On the superhydrophobicity of tetrafluoromethane

Chemical Physics Letters 460 (2008) 470–473

Contents lists available at ScienceDirect

Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

On the superhydrophobicity of tetrafluoromethane Giuseppe Graziano * Dipartimento di Scienze Biologiche ed Ambientali, Università del Sannio, Via Port’Arsa 11, 82100 Benevento, Italy

a r t i c l e

i n f o

Article history: Received 12 May 2008 In final form 20 June 2008 Available online 24 June 2008

a b s t r a c t Tetrafluoromethane, CF4, is markedly less soluble in water than methane and neopentane around room temperature: it is a superhydrophobic solute. An analysis of the physical origin of this superhydrophobicity is performed, exploiting literature thermodynamic data covering the 5–55 °C temperature range. It results that the CF4–water dispersion interactions are markedly weaker in magnitude than those of a ‘hypothetical’ hydrocarbon having the same size of tetrafluoromethane, providing a smaller counterbalancing effect of the work spent to create the cavity in water. The weakness of the CF4–water dispersion interactions is due to the very small polarizability of CF4, which, in turn, is caused by the strong electronegativity of fluorine atoms. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Fluorocarbons are considered to be superhydrophobic because their solubility in water is significantly smaller than that of the corresponding hydrocarbons. For instance, the mole fraction solubility in water, at 25 °C and 1 atm partial pressure of gas, is [1,2]: x2  105 = 0.3802 for CF4, 2.5523 for CH4, 1.077 for C(CH3)4, 0.09975 for C2F6, and 3.4043 for C2H6. These mole fraction solubilities give rise to the following values of the Ben-Naim standard [3] (i.e., transfer from a fixed position in the ideal gas phase to a fixed position into water) Gibbs energy of hydration: DG (in kJ mol1) = 13.1 for CF4, 8.3 for CH4, 10.5 for C(CH3)4, 16.4 for C2F6, and 7.6 for C2H6. From ligand partitioning between n-octanol and water, and from ligand binding it emerged an empirical rule: 1 CF2 group corresponds to about 1.5 CH2 groups in terms of hydrophobicity [4]. There is increasing interest in producing and characterizing superhydrophobic materials, and fluorocarbons seem to be good targets [4]. As a consequence, a molecular level explanation of their superhydrophobicity would be a pre-requisite. In the present Letter, I would like to provide an analysis of the hydration thermodynamics of CF4 exploiting the data by Wilhelm et al. [5], WBW, covering the 10–55 °C temperature range, the gas solubility measurements of Wen and Muccitelli [6], W&M, covering the 5–30 °C temperature range, and those of Scharlin and Battino [7], S&B, covering the 15–45 °C temperature range. Experimental values of DH ; DS ; and DG are listed in Table 1. There is good quantitative agreement for the DG values among the three data sets, whereas there is qualitative, but not quantitative, agreement for the DH and DS values. In line with the general features of hydrophobic hydration [8], (a) DG is large and positive, increas-

* Fax: +39 0824 23013. E-mail address: [email protected] 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.06.057

ing slightly with temperature; (b) DH and DS are large and negative, increasing markedly with temperature. In fact, DC p is a large and positive quantity, amounting, in J K1 mol1 units, to (a) 380 over the 10–55 °C temperature range, on the basis of the DH values of WBW [5]; (b) 433 over the 5–30 °C temperature range, on the basis of the DH values of W&M [6]; (c) 636 over the 15– 45 °C temperature range, on the basis of the DH values of S&B [7] (the uncertainty on these DC p estimates is expected to be large [1]; according to W&M, the uncertainty amounts to 30% of their reported value). It is worth noting that DC p for the hydration of nonpolar solutes is expected to be a decreasing function of temperature on the basis of a large set of experimental data [9]. I preferred to consider DC p as temperature-independent because the precision of the solubility measurements coupled to the small temperature range investigated did not allow a reliable determination of the temperature dependence of DC p . The thermodynamic values reported in Table 1 indicate that, around room temperature, the superhydrophobicity of CF4 is entropy-dominated, even though a significant enthalpy–entropy compensation occurs. By applying a general statistical mechanical theory of hydration [10,11], it emerges that the superhydrophobicity of CF4 is mainly because the work spent for cavity creation is to a little extent counterbalanced by the work gained on turning on the CF4–water attractive interactions. The latter are weak due to the low molecular polarizability of tetrafluoromethane, reflecting the strength of C–F bonds and the strong electronegativity of fluorine atoms. 2. Calculation procedure The theory has already been presented in detail [10,11], and only the main points are summarized to provide a correct perspective. The Ben-Naim standard Gibbs energy change for the transfer

