Pal, Arun K

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IN TERM O LECU LAR FORCES AND VISCOSITY OF SOM E P O L A R  ORGANIC VAPO U RS A B m ; K. PALI n s ia k  Association tob tub Co^^ tivation of Scibnob, Cai<cutta-32.{Received li^irch 23, 1967)ABSTRACT. Viscosity of several pc^ar organic vapours has been measured by a precision all-metal oaoillating-diso viscomet^, over the temperature range 30°-200°C and below a pressure of 10 cm Hg, The results Jhave been utilised to obtain some significant information on inter-molecular forces in thei|S substances.I N T R O D U C T I O NAmongst transport properties like thermal conductivity and thermal diffusion, viscosity is not significantly affected by inelastic collisions. This property, with the recent improvements in the techniques (Kestin et al, 1959; Flynn et al, 1963) can be measured very accurately. Consequently, temperature dependence of viscosity is one of the most important sources of information regarding inter- molecular forces in polyatomic gases. For polar gases a further complication in the intermolecular forces is the angle-dependent dipole-dipole interaction. In order to have precise knowledge of intermolecular forces in polar gases we have taken up a programme for the measurement of viscosity of these gases over a range of temperatures. In this paper we have reported the viscosity data for three polar organic vapours, viz. diethyl ether, ethyl acetate and ter-butyl alcohol over the temperature range 30°—200°0.E X P E R I M E N T A LThe viscosity was measured by an all-metal oscillating-disc viscometer similar in design to that of Kestin and Leidenfrost (1959). The apparatus together with its accessories have been described in detail by Pal et al (1967). At low densities it is possible to calculate viscosity from the following simple expression, (Clifton, 1963),fl =  C?-»[(A/T)-(Ao/ro)]. ” •where if is the viscosity of the gas. A, A, and r, Tj are the logarithmic decrements and time periods of oscillation in the gas and vacuum respectively and (7 is a cons­tant of the apparatus. In order to determine the constant 0, H2 and Ng were taken as the calibrating g ^  (purity better than 99.96%). The viscosity data for these gases were taken from the best available sources (Barua ri al, 1964, Kestin968238S4 Amn K. Palet al, 1963). Diethyl ether, ethyl acetate and ter-butyl alcohol' were of analytical reagent standard and were distilled and dried by specific drying agents. The reproducibility of dampings were within 0.1% and the overall accuracy of our measurements should bo well within 1 %.The viscosity values for these polar gases have been recorded in table 1 . Previous viscosity data are available only for diethyl ether. For this substance the present data are 7-8% lower than those reported by Titani (1633) in the higher temperature range. In the lower temperature range as well (upto 77.8°C) our values are 4-5% lower than those reported by Craven et al (1951). The possible causes have been discussed in detail in a previous paper (Pal et al, 1967).I N T E R M O L E C U L A R  P O T E N T I A L SThe intermolecular potential for polar gases is usually represented by the Stockmayer or 12-6-3 potential which can bo written as,^(r) =  4e[((r/r)“ —(<r/r)®-f-5(<r/r)®], 8 =  i  <?s. f);(2)(2a)g{&v ^2) p) =  2  cos $1 cos sin 6^  sin 6^  cos i (2b)where /ii, /i^  are the dipole moments of the interacting molecules, 6i, 6^  are angles of inclination of the dipoles to the line joining the centres of the molecules, ^ is the azimuthal angle. For /tj, or 0, eq. (2) reduces to the well-known Lennard- Joncs (12:6) potential for non-polar molecules (Hirschfelder et al, 1954). Moncuick et al (1961) have calculated the collision integrals for the 12-6-3 potential by assuming equal probability for aU the relative orientations of the interacting dipoles. In order to fit the viscosity data to the 12-6-3 potential we have followed the procedure of Monchick et al (1961) according to which we have the following equations:log [7] X 10’/Jf*T7«] =  log < Q «.