Comparison of the Complex Dynamic Modulus as Measured by Three

Chapter 3

Comparison of the Complex Dynamic Modulus as Measured by Three Apparatus 1

2

2

James J. Dlubac , Gilbert F. Lee , James V. Duffy , Richard J. Deigan , and John D. Lee 1

2

1

Ship Acoustics Department, David Taylor Research Center, Bethesda, MD 20084-5000 Nonmetallic Materials Branch, Naval Surface Warfare Center, Silver Spring, MD 20903-5000

2

This chapter compares complex dynamic modulus data on two v i s c o e l a s t i c materials obtained with three apparatus: (1) a forced t o r s i o n a l apparatus that determines shear modulus from the r e l a t i v e amplitude and phase at the ends of a harmonically torqued r i g h t c i r c u l a r cylinder, (2) a resonance apparatus that measures the Young's modulus by analyzing the response of a bar sample at extensional resonance, and (3) a cantilever beam bending apparatus that i s used to determine the Young's modulus. Inallof these apparatus, the complex dynamic modulus i s measured over a l i m i t e d frequency range at a number of fixed temperatures. Time-temperature superposition i s then employed to generate master curves of modulus and loss factor at a fixed temperature over a very broad frequency range. The data presented here spans the glass t r a n s i t i o n of the two polyurethane materials. One material has a low, broad t r a n s i t i o n and the other has a high, sharp t r a n s i t i o n . Good agreement was found among the d i f f e r e n t apparatus f o r both materials, but more care must be taken when measuring a sharp t r a n s i t i o n . I tisconcluded that the three apparatus give reasonably consistent data, a sharp t r a n s i t i o n is more s e n s i t i v e t o the t e s t i n g procedure, and the s h i f t i n g algorithm used i n the time-temperature superposition must be considered as part of the t e s t technique when comparing data. This chapter not subject to U.S. copyright Published 1990 American Chemical Society

50

SOUND AND VIBRATION DAMPING WITH POLYMERS

The design of e f f e c t i v e sound and v i b r a t i o n damping m a t e r i a l s assumes an understanding of the mechanisms c o n t r o l l i n g the d i s s i p a t i o n process and knowledge of candidate m a t e r i a l p r o p e r t i e s . The use of v i s c o e l a s t i c m a t e r i a l s as sound and v i b r a t i o n absorbers i s wide-spread and well-known. Accurate measurement of the complex dynamic moduli of these m a t e r i a l s i s t h e r e f o r e v i t a l t o the c o n t r o l of a c o u s t i c and v i b r a t i o n a l energy. This chapter d i s c u s s e s and compares t h r e e apparatus used t o measure the dynamic modulus of v i s c o e l a s t i c m a t e r i a l s . DESCRIPTION OF APPARATUS Various methods (1-3.) have used t o determine the dynamic mechanical p r o p e r t i e s of polymers. Many of the instruments d e s c r i b e d are w e l l known and are widely used ( t o r s i o n a l pendulum, rheovibron, v i b r a t i n g reed, and Oberst beam ASTM D4065-82). Newer instruments l i k e the torqued c y l i n d e r apparatus (4), resonant bar apparatus (5) and Polymer L a b o r a t o r i e s Dynamic Mechanical Thermal Analyzer (6) are becoming more popular i n r e c e n t times. I t i s of i n t e r e s t of t h i s chapter t o show t h a t these newer instruments are accurate and easy t o use. Each device considered i n t h i s chapter determines the complex dynamic modulus from a t h e o r e t i c a l d e s c r i p t i o n of the measurement. These d e s c r i p t i o n s or s o l u t i o n s are d e r i v e d by making assumptions about the experiment. The degree t o which these assumptions are r e a l i z e d determines the accuracy of the measurement. The most important and r e s t r i c t i v e assumptions are those concerning the boundary c o n d i t i o n s , sample geometry and s t r e s s s t a t e . TORSION OF A CYLINDER. The complex dynamic shear modulus can be determined through the r e l a t i v e motion, amplitude and phase, of the ends of a dynamically torqued c y l i n d r i c a l sample (4). F i g u r e 1 i s a setup sketch of t h i s non-resonant experiment. The sample t o be t e s t e d i s bonded t o r i g i d d i s c s t o which are attached accelerometers. An o s c i l l a t o r y torque i s a p p l i e d t o the bottom of the sample through a f o r c e couple c r e a t e d by d r i v i n g two shakers i n phase. The a c c e l e r o m e t e r s s i g n a l s are a m p l i f i e d and f i l t e r e d before being measured by a phase angle voltmeter. A computer uses the a c c e l e r a t i o n amplitude and phase t o i n v e r t the t h e o r e t i c a l s o l u t i o n of the torqued c y l i n d e r t o i n f e r the r e a l p a r t of the shear modulus, G , and the l o s s f a c t o r = G / G where G i s the imaginary p a r t of the modulus. The sample, accelerometers, t o r s i o n s p r i n g , and shakers are a l l i n an environmental chamber. T o r s i o n a l waves are propagated through the sample and are r e s i s t e d at the top p l a t e by a t o r s i o n s p r i n g mounted t o a r i g i d frame. The t o r s i o n s p r i n g a t the top serves two f u n c t i o n s . F i r s t , the s p r i n g prevents s i g n i f i c a n t 1

