Solution Properties of Gellan Gum: Change in Chain Stiffness

Biomacromolecules 2004, 5, 516-523

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Solution Properties of Gellan Gum: Change in Chain Stiffness between Single- and Double-Stranded Chains Rheo Takahashi,*,† Hiroshi Tokunou,‡ Kenji Kubota,‡ Etsuyo Ogawa,§ Tatsuo Oida,| Tokuzo Kawase,| and Katsuyoshi Nishinari† Department of Food and Human Health Sciences, Graduate School of Human Life Science, Osaka City University, Sumiyoshi, Osaka 558-8585, Japan, Department of Biological and Chemical Engineering, Faculty of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan, Showagakuin Junior College, Higashisugano, Ichikawa, Chiba 272-0823, Japan, and Department of Chemistry and Materials Technology, Faculty of Engineering and Design, Kyoto Institute of Technology, Sakyo, Kyoto 606-0962, Japan Received September 23, 2003; Revised Manuscript Received November 6, 2003

Nine samples of gellan gum in the sodium form, ranging in weight-average molar mass from 3.47 × 104 to 1.15 × 105 at 40 °C, were investigated by static and dynamic light scattering and viscometry in 25 mM aqueous NaCl both at 40 and at 25 °C. The ratios of the molar mass at 25 °C (in the ordered state) to that at 40 °C (in the disordered state) were in the range of 1.99 to 2.07, supporting the scheme of the conformational transition of gellan gum between a disassociated single chain and an associated chain composed of two molecules. Focusing on the effects of polydispersity, the intrinsic viscosities, radii of gyration, and hydrodynamic radii were analyzed on the basis of unperturbed wormlike chain models. The persistence lengths were evaluated as 9.4 nm at 40 °C and 98 nm at 25 °C. Introduction Gellan gum is an extracellular polysaccharide produced by the bacterium Pseudomonas elodea and consists of a repeating unit of tetrasaccharide: D-glucose, D-glucuronic acid, D-glucose, and L-rhamnose (Figure 1).1 The most striking characteristic of gellan gum is that it forms a firm and transparent gel in the presence of metallic ions,2 such as Ca2+. Gellan gum exhibits a conformational change from the disordered state (single chain) to the ordered state (double helix) with decreasing temperature, and the gelation is considered to be mediated by the double-helix formation and the association of helices enhanced by the presence of metallic cations.3-6 The physical nature of the gel states is related to the cross-linking structure and the chain properties between the cross-links. The rheological and physicochemical properties of gellan gum in the sol state are also very interesting.7 According to the pioneering work by Dentini et al.8 on gellan gum solution, it has become evident that this polysaccharide behaves as a typical wormlike polyelectrolyte in the ordered state. In the course of the study, the persistence length, q, the most important parameter characterizing the chain stiffness, was estimated as 102 nm at 25 °C for the double-stranded tetramethylammonium (TMA)-gellan.8,9 This q value of 102 nm is comparable to the typical double* To whom correspondence [email protected]. † Osaka City University. ‡ Gunma University. § Showagakuin Junior College. | Kyoto Institute of Technology.

should

be

addressed.

E-mail:

Figure 1. Repeating unit of deacetylated gellan gum (sodium salt).

stranded polysaccharides, such as xanthan10,11 (q ) 120 nm) and succinoglycan12,13 (q ) 50 nm). The common feature of these double-stranded polysaccharides is that the polymer chains are very stiff even in the disordered state. In fact, the q values of xanthan14 and succinoglycan15 in the disordered state have been determined as 21 and 10 nm, respectively. The substantial stiffness of the single-stranded chains, as well as the primary structure, probably makes the formation of double-stranded structure easy. A conversion of deacetylated gellan gum into the TMAsalt has long been considered as an essential procedure to prevent the formation of unnecessary aggregation and microgels.8,16,17 A problem often observed is that gellan does not dissolve even in aqueous salt if the sample contains an excessive amount of gel-promoting cations, such as K+, Mg2+, or Ca2+. Thus, several studies8,16 of dilute solutions of gellan have been reported on TMA-salt-type gellan samples; TMA ion is considerably larger than Na+ sterically and in addition partly hydrophobic. Recently, Drs. Sanderson (Kelco Ltd.), Oomoto, and Asai (San-Ei Gen F. F. I. Inc.) prepared a well-purified sodium-type gellan coded as NaGG3.18 The solubility of NaGG-3 in an aqueous salt solution was very much improved compared with typical commercial

10.1021/bm034371u CCC: $27.50 © 2004 American Chemical Society Published on Web 12/16/2003

