Electrochemical investigations on liquid-state polymerizing systems: Case of sol-gel polymerization of transition metal alkoxides

Article abstract of DOI:10.1021/jp971530t

The polymerization kinetics of zirconium propoxide (and in a few cases of titanium butoxide) were studied in various conditions by following the diffusion of an electroactive probe attached to the metal center. Two different probes were considered, implyi

Full text of DOI:10.1021/jp971530t

J. Phys. Chem. B 1998, 102, 1193-1202
1193
Electrochemical Investigations on Liquid-State Polymerizing Systems: Case of Sol-Gel
Polymerization of Transition Metal Alkoxides
He´le`ne Cattey,† Pierre Audebert,*,† Cle´ment Sanchez,‡ and Philippe Hapiot§
Laboratoire de Chimie et Electrochimie Mole´culaire, UniVersite´ de Franche Comte´, La Bouloie,
Route de Gray, 25030, Besanc¸on, Cedex, France, Laboratoire de Chimie de la Matie`re Condense´e,
URA CNRS no. 1466, UniVersite´ de Paris 6, Place Jussieu, 75005, Paris, Laboratoire d’Electrochimie
Mole´culaire, URA CNRS no. 438, UniVersite´ de Paris 7, 2 Place Jussieu, 75005, Paris, France
ReceiVed: May 7, 1997; In Final Form: October 20, 1997
The polymerization kinetics of zirconium propoxide (and in a few cases of titanium butoxide) were studied
in various conditions by following the diffusion of an electroactive probe attached to the metal center. Two
different probes were considered, implying the complexation of the metal alkoxides with bidentate ligands
functionalized by ferrocene moeties, respectively, a substituted acetylacetone (acac) ligand, and a stronger
complexing ligand as a salicylate ligand. The polymerization kinetics can be followed with good accuracy
on a real time scale by investigating the variation of the diffusion coefficients of the bounded ferrocenes.
This variation can be related to the mass increase of the oligomers formed during the hydrolysis/condensation
process. Electrochemical probing with the functionalized acac ligand shows that some decomplexation of
the ligand occurs during the polymerization process. On the contrary, the salicylate ligand was irreversibly
linked to the metal centers for the alkoxide precursor and also for the larger formed oxopolymers, allowing
an accurate measurement of the mass variation of the electroactive species. The electrochemical results have
been compared with information provided by other techniques. The influence of the electron self-exchange
reaction between species with different diffusion coefficients on the measured diffusion coefficient was
considered in the global analysis.
Introduction
of a given alkoxide to enable the control of the polycondensation
process through a sol-gel route.4a,b The alkoxy groups are
The sol-gel chemistry of silicon alkoxides, and more recently
of transition metal alkoxides, is arousing more and more
interest.1 In addition to numerous spectroscopic investigations
of sol-gel interactions with techniques such as nuclear magnetic
resonance (NMR) spectroscopy,2 we have recently developed
an electrochemical approach to investigate the microviscosity
changes of silica sols and gels. This method is based on the in
situ determination of diffusion coefficients of an included
electroactive species, that can be embedded3 or bounded3b,c to
the silicon species. A further development of this method is to
irreversibly link the electroactive probes to the soluble polymer-
izing species and to investigate the changes in the diffusion rate
of these growing oligomers at different stages of the polymer-
ization process. In this case, the diffusion coefficient would
correspond to the diffusion of the growing oligomer, which
allows us to investigate changes of their sizes. This approach
has the advantage of allowing the investigation of fast changes
in the sol-gel structure during the polymerization process,
which is much more difficult to achieve by a technique like
NMR.
always hydrolyzed prior to the chelating ligand. The complex-
ing power depends both on the nature of the ligand and of the
metal, and it decreases in the orders Zr > Ti > Sn, and salicylate
> acac > carboxylic acid.1 Zirconium is well adapted to our
studies, because a salicylate-chelating ligand is totally resistant
to the hydrolysis, even in pure water.5 Thus, using this ligand,
it is possible to irreversibly bind the electroactive moieties to
zirconium alkoxides and to the condensed species produced
during the hydrolysis/condensation process. On the contrary,
in the case of a weaker complexing ligand, an equilibrium may
exist in solution between the free and the bound form of the
complexant.6
In this study, we have investigated the behavior of zirconium-
based sol-gel systems with complexants, to which a small
amount of the similar complexant that has been functionalized
by a ferrocene has been added. This amount was sufficiently
small to not modify the properties of the system, but can be
used as an electrochemical probe to follow the change in the
size of the oligomeric species. Diffusion kinetics of the attached
ferrocene (i.e., of the oligomer) can be followed by transient
electrochemical techniques (as chronoamperometry), and the
diffusion coefficient can be measured from the current. From
these values, information concerning the average size of the
polymers or aggregates to which the functionalized complexant
has bound itself, can be extracted. Scheme 1 illustrates this
basal work hypothesis. However, during the polymerization
process, oligomers with different sizes will be produced. It is
well known that in similar situations the total current is not
equal to the sum of each individual current because of the
In the case of transition metal sol-gel, the alkoxide precursors
are very reactive, and complexation of the metal is frequently
used to reduce this reactivity to get sols and/or gels and to avoid
the formation of precipitates.4 Exchange of one alkoxy group
by a bidentate ligand like acetylacetone increases the coordina-
tion number of the metal and decreases enough the reactivity
† Laboratoire de Chimie et Electrochimie Mole´culaire.
‡ Laboratoire de Chimie de la Matie`re Condense´e.
§ Laboratoire d’Electrochimie Mole´culaire.
* Corresponding author.
S1089-5647(97)01530-7 CCC: $15.00 © 1998 American Chemical Society
Published on Web 01/23/1998

1194 J. Phys. Chem. B, Vol. 102, No. 7, 1998
Cattey et al.
