J. Phys. Chem. 1995, 99, 274-284
274
Radiowave Dielectric Properties of Xanthan in Aqueous Solutions F. Bordi,? C. Cametti,*y$and G. Paradossis Sezione di Fisica Medica, Dipartimento di Medicina Interna, Universitir di Roma “Tor Vergata”, Rome, Italy, Dipartimento di Fisica, Universith di Roma “La Sapienza”, Rome, Italy, and Dipartimento di Scienze e Tecnologie Chimiche, Universitir di Roma “Tor Vergata ”, Rome, Italy Received: May 4, 1994; In Final Form: September 2, 1994@
The dielectric and conductometric properties of aqueous solutions of xanthan, an ionic polysaccharide consisting of a linear cellulosic backbone with three-sugar side chains, have been extensively investigated over two frequency ranges, from 1 kHz to 10 MHz and from 1 MHz to 1 GHz by means of frequency domain dielectric spectroscopy, at different polyion concentrations and at two different temperatures, above room temperature, in the range where an order-disorder transition occurs. The dielectric spectra have been analyzed on the basis of two contiguous dielectric dispersions described by a Cole-Cole relaxation function, and the parameters have been discussed on the basis of currently accepted dielectric relaxation theories of polyelectrolyte solutions. For the majority of the polyion concentrations employed, a semidilute regime occurs and the two observed dielectric relaxations are ascribed to counterion fluctuations on two different scale lengths, the first associated to the polymer contour length and the second one to an average distance between charged groups of adjacent polyions. Moreover, these measurements suggests that a conformational transition occurs at temperatures above 40 “C with the consequent formation of an extended three-dimensional network. This transition results in a particular behavior of the dielectric relaxation on the polymer concentration.
Introduction
-4-P-D-Glcp-
Xanthan, produced by the fermentation broth of the bacterium Xanthomonas campestris, is a polysaccharide of current interest covering a number of different commercial applications ranging from food to tertiary oil recovery industry. Despite the chemical complexity of the pentasaccharide repeating unit, the regularity of its primary structure is well established. Xanthan is an ionic polysaccharide1s2consisting of a linear cellulosic backbone, i.e., 1 4 linked P-D-glucose residue, with a three-sugar side chain attached to every second glucose of the backbone, therefore yielding a regular comblike polymer. The detailed structure of the repeating unit is shown in Figure 1. In aqueous solution, this molecule undergoes a conformational transition which can be driven by changes in temperature, ionic strength, and degree of ionization of the carboxyl group^.^,^ The temperature-induced transition from an ordered conformation to a disordered one is generally amibuted to a complete or partial separation of the double-stranded form.5 In the past decade, different physicochemical properties of xanthan in aqueous solutions have been extensively studied by means of various experimental techniques, ranging from light scattering measurements6 to hydrodynamic measurements,’ thermodynamic properties such as ion activity,8dependence of the transition temperature on the ionic strength? and calorimetric measurements.1° All these measurements support evidence for the existence at room temperature of an ordered conformation consisting of a rigid double-stranded chain which undergoes a thermally induced transformation toward the dissociation of the strands, even if some recent conductivity measurements still leave this question open.“ On the other hand, the presence of a carboxyl and a pyruvyl group on the polymer side chain makes xanthan a convenient model for an aqueous polyelectrolyte system, and this molecule
-
Dipartimento di Medicina Interna.
* Universid di Roma “La Sapienza”. 8 @
Dipartimento di Scienze e Tecnologie Chimiche. Abstract published in Advance ACS Abstracts, December 1, 1994.
(14)-P-D-GlCp -(1 3
t1
P - D - M w -(1+4)-P-D-Glcp A-( 1 +2)-a-D-Manp 6Ac
Figure 1. Structure of the repeating unit of xanthan.
should represent, in principle, a good approximation to the cylindrical model of the commonly accepted polyelectrolyte aqueous solution theory. Our interest in the transport properties of charged biopolymers in aqueous solution^^^^^^ has brought to our attention the lack of a detailed study on the dielectric properties of xanthan solutions. Therefore we have undertaken a systematic investigation of the radiowave dielectric properties of xanthan aqueous solutions, in two different temperature ranges, at T = 20 “C, where the polymer should display an ordered conformation, and at temperatures higher than the transition temperature (T FZ 40-45 “C) as detected for our samples by optical methods such as rotatory activity, where at least a partial chain dissociation should occur. In particular, we believe it is of interest to study a fraction of xanthan whose molecular weight allows the polymer some extent of coiling, with the contour length larger than its persistence length. Moreover, we have obtained some insights on the high-frequency (up to 1 GHz) dielectric behavior of this polymer for evaluation of the influence of the ion fluctuation within the polymer subunits or more generally within some characteristic lengths, in an attempt to clarify the somewhat controversial molecular mechanism for the highfrequency relaxation. The polymer concentration has been varied within the semidilute regime in both conformations, particularly to ascertain whether the order-disorder transition results in some aggregation phenomena as suggested by Hacche et al.5 and by our dynamic light scattering measurements (data
0022-365419512099-0274$09.00/0 0 1995 American Chemical Society
Radiowave Dielectric Properties of Xanthan
TABLE 1: Molecular Parameters of Xanthan Aqueous Solutions Obtained from Light Scattering Measurements. Polymer Concentration Ranging from 0.1 to 1.0 mg/mL, in mom of NaCl, with (hldc), = the Presence of 5 x 0.144 mwg (8.0 f 0.4)x 1P 85 f 5 (4.0f 0.5) x not shown) carried out on the same polymer, in the same experimental conditions. Finally, the low-frequency conductometric behavior of xanthan aqueous solutions has been studied in the absence of added salt, and the results have been discussed in light of the Manning potyelectrolyte theory.l 4 3 This work represents, to our knowledge, the first systematic investigation of the dielectric and conductometric properties of xanthan in aqueous solutions in an effort to gain insight into the behavior of this polyelectrolyte system in terms of dependence on concentration and temperature.
