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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A systematic analysis of electrochemical processes involving metal complexes.
Starting with general considerations on equilibria in solutions and at interfaces as well as on mass transport, the text acquaints readers with the theory and common experimental practice for studying electrochemical reactions of metals complexes. The core part of the book deals with all important aspects of electroplating, including a systematic discussion of co-deposition of metals and formation of alloys. It also discusses such related subjects as oxide layer formation and hydrogen evolution as a side reaction.
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Seitenzahl: 545
Veröffentlichungsjahr: 2015
Ähnliche
Table of Contents
Cover
Related Titles
Title Page
Copyright
Preface
Symbols and Abbreviations
Chapter 1: Introduction
1.1 Equilibrium Properties of Complex Systems
References
Chapter 2: Equilibrium Electrode Potentials
2.1 Electrodes of the First Kind
2.2 Equilibria Involving Ions of the Intermediate Oxidation State
2.3 Electrodes of the Second Kind
2.4 Open-Circuit Potentials: Examples of Experimental Investigations
References
Chapter 3: Mass Transport
3.1 Two Models of Linear Mass Transport
3.2 Other Cases of Diffusional Mass Transport
3.3 Mass Transport of Chemically Interacting Particles
3.4 Concentration Profiles
References
Chapter 4: Peculiarities of Electrochemical Processes Involving Labile Complexes
4.1 Steady-State Voltammograms
4.2 Potential Transients
4.3 Current Transients
References
Chapter 5: Quantitative Modeling of Quasi-Reversible Electrochemical Processes Involving Labile Complexes of Metals
5.1 Kinetic Equations
5.2 Employment of Voltammetric Data
5.3 Techniques Based on the Control of the Intensity of Forced Convection
References
Chapter 6: Determination of Mechanism of Electrochemical Processes Involving Metal Complexes
6.1 Determination of the Mechanism by Reaction Orders
6.2 Method of Isopotential Solutions
References
Chapter 7: Adsorption
7.1 Thermodynamic Aspects
7.2 Model Aspects
References
Chapter 8: Electrochemical Processes in Real Systems
8.1 Experimental Details
8.2 Cyanide Systems
8.3 Ecological Systems Containing Hydroxy Acids
Appendix
References
Chapter 9: Electrochemical Deposition of Alloys
9.1 Mass Transport during the Codeposition of Metals
9.2 Codeposition of Cobalt and Tin
9.3 Deposition of Brass Coatings
9.4 Deposition of Bronze Coatings
9.5 Codeposition of Cobalt and Molybdenum
References
Chapter 10: Spontaneous Formation of Photosensitive Cuprous Oxide Layers
10.1 Two Mechanisms of Cu
2
O Formation
10.2 Composition of Oxide Layers
10.3 Kinetics of Cu
2
O Formation
10.4 Electrochemical Reduction of Oxide Layers
10.5 Photoelectrochemical Properties of Oxide Layers
10.6 Photoelectrochemical Stability of Oxide Layers
10.7 Influence of Oxide Layers on Kinetics of Cu(II) Reduction
References
Chapter 11: Hydrogen Evaluation Involving Ligands as Proton Donors
References
Concluding Remarks
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Stability constants of Cu(II)–glycine complexes obtained at different ionic strength with nitrate [9] and perchlorate [10] as background electrolytes.
Figure 1.2 Distribution of Ag(I) cyanide complexes versus concentration of free (a) and total (b) cyanide. The total Ag(I) concentration in the part b is equal to 0.05 M (solid lines) and 0.1 M (dotted lines).
Figure 1.3 Distribution of Zn(II) cyanide and hydroxide complexes versus pH. Total Zn(II) and cyanide concentrations are equal, respectively, to 0.4 and 1.8 mM (a) and to 0.01 and 0.1 M (b).
Figure 1.4 Distribution of Ag(I)–thiocyanide complexes versus total Ag(I) concentration.
c
L
= 3 M,
T
= 293 K.
Figure 1.5 Distribution of complexes in the model system with dilution of the solution. The ratio
r
is constant and equal to 4.
Figure 1.6 Temperature effect on the distribution of Cu(II)–ethylenediamine complexes. Total metal and ligand concentrations are equal to 0.01 and 0.005 M, respectively, at a pH of 5.3.
Chapter 2: Equilibrium Electrode Potentials
Figure 2.1 Potentiometric titration curves obtained at different stability of ML
+
complexes (log
K
values are given at the respective curves). 0.1 M solutions of M
+
(20 ml) and ligand (volume
V
) are used. Dilution effects are accounted for.
Figure 2.2 Variations of Zn equilibrium potential with pH of Zn(II) cyanide solutions at
c
M
and
c
L
, which are equal, respectively, to 0.4 and 1.8 mM, (curve 1); 0.01 and 0.1 M (curve 2).
Figure 2.3 Variations of the equilibrium potential of Cu electrode with dilution of Cu(II)–ethylenediamine solutions. The ratio
r
=
c
L
/
c
M
is kept constant and equal to 4.
Figure 2.4 Variations of concentrations of Ag(I) cyanide complexes in a series of isopotential solutions. Total concentrations of Ag(I)and cyanide are shown by dotted lines.
Figure 2.5 Diagram explaining the transition of complex system to equilibrium state A, when the condition holds. The P1 → A transition involves the direct reaction (2.18) with dissolution of metal; and the P2 → A transition involves the reverse reaction.
Figure 2.6 Molar fraction of M(II) converted into M(I) during equilibration versus stability constant of ML
+
species. Differences in formal potentials, , are as follows: −0.06 (1), 0.06 (2), 0.12 (3), and 0.2 V (4). Initial concentrations of M(II) and ligand are 0.01 and 0.02 M, respectively.
Figure 2.7 Changes in electrode potential in the equilibration process versus stability constant of ML
+
species. Differences in formal potentials, , are as follows: −0.06 (1), 0.06 (2), 0.12 (3), and 0.2 V (4). Initial concentrations of M(II) and ligand are 0.01 and 0.02 M, respectively.
Figure 2.8 pH dependencies of Cu
2
O amount formed in the Cu|Cu(II), ethylenediamine system. Initial concentration of Cu(II) is equal to 0.01 M; the total ligand concentration is indicated.
Figure 2.9 Phase diagram of the Cu|Cu(II), ethylenediamine system simulated at
c
Cu(II)
= 0.01 M.
Figure 2.10 Distribution of Cu(I) cyanide complexes versus the total ligand concentration at 293 (solid lines) and 323 K (dotted lines).
c
Cu(I)
= 0.01 M, pH 10.2.
Figure 2.11 Variations of experimental open-circuit potentials (symbols) and simulated equilibrium potentials (lines) with temperature; pH is 10.2,
c
M
= 0.01 M. The ratio r =
c
L
/
c
M
is indicated at the respective curves.
Figure 2.12 Variations of experimental open-circuit potentials (symbols) and simulated equilibrium potentials (lines) with temperature; pH is 10.2,
c
M
= 0.01 M. The ratio r =
c
L
/
c
M
is indicated at the respective curves.