Biomacromolecules, Vol. 5, No. 2, 2004 517

Chain Stiffness of Gellan

samples, and it was possible to carry out the light scattering measurements in aqueous NaCl solution without further treatment; the formation of aggregates and microgels was not observed.17 The q values of NaGG-3 in 25 mM NaCl have been estimated previously as 17 nm at 40 °C (in the disordered state) and 98 nm at 25 °C (in the ordered state). The q value of 98 nm for the ordered Na-gellan is coincidentally close to the early estimation of Dentini et al.8 on TMA-gellan. However, the prior attempts to estimate the chain rigidities of Na-gellan in both the disordered and ordered states have been inconclusive because the q value was determined from only one fraction. The exact estimation of the q value of gellan gum has been limited by difficulty in the preparation of monodisperse samples with a series of molar mass. Consequently, a study of Na-gellan through a wide molar mass range has not been reported so far. Here we report the study of the order-disorder conformational change of deacetylated gellan gum in 25 mM aqueous NaCl solution. First, the molar mass dependence of the intrinsic viscosities, radii of gyration, and hydrodynamic radii in both the disordered and ordered states was analyzed on the basis of wormlike chain models. Wormlike chain parameters, including the persistence length, were estimated focusing on the polydispersity effects using wellpurified sodium salt gellan gum samples. Finally, with the model parameters thus determined, the conformational properties of gellan gum in both disordered and ordered states were examined. Experimental Section Materials. A purified sodium-type gellan gum sample, NaGG-3, was supplied by San-Ei Gen F. F. I., Osaka, Japan. The contents of the metallic ions of Na+, K+, Ca2+, and Mg2+ were 2.59%, 0.009%, 0.02%, and 0.001%, respectively, by the elemental analysis. It is characteristic of NaGG-3 that all of the metallic ions except Na+ were removed exhaustively. The original deacetylated gellan gum sample, NaGG3,17 was dissolved in water (0.1 wt %) and exposed to 20 kHz/400 W ultrasonic irradiation (Branson Sonifier II model 450) for 1-5 min. Each of the sonicated fractions was centrifuged at (8 × 103)g for 1 h. The supernatant was poured into a large quantity of isopropyl alcohol to precipitate gellan. Aqueous solutions of each fraction were treated by the mixed-bed-type ion exchanger and neutralized with 0.1 M NaOH to convert into Na-type. Dry Na-gellan samples were obtained by freeze-drying the solutions for 1 week. Nine samples were chosen for the present study and were designated NAG-A, NAG-B, ..., and NAG-I in order of decreasing molar mass (Table 1). On average, the contents of the metallic ions of the final products were as follows: Na+ 3.1%, K+ 0.005%, Ca2+ 0.002%, and Mg2+ 0.0005%. A known weight of sample was dissolved in 25 mM aqueous NaCl solution to prepare the desired sample solutions. The sample solutions were heated at 95 °C for 1 h to avoid unnecessary aggregations or microgels17 after swelling at 50 °C for 12 h. The sample solutions were dialyzed against 25 mM aqueous NaCl solution at 40 °C thoroughly. Viscosity and light scattering measurements for the dialyzed solutions

Table 1. Molecular Parameters Characterizing Na-gellan in 25 mM Aqueous NaCl Solution