Experimental Section
(A) Material-Sample Preparation and Characterization. Xanthan (Keltrol lot no. 76735A) was purchased from Kelco. The polymer, dispersed in water and stirred for 12 h, was sonicated for 15 min with a procedure previously described el~ewhere.~The solution was centrifuged to separate the particulate, while the supernatant was added with NaCl and with EDTA to a concentration of 1 M and 0.01 M for the two salts, respectively. The solution was then extensively dialyzed against low-conductivity double-distilled water (electrical conductivity lower than 2-3 x cm-l) to remove EDTA and the excess of NaC1. The polymer concentrationduring dialysis was always kept below 1% (w/v). Then the polymer was precipitated with isopropyl alcohol in the presence of 0.1 M NaCI. After redissolution, the fraction investigated in this work was dialyzed against double-distilled water, and it was brought to a concentration, determined by dry weight analysis, of 0.4% (w/ w). This salt-free stock solution from which all samples were prepared was stored at 4 "C. Acetyl and pyruvyl contents were determined by proton NMR spectroscopy at 70 "C with a relaxation delay of 1 s. A 10 mL of stock solution was freeze-dried, dissolved in DzO, and then freeze-dried again, to replace all the exchangeable protons with deuterium. The cycle was repeated three times. The final concentration of the polymer solution was 6 giL. Protons relative to the acetyl and to the pyruvyl groups were detected at 2.4 ppm and at 1.3 ppm, respectively, using (trimethylsily1)propionic acid sodium s a l t 4 (Carlo Erba) as reference. The ratio between the area of the resonance peak relative to acetyl and to pyruvyl with respect to the reference peak gave the degree of substitution (DS) of each group in the repeating unit. The following results were obtained: DS,,1= 1.0;DSp,l = 0.6. The solution to be investigated was converted to acid form by passing it through an ion exchange resin, Amberlite IR 40 (Merck). The pH of the solution was gradually changed by adding known amounts of standarized 0.1 M NaOH, Titrisol (Merck); the degree of neutralization a was varied from a' = 0.2 to a a' = 1 (full neutralization). The molecular parameters of the xanthan samples investigated are reported in Table 1. These parameters have been obtained from light scattering measurements of xanthan solutions at room temperature, with a polymer concentration from 0.1 to 1 g/L, in the presence of 0.005 M NaCl, with a (dnldc)T, = 0,144 m u
J. Phys. Chem., Vol. 99, No. 1, 1995 275
(B) Dielectric Constant Measurements. Dielectric measurements were carired out in the frequency range from l kHz to 10 MHz by means of a Hewlett-Packard Low-Frequency Impedance Analyzer model HP 4192A using a parallel plate dielectric cell with platinum electrodes coated with platinum black to reduce in the low-frequency region the effects of electrcde polarization. Some additional dielectric measurements have been carried out in the frequency range to 1 MHz to 1 GHz, using a Hewlett-Packard Radiowave Analyzer model HP 4191A in connection with a dielectric cell built up with a short section of a precision 50 Q characteristic impedance coaxial cable and connected directly to the meter by means of a precision APC7 connector. The experimental set-up and the calibration procedure based on measurements of standard liquids of known dielectric constant and conductivity are described in detail elsewhere.16 The temperature of the sample was maintained at 20.0 "C within 0.1 "C. The permittivity E' and the conductivity CJ were calculated from the measured quantities, i.e., the magnitude (ZI and the phase angle 8 of the input impedance of the dielectric cell, considering the basic equivalent circuit composed by a capacitor (C) in parallel with a conductor (G), taking into account the series inductance and the stray capacitance. The total dielectric loss E''tot has been determined from the relation
which takes into account the loss due to the dielectric relaxation mechanism (€''diel) and that due to the dc ionic conductivity (a(W--oYEOw).
The observed dielectric spectra have been described by means of different relaxation functions given by the general expression
composed as the superposition of n different relaxation processes, where cs and E , are the low-frequency and the highfrequency limit of the permittivity respectively, z is the relaxation time, and a and B are parameters which take into account, for each dispersion, the deviation from a single time relaxation process. Equation 2 reduces the Debye equation (aj = 0; B, = l), to the Cole-Cole equation (0 < aj < 1; & = l), to the Cole-Davison equation (aj= 0; 0 5 /3j 5 l), or to the Hawrilak-Negami equation (0 < aj 5 1; 0 < ,L?j I l), respectively, according to the values a, and B, which describe symmetric or asymmetric distributions of the relaxation time for each relaxation process j . The parameters entering into eq 2 have been determined by means of a nonlinear least-squares fitting procedure minimizing the error function
where N is the number of data couples ( E ' ( ~ ) , wm) ,the number of adjustable parameters, and S(E')~the standard deviation of the individual data points. (C) Potentiometric Titration. Each sample investigated was titrated at 20 "C with 0.1 M sodium hydroxide (NaOH) delivered to the desired amount by using a calibrated syringe with a capacity of 20 p L and a vernier division of 0.1 pL. The concentration of the polymer, expressed in terms of carboxylic acid groups per unit volume, was determined according to the
276 J. Phys. Chem., Vol. 99, No. 1, 1995
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180 160 w h
140
Y
.d
E 8 P(
100
80 60
1
i o3 o7 o4 1
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frequency v [Hz] Figure 2. Permittivity 6' of xanthan aqueous solutions as a function of frequency for different polymer concentrations, at the temperature of 20 "C: (0)C = 3.5 mg/mL, (M) C = 3.0 mg/mL, (+) C = 2.0 mg/mL, (A)C = 1.0 mg/mL. The pH of the solutions was 7.5. The full lines represent the calculated values with the dielectric parameters derived from the fit of eq 4, as the sum of two contiguous Cole-Cole dielectric dispersions.
moles of NaOH delivered in the solution at the end point of the titration. The pH values were measured with a pH meter model PHM84 (Radiometer), calibrated with standard buffer solutions of pH = 4.01 and pH = 7.01. The degree of neutralization a was determined in the manner described by Zhang et all7 (D) Counterion Activity Coefficient Measurements. Na+ activity coefficient of xanthan solutions in the absence of extemal ionic strength was measured at neutral pH in a thermostated cell, by calibration of an ion selective electrode (Radiometerm G502Na) by means of NaCl standard solutions in connection, as reference, with a calomel electrode (Radiometer, K401). A Radiometer PHM84 was employed as potentiometer. The reproducibility of the calibrations was always within 0.5 mV and the slope of the linear regression of the electromotive force (emf) vs log(mo1arity of Na+) was always larger than 50 mV/log(molarity of Na+) at T = 20 "C in a concentration range of NaCl ranging from 10 to 0.1 mM. Activity coefficient values of xanthan solutions were obtained as the ratio of the concentration of sodium ion detected by the selective electrode and the concentration of the polymer expressed as mol of chargek.
