# Glucono-Delta-Lactone-Induced Alginate Gelation: New Insights into the Effect of the Cross-Linker Carrier Type on the Hydrogel Mechanics

Imen Ben Djemaa, Fouzia Boulmedais, Stéphane Auguste, Malgorzata Tarnowska, Sébastien Andrieux, Wiebke Drenckhan-Andreatta

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## ► To cite this version:

Imen Ben Djemaa, Fouzia Boulmedais, Stéphane Auguste, Malgorzata Tarnowska, Sébastien Andrieux, et al.. Glucono-Delta-Lactone-Induced Alginate Gelation: New Insights into the Effect of the Cross-Linker Carrier Type on the Hydrogel Mechanics. Langmuir, 2024, 40 (20), pp.10492-10501. 10.1021/acs.langmuir.3c03959 . hal-04674099

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# Glucono-Delta-Lactone induced alginate gelation: new insights into the effect of the crosslinker carrier type on the hydrogel mechanics

Imene Ben Djemaa<fnref n="1" />,<fnref n="2" />*, Fouzia Boulmedais<fnref n="1" />*, Stéphane Auguste<fnref n="2" />, Malgorzata Tarnowska<fnref n="2" />, Sébastien Andrieux<fnref n="1" />, and Wiebke Drenckhan-Andreatta<fnref n="1" />

## Abstract

Physical alginate hydrogels commonly rely on “internal gelation” to introduce the cross-linker, i.e. calcium (Ca(II)) ions. These are released in a homogeneous manner using a pH-sensitive Ca(II) carrier and Glucono-Delta-Lactone (GDL) as the acidifier. Yet, it remains unclear how the carrier of the cross-linker affects the gelation process and final hydrogel properties. We therefore investigate two internal gelation methods using either Ca(II)-chelating ligand complexes or insoluble Ca(II)-based salts. Ionometry coupled with pH measurements reveals the release process of Ca(II) ions upon acidification, which is well described by simulations using the Hyperquad Simulation and Speciation program. We show that these findings correlate well with the evolution of the mechanical properties of the hydrogels. Although the two pH-triggered gelation methods appear to be similar, we demonstrate their differences in terms of gelation kinetics and final cross-link density. The nature of the ligand or the salt affects significantly the fraction of the released Ca(II) ions and hence the mechanical properties of the final hydrogel for a given GDL concentration. Furthermore, for the first time, we demonstrate the competition between GDL and alginate in binding with Ca(II) ions. This study therefore provides different tools for the efficient formulation of alginate hydrogels.

Keywords: Alginate hydrogels; Internal cross-linking; Calcium chelators; Ionometry; Rheology, Glucono-Delta-lactone

## Contents

<table><tr><td>1.</td><td>Introduction</td><td>1</td></tr><tr><td>2.</td><td>Materials and methods</td><td>1</td></tr><tr><td>2.1.</td><td>Alginate hydrogels</td><td>1</td></tr><tr><td>2.2.</td><td>Rheological characterisation of alginate hydrogels</td><td>2</td></tr><tr><td>2.3.</td><td>Simulation of calcium speciation diagrams as a function of pH</td><td>2</td></tr><tr><td>3.</td><td>Results and discussion</td><td>3</td></tr><tr><td>3.1.</td><td>Ca(II)-chelating ligand complexes</td><td>3</td></tr><tr><td>3.2.</td><td>Calcium-based salt particles as the cross-linker carrier</td><td>7</td></tr><tr><td>3.3.</td><td>Characterisation of the formulated hydrogels</td><td>8</td></tr><tr><td>4.</td><td>Conclusion</td><td>8</td></tr><tr><td></td><td>References</td><td>10</td></tr></table>

<footnote n="1">¹ Institut Charles Sadron, CNRS UPR22-University of Strasbourg, CEDEX 2, 67084 Strasbourg, France</footnote>

<footnote n="2">² Urgo Research Innovation and Development, CEDEX, 21300 Chenôve, France</footnote>

<footnote>* Corresponding authors: Fouzia.boulmedais@ics-cnrs.unistra.fr; imen.ben-djemaa@etu.unistra.fr</footnote>
# 1. Introduction

Extracted from brown seaweed, sodium alginates are water-soluble anionic polysaccharides composed of long linear β-d-mannuronic acid (M) and α-l-guluronic acid (G) residues. Owing to their biocompatibility, low toxicity, relatively low cost, and mild gelation in the presence of divalent cations such as calcium cations (Ca(II)), alginate hydrogels are widely used in encapsulation technologies for applications in biomedicine, tissue engineering or food science ¹⁻⁵. The formation of alginate gels is due to the binding of Ca(II) with G residues forming eggbox structures ⁶. Gel formation can be “external” or “internal” depending on how the cations are supplied. External gelation is achieved by the diffusion of Ca(II) from the outside to the inside of the alginate solution. Internal gelation is based on the gradual release of Ca(II) within the alginate solution, resulting in structural homogeneity of the hydrogel thanks to a uniform distribution of the cations ⁷. It is commonly based on the use of a pH-sensitive Ca(II) carrier that is in an inactive form, e.g. a Ca(II)-chelating ligand complex ⁸⁻¹¹ or insoluble Ca(II) salt ¹²⁻¹⁵, at neutral or basic pH which release Ca(II) at acidic pH (Figure 1). Ca(II)-chelating ligand complexes, usually obtained with ethylene diamine tetraacetic acid (EDTA) or ethylene glycol tetraacetic acid (EGTA), are stable above pH 7 and release Ca(II) upon ligand protonation. Insoluble calcium salts, such as calcium carbonate, become soluble at acidic pH making Ca(II) available to interact with alginate. In most cases, the acidification is achieved by the addition of glucono-delta-lactone (GDL). GDL is an internal ester which undergoes lactone hydrolysis in the presence of water to form gluconic acid (HGluc). This weak acid further dissociates into gluconate (Gluc) according to the following reaction :

$$GDL + H_2O \leftrightarrow HGluc \leftrightarrow Gluc^- + H^+$$

<figure><img src="image_3.png" /><figcaption>Figure 1: Schematic representation of the two most common methods of internal gelation of alginate hydrogels based on Ca(II)-ion release upon acidification using (I) Ca(II)-chelating ligand complex, e.g Ca(II)-EGTA and (II) insoluble Ca(II) salt, e.g. calcium carbonate.</figcaption></figure>

Depending on the application requirements, the final properties of alginate hydrogels are mainly adjusted by tuning the alginate molecular weight, the M/G ratio, the type of gelation, and the alginate concentration. In this study, we demonstrate the importance of the choice of the pH-sensitive Ca(II) carrier in controlling the viscosity of the pre-gelling solution, its gelation kinetics, and the rheological properties

of the formulated hydrogel. We studied the kinetics of Ca(II) release from different Ca(II)-chelating ligand complexes and insoluble calcium salts upon acidification with GDL, compared them with simulations of the association equilibria, and correlated them with the rheological properties of the formulated alginate gel. For this purpose, systematic ionometry and pH measurements were performed as well as the rheological characterisation, for different Ca(II)-chelating ligand complexes (Section 2.1) and insoluble Ca(II)-based salts (Section 2.2). In both cases, the presence of Gluc affects the final amount of Ca(II) released. Finally, all the results obtained are correlated with the rheological properties of the formulated hydrogels (Section 2.3). We show for the first time that the kinetics of the Ca(II)-ion release and the amount available for cross-linking depends on the chosen pH-sensitive Ca(II) carrier; and we show how the understanding of these two parameters allows to optimise the rheological properties of the obtained gels.