1

fl

f

f1

3. DLUBAC ET AL.

Complex Dynamic Modulus Measured by Three Apparatus

bending o f t h e sample due t o a chance misalignment o f the shakers. T h i s i s p o s s i b l e s i n c e the "X" shape o f t h e s p r i n g has a bending s t i f f n e s s much g r e a t e r than i t s torsional stiffness. Secondly, the t o r s i o n s p r i n g f o r c e s the sample t o d i s t o r t while a l l o w i n g a measurable motion a t the top p l a t e . The frequency range o f the torqued c y l i n d e r apparatus i s 50 Hz t o about 1500 Hz. The temperature range o f the experiment i s -40°C t o 70°C. The maximum temperature i s l i m i t e d by the d u r a b i l i t y o f the shaker diaphragms. Though a thorough study o f the modulus and l o s s f a c t o r measurement ranges has not been conducted, c u r r e n t experience i n d i c a t e s t h e range o f the r e a l p a r t o f t h e shear modulus, G , i s 10 t o 10 dyn/cm ; t h e range o f l o s s f a c t o r i s from 0.05 t o 1.2. The instrument i s capable o f h a n d l i n g samples from 20 t o 90 mm i n diameter by 30 t o 150 mm i n h e i g h t . F o r these t e s t s , t h e sample dimensions were 50 mm diameter by 50 mm i n h e i g h t . An advantage o f such l a r g e samples i s t h a t measurements can be made o f the e f f e c t i v e shear modulus o f m a t e r i a l s with l a r g e inhomogeneities. A disadvantage i s t h a t thermal e q u i l i b r i u m takes longer t o achieve. T h i s lengthens the t e s t time r e q u i r e d . Measurements on the torqued c y l i n d e r apparatus a r e made i s o t h e r m a l l y , from 50 t o 1500 Hz, i n 5°C i n t e r v a l s s t a r t i n g a t -40°C. Thermal e q u i l i b r i u m time between temperature changes i s about 1.5 hours. T y p i c a l l y , a m a t e r i a l can be evaluated i n about 20 hours u s i n g t h i s method. For the worst case, c a l c u l a t i o n o f temperature r i s e w i t h i n the sample due t o mechanical energy d i s s i p a t i o n i s about 1°C. With heat l o s s from the sample, t h i s v a l u e should be lower. 1

7

11

2

EXTENSION OF A BAR. The complex dynamic Young's modulus can be i n f e r r e d through the response o f a sample b a r a t e x t e n s i o n a l resonance. The resonance apparatus (5) i s shown s c h e m a t i c a l l y i n Figure 2. An e l e c t r o m a g n e t i c shaker i s used t o d r i v e a t e s t sample (6.35 by 6.35 by 100 mm) a t one end while the other end i s allowed t o move f r e e l y . M i n i a t u r e accelerometers are a d h e s i v e l y bonded on each end t o measure the d r i v i n g p o i n t a c c e l e r a t i o n and the a c c e l e r a t i o n o f the f r e e end. The weight o f t h e accelerometer and mounting b l o c k i s about 3 grams. The output s i g n a l s from the accelerometers a r e a m p l i f i e d by charge a m p l i f i e r s . The output from the charge a m p l i f i e r s are routed t o a dual channel Fast F o u r i e r Transform (FFT) spectrum a n a l y z e r . The analyzer d i g i t i z e s and d i s p l a y s the measured s i g n a l s as the amplitude and phase o f t h e acceleration ratio. The analyzer a l s o p r o v i d e s a random n o i s e source t o d r i v e the shaker and i s e f f e c t i v e over a frequency range o f t h r e e decades (25 Hz t o 25,000 Hz). The data are always sampled and rms averaged a t l e a s t 8 times, f o r low n o i s e data, and up t o 256 times, f o r noisy data. A minicomputer i s used t o c o l l e c t and s t o r e t h e data from the analyzer f o r l a t e r c a l c u l a t i o n s .

