1816
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 9
LITERATURE ClTED
” 0
20
40 KO 80 100 SPECIFIC SilRfACE AREA
120
140
160
180
(rn2/g)-EM
Figure 18. Relation of abrasion resistance to surface area
As expected, the conclusions which may be drawn from adsorption and bound rubber experiments are similar, the consensus being that the majority of carbon blacks do not differ appreciably from each other in their specific adsorption and reinforcing characteristics toward elastomers. As a consequence, the main effect on reinforcement aB exemplified by abrasion resistance is simply derived from the state of subdivision-Le., particle size or surface area. I n those instances where the simple surface area dependence of abrasion fails, abnormalities in the adsorption-desorption behavior are observed. These are found mainly in Graphon, and to a lesser extent in channel and thermal blacks.
Amborski, L. E., Black, C. E., and Goldfinger, G., Rubber Chem. and Technol., 23, 417 (1950). Amborski, L. E., and Goldfinger, G., Rec. trav. chim., 68, 733 (1949); Rubber Chem. and Tdchnol., 23, 803 (1950). Barton, B. C., Smallwood, H. M., and Ganshorn, G. H., J . Polymer Sei.. 13,487 (1954). Dannenberg, E. M., and Collyer, H. J., IND.EKG.CHEM.,41, 1607 (1949). Fielding, J. H., Zbid., 29, 880 (1937). Flory, P. J., J . Chem. Phys., 18, 108 (1950). Flory, P. J., and Rehner, J., Jr., Ibid., 11, 521 (1943). Frisch, L. H., and Simha, R., J . Phys. Chem., 58, 507 (1954). Frisch, L. H., Simha, R., and Eirich, F. R., J . Chem. Phys., 21, 365 (1953). Goldfinger, G., Rubber Chem. and Technol., 18,286 (1945); 19, 616 (1946). Hobden, J. H., and Jellinek, H. H. G., J . Polymer Sei., 11, 365 (1953). Jenckel, E.,and Rumbach, B., 2. Elektrochem., 55, 612 (1961). Kolthoff, I. M., and Gutmacher, R. G., J . Phys. Chem., 56, 740 (1952). Kolthoff, I. M., Gutmacher, R. G., and Kahn, A , , Ibid., 5 5 , 1240 (1951). Rehner, J., Jr., and Gessler, A. M., Rubber Aoe, 74, 561 (1954). Schaeffer, W. D., Polley, M. H., and Smith, R. W., J . Phys. Colloid Chem., 54, 227 (1950). Simha, R., Frisch, L. H., and Eirich, F. R., J . P ? ~ y sChern., . 57, 584 (1953). Sperberg, L. R., Svetlik, J. F., and Bliss, L. A., IND.ENG.CHEM., 41, 1641 (1949). Sweitser, C . W., Rubber Age. 72, 55 (1952). Sweitzer, C. W., Goodrich, W. C., and Burgess, K. A., Ibid., 65, 651 (1949). Sweitaer, C . W., and Lyon, F., IND. EKG.CHEM.,44, 125 (1952). Treiber, E., Porod, G., Gierlinger, W., and Schwa, J., Makromol. Chem., 9, 241 (1953). Watson, W. F., Proc. Third Rubber Technol. Conf., London, June 1954 (to be published). R E C ~ I V Efor D review November 18, 1954.
ACCEPTED February 10, 1955.
Rheology of Filled Siloxane Polvmers J
E. L. WARRICK Mellon Institute, Pittsburgh, Pa.
R
HEOLOGICAL studies of siloxane polymers and of filled polymer systems a t low volume loadings have led t o a classification of fillers and t o a better understanding of the action of fillers. Dimethylpolysjloxanes below a molecular weight of 20,000 are Newtonian fluids. Larger polymers deviate from Sewtonian behavior as viscoelastic fluids. For such non-Newtonian liquids, the superposition technique as outlined by Ferry (‘7) and later by DeWitt ( 4 ) produces, for a given polymer, a single curve of relative viscosity versus reduced rate of shear for all temperatures. The effect of temperature on t h e zero shear viscosity as measured by the energy of activation for viscous flow is dependent on the viscosity of the fluid. This may be an effect of polymer entanglement. T h e effects of fillers may be noted first in the various volume loading laws of Einstein ( 6 ) , Guth (8),and others. Here, a s in their reduced viscosity-reduced rate of shear plots, systems containing “active” fillers show marked deviations from the behavior of “inert” fillers. Superposition technique shows that systems containing inert fillers do not differ appreciably from the unfilled polymer, whereas active fillers even a t very low volume loadings (2 volume %) show greater non-Newtonian deviations.
