J . Chem. SOC., Faraday Trans. 1, 1984, 80, 549-551 Self-diffusion and Volumetric Measurements for Oc tame thylcyclo te trasiloxane under Pressure at 3 23 K BY ALLAN J. EASTEAL AND LAWRENCE A. WOOLF* Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 2600. Australia Received 8th April, 1983 Self-diffusion coefficients have been measured for octamethylcyclotetrasiloxane (OMCTS) up to 58.4 MPa at 323 K and volume ratios have been determined at the same temperature to 81 MPa and fitted to a modified Tait equation. From the density of liquid OMCTS at the freezing pressure at 323 K, an equivalent hard-sphere diameter of 0.777 nm has been estimated and used in a rough hard-sphere interpretation of the diffusion data. Octamethylcyclotetrasiloxane (OMCTS) is of considerable interest because it is a large globular molecule. Self-diffusion measurements on OMCTS have been made by Levien and Mills’ at atmospheric pressure for the temperature range 288-318 K, and tracer1 and mutual2 diffusion coefficients for mixtures of OMCTS with benzene and carbon tetrachloride have been measured for the same temperature range.Substantial measurements of thermodynamic properties at atmospheric pressure have been made by Marsh and c o ~ o r k e r s . ~ Shear viscosity measurements were made by Dickinson4 at 30 and 52 MPa, at 323 K, but because of the lack of p V data he was forced to estimate densities at those pressures in order to interpret the viscosity data. As part of the present work on the self-diffusion of OMCTS under pressure, the density of the liquid has been measured at 323 K at pressures up to ca.20 MPa beyond the freezing pressure. EXPERIMENTAL The OMCTS used was Fluka ‘purum’ grade (> 98% purity) material which was stored over a molecular sieve. The p V data were obtained from volume-ratio measurements made at ca. 2.5 MPa intervals up to 30 MPa and at CQ. 10 MPa increments from 30 to 81 MPa, using a calibrated bellows vol~morneter.~ The self-diffusion measurements were made using the n.m.r. spin+ho technique. The volume-ratio data are estimated to have a precision of +0.02% and the diffusion data a precision of f 1 %. Pressures were measured using Heise-Bourdon gauges; for the diffusion measurements the pressures should be accurate to f0.3 MPa and for the p-V data to kO.025 MPa up to 25 MPa and f0.4 MPa above 25 MPa.Temperatures were maintained at 323.15 & 0.01 K and measured by platinum resistance thermometry. RESULTS AND DISCUSSION The p-V data were represented by p / ( l - k ) = a,+a,p+a3p2 0) < 81 MPa) (1) where k is the volume ratio [(volume at pressure p)/(volume at 0.1 MPa)], a, = 629.96326 MPa, a, = 5.30341503 and a3 = -0.010613265 MPa-l, with a root- 549550 SELF-DIFFUSION UNDER PRESSURE Table 1. p V data for octamethylcyclotetrasiloxane at 323.2 Ka 0.1 5 10 15 20 30 40 50 60 70 80 0.9998 0.9992 0.9853 0.9788 0.9727 0.961 5 0.95 15 0.9424 0.9341 0.9262 0.9 189 921.gb 928.8 935.4 941.7 947.6 958.6 968.7 978.0 986.8 995.1 1003.1 1.58 I .47 1.38 1.29 1.22 1.09 0.999 0.923 0.864 0.8 17 0.718 a k is the volume ratio and K is the isothermal compressibility; density at 0.1 MPa from K.N. Marsh, Trans. Faraday SOC., 1968, 64, 883. Table 2. Self-diffusion coefficients of OMCTS at 323 Ka D / 10-9 p/MPa m2s-' na3 A D 0.1 0.60 1 0.8794 0.204 5.02 0.547 0.8862 0.196 13.6 0.46 1 0.8970 0.180 22.6 0.403 0.9069 0.171 34.3 0.342 0.9188 0.162 48.5 0.281 0.93 18 0.152 58.4 0.246 0.9403 0.146 a Number density no3 is based on a molecular weight of 0.2966 kg mol-l and a diameter, 0, of 0.777 nm. mean-square deviation in p / ( 1 - k) of 0.09%. Volume ratios, densities and com- pressibilities, IC = - (a In klap),, obtained by analytic differentiation of eqn (1) are given at rounded