CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201400096
Thermodynamics of Micellization from Heat-Capacity Measurements Bojan Sˇarac,* Marija Besˇter-Rogacˇ, and Jurij Lah*[a] Differential scanning calorimetry (DSC), the most important technique for studying the thermodynamics of structural transitions of biological macromolecules, is seldom used in quantitative thermodynamic studies of surfactant micellization/demicellization. The reason for this could be ascribed to an insufficient understanding of the temperature dependence of the heat capacity of surfactant solutions (DSC data) in terms of thermodynamics, which leads to problems with the design of experiments and interpretation of the output signals. We address these issues by careful design of DSC experiments per-
formed with solutions of ionic and nonionic surfactants at various surfactant concentrations, and individual and global massaction model analysis of the obtained DSC data. Our approach leads to reliable thermodynamic parameters of micellization for all types of surfactants, comparable with those obtained by using isothermal titration calorimetry (ITC). In summary, we demonstrate that DSC can be successfully used as an independent method to obtain temperature-dependent thermodynamic parameters for micellization.
1. Introduction It has been well established that an understanding of the thermodynamic nature of micelle formation from surfactant monomers is relevant in such areas as biological self-assembly processes, folding of proteins, and protein–protein and protein– nucleic acid interactions, as well as for many industrial applications.[1] The most suitable method of determining the basic thermodynamic properties of micellization is calorimetry because it is the only method that directly measures the true model-independent enthalpy changes. Isothermal titration calorimetry (ITC) measures the concentration dependence of heat effects at constant temperature and has been frequently used in quantitative thermodynamic studies of micellization.[2] In contrast, corresponding studies of the temperature dependence of the heat capacity at a fixed surfactant concentration by using differential scanning calorimetry (DSC) are rather scarce. There are numerous reasons for that fact. From the ITC enthalpogram, one may directly obtain two important characteristics of the micellization process, that is, the enthalpy of micellization (DHM) and the critical micelle concentration (cmc). Furthermore, from ITC curves measured at different temperatures, one can also obtain the heat capacity of micellization (Dcp,M).[3] Moreover, the standard Gibbs free energy (DGoM ), standard enthalpy (DHMo ), and standard entropy (DSoM ) of micelliza[a] Dr. B. Sˇarac, Prof. Dr. M. Besˇter-Rogacˇ, Prof. Dr. J. Lah Department of Physical Chemistry Faculty of Chemistry and Chemical Technology Asˇkercˇeva 5 SI-1000, Ljubljana (Slovenia) Fax: (+ 386) 1-2419-425 E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201400096.
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tion and the micellar aggregation number (n) may be estimated by using a mass-action model analysis of the ITC curve.[4] In addition, due to the relatively high concentration of surfactant titrated into the calorimetric measuring cell, problems like low signal strength, low signal-to-noise ratio, or a baseline drift are rather scarce. On the contrary, DSC measurements on surfactant solutions are frequently affected by the above-mentioned problems and, in general, DHM, cmc, and Dcp,M cannot be estimated from DSC thermograms in a model-independent manner. For the cmc, the explanation is trivial; the DSC experiment is performed at fixed surfactant concentration. On the other hand, DHM and Dcp,M correspond to the enthalpy and heat-capacity change that accompany the transition of surfactant from a pure monomeric to a pure micellar state. Because, generally speaking, thermally induced transitions of a surfactant monitored by DSC do not reflect a transition between a pure monomeric and a pure micellar state, DHM and Dcp,M cannot be estimated as the area under the thermogram (DHM) or on the basis of extrapolation of pre- and post-transitional baselines (Dcp,M). In this light, the main problem for successful model-independent or model-dependent analysis of DSC micellization/demicellization data is a reasonable estimation of heat capacity versus temperature curves for pure surfactant monomers or pure micelles. As a consequence, DSC studies are seldom used for quantitative thermodynamic characterization of micellization/demicellization processes.[5] However, even in these otherwise high-quality studies, DSC was not used as an independent method for the determination of DGoM , DHMo , DSoM , n, and the standard heat capacity of micellization (Dcop;M ). Herein we show that DSC thermograms alone may contain sufficient information for the determination of the thermodynamic parameters of micellization. To approach this goal, we recently suggested one possible way of analyzing DSC thermoChemPhysChem 2014, 15, 1827 – 1833
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CHEMPHYSCHEM ARTICLES grams to obtain DGoM , DHMo , DSoM , Dcop;M , and n for a series of nonionic surfactants.[4b] In the next step we generalize the quantitative thermodynamic analysis of DSC micellization– demicellization data for both ionic and nonionic surfactants. Therefore, we have studied thermally induced micellization/ demicellization in four model systems (Scheme 1): nonionic
www.chemphyschem.org nary titration experiments. Usually the cmc value exhibits a U-shaped dependence on temperature (Figure 1). Therefore, by choosing a suitable concentration of the surfactant (e.g., cmc at room temperature), it is very likely that during the DSC experiment two peaks should be observed. The first, at low temperature, corresponds to micellization and the second, at higher temperature, corresponds to the demicellization process[5d, 7] (the arrows in Figure 1 denote the direction of the de-
Scheme 1. Structural formulae of the investigated surfactants.
surfactant pentaethylene glycol monooctyl ether (C8E5) in water, cationic surfactant dodecyltrimethylammonium chloride (DTAC) in 0.1 m NaCl solution, and anionic surfactants sodium dodecyl sulfate (SDS) and sodium lauroyl sarcosinate (SARC), both in water. The last belongs to the family of amino acidbased surfactants, which are biodegradable and biocompatible and, to our knowledge, this is the first DSC study on SARC. We suggest how reasonable estimates of heat capacity versus temperature curves can be obtained for pure surfactant monomers and how they may be used in global thermodynamic analysis of DSC thermograms. Comparison of the thermodynamic parameters of micellization obtained by analysis of DSC and ITC data enabled us to discuss the advantages and disadvantages of using DSC in the quantitative thermodynamic characterization of surfactant micellization/demicellization processes.
2. Results and Discussion 2.1. Detection of Micellization/Demicellization Processes by Using DSC For successful detection of micellization/demicellization processes by using DSC, the surfactant solution under investigation has to fulfill two basic conditions. The first requires that the population of micellar aggregates and monomeric surfactant molecules changes with temperature and the second requires that these changes are accompanied by uptake or release of measurable heat.[4b] In this light, an independent variable that can be varied to fulfill these two conditions is surfactant concentration in the sample cell. If the selected concentration of surfactant is close to the cmc value (e.g., at room temperature), one may expect that changes in temperature will induce surfactant micellization or demicellization.[5d] Estimates of cmc values may be obtained from the literature, from empirical relations that take into account the nature of surfactant and composition of surfactant solution,[6] or from prelimi 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 1. Scheme of the micellization/demicellization process observed in the DSC experiments. Black arrows indicate transition from monomeric to micellar state and vice versa. The solid grey line represents data from ref. [3].
