1345

Reduced Adsorption Isotherm for Surfactant Mixtures JOHN F. SCAMEHORN 1, ROBERT S. SCHECHTER 2, Department of Chemical Engineering, and Wl LLIAM H. WADE, Department of Chemistry, University of Texas at Austin, Austin, TX 78712-1186

ABSTRACT The adsorption of surfactants of similar structure on mineral oxide surfaces can be described by a single adsorption isotherm when plotted against reduced concentration. The total adsorption of mixtures of these surfactants and the adsorption of each individual surfactant in the mixture can be estimated from this reduced adsorption isotherm. No mixture data are required for this calculation. The method of calculating the reduced concentration for pure surfactants and surfactant mixtures is discussed. Adsorption data of three isomerically pure alkylbenzene sulfonates and binary mixtures of these surfactants on alumina and kaolinite is used to illustrate this correlation.

INTRODUCTION Surfactant adsorption on minerals is of current interest because of its importance in those processes which use micellar solutions for the enhanced recovery of oil. While the total amount of surfactant adsorbed on the reservoir matrix is of prime importance, the preferential adsorption of some surfactant species is also of concern. This selective adsorption can result in the chromatographic separation of the different surfactant types which have been blended to yield an effective oil recovery agent and, thereby, greatly reduce the efficiency of the process. Isotherms representative of surfactant adsorption from aqueous solutions on mineral oxide surfaces can be characterized by four distinct regions. For very dilute solutions and sparse surface coverages, Henry's law is obeyed. At a critical solution concentration, the isotherm deviates markedly from linear behavior, signaling the transition from the first to the second region, with adsorption increasing rapidly as the solution concentration is increased. In the third region, adsorption increases less rapidly with increasing concentration. In the fourth region, a plateau is reached and adsorption is independent of the surfactant concentration. This plateau is generally reached at the surfaetant critical micelle concentration (CMC), although it is possible to saturate the surface at concentrations less than the CMC. A number of attempts to model surfactant adsorption have been reported. The finite layer BET model (1), the Langmuir adsorption isotherm (2-7), and the Tempkin adsorption model (2,3) have all been used to describe ionic surfactant adsorption, but none of these accurately represents the characteristic isotherm shapes. Scamehorn et al. (8) and Cases et al. (9) have developed theoretically based models which do represent real isotherm shapes. Their development assumes that hemimicelles, which are surface aggregates of surfactant molecules, form by a phase transition mechanism p r o m o t e d by the lateral attraction between the surfactant's hydrocarbon tails. Scarnehorn et al. (8) concluded that the surface aggregates tend to be bilayered structures and that adsorption saturation occurs prior to reaching the CMC only when bilayer coverage is complete. 1Present address: School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, OK 73019. 2To whom correspondence should be addressed.

The striking feature of this physical model of surfactant adsorption is the dominant role accorded lateral interactions between the surfactants' hydrocarbon tails. These are the same interactions (the hydrophobic effect (10)) responsible for the aggregation of surfactants into micelles. For these systems, almost all adsorbed surfactant is present in the form of hemimicelles (8). The change in free energy per methyl group found for micelle formation is comparable to that for hemimicelles (8,11-13). It is this similarity which is responsible for the success which reduced adsorption isotherms have enjoyed (1,9,14,15). A reduced isotherm is one in which the adsorption is shown as a function of reduced surfactant concentration, where the reduced concentration is the concentration divided by a "critical c o n c e n t r a t i o n " - usually the surfactant CMC. The value of a reduced isotherm lies in its generality. All surfactants of a given homologous series would yield the same reduced isotherm. This paper develops reduced adsorption isotherms, which describe the total adsorption of a surfactant mixture. This novel application of the reduced adsorption isotherm concept requires no mixture data and only meager single surfactant system data to predict adsorption of all surfactant components in a mixture. The restriction on this model is that it is only applicable below the CMC and to surfactants belonging to a homologous series.

EXPE R I M E N T A L PROCEDU RES The surfactants used were: sodium 4-([3'] nonyl) benzene sulfonate (3-~-CgABS), sodium 4-([3']decyl) benzene sulfonate (34b-CIoABS) , and sodium 4-([4'] dodecyl) benzene sulfonate (4~b-CIzABS). These compounds, the other materials used, and the procedures employed are discussed in detail elsewhere (8).