SCHEME 1: Diagram Symbolizing the Polymerization
steps from ferrocene according to the following sequence. The
synthesis of the other ligands, where the length of the chain
varies (Fc-acac: n ) 4, 6, and 11), occurs identically and has
been omitted. All structures were confirmed by 13C NMR and
mass spectroscopy.
via the Sol-Gel Process, with Functionalized Monomersa
1-(6-Bromohexanoyl)ferrocene. First, 8.72 g (6.54 10-2 mol)
of AlCl3 was added at 5 °C under N2 to 13.37 g (7.19 × 10-2
mol) of ferrocene dissolved in CH2Cl2. Then 10 mL (6.53 ×
10-2 mol) of 6-bromohexanoyl chloride dissolved in CH2Cl2
was added in a dropwise manner to the preceding mixture. The
solution was stirred for 10 min, and then returned to ambient
temperature. The 1-(6-bromohexanoyl)ferrocene was obtained
after hydrolysis on an ice/water mixture, an extraction with
CH2Cl2, and chromatography (pentane 50%/diethyl oxide 50%).
An orange oil was obtained: yield, 61%; F ) 33 °C; 1H NMR:
4-5.5 ppm, m, 9H (ferrocenic protons); 3.4 ppm, t, 2H
(-CH2Br-); 2.75 ppm, t (-CH2-CO-); 1.90 ppm, q (-CH2-
CH2-Br); 1.70 ppm, q (-CH2-CH2-CO-); 1.50 ppm, q
(central -CH2-).
1-(6-Bromohexyl)ferrocene. A standard Clemmensen reduc-
tion procedure was followed. First, 6.10 g (2.25 × 10-2 mol)
of HgCl2, 50 mL of distilled water, and 8 mL of concentrated
HCl were added before introducing 79.15 g (1.21 mol) of
activated zinc powder. The solution was stirred for 5 min and
decanted. A mixture of 25 mL of water, 30 mL of concentrated
HCl, and 60 mL of cyclohexane was added to the first solution
with strong stirring. Then, 14.59 g (4.02 × 10-2 mol) of 1-(6-
bromohexanoyl)ferrocene was added. The mixture was heated
at 100 °C for 6 h. Care should be taken to maintain a strong
agitation or extensive deacylation may occur as a side reaction.
The 1-(6-bromohexyl)ferrocene, again as an orange oil, was
obtained after extraction with CH2Cl2 and flash chromatography
(pure pentane): yield (after chromatography), 64%; F ) 33 °C,
1H NMR: 4 ppm, m, 9H (ferrocenic protons); 3.4 ppm, t, 2H
(-CH2Br-); 2.35 ppm, t (-CH2-Fc); 1.90 ppm, q (-CH2-
CH2-Br); 1.30-1.60 ppm, m, 6H (central -CH2s).
a The ferrocene species bind progressively to higher oligomers.
possible electron transfers between small and big oligomers.
This problem has been addressed by single-step chronoamper-
ometry in the case of a mixture of two molecules.7 In our study,
we have extended these calculations to the case of n species
with fast isotopic electron exchange, and especially to the most
encountered case of a Gaussian distribution of diffusing species.
The relation between the average diffusion coefficient and the
diffusion coefficient of the averaged mass species can be
estimated from this model.
We have prepared the following functionalized complexants,
where each of the complexing moieties are covalently bonded
to a ferrocene species, with n taking selected values between 4
and 11:
4-[6-Amino-(1-ferrocenyl)hexyl]salicylic acid (Fc-sal). First,
0.41 g (2.68 × 10-3 mol) of salicylic acid was dissolved in 3
mL of dry acetonitrile (3 Å molecular sieves), and 0.82 g (6.77
× 10-3 mol) of 2, 4, 6-collidine and 0.85 g (2.43 × 10-3 mol)
of 1-(6-bromohexyl)ferrocene were added (addition of a few
tenths of a milligram of oven-dried magnesium sulfate may be
required). The mixture was heated for 6 to 8 days with stirring
at 55 °C. The solution was extracted by diethyl oxide and
washed several times with acidic water. The product was
separated by flash chromatography (first 100% pentane, then
dichloromethane was progressively added up to a 100%
1
proportion). An orange solid was obtained: yield, 11%; H
NMR: 11.05 ppm, s, 1H, -NH-; 6-7.65 ppm, 3H, benzenic
ring; 4.25, t, 2H (-CH2-NH-); 4.1 ppm, m, 9H (ferrocenic
protons); 2.25 ppm, t (-CH2-Fc); 1.75 ppm, q (-CH2-CH2-
NH-); 1.30-1.60 ppm, m, 6H (central -CH2s).
We have used these electrochemical probes to investigate the
polymerization of zirconium propoxide in the presence of either
acetylacetone or ethylacetoacetate as the main complexant, with
various hydrolysis and complexation ratios. The behavior of
sols and gels based on the hydrolysis/condensation of titanium
butoxide was also explored to a much smaller extent.
3-[6-(1-Ferrocenyl)hexyl]pentanedione (Fc-acac). In 5 mL
of DMSO were added 2.87 g (2.87 × 10-2 mol) of acetylacetone
and 1.55 g (2.87 × 10-3 mol) of sodium methylate. Then 5 g
(1.43 × 10-2 mol) of 1-(6-bromohexyl)ferrocene was added and
the mixture was heated at 90 °C for 3 h. The product was
neutralized with acidic water, then extracted with diethyl oxide
and purified by flash chromatography (pentane 70%, diethyl
oxide 30%): yield, 20%; 1H NMR: 16.7 ppm, s, 1H, -O-H,
enol; 4.1 ppm, m, 9H (ferrocenic protons); 3.6 ppm, t, 1H (CH-
(CO-)2); 2.4 ppm, t, 2H (CH2-CHd); 2.3 ppm, t, 2H (-CH2-
Fc); 2.15 ppm, s, 3H (CH3-CdO); 2.1 ppm, s, 3H (CH3-
C(OH)); 1.1-1.4 ppm, m, (central -CH2s).
Experimental Section
Synthesis of the Ligands. The synthesis of two ligands,
respectively, of the 3-[6-(1-ferrocenyl)hexyl]-pentanediene (Fc-
acac) and 4-[6-amino(1-ferrocenyl)hexyl]salicylic acid (Fc-sal)
type, stems from the same precursor with a six-methylene unit
chain [1-(6-bromohexyl)ferrocene], which is produced in two

Sol-Gel Polymerization of Metal Alkoxides
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1195
Figure 2. Cottrell plots obtained by chronoamperometry in the case
of the system with Fc-sal/etacac at a complexation rate equal to 0.37
and a hydrolysis rate equal to 2. Features represents the evolution of
the diffusion coefficient at the beginning of the polymerization reaction
(0) and at the end of the polymerization ((). The insert shows the
voltamogram of the corresponding system obtained at 1V/s.
amount of electroactive probe did not affect the gelification
process at all, as expected.
