Physicochemical model for choosing complexes for chromium-plating solutions based on Cr(III) compounds

Article abstract of DOI:10.1007/s11173-005-0027-0

A prognostic physicochemical model for choosing complexes for chromium-plating solutions is constructed on the basis of a combination of the thermodynamic principles and data on the kinetics of some electrochemical reactions. It is shown that high-quality chromium coating can be produced from solutions of Cr(III) complexes, whose logarithm of stability constants ranges from 10 to 20, and the logarithm of stability constants of Cr(II) complexes formed in electrolysis ranges from 7 to 10. The influence of the nature of ligands on chromium electrodeposition is studied. Using the model proposed, a chromium-plating solution based on a chromium(III) malonate complex is developed. This solution makes it possible to produce high-quality coatings in a wide interval of current densities.

Full text of DOI:10.1007/s11173-005-0027-0

Russian Journal of Coordination Chemistry, Vol. 31, No. 1, 2005, pp. 14–18. Translated from Koordinatsionnaya Khimiya, Vol. 31, No. 1, 2005, pp. 17–21.
Original Russian Text Copyright © 2005 by Vinokurov, Demidov, Bondar’.
Physicochemical Model for Choosing Complexes
for Chromium-Plating Solutions Based on Cr(III) Compounds
E. G. Vinokurov*, A. V. Demidov*, and V.V. Bondar’**
*
Mendeleev University of Chemical Technology, Miusskaya pl. 9, Moscow, 125190 Russia
*
* All-Russia Institute of Scientific and Technical Information, Baltiiskaya ul. 14, Moscow, Russia
Received December 4, 2003
Abstract—A prognostic physicochemical model for choosing complexes for chromium-plating solutions is
constructed on the basis of a combination of the thermodynamic principles and data on the kinetics of some
electrochemical reactions. It is shown that high-quality chromium coating can be produced from solutions of
Cr(III) complexes, whose logarithm of stability constants ranges from 10 to 20, and the logarithm of stability
constants of Cr(II) complexes formed in electrolysis ranges from 7 to 10. The influence of the nature of ligands
on chromium electrodeposition is studied. Using the model proposed, a chromium-plating solution based on a
chromium(III) malonate complex is developed. This solution makes it possible to produce high-quality coatings
in a wide interval of current densities.
INTRODUCTION
The purpose of this work is to construct a physico-
chemical model that can be used to choose the Cr(III)
When developing new solutions containing Cr(III) complexes taking into account their constants of forma-
compounds for the electrodeposition of chromium tion and stability constants of the Cr(II) complexes and
coatings, many researchers proposed amino [1], carb- select ligands for chromium-plating solutions.
oxylic [2], dicarboxylic [3–5], and hydroxycarboxylic
[
6] acids and some other compounds [7] forming com-
3
+
plexes with Cr . However, with a diversity of chro-
mium complexes, it is difficult to choose ligands for
developing “trivalent” chromium-plating solutions.
EXPERIMENTAL
Electrolysis was carried out in a solution of compo-
sition KCr(SO ) , 0.2 mol/l; H BO , 1.0 mol/l; Na SO ,
4
2
3
3
2
4
The studies of chromium electrodeposition from
solutions of the chromium complexes [8–10] revealed
no direct relationship between the stability of the
Cr(III) complexes formed, the cathodic polarization,
and the formation of coatings, whereas the influence of
ligands on chromium electrodeposition is explained by
specific properties of passivation layers on the cathode
surface. At the same time, the rate of electroreduction
1
.0 mol/l. A ligand in a concentration providing the
complete substitution of water molecules in the coordi-
3+
nation sphere of Cr ions was added to the solution.
Mono- and polybasic acids were sources of ligands in
solutions for chromium electrodeposition. The required
concentration of the ligand was calculated with account
of its assumed dentate number (d) and coordination
3+
number of the Cr ions equal to six
3+
–
2+
Cr + e
Cr at a mercury electrode correlates
with the spectral characteristics of some Cr(III) com-
plexes [11]. The authors of [12] attempted to find a rela-
tioanship between the addition of complexones in low
6
d
c = --c .
L
Cr
–
2
concentrations (2 g/l, ~10 mol/l) to chromium-plating
After all components were mixed, the solutions
were heated and stored at 70–80°ë for 20 min, then
cooled and stored for 2 days such that complex forma-
tion is complete. This procedure made it possible to
attain a quasi-equilibrium state and reproducible results
3
+
–
solutions (containing Cr , HCOO , (NH ) SO , and
4
2
4
H BO in concentrations 0.4, 0.66, 1.5, and 0.65 mol/l,
3
3
respectively) and the stability of complexes formed. It
is recommended in [6, 12, 13] to use ligands binding
3+
Cr ions into complexes of moderate stability in chro- of electrodeposition [14]. The required pH values were
mium-plating solutions. However, no quantitative char- achieved using H SO or NaOH solutions. The elec-
2
4
acteristics of the complexes or ligands are reported. trodeposition of coatings was carried out in an interval
When choosing ligands, the stability of the Cr(II) com- of pH 1.5–3.5 with an increment of 0.5 at room temper-
2
plexes, which are intermediate species in the reduction ature and current densities from 2 to 60A/dm with tita-
3
+
of the Cr ions to the metal, is not considered, as a rule, nium dioxide–iridium anodes. The electrolysis time
probably, because these data on the Cr(II) complexes was 5–15 min, which made it possible to obtain coat-
are scarce.
ings 0.5–2 µm thick.
1
070-3284/05/3101-0014 © 2005 Pleiades Publishing, Inc.

