Introduction

Magnetic nanoparticles are widely used for the preparation of novel multifunctional therapeutic and diagnostic agents for different fields of medicine [1–3], including oncology. Conjugation of nanoparticles with corresponding antibody provides nanoparticles with the ability to recognize and “mark” specific microbiological objects, cell populations, microorganisms, and so on. On this basis, the concept has been substantiated for chemical construction of magnetosensitive nanocomposites with multilevel hierarchical architecture, characterized with functions of “nanoclinics” [2] and biomedical nanorobots [3–5] (recognition of microbiological objects in biological environments; the aimed delivery of drugs to target cells and organs using an external magnetic field and deposition; complex chemo-, immuno-, neutron capture, real-time hyperthermic therapy and diagnostics).

To produce magnetosensitive multifunctional nanocomposites (NC), considerable interest of researchers is drawn by magnetite (Fe3O4)/hydroxyapatite (HA) nanostructures of core–shell type, characterized with a unique set of physical, chemical, and biological properties, the ability to create on their basis magnetic liquids (ML) containing anticancer remedies for different functional destination, including cytotoxic drug, anthracycline antibiotic doxorubicin (DOX) [6–17]. In this regard, the urgent task is to study the characteristics of the processes of adsorptive immobilization of DOX on the surface of Fe3O4/HA nanocomposites and its release into the saline, which is used to create ML for medical purposes, while maintaining biological activity of the cytotoxic drug.

It has been shown [18] that for a magnetite-based polydisperse colloidal ML the coordination of experimental and theoretical magnetization curves is possible when assuming that Fe3O4 particles have complex magnetic structure, namely, a low-magnetic surface layer with thickness h 1 ~0.83 nm (the lattice constant of magnetite at 300 K is 0.824 nm). Emergence of the said layer is attributed to chemical interaction of a particle with a stabilizing surfactant [19]. In [11, 20], it was found that the calculations of magnetization curve for ML based on single-domain Fe3O4 in the framework of Langevin’s paramagnetism theory coordinate satisfactorily with the experimental results in assumption that saturation magnetization of magnetite particles depends on their sizes, and from experimentally measured distributions of the nanoparticles in ensemble one can calculate the magnetization curve for ML based on them.

An important issue is to find the size distribution for ensemble of superparamagnetic nanoparticles with complex shell structure from experimental measurements of the magnetization curve. Its successful resolution could open the way for determination of size parameters of nanoarchitecture elements that make multicomponent shell structure of the nanocomposite, built on superparamagnetic nanosized carriers, including those in the composition of magnetic liquids.

Therefore, from the above, it can be argued that investigations of the possibility of using approaches applied in [11, 20], based on the use of Langevin’s paramagnetism theory, for the description of nanocomposites with superparamagnetic cores and complex shell structures of different chemical nature and magnetic liquids based on them, are urgent.

The aim of this work is to investigate the DOX adsorption on the surface of magnetite/hydroxyapatite nanostructures, to synthesis bioactive nanocomposites magnetite/hydroxyapatite/doxorubicin of core–shell type and ML based on them, to study the magnetic properties of nanocomposites and liquids, to analyze the results using Langevin’s paramagnetism theory, and to determine the size parameters of multicomponent shell structure of the nanocomposites.

Experimental

Synthesis of initial magnetite, magnetite/hydroxyapatite nanocomposites, their properties and parameters, doxorubicin adsorption calculation technique are described in [11]. In this work, we used Fe3O4 and Fe3O4/HA samples with the specific surface area S sp ~110 and 100 ± 5 % m2/g, respectively. Presence of HA shell did not practically change the magnetic properties [21] of initial magnetite (the nanocomposite core).

