Soft Matter

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1 PAPER Soft Matter Dielectric relaxations in chitosan solution with varying concentration and temperature: analysis coupled with a scaling approach and thermodynamical functions Chun-Yan Liu and Kong-Shuang Zhao* Received 3rd November 2009, Accepted 8th March 2010 First published as an Advance Article on the web 5th May 2010 DOI: /b922807a The dielectric properties of chitosan in an aqueous solution with no added salts have been measured as a function of concentration and temperature in the frequency range from 40 Hz to 110 MHz, respectively. After reducing the contribution of the electrode polarization effects, the dielectric spectra of chitosan semidilute solutions show two relaxations at 100 khz and MHz, respectively. The observed two dielectric relaxations have been strictly analyzed using the Cole-Cole function and the possible relaxation mechanisms were attributed to the fluctuation of condensed counterions and free counterions, respectively. The dependence of the dielectric increment and relaxation time on concentration was interpreted in light of the scaling properties of polyelectrolyte solutions. It was found that the dependence of relaxation time on the C p follows the expected exponents of the scaling laws, both in the low-frequency and high-frequency cases. The good agreement between experimental results and theoretical analysis suggests that the low- and high-frequency relaxation mechanisms are the fluctuation of condensed counterions and free counterions, respectively. In addition to this, this analysis gives further support to the scaling approach of the dynamic behavior of polyelectrolytes. The temperature dependence of the dielectric spectrum of chitosan solutions showed that the low- and highfrequency dielectric increment generally decreases with the rise of temperature, which is considered to be due to the acceleration of the reorientation motion of the counterions. Moreover, the thermodynamic parameters, such as activation free energy E a, activation enthalpy change DH and activation entropy change DS of low- and high-frequency were calculated from the relaxation time, and discussed from the microscopic thermodynamical view. 1. Introduction Chitosan, as a polycationic polymer as well as a typical biomacromolecule, has been attracting tremendous attention because of its distinctive physicochemical characteristics and related potential applications. Fundamental studies on chitosan solutions are being extensively explored to discover its potential worth. Amongst the research, physicochemical issues in chitosan solutions, such as microscopic dynamics, the interaction between chitosan molecules and the solvent, and the conformation of chitosan chains, have become some of the main focuses of this basic research. 1 4 It is known that when the ph is below the pk a (between 6.2 and 6.8), the amines of chitosan become approximately 90% protonated, resulting in a positively charged polyelectrolyte. In addition, as a typical biological macromolecule, chitosan itself has unique value in many application fields. 4,5 For example, the preparation of aqueous solutions is compulsory before obtaining any kind of material from chitosan, such as films, gels, sponges, fibers, particles, etc. and the adsorption properties and biological activity of chitosan are only reflected in aqueous solution. Thus, the study of the solution properties of chitosan is of major interest in order to gain a better understanding of its physicochemical and biological properties. Therefore, researchers College of Chemistry, Beijing Normal University, Beijing, , China attention has been focused on the behavior of chitosan in solution, especially the influencing factors of the chitosan solution properties. Specifically, the main influence factors are the chitosan molecular weight, deacetylation degree (DD), ionic strength, chitosan concentration, temperature and ph. These factors directly influence the viscosity, rheological properties, the conformation and inherent flexibility of chitosan chains, and so on. Their roles have already been extensively studied using several techniques, such as size exclusion chromatography, laser scattering, and viscosimetry, etc. 5,6 11 The dielectric relaxation spectroscopy (DRS) method is still one of the most important techniques for studying the structure and dynamics of polyelectrolyte solutions, because it can investigate the relaxation processes occurring in polyelectrolyte solutions. In this respect, DRS represents a powerful tool providing information such as the static conformation of the macromolecule, 12,13 the motion of the side groups and the chain, 14 and the interactions between the polyions and the counterions. 12 In addition, the DRS method has many desirable features, such as fast measurement, simple equipment and low requirements. Therefore, the DRS method attracted much attention early in the study of polyelectrolytes. For example, the dielectric properties of chitosan and its derivatives have been previously investigated by Bordi and co-workers. 14, 15 In recent years, the study of polyelectrolyte solutions has been greatly developed. Considerable theoretical work has been devoted to 2742 Soft Matter, 2010, 6, This journal is ª The Royal Society of Chemistry 2010

