VISCOSITYOF MOLTEXBi-Bi HALIDE SOLUTIOXS
1737
The Viscodty of Molten Bismuth-Bismuth Halide Solutions1 by Jordan D. Kellner Atomics International, A Division of X o r t h American Rockuell Corporation, Canoga P a r k , California 91304 (Received -7Vol;ember 15, 1967)
The viscosities of solutions of bismuth in BiBrs and in BiC13 were measured by a capillary technique up to 600". When compared to the data for the iodide reported earlier, the viscosity is greatest for the iodide solutions and least for the chloride solutions. The Arrhenius coefficients are greatest for the chloride system and least for the iodides and increase with decreasing temperature for the chloride and bromide solutions. These results are shown to be consistent with the "free-volume" model of transport in ionic melts. Introduction I n a previous paper,2 the viscosities of Bi-BiI, solutions were measured at temperatures ranging from 400 to 500O. The consolute temperature of 458" in this system made it possible to measure the viscosities of all compositions with Pyrex capillary cells. In this paper the work is extended to include the bismuthbismuth bromide system above the consolute temperature of 538", across the entire composition range. The bismuth-bismuth chloride system was studied only up to 30 mol % metal and 600" because of its high consolute temperature (780'). Experimental Section The bismuth halides used were obtained commercially and distilled twice under about 0.25 atm of oxygen. These salts and the purified bismuth2 were handled only under dry argon. The technique is identical with that reported previously.2 The cells were constructed of quartz so that temperatures above the consolute temperature (538") in the bromide system could be reached. Due to the high pressures (-10 atm) generated at 600°, heavywalled quartz (4 mm) was used. The tungsten to quartz compression seals used were similar to those described by Grantham and Yosime3 The cell was calibrated at room temperature with 10% glycerinewater solution, double-distilled water, heptane, acetone, and ether. I n all calibrations a straight line was obtained when v / p , the ratio of the viscosity to the density, was plotted us. time. Only three different cells mere used in all the determinations, one of them for about 75% of the compositions studied. The calibration curves were checked before each run, and virtually no changes were noted. The corrections that must be applied for the difference in temperature of unknown and standard liquid were less than the estimated error and were not applied. Results and Discussion The viscosities of Bi-BiBr3 solutions containing 0, 15, 30, 45, 50, 60, and 80 mol % Bi and BiC13 solutions
containing 0, 15, and 30 mol % Bi were determined a t temperatures ranging from 220 to 600". Higher concentrations of metal in BiC13were not run because of the limited solubility of the metal in the salt at these temperatures. The viscosity of pure bismuth could not be determined with this apparatus because of the very low value of the kinematic viscosity ( v / p = 0.12 cSt at 500"). The flow velocity of bismuth through the capillaries used was great enough to cause turbulent flow with a resultant scatter in the data. Therefore, the literature value4 for the viscosity of pure bismuth was used. The kinematic viscosities calculated from the calibration equation were combined with density data to obtain the viscosity values. Up to 40 mol % Bi, the data of Keneshea and Cubicciotti5 for the densities of chloride and bromide solutions were used. The densities of more concentrated solutions were obtained by interpolation using a value at 70 mol % for the The viscosities bromide6 and a value for bismuth.' are shown in Table I for the bromide system and in Table I1 for the chloride. Figure 1 shows the values for the three pure halides. ,4smooth curve was drawn through a plot of time of flow us. temperature for each solution, and the time of flow at 10" intervals from the smoothed curve was used to calculate the viscosity data. The standard deviation of the measured flow time from the smooth curves was 0.06 sec for flow times of about 40-100 sec. Based on this factor and an estimated error in temperature measurement, the data are estimated to be accurate to within 2%. The data obtained for the Bi-BiC1, solutions and for pure BiC13 are lower by more than a factor of 10 than those given (1) This work was supported by the Research Division of the U. S. Atomic Energy Commission. (2) J. D. Kellner, J . P h y s . Ckem., 71, 3254 (1967). (3) L. F. Grantham and S. J. Yosim, J . Chem. Phys., 38, 1671 (1963). (4) F. Sauerwald and K. Topler, 2. Anorg. Chem., 157, 177 (1926). ( 5 ) (a) F. J. Keneshea and D. Cubicciotti, J . P h y s . Chem., 62, 843 (1958); (b) ibid., 63, 1472 (1959). (6) L. E. Topol and F. Y. Lieu, ibid., 68,851 (1964). (7) E. Gebhardt and K. Kostlin, 2. Metallk., 48, 601 (1957). v o l u m e Y8,Number 6
M a y 1968
1738
JORDAN D.KELLNER ~ 2.75
I
I
I
l
I
I
I
/
Ir
T E M P E R A T U R E (’C )
5.4
I
600
550
I
I
500 I
1.2
1.3
450 I
400 1
350
300 I
I
2.50
1.1
1.4
1.5 VT
1.6
1.7
1.8
x 103
Figure 2. Plots of In viscosity vs. 1/T for BiCla, BiBra, and BiIa.