Investigation of nanomaterials biocompatibility was carried out by studying their influence on cell viability of baker’s yeast Saccharomyces cerevisiae [22, 23] with the help of Goryaev chamber using optical microscopy (biological microscope of Bresser Erudit type), and methylene blue dye by registration of concentration change for cells growing at the temperature of 22 °C in suspensions containing nanocomposites, yeast cells, minimal synthetic nutrient medium (MSM) [24], saline (PS). Numerically viability (K) was evaluated by the formula: K = M 1/(M 1 + M 2) × 100 %, where M 1 is a number of living cells, M 2 is a number of dead cells. The data obtained was compared to the results of control samples studies.

Bioactivity of NC Fe3O4/HA modified with DOX was evaluated from their cytotoxic influence on S. cerevisiae cells [25, 26] and a decrease in cell proliferation rate [24]. These effects are, in particular, due to participation of doxorubicin in redox cyclic reactions and a corresponding increase in quantity of free radical molecules, to induction of oxidative stress, and to cell cycle delay in G1- and S-phase. The concentration of cells (n, mL−1) was calculated by the formula of Goryaev chamber: n = N × 2.5 × 105, where N is a number of cells above a large square of the chamber.

Investigation of isotherm of DOX adsorption on the surface of Fe3O4/HA NC was performed as follows. Samples (g) of Fe3O4/HA NC of 30 mg were mixed with DOX solutions (V = 5 mL) of different concentration. DOX adsorption was carried out in saline (PS) for 2 h in dynamic mode at room temperature and pH = 7.0. The quantity of the substance adsorbed on the surface of nanocomposites was determined by measuring DOX concentration in the contact solutions before and after adsorption. The concentration was measured with the help of a spectrophotometer Spectrometer Lambda 35 UV/Vis Perkin Elmer Instruments at λ = 480 nm using a calibration graph. In this work the lyophilized preparation DOXORUBICIN-TEVA (Pharmachemie BV, The Netherlands) was used.

To study the time dependences of DOX adsorption on the surface of Fe3O4/HA NC, as well as to study the isotherms, we used the samples (30 mg) of Fe3O4/HA nanocomposite, which were mixed with DOX solutions in saline (V = 5 mL) of varying concentration, DOX adsorption was carried out in dynamic regime using a shaker at room temperature. The quantity of the substance adsorbed on the surface of nanocomposites was determined by measuring DOX concentration in contact solutions in fixed time (from 30 min to 24 h).

Calculation of the hydroxyl groups concentration on the HA surface in Fe3O4/HA nanocomposite was determined by thermogravimetric analysis using a derivatograph Q-1500.

Results and discussion

Adsorption studies

Doxorubicin [27] is the antitumor antibiotic agent of anthracycline type, widely used in modern oncotherapy. The mechanism of action is interaction with DNA, formation of free radicals, and direct influence on cell membranes with suppression of nucleic acids synthesis. It is characterized by an appreciable antiproliferative effect.

The DOX absorption spectrum measured in a physiological liquid environment is shown in Fig. 1.

Fig. 1
figure 1

Absorption spectrum of doxorubicin in PS environment. a Calibration graph

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The spectrum has several maxima: 204, 233, 254, 290, 480 cm−1, a slope angle of the line of calibration graph for doxorubicin in the saline environment was optimal for the wavelength λ = 480 nm (Fig. 1a), at which we carried out the quantitative measurements of doxorubicin concentration.

Analysis of the isotherm of DOX adsorption on the surface of Fe3O4/HA NC (Fig. 2) shows that increase in equilibrium DOX concentration does not lead to adsorption saturation of the surface of Fe3O4/HA adsorbent. Concavity (S-similarity) of an initial part of isotherm relatively to the concentration axis and lack of saturation in the investigated range of equilibrium concentrations can be attributed to the polymolecular nature of adsorption and low porosity of the nanocomposite surface. In addition, S-similarity of isotherm can be caused to some extent by co-adsorption of sodium chloride because DOX adsorption was performed from saline.

