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Adsorption kinetics of a non-ionic surfactant on the stationary mercury electrode
Colloids arlci Su~-fi~es. 66 (1992) 249-258 Elsevier Science Publishers B.V.. Amsterdam
249
Adsorption kinetics of a non-ionic surfactant on the stationary mercury electrode Z. Adamczyk and G. Para Institute of Catalysis and Surface Chemistry. Polish Academy ofSciertces, 30-239 Krakh, PolarId
(Received 12 November
ul. Niezapowitrajek I,
1991; accepted 24 April 1992)
Abstract Adsorption kinetics of the non-ionic rm~rs-2-hcptyl-5-hydroxy-l,3-dioxanc surhctant on the stationary mercury ckctrodc was invcstigatcd by a.c. polarography (tcnsammctry) with 0.4 M KC1 solutions used as supporting electrolyte, The experimental results obtained for various bulk surfactant concentrations were interpreted in terms of the exact numerical solutions of the governing mass-translcr equation. A good agreement bctwecn the experimental kinetic mcasurcmcnts and the thcorctical predictions was found, especially for longer adsorption times. The equilibrium adsorption isotherm ofTHHD was also determined. It was proved that the experimental isotherm can be adequately described by the localized adsorption Langmuir model with K, = 0.15 cm (this value corresponds to AC = -40 kJ rnol-I). The non-localizc\f adsorption model proved to bc inadcquatc. K~pords:
Adsorption
kinetics;
mercury
electrode;
non-ionrc
surfactant.
Introduction Non-equilibrium processes occurring at liquidliquid or liquid-gas interfaces in contact with surfactant solutions are of great practical significance, e.g. in important large-scale technological operations such as emulsification, emulsion coalescence and breakup, oil recovery, froth flotation, extraction, detergency, etc. Interface dynamics also plays an important role in many physiological phenomena, e.g. breathing. The kinetics of these processes depends considerably on the relative surclce tension of the coexisting interfaces which is II turn determined by the surfaciant adsorption rr.te. In contrast to the extensive experimental knowledge of static adsorption (adsorption isotherms), kinetic aspects of adsorption have been relatively Corrcsporzderw 10: Z. Adamczyk. 1nsti:utc and Surface Chemistry, Polish Academy of Niczapominajck 1, 30-239 Krakbw, Poland. 0166-6622/92/505.00
0
1992 -
Elsevicr
of Catalysis Scicnccs. ul.
Scicncc
Publishers
little studied in a precise, quantitative manner. This is because adsorption of surfactants can only be determined by means of indirect experimental methods of limited accuracy. One can mention the surface tension measuring techniques used in classical long-lasting adsorption measurements Cl,2], the oscillating-jet method suitable for very short transitions [3,4], and the electrochemical methods using the dropping L-5-7) or stationary [8,9] mercury electrodes. A comprehensive recent review of experimental and theoretical techniques aimed at adsorption studies can be found in Ref. [lo]. It seems that the electrochemical methods are the most reliable and accurate for moderate and longer times, enabling one to determine not only the overall equilibrium adsorption rate constant K, but also adsorption kinetics for various bulk surfactant concentrations. Therefore, the main goal of this paper should be a quantitative description of surfactant adsorption kinetics at the stationary mercury electrode (SME) using the precise tensamB.V. All rights
rcscrvcd.
metric method. As the model substance we shall use the high purity heptyl derivative of 1,3-dioxycyclane which can, potentiaily, be used in froth flotation of non-ferrous ores or as a hydrophobic intermediate for the synthesis of ionic and nonionic detergents. Experimental Mnterials
In our adsorption kinetics measurements we used the high purity isomer rrcrrzs-2-heptyl-5hydroxy- I ,3-dioxane (THHD) kindly supplied by the Institute of Organic and Polymer Technology, Technical University of Wroclaw (Poland). The isomer was isolated from the reaction mixture by repeated fractional distillation [? 11. The purity of the sample was better than 99.9% as checked by gas-liquid chromatography (GLC). Chemically purified mercury was cleaned using concentrated sulfuric acid, dried and distilled twice under vacuum. After the distillations, the mercury stock sample was stored in sealed ampules under argon atmosphere. The potassium chloride used as supporting eIectrolyte was recrystallized six times and then calcined for 8 h at 500°C. Special care was taken in order to produce distilled water of high purity needed for our precise measurements. The water was obtained in a multistage distillation procedure involving at least 6 steps with pyrodistillation over a platinum catalyst as a crucial stage [12-J. Procedtrre
The electrical cell used for the diff?rentlal capacitance measllrements on the SME was of a standard three-electrode type [13,14]. It consisted of the stationary (hanging) mercury electrode produced on the tip of a capillary (inner diameter 0.014 cm) above a mercury pool used as the counter electrode. The size of the mercury drop could be easily regulated by using a precise needle valve. The 0.4 M calomel electrode was used as the reference
electrode. It was connected to the ccl1 via a salt bridge filled with 0.4 A4 KCI. The equivalent electric circuit of the cell is shown schematically in Fig. 1. The measurements of the adsorption process occurring at the SME were carried out acccrding to the alternating current polarography principle (tensammetry). A small alternating current (a.~.) signal (amplitude about 10 mV and Zequency 40 Hz) was superimposed upon the steady polarization potential fed from !he potentiostat. Using the amplifier-phase detector system, the capacitance component of the a.c. flowing through the cell was selectively measured. The amplitude cf this current was proportional to the differential capacity of the eicctric double-layers on the SME and the counter electrode connected in series. Since the latter capacity exceeds cocsiderably the SME capacity, the registered signal was proportional to the SME capacity alone, provided that the ohmic resistance of the cell remained low (which was the case due to the high concentration of the supporting electrolyte). The measurements were carried out according to the three-stage procedure: first the electrode was polarized to such a potential value (usually - 1.7 V) that no surfactant adsorption or chemical reaction took place; then a mercury drop of a given size was produced on the tip of the capillary; finally the polarizing voltage was switched to a new value at which adsorption occurred (about -0.7 V). The resulting signal from the phase detector was registered and processed by a computer. Because the overall response time of the electric circuit is of the order of 1 s, the kinetic curves showing the dependence of the differential capacity of the SME on time can be easily recorded by using our method. Theoretical Governing
equations
The experimental the above-described
results obtained according to procedure were quantitatively
PRINTER I
VOLTMETER
Fig.