Viscometric properties of polysiloxanes were studied by Currie and Smith ( 9 ) using extrusion through a capillary as a measuring method. They studied fluids well below the Newtonian limit up t o those of roughly 100,000 molecular weight, well above the Newtonian limit. When their data are plotted, log D (log shearing rate) versus log (log shearing stress), a series of straight lines is obtained, as shown in Figure 1. On such a plot a line of 45’ slope represents a Newtonian fluid, and therefore a D C 200 fluid of 1000 cs. or approximately 20,000 molecular weight is nearly Iiewtonian in behavior. Above this viscosity, the fluids increase in their deviation from Newtonian behavior. A measure of this deviation is the slope of line C a s defined by
c = -A log D A log r
which is equivalent to
D = KrC where D = 4 Q / T Rand ~
7
=
PR/2 L
This is the type power law first explored by Nutting
(IO)
September 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
and later modified by Ostwald (11), DeWaele (S), Scott Blair (la), and others. Dimethylpolysiloxane systems, both filled and as pure polymers, obey this empirical relation rather well. I n our studies of the rheological properties of siloxanes, a capillary extruSion rheometer, a Severs Model A 300 manufactured by the Castor Laboratory Equipment Co., 741 Shady Lane, Pittsburgh 34, Pa., was used. The instrument consists of a gas pressurized cylinder immersed in a silicone oil bath for temperature control. The bath fluid was recirculated by a pump and controlled t o + l . O o C. by a bimetallic thermoregulator. Two orifices served t o cover the range of shear rate needed in these studies. Both were 5.08 cm. long; one was 0.1608 cm. in diameter and the other was 0.3413 cm. Pressures were read on a gage calibrated by dead weights. The polymers used were dimethylpolysiloxanes ranging from 220,000 t o 427,000 molecular weight (as measured by intrinsic viscosity). The constants used for the calculation of average molecular weight from intrinsic viscosity were those of Barry ( 1 ) . These polymers were not fractionated and consisted of materials of quite a wide range of molecular weights, though no data are available by which an estimate of the distribution of molecular weights may be made, This range is from a fluid of 1,000,000 centistokes t o a semisolid material. D a t a were collected as grams of polymer extruded per second a t pressures expressed in pounds per square inch. These were converted t o volume and c.g.s. units using the density of the material and the orifice dimensions. The data so obtained were plotted D / r (rate of shear divided by shearing stress or apparent fluidity e*) versus the shearing stress as suggested by Spencer (15). The extrapolation to zero shearing stress to obtain a zero shear fluidity as suggested by Spencer is made difficult by the rapid curvature near the origin. This extrapolation is based on the fact that viscoelastic fluids become Newtonian a t low shear rates and should yield one char“Newtonian” or zero shear visacteristic of the material-its cosity. The plots for a fluid of 427,000 molecular weight are shown in Figure 2. A somewhat better method, involving no extrapolation, is t o obtain a falling ball viscosity which is essentially a viscosity determination a t extremely low rates of shear. DeWitt and coworkers (9) showed that falling ball values agreed well with extrapolated data for lower viscosity fluids. The energy of activation for viscous flow may be obtained by plotting log of the zero shear viscosities versus 1/T or by means of the method originated by Smallwood (14). From Eyring’s absolute reaction rate theory, Smallwood developed a relationship ?* =
A plot, therefore of
I
.
Are(a - b r l / T
q * / r (apparent viscosity over the shearing
I
I
10’
IO1
RATE
Figure 1.
