Range of total ionic strength (mmol/dm3) of λ‐carrageenan solutions, range of contribution (%) of added Na+ to the total ionic strength, the amount (meq) of Na+ necessary to neutralize the charges in λ‐carrageenan solutions (Na+nc), and concentration (meq/mL) of Na+ present in the commercial preparation (Na+cp)
Abstract
Small amplitude oscillatory and steady shear measurements at 25°C were used to investigate the rheological behavior of λ‐carrageenan solutions at pH 7.0 ± 1.0 without and with added sodium counterion. The dynamic moduli, G′(ω) and G″(ω), show the typical behavior of macromolecular solutions in which the viscous character predominates. The steady shear flow exhibits a Newtonian zero‐shear viscosity (η0) region followed by a shear‐thinning zone. Viscosity data can be well described by the Carreau‐Yasuda model. Without added Na+, the intrinsic viscosity, [η], and the critical overlap concentration, C*, are 204 dL/g and 0.21%, respectively. With 20 mmol/dm3 Na+, [η] = 14.7 dL/g and C* = 0.38%. For concentrations below C*, the viscous character is more sensitive to the presence of added Na+, and the opposite occurs when the concentration exceeds C*. The dynamic moduli and viscosity increase with the increase of polysaccharide concentration, but they decrease with added Na+, confirming the polyelectrolyte nature of λ‐carrageenan. Empirical shift factors were used to obtain master curves for the dynamic moduli and apparent viscosity for different polysaccharide and added Na+ concentrations.
Keywords
- carrageenan
- polysaccharides
- rheology
- viscoelasticity
- viscosity
1. Introduction
Recently, the nondigestible polysaccharides of natural origin have received great interest from the perspective of human health although they have been widely used for a long time [1, 2]. Carrageenans are among these polysaccharides. They are nondigestible linear sulfated polysaccharides extracted from red algae (
The functionality of carrageenans resides mainly in their structure and polyelectrolyte properties that allow them to interact with other components; they are anionic polysaccharides highly unstable in their free acid form and are commonly commercialized as a mixture of sodium, potassium, and calcium salts. Carrageenans are composed of alternating units of β‐d‐galactopyranoside linked to position 3 (G units) and α‐d‐galactopyranoside attached to position 4 (D units) or 3,6‐anhydrogalactose attached to position 4 (DA units). They form repetitive disaccharide “ideal” units, commonly called carrabioses, giving rise to each type of carrageenan. According to IUPAC rules, the name of λ‐carrageenan is carrageenase 2,6,2′‐trisulfate (G2S‐D2S, 6S) (Figure 1). The λ‐carrageenan lacks DA units and has a 4C1 conformation that causes the creation of twisted zones or segments in the polysaccharide chain. As a consequence, the formation of helices is not possible and gels are not formed but only viscous solutions. As it occurs with the other types, the solubility of λ‐carrageenan depends on temperature, pH of the solvent, type, and concentration of counterions, and other solutes. λ‐Carrageenan is soluble in water at room temperature because the polysaccharide‐polysaccharide interactions are weak [7]. Most of the early investigations were focused on the characterization of the structure and size of λ‐carrageenan by infrared spectrometry, nuclear magnetic resonance, and light scattering [8–10]. The synergistic effects on the rheological properties of λ‐carrageenan combined with other polysaccharides, such as locust bean gum [11], whey protein concentrate [12], and inulin [13], have been studied in complex food systems. However, to the best of our knowledge, the different aspects investigated in this work for λ‐carrageenan have not been previously reported.
Rheological techniques are widely used for the characterization of products and food additives. The variation of shear stress with shear rate or apparent viscosity with shear rate indicates if the flow behavior is Newtonian, shear‐thinning, or both. Small‐amplitude oscillatory tests within the zone of linear viscoelasticity (ZLV) are used to determine the variation of the storage modulus,
The objective of this work is to discuss the flow behavior and viscoelastic properties of λ‐carrageenan in aqueous solution, without or with the addition of sodium to characterize the polyelectrolyte behavior of the polysaccharide, and evaluate the effect of its concentration and that of the counterion on these behaviors. The overlap concentrations separating the dilute from the semidilute regimes were also determined. The flow behavior was described with empirical models. Shift factors for generating master curves of the mechanical spectra and flow curves are proposed for different λ‐carrageenan and added Na+ concentrations. These results are useful to understand better the thickening properties of this important polysaccharide.