Results (A) Dielectric Behavior of Xanthan Solutions as a Function of Polymer Concentration. The dielectric properties of xanthan in aqueous solutions have been measured in the frequency range 1 lcHz to 10 MHz at different polymer concentrations in the interval from 0.01 to 4 mg/mL. In this set of measurements, the pH of the solution was kept constant at the value of 7.5 and the temperature fixed at 20 "C within 0.1 "C. The dielectric spectra at some selected polymer concentrations are shown in Figure 2. The experimental points E' = A w ) were fitted to a function corresponding to the superposition of two independent ColeCole equations
as is usually done for polyelectrolyte solutions, when the dielectric dispersion extends over more than three decades of frequency. Here, A Eand ~ A Eare ~ the dielectric increments of the two dispersions occumng at relaxation times z1 and z2 with relaxation spread parameters a1 and a2, respectively, and w is the angular frequency of the applied electric field. At the polymer concentration of the solutions employed, the high-frequency permittivity E , should not deviate appreciably from that of the solvent, which in turn can be considered equal to that of the pure water (E, = 80.01 at T = 20 "C). Moreover, we have analyzed the experimental data considering different relaxation functions such as, for example, a single Cole-Cole equation or the superposition of a single ColeCole and Debye function, but marked deviations are observed in the real residuals as a function of frequency, suggesting that eq 4 appears to be the more appropriate dielectric function in order to describe the present result. A quantitative picture of the deviations observed as a consequence of the dielectric function employed in the fitting procedure is shown in Figure 3 for the dielectric spectrum recorded at pH = 7.5 and polymer concentration of 2 mg/mL. As can be seen, the relative residues progressively reduce as the fitting function varies from a single Cole-Cole to a superposition of two Cole-Cole functions. The dielectric parameters, Le., the dielectric increments A E ~ and AQ, the relaxation times t l and z2, and the relaxation time parameters aland a2 as a function of the polymer concentration deduced from the fit to two Cole-Cole dispersions according to eq 4 are shown in Figures 4, 5 , and 6, respectively. (B) Dielectric Behavior of Xanthan Solutions as a Function of pH. The dielectric properties of a xanthan in aqueous solution with a polymer concentration of 1.44 mgmL have been
Radiowave Dielectric Properties of Xanthan
J. Phys. Chem., Vol. 99, No. I , I995 277 Y
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Frequency v [Hz] Figure 3. Real residuals for xanthan solution (C = 1.44 mg/mL) obtained as the difference of the experimental and calculated data with different dielectric relaxation functions: a single Cole-Cole function (ICC); the superposition of a Cole-Cole and a Debye function (ICC 1D); the superposition of two Cole-Cole functions (1CC 1CC).
+
+
60
40
* 0 1
2
3
4
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polyion concentration C [mg/ml] Figure 4. Dielectric increments of the low-frequency (Ael) and of the high-frequency (Aez) dielectric dispersion of xanthan aqueous solutions as a function of polymer concentration, at the temperature of 20 "C. The full lines represent the calculated values according to eqs 7 and 9 for a semidilute regime. The pH of the solvent is 7.5.
0
t
0.6 0
1
2
3
4
5
polyion concentration C [mg/ml] Figure 6. Spread relaxation time parameters of the low-frequency (al) and high-frequency (az)dielectric dispersions of xanthan aqueous solutions as a function of polymer concentration at the temperature of 20 "C. The full lines represent a polynomial fit to guide the eye only.
all the samples investigated. The electrical conductivity u of the same solutions at the same selected values of pH is shown in the inset of Figure 7. In this case, the curves do not display any change with the frequency, owing to the high dc ionic conductivity of the samples investigated. In fact, the conductivity contribution due to the dielectric relaxation
a,,, = OEOE'r,e,
1 0
0.7
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1
2
3
4
5
polyion concentration C [mg/ml] Figure 5. Relaxation times of the low-frequency (tl) and the highfrequency (72) dielectric dispersions of xanthan aqueous solutions, as a function of polymer concentration at the temperature of 20 "C. The full lines represent the calculated values according to eqs 6 and 8, respectively, for a semidilute regime.
measured in the frequency range from 1 kHz to 10 MHz, varying the pH of the solution from 2.5 to 9.5. Typical dielectric spectra of the permittivity E' of 1.44mg/mL of xanthan solution at four selected values of pH are shown in Figure 7. Similar spectra, showing a well-pronounced dielectric dispersion occurring at least over four decades of frequencies, have been obtained for
calculated at the relaxation frequency of the order of 2 x lo4 Hz and with err = 15 is of the order of 1 i (2 x C2-l m-l, 3 orders of magnitude lower than that due to the dc ionic conductivity and hence too small to be observed within the accuracy of our experimental set-up. The dielectric parameters, i.e., the dielectric increments A E ~ and AEZ,the relaxation times z1 and z2, and the relaxation time parameters a1 and az characterizing the two Cole-Cole dielectric dispersions, according to eq 4 as a function of the pH of the solution are shown in Figures 8, 9, and 10, respectively. (C) Full Dielectric Spectrum in the Frequency Range from 1 lrHz to 1 GHz. As stated above, at some selected polymer concentrations, we have extended the dielectric measurements up to 1 GHz, over six decades of frequency, to completely define in a wide frequency interval the dielectric behavior of these solutions. A typical spectrum, for the polymer concentration of 4 mg/mL and pH = 7.5, at the temperature of 20 OC is shown in Figure 11. As can be seen, in the whole frequency range, the deconvolution of the spectrum yields clearly the presence of two contiguous dielectric dispersions, and no other dielectric dispersion occurs before that of the aqueous phase at microwave frequencies18 (the relaxation frequency of pure water is Y = 17 GHz at 20 "C). Furthermore, Figure 11 shows the very good agreement between the permittivity values deduced from the two different experimental set-ups employed in the overlapping region at about 10 MHz. (D) Effect of Temperature on the Dielectric Behavior of the Xanthan Solutions. Low-Frequency Region of the Dielectric Spectrum. The dielectric properties of xanthan solutions of different polymer concentrations, between 5 x and 4 mg/mL, have been measured in the frequency range from 1 kHz to 10 MHz, at three different temperatures, 20, 41, and 75 "C. In this frequency range, the dielectric dispersion is almost completely resolved and both the low-frequency and the high-frequency relaxation mechanisms can be observed. Some typical spectra of xanthan solutions at some selected polymer
278
Bordi et al.