OF S H E A R , SEC:’
Shear of dimethylpolysiloxanes
I
1817
THESE STUDIES H A V E LED T O a better understanding of behavior
...
of fillers as reinforcing agents in silicone rubber
. . . a classification of fillers into ac-
I
tive and inactive groups
stress) versus 1/T should be a straight line of slope a - br. Such plots are shown in Figure 3 for the same high molecular weight (427,000) polymer used in Figures 1 and 2. Points a t equal shearing stresses form a series of straight lines. The slopes of these lines were plotted against shearing stress (Figure 4). Clearly shearing stress does decrease the Eviso. However, we cannot use the whole of Smallwood’s treatment, for in the equation the constant, A , turns out to be dependent on shearing stress Thus far we have q , E,,, and the whole fluidity curve as definitive of the viscoelastic fluid. It is interesting to note how the E,,,, varies with molecular weight or viscosity of the fluid as shown in Figure 5 . E,,,, values plotted here are those obtained by extrapolation to zero shearing stress. The low viscosity points are for a series of pure materials whose size is such that they are moving as whole molecules. Early data led us to bel i e v e t h a t E,,., leveled off a t such a value as to indicate a flow unity of around eight siloxane units. However, over a wide range of viscosities it appears t h a t there is a rise in The double circles are given t o estimate distances 50 100 150 200 from the curve. PRESSURE, P, in p s i The inner circle in Figure 2. Extrapolation for Xeweach case is 100 tonian’viscosities of 427,000 moleccalories in diameter ular weight dimethylpolysiloxane (&50 calories uncertainty) and the outer is 200 calories across. The slight rise of something less than 1000 calories may be attributed to the effects of polymer entanglements. To use the whole fluidity curve as characteristic of the material, it would be helpful to eliminate the effect of temperature and obtain one curve, characteristic of the material. Spencer and Dillon ( 1 5 ) suggest one method of doing this by plotting +*/+ versus r (fluidity ratio versus shearing stress). This seems to eliminate the effect of temperature on the Newtonian viscosity, €or they obtain a single curve for polystyrene over the temperature range 165” to 250” C. To obtain the apparent fluidity +* in this ratio, Spencer divides N
D w / r w . The shearing rate a t the wall, D , or
?Iw, is obtained
in a manner first suggested by Rabbinowitsch ( I d ) . This requires the C value obtained as the slope of the log Q versus log P curve obtained originally.
Therefore
Vol. 47, No. 9
INDUSTRIAL AND ENGINEERING CHEMISTRY
1818
@*
=
-
rl
-*
'9
=
~
$Iw.
dynamic viscosity against the reduced frequency, mul, is a single curve for a given material at all temperatures and frequencies. I n Ferry's technique the dynamic viscosity is a function of the reduced frequency and at a temperature, T , is rel?ted to the dynamic viscosity a t a temperature, TO,by
T %* To
?**(a)= aT -
Such plots for dimethylpoly-
4 r l Tw siloxanes are not single curves but rather envelopes over the temperature range 40" to 150" C., as shown in Figure 6.
(WUi)
where the steady state viscosities are related. 9 = UT
T
-
To
70
Substituting
DeWitt ( 4 ) has shown that a similar relation is t o be expected for steady flow viscosities in non-Newtonian systems where t h e variable is D, and the relation becomes
T h a t is, the ratio of the apparent viscosity t o the Newtonian viscosity at one temperature is related t o the same ratio at another temperature by t h e same form of an equation in which the rate of shear is now multiplied by a factor, a~
Figure 3. Smallwood plots for 427,000 inolecular weight dimethylpolysiloxane
The curves for a dimethylpolysiloxane of 25,000 molecular weight are coincident with the shear stress axis since this is about the upper limit (of molecular weight) a t which polysiloxanes are Xewtonian fluids. -4t higher molecular weights the envelopes move further from this axis. I n both illustrations the higher temperature flow curve is more nearly Newtonian. The envelope does not lend itself to further treatment in characterizing either the polymers alone or systems containing fillers. Ferry ( 7 ) has developed a superposition technique which shows the equivalence of frequency and temperature in dynamic viscosity measurements. By his method the curve of reduced
45
t
A
Here the viscosities are Sewtonian or zero shear values for the corresponding temperatures, T and To. Thus curves at one temperature should be superimposable by merely shifting along the rate of shear axis by an amount, aT. DeWitt and coworkers (9) showed this for dynamic viscosity measurements of a dimethylpolysiloxane of 12,500 cs. viscosity (approximately 60,000 molecular weight). The value of this superposition method for capillary extrusion data is shown in Figure 7 , where curves for a dimethylpolysiloxane of molecular weight 220,000 are superimposed over the temperature interval 40" to 150' C. These are referred t o 40" C. and unit viscosity. Similar data for a polymer of 427,000 molecular weight are compared Yith the previous lower molecular weight polymer. Sssuming in principle that one curve of ?*/q should be obtained for all dimethylpolysiloxanes regardless of source, then clearly some additional U T factor would be necessary to permit these two polymer shear curves to coincide. Part of this shift may be molecular weight as already indicated by DeWitt ( 6 ) . How-
0
I
-2 50 SHEAR
Figure 4.