Chapter 3: Mass Transport
Figure 3.1 Linear approximation
(
1) and real (2) concentration profile in the diffusion layer.
Figure 3.2 Effective thickness of diffusion layer versus potential sweep rate in logarithmic coordinates. The data obtained under natural convection conditions for different redox systems as indicated.
Figure 3.3 Values of Ψ(
u
) obtained at different thickness of diffusion layer .
Figure 3.4 Steady-state concentration profiles at
i
=
i
d
,
c
M
= 0.01, and
c
L
= 0.04 M. When
i
=
i
d
/2, ordinate should take up the position indicated by a dotted line.
Figure 3.5 Concentration profiles obtained at
i
=
i
d
for ligand-deficient system .
Figure 3.6 pH changes in the diffusion layer formed at
i
=
i
d
in the system containing LH
+
species. Bulk pH values are indicated at the respective curves.
c
M
= 0.01 and
c
L
= 0.04 M.
Figure 3.7 Calibration graph of Sb|Sb
2
O
3
microprobe. Results obtained for three individual samples (different symbols) are approximated with one general line.
Figure 3.8 pH changes in the diffusion layer of Cu|Cu(II), glycine system. Cathodic
i
= 2.5 mA cm
−2
,
c
M
= 0.01 M,
c
L
= 0.04 M. Bulk pH values are given at the respective curves. Arrows show the position of pH drop according to theoretical predictions.
Figure 3.9 Dynamics of concentration profiles of M
+
ions. Simulation with
c
M
= 0.01 M,
c
L
= 0.02 M, log
K
1
= 2,
k
1
= 100 mol
−1
dm
3
s
−1
.
Figure 3.10 Comparison of normalized steady-state concentration profiles simulated at
i =
0.5
i
d
for IL (solid lines) and LL (circles) systems. The concentration gradients, obtained for IL system at
x
= 0, were used as boundary conditions for LL system.
c
M
= 0.01 M,
c
L
= 0.02 M.
Figure 3.11 Effective stability constants
K
*
, as functions of coordinate
x
. The thickness of the hypothetical reaction layer,
δ
r
, is indicated with crosses. Its dependence on
k
−1
determined by Eq. (3.38) is shown in the inset (logarithmic presentation).
Figure 3.12 Effective stability constants
K
*
in the case of different charge transfer reactions: the reduction of M
+
aqua complexes (a) and that of ML
+
species (b).
Figure 3.13 Effective stability constants β
*
and concentration profiles of M
+
ions (inset). The thickness of the reaction layer is indicated with crosses. The thickness of the hypothetical reaction layer,
δ
r
, is marked with crosses. The case of M
+
reduction at a large excess of ligand.
Chapter 4: Peculiarities of Electrochemical Processes Involving Labile Complexes
Figure 4.1 Variations of equilibrium potential on addition of simple metal salt to 0.1 M ligand solution. It is supposed that ML
+
complexes of different stability can be formed. log
K
values are given at the respective curves.
Figure 4.2 Normalized reversible cathodic voltammograms simulated at different stability of ML
+
complexes (log
K
values are given at the respective curves). Variations of the overvoltage at with log
K
(see dotted lines) are given in the inset.
Figure 4.3 Normalized reversible cathodic voltammograms simulated at different ratios that are indicated at the respective curves.
Figure 4.4 Normalized reversible cathodic voltammograms simulated for Cu|Cu(II), glycine system with , . Bulk pH is indicated at the respective curves. The effect of sulfate (0.3 M) is presented by dotted lines.
Figure 4.5 Cathodic voltammograms obtained for Cu|Cu(II), glycine system at different rotating velocities of RDE as indicated. Comparison between experimental (symbols) and simulated (lines) data.
Figure 4.6 Cathodic voltammograms obtained for Co|Co(II), citrate system [8] at different ratios and , pH 7.2, 25 °C. Variation of prewave height versus overequivalent ligand concentration is shown in the inset. Triangular symbols indicate
i
values obtained with elimination of hydrogen evolution current.
Figure 4.7 Anodic voltammograms simulated for model system at different ratios . Anodic
i
is normalized with respect to the cathodic limiting current density
i
d
.
Figure 4.8 Anodic RDE voltammograms obtained for Cu(II)–glycine solutions at 300 rpm and different glycine concentrations as indicated. Inset contains
i
lim
values determined at and plotted versus overequivalent ligand concentration.
Figure 4.9 Comparison of RDE voltammogram and CPM transients obtained for Cu(II)–glycine solutions of indicated composition.
Figure 4.10 Relationship between the concentration of free metal ions M
n
+
and that of total metal
c
M
(simulated at constant
c
L
). Variations of real (1) and effective (2) potential sweep rate with time are shown in the inset.
Figure 4.11 Reversible cathodic RDE chronovoltammograms simulated at , pH 11, 1000 rpm. Effect of the ligand/metal ratio.
Figure 4.12 Reversible cathodic RDE chronovoltammograms simulated at , pH 4, 1000 rpm. Effect of the potential sweep rate.
Chapter 5: Quantitative Modeling of Quasi-Reversible Electrochemical Processes Involving Labile Complexes of Metals
Figure 5.1 The ratio of partial current densities versus the overvoltage at various potential sweep rates.
Figure 5.2 RDE voltammogram (VA) and normalized Tafel plot (NTP) obtained for the system Cu|Cu(II), glycine.
Figure 5.3 NTP obtained for Cu|Cu(II), glycolic acid system at pH 2.4 and different potential sweep rates (symbols). Regression of similar results obtained at pH 2.9 is presented by dotted line. Dimensions: , .
Figure 5.4 Comparison of
i
p
simulated for model system (symbols) with those obtained by Eqs. (5.29) and (5.30) (lines).
Figure 5.5 Tafel plots obtained for Ag|Ag(I), NH
3
system at pH 11.05 and constant surface concentrations,
c
Ag(I),s
, as indicated.
Figure 5.6 Dependencies of polarization resistance on in the series of isopotential Cu(II)–glycine solutions with constant and various L
−
concentrations indicated at respective lines.
Figure 5.7 Dependencies of
C
s
on the cathodic current density
i
at and different angular frequencies of alternating current indicated at the respective lines.
Figure 5.8
C
s
values (Figure 5.7) extrapolated to (left ordinate) and the slope
k
of dependencies (right ordinate) versus .
Chapter 6: Determination of Mechanism of Electrochemical Processes Involving Metal Complexes
Figure 6.1 Variations of the exchange current density
i
01
with the free ligand concentration in the IPS series.
Chapter 7: Adsorption
Figure 7.1 Distribution of complexes in the bulk of solution (a) and in the adsorption layer (b) versus the total ligand concentration. The first and the second variants of simulations (see text) are presented by full and doted lines, respectively.
Figure 7.2 Surface coverages versus the total ligand concentration.
