# Effect of Temperature on the Dynamic Properties of Mixed Surfactant Adsorbed Layers at the Water/Hexane Interface under Low-Gravity Conditions

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{13}DMPO), the measured interfacial tension of the aqueous mixed surfactant solutions against hexane increases when the temperature decreases between 30 °C and 20 °C. However, with a further temperature decrease between 20 °C and 15 °C, the reverse effect has also been observed at some concentrations, i.e., a decrease of interfacial tension. Additionally, the corresponding dilational interfacial visco-elasticity shows some discrepant temperature effects, depending on the bulk concentration and oscillation frequency. The experiments have been performed with a capillary pressure tensiometer under the conditions of micro-gravity. The reason for the positive and negative interfacial tension and visco-elasticity gradients, respectively, within certain ranges of the temperature, concentration and mixing ratios, are discussed on the basis of all available parameters, such as the solubility and partitioning of the surfactants in the two liquid phases and the oscillation frequency.

## 1. Introduction

_{13}DMPO at a fixed TTAB concentration and of TTAB at a fixed C

_{13}DMPO concentration. In these surfactant mixed solutions, the ionic surfactant TTAB is soluble only in the aqueous phase, whereas the non-ionic surfactant C

_{13}DMPO is present in both adjacent liquids, according to the corresponding equilibrium partitioning.

## 2. Materials and Methods

_{13}DMPO), (CAS 186953-53-7, purchased from Gamma-Service, Berlin, Germany) and the cationic tetradecyl trimethyl ammonium bromide (TTAB), (CAS 1119-97-7, purchased from Sigma-Aldrich, St. Louis, MO, USA), dissolved in pure MilliQ water. The surfactants were injected step-by-step by using two syringes, working according to a pre-established sequence. The sequence included measurements with increasing C

_{13}DMPO concentrations c

_{1}= 4.0 × 10

^{−7}, 8.0 × 10

^{−7}, 4.0 × 10

^{−6}, 8.0 × 10

^{−6}and 2.2 × 10

^{−5}mol/dm

^{3}at a fixed TTAB concentration of c

_{2}= 4.5 × 10

^{−5}mol/dm

^{3}, continued by measurements with increasing TTAB concentrations c

_{2}= 4.5 × 10

^{−5}, 2.2 × 10

^{−4}, 4.5 × 10

^{−4}, 2.2 × 10

^{−3}and 4.5 × 10

^{−3}mol/dm

^{3}at a fixed C

_{13}DMPO concentration of c

_{1}= 2.2 × 10

^{−5}mol/dm

^{3}.

_{13}DMPO was selected due to knowledge gained on it as a single component in previous experimental and theoretical studies [19,20]. TTAB was chosen because of the large knowledge on it as an individual component [21] and because of its favorable Kraft temperature, which is below the available temperature range of the experimental tools. Information about the purity of the two used surfactants is given elsewhere [16].

^{−1}), due to occasional push–pull disturbances for the drop caused by the instrumental set parameters. In contrast, the accuracy of the interfacial-viscoelasticity values was much better (i.e., up to ±0.4 mN m

^{−1}) because of the simultaneous appearance of the disturbances of interfacial tension and the corresponding interfacial area. Additional information about the instrument and measurement procedures can be found in [16,22].

## 3. Theoretical Backgrounds

#### 3.1. Interfacial Tension Measurements

_{13}DMPO and TTAB) adsorb at the n-hexane/water interface and form a mixed interfacial layer. The resulting interfacial tension is a function of partial surfactant adsorptions (surface concentrations). When the limiting adsorptions (i.e., surface excesses) of two surfactants are not very different, Γ

_{1∞}≈ Γ

_{2∞}, the interfacial tension can be approximately described by Equation (1) [16,23]:

_{0}is the interfacial tension of the pure hexane/water interface (about 51.1 mN/m [19,21]), Γ

_{1}and Γ

_{2}are the surfactant adsorptions, ${\mathrm{\Omega}}_{1}=1/{\mathsf{\Gamma}}_{1\infty}$ and ${\mathrm{\Omega}}_{2}=1/{\mathsf{\Gamma}}_{2\infty}$ are their molar areas in a densely packed state, and $\mathrm{\Omega}=\frac{{\mathrm{\Omega}}_{1}^{2}{\mathsf{\Gamma}}_{1}+{\mathrm{\Omega}}_{2}^{2}{\mathsf{\Gamma}}_{2}}{{\mathrm{\Omega}}_{1}{\mathsf{\Gamma}}_{1}+{\mathrm{\Omega}}_{2}{\mathsf{\Gamma}}_{2}}$ is the average molar area. Under equilibrium conditions, the surfactant adsorptions are functions of their bulk concentrations:

_{13}DMPO is soluble in both liquid phases. In particular, it is more soluble in n-hexane, and the respective distribution coefficient is about 30 [20,25].