STRESS,
100 psi
150
Effect of shear on Evise
2
0 LOG
VISCOSITY,
4
6
poises 40'C.
Figure 5. Effect of polymer size on energy of activation for viscous flow
INDUSTRIAL AND ENGINEERING CHEMISTRY
September 1955
ever, the ratio of molecular weights is only 1.94, and it appears that a shift of something like a factor of 10 is needed. It must be remembered that these are whole polymers of unknown molecular weight distribution. The actual molecular weight distributions, particularly the amounts falling below the Kewtonian limit, will be quite important in determining the actual position of the relative viscosity curve.
"n >'
0"L 0.10
-
LLo o : >
40-C.
80°C.
n MW 427,000
0 150°C.
w
b le
I
REDUCED
MW 2 2 0 , 0 0 0
15
I O SHEAR
2.0
STRESS, 105dynes/cm!
Figure 6. Shear behavior of dimethylsiloxane polymers
JVithout further inquiry into the validity of the superposition tcchnique for all kinds and conditions of dimethylpolysiloxanes, systems containing fillers may be compared with the unfilled polymer. Data have been obtained for two levels of loading (5 and 10 volume yo)for titanium dioxide of 152 mp particle size, one loading (3.75 volume %) of copper phthalocyanine of 49 mp particle size, one loading (2 volume %) for Degussa Aerosil silica of 25 mM particle size in a dimethylpolysiloxane of 427,000 molecular weight. Before comparing these systems on the basis of Ferry's reduced variables, note the "bodying" action as compared with that predicted by theory of Einstein (6) and Guth ( 8 ) : Volume
% ...
Filler
Nonc Titanium oxide
di-
Copper, phthalocyanine Derussa Aerosil silica
Einstein (0) Coefficientu
H
Obsvd.
I
...
1.64
...
...
5 10
11.9 25.5
2.62 5.82
1.72 1,80
1.90 2.07
3.75
28.5
3.29
1.70
1,84
21.3 1.67 1.81 600 2.33 1.67 1.81 2 (heated) 21 a Coefficient needed to replace 2.5 in Einstein's relation, q = 7 0 (1 2.5 u / V ) , t o achieve agreement.
106
SHEAR,
ATSW
secT'
1 br
\
Q FILLER
Figure 8.
Polymer-filler reaction
2
+
None of the fillers fit either bodying law very well. IIowever, it is clear that Degussa .4erosii silica is in a distinctly different class from either titanium dioxide or copper phthalocyanine. Just on the basis of this effect, one might classify Degussa Aerosil silica as an active filler and titanium dioxide and copper phthalocyanine as inert fillers. This is especially true since heating the Degussa-filled polymer for 24 hours a t 250" C. causes the filler to revert t o the inert class. Some reaction, such as that shown in Figure 8, may be occurring. With plots of v*/v for the filled polymer against the reduced rate of shear,
OF
-
0
G u t h (8)
RATE
capillary wall rather than the nominal value, D),the filled system may be compared with pure polymer (Figure 9). These curves illustrate still further the classification of fillers into inert and active. Inert fillers seem to yield systems with reduced viscosity-rate OP shear plots which are identical with the unfilled polymer. Active fillers as typified by Degussa Aerosil yield systems which are more non-Newtonian than the unfilled polymer. Polymer filler forces, therefore, must be acting as effective links between polymer chains. These effective links are not broken a t low shearing stress but are ruptured a t high shear stresses. Other work in swelling of more highly filled dimethylsiloxane polymer systems shows that the bonds between polymer and active fillers are not broken by swelling (16). Zapp and Guth ( 1 7 ) showed that swelling of butyl polymer containing fillers served to break bonds to the less active mineral fillers while those to carbon black were not broken. I n effect, reinforcing fillers (or active ones) are those capable of forming bonds to polymer molecules which are not broken by low shearing stresses or by swelling in solvents of maximum swelling power for the polymer concerned.
Viscosities, ____ ~106 . Poises - ~ Einstein (6)
I
io 5
Reduced viscosity versus reduced rate of shear for dimethylpolysiloxanes
Figure 7.
