Dynamic surface tension of micellar solutions studied by the maximum bubble pressure method

A theoretical model for the dynamic surface tension of an air bubble expanding in micellar surfactant solution is proposed. The model accounts for the effect of expansion of the bubble surface during the adsorption of surfactant molecules (monomers) and the effect of disintegration of polydisperse micelles on the surfactant diffusion. Assuming small deviations from equilibrium and constant rate of expansion analytical expression for the surface tension and the subsurface concentration of monomers as a function of time is derived. The characteristic time of micellization is computed from the experimental data for two surfactants (sodium dodecyl sulfate and nonylphenol polyglycol ether) obtained by the maximum bubble pressure method.     

Dynamic surface tension of micellar solutions studied by the maximum bubble pressure method

A theoretical model for the dynamic surface tension of an air bubble expanding in surfactant solution is proposed. The model accounts for the effect of convection on the surfactant diffusion and the effect of expansion of the bubble surface during the adsorption of surfactant molecules. Assuming small deviation from equilibrium and constant rate of expansion, an analytical solution for the surface tension and the subsurface concentration as a function of time is derived. The parameters of the model are computed from experimental data for sodium dodecyl sulfate obtained by the maximum bubble pressure method.     

The measurement of dynamic surface tension by the maximum bubble pressure method

The principle of maximum pressure in a bubble for measurements of dynamic surface tension is realized in a fully automatically operating apparatus. The set-up yields data in the time interval from 1 ms up to several seconds and can be temperature controlled from 5° to 80°C. Experimental data obtained for different surfactants and gelatine in water and/or water/glycerine mixtures at different temperatures are discussed. A direct comparison with results from oscillating jet and inclined plate experiments shows excellent agreement.     

Adsorption kinetics at air/solution interface studied by maximum bubble pressure method

A general dynamic surface adsorption equation (t) for maximum bubble pressure method was derived by solving Ficks diffusion equation for the bubbles under different initial and boundary conditions. Different from the planar surface adsorption(Ward-Tordai equation), the derived dynamic surface adsorption (t) for the short time consists of two terms, one of them reflects the geometric effect caused by the spherical bubble surface. This kind of effect was discussed.The equilibrium surface tension _eq and the dynamic surface tension (t) of aqueous C₁₀E₈ (CH₃(CH₂)₉(OCH₂CH₂)₈OH) solution at temperature 25 °C were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. In the region of t0 (short time limits) a good agreement of experimental results with the theory was reached and the adsorption was controlled by diffusion. However, for the long time limits, a mixed diffusion-kinetics controlled process was proved.     

Dynamic surface tension measurements of surfactant solutions using the maximum bubble pressure method – limits of applicability

One of the essential differences in the design of bubble pressure tensiometers consists in the geometry of the measuring capillaries. To reach extremely short adsorption times of milliseconds and below, the so-called deadtime of the capillaries must be of the order of some 10 ms. In particular, for concentrated surfactant solutions, such as micellar solutions, short deadtimes are needed to minimize the initial surfactant load of the generated bubbles. A theoretical model is derived and confirmed by experiments performed for a wide range of experimental conditions, mainly in respect to variations in deadtime and bubble volume.     

Dynamic surface tensions of micellar Triton X-100 solutions

Considering surfactant solutions at concentrations exceeding the CMC, another relaxation process besides diffusion occurs, also affecting the dynamic surface tension. The latter equilibration process concerns a micellisation/demicellisation process, representing the disintegration of micelles into monomers. The micellisation kinetics are accounted for by adding a single source term to the diffusion equation of the free monomers.

In the present paper the integration of the diffusion equation is avoided by using the concept of the diffusion penetration depth. Nevertheless, when this approximation is made, good agreement is achieved between experiment and theory for micellar Triton X-100 solutions. Moreover, it follows that diffusion of micelles may not be neglected.     

