Scientific paper Viscosity of Aqueous Solutions of Tetramethyl-, Tetraethyl-, Tetra-n-propyl-, Tetra-n-butyl-, and Tetra-n-pentylammonium Cyclohexylsulfamates from 293.15 K to 323.15 K Cveto Klofutar,1 Jaka Horvat,2 Marija Be{ter-Roga~3 and Darja Rudan-Tasi~1'* 1 Biotechnical Faculty, University of Ljubljana, SI-1000 Ljubljana, Slovenia. 2 Acies Bio d. o. o., Tehnolo{ki park 21, SI-1000 Ljubljana, Slovenia. 3 Faculty of Chemistry and Chemical Technology, University of Ljubljana, SI-1000 Ljubljana, Slovenia. * Corresponding author: E-mail: darja.rudan.tasic@bf.uni-lj.si Received: 17-11-2008 Dedicated to Professor Josef Barthel on the occasion of his 80'' birthday Abstract The viscosities of aqueous solutions of tetramethyl-, tetraethyl-, tetra-n-propyl-, tetra-n-butyl-, and tetra-n-pentylammo-nium cyclohexylsulfamate were determined at 293.15, 298.15, 303.15, 313.15 and 323.15 K. The relative viscosity was analysed and interpreted in terms of the Kaminsky equation, nr= 1 + Ac''2 + Bc + Dc2. The viscosity A-coefficient was calculated from Falkenhagen-Dole theory and its temperature coefficient estimated. The viscosity B-coefficients of the solutes are positive and relatively large, while their temperature coefficients are negative and decrease with increasing molecular weight of the solutes. The viscosity D-coefficient was discussed in terms of higher terms of the long-range Coulombic forces and hydrodynamic effects, as well as structural solute-solute interactions. The limiting thermodyna-mic functions of activation for viscous flow of solute, i. e. the Gibbs free energy, enthalpy and entropy, were evaluated using the theoretical approach given by Feakins et al. From the limiting partial molar functions of activation of the solute the contribution to the activation functions of solvent molecules were calculated using the corresponding limiting functions of activation for charge transport of solute ions. Keywords: Viscosity data, viscosity A-, B- and D-coefficients, activation parameters, cyclohexylsulfamates, aqueous solutions 1. Introduction The thermodynamic and transport properties of very dilute electrolyte solution are important in chemistry and biology. Studies of the viscosities of such solutions were among the earliest in the field of solution chemistry and have strongly influenced the development of our view of the solution process. The viscosity B-coefficient of the Jones-Dole equation1 has been a subject of considerable interest and has been measured for a wide range of electrolytes in aqueous and non-aqueous solutions.2 It is the quantity which defines the degree of water structuring around the ions. The viscosity B-coefficient is positive for all cosmotropic ions and negative for chaotropic ions. The B-coefficient though operationally useful, however, is simply an empirical parameter and provides no framework for interpretation. As was shown by Feakins et al.,3 4 the viscosity B-coefficient can be related to the limiting partial molar volume of solute and solvent, as well to the limiting Gibbs free energy of activation for viscous flow of the pure solvent and solute. Furhermore, it was suggested that the activation Gibbs free energy for movement of the solute could be approximated by that for diffusion or conductance of the solute5 or by that for viscous flow of the solvent.4 Some properties of tetra-n-alkylammonium cyclo-hexylsulfamates are now of considerable interest in