A Nonlinear Rupture Theory of Thin Liquid Films with Soluble Surfactant

The effects of soluble surfactant on the dynamic rupture of thin liquid films are investigated. A nonlinear coupling evolution equation is used to simulate the motion of thin liquid films on free surfaces. A generalized Frumkin model is adopted to simulate the adsorption/desorption kinetics of the soluble surfactant between the surface and the bulk phases. Numerical simulation results show that the liquid film system with soluble surfactant is more unstable than that with insoluble surfactant. Moreover, a generalized Frumkin model is substituted for the Langmuir model to predict the instability of liquid film with soluble surfactant. A numerical calculation using the generalized Frumkin model shows that the surfactant solubility increases as the values of parameters of absorption/desorption rate constant (J), activation energy desorption (nu(d)), and bulk diffusion constant (D(1)) increase, which consequently causes the film system to become unstable. The surfactant solubility decreases as the rate of equilibrium (lambda) and interaction among molecules (K) are increased, which therefore stabilizes the film system. On the other hand, an increase of relative surface concentration (the index of a power law), beta(n), will initially result in a decrease of corresponding shear drag force as beta and n increase from 0 to 0.3 and 0.85, respectively. This will enhance the Marangoni effect. However, a further increase of beta and n to greater than 0.3 and 0.85, respectively, will conversely result in an increase of the corresponding shear drag force. This will weaken the Marangoni effect and thus result in a reduction of interfacial stability. Copyright 2000 Academic Press.     

Effect of interactions between the adsorbed species on the properties of single and mixed-surfactant monolayers at the air/water interface

Experimental data on surface tension available from the literature and generated in the present study are analyzed to estimate the applicability of adsorption models, based on the Frumkin equation, to nonionic and ionic surfactants and their mixtures. Optimization programs based on the least-squares method in media of Delphi V and Pascal VII are used. The effect of interactions between the adsorbed species on surface tension is considered in all cases. The results are compared to those obtained with the simpler Szyszkowski equation, employed in numerous studies of nonionic surfactants, when interactions are neglected. Cases where the Frumkin model can be successfully employed with ionic surfactants and mixtures are presented and the conditions of its applicability are analyzed. Related characteristic quantities (maximum adsorption, standard free energy of surfactant adsorption, energy of interaction between adsorbed species, standard free energy of counterion adsorption, degree of coverage by surfactant/counterion associates) are established as a function of: The properties of an adsorption layer from a mixture of nonionic and ionic surface-active species are compared to those of the single surfactants.     

Self-aggregation of cationic surfactants onto oxidized cellulose fibers and coadsorption of organic compounds

In this work, the adsorption of cationic surfactant and organic solutes on oxidized cellulose fibers bearing different amounts of carboxylic moieties was investigated. The increase in the amount of -COOH groups on cellulose fibers by TEMPO oxidation induced a general rise in surfactant adsorption. For all tested conditions, that is, cellulose oxidation level and surfactant alkyl chain length (C12 and C16), adsorption isotherms displayed a typical three-region shape with inversion of the substrate zeta-potential which was interpreted as reflecting surfactant adsorption and aggregation (admicelles and hemimicelles) on cellulose fibers. The addition of organic solutes in surfactant/cellulose systems induced a decrease in surfactant cac on the cellulose surface thus favoring surfactant aggregation and the formation of mixed surfactant/solute assemblies. Adsorption isotherms of organic solutes on cellulose in surfactant/cellulose/solute systems showed that solute adsorption is strictly correlated to (i) the surfactant concentration, solute adsorption increases up to the surfactant cmc, where solute partitioning between the cellulose surface and free micelles causes a drop in adsorption, and to (ii) solute solubility and functional groups. The specific shape of solutes adsorption isotherms at a fixed surfactant concentration was interpreted using a Frumkin adsorption isotherm, thus suggesting that solute uptake on cellulose fibers is a coadsorption and not a partitioning process. Results presented in this study were compared with those obtained in a previous work investigating solute adsorption in anionic surfactant/cationized cellulose systems to better understand the role of surfactant/solute interactions in the coadsorption process.     

