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Inverted Current-Time Transients. A New Method for the Determination of the Potential of Maximum Adsorption in Condensed Layers C. Donner,* St. Kirste, L. Pohlmann, and H. Baumga¨rtel Institute of Physical and Theoretical Chemistry, Free University Berlin, Takustrasse 3, 14195 Berlin, Germany Received June 2, 1998. In Final Form: September 4, 1998 The role of the potential of zero charge (PZC) and of the potential of maximum adsorption Em during the adsorption of neutral molecules at the electrode surface is not yet well understood. The phase transition of the adsorbed molecules to a condensed state adds further complications. But under certain circumstances this process can be utilized to obtain additional information about the adsorbate system and the electrochemical double layer. On these grounds a new method for the determination of the potential of maximum adsorption in condensed layers is proposed. This method is based purely on a qualitative analysis of the shape of current-time transients, which change their sign at the potential of maximum adsorption and become inverted. From this datum and the corresponding capacity-potential curves of the adsorbate system and of the pure electrolyte one can construct the true charge-potential characteristics of the system and obtain the value of the PZC. This method was applied to the system thymine/mercury/ 0.1 M NaClO4. One result is that in this system the potential of maximum adsorption is a function of the temperature, the pH-value, and the prepolarization potential. This latter result can only be explained in terms of a kinetic argumentation.
1. Introduction Adsorption processes followed by first-order phase transitions of organic neutral molecules are the object of a number of investigations in past and present. Beginning with experiments on mercury electrodes,1-5 the development of surface sensitive methods entailed an increasing number of experiments carried out on single-crystal electrodes.6-8 Consequently, the most knowledge about the mechanism of nucleation and growth, the thermodynamics, and the orientation of molecules in the condensed layer on mercury was obtained by electrochemical and surface tension measurements, whereas the solid electrode surface allows us to compare optical methods (IR methods, X-ray methods), STM microscopy, and electrochemical methods to complete the understanding of condensation processes on electrified interfaces. In this situation concerning structural data of adsorbed molecules on mercury electrodes the knowledge of two characteristic potentials of the system, the potential of zero charge (PZC) and the potential of maximum adsorption Em, gives valuable information about the structure of the adsorbed state (e.g., the dipole moment and the preferred orientation of the adsorbed molecules). Consequently, from the shift of these potentials as a result of a two-dimensional condensation one obtains information about structural reorientations during the phase transition. These data, together with information calculated from electrochemical charge balance measurements,9 are (1) Armstrong, R. D. J. Electroanal. Chem. 1969, 20, 168. (2) Vetterl, V.; de Levie, R. J. Electroanal. Chem. 1991, 310, 305. (3) Retter, U. J. Electroanal. Chem. 1984, 165, 221. (4) Buess-Herman, C. Prog. Surf. Sci. 1994, 46, 335. (5) Kamal, M. M.; Ahmed, Z. A.; Ahmed, M. E.; Ibrahim, M. S.; Temerk Y. M. Bioelectrochem. Bioeng. 1991, 25, 137. (6) Scharfe, M., Hamelin, A., Buess-Herman, C. Electrochim. Acta 1995, 40, 61. (7) Ho¨lzle, M. H:, Wandlowski, Th., Kolb, D. M. Surf. Sci. 1995, 335, 281. (8) Dakourie, A. S., Batina, N., Kolb, D. M Electrochim. Acta 1993, 38, 2467.
the only available structural information for physisorbed thymine films on mercury electrodes. A method commonly used for the determination of the potential of maximum adsorption is based on chronocoulometric measurements. A detailed methodology finally aimed at the determination of the Gibbs energy of adsorption was developed by Lipkowsky.10 It should be noted that the potential of maximum adsorption can also be obtained through measurements of the differential capacity against the potential, because the minimum of these curves corresponds to the maximum surface concentration. These methods, however, fail if two-dimensional condensation processes occur in the adsorbed phase. Then inside the condensation region the differences between the measured quantities (surface pressure, differential capacity) become comparable to the noise level. In the present paper a new method for the determination of the potential of maximum adsorption and also of the PZC inside the condensation region will be presented, which is based on some qualitative features of the currenttime transients. In contrast to the above-mentioned methods it needs the condensation process to work properly. Modern fast potentiostats with a high time resolution allow us to record the kinetics of the complete phase transition process from the very beginning in the form of current-time transients. These transients are usually obtained after performing a potential jump from a potential outside the condensation region to a potential inside this region. However, the interpretation of the results obtained in this way is complicated. Generally, the transition between the noncondensed phase and the condensed one results from a nucleation (9) Saffarian, M. H., Sridharan, R., de Levie, R. J. Electroanal. Chem. 1987, 218, 273. (10) Lipkowski, J.; Stolberg, L. V. In Adsorption of Molecules at Metal Electrodes; Ross, P., Lipkowski, J., Eds.; VCH Publihers: Weinheim, 1992; Chapter 4.
