INS and WLADlMlR PHILIPPOFF Laboratories for Research and Development, Franklin Institute, Philadelphia 3, Pa.
In str um en tuti0 n
Rheological Special i whose pr temperature
of Viscoelastic Materials tion must be used for these in-between materials, a y vary from solidlto liquid, depending on time and
Tm
investigation of mechanical properties of viscoelastic materials generally requires special instrumentation. Ordinary viscometers used for the study of simple viscous liquids and tensile testers employed for elastic solids are no pletely satisfactory for these ‘ tween” materials. Their properties may traverse the entire gamut between solid and liquid, depending only on the time and temperature of the experiment. Furthermore, viscoelastic materials are often investigated as molten bulk polymer or concentrated polymer solutions. Therefore, rheologists have had to develop suitable apparatus that are more nearly machines than instruments. The present discussion deals with instrumentation in use in the Franklin Institute laboratories, representing most of the types of apparatus used for viscoelastic investigation. T h a t instrumentation designed here was developed with the dual aim of providing as wide a range in experimental parameters as possible with each instrument and providing experimental data which could be correlatable on a rheological basis with results from the other instruments. T h e primary interest was in determining the force, deformation, and rate of deformation relationships existing under stationary or quasistationary conditions. Most of the instruments have been described, in part at least, previously.
Steady-State Instruments
T h e study of mechanical properties under “steady-state” conditions is probably the most general technique used in rheology. The material is sheared unidirectionally and continuously until an equilibrium value for shear rate is obtained under a constant shew stress, or the converse. I t is desirable that the instrumentation be so designed that
Figure 1. The rheogoniometer, utilized only for steady-state investigations, is essentially a cone-and-plate viscometer
parameters can be precalculated from the geometry and cross-checked against calibrated values. The parameters of primary interest are the shearing stress, 7, and the rate of shear D (their ratio being called the viscosity, q ) , In addi. tion, some function of the elasticity should be derivable: this may be the recoverable shear strain, s, the shear modulus, G = T / S , or the normal stress, Px1 = T F = G J ~ . Three types of instruments are primarily employed for steady-state experiments. Rotational Viscometer. The first of tional viscometer, which lindrical assemblies designed according to Mooney and Ewart (9). Four assemblies are available: two are monoconical concentric cylinders which have been described in detail
(79); the other two are biconical concentric cylinders (2) which represent an extension of the Mooney-Ewart design. Experimental parameters have been discussed previously (76, 27), and numerous experimental results have been presented (7, 73). Capillary Viscometer. The second instrument is the high-pressure (gas) capillary tube viscometer. Nineteen stainless steel capillary tubes are available, ranging in diameter from 1.3 to 0.03 cm. and in length from 30 to 0.04 cm. This instrument has been described in the literature (ZO), and operating procedure has been given (7 7). Additional experimental data have been presented (7, 73, 78). Weissenberg Rheogoniometer. T h e third instrument is the rheogoniometer which was conceived as yielding, in VOL. 51, NO. 7
JULY 19591
8711
RATE OF S H E A R AND SHEAR STRESS RANGES LOG
D
-I
0 LOG
I
2
[ SHEARING
3
4
5
7
6
STRESS, DYN / C M 2
S L O G
]
Figure 2. Operating range of the viscometers can be expressed in terms of shearing stresses and shear rates obtainable
ideal form, complete rheological data by measuring the development with time of stresses and strains throughout the whole solid angle (6). It has been designed with a flexibility of operation that permits both steady-state (continuous unidirectional shear) and dynamic (harmonic oscillatory shear) experiments to be performed. T h e rheogoniometer in these laboratories has been used only for steady-state investigations of viscoelastic materials. This instrument, so utilized, is essentially a cone-and-plate viscometer (Figure 1). Rheological parameters and theoretical fundamentals have been discussed in the literature (2, 6, 76, 2 3 ) ; experimental results have also been given (7, 73, 78). Operating range for this instrument, as well as for the two viscometer assemblies, are shown in Figure 2 in terms of over-all shearing stresses and rates of shear obtainable with the present assemblies.
Figure 3.