RESULTS AND DISCUSSION Pure Component Systems Adsorption is plotted against reduced concentration for ABS isomers on alumina and kaolinite in Figures 1 and 2, respectively. The critical concentrations used to calculate the reduced concentrations were selected so that the adsorption data intersected the plateau adsorption value, which is observed at high surfactant concentrations, at a reduced concentration near unity, and so the data for the different isomers coincides closely on each substrate. However, since the plateau adsorption is a function of alkyl chain length (8), the reduced isotherm concept cannot be expected to apply precisely in the high concentration region. At low concentrations, Ilenry's law is obeyed (8). However, this region is experimentally inaccessible for most of the surfactants in Figures 1 and 2 under the conditions used. Therefore, to test the validity of the single component reduced isotherm in the Henry's law region, adsorption data were obtained at a low solution/solid ratio (and therefore slighdy different pH) as shown for

JAOCS, vol. 60, no. 7 {July 1983)

1346 J.F. SCAMEHORN, W.H. WADE AND R.S. SCHECHTER ~000." .~.

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r

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FIG. 3. Adsorption of single surfactants on alumina in die Henry's law region.

FIG. 1. Adsorption of shagle surfactants on alumina. SURFACTANT

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FIG. 2. Adsorption of single surfactants on kaolini~.

the two substratcs in Figures 3 and 4. Since the CMC is nearly independent of pH for these compounds (8), the critical concentration is assumed to be also, and the same critical concentration is used to calculate reduced concentration in Figures 3 and 4 as was obtained from the data in Figures 1 and 2. The lines drawn in Figures 3 and # correspond to Henry's law (a slope of one on log-log paper) and can be seen to fit the data over a wide concentration range. Since pH affects adsorption, adsorption densities are not the same in Figures 1 and 3 and in Figures 2 and 4; but at a given pH, the reduced adsorption isotherm has been shown to describe all three surfactants used, with the critical concentration being independent of pH. A single reduced adsorption isotherm has been shown to apply for the homologous series of surfactants being used. Reduced adsorption isotherms have been reported JAOCS, vol. 60, no. 7 (July 1983)

I

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l

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FIG, 4. Adsorption of shagle surfactants on kaoliniee in the Henry's law region.

by other investigators (1,9,14,15). The CMC was used as the critical concentration in those studies. The critical concentrations used here represent the "best fit" (by visually adjusting the curves), and these are compared to the CMC in Table 1. There is a deviation between those quantities for 3-~CgABS and 4-~CIeABS isomers; however, the agreement between reduced isotherms found using the CMC as the critical concentration is only slightly poorer. Thus, when there is a need to minimize the number of experiments, the CMC represents an adequate choice for the critical concentration. Surfactant Mixture Adsorption

The total adsorption of surfactant from an aqueous solution containing a mixture of surfactants is hypothesized to correspond to the same reduced isotherm as that of

1347 ADSORPTION OF SURFACTANTS TABLE I Comparison of CMC and Critical Concentration

(#mol/L)

3-O-C9ABS

3-0-C10ABS

4-@Ct2ABS

CMC

1694

727

90.4

Critical concentration lalumina)

2302

727

72.7

Critical concentration (kaolinite)

2276

727

51.8

tion is quite well represented by the reduced adsorption isotherm. One difficulty, which may n o t be immediately clear, is that to calculate the final solution concentration and mole fraction of surfactant, one requires a knowledge of the adsorption of the individual surfactants, not simply the total adsorption. Figures 5 and 6 have been constructed based on measured values of the final solution mole fractions. These can, of course, be calculated by material balances given the solution to solid ratio and a method of calculating the individual adsorptions. To obtain the fraction of each surfactant comprising the adsorbate, again we use the similarity between hemimicelles and micelles and propose that ideal mixed hemimicelles form on the surface. Thus, CCPM

zi - -

the pure components comprising the mixture. By total adsorption is meant the sum of the adsorptions of the individual surfactants. The validity of this hypothesis depends, as will be seen, on making an appropriate choice of critical concentration and on each of the surfactants having the same reduced isotherm. This latter condition usually, but not necessarily, requires that surfactants having the same hydrophilic moiety be considered. To d e f n e a critical mixture concentration, the similarity between micelle and hemimicelle formation is again emphasized. In the presence of a large amount of added electrolyte, the monomer-micelle equilibrium in a mixture of ionic surfactants can be represented by treating t h e system as a mixture of nonionic surfactants, since the electrolyte contributed from the dissociation of the surfactant is small compared to the total present; this condition was satisfied for all experiments reported here. An equation has been presented (16-18), which yields the CMC of such a surfactant mixture, assuming the micellar phase to be ideal. This same equation will be used to calculate a mixture critical concentration except that the critical concentrations of each of the pure components rather than their CMC will be used when these are different. Thus, for a n component surfactant mixture:

=

-

xi

i = 1. . . .

