Marshall, W. T., Hurn, R. W., Society of Automotive Engineers, Paper 680528, 1968. Martin, G. B., Pershing, D. W., Berkau, E . E., "Effects of Fuel Additives on Air Pollutant Emissions from Distillate Oil-Fired Furnaces," Environmental Pollution Agency, 1971 McConnel, G., Howells, H. E., Society of Automotive Engineers, Panpr 67nOF)l. - - - - - 1967. --r--
Miller, C. O., ibk:Paper 670093, 1967. Millington, B. W., French, C. C. J., ibid., Paper 660549, 1966. Norman, G. R.. ibid.. PaDer 660339, 1965. Randall,' N. P.; Pecora, B. J., Hersler, R. Y., Hopkins, S.,Proc. Amer. Petrol. Inst., 111, 1-12 (1960).
Shayeson, M. W., Society of Automotive Engineers, Paper 670866,1967. Sobolev, E. P., Rubinshtein, I. A., Khim. Tekhnol. T o p l . Masel, 54, 13 (1968). Tessier, K. C., Bachman, H. E., American Society of Mechanical Engineers, Paper 68-WA4/DGP-4,1968a. Tessier, K. C., Bachman, H. E., ibid., Paper 68-WA IDGP-5, 196%. RECEIVED for review April 19, 1972 ACCEPTEDSeptemberl2, 1972
Compound Redistribution Reactions Edmund 1. Niedzielski Jackson Laboratory, Organic Chemicals Department, E . I . du Pont de Kemours & Co., P.O. Box 526, TPilmington Del. 19899
Compound redistribution mixtures of [(R0)2PSS]aZnnOHand [(RO)ZPSS]zZn offer improvements in physical properties-viscosity, pour points, solubility in mineral oil, and crystallization during storage-which are not possible with the individual compounds of the same molecular weights. A number of variables among the mixed compounds affect the properties of these mixtures, namely, the formula weight, the proportion of the small size, or limiting, ligands and the number of different ligands incorporated in the original reaction mixture, and the size and structure of the nonlimiting ligands. A simplified multinomial model i s the basis for calculating the number of mixed compounds and correlating the properties and the concentration of the limiting mixed compounds in such mixtures. Application of the model to related mixtures of [(R0)2PSS]&b i s also discussed.
C o m p o u n d redistribution or scrambling reactions are multistep processes in which a n exchange reaction occurs during each step of the process. In contrast with simple redistribution reactions (in which monofunctional ligands or substituents may be redistributed on polyfunctional groups) , compound redistribution reactions are more difficult to define chemically because the experimental methods for determining the equilibrium composition are limited (Lockhart, 1970; lfoedritzer, 1968). I n fact, the difficult analytical problem seems to have been responsible for the enigma concerning compound redistribution reactions, especially those involving mixed compounds of metal 0,O-dialkyl phosphorodithioates prepared from 0,O-dialkyl hydrogen phosphorodithioates redistribution mixtures (Higgins and LeSeur, 1961). S e u t r a l zinc 0,O-dialkyl phosphorodithioates have been used in the past two decades as multifunctional inhibitors in lubricating oils. Many commercial offerings have been redistribution mixtures derived from a mixture of alcohols, two or three in number and containing a t least three carbon atoms. X study of redistribution mixtures was undertaken when it was found that oil-free mixtures of the basic zinc double salt of 0,O-dialkyl phosphorodithioates could be prepared, which did not crystallize on standing despite the presence of some smaller size ligands. I n the absence of any data on the equilibrium composition of such mixtures, the only method available for predicting the composition would be the multinomial theory (Feller, 1950; Kendall, 1952). The reliability of the multinomial theory, however, tends to suffer as the exchange reactions 434
Ind. Eng. Chem. Prod. Res. Develop., Vol. 11, No. 4, 1972
become more complex. There are a number of reasons for the decrease in reliability-occurrence of side reactions and the influence of irreversible decompositions, skewness of the distribution when widely varying proportions of the different ligands are used, and the unequal bond energies of the different ligands. Multinomial Theory
The equilibrium composition of a mixture of compounds with central atom AI (functionality n) and ni ligands ( X , Y , Z) may be calculated statistically (Calingaert and Beatty, 1943). The number of different compounds which can form is
+
(n m - I)! n ! ( m - l)! The concentration of the mixed compounds JILYaYbZ,, etc., will be
where fi = mole fraction of X , f, = mole fraction of Y , etc., . . + j = n. and wherea b c
+ + +
Simple Redistribution Reactions
-4classic example of a simple redistribution reaction is the exchange between l I e r P b and EtaPb in the presence of a catalyst (Calingaert and Beatty, 1943). The reaction of a n
Table 1. Effect of Number of ligands (m) on Number of Redistribution Compounds
1 2 3 4
1 6 21 55 120 231 406 666 1035 1540
1 3 6 10 15 21 28 36 45 55
5 6 7 8 9 10
equimolar mixture yields five compounds in the proportions given 8MerPb
+ 8EtrPb
+ 41Lle3EtPb + 6Me~EtzPb+ 4MeEtaPb + EtrPb
+
MerPb
+ 4EtOH + P4S10
+
(Me0)zPSSH
2(MeO)(EtO)PSSH
+
+ (Et0)zPSSH + 2HzS
(4)
The resulting 0,O-dialkyl hydrogen phosphorodithioate contains a monofunctional ligand which is capable of further reaction with polyfunctional metal compounds. Compound Redistribution Reactions
The number of metal 0,O-dialkyl phosphorodithioate compounds resulting simultaneously from the reaction of a polyfunctional metal compound with a redistribution mixture of 0,O-dialkyl hydrogen phosphorodithioate is dependent on the following: The number of 0,O-dialkyl hydrogen phosphorodithioate intermediates present (i), Le., ,
2 =
+
(2 m - l)! 2!(m - I)!
