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## Boletín de la Sociedad Chilena de Química

##
*versão impressa* ISSN 0366-1644

### Bol. Soc. Chil. Quím. v.45 n.4 Concepción dez. 2000

#### http://dx.doi.org/10.4067/S0366-16442000000400006

**DETERMINATION OF THE COUNTERION-POLYION PARAMETER **

FOR MALEIC ACID-OLEFIN COPOLYMERS. EFFECT**OF THE **

ALKYL SIDE CHAIN LENGTH.

FOR MALEIC ACID-OLEFIN COPOLYMERS. EFFECT

ALKYL SIDE CHAIN LENGTH.

*RAUL G. BARRAZA* AND ROCIO MARTINEZ***

*Departamento de Química, Facultad de Ciencias Universidad de Chile

Las palmeras 3425, Casilla 653, Santiago, Chile.

** Escuela de Química. Facultad de Ciencias Naturales, Matemáticas y del Medio

Ambiente. Universidad Tecnológica Metropolitana

Av. J.P. Alessandri 242. Santiago. Chile

(Received: January 27, 2000 - Accepted: July 31, 2000)

**ABSTRACT**

The interaction between a polyion and its counterion has been studied for a series of potassium salts of poly(maleic acid-co-vinyl-n-alkyl), PA-nK2, with n=8,10,12, 14 and 16 carbon atoms in the side chain. The polyion-counterion interaction parameter was determined from electrical conductivity measurement. This parameter is a function of the side chain length, and its variation is ascribed to a change in the average distance between charges.

**Key Words**:** **amphipatic polyelectrolytes, electrical conductivity, interaction parameter, polyelectrolyte hydrophobic microdomains, Mannings theory

**RESUMEN**

Se estudia la interacción entre el poliion y sus contraiones para una serie de sales de potasio derivadas de poli( ácido maleico-co-vinil-n-alquilo), PA-nK2, con n= 8,10,12,14 y 16 átomos de carbono en la cadena lateral. Se determina el parámetro de interacción poliion-contraión, a partir de mediciones de conductividad eléctrica. Se encuentra que este parámetro es función de la longitud de la cadena lateral, atribuyendo esta variación a un cambio en la distancia promedio entre cargas.

** INTRODUCTION **

The physicochemical properties of polyelectrolytes, in aqueous solutions, such as electrical conductivity, interfacial activity, and formation of microdomains are mainly determined by the linear charge density. According to Mannings counterion condensation theory^{1-3}) this parameter is given by the following relationship:

x = e^{2}/bDkT | (1) |

where e is the proton charge, b is the average distance between charges, D is the dielectric constant of the pure bulk solvent, k is the Boltzmanns constant and T is the absolute temperature. The theory stated that when x > |Z_{c}|, where Z_{c} is the counterion charge, enough counterions condense onto the polyion to yield the critical value x = |Z_{c}|. If x < |Z_{c}|, then dissociation occurs to give x = |Z_{c}|. x is theoretically related to the counterion-polyion interaction, f , by means the following equation: .

f = 0,866(x |Z_{c}|)^{-1} | (2) |

This relationship was obtained by considering that the polyelectrolyte adopts a fully extended configuration at infinite dilution. Under these conditions, the distance among charges, b, is only determined by geometrical factors.

On the other hand, f is related to the electrical equivalent conductivity, L, through the Kohlrauschs law of the independent migration of ions, which take the form:

L= f (l_{i}^{o} + l _{p} ) | (3) |

where, l_{i}^{o} and l _{p} are the equivalent conductivity of the counterion and polyion, respectively.