scribed processes). If we lower the concentration of the surfactant in the experiment, the micellization process occurs at higher temperature, whereas the demicellization starts at a lower temperature than before. Thus, by subsequent lowering of the surfactant concentration the peaks tend to merge together and, due to negligible DHM, disappear at a concentration that corresponds to the minimum of the cmc versus T curve. Consequently, at surfactant concentrations below the minimum of the cmc versus T curve, the thermograms become very similar. This observation can be ascribed to the fact that no micellization or demicellization process takes place under such conditions. Thus, these thermograms correspond to the heat capacity versus T curves for pure surfactant monomers. In our experiments, the reference DSC cell was filled with such a solution of pure monomers and the sample cell was filled with solution of higher surfactant concentration. This design of experiments enabled us to obtain thermograms that reflect mainly the micellization/demicellization processes. Figure 2 (black circles) shows the DSC thermograms for C8E5, SDS, and SARC in water and DTAC in 0.1 m NaCl at three surfactant concentrations (see Figure 2). It is evident that micellization (and demicellization) of all surfactants is induced by increased temperature, but at different temperature ranges. For C8E5, temperature-induced micellization is visible at temperatures between 290 and 330 K (Figure 2a). The demicellization ChemPhysChem 2014, 15, 1827 – 1833
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www.chemphyschem.org KM ¼
Figure 2. Model analysis of DSC thermograms for a) C8E5, b) DTAC, c) SDS, and d) SARC. Circles: experimental data, dashed lines: individual fits, and solid lines: best global fits of the RTS model function [Eq. (5)].
process cannot be observed for C8E5 due to phase separation of the surfactant solution at around 340 K (see the Supporting Information in [4b]). This problem was not encountered for the other surfactants. Here, the measurements were performed up to 372 K and detection of both processes (micellization and demicellization) was possible. However, the quality of DSC signals at temperatures below 280 K was insufficient for further analysis. Therefore, only a part of the peaks corresponding to temperature-induced micellization of DTAC, SDS, and SARC could be observed.
2.2. Micellization as a Reversible Two-State (RTS) Process
ð1Þ
in which S + , C , and Mp + represent surfactant monomers, counterions, and micelles, respectively. To this process an apparent equilibrium constant, given by Equation (2): 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ð2Þ
can be assigned at any T. It involves equilibrium molal concentrations of species S + , C , and Mp + . For a description of micellization of a nonionic surfactant in water (C8E5), S and M are uncharged and C is absent from the solution. Thus, for C8E5 the same equation for Km is valid for p = n. It is convenient to express Km in terms of total molal concentration of surfactant (m) the fraction of surfactant in micellar form (a = nmM/m), and the degree of micelle ionization (p/n) by using Equation (3), in which mX represents the molality of the added electrolyte (mNaCl = 0.1 mol kg-1 in the case of DTAC). The degree of micelle ionization was determined by using highperformance conductivity measurements described elsewhere.[9]
am1n nð1 aÞn ðmð1 að1 p=nÞÞ þ mX Þnp
ð3Þ
In our DSC experiments, the measured solution in the calorimetric sample cell consisted of two components; a solvent (water or 0.1 m NaCl) and a solute (C8E5, DTAC, SDS, SARC). According to Equation (1), the enthalpy of solution for an ionic surfactant in the sample cell can be expressed, at given p, T, and composition, by Equation (4): 2 ¼ H 1 þ n2 ½ H S þ H C þ aDHM H ¼ H 1 þ n2 H
Many models exist for the quantitative description of micellization/demicellization processes. The most commonly applied are the phase-separation model and the mass-action model.[1b, 8] The former considers micelles as a separated phase (micellar aggregation number is infinite) and assumes complete binding of counterions to the surface of the micelles. The latter explicitly takes into account the micellar aggregation number (n) and the effective charge of the formed micelle (p), is more general and thus more appropriate for description of micellization. According to the mass-action model, the micellization of the cationic surfactant (e.g., DTAC) can be described by Equation (1): nSþ þ ðnpÞC $ Mpþ
KM ¼
mM mnS mnp C
ð4Þ
in which H1 represents the contribution of the solvent (water or electrolyte solution), n2 the total amount of surfactant monomers, and H¯2 the partial molar enthalpy of surfactant[4a] characterized by partial molar enthalpies of the monomeric surfactant (H¯S), counterions (H¯C) and micelles (H¯M) that define the enthalpy of micellization (DHM = H¯M/n-H¯S-(1-p/n)H¯C). The output of DSC is a raw signal expressed in terms of power (also referred as heat flow), which is converted to the partial molar heat capacity of the solute (c¯p,2 ; see the Supporting Information in ref. [4b]). The same quantity could be extracted for the twostate model by taking the temperature derivative of H¯2 from Equation (4) at constant p and composition. The corresponding relative partial molar heat capacity of surfactant, normalized to zero micellization (Dcp), may be expressed in terms of the model function[4b] that assumes concentration independence of the enthalpy of micellization (DHM) and heat capacity of micellization (Dcp,M), which means that DHM ¼ DHMo (standard enChemPhysChem 2014, 15, 1827 – 1833
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thalpy of micellization) and Dcp,M = Dcop;M (standard heat capacity of micellization) [Eq. (5)]: Dcp ¼ cp;2 cp;S cp;C ¼ aDcop;M þ DHMo
@a @T n1 ;n2 ;p
ð5Þ
The model function [Eq. (5), right-hand side] for the description of DSC data is defined as follows. An expression for the temperature derivative ½@a=@T n1 ;p2 ;p is derived from the equation for standard Gibbs free energy of micellization DGoM ¼ ðRT=nÞ ln KM and the Gibbs–Helmholtz relation [Eq. (6)]: @a DHo 1 þ aðn 1Þ nð1 p=nÞ þ ¼ n 2M @T n1 ;p2 ;p RT að1 aÞ 1 að1 p=nÞ þ mX =m ð6Þ In the case of nonionic surfactant C8E5, the measured solution consists only of water and surfactant. Therefore, the last term in parenthesis is equal to zero.[4b] The temperature dependence of DGoM is obtained by using the integrated Gibbs–Helmholtz equation [Eq. (7)]: DGoM ¼ T
DGoM;Tr 1 1 Tr T o o þ DHM;T 1 þ Dc ln p;M r T Tr Tr Tr T ð7Þ
o in which DGoM;Tr and DHM;T are the standard Gibbs free energy r and standard enthalpy of micellization at the selected reference temperature Tr. The temperature dependence of DHMo is obtained from Kirchhoff’s law [Eq. (8)]:
o , conductivity measurements.[11] The best-fit values of n, DHM;T r o o o DGM;Tr , and Dcp;M were further used to calculate DGM and DHMo [from Eqs. (7) and (8)] and TDSoM ¼ DHMo DGoM at different temperatures (Figure 5). We performed fitting of the model function (by using adjusto able parameters n, DHM;T , DGoM;Tr , and Dcop;M ) to each individual r experimental Dcp versus T curve separately (individual fitting) and simultaneous (global) fitting of the model function to all Dcp versus T curves measured at different concentrations for all studied surfactants. Both approaches led to reasonably good agreement of the model function with experimental data (Figure 2). The model predicted temperature dependences of fractions of different surfactants in the micellar form (Figure 3) are in agreement with our qualitative predictions obtained by observation of DSC thermograms (Figure 2; see Section 2.1). As expected, the experimental curves are slightly better described by individual fits of the model function (four parameo ters: n, DHM;T , DGoM;Tr , and Dcop;M for the description of each r curve; see Table S1 in the Supporting Information) compared o , DGoM;Tr , and Dcop;M with the global fit (four parameters: n, DHM;T r for the description of all the curves measured at different concentrations; see Table 1). However, our analysis shows that global fitting, characterized by a much higher number of experimental points per fitting parameter, results in a significantly lower reciprocal correlation between adjustable parameters and in higher accuracy of parameters compared with individual fitting. Because the physical meaning of the thermodynamic parameters of micellization for C8E5 and DTAC (at 298.15 K: DGoM < 0, DHMo > 0, DSoM > 0, Dcop;M < 0; see Table 1) has already been discussed elsewhere[3, 4b, 9] we just mention a few additional inter-
o DHMo ¼ DHM;T þ Dcop;M ðT Tr Þ r
ð8Þ It follows that the fraction a and model function for DSC [Eq. (5), right-hand side] may be, at any temperature, described in terms of adjustable parameters n, o DHM;T , DGoM;Tr , and Dcop;M .[4b] Their r best-fit values can be obtained by fitting of the model function to the experimental data by using the Levenberg–Marquardt nonlinear regression algorithm.[10] The description of the DSC model function in the case of ionic surfactants also requires knowledge of p/n. Due to a high reciprocal correlation with the other parameters, p/n cannot be treated as an adjustable parameter.[4a] Therefore, p/n was used in the fitting procedure as a fixed value that was obtained from
Figure 3. Fraction of surfactant in the micellar form obtained from global model analysis of DSC data (Figure 2) for all studied surfactants. Lines are labeled with the corresponding surfactant concentrations.
