Heat and Entropy of Adsorption and Association oflong-Chain Surfactants at the Alumina-Aqueous

Solution Interface

by P. Somasundaran and D. W. Fuerstenau

Adsorption isotheT11t8 for dodecyl sulf<mate Of1 alurnina were deteT111ined at 4S"Cand. 2S'C and the data was used for calculating the partial molar heat and entropy ofadsorbed iOflS under various concentratiCYn$. Changes in .1H afid. .1S observed at cer-tain concentrations agree with the postulate of interaction of surfactant ions to fonntwo-dimensional aggregate$ at the solid-liquid interface. Values of the total~H and ~S for the aggregation proceS.t calculated using the Clausius-ClapeyrOtiequation is used to interpret the interactions of surfactant ions with each other aswell as with the solvent molecules.

Froth flotation separations are sometimes conductedunder conditions of relatively high or low tempera-ture.J-4 It is known that the performance of these opera-tions is dependent on the properties of various interfacesin the bubble-particle-solution system and these inter-facial properties generally involve the adsorption of sur-factants or collectors from solution, However, eventhough extensive applications have been made of ther-modynamics to the adsorption of gases by solids,t-..there has been very little thermodynamic study"-J': in thepast on the adsorption from aqueous solution of collec-tors on minerals. A number of factors may be responsi-ble for this. For example, unlike the adsorption of gaseson solids, adsorption from solution is influenced by thesolvent species in addition to the adsorbate species.J&-~Another problem is the possible variation of the surfa~echarge of minerals...a as well as variation of hydrationof adsorbate species with temperature,"

In this investigation, we have made an attempt tostudy the thermodynamics of the adsorption of sodiumdodecyl sulfonate on alumina. In our previous studieS,aadsorption isotherms of sodium dodecyl sulfonate onalumina were determined as a function of concentrationand pH, and the data were interpreted in tel'tns of amodel wherein the surfactant ions are adsorbed as indi-vidual ions from dilute solutions, but when a certaincritical concentration is exceeded, adsorbed ions inter-act with each other to form two-dimensional aggregatescalled hemimicelles at the interface. In the presentstudy we have obtained information on the thermody-namic quantities of the hemlmicelle association at thesolid-liquid interface.

alumina occurs at pH 9.1.- Hence, fora system contain-ing alumina particles in a dilute solution of an anionicsurfactant in the neutral pH range, the electrical doublelayer will contain surfactant ions adsorbed at the inter-face as counter ions. At low concentrations, surfactantadsorption appears to occur by electrostatic attractiononly. However, increasing the bulk concentration of thesurfactant increases the adsorption to such an extentthat interaction begins to occur among the hydrocarbonchains of the adsorbed surfactant ions at the interface.Correlation of various interfacial properties for thequartz-dodecylammonium acetate system" and alumina-sodium dodecylsulfonate system-'- has shown thatmarked changes in these parameters take place at acritical solution concentration.

The process of adsorption of dodecyl sulfonate ions,X, on alumina can be considered as follows:

X (solD, a. = 1) -+ X (solD, a = C,)

(.1.(;°)" = RTlln Cl

X (solD, a = C,) ~ X (surf, r)

.1G = 0(1)

TheoryAdsorption of sodium dodecyl sulfonate on alumina

can be explained on the basis of an electrical doublelayer model. The surface charge on alumina results fromthe interaction of H' and OH- with broken aluminum-oxygen bonds at the surface. The point of zero charge of

P. SOMASUNDARAN, Member AIME, is Associate Professor of Min-

erai Engineering, Henry Krumb School of Mines, Columbia University,

New York. D. W. FUERSTENAU, Member AIME, is Professor andChairman, Dept. of Material Science and Engineering, University ofCalifornia, Berkeley, Calif. TP 718215. Manuscript, May 14, 1971.Discussion of this poper, submitted in duplicate prior to Dec. 1 S,1972, will appear in SME Transactions, March 1973, and in AIMETransactions, 1973, Vol. 254.

