Langmuir 1993,9, 973-979
973
A Thermodynamic Study of the Solvophobic Effect in Formamide Solutions of Nonpolar Molecules Marie Sjoberg,’ Rebecca Silveston, and Bengt Kronberg Institute for Surface Chemistry, P.O.Box 5607, S-114 86 Stockholm, Sweden Received August 8, 1992. In Final Form: December 7, 1992 The thermodynamics associated with the solvophobic effect in solutions of nonpolar molecules in formamide were examined using high-performanceliquid chromatography (HPLC). The transfer of a series of alkylbenzenesfrom formamideto hydrocarbonenvironmentwas studied in the temperaturerange 5-80 O C in order to obtain the molar free energy, entropy, and enthalpy of transfer. The HPLC system consisted of poly(dimethylsiloxane),PDMS, coated glass beads as the stationary phase and formamide as the mobile phase. The free energy and the enthalpy of transfer were found to be negative, while the entropy of transfer was positive. In general, the thermodynamic transfer quantities for formamide are both smaller in magnitude and less temperature dependent than those previously determined with water as the mobile phase. The relatively small ACp of transfer in the case of formamide indicates that there is negligible structuring of the formamide molecules around the nonpolar molecules, in contrast to the water case. The positive entropy of transfer in the case of formamide is attributed to complex formation between the alkylbenzenesand formamide. The driving force for the solvophobic effect seems to arise from the same source as the hydrophobic effect, namely the large cohesive energy of the solvent. This interpretation was used to explain differences in surfactant aggregation in formamide and water.
Introduction The driving force for surfactant aggregation in water is closely related to the low solubility of the hydrocarbon chains of the surfactant in water. This is commonly referred to as the hydrophobic effect. The molecular and thermodynamic origin of this phenomenon in water has been studied and debated for sometime.’* Morerecently, surfactant aggregation has also been observed in polar solvents other than water, such as formamide,”ll hydrazine,12ethylene glycol,l3and glycerol.lk16 Consequently, these solvents also give rise to a solvophobic interaction that promotes surfactant association. However, it is not completely clear which solvent properties are involved. The aggregation of nonionic and ionic Surfactants in (1) Tanford, C. The Hydrophobic Effect Formation of Micelles and Biological Membranes, 2nd ed.; John Wiley: New York, 1980. (2) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1946,13,507. (3) NBmethy, G.;Sheraga, H. A. J. Chem. Phys. 1962,36,3382. (4) Shinoda, K.; Fujihara, M. Bull. Chem. SOC.Jpn. 1968,41, 2612. Shinoda, K. J . Phys. Chem. 1977,81, 1300. Shinoda, K. Principles of Solution and Solubility; Dekker: New York, 1978. Shinoda, K.; Kobayashi, M.; Yamaguchi, N. J. Phys. Chem. 1987,91,5292. ( 5 ) Franks, F. Water A Comprehensiue Treatise;Plenum Press: New York and London, 1975; Vol. 4, Chapter 1. (6) Coetae, M.; Patterson, D. J . Chem. SOC.,Faraday Trans. 1 1988, 81, 2381. (7) Ben-Naim, A. Water and Aqueous Solutions; Plenum Press: New York, 1974. (8) Hvidt, A. Biochim. Biophys. Acta 1978,537,374. Hvidt, A. Physiol. Chem. Phys. Med. NMR 1983,15,501. Hvidt, A. Annu. Reu. Biophys. . . Bioeng. 1983, 12, 1. (9) Lattes, A.: Rico. I. Colloid Surf. 1989.35.221. Rico, I.: Lattes. A. J . Phys. Chem. 1986,90,5870. Auvray,X.; Petipaa, C.; Anthore, R.; Rico,
I.; Lattes, A.; Ahmah-Zadeh Samii, A.; de Savignac, A. Colloid Polym. Sci. 1987,265,925. Belmajdoub, A.; ElBayed, K.; Brondeau, J.; Canet, D.; Rico, I.; Lattes, A. J . Phys. Chem. 1988, 92,3569.
