4630
J. Phys. Chem. 1996, 100, 4630-4636
Voltammetric Studies of Transport of Thallium(I) Counterions in Solutions of Polyelectrolytes in Mixed Solvents Malgorzata Ciszkowska and Janet G. Osteryoung* Department of Chemistry North Carolina State UniVersity Raleigh, North Carolina 27695-8204 ReceiVed: October 9, 1995; In Final Form: December 1, 1995X
Transport of thallium(I) counterions was studied in solutions of poly(styrenesulfonic acid), PSSA, in mixed solvents by steady-state voltammetry at mercury microelectrodes. The diffusion coefficient values of TlI obtained in polyelectrolyte solutions were compared to those from solutions of p-toluenesulfonic acid, p-TSA, the simple acid, monomer analogue of PSSA. The dependence of the transport of TlI counterions on the dielectric constant, , of the solvent was investigated for such solvents as ethanol-, methanol-, and 1,4dioxane-water mixtures over a wide range of -values. The diffusion coefficient of thallium(I) counterions in PSSA normalized by the diffusion coefficient in solution of the simple acid, p-TSA, was found to change proportionally to the change in the dielectric constant value of the solvent. This dependence is close to that predicted by Manning’s theory. The results were obtained over a wide range of concentrations of counterions and over a wide range of concentrations of various supporting electrolytes.
Introduction Solutions of polyelectrolytes can be treated as model systems for the description of dynamic properties of simple ions in such important media as membranes, micelles, biological fluids and tissues, and other charge aggregates. The high charge density of polyelectrolytes leads to strong electrostatic interactions between polyions and simple ions present in solutions. These interactions result in changes in the transport properties of simple ions. The transport of counterions, simple ions with charge opposite to the charge of the polyions, is suppressed in the presence of polyelectrolytes. This effect is the strongest in solutions of very low ionic strength, for example, solutions without added simple electrolytes. The interactions between counterions and polyelectrolytes are called “counterion binding” or “counterion condensation”.1-3 Various techniques have been used to study the transport and the interactions of simple ions in solutions of polyelectrolytes, including the radioactive tracer method,4,5 pulsed-field-gradient spin-echo (PFGSE) NMR6,7 and voltammetry at regular electrodes.8-10 In a series of papers we have introduced voltammetry with microelectrodes as a very useful, fast, and inexpensive technique for studying the transport of ions in solutions of polyelectrolytes.11-15 We examined several counterions over a wide range of polyelectrolyte and supporting electrolyte concentrations using two modes: first, voltammetry of the counterion from the dissociation of a polyelectrolyte (hydrogen ion in poly(styrenesulfonic acid))11,12,15 and, second, voltammetry of a probe counterion (metal cations, Tl+, Cd2+, or Pb2+ in poly(styrenesulfonic acid).13,14 The results obtained for the transport of thallium(I) counterions in poly(styrenesulfonic acid) by voltammetry with mercury film microelectrodes were compared to results from pulsed-field-gradient spinecho (PFGSE) NMR.14 The results, identical within experimental uncertainty, show that the electrochemical measurements are free of artifacts associated with the intrinsic interfacial nature of the experiment and confirm the identity of self- and gradientdiffusion coefficients under the range of conditions employed. There are several theories describing the transport properties of simple counterions in polyelectrolyte solutions. The theoretiX
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4630$12.00/0
cal treatments have been based most often on the assumption that the polyions may be modeled as charged lines16,17 or infinite cylinders.18,19 Our studies, performed for various polyelectrolytes,11-15 indicate that the experimental data are the closest to those calculated based on the line charge model of polyelectrolytes given by Manning.16,17 According to this theory, counterions condense on the polymer to reduce the net charge to achieve the value of unity for the dimensionless charge density parameter λ. The changes in transport properties of counterions depend on the nature of the polyelectrolyte and the nature of the solvent:
D/D0 ) F(γ)[1/λ + γ]/[1 + γ]
(1)
λ ) e02/4π°bkT
(2)
with
where D is the observed diffusion coefficient, D0 is the diffusion coefficient in a solution free of the polyion, γ is the ratio of the concentration of simple electrolytes to the concentration of the counterions, F(γ) is a factor (depending on γ) that approaches limiting values of 0.866 and unity for small and large γ, respectively, e0 is the elementary charge, ° is the permittivity of vacuum, is the dielectric constant (relative permittivity) of the solvent, b is the length of the polyion per ionized group, k is the Boltzmann constant, and T is the absolute temperature. According to eqs 1 and 2, a decrease of the dielectric constant of the solvent decreases the diffusion coefficient of the counterions in the polyelectrolyte solution. In another words, the strength of electrostatic interactions between polyions and counterions is inversely proportional to the value of the dielectric constant. Although this dependence of the apparent diffusion coefficient on the dielectric constant is a specific feature of Manning’s treatment, it is more generally a feature of interactions described by the Poisson-Boltzman equation. The Poisson-Boltzman theory describes the strength of the interactions between polyions and counterions as a function of the dielectric constant of the solvent and the local energy of these interactions as follows2
U(r) ) (z2e2/4π°r) e-r/λD © 1996 American Chemical Society
(3)