Fig. 2
figure 2

Isotherm of doxorubicin adsorption on the surface of Fe3O4/HA NC

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Distribution coefficient (Ε, mL/g) of doxorubicin between the surface of nanocomposite and solution was 366.8 mL/g at A = 91.7 mg/g.

Upon studies of DOX adsorption on the surface of Fe3O4/HA NC as function of time (Fig. 3), it was revealed that during the first 2 h 60–70 % of the substance is adsorbed, and for 24 h the adsorption was almost complete (93–97 %). And this applies to the entire range of the investigated DOX concentrations. The dependence of the extraction extent (R, %) of doxorubicin on concentration of solutions and adsorption time is given in Table 1.

Fig. 3
figure 3

Time dependence of DOX adsorption on the surface of Fe3O4/HA NC in PS. Initial concentration of DOX solutions С, mg/mL: 1 0.13, 2 0.26, 3 0.32, 4 0.52, 5 0.64, 6 1.04

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Table 1 Extraction extent of doxorubicin (R) on the surface of Fe3O4/HA NC depending on the concentration of solutions and adsorption time (t)
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The results of studies on the dependence of desorption (A D , mg/g) on time and the percentage of desorbed substance (A D , %) are given in Fig. 4 and Table 2. Experimental dependencies of desorption on time indicate that the doxorubicin release decreases with increasing its quantity on the surface of NC. When the quantity of adsorbed DOX is 20–50 mg/g, 80–60 % of DOX, respectively, is desorbed, whereas at large quantities of adsorbed DOX (100–150 mg/g) the release almost do not occur. This situation can be explained by the peculiarities of interaction and the emergence of sufficiently strong bonds between the specific functional groups on HA surface and doxorubicin molecules: hydroxyl and carbonate groups of Fe3O4/HA NC surface can form strong hydrogen bond with hydroxyl and amino groups of DOX; upon the desorption, in samples with lower concentration of DOX, the drug is desorbed faster through partial dissociation of hydrogen bonds [28].

Fig. 4
figure 4

DOX desorption (А D) from Fe3O4/HА/DOX NC surface in PS vs time (t) at different initial amounts of immobilized DOX

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Table 2 Dependence of DOX (A D ) desorption from Fe3O4/HA/DOX NC surface in PS on time (t) at different initial amounts (A) of immobilized DOX
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The basic amount of DOX is desorbed during the first 20 min for all the investigated concentrations.

Biocompatibility and bioactivity of nanocomposites

Biocompatibility of Fe3O4/HA NC is a known fact [3–11]. In this paper, biocompatibility and bioactivity of the produced samples was monitored by their effect on viability of baker’s yeast S. cerevisiae cells [11].

In the study of bioactivity of the original drug doxorubicin, we revealed experimentally that its solution in saline at the concentration of 0.5 mg/mL resulted in almost total death of yeast cells (95 %) for 3.5 days. In the technique for determination of cytotoxicity, it is accepted to use IC50 dose at which there is a death of ~50 % of the cells [29]. Therefore, to test bioactivity, a quantity of Fe3O4/HA/DOX nanocomposite material (~20 mg) with immobilized doxorubicin (~50 mg/g), that was used to form a suspension, was chosen from the data of Fig. 4 and Table 2 in calculation that the concentration of released DOX in research suspensions was ~0.25 mg/mL.

Fifteen samples in total were investigated, five in each series

  1. 1.

    suspension of yeast cells (initial concentration n 0 ≈ 2.5 × 107 mL−1) in PS with MSM (Fig. 5a);

    Fig. 5
    figure 5

    Typical images of fragments of Goryaev chamber with yeast cells: in beginning of studies (a), after interaction of yeast cells with Fe3O4/HA NC (b), after interaction of yeast cells with Fe3O4/HA/DOX NC (c). The interaction time is 3.5 days, T ~300 K, the concentration of cells: а 2.5 × 107 mL−1, b 1 × 108 mL−1, c 3 × 107 mL−1

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  2. 2.

    suspension of yeast cells (initial concentration n 0 ≈ 2.5 × 107 mL−1) in PS with MSM, containing 20 mg of Fe3O4/HA NC;

  3. 3.

    suspension of yeast cells (initial concentration n 0 ≈ 3.5 × 107 mL−1) in PS with MSM, containing 20 mg of Fe3O4/HA/DOX NC.

