11764
J. Phys. Chem. 1995,99, 11764-11769
Transport of Thallium(1) Counterion in Polyelectrolyte Solution Determined by Voltammetry with Microelectrodes and by Pulsed-Field-Gradient, Spin-Echo NMR Malgorzata Ciszkowska, Lei Zeng, E. 0. Stejskal, and Janet G. Osteryoung" Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204 Received: April 3, 1995; In Final Form: June 9, 1995@
Steady-state voltammetry at microelectrodes and pulsed-field-gradient spin-echo NMR are compared as techniques for measurement of diffusion coefficients in solutions of polyelectrolytes. The NMR technique is well established in this application and thus is employed as a reference technique. We used T l' as a counterion probe, poly(styrenesu1fonic acid) (PSSA) as polyelectrolyte, and LiC104 as supporting electrolyte, to investigate the interactions of counterions with polyions in systems for various concentration. We measured 205Tl+selfdiffusion coefficients by NMR and compared the NMR results with the results for gradient diffusion from voltammetry with microelectrodes. Identical results 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 gradient-diffusion coefficients under the range of conditions applied.
Introduction The interactions between counterions and polyions in solutions have been studied and discussed for more than 40 years.'.2 The transport of counterion is suppressed in the presence of such polyelectrolyte systems as charged polyions, micelles, biological membranes and fluids, and other charge aggregates, with most noticeable changes in the diffusion coefficient value in solutions of low ionic ~ t r e n g t h . ~The . ~ reason for this behavior is strong, long range, nonspecific interaction of an electrostatic nature between simple ion and polyelectrolyte ion. These interactions are called "counterion binding" or "counterion condensation". There are several theories describing the transport properties of simple counterions in polyelectrolyte solutions. The theoretical treatments have been based most often on the assumption that the polyions may be modeled as charged line@ or infinite cylinder^.^-^ Various techniques have been used to study the transport and the interactions of simple ions in solutions of polyelectrolytes, most notably the radioactive tracer method,I0-l4 NMR,'5-20 potentiometry,2'.22and ~ o l t a m m e t r y . ~ ~ - ~ * NMR Spectroscopy. The NMR spectroscopic method has been applied in ion interaction studies for more than 3 decades. The techniques include (a) quadrupole relaxation time measurements (limited to certain ions), which are very sensitive to interactions with large molecules and yield information about interactions and dynamics of both monovalent and divalent ions;29-31 (b) chemical shift studies, applied to ions having chemical shifts sensitive to any concentration changes of ions and p o l y i o n ~and ; ~ ~(c) the study of the binding of paramagnetic ions through their effects on the relaxation or chemical shift of water proton^.^^.^^ However, the pulsed-field-gradient spin-echo NMR (PFGSE NMR) self-diffusion technique has proven to be one of the most valuable in studying the association phenomena in polyelectrolyte systems, especially in quite complex biological and nonbiological systems. Self-diffusion coefficients for electrolytes in solutions obtained from 'H magnetic resonance have been determined e x t e n ~ i v e l y ,and ~~,~~ some alkali metal ionic self-diffusion coefficients in electrolyte solutions also have been m e a ~ u r e d . ~ ~ . ~ ~ The PFGSE NMR experiment combines a spin-echo experiment (9O0-z-180"-z-observe), in its simplest form, with two @
Abstract published in Advance ACS Absrracts, July 1, 1995.
0022-3654/95/2099- 11764$09.00/0
field gradient pulses on either side of the 180" pulse. The two gradient pulses are used to create a linear gradient magnetic field which can vary the precession frequencies of nuclear spins, determined by the position of the nuclei in the field. For incoherent random motions such as those in self-diffusion, a random phase shift of individual nuclear spins causes more or less incomplete refocusing and spin-echo attenuation at the time of the echo. The spin-echo amplitude is exponentially related to the gradient pulse strength and the self-diffusion coefficient and can be written as the relation39
In A , = -y2g26'D(A - 6/3)
+ In A,
where g represents the strength of the gradient, 6 is the gradient pulse duration, A is the time interval between the two gradient pulses, y is the gyromagnetic ratio of the nucleus, and D is the self-diffusion coefficient. The quantities A , and A0 are the spinecho amplitudes with and without applied gradient pulses, respectively. The diffusion coefficient, D,can be determined from the slope of the plot In A I verms [y2g2d2(A- 6/3)] with various gradient pulse strengths. Voltammetry. Classic polarography was used to study the transport of metal cations in polyelectrolyte solutions 30 years ago, but because of instrumental limitations the experimental results obtained were not r e p r o d ~ c i b l e . ~Voltammetry ~-~~ with regular-size (0.01-1 cm2) electrodes has been applied to measure the transport of counterions in polyelectrolyte^.