J. Phys. Chem. 1987, 91, 1971-1977 components thus obtained are of the low-pressure form. The Tg2 values below 200 MPa in the R = 20 solution are all obtained in procedure 2 and thus they seem to reflect the high pressure forms of ice, at least to some degree. Before we discuss the effects of the compositional changes in the vitrified TgIcomponent on T g l ,it is better to refer to the high-pressure work recently done by MacFarlane et aLzo They measured the T ~ofSthe LiCl.RH20 solutions ( R = 3.5, 4.5, 8.5, and 10) as a function of pressure up to 400 MPa. An interesting point is that a liquid-liquid phase separation was observed only in the LiCl solution of R = 4.5. In their experimental procedure, vitrification was made at low pressures and as soon as Tghad been recorded in a heating process, the pressure was increased and the pressure vessel was again immersed in liquid nitrogen. They noted that care was taken to avoid temperatures more than 20 OC above Tg. Therefore, we consider that as phase separation proceeds very slowly just above Tg the glass made at low pressures does not develop into a phase-separated glass even in repeated quenchwarm cycles. In fact, our preliminary high-pressure experiments on aqueous lithium chloride and bromide solutions ( R = 5) vitrified at low pressuresI9 revealed that a phase separation did not develop up to high pressures even in the repeated Tgmeasurement cycles only if the glass was not warmed above Tg 10 K. This is presumably due to the high viscosity of the solution just above Tg. The cause of the discrepancy between our Tgresults on the lithium chloride solution ( R = 5) and those on the R = 4.5 solution by MacFarlane et aLZ0is not clear at the moment. On the other hand, our Tg results for the R = 8 solution show the phase separation (Figure 5). In our experiment for the R = 8 solution, all Tgvalues were obtained in procedure 1. Although Tg for the R = 8.5 solution obtained by MacFarlane et a1.20increases linearly with pressure, those of the phase-separated glass of the R = 8 solution show some curvatures in their pressure dependences. Thus, we conclude that there occurred compositional changes in
+
1971
the phase-separated glass with pressure, which had a large effect on the Tg vs. P relation. From the Tg2vs. P curves for the glassy lithium chloride solutions ( R = 12 and 20), we estimated that Tg for a bulk glassy water of the high pressure form should be close to -137 f 2 OC. This finding will give important impetus to resolve the paradoxical problem of the glass transition of bulk water, for which so many a t t e m p t ~ ~have l - ~ ~been devoted to find a solution. This point will be reported ~ e p a r a t e l y . ~ ~ Finally, we note that a similar two Tgphenomenon was observed in aqueous aluminum chloride solutions ( R = 30 and 60) at high pressures and low temperature^.^' Thus the liquid-liquid immiscibility phenomenon in aqueous lithium chloride solutions at high pressures and low temperatures is additional evidence for the notion that water and liquid silicon dioxide are similar in their thermodynamic and transport properties which are so different from normal liquids.
Acknowledgment. This work was carried out in Prof. Angell's laboratory. I am thankful to Professor C. A. Angell for his encouragement and valuable suggestions. Registry No. LEI, 7447-41-8. (31) Angell, C. A.; Shuppert, J.; Tucker, J. C. J . Phys. Chem. 1973, 7, 3092. (32) Johari, G. P. Phil. Mug. 1977, 35, 1077. (33) Rice, S. A.; Bergren, M.; Swingle, L. Chem. Phys. Lett. 1978.59, 14. (34) Mayer, E.; Briiggeller, P. J . Phys. Chem. 1983, 87, 477. (35) MacFarlane, D. R.; Angell, C. A . J . Phys. Chem. 1984, 88, 759. (36) Kanno, H., to be published. (37) Two glass transitions were observed above 100 MPa for aqueous AICl, solutions of R = 30 and 60. It seems that a liquid-liquid immiscibility may be observed in many an aqueous electrolyte solution at high pressures and low temperatures if only the solution can be sufficiently cooled without crystallization.
Ion Binding Characteristics of Chondroitin Sulfate A Having Two Counterion Species. Effects of Alternate Arrangement of Carboxylic and Sulfuric Groups Masakatsu Yonese,* Hideya Tsuge, and Hiroshi Kishimoto Faculty of Pharmaceutical Sciences, Nagoya City University, Tanabe-Dori, Mizuhoku, Nagoya 467, Japan (Received: August 22, 1986; In Final Form: December 8, 1986)
Molal osmotic coefficients, 4, and counterion activity coefficients, yi, of salt-free chondroitin 4-sulfate (ChS-A), which has two counterion species, such as Na and Ca, H and Na, and H and Ca ions (NaCa-, HNa-, and HCaChS-A), were determined at 25 OC by vapor pressure osmometry and potentiometric measurements. yCafor NaCaChS-A increased with increasing fraction of Ca ion, xca. yca for HCaChS-A showed a maximum at xca = 0.5 and its activity was almost constant in the region 0.5 < xCa< 1 .O. The experimental values of 4 and yi for dilute ChS-A solutionswere in good agreement with Manning's theoretical values, which were obtained by selecting 0.63 nm for the distance between the neighboring charged groups and by approximating that protonated carboxylic groups do not function as charged groups. Furthermore, 4 and yi for the imaginary mucopolysaccharides,which consist of the same repeating unit as ChS-A except for possessing only either sulfuric or carboxylic groups, were theoretically examined to elucidate the effects of the alternate arrangement of carboxylic and sulfuric groups in ChS-A on ion binding.
