April, 1946
VAPOR PRESSURE-VISCOSITY
tropy are different from those functions for the liquid has been fitted to isotherms in the range of relative pressures of 0.05 to 0.98. For porous solids equations have been presented for adsorption on solids in which the area available to each [COSTRIBUTION FROM
THE
601
RELATIONS IN h'fETHYLPOLYSILOXANES
succeeding layer is less than the previous one. A new-type equation has been developed for adsorptions limited to n-layers which has better properties than the n-equation of B. E. T.3 PITTSBURGH, PA.
RECEIVED DECEMBER 29, 1945
RESEARCH LABORATORY OF THE GESERAL ELECTRIC Co. ]
Vapor Pressure-Viscosity Relations in Methylpolysiloxanes BY DONALD F. WILCOCK Liquid methylpolysiloxane mixtures, or silicone chlorosilane. The linear compounds MzD5 to MzDpwere by fractionally distilling through a packed column oils, exhibit unusually small changes in viscosity isolated a t reduced pressure the volatile portions from equilibrated4 with temperature. Their viscosities a t 100'F. silicone oils. The fractions were carefully redistilled, but are only about two and one-half times those a t it was not possible to eliminate completely small amounts 21.0'F.) while the corresponding factor for a of the corresponding cyclic compounds which were present, a t distillation temperatures near 200 the boiling petroleum oil of viscosity index 100 is about because points of the cyclic compounds approach those of the eight. This behavior of silicone oils suggested corresponding linear compounds as the number of units is investigation of the relations between the viscous increased (see Fig. 2) The method of specific refraction5 was used to determine the percentage of cyclic methylproperties and the vapor pressure-temperature polysiloxanes present as impurity, with the results shown characteristics of those smaller polysiloxane mole- in Table I. The compound M2D5 was not redistilled, and cules which may be separable as pure compounds. consequently was less pure than the others. The viscosities a t several temperatures of a TABLE I number of the linear and cyclic methylpolysilANALYSIS OF KEWLIKEARMEFHYLPOLYSILOXANES oxanes have been reported by Hurd,l and these Refractive Wt. same compound:; were available for determination ComDensity indexo Specific Me: Si %, of vapor pressures. I n addition the eight-silicon pound 20° at 20 ref. ratio chain ring, hexadecaniethylcyclooctasiloxane,2and the 1.3365 0.2640 2.234 82 MzD) 0.911 seven- to eleven-silicon chain compounds, hexa1.3970 ,2638 M2D6 ,913 2.230 92 decamethylheptasiloxane to tetracosamethylun,918 1.3980 MzD, .2629 2.212 96 decasiloxane, were isolated and their vapor pres1.3988 .2615 MzD8 ,925 2.186 93 sures, viscosities and densities were determined. 1.3994 ,2604 2 165 91 MzDg .930 Analysis of these data has yielded general equaVapor pressures were determined by noting the boiling tions relating vapor pressure to temperature and point of each compound a t several pressures. -4 14" X to the number of silicon-containing units. Similar 1/Z jacketed distillation column packed with 3 / a z " stainless equations relating viscosity to temperature and steel helices was fitted just above the reflux condcnser to the number of units have also been obtained. with a side tube connection leading to a McLeod gage of reading pressures as high as 50 mm. Pressure Estimates of th.e average size of the segmental capable a t the head of the column was regulated with a manostat unit of flow in the large polymeric chains likewise capable of holding pressure within 0.1 mm. Pressures have been made by comparison of the viscous above 50 mm. were read from a manometer. Each compound was placed