Indian Journal o f Chemistry Vol. 40A, February 200 1. pp. 130-134

QSAR modeling of flotation collectors Part 1-Application of valence connectivity indices to the flotation of a uranium ore using substituted-cupferrons 1

R Natarajan*

Campi on Higher Seconda:·y School, Tiruchirappalli , Tamil Nadu , India 620 00 1

and

I Nirdosh

Chemical Engineering Department, Lakehead Uni versity , Thunder I3ay, Ontario, Canada P7B 5E I.

(For correspondence, e-mai l: rnat @tr.dot. net.in )

Received 3 1 July 2000; revised 20 September 2000

Cupferron and substituted-c upferrons are used as collectors for the fl o tation of a Canad ian uranium ore . Va lence connectivity indices are calculated for these co mpounds and stepwi se multipl e regression analysis is perfo rn ed to se lec t a best regression mode l to predict the separat ion e fficienci es. Four of the compounds, p -flu oro, p-ch loro. p-mothoxy and 2.4.6-trimcthy l-cupferrons are found to be the out lie rs. Stepwise regressio n analysis using the topo log ica l indices selects

fifth order connecti vity index, ·\v to form a regression model with the hi ghest F-score and a correlatio n coe ffic ient of 0 .908.

Froth flotat ion is an important step in processing low­grade orcs. It is used in the selecti ve separati on of mineral components fro m a polymineral dispersion of ground ore in water us ing air bubbles. Hydrophobized mineral parti cles attach themselves to the air bubbles and are carried to the surface of the slutTy in the fo rm of froth, which is mechanically removed and is termed concentrate. Other nonhydrophobized minerals remain in the dispersion which is called tailings . A mineral is hydrophobized by a surface-active compound called the co/lector. Efficiency of froth flotation depends on the characteristics of the collector and inter alia on its molecular structure. Therefore , structure-activi ty relationsh ip (SAR) is high ly probable in the case of a flo tation collector, and mineral separation efficiency of the collector can be corre lated to its structural parameters.

Quantitative structure-activity relationship (QSAR) approach is based on the mathematical characterization of molecular structures of the compounds under consideration. A molecule has to be represented by numerical descriptor(s) capable of encodi ng the characteristics of the molecular

tTh is seri es of p:.Jpers is dedi cated to our n!Clllor Dr. S. V. Muthuswam i. Willowdalc, Toronto. Canada

structure. Such descriptors called topological indices or graph inl'a riants are generated by the application of graph theory' . The most commonly used topological indices are the molecu lar connectivity indices . The concept of molecular connectivity and the calcu lation of connectt vt ty indices were introduced by Randic2

. They are used in predicting several physicochemical propert ies of organic compounds3

, biological propenies4 and env ironmental toxicity of chemicals5

·6

·7

. In our earli er attempt8 to test the applicability of QSAR approach fo r froth flota ti on, separation efficiencies of alkylcupfenons as urani um col lectors were plotted ag:.! inst the Randic connectivi ty indices. The scatter plot obtained ind icated the presence of a linear relation between some of the topological indices and separation efficiency of the coll ector. Th is paper is a continuation of this study wherein valence connectiVIty i11clices are used as independent parameters in mul tiple regress ion analysis wh il e separation efficiencies of substituted-cupfen ons for the flotation of a uraniu m ore arc ust>d as the dependent parameters .

Connectivity Indices Molecular connect iVI ty indices (MCJ) are

calculated from the hydrogen- suppressed molecular

NATARAJAN eta/.: QSAR MODELING OF FLOTATION COLLECTORS 131

Table !--Calculation of valence 8 for atoms in groups frequently encountered in organic chemistry

Atom (Zv - h)/(Z - z v - I) ov

-C H3 (4-3)/(6 -4-1 ) I -CHr (4-2)/(6-4- 1) 2 =CH2 ( 4 - I)/( 6 - 4 -I) 2 CR4 (4-0)/(6-4- 1) 4 -NH2 (5- 2)/(7- 5 - I) 3 -NH- (5 - I )/(7 - 5 -I) 4 NR3 (5- 0)/(7- 5 -I) 5 -OH (6- 1)/(8 - 6 -I) 5 -0- (6- 0)/(8- 6 - I) 6 =0 (6 - 0)/(8 - 6 -I ) 6 -F (7 - 0)/(9 - 7- I) 7 -CI (7 - 0)/( 17 - 7- I) 0.78 -Br (7 - 0)/(35- 7- I) 0.26