^^-^^ However, because of the large size of the electrode and the high currents measured, the method has been restricted to rather high levels of simple electrolyte in solution, where the interactions between counterion and polyelectrolyte are weak. Recently, a new voltametric method with either platinum or mercury film microelectrodes has been used to study the transport of hydrogen and metal cations in poly(styrenesu1fonic acid)26-28(PSSA) and in biological polyelectrolytes, such as chondroitin sulfate, 1- and K-carrageenan, and dextran sulfate,43in solutions with no added simple salt. The use of a microelectrode under steady-state conditions allows measurements in solutions of low ionic strength. The measured currents are low, in the range of nanoamps or picoamps, and consequently, the ohmic drop is low too. Additionally, the steady-state current at microelectrodes is
0 1995 American Chemical Society
Transport of T1+ in Polyelectrolyte Solution proportional to the diffusion coefficient, D, and for a disc microelectrode is described by the relation''''
is = 4nFCDr where n is the number of electrons transferred, F is the Faraday constant, C is the concentration of electroactive substrate, and r is the radius of the microelectrode. Thus, the diffusion coefficient of the electroactive ions can be calculated easily from the limiting steady-state current value, if the concentration of ion and the size of microelectrode are known. Also, because the current is proportional to the diffusion coefficient value, the measured signal is sensitive to the changes in the diffusion coefficient. Thallium(1)Ion in NMR Measurements. Thallium occurs as two magnetically active isotopes, thallium-203 and thallium205. They are both sensitive spin l/2 nuclei, with 205Tlpreferred for spectroscopy because of its higher natural abundance (70.5%). The relative receptivity for 205Tlis 0.1355, compared with unity for 'H, and the ionic concentrations are relatively low, which means the operational techniques are quite different from IH-NMR and more like those appropriate to low-y, rarespin NMR, although the relaxation times are not particularly long. The chemical shift range over which compounds of this element resonate is larger than most (about 5500 ppm) and is sensitive to environmental changes. With longer relaxation times, the line widths are generally smaller than those of other group I11 nuclei, so that thallium can be observed in a wide range of chemical environments. We have not found reports on thallium ion self-diffusion coefficients measured by the PFGSE NMR techniques, even though both 203Tl+ and *05Tl+ ions have relatively high gyromagneticratios and sufficiently long relaxation times. That may be due to the requirement for an NMR probe with an unusual resonance frequency, about 57.7 MHz referred to 'H TMS resonance at 100 MHz, and the requirement of the pulsedfield-gradient accessories. Thallium(1) Ion in Voltammetry with Mercury Electrodes. The reduction of Tl+in aqueous solutions at mercury electrodes is a fast, one-electron process that is often used in voltammetry as a model system for reduction of monovalent metal cation. The half-wave potential for reduction of TI+ is -0.455 V versus saturated calomel electrode, SCE, (0.1 M NaNO3, 25 0C),45 which means that the current signal for Tl+ reduction is in the middle of the potential window for the Hg electrode (e.g., from f 0 . 2 5 V to -1.80 V in 0.1 M NaNO3 46). The solubility of thallium in mercury is high, 42.7 at. % at 25 0C:7 Consequently, there is no crystallization of thallium in the mercury phase up to high concentrations of thallium, and voltammetric experiments can be performed over a wide concentration range. Thallous ion is stable in aqueous solutions, and no precipitation is observed even in solutions of relatively high concentration. The aim of this paper is to compare these two methods for studying the diffusion of ions in a situation where they are both applicable, since there are many cases in which only one of the two methods will work. If it can be shown that these two methods study the same phenomenon, despite the different principles on which they are based, and produce equivalent results, then the range of ions which may be studied can be increased by using both techniques. In addition there are two specific questions which arise with regard to the voltammetric measurements, both related to the obligatory interfacial nature of the experiment. The voltammetric measurement of diffusion coefficient relies on establishing a concentration gradient at the electrode, which produces a flux of reactant proportional to current. Thus the gradient is a
J. Phys. Chem., Vol. 99, No. 30,1995 11765 special environment, which may yield values of diffusion coefficient that differ, due to local variation in activity coefficient, from the self-diffusion coefficients of NMR. The polyelectrolyte may also interact specifically with the electrode surface in ways that do not reveal themselves by qualitative departure from expected behavior but nevertheless affect the results quantitatively. Comparison of results from independent techniques can show that these effects are negligible.