in the still pot and slowly distilled a t and vapor pressare properties. constant pressure until the vapor temperature a t total For the sake of clarity and conciseness, the reflux was within 0.1"of the temperature during partial proper names of the methylpolysiloxane com- takeoff. The temperature \vas then noted and the process pounds will be abbreviated by use of a shorthand repeated at other pressures. The experimental values are system of nomenclature based on the function- summarized in Table 11. Kinematic viscosities were determined in modified Ostality of the basic silicon-containing units which wald pipet viscometers a t 100 * 0.1"F. and 210 =t 0.1' appear in the :molecules. The bifunctional re- F., with a precision of 0.5y0. Absolute viscosities were petitive unit, (C:H3)2SiO, is termed a D-unit, and calculated from the kinematic values and the densities. the monofuncticlnal terminal group, (CH3)3SiOl/,, Densities were determined in a 4.5 cc. dilatometer a t 20 * 0.1 ' with a precision of 0.05%. Refractive indices is termed an M.-unit. Using this system, simple were measured with an Abbe-type refractometer a t cyclic molecules are written D,, and linear 20 * 0.1 a using the sodium D-line. molecules are written MzD,-*, x being the total Vapor Pressures number of silicon containing units. The vapor pressure-temperature curves for Experimental The cyclic compound Dg was isolated by Patnode3 by both the cyclic and linear series of compounds are fractional distillation of the hydrolyzate of dimethyldi- plotted in Fig. 1. These log p vs. 1/T curves are __ straight lines for both the linear and cyclic com(1) Charles B. Hurd, THIS JOURXAL, 66, 364 (1946). O
I
(2) For a discussioi of organosilicon nomenclature, see R. 0. Sauer, J . Cheni. Ed., Zl, 303 (1944). (3) Winton Patnodr and D. F. Wilcock. THISJOURNAL, 68, 358
(1046).
'
(4) The process of equilibration, see ref. 3, involves an equilibrium rearrangement of the M and D units into a system comprising linear polysiloxanes using sulfuric acid as a catalyst. ( 5 ) Sauer, THIS JOURNAL, in press.
DONALD F. WILCOCK
692
TABLE IT BOILING POINTSOF METHYLPOLYSILOXANES B. p., “ C . Compound Press., mm. Hg ( 1 / T ) x 10’ D4 D5 De
D7
D*
Mz
MID
M A Mz1)a MzI),i
MzDe
758 20 760 20 100 “0 4.2 99.5 20 4.8 39.2 4.9 1.9
175.8 73.4 210 101 170.0 128.2 95.2 193.0 150.7 118.8 192.0 141.6 124.8
2 228 2,886 2.07 2.67 2.2G 2.49 2.716 2.146 2.360 2.552 2.150 2.412 2.514
757 161.5 100 74 7 154 40 760 20 760 20 101 49 20 5.0 40 20 10 3.2 39.3 20.0 5.1 2 7 lG.O 4.9 4.05 2.7 0.29 10.0 4.1 2.7 1.1 0.45 4.7 1.1 0.30
100.1 54.1 42.7 151.7 99.0 66.5 194 88 229 117 184.2 165.0 141.4 112.0 184.5 165.2 149.0 125.9 202.0 185.6 153.3 141.2 198.8 172.5 170.1 160.6 122.2 202.8 182.6 176.1 161.3 146.8 201.8 176.3 153.1
2.680 3.057 3.167 2.355 2.688 2.946 2.14 2.77 1.99 2.66 2 187 2.283 2.413 2.597 2.186 2.282 2.370 2.506 2.105 2.180 2.346 2.414 2.120 2.245 2.257 2.306 2.530 2.102 2.195 2.227 2.303 2.382 2.106 2.226 2.347
Dounds and have been extrapolated to room iemperature. The vapor pressures are plotted in Fig. 2 as a function of the number of units for temperatures of 30, 100 and 200’. The vapor pressure decreases logarithmically in each series with increase in the molecular size. The latent heat of vaporization, AHvap, increases regularly with the molecular size in both
VOl. 68
the linear and cyclic series. It has been determined for each compound by the ClapeyronClausius equation, and is plotted in Fig. 3 as a funktion of the number of units. The straight lines were fitted by the method of least squares, and their equations are Cyclic: AHvap= 5.45 Linear: AHvap= 4.70
+ 1.35% (kcal.) + 1 . 6 5 ~ (kcal.)
