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Journal of the Chilean Chemical Society

versión On-line ISSN 0717-9707

J. Chil. Chem. Soc. v.48 n.1 Concepción mar. 2003 



1- Departamento de Química, Facultad de Ciencias, Universidad de Chile,
Las Palmeras 3425, Casilla 653, Santiago, Chile
2- Departamento de Química, Facultad de Ciencias Físicas y Matemáticas,
Universidad de Chile, Santiago, Chile
(Received: July 12, 2002 - Accepted: December 2, 2002)


Measurements of the electrical equivalent conductivity of potassium salts of poly(maleic acid-co-1-olefins), PA-nK2 with n = 12, 18 has been carried out in methanol-water mixtures in the whole range of composition. The relative interaction parameter f*, was determined as a function of the mole fraction of methanol. The values of f* do not follow the same tendency of the limiting equivalent conductivity. This unusual behavior was rationalized in terms of a methanol-induced conformational transition that takes the polymer chain from a compact to an expanded structure. As a consequence of this transition the average charge distance in the polyion increases with increasing mole fraction of methanol. This brings about a decrease of the linear charge density parameter, and therefore an increase of the fraction of polymer charges dissociated from their counterions. The existence of the conformational transition of the PA-nK2 copolymers was confirmed through fluorescence probing experiments.

Key Words: Polyelectrolytes, electrical conductivity, counterion condensation, conformational transition


The electrical conductivity of solutions containing polyelectrolytes results from the contributions made by the small ions and the polyion. Assuming that the mobility of the counterions are the same that in solutions of simple electrolytes, it has been proposed that the equivalent conductivity is given by a corrected expression of the Kohlrausch law of the independent ion migration.


where l 0P and l 0C denote the equivalent conductivity of the polymer and the counterion, respectively; and f denotes the fraction of polymer charges dissociated from their counterions. Thus, measurements of electrical conductivity has proved to be a powerful tool to asses the degree and mechanism of counterions association to polyelectrolytes in aqueous solution.

According to the Manning’s counterion condensation theory1-4) the charge fraction f of a polyion is defined as the polymer charge uncompensated by bound counterions, and is given by


where ZC is the counterion charge, and x denotes the linear charge density of the polyion which is defined as


where e is the proton charge, e represents the dielectric constant of the medium, k is the Boltzmann constant, T the temperature and b is the average axial charge-to-charge distance along the fully extended conformation of the polymer chain. According to the Manning theory, the counterions are completely dissociated from the infinite line charge polyelectrolyte when x < |ZC |-1. When x > |ZC |-1 counterion condensation takes place until the effective x value is equal to |ZC |-1 and the remaining dissociated counterions interact with the infinite line charge via Debye-Hückel forces.

On the other hand, the parameter f can be experimentally determined according to the method proposed by Eisenberg5), but this is only applicable if there is two different counterions interacting with the polyelectrolyte in a similar way. Obviously, it is very hard to fulfill this condition, and an alternative method has been suggested6). This method assumes that the equivalent conductivity of the polymer is given by the Manning theory as


where k is the Debye-Hückel length, a the radius of the polyion, and A = ekT/(3phe), with h denoting the absolute viscosity of the solvent. Introducing this expression in equation 1 we obtain


where ^exp and ^theo are the experimental and theoretical equivalent conductivities, respectively. Thus, the parameter f* is a measure of the charge fraction of the polyion referred to the one it would have in the fully extended conformation at the same polymer concentration. Evaluation of the relative interaction parameter has been used to study the counterion association to poly(N,N-dimethyl-N-(2-hydroxypropyl)-ammonium)6), and poly(1,1-dimethyl-3,5-dimethylene piperidinium)7) in the whole range of methanol/water composition. Changes of f* observed for the former polymer, at low content of methanol, have been ascribed to variations in the average charge distance b in the polyion. This effect has been applied to the study of conformational transition of hydrophobically modified polyelectrolytes. For poly(maleic acid-co-1-olefins) PA-nK2, with n ranging from 10-18, it was found that the relative interaction parameter increases with increasing length of the alkyl side chain8). On the other hand, fluorescence probing studies have demonstrated that PA-nK2 with n ³ 8 form micelle-like aggregates9). Therefore, the behavior of f* for these systems was attributed to the formation of larger aggregates by the polymers carrying the longer side alkyl chains.