(10) Binana-Limbele, W.; Zana, R. Colloid Polym. Sci. 1989,267,440. (11) SjBberg, M.; Henriksson, U.; Wirnheim, T. Langmuir 1990, 6, 1205. JonstrBmer, M.; SjBberg, M.; Whnheim, T. J. Phys. Chem. 1990, 94, 7549. SjBberg, M.; Jansson, M.; Henrikeeon, U. Langmuir 1992, 8, 409. (12) Ramadan, M.; Evans, D. F.; Lumry, R. J. Phys. Chem. 1983,87, 4538. Ramadan, M.; Evans, D. F.; Lumry, R.; Philson, S. J. Phys. Chem. 1985,89, 3405. (13) Ray, A. J . Am. Chem. SOC.1969,91, 6511. (14) Friberg, S. E.; Liang, Y. C. Colloid Surf. 1987, 24, 325. (15) Evans, D. F.; Yamauchi, A.; Wei, G. J.; Bloomfield, V. A. J . Phys. Chem. 1983,87, 3537. (16) Fletcher, P. D. I.; Gilbert, P. J. J . Chem. SOC.,Faraday Trans. f 1989,85, 147.
formamide has been studied previously. Phase-diagram studies show the existence of liquid crystalline phases in formamide,17J1 at high surfactant concentration. This suggests a possible micelle formation at lower concentrations as well. The systems were studied with different NMR techniques, relaxation rate measurements and selfdiffusion measurements. The results showed that longchained surfactants, such as hexadecyltrimethylammonium bromide (ClsTABr)and polyethyleneglycol dodecyl ethers (C12En)do form micelles in formamide.” However, the cmc values are 1-2 orders of magnitude higher in formamide than in water and the process of micellization also seemsto be less cooperativethan in water. Moreover, the micelles formed were found to be considerablysmaller in formamide than in the corresponding water systems. The aggregation number for ClsTABr in formamide is about one-third of that in water for example.ll These investigations show that the solvophobic effect in formamide is not of the same magnitude as the hydrophobic effect in water. The purpose of this paper was to investigate whether or not these two effects have a similar thermodynamic origin. A liquid-liquid chromatography technique has previously been used to obtain the thermodynamic quantities associated with the hydrophobic effect, that is the free energy (AG”), the enthalpy (AH”), and the entropy ( 0 3 for transferring a hydrocarbon molecule from an aqueous solution to a nonpolar environment.18 These transfer quantities reflect the change in probe-solvent interaction when the probe molecule is transferred between solvents. The nonpolar environment was simulated in HPLC by using a liquid polymer, poly(dimethylsiloxane),coated onto glass beads as the stationary phase, while the mobile phase was water. A series of alkylbenzenes (increasing in hydrocarbon chain length) were studied over a temperature range 0-85 OC. From the partition coefficients measured, AGtr could be calculated for the transfer process. From the temperature dependence of Act: it was then possible to calculate AHtr and AStr. At room temperature, the (17) Wirnheim, T.; JBneeon, A.; SjBberg, M. Prog. Colloid Polym. Sci. 1990,82, 271. Wirnheim, T.; JBnsson, A. J. Colloid Interface Sei. 1988, 125, 627. (18) Silveston, R.; Kronberg, B. J . Phys. Chem. 1989, 93, 6241.
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974 Langmuir, Vol. 9,No. 4, 1993
entropy of transferring a hydrocarbon molecule from water to PDMS is large and positive while the enthalpy is around zero, resulting in a large and negative free energy of transfer. It was found that A Z P and A P vary strongly with temperature and compensateto give a relatively weak temperature dependence of Act'. The temperature dependence of these terms was interpreted as being dominated by water structuring,l*and the enthalpy-entropy compensation is typical of systems where structure is created or de~tr0yed.l~ The contribution to the total free energy of transfer due to water structuring was found to be positive for the transfer of a hydrocarbon from water into a nonpolar environment. In other words, water structuring has the effect of making hydrocarbons more soluble in water. It is in fact the large cohesive energy of water itself that is responsible for the low solubility of hydrocarbons in watere20t4 In order to comparethe solvophobiceffectin formamide with the hydrophobic effect in water, similar HPLC experiments have been performed with formamide as the mobile phase in place of water. The role of the cohesive energy, i.e. the energy associated with the net attractive interactions within the solvents, in these effects is discussed.