J. Phys. Chem., Vol. 99, No. I , 1995
140
130 120
110
frequency v [Hzl
100 90
frequency v [Hz] Figure 7. Permittivity e' of xanthan aqueous solutions as a function of frequency for different values of pH, at the temperature of 20 "C: (A)pH = 2.81, (+) pH = 3.11, (H) pH = 3.51, (0)pH = 4.68. The polymer concentration is C = 1.44 mg/mL. The full lines represent the calculated values according to eq 4, where the dielectric dispersion over the whole frequency interval is modeled with two Cole-Cole dielectric dispersion functions. The inset shows the behavior of the electrical conductivity u. Owing to the high dc ionic conductivity, the conductivity contribution due to the dielectric relaxation, u,j,,l= WEOE", cannot be detected within the accuracy of the measurements and the curves do not show any dependence on the frequency.
4
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2
3
4
5
6
7
8
9
10
PH
2
3
4
5
6
7
8
9
1
0
PH
Figure 8. Dielectric increments of the low-frequency (Ae1 (0))and high-frequency (Aez (H)) dielectric dispersions as a function of pH for xanthan aqueous solution, for a polymer concentration of 1.44 mg/mL and at the temperature of 20 "C. The full lines are calculated according to the counterion fluctuation model on the basis of eqs 10 and 13.
Figure 9. Relaxation times of the low-frequency (TI)and the highfrequency (TZ) dielectric dispersion as a function of pH for xanthan aqueous solution, for a polymer concentration of 1.44 mg/mL and at the temperature of 20 "C. The dotted lines are drawn to guide the eye, only.
concentrations for two different temperatures (41 and 70 "C) are shown in Figure 12. In aqueous solution, xanthan undergoes a temperature-driven confotmationaltransition, depending on various physicochemical parameters such as polymer molecular weight, pH, and added salt concentration. The transition temperature defines two different conformations of the polyion, a double-stranded ordered form at lower temperature and a complete or partial melting of the double helix in the disordered fotm. Under the experimental conditions employed, the transition temperature detected, for example, by means of optical rotatory activity is about 40 "C. As can be seen in Figure 12, at temperatures close to or higher than that of the transition temperature, the dielectric increment decreases as the polymer concentration is increased, this behavior being opposite to that observed at the temperature of 20 "C, well below the transition temperature. This is strong evidence suggesting that the transition is associated with a severe rearrangement of the molecular structure and raising the possibility of yielding information on the molecular conformation of xanthan molecules from dielectric measurements.
(E) Effect of Temperature on the Dielectric Behavior of the Xanthan Solutions. High-Frequency Region of the Dielectric Spectrum. We have investigated the dielectric behavior of the xanthan solutions at two different temperatures, T = 20 "C and T = 75 "C, in the frequency range from 1 MHz to 1 GHz for different polymer concentrations, in the interval from 0.1 to 4.0 mg/mL. Some typical dielectric spectra at some selected polymer concentrations are shown in Figure 13. As stated above, xanthan undergoes an order-disorder conformational change driven by the temperature consisting in a partial melting of its double helix and this behavior should be reflected in the dielectric properties. (F) Conductometric Behavior of the Xanthan Solutions. The electrical conductivity of xanthan aqueous solutions in the absence of added salt has been measured in the frequency range from 1 kHz to 10 MHz, at the temperature of 20 "C. The pH of the solution was varied from pH = 2.5 to pH = 9.5. Figure 14 shows the behavior of the low-frequency electrical conductivity of xanthan solutions as a function of pH.
J. Phys. ?hem., Vol. 99, No. I, 1995 279
Radiowave Dielectric Properties of Xanthan
described by the following empirical relationships
Aei -_-
cp
0.7
t .t'
PH Figure 10. Spread of the relaxation times of the low-frequency (al) and the high-frequency (a2) dielectric dispersion of xanthan aqueous solution as a function of pH at the temperature of 20 "C. The polymer concentration is C = 1.44 mg/mL,. The full lines are the spline curve
through experimental data drawn for visual purposes, only. I
C=4.0 mg/ml
pH = 7.5
" I 120
&
100
80
1
4
\
1 2 I
103
104
(5)
where Ai and Bi are two constants taking into account the intermolecular interactions and Cp the polymer concentration/ L. In a similar way, the dependence of the relaxation times on the polymer concentratiw is given by the following expressions z. =
.-c .-s
Ai 1 +BiCP (i = 1 , 2 )
105
io6
107
108
109
Frequency v [Hz] Figure 11. Full dielectric spectrum of a xanthan solution (C = 4.0 mg/mL, pH = 7.5) at the temperature of 20 "C as a function of frequency in the full range investigated from 1 kHz to 1 GHz. The full line represents the measured value of the aqueous phase.
