Adsorption of alcohols at an air—solution interface: A pseudoregular monolayer model

Adsorption of Alcohols at an Air-Solution Interface: A Pseudoregular Monolayer Model R. B E N N E S Groupe de Recherche N ° 28. Centre National de la Recherche Scientifique. B.P. 5051, Montpellier Cedex 34033 France AND

E. BOU KARAM Faculty o f Science H, Mansourieh, Metn Nord, Lebanon Received S e p t e m b e r 24, 1979; accepted O c t o b e r 4, 1980 A m o n o l a y e r model of c o n s t a n t t h i c k n e s s h a s been utilized to explain the adsorption of n-propanol, t-butanol, s-butanol, and n-butanol at an a i r - a q u e o u s solution interface. T w o coefficients t h e one B% characterizing the interfacial properties and the other B ~ those of the bulk solution h a v e been correlated. Attention is drawn to the relation b e t w e e n B * and the hydration of the alcohol molecules in solution.

INTRODUCTION

The adsorption of n-alkanols (C~ to Cg), on mercury at zero charge, has been reported in a previous paper (1). The isotherm was established using as a basic hypothesis the idea of an adsorbed monolayer whose behavior, with regard to the activity coefficients at the interface, is that of a regular solution. Here we have chosen, for two reasons, to study the air-solution interface. Firstly, it is thus possible to work in the absence of a salt and hence to obviate any difficulties due to the variation of the chemical potential of the salt, which it must be remembered can be quite considerable (2-4) in the case of very soluble alcohols. Secondly the fact that the superficial tension of the pure substance can be measured considerably simplifies matters and the use which can be made of the results obtained, while at the same time it makes a more thorough study of the isotherm possible.

Nevertheless the two interfaces, airsolution and mercury-solution, lead to complementary results. If indeed it seems that the first interface is not really suited to the study of long-chain molecules and their interaction with water, as a nonnegligible part of these molecules is actually situated in the gaseous and not in the aqueous phase, on the other hand the second interface is not particularly well adapted to the study of short-chain molecules as here an interaction between the mercury and the polar head may well occur. The aim of the work described in this paper was to try and show how the solute-solvent interactions at the interfacial layer are related to the properties of solutions. The approach used is in line with the series of studies which have made use of Eriksson's equations (5) for adsorbed monolayers. In view of what was said above concerning the air-solution interface, and the

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Journal of Colloidand Interface Science, Vol. 81, No. 2, June 1981

305

ADSORPTION AT AIR-SOLUTION INTERFACE

study of long-chain compounds, we have intentionally restricted this study to shortchain alcohols with almost spherically shaped molecules. Finally we make use of the hypothesis, as is generally done in the case of elect r o d e - solution interfaces, that in this region the activity coefficients can be formally expressed as in regular bulk solutions.

F2,1 = - O y / R T 0 In x~ given by the Gibbs equation and the two relations F2,1 = F2 - FlX2/Xl, 1 = F2Ag + FIA~.

It is thus possible to calculate the molar fractions in phase o-, i.e., F, x ~ - - -

F2 x g - - -

and

F1 + F2 THEORETICAL CONSIDERATIONS

The equation for the adsorption in a superficial phase or, of a constituent i, in the bulk phase o~, is (5, 6) A~T - A~°y ° = R T in --a~, a~

[1]

AGO RT

_

/ a1 ~ /

We shall now utilize Eq. 1 making the following hypotheses: The o- solution is considered as being regular, i.e., one neglects any contraction on mixing and Ag ~ Ag o and A~ ~ A~°; A~ ° and A~ ° are given by (7)

)

2',

A ~ ° = V~/T,

[6]

where v~ and v°~ are the molar volumes in the volumic phase which are considered as equal to those in the superficial phase. By analogy with regular bulk solutions the activity coefficient at the interphase is given by (8, 9) l n f g = B'~(x~) 2,

[71

while in solution it is Ot 3 I n f ~ = B~(x~) 2 + B2(Xl) + "'" • [8a]

J

a~/aa~n

= In ~ ( ~ l )

and

The solution being generally dilute, one can write ln f ~ = ~ B~ = B ~. [8b]

a,~o "~i ~,0 - AgOyO

R T ~ ~2 A~ r i

[5]

