Colloids and Surfaces A: Physicochem. Eng. Aspects 419 (2013) 194–200
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Amphiphilic nanostructures in aqueous solutions of triethyleneglycol monododecyl ether Dimi Arabadzhieva, Borislav Soklev, Elena Mileva ∗ Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
h i g h l i g h t s
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a b s t r a c t
In aqueous solutions of C12 E3 premicelles cause onset of two plateaus and one kink of surface tension isotherm. In aqueous solutions of C12 E3 premicelles cause onset of maxima in surface dilational elasticities. In aqueous solutions of C12 E3 premicelles cause onset of unstable black patterns (dots) in foam films.
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Article history: Received 31 August 2012 Received in revised form 11 November 2012 Accepted 24 November 2012 Available online 4 December 2012 Keywords: Adsorption Tensiometry Surface rheology Foam films Self-assembly Triethyleneglycol monododecyl ether
a b s t r a c t The aim of the present study is to relate the surfactant adsorption layer properties at air/solution interface to the drainage parameters of microscopic foam films in the case of aqueous solutions of the non-ionic amphiphile triethyleneglycol monododecyl ether (C12 E3 ). The scope of the research covers adsorption dynamics, construction of equilibrium surface tension isotherm, studies on dilational rheology of the interfacial layers and foam film drainage kinetics. It is established that in the premicellar concentration domain (for surfactant concentrations higher than the range where the Henry’s law is operative but one–two orders of magnitude lower than the conventional CMC-values) there are considerable irregularities of the adsorption layer properties: two plateau regions and a kink are registered in the experimental surface tension isotherm, unusual changes of the surface rheological characteristics. The systematic investigations of the microscopic foam films reveal that the courses of basic kinetic parameters against the amphiphile concentration run in synchrony with the changes in the adsorption layer anomalies. This fact is related to the presence of premicellar surfactant aggregates. The results are juxtaposed to previously obtained characteristics of aqueous solutions of the non-ionic amphiphile tetraethyleneglycol monododecyl ether under similar experimental conditions (Colloids & Surfaces A, 392 (2011) 233–241). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Nonionic surfactants from the group of oligoethylene glycol mono-n-alkyl ethers Cn Em have been a topic of intensive research (e.g. [1]). Most of these compounds are relatively water soluble and biodegradable and they find applications in the production of
∗ Corresponding author at: Institute of Physical Chemistry, Bulgarian Academy of Sciences, “Acad. G. Bonchev” Str., bl.11, Sofia 1113 , Bulgaria. Tel.: +359 2 979 3583/870 0257; fax: +359 2 971 2688. E-mail address:
[email protected] (E. Mileva). 0927-7757/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.colsurfa.2012.11.058
pharmaceuticals, cosmetics, dyes, etc. The key factor in the design and fine-tuning of the surfactant formulations based on Cn Em is the possibility to regulate the hydrophilic–lipophilic balance (HLB) in aqueous solutions by varying the lengths of the hydrophilic and the hydrophobic chains. It is well-known that in aqueous solutions and above a certain threshold quantity – the critical micellar concentration (CMC) – the amphiphilic molecules organize into a range of self-assemblies. The nanostructures may be identified by sharp changes in various bulk and interfacial properties (e.g. electrical conductivity, surface tension isotherms at solution air/interface, etc.). Analogous effects have also been detected when the surfactant concentrations are within the intermediate (premicellar)
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concentration domain (the surfactant quantity is higher than the concentration where the Henry law is operative but still one or two orders of magnitude below the conventional CMC). Earlier investigations on aqueous solutions of sodium alkyl sulfates with different chain lengths have reported well-outlined kink and plateau portions in the surface tension isotherms [3,4]. Later systematic studies on microscopic foam films obtained from aqueous solutions of the anionic surfactant sodium dodecyl sulfate (SDS) have revealed a complete synchrony in the onset of adsorption layer deviations and a specific run of the film drainage characteristics [5–13]. Besides, within the intermediate (pemicellar) concentration domain specific black patterns – black dots and ‘unstable’ black spots – are observed; the film drainage is significantly retarded, etc. Similar data about aqueous solutions of tetraethylene glycol monododecyl ether (C12 E4 ) from the intermediate concentration domain are described in Ref. [2]. The major findings have been: (a) the surface tension isotherm has two plateau portions; (b) the