471

G. Graziano / Chemical Physics Letters 460 (2008) 470–473 Table 1 Experimental values of the Ben-Naim standard thermodynamic functions for the hydration of CF4, determined from solubility measurements, over the 10–55 °C temperature range by WBW [5] (part A), over the 5–30 °C temperature range by W&M [6] (part B), and over the 15–45 °C temperature range by S&B [7] (part C) T (°C)

DH (kJ mol1)

DS (J K1 mol1)

TDS (kJ mol1)

DG (kJ mol1)

A

10 25 40 55

18.5 12.8 7.1 1.4

106.3 86.9 68.0 50.3

30.1 25.9 21.3 16.5

11.6 13.1 14.2 15.1

B

5 15 25 30

22.0 17.8 13.4 11.2

118.6 104.1 88.9 81.8

33.0 30.0 26.5 24.8

11.0 12.2 13.1 13.6

C

15 25 35 45

18.6 12.2 5.9 0.5

106.5 84.9 63.9 43.7

30.7 25.3 19.7 13.9

12.1 13.1 13.8 14.4

of a solute molecule from a fixed position in the ideal gas phase to a fixed position in water at constant temperature and pressure is

DG ¼ DGc þ DGa

ð1Þ

where the first term is the reversible work to create a cavity suitable to host the solute molecule in water; the second term represents the reversible work to turn on the attractive potential between the solute molecule inserted in the cavity and the surrounding water molecules. The latter can be expressed as [11]:

DGa  hwa ic  ½hj2 ic =2RT

ð2Þ

where wa is the attractive solute–water potential energy and j = wa  hwaic. Note that: (a) hwaic is the attractive energy between the solute molecule inserted in the cavity and the surrounding water molecules that have not yet reorganized in response to switching on the wa attractive potential [11] (i.e., in this statistical ensemble the wa potential acts as a ghost); (b) this implies that hwaic  Ea accounts for the solute–water dispersion attractions and a fraction of dipoleinduced dipole attractions, because in this ensemble the dipoles of water molecules will rarely possess the orientation to attractively interact with the nonpolar solute in the cavity [11,12]. When the attractive solute–water potential is weak in comparison to water– water H-bonds, the fluctuations in the value of hwaic are small, and the second term on the right-hand side of Eq. (2) can be neglected [11]. The condition of small fluctuations in the value of hwaic is verified for nonpolar compounds in water [11,12], and DGa is simply given by the average solute–water interaction energy:

DGa  hwa ic  Ea

ð3Þ

The Gibbs energy cost to create a cavity is calculated by means of the formula provided by scaled particle theory, SPT [13]. According to the above theoretical approach, DGc is the work to create the cavity in the real liquid, and the pressure to be used in SPT formula is the experimental one, 1 atm, the hydrostatic pressure over water [13]. The cavity size is defined as the diameter of the spherical region from which any part of any solvent molecules is excluded (i.e., it corresponds to the size of the solute molecule). It is well known that SPT results are sensitive to the r values selected for the solvent and solute molecules [14]. For water, I selected r = 2.80 Å [15], which is close to the location of the first peak in the oxygen–oxygen pair correlation function of water [16], and allows a satisfactory description of the cavity size distribution function of water by means of SPT. The 2.80 Å effective diameter has been considered to be temperature-independent. The experimental values of water density over the 5–55 °C temperature range have been used in SPT calculations [17].

