Chemical Physics Letters 460 (2008) 470–473

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Chemical Physics Letters

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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 a b s t r a c t

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

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.06.057

* Fax: +39 0824 23013.E-mail address: graziano@unisannio.it

Tetrafluoromethane, CF4, is markedly less soluble in water than methane and neopentane around roomtemperature: it is a superhydrophobic solute. An analysis of the physical origin of this superhydrophob-icity is performed, exploiting literature thermodynamic data covering the 5–55 �C temperature range. Itresults 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 counterbal-ancing effect of the work spent to create the cavity in water. The weakness of the CF4–water dispersioninteractions is due to the very small polarizability of CF4, which, in turn, is caused by the strong electro-negativity of fluorine atoms.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Fluorocarbons are considered to be superhydrophobic becausetheir solubility in water is significantly smaller than that of the cor-responding hydrocarbons. For instance, the mole fraction solubilityin 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 solubil-ities 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 fixedposition into water) Gibbs energy of hydration: DG� (inkJ mol�1) = 13.1 for CF4, 8.3 for CH4, 10.5 for C(CH3)4, 16.4 forC2F6, and 7.6 for C2H6. From ligand partitioning between n-octanoland water, and from ligand binding it emerged an empirical rule: 1CF2 group corresponds to about 1.5 CH2 groups in terms of hydro-phobicity [4]. There is increasing interest in producing and charac-terizing superhydrophobic materials, and fluorocarbons seem to begood targets [4]. As a consequence, a molecular level explanationof their superhydrophobicity would be a pre-requisite.

In the present Letter, I would like to provide an analysis of thehydration thermodynamics of CF4 exploiting the data by Wilhelmet al. [5], WBW, covering the 10–55 �C temperature range, thegas solubility measurements of Wen and Muccitelli [6], W&M, cov-ering the 5–30 �C temperature range, and those of Scharlin andBattino [7], S&B, covering the 15–45 �C temperature range. Exper-imental values of DH�; DS�; and DG� are listed in Table 1. There isgood quantitative agreement for the DG� values among the threedata sets, whereas there is qualitative, but not quantitative, agree-ment for the DH� and DS� values. In line with the general featuresof hydrophobic hydration [8], (a) DG� is large and positive, increas-

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ing slightly with temperature; (b) DH� and DS� are large and nega-tive, increasing markedly with temperature. In fact, DC�p is a largeand positive quantity, amounting, in J K�1 mol�1 units, to (a) 380over the 10–55 �C temperature range, on the basis of the DH� val-ues of WBW [5]; (b) 433 over the 5–30 �C temperature range, onthe 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 re-ported value). It is worth noting that DC�p for the hydration of non-polar solutes is expected to be a decreasing function oftemperature on the basis of a large set of experimental data [9]. Ipreferred to consider DC�p as temperature-independent becausethe precision of the solubility measurements coupled to the smalltemperature range investigated did not allow a reliable determina-tion of the temperature dependence of DC�p.

The thermodynamic values reported in Table 1 indicate that,around room temperature, the superhydrophobicity of CF4 is en-tropy-dominated, even though a significant enthalpy–entropycompensation occurs. By applying a general statistical mechanicaltheory of hydration [10,11], it emerges that the superhydrophobic-ity of CF4 is mainly because the work spent for cavity creation is toa little extent counterbalanced by the work gained on turning onthe CF4–water attractive interactions. The latter are weak due tothe low molecular polarizability of tetrafluoromethane, reflectingthe strength of C–F bonds and the strong electronegativity of fluo-rine atoms.