2. Experimental
A food‐grade commercial preparation of λ‐carrageenan as provided by a local supplier (FMC Biopolymer, Mexico) was used without further treatment. Other materials included sodium chloride ACS reagent grade (Mallinckrodt Baker, Mexico) and deionized water. The content (ppm) of sodium, potassium, calcium, and magnesium ions in the commercial preparation of the polysaccharide, determined by atomic absorption, was Na+ = 30,863; K+ = 15,595; Ca2+ = 972, and Mg2+ = 1882.
2.1. Preparation of λ‐carrageenan solutions
λ‐Carrageenan solutions with concentrations of 0.002, 0.006, 0.01, 0.08, 0.5, 0.8, 1.0, 1.5, and 2.0% by weight were prepared without and with added Na+ considering the moisture content of the polysaccharide. The necessary amount of λ‐carrageenan to make 50 g of a solution was dispersed as fine rain with a vibrating spatula in the appropriate solvent at 70°C under magnetic stirring at 1000 rpm (Barnstead International, model Super‐Nuova SP131825, USA) until complete dissolution. The water that evaporated was compensated with the corresponding solvent. The solutions were stored in refrigeration at 3°C until analysis. Solutions with 0.002–2.0% λ‐carrageenan were prepared in 0, 20, 30, 50, 70, 80, 100, 120, and 140 mmol/dm3 NaCl. Besides, 1.5 and 2.0% λ‐carrageenan solutions were prepared in 160, 180, 200, 220, 240, and 260 mmol/dm3 Na+. Only for 2.0% λ‐carrageenan, solutions with 300, 350, and 400 mmol/dm3 Na+ were prepared too. The pH was 7.0 ± 1.0.
2.2. Ionic strength of λ‐carrageenan solutions without and with added sodium counterion
Given the anionic nature of λ‐carrageenan, the ionic strength of the aqueous environment is crucial. Table 1 shows the range of total ionic strength of all solutions without and with added Na+, the range of contribution of added Na+ to the total ion strength, the amount of sodium ion required to neutralize the charges in the different polysaccharide solutions, and the concentration of Na+ present in the commercial preparation.
C |
Imin–Imaxa | Contribution (%)b | Na+nc (meq) | Na+cp (meq/mL) |
---|---|---|---|---|
0.002 | 0.024–70.0 | 99.8 |
0.00952 | 2.98 × 10-5 |
0.006 | 0.072 |
99.3 |
0.0286 | 8.95·× 10-5 |
0.01 | 0.119 |
98.8 |
0.0476 | 1.49 × 10-4 |
0.08 | 0.95 |
91.3 |
0.381 | 1.19 × 10-3 |
0.50 | 5.97 |
62.6 |
2.38 | 7.46 × 10-3 |
0.80 | 9.50 |
51.3 |
3.81 | 1.19 × 10-2 |
1.0 | 11.9 |
45.7 |
4.76 | 1.49 × 10-2 |
1.5 | 17.9 |
35.8 |
7.14 | 2.24 × 10-2 |
2.0 | 23.9 |
29.5 |
9.52 | 2.98·× 10-2 |
The contribution of the internal counterions to the total ionic strength becomes significant only for high levels of the polysaccharide. Below 0.5% λ‐carrageenan, the total ionic strength is practically given by the added Na+, regardless of the concentration of added Na+. Above 0.5% λ‐carrageenan, the contribution of added Na+ depended on the concentrations of the polysaccharide and added Na+. The contribution of the internal counterions is always greater than that of added Na+ for concentrations of added Na+ ≤ 30 mmol/dm3. On the other hand, the Na+/λ‐carrageenan stoichiometric ratio is 4.76 meq/g. This value can be obtained considering a molecular weight of 630.41 for the sodium salt of the repeating unit of λ‐carrageenan and indicates the amount of sodium ion needed to neutralize the charges in 1 g of polysaccharide.
2.3. Rheometry
The rheological behavior of λ‐carrageenan solutions without and with added Na+ was determined in a rheometer (ARES‐RFS III, TA Instruments, Delaware, USA) using the Couette double‐wall concentric cylinders fixture with a diameter ratio of 0.95, and 1.0 mm gap between cylinders. All determinations were performed in duplicate at 25 ± 0.5°C. Rheological data are presented as means of at least two repetitions with a standard deviation not greater than 5.0%.
