J . Chem. SOC., Faraday Trans. 1, 1986, 82, 2605-2614 Thermodynamics of the Adsorption from Aqueous Alcohol Solutions by Graphitised Carbon (Graphon) Douglas H. Everett* and Alistair J. P. Fletcher? Department of Physical Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 ITS Adsorption isotherms have been determined for the system [water (1)- methanol (2)] on graphitised carbon (Graphon) at five temperatures in the range 298.15-338.15 K, and for the system [water (l)-ethanol(2)]/Graphon at six temperatures from 298.15 to 348.15 K. The data have been subjected to a thermodynamic analysis to obtain values of the interfacial tension at the liquid/solid interface and for the enthalpy and entropy of immersion of Graphon into liquid solutions, relative to the corresponding quantities for one or other of the pure components.The condition for thermodynamic equilibrium at the three-phase line of contact in a system comprising liquid A, liquid B and a rigid solid S, where A and B are immiscible, is given by Young’s equation: where 8 is the contact angle measured through liquid A, aAS and oBs are the surface tensions of liquid A and B, respectively, at the A/S and B/S interfaces, and oAB is that at the AB interface. As is well known, it is not possible to measure uAS and aBS separately, so that no direct experimental confirmation of Young’s equation is possible. However, as pointed out previously,l if A and B are both miscible with C, then by measuring the adsorption from mixtures of A-C and B-C over the whole concentration range it is possible, by integration of the Gibbs adsorption isotherm, to obtain ( o ~ ~ - o ~ ~ ) and (ass - a,,).The difference (oBS - oAS) can thus be obtained and when aAB is known, the contact angle 8 can be calculated by a thermodynamic route. The present work is designed to test this procedure by calculating the contact angle for the system benzene/water/Graphon from measurements on (benzene+thanol)/ Graphon and (water-ethanol)/Graphon or from (benzene-methanol)/Graphon and (water-methanol)/Graphon; and for the system n-heptane/water/Graphon using ad sorption measurements for (n- hep tane-e t hanol)/Grap hon and (wa ter-e t hanol)/ Graphon. The methanol route is inapplicable for n-heptane since n-heptane and meth- anol are not completely miscible. The contact angles obtained in this way will then be compared with those measured directly, and published previously.2 This paper reports measurements on the systems (water-methanol)/Graphon and (water-ethanol)/Graphon.A reanalysis of our earlier work3 on (benzene-ethanol)/ Graphon and (n-heptane-ethanol)/Graphon together with new data on (benzene- methanol)/Graphon are presented in a second paper, while the third paper of this group considers the application of the data to the wetting characteristics of the systems benzene/water/Graphon and n-heptane/water/Graphon and comparison with direct observation. GBs - GAS = OAB cos 8 (1) t Present address: B.P. Research Centre, Sunbury. 26052606 Adsorption of Aqueous Alcohols on Carbon Experimental The apparatus and its mode of operation for non-aqueous systems has been described previ~usly.~ When used for aqueous solutions the phosphor-bronze bellows pumps tend to corrode and they were replaced by a mechanical piston pump oscillating a column of mercury (fig.I). The same sample of Graphon (rn = 19.665 g) was used throughout and was taken from the same batch (a gift from the Cabot Corporation) as that employed previo~sly.