Experimental Methods Chemicals and Solutions. All reagents excepting poly(styrenesulfonic acid) were of reagent grade purity and were used as received. Thallium(1) nitrate (Alfa) was used as a source of thallium(1) cation. Electrolyte concentration adjustments were made with lithium perchlorate (Aldrich). Poly(styrenesulfonic acid) (MW 70 000; Polysciences Inc.) contains approximately 5% aqueous sulfuric acid. It was purified by a 36-h dialysis with a 10-fold excess volume of water using a MWCO 12 000-14 000 membrane (SpectralPor4, Spectrum Medical Industries), and the water was changed six times. The concentration of PSSA reported in this work (we call it also the equivalent concentration of PSSA) is the concentration of hydrogen ion in PSSA solution. The charge density of PSSA is 2.6.1° The concentration of stock solutions was determined by conductometric titration against standard sodium hydroxide solution using a YSI Model 31 conductivity bridge (Yellow Springs Instrument Co.). Ultrapure water (Milli-Q, Millipore Corp.) was employed in all rinses, dialyses, and preparations of solutions. The background concentration of cations different than thallium(1) or hydrogen ion was determined by the procedure described previously27and was close to 10 pM. NMR Experiments. The stimulated echo (STE) radio frequency (rf)pulse sequence was used in place of the ordinary spin-echo sequence. In this sequence (90"-t-90"-t-90"z-observe) with the two gradient pulses located during the two t-intervals, advantage is taken of the fact that during the t-interval the echo decays according to TI rather than the usually shorter T2.48 In the measurements described here, we used t = 10.0 ms and t = 50.02 ms, and the interval between the two field gradient pulses (A) was fixed at 60.02 ms, with a gradient pulse duration (6) of 2.00 ms.49 Only the magnitude of the gradient was varied. Under these conditions J modulation as well as T2 and T I effects are constant and signal amplitudes follow eq 1 as the magnitude of the gradient g is varied. The homemade NMR probe was adjusted to the 205Tlresonance frequency, which is 57.633 MHz in the IBM NRlOOAF spectrometer ('H frequency = 100.13 MHz), and a pair of antiHelmhoIz coils were used to provide a linear field gradient. The temperature of the experiments was controlled by passing room temperature air through the NMR probe and was 26 "C. The concentration of T1+ in the different sample solutions was as low as 10 mM. Also the gyromagnetic ratio, y, of 205Tlis 1.569 x lo8 rad s-I T-I, relatively low compared to 'H ( y = 2.675 x lo8 rad s-l T-I), and the natural abundance is also less (70.5%). These facts caused the overall signals of 205Tl+ in the various solutions to be weak, requiring a narrow sweep width (below 600 Hz) to reduce the noise power relative to the signal; this measure also increased the digital resolution. Voltammetric Experiments. Voltammetric measurements were carried out with a three-electrode system in a jacketed cell (25 "C) enclosed in an aluminum Faraday cage. Solutions were deoxygenated before voltammetric scans and blanketed with a stream of water-saturated argon. A mercury film disc microelectrode of 15 p m in radius, r, was used as a working electrode. Silver disc microelectrodes (Project Ltd., Warsaw,
11766 J. Phys. Chem., Vol. 99, No. 30, 1995 Poland) were used as substrates for the mercury films. The mercury film thickness, I , was 1 pm. Mercury was deposited at -0.5 V (versus saturated calomel electrode, SCE) from a solution of 5 mM Hg(II) in 0.1 M HC104. The procedure for preparation of this silver-based mercury film microelectrode has been described in detail.50 After mercury deposition, the electrode was washed carefully with a large amount of water. The surface of the mercury film was inspected with an inverted microscopy (Leitz Wetzler, Germany) before using. A platinum quasi-reference electrode was used under experimental conditions described p r e v i o u ~ l yto , ~prevent ~ leakage of ions into the cell. The counter electrode was platinum. Staircase voltammograms were obtained using a Model 273 potentiostat (EG&G PARC) connected with a Keithley Model 427 current amplifier and controlled by software via a PC 486 computer. Staircase voltammetry parameters were as follows: step height (AE) = 5 mV, frequency @ = 1 Hz. Under these conditions the limiting current for a 15-pm Hg film disc electrode should not exceed the steady-state value by more than 3%.51 The deposition of mercury on the Ag disc electrode was performed in a three-electrode system with Pt wire counter electrode and SCE reference electrode, with Model 173 potentiostat connected with Model 179 digital coulometer (EG&G PARC).
Results and Discussion In our studies, thallium(1) cation was used as a probe counterion in polyelectrolyte solutions. That is, the concentration of metal cation was much lower than the concentration of polyacid. Under these conditions, when the concentration of hydrogen ion (from dissociation of PSSA, a strong acid) in the solution is 20 or more times higher than the highest concentration of thallium(1) cation, we can expect the same interactions between polyion and both hydrogen and thallium counterions. Additionally, in voltammetric measurements no migration effects are observed. The theory predicts that the limiting current of the one-electron reduction of a monovalent cation in the presence of 20-fold excess of 1:l supporting electrolyte (under our experimental conditions CSE= CH+, and CH+2 20Cn+) is 1.012, the diffusional current ~ a l u e . ~Therefore, ~ . ~ ~ we can assume that the steady-state current of reduction of thallium(1) cation is controlled only by diffusional transport, as described by eq 2. Voltammetric studies with mercury microelectrodes of the transport of thallium(1) cation as a probe counterion in PSSA solution were described in ref 28. U-value. Interactions between counterion and polyelectrolyte are usually evaluated by the ratio of the diffusion coefficient of the counterion in the presence and in the absence of polyelectrolyte. This ratio has the lowest value in solutions of very low ionic strength, where the interactions are the strongest. The ratio of the diffusion coefficient in the presence of polyelectrolyte, D, and in the absence of polyelectrolyte, DO,both in the absence of supporting electrolyte, is known in polyelectrolyte literature as a = D/Do. This value is characteristic for each structure of polyelectrolyte as well as for the charge of the c ~ u n t e r i o n . ~To . ~ determine the a-value for PSSA, and for mono- and divalent counterions, the simple method of concentration calibration plots has been Voltammetry offers the possibility of working over a wide range of concentration of electroactive species. Therefore, we measured the steadystate reduction current for various concentrations of thallium(I) cation in the two limiting conditions with and without polyacid, in solutions with no added simple salt. The reproducibility of the limiting current of reduction waves of Tl(1) cation in the presence of PSSA was better than 2%.
