This study is the continuation of our previous work (Kopaˇc, Abrami, et al., 2021) where the theoretical approach of polymer-polymer interaction to predict the crosslink density of hydrogels was introduced. This theory is further extended to the flow properties of hydrogels that allow the analysis of synergistic effect in hydrogel systems and the understanding of possible anomalous behavior of certain mixtures.
Carbohydrate Polymers 287 (2022) 119352 Contents lists available at ScienceDirect Carbohydrate Polymers journal homepage: www.elsevier.com/locate/carbpol Effect of polymer-polymer interactions on the flow behavior of some polysaccharide-based hydrogel blends Tilen Kopaˇc , Aleˇs Ruˇcigaj , Matjaˇz Krajnc * University of Ljubljana, Faculty of Chemistry and Chemical Technology, Veˇcna pot 113, SI-1000 Ljubljana, Slovenia A R T I C L E I N F O A B S T R A C T Keywords: Zero-shear viscosity Yield stress Shear thinning Hydrogel interactions Blending effects Mathematical modeling This study is the continuation of our previous work (Kopaˇc, Abrami, et al., 2021) where the theoretical approach of polymer-polymer interaction to predict the crosslink density of hydrogels was introduced This theory is further extended to the flow properties of hydrogels that allow the analysis of synergistic effect in hydrogel systems and the understanding of possible anomalous behavior of certain mixtures Various hydrogel structures were prepared accordingly by blending scleroglucan, anionic nanocellulose, Laponite dispersions and alginate solution The relationship between mechanical and flow properties of the hydrogel network was carefully studied and eventually described by mathematical model The linear model equation to predict yield stress of hydrogels in relation to the crosslink density was designed showing a satisfactory agreement between experimental data and model predictions The correlation was adjusted by defining a proportionality coefficient, representing the energy defined per moles of crosslinks that can be used to restore the deformation Introduction Rheology plays an essential part in the field of scientific research as well as in industrial development (Boger, 2009), particularly in the case of complex systems such as hydrogels whose deformation behavior and flow properties cannot be described by the classical approaches belonging to continuum mechanics (the elasticity theory and fluid dy namics) (Lei, Li, Xu, & Liu, 2021) The rheological characterization represents an important tool also to investigate hydrogels' structural characteristics (Cao, Duan, Zhang, Cao, & Zhang, 2021) in order to evaluate their potential use and performance in various biomedical ´ & Khutoryanskiy, 2015) Particularly in the case of applications (Calo carbohydrate polymer systems, which present several advantages over the synthetic polymers (Farrukh, Mustafa, Hussain, & Ayoub, 2018), the rheology enables a detailed investigation of the mechanical (crosslink density ρx and average mesh size) and flow properties (zero shear vis cosity η0 and yield stress τ0) of hydrogels (Kopaˇc, Abrami, Grassi, Ruˇcigaj, & Krajnc, 2021; Kopaˇc, Krajnc, & Ruˇcigaj, 2021; Kopaˇc, ˇ Ruˇcigaj, & Krajnc, 2020; Lapasin, Abrami, Grassi, & Sebenik, 2017; ˇ ˇ Sebenik, Krajnc, Aliˇc, & Lapasin, 2018; Sebenik, Lapasin, & Krajnc, 2020) So far, theoretical approaches, that can satisfactorily predict the flow behavior of complex hydrogels, are undersupplied in literature, except for very dilute fluids In our previous work (Kopaˇc, Abrami, et al., 2021) a mathematical model that can satisfactory predict the ρx of hydrogel network on the basis of the number of crosslinks formed due to the polymer-polymer interactions (ionic, hydrogen, electrostatic, and other covalent interactions) was developed and validated for polysaccharide hydrogels Motivated by such ρx prediction, we hypothesize that equa tion can be leveled up to predict the η0 and τ0 of similar hydrogel sys ˇ tems The literature (Hoti et al., 2021; Lapasin et al., 2017; Sebenik et al., 2020; Zhao, Mayumi, Creton, & Narita, 2017) reports the effect of ρx on flow behavior of gels based on rheological rotational tests where for the most part, η0 and τ0 increase with the ρx of gels The detailed study of correlations between ρx and η0 or τ0 can be the starting point for further mathematical modeling For this purpose, the comprehensive rheological characterization of (complex) hydrogel systems based on rotational tests is needed to be performed and studied in detail To prove the high applicability of a new mathematical approach for analyzing the τ0 and η0 data, the hydrogel systems based on TEMPO (2,2,6,6-tetra methylpiperidine-1-oxyl) oxidized nanocellulose (TOCNF), sodium alginate (ALG), scleroglucan (SCLG) and Laponite (LAP) were prepared The baseline of the model development is associated to the under standing of polymer-polymer theory in the hydrogel network starting with the careful study of polymers' chemical structures and their possible interactions To fulfil the above orientations, the brief basic * Corresponding author E-mail address: matjaz.krajnc@fkkt.uni-lj.si (M Krajnc) https://doi.org/10.1016/j.carbpol.2022.119352 Received 11 January 2022; Received in revised form March 2022; Accepted March 2022 Available online 15 March 2022 0144-8617/© 2022 The Authors Published by Elsevier Ltd This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 structural description of TOCNF, ALG, SCLG and LAP is needed ALG is a linear copolymer composed of (1 → 4)-linked α-L-guluronic (G) and β-Dmannuronic (M) residues of varying sequence Anionic carboxyl groups give the hydrogel pH responsivity (Way, Hsu, Shanmuganathan, Weder, & Rowan, 2012) in an alkaline release environment and also allowing ˜ o-Maso ´ control of ρx (Lin, Bruzzese, & Dufresne, 2012), porosity (Patin et al., 2019) and flow properties (Kopaˇc et al., 2020) by crosslinking via divalent ions (e.g., Ca2+) (Curvello & Garnier, 2020; Hecht & Srebnik, 2016; Xu et al., 2019) TOCNF is linear polysaccharide, anionic constituent biopolymer The physical and chemical properties of cellulose fibers (Lundahl, Berta, Ago, Stading, & Rojas, 2018) and cellulose-based materials (John & Thomas, 2008; Liang, Bhagia, Li, Huang, & Ragauskas, 2020) are mostly influenced by the formation of intra- and intermolecular hydrogen bonding (Lin & Dufresne, 2014) which are allowed by the presence of three hydroxyl groups on each β-(1–4)-glucopyranosyl unit (Klemm et al., 2011; Liang et al., 2020) Significant amounts of C6 carboxylate groups are selectively formed on each cellulose nanofibril surface by TEMPO-mediated oxidation that gives the anionic character to biopolymer (Isogai, Saito, & Fukuzumi, 2011) and the possibility of ionic crosslinking (Kopaˇc, Krajnc, & Ruˇcigaj, 2021) The nonionic biopolymer SCLG is used as a thickener and suspending agent (Lapasin et al., 2017; Paolicelli et al., 2017) The β-D-glucopyr anosyl units (1,3) linked in the main chain create the internal structure in addition to the three triplex chains which hold the hydrogen bonds together in the center of the triplex Such a conformation is character ized by high stiffness, which is reflected in the special properties of aqueous solutions of SCLG in a wide pH range and even at relatively high temperatures (Lapasin et al., 2017) Intra- and intermolecular hydrogen bonds between the main SCLG chains lead to the formation of stable rigid triple helices in aqueous solutions (Nazmabadi, Shirdast, Sharif, & Aalaie, 