Electrochemical Measurements. After a first experiment
to check the monomer behavior, the electrochemical study was
started as soon as the addition of water has ended (∼20 s). For
main course studies, the electrochemical setup consisted of a
1.2-mm diameter glassy carbon electrode, a platinum counter
electrode, and a calomel electrode connected to a homemade
potentiostat8 equipped with an ohmic drop compensation device.
The chronoamperometry experiments were performed stepping
from 0 to +0.7 V (which is >200 mV beyond the ferrocenes
potential peaks in the sols). The data were collected on a Nicolet
350 digital oscilloscope, the whole experiment duration (data
acquisition) being usually 1 or 2 s. A typical chronoampero-
metric curve is represented in Figure 2, and attests both the
linearity of the Cottrell curve during the chosen time scale.
Figure 1. Gelification diagrams of Zr(OPr)4 for different complex-
ants: upper, acetylacetone (acac); lower, ethyl acetoacetate (etacac).
Gels Preparation. Inside a tube-shaped thermostated cell
were mixed Zr(OnPr)4 (or in a few experiments, Ti(OnBu)4; for
a typical experiment, 5 mL of a 70% Zr(OnPr)4/30% 2-propanol
solution, a chosen x equivalent of complexant (acac or etacac,
x being called complexation ratio in the following, expressed
as [number moles of complexant]/[number moles of Zr(OnPr)4]),
a polar enough cosolvent made of 50% acetonitrile and 50%
methanol (typically 15 mL), and 0.2 g of lithium perchlorate.
Then, 10-3 M of the functionalized complexant (Fc-acac of Fc-
sal) was added, and cyclic voltammetry and chronoamperometry
were performed. Then, a given amount of a 10% water/90%
propanol hydrolysis solution was added with stirring (the amount
of water is defined by the hydrolysis ratio h ) [number moles
of water]/[number moles of Zr(OnPr)4]; because h was allowed
to vary, the volume of the solution varied in accordance, and
concentration corrections were made, consequently, in the
diffusion coefficient determinations. For experiments carried
out with titanium butoxide, only acac could be used as the main
complexant. The hydrolysis ratios were carefully chosen to
avoid precipitates. The gelification diagram (Figure 1) of the
Zr(OnPr)4/acac and Zr(OnPr)4/etacac systems were determined
separately from similar experiments, quoting the gelation times
and nature (sols, clear gels, turbid gels or precipitates), but
without the electroactive probe added. Gels were designated
as “slow” when the gelation time was >1 h, otherwise they
were called “fast” gels. Usually, slow gelling times lead to
transparent gels, whereas fast gelling times lead to opalescent
or turbid gels. In the case of Ti(OnBu)4/acac, the choice of h
covered too narrow a range once x was fixed and the results
(gels, sols) are directly quoted in the tables gathering the results.
In addition, in a few cases, we checked and found that the small
Several experiments were conducted in parallel using ultra-
microelectrodes instead of conventional microelectrodes. In this
case, the electrodes were 10- or 20-mm diameter gold. The
data after digitalization were transferred to a PC computer for
treatment. The diffusion coefficients were extracted using the
equation devised by Shoup and Szabo9 in conditions closed to
the stationary currents (typical experiments were run for times
between 0.5 and 10 s). In such conditions, the current could
be approximate by i ) (8/π2) FSD1/2C/(πt)1/2 + 4FDCr (S,
surface area; D, diffusion coefficient; r, electrode radius). A
plot of i as a function of t-1/2 (measuring the slope and the
intercept, see the Supporting Information section for an example
of such plot) allows an absolute determination of D and C if
the radius of the electrode has been measured before. (With
an ultramicroelectrode, the real radius of the electrode can be
slightly different from the radius of the wire depending on the
making of the electrode and the polishing.) In our experiments,
only the relative variations of D and C were considered, but if
we take the radius of the gold wire as the geometric radius of
the electrode and suppose a perfect disk shape to estimate the
surface, we found values of D in the 10-5-10-6 cm2 s-1 range.

1196 J. Phys. Chem. B, Vol. 102, No. 7, 1998
Cattey et al.
Miscellaneous. Calculations were performed on a PC
computer with the help of a Matlab software. BET experiments
were performed on dry xerogels on a Micromeritics 2100 A
rapid surface area analyzer using N2 as the adsorbed gas.
Elemental analysis were performed on several xerogels after
stabilization of the system and drying in air.