Ciszkowska et al.
TABLE 1: Values of a = DIDO for Monovalent Counterions in Poly(styrenesu1fonicacid) Solutions without Electrolyte ref counterion a = DIDO 126 Na+ 0.25-0.35’
Li+
Ag+
cs+ TMA+
0.29 0.39 0.48 0.62 0.42 0.44 0.30 0.39 0.37
546 556
566 1O b 18‘ 17‘ 546 18‘ 18‘
a Various concentrationsof PSS. Radioactive tracer measurements. NMR measurements. Tetramethylammonium cation.
The height of the waves did not change with time. This kind of change has been observed for reduction waves of hydrogen counterion in PSSA solution at platinum microelectrodes and has been explained as the effect of adsorption of polyelectrolyte at the platinum electrode surface.27 The results obtained for Tl(1) counterion indicate that there is no significant influence of adsorption of polyelectrolyte at the mercury microelectrode surface. When polyacid was not present in the solution, a simple acid, HC104, was added, to keep constant the concentration of the hydrogen ion. According to eq 2, we calculated the diffusion coefficient of thallium(1) cation fiom the slope of the concentration calibration plot. Using this procedure, we obtained the diffusion coefficient value of T1’ in simple solution, (2.22 f 0.07) x cm2 s-I, and in solution with 20 mM PSSA, (7.78 f 0.27) x cm2 s-l, both without simple electrolyte. The a-value calculated from these diffusion coefficients is 0.35 1 for thallium(1) counterion in poly(styrenesu1fonic acid), which is very close to the a-value obtained for hydrogen counterion in PSSA sol~tion.*~.~’ This means that the transport of T1+ in PSSA solution without added supporting electrolyte is 2.85 times slower than in simple solution. The self-diffusion coefficients obtained from PFGSE NMR measurements for 10 mM thallium(1) ion in solution without supporting electrolyte were (1.91 f 0.13) x and (7.21 & 0.50) x loW6cm2 s-’ in simple solution without polyelectrolyte and in 160 mM PSSA solution, respectively. The a-value calculated from NMR experimental results was 0.377. The values from NMR and from voltammetry are close, with a difference of only 7%, which may be taken to be identical within experimental uncertainty. It should be pointed out that the value of 0.351 is the mean value for several concentrations of counterion in polyelectrolyte solution. Taking into account the reproducibility of limiting currents, with relative standard deviation lower than 2%, and the correlation coefficient for concentration calibration plots, better than 0.9998, the a-values calculated from voltammetric measurements are expected to be precise. However, as Figure 2 will show, the result obtained from the NMR measurements would seem to fit the data about as well, to within experimental error. The a-value for thallium(1) counterion in PSSA solution has not been determined before. However, the transport of other monovalent cations has been studied in PSSA solutions. The a-values found previously for various monovalent counterions are presented in Table 1. The a-values are in the range from 0.25 to 0.62. The big difference between reported values of a for the same counterion in the same polyelectrolyte (e.g., Na+ in PSSA) illustrates the complexity of experimental problems connected with measurements of diffusion coefficient of simple
Transport of Tl+ in Polyelectrolyte Solution
J. Phys. Chem., Vol. 99, No. 30, 1995 11767
TABLE 2: Dependence of the Diffusion Coefficient of T1+ in Simple (DO)and PSSA @MA) Solution on the Normalized Concentration of Supporting Electrolyte, LiC104 (X =
I
0
o
CSdct'SSA)
c L l C l Olog4 x~
D~ x 1054cm2 S-I)
DESAx 1054cm2 S-1) (a) Diffusion Coefficients from PFGSE NMR: 0.01 M Tl+(TlNO3) in 0.16 M PSSA, 25 "C 0 -3 1.91 0.721 0.002 -1.9 2.06 0.796 0.02 -0.9 2.04 0.950 0.05 -0.5 1 2.23 1.15 -0.204 1.86 1.17 0.1 0.097 1.89 1.18 0.2 0.5 0.495 1.84 1.45 0.796 1.83 1.72 1 1 .o 1.57 1.50 1.6 (b) Diffusion Coefficients from Voltammetry: 0.15 mM T1+ (flNO3) in 20 mM PSSA, 25 "C 0 -3.3 2.17 0.760 4 x 10-5 -2.7 0.766 2 x 10-4 -2.0 0.771 0.001 -1.3 0.806 0.003 -0.8 0.864 0.01 -0.3 1.91 0.020 0 1.89 1.17 0.050 0.4 1.41 0.1 0.7 1.86 0.152 0.88 1.82 0.159 0.9 1.59 0.200 1 .o 1.80 0.632 1.5 1.68 0.648 1.51 1.72 1.588 1.9 1.49 1.664 1.92 1.52 2.5 18 2.1 1.34 2.636 2.12 1.35