PHYSICOCHEMICAL MODEL FOR CHOOSING COMPLEXES
15
RESULTS AND DISCUSSION
3+
3+
logβ°(Cr L ) > logβ°(Cr A )



n
n
m
m
(
5)
Physicochemical model for choosing ligands for
chromium-plating solutions. The physicochemical
model for choosing ligands was constructed on the
basis of a combination of the thermodynamic principles
and known data on the kinetics of some electrochemi-
cal reactions.
The physicochemical model for choosing ligands in
the development of complex electrolytes for chromina-
tion should take into account the stepwise reduction of
Cr ions to the metal with the formation of stable ions
of intermediate valence. The general scheme of this
process in the absence of the coordination sphere rear-
rangement can be described as follows:
2
+
2+
logβ°(Cr L ) > logβ°(Cr A ).
n
n
m
m
3
+
2+
2
. A ligand should form with Cr and Cr ions the
complexes, whose stability constants are higher than
those of the corresponding hydroxo complexes.
This condition can be described mathematically by
the following system of inequalities:
3
+
3+
logβ°(Cr L ) > logβ°(Cr OH)



n
n
1
3+
(
6)
2
+
2+
logβ (Cr L ) > logβ (Cr OH).
°
°
n
n
1
2
+
3. A ligand should form with Cr ions a complex,
whose stability provides the standard electrode poten-
tial E[°Cr2+ of reaction (2) with a positive value higher
3
+
3 + nz
+ e–
[Cr L ]2 + nz,
2+
[
Cr L ]
(1)
(2)
n
n
L ]
2
+
2 + nz
+ 2e–
Cr + nLz,
n
[
Cr L ]
n
than the potential of the beginning of active discharge
of water molecules E*.
where z is the charge of the ligand.
This condition can be written as an inequality
Hydroxonium ions and water molecules are reduced
simultaneously with the reduction of the chromium
complexes
E° 2+
> E*.
(7)
[Cr Ln]
+
–
2
H O + 2e
H + 2H O,
(3)
°
Cr L ]
3
2
2
Let us express E[ 2+ in terms of the standard elec-
n
–
–
2+
–
2
H O + 2e
H + 2OH .
(4) trode potential of the reaction Cr + 2e
Cr and a
2
2
stability constant of a discharging complex
A model for choosing ligands cannot be constructed
when thermodynamic principles are used only, because
the standard electrode potential of reaction (2) is more
negative than the potentials of reactions (3) and (4),
2.3RT
2+
E° 2+
= E°Cr2+ – ------------- -- logβ°(Cr L )
(8)
n
n
[Cr L ]
n
2F
indicating that the electrodeposition of chromium is and insert this expression into inequality (7). After sim-
thermodynamically impossible.
The accumulation of éç ions in the near-electrode
layer together with an insufficient stability of the Cr
ple transformations, we have
–
2
+
2F
.3RT
3
+
logβ°(Cr L ) < ------------- -- (E° 2+ – E*).
(9)
n
n
Cr
2
2
+
and Cr complexes brings about the formation of vari-
ous hydroxo complexes and, finally, chromium hydrox-
ides, as a result of which the reduction of the chromium (formation of stable ions of intermediate valence), we
complexes in reaction (2) terminates. Therefore, the can formulate another condition.
Since the complexes are reduced in several steps
rate of reduction of water molecules should not be
higher than some critical value determined by the rate
of reduction of the Cr and Cr complexes. The
kinetic stability of water molecules during their reduc-
. A ligand should form with Cr3+ and Cr2+ ions
complexes, whose stability provides the standard elec-
4
3
+
2+
trode potential E°[Cr3+
2+
of reaction (1) such that