# 2. Materials and methods

Low Viscosity sodium Alginate (LVA, M_n = 2.0 10⁵ g/mol ± 1.3 %, M_w = 3.7 10⁵ g/mol ± 0.6 %, Polydispersity = 1.9 ± 1.4 % measured by SEC (see Appendix A of the supporting information), M/G = 1.2 measured by CD spectroscopy), Ethylene glycol-O,O'-bis(2-aminoethyl)-N,N,N',N'-tetraacetic acid (EGTA, C₁₄H₂₄N₂O₁₀), and calcium carbonate (CaCO₃, 5 µm average), were purchased from Alfa Aesar. D-(+)-Gluconic acid δ-lactone (GDL, C₆H₁₀O₆), Calcium chloride dehydrate (CaCl₂, 2 H₂O), Ethylenediaminetetraacetic acid (EDTA, C₁₀H₁₆N₂O₈), Trans-1,2-Diaminocyclohexane-N,N,N',N'-tetraacetic acid monohydrate (CDTA, C₁₄H₂₂N₂O₈ H₂O), N-(2-Hydroxyethyl)ethylenediamine-N,N',N'-triacetic acid (HEDTA, C₁₀H₁₈N₂O₇), Sodium hydroxide, and calcium phosphate dibasic (CaHPO₄, 15 ± 9 µm) were purchased from Sigma Aldrich. Milli-Q water from a Q-POD Dispenser, with a Millipore membrane of 0.22 µm, was used to prepare all the solutions. All chemicals were used without further purification.

## 2.1. Alginate hydrogels

[Ca(II)]max is defined as the calcium concentration corresponding to a maximum cross-linking degree considering the following two hypotheses:

i) one calcium ion available per two carboxylic groups on the available sodium guluronate (G) in the alginate solution.

ii) M+G = 1.

We calculate [Ca(II)]max accordingly,

$$[Ca(II)]_{\max} = \frac{[G]_{mol/L}}{2} = \frac{\left(\frac{1}{1+M/G}\right)[ALG]_{g/L}}{2 \cdot M_w(G)} \quad (1)$$

where the molecular weight of sodium guluronate M_w(G) = 216.12 g/mol. For 1 wt % sodium alginate [G] = 0.02 M.
The calcium concentration of choice is equivalent to two
times [Ca(II)]<sub>max</sub>.

2.1.1. Preparation of calcium solutions

0.04 M Ca(II)-Ligand solutions were prepared by mixing
calcium chloride and ligand in milli-Q water at an equimolar
amount, and the pH was adjusted by addition of NaOH.
Among the different ligands used, only the EGTA-based
solutions were filtered using a 5 µm syringe filter after
complete dissolution of the complex due to the presence of
micron-sized impurities in the EGTA batch. For ionometric
measurements the calcium solutions were mixed with milli-
Q water at 1:1 v/v to obtain 0.02 M in Ca(II)-Ligand. The
sample volume was 100 mL to which we added 2 mL of an
Ionic Strength Adjustor (ISA) following the protocol
provided by Mettler Toledo.

Dispersions of 0.02 M and 0.04 M Ca(II) salts were prepared
by dispersing the particles in milli-Q water respectively for
ionometric measurements and gelling solutions preparation.

2.1.2. Preparation of the gelling solution

2 wt % of sodium alginate was dissolved in water under
mechanical stirring using a paddle mixer and heating at 50°
C for one hour, then left under magnetic stirring at room
temperature for three days.

The calcium solutions at 0.04 M were mixed with the alginate
solutions at 1:1 v/v to obtain the gelling solution, 0.02 M in
Ca(II) ions after complete release.

2.1.3. Preparation of the alginate hydrogel samples

Alginate hydrogels were prepared by dissolving GDL in 19 mL of the gelling solution at a concentration of 1 wt%. The mixture was stirred for 3 - 5 min and immediately poured into a petri dish of 90 mm diameter, sealed and stored at room temperature for around 17 h (one night) to form circular samples of 3 mm in thickness.

2.1.4. Ionometric measurements

To follow the Ca(II) release from Ca(II)-chelating ligand and
Ca(II) salts, ionometric measurements were performed using
a combined calcium-selective electrode with an integrated
reference (Mettler Toledo) combined with the measurement
of the pH using the InLab NMR sensor (Mettler Toledo). The
electrodes were connected to a multi-channel instrument from
SevenExcellence that allows automatic data acquisition of the
two parameters simultaneously in the same sample as a
function of time via the LabX software. The two electrodes
were calibrated before each experiment.

2.2. Rheological characterisation of alginate hydrogels
All rheological measurements were conducted using a
Discovery HR20 rheometer from TA instruments. The
temperature was set at 25 °C. A solvent trap accessory from

TA Instruments was used to avoid evaporation during the
measurements.

2.2.1. Temporal evolution of the elastic modulus

The loaded sample was a gelling solution (see Section 3.1.2) to which GDL was added 5 min before running the experiment. The geometry used was a 40 mm Sandblast parallel plate. The gap was initially fixed at 1 mm but the precise value was adjusted throughout the experiment to maintain the axial force equal to 0.1 N. The frequency was set at 1 Hz, and the strain was at 0.3 %.

2.2.2. Amplitude sweep tests

The loaded samples were previously formed alginate
hydrogels (see Section 3.1.3) stored in their sealed petri-
dishes. The geometry used was a 60 mm parallel plate (Peltier
plate steel). The overall gap corresponds to the height of the
sample (3 mm, see Section 3.1.3) but the precise value was
fixed at the plate position where the axial force is equal to 1
N. The frequency was set at 0.1 Hz, and the strain ranged
from 0.01 to 50 %.

