Relation between the Degree of Acetylation and the Electrostatic

Biomacromolecules 2001, 2, 765-772

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Relation between the Degree of Acetylation and the Electrostatic Properties of Chitin and Chitosan Pierre Sorlier,†,‡ Anne Denuzie` re,‡ Christophe Viton,† and Alain Domard*,† Laboratoire des Mate´ riaux Polyme` res et des Biomate´ riaux (UMR-CNRS 5627), ISTIL, Domaine Scientifique de la Doua, 15 Boulevard Latarjet, 69622, Villeurbanne Cedex, France; and Laboratoire des Biomate´ riaux et Remodelages Matriciels, Institut des Sciences Biologiques et Pharmaceutiques, Universite´ Claude Bernard, 8 Av. Rockefeller, 69373 Lyon Cedex 03, France Received March 6, 2001; Revised Manuscript Received May 21, 2001

A series of chitosan/chitin samples with DA’s varying between 5.2 and 89% was prepared from the reacetylation under soft conditions of a unique chitosan sample allowing the preservation of the chain distribution. The study of the variation of pH for the same concentration of amine groups, at different ionic strengths, on the scale of DA’s allows us to extrapolate the variation of pKa at dissociation degrees (R) 0 and 1. A modeling of all the curves was obtained by means of only one equation. Then, for given concentration of chitosan and ionic strength, it is possible to predict the pH of the solution whatever the DA and R. The role of DA through the participation of hydrophobic interactions and hydrogen bondings on the electrostatic parameters is discussed. The results allow a better understanding of some physicochemical and biological properties of chitosan and chitin. I. Introduction For various reasons, especially problems of environmental impact or toxicity, biopolymers are increasingly being considered as interesting substitutes for synthetic polymers. Among them, glycosaminoglycans such as chitin and chitosan, belonging to the family of β(1f4)-linked polysaccharides appear as highly promising tools. Indeed, their unique structure gives rise to very good biological and mechanical properties. Chitin is largely widespread in biomass,1 and its main application is in the production of its water-soluble derivative chitosan. Chitin and chitosan have exactly the same chemical structure, corresponding to the series of linear copolymers of (1f4)-2-amino-2-deoxy-βD-glucan and (1f4)-2-acetamido-2-deoxy-β-D-glucan. Thus, DA, the degree of acetylation which reflects the balance between the two kinds of residues plays a major role. It also allows us to define the two terms chitin and chitosan2,3 according to their respective solubilities in dilute acidic media (except the case of sulfuric acid). Then, chitosan is the only derivative to be soluble in these conditions and corresponds approximately to DA’s below 60%. The conformations in solution, the physical, physicochemical, and biological properties of chitosan depend on structural parameters such as the molecular weight, DA, and the distribution of the two kinds of residues constituting the chain.3 Thanks to the presence of the primary amine borne by the glucosamine residues, they necessarily depend on its ionization state and then external parameters including pH, ionic strength, and time. As a consequence, the relation * Author for correspondence. E-mail: [email protected]. † Laboratoire des Mate ´ riaux Polyme`res et des Bromate´riaux, Domaine Scientifique de la Doua. ‡ Laboratoire des Biomate ´ riaux et Remodeloges Matriciels, Universite´ Claude Bernard.