Relation between adsorption of some anionic surfactants on barite and solution/air interfaces

The adsorption behaviour of synthesized anionic surfactants with chemical structure RO–Ph–N?N–Ph–X, where R is octyl, dodecyl or cetyl and X is SO₃Na, was analysed. Analysis of the behaviour of the surfactants was made using a modified version of the Frumkin adsorption isotherm. The values of thermodynamic parameters were calculated at the solution/air interface. The relation between adsorption of the surfactants at the solution/air interface and solid/liquid interface was investigated. The surface properties of these synthetic surfactants were studied. The results show that the length of the hydrocarbon chain of these surfactants plays a major role in determining the surface and thermodynamic properties. The results also indicate that there is a good relationship between effectiveness of adsorption of the surfactant and its efficiency as a collector. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple adsorption model for ionic surfactants

In the past, few theoretical attempts have been made to describe quantitatively the adsorption of ionic surfactants at liquid interfaces. Well-known adsorption isotherms due to Frumkin or Hill–de Boer cannot respond to the specific electrostatic and geometric properties of the surfactant molecules. Our approach is based on a combination of the Gouy–Chapman theory with a modified Frumkin isotherm. The modification implies that the system is free to choose an optimal head group area and an optimal arrangement of the surfactant molecules in the interface as a function of bulk concentration. Interaction energies between neighbouring adsorbed surfactant molecules and between surfactant and water molecules are taken into consideration. The minimum of the Gibbs free energy of the system is equivalent to a minimal interfacial tension. Thus, the thermodynamically stable isotherm can be obtained as the lower envelope of the family of σ versus ln c isotherms resulting from different choices of the model parameters, including the area per molecule. According to the Gibbs equation, the Γ versus ln c adsorption isotherm is obtained as the derivative of this envelope. By variation of the model parameters, the envelope of the calculated adsorption isotherms can be fitted to experimental data of the interfacial tension versus bulk concentration. A computer program is used to calculate the σ versus c and the Γ versus ln c curves as well as to fit the parameters. Received: 28 October 1999/Accepted: 8 February 2000     

The standard free energy of surfactant adsorption at air/water and oil/water interfaces: Theoretical vs. empirical approaches

The standard free energy of surfactant adsorption represents the work of transfer of a surfactant molecule from the bulk of solution to an infinitely diluted adsorption layer. This quantity can be determined by non-linear fits of surface-tension isotherms with the help of a theoretical model of adsorption. Here, the models of Frumkin, van der Waals and Helfand-Frisch-Lebowitz are applied, and the results are compared. Irrespective of the differences between these models, they give close values for the standard free energy. The results from the theoretical approach are compared with those from the most popular empirical approach. The latter gives values of the standard free energy, which are considerably different from the respective true values, with c.a. 10 kJ/mol for nonionic surfactants, and with c.a. 20 kJ/mol for ionic surfactants. These differences are due to contributions from interactions between the molecules in dense adsorption layers. It is concluded that the true values of the standard free energy can be determined with the help of an appropriate theoretical model. For the processed sets of data, the van der Waals model gives the best results, especially for the determination of the standard adsorption enthalpy and entropy from the temperature dependence of surface tension. The results can be useful for the development of a unified approach to the thermodynamic characterization of surfactants.     

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) "Aggregation model". Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species.     

Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility

The effect of bulk-soluble surfactants on the dynamics of a drop translating through a cylindrical tube under low-Reynolds-number conditions is investigated. Interfacial surfactant adsorption/desorption is modeled according to the Frumkin adsorption framework, and the bulk-insoluble surfactant limit is recovered as the rate of surfactant sorption becomes large compared to that of bulk diffusion. As the equilibrium surface coverage is increased, the mechanism by which drop mobility is reduced changes from uniform retardation at low surface coverage to the formation of a stagnant cap at high surface coverage. For large capillary numbers, the drop does not achieve a steady shape, and eventually it breaks up either through the formation of a penetrating viscous jet of suspending fluid, or by continuous elongation and pinch-off. Surfactants have a destabilizing effect on transient drop shapes by accelerating the formation and development of the penetrating viscous jet that leads to drop breakup. The critical conditions for drop breakup, as well as the mode of breakup, depend on the manner in which the strength of the flow (i.e., the capillary number) is increased.     

