A comparative study of the physicochemical properties of perfluorinated and hydrogenated amphiphiles

Journal of Colloid and Interface Science 288 (2005) 247–260 www.elsevier.com/locate/jcis

A comparative study of the physicochemical properties of perfluorinated and hydrogenated amphiphiles Elena Blanco a , Alfredo González-Pérez a , Juan M. Ruso a,∗ , Rosa Pedrido b , Gerardo Prieto a , Félix Sarmiento a a Group of Biophysics and Interfaces, Department of Applied Physics, Faculty of Physics, University of Santiago de Compostela,

E-15782 Santiago de Compostela, Spain b Departamento de Química Inorgánica, Facultad de Química, Universidad de Santiago de Compostela, Spain

Received 16 November 2004; accepted 25 February 2005 Available online 9 April 2005

Abstract In this work we studied and compared the physicochemical properties of perfluorinated (sodium perfluoroheptanoate, C7FONa, and perfluorooctanoate, C8FONa) and hydrogenated (sodium octanoate, C8HONa, decanoate, C10HONa, and dodecanoate, C12HONa) amphiphiles. First, we determined their Krafft points to study the solubility and appropriate temperature range of micellization of these compounds. The critical micelle concentration (cmc) and ionization degree of micellization (β) as a function of temperature (T ) were estimated from conductivity data. Plots of cmc vs T appear to follow the typical U-shaped curve with a minimum Tmin . The results show that the surfactants with CF2 /CH2 ratio of 1.5 between alkyl chains (C12HONa–C8FONa and C10HONa–C7FONa) have nearly the same minimum value for cmc against temperature. The comparison between the cmc of hydrogenated amphiphiles and the corresponding perfluorinated amphiphiles must be done at this point. Thermodynamic functions of micellization were obtained by applying different theoretical models and choosing the one that best fit our experimental data. Although perfluorinated and hydrogenated amphiphiles present similar thermodynamic behavior, we have found a variation of 1.3 to 1.7 in the CF2 /CH2 ratio, which did not remain constant with temperature. In the second part of this study the apparent molar volumes and adiabatic compressibilities were determined from density and ultrasound velocity measurements. Apparent molar volumes at infinite dilution presented the ratio 1.5 between alkyl chains again. However, apparent molar volumes upon micellization for sodium perfluoroheptanoate indicated a different aggregation pattern.  2005 Elsevier Inc. All rights reserved. Keywords: Perfluorinated; Hydrogenated; Krafft point; Thermodynamics; Critical micelle concentration minimum

1. Introduction Amphiphilic molecules constitute an important class of chemicals with numerous applications in chemical processing industries, in the formulation of agricultural chemicals, pharmaceuticals, and household products, in mineral processing technologies, and in food processing industries. Among the most noteworthy characteristics of surfactants is their behavior in dilute aqueous solutions, where they selfassemble to form aggregates, above a concentration known * Corresponding author. Fax: +34 981 520 676.

E-mail address: [email protected] (J.M. Ruso). 0021-9797/$ – see front matter  2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.02.085

as the critical micelle concentration (cmc), to achieve segregation of their hydrophobic moieties from water. The physical phenomenon responsible for this behavior is referred to as the hydrophobic effect and is due to a subtle balance between intermolecular energies and entropies. Depending on the type of surfactant and the solution conditions, the aggregates may have a closed structure with spherical, globular, or rodlike shapes [1]. Perfluorocarbons, surfactants where all the hydrogens in the hydrophobic moiety have been replaced by fluorine, have been much less studied than the corresponding hydrogenated surfactants, despite their technical interest due to their potential usefulness [2]. Fluorine is the most electronegative

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of all elements, and its dense electron cloud has very low polarizability [3]. On the other hand, the reduced conformational freedom allowed to perfluorinated tails produces bulky and stiff chains [4]; hence the aggregates of perfluorinated amphiphiles have a tendency to form a structure with less surface curvature [5]. These properties confer special characteristics on these amphiphiles compared with the corresponding hydrogenated ones; thus, aromatic perfluorocarbons have large quadrupolar moments that are similar in magnitude, yet opposite in sign, or aliphatic perfluorocarbons have great compressibilities and viscosities but lower internal pressures and refractive index [6]. However, the best known relationship between these molecules is the one that refers to their cmcs: the cmc of a perfluorinated surfactant is approximately equal to that of a hydrocarbon surfactant with a hydrocarbon chain 1.5 times longer, at a fixed temperature, than the fluorocarbon chain [7]. A comparative study of perfluorinated and nonfluorinated surfactant systems is interesting in many ways—for example, from a theoretical point of view. These two systems can be used to study the hydrophobic effect or to try to predict a priori the physicochemical properties of the perfluorinated compounds on the basis of the properties of their corresponding hydrogenated counterparts. The aim of this work is to study and relate the physicochemical properties of hydrogenated surfactants and the corresponding perfluorinated surfactants as a function of temperature and alkyl chain. For this reason we have chosen the sodium alkanoates (octanoate, decanoate, dodecanoate, and tetradecanoate) and the corresponding perfluoroalkanoates (perfluoroheptanoate and perfluorooctanoate). To carry out this aim, in the first part of this work, the electrical conductivity technique was used over a wide range of temperatures and the results are discussed for comparative purposes, with different thermodynamic models being proposed. The results were then compared for a better understanding of fluorocarbon/hydrocarbon compounds. In the second part, we measured densities and ultrasound velocities to obtain volumetric properties of solutes, such as the partial molar volume or adiabatic compressibility, known to be sensitive to the degree and nature of solute hydration. The partial molar volume of a solute includes the structural volume of the solute in the solvent and the volume change of the solvent in the process of shell formation around the solute [8]. At low solute concentrations, the measured volume and compressibility properties reflect the contribution of both solvent and solute intrinsic properties. Thus, the results have to be carefully interpreted to discriminate between the intrinsic compressibility of a solute and that due to interactions occurring at the interface in contact with the solvent [9]. These quantities can be obtained from experimental data of densities and ultrasound velocities. Thus, densities and ultrasound measurements are used in a wide variety of colloidal solutions: typical surfactants [10], amphiphilic drugs [11], carbohydrates [12], perfluoroalkanoates [13],

r α,ω-ammonicarboxylic acids [14], or mixtures of surfactants [15].

