Design of Spherical Gel-Based Magnetic Composites: Synthesis and Characterization

Abstract

The purpose of the study was the synthesis and the physicochemical characterization of spherical beads of magnetically active composite ferrogels (FGs) with diameters of 2–3 mm for further application to the needs of targeted drug delivery and/or replacement therapy. Spherical FGs based on a physical network of calcium alginate (CaAlg), a chemical network of polyacrylamide (PAAm), and a combined network of calcium alginate and polyacrylamide (PAAm/CaAlg) were analyzed. FGs were filled with γ-Fe₂O₃ magnetic nanoparticles (MNPs) obtained by using the electrical explosion of wire method. A comparative study of the swelling behavior and of the structural features of the polymeric network in CaAlg, PAAm/CaAlg, and PAAm spherical beads was performed. It was shown that the densest network was provided by a combination of chemical and physical networking in PAAm/CaAlg FGs. If the physical network were removed from FGs it resulted in a substantial increase in the average diameter and the swelling ratio of spherical beads and a decrease in the MNPs concentration in the swollen FGs by approximately two times. It was shown that irrespective of the gel composition, the embedding of maghemite nanoparticles led to an increase in the swelling ratio of the polymeric network. This indicated the absence of strong intermolecular interactions between the polymer and the filler. The results obtained might be useful for the design of magnetically active spherical FG beads of a given size and controlled physicochemical properties.

1. Introduction

Soft materials are of great interest in various fields of materials science. In particular, biocompatible polymer hydrogels are a promising group of materials for various biomedical applications due to their unique swelling and collapse properties [1]. Hydrogels absorb and hold huge volumes of water. If magnetic micro- or nanoparticles are embedded into the gel as a filler, then such a composite is called a ferrogel. Ferrogels (FGs) are a type of multifunctional hybrid material that combines the properties of their individual components: magnetic particles and a gel-like polymer network [2]. The unique property of FGs is their mechanical response to an external magnetic field, which expands the range of FGs’ practical application [3,4,5].

Iron oxide magnetic nanoparticles (MNPs) are widely introduced into clinical medicine due to their low toxicity [6,7,8]. Currently, the application of MNPs in MRI diagnostics and hyperthermic treatment of oncological diseases is a routine practice [9,10,11]. The MNPs embedded in gels of different natures increase the biological activity of cells on the surface of FGs [12,13,14]. This makes it possible to consider FGs as scaffolds for tissue engineering and regenerative medicine [15,16,17]).

The shape and size of FGs can vary greatly because it expands the scope of their applications in fundamental and applied research. In particular, FGs in the form of microspheres are the most promising magnetically controlled microsystems for biomedical applications [18,19,20,21,22,23,24,25,26]. Spherical FGs have certain advantages because of their positioning in biological organs and tissues using an external magnetic field. On the other hand, the network of spherical FGs is a container-like structure for a wide range of medical drugs [27,28,29,30]. The presence of a magneto-deformation effect in FGs facilitates the release of drugs from the polymer network under the application of a magnetic field.

The nature of the FGs network can be either physical, formed due to weak intermolecular bonds, or chemical, consisting of stable covalent bonds between macromolecules [1]. FGs based on a physical network are synthesized by gelation of biopolymers, for example, polysaccharides: agarose, gellan, xanthan, and alginate [31]. These FGs serve as targeted delivery systems for oils, vitamins, essential nutrients, etc. [32]. A significant disadvantage of the physical gel network is the high degree of physicochemical heterogeneity of the initial biopolymer, and this affects the quality of the obtained materials and their potential applicability.

Spherical FGs based on a chemical network are also well studied, and methods for their synthesis are classified [33,34,35]. The main problems in the preparation of such composites are the accuracy and the reproducibility of the size and shape of the spheres. In particular, the reverse suspension polymerization method, traditionally used for the synthesis of spherical gels, often leads to a wide distribution of sample sizes [36]. Difficulties in the uniform encapsulation of magnetic particles in a polymer network were also noted [37,38].