Thallium(I) Counterions where z is the valence of the counterion, r is the distance between the counterion and the polyion, λD ) (°kT/2e2I)1/2, and I is the ionic strength of the solution. Over the years, the study of polyelectrolyte solutions has been performed much more extensively in aqueous solutions than in nonaqueous solutions.3 The reason for this is that polyelectrolytes, usually with high charge density, are difficult to dissolve in polar organic solvents. Additionally, many studies were focused on naturally occurring polyelectrolytes such as proteins, nucleic acids, and polysaccharides in their biologically natural, aqueous environment. However, there is a series of papers published by Fuoss and co-workers during the 1940s and 1950s that describes studies on polyelectrolytes in nonaqueous solutions.20-28 The two properties, conductance and viscosity, of such polyelectrolyte systems as poly(4-vinylpyridine), poly(4-vinyl-N-n-butylpyridine), the polyester of succinic anhydride and methyldiethanolamine, and the copolymer of 4-vinylpyridine and styrene have been studied in various solvents such as ethanol, ethanol-water mixtures, methanol, methylethyl ketone, diphenyl ether, nitromethane, and nitromethane-dioxane mixtures. Both parameters, conductance and viscosity, were found to depend on the dielectric constant of the solvent. However, the nature of the results is such that they cannot be compared quantitatively to the predictions of existing theories. Investigation of the transport of counterions in polyelectrolytes in nonaqueous solutions can offer insights into the fundamental properties of polyelectrolytes. As was mentioned before, the strength of electrostatic interactions should vary inversely as the dielectric constant of the medium, as shown by eqs 1 and 2. Organic solvents offer a wide range of dielectric constant values, and the dependence of the electrostatic interactions on the dielectric properties of solvents can be studied. These investigations also can be very important for a better understanding of the transport properties of ions in nonaqueous or mixed solvent solutions of ion exchange systems such as membranes and ion transport and separation in liquid chromatography. The aim of this work was to study the transport behavior of a monovalent counterion, thallium(I), in polyelectrolyte solutions of various dielectric constants. We decided to use mixed, organic-water solvents, which offer a wide range of dielectric constant values and, at the same time, minimize problems with the solubility of polyelectrolytes, with the very high resistance of the solution, and with preventing traces of water in pure organic solvents. The transport of thallium(I) cations in poly(styrenesulfonic acid) was studied in mixtures of water and such organic solvents as ethanol, methanol, and 1,4-dioxane over a wide range of solvent composition and a wide range of various supporting electrolyte concentrations. The experimental results are discussed in light of existing theories for polyelectrolytes. Experimental Section Voltammetry. Voltammetric measurements were carried out with a three-electrode system in a jacketed cell (25 °C) enclosed in an aluminum Faraday cage. A mercury film disk microelectrode of 15 µm in radius, r, was used as a working electrode. Silver disk microelectrodes (Project Ltd., Warsaw, Poland) were used as substrates for the mercury films. The mercury film thickness was 1 µm. The procedure for preparation of a silverbased mercury film microelectrode has been described in detail.29 The surface of the mercury film was inspected with an inverted microscope (Leitz Wetzler, Germany) before use. Some experiments were performed with a platinum disk microelectrode of 5.5 µm in radius as a working electrode. A platinum quasi-reference electrode was used, under experimental
J. Phys. Chem., Vol. 100, No. 11, 1996 4631 conditions described previously,12 to prevent leakage of ions into the cell. The counterelectrode was platinum. Staircase voltammograms were obtained using a Model 273 potentiostat (EG&G PARC) connected to a Keithley Model 427 current amplifier and controlled by software via a PC 486 computer. Staircase voltammetry parameters were as follows: step height (∆E) of 5 mV and frequency (f) of 1 Hz. Under these conditions the limiting current for a 15 µm Hg film disk electrode does not exceed the steady-state value by more than 3%.30 The deposition of mercury on the Ag disk electrode was performed in a three-electrode system with a Pt wire counter electrode and a SCE reference electrode with a Model 173 potentiostat connected to a Model 179 digital coulometer (EG&G PARC). Chemicals and Solutions. All reagents, except poly(styrenesulfonic acid) were of reagent grade purity and were used as received. Thallium(I) nitrate (Alfa) was used as a source of thallium(I) cations. The electrolyte concentration was adjusted with lithium perchlorate (Aldrich) and tetraethylammonium nitrate, TEA(NO3) (Kodak). The monomer analogue of poly(styrenesulfonic acid), p-toluenesulfonic acid (Fluka), p-TSA, was used for comparison as a simple strong acid with the same acidic group. Poly(styrenesulfonic acid) (MW 70 000, 380 units per polymer chain, Polysciences Inc.), PSSA, was purified as described previously.11,12 The concentration of PSSA reported in this work (we also call it the equivalent concentration of PSSA) is the concentration of the sulfonic groups in PSSA. Ferrocene (Eastman Kodak) and 2,2,6,6-tetramethyl-1-piperidinyloxy, TEMPO (Aldrich), were used as uncharged probe molecules. Solutions were made from the following solvents: ethanol (Fisher), methanol (Fisher), 1,4-dioxane (EM Science), and ultrapure water (Milli-Q, Millipore Corporation). All compositions of solvents are reported in weight percent. Solutions of PSSA or p-TSA in mixed solvents were made by dissolution of acid in the appropriate solvent. The thallium(I) counterion concentration was fixed by adding not more than 25 µL of aqueous TlI stock solution into 10 mL of the investigated solution. This amount of water added to the solution changes the concentration of water by not more than 0.25%. Solutions were deoxygenated before voltammetric scans and blanketed with a stream of solvent-saturated argon. Results and Discussion The thallium(I) cation was used as a probe counterion in polyelectrolyte solutions. The method of the voltammetric investigation of the transport of thallium(I) as a probe counterion in aqueous solutions of PSSA has been described in detail13 and compared to results for the self-diffusion coefficient obtained by PFGSE NMR.14 The concentration of the probe counterions should be much lower than the concentration of the polyacid. Under conditions where the concentration of hydrogen ions (from dissociation of PSSA) in the solution is at least 50 times the highest concentration of thallium(I) cations, we can expect the same interactions between polyions and both hydrogen and thallium counterions. Additionally, if the concentration of hydrogen ions is at least 50 times the concentration of TlI, the hydrogen ion acts as a supporting electrolyte for Tl+. Therefore, the transport-limited steady-state current of the reduction of thallium(I) cations is no larger than 1.005 times the diffusional value.31 The diffusion coefficient values obtained in PSSA solutions for various compositions of solvents were compared to those from solutions without polyelectrolyte. In simple solutions, to maintain a constant concentration of hydrogen ions, p-TSA was used as a monomer analogue of PSSA. For both acids PSSA