(1) (2)
where x again refers to the number of units in the molecule. The agreement between the experimental values and those calculated from equations (1) and ( 2 ) is shown in Table 111. The TABLEI11 LATENTHEATSOF VAPORIZATION Compound
D4
D6 D6 D7 D8 Mz
MD MzDz M A
MzD4 MzDs MBDB M?Di MzDs
MzDs
AHvap (kcal. per mole)
Experimental
Calcd.
Deviation
10.9 12.0 13.75 14.9 16.2 8.3 9.45 11.5 12.7 14.6 16.25 17.2 19.4 22.0 22.8
10.85 12.2 13.55 14.9 16.25 8.00 9.65 11.30 12.95 14.60 16.25 17.9 19.55 21.20 22.85
+ .2
-0.05
-
.2
0
+ .05 - .30 + .20 -
+
.20 .28
0 0
+ .70
4- .15 - .80
+ .05
deviations are less than 4% for the chain compounds and less than 2% for the ring compounds. The increment in A H v a p per D-unit is 300 calories greater in the linear than in the cyclic series of molecules. The linear variation of the molar latent heat of vaporization of the methylpolysiloxanes with the number of silicon atoms per molecule is unexpected in view of the fact that the molar heats of vaporization of the straight chain aliphatic hydrocarbons as reported by Do& are a non-linear function of the number of carbon atoms, and in fact reach a maximum value of 9.56 kcal. for the compound C I ~ H ~ O . The linear dependence of AHvapupon the number of silicon atoms per molecule, together with the linear dependence of log p upon the same variable, as shown in Fig. 2, permits the derivation of a useful expression giving the vapor pressure as a function of temperature and composition. The equation log f i ~= 4.10
- 0.31%
x Z 5
(3)
expresses the relation between log p and x at 200’ shown in Fig. 2 for the linear compounds. The integrated form of the Clapeyron-Clausius equation may be written log PL = A
AHnp - 2.303RT -
(4)
(6) M. P. Doss, “Physical Constants of the Principal Hydrocarbons,” The Texas Co., New York City, N. Y..1943.
VAPORPRESSURE-VISCOSITYRELATIONS rn METHYLPOLYSILOXANES
April, 1946
693
At 200°, this becomes log PL = A - 2.18 - 0 . 7 6 1 ~ (6)
Equating (6) and (3) A = 6.28
+ 0.443~ (7)
Substituting (7) in ( 5 ) , the general vapor pressure relation for linear methylpolysiloxanes ( x 3 5) is obtained log
PL
= 6.28
1030 -T
33
[0.443 - - x
Fig. 1.--Vapor pressures of linear and cyclic methylpolysiloxanes.
+
(8)
The general vapor pressure relation for the cyclic methylpolysiloxanes ( x 3 4) is obtained by a similar procedure.
Substituting ( 2 ) in (4) and rearranging logpL = A
1030 360 --T T
(5)
The lines in Fig. 2 for the temperatures 100' and 30' have been drawn using equations (8) and (9) 24 22
20
2 18 33
B
v
2 16
$ 14 12
10
8
0 Fig. 3.-Latent
.OOOl
0
I
Fig. 2.-Vapor
2
4 5 6 7 8 9 NUMBER OF SILICON ATOMS
3
1011
12
pressure us. composition at constant temp.
4 G 8 1 0 1 2 Number of Si atoms. heats of vaporization of linear and cyclic methyl polysiloxanes
Viscous Properties The viscosities of the linear methylpolysiloxanes up to MZD4 and of the cyclic compounds up to D, have been reported by Hurd.l The viscosities of the linear compounds up to MIDp and of the
DONALD F. WILCOCK
694
TABLE IV VISCOL-sPROPERTIES OF LINEARAND CYCLICMETHYL POL\-SILOX ANES Compound
Viscosity in Centipoises 100'F. 210'F.
