Ultrasonic Studies of Polymethyl Methacrylate - Industrial

J. L. Melchor, and A. A. Petrauskas. Ind. Eng. Chem. , 1952, 44 (4), pp 716–719. DOI: 10.1021/ie50508a020. Publication Date: April 1952. ACS Legacy ...
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ULTRASONIC STUDIES OF POLYMETHYL MET LATE J. L. MELCHOR AND A. A. PETRAUSKAS Department of Physics, University of Notre Dame, Notre Dame, Ind.


TUDIES r e p o r t e d i n cuit elements having low T h e velocity of sound versus temperature in polymethyl the literature ( 5 )on the temperature coefficients to methacrylate was studied by a pulsed ultrasonic beam variation with temperature improve its stability. The method. Measurements were made at frequencies of 0.5, of sound velocity in como u t p u t f r equ en c y was 1, 2, 5, and 10 mc., over a temperature range from 15" mercial polymethyl methacchecked before and after to 105" C. Breaks were observed in the curves of velocity rylate (Plexiglas) showed a e a c h measurement w i t h a of sound versus temperature. The temperature at which sudden change in the slope these breaks occurred did not change strongly with freU. S. Signal Corps frequency of the velocity-temperature meter u-hich was calibrated quency. A slight shift t o higher temperatures with inrelationship. It was found crease i n frequency was observed in the region from 0.5 against a National Bureau that this so-called "secondto 5 mc. The observed change in transition temperature of Standards signal. order transition" decreased The crystal holders x-ere over the frequency range covered was only 2" or 3' C., linearly with increasing freand this is barely outside the experimental error. Thermal designed to hold crystals 1 quency in the range from 3 inch in diameter having resoexpansion curves obtained for the same samples of polyt o 11 megacycles, in sharp nant frequencies ranging methyl methacrylate exhibited a break a t approximately conflict with relaxation theothe same temperature. Attenuation measurements a t from 0.5 to 10 me. One is ries which predict an increase frequencies of 0.5, 1, and 2 m c . show an increase in attenushown in the foreground of in the transition temperature ation with increasing frequency and temperature. Figure 3. The receiver and with increase in frequency. transmitter were of identical Accordingly, it was decided construction. The transmitto check this work using a different and more precise method of ter was mounted a t one end of the liquid bath. The receiver was measurement, and also t o extend the work to lower frequencies. clamped to a movable platform, whose position was controlled by a vernier screw drive. This made it possible to vary the receiverEXPERIMENTAL PROCEDURE transmitter distance by values known to 0.001 inch. Figure 3 showP the two crystal holders mounted in position (but raised I n this work the measurement of supersonic velocity was acout of the bath), the movable platform, and the vernier drive. complished by use of pulsed waves. This method is similar to that used by Ivey et aE. ( 3 ) with improved frequency stability. The waves were transmitted and received by piezoelectric crystals arranged in suitable holders and placed in a tank filled with liquid. A pattern of the received wave form was produced on a cathode ray oscilloscope. By observing the shift in this wave form while moving either transmitter or receiver a known distance, the wave length in the liquid could be determined, and SAMPLE TUNED AMPLIFIER SIGNAL CORPS








Figure 2. General View of Apparatus




Figure 1.





Block Diagram of Apparatus

hence Ihe velocity of sound in the liquid. Interposing the sample between the transmitter and receiver resulted in a shift of the wave pattern. Knowing the thickness of the sample, the amount of the shift, and the velocity of sound in the fluid medium, the velocity of sound in the sample was determined. A block diagram of the apparatus is shown in Figure 1, and Figure 2 is a photograph of the apparatus. The oscillator wag of the Hartley type, and was built with cir716