surface dilational elasticities pass through a sequence of maxima and minima; (c) the onset of characteristic ‘unstable’ black patterns in draining microscopic foam films is registered; (d) a relative stabilization of the draining films is observed. The coupling of these results is interpreted as an experimental evidence for the presence of amphiphilic self-assemblies in the premicellar concentration domain. In certain cases the presence of premicelles becomes important because they have an appreciable influence on the properties and the stability of the systems. An important observation is that the experimental peculiarities appear within almost the same molar concentration domain for both ionic and nonionic surfactants. This fact supports the notion that premicellization of low molecular mass surfactants might be a universal bulk solution phenomenon, depending mostly on the number density of the amphiphilic molecules. In the last years a pool of other experimental [14–24,28] and theoretical [25–27] data has emerged, that substantiates this concept. The aim of the present paper is to follow in detail and understand how the surfactant adsorption layer properties at solution/air interface are related to the foam drainage parameters in the case of aqueous solutions of triethylene glycol monododecyl ether (C12 E3 ). A broader concentration range is investigated, including amphiphile quantities at which the initial onset of surfactant nanostructures might be registered. C12 E3 is chosen for two reasons. First, to check if within the premicellar concentration range specific peculiarities between adsorption layer properties and foam film drainage characteristics could be detected and juxtaposed to the anomalies already established for the higher homolog (C12 E4 ) [2]. Second, the length of the hydrophobic tail and all the rest conditions (temperature, added electrolyte) being the same, the goal is to add new knowledge about the specific effect of the size of the hydrophilic head on the overall interfacial and bulk properties of the investigated systems. The properties of aqueous solutions of triethylene glycol monododecyl ether (C12 E3 ) have not been thoroughly investigated in a broader range of concentrations and including lower surfactant quantities, in particular. There have been some structural studies of the interfacial layers [29,30] at the air/solution interface but they concern higher surfactant concentrations. Reliable surface tension data in the low and intermediate concentration domain and therefore, a thorough outline of the equilibrium surface tension curve within wider concentration domain, are still lacking. Systematic interfacial rheology studies and data on foam film drainage behavior are also not available. There is no systematic juxtaposition of the impact of the adsorption layer characteristics on the stability and drainage parameters of microscopic foam films. The scope of the research covers adsorption dynamics, construction of equilibrium surface tension isotherm, studies on surface dilational rheology of the interfacial layers. Microscopic foam films
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of the same solutions are investigated so as to follow the effect of adsorption layer properties on the parameters of the drainage kinetics. 2. Materials and methods Aqueous solutions of the nonionic surfactant triethyleneglycol monododecyl ether (C12 E3 Sigma–Aldrich, ≥98% purity, gas chromatography) are investigated. The concentration range is 5.0 × 10−8 –5.0 × 10−4 M. In all systems sodium chloride (0.1 М NaCl, Merk, 99.9% purity) is added, after being heated at 600 ◦ C during several hours for removal of organic impurities. Triply distilled water is used. For the lowest surfactant concentrations ultra pure water is also applied (CHROMASOLV® Plus, for HPLC, Sigma–Aldrich). Due to the low solubility of the surfactant, the solutions are put in a shaking machine for several hours before the experiments. The adsorption layer studies are performed by profile analysis tensiometer (PAT-1, Sinterface). Details about this instrumentation and its capacity for investigating the rheology of surfactant layers may be found, e.g. in Refs. [31,32]. The method of buoyant bubble in PAT-1 techniques is employed because it is very appropriate for the investigation of aqueous solutions at lower amphiphile quantities. Particular advantage in this case is the fact that the bubble is obtained in a closed cell thus minimizing the possible inaccuracies related to evaporation or entrapment of impurities. For each concentration the solutions are kept for 24 h at 20 ◦ C before the start of the tensiometric studies. Each measurement is performed with a freshly prepared solution of the respective surfactant concentration. Every experimental point is a result of at least four independent measurements. The foam films are obtained and investigated in the microinterferometric thin liquid film setup equipped with Scheludko–Exerowa cell. The details about this instrumentation might be found, e.g. in Ref. [33]. For