7148
J. Phys. Chem. 1996, 100, 7148-7154
Conformational Changes of Xanthan in Salt-Free Aqueous Solutions: A Low-Frequency Electrical Conductivity Study F. Bordi,† C. Cametti,*,‡ and G. Paradossi§ Sezione di Fisica Medica, Dipartimento di Medicina Interna, and Dipartimento di Scienze e Tecnologie Chimiche, UniVersita’ di Tor Vergata, Rome, Italy, INFM “Istituto Nazionale di Fisica della Materia”, Rome, Italy, and Dipartimento di Fisica, UniVersita’ di Roma “La Sapienza”, Rome, Italy ReceiVed: October 19, 1995; In Final Form: February 1, 1996X
The low-frequency electrical conductivity of xanthan in salt-free aqueous solutions has been measured in a wide temperature range, from 5 to 70 °C, covering the interval where a thermal-induced conformational transition in the polymer chain occurs. The polymer concentration has been varied up to 10 mg/mL, from the semidilute region, where polymer chains are partially entangled with each other, to the concentrated region. Deviations from the dilute regime and the conformation of the polyion in a double-stranded helix with a finite radius make the counterion condensation of the Manning model for highly charged polyelectrolytes inapplicable. On the other hand, on the basis of the present conductivity data and of our previous measurements of radiowave dielectric relaxations of the same polymer solution (J. Phys. Chem. 1995, 99, 274) we find that a fraction of counterions, although different from that predicted by Manning, will condense, altering the value of the conductivity of the whole solution. This condensation is largely independent of the polymer chain structure and, to a first approximation, of polyion concentration, the fraction of free counterions assuming a value that increases with temperature from about f ) 0.53 at 20 °C to about f ) 0.75 at 70 °C. With these values and considering an appropriate conductivity expression consisting of additive contributions, i.e., polyion and free counterions, according to the suggestions of the Manning theory, a reasonable agreement with the experimental data can be found.
Introduction Xanthan is an ionic polysaccharide produced in the fermentation broths of the bacterium Xanthomonas campestris, whose structure has been well established.1,2 It consists of a linear cellulosic backbone, i.e., 1f4 linked β-D-glucose residue, with a three-sugar side chain attached to every second glucose of the backbone. In salt-free aqueous solutions or in aqueous salt solutions of low ionic strength, xanthan in a dilute regime undergoes a thermally induced conformational change consisting in a complete or partial melting of its double-helix structure.3,4 Although the details of this transition are not completely understood, there is much experimental evidence to suggest that the polymer conformation varies from a rigid double-stranded chain at room temperature to a less ordered structure derived from a partial or complete dissociation of the strands at higher temperatures, giving rise to clusters involving different numbers of polymer chains. This thermal-induced transition has been recently questioned by Jones et al.,5 who suggested, on the basis of low-frequency electrical conductivity measurements, that the conformational change concerns a single-helix structure at lower temperatures that evolves toward an extended random coil, at higher temperatures. More recently, we have performed a systematic investigation6 of the dielectric and conductometric properties of xanthan * To whom correspondence should be addressed. Fax: +39 6 4463158. E-mail:
[email protected] † Sezione di Fisica Medica, Dipartimento di Medicina Interna, Universita ´ di Tor Vergata, and INFM. ‡ Dipartimento di Fisica, Universita ´ di Roma “La Sapienza”, and INFM. § Dipartimento di Scienze e Tecnologie Chimiche, Universita ´ di Tor Vergata, and INFM. X Abstract published in AdVance ACS Abstracts, April 1, 1996.
