Faraday Symp. Chem. SOC., 1982 17 41-53 Isothermal Transport Properties in Solutions of Symmetrical Tetra-alkyl ammonium Bromides BY LAWRENCE A. WOOLF Diffusion Research Unit School of Physical Sciences The Australian National University Canberra ACT 2600 Australia AND HERMANN WEINGARTNER Institut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe Kaiserstr. 12 D 7500 Karlsruhe West Germany Received 1st September 1982 Density molar conductance transference number tracer diffusion (cation anion water) and mutual diffusion data are reported for aqueous solutions of the following symmetrical tetra-alkyl- ammonium halides at 25 "C up to 2 mol kg-' concentration Me4NBr Et4NBr n-Pr4NBr and n- Bu4NBr. These data were used to obtain information on the interactions between pairs of species c a w (cation anion water) using Hertz's velocity-correlation formalism.Within this formalism the transport coefficients are related to time integrals over velocity cross-correlation functions between the various interaction partners. Results obtained for solutions of tetra-alkylammonium salts differ characteristically from those reported for alkali halides and reflect structural features such as hydro- phobic hydration cation-cation and anion-anion interactions. As pointed out by Frank and Evans,' aqueous solutions of symmetrical tetra- alkylammonium halides show a remarkably high viscosity attributed to particular water structures around the hydrocarbon groups of the cations. Clearly the problem of the cationic hydration in such systems is closely related to the respective problem of the hydration of neutral molecules containing non-polar groups.2 Thus solutions of symmetrical tetra-alkylammonium salts have been used as model systems for studies on hydrophobic interaction^.^ Extensive studies made on the various proper- ties of these systems have included thermodynamic spectroscopic and relaxation techniques3 It is however curious that apart from viscosity data almost no data on transport properties exist.The only systematic investigations have been conducted by Kay and Evan~,~.~ who made extensive studies on the conductance of quaternary ammonium salts in the dilute concentration range. Above concentrations of ca. 0.01 mol kg-l only a little work on transport properties has been reported including data on self-diffusion of cations and water,6 electrical conductance ' and mutual diffusion.8 The present study provides systematic data on isothermal transport properties in aqueous solutions of tetramethyl- tetraethyl- tetrapropyl- and tetrabutyl-ammonium bromides (Me,NBr Et4NBr n-Pr4NBr and n-Bu,NBr) at 25 "C over the concentration range 0.05-2 mol kg-'.The data include self-diffusion coefficients of water cations and anions mutual diffusion coefficients electrical conductance and transference numbers. As a by-product we have obtained some density data. As suggested by various author^,^-^' a comprehensive set of experimental trans- TRANSPORT PROPERTIES port data can be used to obtain information on the interaction between pairs of species in concentrated electrolyte solutions.We will use a formalism first applied by Hertz," who has given a representation of transport coefficients in terms of velocity cross- correlation coefficients (v.c.c.) derived from linear-response theory. As pointed out by Friedman and Mills l2 and other^,'^-'^ these coefficients are more related to the basic physical processes than are other sets of cofficients (e.g. Miller's generalized Zij coefficients which have their basis in the thermodynamics of irreversible processes 9*16). If present specific interactions such as hydrophobic hydration or ion association should reveal themselves in the respective V.C.C. EXPERIMENTAL MATERIALS The tetra-alkylammonium salts were obtained from Eastman Organic Chemicals.They were purified as described below. Me4NBr was repeatedly recrystallized from a 1 1 methanol water mixture