52


The spectrum analyzer i s used t o i d e n t i f y the resonant frequencies o f the sample. The number of resonant modes t h a t can be measured i s dependent on the l o s s f a c t o r o f the m a t e r i a l . At low l o s s , on e i t h e r the g l a s s y s i d e o r the rubbery s i d e o f the g l a s s t r a n s i t i o n , four t o f i v e resonant modes are e a s i l y measured on the a n a l y z e r . As expected, the resonant modes appear a t h i g h e r frequencies i n the g l a s s y s t a t e than i n the rubbery s t a t e . At the g l a s s t r a n s i t i o n o f the m a t e r i a l , where the l o s s i s high, only three t o four resonant modes can be measured. The higher frequency resonant modes (modes 4 and 5) are not d e t e c t a b l e . From the peak amplitude and frequency, t h e r e a l p a r t of the Young's modulus (E') and the l o s s f a c t o r are determined as f u n c t i o n s of frequency and temperature. The resonant apparatus can measure E' from 10 t o 10 dyn/cm and l o s s f a c t o r over the range of 0.01 t o 5.0. In making the measurements, the f o l l o w i n g thermal c y c l e i s used: c o o l the t e s t sample (mounted i n the apparatus) from room temperature t o -60°C. The sample i s allowed t o soak a t -60°C f o r a t l e a s t 12 hours. Measurements are then made as the temperature i s r a i s e d i n 5°C i n t e r v a l s . Approximately 20 minutes a r e allowed a f t e r a temperature change t o o b t a i n thermal e q u i l i b r i u m i n the sample. The operating temperature range i s -60°C t o 70°C. The time r e q u i r e d t o complete the measurements i s about 24 hours. Since the system i s automated, the instrument can run unattended o v e r n i g h t . The frequency range f o r a t y p i c a l s e t of measurements i s from 1 t o 15 kHz. Conservative c a l c u l a t i o n of temperature r i s e w i t h i n the sample due t o mechanical energy d i s s i p a t i o n i s very much l e s s than 1°C. 5

13

2

BENDING OF A BEAM. The complex dynamic Young's modulus can be determined from the forced, non-resonant o s c i l l a t i o n s of a s i n g l e or double c a n t i l e v e r beam. The apparatus considered i n t h i s paper i s the Dynamic Mechanical Thermal Analyzer (DMTA) (6), manufactured by Polymer L a b o r a t o r i e s , Inc. Figure 3 shows t h e experimental setup f o r the s i n g l e c a n t i l e v e r measurement. A t h i n sample i s clamped a t both ends. One end i s attached t o a c a l i b r a t e d shaker through a d r i v e s h a f t . The f o r c e and displacement are measured a t the d r i v e n end f o r each f i x e d frequency. The low frequency/low mass bending s o l u t i o n i s used together with the measured input impedance t o i n f e r the Young's modulus and l o s s f a c t o r . The DMTA operates a t f i x e d frequencies over a broad temperature range. Sixteen d i s c r e t e frequencies from 0.01 Hz t o 200 Hz are a v a i l a b l e . The very low frequencies, below about 0.1 Hz, r e q u i r e a long time t o complete, while frequencies above 30 Hz a r e o f t e n near o r above the system resonance and r e q u i r e s p e c i a l c o n s i d e r a t i o n . Though the system i s capable o f a


DLUBAC ET AL.

F i g u r e 1.

Torqued

cylinder

apparatus.

ENVIRONMENTAL CHAMBER

RANDOM NOISE SHAKER-

SPECTRUM ANALYZER

ACCELEROMETERS

F i g u r e 2.

