J. Phys. Chem. B 2010, 114, 10401–10408
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Interplay of Ion-Specific and Charge-Density Effects in Aqueous Solutions of Weakly Charged Ionenes as Revealed by Electric-Transport Measurements Miha Luksˇicˇ, Barbara Hribar-Lee,* and Vojko Vlachy Faculty of Chemistry and Chemical Technology, UniVersity of Ljubljana, AsˇkercˇeVa 5, SI-1000 Ljubljana, SloVenia ReceiVed: June 9, 2010; ReVised Manuscript ReceiVed: July 13, 2010
In 3,3-ionenes, one quaternary nitrogen is bonded to a chain of three methylene groups on each side, and in 6,9-ionene, it is bonded to a chain of six on one side and nine on the other. We examined how the solution properties of several ionenes changed with increased hydrophobicity of the polyion, depending on the nature of the counterion. We determined the electrical conductivities of aqueous solutions of 3,3-, 4,5-, 6,6-, and 6,9-ionene fluorides and bromides in the range of concentrations from 5 × 10-3 to 1 × 10-1 M and for the temperature interval 5-35 °C. Over these ranges, the conductivities of the ionenes were found to decrease with increasing concentration and increase with increasing temperature. The conductivity of 3,3-ionene bromide was lower than that of its fluoride analogue throughout the whole range of concentrations, whereas for the 6,9-ionenes, the trend was reversed. For 4,5- and 6,6-ionene, we observed a crossover in the concentration dependence of conductivity. The conductivity data were compared with the predictions of Manning’s theory and scaling theory. Separately determined transport-number values were combined with the conductivity data to obtain the fractions of so-called “free” counterions, f. For bromide samples, f increased from 3,3- to 6,9ionene. In the case of fluoride counterions, the fraction of free counterions was the lowest for 3,3-ionene and, within the experimental uncertainty, approximately constant for the other less charged ionenes. Introduction The conductivity of polyelectrolyte solutions is yet another of the properties that separate charged macromolecules from solutions of simple electrolytes.1-3 This important quantity reflects the nature of the interactions between the principal species in solution: in this case, polyions, counterions, and solvent molecules. The combination of conductivity and transportnumber measurements (the latter have to be obtained in a separate experiment) allows for the estimatation of the extent of counterion-polyion association, providing information about the effective charge density of the polyelectrolyte and the extent of hydration of the poly- and counterions.4-15 Ionenes are structurally relatively simple cationic polyelectrolytes with the repeat unit -N+(CH3)2-(CH2)x-N+ (CH3)2(CH2)y-. As the values of x and y are increased (i.e., the chains of CH2 units between charged nitrogens are lengthened), the hydrophobic part of the polyion is enlarged, and its charge density if reduced. In addition to the effects originating from the charge density of the polyion, ionenes also show a diverse behavior depending on the chemical nature of the counterions.16-24 Because synthetic routes enable one to prepare different analogues, x,y-ionenes allow for a systematic investigation of the influence of the charge density of the polyion and the nature of the counterions, as well as their mutual interplay, on the physicochemical properties of such systems. Ionenes can therefore be test substances to help one understand the ionspecific and hydrophobic effects in more complicated (bio)polyelectrolytes dissolved in water. Previous studies of osmotic17,19 and activity20 coefficients of aqueous 3,3-, 4,5-, 6,6-, and 6,9-ionene salt solutions indicated relatively strong binding of counterions to the polyion, stronger * To whom correspondence should be addressed. E-mail: barbara.hribar@ fkkt.uni-lj.si.