different fields of electrolyte solution chemistry and as potential artificial sweeteners. The interactions of an ion with water molecules is highly specific, therefore a correlation can be expected for a group of closely related species such as R4N+-ions. Since no data are available in the literature on the viscosity of aqueous solutions of tetra-n-alkylam-monium cyclohexylsulfamates, we investigated the solution properties of a series of tetra-n-alkylammonium cyclohexylsulfamates. Our previous papers reported the volumetric measurements of some tetra-n-alkylammo-nium cyclohexylsulfamates.6,7 In this work we reported our study of viscosity of aqueous solutions of these compounds from 293.15 to 323.15 K over a sufficiently wide concentration range. Our prime interest was to determine the thermodynamic functions of activation of viscous flow of the solute and solvent and to provide a better understanding of the solute effect on the viscosity of solution. rent thermostat and flow-through cooler CK 300). The absolute viscosity of solution, n (cP = 10 3 kgm1 s 1) was calculated by means of the equation8 (1) where d (kgm 3) is the density of solution, t (s) is the flow time and C and E are constants characteristic of the visco-meter. The viscometer was calibrated with water. The values of C = 3.17 X 109 m2 s2 and E = 3.4 x 10-4 m2 s were determined by a least squares fit to Eq. (1), using the density9 and absolute viscosity of water,10 and the flow times at the experimental temperatures. The bath temperature was maintained to ±0.02 °C. The accuracy of the measured viscosities of 3 x 10-7 kg m-1s-1 was obtained by using the method of propagation of random errors where St = ±0.01 s, Sd = ±( ±2 X 10-5 m2 s. ±0.01 s, Sd = ±0.02 kg m3, SC = 7 x 10-13 m2 s2 and SE = 2. Experimental 2. 1. Materials All tetraalkylammonium salts investigated, i. e. tetramethyl- (Me4NCy), tetraethyl- (Et4NCy), tetra-n-propyl- (n-Pr4NCy), tetra-n-butyl- (n-Bu4NCy), and tetra-n-pentylammonium cyclohexylsulfamates (n-Pe4NCy) were obtained by careful neutralization of cyclohexylsul-famic acid (purchased from Sigma) with the corresponding base (Fluka). The purity of the salts were checked after recrystallization from various organic solvents (Me4NCy from 2-propanol, Et4NCy from ethyl methyl ketone, n-Pr4NCy from ethyl acetate, n-Bu4NCy and n-Pe4NCy from cyclohexane) by analysis of the elements C, H and N (Perkin Elmer, 2400 Series II CHNS/O Analyzer) and also by ion exchange of the cation of the salt by the hydrogen ion (DOWEX, Type 50 WX8); a purity of 99.7% at least (Et4NCy) or better, e. g. 99.9% for n-Bu4NCy was determined. The salts were kept in a vacuum desiccator over P2O5. 2. 2. Preparation of Solutions The solutions investigated were prepared on a molal concentration scale by precise weighing, using a digital balance (Mettler Toledo, model AT201, Switzerland) accurate to within 1 X 10-5 g. Before use the solutions were degassed by ultrasound (ultrasonic bath, Bandelin Sono-rex, type TK 52, Berlin, Germany). 