Influence of the distance between ionizable groups on the protonation behavior of various hexaamines

Article abstract of DOI:10.1039/a907397c

A synthesis route for N,N,N',N'-tetraaminoethyl-1,2-ethylenediamine, N,N,N',N'-tetraaminopropyl-1,2-ethylenediamine, N,N,N',N'-tetraaminopropyl- 1,3-propylenediamine and N,N,N',N'-tetraaminopropyl-1,4-butylenediamine is presented. These molecules differ from each other in the number of carbon atoms between the six amino groups. This results in different protonation behavior. Potentiometric titrations are performed in 0.1 M and 1.0 M KCl, and the six macroscopic protonation constants are obtained from these curves. An Ising model with a limited number of microscopic protonation constants and short-ranged pair interactions describes the protonation behavior quantitatively. The results are compared to those of other, similar molecules. The advantage of the Ising model over empirical relations such as the Taft equations is the more systematic approach with which the titration curves of more complex molecules can be described. The values for the Ising model parameters obtained here can be used to predict the protonation behavior of more complex, in particular larger, polyamines.

Full text of DOI:10.1039/a907397c

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InÑuence of the distance between ionizable groups on the protonation
behavior of various hexaamines
Rene C. van Duijvenbode,a Anton Rajanayagam,a Ger J. M. Koper,*a Michal Borkovec,b
Wolfgang Paulus,c Ulrich Steuerlec and Lukas Haulingc
a L eiden Institute of Chemistry, L eiden University, P.O. Box 9502, 2300 RA L eiden, T he
Netherlands
b Department of Chemistry, Clarkson University, Potsdam, New Y ork 13699-5814, USA
c BASF AG, 67056 L udwigshafen, Germany
Received 13th September 1999, Accepted 19th October 1999
A synthesis route for N,N,N@,N@-tetraaminoethyl-1,2-ethylenediamine, N,N,N@,N@-tetraaminopropyl-1,2-
ethylenediamine, N,N,N@,N@-tetraaminopropyl-1,3-propylenediamine and N,N,N@,N@-tetraaminopropyl-1,4-
butylenediamine is presented. These molecules di†er from each other in the number of carbon atoms between
the six amino groups. This results in di†erent protonation behavior. Potentiometric titrations are performed in
0.1 M and 1.0 M KCl, and the six macroscopic protonation constants are obtained from these curves. An Ising
model with a limited number of microscopic protonation constants and short-ranged pair interactions
describes the protonation behavior quantitatively. The results are compared to those of other, similar
molecules. The advantage of the Ising model over empirical relations such as the Taft equations is the more
systematic approach with which the titration curves of more complex molecules can be described. The values
for the Ising model parameters obtained here can be used to predict the protonation behavior of more
complex, in particular larger, polyamines.
the Ising model, as there are only three di†erent types of ion-
izable sites: primary (RÈNH ), secondary (R NH) and tertiary
Introduction
2
2
In the past empirical relations have been developed to under-
stand the protonation behavior of smaller molecules. These
rest on the assumption that the individual pK (logarithm of
dissociation constant) can be described with the pK@ of the
isolated group in question, and the sum of neighboring group
contributions.1 These latter corrections on the pK@ have been
derived empirically with Hammet and Taft equations.2 The
pK of an individual ionizable site is then calculated for a
certain protonation state. To describe a potentiometric titra-
tion, the procedure must be repeated for all di†erent proto-
nation states of the molecule, and is therefore exclusively used
for smaller molecules, typically with up to three acidÈbase
sites. For the more complex polyelectrolytes the above
approach becomes too difficult mainly because the number of
pK calculations grows with N2N~1 for N ionizable sites.
In parallel to these empirical Taft relations a di†erent
method has been developed to describe the ionization behav-
ior of polyelectrolytes in terms of local charges.3h7 An Ising
model with pairwise interactions was used for this purpose.
The Ising model also assigns to the individual groups in the
system microscopic pK values (given that all other groups in
the molecule are deprotonated) and extends it with interaction
energies between pairs and triplets of protonated sites. The
approach resembles the classical empirical method if only pair
interactions between neighboring sites are taken into account.