4632 J. Phys. Chem., Vol. 100, No. 11, 1996
Ciszkowska and Osteryoung TABLE 1: Diffusion Parameters Calculated from Concentration Calibration Plots of TlI in PSSA or p-TSA Solutions with No Added Supporting Electrolyte in Ethanol-Water Mixtures slopeb (nA mM-1) DTlI (106 cm2 s-1)
ethanol wt %
a
PSSA
p-TSA
PSSA
p-TSA
Rexp c Rcalc d
0 (H2O) 20 50 70 95
78.54 67.0 49.0 37.5 25.7
4.07 2.04 0.91 0.54 0.45
11.63 6.87 4.94 4.09 4.36
7.03 3.52 1.58 0.93 0.78
20.08 11.86 8.53 7.07 7.53
0.350 0.297 0.185 0.132 0.103
0.334 0.285 0.209 0.160 0.109
a represents dielectric constants from ref 32. b From concentration calibration plots, 0.05 e CTlI (mM) e 0.25 for 10 mM PSSA (or p-TSA). c R ) DTlI in PSSA/DTlI in p-TSA with no supporting electrolytes. d Calculated from eqs 1 and 2.
Figure 1. Steady-state voltammograms of reduction of 0.16 mM TlI in 10 mM PSSA solution, with no supporting electrolytes, in waterethanol mixtures where the wt % of ethanol in water are (a) 0, (b) 20, (c) 50, (d) 70, and (e) 95. For the mercury film disk microelectrode r ) 15 µm.
and p-TSA, the sulfonic group is the source of a dissociated hydrogen ion. Therefore, for each composition of the solvent, the degree of dissociation of the poly- and simple acids should be the same. In the following, results are discussed separately in the text for each solvent system. However, in the figures the results are collected together for the various solvent systems examined. Ethanol-Water Solutions. The dielectric constant, , of ethanol-water mixtures changes from 25 for pure ethanol to 79 for pure water (25 °C).32 The reduction waves of thallium(I) cations in ethanol-water solutions containing PSSA are well defined, even under very demanding conditions of no added supporting electrolytes, as shown in Figure 1. The reproducibility of results was not as good as in aqueous solutions,13,14 and the highest relative standard deviation was 6.5% for 0.05 mM TlI, 10 mM PSSA, and no supporting electrolytes in 95% ethanol solution. The difference in halfwave potentials of the waves is the result of the use of a quasi-reference Pt electrode, the potential of which depends on the composition of the solution.12 Voltammetric waves of TlI reduction obtained in the simple acid p-TSA were also very well defined. The reproducibility of the steady-state current was very good, with relative standard deviations better than 2.5%. The wave height of TlI reduction in polyelectrolyte solutions, Figure 1, decreases with increasing ethanol percentage, which illustrates the changes in the diffusion coefficient of the thallium cation. Concentration Calibration Plots. To obtain values of the diffusion coefficient of thallium(I) in various solvents, in the presence and the absence of polyelectrolytes, we studied the dependence of the steady-state current on the concentration of TlI cations. The measurements were performed for the concentration range of TlI from 0.05 to 0.25 mM for five different compositions of ethanol-water solutions: 95%, 70%, 50%, 20%, and 0% ethanol. The concentration of PSSA was 10 mM. In the absence of polyelectrolytes, a constant concentration of hydrogen ions was maintained by the addition of 10 mM p-TSA. For all concentration calibration plots, we obtained linear dependencies of the steady-state current on the concentration of TlI, with correlation coefficients better than 0.9987 and 0.9996 for PSSA and p-TSA solutions, respectively. The slopes of the concentration calibration plots for solutions with no added supporting electrolytes are presented in Table 1. This table also includes the dielectric constants for the ethanol-water solutions employed. The diffusion coefficient of the electroactive species, D, can be calculated from the slope of a concentration calibration plot
according to the dependence of the steady-state current on diffusion coefficient,33
is ) 4nFCDr
(4)
where C is the concentration of the electroactive species (in our studies TlI), r is the radius of the microelectrode, n is number of electrons transferred, and F is the Faraday constant. Diffusion coefficient values calculated for TlI in solutions of PSSA and p-TSA, without supporting electrolytes, are presented in Table 1. As one can see, the diffusion coefficients of TlI in polyelectrolyte solutions are much smaller than in solutions of the simple acid. This indicates the strong suppression of transport of thallium counterions by PSSA. The same effect has been observed in aqueous solutions of PSSA without added supporting electrolytes, and it is due to the strong electrostatic interactions between TlI cations and polyelectrolytes.13,14 To examine if the changes in transport properties of TlI in ethanol-water solutions of PSSA are the result of only electrostatic interactions and to confirm that there is no significant difference in the viscosities of PSSA and p-TSA solutions, we performed experiments with ferrocene as an electroactive probe under the same experimental conditions (no supporting electrolytes, 10 mM concentration of the poly- or simple acid). Ferrocene is present in solution as an uncharged molecule, so there are no electrostatic interactions between ferrocene itself and the polyelectrolyte anions. The diffusion coefficient values calculated from the anodic steady-state currents of 1 mM ferrocene in 70% and 90% ethanol were the same to within 3% for the PSSA and p-TSA solutions. This indicates that for the same composition of the solvent, there is no significant difference between the viscosities of 10 mM PSSA and 10 mM p-TSA. On the basis of this fact, we can conclude that the difference in the diffusion coefficient values of TlI in PSSA and p-TSA solutions is due to the interactions between thallium(I) counterions and polyelectrolytes. Diffusion Coefficient of TlI in Simple Solutions. As one can see from Table 1, the diffusion coefficient of TlI in a solution of the simple acid p-TSA decreases from 20.08 × 10-6 cm2 s-1 to 7.53 × 10-6 cm2 s-1 with a change in solvent from pure water to 95% ethanol in water. To find out if this is connected with the changes in the viscosity of the solution or if this is a result of changes in the size of TlI in ethanol-water solutions, we analyzed the experimental results in light of the StokesEinstein relation
D ) kT/6πRη
(5)
where k is the Boltzmann constant, T is absolute temperature, R is the radius of the diffusing particle, and η is the viscosity of the solution.
