The use of limiting currents in determination of the effect of viscosity in electrochemical
experiments performed in mixtures of water with some organic co-solvents
P. Zumana , D. Rozbrojb, J. Ludvíkb , M. Aleksićc, L. Camaionea, H. Celika
a
b
Department of Chemistry, Clarkson University, Potsdam, NY 13699-5810, USA
J. Heyrovský Institute of Physical Chemistry, Czech Academy of Science, Dolejškova 3, Prague 8, Czech
Republic
c
Department of Physical Chemistry, Faculty of Pharmacy, University of Belgrade, P.O.BOX 146,
Yu - 11000, Vojvoda Stepe 450, Yugoslavia
Abstract
Ratios of limiting diffusion controlled currents recorded in aqueous solutions to those
obtained in mixture with water-soluble organic co-solvents yield values of rel1/2. These values can
be used for evaluation of electrochemical experiments in such media and for distinguishing currents
affected solely by a change in viscosity from those caused by other solvent-solute interactions, e.g.
covalent additions. Limiting currents of Cd2+ ions and of 2-hydroxy-1,4-naphthoquinone proved to
yield most reliable result, values of rel1/2 obtained with Tl+ ions showed somewhat poorer
correlation. The average values of rel1/2 obtained from comparison of limiting currents for mixtures
of water with ethanol and acetonitrile are in very good agreement with average values of rel1/2
reported in the literature and in acceptable agreement for mixtures of water with 2-propanol.
Nevertheless, the electrochemical data show much smaller standard deviations, than the data
reported in the literature, which have shown inconsistencies when data from different sources are
compared. The data obtained for mixtures of water with DMF have not been previously reported.
Key words
Limiting currents, viscosity, water-organic solvent mixtures, polarography
1. Introduction
The electrochemical experiments in mixtures of water with organic co-solvents belong
among common electrochemical routines. Measurements of limiting currents and interpretation of
their dependences on pH, on composition of the solution or on other experimental parameters play a
crucial role e.g. in investigations of reaction mechanisms, equilibria or in studies of solvent – solute
interactions. In these studies, however, the changing viscosity of the solution can have a significant
effect on measured currents. Limiting diffusion-controlled currents, as can be obtained by DC and
normal pulse polarography or hydrodynamic voltammetry using a rotating disk electrode, are a
linear function of the square root of the diffusion coefficient [1-3]. Diffusion coefficient according
to Stokes-Einstein equation is directly proportional to the reciprocal value of the relative viscosity.
Therefore limiting currents are indirectly proportional to the square root of relative viscosity. The
validity of the expression (1)
id = k.rel-1/2
(1)
has been repeatedly confirmed in solutions, where the viscosity was varied in wide ranges by
variations in concentration of the supporting electrolyte [1,2], or by adding to an aqueous solution
high concentration of viscous electroinactive component such as glycerol or sucrose [1,2].
When limiting currents obtained in mixtures of water with varying amount of a miscible
organic solvent should be compared, it is necessary to multiply all measured diffusion limiting
currents by a square root of viscosity. It is recommended to restrict such comparison to mixtures,
which contain less than 50 % v/v of the organic co-solvent. At higher concentration of the organic
component, irregularities are often observed. These can be attributed to a change in solvation of the
electroactive species from that predominantly formed by water molecules to solvent-solute
interactions in which those with the organic components predominate.
In one of our studies in aqueous solutions containing varying amounts of alcohols, it was of
importance to distinguish, which part of the decrease of the limiting current of the reducible species
is due to an effect of viscosity and which part is due to a chemical reaction between the
electroactive species and alcohol. Inspection of tables indicated, that literature offered for a given
composition of the mixtures of water with the alcohols values, which differed considerably from
source to source (Table 1). Tabulated data proved unsuitable for an exact evaluation of the effect of
viscosity and therefore an approach based on measurements of limiting currents of several
reversible electrochemical systems was developed.
To obtain a polarographic diffusion controlled current it is necessary to measure the currentvoltage curve in the presence of a supporting electrolyte, such as 0.1 M acetate buffer, pH 4,7. In
this medium many organic compounds yield a well developed wave and its relative viscosity
(1.035) differs only slightly from that of pure water. - As test substances Tl+ and Cd2+ ions and a
water soluble quinone (2-hydroxy-1,4-naphthoquinone) were used. The reduction of these species
in protic solvents is reversible and recorded i - E curves thus were not affected by kinetic factors.