centrifugally drained and dried at 80 "C under vacuum for 3 days. A similar procedure was used for the purification of Pr4NBr and Bu4NBr in the latter case however with the use of an acetone diethylether solvent system. Et4NBr was precipitated from chloroform by adding diethylether ; the crystals were centrifugally drained and dried under vacuum for 5 days. Water used in the experiments was distilled and passed through an ion-exchange column. It was then heated and partially degassed at a water pump. The specific conductance was 1 x R-l cm-'. Stock solutions and all dilutions were prepared by weight.Some suitably diluted portions were analysed by potentiometric titration against AgN03 solutions. The uncertainty in composition is estimated as 0.1%. 14C-labelled materials were obtained from the Nuclear England Corporation. The tracers were mixed with purified inactive materials and dried after recrystallization as above. 82Br-labelled bromide was obtained as a 0.1mol dm-3 aqueous solution of HBr from the Australian Atomic Energy Commission Lucas Heights Australia. It was diluted in normal water and used without further purification. HTO was obtained from the Radiochemical Centre Amersham. DENSITY MEASUREMENTS Highly accurate density data were required as we intended to analyse concentrations in mutual diffusion experiments via density measurements.Therefore we performed some density measurements with an Anton Paar type densimeter. In general we found close agreement with results reported by Wen and Saito." Therefore values obtained by these authors and our values have been fitted by least squares to the equation n d = do +.Z Alrn'l2. 1=2 The resulting coefficients At and the standard deviations are shown in table 1. do = 0.997 05 g cm+. CONDUCTANCE MEASUREMENTS Conductance measurements were performed with a Leeds and Northrup Jones bridge in conjunction with an oil thermostat. The temperature measured with a certified platinum resistance thermometer was 25 rrt 0.003 "C. Jones and Bradshaw demal KCI standards were used for calibration.'8 16 data points between 0.05 and 2.25 mol kg-' for each system were fitted to polynomials in order to obtain values at rounded concentrations shown later in table 3.L. A. WOOLF AND H. WEINGARTNER TABLE 1.xOEFFICIENTS OF EQN (1) maximum system A2 A3 A4 A5 deviation standard /mol kg-' concentration Me4NBr 0.036710 0.006384 -0.010504 0.002515 1.3 X 3 Et,NBr 0.036 632 2.266 8 -0.004 883 9.789 1 1.3 x 10-4 3 x 10-4 x 10-4 Pr4NBr 0.026043 0.004 022 -0.003 912 1.1 x 10-4 3 Bu4NBr 0.023 673 0.001 008 -0.003 81 1 0.9 x 10-4 3.3 TRANSFERENCE NUMBERS E.m.f. measurements of concentration cells with transference were performed to obtain transference numbers. Standard techniques as described by Spiro l9 for example were applied. Only some additional remarks are given here.The cell was similar to that described by Stokes and Levien." Pairs of Ag AgBr electrodes were prepared by the thermal- electrolytic method.21 Bias potentials were <0.01 mV. The e.m.f. was determined by a certified digital voltmeter with a resolution of 0.001 mV. E.m.f. values of the corresponding cells without transference were calculated from the activity data reported by Lindenbaum and Boyd,22 but for Me4NBr Levien's data were preferred because Wen's comment indicated that the latter data may be more accurate than those of Lindenbaum and Boyd. MUTUAL DIFFUSION COEFFICIENTS Mutual diffusion coefficients were determined by the diaphragm technique as described by Stokes l8 and modified by Mills and W00lf.*~ After some trials we used potentiornetric titration of Br- against AgN03 to analyse the solutions in the top and bottom compartments of the cell; additional density measurements have been performed in some cases.We noted slight differences (1% at maximum) between values obtained from experiments with a glass sinter and those obtained with a platinum sinter. Comparison with the optical data of Pepela et aL8 for solutions of Pr4NBr indicated that use of the platinum sinter gave the correct values.