05
1819
UT
""/ dr
(note the use of the rate of shear a t the
As both Ferry and DeWitt point out, the UT values provide a means of determining the energy of activation for viscous flow. Since U T is the coefficient which permits superposition, its temperature dependence is really the temperature dependence of the polymer UT
= uoexp [A.H(To - Z')/RTToI
a log UT plot versus 1/T does yield a straight line of slope of 5190 calories for the polymer of 427,000 molecular weight. This is higher than Evisacalculated from 7 or by the Smallwood technique which gave 4380 calories. The difference lies in the definition of U T ; this makes AH larger than Evisoby approximately R2' or about SO0 calories. This is, of course, just what is found numerically.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1820
= shearing stress,
Vol. 47, No. 9
P R / 2 L dynes/sq. cm.
= Newtonian or zero shear viscosity a t temperature 2'
/::L
T , rU = Newtonian or zero shear viscosity at temperature To = real part of complex dynamic viscosity a t temperature 7' = real part of complex dynamic viscosity at temperaturr
= apparent viscosity a t temperature
'x.
-
= = = =
POLYMER
o
5 and IO T ~ 0 2
6
C u Phtholocyonine
+
0---2 S I 0 2
e
t I
'
2 S I O Z Heated
%.
e
'n
I
I
.
1
1
.
/
105
Figure 9.
I
1
REDUCED
RATE
OF
I
106
SHEAR,
_I
nTSw s e e .
= shearing stress a t capillary wall '0
10'
Filled dimethylpolysiloxane, 427,000 molecular weight
I n summary, the reduced variable treatment as shown by Ferry and DeWitt serves to define a single curve for the reduced viscosity as a function of the reduced rate of shear for a given dimethylpolysiloxane over a wide range of temperature. Moreover, this technique also serves to separate the effects of fillers into active and inert classifications. NOMENCLATURE
c
D K L P Q R
= slope A log D / A log
To
circulap frequency, 2~ times frequency Newtonian or zero shear fluidity apparent fluidity, D,/T,, energy of activation as temperature coefficient for relaxation times 3 c
T
nominal shearing rate 4 & / ~R3(sec.-') proportionality constant in power lam length of capillary, cm. pressure in capillary, dynes/sq. cm. volume of extruded, cc./sec. = radius of capillary, cm. = reduction factor for relaxation times at temperature 2' UT E,,,,, = energy of activation for viscous flow (from zero shear viscosities) = = = = =
Y
LITERATURE CITED
Barry, A . J., .I.Appl. Phys., 17, 1020 (1946). Currie, C. C., and Smith, B. F., IND.ENG.CHEM.,42, 2467 (1950).
DeWaele, A., Kolloid Z.,36, 332 (1925). DeWitt, T. W., SOC.Rheology, New York, Oct. 29-31, 1953. DeWitt, T. W., Padden, F., and Markorits, H., Phus. Rei., 9 1 , 2 1 7 (1953).
Einstein, A., Ann. phys., (4) 19, 289 (1906). Ferry, J. D., J . Am. Ckem. Soc., 72, 3746 (1950). Guth, E., and Gold, C. O., Phys. Rev., 5 3 , 3 2 2 (1938). Harper, R. C., Rlarkovitz, H., and DeU'itt, T. W., .T. Polptr7 Sci., 8, 435 (1952).
Iiutting, P. J., J . FranklinInst., 1 9 1 , 6 7 9 (1921). Ostwald, W., 2. physik. Chem., 111, 62 (1924). Rabbinowitsch, B., Ibid., 145A, 1 (1929). Scott Blair, G. W., Nature, 1 4 6 , 8 4 0 (1940). Smallwood, H. AI., J.A p p l . Phys., 8 , 5 0 5 (1937). Spencer, R.S., and Dillon, R. E., J . Colloid Sci., 3, 163 (1948). Warrick, E. L., and Lauterbur, P. C., IND. ENG.CHEM.,47, 486 (1955).
Zapp, R., and Guth, E., Ibid.,4 3 , 4 3 0 (1951). RECEIVED for review November 8, 1954.
A C C ~ P T KMDa r c h 14, 1955. Contribution f r o m the multiple fellowship sustained a t Mellon Institiite, Pittsburgh, Pa., by the Corning Glass Works a n d Dow Corning Corp.
Inhibition of Rubber Oxidation by Carbon Black J
I
