MELT VISCOSITY OF POLYISOBUTYLENE
22 1
REFERENCES
(1) BRESENEVA, N. E., AND ROGINSKY, S. Z.: Uspekhi Khim. 7, 1503 (1938). (2) FEIGL, F.: Qualifutiue Analysis by Spot Tests, 3rd English edition. Elsevier Publishing Company, New York (1948). (3) HEVESY,G. VON: 2. Elektrochem. 34, 463 (1928). C.: 2. physik. Chem. B98, 295 (1937). (4) KOCH,E.,AND WAGNER, (5) KOLTHOFF,I. M., AND O'BBIEN,A. S.: J. Am. Chern. Soc. 61, 3409 (1939). (6) KOLTROFF,I. M., AND O'BRIEN,A. S.: J. Chern. Phys. 7, 401 (1939). I. M.,AND YUTZY,H. C . : J. Am. Chem. Soc. 69, 1634 (1937). (7) KOLTHOFF, (8) LANGER,A.: J. Chem. Phys. 10, 320 (1942). A , : Compt. rend. acad. sci. U.R.S.S. 24, 540 (1939). (9) POLESSITSKY, (IO) POLESSITSKY, A , : Compt. rend. acad. sci. U.R.S.S. 24, 668 (1939). (11) POLESSITSKY, A , : Compt. rend. acad. sci. U.R.S.S. 28, 441 (1940).
FURTHER STUDIES O S T H E MELT VISCOSITY OF POLYISOBUTYLENE'. THOMAS G FOX, J R . , ~AND PAUL J. FLORY' Reasarch Moratory, Goodyear Tire and Rubber Company, Akron, Ohio
Received Februaqj 3,1060
Experimental results on the relationships between the melt viscosity of polyisobutylene and the molecular weight and temperature were presented recently (6). The results reported in this paper extend these relationships to lower molecular weights and temperatures. Combining the two sets of results, data are now available over an extremely wide molecular weight range from 530 to 1,480,000, the viscosities being measured at temperatures from 217" to -40°C. The relationship formerly used to calculate the molecular weight of the polyisobutylene fractions from their intrinsic viscosities in carbon tetrachloride (6) has been shown to be slightly in error (7). The previous bulk viscosities are reexamined here in relation to revised molecular weight values. Specific volumes of these polyisobutylenes also have been measured as functions of molecular weight and temperature and the results are correlated with the viscosity data EXPERIMENTAL
1. Materials The polymer fractions were obtained from five polyisobutylene samples, ranging in molecular weight from 3000 to 1,OOO,OOO,by fractional precipitation Contribution No. 171 from the Research Laboratory of the Goodyear Tire and Rubber Company. ' T h e work preaented in this paper comprises a program of fundamental research on rubber and plastice carried out under a contract between the Office of Naval Research, United States Navy Department, and the Goodyear Tire and Rubber Company. Present addreea: Department of Chemistry, Cornel1 University, Ithaca, New York
222
THOXAS G FOX, J R . , A X D PAUL J. FLORY
from benzene with acetone. The four fractions of lowest molecular weight were obtained by a fractional distillation of a low-molecular-weight extract from one of these polymers. The details are given elsexhere (6, 7). The proportions of the respective whole polymers which the various fractions represent are given in table 1. 2. Molecular weight determinations
Molecular weights of the polyisobutylene fractions above 10,OOO were computed either from their intrinsic viscosities, [q], in diisobutylene at 20"C., employing the equation ( 5 ) = 3.60
x
10-4 JP 6 1
(1)
or from their intrinsic viscosities in carbon tetrachloride at 30°C. by the relationship ( 7 ): = 2.9
x
10-4
~
6
3
(2)
Molecular weights of the four lowest fractions mere obtained from cryoscopic measurements in cyclohexane ( 7 ) . Molecular weights in the intermediate range were obtained from intrinsic viscosities in carbon tetrachloride by means of the graphical relationship recently established between these two quantities (7). Intrinsic viscosities obtained before and after the melt viscosity determinations generally agreed within 5 per cent. The molecular weight values reported here (table 1) represent the values obtained after the melt viscosity measurements and were generally reproducible to f 3 per cent. The details of the intrinsic viscosity and cryoscopic measurements have been described elsewhere (6, 7). 3. Melt viscosities