The viscoelastic properties were determined by small‐amplitude oscillatory shear tests. Strain sweeps were run from 0.1 to 100% strain (
The flow properties were determined from steady angular shear tests in the range of 0.03–300 s-1. Flow curves (
and the Carreau‐Yasuda equation [15]
using the nonlinear regressions routines of SigmaPlot© programming software. Only regressions with
2.3.1. Intrinsic viscosity and critical concentration
The intrinsic viscosity was determined from the graphical representation of the Huggins and Kraemer equations, given by Eqs.(3) and (4), respectively,
In these equations
2.3.2. Master curves
Concentration‐dependent shift factors on the ordinate and the abscissa of the flow curves (
3. Results and discussion
3.1. Viscoelastic behavior of λ‐carrageenan solutions without added sodium counterion
The variation with frequency of
For a given constant frequency both moduli increase with the increase of polysaccharide concentration, but this increase is not proportional. For example, at 10 rad/s
3.2. Steady flow behavior of λ‐carrageenan solutions without added sodium counterion
The variation of apparent viscosity with a shear rate and λ‐carrageenan concentration is shown in Figure 3. The dependence between these two quantities for a given shear rate is approximately
3.3. Intrinsic viscosity and critical concentration of λ‐carrageenan solutions without added sodium counterion
The intrinsic viscosity, [
On the other hand, the critical concentration,
Solutions with 0.5, 0.8, 1.0, 1.5, and 2.0% λ‐carrageenan are semidilute. The shear‐thinning behavior becomes more evident than for dilute solutions (Figure 3). In these solutions, polysaccharide‐polysaccharide interactions, in the form of overlaps and interlocks, become increasingly significant while polysaccharide‐water interactions decrease. When the chains are deformed, the entanglements are disturbed. At low shear rate, there is enough time for new entanglements to be formed and their number to remain constant over time. Therefore, viscosity remains practically constant. This phenomenon gives rise to the zero‐shear Newtonian region. The transition to the shear‐thinning zone occurs when the shear rate is greater than the rate of formation of new entanglements [16]. As a consequence, there are fewer polymer‐polymer interactions which facilitate the flow of the solution and cause the viscosity to decrease.
The rate of formation of new interactions is related to the concentration of polymer in solution. The space occupied by the polymer and particularly the available space are related to C[
3.4. Flow models of λ‐carrageenan solutions without added sodium counterion
The Cross and the Carreau‐Yasuda are two of the more traditional flow models. The regression parameters of the two models for each λ‐carrageenan solution without added Na+ are shown in Table 2. In both models, the increase in the zero‐shear viscosity (
Cross | Carreau‐Yasuda | ||||||||
---|---|---|---|---|---|---|---|---|---|
r2 | |||||||||
0.002 | 0.0030 | 0.2789 | 0.944 | 0.9879 | 0.0017 | 0.0193 | 0.2047 | 0.939 | 0.9883 |
0.006 | 0.0030 | 0.0011 | 0.526 | 0.9967 | 0.0028 | 0.0466 | 1.3320 | 0.860 | 0.9984 |
0.01 | 0.0044 | 0.0022 | 0.396 | 0.9962 | 0.0041 | 0.0415 | 1.7380 | 0.813 | 0.9995 |
0.08 | 0.0131 | 0.0019 | 0.189 | 0.9976 | 0.0129 | 0.0160 | 1.2420 | 0.734 | 0.9990 |
0.5 | 0.0631 | 0.0029 | 0.343 | 0.9997 | 0.0627 | 0.0069 | 0.7295 | 0.531 | 0.9998 |
0.8 | 0.1392 | 0.0061 | 0.384 | 0.9997 | 0.1377 | 0.0107 | 0.6746 | 0.489 | 0.9999 |
1.0 | 0.2414 | 0.0095 | 0.363 | 0.9997 | 0.2387 | 0.0225 | 0.7329 | 0.525 | 0.9999 |
1.5 | 0.7602 | 0.0305 | 0.408 | 0.9997 | 0.7593 | 0.0323 | 0.6028 | 0.413 | 0.9998 |
2.0 | 2.0080 | 0.0633 | 0.377 | 0.9998 | 2.0110 | 0.0581 | 0.6147 | 0.361 | 0.9999 |
The parameter
The power‐law model is used to describe only the shear‐thinning region. The description of the flow curves with this model requires the experimental data to be adjusted to Eq. [5].