I. The
dilfcrcntial
electrical schcmc of the cxpcrimcntal capacity measurcmcnts on the SME.
cell used for
interpreted in terms of the theoretical approach discussed in detail previously [15,16]. The governing equations describing adsorption kinetics onto a spherically shaped interface (see Fig. 2) from a stagnant one-component solution has the form [15,17]
dN dt
+
-- 1
d4QNcJ
A(r)
dt
where c is the concentration of the surfactant, r is the time of adsorption, D is the surfactant diffusion coefficient (assumed to be concentration independent), r is the radial coordinate (cf. Fig. 2), N is the surface concentration of adsorbed surfactant, A is the surface area of the interface (which can be time dependent) and J is the normal component of the flux vector. When formulating Eqns (I), convective effects were neglected. The general constitutive expression for the adsorption flux J is [I71 J = k,c’f(N)
- k,g(N)
N
(2)
where k, is the adsorption rate constant, kd is the desorption rate constant, co is the subsurface concentration of the surfactant and f(N) g(N) are the
(1) to the by introducing the characteristic scaling variables, i.e. maximum surface and the this way (I) and tant concentration cb. can be written in the form:
where the dimensionless
0 = N/N, m
?= r/L
L = N,.,,/c,,
T = t/t,, tch = L2/D
are defined as
353
S, is the surface area occupied by one molecule. The general boundary conditions for Eqns(3) are [IS-l71
F’]
at r = rmix/L
(5b)
Equation (5a) i’:an adequately describe both the diffusion-controiicd and barrier-controlled adsorption regimes whereas Eqn (5b) postulates that, owing to natural convection, the surfactant concentration becomes unifcrm at some prescribed disgeometry the tance )‘mix. In practice, for sphe:ical exact value of rmiX is not important and can bc assumed to be infinitely large without affecting the calcuIations. As the initial condition we assume a uniform concentration distribution for r = 0, i.e. for r,/L < rmi,/L
C;= I o=o
‘1 r=O
(6)
I
In order to make the above set of equations complete one should specify also the constitutive dependence of the adsorption flux J on the surface concentration 0, and the subsurface concentration Co, i.e. the concrete expressions for j’(O) and g(0) should be given. For the simplest case of the linear adsorption model (Henry isotherm) f(O) = g(Bj = 1 and the entire transport problem formulated above becomes linear. In this case analytica solutions can be found, e.g. by applying the Laplace transformation [15,18,19]. For the widely used Langmuir modci the blocking function f(G) is expressed as
f(U) = 1 - c’ 0 mxL g(W
=
(7)
1
where OmxL.is the empirical parameter characterizing the dimensionless maximum surface concen-
tration of the adsorbed substance attainable when its bulk concentration tends to infinity. It should be mentioned that the Langmuil model is strictly valid only for localized adsorption on discretely distributed “active centers”. When no a tive centers can be distinguished and the adsorbed phase remains mobile (analogous to the two-dimensional hard-sphere fluid) then the blocking function can be described by the expressio;l [20,21]
J(O)=exp
2(I
+ iln(l
’ 7 ” (1 - 0)’ + s (1 - 0)2 -0)
1
w
Other useful expressions for J(0) and a(U) in the case where la’.eral interactions occur (Frumkin model) can be found in Refs [22,23]. As can be easily seen, Eqns (3) become nonlinear when one of the above expressions for f(0) is used to eliminate J and can only be solved by means of numerical methods as discussed before [ 15,24]. However, useful analytical solutions can be derived in the limit of the diffusion-controlled adsorption regime and short times when the linear model still holds. By assuming this, one can integrate Eqns (3) for the constant-area interface (which is the case for the SME) to give
2. Adunrczyk.
G. ParajColloids
When 4Ar>
Swfaces
1 the solution
66 (1992) 249-258
253
is
to the general procedure described previously [ 171, one can derive the following asymptotic expression valid when (&r/(k, + Ar) >> 1
1 +cos(qr)II
O=R,
l-n
l-
6 cos (qr) + sin (47)
i
12(7)
L
isin(rj7)
-0 - ac = K17-3” Oi - 0’
II(?)
(14)
[
1
b=&/m
a=2f7, II(t)
=
a
with
q=2nb K, =
04;
cos (26&r)
exp(--‘)dt
I,(7)=exp(-b27)erf(b&) a.,; ---i dz
1
OmxL
!K, f &,I_)’ 2,,&4r2
exp(-b27)
2
Ra
sin(2b&t)
exp(-?)dt
s 0
In the case of strong adsorption where K, >> 1 (perfect sink model), Eqns (9) and (10) simplify to the common limiting expression
O=-$/2+Arr
(11)
J-
Jr
Thus, the limiting adsorption
flux is given by
(12) Equations (11) and (12) are identical with those derived by Smoluchowski [25] to describe the fast coagulation of colloid particles. Note that the first term of Eqn (12) characterizes the transient adsorption fux which vanishes for longer times. It is also interesting to derive the limiting expressions for long adsorption times in the case of the Langmuir isotherm when the system is close to the equilibrium &aracterized by the surface concentration
Thus, for ihe spherical geometry the equilibrium surface concentrations are approached proportionally to 7- 3/2, i.e. much faster than for the planar interface when 0x7-“’ [ 19,263. Equations (1 !)-( 14) were also used for testing the accuracy of the numerical solution of Eqns (3) obtained in the general case by applying the implicit Crank-Nicolson method, generalized to accommodate for the non-linear boundary conditions Eqn (5a). The method enabling an exact solution of the diffusion equation for arbitrary isotherms has been described in detail elsewhere [24]. Since in experiments the differential capacity of the eIectrode is measured rather than the surface concentration 0, one shou!d specify a functional dependence connecting 8 with C, the differential capacitances. This can be done in a standard way by exploiting the well-known thermodynamic relationship [27-291 (15) where 4 is the surface charge density on the electrode for a given electrode potential E, I( = kT In C is the chemical potentia1 of the substance in the solution (we assumed ideal beha\,;or of the surfactant solutions because of their high dilution)_ Integration of this dependence with respect to chemical potential gives, 0
(13)
a0
z
q-q*=kTN,
Performing
the linearization
of Eqns (3) according
S( 0
dln C )P
(16)
254
where go is the surface charge density of zero adsorption. Assuming that the adsorption isotherm can be written in the potential-congruent form [27], i.e.
iI= R,c. In this case Eqn (21) simplifies to,
c=co
(I-$ >d”‘$ mn
or
f(O) =
KaCb -
-c N
=
i?,(E)c;
mx
(22)
(17)
m
(where the dimensionless adsorption depends on the electrode potential rearrange Eqn (16) to the form.