This assumption is justiÐed if the interactions are sufficiently
short-ranged.
amines (R N). In the past the Ising model has already been
3
successfully applied to small oligoamines,8 poly(ethylene
imines)6,7 and poly(propylene imine) dendrimers.9 From these
previous studies a lot of information about pair and triplet
interactions has already been obtained; only the microscopic
protonation constants and their dependence on the chemical
environment are still unresolved. These are however of great
importance in future research in order to predict the proto-
nation behavior for more complicated structures.
Therefore we present here the ionization behavior of a
series of similar oligoamines and determine the microscopic or
intrinsic protonation constants for the di†erent chemical
environments and ionic strengths. For that purpose three new
molecules were synthesized with di†erent spacer lengths
between the ionizable sites, and titrations were performed at
two ionic strengths. The macroscopic protonation constants
are compared, and all di†erences in protonation behavior are
directly related to the distance between the various amine
groups. We believe that we demonstrate that the Ising model
is a simpler approach to extract the same information on the
intrinsic protonation constants than the empirical relations,
which are more commonly used in the literature.
Ising model
The Ising model has been used quite extensively throughout
the literature to describe the acidÈbase properties of various
polyamines.4,6h9 The model weighs all possible positions at
which a proton can adsorb onto the molecule in terms of
energy costs. All these so called protonation microstates are
characterized with a set of site variables Ms , . . . , s N where
The advantage of the Ising model is the more systematic
parametrization of the problem; with a few parameters the
macroscopic pK values can be calculated in a straightforward
manner. Amongst the large variety of acidÈbase systems, the
amines are the Ðrst candidate for a more thorough study with
1
N
s \ 0 if deprotonated and s \ 1 if protonated. N is the total
i
i
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number of ionizable sites. Under rather general conditions,
the free energy F of formation of a given protonation state
Ms , . . . , s N can be expanded as
1
N
F(s , . . . , s )
1
1
N
\ ; (pH [ pK )s ] ; e s s ] É É É (1)
i i
ij i j
kT ln 10
2
i
iEj
where kT denotes the thermal energy, pH is the common
negative logarithm of the proton activity, pK is the logarithm
i
of the dissociation constant for site i, and e is the pair inter-
ij
action parameter.
pK reÑects the energy needed to protonate site i consider-
i
ing all other groups are deprotonated. In the case of the hexa-
amines this would be the same as the intrinsic pK in the
empirical Taft equations,2 which covers the energy needed to
protonate a particular site while other groups are deionized.
Higher order terms in the free energy of formation consist
mainly of electrostatic interactions with other ionizable
groups. Assuming short-range interactions the Taylor expan-
sion reduces to pair interactions e only. It can be further sim-
ij
pliÐed taking only pair interactions between neighboring sites
into account. These nearest neighbor pair interactions (NNI)
resemble Taft corrections for the polarity of substituents in
these empirical relations.10h12
The potentiometric titration curve gives the mean average
of all thermal expectations of the state variables correspond-
ing to a certain degree of protonation h, which can be deter-
mined with a partition function $,
Fig. 1 The synthesis route is drawn for both the case of m \ 3 (left
hand side) and m \ 2 (right hand side). The Ðrst step in the latter case
has already been described in ref. 15. In this article the various mol-
ecules will be addressed with (n,m) and therefore a schematic overall
picture of the hexaamines is shown below. n corresponds to the
number of carbon atoms in the core unit between the tertiary amines,
and m relates to the number of carbon atoms in the outer shell,
between the tertiary and primary amines. The di†erent combinations
compared in the present article are listed in Table 1.
z d ln $
h \
(2)
N
dz
where z is the activity of the protons (pH \ [log z).
10
The more classical way of analysis of the titration curve in
terms of macroscopic protonation steps is recovered by
writing the partition function as a polynomial in the activ-
ity:13
the number of carbon atoms in between the sites: n stands for
the spacer length between the two inner tertiary amines, and
m relates to the number of carbon atoms between a tertiary
and primary amine.