0022-3654/96/20100-7148$12.00/0
aqueous solutions in the semidilute regime, with a polymer concentration from 0.1 to 1.0 mg/mL. Our results showed a very complex phenomenology, depending on the polymer concentration, temperature, and degree of ionization. These findings required a careful interpretation, since the dielectric measurements and the conductivity measurements showed apparent contradictory behavior. Whereas, at temperatures higher than 30-35 °C, the low-frequency dielectric increment decreases as the polymer concentration is increased, suggesting that an aggregation process involving a partial separation of the double-stranded structure occurs, the conductivity measurements at a temperature of 20 °C, well below that of the transition temperature, are apparently well accounted for, on the basis of the Manning theory, with a distance of the adjacent charged groups along the polymer chain of b ) 0.605 nm. This value is in good agreement with the value of b ) 0.58 ( 0.04 nm used by Jones et al.,5 corresponding to that of a single-helix configuration. To clarify this point and to give a full description of the conductometric behavior of these solutions at moderate to high polymer concentration (in the semidilute and concentrated regime), we have undertaken an extensive low-frequency electrical conductivity investigation of xanthan aqueous solutions in a wide temperature range, from 5 to 70 °C, and for different polymer concentrations, from 0.6 to 10 mg/mL, to cover the semidilute and concentrated regime. From a phenomenological point of view, our results indicate that the increase of conductivity with temperature can be described with two linear dependencies of different slopes, below and above a particular temperature Tc at which a conformational change occurs. This temperature is found to be in the range from 30 to 35 °C, in very good agreement with the value of Tc ) 33 ( 1 °C obtained by Jones et al.5 for saltfree solutions of similar polymer concentration. © 1996 American Chemical Society
Conformational Changes of Xanthan The conductivity data have been then analyzed in the light of the Manning polyelectrolyte theory,7,8 assuming that, in the limit of zero salt concentration, the counterions will condense onto the polyion to reduce the linear charge density ξ to the initial value ξc ) 1. The results indicate that this theory is quite unsatisfactory in the case of intrinsically bulk rigid polyelectrolytes, and a better description of the conductometric behavior can be achieved if the counterion condensation, depending on the charge density parameter ξ, is replaced by a counterion condensation independent of the polymer conformation and consequently of any structural parameter, but only influenced by the single charged group on the polymer chain (fixed counterion condensation model). In this context, the experimental data can be accounted for with very good agreement, for all the polymer concentrations investigated and over the whole temperature range, by considering an appropriate temperature dependent friction coefficient fE that takes into account charged group interactions within the polymer chains. Moreover, the “average” charge distance b between charged groups derived from the friction coefficient, besides suggesting a double-stranded helix conformation at lower temperatures, in agreement with similar indications offered by a variety of experimental techniques,9,10 shows an increasing value with temperature. This behavior can be taken as evidence for the occurrence of an aggregation process and gives further support to the model proposed by Hacche et al.11 Experimental Section (a) Materials and Sample Preparation. Xanthan (Keltrol lot no. 76735A) was a kind gift of Prof. D. A. Brant, University of California, Irvine. The polymer was dispersed in Milli-Q water (Millipore) at a concentration of 6.0 mg/mL. Sonication at about 4 °C of 500 mL batches with a Sonix apparatus for 15 min in the presence of acetone as radical scavenger at a concentration of 5% (v/v) was performed to reduce the molecular mass of the polymer and to disrupt cellular debris. The suspension was centrifuged for 2 h at 6000 rpm in a Beckmann centrifuge (rotor JA-10). The supernatant was added with NaCl to a concentration of 0.05 mol/L and then precipitated with RPE grade 2-propanol (Carlo Erba, Italy). The precipitated polymer was recovered by mild centrifugation and then simultaneously dialyzed and concentrated until the presence of chloride ions was not detected by AgNO3 assay. Polymer samples were stocked in solution at a temperature of 4 °C. Dry weight analysis gave a concentration for the batch solution of 10 mg/ mL. (b) Electrical Conductivity Measurements. The electrical conductivity measurements were carried out at the frequency of 1 kHz by means of a low-frequency impedance analyzer, H.P. Model 4192A, using a parallel plate conductivity cell with platinum electrodes coated with platinum black to reduce the effect of electrode polarization. The cell constants were determined at each temperature by means of a calibration procedure based on measurements of standard liquids of known dielectric constant and conductivity. (c) Circular Dichroism. The thermal-induced transition was monitored by circular dichroism measurements recording the molar ellypticity (θ) at the wavelength of 205 nm as a function of temperature by means of a J-600 CD spectropolarimeter (Japan Spectroscopy Co.). The polymer concentration was C ) 0.1 mg/mL. Typical results are shown in Figure 1. (d) Light-Scattering Measurements. The molecular parameters of the polymer in aqueous solution were determined by means of static light-scattering measurements in the presence of 0.1 mol/L NaCl at 25 °C. For a dilute solution at polymer
J. Phys. Chem., Vol. 100, No. 17, 1996 7149
Figure 1. Circular dichroism measurements of salt-free xanthan solutions as a function of temperature, at the wavelength of 205 nm.