EVlS
kcal.
In v a
-4.97 -4.92 -4.99 -5.01 -4.89
D4
1.69
il.7ll~l
3.42
D5
2.94 ,5,10
1.11
3.i1 4.10
D6
D7 DB
i.811 lU.7
1.75 2.79 ;3.2d
4.3i
4-50
VoL-68
4.5
In ?a (calcd.)
4.0
-4.95
-4.96 -4.97
-4.98 -4.98 44 -4 29 -4 19 -4 11 -4 04 -3 98 -3 93 -3 89 -3 8.5 -3 82 -4
cyclic: D8 have now been determined, and are reported in Table IV, columns 2 and 3. The viscosities a t 100'F. are plotted in Fig. 4 as a function of the number of units. The logarithm of
-j 3.5 3
4:
v
?2
3.0
2.5
2.0
4 6 8 1 0 20 Number of Si atoms. Fig. 5.--Energies of activation for viscous flow of linear and cyclic methylpolysiloxanes. 2
values of Evis and In ,urn have been calculated, using the Arrhenius equation'
20
qT = ~ ~ e E v i s / R T
10
(18)
and these values are recorded in columns 4 and 5, Table 11. The energy of activation for viscous flow, Evis,is plotted in Fig. 5 against the number of units. It is a linear function of the logarithm of the number of units, the appropriate equations being Linear: Evis Cyclic: E,,,
= =
1.74 0.98
+ 1.49 l o g s + 3.96 log x
(kcal.) (13) (kcal.) (14)
Using these linear relations, (lo), ( l l ) ,(13) and (14),together with ( l a ) , general equations for the viscosities of the linear and cyclic compounds niay be deriyed in a manner analogous to that used in obtaining the vapor pressure relations. The resulting general equations are
0.5
log q~ = -2.04
+ 380 + [ 0.37 + T --
]"j!
log s .(151
11.2
2 5 10 20 Xuniber of Si atoms. Fig. 4.--Viscosities of linear and cyclic methyl polysilosanes. 1
the absolute viscosity is seen to be a linear function of the logarithm of the number of units for each series: the relation being log
VL =
-0.82
+ 1.41 log x
(10)
for the linear compounds, and log
VR =
-1.44 f 2.74 log
X
(11)
for the cyclic compounds, a t T = 311'K. From the viscosities a t 100' and 210°F., the
The values of In rrnin column 6, Table 11, were calculated from (15) and (16) by setting T = a. Ln 7, is nearly constant for the cyclic compounds but varies oyer a wide range for the linear molecules. The viscosities of the cyclic compounds not only are higher than those of the corresponding linear compounds, but also increase more rapidly with molecular size. Mixing two or more linear methylpolysiloxanes lowers the value of Evisfor the mixture below that for a single compound of the same average composition. Three examples are outlined in Table (7) S. Arrhenius, M e d d e l . T e l e n s k a p a k a d . .\ o b u l i m l . , 3, 20 (1916).
VAPORPRESSURE-VISCOSITYRELATIONS IN METHYLPOLYSILOXANES
April, 1946
times for asymmetric or polar molecules. EyringlO shows that AFZ, is given by the relation
TABLE V EFFECT O F MIXINGON E,ia 31 olar composition Viscosity, cp. of mixture x av. 25'C. 75'C. Evia
41'3'MM?D4 58.797, MpDp
4.83
695
Evis
(calcd.)