2. Experimental 2.1. Materials Sodium octanoate and sodium perfluorooctanoate of at least 97% purity were obtained from Lancaster Synthesis Ltd. Sodium decanoate, sodium dodecanoate, and sodium tetradecanoate, with purity over 99%, were obtained from Sigma Chemical Co. All these products were used as received. All measurements were performed using distilled water with conductivity below 3 µS cm−1 at 298.15 K. Sodium perfluoroheptanoate (C7FONa) was prepared from the corresponding carboxylic acid (perfluoroheptanoic acid, C7FOH, Aldrich). A 0.55-g (13.73 mmol) solution of NaOH in 10 ml of water was mixed with a hot solution of 5 g (13.73 mmol) of C7FOH in ethanol. The resulting mixture was stirred and concentrated by evaporation to a small volume (5 ml) and then 10 ml of hot ethanol was added. The resulting solution was concentrated again to a small volume (5 ml) and the salt precipitated by adding 90 ml of chloroform immediately to the concentrated solution. The salt was filtered, redissolved in ethanol, and recrystallized following the related procedure. The final product was vacuum-dried and stored under anhydrous conditions. Yield was 83%. EA (Found: C 21.3%, C9 F13 O2 Na required: C 21.7%). FAB (mnba): 408.9 (100%). 13 C-NMR (CD3 OD, ppm): δ 105.6–116.6 (3C), 120.4 (C), 124.2 (C), 162.9 (C), 170.7 (Ccarbonyl ). 2.2. Methods Conductivities were measured using a Kyoto Electronics Model CM-117 conductometer with a cell type K-121. The cell constant was determined using KCl solutions following the procedure suggested by Monk [16]. All measurements were taken in a PolyScience Model PS9105 thermostatted waterbath, at a constant temperature within ±0.05 K. The determination of the isotherms of conductivity was carried out by continuous dilution of a concentrated sample prepared by weight. The duration of dynamics processes can vary from 10−8 (which is the time it takes a surfactant to leave or enter a micelle) to 10−2 (the time scale of the fusion of micelles), so the equilibrium process is guaranteed in just a few seconds after dilution [17]. Ultrasound velocities and densities were continuous, simultaneous, and automatically measured using a DSA 5000 Anton Paar density and sound velocity analyzer. This equipment possesses a new generation vibrating tube for density measurements and a stainless-steel cell connected to a sound velocity analyzer with resolution ±10−6 g cm−3 and 10−2 m s−1 , respectively. Both speed of sound and density

E. Blanco et al. / Journal of Colloid and Interface Science 288 (2005) 247–260

are extremely sensitive to temperature, so this was controlled to within ±10−3 K through the Peltier effect. The reproducibility of density and ultrasound measurements was ±10−6 g cm−3 and 10−2 m s−1 , respectively.

3. Results and discussion 3.1. Krafft temperature Aqueous surfactant solutions are completely solubilized only above the Krafft point. Initially, the Krafft point was interpreted as the point at which solid hydrated agent and micelles are in equilibrium with monomers, so at a given pressure, in terms of the phase rule, the point is fixed [18]. More recently, Moroi [19] concluded that the Krafft point is the temperature at which the solubility of surfactants as monomers becomes high enough for the monomers to commence aggregation or micellization. In any case, it is an important parameter used to study the appropriate temperature range of micellization. Thus, from a concentration of twice the cmc, the temperature was increased and conductivity was measured simultaneously for each point until equilibrium was reached. In Fig. 1 we show the curves of normalized conductivity (κ/κmax ) against temperature for sodium decanoate, dodecanoate, tetradecanoate, and perfluorooctanoate. Krafft points are not observed when the Krafft point is below the freezing point of water, as in the case of sodium octanoate. For sodium perfluoroheptanoate, electrical conductivity increases from 274.15 to 279.15 K, then being constant until 288.45 K where it begins to increase linearly. We have not found a reasonable explanation for this anomalous behavior yet, and probably it requires further investigation. However, it could be related to the irregular behavior previously reported for even alkyl chain carbon numbers [20] of sodium carboxylates.

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Although there are authors who prefer to use the second break in the slopes [21], we calculated Krafft points from the first break, following the nomenclature recommended by the IUPAC [22]. The Krafft points obtained were 275.24, 286.14, 291.45, and 282.76 K for sodium decanoate, dodecanoate, tetradecanoate, and perfluorooctanoate, respectively. Krafft temperature increases with surfactant chain length. The Krafft value of sodium perfluorooctanoate is approximately equal (from linear fits we have obtained a value of 11.72 carbons in the alkyl chain) to that of sodium dodecanoate, whose hydrocarbon chain is 1.5 longer. 3.2. Effect of temperature on critical micelle concentration In continuing with our study, we obtained the isotherms of molality dependence of electrical conductivity for the compounds under study. For all temperatures, the concentration dependence of the electrical conductivity shows a monotonic increase with a gradual decrease in slope, this being an experimental confirmation of the self-assembly process. Generally, to calculate the critical concentration, the definition of Phillips [23], which is in widespread use [24], was used and seems to be the best method. In agreement with Phillips, the critical concentration is defined by
3  d κ (1) = 0, dc3 where κ denotes the conductivity and c is the critical concentration. Recently, Carpena and co-workers [25,26] proposed a new approach to analyze the conductivity– concentration data of ionic surfactant solutions. The method is based on the fit of the experimental raw data to a simple nonlinear function obtained by direct integration of a Boltzmann-type sigmoid function having the analytical expression f (m) =

A1 − A2 + A2 , 1 + exp(m − cmc/m)

(2)

where m is the amphiphilic concentration, A1 (A2 ) represents the asymptotic value for small (large) values of m, cmc represents the central point of the transition, and m deals with the width of the transition. If the derivative of the original data behaves as a sigmoid, then the original data behaves as a sigmoid should behave as the integral of the sigmoid. A direct integration of Eq. (2) yields F (m) = F (0) + A1 m

 1 + exp(m − m/m) , (3) + m(A2 − A1 ) ln 1 + exp(−cmc/m)

Fig. 1. Normalized conductance, κ/κmax , versus temperature for C10HONa (1), C12HONa (!), C14HONa (P), and C8FONa (2). The corresponding Krafft temperatures are labeled TK .



where F (0) represents the value of F (m) at m = 0. The cmc values obtained by this method for our systems in the temperature range studied are presented in Table 1 (estimated uncertainties ±10%). The cmc data are in good agreement with previous data reported [27,28]. In Fig. 2

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Table 1 Values of critical micelle concentration (cmc in mol kg−1 ) for sodium octanoate (C8HONa), decanoate (C10HONa), dodecanoate (C12HONa), perfluoroheptanoate (C7FONa), and perfluorooctanoate (C8FONa) at different temperatures (T in K) C8HONa