Discussion The radiowave dielectric dispersions generally occurring in linear polyelectrolyte aqueous solutions in the frequency range from 0.1 kHz to 10 MHz are attributed to the polarization of the ionic atm~sphere'~ consisting in a non-uniform distribution of counterions along the whole polyion chain. These dielectric dispersions are composed of two independent contributions, the f i s t of which is due to a counterion fluctuation along the whole polyion chain and the second one is characterized by a counterion redistribution within an appropriate correlation length. We have extensively studied the dielectric behavior of xanthan aqueous solutions in a wide frequency range and in the following we will discuss the main results we have obtained. The effect of the polymer concentration in the range up to 4 mdmL has been investigated at the temperature of 20 "C and pH = 7.5, where the polyion is almost in a fully ionized conformation. Some typical spectra are shown in Figure 2. The dielectric parameters obtained from the deconvolution of the spectra into two contiguous Cole-Cole dielectric dispersions show that the low-frequency dielectric increment A E increases ~ linearly with the polymer concentration and A E remains ~ approximately constant, whereas the relaxation time t 2 shows a more or less pronounced decrease with the polymer concentration. The relaxation time t l remains approximately constant to values of about s. As pointed out by Mandel,20 the concentration dependence of the dielectric increments can be
Ci
1
+ DiCP(i = 1 , 2 )
(6)
In the present case BIG, > 1; DlC, > 1. The decrease of a1 and a2 with increasing polymer concentration is closely related to an entanglement effect of polyions due to the occurrence of a semidilute regime. These concentration dependencies of the dielectric parameters of the observed dispersions are quite analogous to what is found with different synthetic polyelectrolytes2' and low-molecular-weight DNA.22 In the case of charged linear polyions with no added salt, even at moderate polymer concentrations, deviations from a dilute regime occurs and the properties of both the observed dielectric dispersions are markedly affected by the ionic atmosphere arising from tightly bound counterions. Recently, Ito et al.23have studied the crossover behavior in the highfrequency dielectric relaxation of linear polyions in dilute and semidilute regimes and have pointed out that the high-frequency dielectric increment A E ~due , to localized fluctuation of loosely bound counterions within an appropriate correlation length lo, should be, in the semidilute regime, independent of the polymer concentration C and of the polymer molecular weight M,, i.e.
Moreover, the relaxation time z2 of the high-frequency dielectric dispersion should display a dependence as
z2 = c-IM0, As far as the high-frequency dielectric dispersion is concerned, the results shown in Figures 4 and 5 clearly demonstrate that, at polymer concentration higher than 0.5 mdmL the dielectric increment does not depend on the polymer concentration and the relaxation time varies inversely on the polymer concentration, Le., a semidilute regime prevails. As far as the lowfrequency dielectric relaxation is concerned, this dispersion must be ascribed to fluctuations of tightly bound counterions along the polymer chain and its dielectric dispersion is characterized by a dielectric increment given by
Ael
CPL2
(9)
where f is the fraction of counterions strongly bounded to the polyion charged groups, N the total number of charged groups in the polyion, and L a parameter characterizing the effective length over which counterions fluctuate, Le., a characteristic length of the polymer chain depending on the polymer structure and conformation assumed in the aqueous solution. In the regime of dilute solution, this equation, which contains the key parameters of the counterions fluctuation model proposed by Van der Touw and M a ~ ~ d eattributes l , ~ ~ to the parameter L the meaning of the radius of gyration of (Ri)"2 of the polymer defined as
Bordi et al.
280 J. Phys. Chem., Vol. 99, No. 1, 1995
-0
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Frequency v [Hz] Figure 12. Permittivity e' of xanthan solutions at different polymer concentrations as a function of frequency in the low-frequency range from 1 kHz to 10 MHz at two different temperatures: T = 41 "C, (+) 1 mg/mL, ( 0 )2.0 mg/mL, (W) 3.5 mg/mk T = 70 "C, (6)1 mg/mL, (0)2.5 mg/mL, (W) 3.0 mg/mL.
where ql is the distance of the subunit j to the center of mass of the polyion. On the other hand, where the polyions in rod-like confopation are entangled with each other and a different, semidilute regime prevails, we could assume for A61 the same basic equation by substituting the parameter L with some other characteristic length of the polyion. In the following, in order to account for the low-frequency dielectric dispersion observed in the xanthan solution, we shall find that this length L must be identify with the persistence length. At this stage, we point out that, when the ionic character of the polymer, i.e., its charge density, does not change, eq 9 predicts a linear dependence on the polymer concentration C. As can be seen in Figure 4,this requirement is fully verified. These findings reveal that, at the polymer concentration employed, a semidilute regime occurs and that the dielectric properties can be understood in terms of counterions fluctuation whose movements are further restricted by the interactions between different polyions over a characteristic correlation length lo, defined, to a first approximation, as the average distance between adjacent polyions. The influence of the polyion charge density on the lowfrequency dielectric behavior of xanthan solution can be properly
observed in the measurements carried out at a fixed polymer concentration, as a function of pH. In this case, the ionic character of the polymer changes since a change in the pH of the solvent induces a change in the degree of ionization of the polymer which, in turn,induces a change in the average distance d between ionized groups on the polyion chain. We shall discuss in detail the results obtained in the dielectric measurements of xanthan solution, 1.44 mg/mL, at different pH, from pH = 2.5 to pH = 9.5. As far as the low-frequency dispersion is concerned, the dielectric increement ALE^ can be written as24925
where y is the ratio of the effective electric field acting on the polyion to the average field in the system, N the Avogadro number, C, the polyion concentration in [monomoUm3],a the degree of ionization, KBT the thermal energy, zp, the valence of the polyion groups, e the electronic change, and EO the dielectric constant of free space. The term a(1 - a),added to the factor fa,takes into account that, at a moderate degree of ionization (around a = OS), the fluctuation of protons among the carboxyl groups is not negligible.25 In the above equation, the key parameter is the fraction f of counterions strongly bounded to the polyion. If the Manning counterion condensation theory is assumed,l4 this fractionfis defined by
Radiowave Dielectric Properties of Xanthan
J. Phys. Chem., Val. 99, No.
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Frequency v [Hz] Figure 13. High-frequency dielectric spectrum of xanthan solutions at different polymer contents as a function of frequency, from 1 MHz to 1 GHz, at two different temperatures: T = 20 "C, (A)C = 0.8 mg/mL, (0)C = 1.6 mg/mL, (m) C = 2.7 mg/mL, (+) C = 4.0 mg/mL; T = 70 "c, (A) C = 1.0 mg/mL, (0)C = 2.0 mg/mL, (0)C = 4.0 mg/mL. The pH of the solutions was 7.5. , "
conformation at low pH (pH = 2 t 2.5) to a full charged conformation at pH higher than 5. This means that the charge density parameter 6 varies from 6 = 0.124 at pH = 2.76 (a 0.06) to 6 = 2.42 at pH = 5.84 (a 1). At pH values higher than 3.3, the charge density parameter 6 exceeds the critical value
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3.0
3.5
4.0
4.5
5.0
5.5
PH Figure 14. Low-frequency electrical conductivity of xanthan solution as a function of pH of the solvent, at the temperature of 20 "C. The monomoYL. The full line polymer concentration is 0.73 x represents the calculated values according to eqs 17 and 18.