10.1021/la9806404 CCC: $15.00 © 1998 American Chemical Society Published on Web 10/27/1998
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and growth process occurring in a thermodynamically open system. The phase transition requires a supersaturation, which is time-dependent due to the interplay between the growth of condensed islands and the adsorption of molecules from the bulk. The interference of these processes makes it difficult to model the nucleation and growth processes quantitatively because mostly the complete set of necessary parameters is not available.11,12 Furthermore, the measured current is (in the absence of any faradaic process) a charging (or discharging) current of the electrical double layer. Therefore, the current transients depend not only on the applied potential jump but also on the changes in the capacity of the double layer due to the adsorption and condensation processes. Only under special experimental conditions, like significantly different time constants of the adsorption process and the double-layer charging (which are preferably fulfilled for mercury electrodes), can these processes be separated.12 This allows reasonable approximations of the time dependence of the supersaturation and the corresponding kinetic models can be fitted to the experimental coveragetime curves.13,14 But, in general, one has to take into account also the role of the double-layer charging current and of the adsorption process prior to the phase transition. It turns out that an analysis of these additional effects can lead to a new method revealing the position of the potential of maximum adsorption in the condensed state. The method presented here will be applied to the study of two-dimensional first-order phase transitions in the system thymine/H2O/NaClO4/mercury. The paper is organized as follows: In section 2 the theoretical foundation of the method of inverted currenttime transients is given. The application of the method to the system thymine/H2O/NaClO4/mercury is described in section 3. Finally in section 4 the experimental results are discussed in order to extract new structural information of the system investigated. 2. Theory 2.1. Potential of Zero Charge versus the Potential of Maximum Adsorption. According to the Lippmann equation,
∂γ (∂E )
q)-
T,p,µ
(1)
the surface tension γ as a function of the potential reaches its maximum value at zero surface charge density q ) 0. This point is the so-called potential of zero charge (PZC) and can be obtained from the measured γ(E) curves. The typical γ(E) dependencies with one pronounced maximum result from the fact that usually only at one potential does the concentration of anions in the electrical double layer equal the concentration of cations. If surface active substances are added to the solution, they will compete with the adsorbed solvents molecules in the vicinity of the PZC. From this results a potential at which the surface concentration of adsorbed surface active molecules reaches a maximum value. Often it is assumed that this potential of maximum adsorption (Em) and the PZC have the same (11) Pohlmann, L., Donner, C., Baumga¨rtel, H. J. Phys. Chem. 1997, 101, 10198. (12) Donner, C., Kirste, St., Pohlmann, L., Baumga¨rtel, H. Chem. Phys. Lett. 1997, 280, 287. (13) Pohlmann, L., Donner, C., Baumga¨rtel, H. Surf. Sci. 1996, 359, 280. (14) Donner, C., Pohlmann, L., Baumga¨rtel, H. Surf. Sci. 1996, 345, 363.
numerical value. However, both potentials are thermodynamically distinct terms, which may be not identical. The potential of maximum adsorption depends on the dielectric properties as well as on the existence of a permanent dipole moment of the surface active molecules. Under the simplest assumption of a linear superposition of the partial surface charges of the adsorbate free surface q0(E) and the completely adsorbate covered surface q1(E), respectively (this is the so-called Frumkin model of two parallel plate condensers), one obtains for the actual surface charge density qeff:
qeff(Θ) ) q0(E)(1 - Θ) + q1(E)Θ
(2)
Here Θ ) Γ/Γmax is the surface coverage of the adsorbed molecules and Γ the corresponding surface concentration. Γmax is the maximum possible surface concentration of adsorbed molecules (according to the formal limit of infinite bulk concentration cbulk f ∞). It follows from the electrocapillary equation15,16 that the potential-dependent adsorption coefficient B(E) satisfies the following differential equation:
(
)
∂ ln B(E) ∂E
)-
Γ
1 (q (E) - q1(E)) RTΓmax 0
(3)
Then the maximum of the adsorption coefficient B, or equivalently the minimum of the free adsorption enthalpy, is located at the potential E ) Em, where the potentialdependent partial surface charge densities q0(E) and q1(E) are equal to each other. From these different thermodynamic foundations of the PZC and the potential of maximum adsorption Em, respectively, follows that, in general, they have different numerical values. For example, in aqueous solutions the adsorption maximum of n-aliphatic alcohols corresponds approximately to a surface charge density of -1.8 µC/ cm2; i.e., Em is different from the PZC.17 The explicit dependency of the adsorption coefficient B(E) on the potential can be obtained approximately if one assumes a linear relationship between the partial surface charge densities and the potential (Figure 1), i.e., if one assumes constant partial capacities:
q0 ) C0E
q1 ) C1(E - EN)
and
(4)
where C0 and C1 are the partial capacities of the adsorbate free and of the completely adsorbate covered surface, respectively. E is the potential on the rational potential scale (with respect to the PZC of the pure electrolyte), and EN is the shift of the PZC according to a completely adsorbate covered surface (Γ ) Γmax). This shift is caused by an oriented adsorption of adsorbate molecules with a permanent dipole moment and also by the replacement of adsorbed water dipoles, which are slightly oriented at the electrode surface. Then for B(E) follows:16
[
B(E) ) B0 exp -
))]
E 1 1 C E2 + C1E EN RTΓmax 2 0 2
(
(
(5)
Here, B0 is the potential-independent part of the adsorption coefficient. From the condition q0(Em) ) q1(Em) it follows from eq 4 for the potential of maximum adsorption (15) Damaskin, B. B., Petrii, O. A., Batrakov, V. V. Adsorption of Organic Compounds on Electrodes; Plenum Press: New York, 1971. (16) Frumkin, A. N., Damaskin, B. B. Modern Aspects of Electrochemistry; Butterworth: London, 1964; Vol. 3, p 149. (17) Guidelli, R. In Adsorption of Molecules at Metal Electrodes; Ross, P., Lipkowski, J., Eds.; VCH Publihers: Weinheim, 1992; Chapter 1.