3. Results and Discussion The values of viscosity, n (cP), of aqueous solutions of some tetra-n-alkylammonium cyclohexylsulfamates at various temperatures as a function of molality, m (mol kg-1), are presented in Table 1. The relative viscosity, nr= n In0, (where no is the viscosity of pure water) of the investigated solutions was analysed by the Kaminsky relation11 r]^=\ + Ac"- + Bc + Dc- (2) where c is the molarity (mol dm-3) calculated from the known density of solution6,12 as c = md/(1 + mM2 x 10-3) where d is the density of solution, and M2 the molecular weight of the solute. The A-coefficient is a measure of long-range ion-ion interactions (Coulombic forces), the B-coefficient takes into account the ion-solvent interaction and the D-coefficient includes all solute-solvent and solute-solute structural interactions that are not accounted for by the Ac'^ and Bc terms at higher concentration. The viscosity A-coefficient was calculated theoretically from the relation valid in the case of symmetrical electrolytes, where z+= = z.2 (3) and f (X°+, a!') takes the following form 2. 3. Viscosity Measurements The viscosity of the investigated solutions was determined with an Ubbehlode viscometer (Schott Visco Clock CT 52 measuring system, equipped with a transpa- In Eqs. (3) and (4) A* = 111.3 cP (cm2 S mol1) K1'2 (mol dm-3)-1'2, e0 is the relative permittivity of water, T the absolute temperature, function f Aj') depends on the equivalent conductances at infinite dilution of the ions, and and = + In calculation of the viscosity A-coefficient, the relative permittivity of water was taken from ref.,13 while the equivalent conductances of tetra-n-alkylammonium ions were obtained as follows: the equivalent conductances of tetramethyl-, tetraethyl- and tetra- n-propylammonium ions were obtained by analytical interpolation of the primary data of Robinson and Stokes^^ and Kay and Evans,15 while for the tetra-n-butyl-, and te-tra-n-pentylammonium ions the primary data at higher temperatures were obtained from ref.16 For the cyclo-hexylsulfamate ion the equivalent conductances were obtained as the average values taken from refs.17,18 and at 338.15 K from ref.19 The values of viscosity A-coeffi-cients are given in Table 2. The values of viscosity B-, and Table 1. Viscosity of aqueous solutions of tetramethyl- (Me4NCy), tetraethyl- ( Et4NCy), tetra-n-propyl-(n-Pr4NCy), tetra-n-butyl- (n-Bu4NCy), and tetra-n-pentylammonium (n-Pe4NCy ) cyclohexylsulfa-mates at the indicated molalities and temperatures. n (cP) at T (K) (mol kg-1) 293.15 298.15 303.15 313.15 323.15 Me4NCy 0.09138 1.0601 0.9408 0.8416 0.6876 0.5744 0.11244 1.0741 0.9527 0.8520 0.6956 0.5808 0.13420 1.0892 0.9656 0.8632 0.7044 0.5877 0.15568 1.1036 0.9780 0.8740 0.7125 0.5943 0.17841 1.1201 0.9922 0.8860 0.7218 0.6016 0.20017 1.1355 1.0051 0.8972 0.7303 0.6085 Et4NCy 0.06843 1.0702 0.9489 0.8480 0.6917 0.5773 0.09139 1.0937 0.9688 0.8653 0.7051 0.5876 0.11415 1.1167 0.9886 0.8824 0.7182 0.5981 0.13647 1.1404 1.0085 0.8994 0.7312 0.6080 0.15981 1.1645 1.0289 0.9171 0.7444 0.6186 0.18429 1.1909 1.0512 0.9362 0.7588 0.6299 0.20785 1.2171 1.0732 0.9548 0.7729 0.6409 n-Pr4NCy 0.02484 1.0367 0.9197 0.8223 0.5714 0.5614 0.04995 1.0725 0.9499 0.8481 0.6910 0.5763 0.07524 1.1091 0.9809 0.8748 0.7107 0.5916 0.10047 1.1468 1.0127 0.9018 0.7311 0.6071 0.12595 1.1854 1.0453 0.9295 0.7520 0.6231 0.15066 1.2238 1.0775 0.9573 0.7731 0.6388 0.17660 1.2656 1.1128 0.9866 0.7952 0.6560 0.19998 1.3032 1.1444 1.10139 0.8161 0.6714 n-Bu4NCy 0.00984 1.0192 0.9051 0.8101 0.6624 0.5542 0.02418 1.0455 0.9269 0.8289 0.6769 0.5650 0.05076 1.0962 0.9694 0.8655 0.7034 0.5853 0.07495 1.1436 1.0094 0.8993 0.7282 0.6046 0.10106 1.1968 1.0536 0.9365 0.7554 0.6253 0.12504 1.2470 1.0952 0.9712 0.7805 0.6450 n-Pe4NCy 0.01959 1.0429 0.9252 0.8276 0.6757 0.5642 0.02545 1.0556 0.9359 