In general, over the past few decades, the synthesis of magnetic microspheres with a low degree of polydispersity has been worked out to some extent by studies by a number of researchers [39,40,41,42,43]. The most proposed methods are multi-stage and labor-intensive processes that require careful control of synthesis conditions. In addition, the main works in this area were focused on the synthesis of spherical FGs with a diameter of several 10 μm. This size of microspheres limits the immobilization of both prokaryotic and eukaryotic cells and, therefore, excludes the use of such ferrogels in some areas of biology and medicine [36].

In our early studies, the possibility of using ferrogels of various natures for tissue engineering and regenerative medicine was intensively investigated on cylindrical samples with a diameter of 8–15 mm and a height of 3–10 mm. The mechanical, electrical, magnetic, and acoustic properties of these composites, as well as their compatibility with different cell cultures, were considered in detail. Certain advantages of cylindrical FG application for cellular scaffolds were reported in several of our publications, some of which are referred to above [12,13,14,17].

This study addresses the development of biocompatible magnetically active composites of a spherical shape with a diameter of several millimeters for the needs of biomedical applications. Proposed systems are considered prototypes of implants filled with cells and/or drugs for replacement therapy of damaged tissues of hollow organs, which can be positioned using an external magnetic field. The purpose of the study was the synthesis of spherical FGs with a diameter of 2–3 mm based on physical, chemical, and interpenetrating polymer networks filled with iron oxide MNPs, as well as the physicochemical characterization of these composites at various stages of their preparation.

2. Materials and Methods

The study was performed on spherical beads of composite ferrogels based on a physical network of calcium alginate (CaAlg), a chemical network of polyacrylamide (PAAm), and a combined network of calcium alginate and polyacrylamide (PAAm/CaAlg). Blank hydrogels with the same types of networks were studied as well.

Ferrogels were filled with maghemite (γ-Fe₂O₃) nanoparticles, designated as MNPs, which were obtained by the electric explosion of wire (EEW) method using an automatic laboratory setup. The details of the EEW method are given elsewhere [44,45,46]. Briefly, the essence of the method is the evaporation of the portion of the metal wire by a high-voltage pulse of the electrical current. The subsequent condensation of metal vapors in the gas phase gives either zero-valent metallic particles if the gas is inert or oxide particles if the gas contains oxygen.

The shape and the size of MNPs were characterized by transmission electron microscopy (TEM) (JEOL JEM2100, JEOL Corporation, Tokyo, Japan). As individual particles were condensed in the gas phase, their shape was very close to spherical (see Figure 1A). The particle size distribution of MNPs (see histogram in Figure 1B) calculated by the graphical analysis of 2473 images was rather broad. The number average diameter of MNPs was d_n = 22 nm, the weight average diameter was d_w = 83 nm. The specific surface area of MNPs measured by low-temperature sorption of nitrogen (BET equation), using a Micromeritics TriStar3000 analyzer (Micromeritics, Norcross, GA, USA), was 20 m²/g.

The X-ray diffraction (XRD) studies were performed using Discover diffractometer D8 (Bruker Corporation, Billerica, MA, USA) operating at 40 kV and 40 mA at Cu-Kα radiation (λ = 1.5418 Å), with a graphite monochromator and a scintillation detector. Bruker software TOPAS-3 with Rietveld full-profile refinement was employed for the quantitative analysis of the diffractograms. The phase composition of MNPs corresponded to the inverse spinel crystal lattice with space group Fd3m (see Figure 1C). In principle, this structure belongs either to magnetite Fe₃O₄ or maghemite g-Fe₂O₃. In the latter case, some Fe cation sites in the lattice remain vacant. The chemical composition of MNPs was verified by the electrochemical Red-Ox titration (Schott Titroline, SCHOTT Instruments GmbH, Mainz, Germany) and it was found close to γ-Fe₂O₃. The average size of coherent diffraction domains was estimated by using the Scherrer approach. It was found equal to 90 nm in good correlation with TEM data.

The saturation magnetization of MNPs (Ms) was determined by means of vibration magnetometry (Cryogenics, Ltd. VSM, London, UK) and was found to be 375 (emu/cm³). This value and other magnetic properties of MNPs were very close to the values typical of maghemite particles synthesized by the EEW method, which were described in detail earlier [44].

