Journal of Molecular Liquids 156 (2010) 82–88

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Journal of Molecular Liquids

j ourna l homepage: www.e lsev ie r.com/ locate /mol l iq

Association of hydrophobic ions in aqueous solution: A conductometric study ofsymmetrical tetraalkylammonium cyclohexylsulfamates☆

Marija Bešter-Rogač a,⁎, Cveto Klofutar b, Darja Rudan-Tasic b,c

a Faculty of Chemistry and Chemical Technology, University of Ljubljana, SI-1000 Ljubljana, Sloveniab Biotechnical Faculty, University of Ljubljana, SI-1000 Ljubljana, Sloveniac Krog-MIT, Tržaška cesta 43, SI-1000 Ljubljana, Slovenia

☆ Dedicated to Professor Victor Lobo on the occasion⁎ Corresponding author. Faculty of Chemistry and Che

1000 Ljubljana, SI, Slovenia. Tel.: +386 1 2419 410; faxE-mail address: marija.bester@fkkt.uni-lj.si (M. Bešt

0167-7322/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.molliq.2010.03.016

a b s t r a c t

a r t i c l e i n f o

Available online 27 March 2010

Keywords:Electrolyte conductivityElectrolyte solutionsTetraalkylammonium saltsIon associationCyclohexylsulfamatesChemical model

Tetraalkylammonium salts of cyclohexylsulfamic acid were used as model systems to study the ion-pairingprocess of hydrophobic ions.The electric conductivities of aqueous solutions of tetramethyl-, tetraethyl-, tetrapropyl-, tetrabutyl- andtetrapentylammonium salts of cyclohexylsulfamic acid were measured from 278.15 K to 303.15 K (in steps of5 K) in the concentration range ∼0.2 ∙10−3bc (mol dm−3)b∼6 ∙10−3. Evaluation of the limiting molarconductivity Λ∞ and the association constant KA was based on the low concentration chemical model ofelectrolyte solutions, that includes short-range forces. From the temperature dependence of the limiting molarconductivities Eyring's enthalpy of activation of charge transport was estimated. The standard Gibbs free energy,enthalpy and entropy of the ion-pairing process were calculated from the temperature dependence of the ion-association constants. It was found that in the investigated systems the ion association can be interpreted asstrongly enthalpy driven process that does not include any important release of water molecules from thehydration shells of ions. The non-Coulombic contribution to the Gibbs free energy was evident and favours theassociation process.

of his 70th birthday.mical Technology, Aškerčeva 5,: +386 1 2419 437.er-Rogač).

ll rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

It is well known that tetraalkylammonium (TAA) salts dissolved inwater undergo hydrophobic hydration [1], therefore they have beenstill extensively used as model systems for the investigation ofhydrophobic phenomena and various types of interaction. Thesymmetrical TAA ions (R4N+) have long been used as good examplesof spherical ions having a large variation in size [2] and ability to formhydrophobic ion pairs with organic and inorganic ions in water.

Evans andKay [3] studied the conductancebehaviour of symmetricaltetraalkylammonium halides in aqueous solutions and found out thatthe ion association is more expressed for iodides than for otherinvestigated salts. The investigation of hydration and association insolutions of TAA iodides, carried out by Kuba and Hawlicka [4] applyingelectrical conductivity measurements also, indicates a weak butperceivable association of opposite ions in aqueous solutions. Thevalues reported for the association constant, KA, range from 5.6 fortetramethylammonium iodide (Me4NI) to 15.3 for tetrabutylammo-nium iodide (Bu4NI) showing that the size of cation influences the ion-pairing process essentially. KA is considerably higher than those

obtained by Buchner et al. [5] for bromide analogues by dielectricspectroscopy (KA (Me4NBr)=3.0, KA (Bu4NBr)=5.6). Despite the factthat the difference could be ascribed to different experimentaltechniques andmodels used in these works, it leads to the assumptionsthat for TAA salts ion association is affected by the size and nature ofcation and anion as well.

Recently, the experimental and theoretical studies of the associationbetween TAA salts of increasing chain lengthwith an anionic surfactant,sodium dodecyl sulfate (SDS), in water have been carried out byPradines et al. [6,7]. The obtained values of KA are between 24 forMe4NDS and 1.6 ∙104 for Bu4NDS. Such an increase of the associabilitywith chain length shows a predominance of the hydrophobic interac-tions between the alkyl chain of the R4N+ cations and the long chain ofDS− over the electrostatic effect.

Thus, in these studies two types of anions were taking into account:relatively small halide anions on one and a large dodecyl sulfate on theother side and therefore the difference in the size between anions andcations was quite big.

The present work deals with the TAA cyclohexylsulfamates, i.e.with salts where both of the ions, cation and anion, undergohydrophobic hydration and possess quite comparable radii [8].