$ \ ; K zi
(3)
i
i/0
with K the so called formation constants. The macroscopic
pK values (logarithm of acidity constants) are given by
i
i
i
pK \ log K where K \ K /K
contains the average over
all possible microstates, belonging to a certain protonation
state.
m = 3:
N,N,Nº,Nº-tetraaminopropyl-1,2-ethylenediamine
10
i
i
i
i~1
[compound (2,3)]. First, 1175 ml of water and 100 g of ethyl-
enediamine (1.67 mol) are intensively mixed at 40 ¡C and
within 90 min 443 g acrylonitrile (8.35 mol) is added. The
reaction mixture is kept constant at 40 ¡C for 1 h and then
heated for 2 h at 80 ¡C. Afterwards half of the water and the
excess of acrylonitrile were evaporated under reduced pres-
sure, and after cooling the precipitate was isolated by Ðl-
tration. The residue was recrystallized from methanolÈwater
mixture to yield 478 g of N,N,N@,N@-tetracyanoethyl-1,2-ethyl-
enediamine (1.58 mol).
Experimental
Synthesis
A schematic picture of the structure and the synthesis route
for the di†erent compounds studied (see Table
nomenclature) is provided in Fig. 1. The notation (n,m), which
is used to distinguish the di†erent molecules, is correlated to
1 for
Yield: 94%. M.p.: 66 ¡C. 1H-NMR: 2.53 ppm, t, 8H,
ÈCH ÈCN; 2.72 ppm, s, 4H, NÈCH ÈCH ÈN; (CDCl ) 2.92
2
2
2
3
Table 1 Explanation of the abbreviations for the various hexaamines
studied in the present article
ppm, t, 8H, NÈCH ÈCH ÈCN.
2
2
Then 400 ml h~1 of a mixture of 20 wt.% N,N,N@,N@-
tetracyanoethyl-1,2-ethylenediamine and 80 wt.% N-
methylpyrrolidone and 3500 ml h~1 ammonia were passed at
130 ¡C under 200 bar of hydrogen over 4 liters of a Ðxed bed
catalyst of composition 90 wt.% CoO, 5 wt.% MnO and 5
wt.% P O in a 5 liter Ðxed bed reactor.14 Removal of the
solvent under reduced pressure and fractional distillation
resulted in N,N,N@,N@-tetraaminopropyl-1,2-ethylenediamine.
Yield: 95%. B.p.: 218 ¡C (6 mbar). 1H-NMR: 1.46 ppm, m
(broad), 16H, NÈCH ÈCH ÈCH ÈN (8H) and ÈNH (8H); (d-
Nomenclature
(n, m)
(2,2)
(3,2)
(2,3)
N,N,N@,N@-tetraaminoethyl-1,2-ethylenediamine
(PENTEN)
N,N,N@,N@-tetraaminoethyl-1,3-propylenediamine)
2
5
(PTETRAEN)
N,N,N@,N@-tetraaminopropyl-1,2-ethylenediamine
(TAPEN)
N,N,N@,N@-tetraaminopropyl-1,3-propylenediamine
(3,3)
(4,3)
N,N,N@,N@-tetraaminopropyl-1,4-butylenediamine
2
2
2
2
DMSO) 2.38 ppm, m, 8H, ÈCH ÈNH ; 2.42 ppm, s, 4H,
NÈCH ÈCH ÈN; 2.55 ppm, t, 8H, NÈCH ÈCH ÈCH ÈNH .
2
2
(n,m) stands for the hexaamine with n carbon atoms in the core unit,
and m carbon atoms between the primary and tertiary amines (see
also Fig. 1). The abbreviations PENTEN, PTETRAEN and TAPEN
originate from ref. 17.
2
2
2
2
2
2
13C-NMR: 31.1 ppm, NÈCH ÈCH ÈCH ÈN; 41.6 ppm,
2
2
2
ÈCH ÈNH ; (D O) 52.4 ppm, NÈCH ÈCH ÈN; 53.8 ppm,
2
2
2
2
2
NÈCH ÈCH ÈCH ÈNH . ESI-MS: Peak at 289.2 (M ] H)`
2
2
2
2
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(theoretical MW: 288). Amine number: 1134 mg KOH g~1.
Nitrile number: \1 mg KOH g~1.
the titration curves at 0.1 M and 1.0 M KCl are of similar
quality, albeit with a shift in pH, due to screening e†ects.