Prior to the synthesis of ferrogels, a stock suspension of MNPs was prepared in a glass beaker. For this purpose, air-dry maghemite MNPs were mechanically dispersed in an aqueous 5 mM sodium citrate solution and then treated in a FB 15047 ultrasonic bath (Thermo Fisher Scientific, Waltham, MA, USA) for 15 min. Sodium citrate was used as an electrostatic stabilizer to prevent the aggregation of MNPs in the reaction mixture. The average hydrodynamic particle size in suspension determined by the dynamic light scattering (DLS) using a Brookhaven ZetaPlus analyzer (Brookhaven Instruments, Holtsville, NY, USA) was 95 nm. This value was an intensity average of the lognormal distribution determined via DLS. The distribution was broad with a geometric standard deviation of 1.59. Hence, the hydrodynamic diameter significantly deviated from the number and weight average values evaluated using TEM.

In the synthesis of physically cross-linked CaAlg ferrogels, commercial sodium alginate (NaAlg) (Sigma-Aldrich, St. Louis, MO, USA) with a molecular mass of 121.6 kDa was dissolved in the stock suspension of MNPs. The final concentration of NaAlg was 2% and the concentration of MNPs was 10%. This solution was added manually through a 5G syringe needle with a diameter of 0.5 mm dropwise into an aqueous 0.5 M calcium chloride solution. As a result of the replacement of Na⁺ ions with Ca²⁺, the droplets immediately transferred to elastic ferrogel beads due to the precipitation of calcium alginate. The obtained ferrogel beads were kept in saline solution for 2 days for the completion of ion exchange. After that, they were washed in distilled water for 7 days with daily water renewal to achieve equilibrium swelling.

The synthesis of ferrogels spherical beads with a combined physical (CaAlg) and chemical (PAAm) network was performed according to a modification of the technique proposed in [36]. The stock suspension of MNPs with dissolved sodium alginate was taken as a precursor. Acrylamide (AAm, monomer), N,N′-methylenebisacrylamide (MBAA, cross-linker), and N,N,N′,N′-tetraethylmethylenediamine (TEMED, catalyst) were dissolved in it. All the reagents were commercial products (Merck, Schuchardt, Honenbrunn, Germany) and were used as received. The resulting reaction mixture contained 8% (wt) of acrylamide, 2% (wt) of NaAlg, and 10% (wt) of MNPs. The molar ratio MBAA/AAm was 1:50. Then, the reaction mixture was added dropwise into an aqueous solution with 0.5 M calcium chloride and 0.05 M ammonium persulfate (APS, initiator of polymerization). Two simultaneous processes took place hereafter. One was the formation of spherical beads with the CaAlg network due to the Na/Ca ion exchange; the other was the radical polymerization of the chemical PAAm network in the beads under APS/TEMED initiation. The obtained ferrogel beads were equilibrated in the same manner as CaAlg ferrogels.

The resulting CaAlg/PAAm ferrogels were partly used as precursors for the preparation of PAAm ferrogels with the chemical network. Therefore, the physical network of Ca alginate was to be removed. For this purpose, the beads were placed for 7 days in a 0.25 M sodium phosphate solution with 0.1 M sodium ethylenediaminetetraacetate (EDTA), which was the chelating agent for Ca²⁺ ions. Insoluble CaAlg was converted to soluble Na alginate and was washed out of the beads. After alginate removal, the samples were washed with distilled water for 7 days. All preparatory procedures were performed at room temperature.

The techniques described above were also used for the preparation of blank hydrogel beads based on physical, chemical, and combined polymer networks. In those cases, a suspension of maghemite nanoparticles was not introduced into the reaction mixture.

