A. W. PRYOR AND E. G. RICHARDSON
14
VOl. 59
VELOCITY AND ABSORPTION OF ULTRASONICS IN LIQUID SULFUR BY A. W. PRYOR AND E. G. RICHARDSON King's College, Newcastle upon Tune, England Received June 17, 1864
In order to derive some of the visco-elastic properties of liquid sulfur, particularly in the transition region where polymerization takes place, measurements of ultrasonic velocity and attenuation over the range of temperature 100 to 250" have been made. Comparison is made between the "ultrasonic viscosity'' deduced from such measurements and those derived in a conventional viscometer. A model is suggested to account for the acoustic behavior of sulfur above 160'.
Introduction A number of measurements of the viscosity of
the velocity and attenuation of ultrasonics of megacycle frequencies in sulfur over this transition resulfur in the molten state have been made over the gion and to deduce therefrom values of comprespast fifty years, using simple transpiration or slow sibility and ultrasonic viscosity. In view of the oscillatory motion. Sulfur melts at 111' and in known difficulty of removing small traces of impurities and their effects on the flow properties, only the more usual efforts at purification, e.g., boilGraduated ing, as recommended by Bacon and Fanelli,3 Scale were made, it being considered sufficient for our purpose to compare viscosities deduced from abGuide Rod sorption with those obtained in a conventional viscometer on another sample of the same specimen. Anti- backlash
h
Bearing
Thermocouple Leads Accurate Screw 20 t.p.i.
-.-
U
I
Reflector
I
Heater Leads Asbestos Lagging
Thermojunction Crystal on Brass& Asbestos Plates R.F.Leads Spring
-Levelling Screws
Fig. 1.-Ultrasonic interferometer.
this state the element exists ?h the form of 8 atom rings. At 160' polymerization occurs and the viscosity rapidly rises. The sulfur in this stage exists in long chains and traces of hydrocarbons by terminating the chain have, according to Gee,' a marked effect on the viscosity. Farr and McLeod2 found that the viscosity varies with time. The object of the present research was to measure (1) G. Gee, Trans. Faraday SOC.,48, 515 (1952). (2) C. C. Farr and D. B. MoLeod, Proc. Roy. Soc. (London). A97,
80 (1920): A118, 534 (1928).
Ultrasonic Apparatus.-The interferometer built for these measurements is shown in Fig. 1. The container of the specimen is a brass tube 1.38 in. diameter and 7.5 in. long, heavily chrome-plated on the inside to prevent contamination. The tube is covered externally by a layer of asbestos and wound with a heating coil, over which a further layer of asbestos IS placed. The transducer (a 1-in. quartz crystal), spring-loaded against a collar with hole 0.88 in. diameter soldered near the lower end of the tube, is mounted on a brass disc insulated from the (earthed) furnace by an asbestos disc. The crystals were coated above and below by evaporated aluminum or baked silver paste. The steel screw which carries the reflector is of high accuracy, has a pitch of 20 turns per inch and is fitted with anti-backlash bearings of brass. It has a dial at its upper end. Calibration showed the screw to be accurate to better than 1in 1000. The reflector is of aluminum and also carries the ironconstantan thermocouple which gives the temperature of the enclosure. In order that the reflector and transducer can be adjusted in parallelism-a very important point-the interferometer tube is supported on the base of the screwcarrier through three levelling screws, which are adjusted until a good signal echo is returned. An automatic temperature control assures the temperature of the furnace to & 1
'.
1400
c
h
6
P
-P
I
E 1300
.e
0
3
100
150 200 Temp. ('C.). Fig. 2.-Velocities of sound at various temperatures: a, 4 Mc./sec.; 0, 0.4 Mc./sec. (3) R. F. Bacon and R. Fanelli, I n d . Eng. Chem., 34, 1043 (1942).