Chapter 8: Electrochemical Processes in Real Systems
Figure 8.1 Dependencies of polarization resistance on in the series of isopotential Ag(I) cyanide solutions with constant and various CN
−
concentrations indicated at respective curves.
Figure 8.2 Variations of the exchange current density with the free cyanide concentration in the IPS series.
Figure 8.3 Dependencies of 1/
i
lim
versus obtained for Ag|Ag(I), CN
−
system. (1) and 0.045 M (2–4); (1), 0.22 M (2), 0.18 M (3) and 0.1 M (4); pH 13.
Figure 8.4 Cathodic voltammograms simulated for reversible reduction of Au(I) in 0.01 M KAu(CN)
2
solutions containing different amounts of KCN (in mol per cubic decimeter) as indicated.
Figure 8.5 Chronopotentiograms obtained at indicated current densities for Au(I) cyanide solutions. , .
Figure 8.6 Plots of
i
c
τ
(ordinate to the left) and (ordinate to the right) versus 1/
i
c
obtained for Au|Au(I), CN
−
system from chronopotentiometric data.
Figure 8.7 Chronopotentiometric data selected at constant ratios of
t
/
τ
/
as indicated.
Figure 8.8 Normalized Tafel plots obtained from chronopotentiometric data at cathodic current densities,
i
c
, as indicated. Determined from this NTP kinetic parameters are also listed.
Figure 8.9 Distribution of species in 0.01 M Cu(II) solutions containing 0.5 M Na
2
SO
4
and gluconic acid with total concentration of 0.02 M (solid lines) and 0.05 M (dashed lines).
Figure 8.10 LPS voltammograms obtained for Cu(II)–malic acid system at different pH and potential sweep rates as indicated.
Figure 8.11 Comparison between experimental voltammograms (VAs, lines) and transformed EQCM data (symbols). Data for Cu(II)-free solutions are presented by dotted line and black circles.
Figure 8.12 Two equivalent circuits for consecutive transfer of two electrons. Faradaic elements are connected with solid lines. The ohmic resistance of the solution,
R
Ω
, and the double-layer impedance,
Q
dl
, are the non-faradaic elements.
Figure 8.13 Equivalent circuit and experimental Nyquist plots obtained for series of isopotential Cu(II)–glycolic acid solutions.
Figure 8.14 Comparison of impedance spectra measured for solution B (symbols) and calculated for the equivalent circuit (solid lines) with pertinent data from Table 8.1.
Figure 8.15 Changes in Cu(II) surface concentration under linear potential sweep conditions. Transform of the LPS voltammograms by Eq. (8.14).
Figure 5.3
Figure 8.16 Normalized Tafel plots obtained by transformation of LPS (malic and tartaric acid systems) and RDE (gluconic acid system) voltammograms. 0.3–0.5 M sulfate was used as a supporting electrolyte.
Figure 8.17 Variations of the peak current density with the square root of potential sweep rate. Variations of the peak potential with
v
are shown in the inset in semilogarithmic coordinates. The data obtained for Cu|Cu(II), malic acid system at different pH as indicated.
Figure 8.18 The same as in Figure 8.17 for Cu|Cu(II), gluconic acid system.
Figure 8.19 LPS voltammograms obtained for Cu(II) gluconate solutions containing different supporting electrolytes: sulfate (upper part), mixture of sulfate and perchlorate (middle part), perchlorate (lower part).
Figure 8.20 The
iτ
products plotted versus 1/
i
at different pH as indicated. Respective values are given in the inset.
Figure 8.21 Limiting current densities normalized to the total Cu(II) concentration in Levich coordinates.
Figure 8.22 Distribution of complexes and protonated ligands (inset) in the Cu(II)–citric acid system versus pH.
Figure 8.23 Plots of log
i
01
versus pH obtained from NTP (circles) and IPS (stars) data.
Figure 8.24 Normalized Tafel plots obtained by transformation of RDE voltammograms. CuLH
−
species is treated as the EAC.
Figure 8.25 Normalized Tafel plots obtained from RDE voltammograms at different pH. CuL
2−
species is treated as the EAC.
Figure 8.26 Comparison of experimental (symbols) and simulated (lines) voltammograms.
Figure 8.27 Experimental voltammograms of Sn(II) reduction obtained under natural convection conditions at various pH. Simulated reversible voltammograms are given in the inset.
Figure 8.28 Distribution of Sn(II) citrate complexes versus normalized cathodic current density. The data for the SnLH
−
species are given in the inset in semilogarithmic coordinates.
Figure 8.29 Variations of LH
3−
and L
4−
surface concentrations with normalized cathodic current density. The inset contains similar data for surface pH.
Figure 8.30 Comparison between experimental RDE voltammograms (symbols) and theoretical curves simulated with the indicated kinetic parameters. Tafel plots normalized to the ratio are shown in the inset.
Figure 8.31 Cathodic voltammograms obtained for 0.01 M Sn(II) solutions containing 0.02 M (lower curve, ordinate to the left) and 0.05 M (upper curve, ordinate to the right) of gluconate at pH 4.0. Direct measurements (solid lines) are compared with transformed EQCM data (symbols).
Figure 8.32 RDE voltammograms obtained for 0.01 M Sn(II) solutions containing 0.02 M (dotted lines) or 0.05 M (solid lines) of gluconate at indicated pH. The RDE rotating velocity (revolutions per minute) is indicated at the curves.
Figure 8.33 Levich plots obtained for 0.01 M Sn(II) solutions containing 0.02 M (dotted line) or 0.05 M (solid lines) of gluconate at indicated pH.
Figure 8.34 LPS voltammograms obtained for 0.01 M Sn(II) solutions containing 0.02 M of gluconate. The region of the second current peak (pH 2.0, upper part) is shown in a reduced scale (ordinate to the right). Potential sweep rates
v
are indicated at the curves.
Figure 8.35 Variations of the peak current density with the square root of potential sweep rate. The data obtained for 0.01 M Sn(II) and 0.02 M gluconate solution at different pH as indicated.
Figure 8.36 Dependencies of the peak potential on the potential sweep rate in the semilogarithmic coordinates obtained for 0.01 M Sn(II) and 0.02 M gluconate solution at different pH as indicated.
Figure 8.37 Nyquist plots obtained at open-circuit potentials (see Table 8.6) for the Sn electrode exposure for 20 min under open-circuit conditions to 0.01 M Sn(II) and 0.05 M gluconate solutions at different pH. Some characteristic frequencies are given at certain points. Impedance data obtained for the gluconate-free and gluconate-containing solutions at pH 2 are shown in the inset.
Figure 8.38 Faradaic equivalent circuits (full lines) and their description codes. The first three EC are taken from the literature (see text). The 4th EC is used in this book; the non-faradaic subcircuit is depicted with dashed lines.
Figure 8.39 Bode plots of impedance (|Z|) and phase shift (ψ), obtained under open-circuit conditions at different pH as indicated. Experimental data (symbols) are compared with the data (solid lines) simulated for EC whose parameters are listed in Table 8.7.