Table 3 shows the parameters obtained with such fitting and the good correlations obtained. This proficiency of the model is not surprising, but the limitations in comparison with the Cross and Carreau‐Yasuda equations are evident. The consistency index,
0.5 | 0.1331 | 0.76 | 0.9971 |
0.8 | 0.2881 | 0.72 | 0.9955 |
1.0 | 0.5350 | 0.68 | 0.9960 |
1.5 | 1.708 | 0.59 | 0.9982 |
2.0 | 4.556 | 0.51 | 0.9987 |
3.5. Viscoelastic behavior of λ‐carrageenan solutions with added sodium counterion
Figure 4 shows the effect of added Na+ on the dynamic moduli. The ratios
After an initially noticeable decrease, the dynamic moduli remain practically constant with the increase in the total ionic strength, that is, for concentrations greater than 20 mmol/dm3 Na+. On the other hand, this concentration is superior to the stoichiometric counterion/polysaccharide ratio and is sufficient to screen all the charges in the macromolecule.
The effect of the total ionic strength on 0.5% λ‐carrageenan solutions can also be seen in Figure 4. In this case, the rate of diminution due to the increase in the total ionic strength is 60% for both moduli in comparison with a solution with the same polysaccharide concentration but without added Na+. Moduli decrease and then become practically independent of Na+ concentration. However, above 45 mmol/dm3 approximately, the moduli increase around 10%. At this point, it is possible that ions start to compete for water associated with the polysaccharide because ions are not hydrated enough as they are added to the solution which for 0.5% λ‐carrageenan is in the semidilute regime. The addition of Na+ can lead to the formation of a new more elastic structure than the one observed when there is enough water to hydrate all molecules and ions in solution.
The effect of the increase in ionic strength on 0.8% λ‐carrageenan solutions is observed in Figure 5. The dynamic moduli decrease about 25–30% for 20 mmol/dm3 Na+ (
For 1.0% λ‐carrageenan solutions, the diminution in the presence of added Na+ is almost 30% as compared with solutions without added Na+. The minimum
In the case of 1.5 and 2.0% λ‐carrageenan solutions with added Na+, a respective decrease of 10% for
The decrease in dynamic moduli for 1.5% λ‐carrageenan solutions continues until the total ionic strength is 32.9 mmol/dm3. From this point
3.6. Steady flow behavior of λ‐carrageenan solutions with added sodium counterion
Solutions were also examined under steady angular shear to observe the effect of added Na+ on their thickening properties. Newtonian behavior with a viscosity close to 1 mPa s was found in the range of 6–300 s-1 for 0.002, 0.006, and 0.01% λ‐carrageenan solutions with 20 mmol/dm3 Na+ (
In the case of the 0.08% λ‐carrageenan solution with 20 mmol/dm3 Na+ (
In solutions with 0.5% λ‐carrageenan, a similar behavior is observed. The viscosity decreases 60% when the concentration of added Na+ is 20 mmol/dm3 (
For 0.8 and 1.0% λ‐carrageenan solutions, viscosity decreases of 34 to 28%, respectively, are observed with the addition of 20 mmol/dm3 Na+;
For 1.0% λ‐carrageenan solutions, viscosity increases from the minimum ratio up to 132% of its value without added Na+. However, this increase in viscosity is not linear (
For solutions with concentrations higher than 1.0% polysaccharide, a different behavior is observed (Figure 8). The viscosity of 1.5% λ‐carrageenan solutions without added Na+ decreases 12% when the ionic strength is 32.9 mmol/dm3 in comparison with
For the 2.0% λ‐carrageenan solutions, a minimum is observed for an ionic strength of 33.9 mmol/dm3 which corresponds to a 12% decrease (Figure 8B) regarding 23.9 mmol/dm3 without added Na+. From these minimum values, viscosity suddenly increases with increasing the addition of Na+. Hydration of the Na+ counterions and the formation of semiordered and more elastic structures might explain the growth in viscosity to 200 and 270% for 1.5 and 2.0% λ‐carrageenan, respectively. It is possible that for higher external Na+ concentrations (
3.7. Intrinsic viscosity and critical concentration of λ‐carrageenan solutions with added sodium counterion
The intrinsic viscosity of λ‐carrageenan in a 20 mmol/dm3 Na+ solution is 14.7 dL/g. Values reported in the literature are 9.5 dL/g in 100 mmol/dm3 NaCl for
The critical concentration,
