the construction of thermodynamic cycles but uses the Gibbs energies of the formation and dimerization of surfactant monomers in neutral and ionized forms in the aqueous and gaseous phases. The quantum chemical semiempirical PM3 method is applied to perform calculations using a conductor-like screening model, which takes into account the aqueous phase. The calculation shows that aliphatic amines, as well as carboxylic acids, are characterized by a change of the value of the basicity/acidity constant during the film formation. The film formation of surfactants leads to a decrease in their acid-base properties, i.e., the surface p K a values of carboxylic acids and p K b values of amines increase. However, unlike carboxylic acids, there is practically no dependence of the surface p K b value on the alkyl chain length of the aliphatic amine, which is caused by almost identical contributions of one CH 2 fragment to the solvation Gibbs energy of neutral and ionized monomers within the calculation error. The obtained results agree with existing experimental data., Competing Interests: The authors declare no competing financial interest., (© 2020 American Chemical Society.)

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 C n TAB, of the anionic surfactant SDS, and members of the homologous series of the non-ionic surfactants C n DMPO at water/alkane interfaces., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

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.

The dilational visco-elasticity of surfactant adsorption layers was measured at low frequencies by the drop profile analysis tensiometry using oscillating drops. As the studied non-ionic surfactant C 13 DMPO (tridecyl dimethyl phosphine oxide) is soluble in water and in hexane, the partitioning of the surfactant between the two solvents had to be taken into consideration. The diffusion controlled exchange of matter theory was generalized in order to take into consideration the curvature of the interface, the diffusional transport in both adjacent bulk phases as well as the transfer across the liquid interface. Using two configurations, i.e. water drop in hexane and hexane drop in water, it is shown that the frequency dependence of the visco-elasticity modulus and the phase angle can be well described when the correct partition coefficient is applied. The surface activity of the selected surfactant C 13 DMPO is optimum to demonstrate the impact of matter transfer across the interface on the dilational visco-elasticity of interfacial adsorption layers of non-ionic surfactants., (Copyright © 2018 Elsevier Inc. All rights reserved.)

The thermodynamic parameters of formation and clusterization of aliphatic alcohols C n H 2 n +1 OH and carboxylic acids C n H 2 n +1 COOH ( n = 6-16) are calculated using the quantum-chemical semiempirical PM3 method. Four types of dimers are constructed in two directions of the spread monolayer comprising the most energetically advantageous monomer structures. The hydrophobic chains of alcohol and carboxylic acid molecules in the regarded dimers are found to be tilted within 12° to the normal of the spread monolayer. The structures of the mixed and pure surfactant dimers are the basis for the mixed alcohol-carboxylic acid monolayers of the following types: two dimensional (2D) film 1 with single distribution of the individual component in the other one, when the molecules of the first component do not interact with each other but are completely surrounded by the molecules of the second component; 2D film 2 with domain structure, when the film consists of "islands" of the individual components. The dependences of the clusterization Gibbs' energy per one monolayer molecule on the molar fraction of the components for the mixed 2D films 1 formed by surfactants with equal alkyl chain length are found to be limited from top to bottom by the corresponding dependences for pure components. This indicates the absence of synergetic interaction between the hydrophilic head groups of carboxylic acids and alcohols and conforms to the available experimental data. The formation of the described types of mixed films is competitive. The preferential formation of 2D films 1 with single distribution of the first component among the molecules of the second one is possible when the length of the carboxylic acid hydrocarbon chain is longer by Δ n = 1-2 methylene units than that of the corresponding alcohol alkyl chain. According to the fractionally linear law, the highest possible content of the carboxylic acids in such 2D films 1 depends on the Δ n value and does not exceed 33.3%., Competing Interests: The authors declare no competing financial interest.

Drop profile analysis tensiometry used in the oscillating drop mode provides the dilational viscoelasticity of adsorption layers at liquid interfaces. Applied during the progress of adsorption the dynamic surface rheology can be monitored. For β-casein solutions at the same surface pressure values, the larger the dynamic dilational viscoelasticity the longer the adsorption time, i.e., the smaller the studied protein concentration is. For β-lactoglobulin and human serum albumin, the differences in the viscoelasticity values are less or not dependent on the adsorption time at identical surface pressures. The observed effects are caused by the flexibility of BCS, while the globular proteins BLG and HSA do not change their conformation significantly within the adsorption layer.

Dynamic surface tensions and dilational visco-elasticity are easy accessible parameters of liquids. For human body liquids, such as urine, blood serum, amniotic fluid, gastric juice, saliva and others, these parameters are very characteristic for the health status of people. In case of a disease the composition of certain liquids specifically changes and the measured characteristics of dynamic surface tension of the dilational surface elasticity and viscosity reflect these changes in a clear way. Thus, this kind of physico-chemical measurements represent sensitive tools for evaluating the severity of a disease and can serve as control tool for the efficiency of applied therapies. The overview summarises the results of a successful work over about 25years on this subject and gives specific insight into a number of diseases for which the diagnostics as well as the therapy control have been significantly improved by the application of physico-chemical experimental techniques., (Copyright © 2017 Elsevier B.V. All rights reserved.)

The dynamics of surfactant interfacial layers was first discussed more than a century ago. In 1946 the most important work by Ward and Tordai was published which is still the theoretical basis of all new models to describe the time dependence of interfacial properties. In addition to the diffusion controlled adsorption mechanism, many other models have been postulated in literature, however, well performed experiments with well defined surfactant systems have shown that the diffusional transport is the main process governing the entire formation of surfactant adsorption layers. The main prerequisite, in addition to the diffusional transport, is the consideration of the right boundary condition at the interface, given by a respective equation of state. In addition to the classical models of Langmuir and Frumkin, also the so-called reorientation or interfacial aggregation models are to be assumed to reach a quantitative description of respective experimental data. Moreover, the adsorption of surfactants at the interface between water and a gas phase different from air can be strongly influenced by the type of molecules within the gas phase, such as alkane vapours. These oil molecules co-adsorb from the gas phase and change the adsorption kinetics strongly. Besides the discussion of how to apply theoretical adsorption kinetics models correctly, a large number of experimental data are presented and the way of a quantitative analysis of the adsorption mechanism and the main characteristic parameters is presented. This includes micellar solutions as well as mixtures of surfactants of ionic and non-ionic nature., (Copyright © 2016 Elsevier B.V. All rights reserved.)