2.2.3. Viscosity

The loaded samples were gelling solutions (see Section 3.1.2) without the addition of GDL. The geometry used was a cone-plate geometry (diameter of 40 mm, angle of 1°). The gap was fixed at 27 µm. The measurement consisted of two steps, a first shear rate sweep from 0.1 to 1000 s⁻¹, and a second sweep from 1000 to 0.1 s⁻¹, with a logarithmic progression. Three measurements were taken per decade, each for 10 seconds.

2.3. Simulation of calcium speciation diagrams as a function of pH

The Hyperquad Simulation and Speciation (HySS) program ¹⁶ was used to generate speciation diagrams for the studied systems. The simulation principle relies on the equilibria of the different species in the solution and is explained in detail in the dedicated literature.¹⁶ Here we shall summarise only the general idea. By iteratively solving the mass-balance equations, this method calculates concentrations of various species under different conditions, accounting for stoichiometry and equilibrium constants. Speciation diagrams visually represent how the distributions of different species respond to changes in parameters such as pH or the presence of partially soluble precipitates. In the presence of a solid, the Newton-Raphson method is used to iteratively solve a set of linear equations representing mass balance and solubility.

To perform the simulations, the number and type of
components and their concentrations before dissolution are
first specified, then the system is described by a set of defined
equilibrium constants and stoichiometric coefficients. The
chemical formulas of the present species were created
accordingly (Table 1).
The used models for each system and their conditions are presented in Table 1 along with the literature references from which the conditional formation constants were taken. All concentrations were fixed at 0.02 M, except Gluc⁻ 0.056 M, corresponding to 1 wt %. The number of moles of cross-linked alginate n<sub>Ca-ALG</sub> used in Figure 4 were calculated as the sum of the number of moles of calcium binding with one Guluronate unit and the number of moles of calcium binding with two Guluronate units, n<sub>Ca-ALG</sub> = (n<sub>Ca-G</sub> + n<sub>Ca-G₂</sub>).

<table><caption>Table 1: Used conditional formation constants.</caption><thead><tr><th>Formula</th><th>pKa / Log.<br>formation<br>constant</th><th>Components</th></tr></thead><tbody><tr><td>Ca-G</td><td>3.7</td><td></td></tr><tr><td>Ca-G₂</td><td>4</td><td>11</td></tr><tr><td>HALG</td><td>3.65</td><td></td></tr><tr><td></td><td></td><td>Ca(II)</td></tr><tr><td></td><td></td><td>L</td></tr><tr><td></td><td></td><td>Gluc</td></tr><tr><td></td><td></td><td>H</td></tr><tr><td>HGluc</td><td>3.8</td><td>0</td><td>0</td><td>1</td><td>1</td></tr><tr><td>Ca-Gluc</td><td>1.22</td><td>17</td><td>0</td><td>1</td><td>0</td></tr><tr><td>OH⁻</td><td>-13.77</td><td>16</td><td>0</td><td>0</td><td>0</td><td>-1</td></tr><tr><td><b>L = EGTA</b></td><td></td><td></td></tr><tr><td>HEGTA³⁻</td><td>9.46</td><td></td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><td>H₂EGTA²⁻</td><td>18.31</td><td></td><td>0</td><td>1</td><td>0</td><td>2</td></tr><tr><td>H₃EGTAH⁻</td><td>20.99</td><td>11,18,19</td><td>0</td><td>1</td><td>0</td><td>3</td></tr><tr><td>H₄EGTA</td><td>22.99</td><td></td><td>0</td><td>1</td><td>0</td><td>4</td></tr><tr><td>Ca-EGTA²⁻</td><td>11</td><td></td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Ca-EGTAH⁻</td><td>5.33</td><td></td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td><b>L = EDTA</b></td><td></td><td></td></tr><tr><td>HEDTA³⁻</td><td>10.17</td><td></td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><td>H₂EDTA²⁻</td><td>16.28</td><td>20</td><td>0</td><td>1</td><td>0</td><td>2</td></tr><tr><td>H₃EDTAH⁻</td><td>18.96</td><td></td><td>0</td><td>1</td><td>0</td><td>3</td></tr><tr><td>H₄EDTA</td><td>20.96</td><td></td><td>0</td><td>1</td><td>0</td><td>4</td></tr><tr><td>Ca-EDTA²⁻</td><td>10.7</td><td>21</td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Ca-EDTAH⁻</td><td>3.5</td><td></td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td><b>L = CDTA</b></td><td></td><td></td></tr><tr><td>HCDTA³⁻</td><td>11.7</td><td></td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><td>H₂CDTA²⁻</td><td>17.82</td><td></td><td>0</td><td>1</td><td>0</td><td>2</td></tr><tr><td>H₃CDTAH⁻</td><td>21.32</td><td>18,22</td><td>0</td><td>1</td><td>0</td><td>3</td></tr><tr><td>H₄CDTA</td><td>23.72</td><td></td><td>0</td><td>1</td><td>0</td><td>4</td></tr><tr><td>Ca-CDTA²⁻</td><td>12.5</td><td></td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Ca-CDTAH⁻</td><td></td><td></td><td>1</td><td>1</td><td>0</td><td>1</td></tr><tr><td><b>L = HEDTA</b></td><td></td><td></td></tr><tr><td>H-HEDTA²⁻</td><td>9.9</td><td></td><td>0</td><td>1</td><td>0</td><td>1</td></tr><tr><td>H₂-HEDTA⁻</td><td>15.3</td><td>23</td><td>0</td><td>1</td><td>0</td><td>2</td></tr><tr><td>Ca-HEDTA²⁻</td><td>8.1</td><td></td><td>1</td><td>1</td><td>0</td><td>0</td></tr><tr><td>Ca-HEDTAH⁻</td><td>1.4</td><td></td><td>1</td><td>1</td><td>0</td><td>1</td></tr></tbody></table>

# 3. Results and discussion

## 3.1. Ca(II)-chelating ligand complexes

### 3.1.1. Nature of the chelating ligand

At the outset, we analysed the calcium release kinetics and equilibria for the example of a Ca(II)-EGTA complex solution. For this purpose, we prepared a 0.02 M Ca(II)-EGTA solution and followed the calcium release along with pH variation as a function of time after acidification. In an attempt to separate acidification from calcium release kinetics, we used two different acidification kinetics:

(i) The first is representative of the acidification method for alginate gelation, namely the use of GDL (solid) which

slowly releases Gluc upon hydrolysis (Figure 2a). Herein, both acidification and gelation evolve simultaneously.

(ii) The second acidification kinetics is instantaneous when Gluc is added to the complex solution. After complete hydrolysis of GDL in pure water, the solution (in liquid form) is added gradually and the calcium release is followed for a few minutes after each volume addition (Figure 2b). The used acid being the same as previously, this experiment completes (i) by providing insight into the kinetics of calcium release at fixed pH.