3.8. Flow models of λ‐carrageenan solutions with added sodium counterion
The Carreau‐Yasuda model describes better the flow curves of λ‐carrageenan without added Na+. The same happens with added Na+. However, it is not always possible to obtain proper fittings because, in most cases, the zero‐shear region is not observed in the semidilute regime or the shear‐thinning zone in the dilute regime. Table 4 shows the experimental values of the parameters
Na+ (mmol/dm3) | ||||||
---|---|---|---|---|---|---|
0.5 | 70 | 0.022 | 0.018 | 1.426 | 0.82 | 0.9945 |
80 | 0.023 | 0.014 | 1.139 | 0.79 | 0.9994 | |
0.8 | 20 | 0.087 | 0.014 | 0.801 | 0.61 | 0.9996 |
30 | 0.080 | 0.023 | 0.990 | 0.69 | 0.9995 | |
50 | 0.077 | 0.021 | 0.931 | 0.67 | 0.9999 | |
70 | 0.073 | 0.020 | 0.888 | 0.65 | 0.9998 | |
1.0 | 20 | 0.166 | 0.030 | 0.847 | 0.61 | 0.9990 |
30 | 0.159 | 0.009 | 0.643 | 0.42 | 0.9986 | |
1.5 | 20 | 0.658 | 0.046 | 0.691 | 0.47 | 0.9997 |
3.9. Master curves for mechanical spectra and steady flow
The mechanical spectra and flow curves can be expressed with their corresponding master curves for a constant concentration of added Na+ and λ‐carrageenan concentrations of 0.002–2.0%. Two empirical shift factors were determined to produce each master curve. The factor
The modulus
The following shift factors are used to superimpose the flow curves:
As it happens with the mechanical spectra, the factor
4. Conclusion
The results of this investigation make evident the high sensitivity of λ‐carrageenan to the ionic strength of the aqueous environment, mainly given by the added Na+. This sensitivity is primarily attributed to the polyelectrolyte character of the polysaccharide, but hydration effects and competition for the solvent between the polyanion and sodium counterions can also play a role. The solutions of the commercial preparation of λ‐carrageenan without and with added Na+ are viscoelastic fluids with a dominant viscous behavior. However, with added Na+ the elastic character becomes more important when the polysaccharide concentration increases. In the dilute regime, the viscous character is considerably more sensitive to the addition of Na+. In the semidilute regime, the opposite occurs as the addition of Na+ affects more the elastic nature. Also, with added Na+, it is possible clearly to distinguish three types of behaviors of the apparent viscosity and the dynamic moduli. In the dilute regime and the low‐concentration region of the semidilute regime, moduli decrease drastically when the total ionic strength increases slightly over that without added Na+ and then remain substantially constant regardless of the increase in the total ionic strength. In the semidilute regime for moderate carrageenan concentrations, the moduli reach a minimum for intermediate total ionic strengths and then recover when the total ionic strength increases without necessarily achieve their values without added Na+. Finally, in the same semidilute regime but for large concentrations of polysaccharide, the moduli decrease as the total ionic strength increases slightly over that without added Na+ and show a high recovery, which in the case of the storage moduli and the apparent viscosity significantly exceed their level without added Na+.
Considering all this evidence, the existence of different levels of structural organization of the polysaccharide chains together with their close interactions with them and with the solvent and the added Na+ mainly can be postulated. Therefore, the results presented here allow the polyelectrolyte behavior of λ‐carrageenan to be better understood for a significant range of polysaccharide concentrations under broad conditions of total ionic strength. These characteristics take relevance in the case of commercial preparations that under normal circumstances are used without further treatments, e.g., separation of accompanying counterions to produce a particular salt form of the polysaccharide. Such purified forms are used for more fundamental studies and would be the next step in the investigation of the flow properties of the polysaccharide.
Acknowledgments
The authors would like to acknowledge the financial support of Programa de Apoyo a la Investigación y el Posgrado (PAIP) of Facultad de Química‐UNAM (Grant 5000‐9098).
References
- 1.