* Differential diffusion coefficients were calculated from the measured integral ones by the procedure outlined in ref. (23). The final data are listed later in table 3. The estimated accuracies of the values at rounded concentrations are as follows better than 1 % (Pr4NBr and Bu4NBr) 1yo(Et4NBr) 2% (Me4NBr).TRACER DIFFUSION COEFFICIENTS Tracer diffusion coefficients of cations anions and HTO were measured with diaphragm cells by standard techniques outlined in ref. (23). The radiotracers were 14C,82Br and HTO. Measured values of DHTo by a correction factor 1.03,result-were converted to those for DH~O ing from the mass extrapolation procedure applied by Mills.24 Original data for the tracer diffusion measurements are given in table 2 and values at rounded concentrations are sum- marized in table 3. Limiting ionic diffusion coefficients were calculated from the following limiting ionic conductance^:^ 44.42 (Me4N+),32.22 (Et4N+),23.22 (Pr4N+),19.31 (Bu4N+) 78.22 (Br-) where all values are given in cm2 R-' equiv.-'. * This result is supported by some further diffusion measurements using the Schlieren method.These measurements and some additional conductance measurements have been performed at the Institut fur Physikalische Chemie der Universitat Aachen. Prof. H. Schonert is thanked for his hospitality. TRANSPORT PROPERTIES TABLE 2.-sELF-DIFFUSION COEFFICIENTS OF CATIONS ANIONS AND WATER IN SOLUTIONS OF TETRA-ALKYLAMMONIUM BROMIDES AT 25 "C Me4NBr 0 1.182 0 2.081 0 2.30 0.049 98 1.154 0.045 12 1.9664 0.1012 2.370 0.1Ooo 1.136 0.1110 1.903 0.2722 2.421 0.4998 1.072 0.2516 1.841 0.5532 2.334 0.9997 1.01 3 0.5056 1.759 1.0103 2.231 1.9989 0.885 1.015 1.607 1.9978 1.872 1.997 1.402 2.005 1.875 2.917 1.218 3.882 1.017 Et,NBr 0 0.858 0 2.08 1 0 2.30 0.049 95 0.823 0.099 91 1.867 0.1003 2.289 0.099 97 0.816 0.2453 1.699 0.2641 2.154 0.4998 0.734 0.5192 1.516 0.5003 1.985 0.5193 0.728 1.065 1.219 1.023 1.693 1.003 0.622 2.01 6 0.865 1.992 1.260 1.033 0.618 3.032 0.653 2.989 0.993 1.999 0.512 3.821 0.51 1 Pr4NBr 0 0.61 8 0 2.08 1 0 2.30 0.062 75 0.099 97 (0.620) 0.608 0.1006 0.2523 1.700 1.468 0.450 0.868 1.57 1.12 0.1532 0.582 0.6653 1.111 1.088 0.912 0.251 3 0.551 1.043 0.878 1.289 0.765 0.4996 0.466 1.376 0.788 0.9999 0.354 1.998 0.548 1.999 0.21 8 3.756 0.282 Bu4NBr 0 0.514 0 2.08 1 0 2.30 0.065 16 0.499 0.1003 1.652 0.480 1.57 0.098 02 0,486 0.2293 1.415 1.002 1.16 0.2501 0.419 0.5101 1.121 1.362 0.934 0.9991 0.232 1.1032 0.768 2.553 0.790 1.9955 0.137 2.045 0.4020 3.775 0.1892 "min mol kg-' all diffusion coefficients in m2s-'; value not used for further evaluation of data; measured by 'H n.m.r.in Pr4NBr + D20 and corrected by the ratio of self-diffusion co-efficients of the pure liquids (1.26). L. A. WOOLF AND H. WEINGARTNER TABLE3.-ISOTHERMAL TRANSPORT COEFFICIENTS IN AQUEOUS SOLUTIONS OF TETRA-ALKYL-AMMONIUM BROMIDES AT 25 "CAT ROUNDED CONCENTRATIONS m c d D,w D a Dw A 1 1 + m(dlny/drn) Me4NBr 0 0 0.997 05 1SO8 1.182 2.081 2.30 122.67 0.362 1 0.05 0.04956 0.998 93 1.350 1.153 1.964 2.34 104.14 0.349 0.8945 0.1 0.098 56 1.0o0 82 1.308 1.137 1.921 2.37 98.200 0.346 0.863 1 0.25 0.2422 1.006 43 1.266 1.109 1.838 2.42 88.547 0.344 0.8168 0.5 0.4714 1.015 50 1.230 1.072 1.748 2.35 80.096 0.342 0.7861 0.75 0.6884 1.024 01 1.229 1.042 1.677 2.31 74.717 0.341 0.7761 1 0.8943 1.032 11 1.250 1.01 1 1.61 6 2.22 70.634 0.341 0.7766 1.5 1.2758 1.047 08 1.258 0.949 1 SO6 2.05 64.209 0.34 1 0.7980 2 1.6216 1.060 66 1.269 0.885 1.403 1.88 59.165 0.341 0.8397 Et4NBr 0 0 0.997 05 1.214 0.858 2.081 2.30 110.44 0.291 1 0.05 0.049 42 0.998 88 1.070 0.824 1.930 2.29 91.019 0.271 0.8796 0.1 0.098 01 1.O00 67 1.024 0.814 1.858 2.28 84.179 0.269 0,8392 0.25 0.2389 1.005 96 0.949 0.786 1.706 2.15 72.587 0.266 0.7790 0.5 0.4589 1.014 39 0.855 0.733 1.520 1.98 61.968 0.264 0.7417 0.75 0.6624 0.022 44 