even than predicted by the cell-model theory25-27 (cf. Figure 5 of ref 17). The degree of ion binding as reflected in the osmotic and activity coefficient data increases in the order of counterions F- < Cl- < Br- < I- 19,20 and generally with increasing linear charge density of the polyion. The effects of the nature of the counterions in polyelectrolyte solutions are most clearly revealed in measurements of enthalpies of dilution, ∆HD. The experimental data for 3,3- and 4,5-ionene solutions with bromide and chloride counterions are endothermic,16 whereas the corresponding solutions of the (less charged) more hydrophobic 6,6- and 6,9-ionenes produce an exothermic effect. Further, for 3,3-, 4,5-, 6,6-, and 6,9-ionene fluoride solutions we found that heat is released upon dilution.28 The well-established polyelectrolyte theories, such as the cylindrical cell-model based on the Poisson-Boltzmann’s equation25-27,29 or the Manning’s theory,30 have been used to analyze these data. Both approaches predict ∆HD to be negative in all cases, which is in sharp contrast with the experimental data for 3,3- and 4,5-ionene bromides and chlorides.16 To further investigate the differences between solutions with fluoride and bromide counterions, we examined the relaxation times as obtained from dielectric relaxation studies of these solutions.18,19 These results led to the conclusion that fluoride counterions are affected to a lesser extent by the polyion than are bromide counterions.18 All together, the influences of the polyion’s charges and of the hydrophobic parts of the backbone manifest themselves in a complex manner. The osmotic and activity coefficients, most thoroughly studied so far, are thermodynamic properties of solutions in equilibrium. Another perspective on the interactions between polyions and counterions can be provided by analyzing the transport properties. The conductivities of 3,3-, 4,5-, 6,6-, and 6,9- ionenes with various counterions were previously studied by Nagaya and co-workers.21,22 Most of their results apply to polyelectrolytes in mixtures with low-molecular-weight electrolytes. Only a
10.1021/jp105301m 2010 American Chemical Society Published on Web 07/27/2010
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limited number of data on salt-free ionene solutions were reported by them. For example, in Figure 5 of ref 21, the results for pure 4,5-ionenes with various counterions are shown. The study applies to a dilute region of solutions; the highest concentration examined in ref 21 was around 0.004 M. These authors showed that an effective value of the charge density parameter has to be introduced in order to fit experimental data with Manning’s theory. Further, they demonstrated that additivity does not hold for the conductivities of ionene solutions with added simple electrolyte. However, the main focus of their research was not the interplay of charge density and ion-specific effects. Because these effects strengthen with increasing concentration, it seems worthwhile to extend their research to solutions with higher concentrations. The present work focuses on ionene solutions with concentrations between 0.005 and 0.1 M, where ion-specific effects are assumed to be strong. The electrical conductivities and transport numbers of 3,3-, 4,5-, 6,6-, and 6,9-ionene bromides and fluorides in water were measured. We chose these two anions because they widely differ in the way in which they affect surrounding water molecules. Fluoride ion is known to bind its water molecules strongly and is therefore classified as a strong kosmotrope. Bromide ions, on the other hand, are more loosely solvated and consequently belong to the class of ions called chaotropes.31 The main purpose of this work was to investigate how the properties of the individual ions and the increased length of the hydrophobic chain between the polyion’s charges influence the transport properties of 3,3-, 4,5-, 6,6-, and 6,9ionenes in water. Complementing our thermodynamic data, this study should provide a more complete understanding of ionenes and weakly charged polyelectrolytes in general. To the best of our knowledge, the only previous publication regarding the transport numbers of nitrogen-based cationic polyelectrolytes [namely, poly(4-vinyl-N-n-butylpyridinium bromide) and poly(vinylbenzyl trimethylammonium chloride)] is that of Darskus and co-workers.4 This article proceeds as follows: After the Experimental Section explaining the sample preparation and measurements, we present the results for molar conductivity and transport numbers of various ionenes. From the combination of the conductivity data and transport-number measurements, we calculate the fractions of “free” counterions for the various ionene-counterion systems. In a separate section, the experimental conductivities are compared with the predictions of the Manning’s theory and the scaling approach. Relevant findings are summarized in the Conclusions. Experimental Section A detailed description of the synthesis, purification, and sample preparation of ionene bromides and fluorides, together with an estimated average degree of polymerization, is given in ref 18 and will not be repeated here. It is worth mentioning that all samples were subjected to extensive dialysis against distilled water using dialysis tubes with a molecular weight cutoff of 12000 g mol-1. Purification was terminated after 10-15 days when the conductivity of the exchanging water solution remained less than 2 µS/cm. Electrical Conductivity. The electrical conductivities of the ionene solutions were obtained by measuring the resistance of solution in a specially designed arrangement of nine capillary cells with different cell constants,32 calibrated with potassium chloride. The recorded value of the resistance at ν ) 6 kHz {Agilent 4284A, 20 Hz-1 MHz precision LCR meter [inductance (L), capacitance (C), and resistance (R)]} was used to
Luksˇicˇ et al. calculate the specific conductivities of the ionene solutions χ and, from it, the molar conductivities Λ ) χ/c, where c denotes the stoichiometric concentration of the counterions. A highprecision thermostat (Lauda UB 40J, WK 1400) with a reproducibility of better than (0.003 °C was used to maintain a constant temperature chosen from the interval between 5 and 35 °C. The specific conductivity of pure water at 25 °C was measured to be 1
(4) ξ 1 4πNAξbc ξ < 1
(7)
and fM is given by the relations53
{
0.866 ξ>1 ξ fM ) 0.55ξ2 ξ < 1 1π+ξ
(8)
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Luksˇicˇ et al.
