Lab 11: Rheology
I. Purpose
The purpose of this lab is to study the isothermal crystallization behavior of
poly(-caprolactone), PCL as a function of crystallization temperature, angular
frequency, and shearing time using a Rheometeric dynamic mechanical spectrometer.
II. Background
Dynamic rheology is a powerful tool to monitor gelation (or cross-linking) and
microstructural changes in a material, as it allows properties to be probed in at rest
conditions without disruption of the microstructure. In addition, it is quite an effective
method for studying the curing process of thermosetting polymers and for the
examination of the viscoelastic properties and transition temperatures of the cured
products. The formation of polymer gels can be monitored from the time evolution of
viscoelastic material functions, such as dynamic shear moduli, G′ and G", complex
viscosity, *, and loss tangent, tan  (see Figures 1 and 2) at the gel point, where the
entire network process can be divided into two parts separated by the gel point.
Chemical gels are known to be typically formed via gradual branching of linear
chains into a cluster that are interconnected via covalent bonds, leading to a three
dimensional polymer network structure. The network structure can also be formed
physically (physical gels), where the polymer chains are connected together to form the
networks by different kinds of physical forces, such as hydrogen bonds, electrostatic
attraction, and van der Waals forces. Crystallization in polymers occurs through a
nucleation and growth mechanism. Early stages of crystallization of polymers may be
viewed as thermoreversible physical gelation in which molecular connectivity is
introduced by crystallization. The evolution of the dynamic moduli at early stages of
crystallization was found to have the same universal pattern as chemical gelation. The gel
point, tgel can be rheologically obtained by the point of intersection in tan  vs gelation
time for different constant shear frequencies, where tan  is angular frequency
independent and all curves crossover (see Figure 3). The value of tgel can also be
evaluated from the coincidence of G′ and G" at a given angular frequency.
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Figures from S. Madbouly & T. Ougizawa “Rheological Investigation of Shear-Induced Crystalization of
Poly(ε-Caprolactone)” Journal of Macromolecular Science, vol. B42, No. 2, pp. 269-281, 2003.
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Figure 3. The precise gel point of a curing resin is identified by the intersection of tan 
curves generated in several simultaneous frequency sweeps.
III. Introduction to the Rheometer
Rheology is the flow of fluids and deformation of solids under various kinds of
stress and strain. A rheometer, therefore, measures material behavior such as yield stress,
complex viscosity, modulus, creep, and recovery.
1. Instrument components
The AR 2000ex rheometer used in this laboratory contains an electronicallycontrolled induction motor with an air bearing support for all the rotating parts. The air
bearing is one that utilizes air as the lubricating medium. This allows virtually frictionfree application of torque.
The measurement of angular displacement is achieved by an optical encoder. This
device can detect very small movements down to 4×10-8 rad. The encoder consists of a
non-contacting light source and photocell arranged either side of a transparent disc
attached to the drive shaft. On the edge of this disc are extremely fine, accurate
photographically-etched radial lines. Therefore, this is a diffraction grating. There is also
a stationary segment of a similar disc between the light source and encoder disc. The
interaction of these two discs results in diffraction patterns that are detected by the
photocell.
As the encoder disc moves when the sample strains under stress, these patterns
change. The associated circuitry interpolates and digitizes the resulting signal to produce
digital data. This data is directly related to the angular deflection of the disc, and,
therefore, the strain of the sample.
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2. Parallel Plate Measuring System
The parallel plate geometry is often used to measure the viscosity of polymer
melts and suspensions. It can accommodate simple sample geometries and is easy to
maintain. The main disadvantage of a parallel plate system is that the stress is not
uniform across the entire diameter. However, the software compensates for this fact. The
shear stress and shear rate factors given are with respect to the rim.
Stress and shear rate factors for a parallel plate can be used to determine the
maximum stresses and shear rates available with a particular diameter and gap. The
standard diameters of parallel plates available are 20 mm, 40 mm and 60 mm. In our
experiment, a parallel plate with a diameter of 40mm is applied. A schematic of a
parallel plate system is shown below. Information is given for the calculation of the shear
stress and shear rate.
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IV. Sample and Experiments
1. Sample
Poly(-caprolactone) (PCL) represents an important class of semicrystalline,
biodegradable, and biocompatible polyester with melting point and glass transition
temperature of approximately 60 and −60 °C, respectively. The PCL was provided by
Union Carbide Corporation (PCL-767). The molecular weight and polydispersity of the
PCL were 40,400 g/mol and 2.61, respectively. About 1 g of the sample was melted and
pressed between two metal plates at 100 oC to prepare a sample specimen of 25mm
diameter and 1mm thickness.