The electric conductivities of aqueous solutions of tetramethyl-,tetraethyl-, tetrapropyl-, tetrabutyl- and tetrapentylammoniumsalts of cyclohexylsulfamic acid were measured from 278.15 K to308. 15 K (in steps of 5 K) in the concentration range ∼0.2 ∙10−3bc

Table 1Densities, viscosities and relative permittivities of pure water and limiting conductiv-ities of cyclohexylsulfamate anion in water.

T/K d0a 103 ηb εc λ∞ (Cy−)d

278.15 0.99997 1.5192 85.897 16.25283.15 0.99970 1.3069 83.945 19.08288.15 0.99910 1.1382 82.039 22.05293.15 0.99821 1.0020 80.176 25.21298.15 0.99704 0.8903 78.358 28.47303.15 0.99565 0.7975 76.581 31.86308.15 0.99404 0.7195 74.846 35.37

Units: T, K; d0, kg dm−3; η, Pa s; λ∞, S cm2 mol−1.a Ref. [14].b Ref. [16].c Ref. [17].d Ref. [10].

83M. Bešter-Rogač et al. / Journal of Molecular Liquids 156 (2010) 82–88

(mol dm−3)b∼6 ∙10−3. The experimental data were treated in theframework of the low concentration chemical model (lcCM) [9]yielding the limiting molar conductivity Λ∞ and the associationconstant KA. Using the known data of the limiting conductivities ofcyclohexylsulfamate anion [10] the limiting conductivities of thetetraalkylammonium ions were evaluated at all temperatures. Fromthe temperature dependence of the limiting molar conductivitiesEyring's enthalpy of activation of charge transport was estimated.The standard Gibbs energy, enthalpy and entropy of the ion-pairingprocess were calculated from the temperature dependence of theion-association constants. Finally, the non-Coulombic contributionsto the Gibbs free energy were estimated.

2. Experimental

2.1. Materials

All tetraalkylammonium salts investigated, i.e. tetramethyl-(Me4NCy), tetraethyl- (Et4NCy), tetrapropyl- (Pr4NCy), tetrabutyl-(Bu4NCy), and tetrapentylammonium cyclohexylsulfamates (Pe4NCy)were obtained by careful neutralization of cyclohexylsulfamic acid(purchased from Sigma) with the corresponding base (Fluka). Thepurity of the salts was checked after recrystallization from variousorganic solvents (Me4NCy from 2-propanol, Et4NCy from ethyl methylketone, n-Pr4NCy from ethyl acetate, n-Bu4NCy and n-Pe4NCy fromcyclohexane) by analysis of the elements C, H and N (Perkin Elmer,2400 Series II CHNS/O Analyzer) and also by ion exchange of thecation of the salt by the hydrogen ion (DOWEX, Type 50 WX8); apurity of 99.7% at least (Et4NCy) or better, e.g. 99.9% for Bu4NCy wasdetermined. The salts were kept in a vacuum desiccator over P2O5.

The stock solutions for the electric conductivitymeasurementswereprepared on a molal concentration scale by precise weighing, using adigital balance (Sartorius A-200S) accurate to within 3 ∙10−4 g.

2.2. Conductivity measurement

The conductivities of the solutions were determined with the helpof a three-electrode measuring cell, described elsewhere [11]. The cellwas calibrated with dilute potassium chloride solutions [12] andimmersed in the high precision thermostat described previously [13].The temperature dependence of the cell constant was taken intoaccount [12]. The water bath can be set to each temperature using atemperature program with a reproducibility of 0.005 K. The temper-ature in the precision thermostat bath was additionally checked withcalibrated Pt100 resistance thermometer (MPMI 1004/300 Merz) inconnection with a Multimeter HP 3458A. The resistance measure-ments of the solutions in the cell were performed using a precisionLCR Meter Agilent 4284A.

At the beginning of every measuring cycle, the cell was filled with aknown mass of water (∼660 g). After measurement of water conduc-tivity at all temperatures of the temperature program, the stepwiseconcentrationwas carried out by successive additions of knownmassesof stock solution with a gas-tight syringe. After every addition, thetemperature program was run by the computer and all measured data(frequency dependent resistance, temperature) were stored andpartially shown on display to track the measuring process. A home-developed software package was used for temperature control andacquisition of conductivity data. The measuring procedure, includingcorrections and extrapolation of the sample conductivity, κ, to infinitefrequency, has been previously described [13].