The functionality of the metal atom The proportion of the reactants used in the reaction
It is assumed throughout this paper that stoichiometric amounts of reactants are used in each step of the redistribution process. The stoichiometry in the preparation of the metal 0,Odialkyl phosphorodithioates discussed in this paper is the following: 2(RO)zPSSH 3(RO)zPSSH
+
+ ZnO
+ 2ZnCls
[(RO)zPSS]zZn
4NaOH
+ HzO
+ [(RO)zPSS],Sb + H?O
3(RO)zPSSH
+ 1/2Sbz03
+
The number of mixed compounds of [(RO)zPSSIzZn, j , that can result from Equation 6 depends on the sum total of mixed compounds of (R0)zPSSH available for reaction, i.e., (9) The number of mixed compounds of [ (R0)2PSS]3Zn~OH, k , prepared according to Equation 7 is a function of the number of mixed compounds of [(RO)zPSS]zZnand the number of compounds of (RO)2PSSH,Le.,
k
=
i . j
(10)
The number of mixed compounds of [(RO)zPSS]&3b, I , prepared according to Equation 8 is a function of the central atom functionally (m = 3) and the number of compounds of (R0)zPSSH available for reaction, Le.,
I=
+
(3 i - l)! 3!(i - l)!
Table I shows the effect of the number of alcohols on the number of mixed compounds of (R0)zPSSH and the metal 0,O-dialkyl phosphorodithioates when stoichiometric amounts of reactants are used in each reaction step. For example, theory predicts 21 compounds when a mixture of six alcohols is reacted according to Equation 4. When this mixture is reacted further according to the stoichiometry of Equations 6-8, theory predicts 231 compounds of [(RO)zPSS]zZn,4851 compounds of [ (R0)2PSS]3Zn20H,and 1771 compounds of [(R0)2PSSIrSb,respectively. If, instead of reacting all six alcohols a t one time, two separate mixtures of three alcohols each are prepared and reacted with PZSC,and the resulting compounds of (R0)2PSSH are then combined, theory predicts the formation of only 12 compounds. Such a mixture, when reacted similarly according to Equations 6-8, is expected to yield, respectively, 78 compounds of [ (RO)zPSS]eZn,936 compounds of [ (RO)zPSS],ZnzOH, and 364 compounds of [ (RO)zPSS]3Sb.Therefore, optimization of properties of compound redistribution mixtures can be facilitated by incorporating all of the ligands together in the first reaction step rather than by combining separately prepared mixtures.
(6)
Redistribution Mixtures of [(RO)ZPSS]JZ~~OH
(7)
I n a study of the properties of [(RO)2PSS]3ZnpOH mixtures, the question was posed whether low-molecular-weight ligands-R = Me, E t , Pr, Bu-which yield crystalline compounds could be incorporated into such mixtures without
+
[ ( R O ) Z P S S ] ~ Z ~ Z O H4NaC1
1 10 56 220 680 1771 4060 8436 16,215 29 ,260
(3)
Another type of reaction is the simultaneous redistribution reaction in which exchange occurs during the course of the reaction. An example of such a reaction type is the preparation of 0,O-dialkyl hydrogen phosphorodithioate by the reaction of a mixture of alcohols and PZSS (Kosolapoff, 1950). When a n equimolar mixture of MeOH and EtOH is reacted, three compounds in the proportions given are obtained. 4MeOH
1 18 126 550 1800 4851 11,368 23 ,976 46,575 84 ,700
(8)
Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 , No. 4, 1972
435
Table It. Properties of [(R0)2PSS]3ZnzOHCompounds Viscosity, cSt
Solubility in
R
Mol wt
State
21 O°F
100°F
Me i-Bu n-He
619 871 1039
Solid Solid Liquid
... ... 18.1
...
minerol oil
Insoluble Insoluble Very soluble
...
