J. Phys. Chem. 1981, 85,3263-3265
3263
Enthalpy and Entropy Effects in Adsorption from Solution Douglas H. Everett Deparlment of Physical Chemistry, School of Chemistry, The Univers& Bristol, United Kingdom (Received: May 1 1, 198 1)
A detailed thermodynamic analysis of data on adsorption at the surface of graphitized carbon from mixtures of benzene + cyclohexane, n-heptane + cyclohexane, and n-heptane + benzene shows that while the enthalpies of wetting would in all cases predict preferential adsorption of the first named component, entropy effects lead to the preferential adsorption of benzene from mixtures with n-heptane over most of the concentration range. The forms of the entropy of wetting against composition curves for the systems involving n-hexane are closely similar, and indicate that these arise from the loss of rotational degrees of freedom when n-hexane is in the adsorbed stated.
Introduction It has been common practice in the past to base the discussion of experimental data from solution on physical models of the bulk and adsorbed states, for example, ideal adsorption from an ideal solution,l adsorption in which one or both of the surface and bulk regions are nonideal,2 or models of adsorption of molecules of different sizes3 Insufficient emphasis has been placed on a purely thermodynamic analysis which makes no demands on any physical model. In this paper a thermodynamic analysis is presented for the adsorption by graphitized carbon black from three simple mixtures: benzene + cyclohexane, n-heptane + cyclohexane, and n-heptane + benzene. These three systems illustrate strikingly the way in which the preferential adsorption of one component may result from the domination of either an enthalpy or an entropy term. Because the temperature appears explicitly in the entropy term (as TAS), this balance between enthalpy and entropy and hence the preferential adsorption can be reversed by a change of temperature. Thermodynamic Analysis Adsorption from solution may be characterized conveniently by the specific surface excess of a given component (e.g., component 2) defined by4 n2s(n) nOA.xi - -m m
component 2 with respect to component 1,r2(l), is related to I'2(n) by the equation
r,(U = r 2 (4/
1
1
(3)
The surface tension, u, of the liquid/solid interface, defined as (dG'/dA,)T,p,nj.(where G" is the surface excess Gibbs free energy) is related to the relative adsorption by the Gibbs adsorption isotherm: du = -r2(l)dp2 (constant 7')
(4)
where p2 is the chemical potential of component 2 which a t equilibrium is constant throughout the system. It follows that measurements of I',(n) as a function of x i for systems whose bulk activity coefficients (72) are known enable changes in u to be calculated:s
Here u2* is the surface tension of the interface between solid and pure component 2. If the integration is taken over the whole concentration range x t = 1 to 0 then
where Ax2 is the change in the mole fraction of component 2 in the bulk liquid phase when an amount no of solution of mole fraction x20 is equilibrated with a mass m of solid. If the surface area a, associated with unit mass of solid (specific surface area) is known then the areal surface excess (also called the surface excess concentration), I'2(n), is given by
and the difference between the surface tensions of the solid surface in contact with the two pure components can be calculated. To derive the associated enthalpy and entropy differences we note that the surface excess Gibbs energy Go(") (equal to the surface excess Helmholtz energy since, in the Gibbs formulation, the volume of the surface phase is zero) is given by Go(") = ,,As + CPinidn)= H u b ) - TS&) (7)
For a binary mixture, the Gibbs relative adsorption of
or dividing by A, (and denoting areal quantities by lower case symbols and a circumflex) gdd = + xCL.r.(n) = i o ( n ) - T ~ u ( ~ ) (8) I C
(1)
(1)D. H. Everett, Trans. Faraday SOC., 60, 1803 (1964). (2) D. H. Everett, Trans. Faraday SOC.,61,2478 (1965); A. V. Kiselev and V. V. Khopina, ibid., 65,1936 (1969); L. G. Nagy and G. Schay, Acta Chim. Acad. Sci. Hung., 39, 365 (1963); S. Sircar and A. L. Myers, J. Phys. Chem., 74, 2828 (1970). (3) S. G. Ash, D. H. Everett, and G. H. Findeneg, Trans. Faraday SOC., 64, 2639 (1968); ibid., 64, 2645 (1968); ibid., 66, 708 (1970). (4) See, e.g., D. H. Everett in "Colloid Science",Vol. 1, D. H. Everett,
Ed., Spec. Period. Rep., The Chemical Society, London, 1973, Chapter 2.