0.805 0.680 1.373 1.84 55.089 0.262 0.7335 1 0.851 1 1.030 00 0.772 0.633 1.248 1.68 49.908 0.260 0.7397 1.5 1.1907 1.044 12 0.738 0.575 1.043 1.44 42.107 0.260 0.7794 2 1.4883 1.056 96 0.725 0.512 0.881 1.23 36.145 0.260 0.8462 Pr4NBr 0 0 0.997 05 0.953 0.618 2.081 2.30 101.40 0.229 1 0.05 0.049 26 0.998 38 0.816 0.620 1.805 2.19 81.623 0.210 0.8637 0.1 0.097 38 0.999 74 0.764 0.608 1.700 2.12 74.132 0.205 0.8166 0.25 0.2353 1.003 81 0.668 0.551 1.471 1.86 60.719 0.201 0.7540 0.5 0.4459 1.010 51 0.580 0.475 1.224 1.51 47.870 0.195 0.7345 0.75 0.6358 1.01699 0.531 0.415 1.052 1.23 39.576 0.193 0.7517 1 0.8080 1.023 20 0.502 0.354 0.907 0.98 33.586 0.192 0.7845 1.5 1.1091 1.034 70 0.469 0.277 0.702 0.66 25.437 0.191 0.8725 2 0.3636 1.044 86 0.444 0.210 0.550 0.51" 20.218 0.190 0.9776 Bu4NBr 0 0 0.997 05 0.821 0.514 2.081 2.30 97.50 0.198 1 0.05 0.049 12 0.998 23 0.687 0.500 1.785 2.21 75.984 0.177 0.8711 0.1 0.096 81 0.999 41 0.633 0.480 1.658 2.15 66.725 0.172 0.8251 0.25 0.2320 1.002 85 0.534 0.422 1.403 1.86 50.350 0.166 0.7532 0.5 0.4341 1.008 29 0.441 0.340 1.139 1.65 36.824 0.162 0.7002 0.75 0.61 19 1.013 31 0.381 0.275 0.958 1.43 30.1 18 0.159 0.6741 1 0.7697 1.017 92 0.336 0.225 0.808 1.17 26.422 0.158 0.6583 1.5 2 1.0371 1.2548 1.025 83 1.03200 0,258 0.197 0.159 0.138 0.593 0.430 0.82 0.65' 22.415 19.209 0.157 0.156 0.6381 0.6227 rn in mol kg-' C in mol dm-3 d in g ~m-~ A in cm' f2-l equiv.-' all diffusion coefficients in m2 s-l; * maximum of D,within range of experimental error; extrapolated.TRANSPORT PROPERTIES ACTIVITY COEFFICIENTS Accurate data on activity coefficients are needed since a term of the form dlny l+m-=v,+m* dm dm (where y is the activity coefficient and v is the osmotic coefficient) occurs in the evaluation of the mutual diffusion data.After some trials we have used Pitzer's equations 25 and the respective parameters obtained by Pitzer and Mayorga 26 as a representation of the activity data of Lindenbaum and Boyd 22 and Levien.' The expression for the derivative 1 + m(dlny/drn) in terms of Pitzer's equations is discussed in the Appendix; values at rounded concentrations are given in table 3. DISCUSSION GENERAL The question of how to approach a description of transport properties in con- centrated electrolyte solutions has been discussed from different points of vie~.~-I~ We will use Hertz's velocity correlation formalism which utilizes the fact that the phenomenological coefficients of irreversible thermodynamics can be related to time integrals over velocity cross-correlation functions." Velocity cross-correlation coefficientshj for pairs of constituents i,j = c;a,w are defined by fa = La = fcc = fww = where Va* denotes the velocity of particle a of constituent i with respect to the local centre of mass vector notation is not used in eqn (2)-(5).The pointed brackets denote the ensemble average. c is the salt concentration cw the water concentration both expressed in mol ~m-~; N is Avogadro's number and Y is the volume of the so-lution. Eqn (2)-(5) correspond to the definition of the self-diffusion coefficient D in terms of the velocity autocorrelation function of constituent i v,'(t)) dt.(6) Di= T/$v2(0) 1" As shown by Hertz," V.C.C. can be calculated from diffusion conductance and trans- ference data. We have calculated V.C.C. following Hertz's method from the data summarized in table 3 where the following denotations have been used Dt (self-diffusion coefficients) D, (mutual diffusion coefficient) A (equivalent conductance) and t (transference number of the cation). Concentrations are given in molality units rnlmol kg-I and molarity units C/mol dm-3. For explicit expressions the reader is referred to ref. (1 1). Note that the relation of transport coefficients to V.C.C. has been discussed from a different point of view by one of the present authors and by Miller. l6 L. A. WOOLF AND H. WEINGARTNER CATION-ANION CORRELATIONS The concentration dependence offac for the four tetra-alkylammonium bromides is shown in fig.1. It is not the purpose of this paper to give a quantitative account of the shape of these curves. Rather we will compare them with results recently ob- tained for alkali halides 15*27 and with predictions for V.C.C. in certain reference 0. 