) Bi/A°1, di ) Di/D1, τ ) t/θ (where θ represents the
measurement time), and λij ) kijA°1θ. The dimensionless form
of the current ψ would be then ψ ) iθ1/2/FSD11/2A°1, the letters
having their usual signification. We are searching ψ which is
equal to ∑idi(∂ai/∂y)0. From our hypothesis on isotopic fast
exchange, it comes λij ) λji and aibj/ajbi ) 1; therefore the sum
ai + bi is constant throughout the solution. In particular this is
true for j ) 1, which leads to ai ) (A°i/A°1)(1 - b1) ) (A°i/
A°1) a1. Let us call ) γi the ratio A°i/A°1, so it becomes ai )
γi a1. On the other hand, the sum of the partial derivative
equations leads to:
Results
Theoretical Background. During the polymerization proc-
ess, oligomers with different sizes are produced and the solution
contains a distribution of electroactive species with different
diffusion coefficients. Thus, we need to estimate the relation
between the diffusion coefficients of such distribution and the
electrochemical current recovered from chronoamperometry
experiments. In this connection, we need to answer two main
questions. First, how close is the current recovered to the sum
of the currents arising from the contributions of the different
electroactive species with different masses and diffusion coef-
ficients? Second, extracting an average diffusion coefficient
supposes that we are dealing with a centered distribution, which
is the most often encountered case. Therefore, the related
question is: How close is the central diffusion coefficient to
the average measured diffusion coefficient (i.e., extracting the
D value as if a single diffusing species were present in the
solution) in case of a given definite distribution (e.g., a Gaussian
distribution). The first question raises the problem that the total
current is not equal to the sum of the individual currents for
each species when the solution contains a mixture of species
with different diffusion coefficients due to electron exchange
between small and large molecules.10 The problem has been
previously addressed in the context of a mixture of two different
reactants (see for example refs 7 and 11), including the case of
interest for us, the homogeneous isotopic exchange7 (all the
electroactive species have the same standard potentials E°). In
case of a fast electron exchange versus diffusion, it has been
shown that the contribution of smaller species is expected to
increase the current values.7,11 In this particular case, an
analytical solution can be obtained in the context of chrono-
amperometry in the previously nonexamined case of n species
with n different diffusion coefficients D1....Dn. Let us call Ai
the oxidized species, with a bulk concentration equal to A°i,
which can be reduced in Bi at the electrode according to the
reaction: Ai + e- h Bi and also exchange an electron with
any of the reduced species Bj according to:
∂( a )
∑
i
∂2ai
i
)
d
i
∑
∂y2
∂τ
i
replacing the ai by γi a1, it becomes:
∂a1
∂2a1
(
γ )
) ( d γ )
∑
∑
i
i
i i
∂y2
∂τ
i
Thus, since ai ) γi a1:
∂ai
)γ ( γ / d γ )1/2(πτ)-1/2
(1)
(2)
(3)
(4)
i ∑ ∑
i
i i
( )
∂y
0
i
i
and therefore:
ψ ) [( d γ )( γ )]1/2(πτ)-1/2
∑ ∑
i
i
i
i
i
Then, i becomes:
i ) FS[( D A )( A )]1/2(πt)-1/2
∑
∑
i
i
i
i
i
This expression should be compared to the expression:
i ) FS(πt)-1/2 (D )1/2A
∑
i
i
i
which would be obtained without occurrence of the electron
exchange.
kij
Let us now turn toward the second problem of what would
be the current i recovered from a Gaussian collection of species
of mass mi and concentrations Ci reduced at the same potential,
with Dµ being the diffusion coefficient of the most abundant
species of mass µ (midpoint of the Gaussian, concentration Cµ),
with a given standard deviation σ, and with the sum of the
concentrations equal to C°. The expression (2) just derived is
still valid. Let io ) FS C°Dµ1/2(πt)-1/2 be the current recovered
if all the species were µ species, which is derived straight-
forwardly from a chronoamperometry experiment. We can
normalize the currents relative to io:
Ai + Bj S Aj + Bi
kji
The system of differential equations describing this system
can be written as follows:
∂Ai
∂t
∂2Ai
∂x2
) Di
-
k AiBj + k AjBi
ij ji
∑
∑
j
j
with K ) kij/kji ) 1, and with the following initial conditions:
t ) 0, x g 0 and x ) ∞, t g 0: Ai ) A°i and Bi ) 0
i/i0 ) (1/C°Dµ1/2)[( D C )( C )]1/2
)
∑
∑
i
i
i
i
i
∂Ai ∂Bi
x ) 0, t g 0, Ai ) 0 and
+
) 0
1/2
DiCi
Ci
∂x
∂x
(5)
∑
∑
C°
i
( (
))(
)
[
]
DµC°
because we suppose that the potential is negative enough for
the concentration of any oxidizable species to be zero at the
electrode. It is easier to use a dimensionless formulation,
defining the following dimensionless variables: ai ) Ai/A°1, bi
i
If we are in the presence of a Gaussian distribution, hence we
have:

Sol-Gel Polymerization of Metal Alkoxides
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1197
Ci
2
2
x
) (1/ 2πσ) exp[-(mi - µ) /2σ ]µ
C°
designing the average mass and σ the standard deviation. If
the Stokes-Einstein law applies,
Di/Dµ ) (mi/µ)1/3
Therefore, shifting to the integral form of the equation, we have,
in the case where diffusion-coupled electron exchange is
considered:
∞
i/i ) [1/(σ 2π)][( (m/µ)1/3
×
x
∫
0
m°
∞
exp[-(m - µ)2/2σ2]dm)( m° exp[-(m - µ)2/2σ2]dm)]1/2
∫
(6)
where m° represents the smallest mass present in the real
distribution (monomer case if we consider a polymerizing
system). The normalized current in the classical case is given
by:
∞
i/i ) [1/(σ 2π)][ (m/µ)1/6 exp[-(m - µ)2/2σ2]dm] (7)
x
∫
0
m°
In the case where the diffusion coefficient distribution is
Gaussian (instead of the masses distribution as previously
examined), it is easy to check that we can replace eqs 6 and 7
by eqs 6′ and 7′, where the (m/µ)1/3 coefficient is replaced by
simply m/µ. The Figures 3 and 4 display calculated values
according to m°, µ chosen equal to 5 m° and σ. The value of
m° is arbitrarily chosen as 1. Curves 3a and 3b represent the
normalized currents recovered from a collection of diffusing
species with a Gaussian mass distribution, either in a classical
approach (without coupled electron transfer) or with electron-
transfer considered. It is clear that the curves display the same
behavior, and we see that the currents closely reflect the average
species current, until the standard deviation σ does not exceed
40% of the µ value. Figure 3c gives the ratio between the two
currents; that is, focuses on the possible influence of the electron
transfer. It is clear that the effects are very weak, as would be
expected, but the theoretical current in the presence of electron
transfer gets slightly higher when a lot of small species are
present. This result is in accordance with literature predictions
in more simple cases,7 because smaller species can diffuse faster
and after exchange contribute more to the total current. Figure
4a, b, and c represent the three kinds of curves previously
described. However, the case where the diffusion coefficients
(and no longer the masses) of the species have a Gaussian
distribution is the only case where the average diffusion
coefficient is five-fold the monomer one. It can be seen that
qualitatively identical effects are obtained, albeit with a notice-
able enhancement because the dependence of the diffusion
coefficient with the mass is the cubic root.
Figure 3. Theoretical variation of the normalized current ratio I/I0 in
the (a) absence or in the (b) presence of diffusion-coupled electron
exchange, for a collection of electroactive species with a Gaussian mass
distribution, in function of the average mass µ and the standard deviation
σ. See text for I and Io definition. The mass µ is given in units of the
lowest mass present (monomer case) for three selected cases of 3, 5,
and 10. (c) Ratio of the two curves (a) and (b) [R ) I (with electron
exchange)/I (without electron exchange)].