between parameters such as pKa, DA, and R, the degree of dissociation, must be quite well-known to interpret the properties mentioned above. Only a few works were published on this problem, but no one covered all the ranges of DA, both for the same chain length distribution and for a high molecular weight. A first study on the variation of the intrinsic pKa, pK0, performed on chitosans with different molecular weights and DA’s located within 0 and 25% proposed to consider pK0 as close to 6.5 and almost constant in the range studied, for an ionic strength of the media of 0.1 M.4 Various authors working on a given chitosan, different in each study and at different ionic strengths, contributed to give a large spectrum of values ranging from 6.1 to 7.5-7 In most cases, the determination of pK0 was based mainly on potentiometric titration4-6 or exceptionally on 1H NMR.7 The apparent charge density of the polycation chitosan should necessarily change with pH and DA. On the other hand, it seems necessary to consider that, over a given value of DA, the dielectric environment of the amino groups becomes quite different and, then, both pKa and pK0 should vary. To try to answer these important questions, we decided to study the role of DA on pKa and pK0 as a function of the degree of dissociation R on chitosan chains of same length and of DA’s varying in a very large range of values located within 5.2 and 89%. For that, an initial chitosan of DA 5.2% was acetylated under sufficiently soft conditions allowing us to preserve the chain lengths. The variations of pKa for each polymer were studied as a function of R, and the role of the ionic strength, another important parameter, was also accounted for. To extrapolate with a sufficient precision the values of pKa at R ) 0 and 1, we used a mathematical simulation of the experimental results. The results of these studies should be particularly useful to interpret numerous results still remaining unclearly or

10.1021/bm015531+ CCC: $20.00 © 2001 American Chemical Society Published on Web 07/10/2001

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Table 1. Physicochemical Characteristics of the Samplesa

R

DA (%)

DPn

DPw

Ip

0 0.02 0.20 0.30 0.35 0.40 0.50 0.60 0.70 1.10 1.20 1.50

5.2 15.8 23.3 29.7 32.0 35.1 40.1 44.5 50.7 70.6 74.5 89.0

1853 1844 1620 1327 1902 ND ND 1854 1814 1838 1835 ND

2261 2162 1972 1636 2219 ND ND 2150 2087 2113 2158 ND

1.23 ( 0.07 1.17 ( 0.07 1.22 ( 0.07 1.23 ( 0.06 1.17 ( 0.07 ND ND 1.16 ( 0.07 1.15 ( 0.06 1.15 ( 0.06 1.18 ( 0.06 ND

a R is the molar ratio (anhydride/glucosamine), DP and DP are the n w number and weight average degrees of polymerization, deduced from SEC, respectively, and Ip is the polydispersity index.

incorrectly explained. It concerns, for example, the changes in the behavior of chitosan chains as a function of DA: (i) during the gelation process in the course of reacetylation;8 (ii) in the complexation process with metal ions;9 (iii) in the mechanism of interaction with biological media;10 (iv) in the mechanism of flocculation of various kinds of particles,12 etc. II. Materials and Methods Purification of Chitosan. The initial chitosan was a sample prepared from squid pens provided by France Chitine (batch no. 114). The flakes were purified by dissolution of 5 g of sample in 1 L of water, in the presence of the amount of acetic acid necessary to achieve the stoichiometric protonation of the -NH2 sites. The obtained solution was then filtered through a 0.45 µm membrane (Millipore) before addition of aqueous ammonia to fully precipitate the polymer. After repeated washings with deionized water followed by centrifugations, until a neutral pH was achieved, the product was dispersed in distilled water and then dried by lyophilization. The DA of the sample calculated from 1H NMR13 was found to be close to 5.2%, and the weight-average molecularweight, measured by size exclusion chromatography with a laser-light scattering detector on line14 was 369 000 g‚mol-1. N-Acetylation of Chitosan. The N-acetylation of chitosan was performed by means of acetic anhydride as the reactive medium, in a water/alcohol solution.15,16 Thus, 10 mL of an aqueous acetic acid solution (0.5%) containing chitosan (1%) was mixed with 8 mL of 1,2-propanediol. The acetylating medium, composed of a freshly prepared mixture of 2 mL of 1,2-propanediol with a variable volume of acetic anhydride, was added slowly to the above solution and stirred for 24 h. The variation of the molar ratio R (anhydride/ glucosamine)15 allowed us to achieve the different values of DA reported in Table 1. At the end of reaction, the polymer was fully precipitated by addition of aqueous ammonia and washed several times with deionized water at pH 8.5 in order to maintain the amino groups in the -NH2 form. In any case, the precipitation occurred although it became more difficult to achieve it in the range of DA values between 45% and 60%. In the latter case, the yield was much lower. Nevertheless, it was possible to improve the uptake of polymer by means of dialysis of the solution against water at pH 8.5. Whatever the DA, the final product was then lyophilized.