Figure 8.40 Correlation between the pH, the exchange current density, and the capacitance of charged interface. Open-circuit conditions.
Figure 8.41 Nyquist plots obtained for Sn(II)-free solutions at
E
oc
equal to −0.354 V (pH 3) and −0.392 V (pH 5). Some characteristic frequencies are given at certain points.
Figure 8.42 Selected types of the morphology of tin coatings and the respective impedance data.
Figure 8.43 Distribution of complex species in 0.01 M Zn(II) solutions containing 0.5 M of Na
2
SO
4
and gluconic acid (LH) with total concentration of 0.01 M (dashed lines) and 0.05 M (solid lines).
Figure 8.44 RDE voltammograms obtained for 0.01 M Zn(II) solutions containing 0.01 M (dashed lines) or 0.05 M (solid lines) of gluconate at pH 6. RDE rotating velocities (revolutions per minute) are indicated at the curves. Limiting current densities (
i
lim
) versus (Ω is an angular rotating velocity) are plotted in the inset.
Figure 8.45 Surface pH versus
i
/
i
d
simulated at different gluconate concentrations indicated at the respective curves. Reversible cathodic voltammograms are plotted in the inset.
Figure 8.46 Comparison of the experimental voltammogram (circles) with that (solid line) simulated by Eq. (8.51) with kinetic parameters obtained from the NTP presented in the inset.
Chapter 9: Electrochemical Deposition of Alloys
Figure 9.1 Concentration profiles in the steady-state diffusion layer under codeposition conditions. Two cases are shown: (a) less noble metal is not deposited (
i
2
= 0) and (b) both metals are codeposited (
i
2
≠ 0, dashed line).
Figure 9.2 Distribution of Sn(II) (solid lines) and Co(II) (dashed lines) citrate complexes at low (a) and high (b) concentration of ligand.
Figure 9.3 Voltammograms of Sn and Co codeposition recorded under natural convection conditions.
c
Co(II)
= 0.1 M,
c
cit
= 0.1 M, pH 5. Total concentration of Sn(II) (mol dm
−3
) is indicated on the curves. Limiting currents of Sn(II) reduction versus Sn(II) concentration are plotted in the inset.
Figure 9.6 Comparison of RDE voltammogram obtained experimentally at 450 rpm (symbols) with that simulated with given kinetic parameters of Sn(II) and Co(II) codeposition.
Figure 9.4 Distribution of complex species at the electrode surface versus normalized cathodic current density of Sn(II) reduction (
i
Co
= 0).
Figure 9.5 Tafel plots normalized to the ratio of
c
s
/
c
b
, where
c
is the respective concentration of the electrically active complex given at the plots. Transformation of RDE voltammetric data at 450 rpm.
Figure 9.7 Variations of elemental composition in the surface of coatings deposited at 10 mA cm
−2
from solutions containing different total concentration of Sn(II).
Figure 9.8 X-ray diffraction patterns of Sn–Co coatings containing 86 mass% of Co. The sample removed from the substrate.
Figure 9.9 X-ray diffraction patterns of Sn–Co coatings containing 37 mass% of Co. Line of Cu comes from the substrate.
Figure 9.10 Distribution of complex species in 0.01 M Zn(II) + 0.01 M Cu(II) solutions containing 0.5 M Na
2
SO
4
and gluconic acid with total concentration of 0.02 M (dashed lines) and 0.05 M (solid lines).
Figure 9.11 Equilibrium potentials of Cu|Cu
2+
H
2
|H
+
and of Zn|Zn
2+
electrodes calculated from distribution data (Figure 9.10).
Figure 9.12 RDE voltammograms obtained for 0.05 M sodium gluconate solutions at pH indicated at the curves (Cu electrode, 1250 rpm). Limiting current densities (
i
lim
) versus pH are plotted in the inset.
Figure 9.13 Net (solid line) and partial (symbols and dashed lines) voltammograms obtained for the solution of indicated composition. RDE: 1250 rpm. Zinc content in the coatings, obtained at other gluconate concentrations, is presented in the inset.
Figure 9.14 RDE voltammograms obtained for 0.05 M sodium gluconate solutions at pH indicated at the curves (Cu electrode, 1250 rpm). Limiting current densities (
i
lim
) versus pH are plotted in the inset.
Figure 9.15 RDE voltammograms obtained for electrodes in mixed Cu(II) and Zn(II) gluconate solutions at pH 7.0 and different intensity of forced convection (solid lines). The dashed curve was obtained in the absence of Cu(II) and Zn(II). Limiting current densities in Levich coordinates are plotted in the inset.
Figure 9.16 RDE voltammograms obtained at 440 (inset) and 1250 rpm for 0.01 M Zn(II) and Cu(II) solutions at different gluconate concentrations that are indicated at the respective curves.
Figure 9.17 Auger spectra of Cu–Zn coatings deposited at –0.6 V in the solution containing 0.01 M Zn(II), 0.01 M Cu(II), and 0.5 M Na
2
SO
4
at pH 6.0. The thickness (
d
) of surface layer deleted with Ar
+
beam is indicated at the respective curves.
Figure 9.18 Auger spectra of Cu–Zn coatings deposited at the indicated potentials. The solution composition is the same as in Figure 9.17.
Figure 9.19 An example of distribution of elements at different depths (
d
) of Cu–Zn coatings deposited at −0.9 V in the solutions of indicated composition. The partial fraction of ZnO is shown by a dotted line.
Figure 9.20 Upper part: distribution of copper and zinc in the coatings deposited at different potentials in sulfate-free (dotted lines) and sulfate-containing (solid lines) solutions. The content of carbon and oxygen is shown in the lower part. EDS data.
Figure 9.21 SEM images of Cu–Zn deposits obtained at the indicated potentials in the solution with 0.04 M (left side images) and 0.1 M (right side images) of gluconate.
Figure 9.22 XRD patterns for CuZn coatings electrodeposited at different potentials in the electrolyte solution containing 0.1 M of gluconate.
Figure 9.23 XRD patterns for Cu–Zn coatings electrodeposited at a potential of −0.97 V in the solutions with different amounts of gluconate.
Figure 9.24 Cathodic voltammograms obtained for polyether-free Cu(II) solutions (lines) and in the presence of laprol (circles) or PEG-300 (triangles). Rotation velocity of RDE (revolutions per minute) is indicated at the respective curve. Voltammograms for Cu(II)-free 0.6 M H
2
SO
4
solutions were obtained in the absence (line) and in the presence of laprol (circles).
Figure 9.25 Cathodic voltammograms obtained at 440 rpm for 0.01 M Sn(II) solutions containing laprol, the concentration of which (mg dm
−3
) is given at the respective curve. The effect of the intensity of forced convection at −0.38 V is presented in the inset in Levich coordinates.
Figure 9.26 Equivalent circuit and Nyquist plots obtained at different exposure times
τ
of tin electrode in 0.01 M Sn(II) solutions containing 0.02 M of tetraethylene glycol (TEG). The open-circuit potential
E
oc
= −0.25 V is applied.
