Unravelling parameter interactions in calcium alginate/polyacrylamide double network hydrogels using a design of experiments approach for the optimization of mechanical properties

Abstract

Calcium alginate/polyacrylamide double network hydrogels were reported to be exceptionally tough. However, literature reports so far varied the sample compositions mainly by one parameter at a time approaches, thus only drawing an incomplete picture of achievable material properties. In this contribution, sample compositions are varied according to a face-centered central composite experimental design taking into account the four parameters of alginate concentration c_Alg, high/low molar mass alginate mixing ratio R_P, acrylamide concentration c_AAm, and N,N′-methylenebisacrylamide concentration c_MBA. Each sample composition is investigated in triplicate. Thus, 75 samples were investigated by tensile testing, and a detailed analysis of the significant parameters and parameter interactions influencing the mechanical properties is conducted. The data shows that two parameter interactions, involving all four tested parameters, have a large effect on the Young's modulus, the strength, the toughness and the strain at material failure. As a consequence, it becomes evident that the experimental procedure from previous studies did not always result in optimum sample compositions. The results allow optimization of the mechanical properties within the studied parameter space, and a new maximum value of the strength of 710 kPa is reported. The data also give rise to the assumption that other parameters and parameter interactions ignored also in this study may allow further tailoring of mechanical properties.

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Introduction

Hydrogels are highly attractive materials in such diverse fields such as tissue engineering,^1–3 soft robotics,^4–7 drug delivery,^8–10 or sensing.¹¹ This is facilitated by the many advantageous properties of hydrogels like biocompatibility,^12,13 responsiveness,^14,15 or permeability for solutes.^16,17 However, one of the outstanding weaknesses of many hydrogel materials is their poor mechanical stability. Hydrogels typically have rather low Young's moduli in the order of 10 kPa and rarely above 100 kPa,^18,19 and fracture energies often below 10 J m⁻²,^20,21 limiting their application in load-bearing environments. One approach to overcome these shortcomings are the so-called double network (DN) hydrogels, consisting of two intertwined, independent, swollen polymer networks.^22,23

One popular DN hydrogel class is composed of chemically cross-linked polyacrylamide (PAAm) as the first network and physically cross-linked alginate (Alg) as the second network, first described by Sun et al.²⁴ The Alg is most frequently cross-linked with Ca²⁺ ions and the resulting materials are called Ca-Alg/PAAm DN hydrogels. When deforming these materials, crack bridging occurs by the PAAm network simultaneous to energy dissipation by unzipping ionic cross-links in the alginate network.²⁵ As a result, Ca-Alg/PAAm DN hydrogels were shown to have outstanding properties, such as tunable Young's moduli E between just a few kPa up to approx. 1 MPa, and fracture energies of up to approx. 16 kJ m⁻².^24,25 Among others, these remarkable characteristics have led to applications of Ca-Alg/PAAm DN hydrogels in 3D printing,^26,27 tissue engineering,^28–30 stretchable optical fibers³¹ and electronics,^32,33 wet adhesives,³⁴ hydrogel folding,^35,36 sensors,³⁷ and actuators.³⁸

The exact material properties depend on the preparation conditions and the sample composition. Ca-Alg/PAAm DN hydrogel preparation is usually achieved by first forming the PAAm network by free radical polymerization in the presence of sodium alginate (Na-Alg), followed by cross-linking of the Alg with Ca²⁺ ions (Scheme 1). In this context, especially the method to introduce the Ca²⁺ ions into the hydrogels was studied. Initial reports used CaSO₄ particles dispersed in the precursor solution which slowly released Ca²⁺ ions into the formulation.^24,39 However, due to limited solubility of CaSO₄ the achieved cross-link density of Alg was low, so not the entire possible spectrum of mechanical properties was harnessed, and for examples the achieved Young's moduli were relatively low up to approx. 300 kPa.²⁴ Later, instead of using CaSO₄ particles, the pre-formed PAAm hydrogel containing Na-Alg was submerged in rather concentrated CaCl₂ solutions, allowing the Ca²⁺ ions to diffuse into the gel.^{25,26,29,40–42} The resulting high cross-link density of Alg allows the above mentioned high Young's moduli up to 1000 kPa and fracture energies of up to 16 kJ m⁻², albeit not for the same sample composition, if simultaneously the Alg concentration is adjusted accordingly.²⁵ Another method involves a mixture of CaCO₃ particles and D-glucono-δ-lactone (GDL).^43–45 GDL hydrolyzes slowly, thus lowering the pH and decomposing the CaCO₃ to make the Ca²⁺ ions accessible in solution.

