J . Chem. Soc., Furuduy Trans. I, 1982, 78, 2233-2238 Self-diffusion in Liquid Acetonitrile under Pressure BY ROBERT L. HURLE AND LAWRENCE A. WOOLF* Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 2600, Australia Received 6th October, 198 1 Self-diffusion measurements are reported for acetonitrile in the temperature range 238-343 K at pressures up to 300 MPa. Lack of reliable high-pressure density data has restricted tests of theory to the temperature range 268-328 K. Over that range the results show a breakdown of rough hard-sphere theory which is attributed to the strongly dipolar nature of the acetonitrile molecule. A correlation approach based on Enskog smooth hard-sphere theory is found to be less sensitive to the dipole-dipole interactions.Recently self-diffusion measurements under pressure have been reported for liquid carbon disulphide,l which has a linear molecular arrangement. Contrary to the predictions of Chandler,2 the results were satisfactorily represented by the rough hard-sphere theory. The limited computer simulation data available3? indicate that a three-centre Lennard-Jones potential seems likely to provide a good prediction of CS, diffusion. This paper reports self-diffusion data in the temperature range 238-243 K for pressures up to 300 MPa for acetonitrile, which resembles CS, in having almost linear molecules5 but differs in having a substantial dipole moment, 11.3 x C m. The data therefore enable different tests of the hard-sphere models of self-diffusion and also provide an opportunity for a computer simulation of the self-diffusion in CH,CN, employing either an extension of the model used by Singer et a1.6 for CO, (using, in this instance, a three-centre Lennard-Jones potential) or a more realistic but computationally more difficult model which explicitly recognises the dipolar character of the molecule.EXPERIMENTAL The majority of the experiments used an n.m.r. method which has been described in detail elsewhere;7.s in the method used here, the value reported for the diffusion coefficient at each pressure is the mean of four n.m.r. experiments. Results were also obtained at 298 K by a high-pressure diaphragm cell techniques* using 14CH,CN as tracer. (There were no differences, beside experimental error, between the results obtained by the two methods.) The acetonitrile was analytical reagent grade dried over a molecular sieve; experiments with this material gave the same results as similar measurements with a specially purified sample of acetonitrile obtained from a different supplier.The labelled material, from the Radiochemical Centre, Amersham, was used without further purification; counting procedures were standards and a high ratio of active/background was obtained by using ca. 0.4 MBq of tracer for each experiment. Density data were obtained from the literaturelo, l1 and at atmospheric pressure are represented within & 0.05% by: p/g cm-3 = 1.0738,--9.1250 x 10-4(T/K)-2.8186 x 10-7(T/K)2 (228 < T/K c 338). (1) At elevated pressures the densities used were those of Srinivasan and Kay” which are probably accurate to +0.2%; they were extrapolated to f 15 K outside the temperature range reported for them by using the virtual linearity of the molar volume of acetonitrile with temperature.22332234 HIGH-PRESSURE DIFFUSION OF A CETON I TR I L E The molar volume data, including the extrapolated points, are represented to k0.57" by (p/MPa, T / K ) : In(V/~m~mol-~) = 5.209,-2.306, x 10-3p+4.7979 x 10-6p2-2.956, x lOP9p3 + ( 103/T) [ -0.6167, + 7.336, x 103/T) +4.OO2, x 10-4p-0.7256g x 10-6p2] (268 < T/K < 328.2). (2) Temperatures were held constant to kO.01 K and pressures were accurate to kO.4 MPa. The overall accuracy ofthe diffusion data is & 2% for the n.m.r. data and f 2.5% for the high-pressure diaphragm cell results.RESULTS AND DISCUSSION The experimental results are given in table 1. They are fitted within the experimental accuracy by (p/MPa, T / K ) : ln(D/10-9m2s-1) = 4.968-3.078 x 10-3p+7.361 x 10+p2 -8.446 x lOP9p3- 1.O49(1O3/T)+4.348 p(103/T). (3) Examination of table 1 shows the excellent agreement between the n.m.r. and diaphragm cell results; this is a further confirmation of the reliability of the two methods as used in these laboratories. There have been no previous measurements reported for the self-diffusion of