239
VISCOSITY-CHAIN LENQTHRELATIONSHIP IN MOLTEN SULFUR SYSTEMS
Viscosity-Chain Length Relationship in Molten Sulfur Systems
by F. J. Touro and T. I(. Wiewiorowski Freeport Sulphur Company, Belle Chasse, Louisiuna
(Received Auguet 6,1966)
In this paper a theory is presented which quantitatively relates the viscosity of sulfur to the length and concentration of sulfur chains. The theory was successfully applied in correlating available viscosity data with sulfur chain length and concentration for the sulfur-hydrogen sulfide system as well as the pure sulfur system. In addition to the wellknown viscosity reducing effect which hydrogen sulfide has on sulfur at temperatures above 159", the authors predict that an opposite effect, though smaller in magnitude, should be observed below 159". The relationships derived should be generally applicable to other molten sulfur systems containing chain-terminating entities.
Introduction The viscosity of sulfur undergoes significant and Bacon and reversible changes with temperature. Fanelli' obtained viscosity data on highly purified sulfur, observing that, near its melting point (119"), sulfur is a moderately mobile liquid. Upon being heated, its viscosity initially decreases, reaching a minimum at about 157"; it then rises rapidly, reaching a maximum at about 187". With further increase in temperature, the viscosity of molten sulfur decreases slowly. A qualitative explanation of the viscosity curve implies that, below approximately 159", sulfur consists mainly of octatomic ring molecules, and a normal viscosity decrease occurs with an increase in temperature. The sudden rise in viscosity is attributed to the appearance of long sulfur chain molecules. Then, as the temperature rises, the concentration of polymeric sulfur continues t o increase, but the opposing effect of decreasing chain length due to thermal bond scission causes a gradual decrease in viscosity in the temperature range between 187" and the boiling point of sulfur. A quantitative theoretical treatment of the sulfur system has been presented by Tobolsky and Eisenberg.2 These workers have shown that the drastic viscosity change which occurs in molten sulfur at about 159" is a thermodynamically predictable consequence of the ring-chain polymerization equilibrium in sulfur. Bacon and FaneXli' observed that above 159" certain substances have a profound viscosity-reducing effect
on molten sulfur. Notably, small amounts of halogens or hydrogen sulfide reduce the maximum viscosity of sulfur from 93,000 cp. to a few hundred centipoises. Ruberoa carried out a very detailed study of the effect of hydrogen sulfide on the viscosity of sulfur. A theoretical interpretation of chemical equilibria in the sulfur-hydrogen sulfide system has been presented by Wiewiorowski and T o u ~ o .The ~ ability to suppress the viscosity of sulfur is a consequence of a chain termination reaction. For the sulfur-hydrogen sulfide system, the number-average chain length has been calculated over the entire molten sulfur range.4 In this paper the viscosity of sulfur systems is quantitatively related to the length and concentration of sulfur chains.
Theory The theory of viscosity of long-chain molecules is described by Glasstone.6 If q is the viscosity of a solution and qo is the viscosity of the pure solvent, then q - qo divided by qo is the specific viscosity, qap, of the solution. Specific viscosity divided by the concentration, W , is usually a linear function of concentration. The value of the specific viscosity divided by the con(1) R. F. Bacon and R. Fanelli, J. Am. Chem. SOC.,65, 639 (1943). (2) A. V. Tobolsky and A. Eisenberg, ibid., 81, 780 (1959). (3) P. A. Rubero, J. Chem. Eng. Data, 9,481 (1964). (4) T. K. Wiewiorowski and F. J. Touro, J. Phys. Chem., 70, 234 (1966). (5) S. Glasstone, "Textbook of Physical Chemistry," 2nd Ed., D. Van Nostrand Co., Inc., F'rinceton, N. J., 1946,p. 500.
Volume 70,Number 1 January 1966
240
F. J. Tom0 AND T. K. WIEWIOROWSKI
centration, when extrapolated to zero concentration, is known as the intrinsic viscosity, qi. For long-chain molecules, the intrinsic viscosity is related to the number-average chain length, P, of the dissolved substance by the equation
50.
40
-
PVRE %FIRSULFul EWllBRATED WTH H,S AT ONE ATMOSPHERE.
B
w
30-
qi = K(P)b
(1)
where K and b are constants. The theoretical significance of b and its relationship to the chain length merit some mention. A value of b equal to unity indicates that the molecules dangle randomly in the solution. On the other hand, coiling of molecules into spheres decreases the value of b so that, in the limiting case, b approaches zero as the degree of coiling approaches 100%. In applying the above theory to the viscosity of molten sulfur, the sulfur itself must be considered as both the solvent and the solute. Our pseudo-solution consists of octatomic sulfur rings which will be considered as the pseudo-solvent and sulfur chains which will be considered as the pseudo-solute. Viscosity will be a function of temperature, concentration, and chain length; q = f(T,W,P). In order to simplify the equation, the temperature effect can be minimized by considering the ratio of viscosity of the pseudo-solution to the viscosity of the pseudo-solvent, q/qo, both taken at the same temperature. If 1 is subtracted from the above ratio, then the term is the same as the specific viscosity, (q - qo)/qo, and for small temperature intervals should be independent of temperature. With the assumption that sulfur chains behave in the same manner as other chains, eq. 1 should be applicable to the molten sulfur system. Unfortunately, the intrinsic viscosity cannot be determined directly. However, it can be related to specific viscosity and chain concentration by the equation
From eq. 1 and 2 the following relationships can be derived qap =
aW2
+ KWPb
(34
or
v - 9 0 - aW2 + KWPb 70
s
E
20-
0
B 10
4bo
;0
;20
(3b)
(4)
:60
: 4 Q
;SO
TEMPERATURE
;I0
W ;
;90
: Q C
(*K 1
Figure 1. Viscosity of pure sulfur, sulfur equilibrated with hydrogen sulfide a t 1 atm. of HzSpartial pressure, and theoretical sulfur rings vs. temperature.