Thus, f could be determined experimentally by conductimetric measurements, but the knowledge of lp is difficult to obtain by anyone of the available electrochemical methods due to the low mobility of the macroion. However, a relative interaction parameter, f*, defined as:

f*= L_{ exp}/ L_{theo} | (4) |

can be obtained from conductimetric measurements by using a method described previously 4). Basically, the parameters of eq. 4 are given by L_{ exp}= f_{exp} (l_{i}^{o} + l _{p}_{exp}) and L_{theo}= f_{theo}( l_{i}^{o} +l _{ptheo}), and it has been assumed that l _{p}_{exp} is equal to l _{theo} and given by the following equation:

l _{p}_{exp} =l _{ptheo} = 279A |Z_{c}|^{-1}|lnk a|/ [ 1 + 43.2A(|Z_{c}l_{i}^{o} |)^{-1}|lnka|] | (5) |

where the constant A stands for DkT/(3phe), k is the screening Debye-Hückel length, h is the absolute viscosity of the medium, and a is the radius of the polyion. As a result, equation 4 also represents the ratio:

f*=f _{exp}/ f_{theo} | (6) |

Therefore, f* represents the counterion-polyion parameter interaction relative to the one the polyeletrolyte would have in the fully extended configuration, and at the same polymer concentration. This parameter has been extensively used to characterize the nature and extent of counterion binding to poylelectrolyte^{4-5}). In addition, in a study of chloride and bromide association to poly(N,N-dimethyl -N-(2-hydroxy-propyl)ammonium) in methanol/water solution the f* values obtained were interpreted not only in terms of the dissociation degree, a, but also as changes of the average distance among charges^{6-7}). This latter effect was ascribed to a preferential adsorption of methanol onto the polyion. Intrinsic viscosimetry and preferential adsorption measurements corroborated the selective solvatation of the polyelectrolyte. Hence, the f* parameter is a measure of two quantities: the relative extent of polyelectrolyte dissociation, and the deviation from the fully extended configuration.

The main aim of the present work is to analyze the effect of the alkyl side chain length on the interaction parameter for intramolecular micelle-forming polyelectrolytes. The studied systems are a series of potassium salts of poly(maleic acid-co-vinyl-n-alkyl), PA-nK2, with n=8,10,12, 14 and 16 carbon atoms in the side chain.

**EXPERIMENTAL**

The polyelectrolytes were synthesized by radical polymerization using benzoyl peroxide as initiator in benzene solution under atmosphere of nitrogen at 60 ºC. The average molecular weigth, Mw, were estimated by gel permeation chromatography in a Brucker HPLC 21 B using a IBM column. The Mw values are in the range of 8,000 to 12,000.

The water soluble polymer salts were obtained as described before^{10}). The specific conductivity measurements were performed at 25 ºC under nitrogen by using a CDM 83 Radiometer Research Conductimeter. A bright platinum electrode conductivity cell with a constant of 1.295 cm^{-1} was used. These measurements were highly reproducible and were performed at least three times.

**RESULTS AND DISCUSSION**

The Kohlrausch type plots, L_{exp} versus c^{1/2}, obtained for the studied polyelectrolytes are shown in Fig 1. These plots show a clearly dependence on the side chain length, and are smoothly curved downward. This behavior corresponds to an intermediate electrolyte, and it allows determining the respective experimental limiting equivalent conductivity, Lº_{exp}, from these plots. This is accomplished by fitting the data to a three-order polynomial equation, and calculating the value at concentration zero. The obtained results are given in Table 1 where it can be seen that the Lº_{exp} values follow the order PA-16K2 > PA-14K2 > PA-12K2 > PA-10K2 > PA-8K2.

The theoretical determination of the limiting equivalent conductivities, requires the knowledge of the average distance between charges in the fully extended configuration. This parameter was calculated by considering an alternating copolymer 1:1 with each monomeric unit having two carboxylate groups and the following structural parameters: C-C-C bond angle of 109.5º, C-C bond length of 1.54 A^{o}, average distance between the carboxylate groups, of the same repetitive unit, equal to 4.91 A^{o}, and average distance between carboxylate groups. belonging to consecutive maleic groups, equal to 7.45 A^{o}. Therefore, two charge density parameters were obtained from equation 1, which were averaged to yield a final value 1.155. Consequently, equation 2 gives a single value of f^{o}_{theo} = 0.75 for all PA-nK2 polymers in the fully extended configuration. As predicted by eqn. 4, l_{ptheo} will depend slightly on the radius of the polyion, and consequently the obtained L^{o}_{theo} will have a similar dependence on n. This assumption is confirmed by the results shown in table 1, where L^{o}_{theo} follows the order PA-16K2 < PA-14K2 < PA-12K2 < PA-10K2 < PA-8K2. If we assumed that the dissociation degree of the polyelectrolyte does not change with the side chain length, then the different behavior of L^{o}_{exp} and L^{o}_{theo} can be ascribed to an increasing mobility of counterions with a coiled configuration of polyions.