Thallium(I) Counterions
Figure 2. Dependence of the normalized diffusion coefficient (ratio of diffusion coefficient to diffusion coefficient in aqueous solution) for TlI and TEMPO in simple solutions on the composition of organic solvent-water solution: (O, *) 0.2 mM TlI in 10 mM p-TSA; (4, 3) 2 mM TEMPO, 10 mM p-TSA; (curve 1, O, 4) ethanol-water; (curve 2, *, 3) methanol-water. Solid lines were calculated according to eq 5, based on viscosity values,32 assuming a constant radius R for diffusing ion.
Experimental values of the diffusion coefficients of TlI are presented in Figure 2 (O) as the ratio of the diffusion coefficient in an ethanol-water solution to the diffusion coefficient in an aqueous solution. The solid line (curve 1) in Figure 2 represents results calculated from the Stokes-Einstein relation, using viscosity values for ethanol-water mixtures,32 and assuming a constant size for the diffusing species. Additionally, we performed steady-state voltammetric experiments for the oxidation of 2,2,6,6-tetramethyl-1-piperidinyloxy, TEMPO, using a platinum disk microelectrode. The molecule TEMPO is uncharged, and its diffusion coefficient is expected to depend only on the viscosity of the solution. All experiments were performed in solutions containing 10 mM p-TSA. The oxidation waves of TEMPO were well defined and reproducible, with a relative standard deviation better than 1.2%. The diffusion coefficient values for TEMPO calculated according to eq 4, for various compositions of ethanol-water solutions, are presented in Figure 2 (4). One can see that the experimental results obtained for TEMPO are very close to the calculated dependence based on the changes in the viscosity of solution over the range of solution compositions studied. The diffusion coefficient of TlI changes proportionally to the change in viscosity of the solution in 20% and 50% ethanol-water solutions. However, in solutions with an ethanol percentage higher than 70%, the diffusion coefficient of TlI is smaller than would be expected from taking into account only the changes in the viscosity of the solutions. This suggests that for higher concentrations of ethanol, the radius of TlI changes, which can be the result of association of Tl+ with anions present in solution or changes in the structure of the solvation sphere of TlI. The estimated ratio of the radius of TlI in an ethanol-water solution to that in pure water is 1.38 and 1.99 for 70% and 95% ethanol, respectively. This effect is only briefly mentioned in this paper, but it is the subject of continuing study in our laboratory. Dependence on Dielectric Constant of SolVent. The interactions between counterions and polyelectrolytes are usually evaluated by the ratio of the diffusion coefficient of the counterion in the presence of polyelectrolytes, DPSSA, to that in the absence of polyanions (here, in a simple acid solution), Dp-TSA, both in the absence of supporting electrolytes. This ratio, R ) DPSSA/Dp-TSA, in light of Manning’s theory, depends on the nature of the polyelectrolyte and on the dielectric constant of the solvent (see eqs 1 and 2). On the basis of the diffusion
J. Phys. Chem., Vol. 100, No. 11, 1996 4633
Figure 3. Dependence of the ratio R ) DTlI in PSSA/DTlI in p-TSA, with no supporting electrolyte solutions, on the dielectric constant of organic solvent-water mixtures: (O) ethanol-water; (4) methanol-water; (0) 1,4-dioxane-water; (*) water, 0.16 mM TlI, 10 mM PSSA (or p-TSA). The solid curve was calculated according to eqs 1 and 2, and the dashed curve was calculated as an average dependence for all solvents.