acetonitrile under pressure but one value has been given by Zeidler12 at atmospheric pressure and 298.2 K. This value of 5.4 x lop9 m2 s-l is very different from the corresponding value in this work, 4.34 x lop9 m2 s-l, and we assume that it is wrong.Czworniak et al.13 have made some imprecise (experimental uncertainty _+ 510%) light scattering measurements of mutual diffusion at atmospheric pressure and 293 K in benzene + acetonitrile and carbon tetracholoride + acetonitrile mixtures; the activity coefficient derivatives13 for these mixtures show they are very non-ideal. Czworniak et al. were unable to use Chandler's rough hard-sphere theory2 to obtain a satisfactory analysis of the data and so could not resolve the question as to whether the dipole-dipole interactions in acetonitrile are sufficiently strong to cause a breakdown of the rough hard-sphere model. According to the model, the self-diffusion coefficient should depend linearly on the molar volume at constant temperature. The n.m.r. data plotted in fig.1 for several of the temperatures of this work show a definite, although not strong, non-linear behaviour. Note that because of the lack of volumetric data only a 60 K range (268-328 K) of high-pressure molar volumes can be used. The rough hard-sphere theory approximates the self-diffusion coefficient D of the real fluid by that of a rough hard sphere and this in turn is equated to that of a smooth hard sphere DsHs modified by a factor A , to allow for interchange of rotational and translational energy : D = A, D,,,. (4) D,,, is the Enskog dense fluid diffusion coefficient corrected for hard-sphere behaviour by incorporation of the molecular dynamics data of Alder et al:l4 DsHs = (2.527 x lo-'/ 6;) (RT/M)g ( Y - 1.384 V,) ( 5 ) where V, = Na3/2/ 2 is the volume of close-packed hard spheres.The rough hard-sphere model enables determination of the factor A, and the equivalent hard-sphere diameter by an iterative procedure which minimises the variation of A , with molar volume V at each temperature. The results for acetonitrile are given in table 2. The 0 values are close to the 0.410 nm estimates by Czworniak et al.13 using the incremental atomicR. L. HURLE AND L. A. WOOLF TABLE 1 .-SELF-DIFFUSION IN ACETONITRILE UNDER PRESSURE 2235 T / K p/MPa D/10-9 m2 s-l T/K p/MPa D/ 1 0-9 m2 s-l 238.2 5.8 10.5 21.9 35.0 55.1 253.2 0.1 5.2 13.3 40.4 75.2 111.3 145.6 268.2 0.1 13.9 43.4 72.8 74.5 110.2 163.8 2 10.9 283.2 0.1 1.2 19.7 54.8 56.0 66.5 104.4 11 1.3 165.1 235.0 1.70 1.67 I .58 1 S O 1.36 2.28 2.23 2.13 1.91 1.66 1.45 1.28 2.87a 2.69 2.40 2.13 2.11 1.87 1.57 1.35 3.54 3.52 3.19 2.79 2.80 2.68 2.34 2.30 1.94 1.60 298.2 0.1 0.1 16.6 37.5 60.9 94.8 120.5 163.4 182.4 186.8 247.0 253.3 302.1 313.2 0.1 13.8 33.8 75.2 117.2 161.4 198.8 251.2 303.6 328.2 4.8 25.5 54.5 94.8 150.0 230.1 301.2 343.2 7.1 27.4 61.8 108.5 175.3 302.5 4.31 4.35b9 4.03c 3.62 3.29 3.0Y 2.73 2.45" 2.24 2.24 1.91 1.93" 1.67 5.01 4.76 4.37 3.75 3.25 2.88 2.59 2.29 2.04 5.70 5.21 4.70 4.1 1 3.45 2.84 2.44 6.63 6.00 5.29 4.5 1 3.80 2.79 a Mean oftwo experiments (2.88,2.87); mean of two experiments (4.34,4.37); high-pressure diaphragm cell experiment.volume method. The temperature dependence of A , is greater than is normally observed for non-polar liquids and indicates a breakdown of the rough hard-sphere theory .In principle, A , should be independent of both temperature and density. However, in associated systems such as methanol and water the increase of AD with temperature is attributed to the corresponding decrease in the influence of hydrogen bonding on the liquid structure. In pyridine, another fluid with a large dipole moment2236 HIGH-PRESSURE D I FFUS I 0 N 0 F ACE TON IT R I L E 5 .o 4 .O " I v) "€ 2 ' 3.0 0. \ 2.0 1 1 1 1 1 1 1 1 1 1 1 I 1 I 1 1 1 1 1 1 I 1 1 46 48 50 52 54 V/cm3 mol-' FIG. 1 .-Self-diffusion coefficient of acetonitrile as a function of molar volume. TABLE 2.