0.8367 0.6827 0.5695 0.03518 1.0772 0.9541 0.8521 0.6944 0.5783 0.04556 1.1007 0.9738 0.8688 0.7068 0.5881 0.05043 1.1119 0.9833 0.8767 0.7127 0.5924 0.05529 1.1234 0.9927 0.8847 0.7187 0.5973 0.06494 1.1461 1.0118 0.9008 0.7305 0.6064 0.07586 1.1729 1.0338 0.9193 0.7440 0.6168 0.08471 1.1945 1.0521 0.9346 0.7552 0.6255 0.10086 1.2357 1.0858 0.9630 0.7759 - ö-coefficients were obtained by a least-squares analysis of Eq. (2) in the form (5) and are given in Table 2. The relation (2) satisfactory reproduces the experimental values of solution viscosity, n. Standard deviation, ^ (6) calculated for each compound at a definite temperature amounts to an average value of ±2.5 x 10-4 cP. In rel. (6), is the viscosity of solution calculated via rel. (2) and n is the number of experimental points. From Table 2 it can be seen that the values of the A-coefficient are small and in the range of simple 1:1 electrolytes and that the Ac'^ term in rel. (2) appreciably affects the measured viscosities only at the lowest concentration. According to Falkenhagen and Vernon, the value of the viscosity A-coefficient ia always greater than zero.20,21 The values of the viscosity A-coefficient at a definite temperature increase with increasing ionic radius of the tetra-n-alkylammonium ion, contrary to the alkali-metal cyclohexylsulfamates where the viscosity A-coefficient decreases with increasing ionic radius of alkali-metal 22 ions.22 Furthermore, the viscosity A-coefficients of tetramethyl-, and tetraethylammonium cyclohexylsulfamate slightly increases with increasing temperature, that of te-tra-n-propylammonium cyclohexylsulfamate is temperature independent, while the viscosity A-coefficients of te-tra-n-butyl-, and tetra-n-pentylammonium cyclohexylsul-famates slightly decreases with temperature (see Table 2). The dependence of the viscosity A-coefficient on temperature was expressed by the function (7) where Y = A and a0, a1 and a2 are empirical constants depending on the solute, and T0 = 298.15 K. The values of the empirical constants were evaluated by a least-squares procedure. The values of the temperature coefficient, dA/dT = a1, at 298.15 K are given in Table 3. The temperature coefficient dA/dT at 298.15 K almost linearly decreases with increasing ionic radius of the cation. On the other hand, the dependence of dA/dT at the same temperature on the ionic radius of the alkali-metal cation in al- Table 2. Values of viscosity A-, B- and D-coefficients (Eq. 2) of aqueous solutions of tetramethyl-(Me4NCy), tetraethyl- ( Et4NCy), tetra-n-propyl- (n-Pr4NCy), tetra-n-butyl- (n-Bu4NCy), and tetra-n-pentylammonium (n-Pe4NCy ) cyclohexylsulfamates as a function of temperature Salt T A X 103 B D (K) (L^2mol-^2) (L mol-1) (L2 mol-2) 293.15 3.309 0.594±0.002 0.490±0.016 298.15 3.330 0.586±0.003 0.422±0.017 Me4NCy 303.15 3.356 0.579±0.002 0.363±0.013 313.15 3.397 0.568±0.003 0.262±0.022 323.15 3.430 0.535±0.002 0.275±0.011 293.15 3.914 0.959±0.003 0.610±0.020 298.15 3.925 0.932±0.002 0.517±0.017 Et4NCy 303.15 3.947 0.904±0.001 0.470±0.010 313.15 3.988 0.859±0.002 0.380±0.020 323.15 4.026 0.801±0.002 0.380±0.020 293.15 4.640 1.345±0.002 1.340±0.020 298.15 4.640 1.284±0.001 1.240±0.010 n-Pr4NCy 303.15 4.640 1.225±0.001 1.180±0.012 313.15 4.640 1.116±0.001 1.180±0.010 323.15 4.640 1.044±0.002 0.950±0.010 293.15 5.102 1.705±0.015 2.940±0.020 298.15 5.092 1.636±0.007 2.489±0.092 n-Bu4NCy 303.15 5.088 1.587±0.009 2.098±0.118 