On the Adsorption Kinetics of Octanoic Acid at the
Mercury/Electrolyte Interface
U. Retter,*
,†
A. Avranas,
‡
H. Lohse,
†
K. Siegler,
†
and K. Lunkenheimer
§
Bundesanstalt fu ¨ r Materialforschung, Rudower Chaussee 5, D-12489 Berlin, Germany,
Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece, and Max-Planck-Institut fu ¨ r
Kolloid- und Grenzfla ¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin, Germany
Received September 8, 1998. In Final Form: December 21, 1998
The adsorption kinetics of octanoic acid at the mercury/electrolyte interface was investigated by means
of capacity-time transients. For low concentrations of octanoic acid and for the short-term region, the
transients can be theoretically well described with a diffusion-controlled adsorption process according to
the Delahay-Trachtenberg law. The long-term transients for higher concentrations of octanoic acid exhibit
an increase of the capacity with time, which can be modeled with an adsorption-controlled replacement
of a condensed adsorption state by a hemimicelle adsorption state. Criteria are derived for which an
increase of the double-layer capacity with time can be expected.
Introduction
In recent times, the formation of surface hemimicelles
from adsorption layers at the interfaces metal/electrolyte
1-5
and air/water
6-9
has been intensively discussed. This
problem is of fundamental interest, because mostly two-
dimensional phase transitions in adsorption layers were
found but not transitions from monolayers to three-
dimensional microstructures.
Furthermore, the question arises whether the estab-
lishment of the adsorption equilibrium is always combined
with a decrease of the double-layer capacity at the metal/
electrolyte interface or whether, for certain conditions,
an increase can be expected. Interestingly, in this context,
Jehring
10
already found in 1971 that the double layer
increases with time when butanol molecules will be
displaced by poly(ethylene glycol) (PEG) 1000 molecules
at the interface mercury/electrolyte in the establishment
of the adsorption equilibrium.
The present paper is therefore aimed at clarifying the
two problems mentioned. As an example, we selected the
adsorption of octanoic acid at the interface mercury/
electrolyte.
In two previous papers we have investigated the
adsorption of octanoic acid at the air/electrolyte and
mercury/electrolyte interfaces using surface tension and
double-layer capacity measurements.
11,12
In the first paper
we clearly showed the influence of the surfactant’s purity
on its adsorption behavior while in the second one we
calculated the surface area, adsorption energy, and lateral
interaction energy of adsorbed octanoic acid molecules.
The present paper aims at the investigation of short-
and long-term capacity-time dependencies for adsorption
of octanoic acid at the mercury/electrolyte interface. When
short-term capacitance transients corresponding to dif-
fusion-controlled adsorption were analyzed, it was found
that the square root law (momentary surface concentration
proportional to the square root of time) was only valid for
very short times.
13
More refined models should be applied
here, which also include surface concentrations which are
close to the equilibrium ones.
The long-term capacitance transients can reveal rela-
tively small changes of the double-layer structure, and
only recently has an increase of this capacity with time
been observed,
3
the reason of which is not yet quite clear.
Therefore, in the present paper octanoic acid was included
in these investigations.
Theory
Model A: Diffusion Control according to the
Delahay-Trachtenberg Model. Diffusion of neutral
molecules to the electrode can be described by the
Delahay-Trachtenberg law:
14
D is the diffusion coefficient, c
e
is the bulk concentration
of the surfactant, and erfc(x) represents the complement
of the error function erf(x). Here, the degree of coverage
Θ
e
corresponds to the adsorption equilibrium, and Γ
m
is
the surfactant’s maximal possible surface concentration.
In the following, a way is shown how to determine erfc-
(Kt ). The Gaussian error integral is:
* To whom correspondence should be addressed.
†
Bundesanstalt fu ¨ r Materialforschung.
‡
Aristotle University of Thessaloniki.
§
Max-Planck-Institut fu ¨ r Kolloid-und Grenzfla ¨ chenforschung.
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Θ
t
) Θ
e
[1 - exp(K
2
t) erfc(Kt)] (1)
K ) (Dc
e
2
/Θ
e
2
Γ
m
2
)
1/2
(2)
3661 Langmuir 1999, 15, 3661-3665
10.1021/la981179i CCC: $18.00 © 1999 American Chemical Society
Published on Web 04/22/1999