202
ROGERS. PORTER A N D JULIAN F. JOHNSON
Vol. 63
TABLE I1 ANALYTICAL DATA u
Found e.g.,
Lit % Calod. Found
Ni, % Calcd. Found
0.79
7G.5 74.0 72.7 68.9 61.2 38.2 4.6 0 5G.2 70.3 69.3 68.5 72.7 58.9
,770
O.GG .71
.79 . 79 .79 .78 .78 . $8 .77 .78 1.21 1.54
.7G .75 .i 5 . 70 .78 .74 .6i . 75 1.07 1.20
39.2 19.G .09 .23 .69 1.55
77.6 75.0 73.5 69.4 G1.5 38.5 4,8 56.6 71.3 70.6 70,i 73.1 59.0 40.1 20.1
0 1.9
3,s 8.0 15.4 38.4 72.0 76.6
Zn, % Calcd. Found
0 1.9 3.8 7.7 15.5 38.0 70.8 76.5
20.9 6.4 (3.3 6.2 5.0 19.7 39.4 59.0
+
20.9 6.5 6.5 G.4
6.G 20.2 38.4 57.8
,023 ,049 ,100 ,200 ,496 ,938 1.oo .'751 ,925 ,923 ,925 ,082 ,253 ,488 ,741
.08 .20 .68 1.43
z Found e.g.,
moles Li moles (Li Co Ni)
+ +
0.067 . 072 .077 .0iG .076 ,078 ,080 .082 . 070 ,076 ,10G ,123
,009
,022 ,074 ,138
as was observed for Li,Cocl - z)0.3Additional experiments have indicated that this region is not a t all simple, and that cobalt and nickel partition to a certain extent between the two phases. A sample of Li0.5(Coo.sMn0.~)0.50 was also made in order to determine the crystal structure. In this case the mnterial may be considered as a solid solution of orthoi,hombic
TABLE 111 C
co, % Cnlcd. Found
moles _ _ -Co inoles (Co Ni)
a
c/a
Lio.jNio.jO 14.19 2.878 4.03 Lio.s( C 0 ~ . j N i ~ . 5 ) ~ . j O ~ 14.06 2.840 4.95 L~O.~CO~.~O 14.05 2.817 4.99 Lio.S( C O ~ . ~ M I \ ~ . ~ ) ~ . ~14.27 O~ 2.857 4.99 a Data from two phase products. The actual chemical formulas probably do not consist of equal amounts of the transition metal ions.
Li0.~Mn0.50~ and rhombohedral Lio.sCoo.s0.3 Surprisingly, the product was predominantly a rock salt structure. -4s can be seen from Fig. 2, the lattice parameter for this phase is a reasonable one. An impurity phase having a CsC12I Rtructure also was present in the amount of 10-20%. The lattice parameters on the CsC12I phase are larger than that of pure Lio.sCoo.60,a! would be expected on the basis of ionic radii. The relationship between the two phases in the Lio.b(M ~ O . ~ C O ~preparation . ~ ) ~ . ~ Ois not clear a t this time.
Acknowledgment.-The authors take pleasure in acknowledging the work of Mr. D. E. Sestrich, who assisted in the preparation of these materials, Mr. E. W. Beiter, who performed the chemical analyses, and Mr. R. M. Jones and Mr. N. J. Doylet who assisted in the X-ray work. The authors also wish to express their appreciation to Dr. R. R. Heikes for many valuable discussions.
LAMINAR FLOW DEGRADATION OF POLYISOBUTENE * BY ROGERS. PORTER AND JULIAN F. JOHNSON California Research Corporation, Richmond, California Received Julv 86, 1958
A concentrir cylinder viscometer has been used to measure the degradation of polyisobutene in cetane a t high shear rates under laminar flow conditions. Results were obtained for 10% solutions a t 25, 40, and 80" and a t several rates of shear up t o 3 X 106 seconds-'. Temperatures and rates of shear were closely defined and measured. The degradation process is rapid and terminates a t an equilibrium polymer molecular weight which is characteristic for a particular shear stress and decreases linearly with increasing shear stress. Polyisobutene degradation may be clearly attributed to the extending forces in laminar flow.
Shear rates reach a t least lo6 reciprocal seconds ported which overcomes the major limitations of in conveiitioiial machine elements. Viscosities previous variable shear viscometers. Full demeasured a t known rates of shear generally have tails of this concentric cylinder viscometer and its been limited experimentally to shear rates below operation have been described.' This instrument lo4 seconds-l. Recently, however, design of an with minor modifications has been used in this excellent rotatioiial viscometer has been re- work.