All the samples contained 1.3 mL of PS (0.9 % NaCl) and 1 mL of MSM. The samples of series 1 and 2 were used for control and comparison, and series 3—for studies on bioactivity of Fe3O4/HA/DOX NC.

Research data analysis shows that in the yeast suspensions (n 0 ≈ 2.5 × 107 mL−1) in the PS with MSM (control series of type 1) there is a characteristic for yeast [30] cell division that leads to an increase in their concentration in 16 h twice (5 × 107 mL−1). Further rate of their reproduction slowed (possibly because of nutrient reduction). In 3.5 days their concentration was ~108 mL−1. The viability of yeast cells in the experiments of series 1 was not significantly changed and reached ~98–99 %.

Investigation of suspensions of type 2 control series showed rather active division by which the yeast concentration in 16 h was ~6.5 × 107 mL−1, and in 3.5 days, as in the previous case, reached ~108 mL−1 (Fig. 5b). Cell viability, as in the previous case, at all stages of the series 2 samples study was ~98–99 %. These data indicate biocompatibility of Fe3O4/HA NC with respect to yeast cells under the experiment conditions.

Upon the studies of series 3 sample suspensions, a significant inhibition of cell proliferation was revealed (Fig. 5c). So, the concentration of yeast cells in the beginning of the experiment was ~3.5 × 107 mL−1 and was practically not changed for 16 h, only in 3.5 days their number increased up to ~4 × 107 mL−1. During the study, the quantity of dead cells in the samples of series 3 (Fig. 5c) was about 10 %.

Thus, analyzing the results of experiments of series 1 and 2 (Fig. 5b) and comparing them to the data of series 3 (Fig. 5c), we can conclude that Fe3O4/HA/DOX nanocomposites have cytotoxic influence on S. cerevisiae cells and reduce the rate of their proliferation.

It should be noted that the observed features of magnetosensitive NC Fe3O4/HA/DOX influence on yeast cells are characteristic for the interaction of these cells with the free form of doxorubicin [24–26].

Synthesis of magnetic liquids

In the next stage of research, samples of the three types of magnetic liquids based on saline (ML1–3) were synthesized: ML1 − Fe3O4/sodium oleate (Na ol.)/polyethylene glycol (PEG) + PS, ML2 − Fe3O4/HA/Na ol./PEG + PS, ML3 − Fe3O4/HA/DOX/Na ol./PEG + PS. Fe3O4 nanoparticles, as well as Fe3O4/HA NC and Fe3O4/HA/DOX NC particles were stabilized by sodium oleate [31] and polyethylene glycol. It is known that PEG prevents adsorption interactions of components of a liquid with proteins [32], which is important in medical applications of magnetic liquids. For stabilization of the NP and NC surface in the ML composition, the sodium oleate samples of weight m were calculated taking into account the concentration of hydroxyl groups on the surface of magnetite and hydroxyapatite. The calculation was performed using the formula: m = BMg, where B is the concentration of hydroxyl groups (2.2 mmol/g on the surface of initial nanosized magnetite and 1.8 mmol/g on the surface of Fe3O4/HA nanocomposite, as determined from the data of thermogravimetric analysis using a derivatograph Q–1500), M is the molecular weight of sodium oleate (304 g/mol), g is a sample weight of Fe3O4 or NC. Additional modifying with PEG-2000 was carried out in dynamic mode using a shaker; the amount of polymer was 10–15 % of the weight of Fe3O4 NP or nanocomposite sample.