Molar conductivities, Λ=κ /c, of all investigated systems are givenin Table 2 as a function of electrolyte molality, m. The latter relates tothe corresponding (temperature-dependent) molar concentration, c,via c=m ∙d /(1+M2 ∙m), whereM2 is themolarmass of the solute andd is the density of the solution. A linear change of d with increasingsalt content for diluted solutions was assumed, d=d0+b ∙m, where

d0 is the density of water, taken from the literature [14] and given inTable 1. The density gradients, b, was determined by measuring thedensity of stock solutions and the final solution in the conductivitycell, which were determined by the method of Kratky et al. [15] usinga Paar densimeter (DMA 5000) at 298.15 K combined with a precisionthermostat. As usual, the density gradients b for all examinedelectrolytes are considered to be independent of temperature andare quoted in Table 2. Considering the sources of error (calibration,measurements, impurities), the specific conductivities are estimatedto be accurate within 0.2%.

3. Data analysis

The analysis of conductivity data in the framework of the lowconcentration chemical model (lcCM) given in Ref. [9] and theliterature quoted there, uses the set of equations

Λα

= Λ∞−Sffiffiffiffiffiffiαc

p+ Eαc ln αcð Þ + J1αc−J2 αcð Þ32 ð1Þ

KA =1−α

cα2y′�2; y′� = exp − κq

1 + κR

� �;

κ2 = 16πNAqαc; q =e2

8πεεokTð2a–dÞ

KA = 4πNA ∫R

ar2 exp

2qr−W*

kT

� �dr ð3Þ

where Λ and Λ∞ are the molar conductivities at molarity c and infinitedilution, (1−α) is the fraction of oppositely charged ions acting as ionpairs, and KA is the equilibrium constant of the lcCM with upperassociation limit R; y′± is the corresponding activity coefficient of the freeions, (y′±)2=y′+y′−, κ is the Debye parameter, e is the proton charge, ε isthe relative permittivity of the solvent, εo is the permittivity of a vacuumand T is the absolute temperature. The other symbols have their usualmeaning. W*is a step function for the potential of mean force betweencation and anion due to non-Coulombic interactions.

The coefficients of Eq. (1) are given in Ref. [9]. The limiting slope Sand theparameter E are completely calculablewhen the solvent data areavailable [14,16,17] (Table 1). The coefficients J1 and J2 are functions ofthe distance parameter R, representing the distance towhich oppositelycharged ions can approach as freely moving particles in solution.

Analysis of the conductivity data of associated electrolytes arecarried out by setting the coefficients S, E and J1 of Eq. (1) to theircalculated values and then usually using three-parameter fits toobtain the limiting values of molar conductivity Λ∞, the association KA

and the coefficient J2 by non-linear least squares iterations. A three-parameter evaluation is reduced to a two-parameter procedure fornonassociating electrolytes [11], where usually the coefficient J2 is

Table 2Experimental molar conductivities of the investigated TAA cyclohexylsulfamates inwater.

T 278.15 283.15 288.15 293.15 298.15 303.15 308.15

103 ∙m

Λ

Me4NCy, b=0.03860.22473 42.335 49.141 56.349 63.876 71.793 80.010 88.5800.49179 42.050 48.787 55.890 63.311 71.102 79.211 87.6430.82763 41.762 48.358 55.388 62.747 70.460 78.493 86.8381.1844 41.384 47.979 54.940 62.228 69.873 77.837 86.1121.68762 41.044 47.563 54.484 61.697 69.283 77.182 85.3952.25905 40.710 47.200 54.069 61.225 68.760 76.596 84.7562.99099 40.464 46.832 53.640 60.750 68.217 75.944 84.0303.86185 40.045 46.383 53.123 60.224 67.623 75.336 83.3544.86883 39.693 46.026 52.734 59.752 67.089 74.751 82.7146.11486 39.408 45.634 52.294 59.247 66.529 74.108 82.029

Et4NCy, b=0.03740.30258 34.919 40.716 46.803 53.181 59.911 66.946 74.2900.58381 34.736 40.432 46.445 52.739 59.365 66.291 73.5200.9065 34.405 40.037 45.986 52.200 58.763 65.614 72.7641.29698 33.999 39.636 45.545 51.732 58.254 65.038 72.1281.70814 33.842 39.334 45.181 51.313 57.748 64.524 71.5472.16818 33.551 39.056 44.885 51.007 57.423 64.076 71.0622.77916 33.307 38.710 44.492 50.570 56.944 63.600 70.5363.46334 33.040 38.412 44.143 50.177 56.509 63.118 70.0024.29801 32.769 38.092 43.771 49.768 56.043 62.596 69.4285.22359 32.415 37.686 43.315 49.257 55.478 61.973 68.7336.20057 32.138 37.417 43.004 48.904 55.081 61.525 68.248