constant I?, E) one can
(18) Considering the definition of the difTcrentia1 capacitance C = c7q/dE, or,e can obtain from Eqn (18), by differentiation with respect to E, the expression
(19) where Co is the differential capacitance for an uncovered surface. For 0 -+ O,,: considering that (dO/dln R,) + 0, Eqn (19) becomes
c
mx
-
co = kTN,
d’ln Kali dE2 mx
(20)
where C,, is the capacitance for the maximum surface concentration O,,,. Therefore, for an intermediate 0
+ kTN,
(21)
As pointed out by Parsons [27,28] this equation gives a linear dependence of C on 8 (for arbitrary E) in the case of the Henry isotherm only, i.e. when
This relationship, derived originally by Frumkin, was widely exploited for describing adsorption of non-ionic surfactants [23,30-331. Equation (22) suggests that in the case of a linear isotherm the overall electrode capacity can be treated as composed of t,vo capacitors connected in series. Xowever, for an arbitrary adsorption isotherm and wide range of E, the dependence of C on 0 is generally non-linear C27] due to the presence of the term SO/din /?, in Eqn (2ij. Neverthe!ess, for potentials close to the adsorption maximum (if one exists) the t:rm (Zln l?,/i?~E’) obviously bccomcs very small and Eqn (22) can be used with care as discussed previousIy in Ref. 1231. Since in our measurements we have limited ourselves to potentials close to -0.7 V, i.e. corresponding to the adsorption maximum (cf. Fig. 3), the use of Eqn (22) for converting the measured C values to surface concentration seems justified. It should be noted, however, that the value of O,, occurring in Eqn (22) cannot be determined directly and remains an adjustable parameter. Iliesu’lts and discussion At first, a series of tensammetric runs was performed for various bulk surfactant concentrations in order to determine the effective range of the polarization potential at which adsorption of THHD occurs. These results, showing the dependence of the specific capacity of the mercury electrode on the polarization potential E (measured relative to the 0.1 normal caiomel electrode) are presented in Fig. 3. Because in this series of experiments we were interested in determining the efficient adsorption potential only, we used the
Z. Adan~yk.
G. Para~Collnids
Surfaces
66 (1992)
749-258
255
30
20
70
I
I
-0.5
Fig. 3. The dilTcrential
capacity
I
-1.5
-1.0
C of the dropping mercury clcctrode as a func:ion of the polarization 0.1 M calomcl electrode in solutions of various THHD concentrations.
dropping mercury electrode (lifetime 6 s) which is more convenient for this type of experiment. As can be seen in Fig. 3 the presence of THHD produces a depression of the specific capacity of the mercury electrode (which is a direct measure of adsorption as discussed above) within the range of polarization potentials from -0.2 to - 1.2 V. Beyond this potential range (adsorption maximum) one can observe, on the C vs E relationship, the characteristic pseudo-capacitance peaks associated with adsorption-desorption transitions. In this respect the behavior of THHD is similar to other non-ionic surfactants studied previously [7,34,35]. Based on these experiments we have chosen the -0.7 V polarization potential as the best for further adsorption kinetics studies shown in subsequent figures. In Fig. 4 the kinetics of adsorption of THHD at the SME (diameter 0.11 cm) are presented in .the form of the dependence of the reduction in capacitance dC on the adsorption time t. The dimensionless surface concentration d calculated from the capacitance changes according to Eqn (22) is also
!
E [VI E measured
potential
vs the
shown in this figure. The maximum surface concentration N, needed as an empirical parameter for calculating 0 was assumed to be 2.5 * 1Ol4 cm - ’ pre(4.150 10-*“mol cm-’ ) [36]. As mentioned
200
1 IO
a
I 20
30
40
t IminI Fig. 4. The kinetics ofTHHD adsorption on the SME measured for various bulk surfactant concentrations c; (I) 2 - 10S6 M; (2) 5 - IOmh M; (3) 1 - 10m5 M; (4) I - 10m4 M. The solid lines denote the exact numerical solutions obtained by adopting the Langmuir model (k, = 0.006 cm s-l, k, = 0.04 s- ‘_ K, = 0.15 cm). The broken Iincs rcprcscnt the results derived from the nonlocalized adsorption model N, = !.75 - lOI cm-* (2.9 - 10v9 mol cm-‘), D = 5 * 10e6 cm2 s- ‘.
256
viously, the experimental results were interpreted in terms of the exact numerical solutions of the governing diffusion equation (Eqn (3)) (solid lirics in Fig. 4). It can be observed in Fig. 4 that the agreement between experimental and theoretical results is satisfactory for the Langrnuir model, especially for longer adsorption times. The small deviation between theory and experiment observed for shorter adsorption times is probably caused by the convective currents induced at the mercury surface due to the stepwise change of the polarization potential at t = 0. However the two-dimensional hard-fluid model (non-localized adsorption) depicted by the broken lines in Fig. 4 is not adequate for describing the measured adsorption kinetics. The best fit of our experimental results was achieved for I\X= 0.006 cm s- ’ and kd = 0.04 s which gives a value of 0.15 cm for the equiiibrium adsorption constant K,. However, as shown in Fig. 5 the influence of k, and k, on the theoretical kinetic curves is minor (provided that their ratio remains constant), especially for k, > 0.003 cm s- I_ The influence of k,, i.e. the adsorption barrier, can be significant for very short adsorption times and
small bulk surfactant concentrations. For this range of experimental parameters, however, our method is much less accurate which makes it difficult to unequivocally determine the presence of any adsorption barrier. Results shown in Figs 4 and 5 suggest, however, that for practical purposes the adsorption kinetics of THHD can be treated as barricrless, i.e. diffusion controlled. The kinetic curves shown in Figs 4 and 5 enabled IIS to determine that the equilibrium capacity adecreases as a function of the bulk surfactant concentration cb. By converting these data to the 0 values, the adsorption isotherm was determined experimentally (at 22°C) as shown in Fig. 6. As can be seen, the best 5it of the experimental results can be attained assuming the Langmuir model, i.e. (23) with K, = 0.15 cm and OmxL= 0.69. It should be noted that the theoretical isotherm derived from the two-dimensional liquid model, i.e. the non-locaiized Helfand-Frisch-Lebowitz (HFL) adsorption isotherm approa.ch [28] (marked
0.5
20
\ \ 0
10
(3
L 20
30
0
t [min] Fig. 5. Adsorption kinetics on the SME (r = 0.1 I cm) measured in a solution of 5 1 IO-” M THHD. Comparison with thcorctical predictions calculated numerically for various k, and k,, values (K, = 0.15 cm) and the Langmuir model; (I) k,, = 0.0003 ems-*, k,= 0.002 s - ‘: (2) k, = 0.0006 cm s- I, k, = 0.004 s- ‘: (3) k, = 0.006 cm s- I, k,=O.O4s-*; (4) K,=O.O3cms-*, kd = 0.2 s- ‘. (Other parameters arc the same as for Fig. 4.) The broken line dcnotcs the limiting analytical xsults calculated from Eqn (12).
Fig. 6. The adsorption isotherm c;f THHD on mercury mcasurcd al 22°C. The solid lines present the theoretical results calculated rrom the localized adsorption Langmuir model, i.c. 11= I~mrL~K.q,/(NmfJmxL + Kacb)] with K, ~0.15 cm. The broken lines show the theoretical results calculated from the non-localized adsorption model (two-dimensional hard-sphere fluid), i.c. ff,/J(O,) = K,c,,/N, (with J(Q) given by Eqn (8)). for K B = I cm (upper curve), and K, = 0.15 cm (lower curve).