SAMPLE

FRAME

Resonance apparatus.

CLAMP CLAMP

DISPLACEMENT TRANSDUCER CALIBRATED SHAKER _ (CURRENT PROP TO FORCE)

F i g u r e 3. Dynamic mechanical apparatus.

ENVIRONMENTAL CHAMBER DRIVE SHAFT J FIXED FREQUENCY | thermal a n a l y z e r

(DMTA)

54


temperature range from -150°C t o 300°C, runs much above 100°C tend t o o v e r l y s o f t e n the samples of i n t e r e s t and i n some cases the samples begin t o melt. Only the sample, i t s clamps and p a r t of the d r i v e s h a f t are i n the temperature-controlled chamber. The DMTA can measure E' over the range 10 t o 10 dyn/cm and l o s s f a c t o r over the range o f 10" t o 9.99. Length t o t h i c k n e s s r a t i o from 4 t o 6 mm are encouraged i n t h i s experiment t o optimize sample s t i f f n e s s through the e n t i r e range of modulus. Three clamps are a v a i l a b l e with s i n g l e c a n t i l e v e r beam spans ranging from 5 mm t o 18 mm. Sample widths are t y p i c a l l y about 10 mm while the t h i c k n e s s can range up 5 mm. For the measurements reported here, a length about 12 mm and a t h i c k n e s s of 3 mm was used. The dynamic modulus and l o s s f a c t o r data was c o l l e c t e d i s o t h e r m a l l y from 30 t o 0.30 Hz. M a t e r i a l e v a l u a t i o n r e q u i r e s about 4 hours. S p e c i a l care must be e x e r c i s e d i n clamping the DMTA samples i n t o p l a c e . Samples were prepared by bonding aluminum b l o c k s t o each end with epoxy adhesive. The epoxy was chosen such t h a t , together with the bond t h i c k n e s s , the s t i f f n e s s of the adhesive i s always much g r e a t e r than the sample. The advantage of u s i n g the aluminum b l o c k s i s t h a t the assumed sample boundary c o n d i t i o n s are obtained a t a l l temperatures and f r e q u e n c i e s . The b l o c k s a l s o prevent sample p i n c h i n g when d i r e c t l y clamping t o the sample. Sample p r e p a r a t i o n techniques u s i n g aluminum b l o c k s and a s h i f t i n g algorithm are not provided by the manufacturer of the DMTA and were developed independently. Conservative c a l c u l a t i o n of temperature r i s e w i t h i n the sample due t o mechanical energy d i s s i p a t i o n i s l e s s than 1°C. 6

12

2

4

PARAMETER RANGE COMPARISON. Table I summarizes the parameter ranges of the torqued c y l i n d e r apparatus, the resonance apparatus and the DMTA. Since the bulk moduli of the m a t e r i a l s under c o n s i d e r a t i o n i n t h i s paper are much l a r g e r than the Young's or shear moduli, the m a t e r i a l s are considered incompressible. For incompressible m a t e r i a l s , the shear modulus i s one t h i r d of Young's modulus. Comparisons are then made by c o n v e r t i n g Young's modulus t o shear modulus f o r the data measured by the resonance apparatus and the DMTA.

TIME-TEMPERATURE SUPERPOSITION PROCEDURE Almost always the data from the apparatus above i s analyzed by u s i n g the time-temperature s u p e r p o s i t i o n p r i n c i p l e t o form a master curve over a wide frequency range a t a s e l e c t e d r e f e r e n c e temperature. The b a s i s f o r t h i s procedure i s t h a t f o r t h e r m o r h e o l o g i c a l l y simple m a t e r i a l s the e f f e c t of a change i n temperature on

3. DLUBAC ET AL.


Table I . Comparison o f Dynamic Modulus Apparatus DEVICE

FREQ (Hz)

TEMP (°C)

LOSS REAL MODULUS FACTOR dyn/cm 2

Torqued Cylinder

50 t o -40 t o 1500 70

7

10 t o 10 11

0.05 to 1.2

SAMPLE SIZE (mm)