X(soln, a = 1) -+ X (surf. r)

(:1Gor,)r. = RT,ln C.

C, is the concentration of the sodium dodecylsulfonate.in solution in mole per liter corresponding to an adsorp-tion density r mole per sq cm at temperature T,. and(.1Gor,)r. is the relative partial molar free energy ofthe absorbed ions at this temperature. Here we haveconsidered a solute standard state for X in the solutionsuch that the activity coefficient

'Y.r. -+ 1 as C -+ O.

Similarly at temperature T.. the relative partial molarfree energy of adsorbed ions will be

(.1(;0..,)1', = RT, In Ct. (2)

Knowing C. and C, for the same adsorption density, onecan evaluate ~Go at both temperatures, from whichthe heat and entropy terms involved (~iio.{. and d.S°.r,)can be calculated. .1Fio x, and ~so r. are the changes inheat content and entropy due to adsorption as well asdilution to the bulk concentration under consideration.Assuming ideal mixing and hence neglecting heat of

Reprinted from TraltS4ctivrtS of SM!', Septl!1nber 1912, Vol.. 252

\

"dilution dIn HMA -AH-(I)=AHoz. = ,:1fioz... = Hz. - if'Zl (3)

where Ailo z.o. is the change in partial molar heat contentof sulfonate due to adsorption. Hz. is the partial molarheat content of adsorbed ions related to total heat con-tent of the surface (H") by

iiz.=( ~)ar (4;)

dT Rr

where HMA is the hemimicelle adsorption density andc1HN. is the heat of ht:mimicelle association at tempera-ture T. It is the ad~orption density at hemimicelle for-mation that is used in Eq. 9 and not the bulk concentra-tion. This is done so that we obtain thermodynamicquantities for the hemimicelle association only and notfor the total process of adsorption and association atthe solid-liquid interface.

In the case of micelles in bulk, a number of workershave considered the micelle to be a different phase fromthe aqueous solution and on this basis have treatedmicelle formation as a phase change.- Recent experi-ments by Mysels and coworkers-- show that if properexperimental precautions are taken, the activity of thesurfactant increases above the critical micelle concentra-tion and that this increase can be explained with thehelp of a mass action model. It might, however, be notedthat the increase in activity above micelle concentrationis very small and treatments on the basis of a pseudo-phase separation model, even though not strictly correct,can yield useful information.- For long alkyl chains,there is fair agreement between the mass action andphase separation models.-'"

and Ho x, is the molar heat content of the surfactant inthe standard state. The assumption that the heat of dilu-tion in our case is negligible in comparison to the totalhe3t of the process is probably valid but is subject toverification.

In the treatment of entropy terms, the contribution ofentropy of dilution ~S.'I to total ~§o~. can be evaluatedto obtain the entropy of adsorption using the followingequation:

.1§.x. = 4S.'1 + 4S.X...(0)

= - R In C + Sz. - S' z,

11&. .r.ad is the change in relative partial molar entropy ofthe sulfonate due to adsorption, S.r. is the partial molarheat content of adsorbed ions related to total entropy ofsurface and S..r, is the entropy of the surfactant ions inthe standard state. Using Eq. 1, 2, and 3

".". R (In C. - In C.)(8)~'z... = ,r;..",!

1 1---T. T.

Similarly,

(7)

Experimental Procedure

Adsorption tests were carried out on Linde "A"alumina of 14.5 sq m per g surface area determined bymeasurments of adsorption of stearic acid from benzeneand assuming 20.5A' for the stearic acid area. The sodiumdodecylsulfonate used was prepared from dodecylsul-fonate acid obtained from the Shell Development Co.,Emeryville, Calif. The sodium salt obtained was puri-fied by recrystallization from hot absolute ethyl alcohol.Triply distilled conductivity water was used for adsorp-tion studies.

Adsorption of sodium dodecYlsulfonate was deter-mined at pH 6.9 and 25.C and 45.C by determining thedifference in concentration of the surfactant in solutionbefore and after adding alumina under equilibriumconditions. An atmosphere of purified nitrogen wasmaintained during the experiments. The ionic strengthof the system was kept constant at 2 X lO-3M by addinga sufficient amount of O.lM solution of sodium chloride.The sulfonate concentration was determined by themethylene blue method."'"