i 0
1
300
I I I 420 460 500 TEMPERATURE ( ’ 0
I
340
380
I
I
540
580
6.0
620
Figure 1. ‘Viscosity vs. temperature for the pure salts BiCla, BiBra, and BiIa.
5.0
by Atens in 1909. Since Aten’s temperature coefficients are nearly the same as those of the present work, one can only suggest that the units Aten called “absolute units” are really decipoises instead of poises. At any particular temperature the viscosity of the pure salt increases as the size of the anion increases (see Figure 1). This dependence of the vigcosity on the anion size is observedg in most metal halides. This sequence is reasonable in view of the fact that the viscosity of the melt depends mainly on the mobility of the largest ion in contrast to electrical conductivity where the smallest ion is more important. The usual Arrhenius equation
4.0
‘t I
AeElRT
The Journal of Physical Chemi8tTU
-!
c
3.0
2.0
1.0
0
(1)
was used to calculate an “Arrhenius coefficient,” E , of viscosity. The values of the Arrhenius coefficient which have been called in the literature and in the previous paper “apparent activation energy” are shown in Table 111for the three bismuth halide systems. The In 7 us. 1/T plots for the three pure salts are shown in Figure 2. The “Arrhenius coefficient” of viscosity is greatest for the smallest anion, C1- and least for the largest anion, I-. The viscosity isotherms as a function of composition for the metal solution of the bromide and chloride systems are shown in Figures 3 and 4. Most of the isotherms in Figure 3 could not be completed because an immiscibility gap is present a t that temperature and composition. The isotherms in Figure 4 end a t 30 mol % because of the high consolute temperature in this system; however, it seems likely from the similarity of
i
I
0
7
I
0.2
0.4
0.6
0.8
1.0
xB,
Figure 3. Viscosity isotherms for the Bi-BiBra system.
the isotherms for the three halides that a maximum would be found for the chloride isotherms if the melts were studied a t a high enoukh temperature. The maxima appear a t about the same composition in the bromide system and in the iodide system reported earlier.2 The In 7 us. 1/T plots for the metal solution of the bromide and chloride systems are shown in Figures ‘5 and 6. One can see in Table I11 that generally, the “Arrhenius coefficient’’ of viscosity increases with added metal, reaching a maximum at 50% in the iodide Aten, Z. Phylsik. Chem., 66, 641 (1909). (9) G.J. Jam, A. T. Ward, and R. D. Reeves, “lMolten Salt Data,” Technical Bulletin Series, Rensselaer Polytechnic Institute, Troy, N. Y.,1964. (8) A. H. W.