Z. Adanqvk.
G. Pam/Colloids
257
SrcrJaces 66 (1992) 249-258
by the broken lines in Fig. 6) describes the experimental results poorly, a rather surprising result. The agreement of our results with the localized adsorption model (Langmuir isotherm) may suggest that THHD adsorption at the mercury-water interface proceeds for large surface concentrations in a patchwise manner. One should also note the scatter of experimental results at small bulk surfactant concentration (cb < 10 - ’ M) caused mainly by adsorption of contaminants from the base electrolyte solution. This may produce a much larger capacity decrease for from surfactant longer times than predicted adsorption alone. The limited accuracy of the electrochemical methods for dilute surfactant solutions may lead to misinterpretation of equilibrium adsorption data by introducing the somewhat ad hoc Frumkin or Tiemkin isotherms [35] whereas in fact the Langmuir model is fully adequate. From the estimated K, value one can easily calculate the free energy of adsorption of THHD at the mercury surface dr#~using the known equation [ 15,371 K,=
s exp(-$)dx
(24) where
Assuming a parabolic energy distribution at the energy minimum, one can solve the above equation iteratively with the result Ac$=-
kTln(-j$-)
++kTln[I.(%)]
(25) where 6 is the thickness of the energy minimum. Assuming S= 20 10-8cm (2 A) and K,=
0.15 cm, one obtains from the above equation the value of d4 = -16.6 kT, i.e. AG = -40 kJ mol-‘. This is well above the standard free energy of adsorption of THHD at the free interface which is estimated by the surface tension measurements to be - 31.7 kJ mol- ’ [36]. It should be mentioned that in our case (Langmuir model) the d# value is independent of the surface concentration of adsorbed molecules. The experimental results discussed above should be treated as tentative ones performed in order to illustrate the adequacy of our numerical calculation method. Further experiments are planned using an improved electrochemical ceil enabling measurement of adsorption kinetics at short times.
Concluding remarks Our experimental procedure based on a.c. polarography at the SME proved useful for studying the kinetics and thermodynamics of non-ionic surfactant adsorption at liquid-liquid interfaces. It was shown that the experimental results can be quantitatively described by the theoretical calculations performed by using the new numerical algorithm. The numerical method enables one to solve the governing diffusion equation for arbitrary nonlinear adsorption isotherms both for barriercontrolled and diffusion-controlled adsorption regimes. It was also found that the adsorption kinetics of THHD proceeds according to the diffusioncontrolled mechanism and the localized adsorption Langmuir model. The equilibrium adsorption constant value was found to be 0.15 cm which gives a free energy of adsorption dG of -40 kJ mol- ‘. The good agreement of our experimental results with the Langmuir model suggests that the adsorbed molecules become immobile, probably forming an associated patchwise structure. Further precise experiments are necessary to determine adsorption kinetics for short times to confirm this hypothesis.
Acknowledgments The authors are indebted to Professor B. Burczyk from the Technical University of WrocIaw for providing them with t%e clean THHD samples. References 1
R. D&y and J.R. l-icjmmclcin, J Colloid Sci., 13 (19%) 553. J. Colloid Sci., 14 (1959) 2 R. D&y and J.R. Honlmclcin. 401. 3 R. Dcfay and G. Petrc. in E. MatijcviL: (Ed.), Surbcc and Colloid Science. Vol. 3, Wiley, New York. 1971, p. 59. 4 P. Joos, G. Blcys and G. Pctrc, J. Chim. Phys.. 79 (1982) 387. and P.C. Symans, Trans. Faraday Sot., 64 5 R. Parsons (1968) 1077. 6 E. Miiller and E. DSrllcr, Z. Chcm., 21 (1981) 28. 7 B. Burczyk, A. Piasccki, G. Para and A. Pomianowski. J. Colloid lntcrracc Sci., SO (I9Sl) 123. Kaisheva, V. Kaishcv and M. Matsumoto. 8 M.K. .I. Elcctronnai. Chcm., I71 (19S4) 1I I. Y. Ki!:t and T. Takcnaka. 9 M.K. Kaishcva, M. Matsumoto, Langmuir, 4 (1988) 762. and R. Miller, Adv. Colloid lntcrlace Sci.. 10 G. Krctzschmar 36 (1991) 65. I1 A. Piasccki and B. Burczyk, PO]. J. Chem., 54 (1980) 367. 12 B.E. Conway, H. Angcrstcin-Kozlowska. W.B. Sharp and E.E. Criddlc. Anal. Chcm.. 45 (1973) 1331. I3 DC. Grahnmc, J. Am. Chcm. Sot.. 63 (1941) 1207. I4 D.C. Grahamc. J. Am. Chcm. Sot., 68 (1946) 301. Sci., I I8 IS 2. Adamczyk and J. Petficki, J. Colloid Inlcrfxc (1987) 20.
16 Z. Adamczyk, J. Colloid IntcrCacc Sci., I20 (1987) 477. Sci., I33 (1989) 23. I7 Z. Adamczyk, J. Colloid Intcrfxe I8 K. Sutherland. AUSI. J. Sci. Rcs. Ser. A, 5 (1952) 683. I9 R.S. Hunscn, J. Phys. Chcm.. 64 (1960) 637. P. Schaal and J. filbot. J. Chcm. Phys., 91 (1989) 4401, ‘0 Mol. Phys.. 30 (I 975) 97 I, 21: D. Hcndcrson. Sci., 30 (1969) I. 22 J.F. Barct. J. Coiloid Intcrrxc in J.O’M. Bockris and 23 A.N. Frrlmkin and B.B. Damaskin, B.E. Conway (Eds), Modern Aspects of Elcctrochcmistry, Vol. 3, Buttcrworths, London, 1964, Chapter 3. P. Wandzilak and A. Pomianowski. Bull. ?4 2. Adamczyk, Acad. Pol. Sci., Ser. Chem., 35 (1987) 479. Z. Phys. Chcm.. 92 (i917) 139. 2.5 M. von Smoluchowski, Bull. Acad. Pol. Sci.. Ser. Chcm.. 35 (1987) 26 Z. Adamczyk. 417.