2 polyelectrolyte solutions, starting from the scaling theory of de Gennes 16 which has been extended by Dobrynin, 13 Manning s counterions condensed model 17 and Ito s model. 18 In order to understand the relaxation mechanism, lots of experiments have been carried out by Bordi et al., in which the solvent quality factor and concentration region were taken into account. 12,19 24 In addition, other research on the relaxation behavior of polyelectrolyte solutions has also been reported, such as electric double layer theory. 25,26 Despite all that, the above studies show almost the same limitations which have hampered the application of DRS to aqueous polyelectrolyte solutions. Firstly, it is difficult to discuss expressly the mechanism and the contribution of sub-relaxation to the dielectric spectra, because more than one sub-relaxation process presented in polyelectrolyte solutions are often overlapping. Secondly, polyelectrolyte solutions usually show a very high ionic electrical conductivity which causes a giant frequency-dependent strong electrode polarization, masking the relaxation behavior associated with the polymer component at low-frequency range. 12 Therefore, to obtain the real dielectric data at low-frequency and separate the subrelaxation from raw dielectric spectra, rather sophisticated analysis techniques are indispensable. On the other hand, nearly all the research is focused on the temperature-dependent dielectric spectrum of solid chitosan, 1,27,28 but reports on the dielectric study of chitosan solutions are less abundant, especially the study of temperature-dependent dielectric spectrum of chitosan solutions. It is well known that the temperature will inevitably affect the motion of molecules and the interactions between the polyions and the counterions, etc. Therefore, the dielectric measurement of a chitosan solution at different temperatures is useful for exploring the micro-mechanism of the relaxation process and the micro-dynamic information in the chitosan solution. In this work, considering the above difficulty in dielectric research of polyelectrolyte solutions, dielectric measurements for the chitosan solution without added salt were carried out over the frequency range from 40 Hz to 110 MHz at different chitosan concentrations and temperatures. The dielectric spectra, which can reflect real dielectric properties of the chitosan solution, were obtained by subtracting the contribution of the electrodes polarization, and the characteristic dielectric parameters were also estimated by fitting the real dielectric data. These parameters were analyzed by means of a scaling approach, Arrhenius empirical formula and Eyring equation. In order to obtain more dynamics and electrical information on the studied system, attention was focused on the relaxation mechanism and the influence of temperature and chitosan concentration on the relaxation behavior. 2. Experimental and method 2.1 Materials The chitosan used in this work was purchased from Golden Shell Co. Ltd. (China). Its degree of deacetylation (DD) is more than 92% and the molecular weight is about 20 kd. All of the commercially obtained chemicals, acetic acid, ethanol, and KCl, were used without further purification Preparation of solutions Chitosan was dissolved in 1% (v/v) acetic acid and then a series of chitosan solutions of different concentrations (0.01, 0.08, 0.4, 0.8, 1.2, 1.6, 2.4 mg ml 1 ), with the same ph value (about ), were prepared with doubly distilled water at 20 C. The specific resistance of doubly distilled water is higher than 16 MUcm 1. The DRS for each chitosan solution was measured directly after preparation, at 5, 15, 25, 30, 45, 35, 60, 75 and 90 C, respectively Dielectric measurement Dielectric measurements were carried out over a wide frequency range from 40 Hz to 110 MHz using a 4294A Precision Impedance Analyzer (Agilent Technologies). The amplitude of the applied alternating field was 500 mv. The temperature of the sample was controlled by a circulating thermostated water jacket. The cell used for dielectric measurements consists of concentrically cylindrical platinum electrodes. 29 The cell constant C l and stray capacitance C r determined by using two standard liquids (pure water, ethanol) and air were and pf, respectively, by which the raw data of conductance G and capacitance C at each frequency were converted to the corresponding dielectric permittivity 3 and conductivity k according to the following equations: 3 ¼ (C C r )/C l and k ¼ G3 0 /C l (3 0 (¼ F/m) is the vacuum permittivity). Prior to the transformation, all the raw data were subjected to certain corrections for the errors arising from stray capacitance C r and residual inductance L r due to the terminal leads. First, the value of the residual inductance L r was determined by use of standard KCl solutions with different concentrations and the relation C ¼ L r G 2. Then, the values of C and G measured directly were subjected to modification by the following equations: 30 C s ¼ C xð1 þ u 2 L r C x ÞþL r G 2 x ð1 þ u 2 L r C x Þ 2 þðul r G x Þ 2 C r (1) G x G s ¼ (2) ð1 þ u 2 L r C x Þ 2 þðul r G x Þ 2 where the subscript x and s denote the directly measured and modified values, respectively, and u is the angular frequency (u ¼ 2pf, f is measurement frequency) Dielectric analytical method In an applied electric field, the dielectric properties of a polyelectrolyte aqueous solution can be characterized by the complex permittivity 3 * which is defined as: 12,31 3 * ¼ 3 jk=u3 0 ¼ 3 j3 00 k l (3) u3 0 where 3 and k is the permittivity and conductivity of the system as mentioned above, 3 00 is the dielectric loss, k l is the low-frequency limit of conductivity, and j ¼ ( 1) 1/2. The measured dielectric loss k/3 0 u consists of two parts, one part is the contribution of dc electric conductivity k l /3 0 u, and another is the dielectric loss The high ionic electrical conductivity of chitosan solutions (about Sm 1 ) caused a giant frequencydependent electrode polarization which masked the relaxation This journal is ª The Royal Society of Chemistry 2010 Soft Matter, 2010, 6,