-ROUGH HARD-SPHERE AND CORRELATION PARAMETERS FOR ACETONITRILE T/K &/cm3 mol-l a/nm AD &/cm3 mol-l a,/nm 268.2 29.9 0.41, 0.49, 30.2 0.41, 283.2 29.4 0.41, 0.50, 29.7 0.41, 298.2 29.2 0.40, 0.53, 29.2 0.41, 3 13.2 29.0 0.40, 0.53, 28.9 0.40, 328.2 29.0 0.40, 0.55, 28.7 0.40, (7.7 x C m), a strong variation of A , with temperature has been found and attributed to an undefined combination of both (a) changes in quasi-hydrogen-bonding interactions involving the nitrogen atom and ring protons and (6) a strong temperature effect on the re-orientational motions of the molecule.15 Acetonitrile is not associated and the possibility of its non-spherical shape being the cause of the variation of A , seems unlikely, since carbon disulphide has approximately the same shape and the value of A , for that liquid is 0.6 1 k 0.0 1 (268-3 13 K).The principal difference between acetonitrile and CS, is the large dipole moment (1 1.3 x 1 0-30 C m) of the former.BullR . L. HURLE AND L. A. WOOLF 2237 and Jonas15 have interpreted deuteron and nitrogen spin-lattice relaxation times in [2H,]acetonitrile as indicating that the intermolecular potential has little dependence on the orientation of the main symmetry axis. However, an analysis by Bertagnolli and ZeidleP of X-ray and neutron scattering data suggests that the axes of nearest neighbours in acetonitrile tend to be aligned at 90- 125' to that of the central molecule. In CS,, which has no dipole moment, the preferred orientation of nearest neighbours appears to be ~ara1lel.l~ According to Hirschfelder et al. l8 the effective potential energy of dipole-dipole interactions (for large separations) depends inversely on the temperature and the sixth power of the separation.Because A , is virtually independent of density at constant temperature, its variation in table 2 suggests that the large dipole moment of acetonitrile does have a significant influence on its self-diffusion. This inference provides support for Chandler's reasoning2 that strong, rapidly changing inter- actions between particles would adversely affect the validity of the rough hard-sphere theory. This is in contrast to Czworniak et al.13 who interpreted their mutual-diffusion data as indicating that the hard-sphere model was successful for systems containing molecules with dipole moments comparable to that of acetonitrile. An alternative use of hard-sphere theory to correlate self-diffusion data has been provided by Dymond.lg The experimental diffusion coefficient is used to obtain a reduced diffusion coefficient D* = [nD/(nD),,] (V/V,)g (6) where n is the number density for the experiment and the Enskog dilute fluid diffusion coefficient is defined by ( ~ Z D ) ~ = #(RT/zM)+/o2. In terms of experimental quantities A temperature-dependent equivalent hard-sphere correlation diameter oc is determined from the data by establishing the closest fit of D* to a common curve of D* against V/ y0 (= 2/2/no3).The curve obtained for the reduced acetonitrile data is shown in fig. 2 and the values of V/ 6 and oc are given in table 2. Over the five isotherms (268- D* = 1.744 x 106DV-~(M/7y. (7) I I I I / ' I 1 I I I - I I I I 1 1 1.3 1.5 1.7 1.9 FIG. 2.-Reduced self-diffusion coefficient of acetonitrile- A, 268; 0, 283; 0, 298; m, 313; 0, 328 K ; *, reduced diffusion coefficient of equivalent smooth hard sphere.2238 HIGH-PRESSURE DIFFUS I 0 N OF A CE TONI T R I LE 328 K) included in the fit only two points deviate by > 2% (but < 3%) from the curve given by the equation D* = - 0.429, + 0.179,( V/ ?(J + 0.103,( V / b)2.(8) The comparison in table 2 of oC with 0 determined from the rough hard-sphere approach shows that the two sets of diameters are in good agreement. This provides further evidence that the correlation treatment is insensitive to the shape of the molecule; a similar result was found for carbon disulphide. This is the first occasion on which the correlation approach has been used for a molecule with a large dipole moment. There is no indication that the dipole-dipole interactions adversely affect the correlation.This is in contrast to the methanol system20 where there was a less satisfactory correlation of the data and a much greater variation of the correlation diameter. There are few liquids in which the molecule has as large a dipole moment as acetonitrile. The present results show that the rough hard-sphere theory works well despite the obvious effect of dipole-dipole interactions. We thank Mr P. J. Back and Dr K. R. Harris for assistance with the experimental measurements and R. L. H. thanks the Australian Government for a post-graduate research award. L. A. Woolf, J . Chem. Soc., Faraday Trans. I , 1982, 78, in press. D. 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