171.8
Analysis
% 22.4 13.8 11.4
Znt
s, 70 26.9 22.8 19.1
p, % 14.3 11.2
10.4
Table 111. Classification of limiting Combinations of Mixed Compounds of [ (R0)2PSS]3ZnzOH Group
I 11 111
ligand combinations
XEj X5yj x4yZ~X3Y3, XZY4, XYS,Ye X Z , X4Y2,X3Y22,X2Y32, XYJ,Y * Z xzz,X ~ Y ~XzYaz, Z , XYgz,
Mol fraction of mixed compounds
(X 6(X
+
Y)6
+ Y)5Z
15(x f
Y)4z2
Y4z2
Figure 1 . Concentration of limiting mixed (RO)zPSSHderived from multinomial theory and viscosity of [(RO)zPSS]3ZnzOH mixtures
adversely affecting their physical properties-viscosity, pour point, oil solubility, and crystallization during storage under ambient temperature conditions (Wystrach e t al., 1956).The effect of the size of the ligand on the properties of [(RO)2PSSI3Zn2OH is shown in Table 11. A mixture of six alcohols was chosen, MeOH, i-BuOH, and four isomeric hexyl alcohols. The proportion of the alcohols was varied, but the average molecular weight was held constant. Note that the average molecular weight corresponded to the molecular weight of [ ( ~ - C ~ H ~ O ) ~ P S S ] ~ Z a ~crysZOH, talline solid, melting at 138-14OoC and practically insoluble in mineral oil (Bacon and Bork, 1962). Thus, the mixtures of alcohols were reacted according to the stoichiometry of Equation 4. The resulting (R0)zPSSH redistribution mixtures were then reacted further according to Equation 7 to yield mixed compounds of [(R0)2PSS]3Zn2OH. Since the equilibrium composition of either (R0)zPSSH or [(R0)2PSS]3ZnzOHmixtures could not be measured, the multinomial theory was used to correlate the effect of the ligands on the properties of the [(R0)2PSSI3Zn2OH redistribution mixtures. Simplifying Statistical Model
Computing the composition of a redistribution mixture containing as many as 4851 compounds would indeed be a time-consuming venture. Consequently, the multinomial model was simplified so that the composition of the low436
Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 1 ,
No. 4, 1972
molecular-weight ligands, which are property limiting, would be given greater emphasis than the higher molecular-weight ligands, which are nonlimiting. Thus, the two limiting ligands, Me and i-Bu, were designated X and Y,respectively, whereas the nonlimiting ligands were grouped together under 2. The original model of 4851 compounds was abbreviated to 126 combinations, and of these only a small portion would be expected to limit the properties of the redistribution mixtures. The grouping of the X and Y ligands as being distinct from the Z ligands serves the purpose of converting the multinomial model to binomial. The following were the assumptions underlying the application of the binomial model: The size of the ligand had no effect on the redistribution reaction. The different ligands were independent of each other.
If these assumptions were satisfied, only mixed compounds containing ligands X and Y would limit the properties of the redistribution mixtures. For example, of the three groups of mixed compounds listed in Table 111, the Group I combination comprising only ligands X and Y would be more limiting on the physical properties of the redistribution mixture than the Group I1 combination which, in turn, would be more limiting than the Group I11 combination and so on. Since only the proportion of ligands X and Y in the initial mixture was assumed to influence the theoretical composition of both the intermediate and the Group I combinations of mixed compounds, the relationship between composition and properties of the final product mixture would apply to the composition of either the intermediate 0,O-dialkyl hydrogen phosphorodithioates or the mixture of the basic zinc double salts. Table IV compares the concentration of the three mixed compounds of (R0)zPSSH made up of only X and Y ligands and the properties of the resulting redistribution mixture of [ (R0)2PSSHI3ZnzOH. Figure 1 shows that viscosity of the [(R0)2PSSI3Zn2OH redistribution mixture is proportional to the mole fraction of the limiting compounds of (R0)zPSSH. Of the four redistribution mixtures, only the most viscous basic zinc double salt crystallized during ambient temperature storage. Thus, to reduce the crystallizing tendency of the redistribution
Table IV. Effect of Composition of limiting Mixed Compounds of (R0)ZPSSH on Properties of [(R0)2PSSlBZn2OHRedistribution Mixtures Mol froction .. - ... of -. limiting (ROIzPSSH,
Mol fraction
Y , i-Bu
X, Me
a
Z, Heo
(X
+ YIa
Viscosity, cSt 2 1 ODF
Solubility in mineral oil,
Pour
100°F
point,
wt
OF
%
Analysis Znt
0.774 125.4 7654 ...