2. Experimental
Current-voltage curves were recorded using the instruments, manufactured by Polaro
Sensors (Czech Republic), IBM and Sargent (USA), respectively. Dropping mercury electrodes
(DME) used had a drop-time (t1) of 2 to 4 s at an out-flow velocity of about 2 mg.s-1.
Chemicals used for preparation of 0.01M stock solution of thallium sulfate, thallium nitrate,
cadmium sulfate and 2-hydroxy-1,4-naphthoquinone (Lawsone) were reagent grade. 0.1M acetate
buffer pH 4,7 was used as the supporting electrolyte.
Polarographic current-voltage curves of 210-4 M solutions of the electroactive species in a
given, freshly prepared, appropriate mixture were recorded at 25°C after removal of oxygen by a
stream of argon or nitrogen. Every measurement was repeated 3 to 5 times and the mean value used
for the tabulation.
3. Results and Discussion
As the diffusion controlled limiting current in purely aqueous solution equals
i0 = const. x 1/(H2O)1/2
(2)
and that of a mixture containing organic co-solvent
i = const. x 1/(sol)1/2,
(3)
(where H2O and sol are the viscosity of water and mixed solution, respectively), then
i0/i = (sol)1/2 / (H2O)1/2 =
(rel)1/2
(4)
where rel represents the relative viscosity. Hence to determine the (rel)1/2 needed for
multiplication of the measured current i to compare it to a value corresponding to aqueous solution,
the limiting current must be measured in a solution both dissolved in water (i0) and in the mixture of
water and the organic co-solvent (i).
The presence of the organic co-solvent can affect not only polarographic current-voltage
curves, but can also alter the pH of the studied solution. Therefore the buffers for the supporting
electrolyte must be chosen in such a way that the limiting current remains pH-independent at at
least 1 pH-unit compared to the pH of the chosen buffer. For all studied substances the limiting
currents were proved to be pH-independent between pH 3.7 and 5.7.
The choice of electroanalytical techniques yielding limiting current, such as DC or normal
pulse polarography or hydrodynamic voltammetry with a rotating disk electrode offers several
advantages: The measured ratio i0/i is independent of the concentration of the electroactive species,
of the number of transferred electrons, and of the rate of the electrode process (its reversibility).
This makes the above techniques better suitable for this type of studies than techniques yielding
peak or summit currents as in the case of differential pulse, AC or square-wave polarography or
linear sweep or cyclic voltammetry, where the peak current is also affected by the rate of the
electrode process.
Measurements were carried out in solutions containing between 0 and 50% v/v of the
organic solvent. The mixtures with various alcohols were investigated first, as they are often used in
electroanalytical chemistry of organic compounds. For methanol in mixtures with water the
variations in values of rel are too small for obtaining electrochemically reliable values. For tertbutanol the solubility limits the useful concentration range to below about 10 % v/v. Among
alcohols, the investigation was therefore limited to mixtures of water with ethanol and 2-propanol.
In addition to this, mixtures of acetonitrile and dimethylformamide with water were also
investigated, because of their frequent use in electrochemistry as solvents and co-solvents.
When trying to separate the effects of viscosity from other types of interaction of the solute,
the intermediate of its electrolysis or its product, the limiting currents measured in mixed solvents
(i) have to be multiplied by rel1/2 . The values of rel1/2 for some mixtures of organic solvents with
water (electrochemically determined as well as cited from the literature) are summarized in Table 1.
The electrochemical data (i0/i) reported are mean values of at least 3, usually 5 or 6 independent
measurements. The standard deviation of these repetitive scans was in all instances smaller than
3%, the accepted value for accuracy of current measurements by polarographic techniques.
The series of data taken from the literature show a wide variation, depending on the source.
On the other hand, the electrochemically obtained values of rel1/2 showed much smaller variations,
in most cases even below 2%.