Pr4NCy, b=0.02700.25518 28.833 33.804 39.119 44.736 50.665 56.903 63.0590.56902 28.534 33.383 38.568 44.063 49.827 55.864 62.1650.92941 28.017 32.818 37.903 43.289 48.965 54.908 61.1181.3831 27.588 32.278 37.307 42.624 48.222 54.086 60.2141.8266 27.251 31.892 36.870 42.145 47.689 53.487 59.5572.2658 27.066 31.755 36.605 41.810 47.314 53.084 59.1072.8907 26.695 31.302 36.171 41.338 46.792 52.502 58.4693.6913 26.335 30.925 35.667 40.852 46.246 51.894 57.8114.6813 26.036 30.553 35.323 40.366 45.706 51.296 57.1635.9090 25.700 30.166 34.888 39.899 45.232 50.777 56.566

BuN4Cy, b=0.02220.29891 26.401 31.047 35.943 41.155 46.648 52.408 58.4500.58514 26.083 30.593 35.437 40.587 45.997 51.683 57.6280.96993 25.707 30.168 34.944 40.026 45.376 50.992 56.8821.40094 25.490 29.907 34.648 39.691 45.002 50.570 56.3971.86974 25.187 29.566 34.255 39.243 44.497 50.012 55.7972.47333 24.888 29.228 33.861 38.756 43.955 49.416 55.1363.13457 24.602 28.871 33.482 38.345 43.495 48.903 54.5673.85156 24.300 28.587 33.136 37.956 43.058 48.414 54.0294.64714 24.098 28.321 32.832 37.627 42.689 48.006 53.5735.55718 23.863 28.032 32.498 37.245 42.256 47.530 53.032

PeN4Cy, b=0.01650.29135 25.369 29.821 34.563 39.543 44.823 50.375 56.1910.58894 25.070 29.430 34.036 38.935 44.103 49.534 55.2380.90579 24.717 29.047 33.627 38.460 43.582 48.966 54.5961.26609 24.489 28.755 33.276 38.026 43.096 48.421 54.0111.68533 24.252 28.484 32.974 37.695 42.734 48.010 53.5482.23118 23.971 28.163 32.576 37.296 42.281 47.513 53.0022.80796 23.710 27.864 32.263 36.941 41.880 47.070 52.5123.44295 23.491 27.591 31.961 36.608 41.508 46.655 52.0494.23097 23.271 27.305 31.631 36.235 41.088 46.183 51.5235.14515 23.028 27.022 31.308 35.870 40.675 45.723 51.015

Units: m, mol kg−1; T, K; Λ, S cm2 mol−1; b, kg2 dm−3 mol−1.

Fig. 1. Molar conductivities of aqueous solutions of Pr4NCy from 278.15 K to 308.15 K(in steps of 5 K) in the concentration range ∼0.2 ∙10−3bc (mol dm−3)b∼6 ∙10−3; fulllines: lcCM calculations.

Fig. 2. Molar conductivies of Me4NCy (○), Et4NCy (Δ), Pr4NCy (♦), Bu4NCy (◊) andPe4NCy (●) in water at 298.15 K; full lines: lcCM calculations.

84 M. Bešter-Rogač et al. / Journal of Molecular Liquids 156 (2010) 82–88

also fixed. The input data for the calculation of the coefficients are theknown solvent properties found in the literature (gathered in Table 1)and the distance parameter R. The lower limit a of the associationintegral is the distance of closest approach of cation and anion(contact distance)

a = aþ + a– ð4Þ

calculated from the ionic radii of the cations [9] a+=0.347, 0.400, 0.452,0.494 and 0.529 nm for Me4N+, Et4N+, Pr4N+, Bu4N+ and Pe4N+,respectively. For nonsymmetric ions such as MeBu3N+, C3H7O− or thecyclohexylsulfamate anion, the shortest possible distance between thelocalized positive and negative charges is chosen. We used the valuea−=0.176 nmwhichwasestimated for sulfamic acid assuming that thecyclohexyl radical does not change its interionic distance between theproton and thebasic oxygen atom in the zwitterion structure of sulfamicacid [18]. The crystal radius of the cyclohexylsulfamate anion is reportedto be 0.37 nm [19].

From extended investigations on electrolyte solutions in amphi-protic hydroxylic solvents (water, alcohols) it is known that the upperlimit of association is given by an expression of the type

R = a + n · s ð5Þ

where s is the length of an oriented solvent molecule and n is aninteger, n=0,1, 2, … Here, s is the length of an OH-group, dOH, ands=dOH=0.28 nm.

4. Results and discussion

4.1. lcCM calculations

Fig. 1 shows a comparison of the experimental data for theaqueous solutions of Pr4NCy given in Table 2 and the results of thelcCM calculations executed using Eqs. (1)–(3) under the assumptionn=1 for Eqs. (4) and (5), encompassing contact and solvent-sharedion pairs. All other investigated systems show similar dependence. In

Table 3Limiting molar conductivities Λ∞ and association constants KA of investigated TAA cyclohexylsulfamates in water.