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Table 1. Thermodynamic parameters of micellization at 298.15 K obtained by global fitting of the model function [Eq. (5)] to the DSC data (Figure 4).[a]
C8E5 DTAC SDS SARC
DGoM [kJ mol1]
DHMo [kJ mol1]
Dcop;M [kJ mol1 K1]
n[b]
10.39 0.04 12.7 0.1 17.6 0.1 14.09 0.01
18.0 0.2 3.34 0.06 1.6 0.1 3.0 0.2
0.46 0.01 0.47 0.02 0.42 0.01 0.39 0.01
19 1 15 1 20 1 12 4
[a] The value of p/n for DTAC in 0.1 NaCl was set to 0.524,[11] and for SDS and SARC in water p/n was set to 0.41[12] and 0.54 (Figure S1 in the Supporting Information). [b] The values estimated by fitting the model function to DSC data measured at a concentration around cmc (Figure 2) are significantly lower than n values obtained by scattering methods at much higher surfactant concentrations.[13]
esting observations regarding the micellization of the other two surfactants. It can be seen from Table 1 that DGoM;T is most negative for SDS, which may be ascribed to a higher degree of counterion condensation that results in DHMo < 0. Moreover, it can be seen that the thermodynamic parameters for SARC micellization are comparable with those for DTAC. The only quantity that is slightly but significantly different for the two surfactants is Dcop;M . A negative value of Dcop;M is mainly a consequence of removal of water from the surface of the surfactant nonpolar tails upon micellization. Because the tail of DTAC is one methylene group longer than that of SARC, its more negative Dcop;M value may be ascribed to the burial of this atomic group. 2.3. Thermodynamics of Micellization from DSC Measurements According to our analysis, DSC thermograms (Figure 2; circles) measured for the surfactant solutions do not correspond to transitions from pure monomeric to pure micellar states or vice versa (Figure 3). Therefore, the corresponding thermodynamic parameters of transition (micellization) cannot be obtained directly from DSC thermograms in a model-independent manner, as in the case of structural transitions of biopolymers.[14] Consequently, quantitative thermodynamic characterization of the micellization process by using DSC can only be performed in a model-dependent manner by fitting the corresponding model function to experimental DSC data. Our model-based analysis shows that the estimation of partial molar heat capacities of monomeric surfactant [cp;S þ cp;C ; see Eq. (5)] is crucial for determination of reliable thermodynamic parameters of micellization from DSC data. The problem of estimating cp;S þ cp;C was overcome to a large extent by the design of our experiments, in which the reference DSC cell was filled with a solution of low surfactant concentration (pure monomers) and the sample cell was filled with solution of higher surfactant concentration. In this way, Dcp was obtained directly across the whole temperature range. Fitting of the model function to these experimental Dcp versus T curves resulted in good agreement with experimental data for nonionic surfactants. For ionic surfactants, however, the quality of fit 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
was significantly lower, which may be ascribed to the following reasons: 1) low quality of the raw signal; namely, the enthalpy of the transition is relatively low (DHMo ; see Table 1), which leads to a low magnitude of the measured signal and thus to low signal-to-noise ratio; and 2) appropriateness of the applied model; in addition to hydrophobic interactions, the micellization of ionic surfactants is influenced significantly by the electrostatic interactions between ionized groups that contribute to the nonideal behavior of surfactant solutions. This is not taken into account in our model analysis. We have assumed that the partial molar heat capacities of monomers and the corresponding counterions [see Eq. (5)] are the same in the sample solution and in the solution in the reference cell. In this light, we believe that the discrepancy between the model and experiment observed for the ionic surfactant is due to neglect of concentration- and temperature-dependent effects, such as solution non-idealities and temperature dependence of n and p/n. Because taking into account the temperature dependence of n and p/n did not significantly improve the quality of fit, an attempt was made to correct the estimation of partial molar heat capacities of monomers and corresponding counterions by introducing an additional (global) fitting parameter that corrects the slope of c¯p,S + c¯p,C versus T curves. After this correction of Dcp, the model function [Eq. (5)] gives better agreement with the Dcp versus T curves (Figure 2). The relatively low reciprocal correlation between the additional parameter and the other fitting parameters reveals that its introduction does not significantly influence the best-fit values o of other adjustable parameters (n, DHM;T , DGoM;Tr , and Dcop;M ). r A comparison of thermodynamic parameters of micellization obtained from our analysis of DSC data and the literature ITC data[3, 4b, 12] is shown in Figure 4. It is evident that parameters obtained by different methods exhibit reasonable agreement, which is slightly better for the nonionic surfactant. Therefore, we may conclude that DSC can serve as an independent method for quantitative thermodynamic analysis of micellization of nonionic and also ionic surfactants. A shortcoming of using DSC is the fact that the degree of micelle ionization, p/n, cannot be obtained independently from model analysis of thermograms, which is also the case in model analysis of ITC curves.[4a] Therefore, p/n values determined by other methods (e.g., high-performance conductivity measurements in our case) have to be used in the fitting procedure as fixed values. Another deficiency is that, to obtain reasonable estimates of thermodynamic parameters DHM and Dcp, M, the applied model analysis has to treat them as concentration-independent quantities, which thus assumes that they are equal to their standard state values. In the case of model analysis of ITC curves, the concentration dependence of DHM and Dcp,M can be taken into account approximately.[4a] An obvious benefit of using DSC over ITC is that the temperature dependence of DGoM , DHMo , and DSoM can be obtained within a single experiment (individual fitting). The accuracy of these temperature dependences (Figure 5) can be further improved by global fitting of the model function to DSC thermograms measured at different surfactant concentrations (Figure 2). Namely, as can be seen from Table S1 in the Supporting Information, the individual fits ChemPhysChem 2014, 15, 1827 – 1833
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Figure 5. Temperature dependence of the thermodynamic parameters of micellization (DGoM , DHMo , TDSoM ) obtained from the global fitting of the model function [Eq. (5)] to the experimental DSC data.
