J . Phys. Chem. 1985,89, 1657-1658
1657
Diffusion of Trigiycine Sulfate in Aqueous Solution R. L. Kroes,* D. Reiss, Space Science Laboratory, NASA Marshall Space Flight Center, Huntsville, Alabama 3581 2
E. Silberman, and S. Morgan Department of Chemistry, Fisk University, Nashville, Tennessee 37203 (Received: July 2, 1984)
The diffusion coefficient of triglycine sulfate (TGS) in water was measured for several concentrations over a temperature range of 25 to 55 OC. The activation energy for diffusion obtained from these measurementswas 4180 cal/mol. No concentration dependencewas seen. The maximum differencein D for the various ionic species present was determined by Raman spectroscopy to be about 5%.
Introduction Single crystals of triglycine sulfate, (NHzCH2COOH)3(H2S04), are of interest because of their ferroelectric properties and their applications as infrared thermal Good single crystals of TGS can be grown from aqueous solution. Since the uptake of solute by the crystal is rapid, the TGS concentration and the fluid density within the diffusion layer surrounding the crystal is smaller than in the bulk of the solution. In normal earth gravity, this causes the solution within the diffusion layer to rise and to drive convection currents in the bulk. Dimensional arguments indicate that the rate of growth of the crystal in the presence of gravitational convection should be proportional to a fractional power of D, the TGS diffusion coefficient. By contrast, in the absence of accelerations as in the earth orbiting NASA Spacelab, the growth of the crystal can be expected to be diffusion controlled and to depend linearly upon D.4 Since D is an important parameter in distinguishing these two mechanisms, we have measured its value for aqueous solutions of TGS of varying concentration. Experimental Method The diffusion coefficient was measured with the diaphragm cell method described by Northrup and Anson in 1929.5 The cell we used, shown in Figure 1, is our modification of the one used by McBain and Dawson.6 It has a dimeter of 4.7 cm, an upper and lower chamber volume of approximately 100 cm3, and a sintered glass diaphragm of 0.5 cm thickness. The top of the cell is open to allow insertion of a stirrer, and the bottom chamber has a tube which extends above the fluid level in the top chamber. This tube allows for volume changes in the bottom solution during a run. A cover plate with a feed-through for the stirrer shaft can be placed over the cell during operation to prevent evaporation of fluid from the upper chamber. Dilute solutions of TGS were prepared by using degassed ASTM type I water. Degassing was necessary to prevent bubble formation in the bottom chamber during a run. After the refractive index of each solution was measured to established its initial concentration, it was placed in the bottom chamber, and an equal volume of ASTM type I water was placed in the top chamber. The diaphragm was filled with solution by pressing a cork into the extension tube before filling the top chamber. This drove solution into the pores of the diaphragm, eliminating bubbles. The cell was then placed in a thermostatted water bath controlled to fO.O1 OC, as shown in Figure 2, and the magnetic stirrer was inserted into the top chamber until it almost touched the diaphragm. A floating magnetic stirring bar floated against the underside of the dia(1) R. L. Kroes and D. Reiss, NASA TM-82394, 1981. (2) E. H. Putley in 'Semiconductors and Semimetals", Vol. 5 , R. K. Willardson and A. C. Deer, Ed., Academic Press, New York, 1970, Chapter 6. (3) E. T. Keve, Phillips Tech. Rev., 35, No. 9. 247-257 (1975). (4) V. G. Levich, "Physicochemical Hydrodynamics", Prentice-Hall, Englewood Cliffs, NJ, 1962, pp 127-136. ( 5 ) J. N. Northrup and M. L. Anson, J . Gen. Physiol., 12, 543 (1928). (6) G. W. McBain and C . R. Dawson, Proc. R. SOC.London, Ser. A , 148, 32 (1953).
TABLE I: Diffusion Coefficients of TGS Solutions T , "C 105D, cm2/s T, 'C 105D, cm2/s 25 30
35 40
0.87 i 0.14 0.92 i 0.06 1.18 f 0.20 1.40 f 0.06
45 50 55
1.50 f 0.22 1.42 f 0.03 1.58 0.21
*
phragm. These stirrers, running a t approximately 100 rpm, maintain the concentration on the top and bottom surfaces of the diaphragm equal to the bulk concentration of the solution in the chambers, by preventing the formation of stagnant boundary layers. A preliminary diffusion was allowed to proceed for about 0.5 to 1 h to allow a concentration gradient to be established in the diaphragm. The water in the top chamber was then replaced and the diffusion was allowed to proceed for 1 to 4 days, after which the solute concentrations of the top and bottom solutions were measured at 25 OC. The solution in the bottom chamber was not replaced after the preliminary diffusion because a run of 3 h duration made during this study produced no measurable change in the refractive index of the bottom solution, indicating that the concentration change in the bottom solution during the preliminary diffusions is negligible. A comprehesive review of the diaphragm cell method of measuring diffusion coefficients can be found in a 1945 paper by Gordon.' As applied to our cell, the basic assumptins are as follows: The cell diaphragm is considered to be equivalent to a collection of parallel channels of effective length I and total cross-sectional area A . Stirring keeps the solution in each chamber uniform in concentration right up to the entrance to the diaphragm pores. Transport through the pores is solely by diffusion with no convective mixing or streaming. The solution concentrations in the upper and lower chambers change very slowly because of their relatively large volumes compared to the volume diffusing through the diaphragm. This results in an essentially steady-state concentration distribution through the channels of the diaphragm. The diffusion coefficient can be computed from the formulas
where C1 and C3are the concentrations of TGS in the lower chamber before and after the run, respectively, while C, and C, are the concentrations in the upper chamber before and after the run. The time elapsed in the run is t, while the cell constant fl is given by
P=
:(;
+
&)
where Vl is the volume of the lower chamber, and V, is the volume of the upper chamber. The cell constant, (3, must be determined (7) A. R. Gordon, Ann. N. Y.Acad. Sci., 46, 285 (1945). (8) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworths, London, 1959.
0022-3654/85/2089-1657$01.50/00 1985 American Chemical Society
1658 The Journal of Physical Chemistry, Vol. 89, No. 9, 1985
Kroes et al.
a 7 6
5 4
3
2 . -
2
v
N
E
POROUS GLASS
105 9 8 7 G
5 DIFFUSION CELL
4
Figure 1. Diffusion cell. dSTIRRING
TEMPERATURE PROBE
3
MOTOR
f ,,
CIRCULATOR/ TEMPERATURE CONTROLLER
2
106
I
3.1
3.2
I
I
3.3
3.4
I
3.5
Figure 3. Arrhenius plot of the diffusion coefficient of TGS in aqueous solution.
POROUS
DIAPHRAGM
/
DIFFUSION CELL
Figure 2. Apparatus for measuring diffusion coefficients
by calibrating the cell with a solution of known D because the effective length and area of the pores cannot be measured directly. In this case NaCl, with D = 1.484 X lC5cm2/s for concentrations from 0.1 to 1 M ( D varies by