*
Presented before the Petroleum Division of the 134th National Meeting of t h e Anierican Chenrical Society, Chicago, Sept., 1958.
(1) E. 11. Barber, J. R. 1Iuenger and F. J. Villforth, J r , , Anal. Chem., 27, 425 (1955).
Feb., 1058
LAMINAR
FLOWDEGRADATION
Two phenomeiia are encountreredin polymer solutions at high shear rates. A temporary and reversible decyease in viscosity occurs with increasing shenr rate due to polymer deformat,ioii aiid orieiitatioii. A second effect is an irreversihle decrease ill viscosity caused by the breaking of bonds in polymer molecules which reduces the moleculai' weight. M;my studies of mechanical degradation of polymers in solution have been made by such means as ultrasonic irradiation! passage through genr pumps and orifices, niid Most of these methods produce turbulent flow, cavitation and/or the possibility of local thermal or oxidative degradation. This work mas performed to see whether the same degradation occurs a t high shear rates under strictly Iamiiinr flow conditiolis with a negligible possibility of local effects. These are the existing conditions i n many bearings. Degradation studies have beeii made on polyisobuteiie a t shear rates higher than those previously rcported. The degr:idation may be clearly attributed to the extending forces present in laminnr flow. Experimental
OF POLYISOBUTENE
203
8 12 1 G 20 24 28 32 Shear rate, set.-' X Fig. l . - l O ~ o Vistaiies 100 ill cetane, 40".
3G
3
I
5; 20 X m
1G
.e
a
3
12
8 A' 8 c . .* 0
P 4
.3
+=
0
4
150 I
I
100 90 1: >, 80 _. .5 i 0 .. 00 _. '-
P
'5
2
50 .' 40
30 ._ The concentric cylinder viscometer was constructed from 0 working plans which graciously were made available by Mr. E. M. Barber of the Texas Compaiiy. The sensitivity of (/3 20 .. this viscometric procedure has been improved by using strain gages and bridge cii,cuits to record electronicnlly t,orques and r.p.m.'s from which viscosities and shear rates are calculated. 10 The test fluid is contained between the concentric cylinders. The inner cylinder is rotated, and the torque necess a ~ yt'o restrain rotation of the outel, cylinder is measured. The cylinders are approximately one inch in diameter and have an effective length of l - ? / S inches. The thickness of the test film between the cylindei,~,3.05 X 10-4 inch, was calculated from data obtained 011 API oils of known viscosity. Both cylinders are thermostated and temperatures measured by four thei~mocouples placed ~ymmetrically within the outmercylinder a t l/16-inch from the fluid film. 20 Shear rate is equal to the linear velocity of t,he film divided by the film thickness. Since the inner and outer radii of the filni differ by only 3.05 X l o F 4 inch, the shear rate is esLe' sentially constant across the film. Small film thicknesses minimize tempemture gradient's produced in the film by shearing. Temperature gradients in the test fluid increase as the square of the film thickness.' Calculations indicate VISTANEX I20 that the maximum temperature buildup in the film in this I N I T I A L MOLECULPR work was about 1". No correction has been entered for this effect. Small film t,hicknesses result i11 streamline or laminar flow of fluid between the cylinders. Reynolds numbers did not exceed one. It is generally accepted that lamittar flow exists a t Reynolds numbers below 2000. Taylor has developed an equation for calculating the region of turbulent flow for rotational viscometei.s.3 The maximum speed of rotation VISTANEX 100 I N I T I A L MOLECULAR used ill the viscometer WRS much lou.er than the speed calk WEIGHT 1.41x IOE culated from Taylor's equation for the onset of turbulence. The polyisobritenes used were taken from the Vistanex series which were kindly conti4buted by the Enj:~yCompany, G 5 t Inc. Vistmexes 100 and 120 are solids a t room temperature. The po1ymei.s used for making u p cetane and oarbon tetrachloride so1ut)ionswere taken from the cent,er of large blocks of Vistanexes 100 and 120 which had been fi,eshly cut. Vistanexes RIS arid hIH are viscous fluids at room temperature. Aliquots were dipped from clear samples of these two Ion-er molecular weight polymers. , I The cetane usrd was a d u Pont Petroleum Chemical. 0 5 10 15 20 25 30 35 40 The Vist'anexez n-ere dissolved it1 cet,nne by agitation aild Degrading shear rateflX 10-4, sec.-l. heating I~elow80". One iveek was required for tho solutions to become Iio~nogeneous. All solutions were made up to Fig. 3.-Degradatiori of IO yo solutions of polyisobutene in cetane a t 40".