Niu TT, Dong‐Sheng Z, Hai‐Min C, Xiao‐Jun Y. Modulation of the binding of basic fibroblast growth factor and heparanase activity by purified λ‐carrageenan oligosaccharides. Carbohydrate Polymers. 2015; 125 :76–84. DOI: 10.1016/j.carbpol.2015.02.069 - 2.
Chen H, Wang F, Mao H, Yan X. Degraded λ‐carrageenan activates NF‐κB and AP‐1 pathways in macrophages and enhances LPS‐induced TNF‐α secretion through AP‐1. Biochimica et Biophysica Acta. 2014; 1840(7) :2162–2170. DOI: 10.1016/j.bbagen.2014.03.011 - 3.
McHugh DJ. Carrageenan: A Guide to the Seaweed Industry. FAO Fisheries Technical Paper 441. [Internet]. 2003. Available from: http://www.fao.org/docrep/006/y4765e/y4765e0a.html [Accessed: 2016‐05‐30] - 4.
Commission of Codex Alimentarius. GSFA Online. Carrageenan (407). [Internet]. 2012. Available from: http://www.codexalimentarius.net/gsfaonline/additives/details.html?id=49&lang=es [Accessed: 2016‐05‐30] - 5.
Code of Federal Regulations. Title 21: Food and Drugs, Part 172 Food Additives Permitted for Direct Addition to Food for Human Consumption, Subpart G—Gums, Chewing Gum Bases and Related Substances. §172.620 Carrageenan [Internet]. 2013. Available from: www.wcfr.gov [Accessed: 2016‐05‐30]. - 6.
van de Velde F, De Ruiter GA. Carrageenan. In: Steinbúchel A, Rhee SK, editors. Polysaccharides and Polyamides in the Food Industry . Weinheim: Wiley–Blackwell; 2005. pp. 85–111. - 7.
Eliasson A. Carbohydrates in Food. 2nd ed. Boca Ratón: CRC Press; 2006. pp. 244–252. - 8.
De Lestang Bremond G, Quillet M, Bremond M. λ‐Carrageenan in the gametophytes of Chondrus crispus . Phytochemistry. 1987;26(6) :1705–1707. - 9.
Slootmaekers D, van Dijk JAPP, Varkevisser FA, Bloys van Treslong CJ, Reynaers H. Molecular characterization of κ‐ and λ‐carrageenan by gel permeation chromatography, light scattering, sedimentation analysis and osmometry. Biophysical Chemistry. 1991; 41 :51–59. - 10.
Noseda MD, Cerezo AS. Room temperature, low‐field 13C‐N.M.R. spectra of degraded carrageenans: Part III. Autohydrolysis of a lambda carrageenan and of its alkali‐treated derivative. International Journal of Biological Macromolecules. 1993; 15 :177–181. - 11.
Camacho MM, Martínez‐Navarrete N, Chiralt A. Influence of locust bean gum/λ‐carrageenan mixtures on whipping and mechanical properties and stability of dairy creams. Food Research International. 1999; 31 :653–658. - 12.
Lizarraga MS, De Piante D, González R, Rubiolo A, Santiago LG. Rheological behaviour of whey protein concentrate and λ‐carrageenan aqueous mixtures. Food Hydrocolloids. 2006; 20 :740–748. - 13.
Bayarri S, Chuliá I, Costell E. Comparing λ‐carrageenan and an inulin blend as fat replacers in carboxymethyl cellulose dairy desserts. Rheological and sensory aspects. Food Hydrocolloids. 2010; 24 :578–587. - 14.
Cross MM. Rheology of non‐Newtonian fluids: a new flow equation for pseudoplastic systems. Journal of Colloid Science. 1965; 20 :417–437. - 15.
Bird RB, Armstrong CR, Hassager O. Dynamics of Polymeric Liquids. Vol. 1 Fluid Mechanics. New York: John Wiley & Sons Inc.; 1987. 670 p. - 16.
Graessley W. The entanglement concept in polymer rheology. Advances in Polymer Science. 1974; 16 :164–179. - 17.
Almutairi FM, Adams GG, Kök MS, Lawson CJ, Gahler R, Wood S, Foster TJ, Rowe AJ. An analytical ultracentrifugation based system study on the conformation of lambda carrageenan in aqueous solution. Carbohydrate Polymers. 2013; 97 :203–209.