Additionally, the reference PAAm hydrogels at different monomer concentrations (in the range from 0.4 to 1.6 mol/L) were synthesized by free-radical polymerization in an aqueous AAm monomer solution using MBAA as a crosslinking agent. The MBAA/AAm molar ratio was set to 1:50. APS at a concentration of 3 mM was used to initiate polymerization. TEMED at a concentration of 5 mM served as a reaction catalyst. The synthesis was performed at room temperature in cylindrical polyethylene molds with an inner diameter of 10 mm, after which the obtained hydrogels were extracted, placed in a plastic vessel with distilled water, and washed for 7 days.

The swelling degree of ferrogels and hydrogels was determined by thermogravimetry. Therefore, the swollen gels were weighed; then water was removed by drying to constant weight at 80 °C, and the dry residue was weighed again. The swelling ratio was calculated according to the equation:

$$\alpha =\frac{m-m_0}{m_0}$$

(1)

where α is the equilibrium swelling ratio, m is the mass of the swollen gel, m₀ is the mass of the dried gel.

The average diameter of gel beads obtained at different stages of the preparation was determined using a digital micrometer thickness gauge (Weihai Minghui Measuring Tool Co. Ltd., Weihai, China). The data were processed statistically in STATISTICA 12. The two-tailed Mann–Whitney U test was used for the comparative analysis of two independent groups; the statistical hypothesis was assumed to be verified at p ≤ 0.05.

The surface tension of sodium alginate solutions with acrylamide content in the range of 4–12% (wt) was determined using the maximum bubble pressure method [47]. A capillary with a diameter of 2 mm was used in the measurements.

The content of maghemite MNPs in ferrogel beads was determined by thermal analysis: thermogravimetry/differential scanning calorimetry/mass spectrometry. Thermal decomposition of previously dried ferrogel samples was carried out by heating them from 40 to 1000 °C at a rate of 10 K/min in the air using a NETSCH STA403 thermal analyzer with a built-in quadrupole mass spectrometer (NETZSCH Geratebau Gmbh, Selb, Germany). Thus, the weight fraction (γ) of MNPs in dried ferrogels was determined. These values were further used to calculate the concentration of MNPs in the equilibrium swollen gel beads (ω) and the swelling ratio of the polymer network of the ferrogel (α_P) according to the equations [48]:

$$\omega =\frac{\gamma }{1+\alpha }$$

(2)

and

$${\alpha }_P=\frac{\alpha }{1-\gamma }$$

(3)

Evaluation of molecular parameters of PAAm that were necessary for the calculation of the networking density of gels was conducted using the molecular modeling software package CAChe Work System v.7.5.0.85 (Fujitsu Ltd., Tokyo, Japan). The software enables the evaluation of the molar volume and the solubility parameter for polymers based on the group increments.

3. Results and Discussion

Figure 2 shows photos of some ferrogel beads and blank hydrogel beads under the study.

Table 1. The average diameter of gel beads. Standard error of mean corresponds to n = 100.

Composition of the Polymer Gel Network	Mean Diameter Value (mm)
	CaAlg	PAAm/CaAlg	PAAm
ferrogels	2.30 ± 0.09	1.94 ± 0.05	2.39 ± 0.07
hydrogels	2.17 ± 0.03	1.90 ± 0.03	3.09 ± 0.08

gives the values of the average diameter of gel spherical beads depending on the composition of the polymer network in blank hydrogels and corresponding composite ferrogels. The table shows that the CaAlg hydrogel and ferrogel beads have a statistically larger diameter compared to that of the PAAm/CaAlg gels. Meanwhile, after the washout of calcium alginate from PAAm/CaAlg beads, their diameter significantly increased.

According to the preparation technique, which included the dropwise injection of the reaction mixture into CaCl₂ solution (see Section 2), the caliper diameter of the beads in the first place depended on the size of the droplet that was formed when detached from the syringe needle tip. In general, the size of the droplet is proportional to the surface tension of the solution at the water/air interface [47]. Figure 3 presents the surface tension of a series of NaAlg solutions with different concentrations of acrylamide.