T, 10-3Mw, 103A2, RGz, RHz, -1 °C g mol cm3 mol g-2 nm nm

Fz

10-2[η], M25 w/ µ2/Γ h cm3 g-1 M40 w

40 25

115 230

4.49 3.61

Sample NAG-A 35.6 17.7 2.01 0.13 95.9 31.8 3.02 0.14

40 25

94.5 193

5.39 3.34

Sample NAG-B 32.3 83.8

4.33 18.8

2.04

40 25

80.0 161

6.13 4.05

Sample NAG-C 29.3 14.0 2.09 0.11 74.8 25.6 2.92 0.12

3.80 14.6

2.01

40 25

73.3 147

6.01 4.62

Sample NAG-D 27.9 13.0 2.15 0.10 70.5 23.9 2.95 0.11

3.62 13.8

2.01

40 25

67.6 140

6.11 3.38

Sample NAG-E 27.1 66.5 21.4 3.11 0.11

3.24 12.5

2.07

40 25

64.2 133

6.19 3.75

Sample NAG-F 26.7 65.7 21.2 3.10 0.13

3.20 11.3

2.07

40 25

63.8 127

4.81 4.13

Sample NAG-G 26.1 11.9 2.19 0.11 61.2 20.1 3.04 0.11

3.13 11.0

1.99

2.51

1.79

40 25

49.9

5.27

Sample NAG-H 23.2 10.5 2.21 0.12

40 25

34.7

6.65

Sample NAG-I 18.1

5.20 24.1

2.00

were immediately carried out at 40 °C or carried out at 25 °C after being cooled to 25 °C slowly (at 3 °C/hour). The polymer concentration was determined by the quantitative analysis of total organic carbon with a TOC-5000 (Shimadzu Co.). Viscosity Measurements. Intrinsic viscosities [η] were measured in 25 mM aqueous NaCl solution at 40 and 25 °C using an Ubbelohde-type low-shear capillary viscometer. The temperature was controlled with the constancy of 0.01 °C. The flow time of the solvent was ca. 1070 s at 40 °C. Viscosity data were analyzed by the Huggins,19 Billmeyer,20 and Mead-Fuoss21 plots simultaneously to obtain the reliable extrapolation to an infinite dilution. Refractive Index Increments. The specific refractive index increments, [∂n/∂c]µ, of Na-gellan in 25 mM aqueous NaCl solution were measured over 14-46 °C at a wavelength of 488 nm using a double-beam differential refractometer of DRM-21 (Otsuka Electronics Co. Ltd.). The temperature was controlled with the constancy of 0.1 °C. The solution of Na-gellan in 25 mM aqueous NaCl was dialyzed against 25 mM aqueous NaCl solution at 40 °C before the measurements. Light Scattering Measurements. We used a purpose-built light scattering photometer. Both the purpose-built 240channel digital correlator and ALV-5000/E multiple-τ digital correlator were used for the correlation function measurements. Scattered light intensity measurements and the

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correlation function measurements using homodyne mode were carried out simultaneously. A vertically polarized Ar ion laser operated at a wavelength, λ0, of 488.0 nm was used as the incident beam. Vertically polarized scattered light was detected by a photomultiplier tube using the photon-counting method. Benzene was used as a standard for calibrating the scattering photometer.22 A cylindrical cell of 10 mm outer diameter was placed in a thermostated silicon oil bath, the temperature of which was controlled with the constancy of 0.01 °C. Temperature was monitored by a calibrated platinum resistor. Optical purification of the sample was achieved by centrifugation ((3 × 104)g for 2 h) and filtration through Nylon membrane filters (0.45 µm pore size). In the static light scattering measurements, scattered light intensities at the scattering angle over 15°-135° were measured. The correlation functions were measured over 15°-60° in the dynamic light scattering measurements. For the stiff polymer chain, where the chain dimension becomes substantially large, the measurements at low scattering angles are essential to obtain reliable results. Data Analysis. Zimm plots of the square-root form (Berry plot) were employed to obtain the weight-average molar mass, Mw, the z-average radius of gyration, RGz, and the virial coefficient, A2, expressed as [Kc/Rθ]1/2 ) Mw-1/2(1 + RGz2k2/6 + MwA2c)

(1)

where K, c, θ, and Rθ are the optical constant, the polymer mass concentration, the scattering angle, and the reduced excess scattering intensity at θ, respectively. Here, k is the momentum transfer vector defined as k ) (4πn0/λ0) sin(θ/ 2), n0 being the refractive index of a medium. The autocorrelation functions of scattered light intensity, G2(τ), were analyzed by the cumulant expansion and CONTIN methods.23,24 G2(τ) has the following form related to the normalized electric field correlation function, g1(τ): G2(τ) ) C[1 + β|g1(τ)|2]

(2)

where C is a baseline and β is a machine constant relating to the coherence of detection. Generally, g1(τ) is expressed by the distribution function, G(Γ), of the decay rate, Γ, and is expanded by the cumulant expansion g1(τ) )

∫G(Γ) exp(-Γτ) dΓ

(3)

) exp(-Γ h τ)[1 + (µ2/2!)τ - (µ3/3!)τ + ...] 2

3

Figure 2. Temperature dependence of [∂n/∂c]µ of Na-gellan in 25 mM aqueous NaCl solution. The wavelength of the incident light is 488 nm.

(4)

∫

h 2 ) [(Γ - Γ h )2/Γ h 2]G(Γ) dΓ (5) µ2/Γ where ∫G(Γ) dΓ ) 1, Γ h is the average decay rate, and µ2/Γ h2 is the normalized variance. The third cumulant method of eq 4 was used to retrieve a reliable average decay rate. The z-average translational diffusion coefficients, D0z, were estimated from the dynamic Zimm plots of Γ h /k2(kf0) vs c. The z-average hydrodynamic radii, RHz, were calculated using the Einstein-Stokes equation, RHz ) kBT/(6πη0D0,z), where kB is the Boltzmann constant and η0 the solvent viscosity. Results Specific Refractive Index Increments. Temperature dependence of the specific refractive index increment,

Figure 3. Zimm plot of NAG-C in 25 mM aqueous NaCl solution at 40 °C. c0 ) 1.06 × 10-3 g cm-3. The wavelength of the incident light is 488 nm.

