Sound and Vibration Damping with Polymers - ACS Publications

Chapter 8

Selecting Damping Materials from Differential Scanning Calorimetry Glass-Transition Data A. K. Sircar and Michael L. Drake

Downloaded by GEORGE MASON UNIV on December 23, 2014 | http://pubs.acs.org Publication Date: May 1, 1990 | doi: 10.1021/bk-1990-0424.ch008

University of Dayton Research Institute, Dayton, OH 45469

An empirical equation was used to predict the peak loss factor temperature of dynamic viscoelastic measurements from DSC T data. The frequency for DSC T was given an arbituary value of 10 Hz. The equation offers a rough prediction of peak loss factor temperature at dynamic frequency, thus enabling the material scientist to select candidate viscoelastic damping materials from DSC T data. The predicted loss factor temperature is closer to the actual temperature determined from the nomograph plot of the viscoelastic data i f the experimental E is used in the calculation and the same heating rate is used for both the dynamic and DSC test methods. g

-4

g

g

a

Viscoelastic materials are frequently used for vibration and noise damping. The properties of such materials do vary widely as a function of temperature and frequency. Generally, a viscoelastic material is selected, such that its peak loss factor temperature is in the region of the use temperature at a specific resonant frequency. Since glass transition temperature (T ) by dynamic methods is often defined as the peak loss factor temperature and increases with increasing frequency, an obvious question for material scientists and engineers is how does the glass transition temperature of a polymer, as determined by static methods (DSC, DTA, dilatometry) correlate with those by the dynamic methods (dynamic modulus, resonant beam) that use variable frequencies? An answer to this question would enable the material scientists and engineers to select suitable candidate materials for high frequency applications from DSC (differential scanning calorimetry) data, which are more easily determined and are often available in the literature (1-3). 0097-6156/90/0424-0132$06.00/0 © 1990 American Chemical Society

In Sound and Vibration Damping with Polymers; Corsaro, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

8. SIRCAR AND DRAKE

133

Selecting Damping Materials


Experimental Material - The polymers used in this study are given in Table I. A general chemical identification of six of these polymers is shown in Figure 1. Dyad 609 is a proprietary material trade marketed by The Soundcoat Company, Inc. Hypalon, manufactured by DuPont and Vinac B100, manufactured by Air Products, were used as compounded. The exact formulations for the compounded polymers are proprietary. The other polymers shown in Table I and Figure 1 were used without compounding. All materials were used in uncured condition. The polymers and compounds in Table I were selected for study, since the data were already available from previous investigations. Data for both f i l l e d and unfilled polymers will be the subject of a follow-up future investigation. Measurement of Dynamic Modulus - Three different instruments were used to measure dynamic modulus and calculate the viscoelastic parameters of loss modulus, elastic modulus, and the ratio (loss factor, tan 8). They were the Rheometrics Solids Analyzer (RSA II), Dynamic Mechanical Thermal Analysis (DMTA), and the ASTM, E756-83, Beam Test. The capabilities of each test method with regard to the frequency range, temperature and test specimens are shown in Table II. Frequency ranges used for this investigation are 1 to 15 Hz 0.3 to 50 Hz and 200 to 4000 Hz for RSA, DMTA and Beam Test respectively. DMA-983 at frequencies 0.01, 0.1, 0.5 and 1 Hz was used for the polymethyl methacrylate sample. Comparison of the complex modulus data generated by the three different measurement techniques in Table II have been discussed recently by the authors XD.. A stepwise heating of 2 C/minute, with 3 minutes equilibration time at a constant temperature was used for RSA II. DMTA experiments were carried out at TC/minute in ramp mode. Step heating with 30 min. equilibration at each temperature was used for beam tests. A short description of the beam test and the procedure for obtaining a nomograph is described below. w

Beam Test The resonant beam test technique forms the basis of the ASTM Standard E756-83 for measuring the viscoelastic properties of damping materials. Fundamentally, the beam test requires that the resonant frequencies of a metal-beam, mounted in cantilever fashion, be determined as a function of temperature and frequency; the beam is then coated with a polymer and the resonant frequencies and corresponding modal damping of the composite beam are determined as a function of temperature and frequency. From these two data sets, the vibration damping properties of the polymer can be evaluated. The ASTM Standard provides the necessary equations to obtain the complex modulus data from the collected test data and also provides guidelines for the proper choice of the specimens (1.2). The principal difference between the beam test and the other methods used here is that the beam test calculates the material properties from the test results on the metal beam and the composite beam whereas the