Fig. 2 clearly shows the inÑuence of the inner spacer n, the
number of carbon atoms between the two tertiary amines in
the core. All three hexaamines exhibit exactly the same proto-
nation behavior starting from the deprotonated state, up to
pH 8, when the (Ðrst) plateau is reached. The most favored
microstate at that pH is that one with the four outermost,
primary amines protonated. In the next protonation step a
tertiary amine is involved, and the di†erent length scales (n)
among the three hexaamines result in di†erent magnitudes of
the electrostatic interactions. The last step is even more pro-
nounced for the smallest molecule (2,3); electrostatic e†ects
between the two tertiary amines make it impossible to reach
full protonation even at pH 2.
The synthesis routes for the other compounds with m \ 3
[(3,3) and (4,3)] are analogous to the recipe described above.
m = 2:
N,N,Nº,Nº-tetraaminoethyl-1,2-ethylenediamine
[compound (2,2)]. The synthesis of the precursor N,N,N@,N@-
tetracyanomethyl-1,2-ethylenediamine is described in ref. 15.
The compound was recrystallized from methanolÈwater to
eliminate traces of HCN. The hydrogenation step is again
similar to the description above and described in ref. 14.
Potentiometric titrations
Conventional acidÈbase titrations of the hexaamines with dif-
ferent spacer lengths were carried out with a VIT90 Video
Titrator and a combined electrode (Radiometer, Copenhagen).
The electrode was calibrated with bu†er solutions of pH 4 and
7 (titrisol, Merck). All titrations were performed with HCl and
KOH (titrisol, Merck) at (22 ^ 1) ¡C, with KCl as the support-
ing electrolyte (p.a., Merck). The contribution of the hexa-
amines to the ionic strength was negligible; the initial
concentration of ionizable groups was lower than 10~2 M. All
titrations were reproduced with an error of ^1% in the
degree of protonation between pH 2.5 and 11. Backward base
titrations showed no hysteresis. The nitrogen content needed
to normalize the titration curves to the protonated fraction of
ionizable groups was determined with a CHN analyzer.
The ionization constants were obtained from the titration
curves as successive dissociation constants (pK values) by
means of a non-linear least squares Ðt procedure, with the
hexaamine concentration as an additional Ðt variable. The dif-
ference between the additional Ðt variable and the total
number of sites determined with the CHN analyzer was
within 1%. The accuracy of the obtained macroscopic proto-
nation constants was 0.1 pH units.
Fit results of the macroscopic protonation constants for the
three hexaamines at both 0.1 M and 1.0 M KCl are presented
in Tables 2 and 3 respectively, together with data from the
literature for (2,2) and (3,2) at 0.1 M KNO (refs. 16, 17) and
3
(4,3) (refs. 9). Literature data for (3,2) at 1.0 M are not avail-
able. The macroscopic Ðt results are shown together with the
experimental data in Fig. 2 for the case of m \ 3. The Ðt
method does not provide enough accuracy to obtain informa-
tion about the last step in the protonation scheme in the case
of (2,2).
For the hexaamines with m \ 3 the protonation of the
primary amines in the Ðrst four steps should be identical (see
Fig. 2); the short-range interactions are negligible. The
pK ÈpK show Ñuctuations around a mean average of about
1
4
0.1 pH units, an indication of the accuracy with which the
macroscopic constants are obtained. The same holds for the
data sets (2,2) and (3,2). A macroscopic Ðtting of pK with the
4
fugacity expression [eqn. (3)] appears to be slightly inÑuenced
by the input value for pK . This could explain the (minor)
5
di†erence of 0.2 pH units for the two compounds with outer
spacer m \ 2.
For more detailed information about both the method and
the analysis the reader is referred to ref. 9.
Table 2 Successive macroscopic protonation constants pK in 0.1 M
i
KCl are presented for hexaamines with inner and outer spacer length
n and m, respectively (for structure see Fig. 1)
Results and discussion
The protonation curves of (2,3), and (3,3) hexaamines in 1.0 M
KCl, together with data for (4,3) from the literature,9 are pre-
sented in Fig. 2. Protonation involves two steps for the case
n \ 3, and n \ 4 and n \ 2 even show a third step. In all cases
pK
(2,2)
(3,2)
(2,3)
(3,3)
(4,3)
i
1
2
3
4
5
6
10.30
10.08
9.58
8.99
8.42
10.31
9.63
9.26
8.52
2.5
10.81
10.12
9.71
9.06
6.03
2.75
10.94
10.11
9.87
8.91
6.65
4.97
10.83
10.22
9.72
9.13
7.16
6.01
9.63
9.26
8.31
3.1È3.5 1.33
È
È
È
Literature values for (2,2), (3,2) and (4,3) hexaamines are indicated in
italic.9,16,17 Literature pK values for (3,2) are interpolations to 22 ¡C,
based on two di†erent data sets at 20 ¡C and 25 ¡C. All experimental
pK values are obtained with Ñuctuations of ^0.1 pH units.
