Viscosities of liquid fluorocarbons are listed in Table XIV.
If we consider a force of magnitude F, per unit area perpendicular to x9 applied in the direction x to a mass of liquid, we suppose, following Maxwell, that the rate at which the force is equalized by motion of the molecules composing the liquid is
8F\8t = (elx)(8x!8t) - KF, (26) where K is the constant for the rate at which the force is equalized under
no strain. When the motion is steady under a steady force, 8F\8t = 0 and
{e\x)(8x\8t) = KF. (27) e is the coefficient of elasticity equal here to 3//3 where ]3 is the volume
compressibility. Now imagine two elements of the liquid of width z and thickness y, the center lines of which elements lie in adjacent planes parallel to the direction x. The distance between centers of these adjacent planes is then j>. In terms of F the tangential force, FTi per unit area of the two surfaces of a given layer is
F7 = yzFjzx = (yjx)F. (28) Equation (27) is then
(3/j8)(0*/a) = K(x*ly)FT. (29) If one layer is moving with respect to the adjacent layer
(3/jS) • A(8x/8t) = K(x2ly) • AFT. (30) The coefficient of viscosity is defined as
RJ = (&FT)ylA(8xl8t), which from Eq. (30) becomes
r, = (3IPK)(ylx)*. (31) Taking K as KT\H
RJ = (14.6 x io-5/j8r)Cy/*)2» (3 2)
when RJ is in gm c m ^ s e c- 1, j3 is in reciprocal atm, and T is in °K. Applying Eq. (32) to mercury at 25°C, y/x is found to be 0.36, while for CCI4 yjx = 1.44 at the same temperature. In liquid mercury at 25°C it thus appears that, if the element that moves in the rate process corresponding to K is one atom of Hg thick (y), then the number of mercury atoms corres
ponding to the length x that moves is about 3. In CCI4 at 25°C it appears
182 T. M. REED III
T A B L E XIV
VISCOSITIES OF LIQUIDS A N D GASES A. Liquid Viscosities in Millipoises
K-C5F12 (ref. 21) iso-C5Fi2 (ref. 21) cyclo-CsFio (ref. 21) T ( ° K ) viscosity T ( ° K ) viscosity ( T ° K ) viscosity
184.75 49.61 193.76 77.49 283.52 9.139
188.55 43.15 198.23 64.39 285.21 8.857
193.99 35.98 201.88 55.80 285.72 8.758
197.06 32.61 210.26 41.57 289.00 8.274
205.54 25.65 214.07 36.42 293.21 7.670
209.79 22.66 218.95 31.38 294.71 7.489
214.98 19.85 226.45 25.11
221.71 16.91 238.20 18.44
236.55 12.45 253.71 12.93
237.21 12.31 264.00 10.47
254.84 8.856 276.94 8.238
268.42 7.087 286.82 6.954
275.61 6.342 293.16 6.28
279.44 5.996 294.09 6.178
287.27 5.349 294.76 6.107
288.44 5.273 303.3(b.p.) 5.36
293.16 4.94 296.69 4.708 298.06 4.619 302.5(b.p.) 4.38
w-C6Fi4 (ref. 164) C7F16 (ref. 137) 2 - C F3C5F i i ( r e f . 164) T ( ° K ) viscosity T ( ° K ) viscosity T ( ° K ) viscosity
273.16 9.79 298.16 8.955 274.73 10.65
283.16 8.29 293.37 7.86
293.16 7.10 F2 (ref. 45) 303.32 6.77
303.16 6.14 69.2 4.18 313.55 5.87
313.16 5.35 73.2 3.49 323.44 5.12
323.16 4.71 75.3 3.28
78.2 2.99 80.9 2.75 83.2 2.57
P H Y S I C A L C H E M I S T R Y O F F L U O R O C A R B O N S 183
184 T. M . REED III
that the thickness of the element is 1.5 molecules, if the length x is one molecule, or 3 molecules if the length is 2 molecules. In argonjy is somewhat less than x. For w - C i5H32 at 60°C y\x = 1.78. For C6F i 4 at 10°C, y\x = 1.96 and at 50°, y\x = 2.06. For C7F i 6 at 25°C y\x = 2.05. These calculations indicate in these liquids a situation similar to that in liquid CC14.
Returning to Eq. (31) we may obtain an energy of activation E for the movement of a molecule from one equilibrium position to another as
E/R = - 01nK/0(l/r) = + 01ni7j8/0(l/7,)> (33) assuming y\x independent of temperature. Approximate values for this energy of activation are given in the table below:
EjR AE*IR
at at
boiling point boiling point AE^E ( ° K ) (°K)
Ar 107 670 6.3
N2 105 600 5.7
C7F16 570 3300 5.8
W-C15H34 9 9 0 6 0°c 16,000 16.8
P H Y S I C A L C H E M I S T R Y O F F L U O R O C A R B O N S 185 For Ar, N 2 , and C7F16, E is approximately one-sixth of the energy of vaporization, while for the hydrocarbon, E is much less than one-sixth of the energy of vaporization. In this respect hydrocarbons differ from other molecules that do not contain hydrogen. If the extra (negative) intermolecular energy in hydrocarbons were absent, the boiling points of hydrocarbons would be on the order of one-third those they actually possess on the absolute scale. Because of this additional attraction in hydrocarbons the molecules are closer together than normal. Consequently the compressibility is lower, the liquid viscosity is higher and the energy of activation for viscous flow is lower than would be found for these physical properties in the absence of the extra interaction.
The temperature coefficient of viscosity of fluorocarbons is apparently normal for molecules boiling where they do, while the temperature coefficient of viscosity for hydrocarbons is that corresponding to molecules under compression that boil at much lower temperature than their observed boiling points. That is, the energy of activation for viscous flow of hydro
carbons is lower than that to be expected from their boiling points and energies of vaporization. This comparison between the ratio of the energy of vaporization to the energy of activation for viscous flow for hydrocarbons and fluorocarbons has been noted*1 9'2 1'1 3 7'1 5 9) in experimental work. The energy of vaporization divided by the energy of activation for viscous flow, defined in the usual manner as Rd\nr]jd(\IT) is about 4 for hydro
carbons, while this ratio is about 2.5 for fluorocarbons, argon and nitrogen.
This energy of activation for viscous flow has been found by Simons and Wilson*1 5 9) to be about 1000 cal per mole lower than that expected from the boiling points of hydrocarbons when compared with the inert gases and the fluorocarbons.
The energy of activation for viscous flow arises primarily from forces of repulsion rather than from forces of attraction. The unusually high forces of attraction between molecules in hydrocarbon liquids brings the molecules into a state of compression at ordinary pressures, where only a relatively small amount of additional energy (to overcome repulsion) is required to surmount the energy barrier between adjacent cells, and to allow the movement of a molecule from one cell to another. From this point of view there is no direct correlation to be expected to hold for all molecules between the energy of vaporization and the energy of activation for viscous flow. The two energies are indirectly related in a complicated manner through the resultant effects of molecular interaction (primarily attraction) in producing the net value of the lattice energy (or energy of vaporization) on the one hand, and the effects of molecular interaction (primarily repulsion) on the energy barrier between adjacent sites in the liquid. Certainly the net effects of the attraction and repulsion in
186 T . M . R E E D I I I
establishing the equilibrium lattice characteristics, such as cell size and lattice energy, together with additional repulsion encountered as the molecule approaches the boundary of the cell, determine the energy level with respect to the lattice energy of the barrier between sites. This viewpoint has been examined by McLaughlin*1 0 8).