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REDUCEDTOTAL CONCENTRATION FIG. 5. Total adsorption of a 3-O-C1oABS and 4-O-CI2ABSmixture on alumina.

n

11 CCPi i=l CCPM

=

I00. [11

n

n

2; xilq CCPj i=1 j=l where x i is the mole fraction of surfactant i in the solution, CCPi is the critical concentration for pure i, and CCP M is the mixture critical concentration. In this work, the term mole fraction refers to the molar fraction of the total surfactant in the phase of interest (monomer solution, adsorbed phase, or feed solution) and is not the mole fraction relative to the total number of moles of all components present. Thus, xl = 0.5 implies that half of the total number of surfactant molecules present in solution are of type 1. The application of Equation 1 to binary mixtures of 3Sb-CIoABS and 4~b-C12ABS is shown in Figures 5 and 6 on alumina and kaolinite, respectively. The data cover two different feed (solution prior to adsorption) mole fractions. It is important to note that the xi appearing in Equation 1 refers to the final solution composition. These will generally differ from the initial composition since the adsorption of each component will generally differ. It is seen that the agreement between experiment and theory is reasonable. Thus, the total surfactant adsorp-

I.tJ .J

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MOLE FRACTION IN FEED

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REDUCED TOTAL CONCENTRATION

FIG. 6. Total adsorption of a 3-0-CIoABS and 4-O-CI2ABS mixture on kaolinite.

JAOCS,

vol, 60, no. 7 ( J u l y 1983|

1348

J.F. SCAMEHORN, W.H. WADE AND R.S. SCHECHTER where zi is the mole fraction of surfactant i in the adsorbed phase (hemimicelles). The predicted mole fractions calculated using this e q u a t i o n a g r e e satisfactorily with the observed mote fractions as shown in Figures 7 and 8. Since E q u a t i o n 2 is analogous to the e q u a t i o n used by Mysels and O t t e r (19) to describe the equilibrium b e t w e e n surfactant m o n o m e r and micelles, the agreement is considered to be a further substantiation of the p r o f o u n d similarity between micelles and hemimicelles and provides further evidence for the existence of m i x e d hemimicelles first p r o p o s e d by S c a m e h o r n et al. (20). It is i m p o r t a n t to n o t e that E q u a t i o n s 1 and 2 allow calculation of surfactant mixture adsorption and the c o m p o s i t i o n of the adsorbed phase, based solely on single c o m p o n e n t isotherms. If even less accuracy is necessary, the adsorption isotherm of one c o m p o n e n t and the CMC of each c o m p o n e n t present allow calculation of these same quantities (by assuming that the pure comp o n e n t critical c o n c e n t r a t i o n is equal to the CMC). There are at least two constraints limiting the validity of reduced isotherms for predicting the adsorption of surfactant mixtures. The calculations as presented here apply only if the surfactant solution c o n c e n t r a t i o n is less than the m i x t u r e CMC. If this is the case, all of the surfactant is present as m o n o m e r . Above the m i x t u r e CMC, the mole fractions of each surfactant in the m o n o m e r

I0

MOLE FRACTION 4-~-C~2 AqS AOSORBED 09 0.8

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MOLE FRACTIONIN FEED 3-{-C,oABS 4-{-C~zABS [] OI 0.9

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c~

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FIG. 8. Composition of adsorbed phase for adsorption o f 3@-C10ABS and 4-qS-C12ABSmixtures on kaolinite. o z ~ -..'t

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ACKNOWLEDGMENTS o

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actions between unlike c o m p o n e n t s , as for example, m i x t u r e of anionic and n o n i o n i c surfactants (22).