0 1 2 rnlmol kg-l FIG. 1.-Velocity correlation coefficients f, for aqueous solutions of Me4NBr (l) Et4NBr (2) Pr4NBr (3) and Bu4NBr (4). For details see text. systems 11v2* in a more qualitative way. Nevertheless such a procedure should be adequate to detect specific effects if present. In the dilute concentration range fac increases rapidly with increasing salt con- centration. At very high dilution fa must go to zero as a consequence of the in- dependent motions of cations and anions.Miller l6 has considered limiting-law expressions according to which.fac should obey a m1/2 law with a positive initial slope. Roughly an m1/2 dependence seems to be fulfilled but because of the accumulation of errors in the calculation of small V.C.C. this can only be a tentative conclusion. In particular the magnitude of the initial slopes cannot be determined with the desired accuracy. In any case the observed positive correlations are a consequence of the coupling of cations and anions through an electrostatic potential. Effects in more concentrated solutions (>0.25 mol kg-l) indicate a decrease of correlations asfa goes through a maximum. In going from Me,NBr to Bu,NBr this maximum is systematically shifted to lower concentrations and its height decreases.Similar maxima were observed in solutions of alkali halides and the shape of the curves is roughly the same. Therefore we may conclude that there are no dramatic differences between solutions of alkali halides and tetra-alkylammonium bromides with respect to cation-anion correlations. The observed decrease offac with increasing salt concentration is attributed to the mutual averaging of the electrostatic forces by the presence of other ions close to a -0.11 TRANSPORT PROPERTIES given pair. This averaging diminishes the tendency to form ion pairs with a suficiently deep potential well to cause extended correlated motions between cations and anions.Obviously such effects set in at concentrations ca. 0.25 mol kg-'. Intuitively one may relate positive values offac (or more precisely values which are more positive than values predicted for ideal reference systems) to the degree of ion association. It is therefore important to emphasize the differences between the conventional concepts of ion association and our findings. Usually interaction partners are classified as being associated if their distance is smaller than a given reference distance and the degree of ion association is not expected to decrease with increasing concentration.18 At very high concentrations structural definitions may require the presence of solvent- separated or even contact ion pairs due to simple stoichiometric arguments.On the other hand cation-anion encounters are not necessarily related to the presence of correlated motions. In contrast the experimental findings show that extended correlations are absent. Indeed at high concentrations even negative values have been observed for solutions of the structure-breaking salts KI,27CSCI,~~ NaI l5 and RbC1.lS In contrast for LiCl and NaClf, remains positive over the whole con- centration range.27 From a rough extrapolation to high concentrations we conclude that for Me,NBr Et,NBr and Pr,NBr fac may remain positive whereas for Bu,NBr faC becomes negative at ca. 2 mol kg-'. The origin of negative V.C.C. and in particular off, at high concentrations has been discussed by Hertz:27 If specific interactions are averaged out momentum conservation will become the dominating effect which determines the magnitude offac.Indeed relations based on momentum conservation predict negative values off,,.11*28 0 1 2 rnlmol kg-FIG.2.