ions in polyelectrolytes, especially in solutions without supporting electrolyte. Dependence of Diffusion Coefficient of T1+ Cation on the Concentration of Supporting Electrolyte. The values of the diffusion coefficient of thallium(1) cation in solutions of various concentrations of supporting electrolyte, LiC104, with and without PSSA, were determined independently from NMR and voltammetric measurements, and are summarized in Table 2a,b. The diffusion coefficient depends on ionic strength due to the changes in the activity of the ion (aqueous solutions, 25 "C) through the relatiod7
D = DO(l - 0.5115C,1'2/2)
(3)
where D and DOare the diffusion coefficients of the ion in the presence and the absence of supporting electrolyte, respectively, and C, is the concentration (M) of 1:l electrolyte. Equation 3 is valid only for low concentrations of electrolyte; for high concentrations of electrolyte the dependence is more complicated. The diffusion coefficient, D, also depends on the viscosity of solution
D = kBT/6n7R
(4)
where k~ is the Boltzmann constant, T is the temperature, 7 is the absolute viscosity, and R is the hydrodynamic radius of the diffusing particle. The viscosity factor has been determined by PFGSE NMR experiments. The diffusion coefficient of water was measured in solutions containing thallium(1) ions and various concentrations of lithium perchlorate. The viscosity factor was calculated from the ratio of diffusion coefficient of water without supporting electrolyte, DO,and the diffusion coefficient of water
in
31.0'
n
A
; A o A n o M O
,
;
A
0.5 -4
-2
0
log
2
x
Figure 1. Dependence of the diffusion coefficient of thallium(1) ion in the absence (DO) and the presence of the polyelectrolyte, PSSA (DPSSA), on the normalized concentration of simple electrolyte, LiC104, (x= CdCms~).Vohnmetry: (0)0.15 mM u+, no PSSA; (A) 0.15 mM Tl", 20 mM PSSA. PFGSE NMR (0)10 mM Tlf, no PSSA; (0) 10 mM Tl+,160 mM PSSA.
in the presence of supporting electrolyte, D
where 7 and 70 are viscosities of solutions with and without supporting electrolyte, respectively. For the range of the concentration of supporting electrolyte used in our studies, from 0 to 1.6 M LiC104, the viscosity factor changed from 1 to 0.946. Thus, for the highest concentration of lithium perchlorate the change in the diffusion coefficient value due to the change in the viscosity of the solution is 5.4%. The values of the diffusion coefficient presented here were corrected for the changes in the viscosity of the solutions. As one can see from the Table 2a,b, the changes of the diffusion coefficient are opposite in the simple and polyelectrolyte solutions. In simple solutions, the diffusion coefficient decreases with an increase in the concentration of the supporting electrolyte. In solutions of PSSA, the diffusion coefficient of thallium(1) ion increases with an increase in the Lie104 concentration and for a very high concentration of supporting electrolyte decreases due to the decrease in the activity coefficient of thallium(1) sation. The values of the diffusion coefficient obtained by NMR and by voltammetry in the presence and in the absence of polyelectrolyte are compared in Figure 1. The dependence on the ratio of the electrolyte concentration, X = CLiC104/CPSSA, is the same for both techniques, and the values of the diffusion coefficient are close. The interactions between polyion and thallium counterion are revealed by the difference in the diffusion coefficient value in PSSA solution and simple solution, for the same concentration of supporting electrolyte. Therefore, the following results will present a normalized diffusion coefficient, which is the ratio of the diffusion coefficient in the presence of polyelectrolyte to the diffusion coefficient in the absence of polyelectrolyte. Figure 2 presents the dependence of the normalized diffusion coefficient of thallium counterion in PSSA solution on the normalized concentration of supporting electrolyte, LiC104. These results were obtained by PFGSE N M R for one concentration of T1+ and PSSA (10 mM Tl+,160 mM PSSA), and by voltammetry for two concentrations of T1+ and PSSA (0.1 mM Tl+,2 mM PSSA; and 0.05 mM T1+, 10 mM PSSA). The results obtained by the two methods agree closely. Even allowing for the big difference in PSSA concentration (2 and 10 mM for voltammetry versus 160 mh4 for NMR), the normalized diffusion coefficients are close. The biggest dif-
Ciszkowska et al.