On dividing by T and differentiating, making use of the total differential of the surface enthalpy at constant surface area &dd
= T dp(d +
Cpidri(n)
(9)
we obtain for a binary mixture6 (5) G. Schay, L. G. Nagy, and T. Szekrenyesy, Period. Polytechn., Chem. Eng., 6, 91 (1962).
0022-3654/81/2085-3263$01.25/00 1981 American Chemical Society
3264
The Journal of Physical Chemistry, Vol. 85, No. 22, 198 I
Everett
I where h? and hd are the partial molar enthalpies of the bulk phase at xd. Since h: and hk are not known absolutely, they must be defined relatiy to a convenient standard state; the value attributed to h" must also depend on the chosen standard state. It also follows from (8) that since u is absolutely defined, but pi depends on the standard state, $'(") and depend on the choice of standard state. The link between eq 10 and calorimetrically measured enthalpies of immersion is established as follows. The initial enthalpy of the components before immersion is
Hi = n0h1(nz0) + mh:
(11)
where h: is the specific enthalpy of the solid and hl(xzO) the molar enthalpy of the initial liquid mixture. If the whole of the excess enthalpy of the system after immersion is attributed to the interface (i.e., we suppose that h,O is unaffected, or if affected the change is included in H"(")), then HU(") is defined by
Hf = nOhl(xJ)+ H"" + mh:
(12)
I
'C
Figure 1. (u - ul*)/(mJ m-') as a function of xll. (a) [Benzene (1) cyclohexane (2)]/Graphon. Points for 298.15, 313.15, and 328.15 K all fall within the circles plotted. (b) [ n-Heptane (1) cyclohexane (2)]/Graphon at (i) 283.15, (ii) 298.15, (iii) 313.15, and (v) 343.15 K. (c) [Benzene (1) n-heptane (P)]/Graphon at (i) 283.15, (li) 298.15, (iii) 313.15, (iv) 328.15, and (v) 343.15 K. Components numbered so that (u2* a,') > 0 favoring preferential adsorption of component 1, i.e., 8 ( u - ul+)/dxl' < 0.
+
+
+
-
The first term on the left is Awh (eq 14). We define A,$ by the second term in square brackets so that AWL- TA,$ = u (19) It follows that
where xJ is the equilibrium mole fraction after immersion. The enthalpy of immersion or wetting, AwH= Hf - H', is thus
AwH= H'(n) + n0[h'(x2)- h1(x20)]
(13)
where the last term refers to the change in enthalpy arising from the change in solution composition. Expressing the term in square brackets in terms of partial molar enthalpies, and dividing by the surface area, leads to
A& = f i u b )
-
r 2(n)[h2- hl'l
(14)
where A& is the enthalpy of wetting of a unit area by an amount of mixture sufficiently large that Ax2 is small enough for the approximation hl(xd)- h1(x20)= -(hi h?)AxJ to be valid. Comparing eq 14 with 10 leads to =~ ~ f i (15)
a(+vwn
Since adsorption experiments lead to differences in u rather than absolute values, eq 15 is used in practice either in the form7
or
Data Analysis The methods of analysis outlined above are illustrated by a more detailed consideration of the data obtained by Ash, Bown, and E ~ e r e t ton ~ ?the ~ systems (benzene + cyclohexane)/Graphon, (n-heptane + cyclohexane)/Graphon, and (n-heptane + benzene)/Graphon, the adsorption isotherms for which were reported in ref 8 and 9. The accuracy of the analysis is critically dependent on the reliability of the activity coefficient data for the bulk mixtures. Even for the "most studied hydrocarbon system"lo-benzene + cyclohexane-directly measured activity coefficients at the temperatures employed in the adsorption work are not available and use was made of the equations given by Scatchard, Wood, and Mochell' to extrapolate their data to lower temperatures; the extrapolated values at 298.15 K, however, differ significantly from those measured by Li and Lu.12 Similarly Brown and Ewald's13 data for benzene + n-heptane measured at 60 and 80 "C had to be extrapolated to lower temperatures using their empirical equations. However, Fu and Lu'd4 measurements do not agree well with Brown and Ewald; and neither are in very close agreement with those of Harris and Dunlop15 or Werner and Schuberth.16 The values of (a - ul*) obtained for his system are therefore subject to some uncertainty, probably about f0.4 mJ m-2. The cyclohexane + n-heptane system is nearly ideal. According to Crutzen, Haase, and Sieg17it shows small (8) S. G. Ash, R. Bown, and D. H. Everett, J . C h e n . Thermodyn., 5,
.