2. Calculation procedure

The theory has already been presented in detail [10,11], andonly the main points are summarized to provide a correct perspec-tive. The Ben-Naim standard Gibbs energy change for the transfer

Table 2Values of the work of cavity creation calculated by means of SPT, assumingr(H2O) = 2.80 Å over the whole temperature range; values of the CF4–waterinteraction energy, calculated by means of Pierotti’s formula, and considered to betemperature-independent; comparison between the calculated DGc + Ea numbers andthe experimental DG� values (i.e., those from the data of S&B [7], except the value at5 �C that comes from the data of W&M [6], and that at 55 �C that comes from the dataof WBW [5]; see Table 1)

T(�C)

n DGc

(kJ mol�1)Ea

(kJ mol�1)DGc þ Ea

(kJ mol�1)DG�

(kJ mol�1)

5 0.384 31.5 �20.4 11.1 11.015 0.384 32.6 �20.4 12.2 12.125 0.383 33.6 �20.4 13.2 13.135 0.382 34.5 �20.4 14.1 13.845 0.380 35.3 �20.4 14.9 14.455 0.379 36.0 �20.4 15.6 15.1

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

Table 1Experimental values of the Ben-Naim standard thermodynamic functions for thehydration of CF4, determined from solubility measurements, over the 10–55 �Ctemperature 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 mol�1)DS�

(J K�1 mol�1)�TDS�

(kJ mol�1)DG�

(kJ mol�1)

A 10 �18.5 �106.3 30.1 11.625 �12.8 �86.9 25.9 13.140 �7.1 �68.0 21.3 14.255 �1.4 �50.3 16.5 15.1

B 5 �22.0 �118.6 33.0 11.015 �17.8 �104.1 30.0 12.225 �13.4 �88.9 26.5 13.130 �11.2 �81.8 24.8 13.6

C 15 �18.6 �106.5 30.7 12.125 �12.2 �84.9 25.3 13.135 �5.9 �63.9 19.7 13.845 0.5 �43.7 13.9 14.4

G. Graziano / Chemical Physics Letters 460 (2008) 470–473 471

of a solute molecule from a fixed position in the ideal gas phase to afixed 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 suitableto host the solute molecule in water; the second term representsthe reversible work to turn on the attractive potential betweenthe solute molecule inserted in the cavity and the surroundingwater molecules. The latter can be expressed as [11]:

DGa � hwaic � ½hj2ic=2RT� ð2Þ

where wa is the attractive solute–water potential energy andj = wa � hwaic. Note that: (a) hwaic is the attractive energy betweenthe solute molecule inserted in the cavity and the surrounding watermolecules that have not yet reorganized in response to switching onthe wa attractive potential [11] (i.e., in this statistical ensemble thewa potential acts as a ghost); (b) this implies that hwaic � Ea accountsfor the solute–water dispersion attractions and a fraction of dipole-induced dipole attractions, because in this ensemble the dipoles ofwater molecules will rarely possess the orientation to attractivelyinteract with the nonpolar solute in the cavity [11,12]. When theattractive solute–water potential is weak in comparison to water–water H-bonds, the fluctuations in the value of hwaic are small, andthe 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 ver-ified for nonpolar compounds in water [11,12], and DGa is simply gi-ven by the average solute–water interaction energy:

DGa � hwaic � Ea ð3Þ

The Gibbs energy cost to create a cavity is calculated by meansof the formula provided by scaled particle theory, SPT [13]. Accord-ing to the above theoretical approach, DGc is the work to create thecavity in the real liquid, and the pressure to be used in SPT formulais the experimental one, 1 atm, the hydrostatic pressure over water[13].

The cavity size is defined as the diameter of the spherical regionfrom which any part of any solvent molecules is excluded (i.e., itcorresponds to the size of the solute molecule). It is well knownthat SPT results are sensitive to the r values selected for the sol-vent 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 oxy-gen–oxygen pair correlation function of water [16], and allows asatisfactory description of the cavity size distribution function ofwater by means of SPT. The 2.80 Å effective diameter has been con-sidered to be temperature-independent. The experimental valuesof water density over the 5–55 �C temperature range have beenused in SPT calculations [17].