_{13}DMPO concentration due to this high solubility in hexane. However, the hexane drop is very small compared to the volume of water in the matrix cell (about 68.2 cm

^{3}), and therefore the amount of C

_{13}DMPO transferred into the hexane drop is negligibly small. However, the surfactant can diffuse through the capillary (the valve is open during the experiment) to the hexane reservoir (5.6 cm

^{3}). The change in the C

_{13}DMPO concentration due to this effect should also be relatively small, because the surfactants are injected in continuously increasing amounts and the oscillations are performed shortly after the injections. Therefore, the uncertainty in the C

_{13}DMPO concentration should be insignificant [16].

#### 3.2. Interfacial Dilational Viscoelasticity Modulus

_{0}, the response of the interface can be characterized by the interfacial dilational viscoelastic modulus:

_{0}is the initial interfacial area. From the definition Equation (4), one can see that the interfacial viscoelastic modulus is a complex function of frequency, which can be represented as:

_{r}and ε

_{i}are the real and imaginary parts, respectively, and $\left|\mathsf{\epsilon}*(\mathrm{i}\mathsf{\omega})\right|$ and φ are the modulus and phase of the complex viscoelasticity ε*(iω). In the simplest case of harmonic oscillations, the modulus $\left|\mathsf{\epsilon}*(\mathrm{i}\mathsf{\omega})\right|$ is the ratio of the amplitudes of interfacial tension and relative interfacial area oscillations, whereas the phase φ is the phase shift of interfacial tension with respect to area oscillations.

_{0}can be described by Equation (6):

_{01}and Γ

_{02}are the equilibrium adsorptions, ${n}_{j}^{\mathsf{\alpha}}=\sqrt{\frac{i\mathsf{\omega}}{{D}_{j}^{\mathsf{\alpha}}}}$, ${n}_{j}^{\mathsf{\beta}}=\sqrt{\frac{i\mathsf{\omega}}{{D}_{j}^{\mathsf{\beta}}}}$, and ${D}_{j}^{\mathsf{\alpha}}$ and ${D}_{j}^{\mathsf{\beta}}$ are the diffusion coefficients of the surfactants in the outer phase α and inner phase β, respectively. In particular cases, i.e., when either one surfactant is present or a flat interface exists, Equation (6) is reduced to the models discussed in [16,17].

## 4. Results and Discussion

#### 4.1. Temperature Dependence of Interfacial Tension

_{13}DMPO in Figure 1. This can be the consequence of incomplete mixing of the solution in the matrix cell after surfactant injections, or of small nitrogen bubbles trapped in the main valve, which might be present at the initial stage of the experiment [16].

_{13}DMPO concentration of 0.4 μm in Figure 1 and for TTAB concentrations of 0.22 mM and 0.45 mM in Figure 2. In the last two cases, the difference between the results for 15 °C and 20 °C is rather small, of about 0.5 mN/m or less. Such a difference is of the same magnitude as the apparent variation of the interfacial tensions with the frequency for fixed surfactant concentrations and temperatures (as discussed above) or with the oscillation amplitude (see the Supporting Information). Thus, the inverse temperature dependences in these two cases can be a consequence of some disturbances of the measurements. For the C

_{13}DMPO concentration of 0.4 μm in Figure 1, the difference is larger; however, the results can be affected in this case, probably by incomplete mixing or the effect of small nitrogen bubbles, as discussed above. Therefore, this case cannot be considered as experimental evidence of the inverse temperature dependences either. Unfortunately, the conditions of space experiments do not give the possibility for repeat measurements. Separate accurate experiments should be performed to check the obtained results.