11768 J. Phys. Chem., Vol. 99, No. 30, 1995
no \ 4
m m
a" 0.21 0.01 -4
0
-2
log
2
I
x
Figure 2. Dependence of normalized diffusion coefficient of Tlf on normalized concentration of simple electrolyte, LiC104, (X = CJCPSSA). Voltammetry: (0)0.1 mM T1+, 2 mM PSSA; (A) 0.05 mM Tl', 10 mM PSSA. PFGSE NMR: (*) 10 mM Tl', 160 mM PSSA. (-) Calculated according to eq 6, using a-values of 0.351 and 0.377.
ference between the voltammetric and NMR results is 11%.This difference is connected with experimental uncertainty rather than with physical phenomena and indicates that the interactions between counterion and PSSA do not depend on the concentration of polyanion. The transport of hydrogen counterion in PSSA solutions is independent of the concentration of polyelectrolyte in the range from 0.05 to 10.2 mM.26,27 The solid lines in Figure 2 are the dependencies calculated for two a-values, 0.351 (voltammetric result) and 0.377( N M R result), according to the semiempirical equation proposed by Morris et a1.26
+
DID, = (a X)/(X
+ 1)
(6)
where D and DOare the diffusion coefficients in the presence and the absence of the polyion, respectively, X is the ratio of the concentration of the simple electrolyte to the equivalent concentration of the polyelectrolyte, and a is an empirical factor equivalent to the ratio of the diffusion coefficient of the counterion with and without polyelectrolyte, DIDO,both in the solution with no simple electrolyte. This simple equation was confirmed experimentally by voltammetric studies for hydrogen26,27and thallium28counterion transport in PSSA solutions. As one can see in Figure 2, the experimental results obtained by PFGSE NMR agree well with the voltammetry results when compared by means of eq 6. This indicates that eq 6 is a convenient and versatile way to describe the transport properties of counterions over a wide range of concentrations of polyelectrolytes and supporting electrolytes.
Conclusions Both the pulsed-field-gradient, spin-echo (PFGSE) N M R technique and voltammetry with microelectrodes yield values of the diffusion coefficient of T1+ counterion in poly( styrenesulfonic acid) solution. The values agree over a wide range of electrolyte concentration within experimental uncertainty, despite the different principles on which the two methods are based. Since there are many cases in which only one of these two methods will work, this observation suggests that the range of ions which may be studied can be increased by using both techniques. For this reason, we conclude with a comparison of the advantages and limitations of voltammetry and N M R in this application. Limitations on Counterion. Voltammetry. Only counterions which are electroactive in the potential range available for the electrode used (e.g., Pt,Au, Hg, C) can be studied by the
voltammetric method. For example it is not possible to study the reduction of Na+, IC+, Li+, Ca2+, and Mg2+ counterions by voltammetry in aqueous solutions. Especially because we employed here a simple inorganic ion, we emphasize that a wide range of organic electroactive functional groups provide opportunities for employing organic ions in this application. NMR. An ion containing a nucleus with nonzero spin is required. Paramagnetic ions can be expected to be difficult, due to short relaxation times, and quadrupolar nuclei ( I > l/2) with large quadrupole moments may also have inconveniently short relaxation times. For reasons of sensitivity, large gyromagnetic ratio and large natural abundance are also desirable. Highly favorable spin nuclei include 'H, I9F, 3'P, 195Pt, and, of course, 205Tl. Other nuclei that are favorable but would be improved by isotopic enrichment include 29Si, I3C, 15N,207Pb, and lllCd or 'I3Cd. Quadrupolar nuclei that are often receptive include 23Na,27Al, I7O, 'Li, I4N, and 2H. Concentrationof Counterion. Voltammetry. Voltammetry with microelectrodes offers a very wide range of concentrations of the counterions, from M to 0.1 M. For example, very well defined voltammetric waves for reduction of lead(II) cation in a concentration of 0.12 M have been obtained with a mercury micr~electrode,~~ and as low a concentration as 5 ,uM OH- was determined by steady-state voltammetry with mercury microelectrode~.~~ NMR. The strength of the nuclear signal varies widely from one nucleus to another. Thallium is a typical nucleus of modest sensitivity. The 10 mM concentration used in this study represented a compromise between the accuracy of the measurement and the time for the measurement (see below). More favorable nuclei like 'Hand I9F would permit concentrations at least an order of magnitude smaller. Time Required for Experiment. Voltammetry. One voltammetric curve under steady-state conditions takes approximately 2-3 min. For each point in a plot like Figure 2, a minimum of three replicates are required. One plot usually covers 10-15 points. To obtain 15 points thus takes 45 min of measurement. With other operations, such as preparation of solutions, preparation of mercury microelectrode, weighting and additions of supporting electrolyte, deaerating of solution, and others, the time necessary for obtaining one plot like Figure 2 is less than 3 h. NMR. The time required for a single PFGSE diffusion measurement depends on the strength of the nuclear signal and thus varies widely from one nucleus to another. Thallium is typical of most nuclei of modest sensitivity but with favorable relaxation times. A single diffusion measurement (one point in Figure 2), using eight values of the gradient pulse amplitude each replicated three times, took 10 h. Costs. Voltammetry. The cost of equipment for voltammetric experiments (potentiostat and current amplifier connected with PC computer, electrochemical cell, and all electrodes) is in the range of $15 000. NMR. The cost of adding a gradient probe and gradient pulser to the ordinary modem, multinuclear N M R spectrometer is about $25 000 if purchased from the manufacturer. Temperature Control. The control of temperature is important in measurements of diffusion coefficient. The diffusion coefficient depends on temperature through the relation57
D = BRT(1
+ A)
(7)
where B is a constant, R is the molar gas constant, T is the temperature (K), and A is a value which depends on the activity coefficient of the diffusing species. This means that a change of temperature results in a proportional change in the diffusion
J. Phys. Chem., Vol. 99, No. 30, I995 11769
Transport of T1+ in Polyelectrolyte Solution coefficient. In other words, a 1-deg change results in about a 0.3% change in the diffusion coefficient at room temperature.