Figure 4. Thermodynamic parameters (DGoM , DHMo , TDSoM , Dcop;M ) at 298.15 K obtained by global model analysis of DSC data (Figure 2) compared with values obtained by using ITC for C8E5,[4b] DTAC,[3] SDS[12] and SARC.[15]
of the model function to DSC data measured at low surfactant concentrations result in thermodynamic parameters that may be significantly different from those obtained by ITC.
3. Conclusions We performed thermodynamic characterization of micellization of nonionic, anionic, and cationic surfactants in aqueous solutions by using DSC. Despite the apparent weaknesses of the technique, we demonstrated that appropriate design of the experiment and treatment of the data may lead to reliable values for thermodynamic parameters of micellization that are comparable with those obtained by ITC. Using DSC in analysis of thermodynamics of micellization/ demicellization may have an exclusive advantage over ITC and also other techniques. Namely, the aggregation number and thermodynamic parameters of micellization (including Dcop;M ) can be obtained within a single experiment (individual fitting 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
approach). The results of model analysis of DSC data can be further improved by using a global fitting approach. This approach represents a more rigorous test of model appropriateness, because it takes into account all available experimental data simultaneously and results in greater confidence in the obtained thermodynamic parameters.[16] We believe that our approach may lead to a better general understanding of the temperature dependence of surfactant self-aggregation/dissociation processes. In other words, it may help researchers to avoid frequently observed mistakes in the model-independent analysis of DSC data that accompanies surfactant self-aggregation/dissociation and to improve their model-dependent analysis of these data.
Experimental Section Materials Pentaethylene glycol monooctyl ether (C8E5) was purchased from Anatrace (Maumee, OH, USA) as a 50 % solution in water and was used as received. Dodecyltrimethylammonium chloride (DTAC, > 98 %) was also purchased from Anatrace. Sodium dodecylsulfate (SDS, 98,5 %) and sodium lauroyl sarcosinate (SARC, 99 %) were purchased from Sigma Aldrich. According to the producer’s instructions, the compounds were stored in a refrigerator. Sodium chloride was purchased from Merck and kept in a desiccator before use. Demineralized water, distilled in a quartz bi-distillation apparatus (DESTAMAT Bi18E, Heraeus), had a specific conductivity of less than 5 107 S cm1 and was used for preparing solutions. ChemPhysChem 2014, 15, 1827 – 1833
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CHEMPHYSCHEM ARTICLES For each surfactant we prepared four solutions with concentrations of surfactant ranging from 6 to 15 mm, with water as the solvent for C8E5, SDS, and SARC and 0.1 m NaCl for DTAC. All molecules are presented with structural formulae in Scheme 1.
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[2]
Differential Scanning Calorimetry (DSC) DSC was performed by using a Nano-II differential scanning calorimeter (CSC, Lindon, UT, USA). After degassing (20 min) of surfactant solutions (6–15 mm), at least four consecutive scans were performed to check the reproducibility at heating rate of 1 8C min1. The sample cell of the calorimeter was filled with 0.3 mL of solution of surfactant (8–15 mm), whereas the reference cell was filled with the same volume of a 6 mm (C8E5, DTAC), 7 mm (SDS), or 13 mm (SARC) solution of the same surfactant (reference solution: at the stated concentrations, all surfactants exist in a monomeric state). Experiments with C8E5 were performed from 1–63 8C (C8E5 undergoes phase separation at 66 8C), whereas the other measurements were performed from 1–99 8C. Thermograms of Dcp versus T were obtained from raw signals (Figure 2), corrected for the baseline (DSC scans with 6, 7 mm, or 13 mm solutions of surfactants both in the sample and in the reference cell). To check that Dcp versus T curves are independent of the heating rate, we also performed the experiments at a heating rate of 2 8C min1. After subtraction of the corresponding baselines, we obtained the same thermograms as with a heating rate of 1 8C min1, which suggested that the observed transitions may be considered as reversible processes.
Acknowledgements
[3] [4]
[5]
[6] [7] [8]
[9] [10]
[11] [12] [13]
Financial support by the Slovenian Research Agency (grant P10201) is gratefully acknowledged. The work was partially supported by COST Action CM1101.
[14]
Keywords: differential scanning calorimetry · mass-action model · micelles · surfactants · thermodynamics
[15] [16]
[1] a) C. Tanford, The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed., Wiley, New York, 1980; b) R. J. Hunter, Introduction to Modern Colloid Science, Oxford University Press, Oxford, 1993;
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c) M. Malmsten, Surfactants and Polymers in Drug Delivery, Marcel Dekker, New York, 2002. a) G. C. Kresheck, W. A. Hargraves, J. Colloid Interface Sci. 1974, 48, 481 – 493; b) M. T. Bashford, E. M. Woolley, J. Phys. Chem. 1985, 89, 3173 – 3179; c) B. Andersson, G. Olofsson, J. Chem. Soc. Faraday Trans. 1 1988, 84, 4087 – 4095; d) N. M. van Os, G. J. Daane, G. Haandrikman, J. Colloid Interface Sci. 1991, 141, 199 – 217; e) K. Bijma, J. B. F. N. Engberts, Langmuir 1994, 10, 2578 – 2582; f) M. J. Blandamer, P. M. Cullis, J. B. F. N. Engberts, J. Chem. Soc. Faraday Trans. 1998, 94, 2261 – 2267. B. Sˇarac, M. Besˇter-Rogacˇ, J. Colloid Interface Sci. 2009, 338, 216 – 221. a) J. Lah, C. Pohar, G. Vesnaver, J. Phys. Chem. B 2000, 104, 2522 – 2526; b) J. Lah, M. Besˇter-Rogacˇ, T.-M. Perger, G. Vesnaver, J. Phys. Chem. B 2006, 110, 23279 – 23291. a) M. J. Blandamer, B. Briggs, J. Burgess, P. M. Cullis, G. Eaton, J. Chem. Soc. Faraday Trans. 1991, 87, 1169 – 1175; b) M. J. Blandamer, B. Briggs, J. Burgess, M. D. Butt, H. R. Brown, P. M. Cullis, J. Colloid Interface Sci. 1992, 150, 285 – 290; c) G. C. Kresheck, Langmuir 2000, 16, 3067 – 3069; d) P. R. Majhi, A. Blume, Langmuir 2001, 17, 3844 – 3851. J. N. Israelachvili, D. J. Mitchell, B. W. Ninham, J. Chem. Soc. Faraday Trans. 2 1976, 72, 1525 – 1568. G. C. Kresheck, J. Phys. Chem. B 2001, 105, 4380 – 4385. a) J. N. Phillips, Trans. Faraday Soc. 1955, 51, 561 – 569; b) M. J. Blandamer, P. M. Cullis, L. G. Soldi, J. B. F. N. Engberts, A. Kacperska, N. M. van Os, M. C. S. Subha, Adv. Colloid Interface Sci. 1995, 58, 171 – 209. T. M. Perger, M. Besˇter-Rogacˇ, J. Colloid Interface Sci. 2007, 313, 288 – 295. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York, 2001. A. Kroflicˇ, B. Sˇarac, M. Besˇter-Rogacˇ, Acta Chim. Slov. 2012, 59, 564 – 570. A. Chatterjee, S. P. Moulik, S. K. Sanyal, B. K. Mishra, P. M. Puri, J. Phys. Chem. B 2001, 105, 12823 – 12831. a) J. B. Hayter, M. Zulauf, Colloid Polym. Sci. 1982, 260, 1023 – 1028; b) E. Alami, N. Kamenka, A. Raharimihamina, R. Zana, J. Colloid Interface Sci. 1993, 158, 342 – 350; c) J. B. Hayter, J. Penfold, Colloid Polym. Sci. 1983, 261, 1022 – 1030; d) P. C. Griffiths, A. Paul, R. K. Heenan, J. Penfold, R. Ranganathan, B. L. Bales, J. Phys. Chem. B 2004, 108, 3810 – 3816. a) J. M. Sturtevant, Annu. Rev. Phys. Chem. 1987, 38, 463 – 488; b) J. E. Ladbury, B. Z. Chowdhry, Biocalorimetry: Applications of Calorimetry in the Biological Sciences, Wiley-Blackwell, Chichester, 1998; c) J. B. Chaires, Annu. Rev. Biophys. 2008, 37, 135 – 151. B. Sˇarac, unpublished results. I. Drobnak, G. Vesnaver, J. Lah, J. Phys. Chem. B 2010, 114, 8713 – 8722.