Determining Adsorption in Condensed Layers
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Figure 1. Schematic picture showing typical charge-potential dependencies for the pure electrolyte (a) and different adsorbate states: (b) noncondensed state; (c) condensed state without reorientation; (d) condensed state with reorientation.
Figure 2. Capacity-potential curves for the pure electrolyte 0.1 M NaClO4 at pH ) 7 (a) and for the system 14 mM thymine/ 0.1 M NaClO4/mercury at temperatures of 27 °C (b), 24 °C (c), and 22 °C (d). The pit edges represent the dissolution processes in a simple scan experiment starting inside the pit region.
that
Em ) -ENC1/(C0 - C1)
(6)
which is simultaneously the condition for eq 5 to reach the maximum value of the potential dependent adsorption. Then eq 5 can be reformulated into a more compact form (with a redefined coefficient B′0):
[
B(E) ) B′0 exp -
]
C0 - C 1 (E - Em)2 2RTΓmax
(5a)
From eq 6 follows that if the PZC for the adsorbate system shifts into a positive direction relative to the PZC for the pure electrolyte (i.e., the origin of the rational potential scale), then Em is negatively relative to the origin and vice versa. 2.2. Determination of the Potential of Maximum Adsorption Em from Inverted Current-Time Transients. Current-time transients after a potential jump induced two-dimensional condensation process typically have one minimum followed by a current maximum and after then are slowly approaching zero (see, e.g., Figure 4a). Although only pictures of this type are shown in the literature, there are also qualitatively different shapes of current-time transients possible. To elucidate the occurrence of these different shapes, it is convenient to use the charge density vs potential curves for the various adsorption states at an electrode surface (Figure 1). Here the straight line with the steepest slope is the charge curve of the pure supporting electrolyte q0(E). Per definition of the rational potential scale used here the line goes through the origin. If adsorption of some neutral species occurs in the proximity of the PZC, then this leads to a lower differential capacity and therefore a curved chargepotential dependency qads(E), crossing the electrolyte line at the potential of maximum adsorption Em. For the maximum possible surface concentration Γmax the corresponding tangent line q1(E) at the point Em crosses the line of zero charge at the potential EN, which represents the shift of the PZC due to replacement of the water dipoles by the permanent dipoles of the neutral molecules. If in the region of high adsorption a two-dimensional condensation of the adsorbate phase occurs, then inside this region the charge curve will approximate to the tangent line q1(E). This, however, is only true if the molecules in the
Figure 3. Charge density-potential curves for the corresponding capacity-potential curves shown in Figure 2 for (a) the pure electrolyte, (b) the noncondensed state at 27 °C, and (c) the condensed state at 24 °C. The charge density-potential curve for the condensed state at 24 °C (c) was calculated from the capacity in the condensation region and the potential Ecp (as described in the text).