each concentration the capillary of the cell is loaded three to four times with newly prepared solutions. Within each loading at least 100 films are obtained and image-processed. Every loading of the cell capillary is followed by a thermal and adsorption equilibration in the course of at least 1.5 h. A strict control of temperature is ensured and all experiments are carried out at 20 ◦ C. The application of the microscopic foam film instrumentation has several advantages [5,10]. The microscopic dimensions of the thin liquid layer give the possibility to deal with very low surfactant concentrations of the primary amphiphilic solutions. This allows tracing back the conditions where the effects of initial onset of bulk premicellar structures may be registered. The specific kinetic and thermodynamic properties of the films and the disjoining pressure in particular, offer additional options for the impact on the existing bulk premicellar entities. For example, upon time-evolution of films, which originate from surfactant solutions containing self-assembled nanostructures, the immediate vicinity of every premicelle is altered as compared to the respective homogeneous bulk and structural reorganizations and disintegrations are performed. The impact of these events is routinely registered as specific drainage characteristics of the foam. So, due to the ‘mild’ and gradual changes of the conditions in the course of their thinning, the foam films proved to be very appropriate tools for the investigation of the premicellar structures. 3. Experimental results 3.1. Adsorption layer properties The results from the systematic investigations of the dynamic adsorption properties are shown in Fig. 1. For the lowest
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Fig. 1. Dynamic surface tension curves of aqueous C12 E3 solutions. The data are obtained by PAT-1 at temperature 20◦ C and in the presence of electrolyte – 0.1 M NaCl.
surfactant concentrations the equilibrium values are reached for ∼25 h; an extrapolation procedure developed in Ref. [34] is also applied which reproduces the experimentally determined values. In the intermediate concentration range (CS = 1.5 × 10−7 –1.0 × 10−5 M) the dynamic surface tension curves exhibit a tendency of grouping in three bunches of similar run pattern. The experimental surface tension isotherm is presented in Fig. 2. There are three portions of the isotherm where characteristic peculiarities are observed: a plateau at CS ∼ 2.5 × 10−7 –7.0 × 10−7 M; a kink at CS ∼ 8.0 × 10−7 –1.0 × 10–6 M and another plateau region at CS ∼ 5.0 × 10−6– 1.0 × 10−5 M. These specificities embrace a concentration interval which is 1–2 orders of magnitude below CMC. The experimental CMC-value is 5.5 × 10−5 M. The rheological studies are performed after the acquisition of equilibrium surface tension values. The range of the applied perturbation frequencies is 0.005–0.2 Hz. The course of the surface dilational properties against the applied frequency are presented in Figs. 3 and 4. Oscillation amplitudes are kept within the range of 5–10% of the bubble area during the experiments.
Fig. 2. Surface tension isotherm of aqueous C12 E3 solutions. The experiments are performed with PAT-1 at temperature 20◦ C and in the presence of electrolyte – 0.1 M NaCl.
Fig. 3. Surface dilational elasticities of aqueous C12 E3 solutions against the frequency of the applied bubble area perturbations. The experiments are performed with PAT-1 at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl. The frequency range is 0.005–0.2 Hz.
Particularly interesting are the courses of the surface dilational elasticities of the interfacial layers against the surfactant concentration (Fig. 5). There is a series of alternating minima and maxima in the values within the concentration domain where the kink and plateaus in the surface tension isotherm are observed. In the premicellar concentration range the surface dilation viscosities do not attain very high values because the surfactant concentrations do not allow the formation of highly viscoelastic adsorption layers. However, the maximum in the vicinity of the CMC-value is welloutlined (Fig. 6). 3.2. Microscopic foam films Generally in the course of foam film drainage black patterns are observed that may be classified as of two types: The first type (spots, black films) is characteristic of higher concentration ranges of the amphiphile and are precursors of classic black films (common black films (CBF) and Newton black films (NBF)) [33]. These patterns generally evolve into films that survive within longer time intervals (minutes, hours). They are very well described and have been related to the lifetimes and the stability of liquid films [33]. The common feature of the surfactant systems where these precursors
Fig. 4. Surface dilational viscosities aqueous C12 E3 solutions against the frequency of the applied bubble area perturbations. The experiments are performed with PAT1 at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl. The frequency range is 0.005–0.2 Hz.