coefficient values, calculated from the slopes of the concentration calibration plots, we calculated the R-values for five compositions of ethanol-water mixtures. The results are presented in Table 1. As one can see, the values of R decrease with decreasing values of dielectric constant of the solvent. On the basis of Manning’s theory, according to eqs 1 and 2, we calculated the slope of the linear dependence of DPSSA/D0 on the dielectric constant of the solvent for a PSSA solution (b ) 0.275 nm 5) with no added simple electrolytes. This dependence is described by the following equation DPSSA/D0 ) 0.004 257. Under our experimental conditions D0 is equivalent to Dp-TSA. The linear dependence calculated from the experimental results in ethanol-water mixtures is characterized by a slope of 0.004 78, which differs from the theoretical value by only 12%. In Table 1, the experimental values of R are compared to those calculated from eqs 1 and 2. Figure 3 presents the dependence of DPSSA/Dp-TSA -values on the dielectric constant of the solvent. The solid line in Figure 3 is calculated according to Manning’s theory, and the dashed line is the average experimental dependence for all the solvents studied. The slope of the average experimental dependence is 0.004 486. One can see that the experimental results obtained in ethanol-water mixtures are very close to those predicted by eqs 1 and 2. The largest differences between experimental and theoretical results are 17 and 12%, obtained in 70 and 50% ethanol-water solutions, respectively. Dependence on Supporting Electrolytes. We also studied the influence of the concentration of supporting electrolytes on the diffusion coefficient of TlI counterions in polyelectrolyte solutions of various dielectric constants. The addition of simple electrolytes to a solution of polyelectrolytes results in the neutralization of the surface charge of the polyelectrolyte and makes the interactions between polyions and counterions much weaker. Therefore, in the presence of supporting electrolytes the transport of counterions in a polyelectrolyte solution increases, and for a sufficient excess of supporting electrolytes the diffusion coefficient value of the counterion is that without polyelectrolytes.3 As shown previously for aqueous solutions, the very simple semiempirical equation proposed by Morris et al.,11
D/D0 ) (R + γ)/(γ + 1)
(6)
describes very well the dependence of the transport of hydrogen counterions11,12 and thallium(I) counterions13,14 on the concen-
4634 J. Phys. Chem., Vol. 100, No. 11, 1996
Ciszkowska and Osteryoung
Figure 4. Dependence of the normalized diffusion coefficients of thallium(I) in a polyelectrolyte solution, DPSSA/Dp-TSA, on the concentration of supporting electrolytes, LiClO4. γ ) CLiClO4/CPSSA (or p-TSA). The wt % of ethanol in water are (O) 95, (4) 70, (3) 50, (]) 20, and (0) 0 (pure H2O).
tration of supporting electrolytes in poly(styrenesulfonic acid) solution. In this equation D and D0 are the diffusion coefficients of the counterion in the presence and the absence of the polyion, respectively, γ is the normalized concentration of supporting electrolytes (i.e., the ratio of the concentration of simple (supporting) electrolytes to the equivalent concentration of the polyelectrolytes), and R is an empirical factor equivalent to the ratio of the diffusion coefficient of the counterion with and without polyelectrolytes, D/D0, both in a solution with no simple electrolytes. Equations 1 and 6 have the same limiting values for large and small values of γ and approximately the same shape and position on the γ-scale.15 The experimental dependencies of the diffusion coefficient of TlI in a PSSA solution on the concentration of supporting electrolytes, LiClO4, for five compositions of ethanol-water mixtures are presented in Figure 4, which shows plots of the normalized diffusion coefficient vs the normalized concentration of supporting electrolytes, γ. The normalized diffusion coefficient is the ratio of the diffusion coefficient in the presence of polyelectrolytes to diffusion coefficient in the absence of polyelectrolytes (simple acid solution) for the same concentration of supporting electrolytes. The solid lines in Figure 4 were calculated according to eq 6 using R-values obtained from the slopes of the concentration calibration plots (see Table 1) and moved in the positive direction of log γ as needed to fit the experimental points. The shift in the log γ scale for each composition of solvent is different and equals 1.0, 0.55, 0.22, 0.19 and 0.17 for 95%, 70%, 50%, 20%, and 0% ethanol in water. The shifts for 0, 20, and 50% ethanol solutions are very close to each other. A surprisingly large shift was obtained in solutions of 70 and 95% ethanol. This can be related to the association of the lithium cation with anions present in the more concentrated solution of ethanol. Association of ions (formation of ion pairs) occurs often in organic or mixed solvents with dielectric constants lower than 40. The lithium ion is well known as a cation that forms stable ion pairs with many anions in such solvents as ethanol or methanol.34 The association of ions can decrease the apparent concentration or activity of cations of supporting electrolytes in solution, which would manifest itself in a slower rate of decrease of the strength of electrostatic interactions between TlI counterions and polyelectrolytes with increasing ionic strength. In another words, because of ion association, the effective concentration of Li+ in solution is smaller than the analytical concentration of LiClO4, and a larger
Figure 5. Dependence of normalized diffusion coefficients of thallium(I) in polyelectrolyte solution, DPSSA/Dp-TSA, in 70% (A) and 95% (B) ethanol solution on the concentration of supporting electrolytes: (*) TEA(NO3); (O) LiClO4 γ ) CSE/CPSSA (or p-TSA), 0.1 mM TlI, 10 mM PSSA (or p-TSA). The solid line was calculated according to eq 6 with R ) 0.132 (A) and R ) 0.103 (B).