According to the data given in Figure 3 the addition of acrylamide to NaAlg solution in the studied range (4–12% by weight) resulted in a linear decrease in surface tension. Hence, the diameter of droplets of the mixed NaAlg/AAm solution should also decrease with the weight fraction of added AAm. Smaller droplets of NaAlg/AAm solution would provide smaller PAAm/CaAlg beads. According to the data given in Figure 3, the surface tension of the reaction mixture with 8% (wt) of AAm (as taken in the synthesis of hydrogel beads) is approximately 15% (wt) lower than the surface tension of the NaAlg solution. The same proportion of the diameters occurred for corresponding gel beads (see Table 1).

The droplets of NaAlg/AAm reaction mixture were smaller and at the same time, they contained larger amounts of solutes than the droplets of NaAlg. It favored the noticeable decrease in the water uptake of the resulting gel (and ferrogel) beads. The water uptake of the beads or, in other words, the swelling ratio, was calculated according to Equation (1), and the values for different polymeric networks are given in Figure 4. Note that, in all cases, the swelling ratio for ferrogels is substantially lower than that for corresponding hydrogels. First of all, this is due to the fact that the nominal swelling ratio of ferrogels corresponds to the water content related to the sum of the dry weight of the polymer and the mass of embedded solid particles.

Let us first discuss the dependence of the swelling ratio on the composition of the polymeric network. The hydrogel beads based on the physical CaAlg network had a higher value of the swelling ratio compared to the beads with the combined chemical/physical PAAm/CaAlg network (Figure 4). The structure of the combined chemically cross-linked PAAm gel in CaAlg physical gel can be considered an interpenetrating network (IPN) [36], where these two polymeric networks are entangled with each other, thereby increasing the effective degree of networking. This occurred both for hydrogel and ferrogel beads.

If the physical network of CaAlg was removed from the IPN and then the networking density tended to decrease. As shown in Figure 4 the transition to PAAm hydrogel and ferrogel resulted in a significant increase in the swelling ratio of beads. This is because when alginate dissolves and is washed out of the sample, the space between the cross-links increases and the gel network can absorb more water, which ultimately leads to the increase in the swelling ratio and in the size of both PAAm hydrogels and ferrogels. This process is shown schematically in Figure 5.

Removal of calcium alginate from the gel bead with a combined PAAm/CaAlg network is due to the interaction of Ca²⁺ ions with EDTA molecules. The resulting chelate complex is soluble in water, and it is washed out of the sample. This destroys the physical cross-links between the alginate molecules, which convert into the soluble NaAlg salt. Subsequent washing removes the sodium alginate from the sample. Since MNPs were characterized by a relatively broad particle size distribution, the removal of the alginate and subsequent swelling of the PAAm favored the exit of the smallest MNPs from the gel bead.

Thus, the transition from a combined PAAm/CaAlg polymer network to a chemical PAAm network led to a significant change in the composition of the samples, which is reflected in the swelling ability of these gels.

In this regard, the next step was the assessment of the residual content of the MNPs in the studied ferrogels according to the results of thermal analysis of pre-dried samples of gels and ferrogels. The characteristic TG/DSC/QMS curves are shown in Figure 6.

Decomposition of the polymer gel matrix began above 200 °C and occurred over a wide temperature range up to 800 °C. The decomposition process was multistage and was accompanied by exothermic peaks of heat evolution and peaks of the release of volatile decomposition products: water and carbon dioxide. The detailed analysis of the decomposition process is very complicated, and it was beyond the objective of the present study. Meanwhile, some general remarks could be made. The positions of peaks at the temperature axis were not the same for the dried gel and dried ferrogel. The major exothermic peak of CaAlg decomposition (Figure 6a) and the major peak of CO₂ emission were registered in the range of 500–700 °C, with a maximum occurring at 600 °C. In the decomposition of CaAlg/FeO_x ferrogel, a double peak of heat release and a double peak of CO₂ release were observed in the lower temperature region between 200 and 600 °C. That is, the decomposition of ferrogel occurred at lower temperatures than the decomposition of dried gels. Most likely it is an indication of the catalytic effect of iron oxide NMPs on the decomposition of the polymeric matrix.