Voltammetry. In voltammetric measurements we used a jacketed cell, and the temperature of solution was controlled by a thermostat to within 0.1 degree. Temperature control is generally simple, inexpensive, and reliable. NMR. Room temperature air was passed through the NMR probe to control the sample temperature and help carry away any heat arising from the rf pulses or the gradient pulses. We estimate that control was to within about 2 degrees. Control in this manner depends on the constancy of the room temperature. Better knowledge of the temperature of the sample requires rather elaborate modification of the apparatus. Reproducibility of Results. Voltammetry. The reproducibility of the limiting currents for the reduction of thallium(1) cation is very good, with relative standard deviation (rsd) lower than 2%. In general for measurements of this type in the most favorable cases reproducibility is about 1% rsd. Reproducibility is poorer at lower concentrations, and the lower limit of low5 M suggested above would typically yield a reproducibility of about 6% rsd. NMR. It is estimated that the NMR diffusion coefficients are reliable to within about 7% rsd. Acknowledgment. This work was supported in part by the National Science Foundation under Grant No. CHE9208987. The authors acknowledge the assistance of S. J. Gibbs, K. F. Moms, and C. S. Johnson, Jr., University of North Carolina, Chapel Hill, for their help with the design of the gradient coils. References and Notes (1) Huizenga, J. R.; Grieger, P. F.; Wall, F. T. J . Am. Chem. SOC.1950, 72, 4228. (2) Armstrong, R. W.; Struass, M. P. Polyelectrolytes. In Encyclopedia of Polymer Science and Technology, Eds.: Mark, H. F., Gaylord, N. G., Bikales, N. M., Eds.; Wiley-Interscience: New York, 1969; Vol. 10, pp 78 1-86 1 (3) P olvelectrolvtes: science and technoloav: Hara. M., Ed.; Dekker: new^ York,'l993. ' (4) Oosawa, F. Polvelectrolvtes Dekker: New York, 1971 ( 5 ) Manning, G. S.-J. Chem. Phys. 1969, 51, 924; 1967, 47, 2010. (6) Manning, G. S. Annu. Rev. Phys. Chem. 1972, 23, 117. (7) Alfrey, T.; Perg, P. W.; Morawetz, H. J . Polym. Sci. 1951, 7, 543. (8) Fuoss, R. M.; Katchalsky, A,; Lifson, S. Proc. Narl. Acad. Sci. U.S.A. 1951, 37, 579. (9) Nilsson, L. G.; Nordenskiold, L.; Stilbs, P.; Braunlin, W. H. J . Phys. Chem. 1985, 89, 3385. (10) Ander, P. In Water-Soluble Polymers: ACS Symposium Series, Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds.; ACS Symposium Series 467; American Chemical Society: Washington, DC, 1991. (11) Boyd, G. E. J . Phys. Chem. 1974, 78, 735. (12) Ueda, T.; Kobatake, Y. J . Phys. Chem. 1973, 77, 2995. (13) Ander, P.; Kardan, M. Macromolecules 1984, 17, 243 1. (14) Henningson, C. T.; Karluk, D.; Ander, P. Macromolecules 1987, 20, 1286. (15 ) Rose, D. M.; Bean, M. L.; Record, M. T., Jr.; Bryant, R. G. P roc. Natl. Acad. Sci. U.S.A. 1980, 77, 6289. (16) Nilsson, L. G.; Nordenskiold, L.; Stilbs, P.; Braunlin, W. H. J . Phys. Chem. 1985, 89, 3385. I
I ,
