Large amplitude oscillatory shear behavior and gelation procedure of high and low acyl gellan gum in aqueous solution

Carbohydrate Polymers 199 (2018) 397–405

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Carbohydrate Polymers journal homepage: www.elsevier.com/locate/carbpol

Large amplitude oscillatory shear behavior and gelation procedure of high and low acyl gellan gum in aqueous solution

T

⁎

Kefeng Tonga, , Guoping Xiaob, Weifeng Chenga, Jing Chena, Peiwen Suna a b

Shanghai Chicmax Cosmetic Co., Ltd., Shanghai 200233, China Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Gellan gum LAOS Lissajous curves Chebyshev coefficients Gelation

The rheological properties of gellan fluid gels were investigated using large amplitude oscillatory shear (LAOS) technique in both linear and non-linear viscoelastic regimes, with consideration of high acyl (HA)/low acyl (LA) gellan ratio and Ca2+ concentration. The Lissajous curves and Chebyshev coefficients were used to analyze the LAOS data and successfully provided visual and quantitative representation of microstructural differences between HA and LA gellan gum, respectively. Temperature sweep measurements were performed to monitor the gelation procedure of gellan gum solution. The results show that HA gellan gum forms softer but more stable gels than LA gellan gum, especially at high temperature. And a synergistic interaction between HA and LA gellan gum may exist in the presence of abundant Ca2+ ions. The abovementioned study can allow a better understanding of structural characteristic of gellan gum and provide a practical approach to rheological assessment that facilitates the processing and diversified application of mixed gellan gum.

1. Introduction Gellan gum is a microbial linear anionic polysaccharide secreted by the bacterium Sphingomonas elodea, which is composed of tetrasaccharide (1,3-β-D-glucose, 1,4-β-D-glucuronic acid, 1,4-β-D-glucose, 1,4-α-L-rhamnose) repeating units (Ogawa, Takahashi, Yajima, & Nishinari, 2006). In native gellan, also called high acyl gellan (HA gellan), glucose residue-A contains an L-glycerte group at C2 and an acetate group at C6 with an approximate 50% replacement level. Low acyl gellan (LA gellan), which forms firm and brittle gels in the presence of cations (Grasdalen & Smidsrød, 1987), can be obtained with the strong alkali treatment of HA gellan at high temperatures. Both HA and LA gellan molecules can make a conformational transition from disordered random coils to double helices with decreasing temperature (Huang, Tang, Swanson, & Rasco, 2003). Further decrease in temperature leads to the aggregation of double helices to form a three-dimensional network in the presence of either monovalent or divalent cations (Lau, Tang, & Paulson, 2001). The gellan three-dimensional network is stabilized by either direct cross-linking with divalent cations or indirect cross-linking with monovalent cations (Huang et al., 2003), indicating divalent cations have a better ability of inducing gelation than monovalent cations at significantly lower concentrations (Chandrasekaran & Radha, 1995; Rodrı́Guez-Hernández & Tecante, 1999). Actually, ionic cross-linking between divalent cations ⁎

and other polysaccharides such as alginates has already been widely studied and the well-known “egg-box model” (Grant, Morris, Rees, Smith, & Thom, 1973) has been proposed to describe the gelation and structure of alginate gels because of high affinity of the polyguluronate blocks to divalent cations (Braccini & Pérez, 2001; Gacesa, 1988; Russo, Malinconico, & Santagata, 2007). The structural differences between HA and LA gellan gum induce great diversity of textural properties. The HA gellan gum forms softer but much more stable gels than LA gellan gum due to the glycerate group in HA gellan gum (Huang et al., 2003; Mazen, Milas, & Rinaudo, 1999; Morris, Gothard, Hember, Manning, & Robinson, 1996). Mixtures of HA and LA gellan gum can produce gels with a wide variety of intermediate properties depending on the HA/LA gellan ratio (Gonzálezcuello, Ramosramírez, Cruzorea, & Salazarmontoya, 2012). By varying the HA/LA gellan ratio, the mixture can even match the texture of other hydrocolloids. Therefore, gellan gum has been utilized in a wide variety of food products, pharmaceutical, personal care and oral care as a gelling, suspending and texturizing agent because of its small dosage and diversified textural properties compared to other common polysaccharides. Investigating the rheological properties can provide intuitive and quantitative approach to exploring the gelation mechanism as well as the effects of pH value (Moritaka, Nishinari, Taki, & Fukuba, 1992), cations (Huang, Singh, Tang, & Swanson, 2004; Mazen et al., 1999;