condensed state would have the same orientation relative to the surface, as they have it in the expanded state. Otherwise the charge line corresponding to the condensed film will generally lead to a different shift of the PZC E′N and to a different point of intersection with the electrolyte line at E′N. From this shifted film line qF(E) finally results an additional crossing point with the curve of the expanded (noncondensed) adsorbate state at Ecp. In this picture each current-time transient in a potential step experiment into the condensation region from outside corresponds to a trajectory beginning from the charge density of the adsorbed expanded phase at the start potential Ei and ending in the charge density of the film phase at the final potential Ef. From this trajectory one can obtain some qualitative information about the current transients: the sign of the current at every point of the current trajectory corresponds to the sign of the slope of the trajectory. To show this sign dependence of the current on the conditions of the potential jump one can assume for the
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first approximation, that the time constants for the doublelayer charging and for the adsorption kinetics are small in comparison to the time constant of the condensation process and that the surface concentration of the expanded adsorbed phase is much smaller than the surface concentration in the condensed state. (For a fully quantitative description of the different current-time transients, also including the current due to the changes in the expanded adsorbate phase, see ref 18.) Then one can, according to the Frumkin model (see eq 2), define the effective charge density qeff for a partially film covered electrode surface:
qeff ) qads(E)(1 - θ(t)) + qF(E)θ(t)
b
(7)
where θ(t) is the ratio of the film covered surface area S(t) to the whole surface area S0. Here it was assumed that the film-free surface part is covered with the equilibrium concentration of the expanded phase. To obtain the charging current, eq 7 must be differentiated after time:
ieff ) Ceff(θ) dE/dt - (qads(E) - qF(E)) dθ/dt
(8)
Here, Ceff is the effective capacity:
Ceff ) C0(1 - θ(t)) + C1θ(t)
c
(9)
The first part of eq 8 represents the double-layer charging after a potential jump from a prepolarization potential Ei outside to a measurement potential Ef inside the condensation region (see Figure 1). For very fast doublelayer charging (in comparison to the other processes) this part can be solved separately, leading to
idl ) -
(
∆E t exp R RC0
)
C0 ) Ceff(θ(0))
(10)
with the ohmic resistance R of the electrolyte and ∆E ) Ei - Ef. After the double-layer charging is finished the condensation proceeds under strict potential control at E ) Ef. From the second part of eq 8 then follows the charging current attributed to the film formation process:
iF ) -(qads(E) - qF(E)) dθ/dt,
d
Figure 4. Current-time transients measured at a temperature of 24 °C. (a b) The potential steps follow from -1.700 V: (a) measurement potentials; -1.180 V, -1.160 V, -1.140 V, -1.120 V, -1.110 V; (b) measurement potentials, -1.108 V, -1.107 V, -1.106 V, -1.105 V, -1.103 V, -1.101 V. (c d) The potential steps follow from -0.500 V; (c) measurement potentials, -1.000 V, -1.020 V, -1.040 V, -1.060 V, -1.080 V; (d) measurement potentials, -1.140 V, -1.130 V, -1.120 V -1.110 V, -1.100 V, -1.090 V.
E ) Ef
(11)
With the help of eqs 10 and 11 now one can demonstrate the appearance of inverted current-time transients. For this purpose here it will be assumed that the shift of the PZC is positive, EN > 0 (or E′N > 0) and that the potential jump occurs from the negative side into positive direction, Ei < Ef. Then the initial double-layer charging current idl is always positive according to eq 10. The sign of the charging current iF due to the subsequent condensation process, however, depends on the difference qads(E) qF(E) of the partial charge densities (the film growth rate dθ/dt itself is always nonnegative). In this way one can distinguish two cases (compare Figure 1). (i) Ef < Ecp: If the final potential Ef is located on the left side of the intersection point Ecp of the curves qads(E) and qF(E), then current iF according to eq 11 is positive and one obtains for the total current the well-known minimum/ maximum shape of the current-time transients (see Figure 4a), which was reported for a wide variety of electrochemical systems with and without faradaic transitions. (ii) Ef > Ecp: If the final potential Ef is located on the right side of the intersection point Ecp, then the current
Determining Adsorption in Condensed Layers
iF caused by the condensation process becomes negative. In this case the total current is at the beginning positive but then crosses the time axis and becomes negative (see Figure 4b). These curves are called here inverted currenttime transients, because they are due to the sign inversion of the condensation current. By this means one obtains a tool to determine the crossing point potential Ecp from the qualitative analysis of the shape of the current-time transients by variation of the final potential Ef. If the surface concentration of the expanded adsorbed phase is much smaller than the surface concentration in the condensed state (which is valid in most of the cases), then Ecp is very close to the potential of maximum adsorption of the condensed phase E′m. If, furthermore, no reorientations of adsorbed molecules occur during the phase transition, then all three points of intersection coincide: Ecp ) E′m ) Em (in this case the charge density curves q1(E) and qF(E) coincide). On the other hand a difference between Em and Ecp would then indicate an orientational change between the two adsorbate states. Without a mathematical treatment these alterations in the shape of the current-time transients were predicted in ref 19. But the possibility to determine the potential of maximum adsorption and from that the shift of the PZC in a simple way, only by comparing the shapes of the current-time transients at various potentials, was not tested yet. Together with the above-described new method, one now has a complete set of tools to determine experimentally the shapes and positions of all charge density curves shown in Figure 1. This can be done by performing the following experimental steps: (1) First the PZC of the pure electrolyte must be determined by measuring the capacity minimum of the diffuse layer in dilute solutions of the electrolyte. (2) Then the capacity-potential curve of the pure electrolyte at the used concentration is recorded and integrated to obtain the corresponding charge-potential curve q0(E). The PZC obtained in step (1) here serves as an integration constant. (3) The capacity-potential curve for the noncondensed state can be measured in two different ways. (3a) A precise method to determine the capacitypotential curve for the noncondensed state is described in ref 9. If one measures the capacity-time transients for a temperature slightly below the condensation temperature, then the capacity value immediately after a potential step should correspond to the capacity of the noncondensed state, whereas the final capacity represents a surface, which is completely covered with the condensed state. The missing values for the initial capacities in potential regions with high nucleation rates (in the middle of the pit) then can be estimated by interpolation procedures. (3b) Another method, which was used in this paper, is to measure the capacity-potential curve in a simple scan experiment for a temperature slightly above the critical temperature, where a condensed film does not exist. This procedure is justified, because outside the condensation region the capacity curves above and below the condensation temperature are not distinguishable in the investigated temperature region (Figure 2). Therefore the (18) Donner, C, Kirste, S., Pohlmann, L., Baumga¨rtel, H. Portucalensis Conference on Electrified Interfaces, July 5-10, 1998 in Povoa de Varzim; journal publication in preparation. (19) Buess-Herman, C. In Trends in Interfacial Electrochemistry; Silva, A. F., Ed., D. Reidel: Dordrecht, The Netherlands, 1986; p 205.