DYAD 609 Proprietory Material, Soundcoat

Victrex 5200 P Poly(sulfone)

Ultem 1000 Poly(etherimide)

Lexan 141 Bisphenol A Poly(carbonate)

Plexiglass GP Poly(methyl methacrylate)

Poly(vinylacetate) + filler

Hypalon 48 + f i l l e r

Sample Description

-8

219.5

212

143.7

111

35

-9.7

DSC T lO-C/Sin

307

1177

957

899

725

351

288

AE (Exp) from RSA II, kJ/M

16

301

291

202

160

67

14

Predicted T (C-) at 1000 Hz AE=400 kJ/ Mole

33

247

245

169.6

138

71

22.6

Predicted T CC) at 1000 Hz with Exp. AE

54

250

239

165

132

68

23

Peak Loss Factor Temp. *C, Obtained from Nomograph RSA II Data

77

-

74

28

Peak Loss Factor Temp. •C, Obtained from Nomograph Beam Data

TABLE I „ PREDICTION OF DYNAMIC GLASS TRANSITION TEMPERATURE FROM DSC DATA


Measurements were by DMA multiplex at 2°C step heating

Comments

SIRCAR AND DRAKE


H

H I - CH -CH CH -CH -CH - C CI 2

2

2

2

CH^ C S0 C1J Y

2

2

HYPALON, Chloro-sulfonated poly(ethylene) {CH- - CH>2 | n O-C-CH-


v

&

3

Vinac B-100, Poly(vinylacetate) o

?3

I)

-o-CO

LEXAN 141, Poly(bisphenol A carbonate) o

Victrex, Poly(sulfone)

e

s 1

eC

II C _ l

CH,

Ultem, Poly(etherimide)

'I

CH I

-{-CH

-C 2

,

k-

J*

COOCH Plexiglas GP, Poly(methyl Figure 1.

methacrylate)

Chemical Structure of the Polymers Under Study.



Testing Mode

CO

Temperature

Frequency Hz

TEST PARAMETERS

Free layer or sandwich uniform

-73 to 1093°C

100 to 12000

BEAM TEST

ASTM,E-756

Shear & bending

Shear & bending

0.0016 to 16

-150 to 600°C

to 200

RSA - II

RHEOMETRICS

-150 to 800°C

0.01

DMTA

POLYMER LABORATORIES

METHODS FOR DYNAMIC MODULUS MEASUREMENTS

TABLE II


8. SIRCAR AND DRAKE

137


other methods are tests conducted directly on the material samples.


Nomograph The test results of a material damping test are most useful when placed on a reduced temperature nomograph, which plots the limited number of test results to a graph from which one can obtain the damping properties (modulus and loss factor) at any given combination of temperature and frequency. The WLF equation (5) is used to obtain a nomograph for the results of each test. A reference temperature (TJ corresponding to the best data f i t is used in the nomographi^representation of the data. Figure 2 is a reduced temperature nomograph which demonstrates the procedure for reading the nomograph as follows: Select a combination of temperature and frequency, for example, 1000 Hz and 75°C. Find the point for 1000 Hz on the right-hand frequency axis. Proceed horizontally to the temperature line for 75°C. At this intersection, draw a vertical line. Then, read the modulus and loss factor values from the appropriate data curve, at the point of intersection with the vertical line. In this example, modulus G(1000 Hz, 75°C) = 8 x 10 N/m and loss factor (1000 Hz, 75°C) = 1.96. The temperature scale at the top of the reduced temperature nomograph shows increasing temperature from right to left. Labeling of the temperature lines is done in a uniform temperature increment. The temperature increment is identified at the top of the nomogram. The nomograph presentation and data reduction procedure have been described in earlier publications (6.7). Measurement of Glass Transition Temperature bv DSC - Glass transition temperature by the static method (zero frequency) was measured by the DuPont 910 Differential Scanning Calorimeter using a DuPont 2100 Thermal Analysis System. The samples were annealed 50°C above the T of the polymer and quench cooled by pouring liquid nitrogen on the top of the cooling attachment. T was determined at 5, 10, 20 and 40°C per minute rate of heating. The multiple heating rates allowed the extrapolation of T to a zero rate. The extrapolated T value at 0°C/min. heating rate is comparable to that by dilatometry at a low heating rate (0.6 degree/min.) X S 1 - Both the extrapolated T and the T measured at 10°C/min. (determined from least square plot), were used for the calculations, since the latter is more generally available in the literature. The experimental conditions for the dynamic modulus experiments, as described above, were close to zero rate of heating, since the samples were either equilibrated at a constant temperature or heated at a slow rate ( l ° C / m i n . ) . A plot of rate of heating versus T for the polyvinyl acetate compound is shown in Figure 3. 9