In the present study the conductivity behavior of PA-nK2 with n = 12 and 18 has been

determined in methanol/water mixtures. The structure of the repetitive unit of these copolymers is

Thus, the equivalent conductivity of PA-nK2 solutions were measured at different mole fractions of methanol, and the values of f* were obtained as well. The results are rationalized in terms of the changes of polarity and size of the polymer aggregates, produced by solubilization of methanol into the hydrophobic microdomain.


Materials. Poly(maleic anhydride-co-1-olefin) with 1-dodecene and 1-octadecene as olefins (PA-n with n = 12, 18), were obtained by polymerizing maleic anhydride (1 mol) and 1-olefins (1.5 mol) in 1,2-dichloroethane at 70 1C during 6 h, and using benzoylperoxide as initiator. Further details will be given elsewhere10). The average molecular weights were determined by gel permeation chromatography, GPC, using poly(styrene) samples as standard, and ranges between 8,000 and 10,000.

The potassium salts of these copolymers, PA-nK2, were prepared by adding the polymers to an aqueous solution of KOH, while stirring, heated above 85 ºC. After all solids dissolved the salts were precipitated over an excess of methanol, washed with methanol, and redissolved in water. The remaining KOH was eliminated by ultrafiltration in a 50-ml Amicon cell with a PM-5 membrane which retains all molecules with a molecular weight above 5,000. After filtering 20 ml an equal volume of water is added to the cell to keep constant the filtrand volume. This procedure is repeated until a constant conductivity measurement is reached. Finally the solution was vacuum-dried at 40 °C. The degree of hydrolysis was complete, and it was determined by FTIR, measuring the disappearance of the absorption at 1779 cm -1 which correspond to the maleic anhydride residue.

Conductivity Measurements. The specific conductivity measurements were performed under nitrogen at 25 ºC using a Radiometer Research CDM-83 conductivity meter with a platinum cell. The constant cell was 1.295 cm-1.

Fluorescence probing. The concentrations used were 1g/L and 2 mM for the copolymers and pyrene, respectively. All samples were prepared with deionized water. Fluorescence emission spectra were obtained on a ISS PC1 Photon Counting spectrophotofluorometer. The ratio III/I corresponds to the ratio of intensities of peak three (l= 384 nm) to peak one (l = 373 nm). This ratio report on the polarity of the pyrene microenvironment11,12). The fluorescence decay of the singlet excited pyrene was monitored at 400 nm, following excitation with pulses from a LSI nitrogen laser, model VSL-337ND-S (< 4 ns fwhm, 300-mJ 337.1 nm).


Plots of the equivalent conductivity against the square root of polymer concentration obtained for both polymers, and at each mole fraction of methanol, are smoothly curved downward, and their shape is quite similar to those obtained for the same copolymers in aqueous solution8). This behavior is typical of an intermediate electrolyte. Therefore, the limiting values of the conductivity at infinite dilution ^0exp were obtained by adjusting a third order polynomial function to the variation of the equivalent conductivity with the polymer concentration. The values of ^0exp for both copolymers and for each composition of the methanol/water mixture are collected in Table 1, and plotted in Figure 1. As it can be seen in Figure 1 the values of ^0exp are strongly dependent on the mole fraction of methanol. In the inset of Figure 1 are depicted the dependencies of the dielectric constant and the absolute viscosity on the methanol content in the solvent mixture. A decrease of e should induce a decrease in the number of free counterion, whereas an increase of h would decrease the mobility of the charged species. Thus, comparing the form of the curves of figure 1 and the inset, it can be seen that the decrease of the limiting equivalent conductivity with increasing XMeOH is consistent with the variation of e and h. However, when the XMeOH reach a value of 0.7 a breaking point is observed. This effect suggest the existence of two different regimes for the dependence of ^0exp with XMeOH, namely, from pure water to XMeOH = 0.7 and from XMeOH = 0.7 to pure methanol. In addition, it can be seen that the values of ^0exp follows the order PA-12K2 > PA-18K2, except at low methanol concentration where this order is inverted.