Introduction Chondroitin sulfates (ChS) are important components of mammalian connective tissues and are considered to contribute to the control of bone formation due to their binding with Ca2+ and other cations. Several kinds of ChS are found in vivo. Chondroitin 4-sulfate (ChS-A) and 6-sulfate (ChS-C), which are typical ChS, are composed of N-acetyl-D-galactosamine 40022-3654/87/2091-1971$01.50/0
and -6-sulfates together with D-guluculonic acids. To ellucidate functions resulting from the different position of sulfuric groups in ChS-A and ChS-C, their binding characteristics with ions and proteins have been Their various thermodynamic (1) Galeman, R. A.; Blackwell, J. Eiochim. Eiophys. Acfa 1973, 297, 452-455.
0 1987 American Chemical Society
1972 The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987
properties have been studied in our l a b ~ r a t o r y , ~and - ~ the results of molal osmotic coefficients 45 and dilution enthalpies AdilH6s7 showed no significant differences between them. These thermodynamic properties relating to electrostatic interaction were found to be explained by the Manning's theory based on a line charge model.l0 Ion binding properties of ChS are considered to be affected significantly by adding H ions because of the presence of carboxylic groups. In this paper, molal osmotic coefficients and activity coefficients of salt-free ChS-A solutions are studied in the presence of pairs of three counterions, such as H+, Na+, and Ca2+,and the change of Ca or N a ion binding properties due to the addition of H ions are analyzed by using Manning's theory. Furthermore, the effects of the alternate arrangement of carboxylic and sulfuric groups on counterion bindings are discussed.
Materials and Methods Materials. Sodium chondroitin 4-sulfate (NaChS-A), extracted from shark cartilage, was obtained commercially from Seikagaku Kogyo Co., Ltd. (Tokyo, Japan) and its lot no. was WIA 9082. The weight average molar mass was determined to be 2.96 X lo4 g/mol by a LS-8 light-scattering photometer (Toyo Soda Manufacturing Co., Ltd., Japan) coupled with a gel permeation chromatograph, whose columns were TSK-GEL G5000PW and G3000PW (Toyo Soda Manufacturing Co. Ltd., Japan). NaChS-A was passed through a cation-exchange resin column converted into the acidic form (Amberlite IR 120 B) to obtain chondroitin sulfuric acid (HChS-A), from which the objective salts having two counterion species, such as H and Na, H and Ca, and N a and Ca ions (HNaChS-A, HCaChS-A, and NaCaChS-A), were prepared by neutralization with arbitrary amounts of NaOH and/or Ca(OH)2. Since ChS-A degrades in a strong acidic solution, the HChS-A obtained was neutralized immediately, and molal osmotic coefficients and counterion activity coefficients of HNa- and HCaChS-A aqueous solutions were measured as s w n as possible, within 5 h at most. The neutral sample, NaCaChS-A, was stored in a desiccator after freeze-drying. All electrolytes used in this study were a special grade from Katayama Co., Ltd. (Nagoya, Japan), and distilled and deionized water was used for the preparation of aqueous ChS-A salt solutions. Methods. Measurement of Electric Conductance. The electrolytic conductivites K of aqueous solutions of chondroitin sulfuric acids neutralized to various extents by a N a O H were measured at 25 f 0.1 OC by a 4255A universal bridge (Yokogawa Hewlett-Packard, Ltd.) connected to a conductivity cell (Type CG-2001 PL, TOA Electronics, Ltd., Tokyo, Japan). Measurement of Molal Osmotic Coefficient. Molal osmotic coefficients 4 of aqueous chondroitin sulfate solutions were measured at 25 f 0.1 OC by a vapor-pressure osmometry using a Hitachi-Perkin-Elmer Model 115 molecular apparatus as described previou~ly.~ Under the isopiestic condition between NaCl aqueous solution as a reference and a salt-free ChS solution, the value 4 is given by the following equation in the presence of only one counterion species
(2) Galeman, R. A.; Blackwell, J. Biopolymers 1973, 12, 1959-1974. (3) Mathews, M. B. Biochim. Biophys. Acta 1959, 35, 9-17. (4) Tanaka, T. J . Biochem. 1978, 83, 647-653. (5) Yonese, M.; Tsuge, H.; Kishimoto, H. Nippon Kagaku Kaishi 1978, 108-112. ( 6 ) Tsuge, H.; Yonese, M.; Kishimoto, H. Bull. Chem. SOC.Jpn. 1979, 52, 2846-2848. (7) Yonese, M.; Tsuge, H.; Kishimoto, H. Bull. Chem. SOC.Jpn. 1981, 54, 20-24. (8) Tsuge, H.; Yonese, M.; Kishimoto, H. Nippon Kagaku Kaishi 1978, 609-613. (9) Tsuge, H.; Yonese, M. Nippon Kagaku Kaishi 1982, 1583-1587. (10) Manning, G. S. Annu. Rev. Phys. Chem. 1972, 23, 117-140.