TABLE 1: Molecular Parameters of Xanthan Aqueous Solutions Deduced from Static Light Scattering (4.90 ( 0.05) × 105 54 ( 3 (3.00 ( 0.02) ( 10-4
molecular weight, Mw (g/mol) radius of gyration, (Rg)z (nm) second-order virial coefficient, A2 (mL mol/g2)
concentration C, the angular dependence of the excess Rayleigh ratio ∆R(θ) over the solvent is approximately given by12,13
KC 1 1 1 + (Rg)z2q2 + 2A2C ) 3 ∆R(ϑ) Mw
(
)
where
K)
4π2n2 dn 2 N0λ04 dC µ,T
q)
( )
ϑ 4πn sin λ0 2
()
and
∆R(ϑ) )
i(ϑ)solution - i(ϑ)solvent R90(toluene) i90(toluene)
Here, N0 is the Avogadro number, λ0 the wavelength of light in Vacuo, n the refractive index of the solvent, Mw the weightaverage molecular weight of the polymer, (Rg)z the radius of gyration, and A2 the second-order virial coefficient. Measurements of ∆R(θ) as a function of concentrations and angles were carried out with a home-built photometer13 equipped with a HeNe 5 mW laser using toluene as calibration liquid and as refractive index matching liquid. In this configuration, λ0 and R90(toluene), the wavelength of the incident radiation and the Rayleigh ratio of toluene, are equal to 633 nm and 14.0 × 10-6 cm-1, respectively. Other optical constants dependent on the system under study, the refractive index n and the specific refractive index increment (dn/dC)µ,T at constant chemical potential of all diffusible species of the system and temperature, are equal to 1.33 and 0.144 mL/g, respectively. The molecular parameter of xanthan samples investigated are reported in Table 1. The parameters Mw, (Rg)z, and A2 are deduced from a Zimm plot12,13 giving the dependence of KC/ ∆R(θ) on the concentration C at different scattering angles θ. Figure 2 shows a typical Zimm plot of xanthan in 0.1 M NaCl aqueous solution at the temperature of 25 °C, in the range of the polymer concentration between 0.1 and 1 mg/mL. Results (a) Analysis of the Conductivity Data. The electrical conductivity of xanthan solutions at different polymer concen-
7150 J. Phys. Chem., Vol. 100, No. 17, 1996
Figure 2. Typical Zimm plot of xanthan in 0.1 NaCl aqueous solution at 20 °C. The polymer concentration was in the range 0.1-10.0 mg/ mL. The scattering angle has been varied from 15° to 160°.
Figure 3. Electrical conductivity of xanthan aqueous solutions as a function of temperature at various polymer concentrations: (0) C ) 0.60 mg/mL; (]) C ) 0.67 mg/mL; (O) C ) 1.00 mg/mL; (b) C ) 1.70 mg/mL; ([) C ) 2.30 mg/mL; (2) C ) 3.30 mg/mL; (4) C ) 3.30 mg/mL; (1) C ) 5.00 mg/mL; (3) C ) 5.00 mg/mL; (9) C ) 10.0 mg/mL. The values at the concentrations 0.67 (symbol ]), 3.30 (symbol 4), and 5.00 (symbol 3) mg/mL refer to a different and independent polymer preparation. Each curve can be represented by two straight lines intersecting at approximately T ) 30 °C. The full statistical analysis of the data is shown in Tables 1 and 2.