[∂n/∂c]µ, is shown in Figure 2. Although the measured [∂n/∂c]µ increased slightly with temperature, no marked change in [∂n/∂c]µ was observed between the disordered and ordered conditions. The [∂n/∂c]µ values in 25 mM NaCl solution were fitted by the following equation: [∂n/∂c]µ ) [(1.33 × 10-4)T (°C) + 0.151] cm3 g-1 (488 nm) (6) The values of 0.156 and 0.154 cm3 g-1 were obtained for the sodium salt sample NAG-A at 40.0 and 25.0 °C, respectively. Molar Mass and Chain Dimensions of Sodium Gellan. Figures 3 and 4 illustrate the Berry plots for the Na-gellan sample NAG-C in 25 mM aqueous NaCl solution at 40 and 25 °C, respectively. The square-root form was employed because the second virial coefficient, A2, of our gellan sample was fairly large. The dotted lines in Figures 3 and 4 represent the initial slopes to the curves obtained for the experimental [Kc/Rθ]1/2 at infinite dilution by the least-squares fit. The curves fitting to the data points were more convex upward in the ordered state. The downward deviations from the dotted lines reveal the pronounced polydispersity effects or chain rigidity or both. Although the plots for [Kc/Rθ]1/2 at infinite dilution are bent downward, the intercepts and the



Figure 4. Zimm plot of NAG-C in 25 mM aqueous NaCl solution at 25 °C. c0 ) 1.06 × 10-3 g cm-3. The wavelength of the incident light is 488 nm.

initial slopes were determined without substantial ambiguity because those were almost linear in the small k2 region; typically, kRG < 1. From the intercept to the ordinate and the slopes against the concentration and scattering angle, the weight-average molar mass, Mw, z-average radius of gyration, RGz, and A2 were determined. The numerical values determined by the static and dynamic light scattering measurements are listed in Table 1, together with the data of the viscosity measurements. Flory’s viscosity factors, Φ () [η]Mw/(6RGz2)3/2), are substantially smaller at both 40 and 25 °C than those expected for the long flexible chains (∼2.7 × 1023 mol-1) because of the stiff nature of gellan gum molecules.38 Moreover, Φ values at 25 °C are about half of those at 40 °C corresponding to the conformational change. The values of A2 were on the order of 10-3 cm3 mol g-1 at both temperatures, indicating that the aqueous salt solution is a thermodynamically good solvent for Na-gellan. The 40 ratios of the molar mass at 25 °C to that at 40 °C, M25 w /Mw , -3 were in the range between 1.99 and 2.07 (63.8 e 10 M40 w e 115). According to the scheme that gellan exhibits a structural transition from the disordered single chain at high temperature to the ordered double helix at lower temperature, 40 the M25 w /Mw value should be 2. The experimental results of 25 40 Mw /Mw are consistent enough with this scheme; the ordered chain in the aqueous salt is composed of two chains. The ratio of the radius of gyration to the hydrodynamic radius, RG/RH ()F), relates to the segment distribution and solvent permeability reflecting the chain stiffness.25 The large magnitudes of Fz ()RGz/RHz) ≈ 3 at 25 °C should result from the significant chain stiffness of double-stranded gellan molecules. On the other hand, relatively large values, as much as 2, were obtained at 40 °C. Because the ratio is also affected by molar mass polydispersity, a relatively large Fz value does not necessarily mean the stiff nature of polymers. In fact, experimental Fz at 40 °C is comparable with the predicted value of about 2 for polydisperse Gaussian random coils in a good solvent. The magnitudes of the normalized variance, µ2/Γ h 2, shown in Table 1 mean that our Na-gellan samples are relatively polydisperse. The polydispersity is, however, not so different among the present samples. In Figure 5, Mw dependences of the intrinsic viscosity [η], RGz, and RHz are shown. The exponents of the linear fits for

Figure 5. Double-logarithmic plots of the intrinsic viscosity [η], radius of gyration RGz, and hydrodynamic radius RHz as a function of molar mass: (O) gellan at 40 °C; (b) gellan at 25 °C. The slopes of the lines for [η], RGz, and RHz are 0.88, 0.55, and 0.63, respectively, at 40 °C, and 1.26, 0.74, and 0.76, respectively, at 25 °C.