The fraction of released Ca(II), relative to the initial amount of Ca(II)-EGTA complex introduced, was plotted as a function of pH (Figure 2c) from data obtained in Figures 2a,b. Figure 2a shows the evolution of the molar fraction of released Ca(II) ions from the Ca(II)-EGTA complex along with the evolution of the pH after the addition of 1 wt % GDL in its solid form. The two curves follow the characteristic profiles for calcium decomplexation using GDL¹¹. Two processes take place simultaneously in this case, each with its own kinetics: GDL dissolution and hydrolysis and calcium release from the complex. GDL dissolution kinetics are neglected compared with its hydrolysis kinetics. To decouple these kinetics, we follow separately the calcium decomplexation over time at different fixed pHs. For this purpose, instead of solid GDL, we progressively add controlled volumes of Gluc solution to the complex solution (Figure 2b). We observe an immediate Ca(II)-adjustment with the instantaneous pH change, giving plateaus of released Ca(II) at each fixed pH. This indicates that the decomplexation process is instantaneous and that the decomplexation kinetics observed in Figure 2a is solely dictated by the acidification kinetics. It is therefore meaningful to plot the fraction of released Ca(II) as a function of pH (Figure 2c) from the data shown in Figure 2a,b.

A prior study¹¹ simulated a speciation diagram for a Ca(II)-EGTA/alginate-GDL-based formulation. Their simulations considered solely the complexation of calcium with EGTA and Alginate. We reproduced these simulations using the Hyperquad Simulation and Speciation (HySS) program with the models and conditions compiled in Table 1 giving the grey dash-dotted prediction in Figure 2c. We see that our data does not follow neatly this prediction (which was also the case in the work by Sletmoen et al. ¹¹). Gluc, the deprotonated form of GDL, is a well-known complexing agent and was proven to bind with Ca(II) ions with an association constant of 16.6 at 25° C and an electrolyte background of 0.16 M NaCl¹⁷. We therefore included the formation of this complex in our simulations in an attempt to describe better the experimental data and to determine if Gluc is a potential competitor to alginate in Ca(II) complexation. The resulting dashed line in Figure 2c shows a much better agreement of the simulations with the experimental data in the presence of Gluc. This finding suggests that the released Ca(II) from the initial complex is not entirely available in its free ionic form
but that a non-negligible amount (fraction up to 0.3 in this case) is captured by Gluc molecules. This needs to be taken into account when optimising alginate gel formulations. This “drawback” of using GDL as an acidifying agent also raises questions as to which formulation parameters would mitigate or aggravate it, which will be discussed further in Section 3.1.2.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a,b) Kinetics of decomplexation and pH evolution of 0.02 M Ca(II)-EGTA solution during acidification using as an acidifying agent (a) GDL in powder form (at 1 wt % single-dose addition at t = 0 min), or (b) Gluc solution (multi-dose addition, 0.1 wt % every~2 min). (c) Fraction of released Ca(II) ions from Ca(II)-EGTA complex as a function of pH using experimental data from (a) compared with the predictions using the HySS program (dashed lines) in the absence and the presence of Gluc.</figcaption></figure>

Having analysed the decomplexation process of Ca(II) from its ligand using GDL with the example of EGTA, we move on to investigate other ligands of different molecular structures and relative affinities to chelate Ca(II) ions. Figure

3a shows the acidification and Ca(II)-ion release kinetics after the addition of 1 wt % GDL to three different ligand solutions: EDTA, CDTA, and HEDTA (see Table 1). For comparison, we include the data obtained for EGTA (Figure 2a).

<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Kinetics of decomplexation and pH evolution of different Ca(II)-ligand complex solutions during acidification using 1% wt GDL as an acidifying agent. (b) Temporal evolution of the elastic shear modulus G of 0.02 M Ca(II)-complex solutions mixed with 1 wt % alginate after addition of 1 wt % GDL determined by shear rheology. (c) Data from (a) compared with the corresponding simulated curves, using the HySS program in the presence of Gluc.</figcaption></figure>

Focusing initially on the pH evolution over time, one observes faster acidification occurring in the following order: EDTA, CDTA, HEDTA, and EGTA. The different formulations also reach different pH at equilibrium: 3.7 (EDTA), 3.8 (CDTA), 4.3 (HEDTA), and 4.4 (EGTA). It can
therefore be seen that acidification does not only depend on GDL concentration or the working temperature²⁴ but also on the ligand nature. Previous research has not taken this into account and overlooked the importance of the GDL concentration. It has rather been fixed respecting a molar ratio [GDL]/[Ca(II)] of 2 whatever the ligand nature ¹⁴,²⁵⁻²⁷. An implication of our findings is that the working concentration of GDL has to be adjusted depending on the formulation. For example, to reach a specific value of the final pH, one would have to add a higher amount of GDL to an EGTA-based solution than to an EDTA-based solution.

Considering now the release kinetics from the decomplexation curves, we identify again a measurable dependency on the ligand nature. For example, after 200 minutes, the formulations release the following fractions of $n_{Ca(II)}/n_{0,Ca(II)}$: 0.28 (CDTA), 0.32 (EDTA), 0.41 (EGTA), and 0.45 (HEDTA). Projecting this observation to gelation entails that cross-linking kinetics is also controlled by the nature of the ligand regardless of any other formulation parameter. To confirm this implication, we conducted shear rheology measurements on 1 wt % of alginate/Ca(II)-ligand, using the same formulations as in Figure 3a, upon addition of 1 wt % GDL. Figure 3b shows the evolution of the elastic shear modulus $G'$ with time for the four formulations which differ solely by the nature of the ligand (the corresponding viscous moduli are shown in Appendix B of the supporting information). As the cross-linking occurs upon acidification, the elastic moduli increase relatively slowly following different profiles. As expected, the gelation kinetics of the four different ligands follow the calcium release kinetics during the first 260 min in the following order (from slowest to fastest): CDTA, EDTA, EGTA, and HEDTA. The values of the elastic moduli after 12 h also correlate with the results shown in Figure 3a. For example, CDTA, which released the least amount of Ca(II) ions, has lower $G'$ values than EGTA and HEDTA. After 750 min, the rheological curves of EGTA and HEDTA reached a crossover which again agrees with the results from Figure 3a where both ligands released approximately the same fraction of Ca(II) after 260 min: 0.46 and 0.48 respectively. The time corresponding to the crossover of the two elastic moduli is delayed in comparison to the crossover observed in ionometry. We believe that this is due to the gelation kinetics of alginate (which includes the diffusion of Ca(II) ions and alginate chains, complexation Ca(II)/guluronic moieties, etc.).