Scheme 1 Preparation process for Ca-Alg/PAAm DN hydrogels used in this study. First, a hydrogel precursor solution containing acrylamide (AAm), N,N′-methylenebisacrylamide (MBA), the initiator for radical polymerization of the AAm/MBA system, and alginate is prepared. This solution is cured thermally in a mold to obtain a PAAm hydrogel interpenetrated with alginate. After that the hydrogel is submerged in CaCl₂ solution to form the Ca-Alg network within the PAAm hydrogel. Finally, the samples for tensile testing are punched out of the resulting Ca-Alg/PAAm DN hydrogel. The four parameters investigated in this study are focused on the composition of the hydrogel precursor solution and are the concentrations c_AAm, c_MBA and c_Alg of AAm, MBA and alginate, respectively, as well as the ratio R_P of higher and lower molar mass alginate. Other parameters, such as the initiator concentration, the initiator type, the curing time in the mold, the concentration of CaCl₂ in the second curing step, or the sample geometry (list not complete) were not varied.

The description of the sample preparation process demonstrates that a multitude of parameters influence the final properties of the materials. Within the precursor solution, various components are present: The monomer acrylamide (AAm), the cross-linker N,N′-methylenebisacrylamide (MBA), a radical initiator (typically ammonium persulfate, APS), N,N,N′,N′-tetramethyl ethylenediamine as a catalyst, and Na-Alg. The Na-Alg can come from different sources with varying molar mass or molecular structure.⁴⁶ Finally, the concentration and application method of the calcium ion cross-linker is crucial. The sample composition is governed by the concentrations of all components in the precursor solution. It becomes evident that it is difficult to study the whole parameter space for sample preparation, and thus it is difficult to access the optimum conditions, e.g., to maximize the Young's modulus.

As a result, the pioneering studies published so far put forward mainly variations of one parameter at a time and thus provided a starting point to understand the Ca-Alg/PAAm DN hydrogel behavior. Sun et al. varied the AAm fraction in the total monomer content (c_AAm + c_Alg) as well as changed the CaSO₄ and MBA concentrations.²⁴ Others studied different total Alg concentrations in the precursor solutions,^25,26,41 or varied the APS concentration,⁴³ MBA concentration,³⁹ or used different metal ions to cross-link the Alg.^35,40,47 Naficy et al. and Fitzgerald et al. in principle varied two parameters simultaneously (Alg/MBA concentrations and MBA/Ca²⁺ cross-linker concentrations, respectively), however did not go into detail concerning possible parameter interactions.^41,43 In order to illustrate what a two-factor interaction is, the data reported by Li et al. is helpful.²⁵ They showed an increase of E with increasing Alg concentration while keeping the AAm concentration constant. A change of the AAm concentration could of course have an effect on E, but this is not the important point for a two-factor interaction. A two-factor interaction would mean that the change of AAm concentration, on top of its own effect, induces an additional change of the dependence of E with the Alg concentration, possibly causing a large leveraging effect on E. Thus, such two-factor interactions can be expected to be extremely important for optimization of mechanical properties of Ca-Alg/PAAm hydrogels.

However, up to now no studies exist which cover a larger part of the parameter space concerning the sample composition, and as a consequence it is completely unknown in how far parameter interactions influence the outcome of the experiments and induce leveraging effects on the material properties. Therefore, we hypothesize that the ideal preparation conditions for Ca-Alg/PAAm DN hydrogels have not been found yet. In this contribution, we aim to systematically vary the following four important parameters dealing with the composition of the hydrogel precursor solution (Scheme 1) in a design of experiments (DoE) approach,⁴⁸ and investigate their impact on the mechanical properties: (1) Alg concentration c_Alg, (2) fraction R_P of high molar mass Alg in total Alg concentration, (3) AAm concentration c_AAm, and (4) MBA concentration c_MBA. We especially will study two parameter interactions in detail for the first time. We thus hope to contribute to a more comprehensive understanding of the principles that govern the Ca-Alg/PAAm DN hydrogel properties.

Experimental

Materials

The following materials were purchased from Sigma-Aldrich (Germany): Acrylamide (AAm, ≥99%), ammonium peroxodisulfate (APS, ≥98%), calcium chloride dihydrate (CaCl₂·2H₂O, ≥99%), disodium hydrogen phosphate (Na₂HPO₄, ≥99%), N,N′-methylenebisacrylamide (MBA, 99%), N,N,N′,N′-tetramethyl ethylenediamine (TEMED, 99%). The sodium alginates Protanal LF 10/60 and Manucol LD were obtained from FMC BioPolymer (USA). Poly(methacrylic acid) (PMAA) standards for size exclusion chromatography were purchased from PSS Polymer Standards Service (Germany).