The individual values reported in literature differed also widely according to the source and
the data from none of the available sources paralleled completely the electrochemical ones. Some
agreed better at a lower co-solvent concentration, some at higher. Thus for correction of the limiting
current measured in solvent mixtures, values of rel1/2 obtained from electrochemical measurements
seem to be most suitable. It can be pointed out that reported electrochemical data were obtained in
three different laboratories in three different countries with comparable results.
Reduction of thallium (I) ions, which is an excellent internal standard for measurement of
potentials in aqueous media, showed in several instances larger variations in the values of rel1/2
than data obtained for the cadmium (II) ion or the 2-hydroxynaphthoquinone. Tentatively, this may
be attributed to variations in the structure of the solvated shell in the presence of an organic cosolvent. It seems that Cd(II) ions or suitable quinones are better suited for a more accurate
determination of the relative viscosity coefficients.
4. Conclusions
An independent method for the determination of the relative viscosity coefficients in various
mixtures of water with some organic co-solvents was developed. Sets of data for mixtures of water
with ethanol, 2-propanol, acetonitrile and DMF were obtained. In cases of previously investigated
mixtures, it has been demonstrated that measurements of limiting currents yield values of rel
which are more reliable than values reported in the literature. The electrochemical data show better
consistency for each solvent mixture, as reflected by smaller standard deviation. Values of rel
obtained by electrochemical measurements offer for evaluation of the role of solvent composition
on limiting currents the additional advantages of using the same reaction conditions, including the
same supporting electrolyte. Electrochemical measurements open also the possibility of an
extension of their use to solvent mixtures, for which no previously reported data are available, as
demonstrated for the mixtures of DMF with water.
Acknowledgment
The financial support of D.R. and J.L. by the grant project No. 203/02/0983 from the Grant
Agency of the Czech Republic and of P.Z. and L.C. by The Camille & Henry Dreyfus Foundation
are highly appreciated.
----------------------------------------------------------------------------------------------------------------------References
1. J. Heyrovský, J. Kůta, Principles of Polarography, Publ. House of the Czechoslovak Acad. Sci.,
Prague, Czechoslovakia, 1965, p.103.
2. L. Meites, Polarographic Techniques, 2nd Ed., Interscience, New York, USA, 1965, p. 141.
3. W. J. Albery, M. L. Hitchman, Ring-Disk Electrodes, Clarendon Press, Oxford, U.K. 1971.
4. K. Noack, Wiedemann´s Ann. 27 (1886) 289; 28 (1886) 666.
5. H. C. Jones, F. H. Getman, J. Am. Chem. Soc. 31 (1904) 303; 32 (1904) 308, 398.
6. H.C. Jones, F.H. Getman, Carn. Inst. Publ. No. 210 (1915) 202.
7. International Critical Tables
8. J. Timmermans, The Physico-Chemical Constants of Binary Systems in concentrated Solutions,
Vol. 4. Interscience, New York, USA 1960.
9. Handbook of Chemistry and Physics, 52nd Ed. , R.C. Weast, Ed., CRC Press, Cleveland, Ohio,
USA, 1971-2, p. D-188.
10. G. P. Irany, J. Am. Chem. Soc. 65 (1944) 1396.
11. Handbook of Chemistry and Physics, 67th Ed. , R.C. Weast, Ed., CRC Press, Boca Raton, FL,
USA, 1986-7, p. D-249.
Corresponding author:
Professor Petr Zuman
Department of Chemistry, Clarkson University, Potsdam, NY 13699-5810, USA
Tel. +1 315 268 2340; Fax: +1 315 268 6610; e-mail: zumanp@clarkson.edu
Table 1
Square-roots of relative viscosities (sol / H2Ol )1/2 for corrections of limiting diffusion currents in
mixtures of water with ethanol, 2-propanol, acetonitrile and dimethylformamide. Values rel were
determined in 0,1 M acetate buffer pH 4.7.
Ethanol
Electrochemically measured data a
% v/v
Tl(I)
Cd(II)
NQ
10
1.11
1.18
20
1.38
30
b
Data from the literature
Average val.