#### 4.2. Temperature Dependence of Viscoelastic Modulus

_{13}DMPO concentrations of 4.0 × 10

^{−7}and 8.0 × 10

^{−7}mol/dm

^{3}, and for the smallest TTAB concentration of 4.5 × 10

^{−5}mol/dm

^{3}in Figure 3). However, at higher C

_{13}DMPO concentrations (Figure 3) and higher TTAB concentrations (Figure 4), the tendency changes to the opposite—the modulus increases with temperature. The exception to this is the highest TTAB concentration of 4.5 × 10

^{−3}mol/dm

^{3}in Figure 4, where the modulus for 15 °C is again larger than for 30 °C. However, the concentration of 4.5 × 10

^{−3}mol/dm

^{3}is above the CMC for aqueous TTAB solutions (about 3.5 × 10

^{−3}mol/dm

^{3}[60]), so that the mechanisms of the interfacial layer relaxation can be different in this case compared to the lower concentrations. It should also be noted that the magnitude of the modulus is very small in this case (less than 2 mN/m).

_{01}and E

_{02}, the four partial derivatives of the adsorptions with respect to the concentrations, ${a}_{ji}={(\partial {\mathsf{\Gamma}}_{j}/\partial {c}_{i}^{\mathsf{\alpha}})}_{{c}_{k\ne i}^{\mathsf{\alpha}}}$, the two partition coefficients K

_{1}and K

_{2}, and the two equilibrium adsorptions Γ

_{01}and Γ

_{02}. The partial elasticities and the derivatives of the adsorptions with respect to the concentrations can be obtained from the equation of state of the adsorption layer and the adsorption isotherms, such as Equations (1) and (2) or other similar equations. It is clear that, for fixed surfactant concentrations, all these parameters should depend on the temperature, as the respective equations do. However, it is difficult to predict the exact form of this dependence. The partition coefficients and equilibrium adsorptions also vary with the temperature. The second group of parameters are the kinetic coefficients, such as the diffusion coefficients of the surfactants in the two liquid phases, ${D}_{j}^{\mathsf{\alpha}}$ and ${D}_{j}^{\mathsf{\beta}}$, or other kinetic coefficients (if the relaxation of the adsorption layer is not purely diffusion controlled). These kinetic coefficients also strongly depend on the temperature itself and on the liquid’s viscosity (the diffusion coefficients, according to the Stokes–Einstein equation). They can also be influenced by the height of the activation barriers (according to the Arrhenius equation), which is affected by the temperature.

_{ji}, which can also lead to complicated shape deformations of these dependences.

## 5. Conclusions

_{13}DMPO and cationic surfactant TTAB. The aim was to determine the temperature effect on the interfacial properties in multi-component liquid systems. This study was part of a wider study performed aboard the International Space Station (ISS) [16,22]. The measurements were done with a special designed instrument. It allows the generation of oscillations of a pure n-hexane drop in aqueous matrix solutions. The interfacial tension relaxation served as a response to the drop area oscillations. The microgravity environment allowed for perfect harmonic oscillations of all the system characteristics with sufficiently high amplitudes (up to 20% of the relative area variations), avoiding natural convection in the solution and drop deformations due to gravity.

_{13}DMPO in the water/hexane system are not available for comparison. Therefore, the modelling of the temperature dependencies is not possible. However, in this case, experimental data on the temperature dependencies becomes especially valuable, because they can be useful for many practical applications and can be the starting point for further studies in this area.

## Supplementary Materials

_{13}DMPO concentrations of c

_{1}= 4.0 × 10

^{−7}, 8.0 × 10

^{−7}, 4.0 × 10

^{−6}, 8.0 × 10

^{−6}and 2.2 × 10

^{−5}mol/dm

^{3}, and at a fixed TTAB concentration c

_{2}= 4.5 × 10

^{−5}mol/dm

^{3}. Figure S2: Temperature (blue T = 15 °C, magenta T = 20 °C, red T = 30 °C) and amplitude (squares—Ampl. 5%, up triangles—Ampl. 10%, down triangles—Ampl. 20%) dependences for the mean-level values of interfacial tension oscillations as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) at TTAB concentrations of c

_{2}= 4.5 × 10

^{−5}, 2.2 × 10

^{−4}, 4.5 × 10

^{−4}, 2.2 × 10

^{−3}and 4.5 × 10

^{−3}mol/dm

^{3}, at a fixed C

_{13}DMPO concentration of c

_{1}= 2.2 × 10

^{−5}mol/dm

^{3}. Figure S3: Temperature dependence (cyan surface T = 20 °C, red surface T = 30 °C) for the mean-level values of interfacial tension oscillations upper panel) and for the ε*(iω) modulus (lower panel) as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) and as a function of concentration, in the concentration sequence for C