Experimental Section Column Preparation. The HPLC stationary phase consisted of poly(dimethylsiloxane), PDMS (secondary standard from Aldrich Chemical Co., M.W. about 600.000),coated onto nonporous glass beads (30-60rm). The beads were precleaned by washing with water and 95% ethanol before drying at 110 "C. The PDMS was deposited onto the glass beads from a slurry of the beads in toluene. After 15 min of stirring the toluene was evaporated in a Rotavapor and the dried beads were slurried in water with about 10% chromatographic grade methanol. The slurry was packed with a Magnus Scientific Instruments Slurry Packer Co. (England) at 350 atm into two 25 cm X 10 mm i.d. stainless steel columns (named 1 and 2)with watedmethanol as the packing fluid. When the packing process was complete, the methanol used in the slurrysolution was rinsed out withdeaerated water. The water used in the above processes was purified with equipment from Millipore, Inc., and Cuno, Inc. The water was then replaced with chromatographic grade formamide, supplied by Merck Germany, in the HPLC setup. Column Characterization. The amount of PDMS, deposited onto the glass beads was determined by an elemental analysis performed by MikroKemi, Uppsala, Sweden. This was carried out for various columns from our previous work.18 The amount of PDMS in the present columns, 1 and 2, was calculated by relating the retention volume of toluene in water for the previously analyzed column with the corresponding retention volume in columns 1 and 2. Thereby columns 1 and 2 were found to contain 0.161 g and 0.237g (*0.002),respectively. Analysis of the column performance gave about 1600and 2100 theoretical plates corresponding to the theoretical plate height (HETP) of 0.16 and 0.12mm for columns 1 and 2, respectively. The HPLC Setup. The formamidewasdeaerated by bubbling with helium throughout the experiment. The probes, injected into a 20-mL loop,were dilute solutions of chromatographicgrade benzene to butylbenzene from Merck or Aldrich Chemical Co. The eluent was detected by a Waters 410 Millipore refractive index meter. The column temperature was controlled to f0.5 "C. A pressure that varied between 150 and 200 atm provided a constant flow rate of 1.00 0.05 mL/min. The basic information obtained from chromatography experiments is the difference in retention times of an unretarded marker, sodium nitrate, and a probe molecule, benzene to butylbenzene, over the temperature range 5-85 "C. The eluent was continuously accumulated on a balance. The accumulated
*
(19) Patterson, D.; Barbe, M. J. J . Phys. Chem. 1976,80, 2435. (20) Hartley, G. S. Aqueous Solutions of Paraffin-Chain Salts; Hermann & Cie.: Paris, 1936; Vol. 387, p 45.
weight of the mobile phase and the peaks resulting from differences in refractive index were both plotted on a chart recorder such that the net retention volume could be read directly off the chart paper.
Thermodynamic Background The retention volumes were found to be independent of probe concentration, thus assuring that the results are obtained at infinite dilution. Furthermore, the retention volumes were found to be independent of flow rate, thus ensuring that equilibrium conditions prevail. The net retention volume, Vz;,measured is the difference in retention volume of the probe and that of an - v&ker. It is in principle unretarded marker; i.e. T:kbe a combination of both absorption and adsorption of the probe to the PDMS phase, i.e.