Melt viscosities above 1 poise were measured with straight capillary-tube viscometers calibrated as previously described (6). Melt viscosities between 0.01 and 1 poise were measured with a pipet-type viscometer consisting of a 0.6-mm. bore capillary tube with a fine opening (about 0.1 mm.) at the lower end and with a bulb (capacity about 0.5 ml.) about 12 cm. from this tip. Absolute viscosities were calculated from the expression q =
ktp
where t is the measured time to fill the viscometer under a predetermined pressure differential, p , and k is a constant determined from the t p product and the viscosity of benzene a t 30°C. Temperature control was provided by means of vapor baths (=k0.3"C.)above lOo"C., by thermostated oil baths (&O.l"C.) from 0" to 100°C., and by acetone-dry ice baths (&0.3"C.)at all lower temperatures. The viscosities obtained with the straight capillary-tube viscometers (7 > 1 poise) are generally reproducible and accurate to f3 per cent; those measured with the pipet-type viscometers (7 < 1 poise) exhibited a similar reproducibility, but may be accurate only to 10 per cent in the absolute value. In the
X E L T VISCOSITY O F POLYISOBUTYLESE
223
pressure range employed here (‘2-30 cm. of mercury) thc measured viscosity appears to be independent of the applied stress.
4. Specific volumes ‘The pycnometers and the technique employed were similar to those described in a previous publication (1).Densities were determined at a given temperature by filling a weighed pipet of known volume (from 1 t,o 2 ml.) with the liquid polymer at this temperature, and subsequently weighing at room temperature. The reproducibility of the datii was generally f 0 . 1 per cent. RESULTS
1 . I+iscosiiy-iempcralure relationships
IIitherto unreported melt viscosities at 217’C. and at lo\vtv temperatures have been measured for nineteen polyisobutylene fractions with molecular weights ranging from 530 to 42,700 (table 1). The data from a previous investigation (6) for fractions of higher molecular weight are also recorded here, the revised molecular weight values having been calculated by equation Z 4In figure 1 representativedataare plotted as log (qTjq217) vs. l / T (‘K-l) for several fractions, this ratio being employed to facilitate comparison of results for polymers differing in molecular weight. The relationship betiveen log ( q T / q Z 1 7 ) and l / T is nonlinear. Although data for all fractions of high molecular weight are represented bya single curve, fractions of low molecular weight yield a series of curves, the slopes of which are lower the lower the molecular weight. Since this behavior is analogous to that observed for polystyrene fractions (G, 8 ) , this suggests that the 7-T coefficient may be separable into a product of two factors, dependent only on T and on A f , respectively, as in the case of polystyrene (8). That this is true, a t least as a first approximation, is demonstrated in figure 2, where plots of log log ( q T j q 2 1 7 ) us. M-1 at several temperatures from 160” to 0°C. are approximately represented by a set of parallel lines obeying the relationship log TI^/^^^^) = F(T)e-la/M (3) where F ( T ) is a function of temperature only. Plotting (figure 3) the values of F ( T ) for the intercepts at 1/M = 0 os. 1/T2(oK.-2),a straight, line is obtained. Hence, the empirical relationship log ( 7 T / 7 2 1 7 ) = 5.6 X 105(l/T2- 1/4-2)e-163/M (4) is established. Upon differentiating equation 4 an expression is obtained for E,, the “apparent energy of activation for viscous flow” (6):
E T = R d In T/d(l/T)
=
(5.1 X 106/T)e-lGlM
(5)
Although the above equations are perhaps of no theoretical significance, These molecular weights had previously been calculated on the incorrect assumption that the ratio of the viscosity in carbon tetrachloride to that i n diisobutylene is a oonstant independent of molecular weight (6, 7).