Mass transport in micellar surfactant solutions: 2. Theoretical modeling of adsorption at a quiescent interface

Here, we apply the detailed theoretical model of micellar kinetics from part 1 of this study to the case of surfactant adsorption at a quiescent interface, i.e., to the relaxation of surface tension and adsorption after a small initial perturbation. Our goal is to understand why for some surfactant solutions the surface tension relaxes as inverse-square-root of time, 1/t(1/2), but two different expressions for the characteristic relaxation time are applicable to different cases. In addition, our aim is to clarify why for other surfactant solutions the surface tension relaxes exponentially. For this goal, we carried out a computer modeling of the adsorption process, based on the general system of equations derived in part 1. This analysis reveals the existence of four different consecutive relaxation regimes (stages) for a given micellar solution: two exponential regimes and two inverse-square-root regimes, following one after another in alternating order. Experimentally, depending on the specific surfactant and method, one usually registers only one of these regimes. Therefore, to interpret properly the data, one has to identify which of these four kinetic regimes is observed in the given experiment. Our numerical results for the relaxation of the surface tension, micelle concentration and aggregation number are presented in the form of kinetic diagrams, which reveal the stages of the relaxation process. At low micelle concentrations, "rudimentary" kinetic diagrams could be observed, which are characterized by merging of some stages. Thus, the theoretical modeling reveals a general and physically rich picture of the adsorption process. To facilitate the interpretation of experimental data, we have derived convenient theoretical expressions for the time dependence of surface tension and adsorption in each of the four regimes.     

Dynamic Behavior of Surfactants in Solution

Adsorption of various surfactants at the gas liquid interface is studied with equilibrium and dynamic surface tension measurements. The Wilhelmey plate method and maximum bubble pressure method are used for this study. Dynamic surface tension of solutions of different surfactants, sodium lauryl sulfate (SLS), polyoxyethylene glycol 4‐tert‐octyl phenyl ether (Triton X 100), poly‐oxyethylene(20) cetyl ether (Brij 58), and tetraethylene glycol mono‐n‐dodecyl ether (Brij 30), is measured at different concentrations. Adsorption of different surfactants is compared on the basis of equilibrium and dynamic behavior. Effectiveness and efficiency of different surfactants is found from equilibrium surface tension measurement. A new parameter is defined to quantify the dynamic behavior of adsorption, which gives the concentration of surfactant needed to reduce surface tension to half of its maximum reduction within a defined time available for adsorption. The dynamics of surfactant solution is quantified by using this parameter.     

聚二甲基二烯丙基氯化铵及其与CTAB混合物水溶液 的吸附动力学

用最大泡压法分别测定了聚二甲基二烯丙基氯化铵,十六烷基三甲基溴化铵以及两者混合物水溶液的动表面张力。十六烷基三甲基溴化铵的吸附服从扩散-动力学控制机理。发现聚二甲基二烯丙基氯化铵水溶液的表面张力具有独特的时间相关性。吸附的前期服从扩散控制机理,而在吸附的后期,即接近吸附平衡时服从扩散-动力学控制机理。混合物水溶液的整个吸附过程受扩散控制。     

Dynamic surface tension behavior of aqueous solutions ofN-dodecyl-N,N dimethyl aminobetaine chlorohydrate

The adsorption behavior ofN-dodecyl-N,N dimethyl aminobetaine chlorohydrate (DDAB·HCl) at the air/aqueous interface was studied for solutions in pure water and phosphate buffer (pH=7.4). The equilibrium surface tension versus concentration curves were used to estimate the equilibrium adsorption parameters and CMCs. The buffer solution has a lower CMC and shows higher surface activity below the CMC than the pure water solution. Data and calculations of the dynamic tension behavior at constant-area conditions showed that the adsorption processes of DDAB·HCl solutions are about 10 to 300 times slower than those predicted by a diffusion-controlled model. A mixed kinetics adsorption model with a modified Langmuir-Hinshelwood kinetic equation, which considers an activation energy barrier for adsorption, was applied to find the kinetic adsorption parameters. The dynamic tension behavior at pulsating-area conditions with large amplitude was also examined for frequencies up to 90 cycles/min. The tension amplitude responses depended strongly on the concentration and frequency. Comparisons of diffusion-controlled model predictions and pulsating area tension data confirmed the need to use a mixed kinetics model. The latter model can improve the fit over the diffusion-controlled model, but it does not quantitatively match the observed tensions.     