(8)T.- T.

Results and Discussion

The adsorption isotherms of sodium dodecylsulfonateon alumina at pH 6.9 as a function of concentration ofsulfonate at 2S"C and 4SoC is given in Fig. 1. These iso-therms consist of three regions, which have been in-terpreted in terms of the electrochemical double layertheory elsewhere- and will be mentioned only brieflyhere. At lower concentrations, sulfonate ions are ad-sorbed individually and adsorption takes place by anion exchange mechanism. At the end of this region, thesllrfactant ions begin to associate and hemimicelles form.Here, adsorption results from electrostatic attractionplus the free energy decrease due to the association ofhydrocarbon chains of adsorbed surfactant. Whenenough surfactant ions have been adsorbed to balancethe surface charge, further increase in adsorption inthe upper region results only from the van der Waalsassociation between hydrocarbon tails. From Fig. 1 itcan be seen that adsorption at all concentrations studiedis lower at the higher temperature, in line with the pastobservations of physical adsorption on such adsorbents

By evaluating .1fjo Z.o" and :;So Z.o" as a function of theconcentration, it is possible to get the changes in themdue to such phenomena as hemimicellization. Adsorp-tion in the system discussed here is complicated by theinteraction of other components present. When sulfonateions are adsorbed on alumina, in a system at constantionic strength, they will be displacing anions of the sup-porting electrolyte from the double layer and possiblywater molecules bound to the surface. For concentra-tions below the hemimicelle concentration, adsorption ofsulfonate ions takes place by mere ion exchange.- Sincesodium chloride has been added during these experi-ments to maintain constant ionic strength in the system,adsorption of sulfonate ions below the hemimicelle con-centration is accompanied by displacement of chlorideions from the surface. Alkyl sulfonate ions are consider-ably larger than chloride ions, and hence displacementof a relatively large number of water molecules fromthe "iceberg structure" on the surface may also takeplace when the surfactant is adsorbed. The changes intotal thermodynamic quantities due to adsorption cantherefore be expected to be different from the changesin the corresponding quantities for the adsorbed sul-fonate ions oftly.

It is also possible to evaluate the thermodynamicquantities associated with hemimicelle formation byconsidering it as a phase change and using the Clasius-Clapeyron type equation:

276 - SEPTEMBER 1'72Society of Milling Engineers- 41M£ TRANSACTIONS - VOl. 252

~

surfactant ions in the adsorbed state than in the solu-tion, and this is because when the ions are adsorbed onthe surface they have lesser number of degrees of free-dom than they did in solution. Loss of translationalentropy might partly be balanced by the configurationalentropy of the surfactant ions on the surface and thepresence of weak vibration perpendicular to the ~ur-face."

Continuous variations of the heat of adsorption withcoverage have been reported by several workers as dueto the heterogeneous nature of surfaces. ...,. In additionto such changes, we find some sharp changes jn thevalues of .1H and ,1S from Region 1 to Region 2 in accordwith the postulate of hemimicelle formation. The con-tribution to .1ii. X,a. due to hemimicelle formation isfound to be of the order of +3 Kcal per mole and con-tribution to ,18. X,a. due to hemimicelle formation of theorder of +4 e.u. (entropy units). Changes in .1H re-ported jn literature for micelle formation exist in awide range of +5 to -3 KcaJ/mole, ""'l Since these

as carbon." Using Eq. 6, the partial molar heat contentof the adsorbed surfactant ions has been calculated atvarious constant adsorption densities and is presentedin Fig. 2. It is negative throughout the concentrationrange. Data of Fava and Eyring" for detergent adsorp-tion on cotton show similar results. However, by mea-suring the adsorption at one temperature and using thesame sample and same solution for measurement atanother temperature and calculating the heat of adsorp-tion from the ratio of amounts adsorbed at two tem-peratures, the change in equilibrium concentration hasbeen neglected by them. The partial molar entropy ofadsorbed surfactant ions as calculated by Eq. 7 is givenin Fig. 3 and the change in entropy as calculated by Eq.8 is given in Fig. 4. Note that l1§°z,o. is negativethroughout the entire range.