F1 + F2

A ~ ° = v~/'c

where A~ and A~ ° are respectively the partial molar and molar areas of the constituent i in the phase or; y and To the superficial tensions of the mixture and the pure substance i; a~ and a~ its activities in the phases o- and o~ in a symmetrical system which is defined by f~--> 1 for the pure constituent i. For a binary mixture (i = 1, 2) the elimination of y in the two equations derived from relation [1] for the two constituents leads to

[4]

,

[2]

1/

where n = A ~ / A ~ can be considered as the number of displaced water molecules. Equation [2] is known as the " i s o t h e r m " of the mixture. It corresponds to the law of mass action as applied to the equilibrium n(molecules 1)~ + l(molecule 2)~ l(molecule 2) ~ + n(molecule 1)%

[3]

The superficial excesses F2 and Fi are determined using the relative surface excesses

The activity coefficients of the substance studied at infinite dilution are given in Refs. (10, 11). Equation [1] can now be written Y = B,~(x~) 2 - B ~ Ag o -

xg (y

RT

_

y0)

_

I n - ,

[9]

x~

where the last term on the right-hand side includes only known or calculable parameters. On the basis of results for the variation of the surface tension with the concentration one can represent Y = f ( x g ) 2 and hence evaluate B ~ and B% Journal of Colloid and Interface Science, Vol. 81, N o . 2, June 1981

306

BENNES AND BOU KARAM MATERIAL AND METHODS

TABLE I

The surface tension is determined using the Wilhelmy plate technique, with a reproducibility of 0.1 dyn cm. The apparatus used was a precision J. Guastalla torsion balance constructed in the laboratory. The cell temperature is regulated by a thermostat and all the usual necessary precautions characteristic of this type of measurements are taken to ensure a rapid equilibrium between the liquid and vapor phase and to minimize losses by evaporation (12). Solutions were prepared using freshly twice distilled deionized water, one distillation having been carried out on potassium permanganate. The tertiary butanol (t-BuOH) was a Fluka puriss product used as such while the other alcohols were carefully redistilled before use to ensure purity. The results obtained agree perfectly well with those given by other authors, where they exist, as for instance for the same mole fraction and at 25°C for n-BuOH, s-BuOH, and t-BuOH (13).

E x p e r i m e n t a l R e s ul t s C o n c e r n i n g the t - B u O H at A / W

RESULTS

Determination of the Isotherm Parameters Tertiary Butanol

-In x¢

xg

(dyn/em)

-Y

9.23 8.53 7.82 7.14 6.92 6.22 5.81 5.52 5.30 5.11 4.81 4.58

2.07 × 10-2 4.45 × 10-2 7.86 × 10-2 0.130 0.149 0.217 0.267 0.281 0.299 0.310 0.332 0.358

51.4 50.4 48.2 45.1 43.4 38.6 35.4 32.8 31.0 29.4 26.4 24.5

1.316 1.458 1.491 1.557 1.606 1.662 1.707 1.674 1.651 1.629 1.633 1.624

Note. T = 15°C; ~- = 5 A; y ° = 21.2 dyn/cm;A~°/RT = 7.855 10-2 cm2/erg,

ment if one takes into consideration the approximation made. The coefficients B ~ and B% which represent the deviation from ideality in the two phases, increase linearly with the temperature, the respective gradients being 10-2 °K-1 and 2.10 -~ °K-L The variation of B e with the temperature can lead to an interesting comparison. T A B L E II

The adsorption oft-BuOH at the interface has been studied at four temperatures (15, 25, 35, 45°C) and the results are given in Tables I - I V . The results for ~- (5 A) were chosen on the basis of geometric models. B ~ and B e are determined graphically using Eq. [9]. See Table V. The plot of Y = f(x~) 2 gives a straight line, with a tendency for the points to deviate from this line at the higher concentrations. This would seem to show that the hypotheses made are not incorrect in the case of dilute surface solutions. As compared to these values calculating B e = lnx~-~0f~ at 25°C using the data given by Butler (10), one obtains a value of 2.47 which represents a relatively good agreeJournal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