where z, and zp,are the valences of the polyion charged groups and counterions, respectively, and 6 is the charge parameter given by the ratio of the B j e r " length ( 1 = ~ e 2 / 4 n € ~ K ~toT ) the effective distance between two charged groups on the polyion chain, Le.,
where d in the distance in the full ionized conformation and a the degree of ionization. To evaluate the fraction f of bounded counterions, the structure of the polymer in solution must be known. For the polyion in the double-helix with five saccharide residues in the helix pitch of 4.7 nm and an average number of carboxylate groups per residue equal to 1.6, the distance between two charged groups in the fully ionized state is d = 0.294 nm. As the ionic character of the polymer is changed by adding the titrant to the xanthan solutions, the degree of ionization a increases and the polymer chain changes from an uncharged
beyond which, according to the Manning counterion theory, counterion conden~ation'~ occurs. On the other hand, if a polymer in single-helix conformation is assumed, the distance between two charged groups in the fully ionized state is d = 0.588 nm and consequently the charge density parameter varies from 6 = 0.062 at pH = 2.76 (a 0.06) to 6 = 1.21 at pH = 5.84 (a 1) and the counterion condensation occurs at pH higher than 4.45. The degree of ionization a can be calculated from the measured pH of the solution27using the following equation"
-
-
a=a'-t-10-pH CP where a' is the degree of neutralization determined from the titration with NaOH and the concentration of free hydrogen H+ ions evaluated from the pH measurements. In the context of the Manning condensation model and in the limit of high dilution, assuming for the characteristic length L a radius of gyration of about (R;)'" = 85 nm, as determined from light scattering measurement and a fraction of condensed counterions deduced from eqs 11 and 12, we are unable to account for the observed behavior of the dielectric increment A61 as a function of pH. Owing to the entanglement of the polymer and the Occurrence of a semidilute regime, the Manning theory cannot be applied and in particular the fraction f of condensed counterions does not vary with the degree of ionization according to eqs 11 and 12. Incidentally, we note that this disagreement occurs either if the single-helix or the double-helix conformations are considered. In the semidilute regime, eq 10 does not hold exactly since polyion-polyion interactions modify the distance over which
282 J. Phys. Chem., Vol. 99, No. 1, 1995
Bordi et al.
1.0,
2
I
0.2 0.0
1 I 0
1
2
3
4
5
6
7
Polyion concentration C x 10-3 [monomol/l] Figure 15. Sodium activity coefficient as a function of the polymer concentration at the temperature of 20 "C. The pH of the solution was pH = 7.5. The measurements were carried out by means of a ion (Na+) selective electrode calibrated with standard NaCl electrolyte solutions and of a reference calomel electrode. counterions fluctuate and the dielectric relaxation extends over a polyion subunit, whereas the cooperative effects of charged group interactions on the counterion condensation are largely reduced. On the other hand, we stress that it is possible to account for the observed values of the dielectric increment if a fraction of counterions will remain in the neighboring of the charged group of the polyion and this fraction does not change with the degree of ionization, Le., each charged group behaves independently of other groups on the polymer chain. If this is the case, it would be expected for the fraction5 a value largely independent of the pH of the solution. Moreover, we have assumed for L the persistence length6%7 with a value of L = 1.2 x cm. As can be seen in Figure 8, with f = 0.47, the calculated values of the low-frequency dielectric increment A E ~ are in very good agreement with those measured over the entire range of the pH values investigated. In terms of the Manning theory, we would expect that an increase of the polymer ionization should be accompanied by an increase in the counterion condensation up to f = 0.59 for the double-helix structure. Experimentally, we find a value approximately independent of the degree of ionization. A first comment to this result is that the Manning condensation theory does not apply to this polymer, probably due to its deviation form an infinitely thin charged line as assumed in the model, and consequently counterions behave, in the present case, freely or more freely than that predicted by eq 10. It must be noted, however, that in a wide variety of polyelectrolyte systems, including bulky polyions, the Manning model is accurate enough to predict the experimental findings. This point should be further investigated. To gain further support for the magnitude of the counterion condensation in this system, a potentiometric determination of Na+ activity with a selective electrode has been carried out. Figure 15 shows the Na+ activity coefficient as a function of the polymer concentration for a Xanthan solution at pH = 7.0. As can be seen, a value of about Y N ~ += 0.45 is obtained, in very good agreement with the value for the fraction f of condensed counterions used in eq 10. It must be noted, moreover, that this value is considerably lower than that predicted by the Manning theory that, for E = 2.42 corresponding to the polymer in fully ionized double-stranded conformation, provides for the fraction f a value of
- 0.59
f=1---
independent of the polymer ionization. This value corresponds to that measured by means of light scattering and viscosity measurements carried out on xanthan in double-stranded helix conformation and dissolved in 0.1 M aqueous sodium ~ h l o r i d e . ~ ~ ~ The independence of the persistence length of the degree of ionization is based on the marked stiffness of the polymer chain, whose increment due to electrostatic interactions as a consequence of the change in the ionization is negligible. In fact, with a persistence length Lp of the order of 120 nm, the contribution due to electrostatic interaction2*
ZP,ZP,(
Some further comments are in order. In these calculations, we have assumed a persistence length of 1.2 x cm,
L
=- 1
4 w 2 where KD is the Deybe screening length is of the order of 10 nm, well below that of the intrinsic persistence length. As far as the high-frequency dispersion is concerned, the dielectric increment Ac2 of the process attributed to localized fluctuation of loosely bound counterions within distances of the order of lo is given byz3
where LC is the polymer contour length. For the sample investigated, with a molecular weight of 8 x lo5 g/mol considering a double helical repeating unit with a molecular weight of 2 x lo3 g/mol, i.e., twice the molecular weight of the single-stranded repeating unit, Lc assumes a value of 4.1 x cm. The above expression depends on the degree of ionization through the fraction of loosely bound counterions which, in turn, in the semidilute regime, is proportional to the polymer concentration (C,). This particular dependence makes he2 independent of the polymer concentration. Figure 8 shows the calculated values of A E of ~ the xanthan solution at C = 1.44 mg/mL as a function of the pH of the solvent, compared with those experimentally observed. As can be seen the agreement is quite good, over the entire interval of the ionization of the polymer. As far as the relaxation times of both the dielectric dispersions are concerned, the counterion fluctuation theories for polymers in dilute regime state that these quantities are given, to a first approximation, by
and 12
LO
z2 = -
?ZK,TU
where LQ is the end-to-end polyion length, a the radius of the polymer chain, 7 the viscosity of the solvent, and u the mobility of the associated counterion and 10 the distance over which counterions can fluctuate. As pointed out by It0 et al.,23this distance in the semidilute regime can be considered as an average distance between different polyions. For a cylindrical cell model in the semidilute regime, assuming 10 = ~/(zLJV,)*~, with N p the polymer concentration expressed as the number of polyions per unit volume, T,J = 1 c p at T = 20 "C,u = 3 x loll m/s N, a = 12 A, and the end-to-end distance defined as