concentration is needed to change TlI counterion transport in PSSA. To find out how the changes of the diffusion coefficient of TlI in a PSSA solution depend on the type of supporting electrolyte, we used tetraethylammonium nitrate, TEA(NO3), as an electrolyte. Tetraalkylammonium cations are relatively large cations, for which the tendency of association with anions in such solvents as ethanol or methanol is expected to be negligible compared to that for lithium cations.35 The dependence of the normalized diffusion coefficient of TlI in a 70% ethanol solution of 10 mM PSSA on the concentration of TEA(NO3) is presented in Figure 5A. The experimental points obtained for LiClO4 are added for comparison. The solid line is calculated according to eq 6, with R ) 0.130, obtained from the slopes of the concentration calibration plots in 70% ethanol (see Table 1). The experimental results deviate only slightly from the dependence calculated according to eq 6, and they are very similar to those obtained in aqueous solution. Thus, TEA+ gives normal or expected behavior, whereas the influence of a given concentration of Li+ is less than expected. A difference between the influence of LiClO4 and TEA(NO3) on the normalized diffusion coefficient of TlI in PSSA was also observed in 95% ethanol solution. The experimental data for TEA(NO3) and LiClO4 as supporting electrolytes and dependence calculated according to eq 6, with R ) 0.103 from Table 1, are presented in Figure 5B. There is, in this case, a difference between the prediction from eq 6 and the experimental results for TEA(NO3) as the electrolyte, but the shift of the dependence, log γ ) 0.32, is much closer to that observed in low-percentage solutions of ethanol with LiClO4 as the electrolyte. Methanol-Water. The second solvent used in our studies was methanol. The dielectric constant of methanol-water
Thallium(I) Counterions
J. Phys. Chem., Vol. 100, No. 11, 1996 4635
TABLE 2: Diffusion Parameters Calculated from Concentration Calibration Plots of TlI in PSSA or p-TSA Solutions with No Added Supporting Electrolytes in Methanol-Water Mixtures
TABLE 3: Diffusion Parameters Calculated from the Concentration Calibration Plots of TlI in PSSA or p-TSA Solutions with No Added Supporting Electrolytes in 1,4-Dioxane-Water Mixtures
slopeb (nA mM-1) DTlI (106 cm2 s-1)
methanol wt %
a
PSSA
p-TSA
PSSA
p-TSA
Rexp c Rcalc d
40 60 80 90 99
63.3 51.2 41.4 39.1 33.6
1.92 1.42 1.24 1.38 1.37
7.82 7.47 8.28 9.55 10.94
3.31 2.45 2.15 2.38 2.36
13.50 12.91 14.32 16.51 18.90
0.246 0.185 0.150 0.145 0.125
0.269 0.218 0.176 0.166 0.143
slopeb (nA mM-1)
1,4-dioxane wt %
a
9.25 21.0 32.7 44.4
70.0 60.0 50.0 40.0
DTlI (106 cm2 s-1)
PSSA p-TSA PSSA p-TSA 3.04 2.05 1.47 0.99
9.65 8.26 6.98 5.71
5.25 3.54 2.54 1.71
16.67 14.26 12.05 9.86
Rexp c
Rcalc d
0.315 0.248 0.210 0.173
0.298 0.255 0.213 0.170
a represents dielectric constants from ref 32. b From concentration calibration plots, 0.05 e CTlI (mM) e 0.25 for 10 mM PSSA (or p-TSA). c R ) DTlI in PSSA/DTlI in p-TSA with no supporting electrolytes. d Calculated from eqs 1 and 2.
a represents dielectric constants from ref 36. b From concentration calibration plots, 0.05 e CTlI (mM) e 0.25 for 10 mM PSSA (or p-TSA). c R ) DTlI in PSSA/DTlI in p-TSA with no supporting electrolytes. d Calculated from eqs 1 and 2.
solutions changes from 33 for pure methanol to 79 for pure water. The reduction waves of thallium(I) cations in methanolwater solutions containing PSSA or p-TSA, as those in ethanolwater solutions, are very well defined. The reproducibility of the plateau currents was better than 5% and 2% relative standard deviations for PSSA and p-TSA solutions, respectively. Concentration Calibration Plots. We calculated the values of the diffusion coefficient of thallium(I) in the presence and the absence of polyelectrolytes for various compositions of solvent solutions without supporting electrolytes. These values were obtained from the slopes of the concentration calibration plots according to eq 4. The measurements were performed for the TlI concentration range 0.05-0.25 mM in the presence of 10 mM PSSA or 10 mM p-TSA for five different compositions of methanol-water solutions: 99, 90, 80, 60, and 40% of methanol. The linear dependence of the steady-state current on the concentration of TlI was obtained for all solutions, with correlation coefficients better than 0.9990 and 0.9995 for PSSA and p-TSA solution, respectively. The values of the slopes of the concentration calibration plots and the diffusion coefficient values of TlI are summarized in Table 2. For ethanol-water solutions, the diffusion coefficient values of TlI in PSSA solutions are lower than in solutions of simple acid p-TSA. Diffusion Coefficient of TlI in Simple Solutions. The diffusion coefficient of TlI in a solution of the simple acid p-TSA changes with a change in methanol percentage in water, as shown in Table 2. Figure 2 presents the dependence of the diffusion coefficient of TlI on the composition of methanolwater solutions as the ratio of the diffusion coefficient of the electroactive species in an organic solvent-water mixture to the diffusion coefficient value in pure water. The experimental diffusion coefficient values of TlI (*) are compared to values calculated from the steady-state currents for the oxidation of TEMPO (3) and to the dependence calculated according to the Stokes-Einstein relation (solid line of curve 2), eq 5, assuming a constant size for the diffusing species. The diffusion coefficient values of TEMPO in methanol-water solutions agree well with values predicted from the changes in the viscosity of the solution. The value of the diffusion coefficient of TlI is inversely proportional to the viscosity of the solution for methanol percentages lower than 70%. For more concentrated methanol solutions, the diffusion coefficient of TlI is lower than that expected based on the viscosity changes. This suggests that the interactions of TlI in methanol-water solutions are similar to those observed in ethanol-water solutions. The estimated ratio of the radius of TlI in a methanol-water solution to that in pure water is 1.28, 1.45, and 1.77 for 80%, 90%, and 99% methanol, respectively. Dependence on Dielectric Constant of SolVent. The interactions between counterions and polyelectrolytes in metha-