02

This research has received financial support from the following organizations: Amoco Production Co., Ashland Chemical Co., Atlantic Richfield, British Petroleum Co. Ltd., Chevron Oil Field Research, Conoco Inc., Department of Energy, Elf-Petroleum Corp., Exxon Production Research Co., Gulf Research and Development Co., Marathon Oil Co., Mobil Research and Development Corp., Shell Development Co., Stepan Chemcial Co., Suntech Inc., Texaco Inc., Union Oil Co. of California, The University of Texas Engineering Foundation, and Witco Chemical Corp. Professor Schechter holds the Dula and Ernest Cockrell, Sr., Chair in Engineering

MOLE FRACTION3-~-C:eABS ADSORBED

REFERENCES FIG. 7. Composition of adsorbed phase for adsorption of 3-q5-C~0ABS and 4-~-C~2ABS mixtures on alumina.

are different f r o m those in the total solution. Since ads o r p t i o n then depends on the m o n o m e r c o n c e n t r a t i o n rather than the solution c o n c e n t r a t i o n (8), it w o u l d be necessary to consider m o n o m e r - m i c e l l a r equilibrium and to incorporate material balances into the calculations. Trogus et al. (21) have discussed these difficulties in some detail and Scamehorn et al. (20) have d e m o n s t r a t e d the validity of their approach. It is believed that, using this approach, the adsorption could then be calculated f r o m the relationships given here. It is crucial to understand that the x i are m o n o m e r mole fractions, n o t the solution mole fractions, for concentrations greater than the m i x t u r e CMC. A second restriction to be stressed is that although this correlation should be reasonably good for surfactants having the same hydrophilic m o i e t y , it is uncertain h o w widely it may be applied. It w o u l d not, for example, apply to mixtures exhibiting strong synergistic interJ A O C S , vol. 60, no. 7 (July 1983)

1. Tamamushi, B. and K. Tamaki, Proc. 2nd. Int. Congr. Surf. Act., 3:449 (1957). 2. Dobias, B., Colloid Polym. Sci. 256:465 (1978). 3. Dobias, B., Ibid. 255:682 (1977). 4. Trogus, F.J., S. Thach, R.S. Schechter and W.H. Wade, Soc. Pet. Eng. J. 17:337 (1977). 5. Clementz, D.M., and J.L. Robbins, Soil Sci. Soc. Am. J. 40: 663 (1976). 6. Malik, W.U., S.K. Srivastava and D. Gupta, Clay Miner. 9:369 (1972). 7. Tadros, Th. F., J. Colloid Interface Sci. 46:528(1974). 8. Scamehorn, J.F., R.S. Schechter and W.H. Wade, Ibid. 85:463 (1982). 9. Cases, J.M., G. Goujon and S. Smani, AIChE Syrup. Ser. 71: 100 (1975). 10. Tanford, C., The Hydrophobic Effect: Formation of Micelles and Biological Membranes, Wiley, New York, 1973. 11. Fuerstenau, D.W., T.W, Healy and P. Somasundaran, Trans. AIME 229:321 (1964). 12. Somasundaran, P., T.W. Healy and D.W. Fuerstenau, J. Phys. Chem. 68:3562 (1964). 13. Rosen, M.J. and Y. Nakamura, Ibid. 81:873 (1977). 14. Cases, J.M., and B. Mutaftschiev, Surface Sci. 9:57 (1968). 15. Connor, P., and R.H. Ottewill, J. Colloid Interface Sci. 37:642 (1971).

1349 ADSORPTION OF SURFACTANTS 16. Clint, J.H., J. Chem. Soc., Faraday Trans. 1 71:1327 (1975). 17. Shinoda, K., in Colloidal Surfactants, edited by K. Shinoda, B. Tamamushi, T. Nakagawa and T. lsemura, Academic Press. New York, 1963, pp. 68-69. 18. Lange H. Kolloid-Z. 131:96 (1953). 19. Myself, K~J., and R.J. Otter, J. Colloid Sci. 16:474(1961). 20. Scamehom, J.F., R.S. Schechter and W.H. Wade, Ibid. 85:479 (1982).

21. Trogus, F. J., R.S. Schechter and W.H. Wade, Ibid. 70:293 (1979). 22. Scamehom, J.F., R.S. Schechter and W.H. Wade, Ibid. 85:494 (1982).

