J. Phys. Chem. 1996, 100, 797-804
797
Voltammetric Studies of Counterion Transport in Solutions of Chondroitin Sulfate Chariclea Scordilis-Kelley and Janet G. Osteryoung* Department of Chemistry, North Carolina State UniVersity, Raleigh, North Carolina 27695-8204 ReceiVed: July 26, 1995; In Final Form: September 29, 1995X
The transport of hydrogen counterions was studied in solutions of a linear polyelectrolyte, chondroitin sulfate, CS, by voltammetric measurements at a platinum disk microelectrode. The use of microelectrodes enables voltammetry of the counterion in solutions with little or no supporting electrolyte over a wide range of polyelectrolyte concentrations. The voltammetric interactions of counterions with polyions diminish transportlimited current for reduction of electroactive counterions, as shown by comparing results for a polymeric strong acid, poly(styrenesulfonic acid), and simple strong acids. The experimental results agree reasonably well with Manning’s theory, which describes the effect of ionic interactions on the transport of simple ions in the presence of polyelectrolytes. The data agree equally well with a much simpler semiempirical theory. The experimentally determined limiting value (no supporting electrolyte) of the transport ratio, D/Do, is 0.53, where D and Do are the diffusion coefficients of free hydrogen ion with and without CS. The pKa of the carboxyl group of CS is estimated to vary from 3.5 to 5.7 in the range 0.1-0.001 M of ionic strength.
Introduction Transport of simple ions in solutions of polyelectrolytes is of interest for the description of many synthetic and biological systems, such as ion-exchangers, cellular membranes, biological matrices, and colloidal foods. The transport of ions is suppressed in such systems due to long range electrostatic interactions between polyions and counterions. Changes in transport behavior are most noticeable in solutions of low ionic strength, because at higher ionic strength the overall charge of the polyion is shielded by the electrical double layer formed by the ions of the supporting electrolyte. The inference of ionic interactions from transport data requires measurements over a wide range of concentration, extending to solutions nominally without supporting electrolyte. We have demonstrated previously the effectiveness of steady-state voltammetry at microelectrodes for this purpose.1 Small electrode size (diameters on the order of 10 µm) yields steady-state voltammograms on time scales of seconds and makes measurements possible in resistive media, such as solutions without supporting electrolyte. In addition, the steady-state current at microelectrodes is proportional to the flux of reactant. Thus the voltammetric signal is very sensitive to changes in value of the transport coefficient. It has been demonstrated that the height of steady-state voltammetric waves of strong and weak hydrogen acids, at platinum microelectrodes, depends linearly on the formal acid concentration over a wide range of concentration.2 This dependence has been used for analytical purposes, and the height of the hydrogen ion reduction wave of strong simple acids is found to increase with decreasing concentration of supporting electrolyte due to the contribution of migration, as predicted by theory.3-6 Similar behavior also has been observed for metal probe counterions, i.e., cations present in concentrations much lower than the equivalent concentration of the polyacid.7 We have measured transport-limited steady-state currents for reduction of hydrogen ion in solutions of the polysaccharide chondroitin sulfate, CS, an unbranched, linear polymeric acid with both sulfate and carboxylic groups, in which hydrogen ion is the counterion to the negative charges of the polysaccharide. The value of apparent diffusion coefficient obtained from these X
Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-0797$12.00/0
measurements depends on the concentration of electrolyte. This value with no electrolyte divided by the value for a simple acid also with no electrolyte is referred to as the transport ratio, or D/Do. This quantity is predicted by a simple formula for each theory of electrostatic interactions in these systems. It is also in some cases a parameter in the more complex equations that describe the dependence of transport of simple ions on concentration of electrolyte. Chondroitin sulfate was chosen for this study because of its biological importance and because of its small charge density, which distinguishes it from the model compound poly(styrene sulfonate). Chondroitin sulfate is a polyanionic glucosaminoglycan found in the extracellular matrix of mammalian connective tissues. Its primary function is to resist and absorb compressive stresses, whereas the associated collagen is believed to resist and transmit tensile stresses.8 As shown in Figure 1, CS is composed of repeating disaccharide units, glucuronic acid and glucosamine (N-acetygalactosamine). It has been suggested that the cationexchange properties of proteoglycans and glucosaminoglycans may be significant in the distribution and storage of extracellular cations and in the deposition of calcium during calcification.9,10 The underlying objective of this work was to use data on counterion transport to gain insight regarding the conformation of the CS molecule in solution. However, it must be said that the ability of existing theories to predict in detail the effects of electrostatic interactions on transport properties of counterions is limited. Thus to some extent this work explores the correspondence of theory with experiment as opposed to employing well-verified models for the study of structure. Dermatan sulfate, unlike chondroitin sulfates A and C, is found primarily in dermal tissues, but it is also found in a variety of other animal tissues. Dermatan sulfate, CSB, (also known as β-heparin) is the epimer of chondroitin sulfate A. It is mainly composed of disaccharide units of N-acetyl-D-galactopyranose residues alternating with L-iduronic acid or D-glucuronic acid. The polysaccharide chains are linear but they are heterogeneous due to the presence of two types of uronic acid residues and varying degrees of O-sulfation.11,12 Recent studies13 have demonstrated that CSB has increased antithrombotic activity which appears to be related with the content of the conformationally flexible iduronic acid residues. © 1996 American Chemical Society
798 J. Phys. Chem., Vol. 100, No. 2, 1996
Figure 1. Repeating disaccharide units of chondroitin sulfates A, B (dermatan sulfate), and C.