The temperature of the liquid bath surrounding the sample was regulated by a Brown Electronik recording potentiometer, by controlling the current to immersion heaters placed in the bath. Thermometers were used t o determine the bath temperature. To ensure that the temperature in the samples vias the same as that of the bath, thermocouples were embedded in the Plexiglas blocks. A typical sample of Plexiglas is shorn in the foreground of Figure 2. The thermocouple location and the leads may be seen near the upper right-hand corner of the block. All samp1es:of Plexiglas used in these measurements were cut from one large block in order to reduce variations between samples. I n order to obtain the pattern of the wave on the Tektronix scope, the General Radio pulse generator and the horizontal sweep on the Tektronix scope were triggered by the horizontal sweep trigger circuit of a P4-E synchroscope. The pulse generator then


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With increase in temperature and frequency the attenuation in the blocks became larger, so that it was necessary t o use thinner samples in order to obtain a measurable signal. To make certain that the samples were alike, the velocity of sound in all Barnples was compared a t the same temperature and frequency. A new sample, which was not previously immersed in water, gave the same measured velocity as a sample which had been in and out of the water intermittently over a period of approximately one year. Two liquids were used for the bath. At temperatures below 90" C. water was used for the liquid medium. Above 90" C. oil was employed. For the 0.5- and 1-mc. curves the velocities (in the Plexiglas) obtained with water as a medium were compared with those having oil as a medium, both below and above the transition temperature. No difference was found in these measurements. In taking the data, the measurements were made generally in steps of increasing temperature. However, several runs were made starting at the highest temperature and going down, in order to check the reversibility. No time effects were observed, and the curves were found to be reversible within the experimental accuracy of the measurements.

triggered the oscillator. This allowed the oscillator to function for the duration of the pulse, and hence a pulsed sinusoidal wave form was produced. The output voltage of the oscillator was impressed across a quartz crystal transmitter immersed in the liquid medium, The signal was transmitted through the liquid to the quartz crystal receiver, amplified, and fed to the vertical plates of the Tektronix CRO used for analysis.


Figure 3.

Close-up View of Crystal Holders, Movable Platform, and Vernier Drive

Velocities of sound in water and SAE No. 40 motor oil were measured as prerequisites for determining the velocity of sound in Plexiglas. A complete set of points for both media was obtained a t 0.5, 1, 2, 5, and 10 me. As no dispersion was evident, single representative curves were drawn for the two sets of points. The resulting curves are shown in Figure 4. Points were scattered about the sound velocity curve for water with a mean deviation of

As the horizontal sweep on the Tektronix was triggered a t the same time as the pulse in the liquid medium, the position of the CRO signal was determined by the transit time in the medium. An increased transit time meant increased time between horizontal sweep trigger and beginning of vertical plate the right on the CRO. Similarly, a decreased transit time shifted the wave pattern to the left. Therefore, any movement of either transmitter or receiver resulted id a movement of the pulse pattern on the CRO screen. Thus, if the distance of separation between transmitter and receiver was varied one wave length, one wave length passed any fixed point on the CRO. Since the velocity of sound in Plexiglas is greater than in either water or oil (the two liquids used in this work), bhe transit time was decreased when a Plexiglas block was placed between transmitter and receiver. The signal on the CRO screen correspondingly shifted to the left. The receiver was then moved away from the transmitter so as to increase the transit time to its original value-Le., the wave pattern of the CRO was returned t o its initial position on the screen.


1570 ~~~,e-r8'P'6L-'-~~~~b 00 k*

0: W v,

3 g 1530-

0' w













5 1450-


cc w




- 1360z




k -1280::


% sm.

6' I









-> z

P t


where Sis the distance the receiver was shifted to make the transit time the same, D is the block thickness corrected for thermal expansion, and CL is the velocity of sound in the liquid. The velocity of sound in the liquid was determined by moving the receiver through a known distance and counting the number of waves passing a given point on the CRO screen. From this information the wave length, A, was calculated. By accurately measuring the frequency, v, the velocity was found from the expression CL = XV. April 1952

: :*,

,b\ i

%\ 1


0.06%. , T h i s curve was extended through 4 ' C., and no abnormal deviation was noted. Bepause of unavoidable temperature gradients in the motor oil, mean deviation from the velocity curve was 0.6%. The motor oil displays a linear decrease of velocity with increasing temperature. This is the form most often found for liquids. Water, on the other hand, yields a steadily increasing velocity up to a maximum of about 1557 meters per second at 74" C. Willard (7) obtained similar results for water at 10 mc.