Corresponding author. E-mail address: [email protected] (K. Tong).

https://doi.org/10.1016/j.carbpol.2018.07.043 Received 6 March 2018; Received in revised form 9 July 2018; Accepted 13 July 2018 0144-8617/ © 2018 Elsevier Ltd. All rights reserved.

Carbohydrate Polymers 199 (2018) 397–405

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Nomenclature

en t G′ G′′ Gn′ Gn′′ ′ GM GL′ Tn γ γ0 γ˙

γ˙0 δn ηM′ ηL′ νn τ τ′ τ ′′ τn τ0′ τ0′′ ω

n-th order elastic Chebyshev coefficient time storage moduli loss moduli n-th order storage moduli n-th order loss moduli minimum strain modulus large strain modulus n-th order Chebyshev polynomials of the first kind strain strain amplitude strain rate

strain rate amplitude n-th order phase angle instantaneous smallest strain-rate viscosity instantaneous largest strain-rate viscosity n-th order viscous Chebyshev coefficients stress elastic stress viscous stress stress amplitude of n-th harmonic elastic stress amplitude viscous stress amplitude strain frequency

2.2. Preparation of gellan fluid gels

Miyoshi, Takaya, & Nishinari, 1994; Takahiro et al., 2009; Tang, Tung, & Zeng, 2010b), HA/LA gellan ratio and mixed gel (Lee et al., 2003; Miyoshi, Takaya, Williams, & Nishinari, 1996; Rodrı́Guez-Hernández & Tecante, 1999; Simeone, Tassieri, Sibillo, & Guido, 2005) on the textural properties of gellan gels, subsequently improving the performance of gellan gels in the practical application such as particle suspension, pick up and spreadability of cosmetic and texture of food. Traditionally, rheological properties of gellan gum have been extensively studied mainly focusing on flow curves and small amplitude oscillatory shear (SAOS). However, only few large amplitude oscillatory shear (LAOS) tests for gellan gels have been reported. Hellriegel et al. conducted LAOS tests for gellan-based hydrogel but they did not provide sufficient analysis for rheological properties of gellan in non-linear viscoelastic regime (Hellriegel et al., 2014). Lorenzo et al. studied the non-linear viscoelastic properties of mixed gellan gels without consideration of Ca2+ concentration, by using simple non-linear regression method with low accuracy (Lorenzo, Zaritzky, & Califano, 2015). Therefore, a systematic and in-depth LAOS study of gellan fluid gels with consideration of HA/LA gellan ratio and Ca2+ concentration is still needed to be carried out. Furthermore, LAOS technique succeeds to describe the rheological phenomena and characterizing the microstructures of complex fluids in non-linear viscoelastic regime where traditional shear flow experiments and SAOS technique fail, which is helpful in characterizing and improving real processing and application of gellan fluid gels. In this study, the rheological properties of gellan fluid gels were investigated by LAOS technique in both the linear and non-linear viscoelastic regimes, with consideration of HA/LA gellan ratio and Ca2+ concentration. The obtained LAOS data was then interpreted by Lissajous curves and Chebyshev coefficients to reveal the distinction of microstructure between HA and LA gellan gum. Moreover, gelation procedure of gellan gum solution was studied by temperature sweep measurements to facilitate the processing and diversified application of mixed gellan gum.