2020) Furthermore, a single β-D-glucopyranosyl bound to the unit (1,6) on the main chain prevents polymer precipitation and inter molecular aggregation (Coviello et al., 2005; Lapasin et al., 2017) The synthetic hectorite LAP single layer nanoparticles in a form of rigid, disk-shape crystals were used as a rheological modifier LAP hydrogels own a negative charge of faces as a result of Na+ ions disso ciation Besides, the edges of LAP disks are slightly positively charged due to the protonation of hydroxyl groups (Park, Dawson, Oreffo, Kim, & ˇ Hong, 2020; Sebenik et al., 2020) The face-edge attractions cause a gelification process, when the system does not contain salt, and depend on pH, resulting in a gel network also known as a “house of cards” structure (Becher et al., 2019) Therefore, the LAP addition to weak polysaccharide-based system could contribute to faster development of final gel properties (aging), improve the mechanical properties and ˇ shear thinning character of the matrix (Sebenik et al., 2020) At last, the more detailed analysis of the structural formula of TOCNF (Isogai et al., 2011; Liang et al., 2020), ALG (Homayouni, Ehsani, Azizi, Yarmand, & Razavi, 2007), SCLG (Coviello et al., 2005), and LAP (Ruzicka & Zac carelli, 2011) can be found elsewhere In this study, neutral (SCLG) and anionic (TOCNF and ALG) biopolymer-based hydrogels in addition to LAP were prepared in various concentrations and blended in different weight ratios with the addition of assorted crosslinking agent concentrations to form complex hydrogel systems (i.e., ionically crosslinked blends of polysaccharide polymers in addition to the layered inert component) The effect of polymer and crosslinking agent concentration, respectively, and the polymer fraction dependence in the preparation of hydrogels on flow behavior of the complex hydrogel systems was analyzed Prepared complex hydrogel systems were subjected to comprehensive rheological rotational tests in order to broaden the knowledge of the rheological characteristics of different biopolymer-based systems The study of hydrogel samples provided the explanation of polymer-polymer interaction effects on the flow behavior offering the basis for determination of crucial parameters, such as η0 and τ0 As a result, the theoretical outlines of the model development to predict the flow properties were provided following the polymer-polymer interaction theory correlated to experimental insights As an upgrade to a wide range of experimental data, a new mathematical approach to analyze η0 and τ0 is eventually given, which can be equiv alently used to describe the synergistic effect on shear behavior owing to their interrelationship Experimental 2.1 Materials The TEMPO oxidized nanofibrillated cellulose, a linear poly saccharide composed of cellobiose repeating units linked by β-(1–4) glycosidic bonds, was purchased in freeze-dried powder from The Pro cess Development Centre, University of Maine (UMaine PDC), USA The material specifications given by the producer are: (i) chemical formula of [(C6H10O5)x(C6H9O4COONa)y], (ii) powder density of 1.5 g/cm3, (iii) aqueous gel density of 1.0 g/cm3 (1–3 wt%), (iv) carboxylate level is 0.2–2 mmol/g solids, (v) pKa of substituent group is 3.9, and (vi) the fiber dimensions are classified between 20 and 50 nm in width and lengths of up to several microns Scleroglucan Actigum CS 11 was purchased from Cargill France SAS, France The supplier provides 99%min purity, and the average molar mass is 1.2⋅106 g/mol Laponite XLG, synthetic layered silicate with a low heavy metals content was provided by BYK-Chemie GmbH, Germany The supplier specifications provide: (i) disk-shaped crystals with an average diameter of 30 nm and a thickness of nm, (ii) insolubility in water, (iii) hydrates and swells give clear and colorless colloidal dispersions in water, and (iv) obtains a high surface area (BET) of 800 m2/g Sodium alginate, a polysaccharide made up of α-L-guluronic acid (G) content and (1–4)-linked β-d-mannuronic acid (M) monomers, were supplied by Sigma-Aldrich (St Louis, USA) The molar mass of 2⋅104–6⋅104 g/mol and the high (70%) of G content is provided by supplier Calcium chloride (CaCl2) was as received from Merck (Darmstadt, Germany) and sodium azide (NaN3, an assay of ≥99.5%) was supplied by Sigma-Aldrich (St Louis, USA) 2.2 Sample preparation The gels were prepared by slowly added dry TOCNF, ALG, SCLG or LAP in demineralized water with 0.02 wt% of NaN3 (to prevent micro biological contamination) at constant stirring (500 rpm) by using a fourblade propeller stirrer (pH value of sample was 7) After h, the dispersion was placed in an ultrasonic bath for h (to achieve more homogeneous dispersion - ALG in water form clear solution and so was excluded from this process) The dispersions were stirred overnight at 750 rpm at room temperature The complex hydrogel systems were prepared by blending single biopolymer dispersion TOCNF or SCLG and LAP or ALG in different weight ratios For homogenization, the same procedure was used as previously reported The samples were then quantitatively transferred in a 3D printed mold to sample achieve the same characteristics as the rheometer measuring plate (a diameter of 50 mm and thickness of mm) The crosslinking process including spraying the aqueous solution of calcium ions onto the surface of samples in the mold The mold was designed to have two edges: the first and second corresponding to the equal volume of biopolymer sample and crosslinking agent solution, respectively The crosslinked systems were maintained in a refrigerator at 4.2 ◦ C for 48 h to establish the final hydrogel structure (time required for crosslinking process based on Ca2+ ions) Hydrogels were prepared in 1–3 wt% concentration of a single polymer since the most important changes in the structure of the hydrogel network occur in this range Furthermore, at polymer con centration up to wt%, the systems are almost Newtonian and their T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 viscoelastic properties are practically undetectable (Lapasin et al., 2017; ˇ Sebenik et al., 2020) Ionic crosslinking was performed by adding a calcium ion solution to a maximum concentration of wt% In this state, almost all carboxyl groups of TOCNF or ALG participate in the cross linking process so that a higher concentration of crosslinking agent so lution would not (noticeably) affect the rheological properties of the hydrogels (Kopaˇc et al., 2020; Kopaˇc, Krajnc, & Ruˇcigaj, 2021) The sample pH value was The prepared hydrogel systems were kept in the fridge at a temperature of 4.2 ◦ C for 15 days to establish the final hydrogel structure and to avoid the effect of aging which mainly affect the rheological properties due to the formation of hydrogen bonds (ac ˇ cording to the literature (Lapasin et al., 2017; Sebenik et al., 2018)) and SCLG) and LAP (clay) exhibits pronounced shear thinning character (Fig 1) The η0 increases from TOCNF, over SCLG to LAP dispersions Especially in the case of SCLG and LAP, the behavior is plastic with a significant viscosity drop in a narrow stress interval, while TOCNF hydrogels present a longer stress interval of viscosity decrease which appears at lower τ0 The 1st Newtonian plateau of TOCNF (η0) is the consequence of the existence of invisibly small clusters formed during aging which are enabled by entanglements of nanofibers and non covalent and covalent interactions between them (not only hydrogen bonding, also van der Waals