J . Phys. Chem. 1991, 95,4883-4889
Dielectric Behavior of Polyelectrolyte Solutions: The Role of Proton Fluctuation F.Bordi, Sezione di Fisica Medica, Dipartimento di Medicina Interna. Universith di Roma “Tor Vergata”, Rome, Italy
C. Cametti,* Dipartimento di Fisica, Universith di Roma “La Sapienza”. Rome, Italy
and C . Paradossi Dipartimento di Scienze e Tecnologie Chimiche, Universith di Roma “Tor Vergata”, Rome, Italy (Received: February 22, 1990; In Final Form: November 8, 1990) The dielectric properties of chitosan in aqueous solutions have been measured as a function of the degree of ionization in the frequency range from 1 kHz to 10 MHz. The dielectric spectra have been analyzed in terms of two contiguous dispersions described by a ColtCole and Debye relaxation function. The dependence of the dielectric parameters (dielectric increments and relaxation frequencies) on the degree of ionization cannot be understood simply as a result of polarization of the ionic atmosphere around the polyion, on the basis of the polyelectrolytic counterion fluctuation model. The present results suggest that protonic transport through the ionized sites of the polymer is the dominant mechanism responsible for the overall observed dielectric behavior.
Introduction Dielectric properties of polyelectrolyte solutions have been subject to extensive experimental and theoretical studies over the past decades, and recently various reviews have The dielectric behavior of aqueous polyelectrolyte solutions is dominated by the cooperative interactions between the fixed charges on the polyion and the counterions, which are essentially constrained by electrostatic forces near the surface of the polyelectrolyte. Such interactions play a role of great importance in determining the conformation of the macromolecule, which is deeply connected to the biological functions of biopolymers. In this respect, dielectric relaxation spectmrcopy represents a powerful tool providing information not only on the static conformation of the macromolecule but also on the internal motion of the side groups and on the overall dynamics of the chain. At frequencies below 100 MHz, aqueous polyelectrolyte solutions generally exhibit two dispersion regions that are more or less well separated, whose dielectric parameters depend on concentration, molecular weight, and charge density of the polyion, on the flexibility of the chain, and in general on intra- and intermolecular interactions. On the other hand, the contribution of proton fluctuations to the dielectric properties of different compounds containing a number of neutral or negatively charged basic sites, such as -NH2 and -COO-and to which protons are loosely bound, is well established.’ Due to experimental dificulties of separation of ionic and protonic contributions to the conduction mechanisms in solutions, these studies have been mainly carried out on hydrated
powder^.^^^ The existence of conductance pathways unique to protons due to hydrogen-bonded chains (HBC) has been suggested’ to account for the anomaly observed in the proton flux through biological membranes, where the proton permeability exceeds by orders of magnitude that of small ions. Nagle and Morowitz have suggested* that hydrogen-bonded chains of amino acid side groups of proteins can span the membrane forming a “proton wire”, and more recently a model based on this idea was developed and investigated in detail? Moreover, there is experimental evidence (1) Mandel, M.; Odijk, T. Annu. Reu. fhys. Chem. 1984, 35, 75. (2) Anderson, C. F.; Record, Jr., M. T. Annu. Rev. fhys. Chem. 1982.33, 222. (3) Mandel. M. Makromol. Chem. 1984, 123/124,63. (4) South, G. P.; Grant, E. H. Biopolymers 1973, 12, 1937. (5) Hawkes, J. J.; Pethig, R. Eiochim. Eiophys. Acra 1988, 952, 27. Morgan, H.; Pethig, R. J . Chem. Soc., Faraday Trans. I 1986, 82, 143. (6) Careri, G.; Giansanti, A,; Rupley, J. A. froc. Narl. Acad. Sci. U S A . 1986, 83, 6810. (7) Brunger, A.; Schulten, Z.; Schulten, K. Z . Phys. Chem. (Munich) 1983, 136, I . (8) Nagle, J.; Morowitz, H. froc. Narl. Acad. Sci. U.S.A. 1978, 75, 298.