The HA gellan gum, LA gellan gum or mixed gellan gum with different HA/LA gellan ratio (75/25, 50/50, 25/75) was dispersed in deionized water at concentration of 0.5 wt% at 90 °C under 500 rpm for 30 min by using an IKA agitator. After the hydration of gellan gum, the required amount of CaCl2 was added under stirring for additional 5 min. Deionized water at 90 °C was added to make up the evaporative losses. Subsequently, the gellan gum solutions were allowed to be gelated in a water bath at 20 °C (García, Alfaro, & Muñoz, 2015). The fluid gels were then obtained by mechanical treatment with the IKA agitator for 20 min. The fluid gels were stored at 5 °C for 48 h to allow equilibrium prior to the rheological measurements. 2.3. Rheological measurements All rheological measurements were performed with a HAAKE MARS III rheometer (Thermo Scientific, Karlsruhe, Germany) equipped with a parallel-plate with geometry of 35 mm diameter and 1 mm gap. The samples were put between the plates and the exposed edge was sealed with silicone oil to prevent evaporation of water during measurements (Filipčev, Šimurina, Bodroža-Solarov, & Brkljača, 2013). All the samples were left for a rest time of 10 min to relax any normal stresses induced during sample loading (Lorenzo, Zaritzky, & Califano, 2013). 2.3.1. Temperature sweep measurements Temperature sweep measurements were performed to monitor the sol-gel transition in gellan gum solutions (0.5 wt%) with different concentrations of Ca2+ (2, 5, 10 mM), by measuring the variation of elastic modulus G′ as a function of temperature. Instead of gellan fluid gels, the aforementioned hot gellan gum solution was directly loaded onto the preheated plate and equilibrated for 10 min. The temperature was ramped downward between 80 °C and 5 °C at a constant rate (0.5 °C/min) and oscillation frequency (1 Hz) within the linear viscoelastic regime. The gelation temperature corresponds to an inflection point where the dynamic shear elastic modulus G′ increases steeply (Moritaka, Fukuba, Kumeno, Nakahama, & Nishinari, 1991).

2. Materials and methods 2.1. Materials

2.3.2. Large amplitudes oscillatory shear (LAOS) measurements In order to simulate the real processing and application of the gellan fluid gels, large amplitude oscillatory shear (LAOS) experiments were performed to describe the elastic and viscous properties of gellan fluid gels beyond the linear viscoelastic regime. Based on the strain-controlled sweep, sinusoidal strains with variable amplitude were applied at a fixed frequency of 1 Hz. The oscillation raw data were collected with native rheometer control software (Rheowin Job Manager) and processed with MITlaos software (Ewoldt, Hosoi, & Mckinley, 2009).

Food grade commercial high acyl gellan gum (Kelcogel® CG-HA, CAS NO: 71010-52-1) and low acyl gellan gum (Kelcogel® CG-LA, CAS NO: 71010-52-1) were purchased from CP Kelco. Analytical reagent grade CaCl2 (CAS NO: 10043-52-4) and NaCl (CAS NO: 7647-14-5) were purchased from Sinopharm Chemical Reagent Co., Ltd and used without any further purification. The deionized water was used throughout the research.

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Typically, 3rd order Chebyshev coefficients (e3 and ν3 ) are used to determine the material nonlinear viscoelastic behavior:

The Fourier-transform method is often used to analyze LAOS data. A typical sinusoidal strain is given by (Sim, Ahn, & Lee, 2003):

γ (t ) = γ0 sin(ωt )

(1)

where γ 0 is the strain amplitude, ω is the imposed strain frequency. As the strain amplitude γ 0 is small, the stress is sinusoidal and can be expressed in Eq. (2) (Sim et al., 2003). When the sample progresses into the non-linear viscoelastic regime, the response stress is no longer sinusoidal due to contribution of the other harmonics and can be represented as a Fourier series of multiple harmonics of stress contribution in Eq. (3) (Li, Du, Chen, Song, & Guo, 2003):