The vibration tester can be used with a number
of different stressing devices
instrument was developed consisting of a cylinder and piston. T h e test fluid is forced through the cylinder a t a preselected, fixed rate and expelled through a cylindrical nozzle. The jet extrusion apparatus has been described in detail recently ( 5 ) . Investigations conducted with this instrument are concerned primarily with determining the influence of rheological properties of viscous and viscoelastic fluids on their behavior in extruded jets. This covers such aspects as: mechanism of jet disintegration, control of jet breakup, and the relationship between flight velocities obtained and rheological properties existent at the extrusion. Thest. investigations have led to the development, in incomplete form, of equations for calculating rheological properties of viscoelastic fluids from velocity relationships obtained on extrusion. This offers the possibility of eventually correlating jet extrusion parameters to other rheological parameters.
Jet Extrusion Instrument
Among the properties of viscoelastic materials of interest is the behavior of these fluids in free-flying jets. Past work has defined these properties for simple viscous liquids; however, little work has been done on viscoelastic fluids. T o conduct such investigations, a jet extrusion
872
Dynamic instruments
Viscoelastic liquids arc knowii to h a v r mechanical properties depending on the frequency of shear vibrations (14). The viscosity termed 8' decreases with increasing frequency, and the elasticity described by the shear modulus, G'.
INDUSTRIAL AND ENGINEERING CHEMISTRY
increases with frequency. These measurements have been made possible by a number of instruments termed dynamic or vibration testers. Three such instruments are in use in these laboratories. Vibration Tester. T h e dynamic tester (Figure 3) developed here has been partially described (12, 22). Its basic principle lies in the use of a mechanically driven cam shaft, the rotation of which is transformed into a reciprocating motion; the cam has a variable eccentricity. This motion is transferred Lhrough a strain gage to the sample holder and the displacement of the sample relative to the frame of the instrument is recorded. Frequency can be changed by means of gear boxes over a wide range. The instrument allows a number of stressing devices to be used, including a bending (beam) arrangement, a shear arrangement, and a pumping arrangement with two inner cylinders. Results with these three devices have been so correlated that a continuous curve using all three arrangements can be obtained. The vibration tester has been used for a wide variety of materiaIs in a range of temperatures between -20" and 300" C. and at frequencies between 10 cycles and 50 hours per cycle. Compressibility Tester. In addition, there is a compressional arrangement for
NOW-NEWTONIAN FLUIDS rubber and a compressibility cell for measuring the dynamic compressibility or bulk modulus as a function of frequency and temperature (77). These units are incorporated in the machinery of the vibration tester. Torsion Crystal. The torsion crystal apparatus, designed according to principles established by Mason ( 8 ) has been described rather completely (24, 25). I t consists of a cylindrical quartz crystal, which is connected electrically while fully immersed in the fluid under investigation and then excited into resonance. A comparison is made of the resonant frequencies and electrical resistance of the crystal in the test fluid and in either the pure solvent, if the fluid is a solution, or in air. From the change in frequency and resistance, dynamic properties can be calculated. The present setup allows measurements to be made at a fundamental frequency of about 20 kc. Resonant frequencies of 40, 60, and 100 kc. are obtainable with some additions to the instrument. The temperature can be varied as much as desired; then the data can be treated by Ferry’s method of reduced variables ( 4 ) . Some data from the torsion crystal, correlated with other dynamic data, have been published (22).