interactions and electrostatic repulsion due ˇ to negatively charged carboxyl groups (Sebenik et al., 2018)) The clusters arrangement of the TOCNF internal structure in the shear flow direction is therefore shown in a longer stress interval of viscosity decrease (effect of clusters concentration, shape, and distribution) Accordingly, the TOCNF has the most pronounced 2nd Newtonian plateau and the network-of-forces of the TOCNF internal structure are weaker than in the case of stable rigid triple helices in SCLG structure and LAP crystals (η0 values) As opposed to η0, the τ0 occurs in the lower shear stress in the LAP in comparison with SCLG The reason may be attributed to different interactions that predominantly form a structure in both samples The intra- and inter-molecular hydrogen bonds among the main chains of SCLG lead to the formation of a stable structure until the increased shear stress predominates over hydrogen interactions in the SCLG structure (τ0) On the other hand, the LAP forms rigid, diskshaped crystals whose random distribution determines the internal structure (the crystals are folded and occupy the most energy-efficient state) The viscosity is constant until the crystals start to steer in the direction of shear (τ0) Fig shows that the SCLG structure based on hydrogen interactions between polymer-polymer chains and LAP diskshaped crystals structure (predominantly electrostatic interactions) are more solid than the TOCNF dispersion The internal structure in TOCNF is determined by intra- and intermolecular hydrogen bonding (Lin & Dufresne, 2014), which are allowed by the presence of three hydroxyl groups on each β-(1–4)-glucopyranosyl unit The crosslink density of TOCNF is significantly lower than in the case of SCLG, due to lower hydroxyl group content which results in lower number of polymerpolymer hydrogen interactions, which also results in lower η0 and τ0 Differently, the ALG is soluble in water and does not form gels structure in the absence of crosslinking agent and therefore exhibits fluid-like viscoelastic behavior (Fig 1) The values of η0 and τ0 are experimentally difficult to determine uniformly, as they generally depend on the type and experiment per formance rate The η0 values can be determined by extrapolating the experimental points of the flow curve on the log viscosity–log shear stress (or shear rate) diagram The measurements in Fig show a flow behavior where even at very low shear stresses the samples “creep” and become plastically deformed This is the main reason for the difficult determination of η0 and τ0 All samples with plastic flow behavior (SCLG, LAP and TOCNF) are characterized by a very high viscosity due to a strong internal structure (based on polymer-polymer interactions) that resists the shear The η0 values for 2% SCLG, TOCNF and LAP single dispersion were determined at 101000, 7327 and 520,600 [Pa⋅s], respectively (Table S1) Furthermore, yield points are not material constants as they depend as well on the measuring method as well as on the analysis method used The value of τ0 is often determined as a rough approximation by extrapolating the experimental points of the flow curve on log shear stress–log shear rate or log shear strain– log shear stress diagram The τ0 determination via the “tangent crossover method” is illustrated in Fig The τ0 determination via the best straight fitting line (“tangent”) in the linear–elastic deformation range is also realizable Shear stress ramp experiments from 0.1 to 200 Pa were performed in variable measuring point duration logarithmic profile (initial point duration was set at 300 s and final point duration was set at 20 s, along with ramp log +9.63 points/decade) From Figs 2A–C, the τ0 values for 2% SCLG, TOCNF and LAP single dispersion were determined at 32, 1.9 and 22 2.3 Rheological characterization Rheological rotational tests were performed on rheometer Anton Paar Physica MCR 301 equipped with a crosshatched plate with a diameter of 50 mm (PP50/P2) The samples were prepared to corre spond to a thickness of ± 0.1 mm between the plates and were measured at a temperature of 25 ◦ C Flow curve – viscosity (η) was measured over a range of shear stresses (σ ) from 0.01 to 3000 Pa The flow curves were presented in a log vis cosity–log shear stress plot The experimental data were fitted by the Roberts-Barnes-Carew (RBC) model The RBC is the modified original Ellis equation (Roberts, Barnes, & Carew, 2001): η0 η = η∞ [1 + (σ /σ )s ] + 1+(σ/σ1 )p − η∞ [1 + (σ/σ )s ] ( )m + σσc (1) where η is dynamic viscosity, η0 and η∞ are the asymptotic values of the viscosity at zero and infinite shear stress, respectively, σ is shear stress, σ c is critical shear stress, which locates the transition region between two moderate shear thinning regions, m describes the rate of viscosity decrease in the transition region, σ and σ are critical shear stresses in the composite Ellis model, p and s are adjustable parameters (Roberts et al., 2001) Results and discussion 3.1 Flow behavior 3.1.1 Single polymer hydrogel and yield stress determination Single polymer hydrogel based on constituent biopolymers (TOCNF Fig Flow behavior of single polymer systems based on LAP (squares), SCLG (circles), TOCNF (triangles) and ALG (diamonds) The lines represent RBC model fit T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 increase in the mass fraction of SCLG The shape of flow curves is typical for shear thinning behavior of hydrogel blends All the wt% SCLG/ TOCNF systems exhibit an evident plastic behavior (the 1st Newtonian plateau is distinctive) with a significant viscosity drop more typical for a single SCLG hydrogel Furthermore, the 2nd Newtonian plateau is also detected, as the main contribution of the TOCNF biopolymer (see the shape of the flow curve for single TOCNF hydrogel - triangle) to the SCLG/TOCNF hydrogel blends It may be concluded that wt% SCLG/ TOCNF systems form pronounced viscoelastic properties of hydrogels, where the addition of SCLG mainly affects the elastic properties of the hydrogel (hydrogen interactions contributed to stronger network-offorces of internal structure), while the addition of TOCNF gives the hydrogel a viscous character at high shear stresses (due to the presence of the small invisible clusters or flocs which are dispersed in a gel-like ˇ matrix (Sebenik et al., 2018)) (also discussed after in Figs 7A and B) Based on the calculated data from Table S1, the zero-shear viscosity interval is between 9.94⋅103 < η0 < 3.19⋅104 [Pa⋅s], the yield stress interval is determined in the range of 7.84 < τ0 < 30.7 [Pa] In Figs 3C–D, the effect of ALG in the hydrogel blend system is presented The ALG in water forms a clear solution which is the main reason that it does not participate in forming polymer-polymer inter action in addition to various biopolymer (SCLG) or rheological modifier (LAP) In Fig 3C, it is clear that the flow curves of blends containing LAP in 1.0–0.25 mass fractions have a pronounced plastic behavior evident in 1st Newtonian plateau with a significant viscosity drop in a narrow stress interval (same as for single LAP dispersion presented in Fig 3C – square symbols), in addition to the decreasing effect of η0 and τ0 This may be the consequence of diluting effect of ALG in the 2% LAP/2% ALG systems (see also discussion of Figs 7A and B) In addition, the ALG addition gives the more viscous character of systems in high shear stresses where the 2nd Newtonian plateau is clearer (Fig 3C) than in single LAP dispersions (Fig 1) At the lower mass fractions of LAP in the mixture, the plastic behavior is not expressed According to the litera ture (Lapasin et al., 2017), the LAP dispersion of less than 0.75 wt% has properties of fluid or does not show shear thinning and viscoelastic character, therefore the blending would have only a diluting effect and not synergistic interaction between LAP nanoparticles and biopolymer network The same conclusions (diluting effect) may be given for 2% SCLG/2% ALG systems (Fig 3D) where the flow behavior is a function of SCLG concentration dependence changed by the addition of ALG solu tion While dilution effect of ALG can be observed in non-crosslinked samples, the drastic change in ALG participation in hydrogel mixtures on the flow behavior is presented in ionically crosslinked systems (Section 3.1.3) Fig Yield point determination via the tangent crossover method for 2% SCLG (A), TOCNF (B), LAP (C) and ALG (D) single systems [Pa], respectively Fig 2D illustrates obvious fluid behavior of ALG Additionally, η0 and τ0 can also be defined as a model parameter when a rheological model is used to describe plastic flow behavior Such generally well-known rheological models are the Bingham model, Her schel–Bulkley model and Casson model Both methods for η0 and τ0 values determination were used The results of all samples are sum marized in Table S1 3.1.2 Polymer concentration and fraction dependence hydrogel systems Fig 3A presents flow curve of SCLG/TOCNF hydrogels systems The samples were prepared by blending various (1–3 wt%) concentration of SCLG and TOCNF dispersions in equal weight ratios The concentration of biopolymer plays a crucial role in determining final rheological properties of SCLG/TOCNF hydrogels, which can be confirmed by a very wide interval of yield stresses from 1.28 < τ0 < 43.7 [Pa] and also zeroshear viscosity of 4.15⋅102 < η0 < 1.05⋅105 [Pa⋅s] (more data can be found in Table S1) Shear thinning character increases with increasing biopolymer concentration which suggests the existence of invisibly small clusters with significant swell-ability in water Clusters are formed during the process of storage (aging) of prepared hydrogels when pre dominantly hydrogen, van der Waals and electrostatic repulsive forces begin to intertwine in SCLG and TOCNF network structure In this case, the clusters increase, which reduces their distance from each other and further enhances the noncovalent interactions among them After two weeks, the growth of the clusters slows down reaching the final prop ˇ erties of the hydrogel structure (Sebenik et al., 2018) In the case of TOCNF polymers, having modified carboxyl groups on the surface, the clusters are also formed during the ionic or covalent crosslinking pro cess The experimental data show higher η0 when using a higher con centration of SCLG (the effective volume fraction of the dispersed phase is increased) A less important effect on shear thinning character has the concentration of TOCNF, which significantly affects especially on τ0 in low concentration biopolymer systems The flow curve shape of the sample with a wt% concentration of both biopolymers is extremely similar to the single wt% TOCNF hydrogel It may be concluded that hydrogel with SCLG below wt% does not have plastic behavior (Lapasin et al., 2017) The effect of the mass fraction of different biopolymers on the rheological properties of hydrogel mixtures was studied in the case of blending wt% of SCLG and TOCNF (Fig 3B), LAP and ALG (Fig 3C) as well as SCLG and ALG (Fig 3D) (see single polymer hydrogel properties from Section 3.1.1 as reference) The mixtures were prepared in mass fractions of both biopolymers from 0.9 to 0.1 In Fig 3B, flow curves show almost negligible change in η0 between 0.1 and 0.25 mass fraction of SCLG and also 0.5–0.90 On the other hand, τ0 increased with an 3.1.3 Fraction dependence of biopolymer blends on crosslinked hydrogel systems Biopolymer blends from Section 3.1.2 were additionally crosslinked with wt% CaCl2 solution The rheological properties of such complex hydrogel systems are illustrated in Fig Compared to the noncrosslinked systems a η0 increased by up to two decades (see Ta ble S1), demonstrating even more plastic behavior of hydrogel systems On the opposite, the η0 increases with increasing TOCNF or ALG mass fraction in the case of crosslinked systems as a result of crosslinking polymer chains by calcium ions through the carboxylic functional groups on the polymer surface As anticipated, the higher it is concen tration of the carboxylate level, the more plastic behavior could be observed More than that, the non-ionic SCLG cannot contribute to ionic ˇ interaction with TOCNF or ALG (Sebenik et al., 2020) (see also discus sion of Figs 7C and D) Furthermore, the 2nd Newtonian plateau established in non-crosslinked systems (Fig 3) was no longer existed in crosslinked hydrogels (Fig 4) The effect of increasing the τ0 of cross linked systems with increasing mass fraction of TOCNF or ALG biopolymer is also evident (see Table S1) Interestingly, the same or even slightly higher τ0 of non-crosslinked SCLG/TOCNF mixtures with the SCLG mass fraction of 0.9 (29 Pa) T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 Fig Flow behavior of biopolymer concentration and fraction dependence hydrogel systems In the panel A, the different shape (and color) of symbols represents the various concentrations of biopolymer (blends of SCLG and TOCNF in equal weight ratio) in single polymer hydrogel preparation (the legend inside panel A) Panel B (blends of 2% SCLG and TOCNF biopolymers dispersion), C (blends of 2% LAP and ALG) and D (blends of 2% SCLG and ALG) illustrate the flow curve of biopolymers different weight ratio as shown in the legend below figure The lines represent RBC model fit The open symbols correspond to single polymer systems presented in Fig (circles – SCLG, triangles – TOCNF, squares – LAP, and diamonds - ALG) than their analogous crosslinked samples (28 Pa) is measured In other words, SCLG forms many hydrogen bonds between polymer chains and water molecules, which diffuse into the SCLG network in the process of swelling Also, due to the lower mass fraction of TOCNF, a smaller number of ionic bonds during crosslinking are formed because of the lower concentration of carboxyl functional groups Hydrogen bonds are predominant over a few ionic interactions, in this case, reflecting no effect of increasing τ0 in flow curves In a previous study (Kopaˇc, Abrami, et al., 2021) was shown that the hydrogen bonding interaction arising among SCLG triple helices and TOCNF nanofibrils reduces the tendency to prone to establish Ca2+ mediated ionic bonds The opposite could be clearly seen at higher TOCNF mass fractions (Fig 4A) This anomalous behavior of SCLG/TOCNF gels is further studied in detail in Section 3.4 Additionally, to prove the predominant effect of electrostatic inter action over hydrogen bonds, the crosslinked LAP/TOCNF systems (Fig 4B) were prepared The rheological properties of non-crosslinked ˇ LAP/TOCNF are presented in the literature (Sebenik et al., 2020), therefore the η0 and τ0 values are shown only in Table S1 and not also in a graphical form The effect of hydrogen bonds is lower in exchange for electrostatic interactions between LAP nanodisks (positively charged edges of particles) and TOCNF fibrils (anionic side groups) The clay particles of LAP and its aggregated forms are deposited between the ˇ polymer chains of TOCNF (Lapasin et al., 