50 d i a Large samples x 50 = 9.8 x 10 mm 4

Resonant Bar

2.5 t o -60 t o 25,000 70

5

10 t o 10 13

0.01 to 5.0

0.01 to 200

-150 to 300

6

10 t o 10 12

4

10" to 9.99

3

Exten6x6x 150 sion of = 5.4 x a b a r 10 mm 3

DMTA Beam

REMARKS

3

3x10 xl2 = 3.6x 10 mm 2

Bending of a beam

3

complex modulus i s i n d i s t i n g u i s h a b l e from a change i n frequency (7). Thus, making measurements over a range o f temperatures i s e q u i v a l e n t t o making measurements over a range o f f r e q u e n c i e s . The advantage o f t h i s i s t h a t temperature measurements are much e a s i e r t o make than frequency measurements. In most cases, t h e a c t u a l frequency measurements are not made a t the frequency o f i n t e r e s t but one can determine what the p r o p e r t i e s would be a t t h e frequency o f i n t e r e s t u s i n g time-temperature s u p e r p o s i t i o n . S p e c i f i c a l l y , i n t h i s study t h e t h r e e apparatus do not operate i n the same frequency range and a d i r e c t comparison o f r e s u l t s would not be p o s s i b l e without s u p e r p o s i t i o n . Thus the f i n a l comparison depends not only on the instruments but how the data i s analyzed. While the p r i n c i p l e o f s u p e r p o s i t i o n i s w e l l e s t a b l i s h e d , s i g n i f i c a n t d i f f e r e n c e s can r e s u l t i f the implementation of t h e s h i f t i n g i s not done i n a c o n s i s t e n t manner. F o r t h i s reason, t h e s u p e r p o s i t i o n procedure used w i l l be d e s c r i b e d i n some d e t a i l . F i g u r e 4 i l l u s t r a t e s the mechanics o f t h e p r i n c i p l e . Data c o l l e c t e d a t v a r i o u s temperatures i s s h i f t e d along the l o g frequency a x i s t o form a modulus curve over an extended frequency range. The incremental s h i f t along the l o g frequency a x i s , represented by the change i n t h e s h i f t f a c t o r ( l o g a ) , i s summed t o form t h e s h i f t curve as i l l u s t r a t e d i n F i g u r e 5. The mechanics o f s h i f t i n g was performed by u s i n g an a l g o r i t h m implemented on a computer. No attempt was made t o f i t the frequency s h i f t versus temperature t o the W i l l i a m s - L a n d e l - F e r r y (WLF) equation (3.) , though u s u a l l y the f i t i s good i n the g l a s s t r a n s i t i o n region. T

56


DATA

2

3

0

1 2 3 LOG REDUCED FREQUENCY

4

5

F i g u r e 4. Time-temperature s u p e r p o s i t i o n .

LOG FREQUENCY

5

F i g u r e 5. C o n s t r u c t i o n o f a s h i f t

4

TEMP

curve.

The s p e c i f i c algorithm used was as f o l l o w s . The l o g modulus v s l o g frequency data a t each temperature was l e a s t square f i t t e d t o a l i n e a r equation t o determine the slope o f the data. T h i s slope i s equal t o the d i f f e r e n c e i n l o g modulus, a t a given frequency, between two s e t s o f data d i v i d e d by the d i f f e r e n c e i n l o g frequency. The d i f f e r e n c e i n l o g frequency i s the change i n s h i f t factor, l o g a . When implementing t h i s procedure, data at the r e f e r e n c e temperature i s f i x e d , while data a t the other temperatures are s h i f t e d r e l a t i v e t o the r e f e r e n c e temperature. Note t h a t the l o s s f a c t o r data i s not used i n determining the s h i f t . For the apparatus d i s c u s s e d here, the modulus measurements are more accurate than the l o s s measurements and g i v e more r e l i a b l e s h i f t . The l o s s T

3. DLUBACETAL.

Complex Dynamic Modulus Measured by Three Apparatus 57

f a c t o r data are s h i f t e d u s i n g the same l o g a 's t h a t are used f o r the modulus, and the smoothness of the r e s u l t i n g curve i s an independent i n d i c a t i o n of the v a l i d i t y o f the s h i f t function. T