In conclusion, the average experimental diffusion coefficient
that can be extracted from a chronoamperometry experiment
performed on a Gaussian collection of species reflects with a
reasonable accuracy the diffusion coefficient of the central
species. More generally, even when the distribution is not
Gaussian, it is likely that the average D value extracted from
chronoamperometry experiments is close to the real average D
values of the diffusing species.
ethyl acetoacetate (etacac),3c,12 acetylacetone (acac)3c,13 and
salicylic acid (sal)5,6 were efficient ligands, which substituted
readily with the propylate moieties on the metal. Previous NMR
and chemistry studies have shown that the complexation strength
rises in the order etacac < acac < sal. Whereas etacac binds
reversibly, acac binds irreversibly, but may be released by an
excess of water. On the contrary, sal is not released, even in
pure water, because it has been demonstrated that zirconium
Polymerization of Zirconium Propoxide. Choice of the
Ligand. Bidentate ligands are commonly used to dicrease the
zirconium propoxide reactivity. Earlier works have shown that

1198 J. Phys. Chem. B, Vol. 102, No. 7, 1998
Cattey et al.
two different probes were considered: Fc-acac and Fc-sal. When
etacac is the main ligand, both Fc-acac and Fc-sal probes are
expected not to be released from the zirconium polymers, as in
the case of Fc-sal in the Zr(OnPr)4/acac system. Only in the
last case, Zr(OnPr)4/acac with Fc-acac, the competition between
the main acac ligand and the functionalized Fc-acac can be
slightly unfavorable toward hydrolysis. However, in all cases,
propylate is always hydrolyzed first, and the removal of the
ligand from the growing species should not be felt at the early
stage of the condensation. Besides, the difference between the
electrochemistry of Fc-sal and Fc-acac labeled alkoxides when
acac is the main ligand was expected to give valuable informa-
tion on ligand release in the latter case.
Gelification Diagrams. Prior to the electrochemical study,
it was necessary to determine the gelification diagram of the
zirconium propoxide in the presence of the two complexing
ligands that we used; namely, etacac (weak complexing ligand)
and acac (strong complexing ligand). No reports were available
in the former case. Even though some reports existed with acac,
the use of slightly different solvents suitable for electrochemistry
made the determination of the gelification parameters useful.
The Figure 1 shows the results obtained in the case of the two
systems studied; it is clear that both system behave as previously
noticed in analogous cases, with precipitation of zirconium
oxopolymers in all cases with a weak complexing ratio x and
on the contrary, stable sols above a given x value. However,
the intermediate gel zone shows a difference between the two
systems. Although there is no detectable influence of the
hydrolysis ratio h in the case of the relatively strong complexing
ligand acac, h influences the gelification in the case of etacac,
probably as a consequence of the easier hydrolysis of this weaker
ligand.
Electrochemical Results. As expected, the chronoamperom-
etry currents decrease upon sol aging and in the course of the
gels formation. Several complexing ratios (x) and hydrolysis
ratios (h) values were investigated, both in the sol and gel
regions. The results of all electrochemical studies will be
presented in terms of the mean diffusion coefficient variation
extracted from the Cottrell current in potentiostatic conditions.
As explained before, the experimental measured variation is
1/2
*
Cferrocene D . Assuming that the concentration of ferrocene (i.e.,
of the functionalized ligand) does not change during the
polymerization process, the value of the variation of the diffusion
coefficient can be extracted. Most of our experiments were
performed in the sols or gels conditions, all absolute diffusion
coefficients values were in the 10-5-10-6 cm2 s-1 range using
the geometric parameters of the electrode. Only in the very
few cases where the precipitates were studied, we observed
lower D values, which were not lower than 10-7 cm2 s-1
.
Therefore, physical diffusion is the main process in our systems,
as would be expected from such highly solvated medium.3 To
check that the concentration of ferrocene does not change
significantly during the polymerization, we performed the same
set of experiments as previously detailed, using micronic size
ultramicroelectrodes instead of classical millimeter size micro-
electrodes. This method is based on the comparison between
the planar diffusion current and the steady-state current on the
same electrode and allows the determination with the same
experiment of two parameters of the system.14 This procedure
has been used to determine D independently from the electrode
area14 or the number of electron exchange by molecule,14a but
it is also possible to determine D independently from the
concentration of the electroactive species if the radius of the
electrode is known. We thus calculated the variation of the D
Figure 4. Same feature as in Figure 3 for a collection of species with
a Gaussian distribution of diffusion coefficients centered on an average
diffusion coefficient Dµ which is equal to five times the one of the
smallest species.
salicylate is stable, in pure water.5 Our functionalized ligands
can be expected to bind slightly less strongly than the parent
unsubstituted ligand (i.e., when the part of the molecule binding
to the metal has the same chemical structure) mainly because
of steric effects. If we want that the functionalized ligands
remain attached to the oligomers in formation, the main
complexant of the system should be a weaker ligand than the
functionalized one. It is also obvious that the functionalized
ligand must not be removed upon hydrolysis. Two systems were
studied Zr(OnPr)4/etacac and Zr(OnPr)4/acac. For each system,

Sol-Gel Polymerization of Metal Alkoxides
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1199
Figure 6. Variation of diffusion coefficients with time and influence
of the main complexant. Fc-sal was always used as the probe with
either acac (2) or etacac (0) as main complexant.
relatively high D plateau probably reflects the existence of free
Fc-acac released in the solution. On the other hand, the low D
plateau when Fc-sal is the probe should be related to the
existence of highly aggregated species in this case.
Influence of the Complexation and Hydrolysis Ratio. From
the gelification diagrams, it is evident that the complexation
ratio (proportion of the main complexant initially added to the
system) is the most relevant parameter to predict the final state
of the system. It is possible to correlate the D curves, and
especially the D plateaus to the complexation ratio, either with
acac or etacac as the main ligand. However, in the case of
etacac, the gel domain is quite narrow. Thus, changing x values
over a wide range results in the obtention of sols on one hand,
and turbid gels or even precipitates on the other hand. Because
Fc-sal was found to give the most reliable data in our systems
without any release from the oxopolymers, whatever the main
ligand nature, the use of this probe was chosen through the rest
of this work.