From the data shown in Figure 3a and simulations based on the association constants in Table 1, we plot in Figure 3c the fraction of released Ca(II) as a function of the pH for all formulations. The simulated speciation diagrams correlate again very well with the experimental data, demonstrating the reliability of this tool.

One notices that the release profiles for EDTA and CDTA are shifted towards a more acidic pH as compared with EGTA and HEDTA, e.g., a pH of respectively 4.8 and 3.8 ± 0.1 were

needed to release 0.3 of complexed Ca(II). These observations are reasonable since the four ligands differ in their pKa values and association constants with Ca(II) (see Table 1).

It therefore follows that the nature of the ligand has important implications on the final hydrogel properties, specifically its pH and its stability conditions. We thus present an experimental investigation of the effect of the ligand nature on the final gel strength in Section 3.3.

### 3.1.2. Calcium and GDL concentrations

We demonstrated in Section 3.1.1 that Ca(II) can form complexes with Gluc as a sugar-type ligand. It is therefore important to understand how this affects the alginate gelation and if Gluc is a competitor to alginate carboxylate side groups in complexing with the available Ca(II) in solution. For this purpose, we used the simulation parameters which described well our experimental results in Section 2.1.1 (see Table 1) to predict speciation diagrams for a solution of 0.02 M complex in the presence of 1 wt % alginate (ALG) and two different concentrations of GDL (Figure 4a). Being most commonly used for the internal gelation of alginate, we used herein the example of Ca(II)-EGTA complexes. Figure 4a shows the fraction of Ca(II) complexed with alginate (Ca(II)-ALG) and with Gluc (Ca(II)-Gluc), both relative to the initial amount of Ca(II)-EGTA introduced. The fraction of Ca(II)-ALG increases with decreasing pH linked to GDL hydrolysis but does not reach the value of 1. Starting from pH 6, the fraction of Ca(II)-Gluc increases with the released Ca(II) amount (Figure 2c) until Gluc begins to protonate at pH 4.5 (pKa = 3.8).

When the GDL concentration is increased from 1 to 5 wt %, the fraction of Ca(II)-Gluc at pH 4.5 increases from 0.05 to 0.15, which implies a significant amount of cross-linker being not available to participate in the gelation. These results provide further support to our hypothesis that released Ca(II) ions from EGTA are shared between ALG chains and Gluc. It is therefore important to consider this implication when aiming to accelerate or strengthen the gelation by increasing the GDL concentration.

Given that the hydrogel's elastic modulus is proportional to the cross-link density of the hydrogel network (i.e., calcium concentration) ²⁸, one can consider increasing the initial Ca(II)-ligand concentration to increase the amount of free cross-linker. However, it is important to take into account the effect of calcium concentration itself on the speciation diagram, specifically on the properties of the initial gelling solution. To illustrate this, Figure 4b shows the evolution of the fraction of Ca(II)-ALG (relative to the number of moles of guluronic acid in 1 wt % of ALG) as a function of pH for four different Ca(II)-EGTA concentrations. It is obvious that the degree of alginate complexation increases with decreasing pH in the acidic range until reaching a plateau. The plateau value increases with increasing Ca(II)-EGTA concentration.
One notices also that a fraction of 1 can be reached for Ca(II)-EGTA concentration of 0.05 M and higher. It remains the case that increasing the complex concentration enhances the cross-linking degree (i.e., fraction of cross-linked alginate). However, above 0.5 M Ca(II)-EGTA, it should be noted that the initial fraction of Ca(II)-ALG formed at pH 7 is considerable. It is therefore expected that the initial viscosity of the gelling solution is higher than for a complex of lower concentration. To validate this prediction, we carried out shear viscosity measurements for 1 wt % alginate mixed with 0.5 M Ca(II)-EGTA to compare its viscosity with 0.02 M Ca(II)-EGTA, in the absence of GDL. Figure 4c shows for each of the two formulations, a first shear rate sweep from 0.1 to 1000 s⁻¹ followed by a second sweep from 1000 to 0.1 s⁻¹. We first look at the zero-shear-rate viscosities, where the obtained values are ~0.2 and 0.4 Pa.s for 0.02 M and 0.5 M Ca(II)-EGTA, respectively. This increase in viscosity is in good correlation with the simulations shown in Figure 4b. Furthermore, one sees a well-defined plateau for the solution of 0.02 M Ca(II)-EGTA at low shear rates before the viscosity decreases at high shear rates > 10 s⁻¹ following a shear-thinning behaviour. We also notice for this formulation an overlay in the curves of the rising and descending shear rate sweeps. On the other hand, for a concentration of 0.5 M Ca(II)-EGTA, the two sweeps do not overlap and the viscosities at low shear rates did not reach a plateau. Both observations, increased viscosity and strong shear thinning with hysteresis, confirm that for the higher EGTA concentration some of the alginate chains have already been cross-linked at pH 7. This is in agreement with the prediction of the simulation. The predictions of simulations for the other ligands are very similar considering the overall behaviour (see appendix C of the supporting information).

These results provide additional proof of the reliability of the used simulations and an insight into the importance of setting formulation parameters other than the cross-linker and alginate concentrations, with respect to the desired hydrogel properties. However, caution must be applied, as the speciation diagrams have to be adapted to other alginate types or concentrations.

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

**Figure 4: Speciation diagrams simulated using the HySS program.** (a) Fraction of Ca(II)-Gluc and Ca(II)-ALG relative to the total Ca(II) content of the formulation as a function of pH for a solution of 0.02 M Ca(II)-EGTA and 1 % ALG containing two different GDL concentrations, 1 wt % (equilibrium pH at 4.5 as shown in Figure 2a) and 5 wt %. (b) Fraction of Ca(II)-ALG relative to the number of moles of guluronic acid in 1 wt % of alginate as a function of pH for different Ca(II)-EGTA concentrations containing 1 wt % GDL. (c) Shear viscosity as a function of shear rate of mixture solutions of 1 wt % alginate and 0.02 M or 0.5 M Ca(II)-EGTA.
## 3.2. Calcium-based salt particles as the cross-linker carrier

A second internal gelation method consists in using conditionally soluble divalent ion-based salts as cross-linker, for example pH-sensitive calcium salt particles (e.g., dibasic calcium phosphate or calcium carbonate) which release calcium ions upon acidification. There are numerous assets to using this method, for example, the low alkalinity of calcium salt-based solution compared to calcium complex-based solutions, since the pH of this latter is adjusted commonly by addition of sodium hydroxide. This can give a buffering capacity to the solution and hence can be of great importance, particularly when using a weak acid such as carbon dioxide to trigger gelation²⁹. Moreover, the size of the particles can be used to tune the calcium release kinetics, with larger particles leading to slower release due to their smaller surface-to-volume ratio³⁰. However, considering that these salts are initially insoluble in water at pH 7, the initial state of the gelling solution is a dispersion with micrometer-sized particles which sediment if not stirred continuously. A non-homogeneous dispersion of Ca(II) salt in the gelling solution results in hydrogel heterogeneity. Therefore, the acidification rate (i.e., GDL concentration), needs to be rapid enough to hinder particle sedimentation before gelation.