17 2x 29
30 3! 31 33 34 35
36 37
R. Parsons, Trans. Faraday. SIX.. 55 (1959) 999. R. Parsons. J. Elcctronnal. Chem., 7 (1964) 136. R. Payne, in J.F. Daniclli, M.D. Rosenberg and D.A. Cadcnhcnd. (Eds). Progress in Surracc and Mcmbranc Science, Vol. 6. Academic Press, New York. 1973. p. 51. B.B. Damaskin, Elcctrochim. Acta, 9 (1964) 231. A.N. Frumkin, Z. Phys.. 35 (1926) 792. H.A. Laitincn and B. Mosicr. J. Am. Chcm. Sot., SO (1958) 2363. M.W. Brcitcr and P. Dclahay, J. Am. Chcm. Sot., 81 (1959) 9938. H. Jehring. Elcctrosorptionsanalysc mit dcr Wcchsclstrom Polarographic, Akadcmic-Vcrlag. Berlin, 1974. B.B. Damaskin, D.A. Pctrij and V.V. Batrakov, Adsorpcija Organiczcskich Socdincnij no Elcctrodach, Izd. Nauka Moscow, 1968 (in Russian). B. Burczyk. A. Piasccki and L. Wcclas, J. Phys. Chem.. 89 (1985) 1037. D.T. Grow and J.A. Schaciwitz. J. Colloid Intcrfacc Sci., 86 (1982) 739.
249
Adsorption kinetics of a non-ionic surfactant on the stationary mercury electrode Z. Adamczyk and G. Para Institute of Catalysis and Surface Chemistry. Polish Academy ofSciertces, 30-239 Krakh, PolarId
(Received 12 November
ul. Niezapowitrajek I,
1991; accepted 24 April 1992)
Abstract Adsorption kinetics of the non-ionic rm~rs-2-hcptyl-5-hydroxy-l,3-dioxanc surhctant on the stationary mercury ckctrodc was invcstigatcd by a.c. polarography (tcnsammctry) with 0.4 M KC1 solutions used as supporting electrolyte, The experimental results obtained for various bulk surfactant concentrations were interpreted in terms of the exact numerical solutions of the governing mass-translcr equation. A good agreement bctwecn the experimental kinetic mcasurcmcnts and the thcorctical predictions was found, especially for longer adsorption times. The equilibrium adsorption isotherm ofTHHD was also determined. It was proved that the experimental isotherm can be adequately described by the localized adsorption Langmuir model with K, = 0.15 cm (this value corresponds to AC = -40 kJ rnol-I). The non-localizc\f adsorption model proved to bc inadcquatc. K~pords:
Adsorption
kinetics;
mercury
electrode;
non-ionrc
surfactant.
Introduction Non-equilibrium processes occurring at liquidliquid or liquid-gas interfaces in contact with surfactant solutions are of great practical significance, e.g. in important large-scale technological operations such as emulsification, emulsion coalescence and breakup, oil recovery, froth flotation, extraction, detergency, etc. Interface dynamics also plays an important role in many physiological phenomena, e.g. breathing. The kinetics of these processes depends considerably on the relative surclce tension of the coexisting interfaces which is II turn determined by the surfaciant adsorption rr.te. In contrast to the extensive experimental knowledge of static adsorption (adsorption isotherms), kinetic aspects of adsorption have been relatively Corrcsporzderw 10: Z. Adamczyk. 1nsti:utc and Surface Chemistry, Polish Academy of Niczapominajck 1, 30-239 Krakbw, Poland. 0166-6622/92/505.00
0
1992 -
Elsevicr
of Catalysis Scicnccs. ul.
Scicncc
Publishers
little studied in a precise, quantitative manner. This is because adsorption of surfactants can only be determined by means of indirect experimental methods of limited accuracy. One can mention the surface tension measuring techniques used in classical long-lasting adsorption measurements Cl,2], the oscillating-jet method suitable for very short transitions [3,4], and the electrochemical methods using the dropping L-5-7) or stationary [8,9] mercury electrodes. A comprehensive recent review of experimental and theoretical techniques aimed at adsorption studies can be found in Ref. [lo]. It seems that the electrochemical methods are the most reliable and accurate for moderate and longer times, enabling one to determine not only the overall equilibrium adsorption rate constant K, but also adsorption kinetics for various bulk surfactant concentrations. Therefore, the main goal of this paper should be a quantitative description of surfactant adsorption kinetics at the stationary mercury electrode (SME) using the precise tensamB.V. All rights
rcscrvcd.
metric method. As the model substance we shall use the high purity heptyl derivative of 1,3-dioxycyclane which can, potentiaily, be used in froth flotation of non-ferrous ores or as a hydrophobic intermediate for the synthesis of ionic and nonionic detergents. Experimental Mnterials
In our adsorption kinetics measurements we used the high purity isomer rrcrrzs-2-heptyl-5hydroxy- I ,3-dioxane (THHD) kindly supplied by the Institute of Organic and Polymer Technology, Technical University of Wroclaw (Poland). The isomer was isolated from the reaction mixture by repeated fractional distillation [? 11. The purity of the sample was better than 99.9% as checked by gas-liquid chromatography (GLC). Chemically purified mercury was cleaned using concentrated sulfuric acid, dried and distilled twice under vacuum. After the distillations, the mercury stock sample was stored in sealed ampules under argon atmosphere. The potassium chloride used as supporting eIectrolyte was recrystallized six times and then calcined for 8 h at 500°C. Special care was taken in order to produce distilled water of high purity needed for our precise measurements. The water was obtained in a multistage distillation procedure involving at least 6 steps with pyrodistillation over a platinum catalyst as a crucial stage [12-J. Procedtrre
The electrical cell used for the diff?rentlal capacitance measllrements on the SME was of a standard three-electrode type [13,14]. It consisted of the stationary (hanging) mercury electrode produced on the tip of a capillary (inner diameter 0.014 cm) above a mercury pool used as the counter electrode. The size of the mercury drop could be easily regulated by using a precise needle valve. The 0.4 M calomel electrode was used as the reference
electrode. It was connected to the ccl1 via a salt bridge filled with 0.4 A4 KCI. The equivalent electric circuit of the cell is shown schematically in Fig. 1. The measurements of the adsorption process occurring at the SME were carried out acccrding to the alternating current polarography principle (tensammetry). A small alternating current (a.~.) signal (amplitude about 10 mV and Zequency 40 Hz) was superimposed upon the steady polarization potential fed from !he potentiostat. Using the amplifier-phase detector system, the capacitance component of the a.c. flowing through the cell was selectively measured. The amplitude cf this current was proportional to the differential capacity of the eicctric double-layers on the SME and the counter electrode connected in series. Since the latter capacity exceeds cocsiderably the SME capacity, the registered signal was proportional to the SME capacity alone, provided that the ohmic resistance of the cell remained low (which was the case due to the high concentration of the supporting electrolyte). The measurements were carried out according to the three-stage procedure: first the electrode was polarized to such a potential value (usually - 1.7 V) that no surfactant adsorption or chemical reaction took place; then a mercury drop of a given size was produced on the tip of the capillary; finally the polarizing voltage was switched to a new value at which adsorption occurred (about -0.7 V). The resulting signal from the phase detector was registered and processed by a computer. Because the overall response time of the electric circuit is of the order of 1 s, the kinetic curves showing the dependence of the differential capacity of the SME on time can be easily recorded by using our method. Theoretical Governing
equations
The experimental the above-described
results obtained according to procedure were quantitatively
PRINTER I
VOLTMETER
Fig.