Jan., 1955
15
VELOCITY AND ABSORPTION OF ULTRASONICS IN LIQUIDSULFUR
Electronic Circuits.-A pulse signal was employed. Oscillations from a Hartley oscillator are excited by a multi-vibrator. These are gated in the form of short pulses of oscillations and applied to the transducer, which then launches a short train of waves to be reflected. The echo, again energizing the transducer, is amplified a t constant gain in the receiver. (During the emission of the signal the latter must be ut out of action by a "blanking pulse"). The echo is exgbited on a cathode ray oscillograph and brought to a determined level through the operation of an attenuator in the receiver circuit. The determination of the absorption coefficient therefore consists in moving the reflector away from the source while adjusting and reading the attenuator. To measure the wave length-and so, the velocity-the echo is mixed with a fraction of the original oscillations. The superposed amplitude, dis layed on the oscilloscope, will vary as the relative phase ofsignal and echo varies with relative position of source and reflector. This method is very useful when-as in the present instance-a highly absorbent liquid is in question. The frequency is checked to a high degree of precision on a heterodyne wave-meter.
Velocity Results.-Figure 2 shows the results of velocity measurements at two frequencies, 0.4 and 4 Mc./sec. Those at 4 Mc./sec. showed no marked change at the transition temperature; but at the lower frequency, a jump of some 20 m./sec. occurred at 160" which eventually subsided into the 4 Mc./sec. curve above 200". This effect seemed to be a sort of hysteresis and was not apparent coming down in temperature. The velocity in liquid sulfur was earlier measured by Kleppa4 but our results are higher than his by 10 to 20 m./s. The density of sulfur at 115" is 1.82, of polymerized sulfur 1.93 g./cm.* making the adiabatic compressibilities a t 115 and 160" .32.5 X lo6 and 31.5 X lo6 dynes/cm.2, respectively. Natta and Baccareda5 have shown that the ratio velocity of sound/density is an important index for the lengths of chains in polymers. At the two temperatures noted, this ratio has values 0.74 and 0.66, respectively, in their units. Absorption Results.-Results in the form amplitude-absorption coefficient ( a ) us. temperature at frequencies 5.8, 12 and 15 Mc./sec. are given in Fig. 3. All show a rise beginning at 160" and level0.54
uted to the formation and collapse of vapor bubbles in the liquid. In order to make a comparison between the viscous behavior of sulfur at high and near-zero frequencies an oscillating cylinder viscometer was set up, equipped with a furnace, and the viscositieswhich also showed a tendency to after-effects-determined. The results, which agree with the measurements of Farr and McLeod (1920), are shown in Fig. 4.
f
~
I
u
3-
w IO .-m 0 a .c, c
W
V
2 IO -
x
.-cm,
s
5
1
L IO0
140
-
J 180
Temperature Fig. 4.-Viscosity
200
(OC)
coefficients a t various temperatures.
Discussion of Results According to the well-known theory of Stokes6 the absorption of plane waves of sound in a liquid should follow the formula where f is the frequency, c the velocity and v the kinematic viscosity. The latter being the com120 140 I60 Iso 200 220 mon coefficient of viscosity v divided by the denTemperature (ad. sity p we may divide the data of Fig. 4 by 1.9 apFig. 3.-Absorption coefficients of sound a t various tem- proximately to obtain v values for sulfur. peratures. This formula fits few fluids but it is so far true ling off at about 200". Initially, the absorption that in many liquids a / f 2 is constant. Figure 5 could be as much as 0.1 above the final value on shows that in sulfur at 180", a rises steadily with standing. In order to get steady readings it was f 2 in the megacycle gamut, though with a factor necessary to wait some time at each temperature. which has changed after about an hour's standing. Even so, at the higher temperatures difficulties Working back from the formula given above, subwere experienced through fluctuating echos, attrib- stituting our values of a / f 2 ,we can deduce values of v which we might call "ultrasonic viscosity." (4) 0.d. Kleppa, J . Chem. P h y s . , 18, 1303 (1949). (5) G . Natta and M. Bacoareda, J . Polymer Sei., 3, 829 (1948).
(0) Sir G. Stokes, Trans. Camb. Phil. Soc., 3 (1846).
DONALD P. AMESAND PAULG. SEARS
16
-
0.6 c
.-
W
.g 0 5 -
.