1H

NMR Spectroscopy. The chemical structures of the various chitosan samples obtained as above were characterized by 1H NMR. Spectra were recorded on a Bruker 250 spectrometer (250 MHz) at 25 °C. The DA of each sample was determined from the ratio of the area of the methyl protons of the N-acetylglucosamine residues to that of all the H2 to H6 protons of both glucosamine and N-acetylglucosamine residues, as proposed by Hirai et al.13 Potentiometric Titration. Solutions of each sample (10-2 mol‚L-1 of amino groups) were prepared by addition, to a dispersion of polymer in water, of the exact amount of 0.1 M HCl necessary to achieve the stoichiometric protonation of the amine functions. This amount was deduced from the weight of the sample, taking into account the water content (measured from thermogravimetric analysis) and the DA. These solutions were then diluted in KClO4 with different ionic strengths (0.01, 0.05, and 0.1 M) in order to achieve a chitosan concentration of 5 × 10-4 M in amine groups. The potentiometric titration was then performed in a cell thermostated at 25 ( 0.1 °C thanks to a Tacussel Minisis 8000 pH-meter, equipped with a XC 100 radiometer electrode (Ag/AgCl), and by means of 0.1 M NaOH as titrant. Size-Exclusion Chromatrography and Preparation of Chitosan Solutions. Size-exclusion chromatography was performed by means of an IsoChrom LC pump (SpectraPhysics) connected to a Protein Pack glass 200 SW column and a TSK gel 6000 PW. A Waters 410 differential refractometer and a multiangle laser-light scattering detector, operating at 632.8 nm (Wyatt Dawn DSP), were connected on line. A 0.15 M ammonium acetate/0.2 M acetic acid buffer (pH 4.5) was used as eluent. The refractive index increment, dn/dC, was chosen as being equal to 0.172 cm3‚g-1 14. Polymer solutions (0.1% w/v) were filtered on 0.45 µm pore size membranes (Millipore) before injection. Thermogravimetric Analysis. The water content of chitosan samples was evaluated on a DuPont Instrument 2950 thermogravimetric analyzer (TGA), operating at a ramp of temperature of 2 °C/mn under a flow of helium. Mathematical Modeling. A mathematical treatment of the experimental results was used in two cases: first to extrapolate the curves pKa(R) at R ) 0 and 1; then to determine a general equation allowing on to draw all the curves pKa(R) from just the knowledge of DA. For that we used the “nonlinear curve fitting” of the software Origine 6.0. III. Results and Discussion Preparation and Characterization of Chitosan Samples of Various DA’s. A total of 11 samples of chitosan with DA’s ranging between 15.8 and 89% were prepared by acetylation of the same polymer corresponding to a commercial sample of DA 5.2%, purified by solubilization and then precipitation and intensive washings before lyophilization. The reaction of acetylation was performed in an hydroalcoholic medium by means of acetic anhydride as reactive medium, at ambient temperature. These conditions15,16 allowed us to avoid the O-acylations and were sufficiently soft to preserve the chain length distribution. They are necessary to eliminate any influence of both the

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Properties of Chitin and Chitosan

chemical structure and the chain length on the electrostatic properties. The reaction of acetylation performed in homogeneous media also has the advantage to induce a random distribution of the two kinds of residues constituting the polymer chains.17 The various DA values can be achieved by just a change in R, the initial molar ratio between acetic anhydride and glucosamine residues. After isolation, the samples are characterized by 1H NMR spectrometry and SEC, allowing then to have all the parameters reported in Table 1. We can verify that the initial chain length distribution (R ) 0) is relatively well preserved whatever the DA. To prepare solutions of each polymer the most precisely, it is also important to know the exact amount of acid to be added to a given weight of polymer with a given DA. Indeed, all the solutions must exactly correspond to the salt form, without any excess or default of acid and have the same concentration of glusosamine residues. Then, for some cases, showing slight experimental errors, small corrections (below 1%) were necessary to standardize all the curves. This is why, we preferred to represent the variations of pH and pKa as a function of R, the dissociation degree. To avoid changes due to modifications in the solution organization, all the solutions were prepared at a concentration below C*, the critical concentration of chain entanglement. Role of DA on the Variation of pH as a Function of r. Since chitosan is a weak base, especially for the lowest values of DA, it is necessary to correct the value of R′, the experimental neutralization degree, related to the self-dissociation of the ammonium groups according to the relation R ) R′ + [H+]/C