Received: January 31, 2014 Published online on April 23, 2014
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Thermodynamics of Micellization from Heat-Capacity Measurements Bojan Sˇarac,* Marija Besˇter-Rogacˇ, and Jurij Lah*[a] Differential scanning calorimetry (DSC), the most important technique for studying the thermodynamics of structural transitions of biological macromolecules, is seldom used in quantitative thermodynamic studies of surfactant micellization/demicellization. The reason for this could be ascribed to an insufficient understanding of the temperature dependence of the heat capacity of surfactant solutions (DSC data) in terms of thermodynamics, which leads to problems with the design of experiments and interpretation of the output signals. We address these issues by careful design of DSC experiments per-
formed with solutions of ionic and nonionic surfactants at various surfactant concentrations, and individual and global massaction model analysis of the obtained DSC data. Our approach leads to reliable thermodynamic parameters of micellization for all types of surfactants, comparable with those obtained by using isothermal titration calorimetry (ITC). In summary, we demonstrate that DSC can be successfully used as an independent method to obtain temperature-dependent thermodynamic parameters for micellization.
1. Introduction It has been well established that an understanding of the thermodynamic nature of micelle formation from surfactant monomers is relevant in such areas as biological self-assembly processes, folding of proteins, and protein–protein and protein– nucleic acid interactions, as well as for many industrial applications.[1] The most suitable method of determining the basic thermodynamic properties of micellization is calorimetry because it is the only method that directly measures the true model-independent enthalpy changes. Isothermal titration calorimetry (ITC) measures the concentration dependence of heat effects at constant temperature and has been frequently used in quantitative thermodynamic studies of micellization.[2] In contrast, corresponding studies of the temperature dependence of the heat capacity at a fixed surfactant concentration by using differential scanning calorimetry (DSC) are rather scarce. There are numerous reasons for that fact. From the ITC enthalpogram, one may directly obtain two important characteristics of the micellization process, that is, the enthalpy of micellization (DHM) and the critical micelle concentration (cmc). Furthermore, from ITC curves measured at different temperatures, one can also obtain the heat capacity of micellization (Dcp,M).[3] Moreover, the standard Gibbs free energy (DGoM ), standard enthalpy (DHMo ), and standard entropy (DSoM ) of micelliza[a] Dr. B. Sˇarac, Prof. Dr. M. Besˇter-Rogacˇ, Prof. Dr. J. Lah Department of Physical Chemistry Faculty of Chemistry and Chemical Technology Asˇkercˇeva 5 SI-1000, Ljubljana (Slovenia) Fax: (+ 386) 1-2419-425 E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201400096.
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tion and the micellar aggregation number (n) may be estimated by using a mass-action model analysis of the ITC curve.[4] In addition, due to the relatively high concentration of surfactant titrated into the calorimetric measuring cell, problems like low signal strength, low signal-to-noise ratio, or a baseline drift are rather scarce. On the contrary, DSC measurements on surfactant solutions are frequently affected by the above-mentioned problems and, in general, DHM, cmc, and Dcp,M cannot be estimated from DSC thermograms in a model-independent manner. For the cmc, the explanation is trivial; the DSC experiment is performed at fixed surfactant concentration. On the other hand, DHM and Dcp,M correspond to the enthalpy and heat-capacity change that accompany the transition of surfactant from a pure monomeric to a pure micellar state. Because, generally speaking, thermally induced transitions of a surfactant monitored by DSC do not reflect a transition between a pure monomeric and a pure micellar state, DHM and Dcp,M cannot be estimated as the area under the thermogram (DHM) or on the basis of extrapolation of pre- and post-transitional baselines (Dcp,M). In this light, the main problem for successful model-independent or model-dependent analysis of DSC micellization/demicellization data is a reasonable estimation of heat capacity versus temperature curves for pure surfactant monomers or pure micelles. As a consequence, DSC studies are seldom used for quantitative thermodynamic characterization of micellization/demicellization processes.[5] However, even in these otherwise high-quality studies, DSC was not used as an independent method for the determination of DGoM , DHMo , DSoM , n, and the standard heat capacity of micellization (Dcop;M ). Herein we show that DSC thermograms alone may contain sufficient information for the determination of the thermodynamic parameters of micellization. To approach this goal, we recently suggested one possible way of analyzing DSC thermoChemPhysChem 2014, 15, 1827 – 1833
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CHEMPHYSCHEM ARTICLES grams to obtain DGoM , DHMo , DSoM , Dcop;M , and n for a series of nonionic surfactants.[4b] In the next step we generalize the quantitative thermodynamic analysis of DSC micellization– demicellization data for both ionic and nonionic surfactants. Therefore, we have studied thermally induced micellization/ demicellization in four model systems (Scheme 1): nonionic
www.chemphyschem.org nary titration experiments. Usually the cmc value exhibits a U-shaped dependence on temperature (Figure 1). Therefore, by choosing a suitable concentration of the surfactant (e.g., cmc at room temperature), it is very likely that during the DSC experiment two peaks should be observed. The first, at low temperature, corresponds to micellization and the second, at higher temperature, corresponds to the demicellization process[5d, 7] (the arrows in Figure 1 denote the direction of the de-
Scheme 1. Structural formulae of the investigated surfactants.