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temperature dependence of the adsorbed noncondensed state is not significant in the interesting temperature region. After integration the position of the charge-potential curve qads(E) in Figure 3 is determined by the value of charge at very negative potentials, where the organic molecules are desorbed (see ref 10). In this potential region the double-layer behavior is independent of additives in the electrolytes and therefore the charge-potential curves for the pure electrolyte and the noncondensed adsorbate state coincide. The potential of maximum adsorption Em can now be exactly read off at the point of intersection of the two curves. This procedure fails for the condensed state due to the inexact determination of the term qdΘ/dE, corresponding to the frequency-dependent part of the capacity curves (the so-called adsorption-desorption peaks). (4) The double-layer capacity in the condensation region corresponds to the slope of the charge-potential curves for the condensed state. After integration inside the condensation region the missing integration constant can be determined if one knows the position of the intersection point Ecp, where the current-time transients become inverted. This way one finally obtains the line qF(E). As the result of these experimental steps one obtains the entire diagram according to Figure 1 with the position of all points of intersection Ecp, E′m, Em for the condensed as well as for the expanded adsorbate phases. Simultaneously, one obtains the shift of the PZC EN (or E′N). 3. Experimental Section The electrochemical measurements were carried out in the system 14 mmol of thymine/H2O/0.1 M NaClO4 on a stationary mercury electrode. A platinum wire acts as a counter electrode, whereas a Ag/Ag+ electrode with a 0.1 M AgClO4 solution was used as a reference electrode. The use of electrodes of the first kind is appropriate for the measurements of very fast transients. Because only capacity currents were detected, which are very small, the potential of our reference electrode was absolutely stable at 0.740 V vs NHE. The effect of the temperature dependence of the reference electrode was avoided by using a nonisothermal cell construction with a reference electrode held at a constant temperature. The remaining thermodiffusion potential can be estimated to be 0.3 mV/K, so that the error in the temperature interval of 20-27 °C used here would be no more than 2 mV (see ref 20). The current-time transients were created by single potential step techniques as described earlier12 and the current response was detected using the unfiltered output of the potentiostat. The capacity measurements were accomplished by a lock-in technique. The alternating current had a frequency of 80 Hz, the amplitude was 3 mV. The thymine was used as received (Merck for biochemical purposes), the electrolyte salt NaClO4 was of p.a. quality and the water was tridistilled. Before each measurement cycle the cell was purged with argon, at least 30 min. Otherwise traces of oxygen can produce significant artifacts. All measurements were carried out in neutral as well as in basic solutions (pH 10), to check the influence of the dissociation of thymine, which first pKA value is pKA ) 9.5.
4. Results and Discussion To our knowledge the first experimental inverted current-time transients were obtained in the system coumarin/H2O/mercury.21 But due to the slow nucleation kinetics and therefore the stochastic nucleation process in this system, it was not yet possible to apply the here presented procedure to determine the potential of maximum adsorption. On the other hand, the system tymine/ H2O/mercury, which was investigated in detail by de Levie (20) Milazzo, G., Sharma, V. K. Z. Phys. Chem. (N.F.) 1972, 79, 41. (21) Sto¨ckel, P. Diploma Thesis, Free University of Berlin, 1997.
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Table 1. Potentials of PZC, Maximum Adsorption Em, and the Crossing Point Potentials Ecp for the Different Adsorption States in Neutral Solutiona adsorbate state
PZC, V
pure electrolyte noncondensed state condensed state 24 °C, both prepolarization condensed state 22 °C, cathodic prepolarization condensed state 22 °C, anodic prepolarization
-0.960 -0.930 -0.816
-1.000 -1.020
-1.000 -1.090
-0.825
-1.020
-1.085
-0.761
-1.050
-1.180
a
Em, V
Table 2. Potentials of PZC, Maximum Adsorption Em, and the Crossing Point Potentials Ecp for the Different Adsorption States in Basic Solutiona
Ecp, V
The potentials were measured vs Ag/Ag+.
adsorbate state
PZC, V
Em, V
Ecp, V
pure electrolyte noncondensed state condensed stae 22 °C, cathodic prepolarization condensed state 22 °C, anodic prepolarization condensed state 20 °C, cathodic prepolarization condensed state 20 °C, anodic prepolarization
-0.925 -0.846 -0.561
-1.090 -1.090
-1.090 -1.090
-0.540
-1.100
-1.120
-0.561
-1.090
-1.090
-0.445
-1.160
-1.270
a
Figure 5. Charge density-potential curves for the pure electrolyte (a), the noncondensed state 27 °C (b), and the condensed state formed after a potential step from the cathodic (c) and anodic (d) prepolarization potential at 22 °C in neutral solution.
