ULTRASONIC STUDIES OF THORIUM PHOSPHATE JELLIES AT DIFFERENT TEMPERATURES ARVIKD MOHAS SRIVASTAVA, S. PRAKASH, A S D V. MEHRA Departments o j Physzcs and Chemist)y , Universzty of Allahabad, Allahabad, Indca Received July 19, 1050 INTRODUCTION
Gels of thorium phosphate, arsenate, and molybdate were first prepared in this laboratory in 1929 metathetically by the addition of potassium salts of polybasic acids to thorium nitrate solutions. The thixotropic behavior of these gels, as well as their response to the temperature variations, were studied by Prakash (2, 3, 4). Recently the temperatures of zero conductance and infinite viscosity of some of the negatively charged colloidal systems have also been studied, Prasad ( 5 ) has made studies of certain elastic moduli of a few gels, but he has failed to give a complete picture of all the elasticities. I n a recent paper Srivastava (6) has described a new ultrasonic pulse technique for ready, rapid, and accurate determination of the elastic constants of silica, iron silicate, and other gels. The effect of temperature and frequency has been studied by Srivastava (9), and the variations of the elastic constants have shown certain interesting similarities to the behavior of high polymers and other viscoelastic substances. In this paper the method has been applied to a thorium phosphate jelly a t three frequencies. EXPEF'UMENTAL
The technique has been previously used by Srivastava (7, 10) and is based on a modification of the original pulse methods of Pellam and Galt (1) and others. A beam of ultrasonic energy is made to traverse the gel held vertically in a vessel containing a suitable tank liquid. The ultrasonic energy from the quartz crystal passes first through the liquid, usually water, and then through the gel, which can be robated in a vertical plane, to be received by a similar quartz disc; this disc reconverts sonic energy into electrical energy, which can be applied to the oscillograph plates for detection. The rotation of the gel results in a variation of the amplitude of the transmitted energy and eventually falls to a minimum because of the total reflection of the incident beam a t the critical angle of incidence. Two such minima are observed, owing to the total reflection of the longitudinal and shear waves set up in the sample as a result of the two deformations. The resistance to extension and to shear are represented by E and 8, the two elastic constants being interrelated through Poisson's ratio as
E = 2(1
+ 0)s
(1)
so that the knowledge of any two of these yields the third as well. When sound waves traverse the gel they may take up two different velocities, 1413
1414
A. M. SRIVASTAVA, S . PRAKASH, AND V. MEHRA
depending upon the two types of deformation wociated with them. In the case of shear their velocity is
where p is the density of the gel. When the deformation is a simple extension, the velocity of the vibrations in an infinite medium is:
The Poisson ratio is expressed m:
Since the velocities in the gel are greatei than in the liquid, the waves are refracted away from the normal and the two refractive indices are:
e d and e. are the angles of refraction of the longitudinal and shear waves, respectively, and v,, is the velocity in the tank liquid. Upon rotation of the sample slab, 0 increases and 0 d also increases, until at a value O1 of 0, I'?d = 90" and the longitudinal waves are totally reflected. Similarly, a t a further value 0 2 of 0, Os = go", and the shear waves are also extinguished. Then,
Thus a knowledge of 01 and e2 enables us to determine the elasticities, provided the density be predetermined. OBSERVATIONS AND RESULTS
The preparation of the jelly was a comparatively simple matter in this case where, unlike the Weimarn gels, there is little danger of precipitating the mixture. Sodium molybdate (15.00 ml. of a 10 per cent solution) mas mixed with 16.00 ml. of water and 50.0 ml. of thorium nitrate of the same strength. In 2 hr. a very stable and fairly transparent jelly set and did not synerize. The density was 1.26 a t 20°C. Tables 1, 2 , and 3 show the various elastic constants as well as the angles and the ultrasonic velocities. All the velocities are in centimeters per second and all elasticities in dynes per square centimeter. The velocity in water is 1.55 X los for all calculations.