The influence of hexane vapor in the air atmosphere on the surface tension of water and solutions of C 10 EO 8 , C n TAB and proteins are presented. For dry air, a fast and strong decrease of surface tension of water was observed. In humid air, the process is slower and the surface tension higher. There are differences between the results obtained by the maximum bubble pressure, pendant drop and emerging bubble methods, which are discussed in terms of depletion and initial surface load. The surface tension of aqueous solutions of β-сasein (BCS), β-lactoglobulin (BLG) and human serum albumin (HSA) at the interfaces with air and air-saturated hexane vapor were measured. The results indicate that the equilibrium surface tension in the hexane vapor atmosphere is considerably lower (at 13-20mN/m) as compared to the values at the interface with pure air. A reorientation model is proposed assuming several states of adsorbed molecules with different molar area values. The newly developed theoretical model is used to describe the effect of alkane vapor in the gas phase on the surface tension. This model assumes that the first layer is composed of surfactant (or protein) molecules mixed with alkane, and the second layer is formed by alkane molecules only. The processing of the experimental data for the equilibrium surface tension for the C 10 EO 8 and BCS solutions results in a perfect agreement between the observed and calculated values. The co-adsorption mechanism of dipalmitoyl phosphatidyl choline (DPPC) and the fluorocarbon molecules leads to remarkable differences in the surface pressure term of cohesion Π coh . This in turn leads to a very efficient fluidization of the monolayer. It was found that the adsorption equilibrium constant for dioctanoyl phosphatidyl choline is increased in the presence of perfluorohexane, and the intermolecular interaction of the components is strong., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The dynamic and equilibrium surface tension for drops of aqueous C 14 EO 8 solutions at the interface to pure air or pentane, hexane, heptane and toluene saturated air, and the dynamic surface tension of pure water at these interfaces are presented. Two theoretical models were employed: both assuming a diffusion controlled adsorption of the surfactant, and either a diffusion or kinetic barrier governed adsorption of the alkanes. The experimental results are best described by the model which implies a diffusion control for the C 14 EO 8 molecules and the existence of a kinetic barrier for the alkane molecules. The desorption of alkanes from the surface layer after equilibration and their subsequent removal from the measuring cell was studied as well. The desorption process was shown to be slow for heptane and hexane. However, for the pentane vapor the desorption is quite rapid, and after the desorption commences the surface tension becomes equal to that at the interface with pure air.

Surface tension and dilational viscoelasticity of solutions of various surfactants measured with bubble and drop profile analysis tensiometry are discussed. The study also includes experiments on the co-adsorption of surfactant molecules from a solution drop and alkane molecules from saturated alkane vapor phase. Using experimental data for 12 surfactants with different surface activities, it is shown that depletion due to adsorption of surfactant from the drop bulk can be significant. An algorithm is proposed quantitatively to take into consideration the depletion effect which is required for a correct description of the co-adsorption of alkanes on the solution drop surface and the correct analysis of experimental dynamic surface tension data to determine the adsorption mechanism. Bubble and drop profile analysis tensiometry is also the method of choice for measuring the dilational viscoelasticity of the adsorbed interfacial layer. The same elasticity moduli are obtained with the bubble and drop method only when the equilibrium surface pressures are sufficiently small (Π < 15 mN m -1 ). When the surface pressure for a surfactant solution is larger than this value, the viscoelasticity moduli determined from drop profile experiments become significantly larger than those obtained from bubble profile measurements.

Proteins and their mixtures with surfactants are widely used in many applications. The knowledge of their solution bulk behavior and its impact on the properties of interfacial layers made great progress in the recent years. Different mechanisms apply to the formation process of protein/surfactant complexes for ionic and non-ionic surfactants, which are governed mainly by electrostatic and hydrophobic interactions. The surface activity of these complexes is often remarkably different from that of the individual protein and has to be considered in respective theoretical models. At very low protein concentration, small amounts of added surfactants can change the surface activity of proteins remarkably, even though no strongly interfacial active complexes are observed. Also small added amounts of non-ionic surfactants change the surface activity of proteins in the range of small bulk concentrations or surface coverages. The modeling of the equilibrium adsorption behavior of proteins and their mixtures with surfactants has reached a rather high level. These models are suitable also to describe the high frequency limits of the dilational viscoelasticity of the interfacial layers. Depending on the nature of the protein/surfactant interactions and the changes in the interfacial layer composition rather complex dilational viscoelasticities can be observed and described by the available models. The differences in the interfacial behavior, often observed in literature for studies using different experimental methods, are at least partially explained by a depletion of proteins, surfactants and their complexes in the range of low concentrations. A correction of these depletion effects typically provides good agreement between the data obtained with different methods, such as drop and bubble profile tensiometry., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The dilational viscoelasticity of adsorption layer was measured at different frequencies of drop and bubble surface area oscillations for aqueous C12EO5 solutions. The modulus values obtained by the two experimental protocols are the same for Π < 15 mN/m, while for higher surface pressures the values from drop experiments exceed those from bubble profile analysis. The nature of this phenomenon was studied using stress deformation experiments. At high surfactant concentrations the magnitude of surface tension variations is essentially higher for drops as compared with bubbles, leading to an increased viscoelasticity modulus for oscillating drops. The observed effects are analyzed quantitatively using a diffusion controlled exchange of matter model. The viscoelasticity moduli for a number of surfactants (different CnEOm and Tritons, C13DMPO, and SDS) are reported, and it is shown that the discrepancies between the data obtained by the two methods for many surfactants agree well with the predictions made here.