τ (t ) = τ0′ sin(ωt ) + τ0′′cos(ωt ) = γ0 G′sin(ωt ) + γ0 G′′cos(ωt ) ∞

∑

τnsin(nωt + δn ) = γ0

n = 1,odd

(8)

⎧> 0 shear − thickening ν3 = = 0 linear viscous (Newtonian) ⎨ ⎩< 0 shear − thinning

(9)

where strain stiffening and strain softening correspond to an intracycle increase and decrease in G′, respectively. Shear-thickening and shear thinning correspond to intracycle increase and decrease in G′′, respectively. Also, a new interpretation of viscoelastic moduli has been developed in the nonlinear regime based on a local methods (Carmona et al., 2014) (intracycle non-linearities) that allow the viscoelastic moduli at an instantaneous strain to be calculated. By taking the higher harmonic contributions into account, the elastic modulus was put into minimum ′ strain modulus GM and large strain modulus GL′ . Moreover, the in′ and instantaneous largest stantaneous smallest strain-rate viscosity ηM ′ strain-rate viscosity ηL are obtained analogously to define the strain and strain rate dependence behavior. The definitions related to Chebyshev coefficients are:

(2)

∞

∑

τ (t ) =

⎧> 0 strain−stiffening e3 = = 0 linear elastic ⎨ ⎩< 0 strain−softening

[Gn′ sin(nωt ) + Gn′′ cos(nωt )]

n = 1,odd

(3) where τn and δn is the amplitude of shear stress and phase angle of the n-th harmonic, respectively. Gn′ and Gn′′ are the storage and loss moduli of the n-th harmonic, respectively. Only the odd harmonics are included since the stress response is assumed to be odd symmetry with respect to the directionality of strain or strain rate (Carmona, Ramírez, Calero, & Muñoz, 2014). In order to interpret the nonlinearities, which may not be explained fully with the foundational viscoelastic functions G′ and G′′, Ewoldt et al. (Ewoldt, Hosoi, & Mckinley, 2008) suggest an additional orthogonal decomposition of the elastic and viscous stress using Chebyshev polynomials of the first kind based on the orthogonal decomposition of the general stress proposed by Cho et al. (Cho, Hyun, Ahn, & Lee, 2005):

′ GM ≡

dτ dγ

= e1−3e3 + ⋯ (10)

γ=0

∞

γ γ τ ′ ⎛⎜ ⎞⎟ = γ0 ∑ en (ω, γ0) Tn ( ) γ0 ⎝ γ0 ⎠ n = 1 odd

γ˙ τ ⎜ ⎞⎟ = γ˙0 γ ⎝ ˙0 ⎠ ′′ ⎛

∞

∑ n = 1 odd

′

γ˙ νn (ω, γ0) Tn ⎛⎜ ⎞⎟ γ ⎝ ˙0 ⎠

′′

where τ and τ are elastic and viscous stress, respectively. γ˙ Tn ( γ˙ ) 0

GL′ ≡

(4)

(5) γ Tn ( γ ) 0

ηM′ ≡

and

are n-th order Chebyshev polynomials of the first kind, and en and νn are the n-th order elastic and viscous Chebyshev coefficients. The relationships between the Chebyshev coefficients in the strain or strain rate domain and the Fourier coefficients in the time domain are thus given by:

en = Gn′ (−1)(n − 1)/2 n: odd

νn =

Gn′′ n: odd ω

ηL′ ≡

τ γ

= e1 + e3 + ⋯

dτ dγ˙

τ γ˙

(11)

γ =±γ0

= ν1−3ν3 + ⋯ (12)

γ˙ = 0

= ν1 + ν3 + ⋯ γ˙ =±γ˙0

(13)

by analyzing these elastic modulus and instantaneous dynamic viscosities, Lissajous curves can be readily quantified to provide quantitative and meaningful non-linearities responses of the fluid gels in nonlinear regime. Beyond linear viscoelasticity, this nonlinear LAOS experiment generates rich data related to material structure, processing, applications, and functions of gellan gum.