3 behavior at low-frequency range. 12 In order to remove the electrode polarization, the method similar to the literature 33 was adopted. By fitting the Cole-Cole equation, eqn (4), including electrode polarization term Au m to the experimental data, both the dielectric parameters and Au m were determined. 32, 33, 48 The corrected data were then obtained by removing the Au m from the experimental data. 3 * D3 l D3 h ¼ 3 h þ þ 1 þðjus l Þ b l 1 þðjus h Þ þ b Au m (4) h where D3 l (¼ 3 l 3 m ) and D3 h (¼ 3 m 3 h ) are low and high frequency dielectric increment, respectively, s(s ¼ 1/2pf 0 ) is the characteristic relaxation time, f 0 is the characteristic relaxation frequency, b is the Cole-Cole parameter (0 < b # 1, b ¼ 1 is the Debye relaxation) denoting the width of the distribution of relaxation times. The subscripts l, m, and h denote the low, medium, and high frequency limit values, respectively. A and m are adjustable parameters. At last, the dielectric relaxation parameters are obtained by fitting the eqn (5) to the corrected data * D3 l D3 h ¼ 3 h þ þ 1 þðjus l Þ b l 1 þðjus h Þ b h In order to obtain the 3 00 f curve, it is necessary to calculate 3 00 from the k l with eqn (6). The k l can be obtained through the k 00 k plot. The imaginary part k 00 of the conductivity can be calculated from the obtained dielectric parameters 3 h, with eqn (7). (5) 3 00 ¼ (k k l )/u3 0 (6) k 00 ¼ u3 0 (3 3 h ) (7) Fig. 1 (a) The distribution of free and condensed counterions in chitosan semidilute solution, (C) represent the positive charges on the chain, b is the average distance of the two adjacent charged groups. (b) The motion of free and condensed counterions in a chitosan semidilute solution. The bound counterions fluctuate along the chain. The free counterions fluctuate within the range of x B, where j is electric potential and j m is the maximum potential. interactions and polyion-solvent interactions occur, without polyion-polyion interactions. Counterions in the semidilute region are classified into two groups: condensed (or bound) and free counterions, the distributions of which are shown schematically in Fig. 1(a). The condensed counterions are densely distributed around the chitosan chain within a narrow range due to the fixed charges on the chitosan chains and the free counterions are dispersed in a wide range between the chitosan chains, owing to the shielding effect of the condensed counterions on the chitosan charges. 18 According to the literature, 18 the free counterions fluctuate perpendicular to the polyion axis within the range of x B (approximately equal to the average distance between the chains) in the semidilute region, and the condensed counterions fluctuate along the polyion axis. The free counterions are trapped in the electric potential j and come to the maximum when they are close to the chain, as shown in Fig. 1(b). 3.2 The Ito model 3. Model and theory 3.1. Modelling description of counterions in a semidilute chitosan solution Chitosan molecule chains with protonated amine groups are positively charged. 35 According to Manning s condensation theory, 12 counterion condensation should occur for the interaction parameter between two adjacent charges: 36 u ¼ ð1 DAÞl B. 1 (8) b where DA is degree of acetylation, the Bjerrum length l B ¼ e 2 /3 w is the distance between two adjacent charged groups when the Coulomb repulsion energy is equal to, where 3 w is the dielectric constant of water, e is the elementary charge, T is the temperature in Kelvin and k is the Boltzmann constant, 13 l B equals 7.2 A in water at 25 C, and the average distance between two charges b is 5.1 A for a chitosan solution. Therefore, ion condensation in chitosan solution should occur, only when DD ¼ 1 DA > 71%. The DD in this work is more than 92%, so ion condensation should occur in our chitosan solution. According to the literature, 15,37,38 the concentration range of mg ml 1 of chitosan solution in this work belongs to the semidilute region. In this concentration range, only intramolecular Dielectric increment D3, which is related to polarizability and the concentration of the substance, reflects the polarization degree of the polarized substance. The polarizability a can be expressed by the temperature of the system and the dipole moment m as the following: 18 a ¼ m2 (9) For the relaxation at high-frequency, because the relaxation is caused by the free counterions polarization within the correlation length x B, the high-frequency dipole moment m h can be estimated as m h2 ¼ e 2 x B 2 (10) Substitution of eqn (10) into eqn (9), we have the electrical polarizability a h ¼ e2 2 x B (11) According to Manning s condensation theory, the fraction of free counterions f in chitosan solution is defined as f ¼ b, and l B the concentration of free counterions can be given by fc p (C p is the polyelectrolyte concentration). On the other hand, in the 2744 Soft Matter, 2010, 6, This journal is ª The Royal Society of Chemistry 2010