A theoretical basis is provided for the experimental fact that for various surfactant classes the alkyl chain length threshold varies for the formation of condensed monolayers. The existence of the alkyl chain length threshold for a surfactant enabling the formation of monolayers is determined by the entropy increment to the Gibbs' energy, assessed by using the quantum chemical semiempiric method PM3. The value of the clusterization threshold is not stipulated by the surfactant solubility in water, rather by the electron-donor and electron-seeking properties of the head groups. These properties in turn impact the value of the solubility threshold for surfactants. The value of the clusterization threshold depends quadratically on the substituent constants, i.e. it is independent of whether the functional group is a donor or an acceptor of electrons. Rather it depends only on the donor or the acceptor 'force' of the substituent. The square-law dependence of the surface clusterization threshold of the amphiphile on the solubility threshold is evidenced.

Using the quantum chemical semi-empirical PM3 method it is shown that aliphatic alcohols favor the spontaneous clusterization of vaporous alkanes at the water surface due to the change of adsorption from the barrier to non-barrier mechanism. A theoretical model of the non-barrier mechanism for monolayer formation is developed. In the framework of this model alcohols (or any other surfactants) act as 'floats', which interact with alkane molecules of the vapor phase using their hydrophobic part, whereas the hydrophilic part is immersed into the water phase. This results in a significant increase of contact effectiveness of alkanes with the interface during the adsorption and film formation. The obtained results are in good agreement with the existing experimental data. To test the model the thermodynamic and structural parameters of formation and clusterization are calculated for vaporous alkanes C(n)H(2n+2) (n(CH3) = 6-16) at the water surface in the presence of aliphatic alcohols C(n)H(2n+1)OH (n(OH) = 8-16) at 298 K. It is shown that the values of clusterization enthalpy, entropy and Gibbs' energy per one monomer of the cluster depend on the chain lengths of corresponding alcohols and alkanes, the alcohol molar fraction in the monolayers formed, and the shift of the alkane molecules with respect to the alcohol molecules Δn. Two possible competitive structures of mixed 2D film alkane-alcohol are considered: 2D films 1 with single alcohol molecules enclosed by alkane molecules (the alcohols do not form domains) and 2D films 2 that contain alcohol domains enclosed by alkane molecules. The formation of the alkane films of the first type is nearly independent of the surfactant type present at the interface, but depends on their molar fraction in the monolayer formed and the chain length of the compounds participating in the clusterization, whereas for the formation of the films of the second type the interaction between the hydrophilic parts of the surfactant is essential and different for various types of amphiphilic compounds. The energetic preference of the film formation of both types depends significantly on the chain length of compounds. The surfactant concentration (in the range of X = 0-10%) exerts a slight influence on the process of film formation.

The equations of state, adsorption isotherms and functions of the distribution of protein molecules in liquid interfacial layers with respect to molar area and the equations for their viscoelastic behavior are presented. This theory was used to determine the adsorption characteristics of β-casein and β-lactoglobulin at water/oil interfaces. The experimental results are shown to be describable quite adequately by the proposed theory with consistent model parameters. The data analysis demonstrated that the β-casein molecule adsorbed at equilibrium conditions is more unfolded as compared with dynamic conditions, and this fact causes the significant increase of the adsorption equilibrium constant. The theory assumes the adsorption of protein molecules from the aqueous solution and a competitive adsorption of alkane molecules from the alkane phase. The comparison of the experimental equilibrium interfacial tension isotherms for β-lactoglobulin at the solution/hexane interface with data calculated using the proposed theoretical model demonstrates that the assumption of a competitive adsorption is essential, and the influence of the hexane molecules on the shape of the adsorption isotherm does in fact exist., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The influence of the addition of the nonionic surfactants C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations between 10(-5) and 10(-1) mmol/L to solutions of β-casein (BCS) and β-lactoglobulin (BLG) at a fixed concentration of 10(-5) mmol/L on the dilational surface rheology is studied. A maximum in the viscoelasticity modulus |E| occurs at very low surfactant concentrations (10(-4) to 10(-3) mmol/L) for mixtures of BCS with C12DMPO and C14DMPO and for mixtures of BLG with C10EO5, while for mixture of BCS with C10EO5 the value of |E| only slightly increased. The |E| values calculated with a recently developed model, which assumes changes in the interfacial molar area of the protein molecules due to the interaction with the surfactants, are in satisfactory agreement with experimental data. A linear dependence exists between the ratio of the maximum modulus for the mixture to the modulus of the single protein solution and the coefficient reflecting the influence of the surfactants on the adsorption activity of the protein.

A new model based on the quantum chemical approach is proposed to describe structural and thermodynamic parameters of clusterization for substituted alkanes at the air/liquid and liquid/liquid interfaces. The new model by the authors, unlike the previous one, proposes an explicit account of the liquid phase (phases) influence on the parameters of monomers, clusters and monolayers of substituted alkanes at the regarded interface. The calculations were carried out in the frameworks of the quantum chemical semiempirical PM3 method (Mopac 2012), using the COSMO procedure. The new model was tested in the calculations of the clusterization parameters of fatty alcohols under the standard conditions at the air/water interface. The enthalpy, Gibbs' energy and absolute entropy of formation for alcohol monomers alongside with clusterization parameters for the cluster series including the monolayer at air/water interface were calculated. In our calculations the sinkage of monomers, molecules in clusters and monolayers was varied from 1 up to 5 methylene groups. Thermodynamic parameters calculated using the proposed model for the alcohol monolayers are in a good agreement with the corresponding experimental data. However, the proposed model cannot define the most energetically preferable immersion of the monolayer molecules in the water phase.