~-~ It was washed with 0.2 mol dmP3 HC1 to remove sulphide impurities, then several times with distilled water and dried. This was followed by soxhlet extraction with n-hexane, and by drying at 550 K and loP4 Torr for 24 h. The fraction sieved between 18 and 52 mesh per inch was used. The specific surface area determined by the B.E.T. method from N, adsorption at liquid nitrogen temperature was 84.5 m2 gP1.Between runs the absorbent was outgassed at 550 K, loP4 Torr for 24 h. Ethanol and methanol were AnalaR grade (B.D.H.) and were stored over 4A molecular sieve. The water was freshly double distilled in an all-glass still. The surface tension of typical batches was > 72 mN m-,, indicating the absence of surface active impurities. The purity of the components was further tested by passing each individually over the Graphon adsorbent: in no case did the refractometer register a significant change in composition between the reference and adsorption sides of the apparatus. Solutions were made up by weight, from degassed components, by distilling the liquids under vacuum into the preparation flask [fig. 2 of ref. (4)] : the total amount, no, of solution transferred to both the adsorption and reference circuits was obtained by weighing. The precision of the present technique is critically dependent on calibration of the refractometer which is needed to establish Ax:, the change in mole fraction resulting from adsorption.A particular problem arises with the water-alcohol systems since the refractive index passes through a maximum at a mole fraction of ca. 0.35 for methanol,8 u -\ =s+ G F!g. 1. Mercury operated circulating pump : A, precision bore glass tubing; B, stainless-steel piston; C, neoprene piston ring; D, cam operated by fractional HP electric motor; E, return spring; F, G, Youngs’ taps; H, I, glass non-return valves; J, mercury.D. H. Everett and A . J . P. Fletcher 2607 and 0.60 for ethan01.~ In the neighbourhood of the maximum the sensitivity of the refractive index method of analysis falls off so rapidly that adsorption measurements around these concentrations could not be made.The calibration was carried out at the end of each run by adding known amounts of alcohol to the reference side of the apparatus and plotting the refractometer output against the calculated change in mole fraction. At each mole fraction several additions of alcohol were made and the refractometer output plotted against the volume added. These graphs were accurately linear since the mole fraction change was small, and the slope gave the refractometer sensitivity at the mole fraction concerned. Three methods of adding alcohol were used. In the first a known volume of alcohol held in a bypass capillary between two Youngs’ needle valves was introduced into the main system by manipulating the taps; in the second, several small glass ampoules containing a weighed amount of alcohol were introduced into an enlarged section of the reference circuit.At an appropriate moment an ampoule was crushed using an externally controlled plunger. These methods, used for the water-ethanol system, were not entirely satisfactory and for the water-methanol system, degassed methanol was injected from an Agla syringe through a septum, one face of which was coated with PTFE. It was thus possible to make up to six injections covering the range 25-150 mm3. This enabled considerably greater precision to be achieved. Fig. 2 shows the sensitivity plotted as the reciprocal of the mole fraction change per chart recorder unit as a function of mole fraction for both ethanol-water and methanol-water.The form of these curves can be calculated from the known variation of refractive index with mole fraction. This was necessary in the case of the water+thanol system to overcome the scatter of points in the calibration. The refractive index ( n ) us. mole fraction (xi data of Scott9 were fitted to an eighth-order Chebyshev polynomial, 10 5 Is: \ I 2 0 - 5 0 Fig. 2. Refractometer calibration curves for water-methanol and water+thanol mixtures. 