224
THOMAS Q FOX, JR., AND PAUL J. FLORY
TABLE 1 Viscosity-temperature-molenclar weight relationships for polyieobutylene fractions
PB5Fl (23) 1,480,000 PB5F2 (12). 1,150,000 PB5F3 (12) 660,000 PB2F2 (25) 480,000
poirer
217
2.5 X 10'
217 160 115 217 160 112 217
1.0 x 4.9 x 2.2 x 1.2 X 5.5 x 3.0 X 6.6 X 3.0 X 5.2 X 1.2 X 2.6 x 7.8 x 2.0 x 2.0 x 2.9 X
160
141 119 100 78 28 8 217
PB2F4 (15). . . . . . . . . 205,000 PBlF2 (14), . . . . . . . . 112,000 PBlF3 (11). . . . . . . . . 81 ,000
217 217 201 179 217 190 160 138 89 87 78.5 38 17 3.5
PB4F1 ( 2 0 ) . . . . . . . . .
~,~
-9 -
~~
PB4F2 (14) 42,700 PB6F1 (11) 27,600 PB4F3 (7.3) 21,000 PB4F4 (5.0) 18,#)0
Previous datat
'C.
10' 107 10' 10' 10' 10' 10' 10' 10' 10' 107 107
'C.
PBlF4 (12). . . . . . 57,600
PBlF5 (10). . . . . . 40,000 PBlF6 (9). . . . . . . 32,400 PBlF7 (6.4). . . . .
24,600
100 10'0
10'
PBlF8 (7.8) . . . . . 12,900
217 182 138 110 80.5 217 182
138
3,390 1,160 1,w 2,810 1,100 2,090 4,800 10,100 80,700 88,000 1.38 X los 1.83 X 10' 1.0 x 107 4.1 X 10' 2 . 6 X 10'
217 201 182 157 110 217 201 179 156 217
PB7F4 (4.0). . . . 4170
110 79 56 217 160 130 100 30 0 -10
poises
340 485
880 1,750 9,830 119 168 305 634 55.8 22.9 56.1 #)6
643 2,760 6.45 14.2 57.6 184 884 3,530 0.5 2.03 5.n 14.4 2,130 47,300 165,000
-
Present data
~~
217 217 217 217
PB8F4 4ooo 38.8 PB8F5 3390 PB8F6 24.9 3170 8.52 PB8F7 2640
139
(7.0) (6.0) (4.0) (5.4)
217 30 217 30 217 30 217 30
0.75 2,863 0.56 2,1m 0.40 1,483 0.33 1,183
225
MELT VISCOSITY O F POLYISOBUTYLENE
TABLE 1-Concluded
PB6F2 (11) 17,800 PB6F3 (6.0) 12,100 PB6F4 (2.9) 8500 PB7F1 (7.4) 8500
PB7F2 (8.2) 6610
PB7F3 (7.6) 5380
1
j
~
'C.
217 217 217 217 160 130 100 30 217 160 100 77 30 0 -6 217 160 130 100 61 30 0 -13
pdM3
8.45 PB8F8 (4.0) 2190 3.77 Cut No. 4 (10) 1730 1.79 1.54 Cut No. l ( 1 ) 6.21 890 20.5 42 Cut No. 3 (1) 755 7,420 1.04 3.76 38.6 159 4,340 95,000 228,000 0.74 Cut No. 2 (1) 530 3.10 8.9 28.0 210 2,950 66,300 397,000
'C.
pmser
217 30 217 160 30 0 217 160 30 217 190
0.28 870 0.158 0.56 479 10,000 0.042 0.120 72.5 0.032 0.051 0.093 0.23 0.56 36.7 796 19,700 147,000' 0.0166 0.040 0.165 7.2 141 955 35,000
180
la, 100
30 0 -23
-35 217 160 100 30 0 -24 -40
226
THOMAS 0 FOX, JR., AND PAUL J. FLORY
polyisobutylene of cryoscopic molecular weight 5000 are compared with. the viscosities a t different temperatures predicted by equation 4, using only the value of &?,, and the viscosity a t 170°C.The excellent agreement (at least down to 20°C.) between the observed and calculated values suggests that, as in the TOG. 150
I
50
I
-50
6
4
-
Q5 0 -I 0
2
I/T VI x 103 FIQ.1. Log ( m / q t l v ) u8. l/T('K.-') for polyisobutylene fractions of various molecular weights; 0, M > 2ooo; (D, M = 765; 0 , M = 530. The curves are drawn through the experimental points, Le., they are not calculated by subsequent equations.
case of polystyrene (6, S), the q-T coefficient of a heterogeneous polymer is determined by its number-average molecular weight. Values of E T calculated by equation 5 as a function of M for several temperatures are shown in figure 6. Asymptotic values for high M are in substantial agreement with the values of 16.9 kcal./mole obtained between 0" and 50°C. by Mason and coworkers (9, lo), and also with the value of 15.4 kcd./mole between 30" and lOO"C., obtained by A4ndremset al. (1).