C10HONa

C12HONa

C7FONa

C8FONa

T

cmc

T

cmc

T

cmc

T

cmc

T

cmc

300.15 303.15 305.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.3783 0.3733 0.3703 0.3644 0.3549 0.3508 0.3455 0.3433 0.3417 0.3426 0.3457

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.1130 0.1093 0.1060 0.1038 0.1020 0.1013 0.1020 0.1031 0.1058

288.15 293.15 298.15 303.15 311.15 313.15 318.15 323.15 328.15

0.0305 0.0286 0.0272 0.0261 0.0251 0.0248 0.0247 0.0249 0.0255

276.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 326.15 333.15

0.1032 0.0946 0.0902 0.0867 0.0824 0.0808 0.0797 0.0793 0.0799 0.0827 0.0863

293.15 298.15 303.15 308.15 310.15 313.15 315.15 318.15 323.15 328.15

0.0327 0.0313 0.0302 0.0297 0.0294 0.0295 0.0293 0.0293 0.0295 0.0301

hydration, leading to an increase in repulsion between polar head groups. Once we emphasized the importance of this point, we considered that this should be the point where the relationship between the cmc of perfluorosurfactants and hydrosurfactants must be calculated, the point where both factors are compensated. But first we had to choose a good model to analyze the variation of cmc with temperature and to define the minimum with the best accuracy. A first analysis of the relations between cmc and temperature was developed by La Mesa [31]. He assumed that cmcmin and Tmin are reference values for the micellization, so it is possible to fit experimental data to the equation    cmc T γ (4) − 1 = 1 − , cmcmin Tmin  Fig. 2. Normalized cmc, cmc/cmcmin , versus temperature: (A) C8HONa (1), C10HONa (!), and C12HONa (P); (B) C7FONa (2) and C8FONa (").

we show the curves of normalized cmc change with temperature for the present series of surfactants. Each plot appears to follow a U-shaped curved with a minimum at a certain temperature, Tmin . The values of Tmin , calculated by the least-squares fitting of the experimental values of the cmc, were 333.72, 313.70, 317.01, 313.03, and 316.18 K for C8HONa, C10HONa, C12HONa, C7FONa, and C8FONa, respectively. The surfactants with the ratio of 1.5 between alkyl chains (C12HONa–C8FONa and C10HONa–C7FONa) have nearly the same minimum. Zielinski et al. [29,30] have postulated that the occurrence of a minimum on these plots suggests the existence of at least two factors affecting the cmc value in aqueous solution: hydrophilic hydration around the surfactant in the aggregate state and two types of hydration around surfactant molecules in the monomer state, hydrophobic around the alkyl chain and hydrophilic around the polar head group. Thus, the observed minimum reflects the effect of raising the temperature in a balance between a gradual dehydration of the hydration shell around the hydrocarbon chain, promoting micelle formation, and partial dehydration of the hydrophilic

where γ is an exponent whose numerical value is 1.74 ± 0.03 without physical meaning. Although La Mesa used his model to forecast cmc values in a wide range of experimental conditions and with different surfactants, it did not work properly with our systems. Later, Muller [32] described the variation of cmc with temperature by means of the equation

    1 − Tmin cmc Tmin ln = Cp /(1 + β)R + ln , cmcmin T T (5) where Cp is the heat capacity and β the degree of ionization. Although in this equation variables with physical meaning are introduced, the preliminary assumptions (Cp and β constant with temperature) are quite severe. However, Eq. (5) fits relatively well with our experimental data. The values obtained are listed in Table 2. Kang et al. [33] proposed a simple modification of La Mesa’s equation, introducing a constant: (cmc/cmcmin ) − 1 = A|1 − T /Tmin |B . By fitting our results to this equation we obtained the numerical values listed in Table 3. These values seem to be in good agreement with the finding that exponent B should be 2 [34,35]. These authors have also proposed an elegant description of the cmc as a function of temperature; however, we believe that the excessive number

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Table 2 Parameters resulting from the fitting of experimental cmc vs T to Eq. (5) Surfactant C8HONa C10HONa C12HONa C7FONa C8FONa

∗ ln xcmc

Tmin (K)

−5.0945 ± 0.0016 −6.3044 ± 0.0021 −7.7141 ± 0.0022 −6.5516 ± 0.0021 −7.5477 ± 0.0008

334.86 ± 1.29 313.04 ± 0.51 317.57 ± 0.55 312.00 ± 0.26 316.13 ± 0.23

Cp (J mol−1 K−1 ) −188.08 ± 14.26 −361.15 ± 22.77 −536.24 ± 25.14 −444.69 ± 16.53 −445.29 ± 12.22

Table 3 Parameters resulting from the fitting of experimental cmc vs T to equation proposed by Kang et al. (see text) Surfactant

A

B

C8HONa C10HONa C12HONa C7FONa C8FONa

8.33 ± 1.35 9.86 ± 1.00 27.23 ± 3.36 14.69 ± 2.50 24.61 ± 8.68

1.89 ± 0.07 1.77 ± 0.04 1.98 ± 0.05 1.80 ± 0.07 2.03 ± 0.13

of variables in their model has forced them to introduce too severe approximations. For example, the compensation temperature and the temperature at which entropy becomes zero have constant values for most surfactants, but it is possible to find references in the literature that show that these values depend on the surfactant [36,37] and even on the electrolyte concentration [38]. Recently, Rodriguez et al. [37] improved Muller’s equation by assuming that the degree of ionization of the micelles increases linearly with temperature, β = β0 + β1 T , and the standard change in heat capacity varies linearly in the temperature range studied [39,40] according to the equation 0 0∗ CP,m = CP,m + α(T − T ∗ ).