Ln]/[Cr Ln]
tion was characterized further by the potential of the it is more positive than the potential of the beginning of
beginning of active reduction of water molecules (E*), active discharge of water molecules E*.
which was found as a potential that conventionally
The mathematical formulation of this condition can
divided the polarization curve of hydrogen evolution
be written as an inequality
into two regions of high and low resistance to the
charge transfer.
E[°Cr3+
2+
> E*.
(10)
in terms of the stan-
L ]/[Cr L ]
n
n
The concepts presented above make it possible to
formulate the following rules of choosing ligands for
solutions containing chromium complexes.
Let us express E°[Cr3+
2+
L ]/[Cr L ]
n
n
3+
–
dard electrode potential of the reaction Cr + e
Cr and the stability constant of the complexes
3
+
2+
1
. A ligand should form with Cr and Cr ions the
2+
complexes, whose stability constant (β) is higher than
2
+
those of complexes (predominant in the solution) with
2
.3RT
F
β
°
(Cr L )
n
z
anions of a salt (A ) and/or a supporting electrolyte.
E
°
3+
2+
= E°
3+
2+
+ ------------- -- log------------------------- --
[
Cr L ]/[Cr L ]
Cr /Cr
3+
n
n
β°(Cr L )
n
n
The mathematical expression of this condition can
be described by the following system of inequalities:
(11)
RUSSIAN JOURNAL OF COORDINATION CHEMISTRY Vol. 31 No. 1 2005

1
6
VINOKUROV et al.
and insert this expression into inequality (10)
2
.3RT
3+
E° 3+ = E°Cr3+ – ------------- -- logβ°(Cr L )
(15)
(16)
n
n
2
+
3+
Cr Ln
3F
12) and insert this expression into inequality (14)
3F
logβ°(Cr L ) < logβ°(Cr L )
n
n
n
n
(
F
.3RT
–
------------- -- (E° 3+ 2+ – E*).
Cr /Cr
2
3+
logβ°(Cr L ) < ------------- -- (E° 3+ – E*).
n
n
Cr
2
.3RT
Taking into account a certain probability of dis-
3
+
charge of the [Cr L ] complexes with a simultaneous
n
The choice of a ligand that does not aggravate sew-
age purification is also very important for the develop-
ment of solutions for metal electrodeposition. If it is
assumed that heavy metal hydroxides (in our case,
transfer of three electrons, one can formulate one more
condition.
3
+
5
. A ligand should form with Cr ions a complex,
whose stability provides the standard electrode poten-
Cr(OH) ) are formed at the first step of sewage neutral-
3
tial E[°Cr3+ of the reaction
ization by the reagent method, then the following con-
dition can be formulated.
6. A ligand should form with Cr ions a complex,
whose stability constant is lower than the solubility
product (SP) of chromium hydroxide.
L ]
n
3
+
3 + z
+ 3e–
Cr + nLz,
3+
[
Cr L ]
(13)
n
such that it is more positive than the potential of the
beginning of active discharge of water molecules E*.
The mathematical formulation of this condition is
expressed by an inequality
The mathematical formulation of this condition can
also be written as an inequality
3
+
E° 3+ > E*.
(14)
logβ°(Cr L ) < pSP(Cr(OH) ).
(17)
Cr Ln
n
n
3
Since the proposed ligand should simultaneously
meet all above requirements, this can be expressed by
Cr and the uniting all mathematical equation (6), (9), (12), (16),
and (17) into a system of inequalities
Let us express E°Cr3+ through the standard elec-
Ln
3
+
–
trode potential of the reaction Cr + 3e
stability constant of a reducing complex
3
+
3+

