-1 (7- 0)/(53 -7- I) 0.16 -SH ( 6 - I )/( 16 - 6 - I) 0.56 -S- (6 - 0)/( 16 - 6 - I ) 0.67

structure (molecular graph) and each atom (vertex) is assigned an atomic value 8 (degree), which is equal to the number of non-hydrogen atoms attached to it. The first of molecular connectivity indices (MCI) was introduced2 as branching index by Randic. Randic index is calculated from the 8 values using the relation given below:

... (I)

where i and j are the pairs of non-hydrogen atoms connected by a bond (edge) and the summation is over all the bonds in a molecule. The connectivity index thus calculated is known as the first-order index. The zero-order connectivity index is then

"' ( )-0.5 ox = LJ 8; ... (2)

Randic index was generalized9 into a series of connectivity indices where the summations were made over paths of different lengths. The generalized connectivity index "x of length h can be calculated from equation (3).

"x=I(8;8j8k ... 8")-05 .. . (3)

In the calculation of the above mentioned indices neither the nature of the atom nor the bond multiplicity is considered.

To differentiate heteroatoms, Kier and Hall 10

introduced valence connectivity indices. In the valence connectivity, the 8 values are taken as the difference between the number of valence electrons, Z\ and the number of hydrogen atoms connected to it , hi. The valence atomic value of the i1

" atom is:

6 6 6 6 Path Cluster Pathduster Chain

Fig. !-Subclasses of Connectivity Indices

8;v = Z;'' - h; ... (4)

In the case of halogen and sulphur atoms difficulties were encountered whi le using the above scheme. Calculation of 8v is modifi ed as:

where ziv is the number of valence electrons, zi is the atomic number of the i1

" atom and hi is the number of hydrogen atoms bound to it. The valence 8v of atoms in some groups are given in Table I. The valence connectivity indices of di fferent orders can be calculated from equation (3) using 8v instead of 8.

In the case of higher order molecul ar connectivity indices it is essential to indicate the subclass of index. There are four subclasses of connectivity indices corresponding to the sub-graphs path, cluster, path­cluster and chain (Fig. I). The subscripts P, C, PC and CH are used to indicate path, cluster, path-cluster and chain, respectively. If the subclass is not indicated it is assumed to be path-type index.

The cluster-type indices are calculated in analogy with the above indices considering all the bonds connected to a common central atom. The simplest of cluster molecular connectivity indices is the third order index, 3Xvc. This has the structural unit that resembles isobutane. 3Xv c is calculated as follows:

3 x~ =L.(8i8 j8k8, )-05 . .. (6)

where i, j , k and I are the non-hydrogen atoms that form the sub-graph and the summation is for all such sub-units in a molecule.

The fourth order path-cluster connectivity index (

4Xv rc) is the first member of this sub-class. The sub­graph consists of four adjacent edges of which three are joined to the same vertex. This structural sub-unit corresponds to the molecular graph of isopentane. 4Xv PC is calculated as follows:

4 x;c = L(8;8 j8k 8l)111 )-o.5 ... (7)

132 INDIAN J CHEM, SEC A, FEI3RUARY 2001

Table 2-List of Subst ituted-Cupferrons used and their X Val ues

# Compound 1Xv

I Cupfcrron 2.7 17 2 4-Methylcupferron 3. 128 3 3-Methylcupfcrron 3. 128 4 4-Ethylcup fc rron 3.688 5 4-Propylcupferron 4.188 6 4-1 sopropy lcupfc rron 4.071 7 4-Tert .butylcupfcrron 4.378 8 4-Pentylcupferron 5. 188 9 4- 1-Icpty lcupfcrron 6. 188 10 4-0ctylcupferron 6.688 II 4-Nonylcupferron 7.1 88 12 4-Fluorocupfcrron 2.8 17 13 3-Fiuorocu pferron 2.8 17 14 4-Ch lorocupferron 3.!94 15 3-Ch lorocu pf err on 3. 194 16 4-13romoc upferron '.6 10 17 4-Mcthoxycupferron _, _2-10

18 3-Methoxycupfc rron 3.2-10 19 3,5-Di methylcupferron 3.550 20 2,6- Di mcthylcupfcrron 3.538 2 1 2,4,6-Tri mcth ylcup fcrro n 3 .96 1 22 4- l'hcn y lcupf crron 4.788

here i , j. k, I and m correspond to the vertices (non­hydrogen atoms) tlw t form the sub-graph and the summation is over all such sub-graphs in a molecule.

The chain type molecular connectivity index distinguishes the cyclic compounds. It encodes not only the type of ri ng(s) present in a molecule but al so the subsiitution pattern in the rings. The lowest chain type index must be third order. Benzene and mono

substituted benzenes usuall y have six lh order (6Xvc11)

and seven th order Cxvc11 ) cha in type indices, res peel i vel y.