T Λ∞ KA Λ∞ KA Λ∞ KA Λ∞ KA Λ∞ KA

Me4NCy Et4NCy Pr4NCy Bu4NCy Pe4NCy

R=0.803 R=0.856 R=0.908 R=0.950 R=0.985

278.15 43.00±0.03 4.80±0.35 35.69±0.03 5.87±0.37 29.44±0.07 12.06±1.21 27.08±0.03 8.63±0.55 26.01±0.03 8.22±0.64283.15 49.88±0.04 5.07±0.36 41.57±0.04 6.25±0.37 34.46±0.09 11.36±1.25 31.78±0.04 8.49±0.55 30.56±0.03 8.65±0.58288.15 57.15±0.05 5.05±0.41 47.77±0.04 6.16±0.36 39.81±0.17 11.52±1.40 36.80±0.04 8.24±0.51 35.36±0.05 8.54±0.71293.15 64.75±0.07 4.98±0.45 54.34±0.05 5.78±0.36 45.49±0.14 11.34±1.43 42.13±0.05 8.17±0.55 40.43±0.06 8.02±0.79298.15 72.74±0.08 5.05±0.49 61.07±0.06 5.69±0.40 51.45±0.16 11.03±1.53 47.75±0.05 7.96±0.53 45.81±0.07 7.87±0.81303.15 81.04±0.09 5.06±0.52 68.21±0.07 5.64±0.43 57.72±0.19 10.96±1.62 53.64±0.06 7.73±0.52 51. 46±0.09 7.78±0.84308.15 89.68±0.11 5.01±0.56 75.65±0.08 5.64±0.46 64.14±0.18 10.14±1.35 59.81±0.06 7.61±0.50 57.38±0.09 7.72±0.85

Units: T, K; Λ∞, S cm2 mol−1; KA, dm3mol−1; R, nm.

85M. Bešter-Rogač et al. / Journal of Molecular Liquids 156 (2010) 82–88

Fig. 2 the conductivity data for aqueous solutions of Me4NCy, Et4NCy,Pr4NCy, Bu4NCy and Pe4NCy at 298.15 K are presented.

Table 3 showsa comparison of the calculated data for all investigatedsalts. The obtained values of KA are in the range of 5bKAb12 which isevidently higher than those obtained in the aqueous solutions of thelithium, sodium, potassium and ammonium salts of cyclohexylsulfamicacid where KA=3–5 for aqueous solutions of the ammonium salt andKA=1–1.5 in all other systems are reported [10]. It can be concludedthat the ion association in water between two hydrophobic ions(tetraalkylammonium cations and cyclohexylsulfamate anion) is morepronounced than at smaller, less hydrophobic ions; but it still dependson the size as well as on the nature of ions. An inspection of Table 3reveals that KA≈5 forMe4NCy, slightly higher (∼5.5–6) for Et4NCy andreaches the highest values for Pr4NCy (∼10–12). For Bu4NCy andPe4NCy KA values are close together (∼7.5–8.5).

The values of KA for NaCl aqueous solutions, obtained from preciseconductance measurements by using the lcCM, are in the range0.6bKAb2.6 in the temperature range between 278.15 and 308.15 K[20]. Whereas the temperature coefficient dKA/dT is usually positivefor the alkali salt in water solutions, reverse can be observed for R4NCywith cations possessing longer alkyl chains (Pr4N+, Bu4N+, Pe4N+).The increase of the association constant with increasing temperaturein water can be explained by hydration of ions, which is lesspronounced at higher temperatures and therefore the ion pairing islightened. The hydration of these R4NCy is not very pronouncedneither for anion nor for cation. Due to the more expressed thermicmovement at higher temperatures the ion association is slightlyweaker. This finding is in agreement with recently found results onthe ion association of decyltrimethylammonium chloride (DeTACl)and dodecyltrimethylammonium chloride (DTACl) below criticalmicelle concentrations [21], where these micellar systems behave assimple, slightly associate electrolytes. It is reported that association

Table 4Limiting conductivity of the investigated tetraalkylammonium ions in water as afunction of temperature.

T λ∞ (Me4N+) λ∞ (Et4N+) λ∞ (Pr4N+) λ∞ (Bu4N+) λ∞ (Pe4N+)

278.15 26.75 19.44 13.19 10.83 9.76283.15 30.80 22.49 15.38 12.70 11.48

30.93a 21.90a 15.33a 12.56a

288.15 35.10 25.72 17.76 14.73 13.31293.15 39.54 29.13 20.28 16.92 15.22298.15 44.27 32.60 22.98 19.28 17.34

44.42a 32.22a 23.22a 19.3a 17.50b

44.92c 32.66c 23.42c 19.47c 17.47c

303.15 49.18 36.35 25.86 21.78 19.6308.15 54.31 40.28 28.77 24.44 22.01

Units: T, K; λ∞, S cm2 mol−1.a Ref [3].b Ref [22].c Ref [23].

decreases with rise in temperature, what was ascribed also to thermalagitation which tends to make association less probable.