4 semidilute region the C p and N dependence of x B can be expressed as x B f Cp 1/2 N 0 (12) So the high-frequency dielectric increment is expressed as D3 h z a h fc p z e2 x 2 B fc p z b3 w (13) With regard to the dielectric relaxation of low-frequency, its relaxation mechanism is considered to be the fluctuation of the condensed counterions along an essentially stationary polyelectrolyte chain. Therefore, the low-frequency relaxation increment D3 l can be explained as follows. 12 It is clear that there are (1 f)n (N is the degree of polymerization) condensed counterions on each chain of the chitosan molecule. Fluctuations of condensed counterions should create charges of order e[(1 f)n] 1/2 occurring over a distance comparable with the endto-end distance of the chain R. Therefore, the induced dipole moment from thermal fluctuation is expressed as m l2 ¼ ( e[(1 f)n] 1/2 ) 2 R 2 ¼ e 2 (1 f)nr 2 (14) Substitution of eqn (14) into eqn (9) yields the polarizability of each chain a 1 ¼ e2 ð1 f ÞNR 2 (15) Since D3 l should be the product of the dipole moment of all the chains, the number of which is C p /N, D3 l is expressed as 12 D3 l z e2 ð1 f ÞNR 2 C p N z e2 ð1 f ÞR2 C p z ð1 b3 wþ R 2 C p (16) According to Ito s model, 18 the high-frequency relaxation time s h in semidilute solution is given by s h z x B2 /6D (17) where D is the diffusion coefficient of the counterions in solution. By substituting eqn (12) into eqn (17), we have s h fcp 1 N 0 (18) Since low-frequency relaxation arises from the polarization of the condensed counterions along the length of the chitosan chain, the low-frequency relaxation time s l is expressed as According to Ito s model, D3 h can be expressed as eqn (13). Concerning the Bjerrum length given by l B ¼ e 2 /3 w, D3 h can also be expressed as D3 h z l B 3 w fc p x B 2 (22) Combining eqn (22) and (17) to eliminate x B2, finally the D3 h is expressed as D3 h z 6Dl B 3 w fc p s h z pfc p s h (23) where p(¼ 6Dl B 3 W ) is a constant when the temperature is fixed. Next, the eqn (23) can be converted to the following scaling law: D3 h /s h ffc p (24) which holds both in the dilute and in the semidilute concentration regime. 4. Results and discussion 4.1. Dielectric spectra of chitosan solutions of different concentrations Fig. 2 shows the dielectric spectra of chitosan solutions with different concentrations at 25 C. From Fig. 2, it is clearly seen that one dielectric relaxation occurs between about Hz when the chitosan concentration is above 0.1 mg ml 1. Simultaneously, it is also obvious that the value of permittivity decreases sharply with the increase of frequency in a low frequency range (the part is circled by a dashed ring in Fig. 2) and the location of fall shifts to higher frequency with the increase in chitosan concentration. The remarkable falling phenomenon is recognized as a behavior caused by electrode polarization. The effect of removing electrode polarization is illustrated with the dielectric spectra of the chitosan solution at 0.8 mg ml 1. Fig. 3(a) shows the frequency dependence of the real part 3 and imaginary part 3 00 of the 3* of the chitosan solution at 0.8 mg ml 1 as a function of frequency f, at 25 C. It is noted that the permittivity curve and the dielectric loss curve indicated by the solid circles in Fig. 3(a) are the data processing results in which the electrode polarization effect at low-frequency have been eliminated by the method described in section 2.2 and the open circles are the original data. From Fig. 3(a), it can be clearly seen that when the electrode polarization effect is eliminated, the s l z R 2 /6D (19) Moreover, the s l is determined by the friction coefficient D presented in eqn (20) for condensed counterions moving along the stationary chitosan backbone. 40,41 z z D (20) Finally, combining eqn (20) and eqn (19), s l is expressed as s l z zr2 6 (21) From eqn (21), by assuming that the end-to-end distance of the chain R is unchanged with the change of C p, it is found that s l is insensitive to C p. Fig. 2 Frequency dependence of dielectric permittivity of chitosan solutions with different concentrations of 0.01, 0.08, 0.4, 0.8, 1.6, 2.4 mg ml 1,at25 C. This journal is ª The Royal Society of Chemistry 2010 Soft Matter, 2010, 6,

5 Fig. 4 Three-dimensional representations of the frequency and the concentration dependency of (a) the permittivity spectrum and (b) the dielectric loss spectrum, at 25 C, for chitosan solutions over a concentration range of 0.08 mg ml mg ml 1 which have been processed by eliminating the electrode polarization. Fig. 3 (a) A typical dielectric spectra (real part 3 and imaginary part 3 00 of 3*) of the chitosan solution at 0.8 mg ml 1. The red solid line is the bestfit curve calculated from eqn (5). (b) A Cole-Cole plot obtained from the data in Fig. 3(a). permittivity curve shows a clear-cut relaxation at lower frequency, near the 10 5 Hz, which is that hid by the electrode polarization effect. This relaxation process at low frequency was also confirmed by the dielectric loss spectrum, i.e. the 3 00 f curve in the Fig. 3(a), which was obtained by eqn (6) and (7). In addition, the Cole-Cole plot obtained from the data in Fig. 3(a) also demonstrates likewise that there are two relaxations located at low and high frequency as shown in Fig. 3(b). In order to verify the effect of eliminating electrode polarization, the permittivity was fitted with eqn (5), and the best fitting result was expressed as the red solid line of the 3 f curve in Fig. 3(a). All the dielectric data of the chitosan solutions over the concentration range of 0.08 mg ml mg ml 1, which have been corrected by eliminating the electrode polarization, are shown in three-dimensional plots in Fig. 4. From Fig. 4, it can be seen that two obvious relaxation processes exist in the 100 KHz and MHz range, respectively. The low-frequency relaxation appears only when the chitosan concentration is above 0.1 mg ml 1. The dielectric relaxation parameters were obtained by fitting eqn (5) to the corrected data. The best-fit values for different chitosan concentrations are listed in Table 1. The values of low frequency conductivity k l are also listed in Table 1. The change of dielectric parameters listed in Table 1 with the increase of C p indicates that the dielectric behavior presented in this experiment is somewhat different from that which has been reported elsewhere in which no low-frequency relaxation had been observed. 