The Ea  hwaic term is estimated using the simple formula devised by Pierotti [13], in the assumption that the solute–solvent dispersion interactions are represented by the Lennard-Jones 612 potential, and that the solvent density around the solute is uniform and equal to that of pure solvent. For CF4 in water, Ea should consist of dispersion attractions and a fraction of the dipole-induced dipole attractions. I assume that the latter can be absorbed into the parameterization of the dispersion contribution because both terms depend on the inverse sixth power of distance. On this basis the e/k value of water is increased from 85 K to 120 K [18], considering that the dipole moment of water in the liquid phase is markedly larger than that in the gas phase. For CF4, I selected the Lennard-Jones parameters reported by Reid and Sherwood [19], r = 4.66 Å and e/k = 134 K. By considering the van der Waals surface or volume of the CF4 molecule [1], the diameter of the corresponding sphere is 4.84 Å or 4.51 Å; the average value, r = 4.68 Å, is in line with that of Reid and Sherwood. In addition, the selected r value for CF4 agrees with the location of the first peak in the carbon–carbon radial distribution function of liquid CF4 determined by means of both neutron scattering measurements and computer simulations [20,21]. Clearly, the LennardJones parameters of Reid and Sherwood cannot be directly compared to the van der Waals diameters and e/k values assigned to fluorine and carbon atoms in all-atom force fields [21]. The Ea magnitude depends on temperature mainly because the liquid density decreases with temperature. Since the water density decreases by less than 1.5% over the 5–55 °C temperature range [17], the Ea quantity has been considered to be temperature-independent. A similar calculation procedure was used by both W&M [6], and S&B [7]; however, without the framework provided by the statistical mechanical theory of hydration [10–12], the numerical results would not be so transparent. 3. Results and discussion 3.1. Gibbs energy change The calculated values of DGc and Ea are listed in the third and fourth columns, respectively, of Table 2. Notwithstanding the simplicity of the used formulae, the present values are in line with those calculated by means of direct computer simulations in different water models. At 25 °C and 1 atm, DGc (in kJ mol1) = 33.6 from SPT formula; 35.4 in SPC water by means of a thermodynamic integration procedure [22]; 33.8 in TIP3 P water by means of the test particle insertion method [23]; 35.3 in SPC/E water by means of both the test particle insertion method and perturbation theory [24]. On the same line, Ea (in kJ mol1) = 20.4 from Pierotti’s formula; (22.6 ± 2.5) for a poly-atomic model of CF4, and

Table 2 Values of the work of cavity creation calculated by means of SPT, assuming r(H2O) = 2.80 Å over the whole temperature range; values of the CF4–water interaction energy, calculated by means of Pierotti’s formula, and considered to be temperature-independent; comparison between the calculated DGc + Ea numbers and the experimental DG values (i.e., those from the data of S&B [7], except the value at 5 °C that comes from the data of W&M [6], and that at 55 °C that comes from the data of WBW [5]; see Table 1) T (°C)

n

DGc (kJ mol1)

Ea (kJ mol1)

DGc þ Ea (kJ mol1)

DG (kJ mol1)

5 15 25 35 45 55

0.384 0.384 0.383 0.382 0.380 0.379

31.5 32.6 33.6 34.5 35.3 36.0

20.4 20.4 20.4 20.4 20.4 20.4

11.1 12.2 13.2 14.1 14.9 15.6

11.0 12.1 13.1 13.8 14.4 15.1

For CF4, I selected r = 4.66 Å and e/k = 134 K, while for water e/k = 120 K.