where VPDM~ and A P D Mare ~ the volume and the surface area of PDMS exposed to formamide in the column, and KABand KADare the partition coefficients for absorption and adsorption, respectively. It remains to be shown that we are studying absorption exclusively, i.e. that the contribution to the retention volume due to adsorption on the surface of PDMS by the probe molecules is negligible. The maximum value of KADpossible can be estimated with the help of the PDMS surface area available in the column and if one assumes (i) maximum adsorption occurs from a saturated solution of the probe in formamide, (ii) a minimum possible cross-sectionalarea of the probe, and (iii) monolayer adsorption. See Appendix I for the calculation procedure. As calculated above, the contribution due to adsorption was found to be 4%of the total retention volume. As this is within experimental error, we consider adsorption to be negligible. The thermodynamic quantities, A W , AStr,and AHtr,of transferring a probe molecule from formamide to PDMS were obtained by the same procedure as in our previous work with water as the mobile phase, described in detail in ref 18. We therefore only present a brief summarybelow. In our chromatographicsetup, the partitioningof the probe between the mobile formamide phase and the stationary PDMS phase is defined at any temperature as the ratio of the probe molar concentration in each of the phases. We analyze the results in the frame work of the FloryHuggins theory for polymer solutions where the probe concentrations are expressed in terms of volume fractions rather than molar concentrations. Thus, the equilibrium partition coefficient is expressed as
TAa - v:hker VPDMS
VIPDMS(m)
(2)
VIFW
where 41 is the volume fraction and c1 the molar concentration of the probe (1) in the polymer (PDMS) or formamide (F)phase. VIPDMS(-) and VIF(=) are the partial molar volumes of the probe at infinite dilution in the polymer and the formamide, respectively. The free energy of transfer from formamide to PDMS is thus obtained through
Langmuir, Vol. 9, No.4, 1993 975
Thermodynamic Study of the Soluophobic Effect ""
K 40
-
0 %I
130 0
0
30 -
The partial molar volume of the probe at infinite dilution in formamide and PDMS was calculated2lSz2and the logarithmic term containing the ratio of the partial molar volumes in eq 3 was found to be negative and to amount from 0.5 to 3.0% of the total free energy. A W should also include a term, (P - l)(VIF - VIPDMS), to account for the fact that HPLC is conducted above atmospheric in this case a maximum of 200 atm. This term is positive and amounts to 0.5~3~0% of the total free energy for any of the probes in our system. Since the correction term for the pressure effect and the term for the partial molar volumes at infinite dilution are of the same size but of opposite sign, they are not accounted for in the calculation of the total free energy. The total free energy also includes a combinatorial contribution due to the different sizes of the molecules which is of the same order of magnitude as the total free energy of transfer yet of opposite sign. A theoretically more useful expression for the free energy of transfer does not include this contribution. We have thus subtracted this term from the experimental data, using the FloryHuggins theory for polymer solutions; see Appendix 11. The corrected thermodynamic quantities are denoted as Act",AHt*, and TAW'. Thus, the Act*quantity corresponds to the difference in the standard molar free energy of the probe at infinite dilution in the two solvents. The rational for using this quantity is that it is a reflection of the change in interaction with the solvent as the probe is transferred from formamide to PDMS. Finally the enthalpy is obtained from the derivative of the temperature dependence of AGt* in the van't Hoff plot (ACtr'/Tversus 1/77. The entropy of transfer is then obtained from the definition A@* = AHtf - TAP'.
Results and Discussion Figure 1shows that for the transfer from formamideto PDMS, there are distinct differences in the equilibrium constants for the various probes obtained by using eq 2. In Figure 2a, the A W ' , AHt*',and TAW are shown for ethylbenzene which is representative of the other alkylbenzenes studied. The figure reveals that the free energy of transfer is both small and negative with a very weak temperature dependence. The TAW of transfer is positive while the enthalpy is negative. The transfer quantities for ethylbenzene in formamide are compared with the corresponding quantities for water, shown in Figure 2b.18 In general, the transfer quantities for the series of alkylbenzenes obtained in formamide are considerably smaller in absolute size and less temperature dependent than those obtained for water, see Figure 2. Table I lists the values of A@', AHtr',and TUt*for the series of alkylbenzenes in formamide. Note that these values are interpolated at specific temperatures and not at the actual experimental temperatures. It should be noted that when calculating AHt* and AS* in Table I, a second degree polynomial function of Act