_{13}DMPO (at concentrations of 4.0 × 10

^{−7}, 8.0 × 10

^{−7}, 4.0 × 10

^{−6}, 8.0 × 10

^{−6}and 2.2 × 10

^{−5}mol/dm

^{3}at a fixed TTAB concentration of 4.5 × 10

^{−5}mol/dm

^{3}), and of TTAB (at concentrations of 4.5 × 10

^{−5}, 2.2 × 10

^{−4}, 4.5 × 10

^{−4}and 2.2 × 10

^{−3}mol/dm

^{3}at a fixed C

_{13}DMPO concentration of 2.2 × 10

^{−5}mol/dm

^{3}). Graph rotation: Horizontal view = 45°; Vertical view = 15°. Figure S4: Same as Figure S3. Graph rotation: Horizontal view = 120°; Vertical view = 15°. Figure S5: Same as Figure S3. Graph rotation: Horizontal view = 240°; Vertical view = 15°.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Iglauer, S.; Favretto, S.; Spinosa, G.; Schena, G.; Blunt, M.J. X-ray tomography measurements of power-law cluster size distributions in sandstones. Phys. Rev. E
**2010**, 82, 056315. [Google Scholar] [CrossRef] [PubMed][Green Version] - Fredrick, E.; Walstra, P.; Dewettinck, K. Factors governing partial coalescence in oil-in-water emulsions. Adv. Colloid Interface Sci.
**2010**, 153, 30–42. [Google Scholar] [CrossRef] [PubMed] - Gonçalves, L.M.; Kobayakawa, T.G.; Zanette, D.; Chaimovich, H.; Cuccovia, I.M. Effects of micelles and vesicles on the oximolysis of p-nitrophenyl diphenyl phosphate: A model system for surfactant-based skin-defensive formulations against organophosphates. J. Pharm. Sci.
**2009**, 98, 1040–1052. [Google Scholar] [CrossRef] [PubMed] - Al-Sahhaf, T.; Elkamel, A.; Suttar Ahmed, A.; Knan, A.R. The influence of temperature, pressure, salinity, and surfactant concentration on the interfacial tension of the n-octane-water system. Chem. Eng. Comm.
**2005**, 192, 667–684. [Google Scholar] [CrossRef] - He, Y.; Yazhgur, P.; Salonen, A.; Langevin, D. Adsorption–desorption kinetics of surfactants at liquid surfaces. Adv. Colloid Interf. Sci.
**2015**, 222, 377–384. [Google Scholar] [CrossRef] - Girifalco, L.A.; Good, R.J. A theory for the estimation of surface and interfacial energies. Derivation and application to interfacial tension. J. Phys. Chem.
**1957**, 61, 904–909. [Google Scholar] [CrossRef] - Chen, L.J.; Lin, S.Y.; Huang, C.C.; Chen, E.M. Temperature dependence of critical micelle concentration of polyoxyethylenated non-ionic surfactants. Colloids Surf. A
**1998**, 135, 175–181. [Google Scholar] [CrossRef] - Das, C.; Das, B. Thermodynamic and Interfacial Adsorption Studies on the Micellar Solutions of Alkyltrimethylammonium Bromides in Ethylene Glycol (1) + Water (2) Mixed Solvent Media. J. Chem. Eng. Data
**2009**, 54, 559–565. [Google Scholar] [CrossRef] - Geng, F.; Liu, J.; Zheng, L.; Yu, L.; Li, Z.; Li, G.; Tung, C. Micelle Formation of Long-Chain Imidazolium Ionic Liquids in Aqueous Solution Measured by Isothermal Titration Microcalorimetry. J. Chem. Eng. Data
**2010**, 55, 147–151. [Google Scholar] [CrossRef] - Aveyard, R.; Binks, B.P.; Chen, J.; Esquena, J.; Fletcher, P.D.I.; Buscall, R.; Davies, S. Surface and Colloid Chemistry of Systems Containing Pure Sugar Surfactant. Langmuir
**1998**, 14, 4699–4709. [Google Scholar] [CrossRef] - Aoudia, M.; Al-Shibli, M.N.; Al-Kasimi, L.H.; Al-Maamari, R.; Al-Bemani, A. Novel surfactants for ultralow interfacial tension in a wide range of surfactant concentration and temperature. J. Surfactant Deterg.
**2006**, 9, 287–293. [Google Scholar] [CrossRef] - El-Batanoney, M.; Abdel-Moghny, T.; Ramzi, M. The effect of mixed surfactants on enhancing oil recovery. J. Surfactant Deterg.
**1999**, 2, 201–205. [Google Scholar] [CrossRef] - Fu, D.; Gao, X.R.; Huang, B.; Wang, J.; Sun, Y.; Zhang, W.J.; Kan, K.; Zhang, X.C.; Xie, Y.; Sui, X. Micellization, surface activities and thermodynamics study of pyridinium-based ionic liquid surfactants in aqueous solution. RSC Adv.