472

G. Graziano / Chemical Physics Letters 460 (2008) 470–473

(20.9 ± 1.0) for a united-atom model of CF4 (r = 4.66 Å), from molecular dynamics simulations in SPC/E water [25]. The values of the sum DGc + Ea are close to the experimental DG data over the whole 5–55 °C temperature range. Such an agreement has to be considered satisfactory because no optimization of the CF4 molecular parameters has been performed (i.e., the r and e/k values for CF4 come from a classical text on gases and liquids [19]), and the choice e/k = 120 K for water is not ad hoc for CF4 [18]. In addition, the agreement is better than that reached by: (a) Bonifacio et al. [2], by means of the test particle insertion method with Monte Carlo simulations in SPC/E water, using a united-atom model for CF4; (b) Pratt and co-workers [25] by means of the test particle insertion method with molecular dynamics simulations in SPC/E water, using a poly-atomic model for CF4. This can be verified by looking at Fig. 1. To the best of my knowledge, it does not exist an experimental determination of the partial molar volume, PMV, of CF4 at infinite dilution in water. However, by means of a reliable group additivity approach [26], one obtains PMV(CF4) = 56.9 cm3 mol1 at 25 °C in water. This estimate is close to the value, 57.6 cm3 mol1, calculated at 25 °C by means of the analytical expression for the PMV of a hard sphere solute in an infinitely dilute hard sphere mixture derived by Lee from the SPT equation of state for hard sphere mixtures [27], and using the same parameters selected to calculate DGc by means of SPT formula. This is a further indication that SPT works well to describe the hydration thermodynamics of CF4. To understand the molecular origin of the superhydrophobicity of CF4, it is important to recognize that the magnitude of the DGc function in a given liquid at a fixed temperature depends solely on the size of the cavity, because DGc is a property of the pure liquid (i.e., the size, not the chemical nature, of the solute molecule to be hosted in the cavity is important [18]). This means that the magnitude of DGc is identical for CF4 and a ‘hypothetical’ hydrocarbon having the same size of CF4. The DG difference has to be due to the magnitude of the Ea term, or better to the strength of the CF4– water dispersion interactions with respect to that of CH4–water and/or C(CH3)4–water dispersion interactions (considering also the fraction of dipole-induced dipole interactions). It is useful to compare the molecular polarizability of CF4 with those of methane and neopentane. The experimental values of molecular polarizability at room temperature are the following: a = 4.02 Å3 for CF4 (r = 4.66 Å) [28], 2.70 Å3 for CH4 (r = 3.70 Å)

14

13

ΔG

-1

(kJ mol )

15

[29], and 10.50 Å3 for C(CH3)4 (r = 5.80 Å) [29]. To perform a correct comparison one has to consider that the molecular polarizability is directly proportional to the molecular volume [30]. Thus: (a) starting from the a value of CH4, one obtains that a ‘hypothetical’ hydrocarbon of 4.66 Å diameter would have a = 5.40 Å3; (b) starting from the a value of C(CH3)4, one obtains that a ‘hypothetical’ hydrocarbon of 4.66 Å diameter would have a = 5.45 Å3. These two simple calculations agree between each other and indicate unequivocally that the molecular polarizability of CF4 is about 25% smaller than that of a ‘hypothetical’ hydrocarbon possessing the same size of CF4 (note that another experimental datum is a = 2.86 Å3 for CF4 [31]). Since the molecular polarizability is a fundamental factor of dispersion interactions [30], the above analysis leads to the conclusion that the Ea value of CF4 in water is markedly smaller in magnitude than that of a ‘hypothetical’ hydrocarbon possessing the same size of CF4, causing the superhydrophobicity of the latter. In this respect, it is worth noting that Zhou and coworkers [4] pointed out that the dispersion interactions of fluorocarbons with water molecules in the first hydration shell are noticeably weaker than those of hydrocarbons, determining their superhydrophobicity. Since Zhou and co-workers used the allatom force field developed by Watkins and Jorgensen [21], the weakness of the dispersion attractions in the case of fluorocarbons has to be traced to the smaller e/k values assigned to carbon and fluorine atoms with respect to carbon and hydrogen atoms. In fact, Cummings and co-workers fixed [32]: r(CH2) = 3.93 Å, r(CF2) = 4.65 Å, e/k = 47 K for CH2, and 30 K for CF2; in other words, a CF2 group is larger in size than a CH2 group, but has a smaller e/k parameter. On the other hand, following the suggestion of one of the Reviewers, it has to be noted that the polarizable continuum model, PCM, as implemented in the GAUSSIAN package [33], markedly overestimates the dispersion energy of CF4 with water. A further deepening would require an understanding of the reason why the molecular polarizability of CF4 is so small. The answer is not so difficult: the molecular polarizability is inversely proportional to the electronegativity of the constituent atoms [34]. Since Pauling established long time ago that fluorine is the most electronegative atom [35], it is expected that CF4 possesses a very low polarizability. Therefore, the electronic cloud of CF4 is confined along the C–F bonds, which are very strong, and can be distorted to a little extent. This mechanism corresponds to that operative for He and Ne. Even though the atoms of the two noble gases are very small in size, at 25 °C, DG (in kJ mol1) = 11.5 for He, and 11.2 for Ne; for the larger noble gases DG is smaller [36]. By means of SPT formula, one obtains that, at 25 °C, DGc (in kJ mol1) = 13.4 for He (r = 2.63 Å), and 14.6 for Ne (r = 2.79 Å); thus, Ea (in kJ mol1) = DG  DGc = 1.9 for He, and 3.4 for Ne. These numbers indicate that the large and positive DG values are because the solute–water interactions are particularly weak due to the very low polarizability of He (i.e., 0.204 Å3) and Ne (i.e., 0.393 Å3) atoms [29]. 3.2. Enthalpy and entropy changes