Influence of the Main Complexant Nature. Figure 6 shows
the compared behavior of two systems that differ only by the
complexant kind: namely, acac or etacac. It is clear that
although the kinetics appear similar, the D plateaus differ
noticeably. The higher value obtained in the case of acac shows
that, as expected with this stronger complexant, the average
condensation degree is much lower, resulting in the formation
of smaller oligomers. The opposite behavior is observed in the
case of the weaker complexant etacac.
Figure 5. Variation of diffusion coefficients with time and influence
of the probe: (a) etacac, x ) 0.75 and h ) 10; (b) acac, x ) 0.4 and
h ) 4 with as ligands for the two curves, Fc-sal (]) or Fc-acac (2) as
electroactive probe.
values independently from the concentrations of ferrocene as
explained in the experimental section. It is difficult to get
precise absolute values for the diffusion coefficient because of
the uncertainties of the electrode radius14b and area then only
the relative variations were considered. Similar variation of
the extracted diffusion coefficient were observed, showing that
reproducibility is encountered independently from the used
technique (see Supporting Information section for a comparison
of the variations of D by the two methods). In addition, this
precaution ensures that we are indeed dealing with a diffusion
coefficient decrease and not concentration depletion in the gels,
thus corroborating our ground hypotheses.
Influence of the Probe Nature. To elucidate if probe release
had to be taken into consideration and to that extent, we
investigated the electrochemical response of two identical
systems, on one hand with acac and on the other with etacac as
the main complexant. In each case, either the Fc-acac probe
or the Fc-sal probe was used. Figure 5 shows the response of
identical systems (same complexing and hydrolysis ratio), with
etacac or acac as the main complexing agent, and with either
Fc-sal or Fc-acac as the electroactive probe. The curves
displayed in Figure 5a show that, as expected, identical
responses are obtained when etacac is the main ligand, whatever
the probe complexing strength. Both the time dependence and
the plateau of the D(t) curves are the same; the probe release is
therefore negligible in the course of the experiment, and the D
variation is related to the dynamics of the alkoxide hydrolysis
in this case. On the contrary, when acac is the main ligand
(Figure 5b), different curves are displayed for closely related
systems, differing only by the probe nature. It is obvious this
time that the D decrease is much smaller when Fc-acac is used
as the probe, certainly as a consequence of the unfavorable
competition between Fc-acac and acac complexation. The
Influence of x and h. The curves in Figure 7 show that the
D plateaus change very regularly according to the complexation
ratios with etacac as the main complexant. As expected high
complexation ratios lead to weakly condensed, fast diffusing
species, whereas low complexation ratios lead to highly
condensed aggregates and very low D values. The same
behavior is again seen when acac is the main ligand, as shown
in Figure 7b. Again, the D values vary strongly contrariwise
to the complexation ratio. On the contrary, the hydrolysis ratio
appears to have a weak influence on the D values, and
correlatively also with the nature of the condensed species. This
is obvious in the case of acac (as shown in Figure 8), but even
in the case of etacac, D plateaus are found in the same range
whatever the h value. However, we tried to generate oxopoly-
mers and never tried very weak hydrolysis ratios (<2), which
should have lead to small molecular weight clusters.1b
BET Measurements and Elemental Analysis. Gas adsorption
experiments allow the determination of specific surface area
values of the dried xerogels. Of course the structure of the dried
gel is different from the structure of the wet gel, but the size of

1200 J. Phys. Chem. B, Vol. 102, No. 7, 1998
Cattey et al.
TABLE 1: Results Obtained by BET Measurements on
Several Xerogels
complexation
ratio
hydrolysis
ratio
atom
Zr
complexant
BET (m2/g)
Acac
Acac
Acac
Acac
Etacac
Etacac
Etacac
Acac
0.45
0.5
0.5
0.5
0.6
0.7
1
0.5
0.3
0.9
4
2
4
10
10
10
10
15
18
4
130
82
140
231
73
105
92
221
44
Zr
Ti
Ti
Acac
Etacaca
6
a Precipitate.
TABLE 2: D Plateau Values Obtained from the Hydrolysis
of Ti(OnBu)4 with the Fc-acac/acac Couple, In Function of
the Complexation Ratio x and the Hydrolysis Ratio h
Diffusion coefficient
complexation hydrolysis
ratio
ratio
initial
final
Aspect
0.30
0.35
0.40
1.25
1.25
18
19
17
2
1
1
1
1
1
1.00
0.90
0.97
0.88
1.00
slow gel (5 hours)
slow gel (2 days)
slow gel (2 days)
stable sol
4
stable sol
TABLE 3: D Plateau Values Obtained from the Hydrolysis
of Ti(OnBu)4 with the Fc-sal/acac Couple, In Function of the
Complexation Ratio x and the Hydrolysis Ratio h
Figure 7. Variation of diffusion coefficients with time and influence
of the complexation ratio. (a) The couple Fc-sal/etacac was studied
throughout with several different x: x ) 1.25, h ) 2 (O); x ) 0.75, h
) 10 (9); x ) 0.4, h ) 6 ((); x ) 0.2, h ) 2 (0); x ) 0.1, h ) 2 (2);
(b) The couple Fc-sal/acac was studied with two different x: x ) 1.25,
h ) 2 (2); x ) 0.4, h ) 2 (().
diffusion coefficient
complexation hydrolysis
ratio
ratio
initial
final
aspect
0.30
0.35
0.40
1.00
1.25
1.25
19
13
16
2
2
4
1
1
1
1
1
1
0.26
0.53
0.22
0.94
1.00
1.00
slow gel (1.5 days)
slow gel (2.5 days)
slow gel (3 days)
stable sol
stable sol
stable sol
80% of etacac remaining in the final dry xerogel, according to
the initial x and h values.
Polymerization of titanium butoxide. In the case of titanium
butoxide, an exhaustive study was rendered impossible because
of the high reactivity of this alkoxide that made it impossible
to (1) to prepare sols and gels with etacac as the main
complexant (the weak area reported for a precipitate in Table 1
contrasts with the usually relatively high area in the case of
gels) and (2) to allow h to vary significantly once x was chosen.