1 /R is shown as a function of xf, where R = recorder chart units for lop4 change in xi. The curve for ethanol was obtained by fitting points obtained by the first two methods described in the text to the refractive index against composition relati~nship.~ The calibration for methanol was carried out by the third method.0 , Interpolated points for ethanol-water; 0, experimental points for met hanol-wa ter .2608 Adsorption of Aqueous Alcohols on Carbon from which dn/dx was calculated and used to smooth the calibration curve. With water-methanol this procedure was unnecessary. A slow drift of refractometer sensitivity over several months meant that recalibration was needed from time to time. This problem may be overcome using the null method of measurement which was developed in later work.10 Results Specific surface excess isotherms (noAxi/m against xi) were determined at five temperatures in the range 298-338 K for the system [water (IFmethanol (2)]/Graphon and at the temperatures in the range 298-348 K for the system [water (l>-ethanol(2)]/Graphon (fig. 3 and 4).The isotherm data are given in tables 1 and 2. In both cases the alcohol is the preferentially adsorbed component. I I I I A I I I I 0-2 0 4 0.6 0.8 1 .o 4 Fig. 3. Adsorption isotherms for (water-methanol)/Graphon at various temperatures : n"Ax;/m as function ofx,. Points above xi = 0.4 at intermediate temperatures omitted for clarity. 0,298.15; 0, 308.15; A, 318.15; V, 328.15; a, 338.15 K. Analysis of Results Thermodynamic Analysis The thermodynamic analysis was carried out using the integrated form of the Gibbs adsomtion isotherm :I1 where 0 and a,* are, respectively, the surface tensions of a solution of mole fraction x i and of pure component 2 in contact with the solid, y i is the activity coefficient of component 2 in the bulk solution, and a, the specific surface area of the solid.If the integration is taken to xi = 0, the difference a: -0: is obtained.D. H. Everett and A . J . P. Fletcher 2609 I Fig. 4. Adsorption isotherms for (water+thanol)/Graphon at various temperatures : n"Axi/rn as function of xi. 0, 308.15; 9, 328.15; 0, 348.15 K. Curves for 298.15, 318.15 and 338.15 K omitted for clarity. Table 1. Values of (n"Ax~/m)/104 mol g-' for [water (1)- methanol (2)]/Graphon ~ __ ~ xk 298.15 K 308.15 K 318.15 K 328.15 K 338.15 K 0.034 0.078 0.090 0.127 0.193 0.249 0.277 0.302 0.441 0.51 1 0.599 0.646 0.669 0.858 1.327 2.746 2.8 19 3.319 3.586 3.952 4.128 4.083 2.749 2.344 1.913 1.126 0.648 0.335 1.286 2.607 2.692 3.165 3.393 3.699 3.763 3.749 2.749 2.382 1.890 1.106 0.622 0.343 1.258 2.474 2.564 2.998 3.208 3.446 3.480 3.412 2.742 2.4 14 1.863 1.083 0.594 0.350 1.217 2.340 2.436 2.83 1 3.022 3.192 3.140 3.075 2.742 2.449 1.836 1.01 1 0.571 0.357 1.183 2.20 1 2.309 2.67 1 2.837 2.939 2.909 2.737 2.763 2.434 1.808 1.060 0.548 0.364 The results of this analysis are critically dependent on the use of reliable activity coefficient data.For the water-methanol system we have used the data of McGlashan and Williamson,12 who report values of x,, y, (the