1739
VISCOSITYOF MOLTEN Bi-Bi HALIDESOLUTIONS Table I: The Viscosity of Bi-BiBrs Solutions Viscosity,---a-P-
Temp, OC
0% Bi
15%
600 590 580 570 560 550 540 530 520 510 500 490 480 470 460 450 440 430 420 410 400 390 380 370 360 350 340 330 320 310 300 290 280
0.845 0.862 0.880 0.892 0.919 0.935 0 956 0.979 1.00 1.03 1.06 1.08 1.11 1.14 1.16 1.20 1.24 1.27 1.31 1.36 1.41 1.47 1.54 1.60 1.66 1.75 1.83 1.92 2.02 2.13 2.28 2.45 2.66
1.04 1.06 1.08 1.09 1.11 1.13 1.16 1.18 1.22 1.25 1.29 1.32 1.36 1.41 1.45 1.50 1.55 1.60 1.66 1.72 1.80 1.89 2.00 2.12 2.24 2.40
I
-
30%
1.60 1.66 1.73 1.79 1.88 1.95 2.04 2.14 2.24 2.37 2.49
6
35OoC
4OO0C -1
45OoC 5OO0C 550°C 6OO0C
0
0
0.2
0.4
”
0.6
0.0
1.0
“Bi
Figure 4.
Viscosity isotherms for the Bi-BiCls system.
45 %
50%
1.47 1.51 1.54 1.59 1.63 1.68 1.74 1.80 1.87 1.95 2.03 2.12 2.22 2.32 2.44 2.56 2.73 2.89 3.10 3.28 3.62 3.88 4.19 4.47 5.00 5.72 6.51 7.27 8.23 9.31 11.06 12.91 14.81
1.49 1.52 1.58 1.61 1.67 1.73 1.76 1.81 1.89 1.99 2.13 2.39 2.68 2.97 3.22 3.47 3.71 3.97 4.24 4.49 4.72 5.09 5.51 5.94 6.36 7.15 8.24 9.81 11.4 13.0 14.6
60%
80%
1.38 1.41 1.47 1.51 1.58 1.63 1.70 1.75
1.20 1.22 1.25 1.27 1.31 1.35 1.38 1.44
and 60% in the bromide. There is a small increase in the coefficient at low temperatures for all the solutions studied. The iodide data were interpreted according to the “hole” theory of viscosity in the previous paper.2 This model pictures viscous flow as consisting of two steps. First a suitable hole forms from the free volume available to the melt and then the “flow unit” breaks away from its neighbors and enters this space. If one of these processes dominates the other, then “Arrhenius behavior” is observed; L e . , eq 1 holds. The iodide melts can be considered to be “free volume limited,” in that the rate-determining step in the flow process is the formation of a hole. The maximum in the isotherm is caused by a diminution in the free volume as metal is added, the free volume reaching a minimum at about 50 mol Bi. However, the fact that the iodide melts follow the Arrhenius equation is probably a result of the narrow temperature range of the data (-400-500”). I n the chloride and bromide cases where the temperature range is greater than 300“, the temperature Volume 78, Number 6
M a y 1968
JORDAN D. KELLNER
1740 ~
~
~
Table 11: The Viscosity of Bi-BiCls Solutions Viscosity,
Temp, OC
600 590 580 570 560 550 540 530 520 510 500 490 480 47 0 460 450 440 430 420 410 400 390 380 370 360 350 340 330 320 310 300 290 280 270 260 250 240 230 220
c
pi
15%
30%
0.539 0.552 0.562 0.573 0.592 0.606 0.620 0,637 0.655 0.672 0.693 0.718 0.743 0.771 0.807 0.843 0.897 0.937 0.985 1.04 1.10 1.16 1.22 1.29 1.37 1.46 1.54 1.66 1.77 1.90 2.05 2.20 2.36 2.59
0.642 0.656 0.674 0.692 0.721 0.753 0.787 0.820 0.854 0.892 0.930 0.979 1.03 1.08 1.13 1.18 1.25 1.31 1.38 1.46 1.55 1.64 1.73 1.83 1.93 2.05 2.19 2.33 2.52 2.73 2.95 3.24 3.56 3.93 4.42 5.07 5.86 6.77 7.96