Flotation and adsorption investigations of the systemn-dodecanoic acid/mercury at different pH values

The systemn-dodecanoic acid/mercury in 0,1 N KCl solutions has been investigated within pH range 4,0–10,5 in order to characterize the adsorption of surfactant and to determine its influence on the flotation of mercury. Flotation tests have been carried out in a model mercury flotation apparatus developed by Pomianowski and Para. Some characteristic parameters of adsorption (attraction constant of Frumkin isotherm, adsorption coefficient at maximum adsorption potential, free standard adsorption enthalpy and area per molecule) have been determined by a. c. polarographic capacity-potential and capacity-time curves. Flotation recovery as well as attraction constant, adsorption coefficient and surface excess reach maximum at pH5,1. It is explained by the assumption of an ion-molecule associate formation.Publ.-No. 810 from Research Institute of Mineral Processing, Academy of Sciences of the German Democratic Republic, Freiberg     

Model description of specific adsorption of two anions on electrodes

Simultaneous specific adsorption of two anions on the electrode surface is considered. Calculations involve the use of the Frumkin adsorption isotherm for each anion and a model that describes the electric double layer structure based on one or two Helmholtz planes. Dependences of the ion adsorption on both the electrode potential and the solution composition are calculated for different electrode charges, ion sizes, and capacitance characteristics of the electric double layer.     

Counterion Nature and Alkylammonium Halide Adsorption Thermodynamics

Two surfactants were synthesized by reacting hydrogen halides (hydrogen chloride and hydrogen bromide) with 1-dodecylamine. The resultant cationic surfactants, 1-dodecylammonium chloride (DDAC) and 1-dodecylammonium bromide (DDAB), were characterized by NMR spectrometry and FTIR spectroscopy and data related to their adsorption at the fluid liquid/gas interface were obtained employing bubble surface tensiometry, in pure water and in HCl 0.1 M. Data did not fit well to Langmuir isotherm but Frumkin isotherm did adequately describe to process of adsorption. Adsorption isotherms, as well as data related to critical micelle concentration, CMC, indicated that in HCl 0.1 M, the presence of electrolytes and a common ion to DDAC decreased chloride solvation, changing surface packing and adsorption profile for this surfactant.     

Dynamic surface tension of polyelectrolyte/surfactant systems with opposite charges: two states for the surfactant at the interface

The molecular reorientation model of Fainerman et al. is conceptually adapted to explain the dynamic surface tension behavior in polyelectrolyte/surfactant systems with opposite charges. The equilibrium surface tension curves and the adsorption dynamics may be explained by assuming that there are two different states for surfactant molecules at the interface. One of these states corresponds to the adsorption of the surfactant as monomers, and the other to the formation of a mixed complex at the surface. The model also explains the plateaus that appear in the dynamic surface tension curves and gives a picture of the adsorption process.     

Adsorption of ionic surfactants

Two adsorption models for ionic surfactants based on the Frumkin equation are examined to describe the measured surface tension isotherms of a series of alkali dodecylsulphates. In the model A the number of optimization parameters is reduced by additional modeling. The adsorption of counter-ions in the Stern layer is described via forming of ionic bonds, which free energy is significantly higher than that obtained by the model B. Concurrently the lateral interactions on the water/air interface are also found to be orders of magnitude stronger. Thus, the values of the adsorption parameters are more realistic, which supports the model A as a more relevant one.     