For adsorption only due to electrostatic attraction, itis reasonable that :1H is negative since the adsorption isanalogous to ionic bond formation and there is no ac-tivation energy involved for the reaction. The entropyterm suggests that there is a smaller entropy for the

TR"NS"CTIONS- VOL. 252 Society of Mi"i"Q EnQinee". AIME SEPTEMBER 1972 - 277

hemimicelle formation. The Clausius-Clapeyron equa-tion gives the change in total heat and entropy of thesystem during the hemimicelle formation. It can beseen from a comparison of ~ obtained in the two cases.that there is a further disordering in the system otherthan that of the surfactant ions. This can be explainedon the basis of the water structure effects."'" Watermolecules around the unassociated hydrocarbon chainshave a relatively ordered arrangement. When thehydrocarbon chains associate, these water molecules willbe free to become more disordered. It should be re-membered that for each associating hydrocarbon chainthere is more than one water molecule liberated fromthe vicinity of the chain so that, in total. the disorder-ing is higher.

processes to lorm micelles or hemimicelles involve re-portedly destruction of the ordered water structurearound a chain and the formation of hydrocarbon-hydrocarbon interactions, they should be endothermicin general.- The magnitude of this effect should de-crease with temperature in line with the findings ofJones and coworkers,. Flockhart," Goddard and Ben-son," and Adderson and Taylor.1t The observed changein ~S is due to the curled or bent hydrocarbon chainacquiring a more extended and flexible form in thehemimicelle.-

The small decrease in entropy in the upper region isprobably because increase in adsorption in that regiontakes place only by association and not by electrostaticattraction. Hence the effective number of adsorptionsites is decreased. The fact that a minimum of absoluteentropy associated with a monolayer formation" is notfound at the transition point from middle region toupper region dispels a probable argument that thistransition is due to a monolayer formation. The experi-mental points in Region 3, however, are too few to usethe changes in this region for any detailed interpretation.

The partial molar entropy ~. z. of the adsorbed ionsis essentially composed of the configurational entropyof the adsorbed ions and their excess entropy.

J.S.z. = .1S'.'z. + ~z." (10)

,

AcknowledgmentsThe authors wish to thank Raymond Orr for helpful

discussions. This research was supported by grants fromthe National Science Foundation and American Ironand Steel Institute.

.\SI"Z. = - Bin. :: (11)

~

1-'where 8 is the fraction of the surface covered by the ad-sorbed species. Configurational entropy calculated forour case at some typical concentrations is given in TableI along with the resultant excess entropy values.

We have so far examined the change in entropy andheat content of only the surfactant species and not thetotal changes involved. As mentioned earlier, we cancalculate the total thermodynamic quantities associatedwith the hemimicelle formation by considering it as apseudo-phase change and using Eq. 9.

Using the experimental values for adsorption densityat hemimicelle formation at 25"C and 4S'C, we get avalue of +2.3 Kcal per mole for the total heat of hemi-micelle formation. From the relation

4H..(12)48.. = -;;=.

T

the total entropy for hemimicelle formation at 25°C isfound to be +7.5 e.u.

A negative value for 4S, indicating a lower disorderin the system when surfactant ions aggregate, has alsobeen obtained by other workers"" for micelle formation.~H' x... and ASo x calculated by use of Eqs. 6 and 8 arenot identical to, but contained in ~H and 4S calculatedby the use of Clausius-Clapeyron equation. This is be-cause in addition to the change in heat and entropy ofthe adsorbed surfactant ions, there is also change inthe entropy of other components in the system during

Table 1. Confiruratilnal Entrcpy wit" Excess Entr.,y Values forTypical Concentrations

.'d Uon Oe.'llyHole .er Sq Cia

c..a...rall..a:Entropy

Excc..Eatro,y

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