mole fraction in the vapour) and p (the total pressure) at 35, 50 and 65 "C. The activity coefficients were calculated from In72 = WPY,/P,* 4 +(B,,+v,*)(P-P,*)/RT (3)2610 Adsorption of Aqueous Alcohols on Carbon Table 2.Values of (noAxf/m)/104 mol g-' for [water (lj+thanol (2j]/Graphon ~ x i 298.15 K 308.15 K 318.15 K 378.15 K 338.15 K 348.15 K ~~ -~ 0.004 0.910 0.861 0.8 13 0.766 0.720 0.674 0.022 4.343 4.229 4.107 3.924 3.673 3.406 0.029 4.646 4.576 4.440 4.292 4.141 3.902 0.051 4.776 4.736 3.663 4.536 4.369 4.169 0.145 4.128 4.0 16 3.880 3.768 3.588 3.385 0.195 3.477 3.31 1 3.233 3.010 2.860 2.724 0.221 2.980 2.852 2.741 2.641 2.513 2.425 0.305 1.994 1.844 1.749 1.618 1.443 1.365 0.359 1.300 1.247 1.171 1.088 1.03 1 0.970 0.433 0.691 0.623 0.579 0.456 0.384 0.304 0.601 0.318 0.405 0.579 0.738 0.882 1.013 0.772 0.259 0.315 0.382 0.436 0.483 0.517 0.05 1 0.928 0.031 0.033 0.036 0.042 0.048 0.106 4.607 4.53 1 4.434 4.289 4.I37 3.977 6 0 I I l I l l ~ ~ I 0.2 0.4 0.6 0.8 1.0 0 x:Y: Fig. 5. 0.2 0.4 0.6 0.8 1.0 4 r: Fig. 6. Fig, 5. Graphs of (n"Ax!Jrn)/(x: xf 7;) as functions of xf yf for (water-methanol)/Graphon at (a) 298.15; (b) 308.15; (c) 318.15; (6) 328.15; (e) 338.15 K. Above xi?: = 0.6 the curves are indistinguishable. Fig. 6. Graphs of (n"Axf/m)/(x; xi xf) as functions of x i y: for (water-ethanol)/Graphon at (a) 328.15; (b) 338.15; (c) 348.15 K.261 1 D. H. Everett and A . J . P. Fletcher Table 3. [Water (lkmethanol(2)]/Graphon : (a - a:), T(Aw - A, S:) and (A, h - Aw h,*) as functions of xi ~~ T(A, s^- A~ s:) (A, h -A, h:) (a - o,*)/mJ m-2 mJ m-2 mJ m-2 xi 25°C 35°C 45°C 55°C 65°C 25 "C 25 "C 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1 .oo 16.55 13.75 11.45 9.50 7.85 6.50 5.30 4.15 3.40 2.80 2.36 2.03 1.74 1.37 1 .oo 0.49 0.00 35.00 34.07 32.91 29.00 27.85 26.75 24.05 23.00 21.80 19.90 19.10 18.15 5.30 2.90 0.85 9.20 7.75 6.50 5.40 4.40 3.50 2.95 2.54 2.15 1.82 1.44 1.02 0.52 0.00 6.05 3.45 1.30 9.40 7.80 6.45 5.45 4.35 3.45 2.80 2.43 2.10 1.78 1.41 1.04 0.52 0.00 31.71 25.35 20.75 17.30 14.65 12.35 10.60 9.05 7.75 6.45 5.45 4.50 3.60 3.00 2.58 2.22 1.88 1.47 1.04 0.54 0.00 30.52 33.70 24.40 34.85 20.30 29.20 17.15 21.81 14.30 17.62 12.35 11.67 10.60 7.16 9.15 3.14 7.85 0.15 6.65 -0.95 5.60 - 1.87 4.65 - 3.49 3.75 -2.53 3.10 - 2.39 2.65 -2.18 2.39 - 2.50 I .94 - 1.48 1.53 - 1.07 1.06 -0.36 0.54 0.36 0.00 0.00 mean standard deviation : 68.70 63.85 53.24 41.71 34.17 25.42 18.01 12.64 8.00 5.55 3.47 0.66 0.85 0.41 0.18 0.26 0.30 0.64 0.85 0.00 & 0.93 - 0.47 where p ; and v z are, respectively, the saturation vapour pressure and molar volume of pure component 2 and B,, is the second virial coefficient of the pure vapour 2.Terms in B12, the cross-second virial coefficient, were ignored. Values of v; and B,, were taken from ref. (12). To obtain values of In y z at other temperatures, In y z was plotted against 1 / T and, assuming a linear relation, In y z at the required temperatures was obtained by interpolation or extrapolation. Values extrapolated to 25 "C agreed satisfactorily with the measurements of Butler et al.,13 but less well with the results reported by D~1itskaya.l~ For water-ethanol the values of In yz tabulated by Pemberton and Mash15 at 303, 323, 343 and 363 K were plotted against 1/T and interpolated to obtain values at our experimental temperatures.In this system these graphs are curved and the interpolations were made using a flexible spline. The curves of (n"Axf/rn)/(x: xf yf) against xf yf were constructed from the experimental points