(6)

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Table 4 Parameters resulting from the fitting of experimental cmc vs T to Eq. (7) Surfactant C8HONa C10HONa C12HONa C7FONa C8FONa

T∗ (K) 333.4 314.2 317.6 312.0 316.5

∗ ln xcmc

−5.097 −6.308 −7.718 −6.550 −7.547

0∗ CP,m

(J mol−1 K−1 ) −307.55 −507.40 −741.08 −490.93 −524.62

α/R (K−1 ) −1.0511 −1.6367 −1.6203 0.17012 0.00047

Thus, based on these assumptions, they arrived at the following equation:   
∗ 1 T β0 − 2 ∗ ∗ −2− ln xcmc = ln xcmc 1 + β1 T 2−β T β1 T ∗
  β0 − 2 1 1+ + ∗ 2−β β1 T ∗ 
0∗ CP,m T∗ T 1− − ln ∗ + (2 − β)R T T 
∗2 T −T2 T α + T ∗ ln ∗ . + (7) (2 − β)R 2T T The results obtained are listed in Table 4. These results are closer to those obtained experimentally using microcalorimetry [41]. This relatively good agreement between direct microcalorimetric data and results obtained from variation of cmc against temperature is an interesting result. In a recent work [42], it was concluded that the determination of thermodynamic parameters through the cmc is not amenable due to the effects of the temperature on the aggregation number and the shape of the micelle. However, we have attributed this good agreement to the low aggregation number of these surfactants under study [43–49]. Fig. 3 shows the fits of experimental points to the different models and it is pos-

Fig. 3. (A) Reduced variables fit for sodium perfluoroheptanoate using the Kim–Lim equation (solid line) and the La Mesa equation (dashed line). (B) Fits of the temperature dependence of ln xcmc using the Muller equation (dashed line) and the Rodriguez equation (solid line).

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sible to deduce by simple visual inspection that the model proposed by Rodriguez et al. is the best fit for our results. Based on these results we found a relationship (hydrocarbon/fluorocarbon) of 1.47 for C8FONa and C7FONa and this value remained constant for the temperature range studied. The relationship obtained for the heat capacity at the minimum was 1.35 and 1.48 for C8FONa and C7FONa, respectively. 3.3. Thermodynamics of micellization Once we calculated the cmc minimum and the heat capacity at this point the thermodynamic functions for the same point can be easily derived, obtaining ∗ Hm0∗ = RT ∗2 β1 ln xcmc ,
 0∗ β0 − 2 Hm 0∗ 2 + . Sm = T∗ β1 T ∗

(8) (9)

Now the quantities for the temperature range studied can be calculated using 

0 0∗ CP,m (10) = CP,m +α T −T∗ ,



 0 0∗ 0∗ ∗ ∗ 2 Hm = Hm + CP,m T − T + (α/2) T − T , (11) 

0 0∗ 0∗ = Sm + CP,m ln T /T ∗ Sm  

+ α T − T ∗ − T ∗ ln T /T ∗ . (12) Finally, the standard free energy is obtained from 0 G0m = Hm0 − T Sm = (2 − β)RT ln xcmc ,

(13)

where the right-hand side of the equation can be obtained based on both the charged phase separation model (assuming that the aggregation number is large enough this model provides a good approximation for relative comparisons [50,51]) and the mass action model [52]. Numerical values obtained for heat capacity, enthalpy and entropy are listed in Tables 5 and 6. The results show that for all the surfactants studied, while at low temperatures entropy dominates the process of micellization, at higher temperatures the enthalpic contribution becomes significant. Calculated values of Hm0 show that the aggregation of the surfactants becomes increasingly exothermic with increase in temperature. Positive values of Hm0 are generally attributed to the release of structured water from the hydration layers around the hydrophobic parts of the molecule [53] during the formation of aggregates. Such hydrophobic interactions become increasingly insignificant with the partial breakdown of the structure of water as the temperature is increased and the aggregation becomes primarily an enthalpic process; the negative Hm0 values suggest the importance of the London-dispersion interactions as the major force for aggregation [54]. Similar changes from entropic to enthalpic aggregation with temperature increase have been observed for many surfactants [55], amphiphilic penicillins [56] and betablockers [57,58], with similar critical temperatures. The

Table 5 0 0 (J mol−1 ), and enHeat capacity, CP,m (J mol−1 K−1 ), enthalpy, Hm

0 (J mol−1 K−1 ), obtained using Eqs. (10)–(12), for sodium octropy, Sm tanoate, decanoate, and dodecanoate at different temperatures, T (K)

T (K)

0 CP,m

0 Hm

0 Sm

C8HONa 298.15 300.15 303.15 305.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.33 −17.13 −43.34 −60.81 −87.01 −130.68 −174.35 −218.02 −261.69 −305.37 −349.04 −392.71

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

−153.09 −221.09 −289.10 −357.11 −425.11 −493.12 −561.12 −629.13 −697.13

288.15 293.15 298.15 303.15 311.15 313.15 318.15 323.15 328.15

−344.54 −411.86 −479.19 −546.51 −654.23 −681.16 −748.48 −815.81 −883.13

5414 5397 5307 5203 4981 4437 3674 2693 1494 76 −1559 −3413

76.7 76.6 76.3 76.0 75.2 73.5 71.1 68.0 64.3 60.0 55.2 49.8

271 −664 −1939 −3555 −5510 −7806 −10441 −13417 −16733

75.3 72.0 67.7 62.4 55.9 48.6 40.2 30.9 20.8

6475 4584 2357 −207 −5010 −6345 −9919 −13830 −18077

118.8 112.3 104.8 96.3 80.6 76.3 65.0 52.8 39.8

C10HONa

C12HONa

0 values calculated from these two thermodynamic propSm erties decrease progressively with temperature, showing that at temperatures below the cmc minimum the aggregation is 0 . Fig. 4 shows the moddriven solely by the positive Sm erate dependence of standard free energy of micellization vs temperature for these surfactants, observing similar patterns for all the surfactants. These values show quite good agreement with those previously obtained using different models and techniques. Thus, enthalpy values from 5.12 and 17.45 kJ mol−1 at 288 K to 4.8 and 3.67 kJ mol−1 at 318 K have been found for sodium octanoate and decanoate, respectively [59]. Free energies for sodium octanoate change from −12 kJ mol−1 at 290 K to −15kJ mol−1 at 360 K [27]. And for sodium perfluorooctanoate values from −25.53 and 9.19 kJ mol−1 at 293 K to −27.88 and −13.79 kJ mol−1 at 323 K for free energy and enthalpy respectively were found [60]. To correlate the enthalpic and entropic contributions to 0 , the so-called compensamicellization, Hm0 versus Sm tion phenomenon [61,62] was plotted in Fig. 5. The re-

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253

Table 6 0 0 (J mol−1 ), and en(J mol−1 K−1 ), enthalpy, Hm Heat capacity, CP,m

0 (J mol−1 K−1 ), obtained using Eqs. (10)–(12), for sodium pertropy, Sm fluoroheptanoate and perfluorooctanoate at different temperatures, T (K)

T (K)

0 CP,m

0 Hm

0 Sm

C7FONa 276.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 326.15 332.15

−440.23 −450.13 −457.20 −464.26 −471.33 −478.40 −485.47 −492.54 −499.61 −510.92 −520.53