The Ea � hwaic term is estimated using the simple formula de-vised by Pierotti [13], in the assumption that the solute–solventdispersion interactions are represented by the Lennard-Jones 6-12 potential, and that the solvent density around the solute is uni-form and equal to that of pure solvent. For CF4 in water, Ea shouldconsist of dispersion attractions and a fraction of the dipole-in-duced dipole attractions. I assume that the latter can be absorbedinto the parameterization of the dispersion contribution becauseboth terms depend on the inverse sixth power of distance. On thisbasis 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 phaseis markedly larger than that in the gas phase. For CF4, I selectedthe Lennard-Jones parameters reported by Reid and Sherwood[19], r = 4.66 Å and e/k = 134 K. By considering the van der Waalssurface or volume of the CF4 molecule [1], the diameter of the cor-responding 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 firstpeak in the carbon–carbon radial distribution function of liquidCF4 determined by means of both neutron scattering measure-ments and computer simulations [20,21]. Clearly, the Lennard-Jones parameters of Reid and Sherwood cannot be directly com-pared to the van der Waals diameters and e/k values assigned tofluorine and carbon atoms in all-atom force fields [21].

The Ea magnitude depends on temperature mainly because theliquid density decreases with temperature. Since the water densitydecreases by less than 1.5% over the 5–55 �C temperature range[17], the Ea quantity has been considered to be temperature-inde-pendent. A similar calculation procedure was used by both W&M[6], and S&B [7]; however, without the framework provided bythe statistical mechanical theory of hydration [10–12], the numer-ical 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 andfourth columns, respectively, of Table 2. Notwithstanding the sim-plicity of the used formulae, the present values are in line withthose calculated by means of direct computer simulations in differ-ent water models. At 25 �C and 1 atm, DGc (in kJ mol�1) = 33.6 fromSPT formula; 35.4 in SPC water by means of a thermodynamic inte-gration procedure [22]; 33.8 in TIP3 P water by means of the testparticle insertion method [23]; 35.3 in SPC/E water by means ofboth the test particle insertion method and perturbation theory[24]. On the same line, Ea (in kJ mol�1) = �20.4 from Pierotti’s for-mula; �(22.6 ± 2.5) for a poly-atomic model of CF4, and

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), frommolecular dynamics simulations in SPC/E water [25].

The values of the sum DGc + Ea are close to the experimentalDG� data over the whole 5–55 �C temperature range. Such anagreement has to be considered satisfactory because no optimiza-tion of the CF4 molecular parameters has been performed (i.e., ther and e/k values for CF4 come from a classical text on gases and liq-uids [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 methodwith Monte Carlo simulations in SPC/E water, using a united-atommodel for CF4; (b) Pratt and co-workers [25] by means of the testparticle insertion method with molecular dynamics simulationsin SPC/E water, using a poly-atomic model for CF4. This can be ver-ified by looking at Fig. 1.

To the best of my knowledge, it does not exist an experimentaldetermination of the partial molar volume, PMV, of CF4 at infinitedilution in water. However, by means of a reliable group additivityapproach [26], one obtains PMV(CF4) = 56.9 cm3 mol�1 at 25 �C inwater. This estimate is close to the value, 57.6 cm3 mol�1, calcu-lated at 25 �C by means of the analytical expression for the PMVof a hard sphere solute in an infinitely dilute hard sphere mixturederived by Lee from the SPT equation of state for hard sphere mix-tures [27], and using the same parameters selected to calculate DGc

by means of SPT formula. This is a further indication that SPTworks well to describe the hydration thermodynamics of CF4.