The potentials were measured vs Ag/Ag+.
Figure 6. Capacity-potential curves for the pure electrolyte 0.1 M NaClO4 at a pH value of 10 (a) and for the system 14 mM thymine/0.1 M NaClO4/mercury at temperatures of 27 °C (b), 24 °C (c), and 22 °C (d).
and co-workers,9 seems to be simple enough to test the method of inverted current-time transients. It was shown that the above-described method of inverted current-time transients is applicable to determine the potentials Em and the PZC for the different adsorption states in a relatively simple way. The results of the measurements are presented in Table 1 and Figures 3 and 5 for the neutral system and in Table 2 and Figure 7 for the basic system, respectively. In the neutral as well as in the basic system the potential of maximum adsorption Em is at all investigated temperatures more negative than the PZC of the pure electrolyte. That means that at this potential Em the single molecules “see” only a negatively charged electrode. Due to the fact that at Em the Gibbs free energy of adsorption possesses its minimum, it becomes clear that the neutral thymine molecules but not the thymine anions form the condensed film. Thymine in Neutral Electrolyte Solutions. The PZC for the pure electrolyte NaClO4 (E0PZC) was determined from the position of the minimum in the capacitypotential curves for the concentration range 0.0005-0.01 M. The minimum was shifted slightly in comparison to earlier described data for ClO4- anions.22 Therefore we fixed the value of PZC at E0PZC ) -0.960 V vs Ag/Ag+ (determined for 0.01 M NaClO4). The value reported in the literature of the PCZ for 0.1 M NaClO4 determined
with electrocapillary measurements lies about -0.977 vs Ag/Ag+.25 The PZCs vary slightly according to the different measurement methods being used. The capacity curve for the noncondensed state was measured at a temperature of 27 °C, where the condensed state was not even formed. The current-time transients for the phase transitions were recorded at 24 °C for different measurement potentials Ei and for prepolarization potentials Ef both at the cathodic and anodic pit edge (see Figure 4). The prepolarization potentials at the cathodic as well as at the anodic pit edge are located in regions, where no athermal clusters can disturb the condensation process.12 The potential Ecp now can be determined as that measurement potential Ei, where the current-time transients just become inverted. With the potential Ecp ) -1.090 V and the measured film capacity of C1 ) 9.38 µF/cm2 inside the condensation region, one can determine the slope and the position of the curve qF(E) (Figure 3). An experimental limitation consists of the fact that for lower temperatures the kinetics in the middle of the pit is too fast, so that an exact measurement of the currenttime transients is impossible. For the thymine system the above-described procedure was practicable down to a temperature of 22 °C with an acceptable uncertainty. In this case, there is a region of 300 mV between the fastest transients before and after the potential Ecp, where no
(22) Delahay, P. Double Layer and Electrode Kinetics; Interscience Publishers: New York, 1965. (23) Roelfs, B., Bunge, E., Schro¨ter, C., Solomun, T., Meyer, H., Nichols, R., Baumga¨rtel, H. J. Phys. Chem. 1997, 101, 754.
(24) Haiss, W., Roelfs, B., Port, S. N., Bunge, E., Baumga¨rtel, H., Nichols, R. Submitted. (25) Wroblowa, H.; Kovacs, Z.; Bockris, M. O. J. Trans. Faraday Soc. 1965, 61, 1523.
Determining Adsorption in Condensed Layers
Figure 7. Charge density-potential curves for the corresponding capacity curves shown in Figure 6 for the pure electrolyte (a) and the noncondensed state at a temperature of 27 °C (b). (a) Charge density-potential curves for the condensed state at 22 °C for both prepolarization potentials (cathodic prepolarization potential (c); anodic prepolarization potential (d)). The curves were calculated from the capacity in the condensation region and the potential Ecp (as described in the text). (b) Charge density-potential curves for the condensed state and for an anodic prepolarization potential at 22 °C (c) and at 20 °C (d).