(1)

with R the corrected dissociation degree, [H+] the concentration of free protons deduced from pH and C the concentration of glucosamine residues. To have similar electrostatic conditions, the experiments were performed on solutions with the same initial concentration of glucosamine residues, whatever the DA. In Figure 1a are reported the curves giving the variation of pH as a function of R for the various DA’s studied in this work. We notice a linear relation between pH and DA at R ) 0 (Figure 1b). The limit of this very important increase of the initial pH with the DA can be extrapolated to 7.03 when DA tends toward 100%. It signifies that for the highest values of DA, the free amino groups allow us to induce a true alkaline media on all the pH scale except for the very first R values. On the opposite, the value of pH ) 3.74, extrapolated at DA ) 0 agrees with a relative acidic character of the glucosamine residues in these conditions. On increasing R, for DA’s corresponding to 5.2%, 15.8%, and 23.3%, we notice a deviation of the curves already mentioned in a previous paper,4 due to a kinetic process of precipitation of chitosan, but, the precipitation appears at neutralization degrees increasing with DA. Role of DA on the Variation of pKa as a Function of r. The variation of pKa as a function of R is deduced from pH values by means of the Katchalsky’s equation18 pKa ) pH + log

(1 -R R) ) pK - ∆Ψ(R) KT 0

(2)

where pK0 is the intrinsic pK corresponding to an ionic site supposed as isolated and undissociated. is the dielectric constant of the media, ∆ψ(R) is the difference of electrostatic potential between the surface of the polyion and the reference, and KT is the Boltzman term. Figure 2 illustrates the different kinds of behaviors observed while varying DA from 5.2 to 89%. For low DA’s, the titration in the range just below R ) 1 is conformed to the well-known kinetic process of precipitation4,19 which progressively disappears on increasing DA. In addition, it was necessary to extrapolate the curves at R ) 0.01 and R ) 1. Indeed, the reproducibility of the results is more and more difficult related to the self-dissociation of the amine group in the region of the lowest R values, and related to the instability of pH at the proximity of the complete neutralization. To do that in a reliable manner, we decided to simulate all the curves by means of mathematical equations. Unfortunately, the best fittings necessitated the use of different equations according to the value of DA considered. The various equations used are reported in Table 2. The constants a, b, c, d, e, f, and g are different from each other for the different DA values. If we consider Figure 2, we can observe three kinds of behaviors. 1. For the range of very low values of DA, within 0-20%, the curves agree with the behavior of a polycationic polyelectrolyte for which charge density increases upon decreasing DA. Indeed, the term for electrostatic potential in eq 2 has as much importance as DA and R decrease. On the other side, for high neutralization degrees, the curves tend toward an extrapolated value of pK0 which is low for a primary amine, thus reflecting a particular dielectric environment of these functional groups. This behavior must be related to the important involvement, in this region, of hydrogen bonding. This hypothesis is reinforced by the fact that the pKa of simple primary amines decreases when their structures include functional groups which can form H bonds such as hydroxyl groups.20 Then, the pKa values of ethylamine and 2-ethanolamine are 10.80 and 9.50, respectively. The same behaviors can also be observed in the case of carboxylic sites.21 2. On increasing DA, for values close to 20%, we tend toward the behavior of a simple electrolyte with a pKa which varies only to a very low extent on increasing R. The extrapolation of pK0 shows a slight increase compared to the previous range. 3. Over DA 20%, we notice a very important change at the beginning of the curves. Thus, for the values of R close to 0, we observe an inversion of behavior with a value of pKa at the origin which increases considerably with DA and then decreases monotonuously with R. In this region, the polyelectrolyte behavior is replaced by that of isolated charges in which hydrophobic environment increases on increasing DA. If we consider the pKa of simple aliphatic free amines, it increases with the length of the alkyl chains. This change should be emphasized by a typical situation where the self-association of the polymer chains increases in the same way. Indeed, for DA below 25%, solutions are close to true solutions with a low aggregation. Over DA 25%,