19 The relaxation mechanisms, regardless of lowor high-frequency, may be related to the structure of the chitosan chains and ionic migration Detailed analysis of dielectric parameters is as follows. In order to detect the relation between the low- and highfrequency dielectric increment, D3 l and D3 h, and the chitosan concentration C p given in Table 1, we plotted D3 l and D3 h as a function of C p, respectively. The scaling behaviors D3 h fc p and D3 l fc p were obtained from relation curves. According to eqn (13), D3 h is independent of the C p. Therefore, the scaling behavior D3 h fc p deviates from Ito s scaling law D3 h fc 0 p. In addition, according to eqn (16), the D3 l is dependent on the C p. However, the obtained scaling behavior is D3 l f C p in our result, which indicates that the length of the chitosan chain R in eqn (16) may be associated with C p. Fig. 5 shows the dependence of the relaxation time s h of the chitosan aqueous solutions on the chitosan concentration C p. The slope of the line in Fig. 5 is about 1, which indicates 1 a power relationship s h C p. According to eqn (18), the relationship between the high-frequency relaxation time s h and chitosan concentration C p is s h fcp 1 N 0. The scaling law is in good agreement with our experimental result shown in Fig. 5, which suggests that the high frequency relaxation mechanism is indeed the polarization of free counterions within the range of x B. It can be seen from Table 1 that low-frequency relaxation time s l shows no concentration dependence and has about 10 7 s orders of magnitude. From eqn (21), by assuming that the endto-end distance of the chain R is unchanged with the change of C p, it is found that s l is independent of C p, which has been verified by our experimental data shown in Table 1. The good agreement between experimental results and theoretical analysis Table 1 Dielectric parameters of chitosan solution with different concentration obtained by fitting eqn (5) to the experimental data C p /mg ml 1 3 l 3 m 3 h b l b h s l /s s h /s D3 l D3 h k l /s m E E E E E E E E E E E E Soft Matter, 2010, 6, This journal is ª The Royal Society of Chemistry 2010

6 Fig. 7 The concentration dependence of the low-frequency limit of conductivity k l in a chitosan solution with ph between 5.1 and 5.4, at 25 C. Fig. 5 At 25 C, the relaxation time s h as a function of C p, the slope of the line is about suggests that low-frequency relaxation originates from the fluctuation of condensed counterions along the chitosan chain within the end-to-end distance of the chain R. The scaling approach can provide more detailed information on the chitosan solution, such as the fraction of free counterions. From the eqn (24), it is clear that the D3 h /s h is proportional to the concentration of free counterions fc p, and D3 h /(s h C p ) is proportional to the fraction of free counterions f. Therefore, the concentration and the fraction of free counterions can be calculated from the high-frequency dielectric parameters (D3 h, s h ) by eqn (24). Fig. 6(a) shows the dependence of the scaling behavior D3 h /s h on the C p. As can be seen, the slope of the straight line is about , so the scaling behavior is D3 h /s h fc p, which deviates from the expected scaling law D3 h /s h fc p in eqn (24). D3 h /s h fc p suggests an increasing power function relationship between the concentration of free counterions and C p. Since the scaling behavior is D3 h /s h fc p, the fraction of free counterions f is proportional to D3 h /(s h C p ) in our result, not the D3 h /(s h C p ) expected in eqn (24). Therefore, in order to find out the correlation between the fraction of free counterions and the chitosan concentration, we plot D3 h /(s h C p ) vs. C p in Fig. 6(b). From the Fig. 6(b), it is clear that D3 h /(s h C p ) has only a small change with the change of C p, which suggests that the fraction of free counterions f is insensitive to the chitosan concentration C p. Fig. 7 shows the concentration dependence of the lowfrequency limit of conductivity of chitosan solutions at 25 C. Fig. 8 Three-dimensional representations of the temperature dependency of the permittivity spectrum (a) and the dielectric loss spectrum (b) for chitosan solutions of C p ¼ 0.4 mg ml 1 over a temperature range of 278 K 363 K which have been processed by eliminating the electrode polarization. Insets: the permittivity spectrum of chitosan solution of C p ¼ 0.4 mg ml 1, at 278 K. From Fig. 8, it is clearly seen that k l increases linearly with the increase of C p. This can be explained as follows: according to the literature, 42 the condensed counterions lose their activity due to the fixed charges of chitosan and do not contribute to the electric conductivity of the chitosan solution, but to the polarizability. Moreover, polyelectrolyte chains