227
MELT VISCOSITY O F POLYISOBUTYLENE
;
:
:
; 0.60
0 50
150
M-' x 1 0 5
FIQ.2. Log log
( v T / ~ w )vs.
FIO.3. Log log
1/M for polyisobutylene fractions at various temperatures
( q ~ / q n r )us.
(1/!7'*
('IT2-'/4T02)X I O ' 1/43') for polyisobutylene: of infinite molecular
-
weight.
2. Viscosity and molecular weight The revised and extended data confirm the previous conclusion (6) that log 7217 increases nonlinearly with the square root of M (figure 7 ) . On the other hand,
" h
I
0"
"I
I
I
I
I
30
4.0.
5.0
BO
log M log M (for convenience) for polyisobutylene fractions at several temperatures. The curvee were drawn according to equation 4.
Fro. 4. Log
( q ~ / q a rplotted ) u8.
I-
W
T
OC.
Fro. 5
log M
FIQ.6 FIQ. 5. Log q ua. T (T.)for an unfractionatedpolyisobutylene of cryoecopic molecular weight Mxx) from the data of Ferry and Parks (3). Curve drawn according to equation 4. FIQ. 6. ET ua. log M (for convenience) for polykobutylene at aeverd temperatures, as calculated by equation 5. 228
229
MELT VISCOSITY OF POLYISOBUTYLENE
a log log plot of q us. M is linear at any temperature for M 2 17,000 (figure 8). The equation for this relation at 217°C. is log ~ 2 1 7= 3.40 log M
- 13.56;
M 2 17,000
(6)
Combining this with equation 4 and setting the exponential term of this equation equal to 1 for M 2 17,000, the expression for log q a t any temperature is log v T = 3.40 log M 5.6 X 105/T1 - 15.85; M 2 17,000 (7)
+
For polyisobutylene fractions with molecular weights less than 17,000 the rela8.C
I
I
I
I
I
Palyiiobulylane
7.217'
4.c
c Frn 0 -
0.c
800
400
1200
FIG.7. Log vlil us. J" for polyisobutylene fractions. The open and closed circles represent previous (6) and present data, respectively.
tionship at 217°C. (lower curve of figure 8) may for convenience be approximated by the linear relationship log
q217
=
1.75 log M
- 6.55;
M 5 17,000
(8)
Combining this with equation 4 we obtain: log q T = 1.75 log M
+ 5.6 X
1O6(1/T2- 1/m2)e-'"/'
- 6.55; M 5 17,000 (9)
For these fractions of low molecular weight the nature of the viscosity-molecular weight relationship changes in a complicated manner as T decreases (see upper curve of figure 8).
230
THOMAS G FOX, JR., AND PAUL J. FLORY
-411 of the above conclusions are based on results obtained with polymer fractions of comparatively narrow molecular weight ranges for which the various molecular weight averages gn, M,, and aw are similar. On the basis of the results of a previous investigation of polystyrene and polyisobutylene (6, 8) it may be presumed that equations 4,5 , 6, and 7 are applicable to heterogeneous polymers
log M
FIG.8. Log q us. log M for polyisobutylene fractions at 217' and 30°C.The straight lines representing the data a t 217OC. correspond t o equations 6 and 8; the straight line and the curve a t 30°C.were calculated from equations 7 and 9, respectively.
provided the number-average molecular weight be substituted for M in the exponential terms of equations 4 and 5 and for the value of M (17,000) limiting the range of applicability of equations 6 and 7, while the weight-average molecular weight must be substituted for M in thelog M term in each of the latter two equations. On the other hand, for heterogeneous polymers with jl, 5 17,000, &e viscosity a t 217°C. is probably not explicitly determined by either or M , but by some unknown combination of the two, and hence neither equation 8 nor equation 9 can be applied.