313.15 5.070 1.488±0.006 1.338±0.085 323.15 5.047 1.344±0.003 1.448±0.043 293.15 5.380 1.994±0.002 4.309±0.041 298.15 5.367 1.920±0.002 3.652±0.032 n-Pe4NCy 303.15 5.361 1.868±0.003 2.893±0.042 313.15 5.331 1.760±0.002 2.040±0.036 323.15 5.290 1.573±0.004 2.520±0.089 kali-metal cyclohexylsulfamates showed the reverse beha-viour.22 The behaviour of tetra-n-alkylammonium cyclo-hexylsulfamates can be attributed to hydrophobic hydration of the R4N+ ion, by decreasing influence of the R4N+ ion, and to the increasing effect of the alkyl group. Namely, the viscosity A-coefficient is based on the drag that the ion causes that retards to movement of the ion and indirectly diminishes the viscosity of solution. In aqueous system the hydrocarbon residues occupy a space which would otherwise be void and the volume contraction on this account is greater than the expansion of bulk water. Thus, the effect of the alkyl group of the R4N+ ion on water structure is pronounced and increases with the ionic radius of the R4N+ ion or with the number of CH2 -group in alkyl residues. Regarding the temperature coefficient dA/dTaccording to Kaminsky^^ it should be under all circumstances greater than zero which was not the case of n-Bu4NCy and n-Pe4NCy. Values of the viscosity B-coefficients, given in Table 2, are positive and relatively large which is typical for salts with large hydrophobic ions such as the tetra-n-alky-lammonium23 and cyclohexylsulfamate ions.7 The sign of the viscosity B-coefficient depends on the degree of solvent structuring introduced by the ions. A positive value of viscosity B-coefficient is associated with cosmotropic ions (structure makers), while a negative value is associated with chaotropic ions (structure breakers) according to their relative abilities to induce the structuring of water.24 From this point of view, the viscosity B-coefficient, given in Table 2, belongs to the cosmotropic class of ions. Furthermore, the viscosity B-coefficient was found to be linearly related to the limiting partial molar volume, V2 of the tetra-n-alkylammonium cyclohexylsulfamates.612 The viscosity B-coefficients given in Table 2 decrease with increasing temperature for all the investigated compounds. The temperature dependence of the viscosity B-coefficient was expressed by rel. (7) in a linear form and the values of the empirical constants determinated by the least-squares procedure. The temperature coefficients dB /dT= a1 at 298.15 K are given in Table 3. The temperature coefficients dB /dTat 298.15, collected in Table 3, are negative and decrease with increasing molecular weight of the tetra-n-alkylammonium cyclohexylsulfama- tes. A large and negative temperature dependence of the viscosity B-coefficient was also observed by Wen25 who studied the viscosity of aqueous solutions of n-Bu4Br at 20 and 30 °C. It is interesting to note that temperature coefficients dB/dT, determined at the same temperature for the alkali-metal cyclohexylsulfamates, increase with increasing temperature.22 The viscosity D-coefficients, collected in Table 2, are positive and relatively large and increase at a definite temperature with increasing limiting partial molar volume of the solute, from tetra-n-propylammonium cyclohexyl-sulfamate onwards almost linearly. With increasing temperature the viscosity D-coefficient decreases. The temperature coefficient dD/dT was obtained like dB/dT using rel. (7) in a linear form. The