logβ°(Cr L ) > logβ°(Cr OH)
(‡)
n
n
1
2
+
2+
logβ°(Cr L ) > logβ°(Cr OH)
(a')
n
n
1
2
+
2F
.3RT
logβ°(Cr L ) < ------------- -- (E° 2+ – E*)
(b)
n
n
Cr
2
(
18)
2
+
3+
F
.3RT
logβ°(Cr L ) < logβ°(Cr L ) – ------------- -- (E° 3+ 2+ – E*) (c)
n
n
n
n
Cr /Cr
2
3
+
3F
logβ°(Cr L ) < ------------- -- (E° 3+ – E*)
(d)
(e)
n
n
Cr
2.3RT
logβ°(Cr L ) < pSP(Cr(OH) )
3
+
n
n
3
Numerical simulation. After the values of some characteristics of the ligand, for instance, an exponent
physical magnitudes presented in Table 1 are inserted of the dissociation constant (K) of protonated ligand.
into the system of inequalities (18) and the latter is In [17], we presented equations relating the stability
solved by the graphical method, a region Ω (figure) of constants of the Cr(II) and Cr(III) complexes to the sum
admissible values of logarithms of stability constants of of exponents of dissociation constants of protonated
chromium complexes of different valence is obtained forms of the ligands
that meet all (or almost all) requirements for choosing
ligands. The solution of the system is an interval of logβ
Z
logβ°(Cr L) = a (ΣpK ).
(19)
1
Z
m
values for the Cr(III) complexes from 10 (logβmin ) to The parameters of the Panteleon–Ecka equation (λZ)
0 (logβmax ) and for the Cr(II) complexes an interval
from 7 to 9.8.
2
logβ = nlogβ – λ n(n – 1)
°
°
(20)
n
1
Z
were also determined in this work to calculate the sta-
Since the stability constants for some chromium bility constants of the Cr(II) and Cr(III) complexes with
complexes are unknown, it seems reasonable to deter- n bidentate ligands (n = 2, 3), where Z is the valence of
mine boundaries of both the stability constants and the chromium ions, and a and λ are proportionality
Z
Z
RUSSIAN JOURNAL OF COORDINATION CHEMISTRY Vol. 31 No. 1 2005