nol-water solutions, illustrated by the value of R ) DPSSA/Dp-TSA, depend on the composition of the solution (see Table 2). For ethanol-water mixtures, the value of the normalized diffusion coefficient of TlI in a PSSA solution without supporting electrolytes changes proportionally to the changes in the dielectric constant of the solvent. The slope of the linear dependence of DPSSA/Dp-TSA on the dielectric constant of a methanol-water mixture calculated from experimental values is 0.004 04 vs 0.004 257 calculated from eqs 1 and 2. Experimental data for various compositions of methanol-water solutions are presented in Figure 3. The experimental values of the TlI diffusion coefficient in methanol-water solutions of PSSA are lower, approximately by 10-15%, than theoretically predicted values. However, the slope of the experimental dependence is only 5% smaller than the calculated one. 1,4-Dioxane-Water Solutions. The dielectric constant values, , for various compositions of 1,4-dioxane-water mixtures that were used in our studies36 are presented in Table 3. It has been demonstrated experimentally, for the oxidation of ferrocene, that measurable voltammograms can be obtained in which the dielectric constant of a dioxane-water solvent is as low as 10.37 However, the lowest value of for which the voltammetric measurements gave well-defined waves of TlI ion reduction was 40, equivalent to 44.4% dioxane in water. For a higher percentage of 1,4-dioxane in solution (lower -value), the reduction waves of TlI were poorly defined and irreproducible. Therefore, the results in 1,4-dioxane-water solutions are reported here only for dielectric constant values of 40 and higher. Concentration Calibration Plots. Concentration calibration plots were obtained for TlI reduction in solutions of 10 mM PSSA or 10 mM p-TSA. The concentration of TlI was in the range 0.05-0.25 mM, and experiments were performed with no added supporting electrolytes in dioxane-water mixtures with -values of 40, 50, 60, and 70, which are equivalent to 44.4%, 32.5%, 21%, and 9.3% of 1,4-dioxane, respectively. All dependencies of the steady-state limiting current on the concentration of thallium(I) were linear with correlation coefficients better than 0.9989 and 0.9995 for PSSA and p-TSA solutions, respectively. The values of the slopes of the concentration calibration plots and the values of the diffusion coefficient of TlI, calculated according to eq 4, are presented in Table 3. For ethanol-water and methanol-water solutions, the diffusion coefficient values are lower in PSSA solutions than in p-TSA solutions for each composition of the dioxane-water mixture. Dependence on Dielectric Constant of SolVent. Based on the diffusion coefficient data from Table 3, the values of R ) DPSSA/Dp-TSA, describing the transport of the TlI counterion in 1,4-dioxane-water solutions of PSSA, were calculated. Their dependence on the dielectric constant of the solvent is presented in Figure 3. One can see that the R-value changes in proportion
4636 J. Phys. Chem., Vol. 100, No. 11, 1996 to the change in the dielectric constant . The slope of this dependence is 0.004 64 vs the theoretical value of 0.004 257. Although the linear dependence of the R-value on the dielectric constant might not discriminate among alternative models of charge-charge interaction, the close correspondence of the value of the slope to that predicted by Manning is additional support for the model he has proposed. Additionally, the dependence of the R-value on obtained in 1,2-dioxane-water solutions is very close to those previously obtained for ethanol-water and methanol-water solutions of PSSA.
Ciszkowska and Osteryoung in polyelectrolyte solutions on the dielectric constant of the solvent and indicate that this methodology can be used to study the transport properties of other electroactive mono- and multivalent counterions under a variety of experimental conditions, in solutions of various solvents and polyelectrolytes, including naturally occurring, biological polyelectrolytes. Acknowledgment. This work was supported in part by the National Science Foundation under Grant Number CHE9208987. References and Notes
Conclusions The results reported in this paper show that steady-state voltammetry with a microelectrode can be used successfully for the study of the transport of counterions in mixed solvent solutions of polyelectrolytes, even under experimental conditions of no added supporting electrolytes, where the interactions between polyions and counterions are the strongest. The interactions between poly(styrenesulfonate) ions and thallium(I) counterions in solutions without supporting electrolytes were found to depend on the bulk dielectric constant of the solvent. The diffusion coefficient of TlI in a solution of poly(styrenesulfonic acid) normalized by the diffusion coefficient of TlI in a solution of the simple acid, p-toluenesulfonic acid, changes in proportion to the change in the value of the dielectric constant of the solvent. This dependence was observed