Study of magnetic and structural properties of nanocomposites in composition of magnetic liquids

Further researches are based on using the ensemble of superparamagnetic carriers as a probe for determination of parameters and control of nanostructures with complex construction, in particular, in composition of the magnetic liquids [11, 20, 33].

Implementation of the said approach can be achieved using the method of magnetic granulometry [34], based on the comparison of the experimental magnetization curve to Langevin’s curve at the given laws of size distribution of particles and their magnetic parameters, including saturation magnetization of the particles and the thickness of “demagnetized layer”.

To analyze the magnetization curve of ML containing superparamagnetic nanoparticles, a known equation [35] was applied [11]:

$$\frac{M(H)}{{\varphi_{\rho } M_{s} }} = \frac{{\sum\limits_{i = 1}^{k} {n_{i} (d_{i} - 2h_{1} )^{3} L\left( {\frac{{M_{s} H}}{{k_{B} T}}\frac{\pi }{6}(d_{i} - 2h_{1} )^{3} } \right)} }}{{\sum\limits_{i = 1}^{k} {n_{i} d_{i}^{3} } }},\,\;\quad$$
(1)

where M (H) is the magnetization of ML in magnetic field of strength H; M s is the saturation magnetization of a bulk magnetite; φ ρ is the volumetric concentration of solid phase in ML, defined by the density of ML; d i , n i is the average diameter and quantity of Fe3O4 NP in the i interval of the diameter variation row; k is the number of intervals; h 1 is the thickness of “demagnetized layer” of magnetite; L(ξ) ≡ cthξ − 1/ξ is the Langevin function; k B is the Boltzmann constant; T is the temperature.

  1. (a)

    Determination of the size distribution of ensemble of nanosized magnetite particles and the thickness of their demagnetized layer in terms of the shape of magnetization curves of magnetic liquid.

The ensemble of Fe3O4 particles that are characterized by the sizes of 3–23 nm being in superparamagnetic state, has non-hysteresis demagnetization curve, and therefore, zero values of coercive force (H c) and residual magnetization (M r) [11]. These features of magnetization are mainly observed in experiment also for samples of ML based on nanocomposites Fe3O4/HA/DOX/Na ol./PEG + PS (ML3) (Fig. 6a).

Fig. 6
figure 6

Hysteresis loops: a ML3 (for insertions: the top 1, 2, histograms of experimental and lognormal (2.33, 0.298) distribution of Fe3O4 NP by diameters, respectively; the lower ones, TEM images (scale 50 nm) of magnetite nanoparticles ensemble and initial part of hysteresis loop of ML3); b DR3 in paraffin matrix (for insertions: the top, hysteresis loop of Fe3O4 NP; the bottom, initial part of the loop of DR3)

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The specific saturation magnetization σ s of typical ensembles of Fe3O4 NP synthesized for research in this paper was 62.6 ± 2.5 % Gs cm3/g (Fig. 6b, the upper insertion). In the study of static magnetic characteristics (the measurement time was ~100 s), Fe3O4 NP or dry residues (DR) of magnetic liquids were distributed in the matrix of paraffin (to prevent interparticle interaction) under condition m DR /m p ~0.1 (m DR—weight of DR, m p—weight of paraffin). Calculation times of Neel’s relaxation of magnetic moment of Fe3O4 NP with diameters of 3–22 nm are (10−9–102) s, respectively.

According to the experimental curve (Fig. 6a), the coercive force (H c) of ML3 is equal to (2 ± 0.5) Oe. The samples of Fe3O4 NP and DR3 of ML3, distributed in paraffin, are characterized by H c 89.7 Oe and 90.0 Oe, respectively (Fig. 6b). The availability of coercive force in the investigated samples in a liquid state, probably, is due to the presence of a small number of aggregates, joint by dipole–dipole interaction, and in paraffin matrices—a small number of Fe3O4 NP with diameter >22 nm.