«*(T *)> ]-i-t-0 .05377-| log/tloglog T = log T*-1-log {elk),(3)Wwhere  ^ is in g/om. sec, M  the molecular weight in gm/mole, T is in °K and ji in debyes (1 debye = 10~^ ® esu). If the model is capable of representing the data, a plot of the ezperimeptal quantities log vs. log T  should be super-posable by iiranslation of axes on a plot of log[(!r*)*^ <  Q <*i«*(2’*) >]"* vs. log 3'*(<Q(s>»*> being the averaged collision in t^ a ls). The amount cS. txanslai^oiiV isc o c ity  o f  P o la r  O rganic V a p o u rs 825ftlong the abscissa determines elk and that along the ordinate gives which is given by the relation— 2/1* ... (6)I t  has, however, been observed that the viscosity data cannot be fitted satis­factorily to the 12-6-3 potential by the method described above. The discrepancy is more pronounced in the lower temperature region. As a typical example, the experimental and the theoretical plots from oqs. (3) and (4) are shown in figs. 1 ^nd 2 for diethyl ether. I t  is clear from n look at figs. 1 and 2 that the two curves are not a t all superposable at lower temperatures. At higher temperatures the—1.036logT logT*Figure 1. Plot of log vs. log T. Figure 2. Plot of log [2’*a«<0<®»=“*2’*]vs. log T*.plots are almost straight lines and are superposable. This feature is quite under­standable from physical considerations. The assumption of equal probability for all the relative orientations of the interacting dipoles will hold when the time of interaction is large compared to the time between collisions. This condition is likely to be satisfied better at higher temperatures. I t  also appears that parti­cularly a t lower temperatures viscosity i.s affected significantly by the dipole-dipole forces. Thus the suggestion of Monchick et al (1961) that the viscosity is insen­sitive to the dipole-dipolo forces probably holds only at high temperatures.At lower temperatures when the collision time increases, the dipoles may get a chance to reorient during an encounter. Different pairs of molecules wih thus interact with different relative orientations and it is possible to assume an ‘effec­tive’ relative orientation for aU the molecules which will be a function of tempera- ture. This idea can easily be tested by taking 3 to be an independent p a ^ eter  (Itean et al 1961). Under this condition we have the followmg equations... (6)log [7 X 107(AfT)*] =  log ^)]“*+log 266.93—21og <rlogT  =  logT*-flog(c/*!) (7)826 Arun K. Palwhere o<*.*>* (g, T*) is the unaveraged collision integrals which have been eva- loated by Itean et al (1961) and also by Monchick e( al (1961).Table 1Viscosity of diethyl ether, ethyl acetate and ter<butyl alcohol at different temperatures and force constants for the 12-6-3 model by assuming an effective relative orientation of the dipoleSubstance TOQ TJ X10®(g.cm~ .^soo.** )^Potential parametersr(A)30.0 66.5666.2 73.87Diethyl ether 100.0 86.20150.6 96.96200.0 106.606.684 476.4 0.63Ethyl aoetate30.664.6 99.2160.2200.168.1276.2986.6698.78109.605.711 476.8 0.6430.0 67.4166.6 74.34ber*Butyl alcohol 100.0 86.10149.7 96.73200.0 105.256.699 467.1 0.63A series of plots of log vs. log T* for different 8 values werenade. On these plots another plot of vs logT  was superposedby the translation of axes. The value of 8 was determined from the curve which gave the best fit and ejk were obtained from the amount of translations along the ordinate and abscissa respectively. The effective value of g was obtained from the relation9 ^ ' 1811/e* ... (8)where <r is in ejk is in and is expressed in debye However, it may be seen that 8 as obtained by us are positive which correspondV is i^ sU y  o f  P o la r  O rgan ic  V a p o u rs 827to repulsive orientation of the dipole and are physically less probable. This may be due to the offoentre nature of the dipoles. Some progress in this direction has been made for equilibrium properties by Lawley et al (1963).A C K N O W L E D G M E N T SThe author is grateful to Dr. A. K. Barua for his guidance and to Prof. B. N. Srivastava for his kind interest in the vmrk.B E F E B E N C E SBonia, A. K., Afzal, M., Flynn, G. P. md Ross, J., 1964, J. Ohem. Phy»., 41, 374. Clifton, D. Q., 1963, J. Chem. Phy$,, 88, 1123.Craven, P. M., and Lambert, J. D., 1981, Proc. Roy. Soc. (London), A205, 439.Flynn, G. P.; Hanks, E. V., Lemairo, N, A. and Ross, J. F., 1963, J. Chem. Phya., 88, 164.Hirsohfelder, J. 0.; Curtiss, C. F. and Bird, R. B., 1964, Molecular Theory of Oases and Liquids, John Wiloy & Sons, Inc., New York.Itean, B. C.; Glueck, A. R. and Svehla, R. A., 1961, NASA Technical Note, D-481. Kestin, J. and Leidenfrost, W., 1959, Physica, 25, 1033.Eestin, J., and Whitelaw, J. H., 1963, Physica, 29, 336.Lawley, K. P. and Smith, E. B., 1963, Trans. Faraday. Soc., 59, 301.Monchiok, L. and Mason, E. A., 1961, J. Chem. Phys., 85, 1676.Newell, G. F., 1959, Z. angew.. Math. Phys., 10, 160.Pal, A, K. and Barua, A. K., 1967, Trans. Faraday. Soc., 63, 341., 1967, BrU. J. Appl. Phys., (In press).Titani, T., 1933, Bull. Ohem. Soc., Japan, 8, 256.

Intermolecular Forces and Viscosity of Some Polar Organic Vapours

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Intermolecular Forces and Viscosity of Some Polar Organic Vapours

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