E x p e r i m e n t a l Results C o n c e r n i n g the t - B u O H at A / W

-In x#

x~'

(dyn/cm)

-Y

9.23 8.53 7.82 7.14 6.92 6.22 5.81 5.52 5.30 5.11 4.81 4.58

2.28 × 10-2 4.12 × 10-z 7.48 × 10 -2 0.125 0.146 0.217 0.256 0.288 0.310 0,332 0.367 0.391

50.8 49.6 47.6 44.2 43.7 37.9 34.4 32.1 30.2 28.4 25.4 23.2

1.583 1.574 1.616 1.704 1.682 1.813 1.838 1.833 1.832 1.854 1.882

Note. T = 25°C; ~- = 5 A; 7 ° = 20.2 dyn/cm;A~°/RT = 7,592 10-2 cm2/erg.

307

A D S O R P T I O N AT A I R - S O L U T I O N I N T E R F A C E T A B L E III E x p e r i m e n t a l Resu lts C o n c e r n i n g the t - B u O H at A / W

-In x#

x~

y - y2o (dyn/cm)

-Y

9.23 8.53 7.82 7.14 6.92 6.22 5.81 5.52 5.30 5.11 4.81 4.58

1.82 × 10 -3 3.87 × 10-z 7.18 × 10-2 0.122 0.143 0.217 0.258 0.293 0.322 0.347 0.389 0.423

50.0 49.0 46.9 43.4 42.0 3713 33.9 31.3 29.3 27.4 24.5 22.1

1.552 1.681 1.542 1.85 1.892 1.954 1.965 1.993 2.009 2,038 2.065 2.097

N o t e . T = 35°C; r = 5 A; yO = 19.2 d y n / c m ; A ~ ° / R T = 7.345 10 -2 cm2/erg.

Butler (10) gives, for the variation o f the dilution enthalpy at infinite dilution, the value AH~ol = AHhyo + AHvap = - 4 . 0 3 kcal" mole -1. Taking into account the experimental errors the slope o f B ~ = f(T) gives a maximum value of AH~ot = - 4 . 0 6 k c a l . m o l e -1 (i.e., AH~ol = -RT2OB~/OT). The observed increase of B " with the temperature is therefore perfectly rational. T A B L E IV E x p e r i m e n t a l Results C o n c e r n i n g the t - B u O H at A/W

-In x#

x~

y - y~ (dyn/cm)

-Y

9.23 8.53 7.82 7.14 6.92 6.22 5.81 5.52 5.30 5.11 4.81 4.58

1.55 × 10 -2 3.63 × 10-2 6.93 × 10-2 0.119 0.140 0.214 0.259 0.297 0.326 0.336 0.362 0.377

49.3 48.2 46.3 42.6 41.2 36.7 33.1 30.6 28.3 26.6 23.4 16.4

1.553 1.786 1.858 1.98 1.72 2.065 2.106 2.128 2.16 2.128 2.13 2.436

N o t e . T = 45°C; r = 5 A; yo = 18.2 dyn/cm; A g ° / R T = 7.114 10-2 cm2/erg.

Furthermore, one can calculate the free energy of adsorption AG o from the last term in Eq. (2) or then from the second term of this same equation, if this is simplified by taking into account the regularity of the surface monolayer AG O =

A~Ot 2 ~ r,0 2 -

y0),

AH° = a~°T2( Oy°/TOT

[10]

Oy°/T )

[111

and

ASO = ~o{ Oy°

OY~I [12] or or:" The first method leads to AG°/298R = - 3 . 8 and the second AG°/298 R = - 3 . 9 + 0.3. The model proposed is therefore self-consistent within the experimental errors. In Table VI are given, as examples, three thermodynamical values calculated from Eqs. (10), (11), and (12) at two temperatures. Normal Butanol (n-BuOH), Secondary Butanol (s-BuOH), and Normal Propanol (n-PrOH) at 25°C The results in Tables VII, VIII, and IX can be used, as has been done above, to calculate the values of B ~ and B ~. See Table X. The values given show that the adsorption of the alcohols studied is greatest when the generalized solubility is small and the value of B" is large. The deviation from ideality at infinite dilution which is represented by B ~ decreases for a branched chain, for an equal number of carbon atoms. TABLE V Variation of B " and B '~ with the T e m p e r a t u r e Temperature

B~ B~

15

25

35

45

2 0.55

2,15 0,6

2.4 0.75

2.5 0.75

N o t e . E s t i m a t e d e rror _+ 0.10.

Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

308

BENNES AND BOU KARAM TABLE VI

(a~)li m = 1 = (f~)lim(X~)lim.

Variation of Thermodynamical Values with the Temperature in the Case of t-BuOH Temp. (°K)

AG o (kcal-mole -~)

AH ° (kcal. mole -~)

AS ° ( c a l - K -~ mole -~)

298 318

-2.25 -2.20

- 1.45 - 1.35

2.7 2.7

B ~ i n c l u d e s all t h e i n t e r a c t i o n e f f e c t s b e t w e e n 1 a n d 1, 1 a n d 2, 2 a n d 2, a n d o n e n o t e s t h a t it v a r i e s as d o e s B ~. H o w e v e r , this a c t i v i t y c o e f f i c i e n t at t h e s u r f a c e is m u c h s m a l l e r t h a n t h a t in s o l u t i o n . T h e p o s s i b l e c o r r e l a t i o n b e t w e e n B ~ a n d B " is d i s c u s s e d below. DISCUSSION F o r a l c o h o l s w h i c h a r e n o t m i s c i b l e in all proportions with water (e.g., n-BuOH), there exists a limiting mole fraction above w h i c h t h e s o l u t i o n s e p a r a t e s o u t into t w o p h a s e s , t h e o n e r i c h in w a t e r w h o s e a l c o h o l m o l e f r a c t i o n is ~x k ~ 2 / Il i m ~ a n d t h e o t h e r r i c h in a l c o h o l w i t h a m o l e f r a c t i o n (x~) II. T h e limiting c o m p o s i t i o n s a r e o b t a i n e d w h e n t h e c h e m i c a l p o t e n t i a l o f t h e s o l u t e in s o l u t i o n is t h e s a m e as t h a t o f t h e p u r e s o l u t e (10), i.e.,

[13]

F r o m (8b) a n d (13) e x p ( - B ~) = (X2)li ~ i m.

[14]

For the different alcohols studied the term 3,0 - 3' a l w a y s t e n d s to z e r o w h e n t h e c o n c e n t r a t i o n i n c r e a s e s . A s f u r t h e r this t e r m v a r i e s l i n e a r l y w i t h x L at t h e p o i n t o f inters e c t i o n w h e r e 3" = 3"0, - I n (x~)lim = B ~, w h e r e ( X a2)1im r e p r e s e n t s t h e s o l u b i l i t y o f t h e a l c o h o l in q u e s t i o n . F o r this p a r t i c u l a r m o l e f r a c t i o n a~=

1;

at=

1;

and

3' = To.

[15]

I n t h e c a s e o f a m e r c u r y - s o l u t i o n interf a c e (KC1, K B r , K I , o r K F 0.1 M ) in t h e presence of relatively short-chain n-aliphatic a l c o h o l s (C4 to Cs) it h a s b e e n s h o w n (14), using differential capacity measurements, that the h i g h e s t limiting c o n c e n t r a t i o n w h i c h c a n b e r e a c h e d at t h e i n t e r f a c e c o r r e s p o n d s , in all c a s e s o b s e r v e d , to t h e c o n c e n t r a t i o n at w h i c h s e p a r a t i o n into t w o p h a s e s o c c u r s . T h e limiting f a c t o r is t h e r e f o r e t h e s e p a r a t i o n into t w o p h a s e s a n d n o t t h e s u r f a c e concentration. For alcohols which are miscible with w a t e r in all p r o p o r t i o n s t h e s i t u a t i o n is t h e s a m e as t h a t d e f i n e d in E q . [15] a b o v e . H o w -

TABLE VII TABLE VIII

Experimental Results Concerning the s-BuOH at A/W

Experimental Results Concerning the n-BuOH at A/W -In x~

9.21 8.11 6.91 6.22 5.52 5.12 4.95 ~ 4.81 4.61 4.39 4.23 4.09

xg

(dyn/cm)