The plots in Figure 6 also show that the thermal destruction of both CaAlg hydrogels and CaAlg-based ferrogels produced an undegradable residue. The mass loss in the case of CaAlg hydrogel was much larger than in the case of the corresponding ferrogel. Hence, larger was the mass of the undegradable residue of ferrogel. In the case of CaAlg, it was Ca oxide, and in the case of ferrogel, it was a mixture of Ca oxide and maghemite nanoparticles. The residual mass values make it possible to calculate the weight fraction of nanoparticles in the dried ferrogel samples. The results obtained were used to calculate the nanoparticle content in swollen ferrogels with different polymeric networks. These data are shown in

Table 2. Composition and swelling degree of ferrogels. The confidence interval for α is given at p = 0.05 (n = 10).

Ferrogel	Concentration of MNPs in Dried Gel, γ (%)	Concentration of MNPs in Swollen Gel, ω (%)	Equilibrium Swelling Degree, α
PAAm/CaAlg	69.4	9.51	6.3 ± 0.1
CaAlg	83.2	8.67	8.6 ± 0.7
PAAm	71.7	4.91	13.6 ± 1.5

. The calculation of the MNP content in the samples of ferrogel beads was carried out according to Equation (2) based on the measured swelling ratio of the ferrogels.

As can be seen, the largest value of the MNP weight fraction corresponds to the concentration of PAAm/CaAlg double-network composite gel. It is almost equal to the MNP weight fraction in the initial reaction mixture (10% (wt)). Apparently, the interpenetrating network of chemically cross-linked PAAm and physically cross-linked CaAlg was the most dense, enough to retain MNPs with even the smallest sizes (about 5–10 nm). The network of CaAlg ferrogel beads had slightly lower MNP content, which is probably due to a higher degree of swelling of the CaAlg network (Figure 4). The lowest concentration of MNPs was observed for the PAAm-based ferrogel obtained by washing out alginate from the combined network. In this case, the content of the MNPs was twice as low as that in the initial reaction mixture. That is, the removal of the physical network of Ca alginate from the combined PAAm/CaAlg ferrogel led to a significant decrease in the MNP content in the swollen PAAm ferrogel. The swelling ratio also approximately doubled (~2.2 times). Swelling led to an increase in the distance between the cross-links in the polymer network. On one hand, it favored the washout of the smallest MNPs, and on the other hand, it increased the amount of water in the gel interior. Both factors decreased the content of the MNPs in the swollen ferrogel.

Let us evaluate the actual density of PAAm chemical networking in ferrogel beads synthesized using Ca alginate gel as a template.

First, it is necessary to estimate the actual swelling ratio of the polymer network of the ferrogels excluding MNPs from consideration. In other words, it is to determine how much water a polymer network holds by itself, considering solid particles do not absorb water. For this, the swelling ratio of the ferrogel polymer network (α_P) was calculated using Equation (3). The evaluation was based on the fraction of solid particles in the dried ferrogels given in Table 2, and the values of the actual swelling ratio of the polymeric network in ferrogels are given in Figure 7 in comparison with the values for blank hydrogels.

In all three series, the polymer network of the ferrogels demonstrated higher water uptake than the network of corresponding hydrogels. Note that this trend is opposite to that for the nominal swelling ratio as presented in Figure 4. In principle, both scenarios—the increase and the decrease in swelling—can be observed in composite gels with embedded particles. In general, the decrease in swelling is usually related to the strong adhesion of polymeric subchains to the embedded particles. In the present study, the opposite effect—the increase in the swelling of the polymeric network—was observed for these types of composite gels. Most likely this might be explained also from the viewpoint of adhesion but taken in an opposite way. In this case, polymeric subchains did not adsorb at the surface of solid particles, which remained hydrated. Effectively, it led to the repulsion of polymeric chains from the surface and a consequent increase in the swelling of the network.

The increase in the water uptake by the polymeric network in the presence of maghemite MNPs means that the particles do not create additional cross-links in the gel structure and did not lead to the formation of a denser network in the samples. On the contrary, the presence of MNPs contributed to the loosening of the polymer network of gels and decreased its density, which was reflected in the increase in the swelling degree. Apparently, there were no strong interfacial interactions between the maghemite particles and the polymer network, regardless of their composition.

