4034
Langmuir 2003, 19, 4034-4036
Notes Clustering Effect on the Viscosity of Nondilute Sodium Polystyrenesulfonate Solutions Qing Pu and Shing Bor Chen* Department of Chemical and Environmental Engineering, National University of Singapore, Singapore 117576, Republic of Singapore Received December 13, 2002. In Final Form: February 13, 2003
Introduction Polyelectrolytes have received considerable attention for the past few decades, but our understanding of their novel behavior still remains limited. One interesting phenomenon is formation of clusters, each made of a number of polyelectrolytes, at sufficiently high polymer concentration and low enough ionic strength. In this note, we report a correlation between viscosity and dynamic light scattering results for flexible polyelectrolyte solutions in an attempt to better understand the clustering effect. Clustering can take place for both flexible1-5 and semirigid polyelectrolytes.6,7 The existence of clusters has been experimentally evidenced by two diffusion modes in dynamic light scattering1-5,6,7 and by visualization of aggregates in conventional light microscopy.2 The slow mode from dynamic light scattering is ascribed to the diffusion of clusters, whereas the fast mode represents the coupled diffusion of counterions and polyion segments. Upon increase of salt concentration, the fast mode becomes slower and its relative amplitude increases, whereas the slow mode becomes increasingly unimportant.2,3 The change in relative amplitudes of the two modes implies that with more added salt, more polyelectrolytes stay out of the clusters, whose population thus reduces. In the presence of multivalent cations, Dubois and Boue4 investigated NaPSS (PSS, polystyrenesulfonate) chain conformation by small-angle neutron scattering and the zero average contrast method. They found that in comparison to the case with added NaCl, addition of CaCl2 or LaCl3 causes the polyelectrolyte to become more compact. This observed behavior was attributed to the bridging phenomenon or stronger condensation effect of multivalent ions. Zhang et al.5 reported similar observations by comparing the results for salt-free HPSS, NaPSS, KPSS, CaPSS, MgPSS, and CuPSS solutions and also found that the interchain correlation length increases with increasing counterion valence. However, the mechanism for the cluster formation is not yet fully understood. * Corresponding author. E-mail:
[email protected]. (1) Sedlak, M.; Amis, E. J. J. Chem. Phys. 1992, 96, 826-834. (2) Tanahatoe, J. J.; Kuil, M. E. J. Phys. Chem. B 1997, 101, 1083910844. (3) Matsuoka, H.; Ogura, Y.; Yamaoka, H. J. Chem. Phys. 1998, 109, 6125-6132. (4) Dubois, E.; Boue, F. Macromolecules 2001, 34, 3684-3697. (5) Zhang, Y.; Douglas, J. F.; Ermi, B. D.; Amis, E. J. J. Chem. Phys. 2001, 114, 3299-3313. (6) Ferrari, M. E.; Bloomfield, V. A. Macromolecules 1992, 25, 52665276. (7) Buhler, E.; Rinaudo, M. Macromolecules 2000, 33, 2098-2106.
In view of extensive research work using light scattering, we intend to apply viscometry as a supplementary means to examine the cluster behavior for nondilute solutions with various added salts. This note aims to find a correlation between viscosity and light scattering results. Experimental Section The polyelectrolyte used is analytic grade poly(sodium 4-styrene) sulfonate (NaPSS) purchased from Aldrich Chemical Inc. (Milwaukee, WI). The average molecular weight is Mw ) 106 g/mol according to the manufacturer’s analysis. Deionized water with conductivity lower than 1.0 µS/cm was used in the preparation of NaPSS solutions. All salts used in the experiments are of analytical grade, including NaCl, CaCl2, and LaCl3. Dynamic light scattering measurements for NaPSS solutions were conducted using a Brookhaven BI-9000AT digital autocorrelator and a BI-200SM goniometer. The wavelength of the laser light is 514.5 nm, and the scattering angle is fixed at θ ) 90°. Prior to the scattering measurement, each solution was filtered by a syringe filter of 0.45 µm to remove dust. The measured time correlation function of the scattered intensity can be expressed by the Siegert relation,8
G(2)(q,τ) ) B{1 + β|g(1)(q,τ)|2}
(1)
where τ is delay time, q ) 4πn sin(θ/2)/λ is the scattering wave vector, n is the solvent refractive index, λ is the wavelength, B is the measured baseline, β is a constant less than unity, and g(1) is the time correlation function of the scattered field given by
g(1)(q,τ) )
∫
∞
0
f(q,Γ) exp(-Γτ) dΓ
(2)
with f being the distribution function of decay rate Γ. Note that q ) 0.0231 nm-1 in the present study. The apparent viscosity of NaPSS solutions was measured using a Haake RS75 rheometer with a DC50 temperature controller (water circulating bath). A concentric-cylinder (DG41) geometry was used to carry out measurements at 25 °C.