9

9

9

Measurement of Apparent Activation Energy - The apparent activation energy, E , was determined by using the Arrhenius activation energy equation for the dependence of T on frequency in dynamic mechanical measurements. In this equatton, the temperature shift



SOUND AND VIBRATION DAMPING WITH POLYMERS

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8.

SIRCAR AND DRAKE

139


50

45 Tg 10 8

C. :i5

0

10

20

RATE OF H E A T I N G

Figure 3.

30

40

50

(T./MIN.)

Rate of Heating vs Glass Transition Temperature for Poly (vinyl acetate) Compound.


140


of the peak loss modulus and/or loss factor is controlled by the activation energy of the process: K = A exp (-E /RT)

where:


K A E R T

(1)

= reaction rate = frequency « constant = activation energy * gas constant = absolute test temperature

(f)

Taking the log of the equation (1) yields: "a

1

E

1 0 9

f

=

2303R ~T

+

1

0

9

(

2

)

From this equation it can be seen that E can be determined from the slope of log f vs. 1/T plot. An example of the DMTA peak temperature shifts at different frequencies is given in Figure 4 for the f i l l e d Vinac compound. Activation energy plots for RSA II and DMTA exeriments were actual experimental data, while E for the resonant beam method was obtained from data extrapolated from the nomograph. Results and Discussion Wetton XSI has described the mechanical characteristics for vibration damping materials in terms of the frequency and temperature dependence of the viscoelastic properties of polymeric materials. Use of polymeric materials in free-layer and constrained layer damping configurations has been discussed in the literature by Ungar (10 12), Kerwin (13.14). and others (15.16). Empirical Relationship - Empirical relationships correlating glass transition temperature of an amorphous viscoelastic material with measurement temperature and frequency, such as the William Landel Ferry equation (17) and the form of Arrhenius equation as discussed, assume an affine relationship between stress and strain, at least for small deformations. These relationships cover finite but small strains but do not include zero strain, as is the case for the static methods such as differential scanning calorimetry. However, an infinitely small strain can be assumed in order to extend these relationships to cover the glass transition temperature determined by the static methods (DSC, DTA, dilatometry). Such a correlation which uses a form of the Arrhenius equation was suggested by W. Sichina of DuPont (18). fDMA «n

E

a

.

,

= _1

(_L (3) T DSC T DMA g g Equation (3) is nothing more than subtracting the fDMA and fDSC frequencies in the Arrhenius equation (Equation 1). This fDSC

R


8. SIRCAR AND DRAKE

141


relationship predicts that the DMA T (based on the loss peak or loss factor temperature) will be higfler than the DSC T when heated at the same rate. In an attempt to correlate DSC T with that measured by DMA, Si china proposed that the magnitude of the shift of the DMA T versus the DSC T can be estimated from the following equation? 9

(T DSC) 8.314 =_i 400,000

(fDMA)

2

AT 9


where:

in

1 Q

(4)

-4

AT g = T g DMA-Tg DSC, T DSC x T DMA - (T DSC) g g g ' The reference frequency for DSC was assigned a low value (fDSC = 0.0001 Hz). The value does not have any physical significance and was chosen for best data f i t . This equation requires the value of the activation energy for the polymers which generally lies between 200-900 kJ/mole. An intermediate value of 400 kJ/mole is suggested as an approximation, i f the activation energy of the polymer is unknown. The T at specific dynamic frequencies can now be calculated i f the DSe T at the same heating rate is known. It is evident that the equation is not only empirical but is also arbitrary. Also, the activation energy for many polymers differs widely from the assumed value of 400 kJ/mole. 2