0022-3654/91/2095-4883%02.50/0
that “proton wires” within the bilayer are formed even in the absence of proteins, simply because of the association of water molecules through hydrogen bonds. The term “transient hydrogen-bonded chains” (tHBC) has been proposed to distinguish between this proton conductance mechanism, water-mediated, and the protein-mediated mechanism (HBC).IO In this context, to ascertain whether the proton transport mechanism observed in hydrated powders would also be observable in solutions, we have measured the radiowave dielectric behavior of chitosan in aqueous solution at different degrees of ionization and in the frequency range from 1 kHz to 10 MHz. Chitosan, a polysaccharide containing only neutral basic sites (-NH,), constitutes a useful model system for studying counterion interactions in cylindrical ionic biopolymers, in order to point out the proton contribution to the apparent dipole moment of the chain and to the overall dielectric dispersion. This investigation r e p resents an extension of our previous studies”vt2 on ionic polysaccharides ((carboxymethy1)cellulosewith negatively charged carboxylic groups) to polyelectrolytes with similar structural characteristics but with positively charged aminic groups. In fact, the chitosan, due to the amino groups on the chain, exhibits a true polyelectrolyte behavior in a wide range of pH values up to about pH = 7.13 Above this value, massive aggregation occurs and eventually precipitation takes place. Chitosan and chitin are closely related biopolymers, differing only in their N-acetyl content. In fact, chitosan can be ideally considered as an N-deacetylation reaction product of chitin. Actually, depending on the natural sources (shrimp, crab, lobster shell^),'^ the biopolymers called “chitosan” encompass a wide variety of polydispersed chains either in their molecular weight or in their low N-acetyl content. We thought it worthwhile to take advantage of the sporadic N-acetylation of our starting material (about 10% in our case) to perform a limited enzymatic degradation of the chain. To this aim, we degraded the polymer via chitinase,I5 a hydrolytic enzyme system known to have an activity also for chitosan and to cleave it endowisely at the points where N-acetyl groups are present along the chain. We focused our attention on the possibility of comparing the dielectric properties of this stiff, rodlike biopolymer, namely a (9) Nagle, J. J . Eioenerg. Eiomembr. 1987, 19, 413. (10) Deamer, D. W.; Nichols, J. W. J. Membr. Eiol. 1989, 107, 91. (1 I ) Bordi, F.; Cametti, C. Eer. Bunsen-Ges. fhys. Chem. 1985.89, 747. (12) Bordi, F.; Cametti, C. Eer. Bunsen-Ges. fhys. Chem. 1986, 90,447. (13) Domard, A. Inr. J . Eiol. Macromol. 1987, 9, 98. (14) Muuarelli. R. A. A. Chitin; Pergaman Press: New York, 1977. (15) Tominga, Y.; Tsujisaka, Y. Eiochim. Eiophys. Acra 1975,410, 145.
0 1991 American Chemical Society
Bordi et al.
4884 The Journal of Physical Chemistry, Vol. 95, NO. 12, 1991
poly( 1,4)-2-amino-2-deoxy-8-Dglucopyranose, in aqueous solution with suitable theoretical models.
Experimental Section Materials. Chitosan was a Sigma product. The purification was carried out by dissolving the polymer a t a concentration of about 1.5% (w/w) in a wateracetic acid 1% (v/v) mixture and adding successively sodium chloride (Carlo Erba) up to a 0.3 M concentration. The solution was then dialyzed against doubly distilled water; the solution contained in the dialysis bag showed opalescence. At this stage, however, the dialysis bath was free from chloride ions. The sample was freeze-dried. The equivalent weight of the purified material was determined potentiometrically by the Broussignac methodI6 and yielded a value of 180 g/equiv. As an analogue of the repeating unit of chitosan, we used 2-deoxyglucosamine. This product, from Sigma, was employed without further purification. Degradation and Fractionation. Chitosan was dissolved in 0.2 M acetate buffer a t pH = 5.6 to a concentration of 0.2% a t 38 OC. In a typical run, 5 mg of enzyme "chitinase" (Sigma) was added to 500 mL of a chitosan-containing solution. The shear time of the solution fell abruptly after about 1 h to a value equal to one-third of the initial shear time value, before enzyme addition. This feature was already reported by Tominaga et al.I5 as evidence of an endowise cleavage of chitosan. At this point the mixture was added to ammonium hydroxide to a pH about 8.5 to precipitate the polymer. The precipitate was thoroughly washed and redissolved adding HCl to pH = 3.0. Acetone was then added to the solution under stirring. As the solution was becoming cloudy, the supernatant was separated by the precipitate by centrifugation. Four fractions were collected in this way and stored in freeze-dried form. This precipitation process was efficient as a procedure for molecular weight fractionation since aqueous solutions of four fractions with comparable concentration showed viscosity values decreasing with the increasing amount of the precipitant. All fractions characterized in terms of equivalent weight by the Broussignac methodI6 showed a value ranging from 180 to 200 g/equiv, consistent with that of the starting material: Also, the values of pK, at a = 0.5, where a is the degree of dissociation of the protonated form of the polymer, was the same within the experimental errors and equal to 6.2,in agreement with already published r e s ~ l t s . ~IR ~ Jspectra ~ of films casted from 0.5% (w/v) aqueous solutions of the fractions were consistent between them and in agreement with the IR spectrum reported in the literature for protonated chitosan." Dielectric Measurements. Two kinds of samples-monomers and four different fractions of unknown molecular weight, but ranging approximately from lo3 to 1O5-were prepared and used in this dielectric investigation. The interval of the molecular weight of the fractions has been roughly estimated considering the molecular weight of the starting material and the effect of the dialysis following the enzymatic degradation carried out with membranes with a cutoff of IO4. Additionally, we have carried out light scattering intensity measurements on two intermediate fractions of different degrees of polymerization. Although the absolute value of the molecular weights may reflect the difticulties of an accurate determination of the change of the refraction index on concentration,I* our results confirm the expected sequence and the order of magnitude of the molecular weights of the fractions investigated. The polyion concentration was maintained low (within about 2 mg/mL) to prevent possible polyion-polyion interactions. These concentrations ensure a dilute regime where only intramolecular interactions and polyionsolvent interactions O C C U ~ . ~ Fractions ~,~ (16) Broussignac, P. Chim. Ind., Genie Chim. 1968, 99, 1241. (17) Pearson, F. G.;Marchessault, R. H.;Liang. C. Y . J. Polym. Sci. 1960,13, 101. (18) Rinaudo, M.;Domard, A. In Chirin und chlroson; Skjak-Braek, G . , Anthonsen, T., Sanford, P.,Eds.; Elsevier: Amsterdam, 1989. (19) Johnson, G. A.; Nealc, S. M . J . Polym. Sci. 1961, 51, 229. (20) Kwak, J. C. T.; Murphy, 0.F.;Spiro, E. J. Biophys. Chem. 1978, 7, 379.