[Received N o v e m b e r 9, 1 9 8 1 ]

&Surfactants in Coal Technology 1 M.J. SCHICK 2 and J.L. VILLA, Diamond Shamrock Corporation, Process Chemicals Division, Morristown, NJ 07960 ABSTRACT

time. H o w e v e r , basic studies o f t h e u n d e r l y i n g p h e n o m e n a are q u i t e r e c e n t . W i t h t h e curre.~t increasing i n t e r e s t in e n e r g y p r o b l e m s , a n i n t e n s i v e r e s e a r c h p r o g r a m o n t h e utiliz a t i o n o f s u r f a c t a n t s in coal t e c h n o l o g y is in progress in m a n y l a b o r a t o r i e s a n d n u m e r o u s p r o d u c t s have b e e n d e v e l o p e d . A classification o f coals b y r a n k is p r e s e n t e d in T a b l e I in decreasing o r d e r o f c a r b o n c o n t e n t . T h e principal uses o f s u r f a c t a n t s a n d related c o m p o u n d s are listed in T a b l e II a n d will b e discussed in t h i s order.

The principal uses of surfactants and related compounds in coal technology are the control of coal dust, the purification of coal from admixtures by flotation; the dispersion of coal in water for transportation through pipelines and as a fuel system, the dispersion of coal in fuel with subsequent burning of the coat/oil mixture, demineralization of coal, freeze-conditioning agents and side-car release agents for railroad transport of coal. These applications have been reviewed in this order. This overview demonstrates that the use of surfactants in coal technology is rapidly growing with the increasing interest in utilizing coal as a source of energy and that basic studies are in progress to explain the underlying surface chemical phenomenon.

Wetting of Coal Surfaces F u l l e r et al. ( 2 - - 4 ) have e l u c i d a t e d t h e h e t e r o g e n e i t y o f coal surfaces in this s t u d y o f t h e s t r u c t u r e a n d c h e m i s t r y of coals. Fuller (2) h a s s h o w n t h a t c a l o r i m e t r i c analysis is a valuable m e t h o d f o r t h e i n v e s t i g a t i o n o f t h e s t r u c t u r e a n d c h e m i s t r y o f coals. H e a t s of i m m e r s i o n studies i n d i c a t e t h a t l o w e r r a n k e d coals i m b i b e m o r e w a t e r o n t o m o r e p o l a r sites such as c a r b o x y t , p h e n o l i c , etc., t h a n h i g h e r r a n k e d coals. Mineral m a t t e r reacts s t r o n g l y w i t h p o l a r liquids such as w a t e r , giving rise to higher h e a t s o f i m m e r s i o n . A t t a c k b y alkali loosens t h e coal s t r u c t u r e m a r k e d l y to allow enh a n c e d access t o fluid reagents. H e a t s o f w e t t i n g o f coal in liquids m a y b e c o n s i d e r e d a

INTRODUCTION With th,e g r o w i n g i n t e r e s t in utilizing coal as a s o u r c e o f energy, it seems a p p r o p r i a t e t o p r e s e n t an overview o f t h e role s u r f a c t a n t s play in coal t e c h n o l o g y . S u r f a c t a n t s have b e e n used in coal t e c h n o l o g y for a c o n s i d e r a b l e l e n g t h of 1Paper presented at the symposium on Recent Advances in Surfactant and Surface Chemistry, sponsored by the North Eastern Section of the AOCS in Carteret, New Jersey, November 19, 1981. 2 Consultant, 12 West 72nd Street, New York, NY 10023.

TABLE ! Classification o f

Coals

by

Rank (1)

Class 1. Anthracite

2. Bituminous

Group

Fixed carbon limits (%) Equal or greater Less than than

Volatile matter limits (%) Equal or Greater less than than

1. Metaanthracite 2. Anthracite 3. Semianthracite

98 92 86

98 92

2 8

2 8 14

1. 2. 3. 4. 5.

78 69

86 78 69

14 22 31

22 31 -,

Low volatile bituminous coal Medium volatile bituminous coal High volatile A bituminous coal High volatile B bituminous coal High volatile C bituminous coal

3. Subbituminous

1. Subbituminous A coal 2. Subbituminous B coal 3. Subbituminous C coal

4. Lignitic

1. Lignite A 2. Lignite B

-

Calorific value limits (BTU/lb) Equal or greater Less than than

14,000 13,000 11,500 10,500

14,000 13,000 11,500

10,500 9,500 8,300

11,500 10,500 9,5D0

6,300

8,300 6,300

-

Reprinted from ref. 1, p. 6, courtesy of American Institute of Mining, Metallurgical and Petroleum Engineers, Inc.

JAOCS, vol. 60, no. 7 (July 1983)