In the framework of the quantum chemical semiempirical PM3 method the monolayers of the monoethoxylated normal alcohols CnH2n+1OCH2CH2OH with n = 6-16 (CnE1) at the air/water interface are described. The optimized structures of small clusters (dimers, trimers, tetramers, pentamers, hexamers and heptamers) comprising the hexagonal monolayer are obtained. For these aggregates thermodynamic parameters of formation and clusterization are calculated. The correlation dependencies of the clusterization enthalpy, entropy and Gibbs energy on the number of CHHC interactions and interactions between the functional groups realized in the cluster are obtained on the basis of calculated data. The calculated parameters of the hexagonal monolayer unit cell are: a = 4.02 Å; b = 7.94 Å, t = 4°, close to those for an aliphatic alcohol monolayer according to GIXD experiments: a = 5.0 Å; b = 7.5 Å, t = 0-9°. Spontaneous clusterization of monoethoxylated alcohols at the air/water interface under standard conditions is shown to be possible for molecules possessing more than 14 carbon atoms in the alkyl chain, in good agreement with the characteristics of the surface pressure-molecular area (π-A) isotherms. It is found that addition of the -O-CH2-CH2- unit to the hydrophilic part of aliphatic alcohols results in a shift of their spontaneous clusterization threshold to that of the compounds with hydrocarbon chains 3 methylene units longer. The temperature effect of CnE1 is assessed. It corresponds to the spontaneous clusterization temperature decrease of 10-20 K per two methylene units taken from the alkyl chain in agreement with experimental data. The comparison of clusterization Gibbs energy dependencies for small aggregates of CnE1 confirms the experimental fact that the crystalline monolayers are formed by preferential aggregation of trimers.

The influence of the addition of the nonionic surfactants dodecyl dimethyl phosphine oxide (C12DMPO), tetradecyl dimethyl phosphine oxide (C14DMPO), decyl alcohol (C10OH), and C10EO5 at concentrations between 10(-5) and 10(-1) mmol/L to solutions of β-casein (BCS) and β-lactoglobulin (BLG) at a fixed concentration of 10(-5) mmol/L on the surface tension is studied. It is shown that a significant decrease of the water/air surface tension occurs for all the surfactants studied at very low concentrations (10(-5)-10(-3) mmol/L). All measurements were performed with the buoyant bubble profile method. The dynamics of the surface tension was simulated using the Fick and Ward-Tordai equations. The calculation results agree well with the experimental data, indicating that the equilibration times in the system studied do not exceed 30 000 s, while the time required to attain the equilibrium on a plane surface is by one order of magnitude higher. To achieve agreement between theory and experiment for the mixtures, a supposition was made about the influence of the concentration of nonionic surfactant on the adsorption activity of the protein. The adsorption isotherm equation of the protein was modified accordingly, and this corrected model agrees well with all experimental data.

On the basis of experimental data for the homologous series of alkyltrimethylammonium bromides (CnTAB) the equilibrium surface tension isotherms at three types of liquid-fluid interfaces are discussed: solution/air, solution/alkane vapor and solution/liquid alkane interfaces. It is shown that the adsorption characteristics can be described at all three interfaces by the same thermodynamic approach. In the presence of alkane molecules (in the liquid alkane phase or in the alkane vapor phase) the CnTAB adsorption layers can be best described by a co-adsorption of the alkane molecules.

The structural parameters of fatty acid (with formula CnH2n+1COOH, n = 7-16) monolayers at the air/water interface were modeled within quantum-chemical semiempirical program complex Mopac 2012 (PM3 method). On the basis of quantum-chemical calculations it was shown that molecules in the highly ordered monolayer can be oriented at the angle ∼16° (tilted monolayer), or at the angle ∼0° to the normal to the air/water interface (untilted monolayer). The structural parameters of both tilted and untilted monolayers correspond well to the experimental data. The parameters of the unit cell of the modelled tilted monolayer are: a = 8.0-8.2 Å and b = 4.2-4.5 Å (with the corresponding experimental data 8.4-8.7 Å and 4.9-5.0 Å). For the modelled untilted monolayer these parameters are: a = 7.7-8.0 Å; b = 4.6 Å (with the corresponding experimental data 8.4 Å and 4.8-4.9 Å). Enthalpy, entropy and Gibbs' energy of clusterization were calculated for both structures. The correlation dependencies of the calculated parameters on the number of pair intermolecular CHHC interactions in the clusters and the pair interactions between functional groups were obtained. It was shown that the spontaneous clusterization of the fatty carboxylic acids at the air/water interface under standard conditions is energetically preferable for molecules which have 13 or more carbon atoms in the alkyl chain and this result also agrees with the corresponding experimental parameters.

We measured the interfacial tensions of aqueous solutions against different oil phases using drop profile analysis tensiometry (PAT-1, Sinterface Technologies, Germany) for decyl- and dodecyltrimethylammonium bromide (C10TAB and C12TAB) in phosphate buffer (10 mM, pH7). The following alkanes were used as oil phases: hexane, heptane, octane, nonane, decane, dodecane and tetradecane. The obtained equilibrium interfacial tension isotherms were fitted by the Frumkin Ionic Compressibility model (FIC). The surfactants adsorb at the water/oil interface in competition with the oil molecules. At high surfactant surface coverage this competitive adsorption is manifested in two ways. First, for short chain surfactants, the oil molecules are embedded into the adsorption layer. Second, for long chain surfactants, the short alkane chains of the oil molecules are squeezed out from the adsorption layer due to strong mutual interaction between surfactants' chains., (Copyright © 2013 Elsevier Inc. All rights reserved.)

The adsorption of members of the homologous series of alkyl trimethylammonium bromides (C(n)TAB) is studied at water/alkane interfaces by drop profile analysis tensiometry. The results are discussed in terms of a competitive adsorption process of alkane and surfactant molecules. A thermodynamic model, derived originally for the adsorption of surfactant mixtures, is adapted such that it describes a competitive adsorption of the surfactant molecules from the aqueous phase and alkane molecules from the oil phase. This new model involves the interspecies attraction coefficient, which mutually increases the adsorption activities of the alkane and C(n)TAB. The effects of the alkyl chain length n of C(n)TABs and the influence of the number of C atoms in the alkane chain are discussed, and the physical quantities are compared to those determined at the aqueous solution/air interface. The new theoretical model for aqueous solution/oil interfaces is also compared to a theory that does not consider the adsorption of alkane. The proposed new model demonstrates good agreement with the experimental data.