2017; Sebenik et al., 2020), which additionally connects the polymer nanofibers and strengthens the internal structure of hydrogel systems For that reason, the higher η0 and τ0 values of crosslinked LAP/TOCNF hydrogels in comparison to SCLG/ TOCNF systems, especially in low TOCNF mass fractions, may possibly be explained by stronger electrostatic interactions over hydrogen bonds 3.1.4 Effect of crosslinking agent concentration on complex hydrogel systems To study the effect of crosslinking agent concentration on the rheo logical properties of hydrogel systems, 2% SCLG/2% TOCNF and 2% LAP/2% TOCNF samples were blended in the 0.5/0.5 weight ratio and additionally crosslinked with different concentrations of calcium ion solution (0.17–2 wt%) Fig shows almost negligible effect of cross linking agent concentration on flow curves of ionically crosslinked hydrogels Crosslinked hydrogels have a rigid and stable structure even at higher shear stresses (over 100 Pa) The ionic bonds between the TOCNF polymer chains formed during the crosslinking process with calcium ions (Curvello & Garnier, 2020) are obviously predominant over other interactions (explained in Section 3.1.3.) Flow curves are mostly plastic with a drastic drop in viscosity when the structure is destroyed (see the τ0 data from Table S1) The LAP-containing hydrogel systems possess higher values of η0 and τ0 (Table S1) As already dis cussed in Section 3.1.3, the LAP mainly contributes to electrostatic interaction in the mixture unlike SCLG-containing systems where the hydrogen bonds are strengthened In the crosslinked systems, the polymer chains are closer to each other which allows the electrostatic interaction to play a more important role in a strong hydrogel structure (Fig 5) In the light of high η0 and τ0 illustrated in Fig for TOCNFcontaining systems, for ALG-containing systems with SCLG and LAP only a few measurements at different concentration of crosslinker were assessed for verification purposes (data not shown) Accordingly, due to the higher concentration of carboxyl groups in ALG than in TOCNF (more ionic interactions), the presence of ALG in the crosslinked mixture exhibit an even stronger internal structure (higher η0 and τ0) compared to TOCNF gels T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 Fig Flow behavior of crosslinked (constant – wt% addition of crosslinking agent solution) systems, presented in Fig The lines represent RBC model fit The open symbols correspond to single polymer systems presented in Fig (squares - LAP and circles – SCLG) Ottewill, 1982; Chen & Zukoski, 1990) already reports that plateau modulus (Gp) is proportional to the yield stress τ0: τ0 ∝Gp (2) Further on, the average molecular weight between crosslinks Mc can be derived from the following equation, including Gp as is clearly pre sented in recent paper (Yan et al., 2018): Mc = cρRT Gp (3) where c is the polymer concentration, ρ is the density of water, T is the absolute temperature and R is the ideal gas constant which represent the product of Avogadro (NA) and Boltzmann (kB) constant The Eq (3) leads to the crosslink density determination: ρx = ρg Mc (4) where ρg is hydrogel density Accordingly, the Eqs (2)–(4) allow to find the relation between τ0 and ρx It is followed that a proportionality exists between τ0 and ρx: Fig Flow curve of crosslinked wt% SCLG/TOCNF (A) and wt% LAP/ TOCNF (B) hydrogel systems blended in the equal weight ratio The symbols represent the concentration of the added crosslinking agent solution The lines represent RBC model fit τ ∝ ρx (5) In the previous work (Kopaˇc, Abrami, et al., 2021) we presented an equation (Eq (6)) which may be used to predict the crosslink density ρx of hydrogels and analyze data of shear moduli adopted by the rheo logical oscillatory tests The equation is based on the polymer-polymer interaction as well as properties of polymers and crosslinking agents and avoids difficult-to-determine parameters: ( ) n n ∑ ∑ Nhyd,i mp,i − mp0,i Xhyd,i Nion,i mp,i Xion,i − aion ρx = (6) e x + ahyd 2 i=0 i=0 3.2 Model development The previous sections present the results of rheological rotational tests and detailed characterization of hydrogel flow properties The shear thinning behavior was observed since the gels' structure reveals almost constant viscosity at very small shear stresses (η0) followed by the structure deformation at the τ0 Accordingly, mathematical model to predict these flow characteristics of hydrogels is designed based on the following assumptions The literature (Buscall, Goodwin, Hawkins, & T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 presented in Fig are adopted from our previous paper (Kopaˇc, Abrami, et al., 2021) (samples preparation protocol in this research is identical) On the other hand, the τ0 data were determined based on flow curve measurements (illustrated in Figs 3-5) via the tangent crossover method as presented in Fig During the action of shear force, hydrogels can store part of the energy entering the system, and accordingly, after removing the stress, they can restore part of the deformation In this context, parameter S as a coefficient of the energy that can be restored defined per mole of crosslinks was introduced Below the τ0, a hydrogel deforms elastically and returns to its original shape when the applied stress is removed due to energy stored in the network (described by parameter S) The Shyd for hydrogen interactions and Sion for ionic in teractions were determined by fitting the Eqs (8) and (9) to single noncrosslinked and crosslinked polymer hydrogels (SCLG, LAP, TOCNF, ALG), respectively The predetermined biopolymer individual S co efficients values were further endorsed in mixtures as proposed in Eq (7) to calculate the yield stress of complex hydrogel of (crosslinked) polymer mixtures Furthermore, Sdil was determined in fitting the Eq (10) of non-crosslinked ALG-containing mixtures The results of the model fitting parameters are presented in Table The Eq (7) proved to be a satisfactory model prediction of τ0 (see red lines in Fig 6) in most of the samples except for ionically crosslinked SCLG-containing systems whose unforeseen behavior is detailly dis cussed in Section 3.4 It may be observed that the SCLG internal struc ture, predominantly formed based on the hydrogen interactions (Shyd), are able to restore more energy than LAP and TOCNF per moles of crosslinks On the other hand, in the case of crosslinked TOCNF and ALG hydrogels, where the ionic interactions are predominant, the Sion is significantly lower than Shyd This means that internal structures based on ionic interactions have less potential to restore after deformation compared to hydrogen interactions-based structures On the other hand, it has to be noted that ionic interactions are much stronger than hydrogen interactions along with the usually higher ρx of ionically crosslinked hydrogels (the affinity to create crosslinks are higher) While the shear stress should be significantly higher to deform the gels' structure in crosslinked hydrogels than in non-crosslinked (where the hydrogen interactions are predominant), the parameter S defined here only refers to the energy that can be used to restore the deformation (elastic character) The magnitude of shear stress is therefore hidden in ionic and hydrogen polymer-polymer interactions (see Eqs (6) and (7)) Moreover, not only polymer-polymer interaction but also the (differ ently shaped) building blocks that form a hydrogel significantly affects the flow