To understand the molecular origin of the superhydrophobicityof CF4, it is important to recognize that the magnitude of the DGc

function in a given liquid at a fixed temperature depends solelyon the size of the cavity, because DGc is a property of the pure li-quid (i.e., the size, not the chemical nature, of the solute moleculeto be hosted in the cavity is important [18]). This means that themagnitude of DGc is identical for CF4 and a ‘hypothetical’ hydrocar-bon having the same size of CF4. The DG� difference has to be due tothe magnitude of the Ea term, or better to the strength of the CF4–water dispersion interactions with respect to that of CH4–waterand/or C(CH3)4–water dispersion interactions (considering alsothe fraction of dipole-induced dipole interactions).

It is useful to compare the molecular polarizability of CF4 withthose of methane and neopentane. The experimental values ofmolecular 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)

0 20 40 60 80

11

12

13

14

15

ΔG

(kJ

mol

-1 )

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 ofW&M [6], covering the 5–30 �C temperature range (continuous line); (c) experi-mental 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 calculatedby Bonifacio et al. [2] (filled squares connected by segment); (e) estimatescalculated by Asthagiri et al. [25] (filled diamonds connected by segments).

[29], and 10.50 Å3 for C(CH3)4 (r = 5.80 Å) [29]. To perform a cor-rect comparison one has to consider that the molecular polarizabil-ity 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) start-ing 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. Thesetwo simple calculations agree between each other and indicateunequivocally that the molecular polarizability of CF4 is about25% smaller than that of a ‘hypothetical’ hydrocarbon possessingthe same size of CF4 (note that another experimental datum isa = 2.86 Å3 for CF4 [31]). Since the molecular polarizability is a fun-damental factor of dispersion interactions [30], the above analysisleads to the conclusion that the Ea value of CF4 in water is markedlysmaller in magnitude than that of a ‘hypothetical’ hydrocarbonpossessing the same size of CF4, causing the superhydrophobicityof the latter. In this respect, it is worth noting that Zhou and co-workers [4] pointed out that the dispersion interactions of fluoro-carbons with water molecules in the first hydration shell arenoticeably weaker than those of hydrocarbons, determining theirsuperhydrophobicity. Since Zhou and co-workers used the all-atom force field developed by Watkins and Jorgensen [21], theweakness of the dispersion attractions in the case of fluorocarbonshas to be traced to the smaller e/k values assigned to carbon andfluorine 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/kparameter. On the other hand, following the suggestion of one ofthe Reviewers, it has to be noted that the polarizable continuummodel, PCM, as implemented in the GAUSSIAN package [33], mark-edly overestimates the dispersion energy of CF4 with water.

A further deepening would require an understanding of the rea-son why the molecular polarizability of CF4 is so small. The answeris not so difficult: the molecular polarizability is inversely propor-tional to the electronegativity of the constituent atoms [34]. SincePauling established long time ago that fluorine is the most electro-negative atom [35], it is expected that CF4 possesses a very lowpolarizability. Therefore, the electronic cloud of CF4 is confinedalong the C–F bonds, which are very strong, and can be distortedto 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 insize, at 25 �C, DG� (in kJ mol�1) = 11.5 for He, and 11.2 for Ne; forthe larger noble gases DG� is smaller [36]. By means of SPT formula,one obtains that, at 25 �C, DGc (in kJ mol�1) = 13.4 for He (r =2.63 Å), and 14.6 for Ne (r = 2.79 Å); thus, Ea (in kJ mol�1) =DG� � DGc = �1.9 for He, and �3.4 for Ne. These numbers indicatethat the large and positive DG� values are because the solute–waterinteractions are particularly weak due to the very low polarizabil-ity of He (i.e., 0.204 Å3) and Ne (i.e., 0.393 Å3) atoms [29].

3.2. Enthalpy and entropy changes

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

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

radial distribution function is considered to be a non-ambiguousindication of dewetting [37,38]: if this height is smaller than one(i.e., the peak is absent), dewetting occurs. In the case of CF4, thecarbon–water oxygen radial distribution functions, obtained bymeans of computer simulations in different water models, presenta first maximum centered at 4.1 Å of 1.9 height [2,25]. This maxi-mum height demonstrates that dewetting does not occur.