Equation 4 expresses the chain length, P, as a function of specific viscosity and chain concentration. Since a is difficult to evaluate and since the term aW is insignificant at high viscosities, it is neglected in our calculations.
Results and Discussion K and b were determined utilizing the data on viscosities, chain lengths (in terms of Ss units), and concentrations for pure sulfur1r2 and sulfur equilibrated at 1atm. of hydrogen ~ u l f i d e . ~ , ~ K was found to be equal to 1 and b to 0.9. As a result, the following equation was formulated for calculating sulfur chain lengths in molten sulfur systems. (5)
According to the value found for b, sulfur chains can be characterized as having the equivalent of 90% random orientation and 10% coil. The sulfur-ring viscosity, i.e., the viscosity of the pseudo-solvent, was found by extrapolating the pure sulfur data to temperatures beyond the transition temperature (159") using the equation
In 70
Rearranging eq. 3b
The Journal of P h y s k d Chemistry
W 2
42.64
- 6.74 In T
(6)
Table I gives the viscosity of pure sulfur ( q ) , of sulfur equilibrated with hydrogen sulfide (s'), and of the pseudo-solvent (qo) at various temperatures. Also included in Table I are chain concentrations in pure sulfur ( W ) ,chain concentrations in sulfur equilibrated with HzS (W'), chain lengths (P and P') from litera-
VISCOSITY-CHAIN LENGTHRELATIONSHIP IN MOLTEN SULFUR SYSTEMS
241
Table I : Viscosities, Chain Lengths, and Chain Concentrations in Pure Sulfur and Sulfur Saturated with Hydrogen Sdiide a t 1 Atm.
OK,
425 428 430 440 450 460 470 490 510
7,
op.5
OP.
6.93 7.18 7.36 40,000 74,000 92 ,000 85,000 54,000 25,500
16 17 19 26 37 51 65 95 125
6.4 6.0 5.9 5.0 4.3 3.7 3.2 2.4 1.9
W
...
...
3.8 X 10" 0.25 0.54 0.76 1.01 1.38 1.69
Extrapolated from data in ref. 3. a Taken from ref. 2.
in sa
in 88
W'
units*
unite?
unitad
unitsa
0.16 0.22 0.26 0.46 0.68 0.88 1.10 1.45 1.74
16.4 27.6 57.6 112,300 113,900 94,500 75 ,800 46,000 28 ,400
10.0 11.0 12.4 17.0 22.9 27.0 31.7 37.4
12.0 10.5 10.8 11.6 14.6 19.5 24.1 38.2 55.4
P* =
?)OW']1.1.
t ~ r e and , ~ ~chain ~ lengths (P* and P'*) calculated from viscosity data using eq. 5. The general agreement between P and P* and between P' and Pr* was good considering the approximations which were used in deriving eq. 5. Two assumptions which could account for deviations are restated: (1) the term aW was neglected and may be significant for short chains; (2) temperature effects were neglected but undoubtedly may contribute some error over the relatively large temperature range which was covered. A plot of the viscosity of pure sulfur, of the pseudo-solvent, and of sulfur equilibrated at 1 atm. of hydrogen sulfide overpressure is presented in Figure 1. Although hydrogen sulfide is commonly referred to as a viscosity-reducing agent for sulfur, the results presented in Table I indicate that, below the transition
PI*,
p*, in sa
70,
CP.
P',
in sa
p, Temp.,
[(q
...
... ...
100,000 100,000 103,000 80,600 47,400 21 ,300
- qo)/q0W]1J.* Taken from ref. 4.
42.5 a
P'*
= Kq'
- TO)/
temperature (159"), an increase in viscosity should be observed. This is a consequence of the higher chain concentration encountered in the sulfur-hydrogen sulfide system as compared to the pure sulfur system at temperatures below 159". Above the transition temperature, the viscosity of pure sulfur increases drastically compared to the moderate increase in viscosity of the sulfur-hydrogen sulfide system. This is a consequence of the formation in pure sulfur of chain molecules having a length of lo5 Ss units. In the sulfur-hydrogen sulfide system not only chain termination occurs but also a shift in the ring-chain equilibrium towards a higher concentration of shorter chains. The number-average chain length is three to four orders of magnitude lower than in pure sulfur giving rise to the differences in the viscosities of the two systems.
Volume 70,Number 1 Janwrsy 1066