239 - - (1973). - - . -,.
(6) G. Schay, J. Colloid Interface Sci., 42, 478 (1973); S. Sircar, J. Novosad, and A. L. Myers, Ind. Eng. Chem. Fundam., 11,249 (1972); cf. also ref 7. (7) C. E. Brown and D. H. Everett in "Colloid Science", Vol. 2, D. H. Everett, Ed., Spec. Period. Rep., The Chemical Society, London, 1975, Chapter 2; D. H. Everett and R. T. Podoll, ibid., Vol. 3, 1979, Chapter 2.
(9) S. G. Ash, R. B o w , and D. H. Everett, J. Chem. SOC., Faraday Trans. 1 , 71, 123 (1975). (10) J. S. Rowlinson, "Liquid Mixtures", Butterworth, London, 2nd ed., 1969, p 136. (11) G. Scatchard, S. E. Wood, and J. M. Mochel, J . Phys. Chem., 43, 119 (1939). (12) I. P-C. Li and B. C-Y. Lu, J. Chem. Eng. Data, 18, 305 (1973). (13) I. Brown and A. H. Ewald, Austr. J. Chen., A4, 198 (1951); A5, 530 (1952). (14) S. J. Fu and B. C-Y. Lu, J. Appl. Chem., 16, 324 (1966). (15) K. Harris and P. J. Dunlop, J . Chem. Thermodyn., 2,805 (1970). (16) G. Werner and H. Schuberth, J. Pract. Chem., 31, 225 (1966). (17) J. L. Crutzen, R. Haase, and L. Sieg, 2.Naturforsch A , 5, 600 (1950).
The Journal of Physical Chernistty, Vol. 85, No. 22, 1981 3265
Thermodynamics of Adsorption from Solution
which differs from zero over the whole concentration range by barely twice the estimated experimental uncertainty plays a minimal role in determining the adsorption. This suggests that both kinds of molecule experience similar changes in translational, vibrational, and rotational motion when in the surface region. In the n-heptane +_cyclohexanesystem, heptane with the more negative A& is again more strongly adsorbed-at all copentrations. However, despite the fact that (A&* - A&,*) is over twice as large as for the benzene + cyclohexane system the preferential adsorption is less because of the large contribution from the entropy term T(Ad1*- A d 2 * ) which opposes the enthalpy term. Finally, in the n-heptane benzene system the enthalpy and entropy terms are of similar magnitude. The (A& Awhz*) curve is less negative than for the n-heptane cyclohexane system whereas the T(A$ - Ad2*) curves are almost superimposable for the two systems. The consequence is that while, at low n-heptane concentrations ( x i 1) the dominance of the enthalpy leads to preferential adsorption of n-heptane, at higher n-heptane concentrations (lower benzene concentrations) the slope of the surface tension curve changes sign and benzene becomes the preferentially adsorbed component. At lower temperatures the product T ( A 4 - A d 2 * ) decreases and the range of preferential adsorption of heptane increases; conversely at higher temperatures the entropy term increases and benzene is preferentially adsorbed at all concentrations (Figure IC). The near identity of the entropy curves for the two systems involving n-heptane, and the sign of these terms which corresponds to an increasingly negative contribution of n-heptane to the entropy as the n-heptane concentration increases, suggests that on adsorption n-heptane molecules suffer a larger decrease in entropy than either benzene or cyclohexane molecules. This is consistent with the expectation that a chain molecule in the neighborhood of the surface experiences a decrease in the number of conformations available to it.