Yonese et al. where m and mo are the molality of ChS on a repeating unit basis (mol kg-I) and that of NaCl, 4o is the molal osmotic coefficient of NaCl which can be cited from the literature," and z , zc, and z, (=2) are the stoichiometric charge number per ChS, the charge number of a counterion, and the charge number of the repeating unit, respectively. In the presence of two counterion species denoted by subscripts 1 and 2, the value 4 is given by
4 = /
2mo4o I
\
\
(2)
where zci is the charge number of counterion i and xi is the equivalent molal fraction of counterion species i whose summation is equal to 1. p H Titration of HChS-A and Activity Coefficients of H Ions yH. For pH measurements, a digital ion meter (Orion, Type 701A) connected to pH and reference electrodes (Orion, Type 91-01 and 90-02) was used. HChS-A solutions were titrated in a nitrogen atmosphere at 25 f 0.1 O C by N a O H ( m = 0.0925 mol kg-I) and Ca(OH)2solutions ( m = 0.0197 mol kg-') delivered by microburet. The H ion activity coefficients were obtained from the following equation YH
= 10-PH/2m(1 - xi)
(3)
where x i is equivalent molal fraction of Na or Ca ions, Le., the degree of neutralization. Measurements of Activity Coefficients of Na and Ca Ions. Activity coefficients of Na and Ca ions, yNaand yCa,were measured by a potentiometric method: a digital ion meter (Orion, Type 701A) connected to a Na electrode (Orion, Type 94-1 1) or a Ca electrode (Orion, Type 93-20). The electromotive forces between the reference and the ionic selective electrode in ChS-A solutions were measured after attaining constant values, Le., after 12 min for the N a electrode and after 6 min for the Ca electrode. The values of Y~~ for NaCaChS-A were determined from a calibration curve obtained from standard NaCl solutions ranging from to 1.0 mol kg-' by assuming that the individual activity coefficients of yNaare equal to the mean activity coefficients of NaCl cited from tables." The values of yCafor HCa- and NaCaChS-A were determined from a calibration curve obtained from standard CaCI, solutions ranged from to 0.1 mol kg-I. The individual activity coefficients of Ca ions, yCa,were calculated from the Debye-Huckel formula (eq 4) by using Kieland's effective diameter of hydrated ions.12 (4) where A and B are 0.51 15 and 0.3291 X 1Oloat 25 "C, respectively, Z is the ionic strength, and ri is the effective diameter of the hydrated i ion (rCa = 6, rcI = 3 A). Comparing the mean activity coefficients of CaC12,y*,calculated from yCaand yc, with the reference values13 showed that the errors were less than 2% in the concentration region m < 0.015.
Results Electric Conductances of HNaChS-A. Electrolytic conductivities K of HNaChS-A solutions were measured during the neutralization process of HChS-A ( m = 0.0558 mol kg-I) by the addition of NaOH solution ( m = 2.99 mol kg-I), and the results are shown in Figure 1 as a function of the molal fraction of Na, xNa. In the range 0 C xNa C 0.5, K decreased with xNa,and in the range 0.5 C xNaC 1.0 it increased gradually. Upon further addition of NaOH, the K increased more rapidly due to the increase of free Na and OH ions. These results confirmed that, in the range 0 C xNaC 0.5, hydrogen ions restricted electrostatically by sulfuric ( 1 1) Robinson, R. A,; Stokes, R. H. Electrolyte Solution; Butterworth: London, 1959; p 481. (12) Kielland, J. J . Am. Chem. SOC.1937, 59, 1675-1678. (13) Parsons, R. Handbook of Electrochemical Constants; Butterworths: London, 1959; p 20.
Ion Binding Characteristics of Chondroitin Sulfate
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
t
0 " 0
0
0.5
1.0 Na Figure 1. Specific conductance, K , of chondroitin sulfates (HNaChS-A) neutralized by various amounts of NaOH vs. molal fraction of Na ion, xNS. Specific conductances were measured during the neutralization process of HChS-A (m = 0.058 mol kg-l). 0
1.0 XNa Or XCa Figure 2. Molal osmotic coefficients, 6,of chondroitin sulfates HNa- and HCaChS-A vs. equivalent molal fraction of Na and Ca ion, xNaand xCa: 0, HNaChS-A; X, HCaChS-A. 6 of HNaChS-A (m = 0.055 mol kg-') and HCaChS-A ( m = 0.012 mol kg-') were measured at 25 OC. Solid curves show theoretical 6 values for HNaChS-A calculated from eq 17 and 20, and those for HCaChS-A calculated from eq 23, 26, and 29.
