Langmuir 1999, 15, 4135-4138
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Low- and High-Frequency Electric Birefringence Relaxations in Linear Polyelectrolyte Solutions† Yuko Nagamine,* Kohzo Ito, and Reinosuke Hayakawa Department of Applied Physics, Graduate School of Engineering, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan Received September 3, 1998. In Final Form: March 22, 1999 To clarify the molecular mechanism of the counterion fluctuations in linear polyelectrolyte solutions, we have studied the dependence of the low-frequency electric birefringence relaxation on the degree of polymerization N and the monomer concentration Cp of sodium polystyrenesulfonate (NaPSS) in aqueous solution and the dependence of the low-frequency (LF) and high-frequency (HF) relaxations on the neutralization ratio R of polystyrenesulfonic acid (HPSS) in aqueous solution by the frequency-domain electric birefringence (FEB) method. The experimental results of the N and Cp dependence of the LF relaxation definitely show that the LF relaxation strongly depends on N but is weakly dependent on or almost independent of Cp, which indicates that the LF relaxation arises from the counterion fluctuation along the polyion. Also, it turns out from the experimental results of the R dependence of the LF and HF relaxations that the LF relaxation is ascribed to tightly bound counterions in the vicinity of a polyion and that the HF one is due to loosely bound counterions away from the polyion. These results support the molecular mechanism that the LF and HF relaxations come from the fluctuation of the tightly bound counterions along the polyion axis and from the fluctuation of the loosely bound counterions perpendicular to the polyion axis, respectively.
Introduction The dielectric relaxation spectroscopy for the linear polyions in the semidilute region shows two kinds of relaxation processes, that is, the low-frequency (LF) relaxation in the kilohertz range and the high-frequency (HF) one in the megahertz range.1,2 Although there have been many studies on these processes so far, the molecular mechanism of them still remains controversial: It is obscure how counterions contributing to each relaxation are bound to the polyion and in which direction they fluctuate. Some groups have recently measured the optical anisotropy of linear polyelectrolyte solutions under an electric or shear field and suggested that the LF relaxation is due to the motion of counterions perpendicular to the polyion and that the HF one is ascribed to the counterion motion parallel to the polyion.3,4 On the other hand, the experimental results of the dielectric relaxation have indicated the opposite model that the LF and HF modes arise from the counterion motions in the directions parallel and perpendicular to the polyion axis, respectively.5-7 Moreover, we studied the HF relaxation in detail by dielectric relaxation spectroscopy in the high-frequency region and found crossover behaviors of the dielectric increment and the relaxation time between the dilute and semidilute regions.8 This indicates that the HF relaxation * Corresponding author. Fax: 81-3-5689-8269. Telephone: 81-3-3812-2111 (ex. 6853). E-mail:
[email protected]. † Presented at Polyelectrolytes ‘98, Inuyama, Japan, May 31June 3, 1998. (1) Oosawa, F. POLYELECTROLYTES; Marcel Dekker: New York, 1971. (2) Mandel, M.; Odijk, T. Annu. Rev. Phys. Chem. 1984, 35, 75. (3) Kramer, H.; Graf, C.; Hagenbu¨chle, M.; Johner, C.; Martin, C.; Schwind, P.; Weber, R. J. Phys. II 1994, 4, 1061. (4) Oppermann, W. Makromol. Chem. 1988, 189, 927. (5) Minakata, A.; Imai, N. Biopolymers 1972, 11, 329. (6) Muller, G.; Van Der Touw, F.; Zwolle, S.; Mandel, M. Biophys. Chem. 1974, 2, 242. (7) Minakata, A. Ann. N. Y. Acad. Sci. 1977, 303, 107. (8) Ito, K.; Yagi, A.; Ookubo, N.; Hayakawa, R. Macromolecules 1990, 23, 857.