Experimental Section Reagents. Chondroitin sulfate A (>55%; chondroitin sulfate C 1 (14) where ∞
A(λ,γ) )
∞
[πλ-1(m12 + m22) + 1 + 2 γ]-2 ∑ ∑ m1 ) -∞ m2)-∞ (m1,m2)*(0,0)
where a is the fraction of carboxylic acid groups dissociated and b (nm) is the spacing between sulfate and carboxylate moieties. The value of b has been estimated as 0.47,42-44 0.63,45 0.48,46 and 0.5147 nm. From Table 2 and eq 10, D/Do ) 0.531, λ ) 1.63, and, with pKa ) 5.5, a ) 0.01, eq 12 gives b ) 0.44 nm. Carboxyl-Reduced Chondroitin Sulfate. The lack of a reliable theory of ion transport for simple weak acids complicates the interpretation of data for CS. Thus we transformed the carboxylate groups to alcohols as described in the experimental section. The resulting polyelectrolyte should be a strong polyacid with charge spacing twice that of the original chondroitin sulfate sample. The results for this functionalized chondroitin sulfate, CS(CH2OH), listed in Table 2, show that the value of D/Do is larger than that of the native chondroitin sulfate sample but not, as might be expected, twice as large. This result suggests some degree of aggregation, even at these low concentrations.8,48
(15) where m1 and m2 are integers. The dependence of the transport-limited current on electrolyte ratio, γ, has also been described by means of a semiempirical equation:1
il(γ + 1) ) i(γ + R)
(16)
where il is the limiting current in the presence of a strong polyacid and i is the limiting current for a strong simple acid under the same conditions. Clearly R is the limiting value of il/i at zero added electrolyte and thus can be identified as the limiting value of the transport ratio, D/Do. For chondroitin sulfate, R is 0.531, as reported in Table 2. This simple equation has the same limiting values as that of Manning (eq 14). In reference to eq 14,
Voltammetric Studies of Counterion Transport
R ) lim[1 - (1/3)A(1;λ-1 γ-1)]
J. Phys. Chem., Vol. 100, No. 2, 1996 803
(17)
γf0
In comparison with eq 10, for aqueous solution at 25 °C, R ) 0.866/λ. Experimental currents for transport-limited reduction of hydrogen ions in CS were normalized to currents predicted by eq 7 in the absence of polyelectrolyte. Figure 6 shows a semilogarithmic plot of these transport-limited currents for different CS concentrations and the calculated values according to eq 16 (solid line). The dashed line was calculated according to eq 14. The experimental values appear to agree reasonably well with the predicted values of both equations within experimental error. If the experimental curve is extrapolated to the limiting value (no supporting electrolyte), R is estimated to be 0.52, which is close to the value of 0.53 determined from the concentration calibration plots. The maximal difference between the predictions of eqs 14 and 16 in this case is about 4%. Recall that in order to normalize each experimental il/i Versus log γ point, il first has to be divided by the diffusional current, id. A different pKa value has to be approximated from eqs 1 and 2 for each point in order to calculate id according to the free hydrogen ion concentration for each value of supporting electrolyte. The pKa-value is also used to calculate γ. In estimating pKa, the supporting electrolyte concentration was used to calculate ionic strength, for all values of γ. Influence of Counterion Size and Charge. In order to ensure that the dependence on electrolyte ratio is not specific for lithium perchlorate, the dependence of the transport-limited currents was studied with other supporting electrolytes. Figure 7 displays the dependence of normalized limiting currents on logarithm of γ for different 1:1 supporting electrolytes in solutions of the same CS concentration. As expected, the dependence is approximately the same for all supporting electrolytes studied. Only the tetraethylammonium cation deviates from the behavior for 1:1 electrolytes by more than can be attributed to experimental error. Our results were normalized thus far according to eq 7, which describes the dependence of limiting currents on γ in the case of 1:1 supporting electrolyte. For the case of 2:1 supporting electrolyte our results need to be normalized by the theoretical dependence of a strong simple acid also in a 2:1 supporting electrolyte. For the ratio of limiting to diffusional current for the reduction of R+ to form P in a solution containing RY and CA2 as the supporting electrolyte, where A is a singly charged anion,49
-il/id ) 2(x - 1) - γ(x-2 - 1) + 4γ(x - 1)
Figure 6. Normalized limiting currents for various ratios of electrolyte (LiClO4) to hydrogen ion concentration (γ) for hydrogen ion reduction. (4) 1.0, (*) 0.4, and (0) 0.04 mM chondroitin sulfate solution, calculated according to (s) eq 16 for D/Do ) 0.531 and (- - -) Manning’s theory, eq 14 for λ ) 1.63.