-Velocity correlation coefficients f,= for aqueous solutions of Me4NBr (l) Et4NBr (2), Pr4NBr(3) and Bu4NBr (4). For details see text. L. A. WOOLF AND H. WEINGARTNER 0 i -0. -0. 0 1 2 rnlmol kg-’ FIG.3.-Velocity correlation coefficients ,La for aqueous solutions of Me4NBr (l) Et4NBr (2) Pr4NBr (3) and Bu4NBr (4). For details see text. In summary we believe that there are no indications for specific interactions between cations and anions which exceed those present in solutions of alkali halides. CATION-CATION AND ANION-ANION CORRELATIONS As noted by Hertz It and Friedman and Mills,” time integrals over velocity cross- correlation functions may take negative values in contrast to the behaviour of the respective time integrals over velocity autocorrelation functions (i.e.the self-diffusion coefficients) which must be positive. Hertz has attributed negative values off, to the requirement of momentum conservation. On this basis Hertz has derived ex- pressions for so-called “ standard coefficients” 28 fi, which predict the actual values f;:,in near-ideal systems rather well.27929 Applying Hertz’s approach we expect negative values offaa andf,. over the whole concentration range. Indeed for solutions of alkali halides these coefficients are negative and decrease monotonically with in- creasing salt concentration their values being more negative for structure-forming than for structure-breaking The curves shown in fig.2 and 3 for Me,NBr show the expected behaviour ofha andf, in solutions of KBr as interpolated from the experimental results for KC1 and KI.27 Turning to results for fc in solutions of tetra-alkylammonium bromides rather specific features are observed (see fig. 2). The limiting slopes are negative as expected. However at higher concentrations onlyf, values for Me,NBr and Et,NBr are in accordance with the expected monotonic decrease with increasing salt concentration. Curves obtained for Pr4NBr and Bu,NBr show minima at ca. 0.7 and 0.3 mol kg-’ respectively. For Et4NBr a minimum slightly above 2 mol kg-I is indicated from its TRANSPORT PROPERTIES behaviour at ca.2 mol kg-l. Obviously the initial decrease offcc is superimposed by a positive contribution the inset of which is shifted to lower concentrations in going from Et,NBr to Bu,NBr. One scarcely needs detailed consideration of the behaviour of reference systems to recognize the peculiarities occurring in these systems. Even if fCc values do not become positive on an absolute scale the marked positive deviations from the behaviour of alkali halides are obvious. We believe that these findings are a definite manifestation of particular cation-cation (hydrophobic) interactions in such systems which have often been proposed in the literat~re.~ Whereas cation-cation interactions have been considered to the authors' know- ledge no similar statements on the existence of anion-anion interactions are reported.It is therefore interesting to note that our method yields correlated motions between anions of a similar magnitude as observed for cations. The predicted negative slope and the montonic decrease ofha is only observed for Me,NBr. For the other tetra- alkylammonium bromides a minimum ofha is observed which is located at ca. 0.5 mol kg-'. The anomalous behaviour offaa seems to be more pronounced than the corresponding behaviour offcc for BudNBrf, extrapolates to positive values at con- centrations slightly above 2 mol kg-'. Thus we arrive at the conclusion that apart from cation-cation interactions discussed in the literature there is strong evidence for specific anion-anion interactions.It is however not easy to see whether the occur- rence of correlated motions between anions is a necessary consequence of the presence of correlated motions between cations and vice versa in particular since fa does not show anomalous behaviour. WATER-WATER CORRELATIONS fww coefficients in solutions of tetra-alkylammonium bromides are