is attributed to the fluctuation of loosely bound counterions spreading over the average distance between polyions. To settle the model and clarify the molecular mechanism, we need to obtain more detailed information on the LF and HF relaxations. A definite picture of the LF and HF dynamics of the counterions around the polyion can be obtained by frequency-domain electric birefringence (FEB) spectroscopy.9 This is because the FEB spectra are not influenced by large conductivity of solutions, which is serious for dielectric relaxation spectroscopy in the lowfrequency range. By using the FEB technique, we can obtain information on the polyion conformation from the rotational relaxation frequency fR and on the counterion fluctuations from the LF relaxation frequency fL and the HF relaxation frequency fH. In this report, we measure the dependence of fL on the degree of polymerization N and the monomer concentration Cp of sodium polystyrenesulfonate (NaPSS) in aqueous solution and the dependence of fL and fH on the neutralization ratio R of polystyrenesulfonic acid (HPSS). The N and Cp dependence of the LF relaxation gives us information on the fluctuation direction of the bound counterions contributing to the LF relaxation. On the other hand, the R dependence of the LF and HF relaxations reveals the distribution of counterions contributing to the LF and HF relaxations as follows. As R increases, the counterion H+ of HPSS is replaced by (C4H9)4N+ but the total number of counterions is kept constant within 0 e R e 1. Hence, two kinds of monovalent counterions, H+ and (C4H9)4N+, coexist with different ratios proportional to R in the solutions of PSS- polyions. According to the theoretical calculation with the Poisson-Boltzmann equation for the linear polyelectrolyte solution including two species of monovalent counterions with different sizes,10 the smaller counterion is closer to the polyion axis and the larger one (9) Ookubo, N.; Hirai, Y.; Ito, K.; Hayakawa, R. Macromolecules 1989, 22, 1359. (10) Dolar, D.; Sˇ kerjanc, J. J. Polym. Sci., Polym. Phys. Ed. 1976, 14, 1005.
10.1021/la9811564 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/20/1999
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Figure 1. Typical example of the dc component ∆ndc and the 2ω component ∆n*2ω of the FEB spectra for NaPSS solution at Cp ) 1.0 mM, N ) 2.0 × 103, and E0 ) 1.0 × 103 V/m.
is away from the polyion. This means there is a separately localized distribution of the two kinds of monovalent counterions with different sizes in the linear polyelectrolyte solution. The change of the counterion species or the localized distribution with varying R is expected to affect the relaxation frequencies fL and fH in the FEB spectra. This information will lead to a detailed understanding of the molecular mechanism of the LF and HF relaxations. Experimental Section Three kinds of monodisperse (Mw/Mn e 1.1) samples of dialyzed NaPSS (N ) 1.0 × 103, 2.0 × 103 and 3.8 × 103) were purchased from Pressure Chemical Co. The Cp dependence was measured within the Cp range 0.06-4 mM in the dilute and semidilute regions. The HPSS solutions used for the measurements of the R dependence were prepared by passing the NaPSS samples through a mixed-bed ion-exchange column and were used for measurements after dilution with deionized pure water and addition of (C4H9)4NOH. The Cp of the HPSS solutions was fixed to 0.5 mM. The neutralization ratio R is defined by
R ) Ct/Cp
(1)
where Ct is the concentration of (C4H9)4NOH in the solutions. Then the total number of counterions in the solutions is constant at 0 e R e 1 while it increases with R at R > 1 and the excess amount of (C4H9)4NOH behaves as added salt. The birefringence response ∆n in the frequency range 1 Hz to 10 MHz was measured by using the FEB method.9 In the FEB method, the sinusoidal electric field E with an angular frequency of ω is applied to the sample with anisotropy of electrical and optical polarizabilities, and the dc component ∆ndc and the complex amplitude ∆n2ω* ) ∆n′2ω - i∆n′′2ω of the 2ω component of ∆n are detected. From ∆ndc, we can obtain the induced relaxation frequencies fL and fH of the LF and HF relaxations, respectively, if fL and fH are much larger than the rotational relaxation frequency fR of the polymer chain (polyion).9 From ∆n2ω, on the other hand, we can obtain fR only, which gives us the information on the polyion conformation. The amplitude E0 of the electric field E used was 0.6. The theoretical calculation with the Poisson-Boltzmann equation for the rodlike polyelectrolyte solution without added salts indicates the dependence of the counterion distribution on the counterion size, namely, the counterion species: The smaller counterions are bound closer to the polyion than the larger ones.10 Hence, if two kinds of monovalent counterion species H+ and (C4H9)4N+ with different sizes are mixed, the smaller counterion H+ is localized in the inner region closer to the polyion and the larger (C4H9)4N+ occupies the outer region away from the polyion. The experimental results at R ∼ 0.5 clearly show that H+ contributes to the LF relaxation and (C4H9)4N+