MATERIALS Polyurethanes were chosen f o r t h i s study because these m a t e r i a l s are becoming more widely used i n sound and v i b r a t i o n damping and because they o f f e r a wide range of m a t e r i a l p r o p e r t i e s a g a i n s t which t o compare the apparatus. In p a r t i c u l a r , of the two m a t e r i a l s chosen f o r t h i s study, one has a broad g l a s s t r a n s i t i o n and the other has a narrow g l a s s t r a n s i t i o n . Therefore, with these two samples, a more s t r i n g e n t t e s t can be made on the apparatus. The polyurethanes are prepared from a prepolymer of poly(tetramethylene e t h e r ) g l y c o l (nominal molecular weight of 1000) and 4,4 -diphenylmethane d i i s o c y a n a t e i n which the molar r a t i o of the two components i s 1 t o 3. The prepolymer i s c h a i n extended with e i t h e r 1,4-butanediol, forming a polymer designated as HOI, or with, a 50/50 mixture of 1,4-butanediol and 2,2-dimethyl-1,3-propanediol, which i s designated as H14. The s y n t h e s i s and d e t a i l s of the chemical components are d i s c u s s e d i n another chapter of t h i s book ( J . V. Duffy, et a l . , E f f e c t s of D i o l Chain Extenders S t r u c t u r e on the Dynamic Mechanical P r o p e r t i e s of PTMG Polyurethanes). A c a u t i o n a r y note when u s i n g polyurethanes. There can be c o n s i d e r a b l e v a r i a t i o n i n p r o p e r t i e s depending on the p r o c e s s i n g technique even when the chemical composition i s nominally the same. For t h i s reason, i t i s important t o do q u a l i t y c o n t r o l checks t o v e r i f y t h a t the m a t e r i a l evaluated i n the three apparatus i s i n f a c t the same. Two good ways t o c h a r a c t e r i z e polymeric m a t e r i a l s are the d e n s i t y and g l a s s t r a n s i t i o n temperature. The g l a s s t r a n s i t i o n temperature i s p a r t i c u l a r l y important s i n c e i t governs the dynamic mechanical response of the m a t e r i a l . Density and g l a s s t r a n s i t i o n temperatures are l i s t e d i n Table I I . Glass t r a n s i t i o n temperature, T , values were determined i n a d i f f e r e n t i a l scanning c a l o r i m e t e r and d e n s i t y v a l u e s were obtained by water immersion. 1

g

Table I I . polymer H01 H14

Material Properties 3

d e n s i t y , g/cm 1.139 1.107

T ,°C g

-48 0

One of the f i r s t attempts t o compare the apparatus was not s u c c e s s f u l because the m a t e r i a l used f o r the t h r e e t e s t samples was found t o have a s i g n i f i c a n t l y d i f f e r e n t g l a s s t r a n s i t i o n temperature. T h i s m a t e r i a l was then e l i m i n a t e d from f u r t h e r c o n s i d e r a t i o n .

58


RESULTS Figures 6, 1 and 8 are shear modulus and l o s s f a c t o r master p l o t s f o r HOI as c o l l e c t e d by each o f the three apparatus. Note t h a t the l e f t o r d i n a t e i s l o g G', t h e r i g h t o r d i n a t e i s l o s s f a c t o r and the a b s c i s s a i s l o g frequency. In each case, the p l o t t i n g r e f e r e n c e temperature i s 10°C. The s h i f t e d data c o l l e c t e d by the torqued c y l i n d e r apparatus i s shown i n F i g u r e 6. The i n d i v i d u a l temperature runs are apparent as groups o f data, e s p e c i a l l y i n the g l a s s y r e g i o n . T h i s i s a d i r e c t consequence o f the l i m i t e d frequency range o f t h e apparatus. Overlapping data c o u l d be obtained, i f the measurement was made a t more c l o s e l y spaced temperatures, thus g r e a t l y i n c r e a s i n g the time r e q u i r e d f o r t h e measurement. There i s almost no s c a t t e r i n the G data, but there i s some s c a t t e r i n the l o s s f a c t o r data near the t r a n s i t i o n . These r e s u l t s are t y p i c a l i n t h a t modulus measurements g e n e r a l l y show l e s s s c a t t e r than l o s s f a c t o r measurements and are considered t o be more accurate. F i g u r e 7 contains the s h i f t e d data o f the resonant bar apparatus f o r HOI. The data obtained a t each temperature with t h i s device covers a s l i g h t l y broader frequency range than the torqued c y l i n d e r apparatus, r e s u l t i n g i n o v e r l a p p i n g o f the data when s h i f t e d . The G* data c o n t a i n s very l i t t l e s c a t t e r , but t h e r e i s moderate s c a t t e r i n the l o s s f a c t o r data. F i g u r e 8 i s a p l o t o f the HOI data obtained with the DMTA. The data c l e a r l y overlap due t o the r e l a t i v e l y broad frequency range o f o p e r a t i o n o f t h i s d e v i c e . The G data c o n t a i n s very l i t t l e s c a t t e r , but t h e r e i s moderate s c a t t e r i n the l o s s f a c t o r data. 1