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Fig. 7. Critical thickness of rupture of the foam films against the surfactant concentration of aqueous C12 E3 solutions. The experiments are performed with the microinterferometric foam film techniques of Scheludko–Exerowa. Fig. 5. Surface dilational elasticities of aqueous C12 E3 solutions against the surfactant concentration. The experiments are performed with PAT-1 in the frequency range 0.005–0.2 Hz, at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
of black films are observed is that the surfactant coverage on the liquid/air interface of the initial solutions is almost closely packed. From this point of view, these black formations mark a specific stage of the evolution of black (plane–parallel) films, namely the transition to a new thickness of relatively stable configuration: CBF or NBF. With certain aqueous amphiphilic solutions and in the intermediate concentration range, black patterns of a second type, black dots and ‘unstable’ black spots, are observed [2,5–13]. These black formations appear when there is some deficiency of the surfactant in the adsorption coverage on the interfaces for miscellaneous reasons. They have lifetimes of no more than several seconds. The respective foam films drain quickly and rupture. Within the concentration domain of the adsorption layer peculiarities, all microscopic foam films drain within 1–2 min
and rupture. The critical thickness of rupture does not show any substantial peculiarity and is virtually constant (Fig. 7). Similar results have been obtained in the cases of aqueous solutions of C12 E4 in Ref. [2] and SDS in Refs. [5–13]. In the present study unstable black patterns in the form of black dots are registered within the whole range of premicellar concentrations. These patterns are small black formations which do not increase throughout their lifetime. The initial onset of these dots marks the concentration at which the plateau and kink portions in the surface tension isotherm are situated. The films within the first plateau and the kink are characterized usually by a single black dot (Fig. 8). The dots survive for ∼5 s for the concentration values of the first surface tension plateau portion. The dots continue to exist up to ∼17 s within the kink region of the surface tension isotherm. It is within the concentration range of the second plateau region that the number of the dots (>5), as well as their lifetimes, increase significantly (∼30 s). The course of the mean film thickness against the drainage time is shown in Fig. 9. Two–three curves are shown for each concentration. They are taken from a pool of at least 30 similar measurements for every concentration value. At high film-thicknesses where the disjoining pressure is still not operative, the curves run in a bunch together. At thickness values where the influence of the disjoining pressure is to be expected, the major bunch separates into three branches that stretch apart. These branches outline the concentration domains where the kink and plateau portions of the surface tension isotherm are situated. The mean drainage time of foam films of radii ∼100 m against the surfactant concentration is presented in Fig. 10. On the same graph these results are juxtaposed to = − 0 ; where 0 is the equilibrium surface tension of aqueous solution of the electrolyte and is the equilibrium surface tension of aqueous solution of the surfactant. A distinct concentration synchrony of the onset of peculiarities in the run of the drainage curves and the kink and plateau regions of the isotherm is observed. Similar effects have already been found for aqueous solutions of n-heptanol in Ref. [35], C12E4 in Ref. [2] and SDS in Ref. [5–13]. 4. Discussion of the results
Fig. 6. Surface dilational viscosities of aqueous C12 E3 solutions against the surfactant concentration. The experiments are performed with PAT-1 within the frequency range of 0.005–0.2 Hz, at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
The new experimental results related to the properties of aqueous solution of C12 E3 concern the intermediate (premicellar)
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Fig. 8. Image analysis of ‘unstable’ black patterns (black dots) in microscopic foam films of aqueous C12 E3 solutions. Surfactant concentration is (a) 5 × 10−7 M; (b) 1 × 10−7 M. The experiments are performed with the microinterferometric foam film techniques of Scheludko–Exerowa. at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