[η], RGz, and RHz are 0.88, 0.55, and 0.63 for the disordered gellan and 1.26, 0.74, and 0.76 for the double-stranded gellan, respectively. These values are obviously larger than the values expected for flexible chains, and therefore, the large Fz values obtained at 40 °C are safely attributed to the substantial effects of chain stiffness. Discussion Chain Stiffness in the Disordered State. If the singlestranded Na-gellan molecule in 25 mM aqueous NaCl solution is modeled by unperturbed wormlike chains, the intrinsic viscosity [η] is determined by the persistence length, q, the contour length, L, and the cylinder diameter, d.26,27 The contour length is related to the molar mass, M, by L ) M/ML, ML being the shift factor (molar mass per unit contour length). According to Bohdanecky´,28 the Yamakawa-FujiiYoshizaki theory26,27 for the intrinsic viscosity of an unperturbed wormlike cylinder, [η]0, can be expressed in a good approximation as (M2/[η]0)1/3 ) A + BM1/2

(7)

A ) (1.518 × 10-8)A0ML (g1/3 cm-1)

(8)

B ) (1.518 × 10-8)B0(ML/2q)-1/2 (g1/3 cm-1)

(9)

where

A0 in eq 8 and B0 in eq 9 being the known functions of d/(2q) and having been tabulated by Bohdanecky´.28 In this case, the Bohdanecky´ plot of (Mw2/[η])1/3 vs Mw1/2 should give a straight line. When the excluded-volume effect is significant for high molar mass samples, this plot should bend downward at large Mw1/2. The Bohdanecky´ plot constructed from the present data in 25 mM NaCl solution at 40 °C is plotted in Figure 6. The plotted points follow a straight line, yielding the wormlike chain parameters of q ) 9.1 nm, ML ) 355 nm-1, and d ) 0.9 nm. Here, we note that eq 7 contains three unknowns of q, ML, and d so that, for an estimation of all of these

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Takahashi et al.

Figure 6. Bohdanecky´ plot constructed from the data at 40 (O) and 25 (b) °C.

parameters from [η] data, one needs additional information, that is, the relation of M/[η]0 vs M1/2 or the partial specific volume, Vj, of the polymer.28 We used the relation d ) (6MLVj/ (πNA))1/2 and Vj ≈ 0.7 (assumed value for polysaccharides),8,29 where NA is Avogadro’s number. Because the contour lengths are not so large compared with the assumed value of q ) 9.1 nm, the excluded-volume effect on [η] can be safely neglected.30,31 The ML value of 355 nm-1 is consistent with the primary structure of Na-gellan gum, confirming that the wormlike cylinder is a good model for our samples. The d value of 0.9 nm is also reasonable if possible hydration of water molecules on the polymer chain is considered.32-34 The stiff nature of the disordered gellan should be related to the fact that a gellan solution exhibits unique rheological behavior and forms a firm gel. Consideration of Polydispersity Effects. The above data analysis based on the Yamakawa-Fujii-Yoshizaki theory26,27 shows that the Na-gellan gum chain in 25 mM aqueous NaCl solution behaves as a typically stiff chain even in the disordered state. The above calculation, however, does not take into account the polydispersity effect on the measured [η]. Although the polydispersity effect on [η] is generally small, the above wormlike chain parameters may be somewhat misestimated; the z- to weight-average molar mass ratio, Mz/Mw, of our samples is between 1.44 and 1.56, if calculated by the relation of Mz/Mw ≈ 1 + 4(µ2/Γ h 2).35 To reanalyze the measured [η] data, we take into account the polydispersity effects using the Schulz-Zimm distribution function defined as fw(M) dM )

[

]( ) [

(m + 1)m+1 M m! Mw

m

]( )

M M exp -(m + 1) d Mw Mw (10)

m being the distribution parameter related to number-average molar mass Mn, Mw, and Mz by Mw/Mn ) 1 + 1/m or Mz/Mw ) (m + 2)/(m + 1). Then, intrinsic viscosity of a polydisperse wormlike cylinder is expressed by [η] )

Γ(m + 1 + a)

[η]0

(m + 1)aΓ(m + 1)

Figure 7. Comparison between the experimental and theoretical intrinsic viscosities. The solid lines represent the theoretical values for the polydisperse wormlike cylinders calculated from the Yamakawa-Fujii-Yoshizaki theory26,27 with eq 11 for q ) 9.4 nm, ML ) 355 nm-1, d ) 1.0 nm, and m ) 1 (40 °C) and q ) 98 nm, ML ) 650 nm-1, d ) 2.4 nm, and m ) 1 (25 °C). The dotted lines refer to the monodisperse case.

the gamma function. We take m to be 1 so that Mz/Mw comes close to 1.5. In this case, the measured [η] are 2.4% smaller than [η]0. The wormlike chain parameters for monodisperse Na-gellan are determined as q ) 9.4 nm, ML ) 355 nm-1, and d ) 1.0 nm if the polydispersity effect on the measured [η] is compensated by eq 11. Figure 7 shows that the theoretical solid curves for the polydisperse wormlike cylinder closely fit the measured [η] throughout the entire molar mass range examined. It can be seen that the explicit consideration of polydispersity effects changes the wormlike chain parameters for [η] at most only 3%. On the other hand, the contribution of molar mass polydispersity to RGz should not be negligible because the mean-square radius of gyration is experimentally obtained as the z-average value. Radius of gyration of Schulz-Zimm polydisperse samples is given as36 RGz2 (2q)