Figure 9.27 Variations of the exchange current density
i
0
(ordinate to the left) and the effective double-layer capacitance
C
dl
(ordinate to the right). Sn electrode was kept for the time
τ
in the Sn(II) solution of indicated composition.
Figure 9.28 Adsorption isotherms obtained for tin electrode from impedance (triangles) and voltammetric (circles) data. Experimental data are fitted to Frumkin isotherm (solid lines) with the listed parameters.
Figure 9.29 Comparison of Nyquist plots obtained for the copper (upper part) and tin (lower part) electrodes in 0.01 M Cu(II) or Sn(II) solutions containing laprol and 30 μM of different halides. Open-circuit conditions.
Figure 9.30 Normalized Tafel plots obtained for 0.01 M Cu(II) containing different amounts of tetraethylene glycol and 30 μM of chloride (upper part, ordinate to the left) or bromide (lower part, ordinate to the right).
Figure 9.31 Image of surface cluster. Two TEG molecules form complex with Cu
+
ion that is attached to copper surface via specifically adsorbed halide X
−
.
Figure 9.32 Cathodic RDE voltammograms transformed into NTP. 0.01 M Cu(II) solutions contain 10 mM of different EG oligomers as indicated.
Figure 9.33 Variations of exchange current densities
i
01
obtained for 0.01 M Cu(II) solutions containing 30 μM Br
−
and indicated PEGs. Their amount is transformed into “concentration of unit chains.”
Figure 9.34 Nyquist plots obtained for tin electrode in 0.01 M Sn(II) solutions containing 0.01 M of different EG. High-frequency region is shown in the inset. Open-circuit potential
E
oc
= −0.25 V, exposure time
τ
= 30 min.
Figure 9.35 Effect of PEG-6000 on voltammograms of copper and tin codeposition. The concentrations of PEG (in mg dm
−3
) are given at the respective curves. Cu-coated RDE, 1250 rpm.
Figure 9.36 Cyclic voltammograms obtained for the solution of indicated composition. Direct and reverse scans are presented by solid and dashed lines, respectively. The onset of reverse scans is indicated by circles. The positions of equilibrium potentials of Cu|Cu
2+
and Sn|Sn
2+
electrodes are given on abscissa axis.
Figure 9.37 Effect of forced convection on voltammograms recorded using rotating disc electrode (RDE) at different reverses per minute (rpm). The positions of equilibrium potentials of Cu|Cu
2+
and Sn|Sn
2+
electrodes are given on abscissa axis. The inset demonstrates the Levich behavior of peak currents. The dashed line represents limiting currents obtained for Cu(II) reduction in Sn(II)-free solutions.
Figure 9.38 XRD patterns of Cu–Sn coatings deposited at indicated potentials in the solutions containing 0.01 M Cu(II), 0.01 M Sn(II), 1 M H
2
SO
4
, and 0.1 g dm
−3
PEG-40000.
Figure 9.39 Phase composition of bronze coatings obtained at −0.1 V in the solutions containing different polyethylene glycols. XRD data are normalized with respect to XRD peak 111 of α-CuSn
fcc
phase.
Figure 9.40 Dependencies of oscillation amplitude,
i
A
(ordinate to the left), and its frequency,
f
(ordinate to the right), on electrode potential,
E
. A typical shape of current oscillations is shown in the inset.
Figure 9.41 Nyquist plots obtained at different potentials for the solution containing 0.1 M Cu(II), 0.2 M Sn(II), 1 M H
2
SO
4
, and 5 g dm
−3
laprol. A frequency in Hertz is given at some points. The data shown in parts
a–c
of the Figure were obtained at potentials indicated by the respective symbols on the voltammogram (inset). Electrode surface ∼0.3 cm
2
.
Figure 9.42 Influence of an external resistance (indicated at the curves) on the shape of voltammograms.
c
Cu(II)
= 0.09 M.
Figure 9.43 Linear stability diagrams. Experimental plots show the onset of oscillations observed by insertion of an external resistor,
R
ext
, at constant applied voltage,
V
. Duration of electrolysis equals about 10 min (dashed line) and 20 (solid line) min. Coordinates of points indicated by crosses were determined from the impedance data.
Figure 9.44 Distribution of complex particles in solutions containing 10 mM Co(II), 10 mM Mo(VI), and (left side) 15 mM or (right side) 40 mM citric acid.
Figure 9.45 Dependencies of equilibrium potentials of partial processes on pH of solutions containing 10 mM Co(II), 10 mM Mo(VI) and different concentrations of citric acid (mM) as indicated.
Figure 9.46 Cathodic voltammograms obtained in solutions containing 0.04 M tartaric acid and 0.3 M K
2
SO
4
with pH 3.0 at different potential sweep rates (
v
) as indicated. Inset: dependence of peak current on at different pH.
Figure 9.47 Cathodic voltammograms obtained in solutions containing 0.12 M malic acid and 0.25 M MgSO
4
with pH 5.0 at different potential sweep rates (
v
) as indicated. Inset: dependence of peak current on at different pH.
Chapter 10: Spontaneous Formation of Photosensitive Cuprous Oxide Layers
Figure 10.1 Frequency variations of quartz crystal oscillations recorded in 0.01 M Cu(II) solutions containing 0.04 M glycolic acid (pH 5.9), 0.04 M β-alanine (pH 5.6) or 0.005 M ethylenediamine (pH 5.3), and 0.3 M K
2
SO
4
as a supporting electrolyte. Open-circuit potentials
E
oc
are equal to 0.20, 0.24, and 0.25 V, respectively. Data obtained for corrosion system (0.5 M Na
2
SO
4
, pH 5.6) are shown at right ordinate.
Figure 10.2 Frequency variations of quartz crystal oscillations recorded in 0.01 M Cu(II) solutions containing 0.04 M maleic acid and 0.3 M K
2
SO
4
at different pH as indicated. Open-circuit conditions,
E
oc
= 0.23 V.
Figure 10.3 Comparison of voltammetric (line) and EQCM (circles) data obtained for a Cu(II)–ethylenediamine solution of composition as indicated with
v
= 5 mV s
−1
. The Cu electrode was exposed to the solution under open-circuit conditions for 20 min.
Figure 10.4 Variations of
E
p
with log
v
at the various exposure times
τ
indicated on the curves.
Figure 10.5 Variations of peak current with potential scan rate at the various exposure times
τ
indicated at the curves. The charge
Q
employed for Cu
2
O reduction is given in the inset.
Figure 10.6 Voltammograms recorded at 20 °C in solutions containing 0.01 M Cu(II), 0.005 M ethylenediamine, and 0.3 M K
2
SO
4
(pH 5.3). Prior to experiments, copper electrodes were exposed to the same solution at temperatures indicated at the curves.
Figure 10.7 Onset of the photopotential under open-circuit conditions in a β-alanine solution of composition as indicated.