"V
IO'
I O
IO'
lob
10'
v [Hzl Figure 1. Permittivity c' of 2-deoxyglucosamine (concentration 1.79 mg/mL) as a function of frequency, at 20 'C: (A)pH = 6.97;(m) pH = 8.50. Measurements were carried out at different values of pH from 5.5 to 8.5. The corresponding permittivity curves are omitted for clarity of presentation. The full lines represent the calculated values according to a single Cole-Cole relaxation function. The permittivity (0)of a simple salt solution (NaCI, lo-' M) is also shown to indicate the absence of electrode polarization effects in the low-frequency region of the spectrum.
60 IO'
10'
10'
10'
I'
v [Hzl Figure 2. Permittivity c' of solution of chitosan (polymer fraction of
intermediate molecular weight; at a concentration of 2.04 mg/mL) as
a function of frequency, at 20 'C: (M) pH = 6.94;(A) pH = 5.45. Measurements were carried out at different values of pH from 5.5 to 7.3. The corresponding permittivity curves are omitted for clarity of presentation. The full lines represent the calculated values according to a
low-frequency Cole-Cole and a high-frequency Debye relaxation function. The permittivity (0)of a simple salt solution (NaCI, IO-' M) is also shown to indicate the absence of electrode polarization effects in the low-frequency region of the spectrum. of intermediate molecular weight were prepared both in the H+ and in the deuterated form (dissolved in DzO)in order to point out a possible isotopic effect on the relaxation frequencies, since this effect constitutes a clear indication in the attribution of the relaxation process to proton fluctuations. The complex dielectric constant was determined by means of standard methods using a L.F. impedance analyzer ( H P Model 4192A) in the frequency range from 1 kHz to 10 MHz. The dielectric cell consists of two platinum parallel plate electrodes covered with platinum black to reduce the electrode polarization. The cell constants have been determined by calibration with standard liquids of known conductivity and permittivity. The calibration procedure we adoptedz1requires measurements as a function of frequency of three different liquids to determine at each frequency the values of the capacitance and inductance that model the frequency behavior of the measuring cell. To ascertain whether the bulk ionic charge accumulation at the metal-electrolyte interface could give rise to residual electrode polarization effects, we have measured the permittivity of simple electrolyte solutions of electrical conductivity close to that of the polymer (21)
Bottomley, P. A. J . Phys. E.:
Sci. Insrrum. 1978, 11, 413.
The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 4885
Dielectric Behavior of Polyelectrolyte Solutions
TABLE I: Madd Panmeten rad Limib for Some Typical Dielectric Relaxation Curved
Monomer Solution, pH = 8.5 dielectric model
parameters
1D’ 70 f 2 40 3
At
*
kHz
v,
1Cb 75 2 40 3 0.13 0.04 2.3 2.0
*
a
STD cov
parameters ACl At2 YI, kHz ~ 2 MHz ,
3.2 2.8
Polymer Solution (Fraction d), pH = 5.45 dielectric model 1 Cb 1c + 1C‘
lD4 37
3
56 f 7
67
10
50 f 8
42 & 3 7*2 39 7 1.2 f 0.3 0.29 f 0.01 0.009 f 0.009 2.25 2.04
0.49 f 0.08
a1 a2
STD cov
4.33 3.93
3.02 2.74
lC+lDd 42 f 2
5f1 44 f 5 1.36 0.7 0.29 0.02
*
1.85 1.68
lD+ 1C 23 i 3 24 f 4 188 20 1 . 1 f 0.5 0.14 2.63 2.39
0.05
.A single Debye-type function. b A single ColtCole-type function. C T wColtCole-type ~ functions. *A low-frequency Cole-Cole followed by a high-frequency Debye-type function. ‘A low-frequency Debye-type followed by a high-frequency ColtCole-typefunction. /The uncertainties quoted represent the 95% confidence interval.