2

)

1 m + 2 Lw 1 1 2q - + 6 m + 1 2q 4 4 Lw -m m + 1 1 - [1 + 2(Lw/2q)/(m + 1)] (12) m 8(L /2q)2 w

where Lw is the weight-average contour length. In Figure 8, the theoretical curve of radius of gyration for Na-gellan in 25 mM NaCl at 40 °C calculated from eq 12 for the polydisperse wormlike chain is compared with the experimental RGz. Here, q, ML, and m are adopted as 9.4 nm, 355 nm-1, and 1, respectively. The experimental RGz shows a good agreement with the predictions of eq 12 throughout the entire molar mass range examined. Furthermore, the data of z-average hydrodynamic radii, RHz, are also well fitted by the wormlike cylinder model37 with the wormlike chain parameters estimated above if the polydispersity effect is compensated by

(11)

where a is the exponent value a ) 0.88 of [η] and Γ(x) is

RHz )

(m + 1)1-bΓ(m + 1) RH,0 Γ(m + 2 - b)

(13)



Table 2. Molecular Parameters Characterizing Na-gellan in 25 mM Aqueous NaCl 10-3Mw, g mol-1

Figure 8. Comparison between the experimental and theoretical radii of gyration. The solid lines represent the theoretical values for the polydisperse wormlike chains calculated from eq 12 for q ) 9.4 nm, ML ) 355 nm-1, and m ) 1 (40 °C) and q ) 98 nm, ML ) 650 nm-1, and m ) 1 (25 °C). The dotted lines refer to the monodisperse case.

where b is the exponent value b ) 0.76 of RHz and RH,0 is the hydrodynamic radius of an unperturbed monodisperse wormlike chain (Figure 9). Again, we confirm that the Schulz-Zimm polydisperse wormlike chain with parameter set of q ) 9.4 nm, ML ) 355 nm-1, d ) 1.0 nm, and m ) 1 is a good model for our disordered Na-gellan samples. Reproducibility Test. As seen above, [η], RGz, and RHz of the disordered gellan are well expressed by the wormlike chain models if the molar mass distributions of our samples are approximated by the Schulz-Zimm distribution function with Mz/Mw ) 1.5. The polydispersity effects, however, depend not only on the degree of polydispersity but also on the shape of the molar mass distribution.34 We therefore reanalyze the data of [η], RGz, and RHz by another procedure: that is, dynamic light scattering-CONTIN analysis.33,38,39 First, the molar mass distributions were retrieved from the decay rate distributions obtained from Laplace inversion analyses,33,39 and the Yamakawa-Fujii theory37 for RH with the wormlike chain parameters of q ) 9.4 nm, ML ) 355

RGz, nm

RHz, nm

CONTIN experimental ratioa

Sample NAG-A at 40 °C 117 4.99 115 5.20 1.02 0.96

37.0 35.6 1.04

17.9 17.7 1.01


Sample NAG-C at 40 °C 82.4 3.99 80.0 3.80 1.03 1.05

30.2 29.3 1.03

13.7 14.0 0.98


Sample NAG-G at 40 °C 64.0 3.26 63.8 3.13 1.00 1.04

27.4 26.1 1.05

12.3 11.9 1.03


Sample NAG-A at 25 °C 225 22.9 100 230 24.1 95.9 0.98 0.95 1.07

31.5 31.8 0.99


Sample NAG-C at 25 °C 156 14.3 161 14.6 0.97 0.98

79.3 74.8 1.06

24.3 25.6 0.95


Sample NAG-G at 25 °C 130 10.8 127 11.0 1.02 0.98

61.0 61.2 0.98

19.7 20.1 0.98

a

Figure 9. Comparison between the experimental and theoretical hydrodynamic radii. The solid lines represent the theoretical values for the polydisperse wormlike cylinders calculated from the Yamakawa-Fujii theory36 with eq 13 for q ) 9.4 nm, ML ) 355 nm-1, d ) 1.0 nm, and m ) 1 (40 °C) and q ) 98 nm, ML ) 650 nm-1, d ) 2.4 nm, and m ) 1 (25 °C). The dotted lines refer to the monodisperse case.