1415
ULTRASONIC STUDIES O F THORIUM PHOSPHATE J E L L I E S
555s xxxx
xxxx m m va w t -m*m m. c .u s. c .i m m m m
g mc h.” 3
3
w a m h h h r n
0 0 0 c ‘
0 0 0 0
SNN, Y h h h h
1416
A . hl. SRIV.4STAVA, S. PRAKASH, AND V. MEHRA
DISCUSSION
The values of velocity of propagation of the longitudinal waves have been plotted as a function of temperature (figures 1 and 2); the curves show a gradual diminution of the velocity at higher temperatures. These values do not become cdnstant at 50°C. but show a variation and a tendency to fall still further. Srivastava (8) obtained a result for iron silicate gels in which the values became constant after about 70°C., but in the present case temperatures above 50°C. were not permissible as the gel tends to dissociate. Young's modulus shows a gradual variation but that too is not constant at 50°C. The decrease of the modulus at higher temperatures shows the gel to be unlike a solid. The increase of the modulus at greater frequencies is seen from the tables. This goes to disprove any possibility of a breaking up of the gel structure by the passage of ultrasonic energy. .4s n matter of fact, the pulse technique is especially suited
S
E
TEMPERATURE
TEMPERATURE
FIG.2 FIG.1. Variation of Vd with temperature for thorium phosphate gel. Curve I, 2.28 megaFIG.1
cycles per second; curve 11,0325 megacycle per second. FIG.2. Variation of E and S with temperature for thorium phosphate gel at a frequency of 0.625 megacycle per second.
to this kind of work, because it does not damage the samples, as would happen if a direct concentrated beam of energy were passed for a longer time. Volume elasticity or the bulk modulus, K I , is also tabulated; its reciprocal yields the compressibility of the gel under the different conditions. These values agree with the expected values on the supposition that 90-95 per cent of the gel is water, Work is in progress in this direction. SUMMARY
Using the new ultrasonic pulse technique a t frequencies of 2.50, 2.25, and 0.625 megacycles per second, ultrasonic velocities have been determined from which all the elasticities are calculated. The effect of temperature and of frequency on the velocities and elastic constants has been studied. The thorium phosphate gel resembles some high polymers and other viscoelastic substances in behavior.
BASE-EXCHANGE CAPACITY OF SILICA AKD SILIC.ITES
1417
Thanks are due Dr. R. N. Ghosh, DSc., F.N.I., Fellow of the Acoustical Society of America, for his valuable help and suggestions in the progress of these experiments. REFERESCES PELLAM, J. R., A S D Gavr, J . K . : J . Chem. Phys. 14, 608 (1946): PRAKASH, S.: J . Phys. Chem. 36, 2483 (1932). S., A S U B r s w ~ s N. , S . :J . Indian Chem. SOC.8, 549 (1931). PR.+KASH, PRAKASH, S., A S U DUR. S . R . : J . Indian Chem. s o c . 6, 587 (19'29). PRAS.AD, G . : Kolloid-Z. 33, 279 (1923); see also J. Phys. Chem. 36, 2994 (1932). SRIVASTAVA, A. M.:Proc. Natl. .4cad. Sci. India 18, 65 (1949). ( i ) SRIYASTAVA, A . M :Conipt. rend. 231. 1223 (1950). (8) SRIVASTAVA, .4.31.: Iiolloid-Z. 118.146 (19600);D. Phil. Thesis, University of Allnhnbad. (9) SRIVASTAVA, A. 11.:J. Am. Chem. SOC.73, 489 (1951). A . hf.: Proc. Natl. Acnd. Sci. India, in course of publication. (10) SRIVASTAVA, (1) (2) (3) (4) (5) (6)
BASE-EXCHAXGE CAPACITY OF SILICA AND SILICATE MISERALS A. K. GANGULY 1-nit'ersity College of Science and Technology, Calculta, India
Received J u l y 17, 1960 INTRODUCTION
Base exchange as an important property of soils, clays, and clay minerals has long been recognized. An unequivocal definition of base-exchange capacity has, however, not been forthcoming; in fact, its ill-defined nature is responsible for the iiumerous methods now available for determining it. A large number of investigators have made comparative studies of the methods of measuring baseexchange capacity and have demonstrated the lack of agreement between the various methods. Mukherjee and Ganguly (9) and Mukherjee and Gupta (11) have made detailed investigation into the causes of these discrepancies, as applied to the soils and clays, and have formulated three important factors which determine base-exchange capacity. The three factors are the pH, the nature and concentration of the reacting cation, and the time of interaction. The concepts of the crystallinity and the layer lattice structure of the clay minerals which constitute the soil colloids have gradually become the pivot to which most of the properties of soil colloids have been linked. Mukherjee and Ganguly (10) have recently developed, on the bmis of published data, a systematic approach to the problem of ion exchange in silicate minerals related to soils and clays from the standpoint of their crystalline character. In accordance with these concepts, base exchange is primarily the result of isomorphous replacements in the crystal lattice, which are possible, so far as is known, in the case