solution investigated. As can be seen in Figures 1 and 2, no dependence on frequency has been observed in the permittivity of NaCl electrolyte solutions in the low-frequency region of the dielectric spectrum. Moreover, the scatter of the measured values around the expected one is confined within a few units, and this uncertainty can be assumed as the overall accuracy of the whole experimental setup. At each run, 5 1 logarithmic scale data points were collected for the frequency range investigated. The combined sources of errors due to the small value of the intrinsic phase angle at lower frequencies and at higher ionic conductivity of the sample reflect in dielectric measurements with an uncertainty lower than 2% at frequencies below 10 kHz. It reduces to less than 1% at frequencies above 100 kHz. In the whole frequency range investigated, only the permittivity c’ was measured. The imaginary part of the complex dielectric constant leads to a small increase of the conductivity, owing to the high ionic strength of our solutions. Consequently, we have quoted only the dc electrical conductivity of the samples under testing. The temperature was maintained constant at the value of 20 OC within 0.1 O C . The polymer solutions were neutralized with NaOH or NaOD to various degrees of neutralization. The pD values were obtained from the readings of the pH meter taking into account the appropriate correction.22
Results The analysis of the data was camed out as follows. An attempt was made to fit the data of the polymer solutions to a single dispersion using the Cole-Cole equation, although the whole dispersion pattem was quite broad. Typical results for each sample examined yielded a value of the parameter a,a measure for the width of the relaxation time distribution, ranging from 0.3 to 0.55. These values indicate that the assumption of a single relaxation process is not entirely sufficient and suggest that at least two relaxation processes are involved. Consequently, it was assumed that the complex dielectric constant t * = e’ - it” is given as the sum of two Cole-Cole relaxation functions c‘
= c,
+ 1+
At 1
UTI)'-^^
At2 + 1 + (iw72)1-02
(1)
where e, is the limiting value of the high-frequency permittivity, Atl and Af2 are the dielectric increments of the dispersions (22) Marshall, A. G. Biophysical Chemistry; Wiley: New York, 1978.
characterized by relaxation times 7 , and T ~ respectively, , and w is the angular frequency. If both the low-frequency and highfrequency dispersion are characterized by a single relaxation time, a,= 0 and eq 1 reduces to the ordinary sum of two Debye-type dispersion equations. To determine the most appropriate values of the dielectric parameters in eq 1, we have employed a least-squares fitting procedure minimizing the quantity n
s = C(e’,t4(4 - c’Ca(w&)* 1 We found that, for all the samples investigated, the Cole-Cole parameter of the high-frequency dispersion is very small and in some cases zero within the uncertainty. Consequently, in order to reduce the number of the free parameters, a2was fixed at zero. A further attempt in finding the distribution function was made consisting of a principal Debye-type region in conjunction with a Cole-Cole high-frequency dispersion. For the majority of the present results, this procedure did not yield significantly better results, and consequently we discarded this possibility. The appropriate choice of the different model functions we have considered is based on the variance of the fit yielding a value of the reduced x2 that provides a better statistically significance for a Cole-Cole low-frequency dispersion followed by a Debye highfrequency dispersion. In the case of the monomer solution samples, the dispersion curves occur over a narrow frequency range, suggesting the existence of a single relaxation process. Thus, we have analyzed the dielectric dispersion of the monomer solutions on the basis of a single Cole-Cole distribution function. This analysis results in a parameter a lying between 0.11 and 0.16. The model parameters and their limits for some typical dielectric relaxation curves are shown in Table I. Some examples of the measured dielectric spectra and the curves calculated according to eq 1 for the monomer solution and a polymer solution of intermediate molecular weight at two different degrees of ionization are shown in Figures 1 and 2. In the fitting procedure we adopted, c, is treated as an unknown parameter. Its value does not deviate appreciably from that of the aqueous phase, indicating that, in these samples, it is not possible to detect other dispersion mechanisms at higher frequencies besides that due to the dipolar orientational polarization of water molecules occurring at microwave frequencies. The dielectric increment of the low-frequency dispersion increases with increasing the degree of neutralization (as shown in Figure 3) at first rapidly and then gradually, showing a saturation effect. These features are qualitatively similar to those reported
4886 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 *o __ .. ... -. __ . . __ .- - . --- I
Bordi et al.
,
60
d 4 K 4
so .
I t
h.
1 A=,
I
7 .O
6 .O
20,10
8.0
..
pH
Figure 6. Relaxation frequency of the low-frequencydielectric dispersion as a function of pH derived from the fitting procedure adopted. The different curves refer to polymers of different molecular weight: (A) monomer: the symbols 0, A, 0 indicate different polymer fractions of increasing molecular weight.
6t
;
0,2 .O
5.5
6.0
6.5
7 .O
7s PH
Figure 4. Dielectric increment of the high-frequency dispersion, normalized to the polymer concentration, as a function of pH derived from the fitting procedure adopted. The symbols @ 0, A, and 0 indicate different polymer fractions of increasing molecular weight.
~
o'!.O
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
PH Figure 5. The ColtCole parameter of the low-frequency dielectric dispersion as a function of pH derived from the fitting procedure adopted. The different curvca refer to polymers of different molecular weight: (A) monomer; the symbols 0. A, and 0 indicate different polymer fractions of increasing molecular weight.