properties Therefore, a wide difference between the Shyd of SCLG and TOCNF appears although the hydrogen interactions are pre dominant in both systems (see Table 1) The higher values of Shyd of SCLG than LAP and TOCNF may indicate that by the additional forma tion of the network structure SCLG helices contribute to higher resis tance to flow than LAP nanodisks and TOCNF clusters, respectively In non-crosslinked ALG solutions the hydrogels' structure is not formed since ALG is water-soluble and as such non-swellable (see Fig 1) In this case, ALG participates in the diluting process in the mixture of SCLG or LAP dispersion with ALG solution In ALG polymer solutions, the internal structure of the liquid is formed by polymer molecules that are randomly distributed and occupy the most energy-efficient confor mation (Lee & Mooney, 2012) Therefore, dilution with such solutions (η of wt% ALG solution at 25 ◦ C is 29 mPa⋅s) is significantly different from dilution with water (η of water at 25 ◦ C is 0.89 mPa⋅s) The shear thinning character of SCLG or LAP dispersions decreases linearly with increasing the water content, due to the decreasing polymer concen tration (as formulated, Sdil for water should be equal to zero) Compared to water dispersions of SCLG or LAP, the material becomes less elastic by introducing ALG solution since ALG molecules dispersed in the SCLG network or LAP hydrogel cannot contribute to the crosslinking process and may present barriers in the formation of a hydrogel network Consequently, Shyd, having an elastic character, is here reduced by the value of Sdil where N is substituent groups content on the polymer surface (OH, COOH, NH2, etc.) defined per gram of dry polymer [mmol/g], mp and mp0 are the mass concentration of dry polymer in the solvent and a minimum mass concentration of polymer with the ability of hydrogel formation [g/m3], ahyd is the hydrogen bonds functionality affinity [/], the aion is the functionality affinity [wt%] of the ionic crosslinking agent, x is the crosslinker concentration [wt%], i and n is the particular poly mer and the number of polymers in the hydrogel system, respectively, and Xion,i is the mass fraction of polymer i in the hydrogel system The development of Eq (6) for particular hydrogel system and the detail explanation of symbols as well as its determination can be observed in (Kopaˇc, Abrami, et al., 2021) According to the relation between τ0 and ρx presented in Eq (5), the mathematical model to predict yield stress of complex hydrogel systems can be proposed by analogy to Eq (6): ( ) n n ∑ ∑ Nhyd,i mp,i − mp0,i Xhyd,i Nion,i mp,i Xion,i − aion τ0 = Sion Shyd (7) e x + ahyd 2 i=0 i=0 where S is the coefficient of proportionality in units J/mol and may represents the energy defined per moles of crosslinks that can be used to restore the deformation It is defined as a function of polymer-polymer interaction type (predominant effect of ionic (Sion) and hydrogen (Shyd) interactions) and shapes of building blocks (depends on consistent polymer or clay, etc.) in the gel system In polymer dispersions or so lutions, the internal structure is formed by polymer molecules that are randomly distributed and occupy the most energy-efficient conforma tion Chains can be intertwined, there may be electrostatic repulsive or attractive forces between them, and parts of the chains can be inter connected (crosslinked) These effects significantly affect the S value (more detailed discussion of this parameter is further provided in Sec tion 3.3.) Eq (7) can be further simplified for single: (i) polymer systems giving origin to hydrogels relaying on inter-chains hydrogen bons (Eq (8)), and (ii) ionically crosslinked hydrogel systems (Eq (9)), and can be written as analogy to model development in (Kopaˇc, Abrami, et al., 2021): ( ) Nhyd mp − mp0 ahyd τ0 = Shyd (8) τ0 = Sion Nion mp − e aion x (9) As it was possible to deduce from experimental observations, other phenomena can be introduced and discussed in the development of mathematical model, namely dilution effect In samples where one of the polymers does not participate in ionic, hydrogen, or any other in teractions process (e.g., ALG solution without crosslinking agent), the dilution effect described by the Sdil is introduced in Eq (10) It is spec ulated that the internal structure of the polymer solutions plays an important role in the formation of the hydrogel network ( ) ( )) ( Nhyd mp − mp0 (10) ahyd ∙ Shyd Xhyd − Sdil − Xhyd τ0 = The Eq (10) is written for two-component non-crosslinked hydrogel systems (e.g., SCLG/ALG) where the first term represents the effect of hydrogen bonding interactions between SCLG chains on τ0 and the second term is the dilution effect contribution wherein the ALG polymer molecules inhibit hydrogen interactions between SCLG chains and reduce the Shyd of SCLG due to the steric hindrances 3.3 Analysis of zero–shear viscosity and yield stress (model verification) As an upgrade to a wide range of experimental data, the proposed mathematical approach to analyze τ0 in a form of Eq (7) was used to describe the synergistic effect on shear behavior owing to their inter relationship For this evaluation, the experimentally determined ρx data T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 Fig Correlation between crosslink density and yield stress The τ0 data were determined by the same procedure as shown in Fig and refers to hydrogel samples presented in Figs and The ρx data were adopted from our publication (Kopaˇc, Abrami, et al., 2021) where the same samples (the same procedure of preparation) were prepared The red lines represent the Eq (7) model prediction and numbers represent a mass fraction of first written polymer or clay in the mixture (in panel C the numbers represent the concentration of both polymers in 0.5/0.5 mass fractions) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) formation in a mixture with SCLG Therefore, the presence of ALG in SCLG systems has only a diluting effect, to the point, where gel's for mation is no longer possible (see also Fig 3D for reference) which is for fractions lower than 0.25 of wt% SCLG or 0.5 wt% SCLG (according to the literature (Lapasin et al., 2017), SCLG water dispersions under 0.75 wt% are almost Newtonian or slightly shear thinning with undetectable viscoelastic properties) Differently, in SCLG/TOCNF samples, due to TOCNF nanofibers hydrogen interaction contribution, the hydrogel structure is observed for all fractions (from 0.9 to 0.1) of wt% SCLG Interestingly, although the different effects of ALG and TOCNF on ρx of SCLG based systems, the same linear trend on log η0 vs ρx plot can be observed in both cases It can be figured out that the fraction (concen tration) of polymers contributes to the size of invisibly small clusters which are enabled by entanglements of nanofibers and (non)covalent interactions between them and the size of beads which are formed due to triple helical tertiary structure (triplex) in TOCNF and SCLG systems, respectively Similar hydrogel systems as in previous case were prepared by changing SCLG with LAP (Fig 7B) The presence of ALG has only diluting effect also in the non-crosslinked mixture with LAP This phe nomenon is obvious at 50/50 mixture of LAP/ALG (see circle 0.5 in Fig 7B), where the trend is out of linearity on log η0 vs ρx diagram in comparison to mixtures with higher LAP content On the other hand, the TOCNF reduces the effect of the edge-face, edge-edge, and face-face interactions between LAP particles