Size exclusion chromatography

The molar mass distribution of the two alginates Protanal LF 10/60 and Manucol LD were investigated at 40 °C by size exclusion chromatography using a 1260 infinity GPC-SEC analysis system (Agilent Technologies, USA) equipped with a Suprema Linear M column (PSS Polymer Standards Service, Germany) in the range of 1 kDa to 1000 kDa. A 0.07 M solution of Na₂HPO₄ in ultrapure water was used as the eluent and to dissolve the respective alginates (1 mg mL⁻¹). The flow rate was set to 1 mL min⁻¹, the injection volume was 50 µL. For universal calibration of the measuring system polymethacrylic acid standards were dissolved and measured with a concentration of 1 mg mL⁻¹ in Na₂HPO₄ (0.07 M) combining refractive index (RI) and viscometer detectors.

General procedure for preparation of hydrogel samples for tensile tests

Ca-Alg/PAAm DN hydrogels were prepared according to the experimental plan described below using a two-step method in which first the PAAm network is produced in the presence of sodium alginate (Scheme 1).^40,49 For this purpose, the sodium alginates Protanal LF 10/60 and Manucol LD were mixed at the required concentrations with ultrapure water (30 mL) and stirred at 40 °C for 30 min. Subsequently, the mixture was agitated on a roller mixer at room temperature until the alginates were fully dissolved (typically approx. 1 h). Then AAm, MBA as well as APS were added in the required amounts and dissolved on the roller mixer for 15 min at room temperature. The solution was degassed in an ultrasonic bath at 40 °C for 15 min. This was followed by the addition of TEMED, which was dissolved using a roller mixer for one minute. The entire solution was pipetted into a mold consisting of two quartz glass panes separated by a silicone spacer (2 mm height) greased with polytetrafluoroethylene (PTFE) paste for better adhesion. Cross-linking of the PAAm network was carried out for 48 h at room temperature. After that, the gel was transferred into a Petri dish and covered entirely with 100 mL of a 0.5 M CaCl₂ solution. The sample was swollen for 48 h at room temperature, replacing the entire volume of the CaCl₂ solution after 24 h. After the swelling process, specimens for tensile tests in the shape of the S3A sample (DIN 53504 : 2017-03) (Fig. S1, ESI†) were punched out of the DN hydrogels and examined.

Experimental plan for the variation of the hydrogel composition

Preparation parameters varied according to a DoE were the total alginate concentration c_Alg, the fraction R_P of the Protanal LF 10/60 concentration of the total alginate concentration, the concentration c_AAm of AAm, and the concentration c_MBA of MBA. The concentrations of the initiator APS and the catalyst TEMED were fixed relative to c_AAm and were 0.42% and 0.25% of c_AAm, respectively. The ranges of the parameter values are given in Table 1.

Table 1 Minimum (min), maximum (max) and center point (center) parameter values used for investigation of Ca-Alg/PAAm DN hydrogels together with their dimensionless coded values. Coded values are calculated according to eqn (S1) (ESI) so that the minimum parameter values correspond to −1 and the maximum parameter values to 1

	Min	Center	Max
c Alg [wt%]	1	3	5
R P	0.17	0.5	0.83
c AAm [wt%]	6	12.5	19
cMBA [wt%]	0.01	0.02	0.03
Coded values	−1	0	1

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In this study, parameter values were varied according to a face-centered central composite design, resulting in 25 different sample compositions (Table S2, ESI†).⁴⁸ Each sample composition was prepared in triplicate, so that in total 75 independently prepared samples were investigated for their mechanical properties in a randomized order (Table S3, ESI†). For the mechanical tests, five samples were punched from each of the 75 samples and characterized in a tensile test.