trations from 0.6 to 10.0 mg/mL as a function of temperature is shown in Figure 3. To determine the temperature at which the transition occurs, we have performed a standard regression analysis consisting in fitting a pair of straight lines to the data, giving different arbitrary values θc to the transition temperature Tc close to that where the inflexion appears. The results for a typical set of data (polymer concentration C ) 10 mg/mL) are shown in Table 2. The transition temperature Tc is that value to which corresponds a pair of straight lines with a slope of a minimum standard error. For the set of data, corresponding to polymer concentrations from 0.6 to 10 mg/mL, the transition temperature is between 30 and 35 °C. However, a further possibility must be considered. Since the conductivity varies continuously with temperature, a polynomial rather than two straight lines may better represent the data, according to the expression
Bordi et al. The above analysis, based on two linear dependencies, has been carried out for all the polymer concentrations investigated, and the results are shown in Table 3, where the slopes of the two straight lines and the corresponding correlation coefficients are indicated. As can be seen, for temperatures above 30 °C, the conductivity data are well accounted for by a linear dependence whose slope is markedly different from that deduced from measurements at temperatures less than 30 °C. Circular dichroism measurements on salt-free solutions show that ellipticities at a wavelength of λ ) 205 nm confirm that a thermal-induced transition occurs at a temperature between 30 and 40 °C, as shown in Figure 1, where molar ellipticity moves sigmoidally from positive values to zero, as the temperature increases. These results agree with optical rotation measurements14,15 made by Norton et al., where the change in the optical rotation is progressively shifted at higher temperatures with increasing ionic strength. At the lowest potassium ion concentration investigated by these authors (4.3 mM), the transition occurs at about 45 °C. In the present case, considering the ionic strength of the solution (concentration C ) 2 mM) as given exclusively by the presence of counterions (Na+) derived from the polymer dissociation, the dependence of the transitionmidpoint temperature on ionic strength, according to the values of Norton et al.,14 gives a value of 33 °C, in very good agreement with the value corresponding to the change observed in the slope of the electrical conductivity curves. (b) The Conductivity Behavior of a Salt-Free Polyelectrolyte Solution: Review of the Basic Equations. In light of the polyelectrolyte theory, the electrical conductivity of a polyion aqueous solution in the absence of added salt depends on the value assumed by a critical parameter, the charge density parameter ξ, given by the ratio of the Bjerrum length lB to the effective distance b between two charged groups along the polymer chain:
ξ)
lB e2 ) b KBTb
where is the permittivity of the aqueous phase and KBT the thermal energy. This parameter defines the regime of the counterion condensation. The electrical conductivity σ is given by the following expression:
σ ) ∑ni(zie)ui
where ni is the numerical concentration of the generic charge carrier i, each of them with an electric charge zie and mobility ui. Equation 1 assumes two distinct values whether or not the counterion condensation occurs, i.e., in dependence on the value assumed by the charge density parameter ξ. In the presence of counterion condensation (ξ > 1/(z1zp), where z1 and zp are the valences of counterions and ionized polymer groups, respectively) the fraction f of free counterions is given by
σ(T) ) a + bT + cT2 From this analysis, it results that, although the quadratic coefficient is significantly different from zero (for example, in the solution with a polymer content of 10.0 mg/mL, c ) (1.74 ( 0.24) × 10-5 Ω-1 m-1 °C-2), the correlation coefficient of the fit (r ) 0.9987), even allowing for one degree more of freedom, is not significantly higher than the average value (r ) 0.9978) obtained from the two straight lines intersecting at the transition temperature of Tc ) 30 °C.
(1)
i
f)
0.866 |zp|ξ
and eq 1 can be written in the form
σ ) (fNz1e)Npu1 + (fNzpe)Npup
(2)
where Np is the polymer concentration (number of polyions per unit volume), N is the number of ionized groups on the polymer
Conformational Changes of Xanthan
J. Phys. Chem., Vol. 100, No. 17, 1996 7151
TABLE 2: Standard Regression Analysis of the Conductivity Data as a Function of Temperature T with Two Straight Lines Intersecting at Temperature Tc T e θc T g θc trial transition temperature slope standard error correlation slope standard error correlation inflection temperature Tc (°C) θc (°C) (Ω-1 m-1 °C-1) (Ω-1 m-1 °C-1) coefficient r (Ω-1 m-1 °C-1) (Ω-1 m-1 °C-1) coefficient r T < θc T > θc 20.0 25.0 30.0 35.0 40.0
0.001 22 0.001 35 0.001 44 0.001 54 0.001 70
0.000 12 0.000 09 0.000 07 0.000 07 0.000 10
0.9949 0.9957 0.9962 0.9951 0.9906
0.002 434 0.002 530 0.002 614 0.002 660 0.002 635
0.000 07 0.000 06 0.000 04 0.000 03 0.000 04
0.9965 0.9983 0.9994 0.9996 0.9994
Tc ) 30 °C
Tc ) 35 °C
TABLE 3: Analysis of the Slopes of Two Straight Lines Accounting for the Conductivity Data below and above a Critical Temperature Tc (In This Run, 30 e Tc e 35 °C) σ(T) ) σ0 + aT T e 30 °C C (mg/mL) 0.60 0.67* 1.0 1.7 2.3 3.3 3.3* 5.0 10.0 a
a
a
(Ω-1
m-1
°C-1)
T > 30 °C
correlation coefficient r
(154 ( 5) × 10-6 (156 ( 5) × 10-6 (199 ( 6) × 10-6 (409 ( 10) × 10-6 (415 ( 8) × 10-6 (669 ( 25) × 10-6 (699 ( 35) × 10-6 (908 ( 30) × 10-6 (1435 ( 73) × 10-6
0.9978 0.9978 0.9982 0.9987 0.9994 0.9972 0.9958 0.9980 0.9962
a
(Ω-1
m-1
°C-1)
correlation coefficient r
(186 ( 6) × 10-6 (221 ( 4) × 10-6 (242 ( 3) × 10-6 (496 ( 12) × 10-6 (545 ( 3) × 10-6 (926 ( 9) × 10-6 (873 ( 9) × 10-4 (1220 ( 6) × 10-6 (2660 ( 30) × 10-6
0.9966 0.9994 0.9995 0.9990 0.9999 0.9997 0.9997 0.9999 0.9995
The asterisk marks a different and independent sample preparation.