..
by Minakata et It must be noted, however, that the magnitude of the dielectric increment of the various fractions differs significantly from each other, indicating the existence of the effect of fractionation and suggesting that the low-frequency dielectric dispersion depends on the molecular weight of the polyion. The high-frequency dielectric dispersion shows a dielectric increment approximately independent of the different fractions and of the degree of the neutralization (Figure 4). The width of the low-frequency dielectric relaxation represented by the Cole-Cole parameter a is shown in Figure 5 . As can be (23) Minakata,
A.; Imai, N.Blopolymers
1972, J J , 329.
1
0, .O
5.5
6 .O
6.5
7.O
7.5
PH Figure 7. Relaxation frequency of the high-frequency dielectric dispersion as a function of pH derived from the fitting procedure adopted. The symbols @ 0,A, and 0 indicate different polymer fractions of increasing molecular weight. seen, all the fractions behave similarly, indicating a progressive change toward a single Debye-type dispersion as the degree of neutralization is increased. The relaxation frequencies uI vary monotonously with the size of the macromolecules as shown in Figure 6, qualitatively in agreement with the molecular weight dependence of the dielectric increment of this dispersion. The high-frequency dispersion is characterized for all the degrees of ionization by a molecular weight independent relaxation frequency u2 (Figure 7). These findings are in agreement with similar results obtained by Sachs et ahu on poly(vinylsu1fonic acid) and by Allen et al.zs and Bordi et a1.'1,12on (carboxymethyl)cellulosein aqueous electrolyte solutions. It must be noted, however, that in the above-mentioned studies the change of the relaxation frequency and the dielectric increment as a function of the molecular weight is in the opposite direction compared with the variation we found in the systems investigated here. In the present case, the relaxation frequency vI increases in progressing from the fraction of lower molecular weight to fraction of higher molecular weight, whereas the dielectric increment Ae, shows a behavior in the opposite direction. Discussion The polyelectrolyte system investigated displays two dielectric dispersions associated with two different molecular relaxation mechanisms, as suggested by their different dependence on the molecular weight. The question now arises as to how to identify (241 Sachs. S. B.:Raziel. A.: Eisenbera, - H.;Katchalsky. A. Tram. Faraday Soc. 1%9,65,71. (25) Allen, D. J.; Neale, S.M.;Tait, P.J. T. J . Polym. Sci. A2 1972, 10, 433.
Dielectric Behavior of Polyelectrolyte Solutions the molecular mechanisms of the observed dielectric relaxations. A semiquantitative approach to explain the dispersion regions is based on the effect of polarization of the condensed ions surrounding the polyion. Following the Van der Touw and Mandel the polyelectrolyte is pictured as a sequence of identical radlike subunits with a certain fraction of counterions loosely bounded to the polyion. The counterions are constrained in a cylindrical potential wall around each subunit due to the electrostatic field arising from the net charge on the chain. While ion motion along the subunit is unrestricted, electrostatic forces prevent ions from leaving the neighborhood of the polyion. Between two consecutive subunits there are potential barriers due to the angle they form with each other and which cause a certain hindrance to the motion of ions along the whole chain. Within this model, the low-frequency dispersion is associated with the counterion polarization along the overall polyion (the polyelectrolyte backbone), giving rise to large polarization of the ionic atmosphere, whereas the higher frequency dispersion is determined by the counterion redistribution along the subunit. According to this description, counterion distribution fluctuation leads to a relatively faster process characterized by a relaxation frequency v2 related to the counterion distribution within the subunit and to a relatively slower process characterized by a relaxation frequency vI which tends to cause a redistribution of counterions along the whole polyion. On the basis of this model, the high-frequency and the lowfrequency dielectric increments At, and Ae2 are expected to be proportional to the average square end to end distance (L2)of the whole polyion and to the square of the length b of the subunits, respectively. This theory holds when the charge distribution on the polyion is symmetric and independent of time and thus does not contribute to the dipole moment associated with the charge distribution. In the present case, specially at low degree of dissociation, the fluctuation of protons among the aminic groups, involving intramolecular movements of protons associated with migration and redistribution of charges at the polyion surface, must be taken into account. A correction to the van der Touw and Mandel model has been developed by the same author^,^' considering additional contribution to the dielectric increments arising from proton fluctuation. The dielectric increments of the low- and high-frequency dispersions are given by
The Journal of Physical Chemistry, Vol. 95, No. 12, I991 4887 101
I
A OA 0
0.8
0.6
I
A A
OA 0
A A
0A .n
A
0A .Q
A
t
0 .
A
AU
0,4
A
0 .
A A
AQ 0
A
.