**2019**, 9, 28799–28807. [Google Scholar] [CrossRef][Green Version] - Szymczyk, K.; Szaniawska, M.; Krawczyk, J. Temperature Effect on the Adsorption and Volumetric Properties of Aqueous Solutions of Kolliphor
^{®}ELP. Molecules**2020**, 25, 743. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ivanova, A.A.; Cheremisin, A.N.; Barifcani, A.; Iglauer, S.; Phan, C. Molecular insights in the temperature effect on adsorption of cationic surfactants at liquid/liquid interfaces. J. Mol. Liq.
**2020**, 299, 112104. [Google Scholar] [CrossRef] - Loglio, G.; Kovalchuk, V.I.; Bykov, A.G.; Ferrari, M.; Krägel, J.; Liggieri, L.; Miller, R.; Noskov, B.A.; Pandolfini, P.; Ravera, F.; et al. Dynamic properties of mixed cationic/nonionic adsorbed layers at the n-hexane/water interface: Capillary pressure experiments under low gravity conditions. Colloids Interfaces
**2018**, 2, 53. [Google Scholar] [CrossRef][Green Version] - Kovalchuk, V.I.; Aksenenko, E.V.; Makievski, A.V.; Fainerman, V.B.; Miller, R. Dilational interfacial rheology of tridecyl dimethyl phosphine oxide adsorption layers at the water/hexane interface. J. Colloid Interf. Sci.
**2019**, 539, 30–37. [Google Scholar] [CrossRef] - Passerone, A. Twenty Years of Surface Tension Measurements in Space. Microgravity Sci. Technol.
**2011**, 23, 101–111. [Google Scholar] [CrossRef] - Ferrari, M.; Liggieri, L.; Ravera, F.; Amodio, C.; Miller, R. Adsorption kinetics of alkyl phosphine oxides at the water/hexane interface 1. Pendant drop experiments. J. Colloid Interface Sci.
**1997**, 186, 40–45. [Google Scholar] [CrossRef] - Liggieri, L.; Ravera, F.; Ferrari, M.; Passerone, A.; Miller, R. Adsorption Kinetics of alkyl phosphine oxides at water/hexane interface 2. Theory of the adsorption with transport across the interface in finite systems. J. Colloid Interface Sci.
**1997**, 186, 46–52. [Google Scholar] [CrossRef] - Mucic, N.; Kovalchuk, N.M.; Pradines, V.; Javadi, A.; Aksenenko, E.V.; Krägel, J.; Miller, R. Dynamic properties of C
_{n}TAB adsorption layers at the water/oil interface. Colloids Surf. A**2014**, 441, 825–830. [Google Scholar] [CrossRef] - Pandolfini, P.; Loglio, G.; Ravera, F.; Liggieri, L.; Kovalchuk, V.I.; Javadi, A.; Karbaschi, M.; Krägel, J.; Miller, R.; Noskov, B.A.; et al. Dynamic properties of Span-80 adsorbed layers at paraffin–oil/water interface: Capillary pressure experiments under low gravity conditions. Colloids Surf. A Phys. Eng. Asp.
**2017**, 532, 228–243. [Google Scholar] [CrossRef] - Joos, P. Dynamic Surface Phenomena; VSP: Dordrecht, The Netherlands, 1999. [Google Scholar]
- Fainerman, V.B.; Miller, R.; Aksenenko, E.V.; Makievski, A.V. Equilibrium Adsorption Properties of Single and Mixed Surfactant Solutions. In Surfactants Chemistry, Interfacial Properties, Applications, Studies in Interface Science; Fainerman, V.B., Möbius, D., Miller, R., Eds.; Elsevier: Amsterdam, The Netherlands, 2001; Volume 13, chapter 3. [Google Scholar]
- Fainerman, V.B.; Sharipova, A.A.; Aidarova, S.B.; Kovalchuk, V.I.; Aksenenko, E.V.; Makievski, A.V.; Miller, R. Direct determination of the distribution coefficient of tridecyl dimethyl phosphine oxide between water and hexane. Colloids Interfaces
**2018**, 2, 28. [Google Scholar] [CrossRef][Green Version] - Loglio, G.; Tesei, U.; Cini, R. Spectral Data of Surface Viscoelastic Modulus Acquired via Digital Fourier Transformation. J. Colloid Interface Sci.
**1979**, 71, 316–320. [Google Scholar] [CrossRef] - Miller, R.; Liggieri, L. Interfacial Rheology, 1st ed.; CRC Press: Boca Raton, FL, USA, 2009; Volume 1, pp. 1–37. [Google Scholar]
- Defay, R.; Prigogine, I.; Sanfeld, A. Surface thermodynamics. J. Colloid Interface Sci.