1

9

Test of the Empirical Equation - Table I compares the calculated T values at 1000 Hz using the DSC data at a heating rate of 10°C per min. T was calculated using both the assumed activation energy of 400 kJ/mole as well as the experimentally determined values by RSA II multiplex experiments. The predicted data were compared with the extrapolated peak loss factor temperature from the nomographs of RSA II and beam data. It was evident that: (1) the assumed activation energy of 400 kJ/mole gives a good prediction only in the case of the polyvinyl acetate compound where the experimental activation energy was approximately the same. (2) The prediction improved when experimental E was substituted for the assumed value. (3) Further improvement was observed when DSC T at zero heating rate was substituted for 10*C/min. as will be evident from Table III. Considering the empirical nature of equation (3) and the arbitrary value used for DSC frequency, the correlation is quite good. Thus, the method should allow a rough prediction of the loss factor temperature at higher frequencies from DSC T data, provided E is close to 400 kJ/mole or experimentally determined E values are used. It may also be observed in Table I that the loss factor temperatures from the beam nomograph are slightly higher than those from the RSA II nomograph. This may be due to the different reference temperatures used to plot the nomographs. This will be discussed later. An exception to the above was the Dyad 609. Dyad 609 is a proprietary material with unknown composition. We had difficulty


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8. SIRCAR AND DRAKE

measuring a DSC T for Dyad 609. Supplier's data (19) show a brittleness temperature of -30°C, but a peak loss factor temperature of 82°C. In all probability Dyad 609 is a multicomponent system with different glass transitions and thus not amenable to the above calculation procedure. Table III also shows that E increases with increasing DSC T . This would be expected from restricted segmental mobility of tfle high T samples. Lewis X l i found that Arrhenius plots of log frequency versus reciprocal dynamic glass transition temperature for restricted and nonrestricted polymers converges to a different point in the frequency/temperature scale. From this finding, equations were derived to predict static T from the dynamic T value and vice versa. g


143


9

Activation Energy Using Loss Modulus or Loss Factor Curve Activation energy can be determined either from peak loss modulus or peak loss factor temperature. Table IV compares the data obtained by either methods along with the correlation coefficient of the linear regression plots for determining activation energy. It is evident that either method is equally satisfactory, as would be expected. Activation Energy bv Different Measurement Techniques - Table V compares activation energy data obtained by three different experimental methods for three different samples. Corresponding Arrhenius plots are shown in Figures 5 and 6. In both figures the log frequency vs. reciprocal temperature plot for RSA II and DMTA are parallel to each other, giving very close E values. The same reference temperature gives a good nomograpn for the complex modulus data obtained from these two methods. However, the beam data has a good nomograph f i t at a lower reference temperature and an acceptable nomograph i f the RSAII-DMTA reference temperature is used. If the E is calculated from the beam data nomograph generated with the T. used for the other two test methods, then the E values determined from all these tests are approximately equal. However, i f the nomograph generated with the Jj chosen from only the beam data is used, the E value derived is^about one-third of the value from the other two methods, as is evident from Figures 5 and 6 and Table V. The reason for this apparent anomaly is not known. Activation Energy from DSC Heating Rate The variation of apparent T with DSC heating rate has generally been attributed to the thermal lag of the sample, which increases in step with the heating rate (20-22). This thermal lag is composed of a machine path error and a sample error which are dependent on the characteristics of the instrument and the sample, respectively (21). However, T itself is a rate dependent parameter, and a dependence on scan rate involving a relaxation activation energy is to be anticipated over and above any thermal lag errors. The determination of activation energy from the rate expressions involving heating X S 1 and cooling rate (5,23) in DSC has been attempted earlier. Unfortunately, such determinations



Acrylate Polymer by Sound Coat

Poly(methyl methacrylate)

Poly(carbonate) of Bisphenol A

Poly(etherimide)

Poly(sulfone)

Plexiglas GP

Lexan 141

Ultem 1000

Victrex 5200 P 1077

860

933

725

252

~

282

Hypalon 48 Formulation + Filler

Vinac B100 Polyvinyl acetate) Formulation + Filler

334

Loss Modulus

1177

957

899

307

351

288

287

Loss Factor

Activation Energy, kJ/M

Hypalon 48 Formulation + Filler

Identification

Dyad 609

Sample

0.99

0.98

0.99

0.99

0.96

-

0.93

0.99

Loss Modulus

0.99

0.99

0.98

0.99

0.99

0.98

0.97

Loss Factor

Correlation Coefficient

COMPARISON OF ACTIVATION ENERGY DATA BY LOSS MODULUS AND LOSS FACTOR PEAKS FROM RSA II DATA

TABLE IV


8. SIRCAR AND DRAKE

3

E A

B

A

2.4

c

D x

/1 irk

1.8

/

1.2


145


/ 0.6

/

/

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/

Sound and Vibration Damping with Polymers - ACS Publications

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