Radiowave Dielectric Properties of Xanthan
with 4 = 1.2 x cm and LC = 4.1 x cm, eqs 14 and 15 yield for the relaxation times z1 and z2 values of the order of and 2 x lo-* s, respectively, which are in good agreement with those experimentally observed. Taking into account that several assumptions have to be made, these values are in reasonable agreement with the corresponding findings obtained from the dielectric increments A E and ~ AE~ and this fact can be considered as an indication of the selfconsistency of the charge fluctuation model. At temperatures higher than 40 "C, where at least a partial melting of the double-helix structure occurs, the dielectric properties of xanthan solutions are characterized by a unusual feature, evidenced by the behavior of the dielectric increment as a function of the polymer concentration. We have measured the permittivity 6' of xanthan solutions in the frequency range from 1 lcHz to 10 MHz, at two different temperatures, 40 and 75 "C, at various polyion concentration from 0.2 to 4.0 mg/ mL. We observed that, at the higher polymer concentration, the dielectric increment of the low-frequency dielectric dispersion decreases as the concentration is increased. This particular behavior can be accounted for by a different aggregation process which gives rise to a structure of increasing overall size as the polymer concentration increases. These findings are in qualitative agreement with the picture proposed by Hacche et ala5Close to the melting temperatures, but above the room temperature, the chains of the double-stranded structure are not completely separated and, at the same time, they are not longer in register, Le., they are spatially mismatched. As a consequence, a large number of bonding sites are formed, thus making possible interand intrachain reversible aggregation. The tendency toward this association as well as the temperature at which the process occurs should be dependent on the molecular weight and on the stiffness of the chains. This process is enhanced as the polymer concentration is increased. A similar behavior has been observed by Gupta29*30 who studied the aggregation process of poly(?-benzyl-L-glutamate) in dioxane as a function of the polymer concentration. He found that the dielectric increment normalized to the polymer concentration as a function of concentration presents a maximum, whose position depends on the molecular weight. Recently, electron micrographs by Stokke et showed the existence of multichain clusters in xanthan samples obtained in "dissociative" preparations. Although conditions and sample preparations used in that work differ considerably from ours, an aggregation process, next to the partial melting of the doublehelix structure and caused by side-by-side pairing of singlestranded segments, leads to the formation of a three-dimensional network, whose extension increases with the polymer concentration. Hacche et al.5 discussed the temperature behavior of a xanthan fraction studied by the static light scattering technique with a molecular weight of 2 x lo5 g/mol. In their measurements, as the temperature was raised to allow for reversible dissociation of the double-stranded chains, the light scattering data showed a behavior compatible with the presence of clusters consisting of more than single-stranded chains together with partially dissociated double-stranded molecules. The interpretation of these measurements was made difficult by the large increase of Donnan contributions to the second virial coefficient at temperatures higher than 25 "C. Our permittivity data are in qualitative agreement with Hacche et al. findings5 and support an aggregation mechanism of the kind discussed more than a decade ago by Shibata and S c h d 2 on a statistic basis. In their
J. Phys. Chem., Vol. 99, No. I , 1995 283
model, the possibility of aggregation in a narrow range of temperature is related to the intrinsic stiffness of the conformations adopted by the triple helix of collagen and the double helix of DNA. Both these biopolymers have a persistence length of the same order of magnitude of xanthan. Network formation was also predicted by Higgs et al.33on the basis of the helix-coil transition for an ensemble of infinite chains at an intermediate, lower temperature than the melting temperature. Finally, we will briefly discuss the results of the lowfrequency electrical conductivity measurements we have performed. In salt-free solutions and in the dilute regime, the conductivity behavior of xanthan solutions can be described in light of the polyelectrolyte theory, depending on the value of the charge density parameter 5 by the expression^^^*^^
where the electrical conductivity u is expressed in 51-' cm-', the polymer concentration C, in monomolll, the equivalent conductances 2; and A, of the counterions and polymer, respectively, in 51-l cm-l equiv-'. The calculation of A, in the two above conditions, in the absence and in the presence of counterion condensation, yields36
(20) for
1
e =. -and 5 < -1%, lib11
1
I
respectively. The other symbols
have their usual meaning and the strange-looking numerical factors appearing in the above formulae originate in the conversion factors to cgs electrostatic units. Before coming to a comparison with our experimental data, we want to point out that Jones et al." have recently analyzed conductivity measurements of salt-free xanthan solutions, at a polymer concentration of C, = 3.3 x M, on the basis of the Manning polyelectrolyte-conductivity theory assuming a charge-spacing of (0.58 f 0.04) nm, which corresponds to a single-helix conformation, in contrast with different experimental evidences that support a double-helix ordered structure. Moreover, these authors suggest the presence of a transition between the single helix to the random coil as the temperature is increased beyond 35-40 "C. Our measurements, shown in Figure 14, have been carried out at the temperature of 20 "C for different values of the pH of the solvent, resulting in a different ionization of the polymers chain. The calculation of the expected values on the basis of the above equations depends on the conformation assumed by the polymer in solution and in particular on the distance between
284 J. Phys. Chem., Vol. 99, No. 1, 1995
charges which defines the parameter E and its changes at different degrees of ionization. Moreover, owing to the simultaneous presence of different counterions, Le., H+ and Na+ in the neighboring of each group, the equivalent conductance of the polyion A, has been obtained from eqs 19 and 20 by weighing the different contributions according to the relative counterion concentrations. Within this context, we want to stress that in order to describe the full behavior of the conductivity as a function of pH, we must assume a distance between two adjacent charges of d = 0.605 nm. As can be seen in Figure 14 with this value for d , the agreement with the experimental data is quite good. It must be noted that d = 0.605 nm is in agreement with the value of d = (0.58 f 0.04) nm used by Jones et al.,” thus providing support for a single-helix conformation. This results contradicts those derived from the dielectric measurements and the results obtained by various authors with different experimental methods, where a double-stranded conformation seems highly probable. The reason for this discrepancy between conductometric and dielectric measurements is not yet understood. A fist comment is in order, Le., the Manning conductivity theory cannot be applied directly, since the polyion conformation deviates from that of a thin charged line and secondly, in semidilute regime, polyions associate to form regions where a branched network structure prevails. These aspects conceming the link between the dielectric and conductometric measurements must be further investigated by means the addition of simple salt in order to modulate the effect of counterion condensation in excess of ions. This problem deserves a more detailed treatment.