Uniaxial tensile tests

The mechanical characterization of the Ca-Alg/PAAm DN hydrogels was carried out by uniaxial tensile tests using the Allround-Line table-top testing machine (Zwick Roell, Germany). Sample clamping without damage was achieved with a custom-made clamping tool (Fig. S2, ESI†). Tests were prepared by pre-loading the samples with a strain rate of 5 mm min⁻¹ until a force of 0.1 N was reached. Subsequently, samples were stretched with a strain rate of 200 mm min⁻¹ until rupture. For the calculation of the tensile stress σ, the measured normal force F was divided by the cross sectional area A of the unstrained sample:

Here, b is the sample width (4 mm) as defined by the sample geometry (Fig. S1, ESI†) and d is the sample thickness. Because d depends on sample swelling during preparation it was measured for each sample composition with a light microscope. From the resulting stress–strain curves, the mechanical properties of Young's modulus E, strength σ_max, toughness U_T, and strain at break ε_max were determined. E was taken as the slope of the initial linear region of the stress–strain curve and was calculated by linear regression. For the regression, the data was first smoothed with a Savitzky–Golay filter⁵⁰ and as many data points were included until the coefficient of determination R² dropped to 0.995. The strength σ_max was found as the highest occurring stress, while U_T describes the energy absorption of a material during plastic deformation until it fails and was determined by the area underneath the stress–strain curve. The strain at break ε_max was the maximum reached strain.

Statistical analysis and model fitting

A full linear model was used to describe each of the experimental responses, for the corresponding expression see eqn (S2) (ESI†). The model contained 11 regression coefficients, i.e. four front factors of the terms proportional to only one parameter (a_Alg, a_R, a_AAm, a_MBA), six front factors of two parameter interaction terms (b_Alg,R, b_Alg,AAm, b_Alg,MBA, b_R,AAm, b_R,MBA, b_AAm,MBA), and one intercept (r₀). The statistical evaluation was carried out by analysis of variance (ANOVA) taking into account all 75 independently prepared samples with their coded parameter values. Non-significant model terms with p > 0.05 were excluded, except if they were needed to keep the model hierarchical. Experimental data in figures are generally given as mean of the measured values ± standard deviation.

Results and discussion

Experimental plan

Due to the complex composition, a multitude of parameters is relevant for sample preparation and consequently for the properties of Ca-Alg/PAAm DN hydrogels. In order to end up with a manageable experimental plan, we had to select a limited number of parameters which likely influence the results significantly and which could be well controlled (Scheme 1). For this purpose, we compiled an overview of some preparation conditions used in the literature (Table S1, ESI†). From these conditions, together with the mechanical characterization data from the corresponding publications, we concluded that the four parameters Alg concentraton c_Alg, fraction R_P of high molar mass Alg in total Alg concentration, AAm concentration c_AAm, and MBA concentration c_MBA were important parameters for which also no data on two parameter interactions were collected so far.

In order to vary R_P, two Alg variants with different molar masses were needed. Therefore, the molar masses of the two Alg variants Protanal LF 10/60 and Manucol LD were investigated by size exclusion chromatography (SEC) (Table 2). Indeed, Protanal LF 10/60 exhibited much larger molar masses than Manucol LD, thus making the two polymers suitable to investigate the effect of the fraction of higher molar mass Alg in the Alg mixture.

Table 2 Number average molar mass M_n, mass average molar mass M_w, and molar mass dispersity Đ of the two used Alg variants used in this study

	Protanal LF 10/60	Manucol LD
M n [g mol^−1]	1.70 × 10^5	2.04 × 10^4
M w [g mol^−1]	3.10 × 10^5	1.00 × 10^5
Đ	1.83	4.93

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Apart from the four varied parameters, all other parameters were fixed. It is conceivable that the unaltered parameters like radical initiator concentration, TEMED concentration, Ca²⁺ ion concentration and application method, the kind of cross-linking ion (Ca²⁺ or other metal ions), or sample preparation methodology also have significant effects and are also heavily involved in parameter interactions. However, the envisioned experimental plan with four parameters results in 25 different parameter settings. Due to the general variance observed in tensile tests of hydrogels, we decided to prepare three independent samples for each composition, so that in total 75 samples were investigated. A further increase of investigated parameters would rapidly increase the number of samples, making a realization impractical.

The tested value ranges of the parameters (Table 1) were derived from the values listed in Table S1 (ESI†), and to support these we conducted preliminary experiments. The goal was to make sure that it is possible to prepare defect-free Ca-Alg/PAAm DN hydrogel samples under all parameter settings that could also be submitted to mechanical tests, so that a detailed analysis of the parameter effects and, more importantly, parameter interactions was possible. The tensile tests described in the following section rely on defect-free samples. The main cause for defects were air bubbles entrapped in hydrogel precursor solutions of high viscosity, most relevant for the combination of a high c_Alg and a high R_P and therefore limiting the maximum c_Alg to 5 wt%.