23 1
MELT VISCOSITY O F POLYISOBUTYLENE
The linear relationship between log q and log [7]for unfractionated highmolecular-weight polyisobutylene at li0"C. reported recently by Baldwin ( 2 ) is approximately equivalent to equation 7 . Minor differences which occur may be attributed to the difference between 2, and 111, far these heterogeneous polymers and to the possible change in the ratio of these quantities with molecular weight. The results of Mason et al. (9, 10) cannot be compared with the present data, since the viscosity-average molecular weight values they reported appear to have been calculated from equation 1 , which is inapplicable in the very low molecular weight range with which they \yere conrerned. M x 10.' I
k
\ -
2
3
5T . 217'40
2
1225
E
t
I
I
I
IO
20
30
M"X lo5
FIG.9. Specific volume at 217°C. for polyisobutylene fractions us. molecular weight (upper curve) and us. M-1 (lower curve).
5. Spmjic volumes The specific volumes of fifteen polyisobutylene fractions, ranging in If from 3540 to 115,000, were determined at 217°C. and in some cases a t lower temperatures by the constant-volume pipet method. The specific volume a t 21i°C., ~ 2 1 7 ,decreases with increasing molecular weight in the lower range but becomes relatively constant for M 1 15,000 (upper curve of figure 9). As in the case of polystyrene, the specific volume increases linearly with 1,'ilf. Data at 217'C., shown in the lower portion of figure 9, support the relation Vz17
=
1.225
+ 32/M
(10)
where the units of V Z ~ , are milliliters per gram. The volume-temperature coefficient, dv/dT = 6.8 X lop4,appears to be independent of molecular weight over the above range. Hence UT =
1.077
+ 6.8 X lo-' T + 3 2 j X
serves t o express u as a function of both T (in "C.) and M .
31)
232
THOMAS
c)
FOX, JR., AND PAUL J. FLORY DISCUSSION
The present observations demonstrate the existence of a close relationship between the molecular weight dependence of three properties: the specific volume, the viscosity-temperature coefficient, and the viscosity a t constant temperature. The first two properties change rapidly with increasing molecular weight in the low range, but in each case approach an asymptotic limit which is essentially I
3.0
I
1
I
I
40
50
log M , FIQ.10. Log us. log M for polystyrene fractiona (6,s). The straight lines correspond to equations 12 and 13.
reached at M,,S 17,000. A marked change in the viscosity-molecular weight relationship occurs a t approximately this same value of the molecular weight. Similar observations on polystyrene have been reported in previous papers (6,8).I n this case the asymptotic values of the specific volume and the viscositytemperature coefficient were reached around B. 30,000. In figure 10 a heretofore unpublished plot of log qz17us. log M for polystyrene fractions is linear for M 2 5O,OOO,Le.,
=
- 13.40;
log 7217 = 3.4 log 2"
2
50,000
(12)
An equation of this form, differing only in the additive constant, should apply at any other temperature (> 100°C.)for all molecular weights above 50,OOO.