Combining the limiting ion conductivities Λ∞ of Table 3 and theknown limiting values of anion λ∞(Cy−) [10] listed in Table 1

λ∞ T;R4Nþ� �

= Λ∞ T;R4NCyð Þ−λ∞ T;Cy−ð Þ ð6Þ

yields the limiting cation conductivities of all investigated R4N+

cations, λ∞(R4N+), and their temperature dependence; see Table 4.The agreement with the literature data at 298.15 K [3,22,23] and283.15 K [3] is reasonable.

From the Walden rule [9]

λ∞ Tð Þη Tð Þ = Fejzj6πrh

ð7Þ

the hydrodynamic radii rh could be estimated (F is the Faradayconstant and z the ionic charge). All hydrodynamic radii are collectedin Table 5. It is well known [9], that the hydrodynamic radii, calculatedfrom limiting conductivities (rh) are distinctly different from thoseobtained for the smaller TAA ions from the structural model (a+). Theratio a+/rh for all investigated cations at 298.15 K are given in Table 5and are in excellent agreement with the values from the literature [9].

The reported hydrodynamic radii for the cyclohexylsulfamic anionare between 0.332 nm at 278.15 K and 0.322 nm at 308.15 K [10].They are in reasonable agreement with the reported crystal radius ofthe anion (rcry=0.37 nm) and with the value obtained fromvolumetric properties, rh=0.334 nm at 298.15 K [19]. Thus no explicithydration can be assumed. As it has been discussed in our previouswork, the hydrophobicity of the cyclohexylsulfamic anion seems topredominate in its intrinsic hydrophilic/hydrophobic balance.

Walden rule treats the ionic migration as a movement of a rigidspherical ion throughviscous continuumthereforeno further informationon the molecular scale transport process could be estimated.

Table 5Hydrodynamic radii, rh, of tetraalkylammonium ions in water from Walden's rule as afunction of temperature.

T Me4N+ Et4N+ Pr4N+ Bu4N+ Pe4N+

rh278.15 0.202 0.277 0.409 0.498 0.552283.15 0.203 0.279 0.407 0.493 0.546288.15 0.205 0.280 0.405 0.488 0.541293.15 0.207 0.281 0.403 0.483 0.537298.15 0.208 0.282 0.400 0.477 0.531303.15 0.209 0.283 0.397 0.472 0.524308.15 0.210 0.283 0.396 0.466 0.517

a+ / rhThis work 1.67 1.42 1.13 1.03 1.00Ref. [9] 1.69 1.42 1.15 1.04 1.00

Units: T, K; r, nm.

Fig. 3. Plots of lnλ∞ + 23 lnd0 as a function of 1/T for Me4N+ (○), Et4NCy (Δ), Pr4N+ (♦),

Bu4N+ (◊) and Pe4N+ (●) ions in water. From the slope the Eyring's enthalpy ofactivation of the charge transport, ΔH*, was obtained.

Table 6Coefficients of polynomials ΔGA

0(T)=A0+A1(298.15−T)+A2(298.15−T)2 and ΔHA0

(298.15 K) for Me4NCy, Et4NCy, Pr4NCy, Bu4NCy and Pe4NCy in water.

A0=ΔGA0 (298.15 K) A1=ΔSA0 (298.15 K) A2 ΔHA

0 (298.15 K)

Me4NCy −4021±20 12.8 −0.263 −1829Et4NCy −4361±42 5.33 −0.227 −2721Pr4NCy −5949±31 5.96 −0.299 −3273Bu4NCy −5138±7 6.27 −0.068 −4174Pe4NCy −5161±37 6.50 0.245 −3176

Units: A0, J mol−1; A1, J mol−1 K−1; A2, J mol−1 K−2; ΔHA0, J mol−1.

86 M. Bešter-Rogač et al. / Journal of Molecular Liquids 156 (2010) 82–88

The temperature dependence of limiting conductivity yieldsEyring's enthalpy of activation of charge transport, ΔH⁎ [24]

lnλ∞ +23lnd0 = −ΔH*

RT+ B; ð8Þ

where B is the integrations constant.Values ΔH*=16.67±0.3, 17.14±0.3, 18.44±0.3, 19.22±0.3 and

19.14±0.3 kJ/mol for Me4N+, Et4N+, Pr4N+, Bu4N+, and Pe4N+,respectively were obtained (Fig. 3). The reportedmolar ionic enthalpyof activation for the cyclohexylsulfamate anion is 18.34 kJ/mol [10].