Figure 10.8 Photopotential generated with light pulses of different wavelengths. Respective arrows indicate the start and the end of light perturbation. The initial exposure time
τ
= 10 min.
Figure 10.9 Dependencies of photopotential on quantum energy at different power densities and wavelengths of monochromatic light. Open-circuit conditions.
Figure 10.10 Cyclic voltammogram recorded under chopped illumination conditions. Polychromatic irradiation, the initial exposure time
τ
= 20 min.
Figure 10.11 Inversion of photocurrent. The initial exposure time
τ
= 1 h.
Figure 10.12 Energy correlation between band edges and the Fermi levels of electrode reactions in aqueous solution of 0.01 M Cu(II) and 0.04 M β-alanine at pH 5.5.
Figure 10.13 Typical photo (ordinate to the left) and EQCM responses observed in the β-alanine system. Laser illumination (
λ
= 488 nm,
N
= 0.1 W cm
−2
) was applied at
t
> 0.
Figure 10.14 Variations of surface pH under chopped illumination conditions in the β-alanine system at different distances Δ
x
between the Cu surface and an Sb|Sb
2
O
3
microelectrode.
c
Cu(II)
= 0.01 M,
c
L
= 0.04 M, bulk pH 5.6.
Figure 10.15 Morphology of freshly prepared copper coating (a) and of that exposed for 30 min in the solution containing 0.01 M Cu(II), 0.04 M gluconate, 0.3 M K
2
SO
4
at pH 5 (b). Respective Nyquist plots obtained at the open-circuit potentials are shown in the insets.
Figure 10.16 Nyquist plots recorded in 0.01 M Cu(II) solution at pH 4.9.Before measurements, the copper electrodes were exposed for the times indicated in the solutions containing: (a) 0.01 M Cu(II), 0.005 M ethylenediamine (pH 5.3) and (b) 0.01 M Cu(II), 0.04 M β-alanine (pH 6.1). 0.3 M K
2
SO
4
was present in all the cases.
Figure 10.17 Experimental impedance spectrum taken from Figure 10.16a at
τ
= 30 min (symbols) and that simulated for given equivalent circuit (lines) at the following values of its parameters:
R
Ω
= 0.26 Ω cm
2
,
R
ox
= 122 Ω cm
2
,
Y
ox
= 5.3 × 10
−5
Ω
−1
cm
−2
s
0.628
,
R
1
= 307 Ω cm
2
,
Y
W1
= 8.34 × 10
−3
Ω
−1
cm
−2
s
0.5
,
R
2
= 10 Ω cm
2
,
Y
W2
= 1.42 × 10
−4
Ω
−1
cm
−2
s
0.5
, and
Y
Qdl
= 2.25 × 10
−4
Ω
−1
cm
−2
s
0.776
.
Figure 10.18 Experimental voltammograms for pH 8.3 recorded at different rotation velocities as indicated.
Figure 10.19 Comparison between experimental (symbols) and theoretical (solid lines 1 and 2) voltammograms simulated with two different sets of kinetic parameters.
Chapter 11: Hydrogen Evaluation Involving Ligands as Proton Donors
Figure 11.1 Comparison of voltammetric data obtained at different potential sweep rates
v
for Cu(II)-containing (solid lines) and Cu(II)-free (symbols) solutions. The limiting currents of Cu(II) reduction (dotted lines) served as base lines for the latter data.
Figure 11.2 Voltammograms obtained for 0.02 M gluconic acid solutions containing 0.5 M Na
2
SO
4
at different pH. Potential sweep rates are indicated at the respective curves.
Figure 11.3 Comparison of voltammetric data obtained at
v
= 0.2 V s
−1
for 0.02 M gluconic acid solutions containing different supporting electrolytes as indicated.
Figure 11.4 Peak current densities versus obtained at different pH for 0.04 M malic and tartaric acid solutions.
Figure 11.5 Peak current densities versus obtained at different pH for 0.02 M (dashed lines) and 0.05 M (solid lines) gluconic acid solutions.
Figure 11.6 Normalized Tafel plots obtained at different potential sweep rates for 0.04 M glycolic (upper part) and tartaric (lower part) acid solutions. Indicated kinetic parameters are calculated from general regression lines.
Figure 11.7 Experimental slopes versus total concentration of proton donors. Summation of the data obtained for different solutions at 2.5 < pH < 4.0.
Figure 11.8 Dependencies of peak potentials on potential sweep rate presented in semilogarithmic coordinates. The data are obtained for 0.02 M gluconic acid solutions containing Cu(II) (part a) and for Cu(II)-free solutions (part b) the composition of which is given in the Table 11.2.
List of Tables
Chapter 3: Mass Transport
Table 3.1 Differential equations for various electrode geometries
Table 3.2 Expressions of
F
(
i,x,t
) function for
i
(
t
) signals of different forms
Table 3.3 Rate constants for [30, 31]
Table 3.4 The main set of parameters used in simulations
Chapter 5: Quantitative Modeling of Quasi-Reversible Electrochemical Processes Involving Labile Complexes of Metals
Table 5.1 Conditions for constant surface concentrations
Table 5.2 Values of
β
4
and
k
s
determined for Ag|Ag(I), SCN
−
system from impedance data
c
M
= 0.05 M
Chapter 6: Determination of Mechanism of Electrochemical Processes Involving Metal Complexes
Table 6.1 Characteristics of Cu(II)–glycine isopotential solutions series (pH 3.5)
Chapter 8: Electrochemical Processes in Real Systems
Table 8.1 Characteristics of isopotential solutions involving Ag(I) cyanide complexes
Table 8.2 Complex species predominating in acid Cu(II)–HA solutions containing an excess of ligand (
r
=
c
L
/
c
M
= 4) at pH < 6
Table 8.3 Composition of IPS and parameters of the equivalent circuit
Table 8.4 Stability constants used in simulations
Table 8.5 Kinetic parameters for two mechanisms of Cu(II) reduction in the solutions containing 0.025 M Cu(II), 0.175 M citrate, and 0.3 M K
2
SO
4
as a supporting electrolyte
Table 8.6 Effective diffusion coefficients evaluated by different methods
Table 8.7 Parameters of the equivalent circle
R
Ω
([
R
ct
W
(
R
a
Q
a
)]
Q
dl
) and related parameters determined for nonpolarized Sn electrode in 0.01 M Sn(II) solution containing 0.05 M gluconate and 0.5 M Na
2
SO
4
at different pH.
R
Ω
= 1.87 ± 0.04
Ω
cm
2
Table 8.8 Quantitative characteristics of equilibria in Zn(II) sulfate solutions containing gluconic acid (LH)
Chapter 9: Electrochemical Deposition of Alloys
Table 9.1 Cumulative stability constants of Sn(II) and Co(II) citrate complexes used in simulations
Table 9.2 Binding energies detected in XP and Auger spectra
Table 9.3 Effect of polyethylene glycols HO–(CH
2
–CH
2
–O–)
m
H on kinetic parameters of Cu
2 +
+ e → Cu
+
charge transfer process. 0.01 M Cu(II) solutions containing 30 μM Br
−
and indicated quantities of PEG
Table 9.4 Cumulative stability constants of Co(II) and Mo(VI) citrate complexes
Chapter 11: Hydrogen Evaluation Involving Ligands as Proton Donors
Table 11.1 Selected stability constants of organic acids
Table 11.2 Equilibrium characteristics acid solutions and kinetic parameters of hydrogen evolution
Related Titles
Gileadi, E.