12

11 0

20

40

60

80

temperature (˚C ) Fig. 1. Values of DG for the hydration of CF4: (a) experimental data of WBW [5], covering the 10–55 °C temperature range (open squares); (b) experimental data of W&M [6], covering the 5–30 °C temperature range (continuous line); (c) experimental data of S&B [7], covering the 15–45 °C temperature range (dashed line); (d) estimates calculated in the present article (filled circles); (d) estimates calculated by Bonifacio et al. [2] (filled squares connected by segment); (e) estimates calculated by Asthagiri et al. [25] (filled diamonds connected by segments).

Even though CF4 is a superhydrophobic solute, its hydration process shows the common thermodynamic signatures of hydrophobic hydration, with no indication of dewetting or partial dewetting at room temperature. In particular, at 25 °C, both DH and DS are large and negative quantities, whereas they should be positive in the case of dewetting, as emphasized by Chandler [37], Ashbaugh and Pratt [38]. Since there is nothing special in the superhydrophobicity of CF4, the fundamental variable of dewetting is the molecular size [37]. The effective diameter of CF4, 4.66 Å, is markedly smaller than that of C(CH3)4, 5.80 Å, for the hydration of which I have already pointed out the non-occurrence of dewetting [39]. The height of the first peak in the solute–water oxygen