Tensile tests and resulting stress strain curves

Representative stress strain curves measured for some individual Ca-Alg/PAAm DN hydrogels prepared in this study are shown in Fig. 1. Different shapes of the stress strain curves were observed. Some samples showed a very steep increase of the stress σ and subsequent failure at rather low strains ε (curve 1 in Fig. 1). In other cases, samples could be stretched to very high strains before failure while still at rather low stresses (curve 6 in Fig. 1). Within the entire dataset, various stress strain curves between these two extremes were measured (curves 3, 4 and 5), with the maximum stress observed in curve 2 (Fig. 1). The stress strain curves could generally be tuned well by adjusting the sample composition, and their general appearance was similar to previous literature reports.^24,25,40 In order to further analyze the data, the Young's modulus E, the strength σ_max, the toughness U_T, and the strain at break ε_max were extracted for all samples and will be discussed in the following section.

Fig. 1 Representative stress strain curves of individual Ca-Alg/PAAm DN hydrogels prepared in this study. (1) c_Alg = 5 wt%; R_P/M = 0.83; c_AAm = 6 wt%, c_MBA = 0.01 wt%, (2) c_Alg = 5 wt%; R_P/M = 0.83; c_AAm = 19 wt%, c_MBA = 0.03 wt%, (3) c_Alg = 5 wt%; R_P/M = 0.5; c_AAm = 12.5 wt%, c_MBA = 0.02 wt%, (4) c_Alg = 3 wt%; R_P/M = 0.5; c_AAm = 12.5 wt%, c_MBA = 0.02 wt%, (5) c_Alg = 5 wt%; R_P/M = 0.17; c_AAm = 19 wt%, c_MBA = 0.01 wt%, (6) c_Alg = 1 wt%; R_P/M = 0.83; c_AAm = 19 wt%, c_MBA = 0.01 wt%.

It has to be noted that for the tensile tests, a secure clamping of the specimens in the testing machine must be achieved. In contrast to previous reports,^24,25 we avoided gluing of the hydrogels because we observed optical changes on the glued sample surface and increased brittleness of the sample. Instead, we used a specially designed clamping tool (Fig. S2, ESI†). With the help of a spring, a sufficient and reproducible clamping force is achieved even with changes in the thickness of the specimen during testing.

Analysis of mechanical properties

The results for the mechanical properties E, σ_max, U_T and ε_max are shown in Fig. 2. Additionally, all individual results for the 75 investigated samples as collected chronologically are listed in Table S3, the order a result of randomization of parameter settings (ESI†). The data was assessed by analysis of variance, the corresponding p-values of the various model coefficients are listed in Table 3. Additionally, the regression coefficients after fitting the data with eqn (S2) (ESI†) are collected in Table 4. Model diagnosis graphs are shown in the ESI† (Figures S5 to S8).

Fig. 2 (a) Young's modulus E, (b) strength σ_max, (c) toughness U_T and (d) strain at break ε_max of Ca-Alg/PAAm DN hydrogels at all compositions tested in this study. The blue and grey surfaces represent selected values of the respective regression models and help with identification of general trends. In (a), (c) and (d), they were drawn for c_AAm = 19 wt% (grey) and c_AAm = 6 wt% (blue) with c_MBA = 0.01 wt%, and in (b) they were drawn for c_MBA = 0.03 wt% (grey) and c_MBA = 0.01 wt% (blue) with c_AAm = 6 wt%. The legend in (a) is valid for (b), (c) and (d), too. On the axes are the total alginate concentration c_Alg and the fraction R_P of the Protanal LF 10/60 concentration of the total alginate concentration. The different parameter settings for c_AAm are distinguished by the symbol geometry (square, circle and triangle for 6.0 wt%, 12.5 wt% and 19.0 wt%, respectively), the settings for c_MBA by the symbol color (black, green and blue for 0.01 wt%, 0.02 wt% and 0.03 wt%, respectively).

Table 3 All p-values for the individual model terms resulting from the analysis of variance of the different experimental responses. Non-significant (n.s.) model terms were excluded from further analysis of the experimental results by regression unless they were needed to keep the model hierarchical

	a Alg	a R	a AAm	a MBA	b Alg,R	b Alg,AAm	b Alg,MBA	b R,AAm	b R,MBA	b AAm,MBA
E	<10^−4	<10^−4	<10^−4	0.13	<10^−4	<10^−4	n.s.	0.002	n.s.	0.015
σ max	<10^−4	<10^−4	n.s.	0.02	<10^−4	n.s.	2 × 10^−4	n.s.	n.s.	n.s.
U T	<10^−4	<10^−4	<10^−4	0.29	n.s.	<10^−4	0.017	0.010	n.s.	0.027
ε max	<10^−4	0.42	<10^−4	<10^−4	0.002	0.023	<10^−4	n.s.	n.s.	<10^−4