temperature coefficients dD/dT = a1 at 298.15 K are negative and relatively large and are given in Table 3. From this table it can be seen that their values decrease with increasing molecular weight of the solute. As was shown by Desnoyers and Perron,^26 the Dc2 term in Eq. (2) includes all solute-solvent and solute-solute interactions that are not accounted for by the Ac'^ and Bc terms at higher concentration. According to these authors, the main contribution to the viscosity D-coefficient should include the higher terms of the long-range Cou-lombic forces. Furthermore, the viscosity D-coefficient is also influenced by the higher terms of the hydrodynamic effect. These terms are the leading contribution to the Dc2 term in Eq. (2). According to this approach, the viscosity D-coefficient should always be positive and given by26 (8) The calculated values of viscosity D-coefficients, using rel. (8) are: 0.462 (mol L-1)-2 for tetramethyl-, 0.747 (mol L-1)-2 for tetraethyl-, 1.150 (mol L-1)-2 for tetra-n-propyl-, 1.606 (mol L-1)-2 for tetra-n-butyl-, and 2.152 (mol L-1)-2 for tetra-n-pentylammonium cyclohexylsulfamate at 298.15 K. For tetramethyl- and tetraethylammo-nium cyclohexylsulfamates the calculated values are higher than the experimental ones, while for tetra-n-propyl-, tetra-n-butyl-, and tetra-n-pentylammonium cyclohexyl- Table 3. Temperature coefficient of the viscosity A-, B- and D-coefficients of tetramethyl- (Me4NCy), tetraethyl- (Et4NCy), tetra-n-propyl- (n-Pr4NCy), tetra-n-butyl- (n-Bu4NCy) and tetra-n-pentylammoni-um (n-Pe4NCy) cyclohexylsulfamates in aqueous solutions at 298.15 K. Salt (L^2 mol-^2 K-1) (L mol-1 K-1) (L2 mol-2 K-1) Me4NCy 4.73±0.24 1.8±0.3 0.7±0.2 Et4NCy 3.57±0.40 5.2±0.1 0.8±0.2 n-Pr4NCy 0.0 10.1±0.6 1.1±0.2 n-Bu4NCy -(1.78±0.12) 11.6±0.5 5.2±1.2 n-Pe4NCy -(1.90±0.29) 13.5±1.0 6.3±2.3 sulfamates the calculated values are lower than the experimental ones. The relation (8) does not correctly predict the temperature dependence of the viscosity ö-coefficient since the y2 values of tetra-n-alkylammonium cyclohexyl-sulfamates increase with temperature,6,12 while the viscosity ö-coefficient decreases with increasing temperature (see Table 2). According to Eyring^^ the viscosity B-coefficient can be related to the thermodynamic functions of activation for viscous flow. In this model the molecules of solvent and ions of solute move one by-one from their equilibrium positions through their transition states in which in-termolecular bonds are stretched to their equilibrium positions. Feakins et al, e. g.3,4 have successfully applied the transition state theory to the viscosity of electrolyte or non-electrolyte solutions in aqueous or non-aqueous media. They showed that the viscosity B-coefficient can be given by (9) where v = 2 for a fully dissociated univalent electrolyte, V0 is the limiting partial molar volume of solvent, A*^- 2 and A*G 1 are the limiting Gibbs free energy of activation for the viscous flow of solute and solvent, and R is the gas constant. The use of rel. (9) provides a framework for interpreting the effects of the solute on the solution viscosity since it is more rigorous than the direct consideration of the viscosity B-coefficient and its temperature coefficient. So, for example from rel. (9) it follows that a negative viscosity B-coefficient will result when vV 0 < V 0 and A*G 2 2, can be calculated from the relation (14) The limiting entropy of