groups are neutralized by N a ions and in the range 0.5 d xNad 1.O hydrogen ions bound to carboxylic groups are neutralized.14 Molal Osmotic Coefficients of HNa-, HCa-, and NaCaChS-A. Molal osmotic coefficients of HNa-, HCa-, and NaCa-ChS-A were measured by vapor pressure osmometry. The results are shown in Figures 2 and 3 as a function of xNaor xCa.The 4 values for HNaChS-A ( m = 0.055 mol kg-I) were almost constant (6 = 0.36) in the range 0 d xNad 0.5 and increased gradually with increasing xNato 4 = 0.45 at xNa = 1.0. The 4 values for HCaChS-A ( m = 0.012 mol kg-I) showed a minimum near xCa = 0.5. The 4 results for NaCaChS-A obtained from two different concentrations (m = 0.025 and 0.050 mol kg-') were almost equal as shown in Figure 3. They passed through a maximum value 4 = 0.52 at xCa= 0.33 and then decreased with increasing xCa. The binding specificitiesof the carboxylic groups with H ions result in obvious differences between the values 4 of N a C a - and HCaChS-A. Activities and Activity Coefficients of Counterions of HNa-, HCa-, and NaCaChS-A. Activities of the counterions, ai, were measured at 25 "C by the potentiometric method. Figure 4 shows (14) Casu, B.; Gennaro, U. Carbohyd. Res. 1975, 39, 168-176.
'
"
"
0.5
t
x
9
OO
0.5
"
1.0 XCa Figure 3. Molal osmotic coefficients, 6,of chondroitin sulfates having Na and Ca counterion species (NaCaChS-A) at 25 'C vs. equivalent molal fraction of Ca ion, xCa:0,m = 0.025 mol kg-'; X, m = 0.050 mol kg-l. The solid curve shows the theoretical values calculated by eq 6, 9, and 12.
g
t
"
1973
Q05
m / mol. 0.1 kg-l 0
0.15
Figure 4. Concentration dependencies of counterion activity coefficients ; At m = of Na- and CaChS-A, yNaand yCa,at 25 'C: 0, 7 ~X,~yea. 0 are Manning's theoretical values obtained by using 6 = 6.3 nm as- the distance between neighboring charged groups.
"
0
a5
1.0 XCa Figure 5. Counterion activities of HCaChS-A, uH and aca, and those of NaCaChS-A, aNaand uCarat 25 'C vs. equivalent molal fraction of Ca ion, xca: 0; uca for HCaChS-A; 0 , uH for HCaChS-A; A, uCa for NaCaChS-A; A, aNafor NaCaChS-A. The concentrations of the NaCaChS-A solutions were m = 0.00856 mol kg-' but those of the HCaChS-A solutions varied from m = 0.0151 mol kg-' for xCa = 0 (HChS-A) to m = 0.00856 mol kg-' for xCa = 1 (CaChS-A).
activity coefficients of Na and Ca counterions of Na- and CaChS-A as a function of the concentration of ChS-A, m. They
1974
Yonese et al.
The Journal of Physical Chemistry, Vol, 91, No. 7, 1987 1.0
r
I,,,.;/
n "0
1.o
0.5
k a Figure 6. Counterion activity coefficients of NaCaChS-A, yNaand yea, at 25 O C vs. equivalent molal fraction of Ca ion xca: A, -yea; A, Y N ~ . Solid curves show the theoretical values obtained from eq 7, 10, and 13 for Y~~ and from eq 8, 11, and 14 for yea.
derived by using an infinitely long line charge model is appropriate for discussing the thermodynamic quantities of chondroitin sulfates in dilute solutions. As shown in the previous paper,5 the concentration dependencies of the molal osmotic coefficients of ChS having only one kind of counterion, such as Na-, K-, and CaChS-A etc, were linear and small, and the values extrapolated to infinite dilution were in good agreement with the theoretical values obtained by assigning a distance between neighboring charged groups, b, of 0.63 nm. When the concentrations of ChS, m, were less than 0.05 mol kg-I, the change of the 4 values were found to be within a few percent of the extrapolated values. y,decreased gradually with increasing m, as shown in Figure 4, and in the region m < 0.015 mol kg-' the yl results were in agreement with the extraporated values to m = 0 within a few percent. Then, in this report, we discuss the 4 and yI results by applying Manning's theory to the cases having two kinds of counterions (HNa-, HCa- and NaCaChS-A). Furthermore the ion binding properties of imaginary mucopolysaccharides possessing only the sulfuric or the carboxylic group as charged groups are estimated theoretically and the significance of the alternate arrangement of sulfuric and carboxylic groups on ChS is analyzed. The interactions of polyelectrolytes with counterions consist of two modes: the Debye-Huckel ion atmosphere and condensation on the charge groups. The key parameter for the counterion condensation in Manning's theory is defined by eq 5 and is proportional to the line charge density,'0,'6 that is, the reciprocal of the distance between the neighboring charged groups,
b = e2/(4nckTb) "0
1.o
0.5 XCa
Figure 7. Counterion activity coefficients of HCaChS-A, YH and yea, at 25 OC vs. equivalent molal fraction of Ca ion, xca: 0, yea; 0 , YH. Solid curves show the theoretical values obtained from eq 24, 27, and 30 for yH, and from eq 25, 28, and 31 for yea.