Acknowledgment. This work was supported by “Minister0 dell’universita e della Ricerca Scientifica e Tecnologica” [MURST] and “Consiglio Nazionale delle Ricerche”, Italy. Sample preparations and light scattering measurements were performed in the Laboratory of Dr. D. A. Brant, University of California, Imine. References and Notes (1) Jansson, P. E.; Kenne, L.; Lindberg, B. Carbohydr. Res. 1975,45, 275. (2) Melton, D. L.; Mindt, L.; Rees, D.; Sanderson, G. R. Carbohydr. Res. 1976, 46, 245.
Bordi et al. (3) Ress, D. A. Pure Appl. Phys. 1981, 53, 1. (4) Norton, I. T.; Goodall, D. M.; Moms, E. R.; Rees, D. A. J. Chem. Soc., Chem. Commun. 1980, 545. (5) Hacche, L. S.; Washington, G. E.; Brant, D. A. Macromolecules 1987, 20, 2179. (6) Paradossi, G.; Brant, D. A. Macromolecules 1982, 15, 874. Sato, T.; Norisuye, T.; Fujita, H. Polym. J . 1984,16,341.Liu, W.; Norisuye, T. Biopolymers 1988, 27, 1641. (7) Sato, T.; Norisuye, T.; Fujita, H. Macromolecules 1984,17, 2696. ( 8 ) Rinaudo, M.; Milas, M. Biopolymers 1978, 17, 2663. (9) Dentini, M.; Crescenzi, V.; Blasi, D. Int. J . Biol. Macromol. 1984, 6, 93. Christensen, B. E.; Knudsen, K. D.; Smidsrod, 0.; Kitamura, S.; Takeo, K. Biopolymers 1993,33, 151. Christensen, B. E.; Takeo, K.; Kuge, T.; Stokke, B. T. Biopolymers 1991, 31, 1243. (10) Paoletti, S.; Cesaro, A.; Delben, F. Carbohydr. Res. 1983, 123, 173. (11) Jones, S. A.; Goodall, D. M.; Cutler, A. N.; Norton, I. T. Eur. Biophys. J. 1987, 15, 185. (12) B o d , F.; Cametti, C.; Paradossi, G. J . Phys. Chem. 1992,96,8 194. (13) Bordi, F.; Cametti, C.; Paradossi, G. J . Phys. Chem. 1992,96,913. (14) Manning, G. S. Q. Rev. Biophys. 1978, 11, 179. (15) Manning, G. S. Ann. Rev. Phys. Chem. 1972, 23, 117. (16) Takashima, S.; Casaleggio, A.; Giuliano, F.; Morando, M.; Arrigo, P.; Ridella, S. Biophys. J. 1986, 49, 1003. (17) Zhang, L.; Takematsu, T.; Norisuye, T. Macromolecules 1987,20, 2882. (18) Hasted, J. B. Aqueous Dielectrics;Chapman & Hall: London, 1973. (19) Mandel, M.; Odijk, T. Ann. Rev. Phys. Chem. 1984, 35, 75. (20) Mandel, M. Ann. N.Y. Acad. Sci. 1977, 303, 74. (21) Miiller, G.; Van Der Touw, F.; Zwolle, S.; Mandel, M. Biophys. Chem. 1974, 2, 242. (22) Vreugdenhil, T.; Van Der Touw, F.; Zwolle, S.; Mandel, M. Biophys. Chem. 1979, I O , 67. (23) Ito, K.; Yagi, A.; Ookubo, N.; Hayakawa, R. Macromolecules 1990, 23, 857. (24) Van Der Touw, F.; Mandel, M. Biophys. Chem. 1974,2,218; 231. (25) Paoletti, S.; Van Der Touw, F.; MGdel, M. J . Polym. Sci.: Polym. Phys. Ed. 1978, 16, 641. (26) Moorhouse, R.; Walkinshaw, M. D. In Extracellular microbiol polysaccharides; Sandford,P. A., Lankin, A,, Eds.;ACS Symposium Series 45; American Chemical Society: Washington, D.C., 1977; p 90. (27) Penafiel, L. M.; Litovitz, T. A. J . Chem. Phys. 1992, 96, 3033. (28) Odijk, T. Macromolecules 1979, 12, 638. (29) Gupta, A. K. Biopolymers 1976, 15, 1543. (30) Marchal, E. Ann. N.Y. Acad. Sei. 1977, 303, 123. (31) Stokke, B. T.; Smidsred, 0.;Elgsaeter, A. Biopolymers 1989, 28, 617. (32) Shibata, J. H.; Schurr, J. M. Biopolymers 1981, 20, 525. (33) Higgs, P. G.; Ball, R. C. J . Phys. (Fr.) 1989, 50, 3285. (34) Manning, G. S. J . Phys. Chem. 1981, 85, 1506. (35) Manning, G. S. J. Phys. Chem. 1975, 79, 262. (36) Manning, G. S. Biopolymers 1970, 9, 1543.