I. The
dilfcrcntial
electrical schcmc of the cxpcrimcntal capacity measurcmcnts on the SME.
cell used for
interpreted in terms of the theoretical approach discussed in detail previously [15,16]. The governing equations describing adsorption kinetics onto a spherically shaped interface (see Fig. 2) from a stagnant one-component solution has the form [15,17]
dN dt
+
-- 1
d4QNcJ
A(r)
dt
where c is the concentration of the surfactant, r is the time of adsorption, D is the surfactant diffusion coefficient (assumed to be concentration independent), r is the radial coordinate (cf. Fig. 2), N is the surface concentration of adsorbed surfactant, A is the surface area of the interface (which can be time dependent) and J is the normal component of the flux vector. When formulating Eqns (I), convective effects were neglected. The general constitutive expression for the adsorption flux J is [I71 J = k,c’f(N)
- k,g(N)
N
(2)
where k, is the adsorption rate constant, kd is the desorption rate constant, co is the subsurface concentration of the surfactant and f(N) g(N) are the
(1) to the by introducing the characteristic scaling variables, i.e. maximum surface and the this way (I) and tant concentration cb. can be written in the form:
where the dimensionless
0 = N/N, m
?= r/L
L = N,.,,/c,,
T = t/t,, tch = L2/D
are defined as
353
S, is the surface area occupied by one molecule. The general boundary conditions for Eqns(3) are [IS-l71
F’]
at r = rmix/L
(5b)
Equation (5a) i’:an adequately describe both the diffusion-controiicd and barrier-controlled adsorption regimes whereas Eqn (5b) postulates that, owing to natural convection, the surfactant concentration becomes unifcrm at some prescribed disgeometry the tance )‘mix. In practice, for sphe:ical exact value of rmiX is not important and can bc assumed to be infinitely large without affecting the calcuIations. As the initial condition we assume a uniform concentration distribution for r = 0, i.e. for r,/L < rmi,/L
C;= I o=o
‘1 r=O
(6)
I
In order to make the above set of equations complete one should specify also the constitutive dependence of the adsorption flux J on the surface concentration 0, and the subsurface concentration Co, i.e. the concrete expressions for j’(O) and g(0) should be given. For the simplest case of the linear adsorption model (Henry isotherm) f(O) = g(Bj = 1 and the entire transport problem formulated above becomes linear. In this case analytica solutions can be found, e.g. by applying the Laplace transformation [15,18,19]. For the widely used Langmuir modci the blocking function f(G) is expressed as
f(U) = 1 - c’ 0 mxL g(W
=
(7)
1
where OmxL.is the empirical parameter characterizing the dimensionless maximum surface concen-
tration of the adsorbed substance attainable when its bulk concentration tends to infinity. It should be mentioned that the Langmuil model is strictly valid only for localized adsorption on discretely distributed “active centers”. When no a tive centers can be distinguished and the adsorbed phase remains mobile (analogous to the two-dimensional hard-sphere fluid) then the blocking function can be described by the expressio;l [20,21]
J(O)=exp
2(I
+ iln(l
’ 7 ” (1 - 0)’ + s (1 - 0)2 -0)
1
w
Other useful expressions for J(0) and a(U) in the case where la’.eral interactions occur (Frumkin model) can be found in Refs [22,23]. As can be easily seen, Eqns (3) become nonlinear when one of the above expressions for f(0) is used to eliminate J and can only be solved by means of numerical methods as discussed before [ 15,24]. However, useful analytical solutions can be derived in the limit of the diffusion-controlled adsorption regime and short times when the linear model still holds. By assuming this, one can integrate Eqns (3) for the constant-area interface (which is the case for the SME) to give
2. Adunrczyk.
G. ParajColloids
When 4Ar>
Swfaces
1 the solution
66 (1992) 249-258
253
is
to the general procedure described previously [ 171, one can derive the following asymptotic expression valid when (&r/(k, + Ar) >> 1
1 +cos(qr)II
O=R,
l-n
l-
6 cos (qr) + sin (47)
i
12(7)
L
isin(rj7)
-0 - ac = K17-3” Oi - 0’
II(?)
(14)
[
1
b=&/m
a=2f7, II(t)
=
a
with
q=2nb K, =
04;
cos (26&r)
exp(--‘)dt
I,(7)=exp(-b27)erf(b&) a.,; ---i dz
1
OmxL
!K, f &,I_)’ 2,,&4r2
exp(-b27)
2
Ra
sin(2b&t)
exp(-?)dt
s 0
In the case of strong adsorption where K, >> 1 (perfect sink model), Eqns (9) and (10) simplify to the common limiting expression
O=-$/2+Arr
(11)
J-
Jr
Thus, the limiting adsorption
flux is given by
(12) Equations (11) and (12) are identical with those derived by Smoluchowski [25] to describe the fast coagulation of colloid particles. Note that the first term of Eqn (12) characterizes the transient adsorption fux which vanishes for longer times. It is also interesting to derive the limiting expressions for long adsorption times in the case of the Langmuir isotherm when the system is close to the equilibrium &aracterized by the surface concentration
Thus, for ihe spherical geometry the equilibrium surface concentrations are approached proportionally to 7- 3/2, i.e. much faster than for the planar interface when 0x7-“’ [ 19,263. Equations (1 !)-( 14) were also used for testing the accuracy of the numerical solution of Eqns (3) obtained in the general case by applying the implicit Crank-Nicolson method, generalized to accommodate for the non-linear boundary conditions Eqn (5a). The method enabling an exact solution of the diffusion equation for arbitrary isotherms has been described in detail elsewhere [24]. Since in experiments the differential capacity of the eIectrode is measured rather than the surface concentration 0, one shou!d specify a functional dependence connecting 8 with C, the differential capacitances. This can be done in a standard way by exploiting the well-known thermodynamic relationship [27-291 (15) where 4 is the surface charge density on the electrode for a given electrode potential E, I( = kT In C is the chemical potentia1 of the substance in the solution (we assumed ideal beha\,;or of the surfactant solutions because of their high dilution)_ Integration of this dependence with respect to chemical potential gives, 0
(13)
a0
z
q-q*=kTN,
Performing
the linearization
of Eqns (3) according
S( 0
dln C )P
(16)
254
where go is the surface charge density of zero adsorption. Assuming that the adsorption isotherm can be written in the potential-congruent form [27], i.e.
iI= R,c. In this case Eqn (21) simplifies to,
c=co
(I-$ >d”‘$ mn
or
f(O) =
KaCb -
-c N
=
i?,(E)c;
mx
(22)
(17)
m
(where the dimensionless adsorption depends on the electrode potential rearrange Eqn (16) to the form.