Results and Discussion An important parameter for ionic solutions is the Debye screening length defined by
κ-1 )
(
)
r0kBT 2e2I
1/2
(3)
where I ) (Σi cizi2)/2 is the ionic strength, 0 is the permittivity in a vacuum, r is the dielectric constant of the solvent, kBT is the thermal energy, e is the elementary charge, and ci and zi are the concentration and valence of ion species i. Note that the dissociated counterions from polyelectrolytes also contribute to the ionic strength. Assuming total sulfonation and ignoring ion condensation, the ionic strength for our solutions can be written as Iwc ) CP/2 + z(z + 1)CS/2, where CP and CS are the molar concentrations of the monomers and added salt (XClz), respectively. Our analysis of experimental results is based on constant Iwc. We will report results only for 10 g/L NaPSS solutions, although weakening of the slow mode (8) Ray, J.; Manning, G. S. Macromolecules 2000, 33, 2901-2908.
10.1021/la026994j CCC: $25.00 © 2003 American Chemical Society Published on Web 03/19/2003
Notes
Langmuir, Vol. 19, No. 9, 2003 4035
Table 1. Relaxation Times (τf and τs) and Relative Amplitudes (Af and As) of Fast and Slow Modes for 10 g/L NaPSS Solutionsa z(z + 1)CS/2 (M)
salt
Ic (M)
τf (µs)
τs (ms)
As
0.006
NaCl CaCl2 LaCl3 NaCl CaCl2 LaCl3
0.0147 0.0127 0.0117 0.0387 0.0287 0.0237
25.6 25.3 21.6 54.9 49.1 41.7
8.57 5.87 6.39 5.05 3.23 2.53
0.90 ( 0.033 0.79 ( 0.014 0.81 ( 0.080 0.69 ( 0.007 0.53 ( 0.003 0.33 ( 0.002
0.03
a
Note that Af ) 1 - As and Ic ) aCP/2lB + zCS.
at lower polyion concentrations was observed as reported in the literature.1,3,5 We conducted dynamic light scattering for 10 g/L NaPSS (CP ) 0.048 M) solutions at two values of Iwc and observed two decay rates in the time correlation function, similar to what was shown in the literature.1-5,6,7 To quantify the bimodal behavior, we analyze g(1) by double-exponential fitting. For those that cannot be fitted well, CONTIN analysis is applied to obtain f for further calculation. Table 1 presents the relaxation times and relative amplitudes of the two modes. Each of these values is the average from three measurements on the same solution. It can be found that the relative amplitude of the slow mode decreases with increasing ionic strength, indicating that at higher ionic strength, more polyelectrolytes stay out of clusters, whose population hence becomes smaller. In this sense, the relative amplitude appears to be a strength indicator of the interchain association. It can also be seen that the relaxation time of the slow mode is smaller for the solutions with added LaCl3 and CaCl2 than with added NaCl. NaPSS is a strong polyelectrolyte. The distance between two neighboring ionizable sites (a ) 0.252 nm) is smaller than the Bjerrum length lB ) e2/4πr0kBT (∼0.7 nm for aqueous solution at 25 °C). According to Manning’s theory,9 part of the counterions will become immobile (condensed) near chain charge sites, thereby reducing the polyion charge density. We use the simplest model4 to find that the salt concentrations in our experiments are low enough such that all added multivalent cations simply replace some of the condensed Na+, without affecting the effective charge density of the chains ()e/lB). Accordingly, the ionic strength considering the ion condensation can be estimated by Ic ) aCP/2lB + zCS.4 The corresponding estimates are listed in Table 1. In the framework of counterion condensation, Ray and Manning10 formulated a model for charged, rodlike segments in parallel, which predicts an attractive inter-rod interaction when the separation distance becomes of the order of the Debye length. This attraction results from the free energy reduction owing to sharing of the condensed ions between the segments. Their formulation assumes that the segments are much longer than the Debye length, so each can be approximated by an infinitely long cylinder. The model predicts that the segment association is stronger for counterions with lower valence and becomes weaker at higher ionic strength. NaPSS has a persistence length of about 5 nm,11 and the Debye lengths for our solutions are no greater than 2.6 nm. As such, the assumption of their model is not well satisfied for our samples. Nevertheless, this model can give predictions mostly in qualitative agreement with our experimental results. (9) Chu, B. Laser Light Scattering: Basic Principles and Practice, 2nd ed.; Academic Press: New York, 1991. (10) Manning, G. S. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 909922. (11) Spiteri, M. N.; Boue, F.; Lapp, A.; Cotton, J. P. Phys. Rev. Lett. 1996, 77, 5218-5220.