2. Experiments:
The viscoelastic measurements will be carried out using a Rheometeric dynamic
mechanical spectrometer (model AR 2000) using two 25-mm diameter parallel plates
with strain rate of 1%. The experiments involved the following steps;
a. Rapid heating of the sample disc to the melting temperature, Tm = 80 oC.
b. Holding the molten sample at Tm for the period tm = 3 min to obtain an isotropic
melt and erase the memories of previous treatments.
c. Cooling the sample at 2 oC/min cooling rate under constant different angular
frequencies (10-100 rad/s) and 1% strain. This step can be used to evaluate the
gelation temperature, Tgel.
d. Once Tgel is determined, steps 1 and 2 will be repeated again and the molten
sample will be quenched to crystallization temperature, Tc, should be very close to
the value of Tgel.
e. The isothermal crystallization process will be carried out under different angular
frequencies (10-100 rad/s) and 1% strain.
V. Procedure
1. PRE-TEST SYSTEM CHECK: Check the Cooling System:
a. Air flow: Close doors and check air flow gage behind rheometer. You should hear
a hissing sound from the rheometer.
b. Active Cooling: Check LN2 level in tank and make sure connectors are tight.
2. INSTRUMENT SETUP:
Parallel Plates: install plates (used or new) which have been cleaned with solvent and
Kimwipes.
a. Top plate:
Install the plate into the shaft (at the end where two machine screws are located),
pushing down until the plate is flush with the rim. Holding the plate to the shaft,
use an Allen wrench to snug machine screws. NOTE: Machine screws securing
the parallel plates should not be over-tightened!
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Install shaft: hold shaft still with one hand and insert it into head at the bottom of
upper part of the rheometer. Then tighten the thumb screw at the top of the
rheometer with the other hand.
b. Lower plate: Place lower plate into the center hole on the stage and hold down as
you snug the two machine screws with the allen wrench.
3. SOFTWARE INPUTS:
a. The “Dashboard” tab (AR-2000): This screen displays the rheometer conditions
before testing and parameters changes during running.
Temperature: If test is to occur at a temperature other than room temperature,
begin to heat or cool the plates beforehand by double-clicking the
Temperature box in the Required Value column.
Set
Temperatu
re
AR2000
tab
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b. 25 mm ETC Disposable Aluminum Plate tab: at this time, these are the only
plates being used on the rheometer. Don’t change any parameters in this tab unless a
different geometry is being used.
c. Zero the gap: after Software inputs are set and temperature in the rheometer has
stabilized at the starting temperature, you need to zero the gap.
i. Click the Zero the Gap button,
, located on the left side of the panel.
ii. Using the down arrow on the left-side of the dashboard screen, lower the plates
until the Gap value is < 5mm.
iii. Making sure the gap is less than 5 mm, click Continue.
iv. When the gap is zeroed, a message will read:
Click OK. Zero the gap is finished.
4. SAMPLE PREPARATION AND LOADING:
a. Raise the upper plate several centimeters (enough to put the sample disk on the
lower plate).
b. Slowly push sample onto the center of the lower plate.
c. Lower the head, until the head near sample surface, then slowly lower it until the
sample completely fills the plates (~500 microns).
g. When gap is set, close oven doors, check parameters, and click the green arrow
denoting Start the run.
The real gap may much less or larger than pre-set 500 microns, and a message
will read: “Set the correct gap before proceeding?”
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Click “No” anyway, and experiment will start. The software compensates the
gap value.
5. Procedure:
a. Conditioning Step: This is where the initial temperature and liquid nitrogen
controls are located. Turn on/off the liquid nitrogen for the test by clicking the
advanced tab and checking (off) or unchecking (on) the Purge gas only (no active
cooling) box. Under Settings tab, change equilibration duration to 3 min, in order to
reach thermal equilibrium of your sample prior to the test.
b. Temperature Ramp Step: In this type of test, temperature is the ramping variable.
Enter initial and final temperatures at 80 and 20 oC and ramp rate at 2 oC /min. After
that, set strain at 1% and multiple angular frequencies from 10 to 100 rad/s (log
mode).
c. Time sweep Step: This is the test type used in our experiment. Under test tab, test
type is set to Time Sweep. There are four main variables, Duration,
Temperature, %strain and angular frequency. In our experiment, set 30 min duration
time, temperature at 40 oC, strain at 1%, and multiple angular frequency from 10 to
100 rad/s (log mode).
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d. Post-Experiment Step: This step is handy if you won’t be at the controls when
the test is completed. Set a temperature for your choice by entering it in the box.
e. File name tab: enter desired sample and file names, checking to see them in the
directory.
6. POST-TEST:
a. When run is over, set temperature value to 80 °C to melt the sample.
b. Remove sample: raise head several centimeters and then holding the shaft above the
top plate in place, loosen the screw at the top of the rheometer by hand. Remove shaft as
before. To remove plate, loosen the two machine screws holding the plate to the shaft
and pull plate off. The lower plate can be removed by loosening the two machine screws
and lifting off of the stage. Then wash plates using solvent and kimwipes.
VI. Assignment/Discussion Items
1.
2.
3.
Determine the value of Tgel at different angular frequencies.
Describe the gelation time dependence of G′, G", *, and tan  at different
angular frequencies at T = 40 oC.
Calculate the value of tgel at T = 40 oC by two different methods.
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