chain, and zie and u1 and zpe and up are the electrical charge and the mobility of counterions and ionized polymer groups, respectively. Equation 2, rewritten in the standard form, reads
σ ) 10-1
0.866 C (λ + λp) |zp|ξ n 1
KD ) (3)
where the conductivity σ is expressed in Ω-1 m-1, λ1 and λp are the equivalent conductances of counterions and polyion expressed in Ω-1 cm2 equiv-1, and Cn is the polyion concentration expressed in monomol/L. In the absence of counterion condensation (ξ < 1/z1zp), eq 2 results in the following expression:
(
σ ) 10-1 1 +
)
2
0.55ξ C (λ + λp) π+ξ n 1
(4)
According to Manning,7,8 the equivalent conductance λp of the polyion is given by
KBT 278.6 |log(KDa)| 3πηe|zp| λp ) KBT 1 1 + 43.27 |log(KDa)| 3πηe|zp| λ1
the dielectric constant and viscosity of the aqueous phase, KBT is the thermal energy, a is the radius of the polymer chain, and
(5)
and
[ ( )] ( )
0.55ξ2 KBTξ |log(KDa)| π + ξ 3πηe|zp| (6) λp ) 0.55ξ2 KBTξ 1 1 + 1.55 × 10-7 |log(K a)| D π + ξ 3πηe2 λ1 321.67 1 -
for ξ > 1/zpz1 (eq 5) and ξ < 1/zpz1 (eq 6), respectively, i.e., in the presence and in the absence of counterion condensation. The strange-looking numerical factors appearing in eqs 5 and 6 derive from the conversion of all the quantities employed to cgs electrostatic units. In the above expression, and η are
x
4πe2N0Cc 103KBT
is the inverse of the Debye screening length, where N0 is the Avogadro number and Cc is the concentration of counterions in the bulk solution. This value is related to the polymer concentration Cn (in monomol/L) through the relation
{
(
N0Cn
)
0.55 ξ2 ξe1 π+ξ 10 Cc ) N C 0 n 0.866 ξg1 103 ξ 3
1-
These equations give the full description of the electrical conductivity behavior of a polyelectrolyte solution, within the counterion condensation model of the Manning theory.7,8 (c) The Structure of the Polymer Chain in Aqueous Solution. To evaluate the electrical conductivity from eqs 3 and 4, the structural parameters of the xanthan chain should be known. In the double-helix conformation, with five pentasaccharide residues in the helix pitch of 4.7 nm and an average number of carboxylate groups per residue equal to 1.6, the “apparent” distance b between two charged groups in the fully ionized state is b ) 0.294 nm.16,17 This distance increases to the value of b ) 0.588 nm for a single-helix chain. Conversely, if the polyion is assumed in the fully extended double-chain geometry, with a projected pentasaccharide residue length of 1.03 nm,17 the distance between two charged groups is b ) 0.233 nm, which increases to b ) 0.644 nm in the case of the fully extended single chain. For each of these polymer conformations, the charge density parameter ξ assumes values larger than unity, the critical value above which the counterion condensation should begin. In the above cases, this parameter varies from ξ ) 1.11 in the fully extended single chain to ξ ) 2.42 in the double-helix conformation.