current-time transients could be detected. But with the assumption that Ecp is in the middle of this nonmeasurable potential region, this potential can be estimated. For the neutral system the following can be concluded from the experimental data (Table 1): In the noncondensed state as well as in the condensed state the PZC shifts to more positive potentials in comparison with the pure electrolyte. The difference between the PZC of the condensed and the noncondensed state (114 mV) is similar to the difference described in ref 9 for the thymine condensation in a NaCl electrolyte system. De Levie suggested a planar orientation of thymine in the condensed film and therefore thymine itself would not yield a dipole contribution.9 The same orientation was found for thymine on Au(111) in the physisorbed film.23,24 On the other hand a positive shift of the PZC presupposes a positive net dipole momentum as a result of the dipole contributions of the adsorbate minus the dipole contributions of the displaced solute molecules, which in our case are water molecules.10 If one assumes that the orientation of thymine at the electrode in the condensed state and in the noncondensed
Langmuir, Vol. 14, No. 24, 1998 7005
state is approximately the same, then this would mean that the positive net dipole momentum contribution following from our experimental results can only be due to the displacement of water molecules being oriented with the negative end against the surface at the PZC in the pure electrolyte.17 Contrary to the pyridine adsorption on Au (111), where the more flat orientation in no way influences the position of the PZC,10 in the thymine system on mercury the displacement of negative oriented water plays the most important role for the position of the PZC. But the position of the potential of maximum adsorption Em and its shift with the adsorbate state contains additional information for the structure discussion in comparison to the PZC data. If one considers the difference between the potentials of maximum adsorption Em for the noncondensed (-1.000 V at 1.06 µC cm-2) and E′m for the condensed state (-1.020 V at 1.90 µC cm-2), respectively, the drift into the negative direction due to the condensation can only be explained by a change in the orientation of adsorbed molecules between the two states. And it can be directly concluded that the net dipole contribution of the thymine molecules in the condensed state must be more positive than that in the noncondensed state. From this information it cannot be decided whether the orientation of adsorbed thymine in the noncondensed state is slightly upright with its negative end at the surface and planar in the condensed state or thymine is planar oriented in the noncondensed state and slightly upright oriented with its positive end against the surface in the condensed state. In combination with the surface coverage measurements in ref 9 and the STM and SNIFTIRS measurements on Au(111)24 one would prefer the first interpretation. On no account are the molecules perpendicular oriented with their maximum dipole contribution in normal direction to the surface. In this case the net dipole contribution of thymine would be greater than the greatest net dipole orientation of water at the surface and no potential of maximum adsorption could be measured.17 For 22 °C and a cathodic prepolarization condition Ecp is located at -1.085 V. Having the approximations in mind, one can conclude that the small difference of 5 mV between the Ecp (and therefore between the PZC and the Em) at 24 and 22 °C, respectively, is not significant. Surprisingly, the analysis of the single potential step measurements at 22 °C with a prepolarization potential Ei, which is located at the anodic pit edge, leads to different results. Using the approximations described above, one can estimate a potential Ecp ) -1.180 V, which is nearly 100 mV more negative than the corresponding value estimated according to a cathodic prepolarization potential. Correspondingly, the value of the PZC shifts into positive direction to -0.761 V (Figure 5) and E′m into negative direction. How can these differences be explained? Clearly, the cause can only be the occurrence of an additional metastable or kinetically hindered condensed state. Otherwise the occurrence of different PZCs would suggest that the equilibrium orientation of the molecules in the condensed film varies depending on the start conditions. Therefore it was proposed that the dissociation of the thymine molecule plays an important role: At a temperature of 24 °C the PZC of the noncondensed state is near the anodic pit edge: At all measurement potentials the molecules “see” only a negatively charged electrode surface. Due to the vicinity of the condensation temperature the whole kinetics at 24 °C is slow and consequently the eventually adsorbed thymine anions at
7006 Langmuir, Vol. 14, No. 24, 1998
the anodic start potential Ei have enough time to desorb at the measurement potential Ef. It follows that at this temperature the potential of maximum adsorption E′m (and equally the PZC) is the same for both cathodic and anodic prepolarization potentials. Another situation is present at a temperature of 22 °C, where different PZCs and potentials of maximum adsorption Em were detected depending on the prepolarization potential. Under these conditions the PZC of the noncondensed state is inside the pit region, and the whole condensation kinetics in the middle of the pit is much faster than that at a temperature of 24 °C. It turns out that there are two different causes acting in combination and leading to the shift of the potential of maximum adsorption Em: When the prepolarization potential is at the positive pit edge, a definitive amount of thymine anions will be located at the surface. At the final potential the film formation takes place so fast that there is not enough time for the desorption of all thymine anions. Therefore the condensed film may contain a defined amount of thymine anions. In such a film the electrostatic repulsive forces between the anions themselves and between the anions and the negative charged surface cause an increase of the energy content of the adsorbed film. Consequently, the potential E′m, which corresponds to the minimum energy of the adsorbed film, has to be shifted to more negative potentials where the desorption of anions is so fast that the film consists only of neutral thymine molecules. Hence the PZC shifts to more positive potentials. On the contrary, if one performs a potential jump from the cathodic pit edge, then there are no adsorbed thymine anions present at the surface to be incorporated into the forming film. In this case E′m is not shifted. From this measurement one can conclude that the composition of the condensed thymine film in neutral solutions is dependent on the scan direction due to the presence of a definitive amount of thymine anions at anodic potentials. The thymine anions are embedded in the film and cause a shift of E′m in the negative direction. Basic Electrolyte Solutions. This explanation is supported by the experiments in the basic electrolyte solution (Table 2). The PZC for the pure base electrolyte is about 35 mV more positive than the PZC in the neutral solution at E0PZC ) -0.925 V vs Ag/Ag+. This is approximately in agreement with the pH-shift described in ref 22. Contrary to the neutral system, where the PZC of the pure electrolyte is located inside the pit region, the PZC of the pure electrolyte in a basic system is for a temperature of 24 and 22 °C in the metastable region or at the pit edge, respectively, and only for a temperature of 20 °C inside the pit region. At higher pH-values the condensation region is smaller than in neutral solutions, although the condensation temperature itself remains unchanged. From Figure 6 it is clearly seen, that the cathodic pit edge is at the same place, whereas the anodic pit edge is shifted considerably to more negative potentials. Generally, in a basic solution the absolute ratio between neutral thymine and thymine anions is much lower. A rigorous comparison between the temperature behavior of the thymine system in neutral and base electrolytes is not practicable due to the slower condensation kinetics in the basic system. Thus, the kinetics in the whole condensation region could be obtained at 22 °C in basic solutions, whereas in the neutral solution at these temperature the experimentally accessible time resolution was too low to measure the fast current transients in the middle of the pit region. If the potential steps start at the
Donner et al.
