Temperature and Length Scale Dependence of Tetraalkylammonium

We have studied the temperature and length scale dependence of the energetics of the pair interaction of well-established hydrophobic solutes ...
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J. Phys. Chem. B 2008, 112, 2040-2044

Temperature and Length Scale Dependence of Tetraalkylammonium Ion-Amide Interaction Andrey V. Kustov* and Valeriy P. Korolev Institute of Solution Chemistry of Russian Academy of Sciences, IVanoVo State UniVersity of Chemistry and Technology, IVanoVo 153045, Russia ReceiVed: September 21, 2007

We have studied the temperature and length scale dependence of the energetics of the pair interaction of well-established hydrophobic solutes tetraalkylammonium bromides with hydrophilic formamide (FA) and hydrophobic hexamethylphosphoric triamide (HMPT). Our results do indicate the anomalous length scale dependence of the tetraalkylammonium cation-amide interaction in water. As the cation size is increased, the unfavorable enthalpy of interaction is increased rather linearly until the maximum is reached, after which there appears to be a reversal of the trend. We believe that this phenomenon arises from the impossibility of water to maintain its H-bond network near large tetraalkylammonium cations that leads to the formation of a somewhat disordered solute hydration shell. The energetic cost for overlapping this shell with the amide hydration shell in water is noticeably smaller than that for tetraalkylammonium cations of a moderated size.

I. Introduction Hydrophobic effects are widely believed to play an important role in various chemical phenomena such as the formation of gas clathrates, complexation, molecular recognition, etc.1-3 Hydrophobic interaction is also identified as a primary source of stability of globular proteins and the formation of micelles and bilayer membranes.4-6 These water-induced effects have, however, multifaceted nature1,6-10 which depends strongly upon the solute size. Recent theoretical studies have highlighted the existence of a crossover in the length scale dependence of hydration of apolar species.6-10 For small solutes the hydration free energy scales linearly with the excluded volume, whereas for large hydrophobes it scales linearly with the surface area exposed to the solvent.7,8 The crossover to the large length scale regime is associated with a depletion of water density around an extended surface. Accommodation of small hydrophobic units in water creates excluded volume without any disruption of water structure since water-water hydrogen bonding simply goes around the solute.6-8 In contrast, large assemblies of oil molecules disrupt the H-bond network of water, inducing the loss of hydrogen bonding near the surface. This collective energetic effect causes the depletion of water density near an extended hydrophobic surface, which can induce a strong tendency to segregate large apolar species from water.9,10 Thus, small hydrophobic units are rather separated by water in a dilute solution,1,2,6 whereas large hydrophobes or assemblies of small solutes disrupt H-bonds between neighboring water molecules which move away from an extended hydrophobic surface and, hereby, facilitate the solute-solute attraction.6-8 These results allow to expect that the interaction between two hydrophobic solutes of a moderated size in water should differ from the interaction between two large species. In particular, the energetic cost arising from the partial disruption of the solute hydration shell and a loss of some solute-water interactions1,2 are expected to be smaller for an extended surface than for species of a modest size. * Corresponding author. E-mail: [email protected].

The present study focuses on the temperature and length scale dependence of the enthalpies of the pair interaction between well-established hydrophobic solutesssymmetrical tetraalkylammonium salts11-14sand amides in water. The amides are hydrophobic hexamethylphosphoric triamide (HMPT, (CH3)6N3PO)2 and hydrophilic formamide (FA, NH2CHO),2 the salts being from n-Et4NBr up to n-Hep4NBr. The main goal of our research is to analyze the dependence of tetraalkylammonium salt-amide pair interaction upon hydrophobic cation size and to check the existence of effects mentioned above in the case of hydrophobic electrolyte-amide interactions. II. Experimental Section FA (Reachem), HMPT (Fluka), water, Et4NBr, and Bu4NBr (Merck, >99%) were purified as in our previous studies.14,15 Hex4NBr and Hep4NBr (Aldrich, >99%) were dried in vacuum at 308 K for 72 h with a trap with liquid nitrogen and then used without further purification. The calorimetric measurements have been carried out with an ampule calorimeter fitted with a 70 cm3 vessel.16,17 The vessel is equipped with a calibration heater, a titanium stirrer, and a thermistor. A glass ampule containing a solute is attached to the stirrer and crushed against the vessel bottom to initiate the dissolution process. Thermistor resistance is measured by the standard temperature measuring instrument.16 The signal of the instrument is converted to the degrees of The International Temperature Scale of 1990. The detection limit of the apparatus is 10 µK. The temperature instability in the bath is less than 1 mK. The enthalpies of solution are measured by a comparative method. An electrical calibration is carried out before each experiment. The calorimeter has been tested by measuring the enthalpies of solution of potassium chloride (KCl) and 1-propanol (1-PrOH) in water at 298.15 K according to recommendations given elsewhere.18 Our results (∆Hm(sol) (m ) 0.111 mol/kg) ) 17.61 ( 0.02 kJ/mol and ∆H0(sol) ) -10.18 ( 0.03 kJ/mol for KCl and 1-PrOH,