Studies on Dynamic Surface Tension of an Outstanding Microemulsifier in Supercritical CO2 and Its Wetting Performance

Dodecyl polyoxyethylene(4) polyoxypropylene(5) ether (LS45) is an outstanding microemulsifier in supercritical CO₂. The dynamic surface tension (DST) of this nonionic surfactant was investigated by using the maximum bubble pressure instrument. The effects of concentration and temperature on DST parameters (n, t_i, t*, t_m, and R_1/2) and its adsorption mechanism were discussed by Rosen's empirical equation and the asymptotic Ward and Tordai equation for the LS45 solution system. Finally, the parameters at 1 s related to Draves's wetting performance, pC_20(1s), C_1s (i)*, and C_1s*, analyzed. The results showed that were with increase of bulk concentration and temperature, dynamic surface activity increased. Parameters at 1 s indicated that LS45 is of high surface activity and a very good wetting agent. One‐second related parameters, C_1s (i)* and C_1s*, are valuable in the treatment of practical applications of surfactants. Optimum wetting can be expected at the concentration of 4.8×10^?4 mol/dm³ for LS45 solution.     

Capillary constant and surface tension of methane-nitrogen solutions: 1. Experiment

The differential version of the method of capillary rise has been used to measure the capillary constant and calculate the surface tension of methane-nitrogen solutions. Experiments have been conducted in the temperature range from 95 to 170 K at pressures up to 4 MPa. Experimental data on surface tension have been compared with the results of calculations by thermodynamic models. Equations are given which describe the dependence of the capillary constant of a solution on its temperature and composition.     

On the determination of dynamic surface tensions by means of a modified bubble pressure method

A method for the determination of the dynamic surface tension of surfactant solutions is presented which allows to cover adsorption times down to 10 seconds. This method is based on the determination of the pressure inside two communicating bubbles. There is no deformation of the solution/air interface during the experimental procedure. Hence, in evaluating the kinetic data no surface area enlargement has to be taken into account. An automatically operating procedure should allow to cover adsorption times down to approximately one second and should improve the measuring accuracy substantially. Experimental investigations with aqueous n-decanoic acid solutions using the method proposed provided evidence that decanoic acid is adsorbed by a diffusioncontrolled mechanism.     

Determination of the surface tension of surfactant solutions applying the method of Lecomte du Noüy (ring tensiometer)

Summary Starting from a comparative assessment of the outstanding works on the ring method (du Noüy) for the determination of the surface tension of liquids and its solutions it is shown that the application of this method to surfactant solutions can lead to substantial errors if one follows conventional conditions. These errors are mainly connected with so far unknown phenomena occurring during the raising of the ring and concerning the influence of the hydrophilic vessel wall above the solution level and the stretching of the solution surface. This is demonstrated quantitatively with surfactant solutions of different kind and concentration. These effects can be explained theoretically very simply by introducing certain assumptions on the behaviour of a surfactant adsorption layer on the inner vessel wall. Conditions leading to the elimination of these errors are given, thus enabling the application of the ring method to the determination of the surface tension of surfactant solutions.With 10 figures and 3 tables     

Kinetics of the surface tension of micellar solutions: Comparison of different experimental techniques

The kinetics of the surface tension of micellar solutions of nonionic surfactant Triton X-100 is measured experimentally by means of three different techniques: oscillating jet, maximum bubble pressure and inclined plate. They allow to study the micellization kinetics at various time scales (from a few milliseconds to a few seconds) in fairly large concentration region up to 50 times CMC. The experimental data are satisfactorily explained by a theoretical model accounting for the kinetics of micellization, diffusion of surfactant species and expansion of the bubble interface. By this model are computed the characteristic times of diffusion and micellization, which are of comparable magnitude (about 5 to 200 ms), and the Gibbs' elasticity. The micellization time constant corresponds to the slow relaxation process known to coincide with the disintegration of micelles. Comparing our data with other data from literature one can conclude that more realistic information for the micellization kinetics is obtained by the maximum bubble pressure and the oscillating jet method. The inclined plate seems too slow to measure the relaxation processes in micellar solutions of this surfactant.     