A decrease in the density of the gel polymer network is equivalent to an increase in the average length of the linear polymer subchains between the cross-links, which is characterized by the number of monomeric units (N_C) in the subchains. This value can be calculated using the Flory–Rehner theory [49]. The corresponding equation expressed in terms of the swelling ratio gives [12]:

$$N_C=\frac{V_1(0.5{\alpha }_0{\alpha }_P^{-1}-{\alpha }_0^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\alpha }_P^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.})}{V_2(\ln \left(1-{\alpha }_P^{-1}\right)+{\alpha }_P^{-1}+\chi {\alpha }_P^{-2})}$$

(4)

where V₁ and V₂ are the molar volumes of the solvent and polymer, respectively, χ is the Flory–Huggins parameter for the polymer-solvent system, α₀ is the swelling degree of gel as provided by the composition of the reaction mixture in the synthesis, α_P is the swelling ratio of the polymeric network (without considering MNPs). We used V₁ = 18 cm³/mol (water), V₂ = 56.2 cm³/mol PAAm). Flory–Huggins parameter χ = 0.12 was calculated in a conventional way [50] based on the solubility parameters of water (24.9) and PAAm (29.0).

If the number of monomeric units in a linear subchain is known, we can estimate the average distance L between neighboring cross-links. For this purpose, we proceeded with the assumption that the conformation of the electrically neutral polyacrylamide subchains in the swollen network is close to a Gaussian coil [50]. In this case, the mean square distance between the ends of the Gaussian chain <R²> is calculated as:

$$〈R^2〉=n{l}^2\frac{1-cos\vartheta }{1+cos\vartheta }\bullet \frac{1+cos\phi }{1-cos\phi }$$

(5)

where n is the number of bonds in the polymeric chain, l is the bond length, ϑ is the valent angle, and φ is the angle of hindered rotation.

We took l = 0.154 nm for the ordinary C–C bond, ϑ = 109.5° for the valent angle, φ = 68° for the angle of hindered rotation [50], and n = 2N_C for the number of bonds. The latter is two-fold larger than N_C as it includes the bonds in monomer units and bonds between them. The average distance between neighboring cross-links in the network is: L = <R²>^1/2. Calculated values of L for PAAm hydrogel and ferrogel are given in

Table 3. Parameters of the networking density for gel beads based on PAAm chemical network and model PAAm hydrogel.

Gel	αP	NC	L (nm)	L0 (nm)	L0/L
PAAm ferrogel bead	48.1	950.0	13.9	239.4	17.2
PAAm hydrogel bead	37.4	594.3	11.0	149.8	13.6
Model PAAm gel (1.4 M 1:50)	11.9	59.2	3.5	14.9	4.3

. The values of the average length of the fully-stretched subchains between the cross-links L₀ are also give, calculated based on the average number of monomer units in the subchain.

It is evident from Table 3 that the chemical network of PAAm hydrogel synthesized on the CaAlg template is very loose. The average distance between cross-links is about 10 nm. Therefore, maghemite MNPs that have a smaller diameter than this can be washed out of the ferrogel network. The L₀/L ratio reflects the ability of the subchain to uncoil and stretch under external force [12]. It is noticeable that this ratio is higher in the case of the ferrogel compared to the hydrogel containing no nanoparticles.

The parameters of the PAAm hydrogel and ferrogel beads synthesized on the alginate template were compared with the parameters for the model PAAm hydrogel. The model PAAm hydrogel was synthesized separately at the same initial concentration of AAm in the reaction mixture (1.4 M) and the initial cross-linking degree (1:50) as in PAAm/CaAlg beads. The reaction mixture, however, contained no alginate and no physical networking took place. The parameters of networking for the model PAAm gel are also given in Table 3. One can see that the average distance between the cross-links in the model hydrogel with the initial composition parameters is much smaller than in the case of PAAm gel beads. It means that the network structure of the PAAm gel beads deviates significantly from the structure initially set by the composition of the reaction mixture.