0.879 0.907 0.944 0.984 1.03 1.07 1.12 1.17 1.22 1.28 1.35 1.43 1.50 1.59 1.68 1.78 1.87 1.97 2.08 2.19 2.31 2.49 2.67 2.94 3.14 3.34 3.64 3.99 4.41 4.85 5.43 6.02 6.77
4.0
-
3.6
-
---Temperature 300-400
XBi
-
range, 'C
400 5 00
500-600
Bi-BiIs
0 0.15 0.30 0.45 0.50 0.55 0.60 0.70 1.00
1.72 2.04 2.08 4.79 6.53 6.45 5.56 1.35 1.84 Bi-BiBrs 3.68 4.78
0 0.15 0.30 0.45 0.50 0.60 0.80 1.00
8.40 10.8
0 0.15 0.30 a
2.98 3.44 4.57 5.62
2.98 3.01
1.30
1.84
3.79 3.90 4.70 4.26 2.21
Bi-BiCla 4.8 7.7" 6.97
4.8 5.2 5.75
3.4 5.2 5.75
220-300'
, ,
600 550 500 5
,
2
TEMPERATURE ('0
450
~
4yO
370
3qO
2:O
2:;
4'41 \' 4.2
300
500
I/T x 103
-
3.2 -
2,81 2.4
.45% Bi
2.0
1.0
-
~~~~~
1
TEMPERATURE ( O C ) 400
600
4.8
CP
0%
~-
Table 111: Arrhenius Coefficient of Viscosity (kcal/mol)
I
I
I
1.1
1.2
1.3
I 1.4
I
I
1.5
1.6
1.7
1,8
VT x 103
Figure 5 . Plots of In viscosity us. 1/T for the Bi-BiBra system. (The 50% data were omitted for clarity.) The Journal of Physical Chemistry
i 1.9
Figure 6. Plots of In viscosity us. 1 / T for the Bi-BiCls system.
coefficient of viscosity is dependent on temperature (see Table 111). Also, the Batchinski equation is not followed in the bromide and chloride cases, whereas it is followed in the iodide system. However, if a short 100" range is chosen, then the Batchinski equation holds equally well in all three systems. The increase in Arrhenius coefficient may be due to the equilibrium that exists at low temperatures in the chloride and bromide systems between the monomer subhalide BiX
1741
VISCOSITY OF MOLTEN Bi-Bi HALIDE SOLUTIONS 7
I
I
1
8,5
i- L
8.0
-
7.5
-
7.0
-
6.5
-
I
8.5
I
I
I
o I
c 0
7.5
0 0
A
O%Bi 15%Bi 30%Bi 45%Bi 50%Bi 60%Bi 80%Bi
‘
5 T
p.
1
-
6.0
5.5
15% B i
-
6.0 I
I
I
I
2
3
4
5
Figure 8. Plot of In , / T ’ i 2us. 1/(T for the Bi-BiCls system.
- TO)
5.0
5.5
t
5.0
I
2
I
I
3
4
I T -To
5
I
- To)
and polymeric form, probably (BiX),.lO In the past, an increase in the Arrhenius coefficient a t low temperatures was taken to be caused by complexing. However, it is of interest to see how the data fit the free-volume model of Cohen and TurnbulL’l These authors derive the following expression which is similar to an empirical equation used earlier by Doolittle12 for the diffusion coefficient, D ,in a fluid of hard spheres
D
= ga*u exp(- yv*/vr)
(2)
where g is a geometric factor, a* is approximately equal to the molecular diameter, u is the gas kinetic velocity, y is a factor between and 1 to correct for overlap of free volume, v* is the minimum hole volume necessary for a migration to occur, and vf is the free volume. Hogenboom, Webb, and Dixon13 point out that the viscosity relation, using the Stokes-Einstein equation and eq 2 , should be In v/T’” = In A
+ BVf
(3)
where B is yv*. As pointed out by Barlow, Lamb, and Matheson,14this equation is equivalent to In T/Ti’’ = In A
K + T- To
I x~03 T-To
6
lo3
~ 1/(T Figure 7. Plot of In V / T ” US. for the Bi-BiBra system.