cathodic pit edge, the Em is at -1.090 V, independent of the temperature. There is no difference between the Em of the noncondensed and of the condensed states, respectively, and therefore Em and Ecp are located at the same potential. One can conclude that no significant orientational changes will take place during the condensation process. At first sight it seems that the film composition is the same as in neutral solutions, as long as the potential step takes place from the cathodic pit edge. But one should not forget that the PZC of the pure electrolyte and the one of the noncondensed state are much more positive for high pH-values. And, as a consequence, the charge of the surface at the same potential -1.090 V is more negative in the basic as in the neutral electrolyte. This means that the surface must be more negatively charged to minimize the adsorption energy in a basic solution (Figure 7a). Otherwise the position of the negative pit edge is not influenced by the pH-value, and it is not very likely that at the prepolarization potential of -1.700 V a significant amount of the thymine anions is present at the surface. An explanation can be found, if one examines the adsorption rate of anions at the measurement potential. Due to the absolute higher amount of thymine anions in a basic solution, the probability to adsorb a definitive amount of these at the measurement potential is higher as in neutral solutions. This small amount of anions is the cause for the relative shift of Em to a more negative charged surface, where the adsorption rate is vanishingly small. But what happens at the anodic pit edge? The anodic pit edge is shifted into the cathodic direction in the basic solution. At this edge the thymine anion concentration is significantly higher than in the neutral solution. But from electrostatic considerations one can conclude that above a critical amount of anions in the condensed layer, the film would become unstable due to repulsive forces. At more negative potentials, the rate of adsorption of the neutral form increases and the ratio of the two forms of thymine (anion/neutral form) in the film composition decreases below a critical value, so that the condensation can take place. The shift of Em due to temperature (-1.09 V for 22 °C and -1.16 V for 20 °C) is greater than in the neutral solution, but the mechanisms, namely the fast film formation on one hand and the desorption of thymine anions on the other hand, lead to the effect of the same shift. 5. Conclusions In the present paper we proposed a new method to determine the potential of maximum adsorption in condensed layers. The method is based purely on the qualitative analysis of the shape of current-time transients. At the crossing point potential Ecp the shape of these transients becomes inverted and a determination of this potential is possible as long as the time and current resolution of the instrumentation is high enough. From this and the knowledge about the pure electrolyte chargepotential curve, the potential of maximum adsorption Em can be determined. This method was applied to the thymine condensation on mercury in a temperature region of about ∆T ) (5-7) K below the condensation temperature depending on the pH-value of the solution. Contrary to the usually found cases, where the Em is independent of the surface coverage of the adsorbate, in our case a significant shift was found depending on the
Determining Adsorption in Condensed Layers
prepolarization potential, the temperature and the surface coverage. The first two find their explanation in kinetic arguments and the latter can be explained by an orientational change of the adsorbate molecules. Conclusions for the orientation and the composition of the film can be made by analyzing the shift in the position of Em (rather than in the position of the PZC). Appendix. List of Used Symbols Epzc0:
potential of zero charge (PZC) of the pure supporting electrolyte EN, E′N: shift of the PZC according to a completely adsorbate covered surface, without and with reorientation during the condensation, respectively Em, E′m: potential of maximum adsorption, without and with reorientation Ecp: potential at the intersection point of the charge curve of the reoriented condensed film with the charge curve of the expanded state of adsorbed molecules Θ(t): surface coverage of the adsorbed molecules
Langmuir, Vol. 14, No. 24, 1998 7007 θ(t): ratio of the film-covered surface area S(t) to the whole surface area S0 Γ, Γmax: surface concentration and the maximum possible surface concentration of adsorbed molecules q0, q1, qF: partial surface charges (per area) of the adsorbate free surface and for the completely adsorbate covered surface, without and with reorientation, respectively qads: real surface charge (per area) according to the potential-dependent equilibrium surface concentration of the adsorbate in the expanded state C0, C1, CF: the same for the partial capacities per surface area B(E): adsorption coefficient Ei, Ef: start (prepolarization) potential and final (measurement) potential R: ohmic resistance of the electrolyte idl, iF: double-layer charging current density according to the potential jump (dl) and to the film formation process (F), respectively LA9806404