for ethanol-, methanol-, and 1,4-dioxane-water mixtures. For example, in a solution of an ethanol-water mixture with a dielectric constant ) 25, the diffusion coefficient of TlI in PSSA was found to be one-tenth the value in the simple acid solution, which means that the transport of TlI in PSSA was 10 times slower than that in p-TSA. This is much lower than the value of 0.35 obtained in aqueous solution, ) 79, for the same system. Similar changes in transport properties of counterions in polyelectrolyte solutions with changes in the dielectric constant of the solvent are predicted by Manning’s theory.16,17 The slope of the average dependence of the normalized diffusion coefficient of TlI in a PSSA solution for various compositions of investigated solvents is 0.004 49, while the theoretical dependence has the slope of 0.004 26. The diffusion coefficient of TlI in a simple acid solution also depends on the composition of the solvent. The variations in the diffusion coefficient value are a result of the changes of the solution viscosity, and additionally, for a higher percentage of such solvents as ethanol and methanol, they are probably a result of the change in the size of TlI by either association of Tl+ with anions present in the solution or the transformation of the solvation sphere of TlI. Transport of the TlI counterion in mixed solvent solutions of PSSA depends on the concentration and on the type of simple (supporting) electrolyte added to the solution. With the increase of the concentration of electrolytes, the diffusion coefficient of TlI increases and, for a sufficient excess of electrolytes, reaches the value of the diffusion coefficient in the simple acid solution. The influence of the same concentration of electrolytes on the transport of TlI counterions in PSSA depends on the type of cation of the electrolyte. The lithium cation was found to influence the diffusion coefficient of TlI in polyelectrolytes less effectively than the larger tetraethylammonium cation. These results were obtained for only one type of counterion, TlI, in poly(styrenesulfonic acid), a synthetic, model polyelectrolyte, and the investigations were performed using mixtures of water and only three selected organic solvents: ethanol, methanol, and 1,4-dioxane. However, these results show the strong dependence of the transport of monovalent counterions
(1) Armstrong, R. W.; Strauss, M. P. Polyelectrolytes. In Encyclopedia of Polymer Science and Technology; Mark, H. F., Gaylord, N. G., Bikales, N. M., Eds.; Wiley-Interscience: New York, 1969; Vol. 10. (2) Dautzenberg, H.; Jaeger, W.; Ko¨tz, J.; Philipp, B.; Seidel, C.; Stscherbina, D. Polyelectrolytes: Formation, Characterization and Application; Hanser/Gardner Publications, Inc.: Cincinnati, OH, 1994. (3) Polyelectrolytes: Science and Technology; Hara, M., Ed.; Marcel Dekker: New York, 1993. (4) Ueda, T.; Kobatake, Y. J. Phys.Chem. 1973, 77, 2995. (5) Ander, P. Water-Soluble Polymers; Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds.; ACS Symposium Series 467; American Chemical Society: Washington, DC, 1991. (6) Qian, C.; Asdjodi, M. R.; Spencer, H. G.; Savitsky, G. B. Macromolecules 1989, 22, 995. (7) Nilsson, L. G.; Nordenskio¨ld, L.; Stilbs, P.; Braunlin, W. H. J. Phys.Chem. 1985, 89, 3385. Nilsson, L. G.; Nordenskio¨ld, L.; Stilbs, P. J. Phys.Chem. 1987, 91, 6210. (8) Carter, M. T.; Rodriguez, M.; Bard, A. J. J. Am. Chem. Soc. 1989, 111, 8901. (9) Jiang, R.; Anson, F. C. J. Phys. Chem. 1992, 96, 452. (10) Van den Hoop, M. A. G. T.; Van Leeuwen, H. P. Anal. Chim. Acta 1993, 273, 275. Benegas, J. C.; Van den Hoop, M. A. G. T.; Van Leeuwen, H. P. Biophys. Chem. 1995, 54, 35. (11) Morris, S. E.; Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1993, 97, 10453. (12) Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1994, 98, 3194. (13) Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1994, 98, 11791. (14) Ciszkowska, M.; Zeng, L.; Stejskal, E. O.; Osteryoung, J. G. J. Phys. Chem. 1995, 99, 11764. (15) Scordilis-Kelley, C.; Osteryoung, J. G. J. Phys. Chem. 1996, 100, 797. (16) Manning, G. S. J. Chem. Phys. 1967, 47, 2010; 1969, 51, 924. (17) Manning, G. S. Annu. ReV. Phys. Chem. 1972, 23, 117. (18) Alfrey, T.; Perg, P. W.; Morawetz, H. J. Polym. Sci. 1951, 7, 543. (19) Fuoss, R. M.; Katchalsky, A.; Lifson, S. Proc. Natl. Acad. Sci. U.S.A. 1951, 37, 579. (20) Fuoss, R. M.; Cathers, G. I. J. Polym. Sci. 1947, 2, 12. (21) Fuoss, R. M.; Strauss, U. P. J. Polym. Sci. 1948, 3, 246. (22) Fuoss, R. M.; Cathers, G. I. J. Polym. Sci. 1949, 4, 97. (23) Cathers, G. I.; Fuoss, R. M. J. Polym. Sci. 1949, 4, 121. (24) Strauss, U. P.; Fuoss, R. M. J. Polym. Sci. 1949, 4, 457. (25) Fuoss, R. M.; Maclay, W. N. J. Polym. Sci. 1951, 6, 305. (26) Maclay, W. N.; Fuoss, R. M. J. Polym. Sci. 1951, 6, 511. (27) Fuoss, R. M.; Edelson, D. J. Polym. Sci. 1951, 6, 523. (28) Fuoss, R. M. J. Polym. Sci. 1954, 12, 185. (29) Ciszkowska, M.; Donten, M.; Stojek, Z. Anal. Chem. 1994, 66, 4112. (30) Sinru, L.; Osteryoung, J. G.; O’Dea, J. J.; Osteryoung, R. A. Anal. Chem. 1988, 60, 1135. (31) Myland, J. C.; Oldham, K. B. J. Electroanal. Chem. 1993, 347, 49. (32) Timmermans, J. The Physico-chemical Constants of Binary Systems in Concentrated Solutions; Interscience Publishers, Inc.: New York, 1960; Vol. 4. (33) Wightman, R. M. Anal. Chem. 1981, 53, 1125A. (34) Mamantov, G.; Popov, A. I. Chemistry of Nonaqueous Solutions; VCH: New York, 1994. (35) Bachelin, M.; Gans, P.; Gill, J. B. J. Chem. Soc., Faraday Trans. 1992, 88, 3327. (36) Dobos, D. Electrochemical Data; Elsevier Scientific Publishing Co.: New York, 1975. (37) Ciszkowska, M.; Stojek, Z.; Osteryoung, J. G. Anal. Chem. 1990, 62, 349.
JP952990U