5
7
6
8
10
9 PH
Figure 8. Degree of dissociation a as a function of pH for the monomer (A)and for the four fractions (0),(H), (A), and ( 0 ) of increasing
molecular weight. Tis a function of the charge density of the polyion, and therefore it depends on pH. The additional contribution to the dielectric increment involving intramolecular movements of protons associated with a migration and a redistribution of charges at the polyion surface was firstly proposed by Kirkwood and Schumaker28 and more recently by Plum and B l ~ o m f i e l d . ~The ~ high-frequency relaxation can be due to proton transport through different adjacent charged sites along the polyion chains, whereas the low-frequency relaxation can be attributed to proton displacements between charged sites in different positions of the same polyion along the contour length. This rate process involves the dissociation of a proton from a site and the transfer to an adjacent site, along the polymer chain, the transfer being mediated by the presence of the solvent.30 The proton fluctuation model predicts, as experimentally o b served, a pH-dependent dielectric dispersion. We can assume that the charge on each ionized group is neutralized by a proton involving proton transfer in the reaction scheme -NH3’
-
NH2
+ Ht
According to this model, the probability f of a group having a bound proton depending on the solvent proton concentration (and hence on the solvent pH) and on the dissociation constant pK of that group, is given by 1
= 1+
respectively, where 7 is the average fraction of counterions bond to the polyion, CY the degree of dissociation, N the Avogadro number, Cpthe polyion concentration expressed in monomoles per liter, KBT the thermal energy, and eo the dielectric constant of free space. Here 6 is the length of the rodlike subunit and (R:) the mean-square radius of gyration of the subunits with respect to the center of mass of the polyion. The usual radius of gyration of the polyion is given by
(P) = (R,2) + b2/12 As noted by van der Touw and Mandel,27the correction termf(1
-j)originates by multiplying the average fraction f of aminic
groups by the probability (1 -A that a monomeric group carries on average a proton. In our systems, the net charge on the polyion arises from the protonation of the neutral basic groups -NH2 and is a function of the pH of the solution whereas the role of counterions can be played by CI-anions. The average fraction of bound counterions (26) van der Touw, F.; Mandel. M. Biophys. Chcm. 1974, 2, 218, 231. (27) Paoletti, S.; van der Touw, F.;Mandel, M.J . Polym. Sci. 1978, 16, 641.
10pH-pK
Dielectric Behavior of Dqferent Molecular Weight Fractions in Solution. In this case the dielectric spectra of polyions of different molecular weight and at different degrees of dissociation are characterized by two distinct dielectric relaxation processes. From the dielectric increments the value of ( R ; ) and 6 can be obtained through eqs 2 and 3. According to the Manning counterion theory,31the fraction of counterions that condense around the polyion to reduce its effective charge is governed by the charge density parameter where le is the Bjerrum length and d is the average distance between charged groups on the polyion chain. If [ is lower than a critical value (6= l/(zprc) where z, and zp are the valences of counterions and polyion groups, respectively), condensation does not occur and the concentration of counterions is equal to the stoichiometric value. In the present case, the measured degree of dissociation a as a function of pH (Figure 8) varies from a = 0.1 to about a = 0.9, independent of the polymer fraction, and (28) Kirkwood, J. G.; Shumaker, J. B.Prcc. Nurl. Acad. ScL U S A . 1952, 38, 855, 863. (29) Plum, G. E.;Bloomfield, V. A. Biopolymers 1990, 29, 1137. (30) Williams, R.J. P. ANIU. Reo. Biophys. Biophys. Chcm. 1988,17,71. (31) Manning, G. S. Q.Rcu. Biophys. 1978, 11, 179.
4888 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 TABLE 11: Polyion Structural Parameters Derived from Lon- and Hieb-Freaucncv Dielectric Disuersiom
fraction DH M, = 9.5 X lea 6.28
M, = 1.2 X
a
losa
6.48 6.68 6.92 7.13 6.04 6.20 6.33 6.49 6.66 6.85 7.03
a
0.51 0.62 0.70 0.82 0.88 0.45 0.50 0.55 0.60 0.67 0.78 0.86
ea3 17 16 14 14 13 21 16 16 13 13 12 13
ea2 62 56 52 50 49 64 58 54 51 46 45 45
calc 52.5 51.5 51.0 44.0 42.5 59.7 58.5 57.0 55.5 53.5 50.8 49.3
Estimated from light scattering measurements.