i
Table 3 Successive macroscopic protonation constants pK at 1.0 M
i
KCl are presented for (n,m) hexaamines. (n,m) stand for the inner and
outer spacer length between the six ionizable sites (Fig. 1)
pK
(2, 2)
(2, 3)
(3, 3)
(4, 3)
i
1
2
3
4
5
6
10.70
9.94
9.71
8.83
3.6È4.0
È
11.04
10.47
10.14
9.51
6.73
3.40
10.92
10.63
10.15
9.48
7.46
5.77
10.93
10.58
10.06
9.56
7.91
Fig. 2 Degree of protonation h as a function of pH for (n,3) hexa-
amines at 1.0 M KCl, with n \ 2 (K), 3 (|) and 4 (L). The results for
low ionic strength are of similar quality. The titration curve for (4,3) is
taken from ref. 9. The lines through the points are the macroscopic Ðts
of the protonation constants; results are presented in Table 3.
6.77
Literature values for (4,3) are indicated in italic.9 All experimental pK
values are presented with a standard deviation of ^0.1 pH units.
i
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Table 5 The calculated macroscopic protonation constants pK at
A Ðt of the Ising model to the titration data involved micro-
i
0.1 M and 1.0 M KCl for (n,3) hexaamines are shown
scopic pK values and nearest neighbor pair interactions e
i
ij
only (see Fig. 3). The nearest neighbor pair interactions are
taken to be independent of the chemical environment, but
only dependent on the spacer length. e , e and e represent
(2,3)
(3,3)
(4,3)
pK
0.1 M
1.0 M
0.1 M
1.0 M
0.1 M
1.0 M
2
3
4
i
the repulsive interaction between two amines with two, three
and four carbons in between, respectively.
10.55
10.12
9.77
9.34
5.80
3.00
10.89
10.46
10.11
9.68
6.47
3.67
10.55
10.13
9.77
9.34
6.61
5.02
10.90
10.47
10.11
9.67
7.42
5.83
10.57
10.13
9.77
9.34
7.18
5.99
10.93
10.48
10.10
9.66
7.93
6.76
2
3
4
5
6
Previously it was shown that the pair interactions are
largely independent of ionic strength.7h9 The values are based
on results obtained there. The only real Ðtting parameters are
the intrinsic protonation constants for the primary and ter-
tiary amines. Based on the di†erent empirical relations for the
various types of aliphatic amines10h12 these constants are split
up for amines with a di†erent chemical environment and dif-
The calculations are based on the Ising model with parameters pre-
sented in Table 4.
ferent ionic strength. pK(1) is used for the primary amines in
m/3
hexaamines with outer spacer m \ 3, and pK(1) for spacer
m/2
m \ 2. pK(3) is di†erent for all hexaamines because of the vari-
Trends are similar to the Ðt results obtained in Table 4. The
obtained microscopic protonation constants together with the
already determined pair interaction parameters can be used in
future research to predict the protonation behavior for polya-
mines built up from these monomers.
able inner spacer n. Due to the fact that pK and pK could
5
6
not be obtained sufficiently accurately for the hexaamines
with m \ 2 (Table 2), pK(3) was not determined for these
cases. The resulting parameter values for the hexaamines for
both ionic strengths are given in Table 4, and the calculated
macroscopic pK values based on these Ising parameters in
Table 5 for the case of m \ 3. Because of the incomplete Ðt
results for the case of m \ 2 the calculated macroscopic pK
values are left out, although the Ðrst three experimentally
obtained pK values were again reproduced within 0.2 pH
units.