are stationary compared to the free ions. Therefore, the value of k l depends on the free counterions, not the condensed counterions and chitosan chains. The increase of k l with the increase of C p can be considered to be caused by the increase in the concentration of free counterions which has been confirmed and illustrated in Fig. 6(a). From Table 1, it is clear that the value of b h is smaller than that of b l, indicating a wider distribution of relaxation times at high frequency. The wider distribution of high-frequency relaxation times is due to the different spatial confinement of the condensed counterions, indicating that high-frequency relaxation is caused by the free counterions. Herein the correlations between the dielectric parameters (such as dielectric increment, relaxation time, low-frequency conductivity and the distribution of relaxation time) and chitosan concentration were discussed in detail, and the detailed information on the concentration and the fraction of free counterions in chitosan solution were also obtained with the Ito scaling model The temperature dependence of the dielectric spectrum Fig. 6 (a) The scaling behavior D3 h /s h as a function of chitosan concentration C p, the slope of the line is about (b) The relationship between D3 h /(s h C p ) and C p. Fig. 8 shows the three-dimensional representations of the temperature-dependent dielectric spectrum of the chitosan solutions with C p ¼ 0.4 mg ml 1, which is obtained by the same This journal is ª The Royal Society of Chemistry 2010 Soft Matter, 2010, 6,

7 Table 2 Dielectric parameters of chitosan solutions of 0.4 mg ml 1 over a temperature range of 278 K 363 K T/K 3 l 3 m 3 h b l b h s l /s s h /s D3 l D3 h K l dielectric analytical method described in section 2.2. Here we omitted the dielectric spectrum for C p ¼ 0.8 mg ml 1 because they have a similar shape. In both Fig. 8(a) and (b), it is obvious that there are two relaxations at 100 khz and MHz, respectively. To examine the dielectric behaviors of the chitosan solution at different temperatures (from 278 K to 363 K) in detail the dielectric parameters of chitosan solution of 0.4 mg ml 1 were obtained likewise by fitting the dielectric data using eqn (5). The results are listed in Table 2. From Table 2, it can be seen that the values of the distribution parameter of relaxation time b l and b h, change with the rise of T, which are the same as those for the concentration change. For the sake of clarity, the dielectric increment D3 l and D3 h, and the low-frequency limit of conductivity k l listed in Table 2 were plotted against T as shown in Fig. 9(a) and (b), respectively. As can be seen from Fig. 10(a), both D3 l and D3 h decrease with increased temperature. This can be interpreted as being due to the fact that the thermal motion of the counterions is accelerated with the increasing temperature, and the directional fluctuations of the counterions in the electric field are obstructed, resulting in the decrease of the electric polarizability. The decrease of D3 l and D3 h is in good agreement with the relationship of dielectric increment and temperature predicted by eqn (13) and (16). From Fig. 9(a), it can also be seen that both D3 l and D3 h increase over a temperature range of 303 K 308 K for the chitosan solution of C p ¼ 0.8 mg ml 1 and K for the C p ¼ 0.4 mg ml 1. The two temperature ranges are called transition temperature ranges, and the chitosan solutions with different concentrations have different transition temperature ranges. 43 According to Fig. 9(a), three regions for C p ¼ 0.4 mg ml 1 can be distinguished as follows: (1) Before the transition region (T < 298 K). The binding between condensed counterions and charged groups, and hydrogen bonding 44 become weakened, and the reorientation thermal motions of counterions are accelerated with T rising. However, the directional fluctuations of their counterions in the electric field are obstructed. Therefore, the polarizability decreases, leading to the decrease of D3 l and D3 h. (2) In the transition temperature region (298 K < T < 303 K). D3 l and D3 h have a small rise from 298 K to 303 K, suggesting that the polarizability rises. It can be interpreted as follows: a small number of condensed counterions quickly overcome the electrostatic interaction of the fixed charges on the chitosan chains as a consequence of thermal motion, and then become free counterions by thermal activation, causing a small rise in polarizability. Likewise, the thermal motion of free counterions becomes much faster compared to the fluctuation perpendicular Fig. 9 (a) Dielectric increment of the chitosan solution of 0.4 mg ml 1 and 0.8 mg ml 1 as a function of temperature. (b) The low-frequency limit of conductivity k l of the chitosan solution of 0.4 mg ml 1 as a function of temperature T. to the chitosan main axle, causing the small rise in polarizability. Hence, D3 l and D3 h have a small rise within the temperature range. (3) After the transition region (T > 303 K). The condensed counterions continuously move away from the interaction of the chains 45 and free counterions continue to fluctuate fast, resulting in the decrease of D3 l and D3 h with the rise of T, which can be interpreted by eqn (13) and (16). From Fig. 9(b), it is clear that k l rises linearly as the temperature rises. This is because the rise in T makes the condensed counterions change to free counterions and the coefficient diffusion of free counterions increases, causing k l to rise. 46 Temperature is one of the important thermodynamic parameters to detect the dynamic behavior of polyelectrolyte solutions, because the rise of T can affect the thermal motion of molecules and ions, decrease the electrostatic interaction and weaken Fig. 10 (a) Natural logarithmic plot of the product of relaxation time and temperature. (b) Natural logarithmic plot of low- and high-frequency relaxation time as a function of the inverse temperature 1/T for a chitosan solution of two concentrations (C, B indicate s l, s h of C p ¼ 0.4 mg ml 1 ; -, : indicate s l, s h of C p ¼ 0.8 mg ml 1 ) Soft Matter, 2010, 6, This journal is ª The Royal Society of Chemistry 2010