pressures in table 1 and show that although OMCTS has a limited liquid range, it is a very compressible liquid at 323 K.The p-V measurements were made starting from a maximum pressure of 81 MPa after holding the liquid at that pressure for several hours. It was subsequently found that in the presence of sintered stainless steel OMCTS froze consistently and quickly at 60.6 f 0.2 MPa, implying that the liquid can exist for long periods in the metastable region. The self-diffusion results are given in table 2 and were fitted to where bo = -0.505025, b, = -0.021 7412, b,.= 2.041 259 x and b3 = - I .633 207 x with a root-mean-square deviation in 109D of 0.0045.A. J. EASTEAL AND L. A. WOOLF 55 1 It is usual to analyse such self-diffusion data by using the rough hard-sphere model developed by Chandler.' This relates the measured diffusion coefficient D to that of a smooth hard-sphere fluid DsHs by = AD DSHS (3) where A , represents the coupling of translational and rotational motion, DSHS = CDE, with C a number-density-dependent factor which corrects the Enskog dense-fluid- diffusion coefficient D , to correspond to molecular-dynamics simulation results.Application of eqn (3) relies conventionally on estimation of an equivalent hard-sphere diameter a which provides the best constancy of A , up to the maximum number density (no3 = 0.943) allowed by hard-sphere theory. For OMCTS this procedure is of little value because constancy of A , is not attained by varying a before the density limit is exceeded for all except D at 0.1 MPa. An alternative approach utilises the knowledge that a hard-sphere fluid has a liquid/solid phase transition at the reduced density no3 = 0.943.This density can be used with the molar volume Vm of the liquid at that freezing density to provide the hard-sphere diameter from a = (0.943 Vm/L)i. (4) This procedure has been used by Harris and Trappeniers* to obtain a a for methane. Recently Easteal et aL9 have shown that those a provide a prediction of reduced diffusion coefficients for methane from a smooth hard-sphere simulation method which are in excellent agreement with those obtaified from experimental data. For OMCTS the molar volume of the liquid at the freezing pressure of 60.6 MPa is 300.4 cm3 mol-l, which provides a/nm = 0.777. Use of this fixed value of a with the rough hard-sphere model then leads to a set of A , values which are not constant but decrease monotonically with increasing number density (pressure).Note that such variation in A , is not in accordance with the requirement of constancy stated by Chandler.' It does, however, fit in with the intuitive expectation that coupling of translational and rotational motion should increase with the closer packing of the particles consequent on increasing the pressure. A preliminary investigation of self-diffusion data for other globular liquids suggests that a similar dependence of A , on density exists when the a value is determined from freezing-pressure densities. J. Levien and R. Mills, Aust. J. Chem., 1980, 33, 1977. K. N. Marsh, Trans. Faraday SOC., 1968, 64, 894. K. N. Marsh, Trans. Faraday SOC., 1967, 64, 883; K. N. Marsh and R. P. Tomlins, Trans. Faraday SOC., 1970,66,783; B. J. Levien and K. N. Marsh, J. Chem. Thermodyn., 1970,2,227; K. N. Marsh, J. Chem. Thermodyn., 1971, 3, 355. E. Dickinson, J . Phys. Chem., 1977, 81, 2108. P. J. Back, A. J. Easteal, R. L. Hurle and L. A. Woolf, J . Phys. E, 1982, 15, 360. K. R. Harris, R. Mills, P. J. Back and D. S. Webster, J. Magn. Reson., 1978, 29, 473. K. R. Harris and N. J. Trappeniers, Physica, 1980, 104A, 262. A. J. Easteal, L. A. Woolf and D. L. Jolly, Physica, 1983, in press. ' D. Chandler, J. Chem. Phys., 1975, 62, 1358. (PAPER 3/554)