constant I?, E) one can
(18) Considering the definition of the difTcrentia1 capacitance C = c7q/dE, or,e can obtain from Eqn (18), by differentiation with respect to E, the expression
(19) where Co is the differential capacitance for an uncovered surface. For 0 -+ O,,: considering that (dO/dln R,) + 0, Eqn (19) becomes
c
mx
-
co = kTN,
d’ln Kali dE2 mx
(20)
where C,, is the capacitance for the maximum surface concentration O,,,. Therefore, for an intermediate 0
+ kTN,
(21)
As pointed out by Parsons [27,28] this equation gives a linear dependence of C on 8 (for arbitrary E) in the case of the Henry isotherm only, i.e. when
This relationship, derived originally by Frumkin, was widely exploited for describing adsorption of non-ionic surfactants [23,30-331. Equation (22) suggests that in the case of a linear isotherm the overall electrode capacity can be treated as composed of t,vo capacitors connected in series. Xowever, for an arbitrary adsorption isotherm and wide range of E, the dependence of C on 0 is generally non-linear C27] due to the presence of the term SO/din /?, in Eqn (2ij. Neverthe!ess, for potentials close to the adsorption maximum (if one exists) the t:rm (Zln l?,/i?~E’) obviously bccomcs very small and Eqn (22) can be used with care as discussed previousIy in Ref. 1231. Since in our measurements we have limited ourselves to potentials close to -0.7 V, i.e. corresponding to the adsorption maximum (cf. Fig. 3), the use of Eqn (22) for converting the measured C values to surface concentration seems justified. It should be noted, however, that the value of O,, occurring in Eqn (22) cannot be determined directly and remains an adjustable parameter. Iliesu’lts and discussion At first, a series of tensammetric runs was performed for various bulk surfactant concentrations in order to determine the effective range of the polarization potential at which adsorption of THHD occurs. These results, showing the dependence of the specific capacity of the mercury electrode on the polarization potential E (measured relative to the 0.1 normal caiomel electrode) are presented in Fig. 3. Because in this series of experiments we were interested in determining the efficient adsorption potential only, we used the
Z. Adan~yk.
G. Para~Collnids
Surfaces
66 (1992)
749-258
255
30
20
70
I
I
-0.5
Fig. 3. The dilTcrential
capacity
I
-1.5
-1.0
C of the dropping mercury clcctrode as a func:ion of the polarization 0.1 M calomcl electrode in solutions of various THHD concentrations.
dropping mercury electrode (lifetime 6 s) which is more convenient for this type of experiment. As can be seen in Fig. 3 the presence of THHD produces a depression of the specific capacity of the mercury electrode (which is a direct measure of adsorption as discussed above) within the range of polarization potentials from -0.2 to - 1.2 V. Beyond this potential range (adsorption maximum) one can observe, on the C vs E relationship, the characteristic pseudo-capacitance peaks associated with adsorption-desorption transitions. In this respect the behavior of THHD is similar to other non-ionic surfactants studied previously [7,34,35]. Based on these experiments we have chosen the -0.7 V polarization potential as the best for further adsorption kinetics studies shown in subsequent figures. In Fig. 4 the kinetics of adsorption of THHD at the SME (diameter 0.11 cm) are presented in .the form of the dependence of the reduction in capacitance dC on the adsorption time t. The dimensionless surface concentration d calculated from the capacitance changes according to Eqn (22) is also
!
E [VI E measured
potential
vs the
shown in this figure. The maximum surface concentration N, needed as an empirical parameter for calculating 0 was assumed to be 2.5 * 1Ol4 cm - ’ pre(4.150 10-*“mol cm-’ ) [36]. As mentioned
200
1 IO
a
I 20
30
40
t IminI Fig. 4. The kinetics ofTHHD adsorption on the SME measured for various bulk surfactant concentrations c; (I) 2 - 10S6 M; (2) 5 - IOmh M; (3) 1 - 10m5 M; (4) I - 10m4 M. The solid lines denote the exact numerical solutions obtained by adopting the Langmuir model (k, = 0.006 cm s-l, k, = 0.04 s- ‘_ K, = 0.15 cm). The broken Iincs rcprcscnt the results derived from the nonlocalized adsorption model N, = !.75 - lOI cm-* (2.9 - 10v9 mol cm-‘), D = 5 * 10e6 cm2 s- ‘.
256
viously, the experimental results were interpreted in terms of the exact numerical solutions of the governing diffusion equation (Eqn (3)) (solid lirics in Fig. 4). It can be observed in Fig. 4 that the agreement between experimental and theoretical results is satisfactory for the Langrnuir model, especially for longer adsorption times. The small deviation between theory and experiment observed for shorter adsorption times is probably caused by the convective currents induced at the mercury surface due to the stepwise change of the polarization potential at t = 0. However the two-dimensional hard-fluid model (non-localized adsorption) depicted by the broken lines in Fig. 4 is not adequate for describing the measured adsorption kinetics. The best fit of our experimental results was achieved for I\X= 0.006 cm s- ’ and kd = 0.04 s which gives a value of 0.15 cm for the equiiibrium adsorption constant K,. However, as shown in Fig. 5 the influence of k, and k, on the theoretical kinetic curves is minor (provided that their ratio remains constant), especially for k, > 0.003 cm s- I_ The influence of k,, i.e. the adsorption barrier, can be significant for very short adsorption times and
small bulk surfactant concentrations. For this range of experimental parameters, however, our method is much less accurate which makes it difficult to unequivocally determine the presence of any adsorption barrier. Results shown in Figs 4 and 5 suggest, however, that for practical purposes the adsorption kinetics of THHD can be treated as barricrless, i.e. diffusion controlled. The kinetic curves shown in Figs 4 and 5 enabled IIS to determine that the equilibrium capacity adecreases as a function of the bulk surfactant concentration cb. By converting these data to the 0 values, the adsorption isotherm was determined experimentally (at 22°C) as shown in Fig. 6. As can be seen, the best 5it of the experimental results can be attained assuming the Langmuir model, i.e. (23) with K, = 0.15 cm and OmxL= 0.69. It should be noted that the theoretical isotherm derived from the two-dimensional liquid model, i.e. the non-locaiized Helfand-Frisch-Lebowitz (HFL) adsorption isotherm approa.ch [28] (marked
0.5
20
\ \ 0
10
(3
L 20
30
0
t [min] Fig. 5. Adsorption kinetics on the SME (r = 0.1 I cm) measured in a solution of 5 1 IO-” M THHD. Comparison with thcorctical predictions calculated numerically for various k, and k,, values (K, = 0.15 cm) and the Langmuir model; (I) k,, = 0.0003 ems-*, k,= 0.002 s - ‘: (2) k, = 0.0006 cm s- I, k, = 0.004 s- ‘: (3) k, = 0.006 cm s- I, k,=O.O4s-*; (4) K,=O.O3cms-*, kd = 0.2 s- ‘. (Other parameters arc the same as for Fig. 4.) The broken line dcnotcs the limiting analytical xsults calculated from Eqn (12).