1

7

l — . — i — i — i — i — i — . — . — i — . — . — i — « — i — I

-5 -4 -3 -2 -1

0 1 2 3 4

5 6

7 8 9 10

LOG FREQUENCY (Hz)

F i g u r e 6.

Torqued c y l i n d e r data f o r HOI.

DLUBAC ET AL.

E


10

o

CO CO

•n > O H O

o

30

-5 -4 -3 -2 -1 0 1 2 3 4

5 6 7 8

9 10

LOG FREQUENCY (Hz)

F i g u r e 7. Resonance apparatus data f o r HOI.

11

—i

1

i

1

1

1

1

1

r—

1.5

10

o

c

CO 0) -n >

O H O

C3

30

O

.5

j

i

i

i

i

i _

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 LOG FREQUENCY (Hz)

Figure 8.

DMTA data f o r H01.

60


The s h i f t e d data f o r the three d e v i c e s i s compared i n F i g u r e 9 f o r HOI. For ease of comparison the a c t u a l data p o i n t s are not p l o t t e d . At the t r a n s i t i o n frequency, G i s approximately 10 dyn/cm . The spread i n G among the three curves i s minimal a t about 18%. At the t r a n s i t i o n frequency the peak l o s s f a c t o r i s approximately 0.33, s l i g h t l y higher f o r resonant bar with a d e v i a t i o n among the three apparatus of about 24%. Thus f o r HOI, with i t s broad t r a n s i t i o n and low l o s s f a c t o r , t h e r e i s good agreement among the apparatus. For H14, a p l o t t i n g r e f e r e n c e temperature of 10°C was f i r s t used. The agreement between the torque c y l i n d e r and the beam apparatus was q u i t e good. However, the agreement with the resonant bar was poor. I t was reasoned t h a t choosing a r e f e r e n c e temperature c l o s e t o the T (0°C) may not have been a wise c h o i c e . F i g u r e 10 demonstrates the e f f e c t of s h i f t i n g e r r o r s and r e f e r e n c e temperature on the modulus curve. At temperatures near T on a l o g a versus temperature curve, the s h i f t f a c t o r changes r a p i d l y with temperature. Thus, a small change i n the temperatures can r e s u l t i n l a r g e d i f f e r e n c e s i n the s h i f t e d modulus curve. Since the s h i f t f a c t o r curves are s l i g h t l y d i f f e r e n t from each apparatus f o r the same m a t e r i a l due t o e r r o r s i n modulus measurements and s h i f t i n g , then i t i s best t o s e l e c t a temperature where the s h i f t f a c t o r i s l e s s dependent with temperature, which occurs a t higher temperatures. So, a p l o t t i n g r e f e r e n c e temperature of 35°C was chosen. F i g u r e 11 c o n t a i n s a o v e r l a y of the curves f o r the s h i f t e d data of the c y l i n d e r , bar and beam devices f o r H14 a t 35°C. The agreement i s f a i r l y good. The maximum d i f f e r e n c e i n the modulus, about 36%, occurs at the t r a n s i t i o n frequency. The peak l o s s f a c t o r of the resonant bar apparatus i s about 10% higher than those measured by the other systems. 1

