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STAND: Surface Tension for Aggregation Number Determination Pablo F. Garrido, Pilar Brocos, Alfredo Amigo, Luis Garcia-Rio, Jesús Gracia-Fadrique, and Ángel Piñeiro Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b00477 • Publication Date (Web): 05 Apr 2016 Downloaded from http://pubs.acs.org on April 10, 2016
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STAND: Surface Tension for Aggregation Number Determination Pablo F. Garrido1, Pilar Brocos1, Alfredo Amigo1, Luis García-Río2, Jesús Gracia-Fadrique3, Ángel Piñeiro1,* 1
Departamento de Física Aplicada & 2Departamento de Química Física, Universidade de
Santiago de Compostela, Campus Vida, E-15782 Santiago de Compostela, Spain. 3
Departamento de Fisicoquímica, Facultad de Química, Universidad Nacional Autónoma de
México, Ciudad Universitaria, 04510 México D.F., Mexico. *E-mail:
[email protected] Abstract Taking advantage of the extremely high dependence of surface tension on the concentration of amphiphilic molecules in aqueous solution, a new model based on the double equilibrium between free and aggregated molecules in the liquid phase and between free molecules in the liquid phase and those adsorbed at the air/liquid interface, is presented and validated using literature data and fluorescence measurements. A key point of the model is the use of both the Langmuir isotherm and the Gibbs adsorption equation in terms of free molecules instead of the nominal concentration of the solute. The application of the model should be limited to non ionic compounds since it does not consider the presence of counter ions. It requires several coupled non-linear fittings for which we developed a software that is publicly available in our server as a web application. Using this tool it is straightforward to get the average aggregation number of an amphiphile, the micellization free energy, the adsorption constant, the maximum surface excess (and so the minimum area per molecule), the distribution of solute in the liquid phase between free and aggregate species, and the surface coverage in only a couple of seconds, just by uploading a text file with surface tension vs. concentration data and the corresponding uncertainties.
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Introduction Molecular aggregation as well as adsorption to interfaces between media of different polarity are necessary for many natural phenomena and industrial applications including the compartmentalization of living media into cells or liposomes, the rational design of new materials based on two or three dimensional supramolecular structures, and the encapsulation of dirty particles by cleaning products1. All these phenomena rely on organized molecular selfassembly. There is a clear connection between liquid phase molecular aggregation and interfacial adsorption processes, in such a way that they are very difficult to separate from each other: usually, molecules with high affinity to interfaces between media of different polarity also have a clear ability to self-organize in the liquid phase. Given the importance of both processes, there is a large number of experimental (absorption/emission spectroscopy at different frequencies, particle or light scattering, electrical, magnetic, chemical, optical or mechanical properties, calorimetric measurements and a wide range of microscopies) and computational techniques to address them2. Yet, no experimental method is able to simultaneously assess both phenomena. The surface tension of a solution at the liquid/air interface () is defined as the free energy required to enlarge the surface per unit area. depends directly on the concentration and arrangement of molecules at the interface, but the relative and absolute amounts of these adsorbed molecules depend on their concentration in the bulk phase. Thus, this property is extremely sensitive to any concentration change in the liquid, even for involved multicomponent systems where the different chemical species interact and compete for space at the interface with each other and with the possible supramolecular complexes they can form. For many substances, solutions at almost negligible concentrations in the liquid phase may lead to the saturation of the interface. From the experimental point of view, it is really simple to get a reasonable estimation of the surface tension for a given solution just by counting the number of drops falling from a capillary syringe when a given volume is injected at a constant rate. Commercial instruments based on a variety of methods (pendant drop, bubble pressure, Wilhelmy plate, du Noüy ring, capillary rise, drop volume, amongst other) are available to quantify the surface tension of a liquid in a highly precise way3. Some of these methods even allow getting the value of as a function of time under non-equilibrium regimes, including mechanical perturbations of the interface from which it is possible to obtain interfacial viscoelastic properties.4 Surface tension measurements are often employed to get directly the main features of surfactant molecules: the critical micelle concentration (cmc) and the value when the surface is saturated. 2 ACS Paragon Plus Environment