7152 J. Phys. Chem., Vol. 100, No. 17, 1996
Figure 4. Average charge distance b as a function of temperature derived from the Manning electrical conductivity theory (eqs 3 and 5). Each point represents the average value obtained from values at different polymer concentrations from 0.6 to 10 mg/mL. The standard deviation is also shown. The values of the charge distance for a double-stranded helix, a single helix, and a random coil are also indicated.
According to the Manning theory,7,8 the order-disorder transition, resulting in a change of the charge density parameter ξ, should be accompanied by a change in the counterion condensation. In particular, the fraction of condensed Na+ ion should decrease by 0.41 or 0.49 per carboxyl group in correspondence with the transition from a double-stranded helix at lower temperatures to a single-stranded helix or to a singlestranded expanded coil at higher temperatures, respectively. On the other hand, if the ordered structure at lower temperatures consists of a single helix which evolves toward a random coil, as suggested by Jones et al.,5 the decrease of condensed counterions should be about 0.08 Na+ per carboxyl group. As can be seen, only two possible conformational transitions yield appreciable changes in the counterion condensation, i.e., from a double-stranded helix to a single-stranded helix or to a single fully extended strand. (d) Analysis Based on the Manning Equations. The analysis based on the Manning theory (eqs 3 and 6) yields that the charge density parameter ξ and consequently the distance b between two adjacent charges vary as a function of temperature from ξ ) 1.53 to ξ ) 1.30 and from b ) 0.475 nm to b ) 0.590 nm, respectively. To give the full description of the results of the Manning theory, the values of b for all the polymer concentrations investigated are shown in Figure 4. The dependence of the dielectric constant and viscosity η on the temperature of the aqueous phase, considered equal to that of pure water, has been derived from standard handbooks.18 The equivalent conductance of Na+ ions is assumed to be λ1 ) 43.5 Ω-1 cm2 equiv-1 at 25 °C with a temperature dependence of (1/λ1)dλ1/dT ) 2.44 × 10-2 °C-1. The radius a of the polymer was taken to be a ) 12 Å.19 As can be seen, this behavior differs from that expected for a double-stranded helix at lower temperatures and that of a single helix or that of a random coil, at higher temperatures. It must be noted that this discrepancy remains unchanged even if the polymer is assumed to be, at lower temperatures, in a singlehelix conformation, as suggested by the results presented by Jones et al.5 (e) Analysis Based on a “Fixed Counterion Condensation Model”. Although the Manning theory is very successful in describing the conductometric behavior of a wide variety of polyelectrolyte systems, in the present case, this approach fails for two different reasons. First of all, at the polymer concentration investigated, from 0.5 up to 10 mg/mL, the system is in a semidilute or concentrated regime, that is, polymer-polymer
Bordi et al. interactions cannot be neglected. This emerges from the dielectric behavior of the polymer solutions and in particular from the high-frequency dielectric dispersions whose parameters (the dielectric increment and the relaxation time) follow exactly the dependence on the polymer concentration suggested by Ito et al.20 for the crossover region from dilute to semidilute or concentrated regime. These aspects have been extensively investigated by the prsent authors elsewhere.6 The second point concerns the polymer structure that, in the present case, markedly deviates from that of a thin charged line, as assumed in the Manning model, since the ionizable groups lie on the surface of a helix of finite thickness (with a diameter of about 24 Å). Both these points have been also raised by Zhang et al.19 in the interpretation of potentiometric titration data of xanthan solutions, on the basis of the Manning theory. In our previous work6 on the dielectric properties of xanthan, we have pointed out that the dielectric dispersions due to the distribution of counterions along the polymer chain, resulting in a polarization of the ionic atmosphere,21 could be accounted for by the usual dielectric theories of polyelectrolyte solutions if the fraction of bound counterions deviates from the value suggested by Manning, assuming, in this case, a constant value independent of the polymer structure. On the basis of our dielectric measurements,6 we have found at the temperature of 25 °C, for the fraction of