Conclusion
In conclusion, we have shown that intrinsic pK values can be
obtained from well-chosen model oligoamines. More extended
study on the protonation behavior of amines may yield a
more structural relation than the Taft equations for the intrin-
sic protonation constants. With the already established pair
interaction parameters the Ising model has the advantage over
these empirical relations that the protonation constants of an
individual group can simply be calculated at any protonation
state of the molecule. This brings the prediction of the titra-
tion curve for a given structure within reach, even for systems
with a very large number of sites.
Protonation constants for similar compounds with only
four amine groups are also available in the literature18 for
various spacer lengths at 0.1 M. These molecules di†er in that
the two tertiary amines are replaced by secondary amines.
Using the same Ising model with the same pair interaction
parameters (only pK(2) instead of pK(3) on literature data for
molecules with m \ 3 and n \ 2, 3 and 4 gave pK(1) \ 10.10
m/3
and pK(2) \ 9.09, 9.48 and 9.99 in 0.1 M KCl, respectively.
References
1
D. D. Perrin, B. Dempsey and E. P. Serjeant, pK Prediction for
a
Organic Acids and Bases, Chapman and Hall, London, 1981.
2
R. W. Taft Jr, in Steric E†ects in Organic Chemistry, ed. M. S.
Newman, John Wiley and Sons, Inc., New York, 1956, p. 556†.
R. A. Marcus, J. Phys. Chem., 1954, 58, 621.
A. Katchalsky, J. Mazur and P. Spitnik, J. Polym. Sci., 1957, 23,
513.
3
4
Fig. 3 Schematic representation of the hexaamine showing the
various parameters used to Ðt the Ising model to the macroscopic
protonation constants. All hexaamines are treated with a Ðxed nearest
neighbor pair interaction parameter e and e based on previous
5
6
7
T. Kitano, S. Kawaguchi, K. Ito and A. Minakata, Macro-
molecules, 1987, 20, 1598.
n
m
work.8,9 At one ionic strength pK(1) is kept constant for a series of
hexaamines with m \ 3 and m \ 2, but pK(3) is variable. The idea
behind this approach is that the microscopic protonation constants
are strongly dependent on the chemical environment.
R. Smits, G. J. M. Koper and M. Mandel, J. Phys. Chem., 1993,
97, 5745.
M. Borkovec and G. J. M. Koper, Prog. Colloid Polym. Sci., 1998,
109, 142.
M. Borkovec and G. J. M. Koper, J. Phys. Chem., 1994, 98, 6038.
R. C. van Duijvenbode, M. Borkovec and G. J. M. Koper,
Polymer, 1998, 39, 2657.
8
9
Table 4 Values of the Ising parameters needed to Ðt the macro-
scopic pK values of (n,3) hexaamines at 0.1 M and 1.0 M KCl are
presented
10 F. E. Condon, J. Am. Chem. Soc., 1965, 87, 4481.
11 F. E. Condon, J. Am. Chem. Soc., 1965, 87, 4485.
12 H. K. Hall Jr, J. Am. Chem. Soc., 1957, 79, 5441.
13 T. L. Hill, An Introduction to Statistical T hermodynamics, Dover,
New York, 1986.
14 L. Hauling and W. Paulus, EP 790 976, BASF AG, 09.11.1995.
15 H. Distler and K. L. Hock, EP 045386, BASF AG, 08.07.81.
16 P. Paoletti, R. Walser, A. Vacca and G. Schwarzenbach, Helv.
Chim. Acta, 1971, 54, 243.
17 E. Garcia-Espana, M. Micheloni, P. Paoletti and A. Bianchi,
Inorg. Chem., 1986, 25, 1435.
18 R. M. Smith and A. E. Martell, Critical Stability Constants,
Plenum Press, New York, 1989.
Ising model parameters
0.1 M KCl
1.0 M KCl
pK(1)
9.40
9.95
7.50
8.32
8.90
2.20
1.00
0.60
9.79
10.28
8.17
9.13
9.67
2.20
1.00
0.60
m/2
pK(1)
m/3
pK(3) (n,m) \ (2,3)
pK(3) (n,m) \ (3,3)
pK(3) (n,m) \ (4,3)
e
2
e
3
e
4
An explanation of the parameters is given in Fig. 3. Fixed values in
the Ðtting routine are indicated in italic.
Paper 9/07397C
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Phys. Chem. Chem. Phys., 1999, 1, 5649È5652