Figure 5.

Figure 7.

Velocity of Sound in Plexiglas a t 0.5 Mc.

Velocity of Sound in Plexiglas a t 2 Mc.









Figure 6.

Velocity of Sound in Plexiglas at 1 Mc.

creased with increasing temperature, the resulting decrease in detected signal to background ratio caused errors as high as 1% in the high temperature 5-mc. data. For the 10-mc. data, the error was even greater a t times. A4pproximately5 inches' separation was used in this case, causing additional difficulties due to source radiation lobes. To avoid standing waves in the thin samples it was necessary to decrease the duration of the pulse. This caused some difficulty in the determination of the frequency, for the frequency spread is inversely proportional to the pulse length. The build-up time of the quartz crystal did not permit the use of an arbitrarily small pulse length. From the distribution of the points in the 10-mc. data (for which a 0.1-inch block was used) there is an indication of the presence of standing waves. These difficulties collectively caused considerable scatter in the 10-mc. data. The transition temperatures obtained in this work are summarized in Table I, and compared m,ith those obtained by several other methods.

Table I .

Transition Temperatures for Plexiglas under Various Conditions

c. Volume thermal expansion (6) Linear thermal expansion ( I ) 0.5-mc. sound 1-mc. sound 2-mc. sound 5-mc. sound 10-mc. sound Nuclear magnetic resonance (9)











Velocity of Sound i n Plexiglas a t 5 Mc.

For Plexiglas, sound velocity-temperature curves have relatively sharp changes in slope around 74' C. for the frequency range studied. These points of slope discontinuity denote second-order transitions, and are clearly defined in Figures 5, 6, and 7 for 0.5, 1, and 2 mc., respectively. A block of Plexiglas, 2 inches thick, was used for these sets of data. This yielded greater accuracy than that obtained with 1-, 0.5-, 0.25-, and 0.1inch blocks used at higher frequencies. The transition points defined by Figures 8 and 9, representing 5 and 10 mc., respectively, ma? be subject to debate. High attenuation in both oil and Plexiglas accounts for increased scatter of points here. As a n illustration, for 10 mc. and 80' C., the attenuation in oil alone was approximately 12 db. per inch. I n order to obtain a signal above background noise of the amplifier it was necessary t o operate with source and receiver as close together as physically possible. Because the total attenuation in718




Figure 8.

71 1 72 72 74 6 75 75 71

Within the limits of experimental error these data as shown provide no decisive confirmation or negation of the predictions of relaxation theory. There is some indication of increasing transition temperature n-ith increasing frequency in the range 0.5 to 6 mc. Figure 10 shorn-s a curve of relative length versus temperature obtained for the same sample of Plexiglas (1). This curve exhibits a'break a t a temperature of 72" C,,which is in good agreement with the values obtained by the sound measurements. The results also closely agree with those of Robinson (6) and associates, who found the transition temperature of Plexiglas to be 71.1" C. by volume thermal expansion. In the study of transitions in polymers by nuclear magnetic resonance, Holroyd ( 2 )and associates found a transition temperature of 75' C. for a sample of Plexiglas which was cut from the same block used in the velocity of sound measurements. The line width transition is gradual, taking place over a temperature range of about 16" C. The value of 75' C. is the midpoint of this transition region. Figure 11 shows the dependence of attenuation on temperature and frequency, One sees that the attenuation exhibits a rapid increase with temperature a t high temperatures and increases with


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, > 0 7 2 u'

. W





"O >

2500 >.



0 0


w -I


"'\ 2100,0

Figure 9.