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is responsible for the HF one. Thus, it is concluded that the LF relaxation is ascribed to the counterions in the inner region and that the HF one is due to the counterions in the outer region. This agrees with our picture for the classification of the counterions contributing to the LF and HF relaxations as the tightly and loosely bound counterions, respectively, as mentioned above. Next, we consider the features of the changes of fL and fH with varying R: fL rises and fH decreases with increasing R. According to our model, the fluctuation length ξ in eq 5 is evaluated to be the contour length of the polyion in the LF relaxation or the average distance between polyions in the HF relaxation. Since we fixed Cp to 0.5 mM and N to 2.0 × 103 and changed only the monovalent counterion species, the fluctuation length ξ should be constant in the R-dependence measurements. Accordingly, the R dependence of fL and fH reflects the change of µL and µH, which is the mobility of the counterion contributing to the HF relaxation. The experimental results show the increase of fL (i.e., µL) and the decrease of fH (i.e., µH) with increasing R. Since the mobility of a free ion of (C4H9)4N+ is much smaller than that of a free ion of H+, the relaxation frequency ought to decrease as H+ is replaced with (C4H9)4N+. This tendency agrees with the experimental result of the R dependence of µH, which means that the counterions contributing to the HF relaxation are almost in the free state. This is quite reasonable for the “loosely” bound counterions to which we have assigned the HF relaxation. In contrast, the experimental result of fL increasing with R indicates that the mobility µL of the counterions yielding the LF relaxation is quite different from the counterion mobility µ0 in the free state. As discussed before, µL is much smaller than µ0 because the tightly bound counterions are affected by the undulation of Coulombic potential along the polyion. Then, the amplitude of the undulation mainly dominates µL, irrespective of µ0. The amplitude strongly depends on the counterion size: A smaller counterion can be closer to the polyion and feels the Coulombic undulation with a larger amplitude. Hence, if the effect of the undulation is taken into account, µL of H+ can be smaller than that of (C4H9)4N+ in the LF relaxation, which is contrary to the tendency of µ0 but agrees with the observed R dependence of µL. Recently, we reported the dependence of fL and fH of the PSS solutions on counterion species.14 The experimental results showed that fH was proportional to the free mobility µ0 of counterions whereas fL was nearly independent of µ0. This supports the conclusion that fL or µL is dominated by the amplitude of the undulation, which the tightly bound counterion feels in motion along the polyion. As we have mentioned so far, the experimental results were well explained by the molecular mechanism that
the LF relaxation was ascribed to the fluctuation of the tightly bound counterions along the polyion and the HF one was due to the fluctuation of the loosely bound counterions perpendicular to the polyion axis. Here, let us briefly discuss the possibility of the opposite model that the LF relaxation results from the counterion fluctuation perpendicular to the polyion axis.3 The experimental results of the R dependence definitely showed that the tightly bound counterions in the vicinity of the polyion contributed to the LF relaxation. The tightly bound counterions, densely localized in the ravine of the Coulombic potential with a depth of approximately 6kBT and a width of the order of the polyion diameter,15 should fluctuate along the polyion within the long range up to the contour length and perpendicular to the polyion within the short range of the ravine width. Assuming that the fluctuation length is of the order of the polyion diameter, 1 nm, we can roughly evaluate the relaxation frequency of the tightly bound counterion fluctuating perpendicular to the polyion as 8 GHz, which is much faster than even the HF relaxation frequency. As a consequence, it is impossible to assign the perpendicular fluctuation of the tightly bound counterion to the LF relaxation.
(14) Nagamine, Y.; Ito, K.; Hayakawa, R. Colloids Surf., A: Physicochem. Eng. Aspects 1999, 148, 149.
(15) Gue´ron, M.; Weisbuch, G. J. Phys. Chem. 1979, 83, 1991; Biopolymers 1980, 19, 353.
Conclusion We investigated the N and Cp dependence of fL and the R dependence of fL and fH for PSS solutions by the FEB method. From the N and Cp dependences of fL, it turned out that fL was strongly dependent on N but almost independent of Cp. This indicated that the LF relaxation was ascribable to the counterion fluctuation along the polyion. Moreover, the mobility of the bound counterion calculated from fL was much smaller than the free one, implying that the tightly bound counterions in the vicinity of the polyion contributed to the LF relaxation. On the other hand, the R dependences of fL and fH revealed that fL increased and fH decreased nonlinearly with increasing R. These results clearly supported the model of the molecular mechanism that the LF relaxation was attributed to the tightly bound counterions fluctuating in the Coulombic undulation along the polyion in its vicinity and that the HF one was due to the loosely bound counterions moving with the free mobility perpendicular to the polyion axis away from the polyion. Acknowledgment. This work was partly supported by a grant from Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan. LA9811564