Ma terials and Methods Cupferron, ammonium sa lt of N-

nit rosophenylhydrox y lamine (Fig. 2) and severa l subst itutecl-cup fe rrons (l isted in Table 2) arc used as collectors in the fmth not:ttion of a Canadian uranium ore. Procedures fo r the sy nthesis or substit utcd­cupferrons and ex perimental details or the notation tests arc reported elscwherc 11

• Separalion clliciencies of the collectors we re found 12 Io explain maxim um data variability. lienee, separa tion efficiencies or the collec tors were used :ts dependent vari: tb lcs to construct a rc Qression model. Separation efficiency (Es) of a col lector is defined as the dillercncc bct\\'cen the % recovery of the valu:tblc mineral and that or gangue mineral in the lloat conccntratcu. In the c;tsc of !mt·-gmde orcs, Ihc amount of metal even at 95% recovery will be small and the major mass will be that

2Xv 'xv Es jackkn ifed R

1.707 0.346 27 .1 0.763 2.207 0.474 36.3 0.772 2.2 10 0.461 36.4 0.772 2.391 0.542 30.6 0.785 2.788 0.674 33.4 0.793 3.177 0.595 37.4 0.775 4.168 0 .639 37.3 0.777 3.495 0 .895 42.5 0.780 4.202 1.160 52.3 0 .746 4.555 1.285 5 1.7 0.753 4.909 1.410 58.7 0 .693 1.848 0.368 43 .5 0.8 13 1. 85 1 0.365 36.3 0.774 2.284 0.497 47. 1 0.814 2.287 0.481 3 1.1 0.774 2.763 0.639 44.2 0.780 2.069 0.44 1 42 .5 0.794 2.073 0.469 32.9 0.771 2.612 0.498 40.7 0.774 2.717 0.554 32.5 0.777 3. 188 0.577 44.8 0.788 0.284 0 .955 52.4 0.762

Fig. 2-Structure of cupfcrron

of the gangue minerals. Hence, separat ion ef f iciency (Es) can be expressed as Es = % metal recovery - % mass recovery .

Va lence connectivi ty indices were calculaled using the computer program POLL Y 14

• T he indices used in the best regression models are given in Table 2.

Sta li stical anal yses were carried ut using SPSS 10.0 fo r Windows. The v,tlence connect ivity indices we re c:tlcula tcd fo r the cupfcrron acids (ammoni um unit is replaced by hydrogen atom) and are l isted in Table 2.

ncsults and Discussion Cross corre lat ion of the va lence connccttvtty

indices is givc11 in Table 3. It shows that the p:11h­typc connectivity indices arc highly correlated while Ihc clu ster and path/cluster types ar~ not. The cross corrcla lion helps in identifying whether closely

NATARAJAN eta/.: QSAR MODELING OF FLOTATION COLLECTORS 133

Table 3-Cross correlation of valence connectivity ind ices

oXv JXv 2Xv JXv 4Xv sXv 6Xv 3Xvc 'x'c 6Xvc 4 v Xrc 'xvrc 6 \'

Xrc ox'' 1.000 JXv 0.988 1.000 2Xv 0.973 0.942 1.000 JXv 0.991 0.991 0.951 1.000 4Xv 0.967 0.954 0.926 0.967 1.000 'xv 0.966 0.987 0.908 0.977 0.937 1.000 6Xv 0.987 0.994 0.944 0.992 0.953 0.983 1.000 3Xvc 0. 176 0.058 0.380 0. 104 0. 10 1 -0.015 0.076 1.000 5Xvc 0.140 0.037 0.313 0. 104 0.072 -0.054 0.050 0.891 1.000 6Xvc 0.082 0.116 0.052 0.136 0.091 0.21 1 0.103 -0.117 -0.024 1.000

4 v 0.276 0.151 0.449 0.229 0.236 0.072 0.178 0.932 0.922 -0.047 1.000 Xrc ' v 0.274 0.144 0.408 0.228 0.343 0.069 0.166 0.783 0.743 -O.l!S 0.891 1.000 ·x rc 6 v Xrc 0.321 0.195 0.440 0.282 0.404 0.133 0.219 0.724 0.678 -0.072 0.856 0.99 1 1.000

Table 4--Summary of Stepwise Regression Analys is

Model No. Variable(s) R R2 Adjusted R2 F-score Std. error of the Observations deleted *

I 'xv 0.775 0.60 1 0.58 1 2 'xv 0.857 0.735 0.720 3 'xv 0.877 0.769 0.755 4 'xv 0.885 0.784 0.771 5 ' xv 0.908 0.825 0.8 14 6 'xv, JXv 0.94 1 0.885 0.869 7 ' xv. 1X'. 0.958 0.9 18 0.900

2Xv

*Refer Table 2 for# of an observa tion

related or unrelated indi ces are present 111 the regression equation.