Figure 7. Normalized limiting currents of hydrogen ion reduction Versus the normalized concentration (γ) for 1:1 supporting electrolytes. (s) Calculated from eq 16 for D/Do ) 0.531; (0) LiClO4, (×) NaClO4, (O) CsNO3, and (4) TEANO3 in 0.04 mM chondroitin sulfate solution.
(18)
where x is given as the solution to
x ) [(2γ/(2γ + 1)]1/3
(19)
The experimental limiting currents in CS solution for the reduction of hydrogen ion in the presence of divalent counterions were then normalized according to eq 18 and 19 and are presented in Figure 8, along with one example of a monovalent supporting electrolyte for comparison. As expected, the normalized currents rise faster at lower γ values, indicating that the interactions of polyelectrolytes with divalent cations are more pronounced than those with singly charged cations. Conclusions We have extended earlier voltammetric studies on a model system to the biopolyelectrolyte chondroitin sulfate and shown
Figure 8. Dependence of normalized limiting currents of hydrogen ion reduction on the normalized concentration (γ) of 2:1 supporting electrolytes. (s) Calculated from eq 16 for D/Do ) 0.531; (0) LiClO4, (O) Mg(ClO4)2, and (4) CaCl2 in 0.04 mM chondroitin sulfate solution.
that the theory of Manning for electrostatic interactions in such systems predicts reasonably well the limiting transport (i.e., without added electrolyte) of singly charged counterions. In particular, by comparing results with those for poly(styrenesulfonic acid), we find that the decrease in transport is directly proportional to the charge spacing. We have also shown that Manning's theory for the dependence of this effect on concentration of added electrolyte describes well the experimental findings over more than 5 orders of magnitude change in the ratio of concentration of supporting electrolyte to concentration of polyelectrolyte. Finally, we have shown that the results are
804 J. Phys. Chem., Vol. 100, No. 2, 1996 described equally well by a simple semiempirical algebraic equation. Each equation has only one parameter, the value of which can be obtained independently by experiments in solutions with no added electrolyte. The scope of results presented is made possible by steadystate voltammetry at microelectrodes. This technique provides rapid, precise, and accurate measurement of apparent diffusion coefficients over wide ranges of concentration of supporting electrolyte, including solutions without added electrolyte, and wide ranges of concentration of the analyte. This permits strong experimental definition of the limiting cases of no electrolyte and large excess electrolyte, which is essential for determining the dependence on electrolyte concentration in the intervening range. Several lines of investigation are suggested by these results. First, we are extending it to other biopolyelectrolytes, such as the carrageenans, to define more completely the relation between charge spacing and transport ratio. Second, we are investigating selected systems with probe ions. Third, we are exploring in more detail the interaction of multiply charged counterions with polyelectrolytes. This case is of special interest because of the importance of the interaction of calcium and magnesium with biopolyelectrolytes and because there is no theoretical treatment. Finally, we are exploring the effect of dielectric constant on transport ratio. Acknowledgment. This work was supported in part by the National Science Foundation under Grant CHE9208987. We thank Malgorzata Ciszkowska and John O’Dea for helpful discussion and technical assistance. References and Notes (1) Morris, S. E.; Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1993, 97, 10453. (2) Ciszkowska, M.; Stojek, Z.; Morris, S. E.; Osteryoung, J. G. Anal. Chem. 1992, 64, 2372. (3) Amatore, C.; Fosset, B.; Bartlett, J.; Deakin, M. R.; Wightman, R. M J. Electroanal. Chem. Interfacial Electrochem. 1988, 256, 255. (4) Baker, D. R.; Verbrugge, M. W.; Newman, J. J. Electroanal. Chem. Interfacial Electrochem. 1991, 314, 23. (5) Cooper, X.; Bond, A. M.; Oldham, K. B. J. Electroanal. Chem. Interfacial Electrochem. 1992, 331, 877. (6) Oldham, K. B. J. Electroanal. Chem. 1992, 337, 91. (7) Ciszkowska, M.; Osteryoung, J. G. J. Phys. Chem. 1994, 98, 11791. (8) Scott, J. E.; Chen, Y.; Brass, A. Eur. J. Biochem. 1992, 209, 675. (9) Comper, W. D.; Zamparo, O. Biochem. J. 1990, 269, 561. (10) Maroudas, A. Biophys. J. 1970, 10, 365. (11) Poblacio´n, C. A.; Michelacci, Y. M. Carbohydr. Res. 1986, 147, 87. (12) Volpi, N. Carbohydr. Res. 1994, 260, 159, and 255, 133.
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