this implies for a rodlike structure a distance d between protonated groups ranging from about 7.5 to about 25 A. This distance exceeds the Bjerrum length (7 A at T = 20 "C), the charge parameters is lower than its critical value, f = 1, and counterions do not condense. Under these assumptions, as far as the high frequency is concerned, the length of the subunits b, which represents a measure of the stiffness of the chain, varies from 20 to 13 nm as the pH is increased from 6.0 to 7.0,indicating the significant role of electrostatic forces on the expansion of the polyion in dilute solution. Moreover, it is roughly independent of the molecular weight. In as far as the low-frequency relaxation process is concerned, the mean-square radius of gyration decreases progressively as the pH increases, implying that, as expected, the polyion is in a more extended state at lower degree of dissociation (lower pH) owing to electrostatic interactions between charged groups. Typical values of b and (SZ)'l2for two fractions are shown in Table 11. These values can be compared with those calculated from the conformational behavior of chitosan molecules in the dilute regime. In fact, it is well-known that chitosan in dilute solutions behaves as a wormlike polyi0n'~3~ with a flexibility controlled by the degree of ionization and counterion concentration. The conformational properties of the chain are determined by the total persistence length
& = Lp + Le which contains two contributions, the intrinsic persistence length 4 of the equivalent neutral polymer and the electrostatic persistence length Le. According to the theory of Odjik,33Le, in the limit KDL >> 1 and KD-' >> d, can be calculated from
In our case, the intrinsic persistence length estimated from viscosity measurement^^^,^^ is about 30 nm, whereas the electrostatic persistence length, assuming an overall ionic strength of 5 X 1b4 M, varies from about 25 to about 2 nm as the degree of dissociation increases from a = 0.45to a = 0.86. (These typical values refer to fraction D.)If the mean-square radius of gyration is calculated from the Benoit and Doty e x p r e ~ s i o n ~ ~
where L, is the contour length, for a molecular weight of lo5,
Bordi et al. values of the order of 50 nm are obtained. Moreover, the dependence of the radius of gyration for each fraction as a function of pH, and hence on the degree of dissociation, is in reasonable agreement 'with that derived from the dielectric measurements (Table 11). These findings support further confidence on the one hand in a wormlike chain model to describe the chitosan and on the other hand, in the contribution of proton fluctuation on the overall dielectric behavior. The dependence of the observed dielectric parameters of the low-frequency dielectric dispersion upon the molecular weight in the four fractions investigated is of more difficult interpretation in the framework of the van der Touw and Mandel mode1.26*27 With increasing the polyion molecular weight, the low-frequency dielectric dispersion has been found to progressively shift toward higher frequencies with, at the same time, a decrease of the dielectric increment. The process responsible for the overall observed dispersions can be thought of as composed of two different mechanisms. The first may be characterized by the proton transfer between two adjacent ionizable groups along the polyion chain within the subunit. This process, independent of the molecular weight, gives rise to the high-frequency dielectric dispersion. The second dispersion, occurring at lower frequencies, might originate from proton transfer through ionizable groups of different subunits of the macromolecule. It is noteworthy that, in the case of proton exchange between different sites, the proton movement is not restricted radially in a cylindrical shell around the polymer chain as in the case of counterions surrounding a polyion bearing fixed charges, because now the picture of a static electric field around the chain no longer holds. The dielectric increment Aq decreases on the molecular weight, and regardless of the detailed mechanism, this can be attributed to a decrease of the distance between sites of different subunits involved in the proton transfer. As has been pointed out, the polyion contour length ranges from 50 to about 300 nm depending on the molecular weight, whereas the overall persistence length is approximately 30-50 nm depending on the degree of dissociation. These values suggest that a rather folded configuration can be expected with a flexibility that increases, changing the degree of polymerization. These indications agree with a wormlike chain model with a relatively high stiffness. These decreased distances of proton transfer as the molecular weight is increased will in turn result in higher relaxation frequencies for different fractions in the sequence found experimentally. In the case of monomers (2-deoxyglucosamine) in solution, due to the narrow nature of the dielectric relaxation, we have analyzed the dielectric data on the basis of a single relaxation curve. As above noted, the dielectric dispersion arises from the fluctuation and redistribution of protons associated with ionized groups between the charged sites of different monomeric molecules. Proceeding with this assumption and using the measured titration data for the degree of dissociation, one can evaluate the distance between charged groups involved in the proton fluctuation ranging from 80 to about 150 A as the pH varies from 5.5 to 8.5. It is noteworthy that, if a diffusion constant D = 5 X lo4 m2/s is assumed for the proton, the same value of this distance accounts for the measured relaxation frequency. Moreover, this value can be favorably compared with that of about 150 A as the average distance between monomers estimated from the monomer concentration. Obviously, the diffusion of charge must be envisaged as a cooperative process through coordinated movement of protons through neighboring groups of different monomeric molecules. Finally, the change of the fluctuation relaxation frequency for each fraction depends linearly on the concentration of the H+ ions, according to the expression4 u
(32) Kienzle-Sterzer, C.; Rodriguez-Sanchez, D.;Rha, C. i n Chitin, Chitosun und relures Enymes; Zikakis, J. P.,Ed.: Academic Press: New York, 1984. (33) Odijk. T.; Houwaart, A. C. J . Polym. Sci.: Polym. Phys. Ed. 1987, 16, 627. (34) Benoit, H.; Doty, P. J . Phys. Chem. 1953, 57, 958.
= uo(2
+ IOpK-pH)
where u0 is related to the mean lifetime of the unionized group. The observed dependence of the fluctuation relaxation frequency on the pH is in qualitative agreement with the prediction of the above picture, when the measured dissociation constant of the aminic group is considered.