supplemented by points obtained by interpolation of the experimental isotherm. The form of this curve at low values of xi is important. Since experimental points for x i < 0.005 (for which xiyf < 0.03) were difficult to measure accurately, it has been assumed that the isotherm approaches linearity at sufficiently low values of x f . Values of the specific adsorption were interpolated on this assumption. There was some evidence that plots of Q1) (the relative adsorption of 2 with respect to 1) against x i 7: gave more consistent interpolated values. Typical curves of (n"Ax',/rn)/(x: x i 7;) against x i y i are shown in fig. 5 and 6.Integrations were made using either Simpson's rule or the trapezoidal rule with strip widths of 0.005 for xf increasing in steps of 0.05. Values of (0-0;) obtained in this way2612 Adsorption of Aqueous Alcohols on Carbon Table 4. [Water (l)-ethanol (2)]/Graphon : (a - a,*), T(Aw 6 - Aw 6:) and (Aw h - Aw h,*> as functions of x\ ~~~ -~ _ _ _ _ _ ~ ~ _ _ _ _ _ _ _ ~ -. (a - a,*)/mJ rnp2 T(Aw i- Aw S:) (Aw h - Aw h,*) mJ m-* mJ m-2 xi 25°C 35°C 45 "C 0.00 0.005 0.010 0.02 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1 .oo 42.3 39.0 36.0 30.25 18.2 9.30 5.10 3.48 2.51 2.05 1.64 1.39 1.23 1.11 1.02 0.92 0.80 0.67 0.525 0.37 0.21 0.08 0.004 0.000 41.33 38.5 35.2 29.1 17.4 8.95 5.30 3.73 2.84 2.36 1.98 1.75 1.58 1.46 1.35 1.23 1.08 0.92 0.72 0.51 0.3 1 0.13 0.03 0.00 40.21 37.3 33.6 28.25 16.85 8.85 5.50 3.85 3.10 2.58 2.46 2.02 1.87 1.74 1.60 1.41 1.20 0.95 0.71 0.47 0.36 0.12 0.03 0.00 39.36 36.6 33.3 27.0 16.30 8.6 5.55 4.22 3.60 2.92 2.63 2.44 2.30 2.16 1.97 I .73 1.44 1.13 0.82 0.53 0.28 0.1 1 0.03 0.00 55 "C 65 "C 38.24 35.6 32.5 26.80 16.20 9.10 6.10 4.7 1 3.96 3.47 3.17 2.99 2.86 2.72 2.48 2.18 1.85 1.45 1.07 0.73 0.42 0.19 0.04 0.00 75 "C 25 "C 25 "C 36.90 33.95 3 1.05 25.85 15.70 8.90 6.25 4.90 4.20 3.70 3.41 3.25 3.13 2.96 2.68 2.29 1.87 1.44 1.01 0.66 0.36 0.16 0.05 0.00 31.57 29.44 28.15 25.56 14.17 1.68 - 6.98 - 8.84 - 10.56 - 10.15 - 10.73 - 11.45 - 11.72 - 1 1.45 - 10.28 - 8.53 - 6.74 - 4.77 - 3.04 - 1.84 - 0.86 - 0.48 - 0.21 0.00 73.87 68.44 64.15 55.81 32.37 10.98 - 1.88 - 5.36 - 8.04 -8.10 - 9.09 - 10.06 - 10.49 - 10.34 - 9.26 - 7.61 - 5.94 -4.10 -2.51 - 1.48 - 0.65 - 0.40 - 0.20 0.00 mean standard deviation: k 0.77 are collected in tables 3 and 4.From these, enthalpy and entropy quantities were calculated from l1 = -(Aws"- A,.?,*) ( )$. (4) where Aw ,i: and Aw k are the entropy and enthalpy changes associated with the immersion of unit area of solid (denoted by the circumflex) in solution of mole fraction xi, while Aw j:; and Aw h,* refer to immersion in pure liquid 2. In all cases the relationships implied in eqn (4) and ( 5 ) were linear, and the slopes were obtained by linear regression analysis.Tables 3 and 4 present the resuits at 25 "C in the form of (Aw h - Aw h,*) and T(Aw s" - Aw s",*). In fig. 7 (a - a:), (Aw h - Aw h,*) and T(Aw s"- Aw j::) are shown plotted against xi; for purposes of discussiqn and for comparison with data for other systems it is convenient to plot (a - a:), (Aw h Aw h:) and - T(Aw j: - Aw j::) against xi (fig. 8). This figure also includes values of (Aw h - Aw h,*) calculated from preliminary measurements for (water- methanol)/Graphon obtained by Mr A. Jones by immersion calorimetry.D. H. Everett and A . J. P. Fletcher 2613 70 60 50 40 E 30 E Q N I h 5 20 s :< I 10 0 -10 c - r -201 -30 70 60 5 0 LO E c, 3 0 E <"," 20 Q I < - 10 9 h 0 -10 -20 - 3 0 N 1 n 0.5 x: 0.5 x: 0.5 4 Fig.7. Thermodynamic functions at 25 "C for (water-alcohol)/Graphon systems : (a) (0 -or), (b) (Awh-Awh,*), ( c ) T(AWi-Awi,*) as functions of xi. Open points: methanol; filled points: ethanol. 