Surfactant effects on thermocapillary interactions of deformable drops

A three-dimensional boundary-integral algorithm is used to study thermocapillary interactions of two deformable drops in the presence of bulk-insoluble, non-ionic surfactant. The primary effect of deformation is to slow down the rate of film drainage between drops in close approach and prevent coalescence in the absence of van der Waals forces. Both linear and non-linear models are used to describe the relationship between interfacial tension and surfactant surface concentration. In the linear model, non-monotonic behavior of the minimum separation between the drops as a function of the surface Peclet number Pe(s) is observed for equal drop and external medium viscosities and thermal conductivities. For bubbles with zero drop-to-medium viscosity and thermal conductivity ratios, however, the minimum separation increases with Pe(s). There is a nearly linear relationship between the minimum drop separation and elasticity E. In the simplest non-linear equation of state, the product of the temperature and the surfactant concentration is retained by allowing non-zero values of the dimensionless gas constant Lambda. For Lambda=O(0.05), it is possible for the smaller drop to move faster than the larger drop. In the Langmuir adsorption framework, the tendency of the smaller drop to catch up to the larger one decreases as the ratio of the equilibrium to maximum surfactant surface concentration increases. Finally, in the Frumkin model, a minimum in the drop separation occurs as a function of the interaction parameter lambda(F) for trajectories with all other parameters held constant.     

Adsorption behavior of surface-chemically pure N-alkyl-N-(2-hydroxyethyl)aldonamides at the air/water interface

N-alkyl-N-(2-hydroxyethyl)aldonamides (alkyl: n-C6H13, n-C8H17, n-C10H21, n-C12H25, and n-C14H29) were obtained in the reaction of long-chain N-alkyl-N-(2-hydroxyethyl)amines with D-glucono-1,5-lactone and D-glucoheptono-1,4-lactone. The adsorption isotherms were obtained from surface tension measurements of aqueous solutions of surface-chemically pure surfactants. The experimental equilibrium surface tension versus concentration isotherms were evaluated by the Frumkin adsorption equation to get the adsorption parameters, namely, standard free energy of adsorption, deltaG(o)ad, saturation adsorption, gammainfinity minimum surface area demand per molecule adsorbed, Amin, and interaction parameter, Hs. The investigated functionalized alkylaldonamides show improved solubility in comparison with the corresponding sugar derivatives of the primary amines. The introduction of the -CHOH moiety into the saccharide headgroup causes a noticeable increase of the hydrophobic character of surfactant. The minimum surface area demand, Amin, is slightly greater for glucoheptonamides than for the corresponding gluconamides. The practically constant Amin value within the homologue series of the aldonamides indicates that the obtuse hydroxyethyl residue is the determining factor for the arrangement of the adsorbed surfactants in the interfacial layer.     

Effect of Potential on Coadsorption of Two Organic Substances in the Frumkin Model at a Maximum Possible Number of Solutions for the Relevant Set of Isotherms

Effect of the electrode potential on the coadsorption of two organic substances is studied using a set of two mixed Frumkin isotherms and a model of three parallel capacitors in conditions where in the absence of an electric field this system has seven solutions. It is shown that only four of these solutions may correspond to realizable adsorption states. Effect of the electrode potential on the number of possible solutions of the isotherm set, the number of realizable adsorption states, as well as on the composition and properties of a surface layer is considered.     

Charge dependence of adsorption energy of ions at electrodes

Analysis of the energetic and geometric characteristics of the inner part of the electrical double layer has been carried out in the presence of the specific adsorption of ions accompanied by change in the dimensions and dielectric properties of the inner layer. On the basis of the formulae for the electrochemical potential of the adsorbed ion on the electrode surface and for the components of the inner layer capacity, the equations of the Frumkin isotherm and of its parameters have been derived. It has been shown that, in general, the Frumkin isotherm is non-linear at the given electrode charge and the charge dependence of the adsorption equilibrium constant has a parabolic form. The results of the corresponding theoretical calculations have been compared with the experimental data obtained by the study of the specific adsorption of tetra-alkylammonium cations on a bismuth electrode in ethanolic and aqueous solutions. Good agreement of the experimental results with those calculated theoretically confirm the validity of the equations derived.     

Equilibrium differential capacitance and electrocapillary curves within the framework of a generalized model of the surface layer

Equations that describe the equilibrium differential capacitance C and the interface tension of an electrode subjected to the adsorption of organic molecules under the conditions where this adsorption strictly follows a generalized model of the surface layer are derived. Using the developed programs, the dependences of C on the electrode potential φ are calculated at different concentrations of the organic substance. Based on these C vs. φ curves, a set of effective parameters is obtained. With these parameters, the capacitance curves can best be described by the model of two parallel capacitors combined with the Frumkin isotherm.