decreased gradually with increasing m. The values at m = 0 show Manning's theoretical values obtained by using 0.63 nm as the distance between the neighboring charged groups, b. The activities of counterions ai of NaCaChS-A ( m = 0.00856 mol kg-I) and HCaChS-A solutions are shown in Figure 5 as a function of xCa. As the activities of HCaChS-A were measured during the neutralization process of HChS-A by the addition of Ca(OH), SOlutions, the concentrations of HCaChS-A varied slightly with xca, Le., they varied from m = 0.0151 for xCa= 0 (HChS-A) to m = 0.00856 for xCa= 1 (CaChS-A). Taking the changes of the concentrations in consideration gave activities for Ca-, aca, for NaCa-, and for HCaChS-A that differed significantly. The values aca for NaCaChS-A increased with increasing xCabut those for HCaChS-A became almost constant in the region 0.5 < xCaC 1.0. From these results, the activity coefficients of the counterions yi were obtained and are shown in Figure 6 for NaCaChS-A and in Figure 7 for HCaChS-A. The yca values for HCaChS-A possessed a maximum a t xCa = 0.5 and above it decreased with increasing xca to yca = 0.27 at xCa= 1.O. However, the ycavalues for NaCaChS-A showed a monotonous increase with increasing xCaand reached yca = 0.27 a t xCa = 1.0, and the yNavalues increased also with increasing xCa. The pHs of HNa- and HCaChS-A were measured at various xNaand xCa,and the activity coefficients of H ions, T H . of HCaChS-A obtained from eq 3 are shown in Figure 7. The yH values decreased and became asymptotic with 0 with increasing xCa. The results of HNaChS-A were almost equal to those of HCaChS-A. Discussion ChS in dilute solution behaves as a rodlike polyion due to the electrostatic repulsive force between the charged groups and the rigidity of their saccharide structure.15 Then, Manning's theory (15) Nakagaki, M.; Ikeda, K. Bull. Chem. SOC.Jpn. 1968.41, 555-563.
(5)
where e is the protonic charge, E is the permitivity of solvent, and k and Tare the Boltzmann constant and the absolute temperature. At 25 OC, is equal to 0.7135 X 10-9/b. When the valence of counterion i is zci, the critical value of t, talt,for the condensation is za-'. When 3 z,.-', counterions condense to lower the net value of E, Enet, to tnetis obtained from eq 5 by using the distance between effective closest charged groups left uncovered by the condensed counterions. In this discussion, 4 and yI for the ChS-A salts are analyzed by using b = 0.63 nm according to the previous paper.s (1) Molal Osmotic Coefficients and Activity Coefficients of ChS-ASolutions. (1.1). For NaCaChS-A, as = 1.133 at 25 OC, both N a and Ca ions can consense on the charged groups. Ca ions condense predominantly until1 Enet is lowered to &,,, for the Ca ion (=OS). If Enet is greater than tmtfor the Na ion ( = I .O) even after the condensation of all Ca ions, Na ions condense. According to Manning's theory, the following three cases occur:I6 (a) When 0 C xCaC 0.1 17 ( = I all Ca ions condensed but inet is still greater than Emt for the Na ion (=l). Hence, sufficiently many N a ions also condense to lower Fnet to 1. In this case, the theoretical osmotic coefficients, 4, the activity coefficient of the Na ion, yNa,and the activity coefficient of the Ca ion, yea, are given by the following equations:
r'),
4 = (2t)-I(xNa + XCa/2)-' In
YNa
= -!h - In ( f ( l - XCa)) YCa
=0
(6) (7) (8)
(b) When 0.117 (= 1 - El) C xCaC 0.559 (= 1 - ( 2 t ) - ' ) ,the condensation of all Ca ions lowers Enet to 0.5-1.0. Then no N a ions condense. In this case, 4, yNa,and yca are given by the following equations:
4 = (1 - xca)(l - (1 - Xca)F/2)/(1 - X C , / ~ ) In
YNa
= -(1/2)(l - XCa)E YCa
=0
(9) (10)
(11)
(c) When 0.559 (= 1 - (2E)-') C xCaC 1.0, there are sufficient (16) Manning, G. S . Charged and Reactive Polymers, I , Polyelectrolyte, Selegny, E., Ed.; Reidel: Boston, 1972; pp 9-37.