In the present study it is shown that parameters used in the framework of the model for the assessment of the threshold temperature of spontaneous clusterization of nonionic amphiphiles at the air/water interface (T(Cl)) are independent of the amphiphile type used in the developed schemes. The temperature dependence of the clusterization Gibbs' energies of alkyl amides, α-amino acids and 2-hydroxycarboxylic acids obtained in the framework of several schemes is listed. The exploited schemes differ from each other by the degree of their theoretical validity. The values of the clusterization threshold temperature for substituted alkanes can be described by a fractionally linear function versus the number of CH···HC interactions in the framework of the simplest scheme taking into account the found corrections and agree well with available experimental data.

The drop and bubble profile methods are used to study the viscoelasticity modulus of C14EO8 aqueous solutions within a wide concentration range. To determine the equilibrium concentration of the surfactant in the drop bulk, the correction is introduced for the surfactant losses caused by its adsorption on the drop surface. It is shown that with this correction the frequency dependencies of the viscoelasticity modulus measured by either of the two experimental techniques are almost the same. The theoretical model is used, which describes the surfactant dilational rheology assuming the diffusion-governed adsorption. The experimental data for C14EO8 solutions is described by the reorientation model that assumes the two states of surfactant molecules with different molar areas in the surface layer and the intrinsic compressibility of the molecules.

The interfacial behavior of β-casein (βCS) has been investigated in presence of the cationic surfactant dodecyl trimethyl ammonium bromide (DoTAB) at the water/hexane interface and compared to that obtained for the water/air interface. The used experimental technique is a drop profile analysis tensiometer specially equipped with a coaxial double capillary, which allows investigation of sequential adsorption of individual components besides the traditional simultaneous adsorption of two species. This method also provides the dilational rheological measurements based on low frequency harmonic drop oscillations. The tensiometric results show that the equilibrium states of the mixed βCS/DoTAB layers built up on the two different routes do not differ significantly, that is, the general compositions of the mixed layers are similar. However, the results of dilational rheology for the two adsorption strategies are remarkably different indicating different dynamic characteristics of the adsorbed layers. These findings suggest that the respective mixed layers are more proteinlike if they are formed via sequential adsorption and more surfactant-like after simultaneous adsorption. In contrast to the W/A interface, at the W/H interface proteins remain at the interface once adsorbed and cannot be displaced just by competitive adsorption of surfactants.

In the framework of the quantum chemical semiempirical PM3 method thermodynamic and structural parameters of the formation and clusterization of aliphatic alcohols C(n)H(2n+1)OH (n(OH) = 8-16) at 298 K at the water/alkane vapor C(n)H(2n+2), (n(CH(3)) = 6-16) interface were calculated. The dependencies of enthalpy, entropy and Gibbs' energy of clusterization per one monomer molecule of 2D films on the alkyl chain length of corresponding alcohols and alkanes, the molar fraction of alkanes in the monolayers and the immersion degree of alcohol molecules into the water phase were shown to be linear or stepwise. The threshold of spontaneous clusterization of aliphatic alcohols at the water/alkane vapor interface was 10-11 carbon atoms at 298 K which is in line with experimental data at the air/water interface. It is shown that the presence of alkane vapor does not influence the process of alcohol monolayer formation. The structure of these monolayers is analogous to those obtained at the air/water interface in agreement with experimental data. The inclusion of alkane molecules into the amphiphilic monolayer at the water/alkane vapor interface is possible for amphiphiles with the spontaneous clusterization threshold at the air/water interface (n(s)(0)) of at least 16 methylene units in the alkyl chain, and it does not depend on the molar fraction of alkanes in the corresponding monolayer. The inclusion of alkanes from the vapor phase into the amphiphilic monolayer also requires that the difference between the alkyl chain lengths of alcohols and alkanes is not larger than n(s)(0) - 15 and n(s)(0) - 14 for the 2D film 1 and 2D film 2, respectively.

The superposition-additive approach developed previously was shown to be applicable for the calculations of the thermodynamic parameters of formation and atomization of conjugate systems, their dipole polarizability, molecular diamagnetic susceptibility, π-electronic ring currents, etc. In the present work, the applicability of this approach for the calculation of the thermodynamic parameters of formation and clusterization at the water/air interface of alkanes, fatty alcohols, thioalcohols, amines, nitriles, fatty acids (C(n)H(2n+1)X, X is the functional group) and cis-unsaturated carboxylic acids (C(n)H(2n-1)COOH) is studied. Using the proposed approach the thermodynamic quantities determined agree well with the available data, either calculated using the semiempirical (PM3) quantum chemical method, or obtained in experiments. In particular, for enthalpy and Gibbs' energy of the formation of substituted alkane monomers from the elementary substances, and their absolute entropy, the standard deviations of the values calculated according to the superposition-additive scheme with the mutual superimposition domain C(n-2)H(2n-4) (n is the number of carbon atoms in the alkyl chain) from the results of PM3 calculations for alkanes, alcohols, thioalcohols, amines, fatty acids, nitriles and cis-unsaturated carboxylic acids are respectively: 0.05, 0.004, 2.87, 0.02, 0.01, 0.77, and 0.01 kJ/mol for enthalpy; 2.32, 5.26, 4.49, 0.53, 1.22, 1.02, 5.30 J/(molK) for absolute entropy; 0.69, 1.56, 3.82, 0.15, 0.37, 0.69, 1.58 kJ/mol for Gibbs' energy, whereas the deviations from the experimental data are: 0.52, 5.75, 1.40, 1.00, 4.86 kJ/mol; 0.52, 0.63, 1.40, 6.11, 2.21 J/(molK); 2.52, 5.76, 1.58, 1.78, 4.86 kJ/mol, respectively (for nitriles and cis-unsaturated carboxylic acids experimental data are not available). The proposed approach provides also quite accurate estimates of enthalpy, entropy and Gibbs' energy of boiling and melting, critical temperatures and standard heat capacities for several classes of substituted alkanes. For the calculation of thermodynamic functions of clusterization of dimers, trimers and tetramers of fatty alcohols, thioalcohols, amines, carboxylic acids and cis-unsaturated carboxylic acids two superposition-additive schemes are proposed which ensure the correct superimposition of the molecular graphs, including intermolecular hydrogen-hydrogen interactions in the clusters. The calculations involve the thermodynamic parameters of clusterization obtained earlier by the PM3 method. It is shown that the proposed approach reproduces quite accurately the values calculated earlier and is applicable for the prediction of the thermodynamic parameters of the formation of surfactant monolayers., (Copyright © 2012 Elsevier Inc. All rights reserved.)