**1977**, 58, 498–510. [Google Scholar] [CrossRef] - Noskov, B.A.; Loglio, G. Dynamic surface elasticity of surfactant solutions. Colloids Surf. A
**1998**, 143, 167–183. [Google Scholar] [CrossRef] - Ivanov, I.B.; Danov, K.D.; Ananthapadmanabhan, K.P.; Lips, A. Interfacial rheology of adsorbed layers with surface reaction: On the origin of the dilatational surface viscosity. Adv. Colloid Interface Sci.
**2005**, 114, 61–92. [Google Scholar] [CrossRef] - Ravera, F.; Ferrari, M.; Liggieri, L. Modelling of dilational visco-elasticity of adsorbed layers with multiple kinetic processes. Colloids Surf. A
**2006**, 282, 210–216. [Google Scholar] [CrossRef] - Jiang, Q.; Valentini, J.E.; Chiew, Y.C. Theoretical models for dynamic dilational surface properties of binary surfactant mixtures. J. Colloid Interface Sci.
**1995**, 174, 268–271. [Google Scholar] [CrossRef] - Noskov, B.A. Dynamic surface elasticity of polymer solutions. Colloid Polym. Sci.
**1995**, 273, 263–270. [Google Scholar] [CrossRef] - Aksenenko, E.V.; Kovalchuk, V.I.; Fainerman, V.B.; Miller, R. Surface dilational rheology of mixed adsorption layers at liquid interfaces. Adv. Colloid Interface Sci.
**2006**, 122, 57–66. [Google Scholar] [CrossRef] [PubMed] - Aksenenko, E.V.; Kovalchuk, V.I.; Fainerman, V.B.; Miller, R. Surface dilational rheology of mixed surfactants layers at liquid interface. J. Phys. Chem. C
**2007**, 111, 14713–14719. [Google Scholar] [CrossRef] - Liu, F.; Darjani, S.; Akhmetkhanova, N.; Maldarelli, C.; Banerjee, S.; Pauchard, V. Mixture Effect on the Dilatation Rheology of Asphaltenes-Laden Interfaces. Langmuir
**2017**, 33, 1927–1942. [Google Scholar] [CrossRef] [PubMed] - Bykov, A.G.; Ferrari, M.; Kovalchuk, V.I.; Krägel, J.; Liggieri, L.; Loglio, G.; Makievski, A.V.; Miller, R.; Milyaeva, O.Y.; Noskov, B.A.; et al. The surface dilational viscoelasticity of a curved oil-water interface with two surfactants soluble in both the oil and water phase. In Proceedings of the 8th Bubble and Drop Conference (B&D 2019), Sofia, Bulgaria, 24–28 June 2019. [Google Scholar]
- Loglio, G.; Kovalchuk, V.I.; Bykov, A.G.; Ferrari, M.; Krägel, J.; Liggieri, L.; Miller, R.; Noskov, B.A.; Pandolfini, P.; Ravera, F.; et al. Interfacial Dilational Viscoelasticity of Adsorption Layers at the Hydrocarbon/Water Interface: The Fractional Maxwell Model. Colloids Interfaces
**2019**, 3, 66. [Google Scholar] [CrossRef][Green Version] - Costa, M.F.P.; Ribeiro, C. Generalized fractional Maxwell model: Parameter estimation of a viscoelastic material. AIP Conf. Proc.
**2012**, 1479, 790–793. [Google Scholar] [CrossRef][Green Version] - Stankiewicz, A. Fractional Maxwell model of viscoelastic biological materials. BIO Web Conf.
**2018**, 10, 02032. [Google Scholar] [CrossRef][Green Version] - Povstenko, Y. Essentials of fractional calculus. In Fractional Thermoelasticity; Springer International Publishing: Basel, Switzerland, 2015; Volume 219. [Google Scholar] [CrossRef]
- Lutton, E.S.; Stauffer, C.E.; Martin, J.B.; Fehl, A.J. Solid and liquid monomolecular film at oil/H2O interfaces. J. Colloid Interface Sci.