The Journal of Physical Chemistry, Vol. 91, No. 7. 1987
Ion Binding Characteristics of Chondroitin Sulfate condensed Ca ions to lower fnH to htfor the Ca ion (=OS). Then no Na ions are condensed. In this case, 4, yNa,and Y~~ are given by the following equations:
d= (1 - 1/(2(1 + 2(1 In
In
YCa
YNa
= -1/(8(1 - (1 - XCa)€))
(13)
= -1/(2(1 - (1 - xca)€) + In ((€/2 - 1 + XCa)/XCa) (14)
The 9, yNa,and Y~~ calculated from these equations by using b = 0.63 nm are shown in Figures 3 and 6 as a function of xCa together with the experimental results. They were found to be in good agreement with the theoretical values as well as with the values for polyelectrolytes bearing only one kind of charged group, such as polystyrene~ulfonates.~J~ (1.2)In the Presence of Hydrogen Ions. Carboxylic and sulfuric groups of polyelectrolytes are different in counterion binding s p e c i f i c i t i e ~ . ~ JCarboxylic ~~'~ groups interact with hydrogen ions primarily covalently and dissociate according to the dissociation constant, while sulfuric groups interact electrostatically. Therefore, the binding of N a or Ca ions to ChS-A is significantly affected by the presence of hydrogen ions. Since undissociated carboxylic groups do not function as charged groups, the distance between the effective closest charged groups depends actually on the degree of dissociation of the carboxylic groups. in this discussion, we neglect the dissociation of protonated carboxylic groups and analyze the and yi for HNa- and HCaChS-A by extending Manning's theory under the approximation that none of the carboxylic group work as a charged group. Hereinafter, subscripts 1 and 2 denote H and other ions ( N a or Ca ions). In the range 0 Q x2 C 0.5, the sulfuric groups are neutralized predominantly and all carboxylic groups are left unneutralized. Then, b is
+
b = 1.26 X m in 0 Q x2 Q 0.5 (15) In the range 0.5 d x2 d 1.O,the carboxylic groups are neutralized, and b decreases with the degree of the neutralization x2 according to
b = 0.63
and yNaare given by the following equations:
- XCa)€)))(l + 2(1 - xca)E)/(2(2 - xca)O (12)
X
10-9/x2 m in 0.5 Q x2 Q 1.0
(16)
Manning's theoretical values for +', yI', and y i obtained by using the approximation described above are on the basis of the effective counterion concentrations in which H ions bound to carboxylic groups are excluded. Then, to compare with the experimental results shown in Figures 2 and 7, they must be converted to 4, y', and y2 based on the total counterion concentrations which include all H ions of the protonated carboxylic groups. The relations d'and 4, yl' and y l , and y i and y2 are described in detail in the Appendix. (1.2.1)HNaChS-A. Three cases occur here. (a) When 0 d xNaQ 0.5, b is constant (=1.26 nm) because all the carboxylic groups are in the H form. Since f is less than fmt for a 1 valence ion (=1.0), no Na and H ions condense. 4, yH,and yNaare given by the following equations:
d = (1/2)(1 - F/2) YH = (1/2)((1 - 2xNa)/(1 - XNa)) exp(-f/2) YNa
= exp(-E/2)
(17)
(19)
(b) When 0.5 C xNaQ 0.883, b varies inversely as xNaaccording to eq 16, and E is less than 1.O as in case a. @ and Y~~ are given by eq 17 and 19, and Y~ = 0. (c) When 0.883 Q xNaQ 1.0, b is obtained by eq 16 and 5: is greater than 1.0. Then, N a ions condense to lower Fnet to fCrlt for the N a ion (=1.0), and 4, yH, (17) Rinaudo, M. Charged and Reactive Polymers, I , Polyelectrolyte, Selegny, E.,Ed.;Reidel: Boston, 1972; pp 157-192. (18) Strauss, U.P.;Leung, Y . P.J. Am. Chem. Soc. 1%5,87, 1476-1480. (19) Tamaki, K.;Osaki, M.; Ogiwara, M.; Takemura, I. Nippon Kagaku Kaishi 1967,88,711-714.
1975
d = xca(1/(2€))
(20)
YH = 0
(21)
YNa = (I/() exp(-1/2)
(22)
(1.2.2)HCaChS-A. Three cases also occur here. (a) When 0 Q xca d 0.0585, b is constant (=1.26 nm) and ( is 0.556. Then, no H ions condense on the sulfuric groups, and all Ca ions condense but the fnct value does not reach the fCrlt value for the Ca ion (=1/2). 4, yH,and -yea are given by the following equations:
d = (1 - 2xca)(l - (€/2)(1 - 2Xca)/(2 - Xca)) YH = -((I - 2xca)/2(1 - xca))(l - 2xca)€/2 YCa
(23) (24) (25)
=0