We performed the same study on dispersions of CaCO₃ and CaHPO₄ particles of 5 µm and 15 µm particle size, respectively, in pure water. We followed their dissolution as a function of time after the addition of 1 wt % GDL whilst stirring continuously the solution. Figure 5a shows the pH variation along with the evolution of the molar fraction of released Ca(II) over time. Considering first the kinetics of acidification for CaHPO₄, one notices a rapid drop of the pH in 8 min from 7.7 to 5.0 followed by a relatively slow decrease over 170 min from 5 to 3.8, close to alginate protonation pKa = 3.7. CaCO₃ shows a similar profile of acidification when using the same concentration of GDL of 1 wt %, but with a final pH of 6.2.

Comparing the two release profiles of Ca(II), one sees that CaCO₃ dissolves faster than CaHPO₄ with a crossover at 128 min after which the fraction of released cross-linker reaches a plateau at a value of 0.9, whereas CaHPO₄ continues to dissolve until complete release of the initial calcium at pH 4. This can be a result of the differences in particles size between the two salts, 5 µm for CaCO₃ and 15 µm for CaHPO₄, since their dissolution rate is related to the specific surface area of the particles, where smaller particles lead to faster Ca(II) release³⁰.

In Figure 5b, we plot the temporal evolution of the elastic shear modulus G' of the hydrogels formed by adding 1 wt % ALG to the dispersions investigated in experiments summarised in Figure 5a. In the case of CaCO₃, the alginate gelation starts immediately after addition of GDL, and G' reaches a final value of ~ 3.1 kPa. On the other hand, the

gelation of CaHPO₄ starts after a delay of around 20 min after which G' increases linearly with time until reaching a maximum at ~ 3.5 kPa which is ~ 0.4 kPa higher than that of CaCO₃ due to the difference of 0.1 in the final released calcium fraction (Figure 5a). Therefore, the choice of salt may be used as a lever to finetune gelation kinetics.

<figure><img src="image_9.png" /><figcaption>**Figure 5:** Kinetics of decomplexation of 0.02 M CaCO₃ (5 µm in diameter) and CaHPO₄ (15 µm in diameter) during acidification using 1 wt% GDL as the acidifying agent (single-dose addition at t = 0 min). (b) Temporal evolution of the elastic shear modulus G' of gels formed from the same solutions as in (a) after the addition of 1 wt % alginate. The data shown correspond to the values which we consider significant before the syneresis of the gels alters the results by changing the sample gap or causing the hydrogel to rupture.</figcaption></figure>

It is worth mentioning that unlike in the case of Ca(II) complexes, Ca(II)-Gluc complexation does not impact the Ca(II) release as almost all the ions introduced are released after 180 min.

Further investigations revealed that the release rate of gelling ions from Ca(II) particles is not instantaneous at a given pH (see Appendix D of the supporting information), but requires several minutes to reach a stable value of released amount of Ca(II). Thus, plotting the fraction of released Ca(II) from salt particles as a function of pH, as we did in Figure 2c and Figure 3c for calcium complexes, would be meaningless.
### 3.3. Characterisation of the formulated hydrogels

In Sections 2.1 - 2.2, we used rheology to characterise the gelation kinetics, without analysing the final elastic properties. This is because the long gelation times lead to artifacts in the rheological measurements. To ensure complete gelation of the hydrogels, we characterised the final elastic properties of alginate gels, formed ex-situ after 17 h, by performing amplitude sweeps at 1 Hz. The detailed measurement protocol is given in Section 3.2.2. In the literature, the gel strength of alginate hydrogels is commonly correlated to the total amount of Ca(II) ions contained in the formulation through addition either of Ca(II)-ligand ¹¹ (Section 2.1) or Ca(II)-based salt particles ¹⁴,³¹ (Section 2.2). However, what should matter for gelation is the final amount of *free* Ca(II) ions after acidification with GDL. We have shown in Sections 2.1 - 2.2 that the amount of free Ca(II) can be significantly different to the amount initially introduced in the solution. In the following, we will therefore investigate the correlation of the amount of free Ca(II) with the final gel elasticity.

Figure 6a shows shear strain sweeps of the elastic shear moduli *G*' of hydrogels obtained from 1 wt % alginate and 1 wt % GDL mixture using the calcium sources investigated in Section 2.1 (calcium complexes) and 2.2 (calcium particles). All the formulations were prepared with the same initial Ca(II) content (0.02 M). All measurements were duplicated. At low shear strains, the hydrogels demonstrate a linear viscoelastic plateau region where *G'* is independent of the strain. At a critical point, the gels yield, as shown by the decrease in *G'*. For all hydrogels, the yield occurs at a strain of 20 ± 10 %, except for CaCO₃ which yields earlier at 4.8 ± 0.3 %. In Figure 6b, we plot the plateau values obtained in the small-deformation limit of Figure 6a for all formulations as a function of the experimentally determined number of moles of released free Ca(II) ions (n<sub>Ca(II)</sub>). The obtained data is captured well by a linear fit (R² = 0.976), constrained at zero intercept since the elastic modulus of an alginate solution is close to zero in the absence of a cross-linker. The obtained correlation is in good agreement with the literature which introduced the proportionality between elastic moduli of hydrogels and the cross-links density ²⁸, which depends on the amount of free Ca(II) ions available for the cross-linking. Figure 6b shows that the dependency of alginate hydrogel strength on the cross-linking carrier type is controlled by the amount of released free Ca(II) and not by the amount of Ca(II) contained in the formulation, as commonly asserted in the literature. Formulations releasing a maximum of Ca(II) ions lead to the strongest gels. Here this is CaHPO₄, which, surprisingly, is rarely used in the literature ³², compared to CaCO₃ or calcium complexes.