The numbers in Table 1 indicate that the temperature depen-dence of DH� and DS� is strong, giving rise to DC�p (inJ K�1 mol�1) = 380 from the data of WBW [5], 433 from the dataof W&M [6], and 636 from the data of S&B [7]. The latter numbersare larger than that expected on the basis of (a) the experimentalDC�p values for noble gases and hydrocarbons [9], and (b) thewell-established correlation between DC�p and the accessible sur-face area of the solute molecule [1]. The too large magnitude ofDC�p for CF4 could be an artifact due to the quality and/or processingof 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 ex-actly the averages of the three data sets, DH� = �12.8 kJ mol�1 andDS� = �86.9 J K�1 mol�1 (see Table 1).

By comparing the Ea estimate with the DH� value at 25 �C, it isevident that the structural reorganization of H-bonds among watermolecules surrounding the inserted CF4 molecule is an endother-mic process: DHh = DH� � Ea = 7.6 kJ mol�1. This estimate is not sofar from the enthalpy change for cavity creation, 5.6 kJ mol�1, cal-culated by means of SPT at 25 �C. The H-bond reorganization ismainly associated with cavity creation due to the weakness ofthe CF4–water attractions in comparison to the strength ofwater–water H-bonds.

For the hydration entropy one has to consider that the wholequantity is due to water reorganization [40], because the solute mol-ecule is at a fixed position and its rotational and vibrational degreesof freedom are assumed to be unaffected by the gas-to-water trans-fer. However, the entropy contribution due to the excluded volumeeffect is part of the direct perturbing potential, not a response to it ofthe water, and has to be singled out to determine the entropy contri-bution from H-bond reorganization [11]. It has been demonstrated,on statistical mechanical grounds, that DGc is purely entropic in ori-gin [41–44], measuring the entropy loss for the excluded volume ef-fect associated with cavity creation. In fact, the DGc magnitudeproved to be practically the same, at a given number density, in bothdetailed water models and Lennard-Jones fluids constituted by par-ticles having the same size of water molecules [45,46].

The excluded volume entropy contribution DSx ¼ �DGc/T =�112.7 J K�1 mol�1 at 25 �C for CF4, using the present SPT estimateof DGc. The entropy change due to the structural reorganization ofH-bonds among water molecules surrounding CF4 is a positivequantity at 25 �C: DSh ¼ DS� � DSx = 25.8 J K�1 mol�1. The DHh andDSh estimates indicate that (a) the reorganization of H-bonds ischaracterized by enthalpy–entropy compensation, as expected inview of the weakness of CF4–water attractions [11]; (b) H-bondsin the hydration shell of CF4 are slightly more broken than thosein bulk water (i.e., the DHh estimate amounts to about one-thirdof the energy usually associated with a water–water H-bond [35],21 kJ mol�1, and the hydration shell of CF4 consists of about 24water molecules [1]). This finding is in line with both a generalanalysis [10], and one grounded on the Muller’s model [47], of ther-modynamic data for the hydration of nonpolar solutes [9]. Moreimportantly, it agrees with direct structural information recordedby means of neutron scattering and EXAFS measurements [48,49].

4. Conclusion

The present study of the physical origin of the superhydrophob-icity of CF4 points out that the CF4–water dispersion interactions

are markedly weaker in magnitude than those of a ‘hypothetical’hydrocarbon having the same size of CF4, counterbalancing to asmaller extent the large and positive work spent to create the cav-ity in water. The weakness of the CF4–water dispersion interactionscomes from the very small polarizability of CF4, which, in turn, ismainly caused by the strong electronegativity of fluorine atoms.Moreover, the large and negative hydration enthalpy and entropyvalues at room temperature unequivocally indicate that dewettingis not a feature of CF4 hydration. The H-bonds among the watermolecules constituting the CF4 hydration shell are only slightlyperturbed with respect to those in bulk water.

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