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Figure 1. (a) Potentiometric titration curves of chitosan solutions 5 × 10-4 equiv/L as a function of DA in 0.1 M KClO4 (NaOH 0.1 M as titrant). (b) Variation of the initial pH as a function of DA.

the proportion of aggregates increases up to a frontier located near 60%.19,22 Over this value, solutions correspond more and more to dispersions of highly solvated microgels instead of isolated chains. As a consequence, the local concentration of polymer segments becomes very different and certainly contributes to considerably reinforce the hydrophobic interactions. As shown previously,19,22 the local formation of supramolecular structures could participate in this important change. On increasing R, we lose progressively the hydration of the system, in favor of H bonding as in the above two cases, and we tend toward a much lower value of pKa. Nevertheless, the value of pK0 progressively increases with DA. Variation of pKa at r ) 0 and 1 as a Function of DA. It is interesting to consider the variation of pKa at both ends of the scale of the R values. As can be seen in Figure 3, the two situations are quite different. In the first case (Figure 3a), for R ) 0, pKa increases in a linear manner as a function of DA. This behavior reflects

the variations described above but the linearity remains difficult to explain. The extrapolations of pKa at the two ends of the curve are equal to 5.44 and 10.44, for DA ) 0 and 100% respectively. The first value corresponds to a weak acid although the second agrees with that measured for a simple primary amine associated with a short alkyl chain. The value of ethylamine mentioned above is quite similar. In this range, whatever DA, the hydration remains at its maximum for the whole scale of DA’s. In the case of R ) 1, Figure 3b, the situation is quite different and we may notice two distinct cases with an intermediate range corresponding to the transition between the two domains. The location of the various domains corresponds to DA < 30%, 30% < DA < 60%, and DA > 60%. The mathematical simulation of the two regions allows us to extrapolate various values of pK0 in each range. In the first range, 0 < DA < 30%, the values of pK0 extrapolated at DA ) 0 and 100% are 6.46 and 9.49, respectively. This behavior is in agreement



Figure 2. Variation of pKa as a function of R and DA for chitosan solutions (5 × 10-4 equiv/L in 0.1 M KClO4). Open dots are extrapolated points while filled dots are experimental results. Table 2. Equations Used for the Extrapolations of the pKa Values at R ) 0.01 and 1 DA (%)

R

name of the equation

equation (a+(b/R+c))

89

Exp3P1Md

1

p Ka ) e

74.5

ExpDec3

1

pKa ) ae(-R/b) + ce(-R/d) + fe(-R/g)+ h

29.7 to 70.6

Explinear

0.01

pKa ) ae(-R/b) + c + dR

Shah

1

pKa ) a + bR + crR

23.3

Shah

0.01 and 1

15.8

Rational0

0.01 and 1

5.2

Rational3

0.01 and 1

pKa ) a + bR + crR a + bR p Ka ) 1 + cR a+R pKa ) b + cR

with that of a glucosamine residue included in a polyelectrolyte structure in which charge density tends toward that of a monomer included in a structure where the hydrophobicity of the environment increases but where the hydration

of the ionic site would not be largely modified. It is interesting to notice that 9.49 is not far from the pKa of ethanolamine mentioned above. Experimentally, the situation is quite different and we observe a transition range where

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Figure 3. Variation of pKa at R ) 0 (a) and 1 (b), as a function of DA.