Fig.1. Limiting equivalent conductivity of ()) PA-12K2, and (') PA-18-K2 as a function of mole fraction of methanol.

The values of ^0theo were calculated according to equation 1. In this case the interaction parameter ft heo was calculated from equations 2 and 3 by using an average charge distance b equal to 1.1558). The equivalent conductivity of the potassium counterion l 0C were obtained from the limiting equivalent conductivity determined for KCl solutions, and by using the literature data for the equivalent conductivity of the chloride ion13). The values of l 0P were calculated through equation 4. This equation predicts a slightly dependence of ^0P, and consequently of ^0theo, on the radius of the polyion. For a fully extended conformation of the macromolecule the radius has been taken as the length of the side chain. This dependence has been observed in a previous work8). The dielectric constant and the absolute viscosity of each mole fraction of methanol were obtained from a previous work13). The data collected in Table 1 show that ^0theo is larger than ^0exp in the whole range of composition. As mentioned above these PA-nK2 copolymers form hydrophobic aggregates, and therefore the difference in ^0exp values can be attributed to deviations from the fully extended form assumed in the Manning theory.

Table I Theoretical and experimental equivalent conductivity ^0, and relative interaction parameter f* of PA-nK2 as a function of methanol mole fraction.









l 0C (K+)
















































































^0 and l 0C in (Ohm equiv)-1 cm2          

The relative interaction parameter of PA-nK2 solutions at different XMeOH were calculated according to equation 5, and the obtained values are given in Table 1. Figure 2 shows a plot of f* against XMeOH for both polymers. The data indicate that f* increases with increasing content of methanol in the solvent mixture, until it reaches an almost constant value at XMeOH = 0.7. A comparison of figures 1 and 2 shows that ^0exp and f* exhibit breaking- and turning points in the same region of XMeOH. This result is expected because the values of ftheo varies only slightly with the solvent composition (see table 1), and therefore the changes of f* simply reflect the variation of f with the methanol content. The behavior of f* does not correspond with the variation of the dielectric constant, because a decrease of e induces an increase of counterion association, i.e., a decrease of the charge fraction of the polyion. This sort of behavior has been found previously for poly(1,1-dimethyl-3,5-dimethylene piperidinium) with chloride, bromide, and nitrate as counterions7). Thus, to rationalize the behavior of f* represented in figure 2, we must assume that the increase of f* is produced by an increase of the average charge distance in the polyelectrolyte. This concept has been applied before to explain the increase of f* observed for chloride and bromide salts of poly(N,N-dimethyl-N-(2-hydroxypropyl)-ammonium)6). In these systems, measurements of viscosity and adsorption of methanol demonstrated that the increase of b was due to an increment of the hydrodynamic volume of the polyion, induced by preferential adsorption of methanol onto the polymer chain14). In the case of PA-nK2, we can invoke at least two different factors responsible of the increase of the average charge distance in the polyion with increasing content of methanol. In fact, the addition of methanol to an aqueous solution of PA-nK2 will produce two immediate effects: the incorporation of methanol to the hydrophobic aggregates, which increase their size; and a reduction of the hydrophobic effect by a decreasing of the solvent polarity. As a consequence of this reduced repulsive interaction, between the side alkyl chains and the solvent, the aggregate will adopt a more "loose" conformation, increasing the value of b. This factor should be less important for PA-18K2 because the attractive interaction between the alkyl chains will compensate in some degree the reduction of the hydrophobic effect. At low content of methanol it is probable that these two factors make different contributions to the change of f*, explaining the initial decrease of f* for PA-18K2 and the inversion of magnitude. However, from XMeOH = 0.2 to 1.0 both curves are quite similar, suggesting that the main factor in the increasing value of f* is the solubilization of methanol into the aggregates. At XMeOH = 0.7 the interaction parameter reach almost the unity, indicating that at this composition both polymer chains are near to the fully extended conformation. In other words, at this mole fraction of methanol the polymer aggregates have collapsed completely and the chains have adopted a more extended conformation. The change of f* in the region of high content of methanol reflects the variation of the dielectric constant of the mixed solvent (see Figure 1). This behavior is similar to that observed for the above mentioned cationic polyelectrolytes6,7).