40 30 20 10 0 N E -10 h -20 % -30 * .3 -4 0 - 9 0 1 Fig. 8. Ther-modynamic functions at 25 "C for (water-alcohol)/Graphon systems: 0, (a -a:); A, (Aw h -Aw h:); 0, - T(Aw &-Aw 2:); Open symbols, methanol; filled symbols, ethanol. 0, (Aw h - Aw h:) from immersion calorimetry.2614 Adsorption of Aqueous Alcohols on Carbon Discussion Fig. 7 and 8 illustrate the broadly similar behaviour of these two systems. In the first place, the addition of water to ethanol has very little influence on the thermodynamic parameters for adsorption up to a mole fraction of ca.0.4 (fig. 8). Put another way, the addition of alcohol to water results in strong adsorption of alcohol, and a rapid change of the character of the interfacial layer towards that characteristic of the alcohol/Graphon interface. Consideration of the adsorption isotherms shows that ethanol is more strongly adsorbed than methanol, which is consistent with the view that adsorption arises mainly from dispersion forces between alkyl groups and the graphite surface. The secondary maximum at higher mole fractions which develops in the ethanol isotherms at higher temperatures, and which appears as a slight shoulder with methanol, is not readily interpreted. Its influence on the surface tensions is small, but leads to an inflection point in the (0-0;) against x', graphs which is, however, hardly seen on the scale of fig.7. It is also noteworthy that the adsorption isotherms for water-methanol are virtually independent of temperature above a mole fraction of methanol of 0.4, and that the graphs of T i n ) / x ; xi y i against x i y', are superposable above xi y', > 0.6, while for the water- ethanol system the corresponding graphs run closely parallel in the range 0.10-0.6. Fig. 8 also shows that the dominant factor which determines the sign of the preferential adsorption is the enthalpy of immersion, although the opposing entropy term is some 50% of the enthalpy term. A. J. P. F. is indebted to the S.E.R.C. and B.P. for the award of a CASE studentship. References 1 D. H. Everett, Pure Appl. Chem., 1981, 53, 2181. 2 I. Callaghan, D. H. Everett and A. J. P. Fletcher, J . Chem. Soc., Faraday Trans. 1, 1983, 79, 2723. 3 C. E. Brown, D. H. Everett and C. J. Morgan, J . Chem. Soc., Faraday Trans. I , 1975, 71, 838. 4 S. G. Ash, R. Bown and D. H. Everett, J . Chem. Thermodyn., 1973, 5, 239. 5 S. G. Ash, R. Bown and D. H. Everett, J . Chem. Soc., Faraday Trans. I , 1975, 71, 123. 6 D. H. Everett and R. T. Podoll, J. Colloid Interface Sci., 1981, 82, 14. 7 D. H. Everett, in Ahorption from Solution, ed. R. H. Ottewill, C. H. Rochester and A. L. Smith 8 Handbook of Chemistry and Physics, ed. R. C. Weast (C.R.C. Press, Cleveland, 57th edn, 197677). 9 T. A. Scott, J. Phys. Chem., 1946, 50, 406. (Academic Press, London, 1983). p. D-237. 10 D. H. Everett and C. Nunn, J . Chem. Soc., Faraday Trans. I , 1983, 79, 2953. 1 1 D. H. Everett and R. T. Podoll, in Specialist Periodical Report: Colloid Science (The Chemical Society, 12 M. L. McGlashan and A. G. Williamson, J . Chem. Eng. Data, 1976, 21, 196. 13 J. A. V. Butler, D. W. Thomson and W. H. McLennan, J . Chem. Soc., 1933, 674. 14 K. A. Dulitskaya, Zh. Obsch. Khim., 1945, 15, 9. 15 R. C. Pemberton and C. J. Mash, J . Chem. Thermodyn., 1978, 10, 867. London, 1979), vol. 3, chap. 2. Paper 5/ 18 15; Receii3ed 18th October, 1985