Flow Birefringence Instrument The investigation of flow birefringence is important to rheology as an independent way of ascertaining changes in flowing liquids. Recently attempts have been made to correlate the results of flow birefringence measurements, namely the degrep of birefringence, An, and the
extinction angle, x, with mechanical properties (7, 70). Numerous investigations have shown the importance of extinction angle measurements which give the possibility of calculating recoverable shear, s. The flow birefringence instrument of the Franklin Institute (Figure 4) has been designed according to classical principles. It has a concentric cylinder arrangement (inner rotating cylinder) with a beam of linear polarized light traveling miall) in the annulus. Three inner cylinders are used. The bores of the outer cylinder and the inner cylinders are highly polished hardened stainless steel. The inner cylinder is mounted on two pairs of prestressed ball bearings held on the driving shaft with a cone and driven by a synchronous motor through a decade gear selector. The optical arrangement is mounted on a very rigid optical bench, the illumination being adapted from Cerf ( 3 ) . The determination of x is made using the Bravais plate; An is measured by either a Senarmont compensator or a Solei1 compensator. The polarizer is rigidly connected to the analyzer, so that they can be locked together and swung around the beam of light for f 4 5 ’ . Observations are made through a microscope. T h e optical arrangement gives a sensitivity for the measurement of An of 4 X 10-8 units per degree of the Senarmont compensator. Adjustment of the compensator can be made at a sensitivity of around 10- units in An. The Bravais plate gives good operation with colorless solutions and allows x to be measured at small values of An. The probable error in the measurement
of extinction angle is between and The highest rate of shear used was 34,600 seconds-’ with the 0.4-mm. gap; the lowest one was 0.0008 second-’ with a 3.5-mm. gap. The shearing stresses are measured independently in the viscometers described previously. Further discussion of the flow birefringence instrument, together with many experimental results, has been presented (7, 2, 73, 75).
literature Cited
.,
11) Brodnvan. J. G.. Gaskins. F. H.. Philippdff, ‘W., Trans. SOC.Rheology 1 ; . 109 (1957). (2) Brodynan, J. G., Gaskins, F. H., Philippoff, W., Lendrat, E. G., Ibid., in press. (3) Cerf, R., Ph.D. dissertation, University of Strasbourg, France, 1951. (4) Ferry, J. D., Fitzgerald, E. R., Grandine, L. D., Williams, M. L., I N D . ENO.CHEM.44, 703 (1952). (5) Gaskins, F. H., Philippoff, W., Trans. Soc. Rheology 3, (1959); Rept. of Symposium VIII, “Spray Dissemination of Agents”(c), U. S. Army Chemical Center, Edgewood, Md., 1958. (6) Jobling, A., Ph.D. dissertation, University of Cambridge, England, 1955. ( 7 ) Lodge. A. S.. Nature 176, 838 (1955). (8) Mas%, W. P.,Trans. Am. SOC.Mech. Eagrs. 69, 359 (1947). (9) Mooney, M., Ewart, R. M., Physics 5. 350 11934). (IO) Peterlin, A,, Signer, R., Helv. Chim. Acta 36, 24 (1953). (11) Philippoff, W., Am. SOC.Lubricating Enps. Trans. 1, 1 (1958). (12) Philippoff, W., J . Appl. Phys. 24, 685 (1953); 25, 1102 (1954). (13) Z6id., 27, 9 (1956); Nature 178, 811 (1956). (14) Philippoff, W., Physik. Z . 35, 88, 900 11934). (15) Philippoff, W., Rheolog. Acta., in press; Trans SOC.Rheology 3, (1959). (16) Zbid., 1, 95 (1957). (17) Philippoff, W., Brodynan, J., J . Appl. Phys. 26, 846 (1955). (18) Philippoff, W., Galkins, F. H., J . Phys. Chem., in press. (19) Philippoff, W., Gaskins, F. H., J . Polymer Sci. 21, 205 (1956). (20) Philippoff, W., Gaskins, F. H., Trans. Sod. Rheoloqy, .,. in press. (21) Philippoff, W., Gaskins, F. H., Brodnyan, J. G., J . Appl. Phys. 28, 10 \
I
.
.
,
I
(I 957) ,-,~,,.
(22) Philippoff, W., Sittel, K., Ferry, J. D., Plazek, D. J., SPE Journal 11, 7 (1955). (23) .Roberts, J. E., Ministry Supply (Gr. Brit.), Rept. A.D.E. 13/52 (1952) ; D4-54-Rl4.2 (1954) ; Proc. 2nd Intern. Congr. Rheol., 1953, Academic Press, New York, 1954. (24) Rouse, P. E., Jr., Sittel, K., J . ApPl. Phys. 24, 690 (1953). (25) Sittel, K., Rouse, P. E., Jr., Bailey, E. D., Ibid., 25, 1312 (1954). \
Figure 4. Observations are made in the flow birefringes instrument with a microscope
,
RECEIVED for review January 15, 1959 ACCEPTED February 18, 1959 VOL. 51, NO. 7
JULY 1959
873