pK0 decreases and remains unchanged up to 60%. This behavior necessarily reflects the involvement of a second behavior which becomes progressively majoritary and corresponds to values of pK0 lower than those we could expect. This is confirmed in the last range by an extrapolated value of pK0 at DA ) 100% close to 7.32, a relatively low value which remains below but close to that of the monomer.23 These behaviors must be related to the progressive involvement of chain associations corresponding to the formation of aggregates,19,22 up to a limit close to 60% over which the system corresponds more to a dispersion of microgels than to a true solution. Then the second behavior reflects essentially the change in the solvation of the ionic sites associated with the important role played by hydrogen bondings in the limitation of the increase of pK0. Role of the Electrostatic Parameters on the Polymer Properties in Solution. At R ) 0 (figure 2), when DA increases, the increase in pKa allows the rigorous interpretation of some behaviors already published. First of all is the fact that hydrophobic cross-links play the major role in the gelation process observed on increasing the DA of chitosan.24 It also confirms the important increase of the cationicity of the polymers at DA’s over 80%.8 Thus, if we consider a polymer of DA ) 89%, pH 7 corresponds to a dissociation degree below 0.4, although a chitosan of DA < 20% must be considered as being almost neutralized at this pH. This property is particularly interesting for all the interactions in which chitosans are involved, whatever the physical state. We may mention various situations where typical behaviors of chitosan remained unexplained. (i) First is that the electrostatic properties of chitin gels, near the critical DA of gelation, close to 80%, remain important.8 (ii) Second is the fact that, for a given concentration of glucosamine residues, the complexation of metal ions decreases significantly on increasing DA, especially for values over 70%.

Indeed, the complexation of metals by chitosan is essentially due to the formation of dative bonds by means of the free amino groups.25 (iii) It also allows us to interpret the changes in the properties of flocculation by chitosan, especially when we study the role of DA. Then, when the latter is below 28%, there is no significative role of DA, and only the total amount of glucosamine residues is important.12,26 On increasing DA over this limit, the role of DA on the increase of the cationicity becomes very important.12 (iv) Knowledge of the variation of pK0 on increasing DA is also useful to interpret the change in the solubility properties. Thus, it was considered that on increasing DA, the enlargement of the range of pH where chitosan is water-soluble was due to a stiffening of the chains related to the steric hindrance brought about by the increase of the number of acetyl groups. It was also noticed that A2, the second virial coefficient, was decreasing. Our results show that we must also take into account the role of the increase of pK0 on the increase of the stiffness, thanks to electrostatic repulsions induced by the increase of the cationicity of the amine groups. Although A2 decreases, in relation to the hydrophobization of the structure, this change in cationicity also contributes to maintaining the second virial coefficient at a sufficiently high level, thus avoiding an anticipated precipitation. On increasing DA, in the range of low dissociation degrees, we favor the formation of hydrophobic interactions. The presence of amino groups for which cationicity increases with DA maintains the hydrophily of the chains and limits the formation of hydrogen bondings. These conditions, depending on whether the initial concentration of the polymer is below or over C*, allows an easy aggregation or gelation either in the presence or in absence of a cosolvent.24 These physical forms are preferentially formed with regard to precipitation since the hydrophily of the system is maintained, especially by the presence of ammonium groups.



Figure 4. Variation of pKa as a function of R, DA and ionic strength. Parts a-d correspond to DA ) 5.2%, 32%, 50.7%, and 70.6%, respectively, for three different ionic strengths (2, 0.1 M; [, 0.05 M; b, 0.01 M).

When we increase the pH of a solution of chitosan, we contribute to favor the formation of H bonds which certainly replace an important part of hydrophobic interactions thus explaining the decrease of pKa with R. Then, pK0 is more representative of the influence of H bonding although pKa at R ) 0 is more influenced by hydrophobic interactions. Nevertheless, the latter kind of interaction remains present over the entire scale of pH in agreement with the two different behavior laws observed when we study the variation of pK0 with DA, at R ) 1. Role of the Ionic Strength of the Media. To be complete, the study of the electrostatic properties of chitin and chitosan also needs to take into account the role of the ionic strength of the media. We chose to investigate the role of this parameter on four different polymers covering largely the scale of DA’s (5.2%, 32%, 50.7%, and 70.6%). Three ionic strengths corresponding to 0.01, 0.05, and 0.1 M KClO4 were used. The concentration of the polymers was the same as in the above studies, and the contribution to the ionic strength could be neglected. The results are reported in Figure 4. Whatever the DA, the screening effect due to an increase of the ionic strength is always observed. This behavior is responsible for a decrease of the electrostatic potential parameter in Katchalsky’s equation. The consequence is an increase of the value of pK0 when the ionic strength increases. This variation is just as important as the structural charge