An approach to calculation of the threshold temperature for spontaneous clusterization of substituted alkanes (amines, nitriles, alcohols, thioalcohols, saturated and unsaturated carboxylic acids, α-amino acids, carboxylic acid amides, and melamine derivatives) at the air/water interface with dependence on the alkyl chain length was developed. In the framework of this approach, four schemes for the description of the temperature dependencies of the thermodynamic parameters of clusterization of the concerned amphiphilic compounds were proposed. They use the data obtained previously in the framework of quantum chemical semiempirical PM3 method and differ from each other by the degree of their theoretical accuracy. It was shown that the threshold temperature for spontaneous clusterization of the regarded classes of substituted alkanes can be described using a fractionally linear function in dependence on the alkyl chain length. It was found that, in agreement with the presented experimental data, the effect of the alkyl chain elongation of the substituted alkanes by two methylene units correlates with the decrease of the subphase temperature (ΔT) by 10-20 K. The general shape of the obtained dependencies indicates that the difference in the ΔT values for the amphiphilic molecules decreases with increasing alkyl chain length. This implies that the contribution of the intermolecular CH···HC interactions between the alkyl chains of monolayer molecules should be a decisive factor.

The complementary drop and bubble profile analysis and maximum bubble pressure tensiometry are used to measure the dynamic surface tension of aqueous SDS solutions in the presence of hardness salts (CaCl(2) and MgCl(2) in the ratio of 2:1 at concentrations of 6 and 40FH). The presence of hardness salts results in an essential increase of the SDS adsorption activity, which indicates the formation of Ca(DS)(2) and Mg(DS)(2) in the SDS solutions. The surface tension isotherms of SDS in presence of Ca(DS)(2) and Mg(DS)(2) are described using the generalised Frumkin model. The presence of hardness salts accelerates the ageing of SDS solutions as compared with the addition of 0.01 M NaCl due to a faster hydrolysis and hence formation of dodecanol. These results are used to estimate the possible concentration of dodecanol in the studied SDS solutions. The buoyant bubble profile method with harmonic surface oscillations is used to measure the dilational rheology of SDS solutions in presence of hardness salts in the frequency range between 0.005 Hz and 0.2 Hz. The visco-elasticity modulus in the presence of hardness salts is higher as compared with its values in the presence of 0.01 M NaCl additions. The ageing of SDS solutions leads to an essential increase of the visco-elastic modulus., (Copyright © 2012 Elsevier Inc. All rights reserved.)

In the frameworks of the quantum-chemical semiempirical PM3 method, the thermodynamic parameters of trans-isomers of unsaturated carboxylic acids at the air/water interface were studied. Systems with 18-26 carbon atoms in the alkyl chain and different positions of the double bond are considered. Using quantum-chemical semiempirical PM3 method enthalpy, Gibbs' energy of monomers' formation from the elementary compounds and absolute entropy of trans-unsaturated carboxylic acids are calculated. It has been shown that thermodynamic parameters mentioned above for isomers with the same number of carbon atoms in the hydrocarbon chain but different position of double bond are practically the same within the margin of error. For dimers, trimers, and tetramers of the four trans-unsaturated carboxylic acids, the thermodynamic parameters of clusterization were calculated. It is shown that the position of double bond does not significantly affect the values of thermodynamic parameters of formation and clusterization of carboxylic acids with equal alkyl chain lengths. The only exception is the case that the double bond is in the ω-position (extremely distanced from the carboxylic group). In this case, the number of intermolecular interactions between alkyl chains is changed. Spontaneous clusterization of trans- in the standard conditions is possible for molecules that possess more than 16-17 carbon atoms in the alkyl chain. These threshold values exceed the corresponding values that were calculated previously using the quantum-chemical PM3 method for saturated carboxylic acids (12-13 carbon atoms in the alkyl chain) and are a little bit smaller than the corresponding parameters for cis-unsaturated carboxylic acids (18-19 carbon atoms). These values agree with experimental parameters. Also, the calculated structural parameters of trans-unsaturated carboxylic acids' monolayer for the unit cell with a = 6.98 Å, b = 8.30 Å, and for the molecular tilt angle with 64.95° agree with the experimental parameters., (© 2012 American Chemical Society)

The applicability of the superposition-additive approach for the calculation of the thermodynamic parameters of formation and atomization of conjugate systems, their dipole electric polarisabilities, molecular diamagnetic susceptibilities, π-electron circular currents, as well as for the estimation of the thermodynamic parameters of substituted alkanes, was demonstrated earlier. Now the applicability of the superposition-additive approach for the description of clusterization of fatty alcohols, thioalcohols, amines, carboxylic acids at the air/water interface is studied. Two superposition-additive schemes are used that ensure the maximum superimposition of the graphs of the considered molecular structures including the intermolecular CH-HC interactions within the clusters. The thermodynamic parameters of clusterization are calculated for dimers, trimers and tetramers. The calculations are based on the values of enthalpy, entropy and Gibbs' energy of clusterization calculated earlier using the semiempirical quantum chemical PM3 method. It is shown that the proposed approach is capable of the reproduction with sufficiently enough accuracy of the values calculated previously.