activation for viscous flow was estimated from the dependence of A* G- 0 on temperature. The dependence of A* G 2 on temperature was expressed for Me4NCy by function (7), while for other salts only a linear form of rel. (7) was used. The values of constants a1 in rel. (7) were calculated by the least squres procedure and A*S! 0 = -a1 at 298.15 K. Table 6 lists the contribution of tetra-n-alkylammonium cyclohexylsulfamates to the limiting partial molar entropy for viscous flow, A* S> 2. From this table it can be seen that A* S0 values increase with in- creasing molecular weight of the salt and are positive except for Me4NCy. The limiting pjartial molar enthalpies for activation of viscous flow, A*fi 2, calculated from the Gibbs-Helm-holtz relation (15) are given in Table 6. The A*HI 0 values are positive and increase with increasing molecular weight of the solute. According to Tamamushi and Isono^° the following conditions are characteristic of a hydrophobic ion-solvent interaction: A*^0 > A*^ 0, A*f^2 > A*f^0 and A*S0 > A*S0. For the investigated R4NCy solutes these conditions are satisfied for all solutes except for Me4NCy where A*S 0 < A* S> 1. Me4NCy behaves differently from the higher members of the R4NCy series due to its solvation properties.12 The effect of the solute on the acti-vation enthalpy \* Ü 0/- and entropy of the solvent molecules, A H2(1 ^ 1') and A*]- 2(1 ^ 1'), can be estimated from the enthalpy A*fì'0c) and entropy A*!- °(cd) of activation for conductance of the ions. From the limiting molar conductivity of the R4N+ ions, given in refs.,14,15,16 the Eyring's enthalpy of activation of charge transport, i. e. the enthalpy change required for unit displacement of one mole of R4N+ ions, can be evaluated from28 (16) where C is an integration constant and d0 the density of pure water. The enthalpy of activation for conductance of the cyclohexylsulfamate ion, A*H0(cd^ = 18.34 kJ mol 1, was estimated previously.22 In Table 5, A*H{0cd. represents the sum of the ionic enthalpy for conductance of R4N+ ions, calculated via rel. (16) and the corresponding values of the cyclohexylsulfamate ion. From this table it follows that values are positive and slightly increase with increasing molecular weight of the tetra-n-alkylammo-nium cyclohexylsulfamates. The integration constant C of rel. (16) amounts to: 5.179±0.059 (Me4N+), 5.499±0.095 (Et4N+), 5.372±0.074 (n-Pr4N+), 5.356±0.063 (n-Bu4N+) and 5.377±0.034 (n-Pe4N+), respectively. The entropy of activation for conductance, A*S>2!fca) of R4NCy salts was obtained from the Gibbs-Helmholtz relation _(15) and are given in Table 5. The calculated values of A* are low and almost independent of the molecular weight of the solute and their average value amounts to (34.8±2) J mol-1 K-1. Since the enthalpies and entropies of activation for conductance of R4NCy salts are positive, therefore the effect of the solute on the activation enthalpy and entropy of the solvent molecules obtained from the analogous relation as (11), A*li°(1^V) and A*S°(1^V) is higji (see Tat)le 5). So, the positive and high values of A*H0 and A*S 0 given in Table 6, primarily arise from the breaking of solvent-solvent bonds in the transition state. This is in accordance with the fact that very large ions with hydrop-hobic surfaces do not display peripheral hydration.12 The hydrophobic surface of such ions literally repels the water molecules from its surface with the formation of a more ordered and rigid structure of water surrounding the ions.23 4. References 1. G. Jones, M. Dole, J. Am. Chem. Soc. 1929, 51, 2950-2964. 