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Several attempts of getting more information from surface tension measurements have been proposed, including the determination of equilibrium constants for supramolecular complex formation,5 the surface excess6,7 and activity coefficients.8,9 Surface tension measurements are typically employed to characterize surfactant molecules. The average aggregation number (N) together with the cmc, are probably the most important parameters to be considered in the development of surfactant-based commercial products, as well as in fundamental applications involving this kind of molecules. The cmc has been quantitatively defined in different ways but it is generally understood as the free surfactant concentration beyond which all the added molecules become part of nanoaggregate structures called micelles. The combination of both numbers allows determining the concentration of micelles for a given nominal surfactant concentration and its ability to encapsulate a certain cosolute in aqueous solution. Other thermodynamic parameters such as the Gibbs energy, enthalpy or entropy corresponding to the micelle formation process are also key in the characterization of these molecules since they allow the introduction of rational chemical modifications in their structure to modify their stability, diffusion rate and other physicochemical properties. The most accessible experiments aimed to determine micelle aggregation numbers require using a fluorescent probe and a quencher,10 although other methods including light scattering and small angle neutron scattering are also occasionally employed.11,12 The reliability of the results is often dependent on the physicochemical properties of the employed molecules. Additionally, these techniques present some limitations such as the temperature at which the experiment can be carried out and the accessible concentration ranges of the target surfactant. In the present paper we will introduce a model that allows getting the average aggregation number in the liquid phase, the micellization free energy, the adsorption constant, the maximum surface excess (and so the minimum area per molecule), the distribution of molecules into micelles and free monomers in the bulk phase, and the surface coverage, just from surface tension vs. concentration measurements. We have named this model STAND as an acronym of Surface Tension for Aggregation Number Determination since the aggregation number is probably the most significant property provided by the proposed method. We will also show how the model can be easily applied in just a few seconds by using a homemade computational application that is publicly available from our web server. A variety of surfactant molecules, including alkyl glucopyranosides and alkyl maltopyranosides at different temperatures, together with two nonylphenol derivatives are employed to validate the method by comparing the results with complementary information obtained from fluorescence experiments also performed in this work and with other data available in the literature for the same systems.
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Materials & Experimental Methods Materials: Octyl--D-glucopyranoside maltopyranoside
(C10G2),
(C8G1),
decyl--D-glucopyranoside
dodecyl--D-maltopyranoside
(C12G2),
(C10G1), and
decyl--D-
tetradecyl--D-
maltopyranoside (C14G2) were purchased from Anatrace, kept in a dark place at 278 K, and used as received. Nonylphenol polyethylene-7 glycol ether (Tergitol NP7) and nonylphenol polyethylene-10 glycol ether (Tergitol NP10) were purchased from Sigma and used with no further purification. The analysis of nonyl phenol ethoxilates molecular weight distribution was performed in the Mass Spectrometry and Proteomics Core Facility at the University of Santiago de Compostela using a matrix-assisted laser desorption/ionization time-of-flight mass spectrometer (MALDI-TOF MS) with -cyano-4-hydroxicinnamic acid as the matrix. Mass spectra were obtained using a MALDI-TOF Autoflex mass spectrometer (Bruker Daltonix).The weight average molecular weights (Mw) for NP7 and NP10 are 576.07 and 671.35 g·mol1, respectively. Water content was determined with a C20 coulometric Karl Fischer titrator from Mettler Toledo. Ultrapure water (Elix 3 purification system, Millipore Corp.) was used in sample preparation. Solutions were carefully prepared by mass (balance model AT250, Mettler, Switzerland) with the procedure of diluting aliquots from a mother solution, in whose preparation the water content of the surfactants was considered. The relative uncertainty in the concentration (c) of the final solutions was less than 0.2% and 0.01% for the lowest and highest c values, respectively.