shown in fig. 4. In pure water i.e. at m = 0 according to the definitionf, is equal to the self-diffusion coefficient of water multiplied by -1. For m # 0 fww increases with increasing salt concentration. Hertz has noted 27 that the behaviour of the structure-forming alkali halides is very close to the predicted standard values f;,. The respective experimental curves and the standard values are of the same order of magnitude as observed for Me,NBr in the present work.Thus the curve for Me,NBr in fig. 4 at the same time gives a qualitative representation of the behaviour of the structure- forming alkali halides. In contrast for the structure-breaking CsCl positive values of fww have been observed at high concentrations. Positive values off, have therefore been interpreted as an important feature of the structure-breaking effect.27 Turning to tetra-alkylammonium bromidesf, is also less negative than predicted with the exception of Me,NBr. Moreover the curves seem to extrapolate to positive values at high concentrations. In fact in aqueous solutions of non-electrolytes such as acetone and simple alcohols 29~30 positive water-water correlations have been observed also.Thus we conclude that positive water-water correlations are an obvious manifestation of the hydrophobic hydration effect. INTERIONIC CONTRIBUTIONS TO THE EQUIVALENT CONDUCTANCE The anomalous behaviour of the like-ion coefficientsf, andf, has some important consequences for the concentration dependence of the equivalent conductance as will be shown for Bu,NBr. In terms of V.C.C.the equivalent conductance is given by L. A. WOOLF AND H. WEINGARTNER If all cross-terms were to vanish A would be given by the dashed line in fig. 5 which represents the sum of the contributions of the cationic and anionic self-diffusion co- efficientsA’. At concentrations below 0.3 mol kg-l,faa,fcc andf, are still sniall com- pared with the self-diffusion coefficients but they act in the same direction which results in a marked overall reduction of the conductance.Its magnitude can be seen by comparing the experimental curve with the dashed line. At concentrations above 1-4 Iv) “E h -31 0 1 2 rnlmol kg-I FIG.4.-Velocity correlation coefficients fww for aqueous solutions of Me4NBr (l) Et4NBr (2) Pr4NBr(3) and Bu4NBr (4). For details see text. 0.3 mol kg-l the anomalous behaviour offa andf,. sets in. The related effects on the conductance may be estimated as follows the initial curves fork andf, are extra- polated to higher concentrations assuming a similar shape of these curves as ob-served for Me,NBr. The result for the equivalent conductance in a hypothetical solution where specific cation-cation and anion-anion interactions are absent is also shown in fig.5. It is immediately obvious that the observed correlated motions between like ions shift the equivalent conductance to higher values. At 2 mol kg-l ca. 15% of its actual value may be attributed to these effects. At ca. 2 mol kg-l the contributions due tofaoh andf, nearly cancel one another and A is close to the value given by the sum of the ionic self-diffusion coefficients A’. More important at high concentrations A may even become larger than A’ behaviour which has not yet been observed in other systems. TRANSPORT PROPERTIES 100 75 50 25 I 1 1 0.5 1 1.5 (rnlmol kg -I)* FIG.5.-Equivalent conductance in solutions of BuoNBr as a function of the square root of molality.The solid line represents the experimental curve. The dashed line gives the contributions from the ionic self-diffusion coefficients neglecting the cross-terms. The dotted line gives the equivalent conductance estimated for a hypothetical solution where hydrophobic cation-cation association and anion-anion is absent. For details see text. CONCLUSIONS We have characterized the dynamical properties of aqueous solutions of tetra- alkylammonium ions via the correlated translational motions between the various interaction