The data of table 1 show that the limiting values of f* increase with increasing n, approaching the unity (value that corresponds to the fully extended configuration). Figure 2 shows a plot of f^{o}_{exp} against n, and for comparison the value predicted by Manning´s theory is shown as a straight line. The values of f^{o}_{exp} , calculated from f* trough eqn. 6, are clearly dependent of the number of methylene groups in the side chain, they approach monotonically to the theoretical parameter at high values of n. Since, a has been considered independent of n, the lateral chain growing would exclusively affect the hydrodynamic volume of the polyions, i.e. higher values of n would give larger coils. Consequently, the observed behavior of f^{o}_{exp} could be explained in terms of the increase of the average distance between charges with increasing hydrodynamic volume of the polyelectrolyte.

In order to confirm that the ionization degree of the polyelectrolite play no important role in the f_{exp} behavior of the studied polymers, the electrical conductivities for the PA-16K2 were measured at different temperatures. Figure 3 shows Kolrausch´s plots obtained for the polyelectrolyte PA-16K2 at 0, 8, 25 and 40 ºC. As can be seen, the experimental equivalent conductivity of this polymer exhibit a strong dependence on T, but keeping a typical intermediate electrolyte behavior. The extrapolated values of L^{o}_{exp}, and the respective values of L^{o}_{theo}, f* and f^{o}_{exp} are given in table 2. A plot of f^{o}_{exp} and f^{o}_{theo} is shown in Figure 4. Interestingly, these parameters exhibit different behavior with changing temperature, i.e. f^{o}_{exp} increases and f^{o}_{theo} decreases with increasing temperature. The Manning´s theory predicts that f^{o}_{theo} is directly proportional to DT. However, in the range 0 to 40 ºC both parameters have opposite behavior, i.e. with the increasing temperature the dielectric constant of the water decays from 87.9 to 73.2. Thus, the behavior of f^{o}_{theo} is mainly determined by the change of the dielectric constant, while the variation of f^{o}_{exp} is due to the increase of temperature. Consequently, this latter effect can be attribute to an expansion of the hydrodynamic volume with temperature, which produces an increase of the charge distance.

On the other hand, fluorescence probing studies of PA-16K2^{8}), and copolymers of maleic acid and alkylvinylethers with alkyl chains longer than octyl^{9}), have shown that hydrophobic aggregates are formed in the whole range of pH. The same conclusion was reached in a surface activity study ^{10}) of the PA-nK2 polymers where the lowering of the surface tension was found to be inversely dependent on the length of the side chain. This behavior is exactly the opposite of that observed for monoesters derived from copolymers of maleic acid and styrene^{11}), and it was interpreted in terms of the formation of hydrophobic microdomains in the bulk solution. Thus, we can conclude that the behavior of polyion-counterion interaction parameter is mainly dependent on the distance between charges, and that the increase of this parameter can be associated to an increase of the intramolecular micelle size with the number of carbon atoms in the side hydrophobic chain. Also, the effect of the temperature described above can be ascribed to an expansion of the intramolecular micelle due to a thermal weakening of the hydrophobic interaction between the alkyl chains.

**In partial fulfillment of the requirement to obtain the Title of Ingeniero en Ejecución en Química.

**ACKNOWLEDGMENTS**

The authors thank Dr. F. Martínez of the Departamento de Química. Facultad de Ciencias Físicas y Matemáticas. Universidad de Chile for providing the characterized polymers used in this work.

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