The quantum-chemical semiempiric PM3 method is used to calculate the thermodynamic parameters of clusterization for the racemic α-amino acids C(n)H(2n+1)CHNH(2)COOH with n=5-15 at 278 and 298 K. Possible relative orientations of the monomers in the heterochiral clusters are considered. It is shown that, for the racemic mixtures of α-amino acids, the formation of heterochiral 2D films is most energetically preferable with the alternating (rather than "checkered") packing of the enantiomers with opposite specific rotation. The two enantiomeric forms of α-amino acids in the heterochiral 2D clusters are tilted with respect to the normal to the q direction at angles of φ(1)=20° and φ(2) = 33°, whereas the single enantiomeric forms are oriented at an angle of δ=9° with respect to the normal to the p direction. It is shown that the heterochiral 2D film based on the α-amino acid structures oriented at the angle φ(2)=33° with respect to the normal to the q direction possesses a rectangular unit cell with the geometric parameters a = 4.62 Å and b = 10.70 Å and the tilt angle of the alkyl chain of the molecule with respect to the interface t(2)=35°, which is in good agreement with the X-ray structural data a=4.80 Å, b=9.67 Å, and t(2)=37°. The parameters of the lattice structure of monolayers formed by amphiphilic amino acids are shown to be determined by the "a" type of the intermolecular H-H interactions, whereas the tilt angle of the molecules with respect to the interface depends on the volume and the structure of the functional groups involved in the hydrophilic part of the molecule. Spontaneous clusterization of the racemic form of α-amino acids at the air/water interface at 278 K takes place if the alkyl chain length is equal or higher than 12-13 carbon atoms, whereas for 298 K this clusterization threshold corresponds to 14 carbon atoms in the hydrocarbon chain. These values agree with the experimental data., (© 2011 American Chemical Society)

Interfacial tension measurements have been performed at the water/hexane interface on mixtures of the bovine milk protein β-lactoglobulin and positively charged cationic surfactants (alkytrimethylammonium bromides). The addition of surfactants with different chain lengths leads to the formation of protein-surfactant complexes with different adsorption properties as compared to those of the single protein. In this study, the formation of complexes has been observed clearly for protein-long chain surfactant (TTAB and CTAB) mixtures, which has shown in addition to specific electrostatic interactions the relevance of hydrophobic interactions between surfactant molecules and the protein. The modeling of interfacial tension data by using a mixed adsorption model provides a quantitative understanding of the mixture behavior. Indeed, the value of the adsorption constant of the protein obtained in the presence of surfactants has strongly varied as compared to the single protein. Actually, this parameter which represents the affinity of the molecule for the interface is representative of the hydrophobic character of the compound and so of its surface activity. Even if a more hydrophobic and more surface active protein-surfactant complex has been formed, the replacement of this complex from the interface by surfactants close to their cmc was observed.

Even though sodium dodecyl sulphate (SDS) is the most frequently studied surfactant, its properties at liquid interfaces are not easily accessible. This is mainly caused by the fact that in aqueous solution SDS is subject to hydrolysis, by which the homologous dodecanol (C12OH) is formed. Due to its enormously high surface activity it competes with SDS at the interface. We demonstrate here that this "natural" impurity C12OH does not remarkably affect the adsorption dynamics of SDS at the water/hexane interface, due to its high solubility in hexane. Therefore, the dynamic adsorption properties can be determined independent of disturbing dodecanol effects. The surfactant adsorbs diffusion controlled and the interfacial tension isotherm at the water/hexane interface is well described by a Frumkin model. However complementary experiments via direct admixture of dodecanol in hexane indicate a significant decrease in interfacial tension of the water-hexane interface at concentrations higher than 10(-3) mol/l in hexane. This condition may happen when the oil phase is distributed as small droplets in a high concentrated solution of SDS. The distribution coefficient of C12OH between water and hexane is estimated from adsorption experiments to be K(p)=c(o)/c(w)=6.7×10(3)., (Copyright © 2010 Elsevier Inc. All rights reserved.)

Understanding the effects of digestion conditions on the structure of interfacial protein networks is important in order to rationally design food emulsions which can moderate lipid digestion. This study compares the effect of gastric conditions (pH, temperature, and ionic strength) on β-lactoglobulin films at different fluid interfaces: air-water, tetradecane-water, and olive oil-water. The experiments have been designed to simulate the passage into the stomach media. Hence, preformed interfacial protein (β-lactoglobulin) networks have been exposed to gastric conditions in order to establish generic aspects of the digestion process. The results show that the presence of an oil phase affects both the unfolding of the protein at the interface on adsorption and the subsequent interprotein associations responsible for network formation at the interface. Furthermore, the effects of the physiological conditions characteristic of the stomach also altered differently the preformed protein layer at different fluid interfaces. Initially, the effects of temperature, acid pH, and ionic strength on the dilatational modulus of β-lactoglobulin adsorbed layers at tetradecane-water and olive oil-water interfaces were studied in isolation. The presence of salt was found to have a major effect on the dilatational response at the oil-water interface in contrast to the observations at the air-water interface: it enhanced intermolecular association, hence increasing the packing at the interface causing it to become more elastic. Exposure to acid pH (2.5) also increased the elasticity of the interface, possibly due to the fact that strong electrostatic interactions acting at the interface compensated for the reduced level of intermolecular association. However, the increase in dilatational modulus at the oil-water interface was less noticeable upon exposure to combined changes in acid pH and ionic strength, as would occur in the stomach. This is consistent with previously reported observations at the air-water interface. The quantitative differences in the response of the protein networks to gastric media at different fluid interfaces are discussed in terms of the conformation of β-lactoglobulin within the networks formed at each interface based on detailed theoretical modeling of adsorption data.

In the presented work, bubble profile analysis tensiometry is used to study the equilibrium surface tensions and the rheological behavior of solutions of mixed oxyethylated alcohols (C(12)EO(5)/C(14)EO(8)) and their mixtures with polyethylene glycol octylphenyl ethers (Triton X45/Triton X165). For the analysis of the experimental data, a new theoretical model for mixtures of two nonionic oxyethylated surfactants was employed which assumes two states of surfactant molecules with different molar areas in the surface layer and an intrinsic compressibility of the molecules in the state of closest packing. The theoretical models allow an accurate description of the experimental equilibrium surface tensions for all studied mixed solutions. For the analysis of the rheological behavior of the studied mixed surfactant solutions, the theory for a diffusional adsorption mechanism was applied, and a satisfactory agreement between the experimental data and the calculated viscoelasticity modulus and phase angle was achieved.