It has been shown that the ionic migration in a non-structuressolvent is very much a solvent property and that the difference in themobilities of ions is simply the result of different ion sizes [25]. Thus,the observed differences in the Eyring's enthalpy of activation ofcharge transport in the investigated systems could first be ascribed tothe differences in the ion sizes.

All values are distinctly higher than the corresponding Eyringactivation enthalpy for viscous flow for purewater (14.97±0.30 kJ/mol).

The observed order of the molar ionic enthalpy of activation for theions Me4N+NEt4N+NPr4N+≈Cy−NBu4N+≈Pe4N+ could be explainedby the energy needed for the desolvation and rearrangement of watermolecules in the vicinity of the ion and depends on the expressedhydration. Surprisingly, the same – but reverse order –was found for theKA values, confirming the assumption that the hydration plays anextremely important role at the ion association: at less pronouncedhydration the association ismore favourable. The highest associationwasobserved for Pr4NCy, where cation and anion expressed very similarEyring's enthalpy of activation of charge transport and therefore thehydration of these ions is very similar. This finding is in agreement withrecently reported statement that ions prefer to pair with counter ions orionic groups which have comparable hydration enthalpies [26].

4.2. Thermodynamics of the ion-pair process

The association constant KA(T) is linked to the Gibbs' energy of ionpair formation, ΔGA

0(T), by

ΔG0A Tð Þ = −RT lnKA Tð Þ: ð9Þ

ΔGA0(T) is represented for the measured temperature-dependent

association constants of Table 3 with the help of a polynomial

ΔG0A Tð Þ = A0 + A1 298:15−Tð Þ + A2 298:15−Tð Þ2: ð10Þ

Enthalpy and entropy of association here are obtained as follows

ΔS0A = − ∂ΔG0A

∂T

!p

= A1 + 2A2 298:15−Tð Þ ð11Þ

ΔH0A = ΔG0

A + TΔS0A = A0 + 298:15A1 + A2 298:152−T2� �

: ð12Þ

Table 6 compiles the coefficient of the polynomial, Eq. (10). Thevalues of ΔGA

0 and ΔSA0 at 298.15 K are ΔGA0=A0 and ΔSA0=A1.

Fig. 4 shows the Gibbs energies ΔGA0, enthalpies ΔHA

0 and entropiesΔSA0 of ion-pair formation inMe4NCy and Pe4NCy aqueous solutions asboundary systems.

Inall systemsΔSA0 is positiveat all temperatures but very low— aboutten times lower than observed for the ion association in aqueoussolutions of 1.1 or 2.2 electrolytes [20,27] where the ion pairing is anendothermic process resulting from the interplay of the contributions ofdehydration of ions and association to ion pair. Due to the release of theessential amount ofwatermolecules fromorderedhydration shell in thebulk, entropy is positive.

Ion pairing in the investigated systems is an exothermic process,except at Me4NCy at lower temperatures (Fig. 4). Therefore this ionassociation can be interpreted as strongly enthalpy driven processbeing performed without any important release of water moleculesfrom the hydration shells of ions.

According to the Eq. (3) the Gibbs' energy of ion-pair formation,ΔGA

0, can be split into two terms

ΔG0A = ΔGcoul

A + ΔG*A; ð13Þ

where ΔGA⁎=NAW* and ΔGAcoul is obtained from the “Coulombic” part

of the association constant KA in Eq. (3)

ΔGcoulA = −RT lnKcoul

A ð14Þ

KcoulA = 4πNA ∫

R

ar2 exp

2qr

� �dr: ð15Þ

A polynomial type of Eq. (10)

ΔG*A Tð Þ = B0 + B1 298:15−Tð Þ + B2 298:15−Tð Þ2 ð16Þ

is used for evaluation of the ΔGA⁎, ΔHA⁎ and ΔSA⁎ of the ion-pair formationpresented in Table 7, together with the coefficients B0, B1 and B2 of ΔGA⁎

polynomials. It is evident that ΔGA⁎ is small in comparison to the totalvalue of ΔGA, but all values are negative indicating that the non-Coulombic interactions play an important role in the process of ionassociation. For the ion association in aqueous solutions of 2.2 electrolytes[27,28] ΔGA⁎ is positive but small in comparison to the total value of ΔGA,indicating apreference of strong electrostatically bound ionpairs. There isno evidence in the literature for the non-Coulombic contributions to theion association for 1.1 electrolytes in water.

Fig. 4. Temperature dependence of thermodynamic functions of association of Me4NCy and Pe4NCy. (□) ΔGA0; (●) ΔHA

0; (○) TΔSA0.