partners. Intuitively one is attempting to relate these effects to the intermolecular structures present in these solutions. However we believe that the translation of this dynamical information into a structural picture will be a difficult task.There is evidence that the spatial extension of the observed correlations is rather long range.27 Thus the detection of" association " by the aid of the present method is certainly different from the usual concept of association as for example is inherent in Bjerrum's treatment of ion association.18 Nevertheless the main results of the present study are supported by similar conclusions derived from various other experimental results and any structural models should account for the facts presented here. H. W. thanks the authorities of the Australian National University for a visiting fellowship during the tenure of which most of the experimental results have been obtained. Wealso thank the Deutsche Forschungsgemeinschaft for financial support.Helpful discussions with Dr R. Mills and Prof. W-Y. Wen and H. G. Hertz are grate- fully acknowledged. L. A. WOOLF AND H. WEINGARTNER APPENDIX Equations derived by Pitzer 25 have been found to yield accurate representations of experimental data on activity and osmotic coefficients in electrolyte solutions.26 For 1-1 electrolytes at 25 “C these equations are given in ref. (25) and (26). The expression for the derivative (1 + rn dlnyldrn) in terms of Pitzer’s parameters is do = 1 + m-dlny = 1 -0.3920rn3 (1.5 + bm+) p + dm dm (1 + brn+)2 where a = 2.0 and b = 1.2 are characteristic for the class of electrolytes and B(O) 8“)and C9 are characteristic for each electrolyte. Pitzer and Mayorga 26 have fitted their equations to the activity data of Lindenbaum and Boyd,” but the set of parameters for tetra-alkylammon- ium bromides has been corrected in an additional note.26 H.S. Frank and M. W. Evans J. Chem. Phys. 1945,13 507. F. Franks in Water-A Comprehensiue Treatise ed. F. Franks (Plenum Press New York 1975) vol. 4 chap. 1 pp. 1-94. ’W-Y. Wen in Water and Aqueous Solutions ed. R.A. Horne (Wiley New York 1972) chap. 15 pp. 613-661. R. L. Kay and D. F. Evans 1.Phys. Chem. 1965,69,4216. ’R. L. Kay and D. F. Evans J. Phys. Chem. 1966,70,366. H. G. Hertz B. Lindman and V. Siepe Ber. Bunsenges. Phys. Chem. 1969 73 542. B. J. Levien Aust. J. Chem. 1965 18 1161. C. N. Pepela B. J. Steel and P. J. Dunlop J. Am. Chem. SOC. 1970 92 6743. D. G. Miller J.Phys. Chem. 1966 70 2639. lo R. Haase and J. Richter Z. Naturforsch. Teil A 1967 22 1761. H. G. Hertz Ber. Bunsenges. Phys. Chem. 1977 81 656. H. L. Friedman and R. Mills J. Solution Chem. 1981 10 395. l3 K. R. Harris and H. V. J. Tyrell J. Chem. SOC. Faraday Trans. 1 1982 78 957. l4 H. Latrous P. Turq and M. Chemla J. Chim. Phys. Phys. Chim. Biol. 1972,69 1650. ’’ L. A. Woolf and K. R. Harris J. Chem. SOC. Faraday Trans. 1 1978,74,933. l6 D. G. Miller J. Phys. Chem. 1981 85 1137. l7 W-Y. Wen and S. Saito J. Phys. Chem. 1965 69 3659. R. A. Robinson and R. H. Stokes in Electrolyte Solutions (Butterworths London 2nd edn 1970). l9 M. Spiro in Techniques ofchemistry ed. A. Weissberger and B. W. Rossiter (Wiley New York 1971) vol. 1 chap. 4 pp.206-295. ” R. H. Stokes and B. L. Levien J. Am. Chem. SOC. 1946,68 333. 21 D. J. Ives and G. J. Janz in Reference Electrodes (Academic Press New York 1961). 22 S. Lindenbaum and G. E. Boyd J. Phys. Chem. 1964 68 91 1. 23 R. Mills and L. A. Woolf in The Diaphragm Cell (A.N.U. Press Canberra Australia 1968). 24 R. Mills J. Phys. Chem. 1973 77 685. ” K. S. Pitzer J. Phjs. Chem. 1973 77 268. 26 K. S. Pitzerand G. Mayorga J.Phys. Chem. 1973,77,2300; erratum J.Phys. Chem. 1974,78 2698. 27 H. G. Hertz K. R. Harris R. Mills and L. A. Woolf Ber. Bunsenges. Phys. Chem. 1977 81 664. H. G. Hertz 2.Phys. Chem. (Frankfurt am Main) in press. 29 R. Mills and H. G. Hertz J. Phys. Chem. 1980 84 220. 30 H. Leiter Thesis (University of Karlsruhe 1982).