Physical Electrochemistry
Fundamentals, Techniques and Applications
2011
Print ISBN: 978-3-527-31970-1; also available in electronic formats
Schlesinger, M., Paunovic, M. (eds.)
Modern Electroplating
5th Edition
2010
Print ISBN: 978-0-470-16778-6; also available in electronic formats
Endres, F., MacFarlane, D., Abbott, A. (eds.)
Electrodeposition from Ionic Liquids
2008
Print ISBN: 978-3-527-31565-9; also available in electronic formats
Arvydas Survila
Electrochemistry of Metal Complexes
Applications from Electroplating to Oxide Layer Formation
The Author
Prof. Dr. Arvydas Survila
Center for Physical Sciences & Technology
Goštauto str. 9
01108 Vilnius
Lithuania
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Print ISBN: 978-3-527-33877-1
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Preface
Chemical processes involving metal complexes can be found at every step, from the transformations observed in nature and ending with the various chemical industries, purposefully carried out by man. Among the latter are prominent processes occurring at the interface metal/solution, the end result of which is a production of electric energy or production of various products of electrolysis, including metallic coatings having a different purpose.
Qualitative anticorrosive, decorative, abrasion-resistant, and heat-resistant coatings are usually obtained by the electrolysis of solutions containing coordination compounds (complexes) of metals. Electrochemical processes involving these compounds are rather complicated because they proceed through several different stages, such as the mass transfer of chemically interacting particles, adsorption, charge transfer, formation of new phases, and so on.
Various problems of the electrochemistry of these systems have frequently been discussed in the literature including my book: A. Survila, Electrode Processes in Systems of Labile Complexes of Metals (Mokslas, Vilnius 1989), published sometime ago. Since then, a long time has passed and there has been progress in the field of theory and practice, in the field that deserves comprehension and generalization. In this regard, there was an interest to write a book in which all the major stages of electrochemical processes (mass transport, adsorption, charge transfer) are sequentially covered, putting special emphasis on their deep interrelation. I decided on this difficult task, using data published at different times in the literature, as well as theoretical and experimental material accumulated in the last half-century. In addition, it seemed appropriate to present in this book not only basic questions of electrochemistry of metal complexes including the actual plating problems, but also some other phenomena that would be possible to be classified as “related”. I hope that spontaneous formation of semiconducting oxide layers, appearance of current oscillations, specifics of hydrogen evolution could also be of interest to the reader.
The material presented in this book is divided into 11 chapters. A systematic analysis of electrochemical processes involving metal complexes starts with general considerations on equilibria in solutions (Chapter 1). Their main equilibrium properties are considered and general principles of quantitative description of their composition are presented. Acquaintance with the equilibrium properties of complex systems continues in Chapter 2, which analyzes the processes occurring at the interface metal/solution and discusses the electrodes of the first and second kinds. The principles of their quantitative descriptions are presented together with selected experimental data. Along with the known points, the reader will also find a description of other, less known self-extinguishing characteristics of these systems. This part of book is intended to provide background information, sufficient for an intelligible understanding of the material that is developed in next chapters.
Next chapters acquaint readers with the theory and common experimental practice for studying electrochemical reactions of metal complexes. Regularities of mass transport of chemically interacting particles considered in Chapter 3 serve for determining the surface concentrations of complexes and ligands. Furthermore, these data make it possible to reveal the peculiarities of electrochemical processes (Chapter 4) and form the basis for quantitative modeling of electrochemical processes (Chapter 5) and determining their mechanism (Chapter 6).
Theoretical developments are widely used in experimental investigation of real electrochemical systems (Chapters 8 and 9). The core part of the book deals with all important aspects of electroplating, including a systematic discussion of co-deposition of metals and formation of alloys. It also discusses such related subjects as oxide layer formation (Chapter 10) and hydrogen evolution as a side reaction (Chapter 11).
The material presented in this book are designed for a wide range of readers. A major part of the material included in this book was presented at Vilnius University for senior students who have completed introductory courses in chemistry of coordination compounds and electrochemistry, though the first two chapters are easy comprehensible even for younger students. Problems regarding the quantitative description of electrochemical processes and the determination of their mechanism differ in complexity. Some of them are aimed at senior graduate or postgraduate students; others suggest a higher level of competence and, it is hoped will also be of interest to professional electrochemists.
Materials relating to the processes occurring in real systems may be useful for people working in engineering or manufacturing. The same can be said about Chapter 10. Electrochemical mechanisms and the role of ligand in formation of light-sensitive oxide layers may be of interest to researchers who have less contact with the electrochemistry.
In the book, much space is allotted to theoretical and experimental research performed by the author at the Institute of Chemistry (at present, Center of Physical Sciences and Technology, Vilnius, Lithuania) in collaboration with a capital research team. I wish to acknowledge a valuable contribution of my coauthors, whose names appear in the literature references. Two persons I would like to mention particularly. One of them is a nice experimenter Stasė Kanapeckaitė, with whom I had a pleasure to work with successfully for several decades. Another is my wife Audronė Survilienė, who not only carried out a number of important experiments but also created the conditions for the successful work on this book.