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Table 4 All regression coefficients resulting from a regression on all responses with equation S2, taking into account the relevant model terms identified by analysis of variance (Table 3)

	r 0	a Alg	a R	a AAm	a MBA	b Alg,R	b Alg,AAm	b Alg,MBA	b R,AAm	b R,MBA	b AAm,MBA
E	207.3	172.2	88.6	−67.2	−10.1	81.3	−45.9	—	−21.5	—	16.7
σ max	265.5	166.6	117.3	—	21.7	90.6	—	36.8	—	—	—
U T	726.4	281.0	204.8	242.4	−46.3	—	243.7	126.2	135.8	—	−116.5
ε max	494.8	−156.5	−15.1	162.8	−112.9	−58.5	41.9	108.4	—	—	−112.8

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Concerning the Young's modulus E, it is evident from Fig. 2(a) that the reported range is similar to previous literature reports and that varying the three parameters c_Alg, R_P and c_AAm univariately around the center point (all coded parameter values are 0, E = 207.3 kPa) had a substantial effect, while c_MBA only had a minor influence. It was observed that E generally increased with increasing c_Alg and R_P and with decreasing c_AAm. This is also reflected by the p-values (Table 3) and regression coefficients (Table 4) of a_Alg, a_R, a_AAm and a_MBA. This univariate dependence of E was studied before. For example, Nafici et al. and Li et al. showed an increase of E with c_Alg.^25,41 The importance of the Alg network for E is also evident from the dramatic increase of E when exchanging Ca²⁺ with Fe³⁺.⁴⁰ Fitzgerald reported an increase of E with increasing total monomer concentration (c_Alg + c_AAm), but a fixed ratio of c_Alg and c_AAm,⁴³ thus mixing two of the parameters in this study with opposing influences. However, the absolute value of a_Alg is greater than of a_AAm, so their finding is also in line with our study. Similarly, Sun et al. found a decrease of E with increasing fraction of AAm in the total monomer content.²⁴ Interestingly, the two parameters c_Alg and c_AAm are frequently coupled in studies so far.^24,43 The results here clearly show that it is more reasonable to vary c_Alg and c_AAm independently for maximizing or fine-tuning E due to their opposing effects. Concerning c_MBA, Nafici et al. also found it is of minor importance⁴¹ while Fitzgerald et al. reported an increase of E with c_MBA.⁴³ The reason for these seemingly conflicting findings probably is in the range of concentrations investigated: The former study was rather close to the range in this study while the latter study chose much smaller values (see Table S1, ESI†).

The major advantage of the DoE approach in this study compared to a one parameter at a time approach becomes evident when analysing the effect of R_P on E. In this context, it is important to note that Li et al. already varied the ratio of a short chain alginate in the alginate mixture, similar to the variation of R_P in this study.²⁵ However, they found that there is no big variation of E with the alginate ratio in their experiments, quite in contrast to our findings here where a_R was 88.6, indicative of an increase of E with R_P. In order to resolve this contradiction, it is useful to look at the significant two parameter interaction terms in Table 3 and 4. Indeed, four of the two parameter interactions were significant, including b_Alg,R and b_Alg,AAm. This is also reflected by the different slopes of E with c_Alg depending on the values of c_AAm and R_P (Fig. 2(a)). Expressing the experimental parameters from Li et al. in terms of the parameters used in this study, they varied R_P from 0 to 1 with c_Alg = 2.3 wt%, c_AAm = 16.8 wt% and c_MBA = 0.01 wt%,²⁵ which is rather close to the grey surface plotted in Fig. 2(a). Indeed, at c_Alg = 2.3 wt%, the slope for E with R_P is quite low, in line with Li et al., thus resolving the contradiction above. It becomes evident that a high c_Alg leverages up the effect of R_P on E which has not been recognized in the previous literature studies. Another finding by Li et al. was an E of approx. 1000 kPa by increasing c_Alg up to 6.4 wt% while fixing all other parameters. However, our data show that their choice of a rather high c_AAm = 16.8 wt% was not ideal to maximize E: A simultaneous reduction of c_AAm when increasing c_Alg leads to further increase of E due to the two parameter interaction, especially when at the same time a high R_P is adjusted, which Li et al. also did not do. These results clearly demonstrate that the experimental plan in this study allows one to navigate the entire parameter space more efficiently in order to optimize the responses such as E, compared to the univariate approaches followed in the literature so far. Thus, E values between 3.8 kPa and 766.9 kPa were reached.