9

2

1

g

g

T

DISCUSSION The inherent d i f f i c u l t y i n the measurement of the complex dynamic moduli of v i s c o e l a s t i c m a t e r i a l s i s emphasized by the r e s u l t s of t h i s paper. The agreement among the s h i f t e d modulus data as measured by d i f f e r e n t systems i s l i m i t e d by s e v e r a l d i f f i c u l t i e s : (1) measurement i n a c c u r a c i e s of the instruments, (2) d i f f e r e n c e s i n the data r e d u c t i o n techniques used t o apply the time-temperature s u p e r p o s i t i o n p r i n c i p l e and propagation of s h i f t curve e r r o r s and, (3) nonuniformity of the t e s t samples. Though the measurement u n c e r t a i n t y of each device has been checked, and care was taken t o minimize measurement e r r o r s , i n a c c u r a c i e s of measurement cannot be r u l e d out. The higher peak l o s s f a c t o r f o r the resonant apparatus f o r example may be due t o v i b r a t i o n a l energy propagating i n t o the dangling accelerometer c a b l e .

3.

Complex Dynamic Modulus Measured by Three Apparatus 6

DLUBAC ET AL.

7 r i i i i i i i 1 1 1 1 1 i 1 — -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 LOG FREQUENCY (Hz)

F i g u r e 9.

10°

Comparison of a l l t h r e e apparatus f o r HOI.

1 T g

1 35°

TEMPERATURE

F i g u r e 10.

•

I A L O G a

T

1 0

~*j

-»|J^L

LOG FREQUENCY

0

G 3 t

35

E f f e c t of e r r o r s on the modulus curve.


62

In t h i s study a l l data was reduced and s h i f t e d using the same software i n order t o e l i m i n a t e d i f f e r e n c e s between d i f f e r e n t algorithms. I t i s a l s o necessary t o use a s h i f t i n g reference temperature w e l l above T . Good agreement was obtained on samples HOI at 10°C and H14 at 35 °C, both r e f e r e n c e temperatures being w e l l above the r e s p e c t i v e g l a s s t r a n s i t i o n temperatures. Since the f i n a l r e s u l t s are d i s p l a y e d i n the form of master curves, the s h i f t i n g a l g o r i t h m must be considered p a r t of the t e s t procedure and can introduce l a r g e e r r o r s i f not done properly. An obvious and very important c o n s i d e r a t i o n i n dynamic modulus comparisons i s the u n i f o r m i t y of t e s t samples. Candidate m a t e r i a l s should be checked t o be s t a b l e i n time. Sample f a b r i c a t i o n should be meticulous. S p e c i a l care should be given to d i f f e r e n t sample geometries, e s p e c i a l l y when the chemical r e a c t i o n d u r i n g f a b r i c a t i o n i s exothermic. F i n a l l y , comparisons should be made with m a t e r i a l s t h a t possess a r e l a t i v e l y narrow g l a s s t r a n s i t i o n r e g i o n and high l o s s f a c t o r s . These m a t e r i a l s more r e a d i l y d i s p l a y d i f f e r e n c e s among the t e s t apparatus. In choosing among the three apparatus, i t i s seen t h a t the r e s u l t s are comparable when proper care i s taken so t h a t a l l three can be considered e q u i v a l e n t data. A l s o , because a l l three r a t h e r d i f f e r e n t apparatus g i v e f a i r l y s i m i l a r and r e p r o d u c i b l e r e s u l t s , one has g r e a t e r confidence t h a t a l l three are measuring i n t r i n s i c m a t e r i a l s p r o p e r t i e s with acceptable accuracy. g

LITERATURE CITED 1. Ward, I. M., Mechanical Properties of S o l i d Polymers; John Wiley and Sons: New York, 1971. 2. Read, B. E. and Dean, G. D., The Determination of Dynamic Properties of Polymers and Composite; John Wiley and Sons: New York, 1978. 3. Murayama, T., Dynamic Mechanical Analysis of Polymeric Materials; E l s e v i e r S c i e n t i f i c Publishing Company: New York, 1982. 4. Magrab, E. B., J . Res. Natl. Bur. Stds. 1984, 89, 193-207. 5. Madigosky, W. M. and Lee, G. L., J . Acoust. Soc. Am. 1983, 73, 1374-1377. 6. Brown, R. P. and Read, B. E., Measurement Techniques for Polymeric S o l i d s ; E l s e v i e r Applied Science Publishers: New York, 1984. 7. Ferry, J . D., V i s c o e l a s t i c Properties of Polymers; John Wiley and Sons: New York, 1980. RECEIVED January 24, 1990

Comparison of the Complex Dynamic Modulus as Measured by Three

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