8 Table 3 Thermodynamic parameters obtained by the Eyring equation and the Arrhenius empirical formula C p /mg ml 1 DH l /J mol 1 DH h /J mol 1 DS l (J mol 1 K) DS h (J mol 1 K) E a,l /J mol 1 E a,h /J mol hydrogen bonding. To evaluate how the temperature affects the dynamical behavior, we focused on the relation between relaxation time and temperature with the aid of the Eyring equation. 47 Considering the relationship of macro relaxation time and the relaxation rate constant s(¼ 1/k), the Eyring equation can be expressed as h lns ¼ ln DS R þ DH (25) RT where h is the Planck s constant, DH is the activation enthalpy of the relaxation process for the counterions fluctuation, DS is the activation entropy associated with the fluctuation of counterions in an electric field. In order to obtain DH and DS at low-and high-frequency, the eqn (25) was deformed to: h lnst ¼ ln k DS R þ DH RT (26) The lns l T and lns h T were plotted as a function of 1/T in Fig. 10(a) for two chitosan concentrations, respectively. From Fig. 10(a), DH and DS at the low-and high-frequency for the two chitosan solutions were calculated and listed in Table 3. On the other hand, the information on activation free energy Ea can be obtained by the Arrhenius empirical formula K ¼ Aexpð Ea Þ. Considering s ¼ 1/k, the Arrhenius RT empirical formula was deformed to ln s ¼ ln A þ Ea (27) RT We plotted lns l and lns h as a function of 1/T for two chitosan concentrations in Fig. 10(b), respectively. From Fig. 10 (b), Ea at low- and high-frequency for the two chitosan solutions were calculated by eqn (27) and the results were also listed in Table 3. As can be seen from Table 3, Ea, DH, and DS at low-frequency are all different from the ones at high-frequency. This is because the relaxation mechanisms of low-and high-frequency are different from each other. First, the different values of E a,l, E a,h indicate that the energy barrier of low- and high-frequency are different from each other. Moreover, the different energy barriers that counterions need to overcome are reflected in the different scales of fluctuations of condensed and free counterions. The condensed counterions fluctuate along the polyelectrolyte chain within a wider range compared to the correlation length x B which is the length scale of fluctuation of the free counterions. This indicates that the fluctuation of the free counterions overcome a greater energy barrier. Therefore, E a,h is more than E a,l. 39 Concerning DH and DS, their difference for low- and high-frequency relaxation processes can be interpreted, respectively. The DH l of the 0.4 mg ml 1 chitosan solution approximately equals that of the 0.8 mg ml 1 chitosan solution and is about J mol 1. The DH h for the two concentrations are about J mol 1. The different values of DH l and DH h indicate that the thermal fluctuation of free counterions need more thermal activation energy than the condensed counterions. At low frequency, with the rise of T, both the cleavage of the hydrogen bonding and the fluctuation of the condensed counterions need energy, so both the DH l for the two concentrations are over zero. From Table 3, it can be seen that both the DS l of these two concentrations are more than zero, this is because the break of the hydrogen bonding, the acceleration of the fluctuation and the release of the condensed counterions lead to the increase of the confusion degree of condensed counterions. At high frequency, when the T rises, the thermal motions of the free counterions are accelerated. All of the motion above, containing the thermal motion and fluctuation in the electric field, need energy, and the result that DH h is greater than zero is sound. Moreover, DS h is greater than zero, showing that the confusion degree of free counterions increases, which result from the increase of the number and the rapid motion of the free counterions. 4. Conclusion The concentration and temperature dependence of the dielectric spectra of chitosan in aqueous solution with no added salts have been investigated in the frequency range from 40 Hz to 110 MHz. After reducing the contribution of the electrode polarization effects successfully, the dielectric spectra of chitosan in semidilute solutions show two relaxations in the experimental frequency range. The observed two dielectric relaxations were strictly analyzed by the Cole-Cole relaxation function and the dielectric parameters were obtained. The low- and high-frequency dielectric relaxations were considered to be due to the fluctuation of condensed counterions and free counterions respectively, and the two relaxations were interpreted by scaling theory of polyelectrolyte solutions. The relationship between relaxation time s l, s h and the chitosan concentration C p are in good agreement with the scaling laws. The good agreement suggests that lowfrequency relaxation originates from the fluctuation of condensed counterions along the chitosan chain within the endto-end distance of the chain R, and high-frequency relaxation originates from the fluctuation of free counterions perpendicular to polyion axis within the range of x B. In addition to this, this analysis gives further support to the scaling approach of the dynamic behavior of polyelectrolytes. The fact that the fraction of free counterions f is insensitive to C p was also obtained from D3 h, s h by the scaling approach. Only the scaling behaviors D3 h fc p, D3 l fc p, and D3 h /s h fc p in our result deviate from Ito s scaling law. The studies on the concentration dependence of the dielectric behavior of chitosan solutions show that the DRS coupled with scaling theory is a useful approach to This journal is ª The Royal Society of Chemistry 2010 Soft Matter, 2010, 6,