TABLE 2: Values of Parameters Needed to Fit Experimental Conductivities Using Manning’s Theory and Scaling Theory for Solutions of Ionene Bromides at 25 °C Manning’s theory a
scaling theory
b
fMeff c
Ad
fAeff e
0.39 0.51 0.60 0.73
2.71 1.99 1.62 1.33
0.37 0.50 0.62 0.75
ionene
ξ
ξeff
3,34,56,66,9-
1.44 1.05 0.82 0.67
2.24 1.70 1.45 1.19
a Structural value of ξ. b Effective value of ξ needed to bring Manning’s theory in agreement with experimental conductivities. c Effective value of fM estimated from eq 8 using ξeff. d Effective value of parameter A needed to fit experimental conductivities with eq 9. e Effective value of fA calculated from A using eq 12.
Other physical quantities have their usual meanings: e0 is the charge of an electron; ε0 is the permittivity of a vacuum; ε and η are the dielectric constant and viscosity of pure solvent, respectively; k is the Boltzmann constant constant; R is the gas constant; and NA is Avogadro’s constant. We denote the Bjerrum constant as λB (cf. eq 5) and concentration with c. In the above equations, we omitted the valency dependence, because, for the solutions studied here, the valence of the polyion unit is zp ) 1 and that of the counterions zc ) -1. The overall conductivity of the solution, Λ, is calculated according to eq 2 using the effective values of ξ in expressions 4 and 8 (see Table 2). Scaling Theory. In dilute solutions, a polyelectrolyte chain can be pictured as a necklace made of electrostatic blobs of dimension D, where the conformation (statistics) of the chain inside the blob is determined by the thermodynamic interaction between uncharged polymer and the solvent. The conformation of the macromolecule inside the blob is assumed to depend mostly on the quality of the solvent for the neutral polymer. On larger scales, the chain is stretched up to the correlation length ζ. The length of a repeat unit of the chain is b, as in Manning’s theory. The effects of possible counterion condensation are incorporated in the parameter A, which gives the number of monomers between the two effective charges of the backbone. The dependence of the molar conductivity of a polyelectrolyte solution on the concentration, c, is given by52
Λ≈
[
]
2 2 1 NAcζ e0 ln(ζ/D) + Λ∞c A 3πηA
(9)
where
ζ≈
1
√NAcb
×
{
×
{
(A2b/λBj)1/3 poor solvent (A2b/λBj)1/7 good solvent
(10)
and
ζ ≈ D
1
√NAcb3
1 poor solvent 2 -2/7 (A b/λBj) good solvent
(11)
From a comparison of eqs 2 and 9, it follows that the parameter A can be related to the fraction of free counterions f determined by the association theory as
A≈
1 f
(12)
In the following subsection, the fraction of free counterions f is compared with the corresponding quantities obtained from fitting the experimental data by Manning’s and scaling theories. Discussion of the Theoretical Predictions. For solutions of ionene bromides, both theories correctly describe the concentration and charge density dependence of the conductivity (see Figure 4). This is somewhat surprising, considering that Manning’s theory is used here beyond the range of its validity. The theory can be brought into exact agreement with the experimental data for an effective value of ξeff > ξ.20,21,23 The same holds true for parameter A of scaling theory: it has been shown for sodium polystyrene sulfonate that A deviates slightly from the values approximated from the osmotic coefficients52 or, in our case, from the value obtained using eq 12 with f taken from Table 1. Figure 4 shows the predictions of Manning’s theory (panel a) and scaling theory (panel b, good solvent condition) for 3,3-, 4,5-, 6,6-, and 6,9-ionene bromides (lines), together with the experimental data (symbols). The parameters yielding the best agreement between theory and experiment are given in Table 2. One can see that the structural charge density parameter is lower than the effective value, ξ < ξeff. The Manning’s fraction of free bromide counterions (fM, eq 8), calculated on the basis of ξeff is lower than that obtained from association theory (see Table 1). On the other hand, when eq 8 is used to compute fM with the structural values of ξ, Manning’s theory predicts 20-35% higher values of fM compared to those extracted from the experimental data (see Tables 1 and 2). To bring scaling theory in close agreement with the experimental data, parameter A has to be set to higher values then determined from the experimental values of f (eq 12, Table 1). This means that the effective value, fAeff, calculated from eq 12 using an adjusted fitting parameter A, given in Table 2, is smaller than the experimental value (see Tables 1 and 2). For both theories, the deviations in the effective values of f from the experimentally determined values (given in Table 1) are largest in the case of 3,3-ionene bromide and smallest for the 6,9analogue. Because experimental data can be fitted with only one value of the fraction of free counterions throughout the whole range of concentrations, this could be an indication that f is a constant value over this concentration range. This is in agreement with the findings of Darksus et al.,4 who demonstrated that f remains practically constant over a large concentration interval, as well as with our preliminary results for ionene bromides.45 Figure 5 shows the best fit of Manning’s theory to the conductivities of 3,3-, 4,5-, and 6,9-ionene fluorides. Again, the lines represent the theoretical predictions, and the experimental results are shown by symbols. It can be seen that the theory cannot be properly fitted to the experimental data. The same holds true for scaling theory, and the results are therefore not shown here. The concentration dependence is different from that determined experimentally: the experimental Λ value decays much more slowly than predicted theoretically. This is not an isolated result. Several previous measurements of moderately concentrated electrolyte solutions indicated that the molar conductivity approaches a minimum and even increases at higher polyelectrolyte concentrations.5,7,9,15,36 A possible explanation for the disagreement between the theoretical and experimental results could be that the theoretical expression for the conductivity of a polyion is not suitable for more concentrated solutions. Yet another possibility is that f does not remain constant in the whole range of concentrations. The finding that the theories show success in the case of bromide samples and fail in the
Ion Specificity and Charge Density in Ionene Solutions
J. Phys. Chem. B, Vol. 114, No. 32, 2010 10407
Figure 4. Fits of (a) Manning’s theory and (b) scaling theory to molar conductivity as a function of the square root of the concentration of ionene bromides at 25 °C: (b) 3,3-, (O) 4,5-, (9) 6,6-, and (0) 6,9-. Continuous lines are predictions of the theory. For parameters, see Table 2.