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Flgure 2. Thermodynamic functions at 298.15 K: 0 , (a - a2")/(mJ m-,); 0, (Awh- Awh2')/(ml m-2); and 0 , -T(Aw3- A,i,*)/(mJ m-') as function of x i for systems (a) [benzene (1) cyclohexane (2)]/ Graphon, (b) [n-heptane (1) cyclohexane (2)]/Graphon, (c) [nheptane (1) benzene (Z)]/Graphon. Components numbered so that (Awh, A w f 2 )is negative, favoring preferential adsorption of component 1, which corresponds to d(a - a,*)/dx; > 0. Estimated pxperimental uncertalnties in mJ m-2: (a) (a - a,'), f0.05; (AwhAwf2*),i 1 . 5 ; T(Aw& AWg2*),f1.5; (b) and (c), (a - a,"), f0.05; (Awh- Awh2+),f0.3; T(A,b - AwS2*),f0.3. These estimates do not include systematic errors in (a - a,') arising from uncertainties in bulk activity coefficient data which may be as large as k0.2 to f0.4 mJ m-',
-
+
+
+
positive deviations from ideality below 293 K and small negative deviations above. However, Young, Mentzer, Greenhorn, and Chao18report positive deviations of several percent at 298 K. The latter work was confined to one temperature so that the equations of Criitzen et al. were used; the uncertainty in (a - al*) arising from the uncertainty in the activity coefficient data is of the order of 2~0.2 mJ m-2. Figure 1 shows (a - al*)as a function of x t for the three systems, obtained by graphical integration of eq 5. Here the systems are numbered such that (a2* - ul*) > 0 favoring preferential adsorption of component 1, which corresponds to d(a - al*)/dxll < 0. Bearing in mind the uncertainties in the values of az* - ul* arising from the lack of accurate activity coefficient data, we find that the criterion of thermodynamic consistency of the results for the three binary pairs 1,2, 2,3, and 3,l formed from three components 1,2,3,namely, (ul* - az*) + (uz* - u3*) + (u3* - al*)= 0, is met satisfactorily. For the system (benzene + cyclohexane)/Graphon, (a - ul*)is almost independent of temperature indicating that A d - A d l * is small, while for both other systems the surface tension term is strongly temperature dependent. For (benzene + n-heptane)/ Graphon, the slope of (a - al*)against x ; changes sign, the azeocorresponding to a change in the sign of I'l(n); = 0 corresponds to the minimum in (a tropic point - Q*).
In Figure 2 are shown (a - u2*), (A& - A A 2 * ) , and - A d 2 * ) as functions of x $ at 298.15 K. In-this figure the components are numbered so that (A&* A$z2*) is negative, favoring preferention adsorption of component 1 for which d(a - az*)/dx$ > 0. These curves illustrate strikingly the way in which the preferential adsorption is controlled by the interplay of enthalpy and entropy terms. For the benzene + cyclohexane system, benzene is preferentially adsorbed at all concentrations as a result of the larger (more negative) enthalpy of immersion of Graphon in benzene than in cyclohexane. The entropy term -T(A$
(18) K. L. Young, R. A. Mentzer, R. A. Greenhorn, and K. C. Chao,
J. Chem. Thermodyn., 9, 979 (1977).
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Conclusions The analysis presented here indicates clearly that competitive adsorption from solution is a function not only of the energies of interaction of the componentswith the solid surface, but also of the entropy changes accompanying adsorption. The interplay of these factors is expected to play an increasing role as the size difference between the components increases. A reanalysis of data for the system (n-pentane + n-decane)/Graphon and (n-hexane + nhexadecane)/Graphon19 is in hand to examine this question while current experiments20comparing the systems benzene + n-pentane and benzene + isopentane should provide further examples of the enthalpy/entropy compensation. The importance of entropy effects has other implications. Thus the contact angle at a liquid/liquid/solid line of contact depends through Young's equation on the difference between the surface tensions between the solid and the two liquid phases. Theoretical discussions of contact angles2I have in the past concentrated on calculating energies of interaction; the present work indicates that where the two liquids have widely differing molecular structures entropy effects may play a dominant role and cannot be ignored. (19) R.Bown, Ph.D. Thesis, Bristol, 1973. (20) J. Davis, unpublished results. (21) E.g., L. A. Girifalco and R. J. Good, J. Phys. Chem., 61, 904 (1957);F M. Fowkes, Ind. Eng. Chem., 56, 40 (1961); R. J. Good, J. Colloid Interface Sci., 59, 398 (1977).
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