8217 5101 2833 529 −1809 −4183 −6593 −9038 −11518 −15561 −19068

101.6 90.5 82.5 74.6 66.7 58.8 50.9 43.1 35.2 22.6 12.0

C8FONa 293.15 298.15 303.15 308.15 310.15 313.15 315.15 318.15 323.15 328.15

−524.71 −524.69 −524.67 −524.65 −524.64 −524.63 −524.62 −524.61 −524.59 −524.57

993 −1630 −4253 −6876 −7926 −9499 −10549 −12123 −14746 −17368

93.9 85.0 76.3 67.7 64.3 59.3 55.9 51.0 42.8 34.7

Fig. 4. Standard free energy of micellization as a function of temperature for C8HONa (1), C10HONa (!), C12HONa (P), C7FONa (2), and C8FONa ("). 0. sults were fitted to the equation Hm0 = Hm0∗ + Tc Sm Tc is the compensation temperature and reflects the cooperation of enthalpy with entropy for the micellization process. Values obtained for Tc were 326.27, 311.82, 310.41, 304.48, and 310.15 K for C8HONa, C10HONa, C12HONa, C7FONa, and C8FONa, respectively. When hydrated ionic groups of surfactants are bound to surrounding water molecules, the process leads to an energetic stabilization (negative enthalpy changes). At the same time, the motion of water molecules bound to ionic groups causes a decrease in entropy. In this situation, the driving force of micelle

Fig. 5. Enthalpy–entropy compensation plot for aqueous solutions of C8HONa (1), C10HONa (!), C12HONa (P), C7FONa (2), and C8FONa (").

formation comes only from the enthalpic term; that is, the standard Gibbs energy of micellization only has an enthalpic term, Hm0∗ . Then, a quantitative measure of hydrophobicity of the surfactants can be expressed by the value of this intercept. The corresponding values amount to: −19,571.91, −23,065.93, −30,199.09, −22,325.19 and −27,967.15 J mol−1 for C8HONa, C10HONa, C12HONa, C7FONa, and C8FONa, respectively. Comparison of thermodynamic values between the hydrogenated surfactants and the perfluorinated ones is now quite complicated due to the propagation of errors; however, it is possible to obtain some general remarks. All surfactants behave in the same manner; that is, their aggregation at higher temperatures would tend to be a purely enthalpic phenomenon. It has been found that the incremental change in the standard free energy of adsorption for the transfer of a CF2 group from water to the air–water interface is −5.1 kJ mol−1 versus −2.6 kJ mol−1 for a CH2 group [63], values which are really close to those calculated in this study (see Fig. 4) for the standard free energy of micellization: −5.5 and −2.9 kJ mol−1 for CF2 and CH2 , respectively. In the case of hydrocarbon surfactants it has been shown that the total hydrophobic contributions to free energy changes derive from the interactions among chains and interactions responsible for removing the chains from water [60]; thus the roughly similar free energies of micelle formation for C10HONa/C7FONa and C12HONa/C8FONa indicate a significantly greater contribution to the free energy arising from the removal of the chain from water for the fluorocarbon surfactant. In fact, it has been demonstrated that fluorocarbon gases are less soluble in water than the corresponding hydrocarbon ones [64]. Ravey and Stebe [65] have shown that hydrogen and fluorine in the surfactant chain create different cavities in the water, which explains the differences in their hydrophobicity. These authors found ratios (CF3 /CH3 ) of 2, 1.3, and 1.75 for entropy by comparing, entropy, enthalpy, and free energy in their study with nonionic surfac-

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tants. Of course these values are essentially indicative, since they should depend somewhat on temperature and on chain length. For our study we compared values corresponding to Tmin , and from the results an obvious tendency could not be deduced. Nevertheless, a ratio between 1.3 and 1.7 was obtained, which does not remain constant with temperature. 3.4. Densities and molar apparent volumes It is well known that the apparent molar volume, Vφ , is a classical and well defined thermodynamic quantity for binary systems that can be obtained from density measurements using the equation Vφ =

M 103 (ρ − ρ0 ) − , ρ mρρ0

(14)

where M is the molecular weight of the solute, ρ the density of the solution, m the molality, and ρ0 the density of pure solvent. The apparent molar volumes of all the surfactants under study were calculated as a function of molalities at the different temperatures studied. The plots of Vφ versus molality for sodium perfluoroheptanoate and sodium decanoate at different temperatures are presented in Fig. 6 (we have not plotted all temperatures for clarity). The apparent molar volumes show initial smooth behavior followed first by a sharp increase in the region close to the cmc and then by an approach to a saturation value at the highest concentration studied. Analogous behavior was observed for the other surfactants. Since it is generally accepted that the surfactant solutions in the premicellar region behave as singly dispersed systems, they may be described by the relation Vφ = Vφ0 + Av m1/2 + Bv m + · · · ,

(15)

where Vφ0 is the apparent molar volume at infinite dilution, Av is the Debye–Hückel limiting law coefficient, and Bv is

an adjustable parameter related to a pair interaction [66] and equivalent to the second virial coefficient which measures the deviation from the limiting law due to the nonelectrostatic solute–solute interactions. More coefficients are not considered in the case of volume in Eq. (15) [67]. Values obtained for Vφ0 and Bv are summarized in Tables 7 to 11. The uncertainty of the data in the high dilution region does not allow us to obtain accurate values of Bv ; however, qualitative conclusions can be drawn. This coefficient is generally negative except in hydrogen-bonding interactions [10], as expected for 1:1 electrolytes. At high temperatures this parameter assumes positive values [68]. Thus, the sign of the parameter Bv could be associated with the presence of dimers in the premicellar region, a subject of great controversy related to the cmc definition. The micellization of an amphiphile can be explained by stepwise aggregation models: the micelle is distributed from dimers to infinite size, with drugs and bile salts showing less micellar self-association patterns than surfactants. So the formation of higher polymers may often overshadow the dimerization and may lead to difficulties in even detecting them. In fact, dimerization does not cause any inflection in the concentration dependence of certain physical properties [69]. In the literature it is possible to find positive values that lead to dimerization in the premicellar region for the amphiphilic drugs nortriptyline, the tranquilizer phenitiazine, the drugs promazine, chlorpromazine and promethazine, and penicillin V, and the antidepressant imipramine hydrochloride. With these amphiphiles, different techniques, such as calorimetry and osmotic pressure of frontal derivative chromatography, have demonstrated the existence of preaggregation at concentrations well below the cmc [70]. On the other hand, negative values were found for: typical surfactants such as the alkyl sulfates or tetralkylammonium salts [71]; Fukada et al. found negligibly small values for aqueous solutions of Cn AB and Cn TAB at 5 ◦ C [72]; for amitriptilyne

Fig. 6. Plots of molar apparent volume against molality at different temperatures for: (A) C7FONa and (B) C10HONa.