The reason is that the polymerization of AAm in the droplet injected into the CaCl₂ precipitant medium was not instantaneous. Simultaneously, with the polymerization of the PAAm network inside the CaAlg gel bead, the monomeric AAm diffused into the surrounding aqueous solution. Therefore, the network structure of the templated PAAm gel corresponded to a significantly lower actual initial monomer concentration than that initially taken up in the reaction mixture.

To estimate the effective monomer concentration that corresponded to the formation of the PAAm network inside a CaAlg bead, a series of model PAAm hydrogels with a cross-linking degree of 1:50 at different initial monomer concentrations were synthesized separately in the absence of alginate. The swelling ratio was determined for these model gels. The dependence of the swelling ratio on the AAm concentration in the reaction mixture is shown in Figure 8.

A decrease in AAm concentration in the range from 1.6 down to 0.6 M was accompanied by a gradual increase in the swelling ratio (Figure 8a). At further decrease in monomer concentration down to 0.4 M, the swelling degree sharply increased. It is convenient to plot this dependence in coordinates ω_PAAm = f (C_AAm), where ω_PAAm is the PAAm weight fraction in the swollen gel related to its swelling ratio by the equation:

$${\omega }_{PAAm}=\frac{1}{1+\alpha }$$

(6)

This dependence is shown in Figure 8b. In this case, the experimental results are well fitted by the quadratic function of the monomer concentration at the synthesis:

$${\omega }_{PAAm}=-0.023C^2+0.117C-0.039$$

(7)

The obtained equation made it possible to estimate the actual concentration of acrylamide in swollen spherical gel beads synthesized on the alginate template. The calculation based on the swelling ratio of hydrogel and ferrogel PAAm beads (Table 3) showed that the effective monomer concentration was approximately 0.6 M. That is, the initial AAm concentration in the reaction mixture (1.4 M) decreased by more than half that value (to 0.6 M) due to monomer diffusion from CaAlg hydrogel beads during the polymerization of the chemical network. This effect must be taken into account in the synthesis of PAAm hydrogel and ferrogel spherical beads using CaAlg physical network as a template.

Finally, we consider the composites synthesized in this work as promising magnetically active matrixes for biomedical applications. Such materials with a size of several millimeters are well-visualized using medical echography and well-positioned by the application of an external magnetic field. The quality of FG echolocation as well as the force of their attraction to the source of the magnetic field critically depends on the MNP concentration [51,52]. Therefore, the features of MNP interaction with a polymer network considered in this study are a useful basis for designing biomedical devices with desired properties.

4. Conclusions

The physicochemical features of the synthesis of composite spherical beads of ferrogels with physical networking, chemical networking, and interpenetrating networks had been analyzed. The effect of the polymer network composition on the size, swelling ratio, and network structure of the gels was studied. The beads formed by the interpenetrating polymer network of polyacrylamide and calcium alginate had minimal values of average diameter and swelling degree due to a higher effective density of the combined physical (CaAlg) and chemical (PAAm) networking.

If the physical networks of CaAlg were removed by the exposure to a chelating agent and subsequent washing out, then the transition from PAAm/CaAlg ferrogels to PAAm ferrogels was accompanied by significant changes in the swelling ratio and a decrease in the concentration of MNPs. The main reason for such behavior was a significant decrease in acrylamide concentration during the synthesis of spherical gel beads on the CaAlg template due to monomer diffusion into the external solution. Calculation of the characteristic parameters of the polymer mesh based on the Flory–Rehner equation confirmed the decrease in the mesh density in PAAm ferrogels and the substantial elongation of the subchains between the cross-links. Therefore, the smallest MNPs tended to leave the loosened network of PAAm ferrogels.

It was shown that irrespective of the gel composition, the embedding of maghemite nanoparticles led to an increase in the swelling ratio of the polymeric network. This indicated the absence of strong intermolecular interactions between the polymer and the filler.

Future studies of the magnetic properties of the proposed composite spherical beads, their behavior in a magnetic field, including magnetic deformation and positioning, as well as their biocompatibility, are the subjects of the development of this work.