I
(4)
where K = yv*/afi, a being the thermal expansivity, and 8 the mean molecular volume. Equation 4 follows if the specific volume is a linear function of the temperature and if all liquid expansion appears as an increase in free volume. Equation 4 has been used empirically for many years to describe the viscous behavior of liquids. I n Figures 7 and 8, In v/T1’2plotted us. 1/(T - TO)is shown for the bromide and chloride systems. These lines were obtained by a computer program in which In v/Tl/’ and T for each composition were given, and K , To, and In A were determined. The values for these quantities for each composition studied are shown in Table IV. It seems remarkable, as Figures 7 and 8 show, that all the data for all compositions of each halide fall on the same straight line. However, until there is some independent way to calculate these quantities from structural parameters, eq 4 must be considered as merely a three-parameter fit for the data, which would be expected to be better than a two-parameter equation. Nevertheless, the fact that the constants K and In A are the same for all the com(10) (a) L. E. Topol, S. J. Yosim, and R. A. Osteryoung, J . Phys. Chem., 6 5 , 1511 (1961); (b) L. E. Topol and R. A. Osteryoung, ibid., 66, 1587 (1962). (11) M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). (12) A. K. Doolittle, J . A p p l . Phys., 2 2 , 1471 (1951). (13) D. L. Hogenboom, W. Webb, and J. A. Dixon, J . Chem. Phys., 46, 2586 (1967). (14) A. J. Barlow, J. Lamb, and A. J. Matheson, Proc. Roy. Soe. (London), A292, B22 (1966). Volume ‘72, Number 6
M a y 1968
JORDAND. KELLNER
1742
Table IV : Values of the Constants in Eq 4 Tu In A
BiBrs 15% Bi 30% Bi 45% Bi 50% Bi 60yGBi 80% Bi BiCls 15% Bi 30% Bi BiIs 15% Bi 307, Bi 45770 Bi 50% Bi 55% Bi 60% Bi 70% Bi a
-9.72 -9.53 -9.56 -9.52 -9.50 -9.50 -9.51 - 10.97 -10.98 -10.93 (- 8 . 65)a
K
1086 1008 1017 1006 1000 1000 1000 1740 1703 1752 (561)a
OK
A
x
104
0.60 0.72 0.71 0.73 0.75 0.75 0.74 0.17 0.17 0.18 (1.7)a
Average values for all compositions.
positions that contain the same anion is suggestive that To does indeed have a physical meaning, Le., the temperature at which the free volume disappears. The iodide system is not plotted because the short range of values for In 7/T1”makes the choice of To almost arbitrary. However, if one does choose values of To for the iodide melts, to force the data for all
The Journal of Physical Chemistry
compositions to be on the same line, then this line will have a smaller K value, a smaller A value, and intersect the other two curves within a region common to all three systems. The parameters K , In A , and To are given for the iodide system in Table IV in parentheses to emphasize that they are approximate. These three lines have a common intersection because each line contains some points that correspond to a composition of 100% bismuth, and the viscosity of pure bismuth at these temperatures would give In V / T ” ~values of between -7.5 and -7.8. According to the Cohen-Turnbull equation (eq 2), and the Stokes-Einstein relation, A in eq 3 is proportional to rn1/’/a2,where na is molecular weight and a is ionic diameter. Thus, A should increase in the order C1, Br, I as is shown to be the case in Table IV. Since at a temperature T , the viscosity is dependent only on A , K , and T - To in eq 4, and for all solutions containing the same anion, K and A are the same, the differences in viscosity are due to the term (T - TO). This term is proportional to free volume and goes through a minimum as the bismuth concentration increases causing the viscosity to go through a maximum. This picture is consistent with the minimum in free volume found in the iodide system at 55 mole % z and with the fact that the molar volume isotherms show negative deviations from ideality for all three systems.
Acknowledgment. The author is indebted to Mr. Alex Kickols for the computer calculations.