Looking at the next response, the strength σ_max, generally the trends were similar to the trends observed for E (Fig. 2(b)). Indeed, samples with a high E also had a high σ_max, and vice versa (Figure S3, ESI†). The increase of σ_max with c_Alg is again in line with literature reports.^26,41 Also the increase of σ_max with R_P was reported before.²⁵ Nafici et al. also in principle investigated the effect of c_MBA on σ_max, however did not discuss their results accordingly, probably because the effect was very small, if significant at all.⁴¹ The main differences found between σ_max and E in this study were that for σ_max, c_MBA was significant, like also the two parameter interaction of c_MBA and c_Alg (Table 3). However, the effect of c_MBA, although significant, is not dominating due to the rather small regression coefficients a_MBA and b_Alg,MBA. Additionally, c_AAm was not significant, and also did not participate in any parameter interaction. By contrast, like for E, the two parameter interaction term b_Alg,R is of great importance due to its relatively large value. Generally, the knowledge about the significant parameters and parameter interactions and the values of the corresponding regression coefficients (Table 4) again allow to fine-tune σ_max according to the needs of a specific application in the range between 46.2 kPa and 709.8 kPa. To the best of the authors’ knowledge, this is the highest value reported for the tensile strength of Ca-Alg/PAAm DN hydrogels so far, and a direct result of the systematic parameter variation in this study. For example, Li et al. were limited to strengths of approx. 470 kPa although they increased c_Alg up to 6.4 wt% because they missed using high c_Alg and R_P simultaneously.²⁵ Interestingly, the highest strength so far of approx. 550 kPa from Yang et al. was found at rather low c_Alg = 1.56 wt% and also low c_MBA = 0.0076 wt% (Table S1, ESI†) which is in contrast to the findings from the present study and other literature.

The third response, the toughness U_T, is shown in Fig. 2(c). We report U_T as the area under the stress strain curve, like for example also Bakarich et al.^26,27 or Du et al.,⁴⁵ while other literature reports focus on the fracture energy of notched samples.^24,25,35,41 Therefore, only few values are available for direct comparison. Additionally, Bakarich et al. used samples prepared by extrusion-based 3D printing in their tests which usually contain defects, so that generally no consistent trend in U_T was observed.²⁶ For the analysis of our data, we start again at the experimental center point (all coded parameter values are 0, U_T = 726.4 kJ m⁻³) and think first about univariately changing the parameter values. In this case, only the parameters c_Alg, R_P, and c_AAm had a significant effect on U_T while c_MBA was found to be insignificant (Table 3). The corresponding regression coefficients of the three significant parameters are similar (Table 4), showing a similar effect of the three parameters within the studied parameter space. The toughness range achieved by univariate variation of c_Alg, R_P, and c_AAm around the center point thus was between 191.5 kJ m⁻³ and 1346.1 kJ m⁻³, already covered solely by changing the c_Alg value. However, like E and σ_max above, also U_T is heavily influenced by two parameter interactions with rather high values of the corresponding regression coefficients (Table 3 and 4). Therefore, by multivariate variation of all parameters, a U_T range between 21.5 kJ m⁻³ and 2018.0 kJ m⁻³ is accessible, again demonstrating the advantages of a DoE approach. The reported values are somewhat smaller than the maximum value of 5100 kJ m⁻³ given by Du et al.⁴⁵ This can be explained by their very high value of c_AAm = 28% (w/v) and also rather high c_Alg = 4% (w/v). The importance of the two parameter interactions for U_T becomes evident when focusing on b_Alg,AAm. At the lowest c_AAm of 6 wt%, U_T decreases with increasing c_Alg (fixing R_P = 0.5 and c_MBA = 0.01 wt%) with a slope of −88.8 kJ m⁻³ in the coded parameter space, see also the blue surface in Fig. 2(c). Such a trend was also observed by Li et al. for the fracture energy.²⁵ By contrast, at the highest c_AAm of 19 wt% and again fixing R_P = 0.5 and c_MBA = 0.01 wt%, U_T increases with increasing c_Alg with a slope of 398.5 kJ m⁻³.