A gelification diagram (with acac) has, however, been reported
in the literature in slightly different conditions than ours, which
shows that both x and h play an important role, with sols always
obtained at low h values.15 Therefore, only selected experiments
were performed and the results are presented in Tables 2 and
3. Again a D plateau is reached, extremely quickly in this case,
and in all cases but one the first measurement after water
addition reaches the D plateau. Values have been therefore
gathered in Tables 2 and 3 according to the probe kind.
Figure 8. Variation of diffusion coefficients with time and influence
of the hydrolysis ratio on the couple Fc-sal/acac. (a) x ) 0.4, h ) 2
(2); (b) x ) 0.4, h ) 6 (0).
the pores has a relation with the average oxopolymer size in
the fresh gel. Results in Table 1 show that the BET specific
surface area values of the xerogels is in the 100 m2/g range.
There is an increase with the hydrolysis ratio in the case of a
good complexant like acac; on the other hand, the surface area
is practically constant with the weak complexant etacac. The
results of elemental analysis on carbon and hydrogen clearly
show that all ligands remain inside the xerogels in the case of
Fc-sal, and 90% to 100% in the case of Fc-acac, according to
the case where the main ligand is etacac or acac, respectively.
On the contrary, all propylate moieties are hydrolyzed and the
propanol formed is then evaporated out of the final xerogel
(because of the presence of little residual water, oxygen content
does not provide reliable data). About the main ligand, analyses
show the more labile etacac ligand is partly released, 60% to
Discussion
In the framework of the theoretical approach defined, it is
clear that in the zirconium systems the D drop measured by
chronoamperometry is directly related to the size of the polymers
formed. Variations are large enough to provide information
on both the evolution and the final state of the systems. It is
noticeable in the framework of our theoretical approach that
the influence of the electron transfer between small and big
oligomers would be that the apparent diffusion coefficient value

Sol-Gel Polymerization of Metal Alkoxides
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1201
gets closer to the mean value than it would in the case of a
simple additive behavior. Especially in the case of a Gaussian
distribution of the diffusion coefficient, the apparent value stays
extremely close to the average value, when the σ value does
not exceed 40% of the Dµ value, due to the diffusion coupled
electron exchange. We have also checked that integrating the
curves from zero instead of 1 (reducing the monomer mass or
diffusion coefficient to its lowest possible limit) almost does
not changes the curves displayed in Figures 3 and 4.
Kinetic Behavior. The very fast D decay on all curves
proves that the polycondensation reactions begin within seconds
as soon as water addition occurs; therefore confirming the high
reactivity of the alkoxide even with complexant added. To
explain such fast polymerization, it should be admitted that
hydrolysis is almost instantaneous as soon as water is introduced
in the system. It is somewhat surprising that the time to reach
the D plateau, which is characteristic of the condensation kinetics
of the system, appears more dependent on the plateau value
than the ligand nature, suggesting that the condensation has
comparable kinetics whatever the main ligand (probably related
to mixing). Only in the case where acac (which is the best of
the two complexants that we tried) is used, with a low hydrolysis
ratio, is a time-dependent kinetics observable (Figure 5b).
Although the hydrolysis ratio has a very weak influence on the
final D plateau value, it may influence the rapidity at which
this value is attained. Probably both less hydrolyzed species
are formed and their condensation is slower, again especially
in the case where acac is the main ligand. This idea is attested
by the results in Figure 8, which show that the same D value is
reached at clearly different rates due to the difference in the
hydrolysis ratios. On the contrary, Figure 5a (case where etacac
is the main ligand) does not show any appreciable difference
concerning the time at which the plateau is reached, arguing
thus for a relatively rapid hydrolysis of the etacac ligand.
Figure 9. Plot of the (D/D°)3 variation with the complexation ratio x
(couple Fc-sal/etacac), deduced from the data in Figure 6.
D/D° values are proportional to the power 1/3 of the reduced
mass m/m°, m° being the monomer mass. Figure 9 shows that
in the sols and slow gels, the dependence of (D/D°)3 correlates
with the complexation ratio. However, in the domain of the
turbid gels and precipitates, the correlation stops and the linearity
of the plot ceases. If, as expected, the (D/D°)3 is really
correlated to the reduced mass variation, it comes ln(m/m°) )
kx. Then, the average mass of the final polymers would vary
exponentially with the complexation rate, which is not unex-
pected in the case of an aggregating process and a second-order
kinetics in each elementary step. Moreover, the BET surface
area of the dried gels may be correlated with the average
oligomer size, on the (very approximated) basis of sphere
stacking; with most dried gels, the diameter of the spheres would
be in the 50-100 Å range. This result is not in contradiction
with the mass of the oxopolymers experienced by the electro-
chemical study, which falls between 10 and 1000 times the mass
of the functionalized monomer according to the hydrolysis
conditions.
In the case of titanium butoxide, the results in Table 2 show
very clearly that when Fc-acac is the functionalized ligand, there
is no variation at all in the diffusion coefficients, whatever the
conditions chosen (x and/or h values, sols or gels). This result
shows unambiguously that Fc-acac is not able to compete with
acac, this contrasting with the more ambiguous situation met
in the case of zirconium propoxide. The results in Table 3 show,
on the contrary, that in the case of Fc-sal as the functionalized
probe there is a strong variation encountered in the case of
gelling systems (weak x and relatively high h values), whereas
in the case of stable sols, there is almost no drop noticed, as a
probable consequence of the formation of low molecular weight
clusters. This situation shows again that Fc-sal is strongly bound
to the polymerizing species and that with weak complexation
ratios, a sharp drop is noticed as the consequence of the very
fast formation of highly condensed species. This result is
confirmed by the high specific area reported in Table 1 for such
gels.
D Plateau. In all cases, we observed that a limit plateau
was reached for D, which varies both with the system and the
probe nature. In the case where salicylate is the anchor of the
probe, there was no release of the probe. As explained before,
ultramicroelectrode experiments did not show any noticeable
depletion of the electroactive species concentration, and there-
fore the D drop experienced by the chronoamperometry is
related to a slowing down of the diffusion of the grafted
electroactive species. However, the interpretation of this value
is not straightforward, although it should be related to the
average mass of the oligomers when the condensation reaction
has stopped. As often noticed before in different sol-gel
systems, the gel time is not a relevant parameter because a
plateau in the D value is usually reached before the gel time.