11I \
-.r .M
(2) H. H. G. Jellinek, "Degradation of Vinyl Polymers," Acadeiiiio Psess. Inc.. Kew York, N . Y . , 1955. (3) G. I. Taylor, P h l . T i a u s . , 8 8 3 3 , 289 (1922).
10.08 & 0.01 g. per 100 ml. of cetane at room temperature. The accuracy of viscosity measurements obtained from the high shear rate viscometer has been checked with n-dodeo-
204
ROGER8. P O R T E R
AND J u L 1 . 4 ~F.
JOHNSOX
l'ol. G3
TABLE I VISTANEX 100 INITIAL MOLECULAR WEIGHT 1.41 Y IO'
LrISCOSITY
AVERAGERlOLECULAR WEIGHTS
O F POLYISO-
BUTENE
Vistanex specification
Intrinsic viscosity
MS MH
0.30 0 53
100 120
4.4 5.0
Rlol. \vt. 4.00 x 6.18 x 1.41 X 2.24 X
104 104 Ire lo6
Figure 1 shows the effect of shearing on a 10% solution of Vistanex 100 a t 40". The solution was placed in the viscometer and measurements were started a t low rates of shear. KOpermanent degradation was observed after prolonged shearing a t shear rates up to 1.72 X 104 seconds-'. The viscosity as a function of shear rate is shown as curve A in Fig. 1. The shear rate then was increased to 2.41 X lo4 seconds-l. After about 10 I minutes the shear rate was lowered, and the 0 5 10 15 20 25 30 35 40 viscosity again was measured a t lo4 seconds-'. Degrading shear rate X sec.-l. Fig. 4.-Degradation of a 10% solution of polyisobutene in This cycle was repeated until no further change was cetane. observed. At this point equilibrium had been reached. The viscosity as a function of shear rate was determined for shear rates below 2.41 X lo4 l5 seconds-l. These results are shown as curve B in Fig. 1. The shear rate then was increased to 1.38 X 10j cieconds-' and curve C determined. Curve D was obtained in a similar manner. It is interesting to observe that the viscosity decreases from much greater than 5000 centipoises at low shear to 35 centipoises a t 340,000 seconds-'. Measurements showed the viscosity of cetane to be effectively independent of shear rate over the entire temperature and shear rate range investigated. The molecular weight of polymers in the several degradation curves in Fig. 1 'was estimated by measuring the viscosities of four undegraded poly0 isobutenes listed in Table I in 10% solution at lo4 0 5 10 15 seconds-l. Permanent viscosity reductions were Shear stress, (dyne/cm.2) X 10-4. measured a t lo4 reciprocal seconds because the efFig. 5.-Degradation of 10% Vistanex 100 in cetane. fect of molecular weight on viscosity will be ane, n-hexadecane and n-eicosane as well as a number of greatest a t the lowest conveniently measured shear petroleum base stocks whose viscosities are well established. Shear rate factors have been checked on a fluid measured by rate. A scale for calculating molecular weight was established by plotting the logarithm of several workers using different methods over the range of shear rates reported in this work.' Results obtained here molecular weight versus the logarithm of specific are in excellent agreement with the consistent data obtained viscosity which was obtained in 10% solutions a t by others. On the basis of all accuracy, calibration and precision studies, it is felt the viscosities and rates of shear 40" and lo4 seconds-l. Using this plot, shown in are measured in the high shear rate viscometer to better Fig. 2 , a correlation has been obtained between than &2% of the true values. degrading shear rate and the resultant polymer The intrinsic viscosity determinations are believed to be molecular weight. The specific viscosity-molecu. were made in duplicate better than d ~ 5 7 ~ Determinations a t four levels of concentration and extrapolated to zero coli- lar weight correlation is empirical but serves to centration. Capillary viscosities were not corrected to zero compare degraded molecular weights. rate of shear. Figure 3 shows this change in molecular weight Results with rate of shear for 10% solutions of Vistanex Polyisobutene solutions, lo%, weight to volume, 100 and 120. It may be seen that the molecular in cetane were tested in a high shear rate viscom- weights of the two polyisobutenes approach one eter a t 25, 40 and 80" over the shear rate range another a t high rates of shear. It is expected that from 5000 to 34,000 seconds-l. Intrinsic viscosi- a t even higher rates of shear the curves would ties were used to derive viscosit'y average molecular superimpose. The shapes of the curves are due a t weights for the four grades of polyisobutene which least in part to a reasonably large spread i n molecuwere tested. Table I shows the Vistanex speci- lar weights for the Vistanex starting mnterials. fication and the molecular weight calculated from In a theoretical estimation of degradation in lamithe Staudinger equation for polyisobutene in CCl4 nar flow, Frenkel concludes that the square root of a t 30°.4 (4) T. G. Fox, J r . , and P. J. Floty, T H I U J O U R N A83, L , ID7 (1949). I