Interestingly, Sun et al. reported an optimum in fracture energy of approx. 8000 J m⁻² for their Ca-Alg/PAAm DN hydrogels.²⁴ This was found by varying the ratio of c_AAm and total monomer content (c_AAm + c_Alg). Assuming a correlation between U_T and the fracture energy, as it is sometimes observed for hydrogels,⁵¹ we should also be able to find such an optimum in our data for U_T, which is apparently not present in the data shown in Fig. 2(c). However, when fixing the sum of c_Alg and c_AAm to 14 wt%, like done by Sun et al. in their experiments,²⁴ and further using their other parameter settings, we can use our model to calculate a dependency of U_T against the ratio of c_AAm and total monomer content (Fig. 3). The result is very similar to the observation from Sun et al., including the apparent optimum in U_T of 707.6 kJ m⁻³. However, for our data we can safely say that the thus obtained, apparently optimized result is rather far from the real optimum, and it is conceivable that this is also the case for the parameter settings used to maximize the fracture energy reported by Sun et al. Furthermore, the unnecessary coupling of the two parameters c_Alg and c_AAm results in an awkward path through the parameter space, while pretending a univariate parameter variation, thus concealing the individual parameter influences on U_T.

Fig. 3 Comparison of toughness model with fracture energies from Sun et al., Nature 2012, 489, 133. Black line: Toughness U_T calculated with the corresponding regression model from the present study for the experimental conditions used by Sun et al. Parameters values were: c_Alg + c_AAm = 14 wt%; 9 wt% < c_AAm < 13 wt%; c_MBA = 0.0006*c_AAm; R_P = 0.5. Red data points: Experimental values from Sun et al. for the fracture energy of Ca-Alg/PAAm DN hydrogels.

Finally, the fourth response, the strain at break ε_max, is plotted in Fig. 2(d). Within the tested sample compositions, a range of ε_max between 32% and 1283% was observed. When varying multiple parameter values simultaneously, also for ε_max two parameter interactions are highly relevant, similar to the other responses. The highest ε_max was a result of the combination of low c_Alg, a high c_AAm and also a low c_MBA. Obviously, a relatively loosely cross-linked PAAm network at a rather high concentration in combination with a low concentration of the Ca-Alg network facilitates a high extensibility of the Ca-Alg/PAAm DN hydrogels. This is also expressed by the corresponding regression coefficients (a_Alg, a_AAm, a_MBA, b_Alg,AAm, b_Alg,MBA, b_AAm,MBA), all pointing to a larger ε_max for the mentioned combination. As a result, the samples with a very high ε_max had a very low E and vice versa (Figure S4, ESI†). The results are in agreement with previous reports although the maximum strain observed is lower than the highest value of 2300% reported before.²⁴ This can be explained by the differences in the sample preparation procedure. On the one hand, the c_MBA in the previous report was lower than the minimum value in the present study, on the other hand also the cross-linking density of the Ca-Alg network was presumably lower due to the Alg cross-linking method with CaSO₄ particles.²⁴ Interestingly, our results show only a minor effect of R_P on ε_max, quite in contrast to its effect on E, σ_max and U_T. This would generally allow moderate increases in E, σ_max and U_T by increasing R_P without much affecting ε_max.

Conclusions

Previously the composition of calcium alginate/polyacrylamide double network hydrogels was varied by one parameter at a time approaches. We could show by a design of experiments approach that as a consequence the achieved, already outstanding mechanical properties were most likely not a result of a fully optimized material composition. The regression models presented here agree with literature findings so far, and additionally dramatically extend the knowledge about the Ca-Alg/PAAm DN hydrogel system by analysis of two-factor interactions. The data analysis shows the way to further improve the optimization efforts to reach well-defined mechanical properties. The investigation took into account four important parameters relevant for the sample composition, and their parameter values varied within limits which guaranteed successful sample preparation. Thus, the highest value for the tensile strength of Ca-ALg/PAAm DN hydrogels reported so far was found. However, the present study only covers a part of the entire parameter space. It is highly probable that as a consequence, still not the full potential of the calcium alginate/polyacrylamide double network hydrogels is uncovered so far. It is for example conceivable that a higher E modulus than reported so far is achievable by increasing c_Alg above the maximum level used in the present investigation while keeping a low c_AAm and a high R_P – a parameter combination that has not been tested in any study. This hypothesis is now possible due to the model described here for the first time by extrapolating out of the investigated parameter space, therefore is speculative presently and subject to future experimental investigation. Future studies should additionally deal with the other parameters which were also ignored in this study, and further optimize the parameter settings to reach even more outstanding properties for Ca-Alg/PAAm DN hydrogels. We would also like to encourage future studies on inherently complex hydrogel systems to follow experimental plans like a design of experiments approach in order to be able to identify parameter interaction effects.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors kindly thank the German Research Foundation (DFG) for financial support of this work (grant ID SO 1387/2-1).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Literature review about synthesis parameters, details about the experimental plan, all experimental results, details about the tensile test setup, model diagnosis graphs. See DOI: https://doi.org/10.1039/d3ma00740e

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