The upper insertion in Fig. 6a shows the diameter distribution of Fe3O4 NP, obtained in experiment by statistical processing (a program Get Data Graph Digitizer 2.24) of TEM images of initial magnetite (1), and lognormal diameter distribution (2), calculated for the same ensemble using a probability density function, similar to [11]. The average diameter value d 0 = (Σn i d i )/N and the standard deviation (s) of diameter of Fe3O4 NP for a choice of volume N = 274 was 10.77 nm (s = 3.083 nm), logarithm of diameter: 2.33 (s lnd  = 0.298), logarithm of volume: 6.37 (s lnV  = 0.894). For mathematical expectation of Fe3O4 particle diameter M(d) and logarithm of diameter M(lnd), the correlation is just: M(d) = exp[M(lnd) + (σ lnd ) 2 /2], where σ lnd is the standard deviation of logarithm of a particle diameter [36]. The value of thickness of “demagnetized” surface layer h 1 of Fe3O4 NP, calculated according formula (1) was ~0.83 nm.

Figure 7 shows a model of Fe3O4/HA/DOX/Na ol./PEG NC particle with a multilayer shell in which: d = d s + 2h 1 is the diameter of a spherical magnetite particle; d s is the diameter of the area of Fe3O4 NP with σ s which is the characteristic for a bulk magnetite (≈92 emu/g at 300 K); h 1 is the thickness of “demagnetized” layer of Fe3O4 particles; h 2, h 3, h 4 are the thickness of spherical layers of modifier (HA), drug (DOX) and stabilizer (Na ol./PEG), respectively.

Fig. 7
figure 7

Model of a particle of NC with a multilayer shell. It is marked: d = d s + 2h 1 is the diameter of a spherical Fe3O4 NP; d s is the diameter of the area of Fe3O4 NP with σ s, that is characteristic for a bulk magnetite; h 1 is the thickness of the “demagnetized” surface layer of Fe3O4 NP; h 2, h 3, h 4 are the thickness of the modifying layer (HA), drug (DOX), and combined stabilizer (Naol./PEG) in NC structure, respectively

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Using the model (Fig. 7), in terms of the results of experimental measurements and ensemble parameters calculation for nanoparticles of magnetite and dry residues of magnetic liquid of corresponding composition, the shell layers sizes of Fe3O4/HA/DOX/Na ol./PEG nanostructure were determined.

In [11] it has been shown that for ensembles of nanoparticles of “core–shell” type, under condition of cores to be in a superparamagnetic state, formula (1) practically unequivocally binds the size distribution of Fe3O4 NP in ensemble with a shape of hysteresis curve. Taking into account that in conditions of magnetic saturation the Langevin function L(ξ) → 1, and in DR a volumetric concentration of solid phase ~1, formula (1) can be written as

$$\frac{{M_{s}^{\text{NCPM}} }}{{M_{s}^{\text{NPM}} }} = \frac{{\langle \rho_{\text{NCPM}} \rangle \sigma_{s}^{\text{NCPM}} \int\limits_{0}^{\infty } {V_{\text{NCPM}} f(V_{\text{NCPM}} ){\text{d}}V} }}{{\langle \rho_{\text{NPM}} \rangle \sigma_{s}^{\text{NPM}} \int\limits_{0}^{\infty } {V_{\text{NPM}} f(V_{\text{NPM}} ){\text{d}}V} }},$$
(2)

where M NCPM s , M NPM s are the saturation magnetization of ensembles of particles of NC (NCPM) and Fe3O4, respectively; <ρ NCPM>, <ρ NPM> are the average density of ensembles of particles of NC and Fe3O4, respectively; σ NCPM s , σ NPM s are the specific saturation magnetization of ensembles of particles of NC and Fe3O4, respectively; f(V NCPM), f(V NPM) are the probability density functions for the volumes of ensembles of particles of nanocomposite and magnetite, respectively; V NCPM, V NPM are the volume of a particle of NC and Fe3O4, respectively.