- Y

2.02 x 10-2 4.42 x 10-2 0.140 0.276 0.327 0.352

47.8 45.4 40.7 34.8 28.2 24.2 22.2 20.8 18.2 15.8 14.1 12.6

2.00 1.85 2.16 2.52 2.45 2.41

Note. T = 25°C; ~-= 5.5A; T° = 21.5 dyn/cm; A~°/RT = 6.91 10-2 cm2/erg. Journal o f Colloid and Interface Science, Vol. 81, N o . 2, J u n e 1981

-In x~

x¢

8.05 6.91 6.22 5.52 5.12 4.96 4.81 4.61 4.39 4.35 4.09

5.08 × 6.17 × 7.68 × 9.64 × 0.t22 0.148 0.186 0.283 0.367 0.456 0.520

10-2 10-2 10-2 10-2

(dyn/cm)

- Y

42.6 36.8 29.5 21.1 15.9 13.6 11.7 8.6 5.9 3.6 1.8

2.41 1.81 1.81 1.86 2.02 2.2 2.4 2.81 3.02 3.35 3.33

Note. T = 25°C; r = 5.9A; To = 24.1 dyn/cm; A~°/RT = 6.26 10-2 cmVerg.

309

A D S O R P T I O N AT A I R - S O L U T I O N I N T E R F A C E T A B L E IX Experimental Results Concerning the n-PrOH at A/W - To -In x~

xg

(dyn/cm)

- Y

7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5

2.84 × 10-~ 4.70 × 10-2 8.15 × 10-~ 0.137 0.207 0.295 0.336 0.381 0.396

44.5 43.3 41.5 38.5 34.5 29.2 23.4 17.1 10.9

1.46 1.53 1.69 1.87 2.00 2.15 2.11 2.09 1.97

N o t e . T = 25°C; r = 5.4/~; Ag°/RT = 5.57 10-2 cm2/erg.

yo = 24.5

dyn/cm;

ever, here the saturation of the bulk solution has a purely theoretical value termed by Butler (15) "Generalized solubility." Correlation between

B ~ and B ~

Figure 1 shows the relation between the two above coefficients obtained for the alcohols used here. One notes the excellent correlation for the results of t-BuOH at the different temperatures studied. To extend this study, the results for ethyl alcohol given by Butler e t a l . (15) have also been plotted. The curve appears to go through zero forB ~ ~ 0, which point should correspond to the first alcohol, i.e., water. Furthermore, looking into the hypotheses put forward by Butler (10) one notes (Fig. 2) a linear correlation between B ~ and nfi~o, where the latter corresponds to the number of nearest neighbors of water molecules to the hydrocarbon chain in the bulk

solution. In other words in accordance with the simple model proposed by that author, the hydration at infinite dilution, and hence also B% depends on the surface area of the alcohol molecule exposed to an interaction with the water. It is therefore of relatively little importance whether one is dealing with a normal straight or a branched chain, which is also revealed by the correlation between B ~ and B% Since B ~ is related to B ~ which in turn varies with n~2o (Figs. 1 and 2) one can assert that there exists a relationship between the coefficient B ~ and the number of nearest water molecules in the solution, i.e., n~o. This simply means that the activity coefficient at the interface depends on the number of molecules of hydration of the chain in the bulk solution. For the moment this has only been shown to be the case at an air-solution interface for carbon chains up to n-BuOH as longer-chain compounds cannot be studied as has been done here. However, results obtained at a

3

2

1

TABLE X Variation of B% B ", AG °, and rA °

B* n-BuOH s-BuOH t-BuOH n-PrOH

2.4 1.35 0.6 1.1

± ± ± ±

B~ 0.2 0.10 0.1 0.1

3.95 3.20 2.15 2,60

-+ 0.10 ± 0.10 ± 0.10 ± 0. I0

o

AG O

T

(keal/mole)

(/~)

-1.8 -2.05 -2.25 -1.55

± -* ±

0.3 0.30 0.30 0.30

5.9

5.5 5.0 5.4

i

5

B-"

FIG. 1. Correlation of the values found for B ~ and B ~ at aqueous solution interface. From the top downward ©--n-BuOH at 2 5 ° C , s-BuOH at 25°C, t-BuOH at 45, 35, 25, and 15°C; O - - n - P r O H at 25°C; O - - E t O H at 25°C (Butler).