density increases, i.e., when DA decreases (Figure 4a). This dependence remains moderate since for the case where it is the most important, the variation is only of 0.3 pK unit when the ionic strength is multiplied by 10. It is interesting to notice that, for these low DA’s, the variation of the pKa is maintained almost constant over the entire scale of R, in agreement with the polyelectrolyte behavior. On increasing DA, the screening effect becomes less important and the changes must be even more attributed to an increase of the hydrophobic character of both the structures and the media, there also limited by the balance between hydrophobic interactions and hydrogen bondings. The influence of the ionic strength on the hydrophobic interactions is particularly well observed, at low R values, in the intermediate range of the DA’s (Figure 4, parts b and c) and reaches a maximum for the lowest DA values of this range (Figure 4b). In this domain, as discussed above, the hydrophobic parameter is weakly counterbalanced by hydrogen bondings, especially for the lowest value of DA in this region. Mathematical Modeling. The equations and the different parameters used to extrapolate the curves pKa(R) are reported in Table 2. On the other hand, we attempted to find an equation allowing the drawing of all the curves pKa(R) whatever the DA. In Figure 5 are compared the experimental curves and

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value of pKa and then pH from only the knowledge of the degree of acetylation and the ionic strength of the media. IV. Conclusion In this paper, we studied the role of DA and the ionic strength on the variation of pKa whatever the DA and the degree of dissociation. The modelization of all the curves by means of a unique equation allows an easy prediction of the e´lectrostatic parameters in solution. The next important question to answer concerns the problem of the stability of the solutions with regard to their possible self-association with time, for conditions corresponding to a given DA and R. This kind of study is in progress in our laboratory. Acknowledgment. This work is financially supported by a grant from the Ministry of Teaching and Research. We also thank FRANCE CHITINE for the gift of the squid pen sample of chitosan used in this work. Figure 5. Comparison between modeled (s) and experimental curves for some DA (9, 74.5%; 2, 50.7%; O, 40.1%; [, 29.7%; b, 15.8%; 0, 5.2%). Table 3. Values of the Constants of the Polynomial Functions Used to Calculate Eq 3 for Every DA and Correlation Coefficient R2 for Each Function

ADA x1 x2 x3 x4 R2

BDA 10-6

-1.446 × 2.801 × 10-4 1.918 × 10-3 6.028 0.9939

10-6

3.024 × -4.743 × 10-4 9.039 × 10-3 0.4645 0.9530

CDA 1.966 × 10-7 -3.960 × 10-4 6.416 × 10-2 -1.086 0.9089

their mathematical modeling. To clarify the figure, we voluntarily limited the number of curves. The use of a function of the type Shah such as pKa ) ADA + RBDA + CDArR

(3)

allows us to draw all the curves. For each DA, the experimental values of pKa allow the calculation of ADA, BDA, and CDA. It is then possible to draw the curves of variation of these three parameters as a function of DA and to smooth them by means of a polynomial function of degree 3. So, ADA, BDA, and CDA are of the form x1DA3 + x2DA2 + x3DA + x4 (see values and correlation coefficient in Table 3). It is thus possible to fully know the general equation mentioned above. This equation is tested for different values of r. This treatment allows us to estimate the best value for r as close to 10-10. The comparison between the experimental and modelized curves is relatively satisfying if we consider both the involvement of experimental errors and the limits of the predictive model chosen. Some slight discrepancies can be observed for some curves at very low values of R. The same treatment can also be applied to the variation of pKa as a function of the ionic strength for a given DA (not shown). If this model has no theoretical basement, it has the merit to show that, for a given concentration and ionic strength of a solution of chitosan, it is still possible to deduce easily the