(b) When 0.0585 Q xCad 0.5, b = 1.26 nm and = 0.566 as in case a. However, there are sufficient condensed Ca ions to lower Fnct to Fcrit (=1/2). 4, yH,and 7ca are given by the following equations:
d = (1 - 1/(2(1 + 2(1 - 2xca)F))) X (1/(2€) + 1 - 2xca)/(4(1 -xca/2)) (26) YH = -1/(8(1 - E(1 - 2xca))) (27) Yca = -1/(2(1
-
+ In (((2F)F'
- 2Xca)))
- (1 - 2xca))/(2xca))
(28) (c) When 0.5 Q XG Q 1.0, b is obtained from eq 16 and the values of € = 0.7135/(0.63/xG) are greater than 0.5. There are sufficient condensed Ca ions to lower fnet to fCrlt (=1/2). 4, Y ~and , Y~~ are given by the following equations:
d = 1/(4€)
(29)
YH = 0
(30)
= -1/2 - In (2l)
(31)
Theoretical 6 and yI values for HNaChS-A and HCaChS-A obtained from above equations are shown in Figures 2 and 7 together with experimental results. Under the approximation that protonated carboxylic groups do not function as charged groups, the theoretical d, and Y~~ values were found to be in good agreement with the experimental results even in the presence of H ions. Although the experimental yH values for HCaChS-A shown in Figure 7 deviated from the theoretical values near xCa = 0.5 due to the dissociation of H ions from the carboxylic groups, we can say that the counterion binding features can be analyzed with sufficient accuracy under the approximation. Then, in following section, the counterion binding features due to the alternate arrangement of the sulfuric and carboxylic groups will be discussed in light of the theoretical 6 and yI values obtained under the approximation. (2) Ion Binding Properties of Imaginary Mucopolysaccharides. To elucidate the ion binding characteristics resulting from the alternate arrangement of the carboxylic and sulfuric groups of ChS-A, we studied theoretically the and y Ivalues of imaginary mucopolysaccharides (IMPC and IMPS), which consist of the same repeating units as ChS-A except for possessing only carboxylic or sulfuric groups and compared them with the values for ChS-A. (2.1)Imaginary Mucopolysaccharide Possessing only Sulfuric Groups, IMPS. b and for IMPS are 0.63 nm and 1.133. For HNaIMPS, H and N a ions condense to lower Enel to 1. 4, yH, and yNaare independent of the fraction of Na and are obtained by the following equations:
d = 1/2E In
+
YH
= In
?Na
= -1/2 - In
(32) (33)
and yI for NaCa- and HCaIMPS are the same as those for NaCaChS-A described in (1.1). Figures 8-1 1 show the theoretical and T~ values together with those for ChS-A and IMPC.
Yonese et al.
1976 The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987
0 0
0.5
%a
1.0
Figure 8. Theoretical osmotic coefficients, 4, of ChS, IMPS, and IMPC having two counterion species (NaCa- and HCa-) at 25 OC vs. equivalent
molal fraction of Ca ion, xCa: 0,NaCaChS-A, NaCaIMPC, NaCaIMPS, and HCaIMPS; 0, HCaChS-A; A, HCaIMPC. 0.5
1 1 1 / 1 1 1 1 ( I I
1.0 XNa Figure 10. Theoretical activity coefficients of Na ions, Y N ~ , of HNaChS-A, -IMPC, and -IMPS at 25 'C vs. molal fraction of Na, X N ~ : 0, HNaChS-A; A, HNaIMPC; 0,HNaIMPS. 0
1
l'O
0.5
ei
G-e-
0.5
-
0 k a
0.5
0
Na Figure 9. Theoretical osmotic coefficients, 4, of ChS-A, IMPC, and IMPS having H and Na counterions at 25 OC vs. molal fraction of Na ion, xXa: 0, HNaChS-A; A, HNaIMPC; 0,HNaIMPS.
(2.2) Imaginary Mucopolysaccharide Possessing only Carboxylic Groups, IMPC. For NaCaIMPC, the results are the same as those for NaCaChS-A. However, the following discussions for the cases with H ions present proceed under the approximations described in (1.2). Then, the b values are obtained by eq 16 in 0 Q x2 Q 1.O, and the theoretical 4 and y ivalues were corrected on the basis of total counterion concentrations mT according to eq A.6, A.7, and A.8 as mentioned in Appendix. (2.2.1) HNalMPC. Two cases occur. (a) When 0 6 X N ~Q 0.883,F C 1 and then no N a ions condense. @, yH. and Y N are ~ obtained by the following equations:
d = XNa(l -
(34)
Yn = 0
(35)
= -E/2 (36) (b) When 0.883 C xNaC 1.0, E > 1 and then N a ions condense to lower fnet to 1. 4, yH, and yNaare obtained by the following equations: 4 = XNa(1/2F) (37) In
YNa
YH = In Y~~ = -1 / 2 - In [
Theoretical activity coefficients of Ca ions, yc., of HEaChS-A, -IMPC, and -IMPS at 25 OC vs. equivalent molal fraction of Ca, xCa: 0, HCaChS-A; A, HCaIMPC; 0,HCaIMPS. Figure 11.