(6)

(7)

Fig. 1. The gelation curves of gellan gum solutions (0.5 wt%) with different concentrations of CaCl2 (I: 2 mM; II: 5 mM; III: 10 mM). (a) LA gellan gum solution (b) mixed gellan gum solution with HA/LA gellan ratio = 50:50 (c) HA gellan gum solution. 399

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3. Results and discussion

distinguishable because the gelation behaviors becomes to be analogous to those of HA gellan gum solution. At 10 mM of Ca2+, the gel formed by mixed gellan gum solution has higher elastic modulus G′ than the gels formed by HA gellan gum solution and LA gellan gum solution. This synergistic interaction phenomenon between HA and LA gellan gum, which to our knowledge is for the first time observed in gelation research of mixed gellan gum, likely due to the stable interpenetrating polymer network stabilized by abundant Ca2+ ions (Mao, Tang, & Swanson, 2000).

3.1. Temperature sweep measurements As shown in Fig. 1, all the gellan gum solutions form gel structures on lowering the temperature in the presence of CaCl2. Compared to the elastic modulus G′ in Fig. 1(a) and (c), gels formed by HA gellan gum solutions is softer than gels formed by LA gellan gum solutions at corresponding concentration of CaCl2, which have been theoretical explained (Chandrasekaran & Thailambal, 1990). HA gellan gum solution forms gel gently on cooling throughout the temperature range while the gelation curves of LA gellan gum solution show two step-like changes in elastic modulus G′ in the presence of Ca2+. For HA gellan gum, the substituents (such as glycerate group) are considered to stabilize the double helix structure (Matsukawa & Watanabe, 2007). Therefore, HA gellan gum shows higher gelation ability and is much less sensitive to Ca2+ than LA gellan gum, especially at high temperature. Since LA gellan gum solution only shows coil-helix transition but not sol-gel transition, extra cations are needed to stabilize the three-dimensional network. Within the Ca2+ range, increasing Ca2+ concentration results in higher gelation temperature in LA gellan gum solution as shown in Fig. 1. And the gelation temperature of LA gellan gum solution shifts from ca. 35℃ to ca. 55 ℃ while no accurate gelation temperature can be read in HA gellan gum solution. Similar results were reported in LA gellan gum solution with Mg2+ (Tang, Tung, & Zeng, 2010a). Fig. 1(b) indicates that the gels formed by mixed gellan gum solution with Ca2+ exhibit unique rheological properties different from those formed by HA or LA gellan gum solution. The elastic modulus G′ increases apparently with increasing Ca2+ concentration at corresponding temperature. And the gelation temperature is also hardly

3.2. Large amplitudes oscillatory shear (LAOS) measurements In the linear viscoelastic regime, the moduli are constant regardless of strain amplitude for all fluid gels. Each fluid gel undergoes a transition at a critical strain (yield strain) at which G′ decreases dramatically as the strain increases, while G′′ first increases and then decreases, which is defined as weak strain overshoot (LAOS type III) (Sim et al., 2003). As illustrated in Fig. 2 (d), the fluid gels containing more LA gellan gum require a smaller critical strain to disrupt the equilibrium microstructure than those containing more HA gellan gum. It is also evident that the strain overshoot phenomenon appears in only G′′ curves and becomes more pronounced as HA gellan gum concentration increases. The structural cause of the strain overshoot behavior in G′′ is different corresponding to the class of soft materials (Lim, Ahn, Hong, & Hyun, 2013; V. Tirtaatmadja, Tam, & Jenkins, 1997). In this study, the strain overshoot behavior in G′′ perhaps could be related to the reformation ability of the destructed gel network induced by larger imposed strain (Hyun et al., 2011). This LAOS behavior has been investigated using a network model composed of segments and junctions, which is determined by the