concentration domain, namely: (i) the surface tension isotherm has two plateau and one kink regions; (ii) the dependence of the surface dilational elasticities at the air/solution interface on the amphiphile concentration goes through sequential minima and maxima; (iii) the courses of the foam film drainage parameters run in concentration synchrony with the investigated adsorption layer properties. In so far as similar results have already been registered for aqueous solutions of the higher homologue – C12 E4 [2], the juxtaposition of the similarities and the differences outline the specific role of the structural peculiarities. The comparison of the surface tension isotherms for aqueous solutions of C12 E3 and C12 E4 is shown in Fig. 11. The equilibrium surface tension values in the vicinity of CMC are determined mainly by the length of the hydrophobic tail. Since it is the same for both surfactants, the experimental CMC-values are quite similar (5.5 × 10−5 M for C12 E3 and 5.8 × 10−5 M for C12 E4 ). In both
Fig. 9. Evolution of mean film thickness with time for foam films of aqueous C12 E3 solutions. The experiments are performed with the microinterferometric foam film techniques of Scheludko-Exerowa at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
systems kink and plateau regions are obtained in the intermediate concentration domain. These peculiarities are related to the formation of bulk nanostructures (premicelles) within certain range of intermediate concentration domain. The major difference – two plateaus and a kink for C12 E3 , and only two plateaus for C12 E4 – is most probably due to the diverse structure of their hydrophilic head-groups. The bulkier head groups of C12 E4 are presumed to result in the formation of spherically symmetric premicelles [2]. The lower number of the ethylene glycol groups in C12 E3 is expected to enforce the onset of predominantly anisodiametric (disk-like) premicellar nanostructures. This reasoning is in line with the results of recent numerical modeling [26] and with some data about the interfacial adsorption layers obtained by using different instrumentation (e.g. [29,30]). The surface rheological data give additional hints in support of this premicellar notion. During the imposed interfacial disturbances, the surface area of the bubble is periodically increased and
Fig. 10. Mean drainage time of foam films of aqueous C12 E3 solutions against the surfactant concentration. The temperature is 20◦ C, electrolyte is added – 0.1 M NaCl. = 0 − ; 0 is the equilibrium surface tension of aqueous solution of the electrolyte, is the equilibrium surface tension of aqueous solution of the surfactant solution.
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Fig. 11. Juxtaposition of the surface tension isotherms of aqueous solutions from C12 E4 (data taken from Ref. [2]) and C12 E3 . The experiments are performed with PAT-1 at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
compressed, resulting in the appearance of surface tension gradients. The surface dilational elasticity is a measure of the resistance against the creation of a surface tension gradient at the interface and of the rate at which this gradient disappears once the system is again left to itself [31,32]. It is indicative of both the scale of surface tension changes and of the system’s capacity to restore the initial equilibrium values when the disturbance is released. If there are no premicelles, the usual course of the dilational elasticity against the amphiphile concentration encompasses a maximum and a fall-down at the CMC-value. The surface rheology results as presented in Fig. 5, demonstrate that a phenomenon of this type is repeatedly observed in the intermediate concentration range, as well. Several sequential minima and maxima are registered in the curves presenting the relationship between the surface dilational elasticity and the surfactant concentration. It might be hypothized that these maxima could be looked at as a sign of possible formation of different bulk premicelles. Besides, each irregularity of the surface tension isotherm against the surfactant concentration (first plateau, the kink and second plateau) is marked by one maximum in the relationship of the surface dilational elasticity which might be interpreted as related to one type of premicellar structure (Fig. 12). So, the combination of these effects could be considered
Fig. 12. Juxtaposition of the surface dilational elasticities and the surface tension isotherm of aqueous C12 E3 solutions against the surfactant concentration.
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Fig. 13. Juxtaposition of the surface dilational elasticities of aqueous solutions from C12 E3 and C12 E4 (data taken from Ref. [2]). The experiments are performed with PAT-1 at temperature 20◦ C, in the presence of electrolyte – 0.1 M NaCl.