**1969**, 30, 283–290. [Google Scholar] [CrossRef] - Ataev, G.M. Anomalous Temperature Dependence of Interfacial Tension in Water–Hydrocarbon Mixtures. Russ. J. Phys. Chem.
**2007**, 81, 2094–2095. [Google Scholar] [CrossRef] - Ye, Z.; Zhang, F.; Han, L.; Luo, P.; Yang, J.; Chen, H. The effect of temperature on the interfacial tension between crude oil and gemini surfactant solution. Colloids Surf. A
**2008**, 322, 138–141. [Google Scholar] [CrossRef] - Miquilena, A.; Coll, V.; Borges, A.; Melendez, J.; Zeppieri, S. Influence of Drop Growth Rate and Size on the Interfacial Tension of Triton X-100 Solutions as a Function of Pressure and Temperature. Int. J. Thermophys.
**2010**, 31, 2416–2424. [Google Scholar] [CrossRef] - Ferdous, S.; Ioannidis, M.A.; Henneke, D.E. Effects of temperature, pH, and ionic strength on the adsorption of nanoparticles at liquid–liquid interfaces. J. Nanopart. Res.
**2012**, 14, 850. [Google Scholar] [CrossRef] - Hyde, A.; Horiguchi, M.; Minamishima, N.; Asakuma, Y.; Phan, C. Effects of microwave irradiation on the decane-water interface in the presence of Triton X-100. Colloids Surf. A
**2017**, 524, 178–184. [Google Scholar] [CrossRef] - Shibata, Y.; Hyde, A.; Asakuma, Y.; Phan, C. Thermal response of a non-ionic surfactant layer at the water/oil interface during microwave heating. Colloids Surf. A
**2018**, 556, 127–133. [Google Scholar] [CrossRef] - Vochten, R.; Petre, G. Study of the heat of reversible adsorption at the air-solution interface. II. Experimental determination of the heat of reversible adsorption of some alcohols. J. Colloid Interface Sci.
**1973**, 42, 320–327. [Google Scholar] [CrossRef] - Petre, G.; Azouni, M.A. Experimental evidence for the minimum of surface tension with temperature at aqueous alcohol solution air interfaces. J. Colloid Interface Sci.
**1984**, 98, 261–263. [Google Scholar] [CrossRef] - Slavtchev, S.G.; Miladinova, S.P. Thermocapillary flow in a liquid layer at minimum in surface tension. Acta Mech.
**1998**, 127, 209–224. [Google Scholar] [CrossRef] - Legros, J.C.; Limbourg-Fontaine, M.C.; Petre, G. Influence of a surface tension minimum as a function of temperature on the Marangoni convection. Acta Astronaut.
**1984**, 11, 143–147. [Google Scholar] [CrossRef] - Limbourg-Fontaine, M.C.; Petre, G.; Legros, J.C. Thermocapillary movements under at a minimum of surface tension. Naturwissenschaften
**1986**, 73, 360–362. [Google Scholar] [CrossRef] - Savino, R.; Cecere, A.; Vaerenbergh, S.V.; Abe, Y.; Pizzirusso, G.; Tzevelecos, W.; Mojahed, M.; Galand, Q. Some experimental progresses in the study of the self-rewetting fluids for the SELENE experiment to be carried in the Thermal Platform 1 hardware. Acta Astronaut.
**2013**, 89, 179–188. [Google Scholar] [CrossRef] - Savino, R.; Cecere, A.; Paola, R.D. Surface tension driven flow in wickless heat pipes with self-rewetting fluids. Int. J. Heat Fluid Flow
**2009**, 30, 380–388. [Google Scholar] [CrossRef] - Karapetsas, G.; Sahu, K.C.; Sefiane, K.; Matar, O.K. Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature. Langmuir
**2014**, 30, 4310–4321. [Google Scholar] [CrossRef][Green Version] - Tripathi, M.K.; Sahu, K.C.; Karapetsas, G.; Sefiane, K.; Matar, O.K. Non-isothermal bubble rise: Non-monotonic dependence of surface tension on temperature. J. Fluid Mech.
**2015**, 763, 82–108. [Google Scholar] [CrossRef][Green Version] - Balla, M.; Tripathi, M.K.; Sahu, K.C.; Karapetsas, G.; Matar, O.K. Non-isothermal bubble rise dynamics in a self-rewetting fluid: Three-dimensional effects. J. Fluid Mech.
**2019**, 858, 689–713. [Google Scholar] [CrossRef] - Rusanov, A.I.; Prokhorov, V.A. Interfacial tensiometry. In Studies in Interface Science; Elsevier: Amsterdam, The Netherlands, 1996; Volume 3, Chapter 1. [Google Scholar]
- Bergeron, V. Disjoining Pressures and Film Stability of Alkyltrimethylammonium Bromide Foam Films. Langmuir
**1997**, 13, 3474–3482. [Google Scholar] [CrossRef]