Ref.[1]
Refs.[2]
Ref.[3]
Ref.[4]
Ref.[5]
Average value
1.16
1.15  0.029
1.17
1.20
1.07
1.01
1.18
1.13  0.073
1.30
1.30
1.33  0.038
1.35
1.34
1.32
1.29
1.41
1.34  0.040
1.50
1.42
1.46
1.46  0.033
1.52
1.44
1.42
1.46
1.59
1.49  0.062
40
1.63
1.55
1.55
1.58  0.038
1.68
1.53
1.50
1.59
1.68
1.60  0.074
50
(1.80)
1.58
1.60
1.59  0.010
1.75
1.60
1.54
1.64
1.68
1.63  0.069
2-prop.
Electrochemically measured data a
Data from the literature
% v/v
Tl(I)
Cd(II)
NQ b
Average val.
Ref.[6]
Ref.[4]
Ref.[7]
Average value
10
1.15
1.16
1.14
1.15  0.008
1.29
1.20
1.22
1.22  0.016
20
1.30
1.33
1.35
1.33  0.020
1.53
1.41
1.47
1.47  0.045
30
1.46
1.49
1.57
1.51  0.046
1.75
1.58
1.69
1.67  0.070
40
1.66
1.66
1.68
1.67  0.009
1.88
1.74
1.82
1.81  0.057
50
1.80
1.76
1.74
1.77  0.025
1.95
1.82
1.92
1.90  0.055
Electrochemically measured data a
acetonitrile
Data from the literature
% v/v
Tl(I)
Cd(II)
NQ b
Average value
Ref.[4]
10
1.02
1.02
1.01
1.02  0.005
1.05
20
1.03
1.04
1.05
1.04  0.008
1.06
30
1.06
1.04
1.04
1.05  0.010
1.05
40
1.07
1.04
1.02
1.04  0.021
1.03
50
(1.09)
1.02
1.03
1.03  0.010
0.99
1.07  0.016
Mean values
1.04  0.060
Electrochemically measured data a
dimethylformamide
% v/v
Tl(I)
Cd(II)
NQ b
Average value
10
1.12
1.08
1.08
1.09  0.019
20
1.22
1.18
1.19
1.20  0.017
30
1.35
1.26
1.26
1.29  0.042
40
1.44
1.31
1.39
1.38  0.053
50
1.49
1.38
1.45
1.44  0.045
a This work
b 2-hydroxy-1,4-naphthoquinone
Reference:
Ref.1 Nosek, K. Wiedemann´s Ann. 1886, 27, 289; 1886, 28, 666.
Taken from: Timmermans, Jean, The Physico-Chemical Constants of Binary Systems in
Concentrated Solutions, Vol. 4.: Systems with Inorganic + Organic or Inorganic Compounds
(Excepting Metallic Derivatives); Interscience Publishers Inc., New York, USA 1960., p.190.
Ref.2 Jones, H. C.; Getman, F. H. J. Am. Chem. Soc, 1904, 31, 303; 1904, 32, 308, 398.
Jones, H.C.; Getman, F.H.; Carn. Inst. Publ. No. 210, 1915, 202.
Taken from: Timmermans, Jean, The Physico-Chemical Constants of Binary Systems in
Concentrated Solutions, Vol. 4.: Systems with Inorganic + Organic or Inorganic Compounds
(Excepting Metallic Derivatives); Interscience Publishers Inc., New York, USA 1960, p.191-2.
Ref.3 International Critical Tables
Ref.4 Timmermans, Jean, The Physico-Chemical Constants of Binary Systems in Concentrated
Solutions, Vol. 4.: Systems with Inorganic + Organic or Inorganic Compounds (Excepting Metallic
Derivatives); Interscience Publishers Inc., New York, USA 1960.
Ref.5 Handbook of Chemistry and Physics, 52nd Ed. , Weast, R.C., Ed., CRC Press, Cleveland,
Ohio, USA, 1971-2, p. D-188.
Ref.6 Irany, G. P. J. Am. Chem. Soc. 1944, 65, 1396.
Taken from: Timmermans, Jean, The Physico-Chemical Constants of Binary Systems in
Concentrated Solutions, Vol. 4.: Systems with Inorganic + Organic or Inorganic Compounds
(Excepting Metallic Derivatives); Interscience Publishers Inc., New York, USA 1960, p. 223.
Ref.7 Handbook of Chemistry and Physics, 67th Ed. , Weast, R.C., Ed., CRC Press, Boca Raton,
FL, USA, 1986-7, p. D-249.