HO 100


Velocity of Sound in Plexiglas at 10 M a .

Figure 10. Linear Thermal Expansion of Plexiglas

frequency. It is likely that the attenuation reaches a peak at some temperature above 110" C. With the present apparatus, however, sufficiently high temperatures could not be obtained to verify this assumption. Measurements were made a t frequencies of 0.5, 1, and 2 mc. No attenuation data were obtained at higher frequencies, because of difficulties encountered in the measurement of weak signals when the sample of Plexiglas was interposed between the transmitter and the receiver. Even a t a frequency as low as 2 mc. the experimental points are considerably scattered. In this case, deviations from the curve are as high as 1db. per cm. Assuming a sinusoidal time dependence, the solution of the wave equation gives the usual relationships for the effective bulk wave modulus and the effective viscosity coefficient. If the quantity a C / w is much smaller than 1, which is true for the present case, the effective moduli and viscosity coefficients are given by the approximate relations ( 4 )


+ (413)

P =

Sample length 5 inches.







yw =


Sample cross section 0.25 X 0.016 inch

where K and p are the bulk and shear moduli, p is the density in grams per cc., C is the phase velocity in om. per second, OL is the attenuation in nepers per cm., w is the angular frequency in radians per second, and y is the coefficient of shear viscosity. Using these relations with the attenuation data of Figure 11 and the velocity data of Figures 5, 6, and 7, it is found that the effective bulk modulus does not change appreciably with frequency in the range from 0.5 to 2 inc. and is approximately equal to 8.5 X 1010dynes per sq. cm. at 15" C. and 5.5 X 1010 dynes per sq. cm. at 105" C. At 0.5 mc. the viscosity coefficient changes from 1.7 X 109 dynes per sq. cm. at 15" C. t o 4.2 X 10s dynes per sq. cm. at 105" C. At 1 mc. the viscosity coefficient changes from 1.9 X 108 dynes per sq. om. at 15" C. to 7.9 X 109 dynes per sq. cm. at 105" C. The attenuation data for frequencies of 2 mc. and above were not sufficiently accurate ta warrant a computation of the viscosity coefficient.




I I20



Figure 11, Attenuation in Plexiglae 0 . 0.5-mc. points

0. X.

I-mo. points 2-mo. points

studies reported in the literature (6),where the transition temperature was found t o decrease by a considerable amount in the frequency range from 3 to 11mc. ACKNOWLEDGMENT

The authors wish to acknowledge their indebtedness to F. P. Baldwin for the data on relative length versus temperature, and to R. L. Anthony and B. A. Mrowsa for many discussions and suggestions. LITERATURE CITED


The phase velocity of bulk waves and attenuation in Plexiglas 1A have been studied as a function of temperature and frequency. From these data it.was found that relatively sharp breaks occur in the curves of sound velocity versus temperature at approximately 74" C. The temperature a t which these breaks occur does not change strongly with frequency. There is a slight shift toward higher temperatures with increase in frequency in the range from 0.5 to 5 mc. This is in sharp contrast with similar April 1952

Baldwin, E'. P., University of Notre Dame, unpublished data. Holroyd, L. V., Codrington, R. S., Mrowoa, B. A., and Guth, E., J . Applied Phya., 22,696 (1951). (3) Ivey, D. G., Mrowca, B.A., and Guth, E.,Ibid., 20,486 (1949). (4) Nolle, A. W., and Mowry, S. C., J . Acoust. SOC.Am.. 20, 432 (1948). ( 5 ) Protsman, T. F., J . Applied Phys., 20,627 (1949)

(6) Robinson, H.A., Ruggy, R., and Slantz, E., Ibid., 15,343 (1944). (7)Willard, G.W., J . Acoual. 8 0 0 . Am., 19,235 (1947). RBOsIvSD

for review Deoember 26, 1061.

I N D U S T R ~ A LA N D E N G I N E E R I N G C H E M I S T R Y

ACCBPTEYD February 9 , 1952.