Adsorption kinetics of surfactant mixtures from micellar solutions as studied by maximum bubble pressure technique

The adsorption kinetics of micellar solutions of anionic/cationic SDS/DATB mixtures with mixing ratios of 10/1 and 10/2, respectively, are studied experimentally by means of the maximum bubble pressure method. For long adsorption times the adsorption of the highly surface-active anionic/cationic complex leads to a decrease of dynamic surface tension in comparison to the single SDS system. However, the situation is the reverse for short adsorption times where the dynamic surface tension is increased by addition of the cationic surfactant, although the overall concentration is increased. This unexpected behavior is explained by partial solubilization of free SDS molecules into micelles formed by SDS/DTAB complexes. With increasing overall concentration, when eventually the CMC of SDS is reached, the anionic/cationic complex itself is solubilized by SDS micelles. Finally, no complex micelles, which for their part can solubilize an excess of SDS molecules, are present. Hence, the dynamic properties of the solution are no longer influenced by the depletion of SDS molecules and the mixture tends to behave like a pure SDS solution.     

最大泡压法研究C12-2-Ex-C12•2Br在气/液表面的吸附动力学

用最大泡压法考察季铵盐Gemini表面活性剂C₁₂-2-E_x-C₁₂?2Br (x＝1, 2, 3)在气/液表面吸附动力学行为, 研究表明增加表面活性剂体相浓度和温度将加快分子扩散速度, 因此提高了表面吸附的动力学效果. 增加联接链长度x减小了分子预聚集倾向, 溶液中的单分子浓度增加, 有利于初始扩散, 使γ_t降低. 接近饱和吸附时, 由于x较大的单元分子在表面层占据的截面积也较大, 降低了表面层甲基端基的覆盖度, 相对升高了介平衡表面张力. 与对应的同头基同碳原子数的十二烷基三甲基溴化铵(C₁₂TABr)比较, C₁₂-2-E₁-C₁₂?2Br分子更倾向于吸附在表面层上.     

Method of the Green functions in the kinetics of adsorption from micellar surfactant solutions

The kinetics of adsorption from micellar surfactant solutions is considered theoretically from a uniform point of view. Three boundary value problems for the adsorption on flat and on spherical interface are solved analytically by means of the method of the Green functions. In this way the bulk concentration and the adsorption of surfactant monomers are expressed as functions of time. The contribution of the micelles (surfactant aggregates) to the diffusion of the monomers is accounted for as pseudo-first order reaction. The adsorption from surfactant solutions without micelles turns out to be the particular case of the problems considered here. Being general in form, the derived equations can be applied also to other practical problems in heterogeneous chemical kinetics, adsorption of gases, heat transfer, etc.     

An application of the modified Poisson- Boltzmann equation in studies of osmotic properties of micellar solutions

The spherical cell model of colloidal solutions is applied in calculations of the osmotic pressure of micellar systems. The predictions of the nonlinear Poisson-Boltzmann equation (MPB) and of the Modified Poisson-Boltzmann equation (MPB) containing the leading terms of the fluctuation potential and the exclusion volume corrections to the mean potential acting on simple ions are compared with the results of recent computer simulations. Both PB and MPB seem satisfactory for solutions with monovalent counterions while the MPB is preferable for studies of the solutions containing divalent countenons.On leave from the University of Ljubljana, Ljubljana, Yugoslavia