1.738 0.8914 2.75 2.76"
45'7% M2D4 (3 3.470 1.583 3.24 3.54b 54.3'33 Da Oil: M2D,-, 3.7 1.20 ... 2.31 2.59" Calculated by equation (13). 0.457 X 2.89 O.,i43 X 4.10 = 3.54.
where V is the molar volume ( V = Mu), h is the Planck constant and N is the Avogadro number. At T = 100°F., equation (18) may be rewritten as
-+
V. The first, a mixture of a 4-silicon with a tisilicon chain, shows a slight reduction in Evis'below that calculated from (13). The second, a mixture of a 6-silicon chain and a 6-silicon ring, has a value of E v i s considerably lower than that calculated by means of a linear relation between the molar composition and the E v i s values of the pure compounds. The third example is, a low viscosity silicone oil com:prising a mixture of linear compounds of average length 3.7 units. This mixture shows a marked negative deviation from equation (13). 'The Unit'of Flow Eyring833+1U and co-workers have demonstrated that for many molecules the standard free energy of activation for viscous flow, AFZ,, is related to the energy of vaporization a t the normal boiling point AEv;,p, by the equation
= 3.43
+ 1.43 log [ v M q ]
(19)
a t constant temperature and is then in convenient form for calculation. In Table VI, values of AF& calculated by means of equation (19) are tabulated. The values of E v i s are taken from Table 11. The energy of Vaporization of each compound has been calculated from its heat of vaporization by means of the relation AEvsp = A H v p
where RTb.,. is given by Linear: RTb.p. =
- RTb. p.
(20)
+ +
(21)
4620 1610x x 8.68
derived from (8) and (9) by setting p = 760 mm. The calculated values of A E v a p are recorded in Table IV, column 4. I n the last two columns are the values of the ratios AEvap/AF$sand AEvap/ A E v i s for each compound. The average value of the ratio AEvap/AFZs for the cyclic compounds is 2.34, which is very nearly that found by Eyring and co-workers for many series of organic compounds. There apand that for sma.11 molecules AEvap is either three or four times the energy of activation for viscous pears, however, t o be a uniform trend toward flow, E v i s , the factor being three times for sym- larger ratios for larger molecules. This trend is metrical, or nearly spherical, molecules, and four even more marked in the series of linear compounds, where the values range from 2.14 for Mzto 3.76 for M2DB. TABLE VI The ratios AhEva,/ A E v i s show the same trends. RELATIONS IjETWEE:N F L O W AND VAPORIZATION ENERGIES The ratio is about 3 for the cyclic compounds, indicating that these are approximately spherical molecules. The value of 3.3 for M, likewise in2.21 2.89 D4 4.47 3.42 9.96 dicates a nearly spherical molecule. The ratio 3.i1 11.2 2.26 3.02 1)s 3.95 increases rapidly with the length of the chain. D6 5.40 2.32 3.05 4.10 12.5 A similar increase in the ratio of A E v a p to Evis 2.40 3.16 4.37 13.8 D7 5.75 above 4 has been observed in the hydrocarbon 15.1 4.50 2.51 3.36 1)s 0.03 series by Kauzmann and Eyring." They ascribe this behavior to the motion of the chain in seg2.17 7.19 2.14 3.31 M, 3.36 ments, the activation energy for the movement of 2.20 3.58 2.45 8.77 MzD 3.88 a segment being but a fraction of that required 2.42 3.90 3.67 10.4 MZD: 4.30 for the motion of the entire molecule. The size of 2.6(J 4.31 2.78 12.0 M2Ds 3.62 the unit of flow for each molecule was estimated 2.89 13.6 2.80 4.70 M~DJ 4.815 to be that of the member of the series for which 2.96 5.00 3.04 15.2 M,Dj 5.13 A E v a p equaled four times the value of E v i s for 3.19 5.41 3.10 16.8 MpDa 5.27 the molecule in question. This type of calculation 3.38 5.89 15.4 5.44 3.13 M9: has been carried out for the linear methylpoly3.58 6.11 20.0 5.59 3.27 MpD, siloxanes with the results shown in Fig. 6, in which 21.6 3.76 6.59 3.28 5.74 M2Dg the size of the unit of flow is plotted as a function (8) Powel1,Roseveart and Eyring,Znd. Eng. Chem., 33,430 (1041). of the size of the molecule. (9) Ewell anti Eyring, J. Chem. Pizrs., 5 , 726 (1037).