9 explore the electrical properties and micro-dynamic information of polyelectrolyte solutions. The results on the temperature dependence demonstrate that dielectric increments at low- and high-frequency generally decrease with the rise of temperature, which is considered to be due to the acceleration of reorientation motion of the counterions, leading to the decrease in polarizability. By using the Eyring equation and Arrhenius empirical formula, the thermodynamic parameters, activation free Ea, activation enthalpy DH, and the activation entropy DS of low- and high-frequency were calculated from the relaxation time and discussed from the microscopic thermodynamical view. It was concluded that the DH and DS of low- and high-frequency were associated with the fluctuation of counterions, and the release of condensed counterions from chitosan chains influence the low-frequency conductivity k l. The studies on the temperature dependence of polyelectrolyte solutions can provide an effective method to probe the microscopic thermo-dynamical information. Acknowledgements Financial support of this work by the National Natural Science Foundation of China (No and No ) is gratefully acknowledged. References 1 M. T. Viciosa, M. Dionısio, R. M. Silva, R. L. Reis and J. F. Mano, Biomacromolecules, 2004, 5, Keisuke Kurita, Mar. Biotechnol., 2006, 8, E. Guibal, M. Van Vooren, B. A. Dempsey and J. Roussy, Sep. Sci. Technol., 2006, 41, Q. Zhang, L. Zhang and J. Li, Electrochim. Acta, 2008, 53, P. Sorlier, C. Viton and A. Domard, Biomacromolecules, 2002, 3, R. H. Chen and M. L. Tsaih, Int. J. Biol. Macromol., 1998, 23, J. Cho, M.-C. Heuzey, A. Begin and P. J. Carreau, J. Food Eng., 2006, 74, G. A. Morris, J. Castile, A. Smith, G. G. Adams and S. n E. Harding, Carbohydr. Polym., 2009, 76, R. Ravindra, K. R. Krovvidi and A. A. Khan, Carbohydr. Polym., 1998, 36, G. Bertha, H. Dautzenberg and M. G. Peter, Carbohydr. Polym., 1998, 36, M. L. Tsaih and R. H. Chen, Int. J. Biol. Macromol., 1997, 20, F. Bordi, C. Cametti and R. H. Colby, J. Phys.: Condens. Matter, 2004, 16, R A. V. Dobrynin, R. H. Colby and Michael Rubinstein, Macromolecules, 1995, 28, F. Bordi, C. Cametti and G. Paradossi, Macromolecules, 1993, 26, F. Bordi, C. Cametti and C. Paradossi, J. Phys. Chem., 1991, 95, P. G. de Gennes, P. Pincus, R. M. Velasco and F. J. Brochard, J. Phys. (Paris), 1976, 37, G. S. Manning, Acc. Chem. Res., 1979, 12, K. Ito, A. Yagi, N. Ookubo and R. Hayakawa, Macromolecules, 1990, 23, F. Bordi, C. Cametti and A. Motta, Macromolecules, 2000, 33, F. Bordi, C. Cametti, T. Gili and R. H. Colby, Langmuir, 2002, 18, F. Bordi and C. Cametti, Macromolecules, 2002, 35, F. Bordi, C. Cametti and T. Gili, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2002, 66, F. Bordi, C. Cametti and T. Gili, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2003, 68, F. Bordi, C. Cametti, T. Gili, S. Sennato, S. Zuzzi, S. Dou and R. H. Colby, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2005, 72, C.-Y. D. Lu, J. Phys.: Condens. Matter, 2005, 17, S K. Nakamura and T. Shikata, Macromolecules, 2006, 39, D. Meißner, J. Einfeldt and A. Kwasniewski, J. Non-Cryst. Solids, 2000, 275, M. T. Viciosa, M. Dionısio and J. F. Mano, Biopolymers, 2006, 81, T. Hanai, H. Z. Zhang and K. Asaka, et al, Ferroelectrics, 1988, 86, K. Asami, A. Irimajiri, T. Hanai and N. Koizumi, Bull. Inst. Chem. Res. Kyoto Univ, 1973, 51, L. K. H. Van Beek, Dielectric behaviour of heterogeneous systems, in Progress in Dielectrics, ed. J. B. Birks, Heywood Books, London, 1967, vol. 7, pp K. Asami, Langmuir, 2005, 21, T. Mitsumata, J. P. Gong, K. Ikeda and Y. Osada, J. Phys. Chem. B, 1998, 102, K. Asami, Prog. Polym. Sci., 2002, 27, J. Brugnerotto, J. Desbrieres, L. Heux, K. Mazeau and M. Rinaudo, Macromol. Symp., 2001, 168, N. Boucard, L. David, C. Rochas, A. Montembault, C. Viton and A. Domard, Biomacromolecules, 2007, 8, G. A. Johnson and S. M. Nealc, J. Polym. Sci., 1961, 54, J. C. T. Kwak, G. F. Murphy and E. Spiro, Biophys. Chem., 1978, 7, K. Ito and R. Hayakawa, Macromolecules, 1991, 24, M. Mandel, Biophys. Chem., 2000, 85, Y. Nagamine, K. Ito and R. Hayakawa, Langmuir, 1999, 15, Y. Nagamine, K. Ito and R. Hayakawa, Colloids Surf., A, 1999, 148, S. Mafe, J. A. Manzanares, A.-K. Kontturi and K. Kontturi, Bioelectrochem. Bioenerg., 1995, 38, J. Cho, M.-C. Heuzey, A. Begin and P. J. Carreau, Carbohydr. Polym., 2006, 63, J. Cai, H. Liu and Y. Hu, Fluid Phase Equilib., 2000, 170, R. De and B. Das, Eur. Polym. J., 2007, 43, G. Smith, B. Y. Shekunov, J. Shen, A. P. Duffy, J. Anwar, M. G. Wakerly and R. Chakrabarti, Pharm. Res., 1996, 13, M. T. Shaw, J. Chem. Phys., 1942, 10, Soft Matter, 2010, 6, This journal is ª The Royal Society of Chemistry 2010