Arvydas Survila
Vilnius, 2015
Symbols and Abbreviations
Subscripts
a
anodic
b
bulk
c
cathodic
ct
charge transfer
d
diffusion
dl
double layer
eq
equilibrium
fb
flat band
F
Faradaic
H
proton donors and acceptors
inv
inversion
lim
limiting
L
ligand
M
metal
N
Nernstian
O
oxidant
oc
open circuit
p
peak
pol
polarization
r
reaction
R
reductant
s
surface
Ω
ohmic
1/2
half-wave
Roman Symbols
a
activity
{X}
activity of species X
A
area
B
adsorption constant
c
concentration
[
X
]
concentration of species X
C
differential capacitance
D
diffusion coefficient
E
electrode potential
E
0
standard potential
E
o/
formal potential
Δ
E
a
activation energy
f
frequency
F
Faraday constant
G
Gibbs free energy
H
enthalpy
i
current density
i
0
exchange current density
I
ionic strength
j
imaginary unit
J
flux
k
rate constant of homogeneous reaction
K
stepwise stability constant
m
mass
M
molar mass
n
stoichiometric number of electrons involved in electrochemical reaction
average coordination number
N
A
Avogadro constant
Q
charge; constant phase element
r
radius
R
gas constant
R
resistance
s
complex variable
S
entropy
t
time
T
absolute temperature
u
auxiliary variable
v
potential scan rate
V
volume
w
rate of chemical reaction
W
Warburg impedance
x
coordinate (distance)
Y
admittance
z
i
charge number of ion
i
Z
impedance
Z
/
real part of impedance
Z
//
imaginary part of impedance
Greek Symbols
α
charge transfer coefficient
α
j
formation degree of species j
β
cumulative stability constant of complex species
β
H
cumulative stability constant of protonated ligand
γ
activity coefficient
Γ
adsorption (surface excess)
δ
diffusion layer thickness
ϵ
surface charge density
η
overvoltage
μ
electrochemical potential
ν
kinematic viscosity; stoichiometric coefficient
σ
surface tension (energy)
θ
surface coverage
τ
transition time; exposure duration
ψ
shift of electrical phase
ν
angular frequency
Ω
angular rotation velocity
Abbreviations
AES
Auger electron spectroscopy
AME
antimony microelectrode
CPE
constant phase element
DEL
double electric layer
EAC
electrically active complex
EC
equivalent circuit
EDTA
ethylenediamine tetraacetic acid
EDS
energy-dispersive X-ray spectroscopy
EIS
electrochemical impedance spectroscopy
EMF
electromotive force
EQCM
electrochemical quartz crystal microbalance
fcc
face-centered cubic
hcp
hexagonal close packed
IL
ideal lability
IPS
isopotential solutions
LL
limited lability
LPS
linear potential sweep
NTP
normalized Tafel plot
PEG
polyethylene glycol
RDE
rotating disk electrode
SAS
surface-active substance
scc
simple cubic cell
SEM
scanning electron microscopy
SERS
surface-enhanced Raman spectroscopy
UPD
underpotential deposition
VA
voltammetry
XP
X-ray photoelectron
XPS
X-ray photoelectron spectroscopy
XRD
X-ray diffraction
1Introduction
At present, coordination compounds are widely applied in various fields of science and technology. One hundred and fifty years have passed since the time when Cato Maximilian Guldberg and Peter Waage formulated the Law of Mass Action. They suggested that the driving force (chemical affinity) for both forward and backward reactions is equal when the mixture is at equilibrium (today, the expression for the equilibrium constant is derived by setting the chemical potential of forward and backward reactions to be equal). The elaboration of successful theory became one of the cornerstones of coordination chemistry. This branch of science started to develop rapidly only in the middle of the past century after Jannik Bjerrum announced his thesis [1] in 1941, which was later translated into many languages. The key to Bjerrum's method was the use of the then recently developed glass electrode and pH meter to determine the concentration of hydrogen ions in solution. Bjerrum recognized that the formation of a metal complex with a ligand was a kind of acid–base equilibrium: there is competition for the ligand, L, between the metal ion, Mn+, and the hydrogen ion, H+.
Main conceptions of this work, which have not lost their value and importance up to date, provided a strong stimulus for further investigations. The number of publications devoted to the problems of coordination compounds started to grow at a fast rate. The first calculations were done by hand using the so-called graphical methods. The next key development was the use of computer programs. This permitted the examination of more complicated systems. One can judge the intensity of the development of this sphere having compared a small number of works published before 1941, containing abundance of data on the characteristics of various systems collected in several volumes of “Stability Constants” [2–7]. Later, these data were critically assessed when publishing a reference book [8] containing the most reliable values of constants. Currently, a lot of critical reviews were published (most of them in the Pure and Applied Chemistry), and thousands of stability constants can be found in different databases.
Coordination compounds found their application in various areas including plating, which did not lose its importance until now. Much interest in the recent investigations was shown in the problems of an applied nature, underlining the effect of plating parameters such as current density, deposition time, temperature, and pH in relation to the phase composition, structure, and quality of deposit. To gain a better insight into the nature of electrochemical processes involving metal complexes, the kinetic regularities of the processes should be revealed and considered invoking adequate theoretical models. These problems take a considerable place in this book.
We start with the consideration of equilibrium processes taking place in the solutions containing metal complexes. As the relevant theoretical aspects are widely elucidated in the literature, we present only the most general knowledge that is closely related to the problems to be considered.
1.1 Equilibrium Properties of Complex Systems
1.1.1 General Definitions
A molecular entity formed by the reversible association of two or more chemical species (molecules, atoms, or ions) is referred to as complex. Very different kinds of bonds can be involved in this formation, but in the following, the charge transfer complexes will be considered for the most part. These compounds contain the central ion (most commonly a metal ion) that is bound with several groups of electron donors called ligands. They can be both neutral particles and ions.
The number of bonds that the central ion forms with electron-donor species is designated as its coordination number (π-bonds are not considered in determining the coordination number). In turn, depending on the number of bonds that a single ligand particle forms, they are classified as uni- or monodentate, bidentate, and so on, ligands. Ligands, bound with the central particle by coordination bonds, constitute an inner coordination sphere.
The so-called chelates belong to the category of inner-sphere complexes. The chelating ligands have several unshared electron pairs giving rise to two or more coordination bonds. The term chelate is derived from the Greek word for the claw of a crawfish, as the ligand grasps the metal ion like a crawfish grasps its catch with its claws. Such complexes are much more stable than the compounds made of monodentate ligands because of the liberation of a larger number of solvent molecules. This leads to an increase in the number of species present in the system and, therefore, an increase in entropy. An increase in entropy makes the formation of the chelated complex more favorable.
Depending on the number of central particles in a single molecule of a complex compound, complexes are categorized into mononuclear and polynuclear ones. In the latter, metal ions can be bound directly or through a ligand particle (“ligand bridge”).
A certain part of ligands can have no direct contact with the central particle with which they are linked by weaker (electrostatic or van der Waals) interactions or a hydrogen bond. The position of such ligands in space around the central ion is not strictly defined. They constitute a second coordination sphere, and compounds of this type are calledouter-sphere complexes. Main attention in this book is concentrated on the processes involving mononuclear inner-sphere complexes.
1.1.2 Equilibrium in the Solutions of Complex Compounds
Solvated ions, which form when dissolving substances in some solvent W, in essence are coordination compounds with a saturated inner coordination sphere. If the solvent is water, the so-called aqua complexes form. In this case, the number of immediately bound monodentate ligands (H2O molecules) is equal to the coordination number, N, of the metal ion.
Upon addition of ligands X and Y to the solution containing solvate complexes MWn+, the former can displace part of W molecules in the inner coordination sphere forming extra complexes. Usually, this process takes place until equilibrium is established:
1The constant of this equilibrium is called theoverall or cumulative stability constant of the complex. The quantitative expression for cumulative stability constant, βpq, can be greatly simplified by removing those terms that are constant. The number of water molecules attached to each metal ion is constant. In dilute solutions, the concentration of water is effectively constant. Then, the equation written without indicating molecules of the solvent becomes:
Here, {X} should be read as “the activity of X” and likewise for the other terms in curly brackets. The reciprocal quantity is called instability constant. As activity is the product of concentration and activity coefficient (γ), this definition could also be written as
where [X] represents the concentration of species given in square brackets.