Recent work has provided experimental and theoretical evidence that a first order fluid/condensed (LE/LC) phase transition can occur in adsorbed monolayers of amphiphiles and surfactants which are dissolved in aqueous solution. Similar to Langmuir monolayers, also in the case of adsorbed monolayers, the existence of a G/LE phase transition, as assumed by several authors, is a matter of question. Representative studies, at first performed with a tailored amphiphile and later with numerous other amphiphiles, also with n-dodecanol, provide insight into the main characteristics of the adsorbed monolayer during the adsorption kinetics. The general conditions necessary for the formation of a two-phase coexistence in adsorbed monolayers can be optimally studied using dynamic surface pressure measurements, Brewster angle microscopy (BAM) and synchrotron X-ray diffraction at grazing incidence (GIXD). A characteristic break point in the time dependence of the adsorption kinetics curves indicates the phase transition which is largely affected by the concentration of the amphiphile in the aqueous solution and on the temperature. Formation and growth of condensed phase domains after the phase transition point are visualised by BAM. As demonstrated by a tailored amphiphile, various types of morphological textures of the condensed phase can occur in different temperature regions. Lattice structure and tilt angle of the alkyl chains in the condensed phase of the adsorbed monolayer are determined using GIXD. The main growth directions of the condensed phase textures are correlated with the two-dimensional lattice structure. The results, obtained for the characteristics of the condensed phase after a first order main transition, are supported by experimental bridging to the Langmuir monolayers. Phase transition of adsorbing trace impurities in model surfactants can strongly affect the characteristics of the main component. Dodecanol present as minor component in aqueous sodium dodecylsulfate solution dominate largely the fundamental features of the adsorbed monolayer of the mixed dodecanol/SDS solutions at adsorption equilibrium. A theoretical concept on the basis of the quasi-chemical model and assumption of the entropy non-ideality has been developed which can well describe the experimental results of the diffusion kinetics of surfactant adsorption from solutions. The model regards the phase behaviour of adsorbed monolayers on the basis of the experimental results explicitly supported by the first order fluid/condensed phase transition and theoretical models assuming bimodal distribution between large aggregates (domains) and monomers and/or very small aggregates. Another simple theoretical model for the description of the coadsorption of surfactant mixtures, based on the additivity of the contributions brought by the solution components into the surface pressure is shown to be in qualitative agreement with the experimental data of mixed dodecanol/SDS solutions. The theoretical results corroborate the fact that the formed condensed phase (large aggregates) in the mixed monolayer consists mainly of dodecanol., (Copyright 2010 Elsevier B.V. All rights reserved.)

The dynamic surface tensions of mixed SDS/C(12)EO(5) and SDS/C(14)EO(8) micellar solutions measured over a wide time range (0.1 ms to 10,000 s) at various mixing ratios are described satisfactorily by a theoretical model for the kinetics of adsorption of surfactant mixtures using the surfactant adsorption parameters obtained for premicellar mixed solutions. Additional relations used for the description of the adsorption kinetics from micellar solutions were expressions of the effective diffusion coefficient of monomers accounting for the disintegration of micelles. The modeled dynamic surface tensions agree well with the experimental data for all studied surfactant mixtures. The rheological behavior of the same mixtures--the dependencies of the viscoelasticity modulus and phase angle--were studied by using the bubble profile method at harmonic bubble surface area oscillations. The theoretical approach employed for data analysis was the same as for the dynamic surface tension behavior. Again, satisfactory agreement between the experimental data and theoretical calculations of the dilational rheological parameters was found.

Bubble profile analysis tensiometry is used to study the surface rheological behavior of mixed SDS/C(12)EO(5) and SDS/C(14)EO(8) solutions. The experimental dependencies of the viscoelasticity modulus and phase angle are studied in a wide range of surfactant concentrations of the individual sodium dodecyl sulfate (SDS) and C(m)EO(n) solutions and SDS/C(n)EO(m) mixtures at various mixing ratios. By generating harmonic oscillations of the bubble area at low oscillation amplitudes, the relaxation behavior at oscillation frequencies between 0.005 and 0.2 Hz was studied. The applied theoretical approach to describe the dilational rheology of surfactant mixtures requires the specification of the equations of state of the mixed surface layer and the adsorption isotherm of the mixture's components. For the systems studied, the theoretical model considers different adsorption mechanisms for the different surfactants. In particular, the adsorption behavior of oxyethylated surfactants was described by the reorientation model (assumes two adsorption states of surfactant molecules with different molar areas), including an intrinsic compressibility of molecules in the state of minimal area. For the SDS component, the adsorption was assumed to be governed by the Frumkin model, which also accounts for the intrinsic compressibility. Satisfactory agreement between experimental data and theoretical calculations of the viscoelasticity modulus and the phase angle is obtained.

Bubble profile analysis tensiometry is used to study the dynamic and equilibrium surface tensions of mixed sodium dodecyl sulfate (SDS)/C(12)EO(5) and SDS/C(14)EO(8) solutions. For the data analysis, a new theoretical model was employed, which assumes different adsorption mechanisms for each type of surfactants. In particular, the adsorption behavior of oxyethylated surfactants was described by the so-called reorientation model, which assumes two states of surfactant molecules with different molar areas in the surface layer, and additionally an intrinsic compressibility of the adsorbed layer. For the anionic surfactant SDS, a modified Frumkin adsorption model was assumed, which also accounts for the intrinsic compressibility. For the theoretical analysis of the dynamic surface tensions, the theoretical model was based on the numerical solution of Fick's diffusion equation for a spherical geometry of the bubble. The proposed set of theoretical models describes accurately and consistently the experimental results of the equilibrium and dynamic surface tensions of the studied mixed solutions.