Fig. 6. The adsorption isotherm c;f THHD on mercury mcasurcd al 22°C. The solid lines present the theoretical results calculated rrom the localized adsorption Langmuir model, i.c. 11= I~mrL~K.q,/(NmfJmxL + Kacb)] with K, ~0.15 cm. The broken lines show the theoretical results calculated from the non-localized adsorption model (two-dimensional hard-sphere fluid), i.c. ff,/J(O,) = K,c,,/N, (with J(Q) given by Eqn (8)). for K B = I cm (upper curve), and K, = 0.15 cm (lower curve).
Z. Adanqvk.
G. Pam/Colloids
257
SrcrJaces 66 (1992) 249-258
by the broken lines in Fig. 6) describes the experimental results poorly, a rather surprising result. The agreement of our results with the localized adsorption model (Langmuir isotherm) may suggest that THHD adsorption at the mercury-water interface proceeds for large surface concentrations in a patchwise manner. One should also note the scatter of experimental results at small bulk surfactant concentration (cb < 10 - ’ M) caused mainly by adsorption of contaminants from the base electrolyte solution. This may produce a much larger capacity decrease for from surfactant longer times than predicted adsorption alone. The limited accuracy of the electrochemical methods for dilute surfactant solutions may lead to misinterpretation of equilibrium adsorption data by introducing the somewhat ad hoc Frumkin or Tiemkin isotherms [35] whereas in fact the Langmuir model is fully adequate. From the estimated K, value one can easily calculate the free energy of adsorption of THHD at the mercury surface dr#~using the known equation [ 15,371 K,=
s exp(-$)dx
(24) where
Assuming a parabolic energy distribution at the energy minimum, one can solve the above equation iteratively with the result Ac$=-
kTln(-j$-)
++kTln[I.(%)]
(25) where 6 is the thickness of the energy minimum. Assuming S= 20 10-8cm (2 A) and K,=
0.15 cm, one obtains from the above equation the value of d4 = -16.6 kT, i.e. AG = -40 kJ mol-‘. This is well above the standard free energy of adsorption of THHD at the free interface which is estimated by the surface tension measurements to be - 31.7 kJ mol- ’ [36]. It should be mentioned that in our case (Langmuir model) the d# value is independent of the surface concentration of adsorbed molecules. The experimental results discussed above should be treated as tentative ones performed in order to illustrate the adequacy of our numerical calculation method. Further experiments are planned using an improved electrochemical ceil enabling measurement of adsorption kinetics at short times.
Concluding remarks Our experimental procedure based on a.c. polarography at the SME proved useful for studying the kinetics and thermodynamics of non-ionic surfactant adsorption at liquid-liquid interfaces. It was shown that the experimental results can be quantitatively described by the theoretical calculations performed by using the new numerical algorithm. The numerical method enables one to solve the governing diffusion equation for arbitrary nonlinear adsorption isotherms both for barriercontrolled and diffusion-controlled adsorption regimes. It was also found that the adsorption kinetics of THHD proceeds according to the diffusioncontrolled mechanism and the localized adsorption Langmuir model. The equilibrium adsorption constant value was found to be 0.15 cm which gives a free energy of adsorption dG of -40 kJ mol- ‘. The good agreement of our experimental results with the Langmuir model suggests that the adsorbed molecules become immobile, probably forming an associated patchwise structure. Further precise experiments are necessary to determine adsorption kinetics for short times to confirm this hypothesis.
Acknowledgments The authors are indebted to Professor B. Burczyk from the Technical University of WrocIaw for providing them with t%e clean THHD samples. References 1
R. D&y and J.R. l-icjmmclcin, J Colloid Sci., 13 (19%) 553. J. Colloid Sci., 14 (1959) 2 R. D&y and J.R. Honlmclcin. 401. 3 R. Dcfay and G. Petrc. in E. MatijcviL: (Ed.), Surbcc and Colloid Science. Vol. 3, Wiley, New York. 1971, p. 59. 4 P. Joos, G. Blcys and G. Pctrc, J. Chim. Phys.. 79 (1982) 387. and P.C. Symans, Trans. Faraday Sot., 64 5 R. Parsons (1968) 1077. 6 E. Miiller and E. DSrllcr, Z. Chcm., 21 (1981) 28. 7 B. Burczyk, A. Piasccki, G. Para and A. Pomianowski. J. Colloid lntcrracc Sci., SO (I9Sl) 123. Kaisheva, V. Kaishcv and M. Matsumoto. 8 M.K. .I. Elcctronnai. Chcm., I71 (19S4) 1I I. Y. Ki!:t and T. Takcnaka. 9 M.K. Kaishcva, M. Matsumoto, Langmuir, 4 (1988) 762. and R. Miller, Adv. Colloid lntcrlace Sci.. 10 G. Krctzschmar 36 (1991) 65. I1 A. Piasccki and B. Burczyk, PO]. J. Chem., 54 (1980) 367. 12 B.E. Conway, H. Angcrstcin-Kozlowska. W.B. Sharp and E.E. Criddlc. Anal. Chcm.. 45 (1973) 1331. I3 DC. Grahnmc, J. Am. Chcm. Sot.. 63 (1941) 1207. I4 D.C. Grahamc. J. Am. Chcm. Sot., 68 (1946) 301. Sci., I I8 IS 2. Adamczyk and J. Petficki, J. Colloid Inlcrfxc (1987) 20.
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17 2x 29
30 3! 31 33 34 35
36 37
R. Parsons, Trans. Faraday. SIX.. 55 (1959) 999. R. Parsons. J. Elcctronnal. Chem., 7 (1964) 136. R. Payne, in J.F. Daniclli, M.D. Rosenberg and D.A. Cadcnhcnd. (Eds). Progress in Surracc and Mcmbranc Science, Vol. 6. Academic Press, New York. 1973. p. 51. B.B. Damaskin, Elcctrochim. Acta, 9 (1964) 231. A.N. Frumkin, Z. Phys.. 35 (1926) 792. H.A. Laitincn and B. Mosicr. J. Am. Chcm. Sot., SO (1958) 2363. M.W. Brcitcr and P. Dclahay, J. Am. Chcm. Sot., 81 (1959) 9938. H. Jehring. Elcctrosorptionsanalysc mit dcr Wcchsclstrom Polarographic, Akadcmic-Vcrlag. Berlin, 1974. B.B. Damaskin, D.A. Pctrij and V.V. Batrakov, Adsorpcija Organiczcskich Socdincnij no Elcctrodach, Izd. Nauka Moscow, 1968 (in Russian). B. Burczyk. A. Piasccki and L. Wcclas, J. Phys. Chem.. 89 (1985) 1037. D.T. Grow and J.A. Schaciwitz. J. Colloid Intcrfacc Sci., 86 (1982) 739.