Fig. 2. Elastic modulus G’ and viscous modulus G’’ as a function of strain at different Ca2+ concentrations (a) HA:LA = 25:75 (b) HA:LA = 50:50 (c) HA:LA = 75:25 (d) 5 mM Ca2+, different HA:LA gellan ratio. 400

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dissipation of the mechanical energy within one cycle. And only the fluid gel with pure HA gellan gum adopts ellipse throughout the applied train. With increasing concentration of Ca2+ to 5 mM and 10 mM, the area of shapes with pure, 50% and 75% HA gellan gum decreases due to the impact of Ca2+ on the polymer network and the shape is much closer to a rectangle than an ellipse, corresponding to an elastoviscoplastic material (Ewoldt, Winter, Maxey, & Mckinley, 2010). However, the area of shapes with pure LA gellan gum and 25% HA gellan gum is not linear dependent on the Ca2+ concentration, resulting from the combined influence of Ca2+ and HA/LA gellan ratio. The fluid gels with pure LA gellan gum are mainly characterized by plastic behaviors while the fluids gels with pure HA gellan gum tend to dissipate the energy associated with the viscous forces according to the Lissajous shapes at the applied strain. By adjusting the Ca2+ concentration and HA/LA gellan ratio, the Lissajous shapes become more complicated, consequently diversifying the properties of gellan fluid gels. In general, the gellan fluid gel with different HA/LA gellan ratio and Ca2+ concentration show similar weak strain overshoot behaviors (Figs. 2 and 3) though, Lissajous curves take distinctively different shapes (Figs. 4 and 5), fully indicating the essential distinction of internal polymer network between fluid gel with HA and LA gellan gum. Fig. 5 shows the viscous Lissajous curves with stress response versus strain rate. For small strain amplitude, the viscous Lissajous figures are ellipses of a very small minor axis (invisible at the applied scale) at all the Ca2+ concentrations. As the strain amplitude increases into the nonlinear regime, the Lissajous figures adopt increasingly complex shapes and secondary loops appear in most of the viscous Lissajous curves in Fig. 5 (except for Fig. 5(e)), corresponding to the self-intersection and strong nonlinear elastic responses at large strain amplitude (Ewoldt & Mckinley, 2010). The self-intersections have already been studied for several other materials systems (Gurnon, Lopezbarron, Eberle, Porcar, & Wagner, 2014; Gurnon & Wagner, 2012; Renou, Stellbrink, & Petekidis, 2010) and constitutive models (Armstrong, Beris, Rogers, & Wagner, 2016; Giacomin, Bird, Johnson, & Mix, 2011; Hyun, Kim, Park, & Wilhelm, 2013; Mendes & Thompson, 2013; Zhou, Cook, & Mckinley, 2010). And Ewoldt et al. have provided a general physical interpretation of this nonlinear rheological phenomenon by deriving a mathematical criteria simply related to a single viscoelastic ′ < 0 , corresponding to a negative slope in the elastic parameter GM Lissajous curves at instantaneous strain value equal to zero (Ewoldt & Mckinley, 2010).

creation rate and loss rate of network junctions. With rationalizing the responses in terms of creation and loss rate, the network model can qualitatively predicts the various classes of experimental LAOS behavior of complex fluids. The overshoot may be regarded as arising from the balance between the formation and the destruction of the network junctions (Hyun et al., 2011). Obviously, the strain overshoot in Figs. 2 and 3 more depends on the creation rate than the loss rate according to the network model. From the molecular point of view, the structural differences between HA and LA gellan gum may induce the diversity of microstructure, consequently resulting in the extent of strain overshoot phenomenon. The HA gellan gum contains a substitution of a glycerate group (C2) and a partial substitution of an acetate group (C6). The LA gellan gum can be obtained by deacylating the HA gellan gum under alkali conditions. Compared to LA gellan gum, more hydrogen bonding was identified for HA gellan gum partly due to three oxygen atoms in the glycerate group, forming a more stable gel network (Huang et al., 2003). Furthermore, the glycerate group in HA gellan gum can also stabilize the double helix structure, indicating a higher gelation ability than LA gellan gum (Matsukawa & Watanabe, 2007). Therefore, the more HA gellan gum, the more pronounced the strain overshoot behavior.