-
(10) Glasstone, Laidler and Eyring, "Theory of Rate Processes," McCraw-Hill Book Co., Inc., New York, N. Y., 1941.
(11) W. Kanzmann a n d H. Eyring, Txrs
(1940).
JOURNAL,
62, 3113
Vol. 68
DONALD E. WILCOCK
696
1
Fig. 6.-The
3 a 7 9 11 Number of silicon atoms. unit of flow in linear methylpolysiloxanes.
Kauzman.n and Eyring estimate that the average length of the unit of flow for very long hydrocarbon chains becomes constant for molecules longer than 20 to 25 carbon atoms. From Fig. 6, the unit of flow for methyl silicones is seen to approach a constant size of approximately 6 silicon atoms. As a check on this figure, the value of E v i s for high molecular weight silicone oils, which are predominantly linear, approaches asymptotically the value of 3.8 kcal. as the viscosity is increased.12 This value of Evisindicates a limiting flow unit 7.2 silicon atoms in length, which com:pares well with the estimate made above. The relative sizes of the hydrocarbon and silicone oil flow units are compared in Table VII. The sizes are based on the extended form of the chains, and for the silicone units the covalent oxygen angle was assumed. TABLEVI1 COMPARISON OF HYDROCARBON AND SILICONE UNITS OF
FLOW Hydrocarbon
Composition Molecular weight Length, Angstroms Cross-sec$ion,A, sq. Volume, 9.. cubed EYiH, kcal.
CZZHSO 3 50 32
4x 5 640 6-7
Silicone
(CHa)14Si70, 519 23 5 x 8 920 3.8
The two flow units are roughly the same size. However, both the weight and volume of the silicone unit are about fifty per cent. greater than the weight and volume of the hydrocarbon unit, whi'le the activation energy for viscous flow of the hydrocarbon unit is seventy per cent. greater than that of the silicone unit. If one accepts the con(12) &is is 3 70 kcal. for an oil with a viscosity of 50 centistokes at 100°F., and 3.79 kcal. for an oil with a viscosity of IO00 centistokes.
cept that the activation energy E v i s represents the energy necessary to form a hole large enough to accommodate the unit of flow, then methyl silicone oils provide larger holes for a lesser expenditure of energy than do hydrocarbons. Thus, the attractive forces between molecules in the liquid state are lower in methyl silicone oils than in hydrocarbons, a fact which also is demonstrated by the low boiling points of methyl silicones compared to those of hydrocarbons of equivalent molecular weight. Acknowledgment.-The author is indebted t o Dr.. Winton Patnode for furnishing many of the compounds studied and to Dr. R. 0. Sauer for his advice on analysis. Thanks are due Miss B. Sullivan for determining the viscosities.
Summary The linear methylpolysiloxanes with 7, 8, 9, 10 and 11 silicon atoms have been isolated, and their viscosity and vapor pressure curves have been determined. The vapor pressure curves of the shorter linear compounds and of the cyclic compounds up to Dg have been determined. Simple relations have been found which express vapor pressure and viscosity as functions of temperature and composition, For linear molecules these are:
and for cyclic molecules log PR = 7.07 log V R = -2.13
- $!? + b . 2 6 5 - y] x + 214 T - b.04 log x
y]
where x is the number of silicon-containing units. By comparing the energy of vaporization with the activation energy for viscous flow, the unit of flow in high molecular weight silicone polymer fluids has been estimated to be (CH&SiTOT. This is somewhat larger than the unit of flow in hydrocarbons, as estimated by Eyring and coworkers. Since the energy of activation for viscous flow is smaller for silicones, i t is concluded that the attractive forces between molecules in liquid linear polysiloxanes are much lower than those in hydrocarbons of comparable molecular weight. SCEIEXECTADY, K. Y .
RECEIVED SEPTEMBER 26, 1945