References and Notes (1) Roberts, G. A. F. In Chitin Chemistry; Roberts, G. A. F., Ed.; Macmillan Press Ltd.: London, 1992; p 54. (2) Domard, A. In AdVances in Chitin Science; Chen, R. H., Chen, H. C., Eds.; National Taiwan Ocean University Publisher: Taipei, 1998; Vol. III; p 24. (3) Roberts, G. A. F. In Chitin Chemistry; Roberts, G. A. F., Ed.; Macmillan Press Ltd.: London, 1992; p 274. (4) Domard, A. Int. J. Biol. Macromol. 1987, 9, 98. (5) Park, J. W.; Choi, K.-H. Bull. Korean Chem. Soc. 1983, 4, 68. (6) Terbojevich, M.; Carraro, C.; Cosani, A. Makromol. Chem. 1989, 190, 2847. (7) Anthonsen, M. W.; Smidsrød, O. Carbohydr. Polym. 1995, 26, 303. (8) Vachoud, L.; Zydowicz, N.; Domard, A. Int. J. Biol. Macromol. 2001, 28, 93. (9) Piron, E. Ph.D. Thesis, Lyon, France, 1997. (10) Chatelet, C.; Damour, O.; Domard, A. Biomaterials 2001, 22, 261. (11) Vander, P.; Vårum, K. M.; Domard, A.; Eddine El Guedari, N.; Moerschbacher, B. Plant. Physiol. 1998, 118, 1353. (12) Strand, S. P.; Vandvik, M. S.; Vårum, K. M.; Ostgaard, K. Biomacromolecules 2001, 2, 126. (13) Hirai, A.; Odani, H.; Nakajima, A. Polym. Bull. 1991, 26, 87. (14) Domard, A. In Chitin Enzymology; Muzzarelli, R. A. A., Ed.; European Chitin Society Publisher: Ancona, Italy, 1993; p 441. (15) Vachoud, L.; Zydowicz, N.; Domard, A. Carbohydr. Res. 1997, 302, 169. (16) Hirano, S.; Ohe, Y. Agric. Biol. Chem. 1975, 39, 1337. (17) Vårum, K. M.; Anthonsen, M. W.; Grasdalen, H.; Smidsrød, O. Carbohydr. Res. 1991, 211, 17. (18) Katchalsky, A. Pure Appl. Chem. 1971, 26, 327. (19) Vårum, K. M.; Ottøy, M. H.; Smidsrød, O. Carbohydr. Polym. 1994, 25, 65. (20) Handbook of Chemistry and Physics, 69th ed.; Weast, R. C., Astle, M. J., Beyer, W. H., Eds.; CRC Press: Boca Raton, FL, 1988-89. Section D-159. (21) Handbook of Chemistry and Physics, 69th ed.; Weast, R. C., Astle, M. J., Beyer, W. H., Eds; CRC Press: Boca Raton, FL, 1988-89; Section D-161. (22) Ottøy, M. H.; Vårum, K. M.; Christensen, B. E.; Anthonsen, M. W.; Smidsrød, O. Carbohydr. Polym. 1996, 31, 253. (23) Tsukada, S.; Inoue, Y. Carbohydr. Res. 1981, 88, 19. (24) Domard, A.; Vachoud, L. Proceedings of the 8th International Conference on Chitin and Chitosan; Yamagushi, Japan, Sept, 2000, in press. (25) Domard, A.; Piron, E. In AdVances in Chitin Science; Peter, M. G., Domard, A., Muzzarelli, R. A. A., Eds.; Universita¨t Potsdam: Potsdam, Germany, 2000; vol IV, p 295. (26) Demarger-Andre´, S.; Domard, A. Carbohydr. Polym. 1994, 24, 177.

BM015531+

Relation between the Degree of Acetylation and the Electrostatic

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