10.1021/jp0776199 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/31/2008

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TABLE 1: Standard Enthalpies of Solution ∆H0(sol) in kJ/mol for n-Et4NBr, n-Pr4NBr, n-Bu4NBr, and n-Pen4NBr in Water-HMPT Mixtures at 298.15 and 328.15 K n-Pr4NBr (298.15 K) XAa ∆H0(sol) 0 0.000 701 0.000 999 0.003 000 0.005 001 0.010 01 0.030 02 0.050 00

-4.44 -4.2511 b -4.23 -3.95 -3.00 -2.18 -0.41 7.32 13.18

n-Pen4NBr (298.15 K) ∆H0(sol) XA 0 0.013 35 0.020 43 0.035 50 0.041 30 0.071 16

4.02 3.2,19 3.821 18.88 27.37 39.60 44.80 61.89

n-Et4NBr (328.15 K) ∆H0(sol) XA 0 0.005 34 0.014 17 0.025 33 0.033 39 0.052 30 0.074 43

10.22 10.1324 10.69 11.45 12.06 12.64 13.73 14.89

n-Bu4NBr (328.15 K) ∆H0(sol) XA 0 0.011 96 0.022 49 0.030 52 0.047 07 0.073 56

12.87 12.6224 21.16 26.59 30.86 35.61 41.36

a The amide mole fraction. b The average value in the range of experimental results at a solute molality of ∼0.02 mol/kg. The standard enthalpy of solution, therefore, should be smaller by 100-150 J/mol. The coefficients of eq 1 are A0 ) -4.437(0.07), A1 ) 442.2 (12), A2 ) 1780 (242), sf ) 0.13 kJ/mol (n-Pr4NBr, 298.15 K); A0 ) 4.06(0.52), A1 ) 1220 (34), A2 ) -5731 (449), sf ) 0.58 kJ/mol (n-Pen4NBr, 298.15 K); A0 ) 10.28(0.05), A1 ) 77.86 (4), A2 ) -216.7 (48), sf ) 0.07 kJ/mol (n-Et4NBr, 328.15 K); A0 ) 13.19 (0.52), A1 ) 691.9 (34), A2 ) -4223 (436), sf ) 0.59 kJ/mol (n-Bu4NBr, 328.15 K). The values in parentheses from here on represent the standard deviation of the coefficient.

TABLE 2: Standard Enthalpies of Solution ∆H0(sol) in kJ/mol for Hex4NBr and Hept4NBr in Water-FA and Water-HMPT Mixtures at 328.15 Ka n-Hex4NBr in water-FA XA ∆H0(sol)

n-Hex4NBr in water-HMPT ∆H0(sol) XA

n-Hept4NBr in water-FA ∆H0(sol) XA

n-Hept4NBr in water-HMPT ∆H0(sol) XA

0 0.016 54 0.037 50 0.050 86 0.076 30 0.084 03 0.100 6 0.110 6 0.125 5

0 0.005 050 0.009 721 0.013 71 0.025 66 0.037 66 0.059 46

0 0.015 05 0.030 48 0.047 35 0.063 41 0.084 68 0.105 5

0 0.006 17 0.007 97 0.012 66 0.012 66 0.015 85 0.019 66 0.026 21 0.031 72

21.03 21.67 22.50 23.01 23.95 24.15 25.10 25.41 25.99

21.03 28.50 35.05 41.56 51.65 58.37 61.87

59.61 60.20 60.87 62.07 63.58 65.28 68.89

59.61 68.77 71.55 77.10 77.54 83.54 89.22 96.37 102.30

a The coefficients of eq 1 are A0 ) 21.05(0.07), A1 ) 36.49 (3), A2 ) 24.35 (19), sf ) 0.08 kJ/mol (n-Hex4NBr in water-FA mixtures); A0 ) 21.34(0.67), A1 ) 1571(64), A2 ) -15040 (1027), sf ) 0.90 kJ/mol (n-Hex4NBr in water-HMPT mixtures); A0 ) 59.71(0.25), A1 ) 18.05 (11), A2 ) 633.1 (105), sf ) 0.30 kJ/mol (n-Hep4NBr in water-FA mixtures); A0 ) 59.32 (0.61), A1 ) 1582 (85), A2 ) -6823 (2500), sf ) 0.70 kJ/mol (n-Hep4NBr in water-HMPT mixtures).