Fluorescence: Steady-state fluorescence experiments were recorded using a Cary Eclipse instrument. Pyrene of the highest available purity was purchased from Aldrich and was used without further purification. The fluorescence spectrum of pyrene was measured with an excitation wavelength of 334 nm. All emission spectra measured were corrected for emission monochromator response and were background-subtracted using appropriate blanks. Slits and rate of acquisition were chosen for a convenient signal-to-noise ratio. The micelle aggregation number of surfactants can be determined by static luminescence quenching according to the Turro-Yekta method.13 Pyrene was selected as the fluorescent probe and cetylpyridinium chloride (CPC) was assigned to be its quencher. N can be calculated on the basis of the following equation:
[Q] I ln 0 N [S] cmc I 4
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(1)
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where I0 and I are the fluorescent intensities of pyrene in the absence and presence of CPC; and [Q] and [S] are the concentration of CPC and surfactant (slightly above the cmc), respectively. The cmc values required to use equation (1) were obtained from surface tension measurements, unless specified in the results section. This equation relies on the assumptions that the pyrene and CPC molecules are completely solubilized in the micelle phase and that their distributions obey Poisson statistics. As an example, fluorescence results for C12G2 are shown in Figure S1 of the Supporting Information (SI).
Surface tension: Equilibrium surface tensions (σ) were measured with a Lauda drop volume tensiometer (TVT 2 model, Germany) using the standard mode or the quasi-static mode depending on the surfactant characteristics. Capillaries with inner radius of 1.345 mm and 1.71 mm, and a 5 mL syringe were used. Both the equipment and the procedure were described in detail in the past.14,15 Depending on the working concentration and temperature, the surface tensions were determined with an uncertainty ranging from ± 0.01 to ± 0.05 mN·m for the measurements with the standard mode and from ± 0.1 to ± 1 mN·m for the measurements performed with the quasistatic mode, both at the 95% confidence level. The temperature of the external bath to which the measurement cell is connected was controlled within ±0.1 K.
Theory Description of the STAND model The equations employed to analyze surface tension as a function of concentration measurements obtaining a detailed simultaneous characterization of surfactant adsorption and micellization processes are presented in this section.
The monodisperse mass action approach for free surfactant-micelle equilibrium in the bulk phase: Typically, two different types of models are applied to the analysis of micelle formation processes observed by different experimental techniques, namely those based on the pseudophase separation and on the mass action approaches.16,17 The former type of models is normally easier to apply since it assumes the micelles as a different phase in equilibrium with monomers, disregarding the number of surfactant molecules in each nanoaggregate. In contrast, models from the second family may explicitly consider the size of the micelles approaching it from the number of surfactant molecules forming them. These models usually assume that all micelles are identical. Since the surface tension of a given surfactant hardly changes once the interface is saturated, this property is expected to be sensitive only to the micelles formed at concentrations 5 ACS Paragon Plus Environment
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around the cmc. Their size distribution in this region is expected to be narrow enough to justify the monodispersity assumption. Thus, the method proposed herein is based on the monodisperse mass action approach, which assumes the equilibrium between the N surfactant monomers (S) and the corresponding micelles (M): N S ↔ SN ≡ M
(2)
Note that the presence of ions forming part of micelles is not explicitly considered in the previous reaction and so, the application of this model would be less rigorous for ionic molecules. The overall equilibrium constant corresponding to equation (2) is given by: K = [M] / [SF]N
(3)
where [SF] is the molar concentration of free surfactant and [M] the molar concentration of micelles. Thus, the total concentration of surfactant in a given solution can be expressed as: [ST] = [SF] + N [M] = [SF] + N K [SF]N
(4)
Where the loss of concentration due to adsorbed molecules, which would depend on the geometry and composition of the solution container, is considered to be negligible. The free energy for the micelle formation process per mole of surfactant molecule is given by 0 = RT/N) ln(K)
(5)
Equation (5) is often simplified at the cmc by assuming that in that region [M]