10-2[η], cm3 g-1

Ratio is [CONTIN]/[experimental].

nm-1, d ) 1.0 nm. Second, the distribution functions of [η], RGz, and RHz were calculated from the molar mass distributions thus obtained with the Yamakawa-Fujii-Yoshizaki theory for [η],26,27 Benoit-Doty equation for RG,39 and Yamakawa-Fujii theory for RH.37 Finally, Mw, [η]w, RGz, and RHz were calculated from respective distribution functions and compared with the experimental values; further detail has been described elsewhere.33,39 We note that no longer adjustable parameters are used in this calculation. Results are summarized in Table 2 for the samples NAG-A, -C, and -G as typical examples. Although there is a tendency to give slightly larger values of RGz than the experimental ones, the agreements are good enough between the calculated and experimental values, and the deviation is at most only 7% for RGz and 5% for other parameters; overestimation of RGz might be due to a slight uncertainty for the determination of the baseline of correlation functions resulting in overestimation of the higher molar mass contribution. By considering the polydispersity effects properly on the solution properties of disordered gellan, we determine [η], RGz, and RHz selfconsistently and quantitatively as a wormlike chain. Chain Stiffness in the Ordered State. In Figures 7-9, the data of [η], RGz, and RHz for the ordered gellan are compared with the Schulz-Zimm polydisperse wormlike chain models. The data points are well fitted by the respective theoretical curves for [η],26,27 RG,40 and RH37 if the parameter set is chosen as q ) 98 nm, ML ) 650 nm-1, d ) 2.4 nm, and m ) 1. The dynamic light scattering-CONTIN also gives this parameter set (Table 3). The magnitude of q ) 98 nm at 25 °C means a significant chain stiffness in the double-

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Table 3. Wormlike Chain Parameters of Na-gellan in 25 mM NaCl

T, °C

q, nm

ML, nm-1

d, nm

h, nm

40 25

9.4 98

355 650

1.0 2.4

0.47 0.51

helix state. This is in good agreement with the recent report using atomic force microscopy by Morris et al.41,42 Yuguchi et al.43 reported the diameter of Na-gellan in water by means of cross-sectional Guinier analyses by smallangle X-ray scattering as 0.76 nm at 60 °C and 0.98 nm at 10 °C (polymer concentration ) 1.0 wt %). In aqueous 50 mM NaCl solution, diameter of 0.88 nm at 60 °C (polymer concentration ) 1.5%) was also obtained.44 Those magnitudes are a little smaller than the present results, especially for the ordered state. In the present case, the diameter was evaluated from the hydrodynamic transport properties, and larger diameter is reasonable considering the effect of hydration. Conformational Properties. The linear mass density (molar mass per unit contour length), ML, is related to the monosaccharide projection length (monosaccharide length along with the chain contour), h, by h ) M0/ML, M0 being the molar mass of the monomer unit (669 g mol-1). Because each repeating unit of gellan contains four main chain monosaccharides, the values of h for both disordered and ordered Na-gellan are expressed by h)

M0/4 ML/x

(14)

with x ) 1 for the disordered state and x ) 2 for the ordered state. Table 3 summarizes the calculated h values together with the wormlike chain parameters for the disordered and ordered gellan in 25 mM aqueous NaCl solution. The ML value of 355 nm-1 for the disordered gellan yields 0.47 nm for h. This h value is reasonable if single-helical structure is considered. On the other hand, the ML value of 650 nm-1 for the ordered gellan yields 0.51 nm for h. This value is perfectly the same as the result on TMA-gellan8 but 9% larger than the X-ray data of h ) 0.47 nm.45 The ML value of double-stranded Na-gellan should be 712 nm-1 if h ) 0.47 nm. This discrepancy implies that the estimated ML value of 650 nm-1 for the double-stranded gellan might be underestimated (the contour length in the ordered state has 40 been overestimated).46 In fact, although the M25 w /Mw ratio is 40 almost 2 in the Mw range from 6.38 × 104 to 1.15 × 105, the ratio of the contour length at 25 to 40 °C, L25/L,40 is simply calculated as 1.09, suggesting that some portion of the total contour length of polydisperse gellan in the ordered state does not participate in the double-stranded structure completely (Figure 10). Probably the total persistence length evaluated at 25 °C is sum of the contribution of wormlike coils separated from a paired double-helical residue and a double-helical residue itself. In the gelation process, free single chain may interact with neighboring single chain resulting the cross-linking region in addition to the lateral

Figure 10. Model for a gellan dimer composed of polydisperse wormlike chains. Dimer consists of one wormlike double helix the ends of which are linked by single-stranded wormlike chains separated from paired helical residues. Effects of chain stiffness are not considered. Leffective denotes the contour length determined via wormlike chain analyses.