respectively)14 are in good agreement with recommended literature values (17.58 ( 0.02 and -10.16 ( 0.02 kJ/mol for KCl and 1-PrOH, respectively).18 III. Results The experimental enthalpies of solution of n-Et4NBr, n-Pr4NBr, n-Bu4NBr, and n-Pen4NBr in water and a highly aqueous HMPT were obtained in the range of the electrolyte molalities of 0.003-0.01 mol/kg. Since larger tetraalkylammonium salts were slightly soluble and dissolved slowly in water at a room temperature,19-22 we have performed accurate calorimetric measurements only at 328.15 K in highly diluted solutions (0.0007-0.002 and 0.0002-0.0006 mol/kg for n-Hex4NBr and n-Hep4NBr, respectively). The standard enthalpies of solution ∆H0 (sol) given in Tables 1 and 2 have been calculated from the following relationship: ∆H0(sol) ) ∆Hm(sol) + ∆Hmf0(dil), where the enthalpies of dilution ∆Hmf0(dil) are computed in terms of Debye-Hu¨ckel theory in the second approximation.23 The ∆H0(sol) values in pure water reflect the result of five or more measurements, while the enthalpies of solution in mixed solvents represent the result of either two, four, or mainly one experiment. Tables 1 and 2 show a good agreement between our ∆H0(sol) values and the available literature ones.11,21,24 IV. Discussion A. The Pair Interaction at 298.15 K. The formally exact theory of solutions developed by McMillan and Mayer25 and then adapted by Kauzmann26 and Friedman27 relates thermodynamic properties of multicomponent system to certain integrals of the potential of mean force associated with a fixed set

of interacting species in an infinitely diluted solution. The parameters of the virial expansion reflect a contribution of the interaction between pairs, triplets, and a high number of solute molecules to the appropriate thermodynamic property. We extract the enthalpic parameters of the solute-amide pair interaction (hSA) from the experimental data by the method proposed elsewhere.28 The ∆H0(sol) - f (XA) curves have been fitted to the second-order polynomials:

∆H0(sol) ) A0 + A1 XA + A2 XA2

(1)

the A1 coefficient of which, obtained in a least-squares fitting routine, is related to the enthalpic parameter of the salt-amide interaction hSA in the following manner:28,29

hSA ) A1 MH2O/2

(2)

The coefficients of eq 1 are given in the footnotes to Tables 1 and 2. Figure 1 compares the length scale dependence of pair interaction between tetraalkylammonium bromides and various organic nonelectrolytes at 298.15 K. The solute-solute interaction is similar in all cases. Rising the cation size induces the increase of the hSA parameters which become more and more positive. It indicates that the tetraalkylammonium salt-nonelectrolyte interaction is enthalpically repulsive, the repulsion enhancing rapidly for hydrophobic HMPT and 2-methyl-2propanol. In contrast, this effect is much weaker pronounced for hydrophilic FA. Thus, the unfavorable enthalpy of interaction follows the cation and nonelectrolyte molecule hydrophobicity and simply reflects a partial disruption of solute hydration shells when they overlap in a highly diluted solution. We have shown

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Figure 1. Enthalpic parameters of ammonium and tetraalkylammonium bromides pair interaction, hSA, with FA (0),15,28,33 DMF (2),28 2-methyl2-propanol (3),30 and HMPT (9)15,32,33 at 298.15 K. The digits on the curves from here on denote the number of carbon atoms in the cation alkyl length (0 ) ammonium bromide, 1 ) tetramethylammonium bromide, 2 ) tetraethylammonium bromide, etc.). Error bars represent the standard deviation. Lines show the existence of the constant methylene group contribution to hSA values.