  1. (b)

    Determination of thickness of the layer of combined stabilizer (Na ol./PEG)

The synthesized samples of initial Fe3O4 and ML1 composed of Fe3O4/Na ol./PEG + PS were dried at room temperature. The mass proportion of magnetite in the dry residue of ML1 (DR1) was experimentally defined as α expFe3O4  = σ DR1 s /σ NPM s  ± 5 %, and calculated by the formula

$$\alpha_{{{\text{Fe}}_{ 3} {\text{O}}_{ 4} }}^{\text{calc}} = \frac{{\upsilon_{{{\text{Fe}}_{ 3} {\text{O}}_{ 4} }} \rho_{{{\text{Fe}}_{ 3} {\text{O}}_{ 4} }} }}{{\left\langle {\rho_{\text{NCPM}} } \right\rangle }} ,$$
(3)

where v Fe3O4 = ∑n i d 3 i /∑n i (d i  + 2δ)3 is the volume fraction of magnetite in the sample; δ = h 2 + h 3 + h 4 is the thickness of the shell; ρ Fe3O4 is the density of magnetite, <ρ NCPM> is the average density of the ensemble of NC particles, which was found from the formula

$$\left\langle {\rho_{\text{NCPM}} } \right\rangle = \,\frac{{\sum\limits_{i = 1}^{k} {n_{i} \rho_{{{\text{NCPM}}_{i} }} (d_{i} + 2\delta )^{ 3} } }}{{\sum\limits_{i = 1}^{k} {n_{i} (d_{i} + 2\delta )^{ 3} } }}$$
(4)

The density of nanocomposite particles of i interval ρ NCPMi in composition of DR1–3 was determined by formulas (5.1–5.3):

$$\rho_{i}^{12} = \alpha_{2} \rho_{1} + \left( {1 - \alpha_{2} } \right)\rho_{2} ,{\text{where }}\alpha_{2} = \left( {\frac{{d_{i} }}{{d_{i} + 2h}}_{2} } \right)^{3} ,$$
(5.1)
$$\rho_{i}^{123} = \alpha_{3} \rho_{i}^{12} + \left( {1 - \alpha_{3} } \right)\rho_{3} ,{\text{where }}\alpha_{3} = \left( {\frac{{d_{i} + 2h_{2} }}{{d_{i} + 2h_{2} + 2h_{3} }}} \right)^{3} ,$$
(5.2)
$$\rho_{i}^{1234} = \alpha_{4} \rho_{i}^{123} + \left( {1 - \alpha_{4} } \right)\rho_{4} ,{\text{where }}\alpha_{4} = \left( {\frac{{d_{i} + 2h_{2} + 2h_{3} }}{{d_{i} + 2h_{2} + 2h_{3} + 2h_{4} }}} \right)^{3}$$
(5.3)

and ρ 1, ρ 2, ρ 3, ρ 4 are the density of magnetite, HA, DOX and Na ol./PEG, respectively; ρ 12 i , ρ 123 i , ρ 1234 i are the density of a particle of i interval of NC Fe3O4/HA, Fe3O4/HA/DOX and Fe3O4/HA/DOX/Na ol./PEG, respectively. For calculations, we used the values ρ 1 ≈ 5.19 g/cm3 [37], ρ 2 ≈ 2.71 g/cm3 [28], ρ 3 ≈ 1.00 g/cm3, ρ 4 ≈ 1.13 g/cm3 [33]). We considered that the size distribution of Fe3O4 NP of the initial ensemble and its dry residues was identical.

Specific surface area of the ensemble of NC particles was determined by the formula

$$S_{\text{sp}}^{\text{calk}} = 6\frac{{\sum\limits_{i = 1}^{k} {n_{i} (d_{i} + 2\delta )^{2} } }}{{\sum\limits_{i = 1}^{k} {\rho_{{{\text{NCPM}}_{i} }} (d_{i} + 2\delta )^{3} } }}.$$
(6)

According to the model (Fig. 7) in a particle of DR1 only h 4 shell is filled (h 2, h 3 = 0). The results of experimental measurements and calculations of parameters of ensemble of NP Fe3O4 and DR1 are shown in Table 3.