bound counterions, the value 1 - f ) 0.47, independent of the degree of ionization of the polymer. This value accounts for the low-frequency dielectric increment of xanthan solutions in a wide range of pH, from pH ) 2.5 to pH ) 9.5. In the semidilute regime, owing to the entanglement of the polymer, the polymer-polymer interactions alter the distance over which counterions can fluctuate and each charged group is able to condense the same fraction of counterions, independently of the other neighbour groups on the same polymer chain. At this stage, to proceed further, we turn to the expression of the conductivity given by Manning (eqs 3 and 5) considering that now the fraction (1 - f) of bound counterions assumes, as pointed out above, a constant value, independent of the charge distribution on the polymer chain. In this case, the conductivity of the solution can be written, according to eq 3, as
σ ) 10-1{0.866f(λ1 + λp)Cn}
(7)
where the equivalent conductance λp of the polyion is given by
λp )
278.5ef fE ef + 43.1 N λ1
(8)
with
fE 3πηb ) N |log(KDb)|
(8′)
the friction coefficient. The derivation of the above expressions proceeds following the line of the Manning theory, by considering a fixed counterion condensation. As pointed out by Manning,22 the friction coefficient depends on the polyion charge spacing and not on the radius of the polyion chain. To evaluate the fraction (1 - f) of condensed counterions over the entire temperature range investigated, we have measured the counterion (Na+) activity coefficient of xanthan solutions as a function of temperature. The measurements were carried out measuring the activity coefficient of Na+ ions by
Conformational Changes of Xanthan
J. Phys. Chem., Vol. 100, No. 17, 1996 7153
Figure 6. Electrical conductivity of xanthan aqueous solutions as a function of concentration at some selected different temperatures: (O) T ) 15 °C; (0) T ) 25 °C; (4) T ) 40 °C; (]) T ) 65 °C. The plot shows two linear behaviors with different slopes, indicating the occurrence of two different semidilute and concentrated regimes. The full lines are drawn only to guide the eye.
Figure 5. (A) Friction coefficient fE as a function of temperature at different polymer concentrations: (O) C ) 10.0 mg/mL; (0) C ) 5.0 mg/mL; (]) C ) 3.3 mg/mL; (4) C ) 0.6 mg/mL. The full lines are drawn only to guide the eye. (B) “Apparent” value of the distance b between charged groups as a function of temperature at different polymer concentrations: (O) C ) 10.0 mg/mL; (0) C ) 5.0 mg/mL; (]) C ) 3.3 mg/mL; (4) C ) 0.6 mg/mL. The inset shows the behavior of the fraction of condensed counterions as a function of temperature deduced from Na+ coefficient activity measurements for a xanthan solution at the concentration C ) 1.0 mg/mL.
Figure 7. Electrical conductivity of xanthan aqueous solutions as a function of temperature at some selected polymer concentrations. The polymer solutions have experienced different thermal cycles. Without thermal conditioning: (b) C ) 10.0 mg/mL; (9) C ) 5.0 mg/mL; (1) C ) 3.4 mg/mL; (2) C ) 1.7 mg/mL. With thermal conditioning treatment, consisting in a thermal stabilization of 1 h at T ) 50 °C: (O) C ) 10.0 mg/mL; (0) C ) 5.0 mg/mL; (3) C ) 3.4 mg/mL; (4) C ) 1.7 mg/mL. No appreciable differences appear in the electrical conductivity.
means of an ion selective electrode. We obtained values of 1 - f ) 0.47 at 20 °C, which, with an approximately linear dependence, decrease to 1 - f ) 0.25 at 70 °C. Incidentally, we wish to stress that these values are about the same as those deduced from the dielectric dispersions at 20, 41, and 70 °C for different xanthan solutions at concentrations from 1.0 to 3.5 mg/mL (see Figures 8 and 12 of ref 6). Equation 7 furnishes a very good agreement with the experimental data for all the polymer concentrations investigated with the values of the friction coefficient fE/N as a function of temperature, shown in Figure 5. As can be seen, the friction coefficient, which probes the local interactions between different charged groups on the polymer chains, reflects the temperature behavior of the conductivity and in particular shows a pronounced change in its temperature slope around the transition temperature of about 33-35 °C. This change is more pronounced at higher polymer concentrations. Moreover, the “apparent” charged group distance b, derived from the friction coefficient, assumes values not too far from those of a single double-stranded helix at lower temperatures that progressively increases up to values of about 0.6-0.7 nm at higher temperatures, indicating a continuous modification of the structure toward that of an expanded coil accompanied by an increase in the polymer-polymer interactions. This change can be seen as due to an increase of the