(17) Nilsson, L. G.; Nordenskiold, L.; Stilbs, P. J . Phys. Chem. 1987, 91, 6210. (18) Bratko, D.; Stilbs, P.; Bester, M. Makromol. Chem., Rapid Commun. 1985, 6, 163. (19) Qian, C.; Asdjodi, M. R.; Spencer, H. G.; Savitsky, G. B. Macromolecules 1989, 22, 995. (20) Stilbs, P.; Lindman, B. J . Magn. Reson. 1982, 48, 132. (21) Kwak, J. C. T. J . Phys. Chem. 1973, 77, 2790. (22) Kwak, J. C. T.; O'Bien, M. C.; MacLean, D. A. J . Phys. Chem. 1975, 79, 2381. (23) Carter, M. T.; Rodriguez, M.; Bard, A. J. J . Am. Chem. SOC.1989, 111, 8901. (24) Jiang, R.; Anson, F. C. J . Phys. Chem. 1992, 92, 452. (25) Van Leeuwen, H. P.; Cleven, R.; Buffle, J. Pure Appl. Chem. 1989, 61, 255. 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. BioDhvs. Chem. 1995, 54, 35. (26) Moms, S. E.;.Ciszkowska, M.; Osteryoung, J. G. J . Phys. Chem. 1993, 97, 10453. (27) Ciszkowska, M.; Osteryoung, J. G. J . Phys. Chem. 1994,98,3194. (28) Ciszkowska, M.; Osteryoung, J. G. J . Phys. Chem. 1994,98,11791. (29) Forsen, S., Lindman, B. Meth. Biochem. Anal. 1981, 27, 289. (30) Laszlo, P. Angew. Chem. 1978, 90, 271. (31) Gustavsson, H.; Lindman, B.; Bull, T. J . Am. Chem. SOC. 1978, 100, 4655. (32) Linse, P.; Gustavsson, H.; Lindman, B.; Drakenberg, T. J. Magn. Reson. 1981, 45, 133. (33) Spegt, P.; Weill, G. Biophys. Chem. 1976, 4, 143. (34) Gueron, M.; Weisbuch, G. Biopolymers 1980, 19, 353. (35) Stilbs, P.; Lindman, B. J . Magn. Reson. 1982, 48, 132. (36) Harris, K. R.; Mills, R.; Back, P.; Webster, D. S. J . Magn. Reson. 1978, 29, 473. (37) Braun, B. M.; Weigartner, J. J . Phys. Chem. 1988, 92, 1342. (38) Weigartner, J.; Braun, B. M.; Schmoll, J. M. J . Phys. Chem. 1987, 91, 979. (39) Stejskal, E. 0.;Tanner, J. E. J . Chem. Phys. 1965, 42, 288. (40) Tanford, C. J . Am. Chem. SOC.1951, 73,2066; 1952, 74,211; 1952, 74, 6036. (41) Lapanje, S.; Oman, S. Macromol. Chem. 1962, 53, 46. (42) Lapanje, S. Biopolymers 1964, 2, 585; 1966, 4, 85. (43) Scordilis-Kelley, C.; Osteryoung, J. G. Unpublished data. (44) Wightman, R. M. Anal. Chem. 1981, 53, 1125A. (45) Heyrovsky, J.; Kuta, J. Principles of Polarography; Academic Press: New York, 1966. (46) Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications; Wiley: New York, 1980. (47) Solubility Data Series, Kertes, A. S., Ed.; Pergamon Press: New York, 1986; Vol. 25. (48) Tanner, J. E. J . Chem. Phys. 1970, 52, 2523. (49) Zeng, L. Ph.D. Thesis, North Carolina State University, Raleigh, NC, 1994. (50) Ciszkowska, M.; Donten, M.; Stojek, 2.Anal. Chem. 1994, 66, 41 12. (51) Sinru, L.; Osteryoung, J. G.; O'Dea, J. J.; Osteryoung, R. A. Anal. Chem. 1988, 60, 1135. (52) Amatore, C.; Fosset, B.; Bartlet, J.; Deakin, M. R.; Wightman, R. M. J . Electroanal. Chem. 1988, 256, 255. (53) Myland, J. C.; Oldham, K. B. J . Electroanal. Chem. 1993, 347, 49. (54) Fernandez-Prini, R.; Baumgartner, E.; Liberman, S.; Lagos, A. E. J . Phys. Chem. 1969, 73, 1420. (55) Fernandez-Prini, R.; Lagos, A. E. J . Polym. Sci., Part A 1964, 2, 2917. (56) Baumeartner. E. Liberman. S.: Lagos. A. E. Z. Phvs. Chem. (Frankfurt) 1%8, 61, 211. (57) Bockris, J. O'M.; Reddy, A. K. N. Modem Electrochemistry; Plenum Press: New York, 1970{Vol. 1. (58) Golas, J.; Kowalski, 2.Anal. Chim. Acta 1989, 221, 305. (59) Stojek, Z.; Osteryoung, J. G. Anal. Chem. 1988, 60, 131. I
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