<figure><img src="image_10.png" /><figcaption>Figure 6: Elastic shear modulus of alginate gels formulated with different Ca(II) sources by GDL acidification (a) Amplitude sweep measurements (at 1 Hz) on hydrogels, obtained 17 h after the addition of GDL for four different calcium complexes (Section 2.1) and two different calcium particles (Section 2.2). (b) Plateau storage moduli *G'* as a function of released free Ca(II) (n<sub>Ca(II)</sub>) 17 h after adding GDL. ALG and GDL concentrations were set at 1 wt %, and Ca(II) complexes and particles at 0.02 M.</figcaption></figure>

## 4. Conclusion

We used ionometry coupled with pH measurements to compare the kinetics and degree of Ca(II)-ion release from different Ca(II) carriers. Our observations revealed that having identical concentrations of calcium and acidifying agent (here GDL) in the formulations still leads to measurably different release kinetics and final gel properties. For example, in the case of Ca(II)-chelating ligands, Ca(II) release occurred in the following order: CDTA, EDTA, EGTA, and HEDTA. Using the HySS simulation program we demonstrated that Gluc (hydrolysed form of GDL) molecules complex with a part of released Ca(II) in competition with alginate chains. We also addressed the importance of adjusting GDL concentration to the nature of the cross-linkers carrier and not only to the introduced Ca(II) amount as claimed in prior studies. Comparing Ca(II) complexes with Ca(II)-based salt particles, the latter seem to be particularly well suited to applications that require a rapid gelation process in a limited pH range. In particular, we showed the interest in using CaHPO₄ salt, which seems to be neglected
by the community with respect to the use of CaCO₃. Rheology was used to characterise the evolution of the viscoelastic properties of the different hydrogels and their final mechanical properties. We put in evidence a strong correlation between available Ca(II) ions released from the different carriers and the final elastic shear modulus of the corresponding hydrogels. Unlike commonly assumed, it is therefore not sufficient to consider the amount of Ca(II) contained in the formulation, but the amount of actually available Ca(II) ions for the cross-linking of alginate. This combination of findings provides some guidelines for an effective design of alginate-based hydrogels. While we have concentrated here on Ca(II)-based alginate gels, it is obvious that our approach can be easily extended to other gels. In particular, we show that the HySS simulation program ¹⁶ provides a powerful tool to predict the release behavior of different formulations, which could be used more systematically as a guide.

**Acknowledgments** : The authors acknowledge many fruitful discussions with Leandro Jacomine, François Schosseler, Frédéric Faure, and Fabien Canivet. We thank Matthias Pauly, Catherine Foussat and Mélanie Legros from the CARMAC platform for technical help and discussions related to CD and SEC measurements. We thank authors of¹⁶ for giving public access to the HySS computer program. This work has been financed by a CIFRE contract with the company URGO in conjunction with an ERC Consolidator Grant (agreement 819511 METAFOAM). It was conducted in the framework of the Interdisciplinary Institute HiFunMat, as part of the ITI 2021–2028 program of the University of Strasbourg, CNRS and Inserm, was supported by IdEx Unistra (ANR-10-IDEX-0002) and SFRI (STRATUS project, ANR-20-SFRI-0012) under the framework of the French Investments for the Future Program.
References

(1) Shinde, S. D.; Kulkarni, N.; Jadhav, G. S.; Dewangan, B.; Baby, S.; Pophali, S.; Sahu, B. Alginate Based Hydrogel in Drug Delivery and Biomedical Applications. *Alginate Biomaterial: Drug Delivery Strategies and Biomedical Engineering* **2023**, *109–133*.
https://doi.org/10.1007/978-981-19-6937-9_5/FIGURES/2.

(2) Jarrah, R.; Sammak, S. El; Onyedimma, C.; Ghaith, A. K.; Moinuddin, F. M.; Bhandarkar, A. R.; Siddiqui, A.; Madigan, N.; Bydon, M. The Role of Alginate Hydrogels as a Potential Treatment Modality for Spinal Cord Injury: A Comprehensive Review of the Literature. *Neurospine* **2022**, *19* (2), 272–280.
https://doi.org/10.14245/NS.2244186.093.

(3) Puscaselu, R. G.; Lobiuc, A.; Dimian, M.; Covasa, M. Alginate: From Food Industry to Biomedical Applications and Management of Metabolic Disorders. *Polymers* 2020, Vol. 12, Page 2417 **2020**, *12* (10), 2417.
https://doi.org/10.3390/POLYM12102417.

(4) Li, D.; Wei, Z.; Xue, C. Alginate-Based Delivery Systems for Food Bioactive Ingredients: An Overview of Recent Advances and Future Trends. *Compr Rev Food Sci Food Saf* **2021**, *20* (6), 5345–5369.
https://doi.org/10.1111/1541-4337.12840.

(5) James, S. *Ionically Cross-Linked Alginate Hydrogels as Drug Delivery Systems for Analgesics in Broiler Chickens*; 2017.
https://mro.massey.ac.nz/handle/10179/12167
(accessed 2020-06-23).

(6) Grant, G. T.; Morris, E. R.; Rees, D. A.; Smith, P. J. C.; Thom, D. Biological Interactions between Polysaccharides and Divalent Cations: The Egg-Box Model. *FEBS Lett* **1973**, *32* (1), 195–198.
https://doi.org/10.1016/0014-5793(73)80770-7.

(7) Draget, K.; Østgaard, K.; Polymers, O. S.-C.; 1990, U. Homogeneous Alginate Gels: A Technical Approach. *Elsevier* **1990**.

(8) Liu, X.; Qian, L.; Shu, T.; Polymer, Z. T.; 2003, U. Rheology Characterization of Sol–Gel Transition in Aqueous Alginate Solutions Induced by Calcium Cations through in Situ Release. *Elsevier* **2003**.

(9) Yuguchi, Y.; Hasegawa, A.; Padoł, A. M.; Draget, K. I.; Stokke, B. T. Local Structure of Ca(2+) Induced Hydrogels of Alginate-Oligoguluronate Blends Determined by Small-Angle-X-Ray Scattering. *undefined* **2016**, *152*,

532–540.

https://doi.org/10.1016/J.CARBPOL.2016.07.020.
Stokke, B. T.; Draget, K. I.; Smidsrød, O.; Yuguchi, Y.; Urakawa, H.; Kajiwara, K. Small-Angle X-Ray Scattering and Rheological Characterization of Alginate Gels. *1. Ca-Alginate Gels. Macromolecules* **2000**, *33* (5), 1853–1863.

https://doi.org/10.1021/MA991559Q/ASSET/IMAGES/LARGE/MA991559QF00011.JPEG.

(10)

Sletmoen, M.; Draget, K. I.; Stokke, B. T. Alginate Oligoguluronates as a Tool for Tailoring Properties of Ca-Alginate Gels. *Macromol Symp* **2010**, *291–292* (1), 345–353.
https://doi.org/10.1002/masy.201050541.

(11)

Gwon, S. H.; Yoon, J.; Seok, H. K.; Oh, K. H.; Sun, J. Y. Gelation Dynamics of Ionically Crosslinked Alginate Gel with Various Cations. *Macromol Res* **2015**, *23* (12), 1112–1116.
https://doi.org/10.1007/s13233-015-3151-9.