87M. Bešter-Rogač et al. / Journal of Molecular Liquids 156 (2010) 82–88

Moreover, there are no systematic temperature-dependent inves-tigations on the transport properties of TAA salts in water in theliterature. As it has been mentioned in the Introduction, Evans andKay [3] performed conductivity measurements of some TAA halides inwater at 283.15 and 298.15 K. To enable the comparison with thepresent results their data were re-evaluated by lcCM. The ionic radii ofthe halide anions (0.181, 0.196 and 0.220 nm for Cl−, Br− and I−,respectively) [9] were used together with the ionic radii for R4N+

cations for the distance parameters in Eqs. (4) and (5). As expected,values of Λ∞ do not differ significantly from the reported values,therefore in Table 8 only KA and ΔGA⁎ are reported. Evidently, for thesalts with common anion, KA values are increasing with growingcation size (Me4N+bEt4N+bPr4N+bBu4N+). The temperature de-pendence of KA also shows similar behaviour as in our investigation:TAA cations with longer chains (Pr4N+, Bu4N+) show strongertemperature dependence, KA is lower at higher temperature.Obviously KA is affected by the anion also. For Me4N+ the followingorder of KA is evident: Cl−bBr−b I− and for all other salts KA foriodides is systematically higher than for bromides too.

Table 7Coefficients of polynomials ΔGA

⁎(T)=B0+B1(298.15−T)+B2(298.15−T)2 and ΔHA⁎

(298.15 K) for Me4NCy, Et4NCy, Pr4NCy, Bu4NCy and Pe4NCy in water.

B0=ΔGA⁎(298.15 K) B1=ΔSA⁎ (298.15 K) B2 ΔHA

⁎ (298.15 K)

Me4NCy −256±7 −4.6 0.009 −1618Et4NCy −210±21 −11.7 −0.456 −3685Pr4NCy −1547±24 −14.1 0.336 −5761Bu4NCy −487±7 −12.2 0.025 −4148Pe4NCy −279±20 −12.7 −0.340 −4058

Units: B0, J mol−1; B1, J mol−1 K−1; B2, J mol−1 K−2; ΔHA⁎, J mol−1.

Table 8Values of KA and ΔGA

⁎ as obtained from the literature data for some TAA halides byapplying lcCM.

KA ΔGA⁎

283.15 K 298.15 K 298.15 K

Me4NCla 2.19±0.04 2.17±0.12 1881.7Me4NBra 2.73±0.03 2.78±0.03 1353.7Me4NIa 3.24±0.03 2.15±0.73 2147.2Et4NBra 3.25±0.06 3.55±0.06 1292.5Pr4NBra 4.36±0.08 3.92±0.04 1130.8Pr4NIa 6.06±0.07 5.62±0.05 370.7Bu4NBra 5.19±0.06 4.55±0.03 1455.86Bu4NIa 7.37±0.15 6.88±0.06 99.06Pe4NBrb 5.61±0.09 664.0

Units: T, K; ΔGA⁎; J mol−1.

a Ref [3].b Ref [22].

Whereas the pattern of KA for TAA halides and TAA cyclohexylsulfa-mates is somehow similar, this is not true for theΔGA⁎. From Table 7 andEq. (10) it is evident, that at TAA cyclohexylsulfamates ΔGA⁎ is small incomparison to the total value of ΔGA, but negative. Values of ΔGA⁎

obtained for TTAhalides at 298.15 K are positive (Table 8). Thus it canbeconcluded that at cyclohexylsulfamates the non-Coulombic contribu-tion to the ion association is more expressed than for halides andtherefore the association process is more favourable.

5. Conclusion

In this work the ion association in diluted aqueous solutions of fivetetraalkylammonium salts of cyclohexylsulfamic acid was investigatedby electrical conductivity measurements in broad temperature range.

Since R4N+ cation as cyclohexylsulfamate anion are known ashydrophobic type of ions they can serve as model systems for theresearch of ion pairing of hydrophobic ions in water.

The experimental data were treated in the framework of the lowconcentration chemical model yielded the limiting molar conductiv-ities Λ∞ and the association constants KA.

From the temperature dependence of the limiting molar conductiv-ities Eyring's enthalpy of activation of charge transport was estimated.The standard Gibbs free energy, enthalpy and entropy of the ion-pairingprocess were calculated from the temperature dependence of the ion-association constants. It was found that in the investigated systems theion association can be interpreted as strongly enthalpy driven processbeing performed without any important release of water moleculesfrom the hydration shells of ions. The non-Coulombic contribution tothe Gibbs free energy is evident and favours the association process.

Acknowledgement

Financial support by the Slovenian Research Agency through GrantNo. P1-0201 is gratefully acknowledged.

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