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255

Table 7 Apparent molar volumes at infinite dilution, Vφ0 , apparent molar volumes at the cmc, Vφcmc , apparent molar volumes upon micellization, Vφm , Bv , isentropic apparent molar adiabatic compressibilities at infinite dilution, Kφ0 , isentropic apparent molar adiabatic compressibilities at the cmc, Kφcmc , and isentropic apparent molar adiabatic compressibilities upon micellization, Kφm , of sodium perfluoroheptanoate at different temperatures Vφ0

Vφcmc

Vφm

Bv

(K)

(cm3 mol−1 )

(cm3 mol−1 )

(cm3 kg mol−1 )

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

167.84 169.95 171.91 173.88 176.00 176.85 178.66 180.28 181.87 183.26 184.82

178.01 179.93 181.60 183.28 184.86 186.76 187.67 189.20 190.53 191.82 193.08

2.52 2.01 1.54 1.31 1.17 1.03 0.90 0.84 0.76 0.69 0.62

12.57 10.83 11.31 8.96 10.08 8.92 11.91 11.14 11.74 14.29 13.28

T

(cm3 mol−1 )

108 Kφ0

108 Kφcmc

107 Kφm

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

−10.03 −8.65 −2.26 −2.18 −1.92 −1.26 0.94 2.68 2.79 3.96 5.09

−9.43 −7.43 −5.75 −4.57 −2.27 −1.07 −0.01 1.19 2.28 3.34 4.51

2.03 1.81 1.69 1.63 1.49 1.41 1.35 1.27 1.21 1.15 1.09

Table 8 Apparent molar volumes at infinite dilution, Vφ0 , apparent molar volumes at the cmc, Vφcmc , apparent molar volumes upon micellization, Vφm , Bv , isentropic apparent molar adiabatic compressibilities at infinite dilution, Kφ0 , isentropic apparent molar adiabatic compressibilities at the cmc, Kφcmc , and isentropic apparent molar adiabatic compressibilities upon micellization, Kφm , of sodium perfluorooctanoate at different temperatures Vφ0

Vφm

Bv

(cm3 mol−1 )

Vφcmc

(K)

(cm3 mol−1 )

(cm3 kg mol−1 )

293.15 298.15 303.15 308.15 313.15 318.15 323.15

197.4 199.3 201.4 203.5 205.4 206.9 208.4

198.0 200.0 202.1 204.0 205.7 207.6 209.7

15.0 14.5 14.1 13.6 13.1 12.7 12.1

25.3 14.5 14.1 13.6 13.1 12.7 12.1

T

(cm3 mol−1 )

108 Kφ0

108 Kφcmc

107 Kφm

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

−20.27 −12.86 −5.05 −5.00 −3.09 −5.46 −5.34

−5.29 −3.60 −2.23 −0.92 0.17 1.13 2.05

1.92 1.81 1.73 1.67 1.62 1.55 1.39

Table 9 Apparent molar volumes at infinite dilution, Vφ0 , apparent molar volumes at the cmc, Vφcmc , apparent molar volumes upon micellization, Vφm , Bv , isentropic apparent molar adiabatic compressibilities at infinite dilution, Kφ0 , isentropic apparent molar adiabatic compressibilities at the cmc, Kφcmc , and isentropic apparent molar adiabatic compressibilities upon micellization, Kφm , of sodium octanoate at different temperatures Vφ0

Vφcmc

Vφm

Bv

(K)

(cm3 mol−1 )

(cm3 mol−1 )

(cm3 kg mol−1 )

288.15 293.15 298.15 303.15 308.15

131.1 134.1 135.0 136.0 136.9

134.2 135.4 136.7 137.9 138.8

14.2 13.8 13.4 13.1 12.8

−0.89 −0.24 0.10 0.12 0.26

T

(cm3 mol−1 )

and desipramine [73] and for a bolaform surfactant (docosane 1,22-bis(trimethylammonium bromide)) [74] in water at 25 ◦ C. We have only found negative values for sodium octanoate at low temperatures, so based on the previous discussion, the existence of dimers could be expected below cmc. As we pointed out Bv is related to nonelectrostatic solute–solute interactions; thus it could be expected that the value would decrease with solute concentration. However, the lowest values were found for sodium octanoate, where concentrations are highest, indicating that Bv is more pertaining to the alkyl chain length than to the concentration of monomers. Finally, this factor seems to increase by one or-

108 Kφ0

108 Kφcmc

107 Kφm

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

(cm3 Pa−1 mol−1 )

−6.95 −5.44 −4.50 −3.74 −2.99

−4.93 −4.08 −3.33 −2.68 −2.02

1.21 1.05 0.95 0.89 0.81

der of magnitude with the CH2 group, whereas it remains on the same order for the CF2 group. The average group contribution of each methylene group to the apparent molar volumes at infinite dilution was estimated from the slope of Vφ0 against the number of carbon atoms in the alkyl chain, and the value obtained was 15.0 cm3 mol−1 , which is quite close to the generally accepted value of 15.9 cm3 mol−1 for a variety of homologues [72]. Although the average CF2 group contribution was found to be 25.1 cm3 mol−1 , this deviation arises from the differences of the cavities they create in the surrounding water [66]. Tables 7 to 11 show that Vφ0 increases with

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Table 10 Apparent molar volumes at infinite dilution, Vφ0 , apparent molar volumes at the cmc, Vφcmc , apparent molar volumes upon micellization, Vφm , Bv , isentropic apparent molar adiabatic compressibilities at infinite dilution, Kφ0 , isentropic apparent molar adiabatic compressibilities at the cmc, Kφcmc , and isentropic apparent molar adiabatic compressibilities upon micellization, Kφm , of sodium decanoate at different temperatures Vφ0

Vφcmc

Vφm

Bv

(K)

(cm3 mol−1 )

(cm3 mol−1 )

(cm3 kg mol−1 )