on the viscoelastic properties, ˇ through the steric hindrance (Lapasin et al., 2017; Sebenik et al., 2020) It can be observed that LAP/TOCNF system (black circles) possess higher Table The values of proportionality coefficient S (Eq (7)) for a specific hydrogel constituent material The Shyd was adopted by fitting the Eq (8) of noncrosslinked single polymer (SCLG, LAP, TOCNF) hydrogels, Sion was adopted by fitting the Eq (9) of crosslinked single polymer (ALG, TOCNF) hydrogels, and Sdil was adopted by fitting the Eq (10) of non-crosslinked ALG-containing mixtures The predetermined values for SCLG, LAP, and TOCNF were fixed in further model calculations SCLG LAP TOCNF ALG Shyd [J/mol] Sion [J/mol] Sdil [J/mol] 317 151 69 / / / 26 34 / / / 150 Additionally, to analyze in detail the relationship between mechan ical and flow properties of hydrogels, the effect of ρx on η0 was also identified and illustrated in Fig In absence of (ionic) crosslinking agent, the predominant effect on the formation of hydrogel network and consequently on rheological properties have the polymers which in pure dispersion state forms strong gels' structure due to many interactions (hydrogen, electrostatic, covalent, other van der Waals bonds…) present between polymer chains (see Fig for reference) Fig 7A reports the effect of SCLG addition on ρx and η0 of non-crosslinked hydrogel sys tems Due to the previously exposed dilution effect of ALG it can be presumed that ALG solution has no contribution to hydrogel network T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 Fig Zero-shear viscosity (η0) obtained by RBC model against crosslink density (ρx) of various hydrogel systems (different colors) Panel A and B reports the effect of SCLG and LAP, respectively, on rheological properties of non-crosslinked hydrogel system Panel C and D show the predominant effect of ionic polymer (TOCNF and ALG, respectively) on crosslinked samples The numbers represent a mass fraction of first written polymer or clay in the mixture The double color circles correspond to the single biopolymer or clay dispersion (2% SCLG, 2% LAP, crosslinked 2% TOCNF, and crosslinked 2% ALG in panel A, B, C, and D, respectively) summarized from Fig η0 values at the same ρx of the network than in LAP/ALG system (red ˇ polymer nanofibers (Sebenik et al., 2020) which may be the reason for higher η0 values for crosslinked TOCNF or ALG systems containing LAP (unlike nonionic SCLG-containing systems) (see Figs 7C and D) Differently, TOCNF–SCLG hydrogen bonds lead to the scarce effect of calcium ions due to the hydrogen bonding interaction arising among SCLG triple helices and TOCNF nanofibrils that are no longer so prone to establish Ca2+ mediated ionic bonds (see Fig 7C) In the SCLG/ALG systems (Fig 7D), the presence of SCLG reduces ρx as a result of steric hindrances, especially evident in the intermediate region of SCLG frac tions (0.25–0.75) The effect of SCLG in complex hydrogel systems on ρx and τ0 which leads to anomalous rheological behavior is profoundly discussed in the next section Here, it may be concluded, that the pres ence of SCLG in ionically crosslinked hydrogels reduces the ρx because it complicates the ionic interactions between ALG or TOCNF polymer chains (Figs 7C and D) On the other hand, the addition of SCLG con tributes to high values of η0 even at lower ρx (under mol/m3), indi cating that by the additional formation of the network structure SCLG helices contribute to higher resistance to flow circles) This is contributed to building blocks that form a hydrogel in different shapes The LAP/TOCNF system is made of LAP disks which are smaller and more homogeneous than TOCNF fibers which form ag glomerates (the meshes of invisibly small clusters) between which LAP ˇ disks are distributed (Sebenik et al., 2020) It may be also assumed that LAP contributes to the rheological response of the system in the same way as other particulate fillers, although the individual clay nano particles are capable of aggregation (squares in Fig 1) The contact between the particles is also different due to the various external sur faces and therefore the complex LAP/TOCNF building blocks are accordingly the main reason for higher η0 values Figs 7C and D illustrate the effect of TOCNF and ALG presence on ρx and η0 in ionically crosslinked hydrogel systems, respectively It may be figured out that the ρx and η0 are much higher than in the same noncrosslinked samples (Figs 7A and B) At this point, the hydrogel for mation of ALG systems is stimulated by ionic interactions, omitting the previously reported dilution effect of ALG in non-crosslinked samples This leads to the different dynamics of hydrogel properties, which is why the ALG-containing crosslinked systems have higher ρx due to more carboxyl groups on the surface of ALG than in the case of TOCNF Generally, the linear (exponential on a normal scale) growth in log η0 versus ρx can be observed with some deviations marked at lower mass fractions of ionic polymer A very similar trend can be observed in LAP/ TOCNF (red circles in Fig 7C) and LAP/ALG (red circles in Fig 7D) samples which may be explained by the noncompetition of LAP disks with TOCNF or ALG mediated ionic interactions via calcium ions Furthermore, LAP nanodisks are distributed (interpenetrate) within the TOCNF matrix due to electrostatic interactions between positively charged edges of LAP disks and negatively charged carboxyl groups of TOCNF nanofibers The LAP nanodisks act as bridging agents between 3.4 Analysis of synergistic effects in hydrogel systems and anomalous behavior of gels based on scleroglucan and TEMPO nanofibrillated cellulose mixture In Fig the black and red lines represent the systems where the hydrogen and ionic (electrostatic) interactions, respectively, play a pivotal role in the formation of hydrogel network In Figs 8B-D, the predominant effect of ionic interactions over hydrogen bonds (and other interactions, explained in the introduction) are evident even at low ρx (the intersection of the black and red curves is at the point where there is the lowest concentration (fraction) of the polymer with carboxyl groups - i.e., ALG or TOCNF) Meanwhile, in Fig 8A, the linear trendline (black) T Kopaˇc et al Carbohydrate Polymers 287 (2022) 119352 Fig Correlation between crosslink density and yield stress presented for four different types of polymer mixtures in addition of Laponite The values in panel: (i) A refers to Figs 6A and B, (ii) B refers to Figs 6F and I, (iii) C refers to Figs E and H, and (iv) D refers to Figs D and G The black and red circles represent the noncrosslinked and crosslinked samples, respectively The lines correspond to linear fit where black and red color refers to predominant effect of hydrogen and ionic interaction in hydrogel systems, respectively In panel A, the gray color represents the linear correlation between τ0 and theoretically calculated ρx by Eq (6) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) of the SCLG/TOCNF system without a crosslinking agent can be forwardly forecast into the “red region” where the SCLG/TOCNF sam ples were ionically crosslinked It was proven in Fig 8A, where the black circles/lines present the samples without addition of ionic crosslinker (without ionic interactions) Differently, the red circles/lines present the same samples which were ionically crosslinked However, it was spec ulated that the ionic interactions are predominant over hydrogen which results especially in drastic increase