Stepwise multiple regression analysis using all the valence connectivity indices showed that the fifth order path connecti vity index , 5xv. gives the best possible correlation with the correl ation coefficient of 0.775. ln order to identify the "outliers" a modified form of jack-knifing procedure 15

· 16 suggested by

Speece et a/ 17 was followed. In this method, each observation is deleted in turn from the regress ion analysis and the resulting correlation coefficient for the data set containing (n- 1) observat ions is noted. These R-values are g iven as jack-knifed R in Table 2. Very high pos itive deviations are shown by p-chloro-, p-fluoro-, p -methoxy- and 2,4.6-trimethyl - substitu ted compounds. The deviation in the case of first two compounds may be due to the presence of highl y electronegative halogen atoms at the end of the hydrocarbon chai n of the collector molecu les. This will affect the surface-active property of these molecules. Presence of fluorine atom(s) at the end of a hydrocarbon chain is known 18 to affect the surface-

estimate

30.11 5.361 nil

49.85 1 4.516 12, 14 56.477 4.302 12, 14,2 1 61.647 4.185 12, 14, 17 75.435 3.846 12, 14, 17, 21 57.543 3.224 12, 14, 17, 21 56.477 2.8 16 12, 14. 17,2 1

active properties. ln the case of p-methoxy compound the electron donating nature of the group and the consequent increase in electron density at the chelating atoms may be the reason for the deviation . 2,4,6-Trimethylcupferron is an outlier due to steric facto r. ln addition, two of the methyl groups that are ortho to the chelati ng group may cause suppression of gangue and conseq uently separation efficiency will be higher.

The stepwise regression analysis was rerun arter deleting p-chloro- and p-fluoro-cupferrons. The correlation coefficient improved significantly to 0.857 and the regress ion equation was:

Es = 23.887 (5 X'' )+ 23.979 ... (~l

F-score, R2 and standard error of the estimate are given in Table 4. When p-methoxycupferron was also removed from analysis, the correlation coeffic ient improved to 0.885 and the regression model obtai ncn was:

Es = 25.0 17(5 x'' )+ 22.784 ... ,9)

134 INDIAN J CHEM, SEC A, FEBRUARY 200 1

The fourth outlier, 2,4,6-trimethylcupferron was also removed and the stepwise regression performed for 18 observations with all the valence con nectivity indices as independent parameters. Three models were selected with correlation coefficient greater than 0.9. ANOV A results of the models are g iven in Table 4. First model has one independent variable Cxv) while the second has two Cxv and 1Xv) and the third three ex\ 1Xv and 2Xv) independent vari ab les. Detail s of these models are g iven in Table 4 . Correlation coefficient always increased with increase in the number of parameters used . Hence, F-score was taken as the measure to decide the best model. The regression model with the F-score of 75.435 was taken as the best model and the regress ion equation was

Es = 25.523(5 x" )+ 22.014 .. . (10)

The standard error of the estimate in the models is 4.0, which is lower than the experimental error in the flotation tests. Generally, 5% error is a ll owed in flotation tests. Thi s is due to the involvement of a large number of experimental variables such as pH, collector concentration, pulp density, air flow-rate, propeller speed, etc. It is very difficult to monitor all of them and maintain them uniformly in all the tests.

Conclusion Formation of regress ion models to predict

separation efficiencies of flotation collectors using computable properties verifies our hypothesis that froth flotation is amenable to QSAR modeling. Success of this approach has a significant importance in the selection and the screen ing of compounds to be tested as flotation collectors. Thus, a lot of chemicals and testing time can be saved in the synthes is of new collectors for mineral flotation. Though there is good correlation in the models generated, data for a few compounds have to be deleted from the original li st of compounds studied. This is due to the inability of the topological indices used to encode certain structural

details . Hence, further improvement using new parameters is to be attempted to evolve a more general ized model capable of including the entire data obtai ned with all the compounds tes ted.

Acknowledgement Financial support from Natural Sciences and

Engineering Research Council of Canada (NSERC) is acknowledged. Thanks are due to Dr. S. C. Basak and Denise Mills, University of Minnesota, Duluth, USA for calcu lating the topological indices.

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