(12)

Andersen, T.; Melvik, J. E.; Gåserød, O.; Alsberg, E.; Christensen, B. E. Ionically Gelled Alginate Foams: Physical Properties Controlled by Operational and Macromolecular Parameters. *Biomacromolecules* **2012**, *13* (11), 3703–3710.
https://doi.org/10.1021/BM301194F/SUPPL_FIL E/BM301194F_SI_001.PDF.

(13)

Davidovich-Pinhas, M.; Polymers, H. B.-P.-C.; 2010, U. A Quantitative Analysis of Alginate Swelling. *Elsevier* **2010**.

(14)

Kuo, C. K.; Ma, P. X. Ionically Crosslinked Alginate Hydrogels as Scaffolds for Tissue Engineering: Part 1. Structure, Gelation Rate and Mechanical Properties. *Biomaterials* **2001**, *22* (6), 511–521.
https://doi.org/10.1016/S0142-9612(00)00201-5.

(15)

Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. Hyperquad Simulation and Speciation (HySS): A Utility Program for the Investigation of Equilibria Involving Soluble and Partially Soluble Species. *Coord Chem Rev* **1999**, *184* (1), 311–318.
https://doi.org/10.1016/S0010-8545(98)00260-4.

(16)

Kutus, B.; Gaona, X.; Pallagi, A.; Pálinkó, I.; Altmaier, M.; Sipos, P. Recent Advances in the Aqueous Chemistry of the Calcium(II)-Gluconate System – Equilibria, Structure and Composition of the Complexes Forming in Neutral and in Alkaline Solutions. *Coord Chem Rev* **2020**, *417*, 213337.
https://doi.org/10.1016/J.CCR.2020.213337.

(17)
(18) Holloway, J. H.; Reilley, C. N. Metal Chelate Stability Constants of Aminopolycar-Boxylate Ligands. *Anal Chem* **1960**, *32* (2), 249–256.
https://doi.org/10.1021/AC60158A033/ASSET/A C60158A033.FP.PNG_V03.

(19) Crea, F.; De Stefano, C.; Gianguzza, A.; Piazzese, D.; Sammartano, S. Speciation of Poly-Amino Carboxylic Compounds in Seawater. http://www.tandfonline.com/action/journal/Informat ion?show=aimsScope&journalCode=tcsb20 **2015**, *15* (3), 75–86.
https://doi.org/10.3184/095422903782775190.

(20) Martell, A. E.; Hancock, R. D. Metal Complexes in Aqueous Solutions. *Metal Complexes in Aqueous Solutions* **1996**.
https://doi.org/10.1007/978-1-4899-1486-6.

(21) Portzehl, H.; Caldwell, P. C.; Rüegg, J. C. The Dependence of Contraction and Relaxation of Muscle Fibres from the Crab Maia Squinado on the Internal Concentration of Free Calcium Ions. *BBA - Specialised Section On Biophysical Subjects* **1964**, *79* (3), 581–591.
https://doi.org/10.1016/0926-6577(64)90224-4.

(22) Dwyer, F. D. M. *Chelating Agents and Metal Chelates*; 1965.

(23) Kula, R. J.; Rabenstein, D. L. Aminopolycarboxylic Acid Ligand-Exchange Kinetics of Selected Alkaline Earth Ions. *J Am Chem Soc* **1967**, *89* (3), 552–556.
https://doi.org/10.1021/JA00979A014/ASSET/JA 00979A014.FP.PNG_V03.

(24) Cardoso, A. Z.; Alvarez Alvarez, A. E.; Cattoz, B. N.; Griffiths, P. C.; King, S. M.; Frith, W. J.; Adams, D. J. The Influence of the Kinetics of Self-Assembly on the Properties of Dipeptide Hydrogels. *Faraday Discussions*. The Royal Society of Chemistry December 1, 2013, pp 101–116. https://doi.org/10.1039/c3fd00104k.

(25) Mørch, Ý. A.; Donati, I.; Strand, B. L.; Skjåk-Bræk, G. Effect of Ca2+, Ba2+, and Sr2+ on Alginate Microbeads. *Biomacromolecules* **2006**, *7* (5), 1471–1480.
https://doi.org/10.1021/bm060010d.

(26) Donati, I.; Paoletti, S. Material Properties of Alginates; 2009; pp 1–53.
https://doi.org/10.1007/978-3-540-92679-5_1.

(27) Roberts, J. R.; Meissner, E.; Grunlan, M. A.; Rice-Ficht, A. C. *NOVEL IN SITU-GELLING, ALGINATE-BASED COMPOSITES FOR INJECTABLE DELIVERY: TUNING MECHANICAL AND FUNCTIONAL CHARACTERISTICS A Dissertation*; 2014.

https://oaktrust.library.tamu.edu/handle/1969.1/153362 (accessed 2020-06-25).

(28) Calvet, D.; Wong, J. Y.; Giasson, S. Rheological Monitoring of Polyacrylamide Gelation: Importance of Cross-Link Density and Temperature. *Macromolecules* **2004**, *37* (20), 7762–7771.
https://doi.org/10.1021/MA049072R.

(29) Djemaa, I. Ben; Andrieux, S.; Auguste, S.; Jacomine, L.; Tarnowska, M.; Drenckhan-Andreatta, W. One-Step Generation of Alginate-Based Hydrogel Foams Using CO2 for Simultaneous Foaming and Gelation. *mdpi.com* **2022**. https://doi.org/10.3390/gels8070444.

(30) Andersen, T.; Melvik, J. E.; Gåserød, O.; Alsberg, E.; Christensen, B. E. Ionically Gelled Alginate Foams: Physical Properties Controlled by Type, Amount and Source of Gelling Ions. *Carbohydr Polym* **2014**, *99*, 249–256.
https://doi.org/10.1016/j.CARBPOL.2013.08.036.

(31) Donati, I.; Holtan, S.; Mørch, Y. A.; Borgogna, M.; Dentini, M.; Skjåk-Bræk, G. New Hypothesis on the Role of Alternating Sequences in Calcium–Alginate Gels. *Biomacromolecules* **2005**, *6* (2), 1031–1040.
https://doi.org/10.1021/BM049306E.

(32) Jost, V.; Reinelt, M. Effect of Ca2+ Induced Crosslinking on the Mechanical and Barrier Properties of Cast Alginate Films. *J Appl Polym Sci* **2018**, *135* (5).
https://doi.org/10.1002/APP.45754.

(33) Desalination, A. A.-R.-; 2007, undefined. Modeling of Alkaline Scale Formation in Falling Film Horizontal-Tube Multiple-Effect Distillers. *Elsevier*.