**Figure 1.**Temperature dependence (blue up triangles T = 15 °C, magenta down triangles T = 20 °C, red circles T = 30 °C) for the mean-level values of interfacial tension oscillations as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) at C

_{13}DMPO concentrations of c

_{1}= 4.0 × 10

^{−7}, 8.0 × 10

^{−7}, 4.0 × 10

^{−6}, 8.0 × 10

^{−6}and 2.2 × 10

^{−5}mol/dm

^{3}, and at a fixed TTAB concentration c

_{2}= 4.5 × 10

^{−5}mol/dm

^{3}.

**Figure 2.**Temperature dependence (blue up triangles T = 15 °C, magenta down triangles T = 20 °C, red circles T = 30 °C) for the mean-level values of interfacial tension oscillations as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) at TTAB concentrations of c

_{2}= 4.5 × 10

^{−5}, 2.2 × 10

^{−4}, 4.5 × 10

^{−4}, 2.2 × 10

^{−3}and 4.5 × 10

^{−3}mol/dm

^{3}, at a fixed C

_{13}DMPO concentration of c

_{1}= 2.2 × 10

^{−5}mol/dm

^{3}.

**Figure 3.**Temperature dependence (blue up triangles T = 15 °C, magenta down triangles T = 20 °C, red circles T = 30 °C) for the ε*(iω) modulus as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) at C

_{13}DMPO concentrations of c

_{1}= 4.0 × 10

^{−7}, 8.0 × 10

^{−7}, 4.0 × 10

^{−6}, 8.0 × 10

^{−6}and 2.2 × 10

^{−5}mol/dm

^{3}, at a fixed TTAB concentration of c

_{2}= 4.5 × 10

^{−5}mol/dm

^{3}.

**Figure 4.**Temperature dependence (blue up triangles T = 15 °C, magenta down triangles T = 20 °C, red circles T = 30 °C) for the ε*(iω) modulus as a function of frequency (f = 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.5 and 1.0 Hz) at TTAB concentrations of c

_{2}= 4.5 × 10

^{−5}, 2.2 × 10

^{−4}, 4.5 × 10

^{−4}, 2.2 × 10

^{−3}and 4.5 × 10

^{−3}mol/dm

^{3}, at a fixed C

_{13}DMPO concentration of c

_{1}= 2.2 × 10

^{−5}mol/dm

^{3}.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kovalchuk, V.I.; Loglio, G.; Bykov, A.G.; Ferrari, M.; Krägel, J.; Liggieri, L.; Miller, R.; Milyaeva, O.Y.; Noskov, B.A.; Ravera, F.; Santini, E.; Schneck, E. Effect of Temperature on the Dynamic Properties of Mixed Surfactant Adsorbed Layers at the Water/Hexane Interface under Low-Gravity Conditions. *Colloids Interfaces* **2020**, *4*, 27.
https://doi.org/10.3390/colloids4030027

**AMA Style**

Kovalchuk VI, Loglio G, Bykov AG, Ferrari M, Krägel J, Liggieri L, Miller R, Milyaeva OY, Noskov BA, Ravera F, Santini E, Schneck E. Effect of Temperature on the Dynamic Properties of Mixed Surfactant Adsorbed Layers at the Water/Hexane Interface under Low-Gravity Conditions. *Colloids and Interfaces*. 2020; 4(3):27.
https://doi.org/10.3390/colloids4030027

**Chicago/Turabian Style**

Kovalchuk, Volodymyr I., Giuseppe Loglio, Alexey G. Bykov, Michele Ferrari, Jürgen Krägel, Libero Liggieri, Reinhard Miller, Olga Yu. Milyaeva, Boris A. Noskov, Francesca Ravera, Eva Santini, and Emanuel Schneck. 2020. "Effect of Temperature on the Dynamic Properties of Mixed Surfactant Adsorbed Layers at the Water/Hexane Interface under Low-Gravity Conditions" *Colloids and Interfaces* 4, no. 3: 27.
https://doi.org/10.3390/colloids4030027