surfactant pentaethylene glycol monooctyl ether (C8E5) in water, cationic surfactant dodecyltrimethylammonium chloride (DTAC) in 0.1 m NaCl solution, and anionic surfactants sodium dodecyl sulfate (SDS) and sodium lauroyl sarcosinate (SARC), both in water. The last belongs to the family of amino acidbased surfactants, which are biodegradable and biocompatible and, to our knowledge, this is the first DSC study on SARC. We suggest how reasonable estimates of heat capacity versus temperature curves can be obtained for pure surfactant monomers and how they may be used in global thermodynamic analysis of DSC thermograms. Comparison of the thermodynamic parameters of micellization obtained by analysis of DSC and ITC data enabled us to discuss the advantages and disadvantages of using DSC in the quantitative thermodynamic characterization of surfactant micellization/demicellization processes.
2. Results and Discussion 2.1. Detection of Micellization/Demicellization Processes by Using DSC For successful detection of micellization/demicellization processes by using DSC, the surfactant solution under investigation has to fulfill two basic conditions. The first requires that the population of micellar aggregates and monomeric surfactant molecules changes with temperature and the second requires that these changes are accompanied by uptake or release of measurable heat.[4b] In this light, an independent variable that can be varied to fulfill these two conditions is surfactant concentration in the sample cell. If the selected concentration of surfactant is close to the cmc value (e.g., at room temperature), one may expect that changes in temperature will induce surfactant micellization or demicellization.[5d] Estimates of cmc values may be obtained from the literature, from empirical relations that take into account the nature of surfactant and composition of surfactant solution,[6] or from prelimi 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 1. Scheme of the micellization/demicellization process observed in the DSC experiments. Black arrows indicate transition from monomeric to micellar state and vice versa. The solid grey line represents data from ref. [3].
scribed processes). If we lower the concentration of the surfactant in the experiment, the micellization process occurs at higher temperature, whereas the demicellization starts at a lower temperature than before. Thus, by subsequent lowering of the surfactant concentration the peaks tend to merge together and, due to negligible DHM, disappear at a concentration that corresponds to the minimum of the cmc versus T curve. Consequently, at surfactant concentrations below the minimum of the cmc versus T curve, the thermograms become very similar. This observation can be ascribed to the fact that no micellization or demicellization process takes place under such conditions. Thus, these thermograms correspond to the heat capacity versus T curves for pure surfactant monomers. In our experiments, the reference DSC cell was filled with such a solution of pure monomers and the sample cell was filled with solution of higher surfactant concentration. This design of experiments enabled us to obtain thermograms that reflect mainly the micellization/demicellization processes. Figure 2 (black circles) shows the DSC thermograms for C8E5, SDS, and SARC in water and DTAC in 0.1 m NaCl at three surfactant concentrations (see Figure 2). It is evident that micellization (and demicellization) of all surfactants is induced by increased temperature, but at different temperature ranges. For C8E5, temperature-induced micellization is visible at temperatures between 290 and 330 K (Figure 2a). The demicellization ChemPhysChem 2014, 15, 1827 – 1833
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www.chemphyschem.org KM ¼
Figure 2. Model analysis of DSC thermograms for a) C8E5, b) DTAC, c) SDS, and d) SARC. Circles: experimental data, dashed lines: individual fits, and solid lines: best global fits of the RTS model function [Eq. (5)].
process cannot be observed for C8E5 due to phase separation of the surfactant solution at around 340 K (see the Supporting Information in [4b]). This problem was not encountered for the other surfactants. Here, the measurements were performed up to 372 K and detection of both processes (micellization and demicellization) was possible. However, the quality of DSC signals at temperatures below 280 K was insufficient for further analysis. Therefore, only a part of the peaks corresponding to temperature-induced micellization of DTAC, SDS, and SARC could be observed.
2.2. Micellization as a Reversible Two-State (RTS) Process
ð1Þ
in which S + , C , and Mp + represent surfactant monomers, counterions, and micelles, respectively. To this process an apparent equilibrium constant, given by Equation (2): 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ð2Þ
can be assigned at any T. It involves equilibrium molal concentrations of species S + , C , and Mp + . For a description of micellization of a nonionic surfactant in water (C8E5), S and M are uncharged and C is absent from the solution. Thus, for C8E5 the same equation for Km is valid for p = n. It is convenient to express Km in terms of total molal concentration of surfactant (m) the fraction of surfactant in micellar form (a = nmM/m), and the degree of micelle ionization (p/n) by using Equation (3), in which mX represents the molality of the added electrolyte (mNaCl = 0.1 mol kg-1 in the case of DTAC). The degree of micelle ionization was determined by using highperformance conductivity measurements described elsewhere.[9]
am1n nð1 aÞn ðmð1 að1 p=nÞÞ þ mX Þnp
ð3Þ
In our DSC experiments, the measured solution in the calorimetric sample cell consisted of two components; a solvent (water or 0.1 m NaCl) and a solute (C8E5, DTAC, SDS, SARC). According to Equation (1), the enthalpy of solution for an ionic surfactant in the sample cell can be expressed, at given p, T, and composition, by Equation (4): 2 ¼ H 1 þ n2 ½ H S þ H C þ aDHM H ¼ H 1 þ n2 H
Many models exist for the quantitative description of micellization/demicellization processes. The most commonly applied are the phase-separation model and the mass-action model.[1b, 8] The former considers micelles as a separated phase (micellar aggregation number is infinite) and assumes complete binding of counterions to the surface of the micelles. The latter explicitly takes into account the micellar aggregation number (n) and the effective charge of the formed micelle (p), is more general and thus more appropriate for description of micellization. According to the mass-action model, the micellization of the cationic surfactant (e.g., DTAC) can be described by Equation (1): nSþ þ ðnpÞC $ Mpþ
KM ¼
mM mnS mnp C
ð4Þ
in which H1 represents the contribution of the solvent (water or electrolyte solution), n2 the total amount of surfactant monomers, and H¯2 the partial molar enthalpy of surfactant[4a] characterized by partial molar enthalpies of the monomeric surfactant (H¯S), counterions (H¯C) and micelles (H¯M) that define the enthalpy of micellization (DHM = H¯M/n-H¯S-(1-p/n)H¯C). The output of DSC is a raw signal expressed in terms of power (also referred as heat flow), which is converted to the partial molar heat capacity of the solute (c¯p,2 ; see the Supporting Information in ref. [4b]). The same quantity could be extracted for the twostate model by taking the temperature derivative of H¯2 from Equation (4) at constant p and composition. The corresponding relative partial molar heat capacity of surfactant, normalized to zero micellization (Dcp), may be expressed in terms of the model function[4b] that assumes concentration independence of the enthalpy of micellization (DHM) and heat capacity of micellization (Dcp,M), which means that DHM ¼ DHMo (standard enChemPhysChem 2014, 15, 1827 – 1833