3.3. Lissajous curves analysis With the aid of Lissajous curves one can see visual difference in the nonlinear stress response according to the distortion of the elliptical shape of the Lissajous curves, subsequently the changes in viscoelastic properties of gellan fluid gels with the increase in imposed strain amplitude. The elastic Lissajous curves with stress response versus strain are shown in Fig. 4 while the viscous Lissajous curves with stress response versus strain rate are shown in Fig. 5. In the Lissajous curves, the effect of imposed strain amplitude and Ca2+ concentration of HA and LA gellan on the Lissajous curves are studied. As can be seen in Fig. 4, for small strain amplitudes the elastic Lissajous loops is ellipsoidal, indicating that the response of the fluid gels is dominated by elasticity. As strain amplitudes increase into the nonlinear viscoelastic regime, the elastic Lissajous loops deform closer to rectangle gradually. The difference in molecular structure between HA and LA gellan gum result in different Lissajous shapes. In the fluid gels containing 2 mM of Ca2+, the area of figures becomes larger with increasing the HA/LA gellan ratio, which is associated with greater

Fig. 3. Elastic modulus G’ and viscous modulus G’’ as a function of strain at different Ca2+ concentrations (a) LA gellan 0.5 wt% (b) HA gellan 0.5 wt%. 401

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Fig. 4. Elastic Lissajous curves.

viscoelastic responses of gellan fluid gels in LAOS tests in this study. Furthermore, the Chebyshev coefficients and the above mentioned local method were used to quantify the Lissajous curves to provide quantitative viscoelastic responses of fluid gels at instantaneous strains and a

3.4. Chebyshev coefficients analysis Lissajous curves, mathematically known as parametric curves to describe complex harmonic motion, were used to visualize the

Fig. 5. Viscous Lissajous curves. 402

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Fig. 6. The effects of HA/LA gellan ratio and Ca2+ concentration on the normalized 3th and 5th Chebyshev coefficients as a function of strain amplitude.

gellan fluid gels, the increase in Ca2+ concentration results in more gentle increase in e3/e1 and e5/e1 values while contrary trend is observed in pure HA gellan fluid gels. The effect of Ca2+ concentration on the elastic Chebyshev coefficients in mixed gellan fluid gels becomes weaker most likely due to the strong synergy of HA and LA gellan gum in gelation at applied Ca2+ concentration. For all the samples, the ν3/ν1 values based on Eq. (9) grow initially, until they reach a maximum and then decrease to be negative, indicating that gellan gels show a shear thickening behavior followed by a shear thinning behavior after it crosses a certain barrier. This shear thickening behavior is related to the weak strain overshoot response as depicted in Figs. 2 and 3. The ν5/ν1 value curves vary according to the

comprehensive physical interpretation of the deviations from a linear response to the large strain amplitudes. Both normalized elastic Chebyshev coefficients (e3/e1 and e5/e1) and viscous Chebyshev coefficients (ν3/ν1 and ν5/ν1) are analyzed shown in Fig. 6. Almost all the samples show similar behavior of variation in elastic and viscous Chebyshev coefficients. With increasing the strain amplitude, e3/e1 and e5/ e1 values change from nearly zero to positive values, indicating strain stiffening in nonlinear regime based on Eq. (8). The effect of Ca2+ concentration on the Chebyshev coefficients is related to HA/LA gellan ratio in fluid gels. The e3/e1 contribution becomes less significant with increasing HA gellan gum ratio at corresponding Ca2+ concentration, indicating a gradually declining strain stiffening behavior. In pure LA