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

159.67 161.52 163.17 164.68 166.03 167.54 168.77 169.98 171.06 172.25

160.49 162.17 163.79 165.35 166.88 168.31 169.81 171.25 172.70 174.05

13.48 12.59 11.90 11.32 10.79 10.31 9.76 9.30 8.78 8.31

1.37 0.42 0.95 0.74 1.01 0.80 1.32 2.23 3.33 3.21

T

(cm3 mol−1 )

108 Kφ0

(cm3 Pa−1 mol−1 )

108 Kφcmc

(cm3 Pa−1 mol−1 )

107 Kφm

−11.02 −9.30 −8.05 −6.61 −5.72 −4.15 −3.50 −1.93 −0.84 0.65

−10.84 −8.98 −7.49 −6.14 −4.97 −3.96 −3.07 −2.01 −1.09 −0.14

1.75 1.54 1.39 1.28 1.18 1.11 1.05 0.97 0.91 0.85

(cm3 Pa−1 mol−1 )

Table 11 Apparent molar volumes at infinite dilution, Vφ0 , apparent molar volumes at the cmc, Vφcmc , apparent molar volumes upon micellization, Vφm , Bv , isentropic apparent molar adiabatic compressibilities at infinite dilution, Kφ0 , isentropic apparent molar adiabatic compressibilities at the cmc, Kφcmc , and isentropic apparent molar adiabatic compressibilities upon micellization, Kφm , of sodium dodecanoate at different temperatures Vφ0

Vφcmc

Vφm

Bv

(K)

(cm3 mol−1 )

(cm3 mol−1 )

(cm3 kg mol−1 )

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

193.16 194.37 196.16 198.32 200.51 202.23 203.63 204.89

195.83 197.45 198.99 200.47 202.02 203.39 204.98 206.66

12.94 12.57 12.11 11.74 11.29 10.89 10.37 9.78

89.09 85.25 91.96 78.86 57.72 45.58 52.61 60.61

T

(cm3 mol−1 )

temperature for all surfactants, this behavior usually being ascribed to the reduction in the negative contribution to Vφ0 from hydrophobic hydration and electrostriction [28]. In this case, the CH2 /CF2 ratio found for Vφ0 was 1.5 and remained constant with temperature. Based on the same assumptions, similar conclusions could be obtained for Vφcmc , and small differences are attributed to the increase in the ion–ion interactions due to the corresponding concentration increase. In the micellar region the values of Vφ were fitted to the function Vφ = Vφcmc +

Vφm (m − cmc) [B + (m − cmc)]

,

(16)

where B is an adjustable parameter without physical meaning, Vφcmc is the value of the apparent molar volume at the cmc, and Vφ is the difference between the limiting value and Vφcmc and can be identified with the change in the apparent molar volume upon micellization. Values for these parameters are listed in Tables 7 to 11. Vφ values as a function of the CH2 group do not exhibit linear behavior. This fact has been previously reported in the literature as deviation from linearity for surfactants with shorter chain length [75]. This magnitude also decreases with temperature, de Lisi et al. [76] finding negative slopes for Vφ of sodium octyl, decyl, and dodecyl sulfates in water against temperature in the

108 Kφ0

(cm3 Pa−1 mol−1 )

108 Kφcmc

(cm3 Pa−1 mol−1 )

107 Kφm

−9.30 −8.23 −6.92 −5.64 −4.53 −3.24 −2.36 −0.45

−7.86 −6.15 −4.97 −3.83 −3.33 −2.09 −1.05 0.08

1.53 1.45 1.37 1.30 1.23 1.15 1.08 1.01

(cm3 Pa−1 mol−1 )

range 25◦ to 130 ◦ C at different pressures, attributing this negative slope value to the expansibility of the surfactant in the micellar state being smaller than that in the aqueous phase. Attwood et al. [77] found this decrease with temperature for chlorpromazine, an effect which has been attributed to the dehydration of the ionic head group. These authors compared their results with those of other works, finding that negative Vφ values are due to micelle formation of smaller aggregation numbers. Absolute values of Vφ obtained for perfluoroheptanoate are one order of magnitude smaller than those calculated for the other amphiphiles in this study and those reported for typical surfactants [77]. This relatively small increase in free space of perfluoroheptanoate, in transition from monomeric to the micellar state, is a possible consequence of a different arrangement in comparison with the rest of the amphiphiles in this study. In fact, these lower values can be compared with those found for amphiphiles with planar tricyclic rings which form stacked aggregates [73]. 3.5. Sound velocity and compressibilities Density and ultrasound velocity measurements were combined to calculate adiabatic compressibilities using the

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257

Fig. 7. Adiabatic compressibility as a function of amphiphile concentration at several temperatures of aqueous solutions of (A) sodium perfluoroheptanoate and (B) sodium decanoate.

Fig. 8. Isentropic apparent molal compressibility as a function of amphiphile concentration at several temperatures of aqueous solutions of (A) sodium perfluoroheptanoate and (B) sodium decanoate.

Laplace equation 1 β =− V




∂V ∂P

 = S

10−3 , ρu2

(17)

where V , P , and S refer to volume, pressure and entropy, respectively. β is the adiabatic compressibility coefficient, expressed in Pa−1 when the ultrasound velocity u is expressed in cm s−1 and density in g cm−3 . Typical plots of the changes in the adiabatic compressibility of aqueous solutions of sodium perfluoroheptanoate and sodium decanoate with the amphiphile concentration at different temperatures are shown in Fig. 7. Each plot can be divided into two straight-line segments corresponding to the monomeric and micellar forms of the amphiphiles. The slopes of the plots for the monomeric forms are negative for all homologues, while

the sign of the slopes over the cmc depends on the length of the alkyl chain and temperature. The isentropic apparent molar adiabatic compressibility, Kφ , can be calculated from ultrasound measurements as 103 (β − β0 ) (18) + β0 Vφ , mρ0 where β and β0 are the isentropic coefficients of compressibility of the solution and solvent, respectively. Fig. 8 shows plots of Kφ vs molality for sodium perfluoroheptanoate and sodium decanoate; similar plots were found for all amphiphiles under study. The apparent molar compressibility at infinite dilution, Kφ0 , can be calculated using the relation Kφ =

Kφ = Kφ0 + AK m1/2 + BK m,

(19)

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where the parameter AK represents the Debye–Hückel limiting law coefficient and BK is an adjustable parameter that represents the deviations from the limiting law. The parameter AK reported by Zana [78], based on the previous work of Bradley and Pitzer [79], is inconsistent with the experimental data, as reported by Garnsey et al. [80] for electrolyte solutions. This is the reason for applying Eq. (19) with AK and BK as free parameters. In the postmicellar region, an equation similar to (16) was applied. The Kφ values were fitted to the equation Kφ = Kφcmc +