MELT VISCOSITY O F POLYISOBUTYLENE
For polystyrene fractions with M also to be approximately linear
233
< 50,000 the relationship a t 217°C. happens
log $217 G 2.34 log M ,
- 8.44;
M , 5 50,000
(13)
but the relationship becomes much more complicated a t lower temperatures (6, 8). The region of transition in the v-M relationship is not much beyond the range of approach to the asymptotic values in the above properties. The behavior of polyisobutylene is entirely analogous to that of polystyrene, differences occurring only in the magnitude of the quantities involved. Asymptotic values of v T and log ( ~ T / v ~forl ~the ) former are reached a t M values about half those required for the latter, and the viscosity-temperature coefficients are smaller in magnitude for the former; e.g., E T values a t 217°C. are 10 and 28 kcal., respectively, for polyisobutylene and polystyrene. The similarity in behavior of these two polymers suggests that the previously presented interpretation of these relationships for polystyrene (8) applies also to polyisobutylene. Thus, the “local liquid structure,” or configurational arrangement of nearest neighbor segments of a polymer chain about a particular segment, is an important characteristic of a liquid polymer which may play a dominant role in determining many of its physical properties. To understand the effect on a given property of varying a parameter such as the molecular weight, the effect of this variation on the liquid structure must first be considered. Decreasing the average length of the polymer chain is equivalent to the introduction of foreign particles (the end groups) which disturb the local liquid structure in such a way as to produce a less dense, more open structure, the magnitude of this change being proportional to the number of end groups added, i.e., to %;I. Thus the specific volume must increase and the viscosity-temperature coefficient must decrease as 2;’becomes larger. It is clear also that the introduction of the first few end groups, while decreasing the molecular weight enormously, will have no measurable effect on these properties and hence a t a sufficiently high value of they will appear to be independent of molecular weight. The macroscopic viscosity, however, being a sensitive function of n?, (owing to the limitations on the motions of the individual segments imposed by the primary valence linkages), decreases rapidly with decreasing M even above this limiting value of ii?,. Below this limit, the viscosity will reflect also the measurable changes in the structure of the liquid and hence will be a function of 27 as well as of %., The abrupt change in the 7-M relationship seems to be due to the superposition of the appreciable variations in liquid structure with decreasing M occurring below this limit. The lower value of E T and the dependence of this parameter on a lower power of 1/T for polyisobutylene suggest that in the temperature range considered the local configurational structure is less dense for polyisobutylene than for polystyrenz, Le., there is a greater “free volume” relative to the cross-section of the polymer segment in the former case. There is here an implication that the present viscosity data appear to bear out: namely, that E T for polyisobutylene varies according to a power of 1/T higher than 1 as the temperature approaohes the
a,,
.
234
THOMAS G FOX, JR., AND PAUL J. FLORY
second-order transition temperature. I t is not yet clear whether the actual magnitudes of the free volumes for the two polymers differ, nor are the structural factors which determine the free volume well understood. SUMMARY
The study of the melt viscosity of polyisobutylene fractions has been extended to cover the molecular weight range from 530 to 1,480,000 at temperatures from 217" to -40°C. The results are expressed graphically and by empirical equations which represent the data satisfactorily except at the lower temperatures. Specific volumes have been determined at 217°C. and at lower temperatures for polyisobutylene fractions ranging in M from 3400 to 115,000. Both the specific volume and the viscosity-temperature coefficient are found to be simple functions of M-',and in each case as ll.i increases the value of the property approaches an asymptotic limit which is practically reached at 2, G 17,000. An abrupt change in the viscosity-molecular weight relationship occurs at this same value of These relationships are discussed in terms of a concept of the liquid state which has previously been employed in the interpretation of an analogous set of observations obtained with polystyrene. The most striking difference between the flow behavior of the two polymers is observed in the lower value and smaller temperature dependence of the viscosity-temperature coefficient for polyisobutylene.
a,.
The authors wish to acknowledge the assistance of Mr. Robert E. Marshall in carrying out the experimental work. REFERENCES (1) ANDBEWS, R. D.,HOFMAN-BANG, N., AND TOBOLSKY, -4.V.: J. Polymer Sci. 3, 669 (1948). (2) BALDWIN, F. P.:J. Am. Chem. SOC.72, 1833 (1950). J. D.,AND PARKS, G.S.: Physics 6, 356 (1935). (3) FERRY, (4) FLORY,P.J.: J. Am. Chem. SOC.62, 1057 (1940). (5) FLORY, P. J.: J. Am. Chem. SOC.66, 372 (1943). (6)Fox, T . G,AND FLORY,P. J.: J. Am. Chem. Sot. 70, 2384 (1948). (7) Fox, T. G, AND FLORY, P. J . : J. Phys. & Colloid Chem. 63, 197 (1949). (8) Fox, T. G, AND FLORY, P. J.: J. Applied Phys. 21, 581 (1950). (9) MABON,W. P.: J. Colloid Sci. 3, 147 (1948). (10) MASON,W. P., BAKER, W. O., MCSKIMIN, H . J., AND HEISS,J. H . : Phys. Rev. 73, 1074 (1948).