G. Graziano / Chemical Physics Letters 460 (2008) 470–473

radial distribution function is considered to be a non-ambiguous indication of dewetting [37,38]: if this height is smaller than one (i.e., the peak is absent), dewetting occurs. In the case of CF4, the carbon–water oxygen radial distribution functions, obtained by means of computer simulations in different water models, present a first maximum centered at 4.1 Å of 1.9 height [2,25]. This maximum height demonstrates that dewetting does not occur. The numbers in Table 1 indicate that the temperature dependence of DH and DS is strong, giving rise to DC p (in J K1 mol1) = 380 from the data of WBW [5], 433 from the data of W&M [6], and 636 from the data of S&B [7]. The latter numbers are larger than that expected on the basis of (a) the experimental DC p values for noble gases and hydrocarbons [9], and (b) the well-established correlation between DC p and the accessible surface area of the solute molecule [1]. The too large magnitude of DC p for CF4 could be an artifact due to the quality and/or processing of solubility data [1]. Thus, I preferred to analyze the DH and DS values solely at 25 °C, and to consider those of WBW, that are exactly the averages of the three data sets, DH = 12.8 kJ mol1 and DS = 86.9 J K1 mol1 (see Table 1). By comparing the Ea estimate with the DH value at 25 °C, it is evident that the structural reorganization of H-bonds among water molecules surrounding the inserted CF4 molecule is an endothermic process: DHh = DH  Ea = 7.6 kJ mol1. This estimate is not so far from the enthalpy change for cavity creation, 5.6 kJ mol1, calculated by means of SPT at 25 °C. The H-bond reorganization is mainly associated with cavity creation due to the weakness of the CF4–water attractions in comparison to the strength of water–water H-bonds. For the hydration entropy one has to consider that the whole quantity is due to water reorganization [40], because the solute molecule is at a fixed position and its rotational and vibrational degrees of freedom are assumed to be unaffected by the gas-to-water transfer. However, the entropy contribution due to the excluded volume effect is part of the direct perturbing potential, not a response to it of the water, and has to be singled out to determine the entropy contribution from H-bond reorganization [11]. It has been demonstrated, on statistical mechanical grounds, that DGc is purely entropic in origin [41–44], measuring the entropy loss for the excluded volume effect associated with cavity creation. In fact, the DGc magnitude proved to be practically the same, at a given number density, in both detailed water models and Lennard-Jones fluids constituted by particles having the same size of water molecules [45,46]. The excluded volume entropy contribution DSx ¼ DGc /T = 112.7 J K1 mol1 at 25 °C for CF4, using the present SPT estimate of DGc . The entropy change due to the structural reorganization of H-bonds among water molecules surrounding CF4 is a positive quantity at 25 °C: DSh ¼ DS  DSx = 25.8 J K1 mol1. The DHh and DSh estimates indicate that (a) the reorganization of H-bonds is characterized by enthalpy–entropy compensation, as expected in view of the weakness of CF4–water attractions [11]; (b) H-bonds in the hydration shell of CF4 are slightly more broken than those in bulk water (i.e., the DHh estimate amounts to about one-third of the energy usually associated with a water–water H-bond [35], 21 kJ mol1, and the hydration shell of CF4 consists of about 24 water molecules [1]). This finding is in line with both a general analysis [10], and one grounded on the Muller’s model [47], of thermodynamic data for the hydration of nonpolar solutes [9]. More importantly, it agrees with direct structural information recorded by means of neutron scattering and EXAFS measurements [48,49]. 4. Conclusion The present study of the physical origin of the superhydrophobicity of CF4 points out that the CF4–water dispersion interactions