as an experimental indication for the chronological onset of different self-assembled nanostructures upon the successive raise of the surfactant concentration. Analogous results are obtained for the aqueous solutions of the higher homologue – C12 E4 , as well (Fig. 13). Within the intermediate concentration domain the microscopic foam films drain in a regime of high interfacial mobility and rupture in a minute or two. So, the specific film hydrodynamics is coupled with the mass transfer of the stabilizing surfactant via the Marangoni effect [36]. The observed unstable black patterns – black dots – are a clear sign of the thickness inhomogeneities. The latter create an extra option for the onset of local differences in the general coupling mechanism of the film hydrodynamics and the surfactant mass transfer resulting in the relative increase in the mean film lifetimes [2,9,10]. In the thinner portions of the film, the black pattern regions, the local flow is retarded. The mechanism of this retardation is related to the fact that the amphiphilic nanostructures (premicelles) in the film bulk serve as an extra reservoir for surfactant molecules. The flow sweeps the surfactant molecules outside the black pattern region towards the thicker portions of the film. Due to the uneven distribution of these molecules at the interfaces, local surface tension gradient emerges. This causes the onset of additional tangential forces which act in a direction opposite to the fluid outflow. Towards the places of deficiency of amphiphilic molecules, diffusion fluxes are directed. The normal flux from the black pattern bulk results in constant depletion of the amphiphilic molecules. Besides, in the thinner places all existing amphiphilic nanostructures are already destroyed [9,10]. So, a concentration difference comes out between the pattern bulk and the neighbouring thicker portions of the film. A bulk diffusion flux is directed towards the black pattern region. This flux however, covers a longer path until reaching the interfacial portions depleted of surfactant molecules. If there would not be a sufficient number of them, the pattern interfaces should very quickly become bare of amphiphiles and the film would most probably rupture in these thinner places. But in the neighbouring thicker regions there are premicelles. These regions drain further on and these premicelles are destroyed [11,12]. Thus they provide an extra amount of monomers, which can also participate in the feed up of the black pattern interfaces. This gives a certain additional time to the emerged tangential force, opposite to the outflow, to be maintained for a while and the interfacial outflow to be retarded. This results in a retardation of the drainage process within the black pattern region. Upon raise of the surfactant concentration both the lifetimes
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and the number of these black patterns are increased. This results in an increase of the overall lifetime of the respective microscopic foam films at higher concentration values. Generally, the time and lengths scales of the performed film drainage and rheological phenomena are of the same order of magnitude. In the applied instrumentations the experiments and the accumulation of data are designed to begin after reaching adsorption equilibrium at the air/solution interface. Both the film drainage and the surface dilational studies are related to processes that comprise the onset of surface tension gradients and consecutive relaxations of these gradients due to mass transfer of the surfactant molecules. Therefore, the specific peculiarities in the runs of the interfacial layer properties and of the drainage parameters have common origin and are related to dynamic phenomena (specific manifestation of the Marangoni effect), modified by the presence of bulk premicellar self-assemblies. 5. Concluding remarks The presented results are summarized as follows: 1. surface tension isotherm has a kink and two plateau portions in the intermediate (premicellar) concentration domain; 2. surface dilational elasticities go through a sequence of maxima and minima in the premicellar concentration domain, the same where the peculiarities of the surface tension isotherms are observed; 3. the premicellar concentration domain is marked by the onset of “unstable” black patterns – black dots – in the draining films; 4. the film thickness evolution curves and the drainage times run in a concentration synchrony with the irregularities of the interfacial layer properties; 5. the presence of premicelles stabilizes the draining films. The developed experimental protocol of combined adsorption layer and microscopic thin liquid film experiments is very efficient in tracing the initial stages of the self-assembly and the implications resulting from the structure–property relationships. The concerted results present an experimental evidence for the presence of amphiphilic self-assembly in the premicellar concentration domain of aqueous solutions of C12 E3 . This trend of research gives clues for the better comprehension of the interrelation between the surfactant self-assembly, interfacial rheology, and stability of microscopic foam films. Acknowledgements The financial support of National Science Fund of Bulgaria (Project No. DO-02–256) is gratefully acknowledged. References [1] R. Dong, J. Hao, Complex fluids of poly(oxyethylene) mnoalkyl ether nonionic surfactants, Chem. Rev. 110 (2010) 4978–5022. [2] D. Arabadzhieva, E. Mileva, P. Tchoukov, R. Miller, F. Ravera, L. Liggieri, Adsorption layer properties and foam film drainage of aqueous solutions of tetraethyleneglycol monododecyl ether, Colloids Surf. A Physicochem. Eng. Aspects 392 (2011) 233–241. [3] D. Exerowa, A. Scheludko, On the relation between the concentration of formation of black spots in microscopic foam films and the dependence of the surface tension on the concentration of the detergent, Bull. Inst. Phys. Chem. Bulg. Acad. Sci. 3 (1963) 79–87. [4] A. Nikolov, G. Martynov, D. Exerowa, Associative interactions and surface tension in ionic surfactant solutions at concentrations much lower than the cmc, J. Colloid Interface Sci. 81 (1981) 116–124. [5] E. Mileva, D. Exerowa, Foam films as instrumentation in the study of amphiphile self-assembly, Adv. Colloid Interface Sci. 100–102 (2003) 547–562.
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