This argues for the D plateau to be directly related to the
diffusion of the grafted species because if restricted diffusion
were to occur, then gelification and the first stages of aging
would influence the plateau value. As we discussed before,
there is only a slight deviation from the average diffusion
coefficient provided that the distribution of masses was not too
extended and thus the D plateau experienced by the Fc-sal probe
reflects the average diffusion coefficient of inorganic oxopoly-
mers onto which the ferrocenic species have been grafted. This
assertion is supported by the results displayed Figure 7a, where
clearly the plateau currents are inversely proportional to the
complexation ratio. This is in accordance with literature results
because it is known that the lowest is the complexation ratio
and the highest is the size of the oligomers. From the diffusion
coefficient determination, we can try to evaluate the average
size of the oxopolymers formed, continuing to suppose that the
Conclusion
The electrochemical approach where an electroactive species
is bound to the metal center is an efficient technique to follow
the aggregation process occurring during the polymerization of
metal propoxides. Experiments of functionalized ligand bound

1202 J. Phys. Chem. B, Vol. 102, No. 7, 1998
Cattey et al.
(2) (a) Brinker, C. J.; Scherrer, G. Sol-Gel Science, the Physics and
Chemistry of Sol-gel Processing; Academic: San-Diego, 1989; (b)
Babonneau, F. Mater. Res. Soc. Symp. Proc. 1994, 346, 949.
(3) (a) Audebert, P.; Griesmar, P.; Sanchez, C. J. Mater. Chem. 1991,
1, 699; (b) Audebert, P.; Griesmar, P.; Hapiot, P.; Sanchez, C. J. Mater.
Chem. 1992, 2, 1293; (c) Cattey, H.; Audebert, P.; Hapiot, P.; Sanchez, C.
J. Mater. Chem. 1997, 7, 1461.
(4) (a) Sanchez, C.; Ribot, F.; Doeuff, S. In Inorganic and Organic
Polymers with Special Properties, Nato ASI Series; Laine, R. M., Ed.;
Kluwer: New York, 1992; Vol. 206, p 267; (b) Mehrotra, R. C.; Bohra,
R.; Gaur, D. P. Metal b-Diketonates and Allied DeriVatiVes; Academic:
London, 1978; (c) Yoldas, B. E. J. Mater. Sci. 1986, 21, 1086.
to zirconium species in the course of polymerization, showed
that, as expected, the average measured diffusion coefficient
reflects the mass of the oxopolymers formed when the electro-
chemical probe is bound with a strongly anchoring species like
the salicylate function. We have shown that, especially in the
case of the weakly complexing etacac as a ligand, the average
mass of the polymers formed is experienced by the diffusion
coefficient determined from the electrochemical measurements.
In the case of titanium species, we have shown that the
polymerization was extremely fast, and that complexation on
titanium species was less efficient because the Fc-acac probe
does not bind at all in the presence of free acac in the medium.
The theoretical prediction for the response of electroactive
species in the presence or without diffusion-coupled electron
transfer has been solved out and shows that in the case of a
Gaussian distribution, there is only a slight difference between
the current from a real collection of species, and the current
that would be recorded if all the species had the central mass.
Therefore the average diffusion coefficient reflects with a
reasonable accuracy the actual diffusion coefficient of the
midpoint species, even when there is a noticeable dispersion of
the molecular weights of the species.
(5) (a) Kapoor, R. N.; Mehrotra, R. C. J. Am. Chem. Soc. 1960, 82,
3495; (b) Griesmar, P. Thesis, University of Paris 6, July 1992.
(6) (a) Sanchez, C.; In, M. J. Non-Cryst. Solids 1992, 1, 147; (b) French
patents nos. INPI 91 11634, 91 11635 (In, M.; Sanchez, C.; Daniel J. C.);
(c) In, M. Thesis, University of Paris 6, June 1994.
(7) Andrieux, C. P.; Hapiot, P.; Save´ant, J.-M. J. Electroanal. Chem.
1984, 49, 172.
(8) Garreau, D.; Save´ant, J.-M. J. Electroanal. Chem. 1972, 35, 309.
(9) Shoup, D.; Szabo, A. J. Electroanal. Chem. 1982, 140, 237.
(10) Andrieux, C. P.; Save´ant, J.-M. J. Electroanal. Chem 1970, 28,
339.
(11) (a) Miller, S. L.; Orleman, E. F. J. Am. Chem. Soc. 1953, 75, 2001;
(b) Schwall, R. J.; Smith, D. E. J. Electroanal. Chem. 1978, 94, 227; (c)
Andrieux, C. P.; Hapiot, P.; Save´ant, J.-M. J. Electroanal. Chem. 1985,
186, 237; (d) Evans, D. H. J. Electroanal. Chem. 1989, 258, 451.
(12) (a) Deksibar, J. C. J. Non Cryst. Solids 1986, 87, 343; (b) Deksibar,
J. C. J. Mat. Sci. 1985, 20, 44; (c) Livage, J.; Sanchez, C. J. Non Cryst.
Solids 1992, 145, 11; (d) Papet, P.; LeBars, N.; Baumard, J. F.; Lecomte,
A.; Dauger, A. J. Mater. Sci. 1989, 24, 3850.
(13) Saxena, U. B.; Rai, A. K.; Mathur, V. K.; Mehrotra, R. C.; Bradford,
D. J. Chem. Soc., A 1970, 904.
Supporting Information Available: Figures of experimental
data from an experiment using ultramicroelectrodes and of
experimental diffusion coefficients vs time (2 pages). Ordering
information is on any current masthead page.
(14) (a) Amatore, C.; Azzabi, M.; Calas, P.; Jutand, A.; Lefrou, C.;
Rollin, Y. J. Electroanal. Chem. 1990, 288, 45; (b) Denuault, G.; Mirkin,
M. V.; Bard, A. J. J. Electroanal. Chem. 1991, 308, 27.
References and Notes
(1) (a) Livage, J.; Henry, M.; Sanchez, C. Prog. Solid State Phys. 1988,
18, 259; (b) Sanchez C.; Ribot, F. New J. Chem. 1994, 18, 1007.
(15) Bleuzen, A.; Barboux-Doeuff, S.; Flaud P.; Sanchez, C. Mater. Res.
Bull. 1994, 29, 1223.