Kφm (m − cmc) [C + (m − cmc)]

,

(20)

where C is an adjustable parameter without physical meaning, Kφcmc is the value of the apparent molar adiabatic compressibility at the cmc, and Kφm is the difference between the limiting value and the Kφcmc and can be identified with the apparent molar adiabatic compressibility upon micellization. The values obtained for Kφ0 , Kφcmc , and Kφm for the systems under study are listed in Tables 7 to 11. Apparent molar volume at infinite dilution consists of two contributions: the intrinsic volume of the solute molecule and that of the hydration shell. In contrast, apparent molar compressibility data, at infinite dilution, provide insight into the compressibility of the hydration layer around the solute molecule, since the solute intrinsic compressibility is assumed to be zero. In solutes with more negative compressibility, the occurrence of strong hydration is suggested. When the amphiphiles form micelles, the hydrophobic hydration around the alkyl chain disappears and the compressibility of the aggregate becomes the dominant factor. Previous studies of Kφ have shown that this quantity is large and negative for ionic compounds in water, intermediate and positive for mainly hydrophobic solutes, and small and negative for uncharged hydrophilic solutes such as sugars [81]. When the aggregate forms, the released water molecules that were in the vicinity of the hydrophobic part of the molecule become bulk water. The water molecules around the hydrophobic part are highly structured, having a rather low compressibility compared to the bulk water. If the amphiphile becomes longer, more conversion to bulk water of the structured water molecules is observed, obtaining lower compressibilities. Such behavior was confirmed with studies of a homologous series of tetra-n-alkylammonium salts [82], alkyltrimethylammonium bromides and n-alkylsulfates [83], where the isentropic apparent molar compressibilities of the surfactant monomers decrease with increasing chain length due to an increase in the amount of structured water in the vicinity of the hydrocarbon chains. Fukada et al. [72] found that adiabatic compressibilities for aqueous solutions of n-alkylammonium bromide stay almost constant as a function of the number of methyl groups (from 0 to 4) present. Because an increase in the number of methyl groups increases the hydrophobic hydration, leading to a negative contribution to compressibility, some kind of contribution to compensate this hydration can be expected.

This compensation arises from the effect of electrostriction around the ammonium cation, which depends on the radius of ions; the larger the ion is, the smaller the electrostriction (more positive compressibility). Therefore, it might be expected that the perfluorinated compounds would have lower compressibilities than the corresponding hydrogenated ones because of their stronger hydrophobicity. However, the isentropic apparent molar compressibilities at infinite dilution do not confirm this hypothesis; in fact, it is difficult to draw any conclusions from the experimental results: Kφ0 becomes more negative per CH2 group and this variation remains constant with temperature. Meanwhile, the variation with CF2 changes drastically with temperature. This high temperature dependence can be explained on the basis of a balance of two opposite contributions to the adiabatic compressibility: one negative contribution comes from the decrease in the compressibility of water in the hydration shell of the CF2 groups because of the restriction of the number of conformations they adopt, whereas the positive contribution results from the compressibility of the cavity created by the water molecules surrounding the group, the size of this cavity being greater than the van der Waals volume of the group [75]. The values calculated for Kφcmc show different patterns, for all surfactants, this value increasing linearly with temperature. The plots for both perfluorosurfactants are very similar. The same is observed for the longer hydrogenated (decanoate and dodecanoate) compounds, although the plot of octanoate is closer to that of perfluorosurfactants. Finally, values obtained for Kφm show more generalized behavior for all amphiphiles under study. This quantity decreases with T , the changes in Kφcmc being larger, resulting in a net decrease in Kφm . At a fixed temperature, Kφm increases with CH2 groups by a value of 0.12, being 0.26 for CF2 . Now the CH2 /CF2 ratio gives us a value of 1.8.

4. Conclusions In this work we have exposed, discussed, and compared the physicochemical properties of hydrocarbon and perfluorinated amphiphiles. We started by obtaining the Krafft points for our systems where we found that perfluorooctanoate and dodecanoate have practically the same Krafft points. Then we calculated the corresponding cmc for all the systems and we recommend that the minimum of cmc vs temperature is the ideal point to make comparisons between the cmc of perfluorinated and hydrogenated amphiphiles. This point is where the dehydrations of the alkyl chain and the polar head of monomers is balanced; that is, if we do not know the minimums of the two amphiphiles, at a fixed temperature we can be comparing the cmc of one amphiphile, for example, situated at the area of decrease of cmc vs temperature, with one belonging to another amphiphile that can be at an area of growth. For this minimum we have found that perfluorinated amphiphiles, with alkyl chain 1.5 times

E. Blanco et al. / Journal of Colloid and Interface Science 288 (2005) 247–260

shorter than the corresponding hydrogenated amphiphile, have the same cmc. We have obtained the thermodynamic function of micellization for our systems. For this purpose we used four different theoretical models and found that the model that best fit our data was the one proposed by Rodriguez et al. It was not possible to find any clear relationship for the comparison of thermodynamic parameters of hydrogenated and fluorinated compounds. We found that the relationship changed from 1.3 to 1.7 and that it was dependent on temperature and alkyl chain length. For example, perfluoroheptanoate and decanoate have very similar Hm0∗ ; however, Tc is the same for perfluorooctanoate and dodecanoate. In the second part of this study we obtained the apparent molar volumes and adiabatic compressibilities of the systems under study. The CH2 /CF2 ratio found for Vφ0 was 1.5 and remained constant with temperature. Similar conclusions could be drawn for Vφcmc . However, absolute values of Vφ obtained for perfluoroheptanoate were one order of magnitude smaller than those calculated for the other amphiphiles. This relatively small increase is a consequence of a different arrangement in comparison with the rest of the amphiphiles in this study. It was not possible to extrapolate a common pattern for the adiabatic compressibilities due to the high temperature dependence, which can be explained on the basis of a balance of two opposite contributions and the differences created in the surrounding water between CH2 and CF2 groups. The main conclusion of this work is that it is possible to predict the physicochemical properties, in the monomeric state, of a perfluorinated compound based on the corresponding hydrogenated one. However, in the micellar state, the physicochemical properties can be predicted only if both amphiphiles form aggregates of similar structure.

Acknowledgments This research was funded by the Spanish Ministry of Science and Technology through Project MAT2002–00608 (European FEDER support included) and by the Xunta de Galicia (Project PGIDIT03 PXIC 20615 PN).

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