'c
W
VOl. 59
I n order to explain this we assume that above 160" we are dealing with a visco-elastic fluid, whose elasticity a t high frequencies far outweighs the true viscosity. The model shown as inset to Fig. 5 will serve our purpose. Here a dashpot of viscosity r] is in parallel with another dashpot 7' and a spring of elasticity n'. In Fig. 5 the slope of the lines gives the ultrasonic viscosity r]' while r] r]' represents the "steady viscosity." The intercept, absorption at zero frequency, enables the elasticity n' t o be calculated. Thus, the model has a resonant pulsatance oo = n'/r]', = RC' in electrical symbols, and the attenuation can be written
+
o.+
/ 1
1
1
,
1
,
1
,
100
0
1
1
1
1
1
200 x 1 0 ' 2
(Frequency) Fig. 5.-Absorption
Thus, on a graph of a against jz,the slope B = 81r2/3 X q / p c 3 , and the intercept on the ordinate axls where f +0
coefficients vs. (frequency)2.
Doing this for the whole range of temperature to the results of Fig. 3, we can show that below transition the flow viscosity is about one third and above transition about one thousand times the ultrasonic viscosity.
Inserting the slopes and intercepts, we find for example at 180" the following initial and final approximate values for the elements of the model: q, 0.32 to 0.27; q', 300 to 200; n', 5 to 1.7 X loRin c.g.s. units.
THE CONDUCTANCES OF SOME POTASSIUM AND SODIUM SALTS IN DIMETHYLFORMAMIDE AT 25' BY DONALD P. AMESAND PAULG. SEARS Contribution from the Department of Chemistry, University ~jKentucky, Lexington, Icy. Received June 18, 1964
The conductances of dilute dimethylformamide solutions of ten potassium and sodium salts having univalent anions have been measured at 25". For the concentration range of 1-20 X lo-' N , relative1 good agreement exists between the observed and theoretical Onsager behavior for all salts studied except the nitrates. &e limiting equivalent conductances indicate a potassium salt to be 0.7 i 0.4 ohm-' cm.2 more conducting than the corresponding sodium salt and substantiate the Kohlrausch law of independent ion migration in dimethylformamide.
Introduction Although dimethylformamide has become important in the non-aqueous solvent field, there exists in the literatures2 a paucity of information concerning the conductance of salts in this solvent. The purpose of this investigation has been to obtain some additional information concerning the conductance behavior of several pairs of potassium and sodium salts having the same univalent anion and to test the validity of the Kohlrausch law of independent ion migration in dimethylformamide. Experimental 1. Puriiication of Solvent.-Dimethylformamide
(Eastman White Label) was dried over solid potassium hydroxide and fractionally distilled at 5 mm. pressure. The retained middle fractions had conductivities ranging from 0.6-2.0 X lo-' ohm-' cm.+ at 25". (1) L. R. Dawson, M. Golben, G. R. Leader and H. IC. Zimmerman, Jr., J . Electrochem. SOC., 99, 28 (1952). (2) L. R. Dawson, M. Golben, 0.R. Leader and H. K. Zimmerman, Jr., Trona.Kentucky Acad. Sci., 18, 221 (1962).
2. Purification of Salts.-Reagent grade potassium and sodium nitrates and bromides were recrystallized three times from redistilled water and dried for 12 hours in vacuo a t 70". Reagent grade potassium and sodium iodides were recrystalliaed three times from water-ethanol solutions and dried for 12 hours in vacuo at 70". Reagent grade potassium and sodium perchlorates were recrystallized three times from redistilled water and dried in vacuo for 10 hours at 100' and an additional 12 hours a t 130". Reagent grade potassium and sodium thiocyanates were recrystallized three times from redistilled water and dried 48 hours in vacuo at 60". 3. Apparatus and Procedure.-Resistance measurements were made with a Jones bridge (manufactured by the Leeds and Northrup Company) a t a frequency of 1000 cycles per second. Periodic resistance measurements were made also at 500 and 2000 cycles per second; however, no significant frequency dependence for resistance was observed. For resistances greater than 30,000ohms, 30,000 ohms of the bridge resistance was shunted in parallel with the cell and the series cell resistance was computed from the measured parallel resistance. Three flask cells with lightly platinized electrodes, similar to those designed - by- Daaaett, -- . Blair and Kraus.' were em(3) H. M. Daggett, Jr., E. J. Blair and C. A. Kraus, J . A m . Chem. Soc., 7 8 , 799 (1951).