J . Phys. Chem. 1991, 95, 4889-4896
Figure 9. Effect of the deuterium substitution on the relaxation frequencies of the low- and high-dielectric dispersions. The full line rep resents, in a linear plot, a straight line of slope d?.The slopes of the straight lines that fit the low- and high-frequency dispersion separately are 1.5 f 0.3 and 1.42 0.06, respectively. These figure are consistent with a unique process for the relaxation frequencies of the two dielectric dispersions.
Deuterium Substitution Effect. Further support to the involvement of protons in the observed dielectric behavior of the polymer investigated arises from the effect of deuterium substitution. The isotope effect has been measured on two different samples (monomers and a fraction of intermediate molecular weight) dispersed in heavy water at different pD values in the
4889
range from 5.5 to 8.5, under similar experimental conditions. The overall phenomenology observed is very close to that found on similar samples dissolved in normal water. The effect of deuterium substitution is equivalent to a shift of the relaxation time, which should be higher by a factor of d? in D 2 0 than in H20. This is in fact the expected ~ h a n g e ~ in ~ Ja6process involving protons. Figure 9 shows the relaxation frequencies of the low- and high-frequency dispersion process for the polymer solution of chitosan in normal water and heavy water, respectively, the comparison being made a t equal pH and pD values. As can be seen, the relaxation frequencies of both the relaxation processes fall with reasonable agreement on a straight line of slope d?. The fact that the two separate dispersion regions have been observed to shift toward lower frequencies when the deuterium substitution is present agrees with the view that observed dielectric dispersions are due to proton fluctuation along the macromolecular chain. These results represent a good indication that the transport process involving protons through different charge sites on the polyion in solution is the dominating contribution to the dielectric relaxations observed on the samples studied here. However, the details of these mechanisms remain unclear and must be investigated more accurately. (35) Pethig, R. Dielecrric and Electronic Properiies of Biological Marerials; Wiley: Chichester. 1979. (36) Cared, G.;Geraci, M.; Giansanti, A.; Rupley, . . J. A. Proc. Nail. Acad. Sci: U.S.A. 19& 82, 5342.
Phase Behavlor of AOT Microemulsions In Compressible LlquMs Greg J. McFann and Keith P. Johnston* Department of Chemical Engineering, The University of Texas, Austin, Texas 78712 (Received: September 17. 1990; In Final Form: December 1 1 , 1990}
The phase behavior of bis(2-ethylhexyl) sodium sulfosuccinate (A0T)-alkanebrine systems is described over a wide range of pressure, temperature, and salinity for alkanes from ethane to dodecane. The partitioning of AOT between the oil, middle, and brine phases is reported for propane in order to determine the natural curvature. This is important for understanding separation processes with water-in-oil microemulsions. For the lighter, more compressible alkanes, the pressure effect on the hydrophilicity of the surfactant is much larger and in the opposite direction as for the heavier, less compressible ones. In propane at constant temperature and salinity, water-in-oil (w/o) microemulsions have been converted to middle phase microemulsions and then to oil-in-water (o/w) microemulsions by decreasing the pressure. These phase inversions are described in terms of the immiscibilities in the binary systems, and the molecular interactions at the surfactant interface. Although temperature and salinity are used commonly to manipulate interactions primarily on the water side of the interface, these results show it is possible to control interactions on the oil side by adjusting the pressure. The well-established trends in the phase behavior and size of microemulsion drops for dodecane through hexane are not observed for the lighter alkanes. For butane through ethane, a new unusual behavior is identified and attributed to a significant decrease in the strength of the attractive interactions between the surfactant tails and the alkane.
Introduction
The effect of pressure on microemulsion phase behavior for systems composed of surfactant, oil, and brine has been studied previously for liquid solvents,'J but not for highly compressible liquids such as ethane, propane, and butane. For relatively incompressible alkanes, pressure has little effect on the phase be( I ) Turkevich, L. A.; Mann, J. A. Lmgmuir 1990, 6,457. Kim, J. D.: OConnell, J. P.J . fhys. Chem. 1988,92, 3492. Fotland, P.; Skauge, A. J . Dispersion Sci. Technol. 1986, 7. 563. Kim, M. W.; Gallagher, W.; Bock, J. J . Phys. Chem. 1988, 92, 1226. (2) Kahlweit, M.:Strey, R.;Schomacker. R.;Haase, D. Longmuir 1989, 5. 305.
0022-3654/91/2095-4889$02.50/0
havior, unless the system is already near a phase transition a t ambient pressure. However, pressure may have a significantly larger effect for propane even at ambient temperature, because propane's density and solubility parameter are much more adjustable due to its relatively low critical temperature, 96.8 O C . Our objective is to demonstrate and explain large effects on the droplet size and phase behavior of microemulsions in compressible liquids with changes in four principal variables: pressure, temperature, salinity, and molecular volume of the alkane solvent. Because both oil and brine phases are present, the surfactant partitions between the phases, and in some cases, forms a new middle phase. A knowledge of partitioning between the phases is important for understanding separation processes such as the 0 1991 American Chemical Society