association of double-stranded region. This speculation is basically consistent with the fibrous model for the gelation mechanism of double-stranded polysaccharide solution proposed by Gunning and Morris.47 Concluding Remarks The present study demonstrated that the dimensional properties of deacetylated Na-gellan gum are well expressed by the wormlike chain models in the molar mass ranges from 3.47 × 104 to 1.15 × 105 at 40 °C and from 12.7 × 105 to 23.0 × 105 at 25 °C. The data for the molar mass, intrinsic viscosity, radius of gyration, and hydrodynamic radii at 25 °C all appeared to be consistent with the rigid dimerized structure. Generally, in regard to dimerized polysaccharides, single chains can readily form aggregates at high concentration whereas they can seldom contact each other at a very low concentration. Present results of the static light scattering data in Figure 4 show no anomalous concentration effect, indicating that cooling of disordered gellan solutions causes single chains to be dimerized with no substantial random aggregation at the present solvent condition. The chain stiffness changes greatly with temperature (q ) 9.4 nm at 40 °C and q ) 98 nm at 25 °C), but the gellan molecule behaves as a relatively stiff chain even in the disordered state of a single-stranded chain. The substantial stiffness in the single-stranded state makes the double-helix formation easy. To determine the local persistence length of double-stranded


gellan, we need further analysis using monodisperse samples. It is also very interesting to examine the effect of ionic strength on the conformational properties of gellan gum. These studies are now in progress. Acknowledgment. This research was partially supported by the Grants-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan (for JSPS Fellows- 2003 and Grant (A)(1)14208011). R.T. and K.N. thank San-Ei Gen F.F.I. Inc. for the financial support. References and Notes (1) Jansson, P.; Lindberg, B.; Sandford, P. A. Carbohydr. Res. 1983, 124, 135-139. (2) Crescenzi, V.; Dentini, M.; Dea, I. C. M. Carbohydr. Res. 1987, 160, 283-302. (3) Milas, M.; Shi, X.; Rinaudo, M. Biopolymers 1990, 30, 451-464. (4) Nishinari, K.; Miyoshi, E.; Takaya, T.; Williams, P. A. Carbohydr. Polym. 1996, 30, 193-207. (5) Annaka, M.; Takahashi, R.; Nakahira, T.; Tokita, M.; Matsukawa, T. Biomacromolecules 2001, 2, 635-640. (6) Ogawa, E.; Matsuzawa, H.; Iwahashi, M.; Sagara, Y.; Shioya, T.; Kimura, T. Trans. Mater. Res. Soc., Jpn. 2001, 26, 613-616. (7) Nishinari, K. Rep. Prog. Polym. Phys. Jpn. 2000, 43, 163-192. (8) Dentini, M.; Coviello, T.; Burchard, W.; Crescenzi, V. Macromolecules 1988, 21, 3312-3320. (9) Polydispersity effects were compensated by eq 12 in Schmidt, M.; Paradossi, G.; Burchard, W. Makromol. Chem. Rapid Commun. 1985, 6, 767-772. (10) Sato, T.; Norisuye, T.; Fujita, F. Macromolecules 1984, 17, 26962700. (11) Sato, T.; Norisuye, T.; Fujita, F. Polym. J. 1984, 16, 341-350. (12) Kido, S.; Nakanishi, T.; Norisuye, T. Biomacromolecules 2001, 2, 952-957. (13) Nakanishi, T.; Norisuye, T. Polym. Bull. 2001, 47, 47-53. (14) Liu, W.; Sato, T.; Norisuye, T.; Fujita, H. Carbohydr. Res. 1987, 160, 267-281. (15) Nakanishi, T.; Norisuye, T. Biomacromolecules 2003, 4, 736-742. (16) Okamoto, T.; Kubota, K.; Kuwahara, N. Food Hydrocolloids 1993, 7, 363-371. (17) Takahashi, R.; Akutu, M.; Kubota, K.; Nakamura, K. In Progress in Colloid and Polymer Science, Physical Chemistry and Industrial Application of Gellan Gum; Nishinari, K., Ed.; Springer: Berlin, 1999; Vol. 114, pp 1-7. (18) Progress in Colloid and Polymer Science, Physical Chemistry and Industrial Application of Gellan Gum; Nishinari, K., Ed.; Springer: Berlin, 1999; Vol. 114. (19) Huggins, M. L. J. Am. Chem. Soc. 1942, 64, 2716-2718. (20) Billmeyer, F. W., Jr. J. Polym. Sci. 1949, 4, 83-86. (21) Mead, D. J.; Fuoss, R. M. J. Am. Chem. Soc. 1942, 64, 277-282. (22) Pike, E. R.; Pomeroy, W. R. M.; Vaughan, J. M. J. Chem. Phys. 1975, 62, 3188-3192.

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BM034371U

Solution Properties of Gellan Gum: Change in Chain Stiffness

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