1.0
(38)
(39)
(2.2.2) HCalMPC. Two cases occur here also. (a) When 0 Q xCaQ 0.441, < 112 and then no Ca ions condense. and yCaare obtained by the following equations:
d=
(xca/(2
- xca))(l - E )
4, YH, (40)
Yn = 0
(41)
In Yca = -F
(42)
(b) When 0.441 Q xCa< 1.0, E > 1/2 and Ca ions condense to lower fnet to 112. 4, yH, and Y~~ are obtained by the following equations:
4 = (xca/(2 - x ~ a ) ) ( 1 / 4 0
(43)
= In Y~~ = -1/2 - In 2 t
(44)
YH
(45)
The 4 values for ChS-A, IMPC, and IMPS having two counterion species (NaCa, HCa, and HNa) are shown in Figures 8 and 9 The 4 values of these polymers having Na and Ca counterions are same and have a maximum at xca = 0.33 as shown in Figure 8 by the symbol 0.For the HCa and HNa counterions, the 4 values show distinguishable differences between ChS-A, IMPC, and IMPS in the region 0 Q x2 < 0.5, but in the region 0.5 < x 2 C 1.0 the values of ChS-A and IMPC are same. The y,values are prefered to 4 to analyze the binding properties of
J. Phys. Chem. 1987, 91, 1977-1980 each counterion. Figure IO shows the yNavalues for the H N a counterion systems and Figure 11 shows the yCavalues for the HCa systems as a function of xCa. Summarizing the features of yNaand yCa,in the region 0.5 Q x2 Q 1.0 the values for ChS-A are same as those for IMPC, but they differ significantly from those for IMPS. It is worthwhile to note that the yCavalue for HCaChS-A shows a maximum at xCa= 0.5, that is, in the region 0 < xCaQ 0.5 the aca increases with increasing xCabut remains constant in the region 0.5 < xCa< 1.0 as shown in Figure 5. This specific behavior of the Ca ion binding properties of ChS-A in the presence of H ions is one of the characteristics resulting from the alternate arrangement of carboxylic and sulfuric groups and is considered to take part in living functions. However, considering that the pH in vivo is almost neutral, the counterion binding properties of ChS-A do not differ from those of IMPC in the neutral pH region. To elucidate furthermore the biological significance of the alternate arrangements of carboxylic and sulfuric groups, not only counterion binding but also the interaction with proteins, such as collagen, must be taken into consideration.
Appendix The total concentrations of counterions, mT,which include all H ions bound to carboxylic groups and that of counterion 1, m T l , are expressed by
1977
mT = 2(1
- (1 - l / z c 2 ) x 2 ) m
mT1= 2(1 - x 2 ) m
(A. 1) (‘4.2)
The effective counterion concentrations me, which is the summation of the concentration of free H ions, mel,and Na or Ca ions, are obtained by the following equations. When 0 < x2 < 0.5
me = (1 - 2x2( 1 - 1/ z c 2 ) ) m mel = (1
- 2xJm
64.3) (A.4)
When 0.5 Q x2 Q 1.0, the effective concentration of H ions is zero (me] = 0) and me is
me = 2x2m/zc2
(‘4.5)
yl, and y 2 are related to d’, yl’, and y2’ by the following equations:
4,
d’ = (me/mT)+’ YI
(A.6)
= (mei/mTihi’
(‘4.7)
= Yzl
(‘4.8)
72
Registry No. Chondroitin sulfate A, 24967-93-9.
Birefringence Stopped-Flow Study on the Rotational Relaxation Time and Conformation of Sodium Salts of Poly(styrenesu1fonic acid) and Deoxyribonucleic Acid Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto 606, Japan (Received: November 21, 1986)
The birefringence detected stopped-flow (BSF) technique gives valuable information on the rotational relaxation time ( T ) of sodium poly(styrenesu1fonate)s(NaPSS) and deoxyribonucleicacid (NaDNA) in aqueous media. The 7 values for NaPSS from the BSF method agree satisfactorily with those from the conductance stopped-flow method, which has been clarified as an effective technique to study T for NaPSS solution. The effective length and the total persistence length of NaDNA at various concentrations of polymers and foreign salts (0.014.1 M) are evaluated from the T values and compared satisfactorily with previously reported values.
Introduction In preceding articles the author used the spectrophotometric stopped-flow (SP-SF) and conductance stopped-flow (CSF) techniques, for the first time, in order to obtain information on the rotational relaxation time and rotational diffusion coefficient of anisotropic macroions such as ellipsoidal colloids of tungstic acid and sodium poly(styrenesu1fonate) in aqueous suspensions.Iv2 In the present paper the birefrigence detected stopped-flow (BSF) method is reported to be very useful to study the rotational Brownian motion of anisotropic colloids. The anisotropic particles are expected to orient along the flow direction during continuous flow by shearing forces arising from the velocity gradient. We expect that the transmittance of the visible light through the cross nicols would be significantly strengthened by the orientation. ~~~
~~
When the solution flow is stopped, the colloidal molecules revert to rotate freely to a random Brownian distribution. Then, the transmittance would relax and decrease toward an equilibrium point after the stopped-flow. Changes in birefringence are expected to occur for almost all anisotropic colloids including particles showing no spectrophotometric detection. The author believes that the BSF technique is one of the most powerful, reliable, and convenient methods for studying the rotational properties. Here, the BSF technique is applied to aqueous solution of sodium poly(styrenesu1fonate) (NaPSS), and comparison with the data from the C S F method is carried out. Furthermore, the rotational relaxation times of the rather stretched linear macroions, deoxyribonucleic acid (DNA) of high molecular weight, are determined by the BSF method, and the conformation of the molecules is discussed.
~
(1) Okubo, T.J. A m . Chem. SOC.,in press. Polym. Prepr., Jpn. 1986, 35, 1110. (2) Okubo, T., submitted for publication. Polym. Prepr. Jpn. 1986, 35, 1111.
0022-3654/87/2091-1977$01.50/0
Experimental Section Materials. Sodium poly(styrenesu1fonate) (NaPSS) with a molecular weight of 1.2 X lo6 was purchased from Pressure 0 1987 American Chemical Society