Fig. 7. Chebyshev coefficients as a function of strain with 2 mM Ca2+ (a) pure LA gellan fluid gel (b) pure HA gellan fluid gel. 403

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Table 1 Chebyshev coefficients calculated from LAOS data by MITlaos software at 1%, 100% and 1000% strain amplitudes. Strain amplitude % HA gellan fluid gels with 2 mM Ca2+ LA gellan fluid gels with 2 mM Ca2+

1 100 1000 1 100 1000

e1

′ GM

GL′

Pa

72.06 55.18 2.68 72.24 12.08 0.14

ν1

′ ηM

ηL′

4.86 7.71 10.36 10.41 14.53 4.65

4.28 12.69 10.66 9.82 18.62 2.35

Pa·s

76.11 47.05 0.77 72.49 6.089 −0.58

Ca2+ concentration and HA/LA gellan ratio. In the fluid gels containing higher Ca2+ and LA gellan gum concentration, the ν5/ν1 value curves adopt more pronounced minus minimum. Therefore, the characteristics analyzed using the Chebyshev coefficients further confirm the remarkable structural difference between HA and LA gellan gum. With increasing strain amplitude, the non-linearities response should be involved as evidence by the non-ellipsoidal shapes of Lissajous curves. In these cases, single elastic or viscous modulus is insufficient to describe the instantaneous viscoelastic behavior in nonlinear regime. Hence, the local elastic modulus and dynamic viscosity based on Eq. (10) to Eq. (13) as a function of imposed strain amplitude in two typical systems are illustrated in Fig. 7 (pure HA and pure LA gellan fluid gels with 2 mM Ca2+, respectively). And Chebyshev coefficients calculated from LAOS data by MITlaos software at 1%, 100% and 1000% strain amplitudes are shown in Table 1. At low strain am′ plitude, G1′, GM and GL′ converge to the linear elastic modulus G′, corresponding to a linear viscoelastic response. As the strain amplitude increases, all the three local elastic moduli decrease and GL′ decreases ′ , indicating that the elastic response behaves strain stifless than GM ′ becomes negative fening at large strain amplitude. In Fig. 7(a), GM within the nonlinear regime, indicating that the LA gellan fluid gel with 2 mM Ca2+ releases elastic stress faster than new deformation is accumulated. This corresponds to the secondary loops as shown in Fig. 5(a). However, this phenomenon does not appear in HA gellan fluid gel with 2 mM Ca2+ depicted in Fig. 7(b). Furthermore, the viscoelastic response in both of the HA and LA gellan fluid gels is dominated by the viscous properties in nonlinear regime, confirmed by greater ν1 values than e1 values. This implies that flow is the main rheological phenomenon accompanied by an elastic manner due to the nonzero values of e3 in Fig. 6(a) and (e).

72.63 58.37 3.49 72.67 14.18 0.76

4.65 11.68 10.91 9.98 18.66 2.69

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4. Conclusions The LAOS technique was used to investigate the rheological properties of gellan fluid gels, taking into account the influence of HA/LA gellan ratio and Ca2+ concentration. The LAOS data was systematically analyzed using Lissajous curves and Chebyshev coefficients for the first time. The different shapes of Lissajous curves associated with different Ca2+ concentration and HA/LA gellan ratio provided visual representation of microstructural differences between HA and LA gellan gum, which is quantitatively confirmed by Chebyshev coefficients. Results obtained from temperature sweep measurements showed that HA gellan gum forms softer but much more stable gels than LA gellan gum due to the glycerate group in HA gellan gum. A synergistic interaction between HA and LA gellan gum may exist in the presence of abundant Ca2+ ions to provide a higher elastic modulus. In general, the differences in the molecular structure and gelation mechanism of HA and LA gellan gum are hypothesized to be responsible for the different rheological properties of HA and LA gellan gum.

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