connectivity between single polymer chains as a consequence of the partial melting of the double-stranded helix structure. Finally, we will consider the effect of the polymer concentration. Figure 6 shows the electrical conductivity of xanthan solutions as a function of the polymer concentration at various selected temperatures from 5 to 70 °C. As can be seen, two different regimes can be evidenced, corresponding to the semidilute regime, up to about 3.5 mg/mL, and to the concentrated regime, at concentrations higher than 3.5 mg/mL. In both regions, a linear dependence on the concentration is observed, characterized by different slopes, where the less pronounced dependence on concentration in the concentrated regime is caused by the larger polymer-polymer interactions. It is noteworthy, however, that also in this regime the conductivity behavior can be described by a fixed counterion condensation, supporting further evidence that each charged group on the polymer chain behaves independently of the neighbouring groups. A final comment is in order. Recently, Muller and Lecourtier23 have measured the specific viscosity of xanthan in 0.1 M NaCl aqueous solution and have observed that the results are strongly dependent on the preheating temperature. These authors suggest a more elaborate model of the temperatureinduced denaturation, where the thermal treatment could influence, probably irreversibly, also the conductometric behavior
7154 J. Phys. Chem., Vol. 100, No. 17, 1996 of the polymer solution. It consists of two steps, the first of which starts from a native dimeric structure and evolves toward an extended double strand, whereas the second one involves the complete dissociation into separate strands, as indicated by the halving of the molecular weight in light-scattering experiments. Moreover, between ordered and disordered forms, an intermediate conformation can exist, consisting of disordered regions held together by a segment of ordered chains. To ascertain if the conductometric behavior could be influenced by a moderate heat treatment or if some structures could be stabilized by the thermal treatment, we have brought the sample to a partial disordered conformation by heating at a temperature of 50 °C for 1 h and then returning to room temperature. The results are shown in Figure 7, where the electrical conductivity of xanthan samples with a different thermal treatment is compared in the whole temperature interval investigated with solutions of various polymer concentrations. As can be seen, no marked differences are found, suggesting that from the point of view of the conductometric measurements this effect, if any, is negligible. 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. (3) Liu, W.; Sato, T.; Norisuye, N.; Fujita, H. Carbohydr. Res. 1987, 160, 267.
Bordi et al. (4) Rees, D. A. Pure Appl. Chem. 1981, 53, 1. (5) Jones, S. A.; Goodall, D. M.; Cutler, A. N.; Norton, I. T. Eur. Biophys. J. 1987, 15, 185. (6) Bordi, F.; Cametti, C.; Paradossi, G. J. Phys. Chem. 1995, 99, 274. (7) Manning, G. S. Biopolymers 1970, 9, 1543. (8) Manning, G. S. J. Phys. Chem. 1975, 79, 162. (9) Nakasuka, M.; Norisuye, T. Polym. J. 1988, 20, 939. (10) Liu, W.; Norisuye, T. Biopolymers 1988, 27, 1641. (11) Hacche, L. S.; Washington, G. E.; Brant, D. A. Macromolecules 1987, 20, 2179. (12) Zimm, B. H. J. Chem. Phys. 1948, 16, 1099. (13) Bolle, G.; Codastefano, P.; Paradossi, G. IEEE Trans. Instrum. Meas. 1994, 43, 553. (14) Norton, I. T.; Goodall, D. M.; Frangou, S. A.; Morris, E. R.; Rees, D. A. J. Mol. Biol. 1984, 175, 371. (15) Milas, M.; Rinaudo, M. Carbohydr. Res. 1979, 76, 189. (16) Sato, T.; Norisuye, T.; Fujita, H. Macromolecules 1984, 17, 2696. (17) Moorhouse, R.; Walkinshaw, M. D. In Extracellular Microbiology Polysaccharides; Sanford, P. A., Lanicin, A., Eds.; ACS Symposium Series 45; American Chemical Society: Washington, DC, 1977; p 90. (18) Weast, R. C., Ed. CRC Handbook of Chemistry and Physics, 63rd ed.; CRC Press: Boca Raton, FL, 1982. (19) Zhang, L.; Takematsu, T.; Norisuye, T. Macromolecules 1987, 20, 2882. (20) Ito, K.; Yagi, A.; Ookubo, K.; Hayakawa, R. Macromolecules 1990, 93, 857. (21) Van der Touw, F.; Mandel, M. Biophys. Chem. 1974, 2, 218; 1974, 2, 231. (22) Manning, G. S. J. Phys. Chem. 1981, 85, 1506. (23) Muller, G.; Lecourtier, J. Carbohydr. Polym. 1988, 9, 213.
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