2. H. D. B. Jenkins, Y. Marcus, Chem. Rev. 1995, 95, 26952724. 3. D. Feakins, D. J. Freemantle, K. G. Lawrence, J. Chem. Soc. Faraday Trans. 1974, 70, 795-806. 4. D. Feakins, F. M. Bates, W. E. Waghorne, K. G. Lawrence, J. Chem. Soc. Farad. Trans. 1993, 89, 3381-3388. 5. D. Feakins, F. M. Canning, J. J. Mullally, W. E. Waghorne, Pure Appl. Chem. 1989, 61, 133-142. 6. C. Klofutar, D. Rudan-Tasic, Monatsh. Chem. 2005, 136, 1727-1736. 8. 9. 10 11. 12. 13 14 15. 16. 7. C. Klofutar, J. Horvat, D. Rudan-Tasic, Monatsh. Chem. 2006, 137, 1151-1162. . M. R. Cannon, R. E. Manning, J. D. Bell, Anal. Chem. 1960, 32, 355-358. . W. Wagner, A. Pruß, J. Phys. Chem. Ref. Data 2002, 31, 387-535. . J. Kestin, J. V. Sengers, B. Kamgar-Parsi, J. M. H. Levlet Sangers, J. Phys. Chem. ReJ^. Data 1984, 13, 175-183. . M. Kaminsky, Z. Phys. Chem. 1957, 12, 206-231. . C. Klofutar, J. Horvat, D. Rudan-Tasic, Acta Chim. Slov. 2007, 54, 460-468. . D. G. Archer, P. M. Wang, J. Phys. Chem. Ref. Data 1990, 19, 371-411. . R. A. Robinson, R. H. Stokes, Electrolyte Solutions (2nd ed.); Dover Publications, New York, 2002, 465. . R. L. Kay, D. F. Evans, J. Phys. Chem. 1966, 70, 2325-2335. . M. Luci, Ph. D. Thesis, Electrolytic conductance of aqueous solutions of some tetra-n-alkylammonium salts of cyclo-hexylsulfamic acid; University of Ljubljana, 2001. 17. D. Rudan-Tasic, T. Župec, C. Klofutar, M. Bešter-Rogač, J. Solution Chem. 2005, 34, 631-644. 18. D. Rudan-Tasič, C. Klofutar, M. Bešter-Rogač, Acta Chim. Slov. 2006, 53, 324-330. 19. C. Klofutar, M. Luci, M. H. Abramovic, Physiol. Chem. Phys. & Med. NMR 1999, 31, 1-8. 20. H. Falkenhagen, E. L. Vernon, Physik. Z. 1932, 33, 140. 21. H. Falkenhagen, E. L. Vernon, Phil. Mag. 1932, 14, 537563. 22. J. Horvat, M. Bešter-Rogač, C. Klofutar, D. Rudan-Tasic, J. Solution Chem. 2008, 37, 1329-1342. 23. H. S. Frank, W. Y. Wen, Discuss. Faraday Soc. 1957, 24, 133-140. 24. B. Hribar, N. T. Southall, V. Vlachy, K. A. Dill, J. Am. Chem. Soc. 2002, 124, 12302-12311. 25. W. Y. Wen, Ph. D. Thesis, Some Thermodynamic and flow properties of the aqueous solutions and hydrates of two tetra-n-butylammonium salts; University of Pitsburgh, 1957. 26. J. E. Desnoyers, G. Perron, J. Solution. Chem. 1972, 1, 199-212. 27. S. Glasstone, K. J. Laidler, H. Eyring, The theory of rate processes; McGraw-Hill, New York, 1941, p. 477. 28. S. B. Brummer, G. J. Hills, J. Chem. Soc. Farad. Trans. 1961, 57, 1816-1822. 29. K. Hickey, W. E. Waghorne, A. Sacco, J. Phys. Chem. Ser. A 2001, 105, 1093-1096. 30. R. Tamamushi, T. Isono, J. Chem. Soc. Farad. Trans. 1984, 80, 2751-2758. Povzetek Relativno viskoznost vodne raztopine nekaterih tetra-n-alkilamonijevih soli v temperaturnem intervalu od 293,15 do 323,15 K smo interpretirali s Kaminsky-jevo enačbo. Vrednosti koeficientov viskoznosti A, B in D smo razložili z naravo soli, velikostjo ionov, s strukturnimi interakcijami med topilom in topljencem ter dalekosežnimi interakcijami med ioni. Izračunali smo limitne termodinamske funkcije viskoznega toka topila in topljenca in določili njihove prispevke k transportnemu prenosu raztopine. Razliko med preiskovanimi solmi smo razložili kot posledico različne velikosti tetra-n-alkilamonijevega iona in vpliva hidrofobnih lastnosti alkilnih skupin v tetra-n-alkilamonijevem ionu.