elsewhere14 that the standard enthalpy of solution of Bu4NBr in water-HMPT mixtures at 298.15 K differs from the value in pure water at XA< 5 × 10-4 amide mole fraction, where the HMPT/water mole ratio is 1/2000. It indicates that tetraalkylammonium ion and amide hydration shells containing a large amount of water molecules overlap at a very low amide concentration, this process being accompanied by a large and unfavorable enthalpic effect. Figure 1 illustrates that starting with n-Et4NBr the enthalpic interaction parameters scale approximately with cation molar mass; i.e., the methylene group increment is a constant. Although these solutes contain a sufficiently large amount of apolar groups, they appear to be rather small to induce drying at room temperature since they are accommodated by water through small rearrangements. Neutron scattering studies12 and computer simulation13 indicate that there is even some enhancement of water structure near these species. Thus, if larger tetraalkylammonium ions interact with nonelectrolytes in the same way as the cations of moderated size, we could expect the linear dependence shown in Figure 1 to provide a good prediction of their hSA values. However, because of experimental problems mentioned above, we are able to check this idea at higher temperatures only. B. Temperature Dependence of the Pair Interaction. The temperature dependence of the enthalpy of interaction of ammonium and tetraalkylammonium bromides with FA and HMPT is plotted in Figure 2. Et4NBr and Bu4NBr show similar behavior in both systems; i.e., their heat capacity of interaction with both hydrophobic and hydrophilic amides is negative. The heat capacity of interaction between two hydrophilic solutes such as ammonium bromide and FA is positive, whereas it is large and negative for the NH4Br-HMPT interaction. Since the electrolyte-amide pair interaction parameters reflect the sum of cation and anion contributions, it would be useful to eliminate the term of bromide ion. The difference of the hSA values for Bu4NBr and Et4NBr is also plotted in Figure 2. The hSA (Bu4N+-Et4N+)-HMPT parameter is large, positive, and

Figure 2. Temperature dependence of enthalpic interaction parameters, hSA, of NH4Br (9), Et4NBr (b), Bu4NBr (2), and (Bu4N+-Et4N+) (3) with HMPT (a) and FA (b). Lines represent the linear description. Values are taken from refs 15 and 31-34.

independent of temperature. Since the hSA (Bu4N+-Et4N+) value reflects the interaction of eight -CH2- groups with an amide molecule, it is clear that the heat capacity of the -CH2group-HMPT interaction equals zero (see Figure 2a). This explains why the heat capacity of HMPT interaction both with hydrophilic NH4Br and hydrophobic Et4NBr or Bu4NBr is negative. It is obvious that in all cases the negative bromide ion contribution to the cpSA values dominates over the cation one.31 The heat capacity of the -CH2- group-FA interaction is found to be negative (see Figure 2b) due to the influence of a polar part of the amide molecule.32 Thus, an assortment of interactions, and not only hydrophobic one, is very important for the cpSA values, and therefore, the heat capacity of interaction is unlikely to be a useful probe of hydrophobicity. In contrast, Figure 1 clearly shows that the enthalpy of the tetraalkylammonium salt-amide interaction scales linearly with a hydrophobic cation size. Here we could not obtain the heat capacity of interaction for larger tetraalkylammonium salts. However, one can expect that this quantity should not differ strongly from cpSA values obtained for smaller tetraalkylammonium salts at least in the case of HMPT, where the bromide ion is a primary source of the negative interaction heat capacity. C. Length Scale Dependence of the Pair Interaction. Figure 3 illustrates the dependence of the enthalpy of the salt-amide interaction upon cation molar mass at different temperatures.

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Figure 4. Enthalpic parameters per solute surface area, hSA/4πRcation2, for ammonium and tetraalkylammonium bromides interaction with HMPT (9) and FA (b) at 328.15 K. Lines are spline functions. The Rcation values were taken from ref 36. The quantities for Hex4N+ and Hep4N+ were estimated from the linear relationship between the cation van der Waals volumes Vw (cm3 mol-1) and the number of methylene groups in the cation, n, via Vw ) 55.484 + 10.23n, R2 ) 0.999, and sf ) 0.3 cm3 mol-1, where Vw ) 4/3πRcation2NA. The Rcation ) 0.14 nm for NH4+ ion is accepted.

Figure 3. Size dependence of enthalpic pair interaction parameters, hSA, of ammonium and tetraalkylammonium bromides with HMPT (a) and FA (b) at 277.15 (9), 298.15 (b), and 328.15 K (2). Straight lines are shown for clarity.