Figure 1. Viscosity of 10 g/L NaPSS as a function of shear rate at constant ionic strength ignoring ion condensation.
Figure 2. Viscosity of 10 g/L NaPSS as a function of shear rate at constant ionic strength ignoring ion condensation.
To examine whether the amplitude of the slow mode can represent the strength of interchain association, we measured the viscosity for each of those NaPSS solutions at 25 °C. Viscometry was indeed used by Cohen and Priel12 to examine the effect of the ion valence on NaPSS solutions at lower concentrations. They found that the viscosity decreases with increasing cation valence at equal salt concentration, without addressing any clustering effects. We plot in Figures 1 and 2 the apparent viscosity η against shear rate for the two values of Iwc. It can be seen that at lower ionic strength, the viscosity order is NaCl > LaCl3 > CaCl2. This viscosity order is exactly the same as the relative amplitude order of the slow mode. For solutions at this value of Iwc, the relative amplitude of the slow mode is more than 0.79, indicating the importance of clusters relative to isolated chains. As a result, the solution viscosity is largely affected by the population and strength of the clusters as reflected by the relative mode amplitude. This argument is further supported by the close values of viscosity at low shear rates for LaCl3 and CaCl2 as the amplitudes of the slow mode are about equal. At low shear rates, the clusters are distorted only slightly from their equilibrium state. At high shear rates, in contrast, the viscosity becomes nearly the same between NaCl and LaCl3. Since a strong flow can distort the clusters substantially, the viscosity behavior cannot be interpreted simply by the strength of the equilibrium microstructure. At the higher ionic strength, the relative amplitude of the (12) Cohen, J.; Priel, Z. Macromolecules 1989, 22, 2356-2358.
4036
Langmuir, Vol. 19, No. 9, 2003
slow mode is reduced considerably. In particular, the amplitude of the fast mode has exceeded that of the slow mode for the case with added LaCl3. The viscosity order for the three salts again conforms to the order for the relative amplitude of the slow mode. In these solutions, the behavior of the chains out of clusters may play an increasingly important role in the solution viscosity. Similar to chains in a dilute solution, the isolated polyelectrolytes affect the solution viscosity mainly through the coupled primary and tertiary electroviscous effects.13,14 The tertiary effect is associated with the polyelectrolyte conformation. In the presence of multivalent cations, the chains are more compact owing to either the stronger ion condensation or the intrachain ion bridging phenomenon.15,16 The primary effect arises from ion cloud distortion, leading to additional energy dissipation that in(13) Jiang, L.; Chen, S. B. J. Non-Newtonian Fluid Mech. 2001, 96, 445-458. (14) Jiang, L.; Yang, D. H.; Chen, S. B. Macromolecules 2001, 34, 3730-3735. (15) Okamoto, S.; Vyprachticky, D.; Furuya, H.; Abe, A.; Okamoto, Y. Macromolecules 1996, 29, 3511-3514. (16) Ikeda, Y.; Beer, M.; Schmidt, M.; Huber, K. Macromolecules 1998, 31, 728-733.
Notes
creases with decreasing mobility and valence of cations. The coupled effects will result in the viscosity order Na+ > Ca2+ > La3+.13 Taking into account the behaviors of both clusters and isolated polyions, the observed viscosity order at the higher ionic strength can be justified. Conclusion In summary, we have found a promising correlation between the viscosity and the relative amplitude of the slow mode in nondilute NaPSS solutions. The finding shows that viscosity is a good supplementary measure of the clustering strength, in particular when the slow mode becomes important at low ionic strength. Although the mode amplitude is based on scattering density, not exactly representing the mass fraction of chains in clusters, the good qualitative agreement between the amplitude and viscosity does lend support to our exposition. Acknowledgment. The authors are grateful to the National University of Singapore for supporting the work through Grant R-279-000-100-112. LA026994J