t
LAMINAR FLOW DEGRADAT~OS OF POLYISOBUTENE
Fell., 1959
the molecu1:w weight of degraded polymer should vnry inversely with rate of shear.5 Degradation studies also were made on a 10% solution of Vistanex 100 a t 25 and 80". By using similar log-log plots a t 25 and 80" molecular weights have beeii calculated for polyisobutene solutions degraded at a series of shear rates. These results :ire compared in Fig. 4. It is of interest to iiiterpret this degradation in terms of applied shear *tress. Figure 5 shon-s data for Vistanex 100 a t 25, 40 and 80". All points fit a linear correlation for decrease of polymer molecular weight with applied shear stress. The equilibrium niolecular weight for degrnded polymer will also depend 1ine:irly 011 rat,e of energy application. 'Fable I1 summarizes viscosities measured n t lo4 seconds-' on solutions of Vistanex 100 and 120 a t several t'emperatures after degradation a t a series of shear rates. vISCOSITY
TABLE I1 REDCCTIONS DUETO POLYAIER
Degradation shear rate, sec. -1
KO clegradii. 1,20 x L72 x 2.41 x 3.44 x 1.38 X 3.40 x 3.44 x
104 104 10' 10' IO6 105 105
:DEGRADATIOS
Viscosity, centipoise at 104 sec-1 at indicated teiiip. Vistnnex Vistanex 100 120 250
40'
800
40'
2G2 257 252 243 23 1 105 179 145
202
lljG
"0
183 154
235
131 121
127
115
174 151 138
Discussion The geometry of the viscometer ensures con6 results of Bestul' ditions of laniiiiar f l 0 ~ . ~ ~Thc and the low volatility of the solutioris make the presence of cavitation unlikely. Polyisobutene ( 5 ) J. Frenliel, .4cta Phpicociicm. 17RRS. 19, No. 1, 52 ( l W 4 ) . (17)C. Gxzlev, .Ir.. Traits. .I in. #Tor. ,llci,h. l;'iIur,~.,80, 79 (1958). (7) A. B. Bestul, T H I V JOURN.A 61, L .418 (1957).
205
begins to deconipose a t 300°.2 Therefore the thermal contribution to degradation should be negligible a t 80", the highest test temperature. Although thixotropy has beeii for a similar system, it W:LS not obserJ7ed in this work. On the basis of these facts, it is coiicluded that mechanical degradation takes place under laminar flow conditions. Degradation is envisioned as a mechanically induced chemical reaction. The mechanically supplied activ:itioii energy is certainly in excess of the 80 kcal. bond energy of an aliphatic cerboncarbon bond. This is equivalent to 5.5 X 10-l2 ergs per broken bondeg The extending forces on polymer molecules increase as the square of molecular l e i ~ g t h . ~Under stress the longer molecules will therefore be ruptured preferentially. The viscosity average molecular weights reported for degraded polymer must represent highly skewed averages which are weighted in favor of lower molecular weight species. Capillary shearing experiments on Vistallex 100 have been performed by Bestul and Good1nan.8-10 At 40" and a nominal shear rate of 66,000 seconds-1, polyisobutene was degraded from an initial molecular weight of 1.75 X lo6 to 1.13 X lo6. The two sets of data plus others obtained by cnpillary s h e n r i ~ i g ~cannot s ~ ~ be compared directly. In a capillary viscometer the shear rate is not uiiiform, and degradatioii is dependent on the geometry of the capillary.12 However, qualitatively, the results by the two different methods are the same and show the same temperature end molecular n-eight dependence. ( 8 ) .4. B. Bestril, J. A p p l . Phus.. 26, 1069 (1954). (9) P. Goodiiian and A . B. Bestiil. J. PolUnier S c i . , 18, 236 (195.5) ( I O ) A. P. Bestiil. J. Chem. Phi/s., 24, 1190 (195ti). (11) A. B. Bestiil nnd H. V. Belclier, J. A p p l . Phus., 24, 1011 (1953). (12) H S. White and H. V. Belclier, J . Research h'atl. Bur. Slanda i d r , 60, 215 (1938). (13) P. Goodiiian, J. Polumer Sei., 25, 322 (1957).