The results plotted in Figure 3a show that as the alkyl chain length is increased, the enthalpy of the salt-HMPT interaction gradually increases up to Hex4NBr, after which there is likely to be a plateau. In fact, from Figure 1 we could expect that the pair interaction between Hep4NBr and HMPT should be more energetically repulsive than the Hex4NBr-HMPT one. The hSA values, however, for these solutes are almost identical. The length scale dependence of the tetraalkylammonium salt-FA interaction given in Figure 3b illustrates some more interesting features which are worthy of note. First, the hSA vs Mcation curves intersect each other at some Mcation value which is nearly identical to the molar mass of tetramethylammonium ion. It indicates that the enthalpy of Me4NBr-FA interaction is negative and almost independent of the temperature; i.e., the heat capacity of interaction equals zero. Second, the enthalpy of Et4NBr-FA interaction being positive at low temperatures becomes negative in hot water. Finally and generally, this seems rather surprising, but it is really true that both the Hex4NBrFA and Hep4NBr-FA pair interactions are less enthalpically repulsive than the pair interaction between Bu4NBr and formamide. Figure 4 compares the hSA parameters as a function of tetraalkylammonium ion radius Rcation. Although the tetraalkylammonium ion radii have been found to strongly depend on the estimation procedure,35 the result is quantitatively the sames the hSA/4πRcation2 values increase with the size of tetraalkylammonium cation until a maximum is reached, after which there

is a reversal of the trend. What can cause such a solute behavior? Since electrolytes with a common anion are examined, this phenomenon arises from increasing a cation size. The amide interaction with tetraalkylammonium ions of a moderated size is accompanied by a large unfavorable enthalpic effect which increases in magnitude up to some critical Rcation value. Further rise of a solute size, however, appears to result in some disruption of water structure near a solute, which does not occur for smaller cations. This leads to a much less structured solute hydration shell. The enthalpic cost per a solute surface area for overlapping this shell with that of the amide molecule is much smaller than it would be expected from the linear prediction illustrated in Figure 1. This explains the decrease of the hSA values for large solutes. We believe that Figure 4 shows the existence of crossover in hSA(R) as a function of R between small and large symmetrical tetraalkylammonium cations. This phenomenon is observed at rather lower R values than that for excess free energies of hydration;6-8 however, this result seems to be not too surprising. First, we analyze a pair interaction and not hydration. Therefore, a total amount of apolar groups in solute particles could be sufficient to induce at least partial drying. Second and generally, the measurements for large solutes are performed at 328 K, where water is closer to liquid-vapor coexistence than it is at a room temperature. It allows to expect that the crossover above will be observed at lower R values. Another important and unexpected feature, briefly commented on above, is that this phenomenon is observed at lower Rcation values for hydrophilic FA than for hydrophobic HMPT. This fact may be attributed to the formation of stable hydration shell around a large HMPT molecule,2 which is absent in the case of FA. This shell is believed to be additionally structured by a cooperation of hydrophobic hydration of methyl groups and hydrophilic hydration of the polar ≡PO one.2 The existence of the latter group in an amide molecule may shift the maximum given in Figure 4 to higher R values. Thus, the results obtained do indicate for the first time the anomalous length scale dependence of the tetraalkylammonium cation-amide interaction in water. Rising the hydrophobic

2044 J. Phys. Chem. B, Vol. 112, No. 7, 2008 cation size induces increasing the enthalpy of pair interaction until the reversal of the trend is observed. We believe that this phenomenon has the same nature as the crossover founded for free energies of hydration of hydrophobic spheres,6-10 which arises from a depletion of water density near large hydrophobic solutes. It seems to be important to compare the temperature changes of free energies of solution of tetraalkylammonium salts with small and large cations in water, since this quantity is positive for small hydrophobic solutes but negative for a planar surface.8 However, this extension of the research is left for future work. Acknowledgment. This work was supported by the Russian Foundation for Basic Researches (Grants N 02-03-32520, 0303-06582, and 06-03-32169) and Russian Science Support Foundation. References and Notes (1) Blokzijl, W.; Engberts, J. B. F. N. Angew. Chem., Int. Ed. Engl. 1993, 32, 1545. (2) Kessler, Yu. M.; Zaitsev, A. L. SolVophobic Effects; Ellis Horwood: Chichester, 1994. (3) Pratt, L. R.; Pohorille, A. Chem. ReV. 2002, 102, 2671. (4) Tanford, C. The Hydrophobic EffectsFormation of Micelles and Biological Membranes; Wiley-Interscience: New York, 1973. (5) Kauzmann, W. AdV. Protein Chem. 1959, 14, 1. (6) Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570. (7) Huang, D. M.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704. (8) Huang, D. M.; Chandler, D. J. Phys. Chem. B 2002, 106, 2047. (9) Chandler, D. Nature (London) 2002, 417, 491. (10) Chandler, D. Nature (London) 2007, 445, 831. (11) De Visser, C.; Somsen, G. J. Phys. Chem. 1974, 78, 1719. (12) Tuner, J. Z.; Soper, A. K. J. Chem. Phys. 1994, 101, 6116.

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