473

are markedly weaker in magnitude than those of a ‘hypothetical’ hydrocarbon having the same size of CF4, counterbalancing to a smaller extent the large and positive work spent to create the cavity in water. The weakness of the CF4–water dispersion interactions comes from the very small polarizability of CF4, which, in turn, is mainly caused by the strong electronegativity of fluorine atoms. Moreover, the large and negative hydration enthalpy and entropy values at room temperature unequivocally indicate that dewetting is not a feature of CF4 hydration. The H-bonds among the water molecules constituting the CF4 hydration shell are only slightly perturbed with respect to those in bulk water. References [1] P. Scharlin, R. Battino, E. Silla, I. Tuñon, J.L. Pascual-Ahuir, Pure Appl.Chem. 70 (1998) 1895. [2] R.P. Bonifacio, A.A.H. Padua, M.F. Costa Gomes, J. Phys. Chem. B 105 (2001) 8403. [3] A. Ben-Naim, Solvation Thermodynamics, Plenum Press, New York, 1987. [4] X. Li, J. Li, M. Eleftheriou, R.H. Zhou, J. Am. Chem. Soc. 128 (2006) 12439. [5] E. Wilhelm, R. Battino, R.J. Wilcock, Chem. Rev. 77 (1977) 219. [6] W.Y. Wen, J.A. Muccitelli, J. Solution Chem. 8 (1979) 225. [7] P. Scharlin, R. Battino, J. Solution Chem. 21 (1992) 67. [8] W. Blokzijl, J.B.F.N. Engberts, Angew. Chem., Int. Ed. Engl. 32 (1993) 1545. [9] G. Graziano, B. Lee, J. Phys. Chem. B 109 (2005) 8103. [10] B. Lee, Biopolymers 31 (1991) 993. [11] G. Graziano, B. Lee, J. Phys. Chem. B 105 (2001) 10367. [12] G. Graziano, Chem. Phys. Lett. 429 (2006) 114. [13] R.A. Pierotti, Chem. Rev. 76 (1976) 717. [14] K.E.S. Tang, V.A. Bloomfield, Biophys. J. 79 (2000) 2222. [15] G. Graziano, Chem. Phys. Lett. 396 (2004) 226. [16] T. Head-Gordon, G. Hura, Chem. Rev. 102 (2002) 2651. [17] G.S. Kell, J. Chem. Eng. Data 20 (1975) 97. [18] G. Graziano, J. Chem. Phys. 120 (2004) 4467. [19] R.C. Reid, T.K. Sherwood, The Properties of Gases and Liquids, McGraw-Hill, New York, 1966. [20] I. Waldner, A. Bassen, H. Bertagnolli, K. Todheide, G. Strauss, A.K. Soper, J. Chem. Phys. 107 (1997) 10667. [21] E.K. Watkins, W.L. Jorgensen, J. Phys. Chem. A 105 (2001) 4118. [22] T.C. Beutler, D.R. Beguelin, W.F. van Gunsteren, J. Chem. Phys. 102 (1995) 3787. [23] A. Kalra, N. Tugcu, S.M. Cramer, S. Garde, J. Phys. Chem. B 105 (2001) 6380. [24] S. Rajamani, T.M. Truskett, S. Garde, Proc. Natl. Acad. Sci. U.S.A. 102 (2005) 9475. [25] D. Asthagiri, H.S. Ashbaugh, A. Piryatinski, M.E. Paulaitis, L.R. Pratt, J. Am. Chem. Soc. 129 (2007) 10133. [26] L. Lepori, P. Gianni, J. Solution Chem. 29 (2000) 405. [27] B. Lee, J. Phys. Chem. 87 (1983) 112. [28] T.M. Reed, in: J.H. Simons (Ed.), Fluorine Chemistry, vol. 5, Academic Press, New York, 1964, p. 133. [29] E. Wilhelm, R. Battino, J. Chem. Phys. 55 (1971) 4012. [30] P.W. Atkins, Physical Chemistry, fifth edn., Oxford University Press, New York, 1995. [31] E.R. Lippincott, J.M. Stutman, J. Phys. Chem. 68 (1964) 2926. [32] S.T. Cui, H.D. Cochran, P.T. Cummings, J. Phys. Chem. B 103 (1999) 4485. [33] V. Barone, M. Cossi, J. Tomasi, J. Chem. Phys. 107 (1997) 3210. [34] S.K. Burley, G.A. Petsko, Adv. Protein Chem. 39 (1988) 125. [35] L. Pauling, The Nature of the Chemical Bond, third edn., Cornell University Press, Ithaca, New York, 1960. [36] G. Graziano, Can. J. Chem. 80 (2002) 401. [37] D. Chandler, Nature 437 (2005) 640. [38] H.S. Ashbaugh, L.R. Pratt, Rev. Mod. Phys. 78 (2006) 159. [39] G. Graziano, J. Phys. Chem. B 108 (2004) 9371. [40] B. Lee, G. Graziano, J. Am. Chem. Soc. 118 (1996) 5163. [41] B. Lee, J. Chem. Phys. 83 (1985) 2421. [42] G. Graziano, J. Phys. Chem. B 110 (2006) 11421. [43] S. Höfinger, F. Zerbetto, Chem. Soc. Rev. 34 (2005) 1012. [44] R. Mahajan, D. Kranzlmuller, J. Volkert, U.H.E. Hansmann, S. Höfinger, Phys. Chem. Chem. Phys. 8 (2006) 5515. [45] B. Madan, B. Lee, Biophys. Chem. 51 (1994) 279. [46] M. Ikeguchi, S. Shimizu, S. Nakamura, K. Shimizu, J. Phys. Chem. B 102 (1998) 5891. [47] N. Muller, Acc. Chem. Res. 23 (1990) 23. [48] J.L. Finney, D.T. Bowron, R.M. Daniel, P.A. Timmins, M.A. Roberts, Biophys. Chem. 105 (2003) 391. [49] P. Buchanan, N. Aldiwan, A.K. Soper, J.L. Creek, C.A. Koh, Chem. Phys. Lett. 415 (2005) 89.