Fig. 2Relative interaction parameter f* of ()) PA-12K2, and (') PA-18-K2 as a function of mole fraction of methanol.

Fluorescence probing experiments were carried out to corroborate this change of conformation of the polymer aggregates. This method has been used previously to study the pH-induced conformational transition of poly(methacrylic acid)15) and hemiesters of poly(maleic acid-co-styrene)16). The ratio III/I and the fluorescence lifetime t of pyrene were obtained from steady-state and time-resolved measurements of pyrene emission, respectively. Both parameters have been used to report on the polarity of the medium where pyrene is solubilized17). Figure 3 shows a plot of t against XMeOH. The form of this curve is typical of a conformational transition that takes a polymer chain from a compact to an expanded structure. At low content of methanol, XMeOH £ 0.2, the PA-nK2 are forming a micelle-like structure, which provides a hydrophobic environment where pyrene is solubilized, and therefore high values of lifetime are obtained. As discussed above, addition of methanol to the aqueous solution produces two effects: reduces the hydrophobic effect, and increases the volume of the polymer aggregate by distribution of methanol between the aqueous phase and the hydrophobic polymer conformation. The incorporation of methanol to the aggregates makes them more polar and consequently a decrease of the lifetime is observed for XMeOH in the range 0.2-0.8. At this point the lifetime reach a value somewhat lower than that measured in pure methanol, and remains almost constant up to XMeOH = 0.9, suggesting that the aggregate has collapsed and pyrene has been released to the bulk solvent. The final increase of the lifetime observed when the solvent becomes pure methanol can be attributed to the increase of polarity associated to this change (see inset of figure 1). Thus, the changes of lifetime with increasing XMeOH reflect a conformational transition, induced by methanol addition, that takes the polymer chain from a compact to a random coil form. This transition can also be monitored by the ratio III/I which has been used as a measure of the polarity of the environment where pyrene is located11,12). The values of the ratio III/I, (1.05 and 0.75 at low and high content of methanol, respectively), indicate that pyrene senses a hydrophobic medium at low XMeOH, and that at higher values of XMeOH pyrene is released to a methanol rich solvent. These results agree with the behavior shown by the relative interaction parameter, i.e. that at high methanol content the polymer chain is near to the fully extended conformation.

Fig. 3.Lifetime of pyrene in water/methanol solutions of PA-18K2 in the whole range of methanol content.


Electrical conductivity measurements of PA-nK2 methanol/water solutions were performed in the whole range of composition. The variation of the equivalent conductivity and the relative interaction parameter with XMeOH were rationalized in terms of a methanol-induced conformational transition that takes the polymer chain from a compact to an expanded structure. As a consequence of this transition the average charge distance in the polyion increases with increasing mole fraction of methanol. This brings about a decrease of the linear charge density parameter, and therefore an increase of the fraction of polymer charges dissociated from their counterions. The existence of the conformational transition of the PA-nK2 copolymers was confirmed through fluorescence probing experiments.


This work was supported by FONDECYT Grant 1990968, and by DID, Universidad de Chile, Grant ENL-02/05


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