PHYSICOCHEMICAL MODEL FOR CHOOSING COMPLEXES
17
3
+
Table 1. Logarithms of stability constants of the Cr and cients a and λ for the corresponding chromium com-
Z
Z
2+
Cr hydroxo complexes, the solubility product exponent for
Cr(III) (pSP), the standard electrode potentials of the reac-
tions involving chromium ions (E°), and the potential of ac-
tive reduction of water molecules (E*)
plexes into Eq. (21), we find the boundary conditions
for ΣpK : (ΣpK ) = 9.2 and (ΣpK ) = 5.4, which
m
m max
m min
is an obligatory requirement for choosing ligands for
chromium-plating solutions.
Parameter
Value
10.0
References
[15]
Comparison of the results of simulation with
experimental data. For experimental checking, we
chose ligands satisfying the boundary conditions and
overstepping them (Table 2). An admissible interval of
current densities of the electrodeposition of high-qual-
ity coatings (∆i) was determined at pH 2 in solutions
containing the ligands chosen.
3
+
logβ° (Cr OH)
1
2
+
logβ° (Cr OH)
~7
[15]
[15]
[15]
1
pSP(Cr(OH)3)
30.2
–0.41
E° 3+ 2+ , V
The results obtained were used to verify the pro-
posed model. The plot of ∆i vs. logβ for the correspond-
ing coordinatively saturated Cr(III) complexes is pre-
sented in the figure (curve f). This plot has a maximum,
whose position corresponds to the Ω region. The widest
interval of current densities is observed for the elec-
trodeposition of chromium from a solution of the chro-
mium malonate complexes. When using the ligands
Cr /Cr
E° 3+ , V
–0.744
[15]
Cr
E° 2+ , V
–0.914
–1.2
[15]
[16]
Cr
E*, V
3
+
that form complexes with Cr ions, whose stability
coefficients. In Eqs. (19) and (20), a = 0.53, λ = 0.57
2
2
constants are beyond the upper (logβmax = 20) and
lower (logβmin = 10) boundaries of the Ω region, the
admissible interval of current densities narrows
sharply, and chromium deposition even stops com-
pletely in some cases of the indicated conditions.
and a = 0.88, λ = 0.69. To find ΣpK , we solved a sys-
3
3
m
tem of Eqs. (19) and (20)
Z
logβ°[Cr L ]
λ
a
n
n
Z
ΣpK = --------------------------------- + --- -- (n – 1).
(21)
m
n
Z
Thus, our studies confirmed the validity of the
model developed for choosing Cr(III) complexes and
Inserting logβmax , logβmin for the coordinatively
saturated complexes (n = 3) and the values of coeffi- selecting ligands for chromium-plating solutions con-
Table 2. Exponents of dissociation constants of the protonated ligands, logarithms of stability constants of the coordinately
saturated Cr(III) complexes, minimally and maximally admissible current densities, and the range of current densities for the
deposition of high-quality chromium coatings
pK1
15]
ΣpKn
[15]
logβ
[17]
imin
A/dm
,
imax
A/dm
,
∆i,
A/dm
Protonated ligand
c, mol/l
pH
2
2
2
[
–
4
HSO
0.6
0.6
1.94
3.75
1.94
3.75
1.4
2
0
Formic acid
5.76
1.5
2
2
2.5
1.5
2
2
3
17.6
10.6
9.1
3.5
6.8
2.4
2.5
1.5
6.8
2.4
2.1
13.5
6.5
4.5
4.5
21.0
13.2
10.9
5.5
11.3
5.9
4.1
3.5
12.2
7.5
6.7
3.4
2.6
1.8
2.0
4.5
3.5
1.6
2.0
5.4
5.1
4.6
34.1
6.8
6.5
1.6
0
.0
.5
Lactic acid
Oxalic acid
0.6
0.6
3.83
1.19
3.83
5.20
6.0
9.6
.0
.5
.0
Nitrilotriacetic acid
Malonic acid
0.4
0.6
1.89
2.80
14.11
8.50
12.3
1.5
2
2
.0
.5
18.3
1.5
47.6
13.3
11.1
6.1
2
2
3
.0
.5
.0
Trilon B
0.2
2.0
23.0
26.5
2.0
RUSSIAN JOURNAL OF COORDINATION CHEMISTRY Vol. 31 No. 1 2005

1
8
VINOKUROV et al.
0
2+
∆i, A/dm2
mental verification, we developed a chromium-plating
logβ (Cr L )
n
n
solution containing the chromium(III) malonate com-
plex that makes it possible to produce high-quality
coatings in a wide range of current densities.
1
2
0
8
6
4
2
15
a
d
c
e
1
b
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Ω
10
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1
Graphical determination of the admissible region Ω for log-
arithms of stability constants of the coordinatively saturated
chromium complexes of different valence: a–e correspond
to the numbers of inequalities in system (18), and f is the
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trodeposition of high-quality chromium coatings at pH 2 vs.
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the following conclusions. Based on the analysis of
chemical and electrochemical processes that can occur
during electrodeposition of chromium from solutions
of the Cr(III) complexes, we proposed a physicochem-
ical model for choosing complexes and, correspond-
ingly, ligands for chromium-plating solutions. It was
shown that high-quality chromium coatings can be
obtained from solutions of the Cr(III) complexes for
which logβ range from 10 to 20 and logβ of the Cr(II)
complexes formed in electrolysis range from 7 to 10.
The influence of the ligand nature on the process of
chromium electrodeposition was established. The
physicochemical model was experimentally confirmed.
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RUSSIAN JOURNAL OF COORDINATION CHEMISTRY Vol. 31 No. 1 2005