Journal of CoUoid and Interface Science, Vol. 81, No. 2, June 1981

310

BENNES AND BOU KARAM

a

==

7

6

5

4

3

q / ~ j

o%

2

1

i

l

5

3

,

i

7

9

,

11

_

n~

.p

FIG. 2. Variation of B e with the number of nearest neighbors of water molecules to the carbon chain n~o given by Butler (10). m e r c u r y - s o l u t i o n interface in the p r e s e n c e o f a salt s e e m to indicate that for n o r m a l pentyl alcohol a b r e a k s e e m s to o c c u r in the curve. T h e s a m e p h e n o m e n o n has also b e e n o b s e r v e d in o u r l a b o r a t o r y at the merc u r y - a q u e o u s solution interface ( 0 . 5 M NaC1) for n-alcohols, n-acids, and glycol n - a l k y l m o n o e t h e r s , w h i c h s e e m s to s h o w that for s o m e r e a s o n or a n o t h e r a c h a n g e o c c u r s near the fifth c a r b o n atom. CONCLUSION I n spite o f the s o m e w h a t oversimplified nature o f the " regular a d s o r b e d m o n o l a y e r " h y p o t h e s i s it has n e v e r t h e l e s s b e e n s h o w n to constitute an interesting m e t h o d o f app r o a c h i n g the s t u d y o f a d s o r p t i o n p r o b l e m s . In the particular case o f short chain alc o h o l s using this m o d e l it has b e e n possible to determine the activity at the interface and at infinite dilution in solution. T h e results o b t a i n e d are in a g r e e m e n t with t h o s e f o u n d elsewhere. It w o u l d be interesting to follow up this w o r k b y s t u d y i n g n u m e r o u s o t h e r alcohols and their b e h a v i o r at different interfaces in o r d e r to establish w h e t h e r or not the relation B ~ = f ( B ~) goes t h r o u g h a m a x i m u m for n-pentanol. Journal of Colloid and Interface Science,

Vol.

81, No.

2, June

1981

REFERENCES 1. Bennes, R., J. Electroanal. Chem. 105, 85 (1979). 2. Nakadomari, H., Mohilner, D. M., and Mohilner, P., J. Phys. Chem. 80, 1761 (1976); Mohilner, D. H., and Nakadomari, H., J. Electroanal. Chem. 65, 843 (1975). 3. De Battisti, A., and Trasatti S., J. Electroanal. Chem. 54, 1 (1974). 4. Mazhar, A., Bennes, R., Vanel, P., and Schuhmann, D., J. Electroanal. Chem. 100, 395 (1979). 5. Eriksson, J. C., Ark. Kemi 25, 331 (1965); 25, 342 (1965); 26, 49 (1966). 6. Butler, J. A. V., Proc. Roy. Soc. London A 135, 348 (1932). 7. Randles, J. E. B. and Behr, B., J. Electroanal. Chem. 35, 389 (1972); Randles, J. E. B., Behr, B. and Borkowska, Z., J. Electroanal. Chem. 65, 775 (1975). 8. McGlashan, M. L.,J. Chem. Educ. 10, 516 (1963). 9. Prigogine, I., and Defay, R., "Chemical Thermodynamics," Longmans, London, 1969, p. 342. 10. Butler, J. A. V., Trans. Faraday Soc. 33, 229 (1937). 11. Kinoshita, K., Ishikawa, H., and Shinoda, K., Bull. Chem. Soc. Japan 31, 1081 (1958). 12. Guastalla, J., Lize, A., and Davion, N., J. Chim. Phys. 68, 822 (1971). 13. Dunning, H. N., and Washburn, E. R., J. Phys. Chem. 56, 235 (1952), 14. Tronel Peyroz, E., Schuhmann, D., and Bellostas, D., C.R.H. Acad. Sci. S~r. C 289, I (1979). 15. Butler, J. A. V., and Wightman, A., J. Chem. Soc. 2089 (1932).