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thalpy of micellization) and Dcp,M = Dcop;M (standard heat capacity of micellization) [Eq. (5)]: Dcp ¼ cp;2 cp;S cp;C ¼ aDcop;M þ DHMo
@a @T n1 ;n2 ;p
ð5Þ
The model function [Eq. (5), right-hand side] for the description of DSC data is defined as follows. An expression for the temperature derivative ½@a=@T n1 ;p2 ;p is derived from the equation for standard Gibbs free energy of micellization DGoM ¼ ðRT=nÞ ln KM and the Gibbs–Helmholtz relation [Eq. (6)]: @a DHo 1 þ aðn 1Þ nð1 p=nÞ þ ¼ n 2M @T n1 ;p2 ;p RT að1 aÞ 1 að1 p=nÞ þ mX =m ð6Þ In the case of nonionic surfactant C8E5, the measured solution consists only of water and surfactant. Therefore, the last term in parenthesis is equal to zero.[4b] The temperature dependence of DGoM is obtained by using the integrated Gibbs–Helmholtz equation [Eq. (7)]: DGoM ¼ T
DGoM;Tr 1 1 Tr T o o þ DHM;T 1 þ Dc ln p;M r T Tr Tr Tr T ð7Þ
o in which DGoM;Tr and DHM;T are the standard Gibbs free energy r and standard enthalpy of micellization at the selected reference temperature Tr. The temperature dependence of DHMo is obtained from Kirchhoff’s law [Eq. (8)]:
o , conductivity measurements.[11] The best-fit values of n, DHM;T r o o o DGM;Tr , and Dcp;M were further used to calculate DGM and DHMo [from Eqs. (7) and (8)] and TDSoM ¼ DHMo DGoM at different temperatures (Figure 5). We performed fitting of the model function (by using adjusto able parameters n, DHM;T , DGoM;Tr , and Dcop;M ) to each individual r experimental Dcp versus T curve separately (individual fitting) and simultaneous (global) fitting of the model function to all Dcp versus T curves measured at different concentrations for all studied surfactants. Both approaches led to reasonably good agreement of the model function with experimental data (Figure 2). The model predicted temperature dependences of fractions of different surfactants in the micellar form (Figure 3) are in agreement with our qualitative predictions obtained by observation of DSC thermograms (Figure 2; see Section 2.1). As expected, the experimental curves are slightly better described by individual fits of the model function (four parameo ters: n, DHM;T , DGoM;Tr , and Dcop;M for the description of each r curve; see Table S1 in the Supporting Information) compared o , DGoM;Tr , and Dcop;M with the global fit (four parameters: n, DHM;T r for the description of all the curves measured at different concentrations; see Table 1). However, our analysis shows that global fitting, characterized by a much higher number of experimental points per fitting parameter, results in a significantly lower reciprocal correlation between adjustable parameters and in higher accuracy of parameters compared with individual fitting. Because the physical meaning of the thermodynamic parameters of micellization for C8E5 and DTAC (at 298.15 K: DGoM < 0, DHMo > 0, DSoM > 0, Dcop;M < 0; see Table 1) has already been discussed elsewhere[3, 4b, 9] we just mention a few additional inter-
o DHMo ¼ DHM;T þ Dcop;M ðT Tr Þ r
ð8Þ It follows that the fraction a and model function for DSC [Eq. (5), right-hand side] may be, at any temperature, described in terms of adjustable parameters n, o DHM;T , DGoM;Tr , and Dcop;M .[4b] Their r best-fit values can be obtained by fitting of the model function to the experimental data by using the Levenberg–Marquardt nonlinear regression algorithm.[10] The description of the DSC model function in the case of ionic surfactants also requires knowledge of p/n. Due to a high reciprocal correlation with the other parameters, p/n cannot be treated as an adjustable parameter.[4a] Therefore, p/n was used in the fitting procedure as a fixed value that was obtained from
Figure 3. Fraction of surfactant in the micellar form obtained from global model analysis of DSC data (Figure 2) for all studied surfactants. Lines are labeled with the corresponding surfactant concentrations.
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Table 1. Thermodynamic parameters of micellization at 298.15 K obtained by global fitting of the model function [Eq. (5)] to the DSC data (Figure 4).[a]
C8E5 DTAC SDS SARC
DGoM [kJ mol1]
DHMo [kJ mol1]
Dcop;M [kJ mol1 K1]
n[b]
10.39 0.04 12.7 0.1 17.6 0.1 14.09 0.01
18.0 0.2 3.34 0.06 1.6 0.1 3.0 0.2
0.46 0.01 0.47 0.02 0.42 0.01 0.39 0.01
19 1 15 1 20 1 12 4
[a] The value of p/n for DTAC in 0.1 NaCl was set to 0.524,[11] and for SDS and SARC in water p/n was set to 0.41[12] and 0.54 (Figure S1 in the Supporting Information). [b] The values estimated by fitting the model function to DSC data measured at a concentration around cmc (Figure 2) are significantly lower than n values obtained by scattering methods at much higher surfactant concentrations.[13]
esting observations regarding the micellization of the other two surfactants. It can be seen from Table 1 that DGoM;T is most negative for SDS, which may be ascribed to a higher degree of counterion condensation that results in DHMo < 0. Moreover, it can be seen that the thermodynamic parameters for SARC micellization are comparable with those for DTAC. The only quantity that is slightly but significantly different for the two surfactants is Dcop;M . A negative value of Dcop;M is mainly a consequence of removal of water from the surface of the surfactant nonpolar tails upon micellization. Because the tail of DTAC is one methylene group longer than that of SARC, its more negative Dcop;M value may be ascribed to the burial of this atomic group. 2.3. Thermodynamics of Micellization from DSC Measurements According to our analysis, DSC thermograms (Figure 2; circles) measured for the surfactant solutions do not correspond to transitions from pure monomeric to pure micellar states or vice versa (Figure 3). Therefore, the corresponding thermodynamic parameters of transition (micellization) cannot be obtained directly from DSC thermograms in a model-independent manner, as in the case of structural transitions of biopolymers.[14] Consequently, quantitative thermodynamic characterization of the micellization process by using DSC can only be performed in a model-dependent manner by fitting the corresponding model function to experimental DSC data. Our model-based analysis shows that the estimation of partial molar heat capacities of monomeric surfactant [cp;S þ cp;C ; see Eq. (5)] is crucial for determination of reliable thermodynamic parameters of micellization from DSC data. The problem of estimating cp;S þ cp;C was overcome to a large extent by the design of our experiments, in which the reference DSC cell was filled with a solution of low surfactant concentration (pure monomers) and the sample cell was filled with solution of higher surfactant concentration. In this way, Dcp was obtained directly across the whole temperature range. Fitting of the model function to these experimental Dcp versus T curves resulted in good agreement with experimental data for nonionic surfactants. For ionic surfactants, however, the quality of fit 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