in crosslink densities (see different slopes of red and black lines on panels B, C and D) In panel A, the slope of black line (predominant hydrogen interactions) is almost the same as the slope of red line This clearly shows that in the case of SCLG/TOCNF systems the hydrogen bonds play a predominant role even at low con centrations of ionic interaction (Kopaˇc, Abrami, et al., 2021) As a matter of fact, in Fig 6, the (only) nonlinear behavior between τ0 and ρx is revealed in crosslinked 2% SCLG/2% TOCNF gels in different weight ratios of both constituent biopolymers (Fig 6B) A small deviation can be also observed in crosslinked 2% SCLG/2% ALG system (Fig 6H) Apparently, the SCLG biopolymer in mixture with the polymer that could be ionically crosslinked often leads to anomalous behavior of gel's rheological properties Interestingly, a similar deviation was observed in our previous study (Kopaˇc, Abrami, et al., 2021), where the SCLG/ TOCNF hydrogel systems clearly differ from the ρx prediction of the developed model equation (Eq (6)) According to this model prediction, it can be speculated that ρx is underestimated, since the experimentally determined values of ρx are lower than the Eq (6) prediction To support this assumption, the model prediction of τ0 by Eq (7) is added in Fig 8A for reference (gray circles) The observed deviations can be explained by the predominance of hydrogen interactions that probably hinder the formation of ionic bonds in obtaining the hydrogel network Therefore, the competition between TOCNF – Ca2+ − TOCNF mediated ionic in teractions and TOCNF–SCLG hydrogen bonds lead to the scarce effect of calcium ions due to the hydrogen bonding interaction arising among SCLG triple helices and TOCNF nanofibrils that are no longer so prone to establish Ca2+ mediated ionic bonds It is also not negligible that, theoretically, it is possible that more than twice more hydrogen bonds (2.8 mmol/g of hydroxyl group content) can be formed between TOCNF polymer chains than ionic ones (1.2 mmol/g of carboxyl group content) The SCLG has even more hydroxyl pendant groups (4.2 mmol/g of hy droxyl group content) on the surface than TOCNF that are accessible for hydrogen bond formation (Kopaˇc, Abrami, et al., 2021) Moreover, as illustrated in Fig 8C, the presence of SCLG due to the steric hindrance also reduces the effect of the ionic interactions in the SCLG/ALG system on the ρx (viscoelastic properties) On the other hand, except for SCLG, Fig reports that the addition of TOCNF, ALG, and LAP to the polymer mixture produces only a quantitative effect on its viscous behavior, which does not change qualitatively In the LAP-containing systems, the synergistic effects of polymer-clay blending are crucial The linear response shown in Figs 6D, F, G, and I and the apparent switch in the slope of the linear curve (black to red lines) when the crosslinking agent is added (see Figs B and D) may be evidence that the synergistic effect of polymerclay interaction gradually decreases when, despite high concentrations, nanoparticles, distributed within the polymer network, are no longer able to develop an extended aggregation structure (Lapasin et al., 2017) Therefore, an increase of LAP fraction implies 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M., Shirdast, A., Sharif, A., & Aalaie, J (2020) Aqueous/brine solutions viscosity and surface properties of hydrophobically modified scleroglucans: Role of grafted chain length Carbohydrate Polymers, 229, Article 115519 https://doi.org/ 10.1016/J.CARBPOL.2019.115519 Paolicelli, P., Varani, G., Pacelli, S., Ogliani, E., Nardoni, M., Petralito, S., Adrover, A., & Casadei, M A (2017) Design and characterization of a biocompatible physical This study presents a comprehensive flow behavior characterization of the hydrogel systems based on polysaccharide mixtures In noncrosslinked samples, the shear-thinning behavior is more pronounced at higher SCLG and LAP fractions in the mixture (higher concentration) eventually becoming apparently plastic even at the lowest fractions On the other hand, TOCNF and ALG content in non-crosslinked samples contribute to more elastic behavior with pronounced 2nd Newtonian plateau In ionically crosslinked samples, however, the anionic bio polymers TOCNF and ALG content play a predominant role in deter mining rheological properties compared to nonionic polymers, giving evidentially plastic behavior with significantly higher zero-shear vis cosity and yield stress values (extended list is included in Table S1) The detailed flow behavior examination is performed based on polymerpolymer interaction theory, mainly introduced in our previous work (Kopaˇc, Abrami, et al., 2021), where the hydrogen interactions play a pivotal role in hydrogels, until the addition of crosslinking agent, when ionic interactions take precedence over hydrogen bonds Following the rheological observations supported with the theoretical background, the mathematical prediction of yield stress in relation to crosslink density is proposed A detailed analysis of synergetic effect in complex hydrogel systems that predominantly affect the rheological properties of gels leads to the conclusion that there is a linear correlation between cross link density and yield stress At this point, the parameter S is introduced, which serves as the coefficient of proportionality in units [J/mol] and represents a new way of analyzing the rheological properties of complex hydrogels According to the developed model prediction of yield stress, the higher S represents the more reversible (elastic) hydrogel structures in the deformation process under the shear force action The model correlation provides an insight into the interior of the hydrogel network, where various anomalous processes occur, which are difficult to detect with conventional rheological measurements Thus, the scarce effect of calcium ions in SCLG/TOCNF systems was discovered It was found that the hydrogen interaction can predominantly affect the rheological properties over ionic interaction due to the hydrogen bonding interac tion arising among SCLG triple helices and TOCNF nano-fibrils that are no longer so prone to establish Ca2+ mediated ionic bonds Moreover, the dilution effect of non-crosslinked ALG-containing systems was detected where dilution with polymer solution mainly contributes to less elastic hydrogel behavior Supplementary data to this article can be found online at https://doi org/10.1016/j.carbpol.2022.119352 CRediT authorship contribution statement Tilen Kopacˇ: Conceptualization, Methodology, Software, Valida tion, Formal analysis, Investigation, Writing – original draft, Visualiza tion Aleˇs Ruˇ cigaj: Software, Formal analysis, Data curation, Writing – review & editing, Visualization Matjaˇ z Krajnc: Writing – review & editing, Resources, Supervision, Project administration, Funding acquisition Declaration of competing interest The authors declared no conflicts of interest Acknowledgment The authors acknowledge the financial support from the Slovenian Research Agency (research core funding No P2-0191) References Becher, T B., Braga, C B., Bertuzzi, D L., Ramos, M D., Hassan, A., Crespilho, F N., & Ornelas, C (2019) The structure–property relationship in 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of. .. interaction effects on the flow behavior offering the basis for determination of crucial parameters, such as η0 and τ0 As a result, the theoretical outlines of the model development to predict the flow