Figure 5. Fits of Manning’s theory to molar conductivity as a function of the square root of the concentration of ionene fluorides at 25 °C: (b) 3,3-, (O) 4,5-, and (0) 6,9-ionene. Continuous lines are predictions of the theory.
the polyions. From the conductivity and transport-number measurements, we calculated the fraction of free counterions, f, at c ) 0.02 M. For bromide samples, f increased from the more highly charged 3,3-ionene to the less charged 6,9-ionene, whereas for the ionene fluorides, f was smallest for 3,3-ionene and approximately constant for the other analogues. Differences similar to those seen in this study in the charge density trends of the fraction of free counterions were recently observed by Essafi and co-workers by measuring osmotic coefficients in solutions of two anionic polyelectrolytes with the same counterion (cf. Figure 4 of ref 54). In summary, the differences in the solution properties of bromide and fluoride ionenes, as observed in this study, are strong and are qualitatively dependent on the ionene charge density.
case of ionene fluorides is somewhat surprising, because implicit solvent theories have often been seen work better for polyelectrolytes with strongly hydrated counterions.9,16,17,28 We can also speculate that differences arise from different solvation behaviors of bromide and fluoride counterions, as a function of concentration, but the actual mechanism is not known.
Acknowledgment. The authors thank the Slovenian Research Agency (ARRS) for financial support through research programme P1-0201. The authors acknowledge the help of Prof. M. Besˇter-Rogacˇ, Dr. M. Boncˇina, and Mr. A. Kelbl. V.V. is Adjunct Professor in the Department of Pharmaceutical Chemistry, University of California at San Francisco.
Conclusions
Supporting Information Available: Concentration and temperature dependences of the molar conductivities of 3,3-, 4,5-, 6,6-, and 6,9-ionene bromides and fluorides (Tables S1 and S2, respectively); temperature dependence of Λ for given x,y-ionene bromide and fluoride (Figures S3 and S4, respectively); and Walden’s rule for given x,y-ionene bromide and fluoride (Figures S5 and S6, respectively). This material is available free of charge via the Internet at http://pubs.acs.org.
The results communicated in this article indicate significant differences in the behaviors of fluoride and bromide ionenes in water. Whereas the ion-specific effects in aqueous polyelectrolyte solutions have been known for a long time and, therefore, are of no surprise, it was of great interest to learn how an increasing nonpolar part of the polyion modifies the ion specificity. For this purpose, the conductivities and transport numbers of aqueous solutions of 3,3-, 4,5-, 6,6-, and 6,9-ionene bromides and fluorides were determined. The conductivity was measured in the concentration range from 5 × 10-3 to 1 × 10-1 M and for the temperature interval 5-35 °C. Using effective parameters, Manning’s and scaling theories can be brought into good agreement with the experimental data for ionene bromides, but not for fluorides. The molar conductivity of fluoride ionenes first decreased but seemed to level off at higher polyelectrolyte concentrations. This made the agreement with theory, which was used beyond the range of its proposed validity, poor. The experimental data indicated that decreasing the charge density (or increasing the hydrophobicity) of the ionene chain can substantially modify the behavior of fluoride and bromide ions in interaction with ionene. This was reflected in conductivities in the following way: The conductivity of 3,3-ionene bromide was lower than the conductivity of the fluoride analogue throughout the whole range of concentrations, whereas for the 6,9-ionenes, the trend was reversed. Transport-number measurements indicated that the counterions in these solutions, with the exception of 6,9-ionene bromide, transported less current than
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