was significantly lower, which may be ascribed to the following reasons: 1) low quality of the raw signal; namely, the enthalpy of the transition is relatively low (DHMo ; see Table 1), which leads to a low magnitude of the measured signal and thus to low signal-to-noise ratio; and 2) appropriateness of the applied model; in addition to hydrophobic interactions, the micellization of ionic surfactants is influenced significantly by the electrostatic interactions between ionized groups that contribute to the nonideal behavior of surfactant solutions. This is not taken into account in our model analysis. We have assumed that the partial molar heat capacities of monomers and the corresponding counterions [see Eq. (5)] are the same in the sample solution and in the solution in the reference cell. In this light, we believe that the discrepancy between the model and experiment observed for the ionic surfactant is due to neglect of concentration- and temperature-dependent effects, such as solution non-idealities and temperature dependence of n and p/n. Because taking into account the temperature dependence of n and p/n did not significantly improve the quality of fit, an attempt was made to correct the estimation of partial molar heat capacities of monomers and corresponding counterions by introducing an additional (global) fitting parameter that corrects the slope of c¯p,S + c¯p,C versus T curves. After this correction of Dcp, the model function [Eq. (5)] gives better agreement with the Dcp versus T curves (Figure 2). The relatively low reciprocal correlation between the additional parameter and the other fitting parameters reveals that its introduction does not significantly influence the best-fit values o of other adjustable parameters (n, DHM;T , DGoM;Tr , and Dcop;M ). r A comparison of thermodynamic parameters of micellization obtained from our analysis of DSC data and the literature ITC data[3, 4b, 12] is shown in Figure 4. It is evident that parameters obtained by different methods exhibit reasonable agreement, which is slightly better for the nonionic surfactant. Therefore, we may conclude that DSC can serve as an independent method for quantitative thermodynamic analysis of micellization of nonionic and also ionic surfactants. A shortcoming of using DSC is the fact that the degree of micelle ionization, p/n, cannot be obtained independently from model analysis of thermograms, which is also the case in model analysis of ITC curves.[4a] Therefore, p/n values determined by other methods (e.g., high-performance conductivity measurements in our case) have to be used in the fitting procedure as fixed values. Another deficiency is that, to obtain reasonable estimates of thermodynamic parameters DHM and Dcp, M, the applied model analysis has to treat them as concentration-independent quantities, which thus assumes that they are equal to their standard state values. In the case of model analysis of ITC curves, the concentration dependence of DHM and Dcp,M can be taken into account approximately.[4a] An obvious benefit of using DSC over ITC is that the temperature dependence of DGoM , DHMo , and DSoM can be obtained within a single experiment (individual fitting). The accuracy of these temperature dependences (Figure 5) can be further improved by global fitting of the model function to DSC thermograms measured at different surfactant concentrations (Figure 2). Namely, as can be seen from Table S1 in the Supporting Information, the individual fits ChemPhysChem 2014, 15, 1827 – 1833
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Figure 5. Temperature dependence of the thermodynamic parameters of micellization (DGoM , DHMo , TDSoM ) obtained from the global fitting of the model function [Eq. (5)] to the experimental DSC data.
Figure 4. Thermodynamic parameters (DGoM , DHMo , TDSoM , Dcop;M ) at 298.15 K obtained by global model analysis of DSC data (Figure 2) compared with values obtained by using ITC for C8E5,[4b] DTAC,[3] SDS[12] and SARC.[15]
of the model function to DSC data measured at low surfactant concentrations result in thermodynamic parameters that may be significantly different from those obtained by ITC.
3. Conclusions We performed thermodynamic characterization of micellization of nonionic, anionic, and cationic surfactants in aqueous solutions by using DSC. Despite the apparent weaknesses of the technique, we demonstrated that appropriate design of the experiment and treatment of the data may lead to reliable values for thermodynamic parameters of micellization that are comparable with those obtained by ITC. Using DSC in analysis of thermodynamics of micellization/ demicellization may have an exclusive advantage over ITC and also other techniques. Namely, the aggregation number and thermodynamic parameters of micellization (including Dcop;M ) can be obtained within a single experiment (individual fitting 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
approach). The results of model analysis of DSC data can be further improved by using a global fitting approach. This approach represents a more rigorous test of model appropriateness, because it takes into account all available experimental data simultaneously and results in greater confidence in the obtained thermodynamic parameters.[16] We believe that our approach may lead to a better general understanding of the temperature dependence of surfactant self-aggregation/dissociation processes. In other words, it may help researchers to avoid frequently observed mistakes in the model-independent analysis of DSC data that accompanies surfactant self-aggregation/dissociation and to improve their model-dependent analysis of these data.
Experimental Section Materials Pentaethylene glycol monooctyl ether (C8E5) was purchased from Anatrace (Maumee, OH, USA) as a 50 % solution in water and was used as received. Dodecyltrimethylammonium chloride (DTAC, > 98 %) was also purchased from Anatrace. Sodium dodecylsulfate (SDS, 98,5 %) and sodium lauroyl sarcosinate (SARC, 99 %) were purchased from Sigma Aldrich. According to the producer’s instructions, the compounds were stored in a refrigerator. Sodium chloride was purchased from Merck and kept in a desiccator before use. Demineralized water, distilled in a quartz bi-distillation apparatus (DESTAMAT Bi18E, Heraeus), had a specific conductivity of less than 5 107 S cm1 and was used for preparing solutions. ChemPhysChem 2014, 15, 1827 – 1833
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CHEMPHYSCHEM ARTICLES For each surfactant we prepared four solutions with concentrations of surfactant ranging from 6 to 15 mm, with water as the solvent for C8E5, SDS, and SARC and 0.1 m NaCl for DTAC. All molecules are presented with structural formulae in Scheme 1.
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[2]
Differential Scanning Calorimetry (DSC) DSC was performed by using a Nano-II differential scanning calorimeter (CSC, Lindon, UT, USA). After degassing (20 min) of surfactant solutions (6–15 mm), at least four consecutive scans were performed to check the reproducibility at heating rate of 1 8C min1. The sample cell of the calorimeter was filled with 0.3 mL of solution of surfactant (8–15 mm), whereas the reference cell was filled with the same volume of a 6 mm (C8E5, DTAC), 7 mm (SDS), or 13 mm (SARC) solution of the same surfactant (reference solution: at the stated concentrations, all surfactants exist in a monomeric state). Experiments with C8E5 were performed from 1–63 8C (C8E5 undergoes phase separation at 66 8C), whereas the other measurements were performed from 1–99 8C. Thermograms of Dcp versus T were obtained from raw signals (Figure 2), corrected for the baseline (DSC scans with 6, 7 mm, or 13 mm solutions of surfactants both in the sample and in the reference cell). To check that Dcp versus T curves are independent of the heating rate, we also performed the experiments at a heating rate of 2 8C min1. After subtraction of the corresponding baselines, we obtained the same thermograms as with a heating rate of 1 8C min1, which suggested that the observed transitions may be considered as reversible processes.
Acknowledgements
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Financial support by the Slovenian Research Agency (grant P10201) is gratefully acknowledged. The work was partially supported by COST Action CM1101.
[14]
Keywords: differential scanning calorimetry · mass-action model · micelles · surfactants · thermodynamics
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Received: January 31, 2014 Published online on April 23, 2014
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