Table 3 Results of experimental measurements and calculation of parameters of ensemble of NP Fe3O4 and DR1
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As shown in Table 3, thickness of the shell of combined stabilizer Na ol./PEG in composition of dry residue of magnetic liquid Fe3O4/Na ol./PEG + PS is (3.4 ± 0.1) nm.

  1. (c)

    Determination of the thickness of HA layer

To determine the thickness of HA layer we studied the ensemble of NP Fe3O4 and ML2 composed of Fe3O4/HA/Na ol./PEG + PS obtained on its basis, the samples were dried at room temperature, dry residue DR2 was obtained and their parameters were investigated by the technique described above. The results are shown in Table 4.

Table 4 Results of experimental measurements and calculation of parameters of ensemble of NP Fe3O4 and DR2
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As shown in Table 4, the found value of thickness of hydroxyapatite layer h 2 in the structure of Fe3O4/HA/Na ol./PEG is 3.5 ± 0.3 nm, which in our view is satisfactorily consistent with the value of ~4 nm, determined by an independent technique in studies of Fe3O4/HA nanocomposites by photoelectron spectroscopy method [11]. The obtained data may indicate reliability of the results of determination of shell parameters in complex nanoarchitecture of multifunctional magnetosensitive nanocomposites.

  1. (d)

    Determination of the thickness of DOX layer

The ensemble of magnetite nanoparticles and ML3 composed of Fe3O4/HA/DOX/Na ol./PEG + PS obtained on their basis, were dried at room temperature. The dried samples Fe3O4 and dry residue DR3 were studied, as in the previous cases. The research results are given in Table 5.

Table 5 Results of experimental measurements and calculation of parameters of magnetite nanoparticles ensemble and dry ML3 residues
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According to the data of Table 5, the found value of thickness of the layer of medical drug doxorubicin h 3 in the structure of Fe3O4/HA/DOX/Na ol./PEG is 2.0 ± 0.3 nm.

  1. (e)

    Study of sedimentation stability of magnetic liquids

The investigated ML are nanoheterogeneous systems, where diffusion fluxes of particles dominate over sedimentation ones. Over a long period of time (years) in monodisperse sols, the fluxes become equal and a state of diffusion-sedimentation equilibrium (DSE) is set, at which the distribution of particles on height of a vessel is subjected to the hypsometric law [37]:

$${\raise0.7ex\hbox{${v_{h} }$} \!\mathord{\left/ {\vphantom {{v_{h} } {v_{0} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${v_{0} }$}} = \exp \left[ { - \frac{{V_{\text{cp}} (\rho_{\text{cp}} - \rho_{\text{lc}} )gh}}{{k_{B} T}}} \right] ,$$
(7)

where ν h , ν 0 are the concentrations of particles at height h and at the level of bottom of a vessel, respectively; V cp, ρ cp are the volume and density of colloidal particles, respectively; ρ lc is the density of a liquid carrier; g is the acceleration of gravity.

The height at which concentration of particles varies in e times, characterizes the thermodynamic sedimentation stability (TDS) of a colloidal system [37] (hypsometric height L). From Eq. (7) it follows that

$$L = \frac{{k_{B} T}}{{V_{cp} (\rho_{cp} - \rho_{lc} )g}} = \frac{{6k_{B} T}}{{\pi (d + 2\delta )^{3} (\langle \rho_{NCPM} \rangle - \rho_{lc} )g}} ,$$
(8)

where <ρ NCPM> is the mean density of a nanocomposite particle with diameter of core d and thickness of shell δ, calculated by formulas (5.1–5.3).

In polydisperse systems, DSE is set for each fraction of particles. Time of setting DSE (t b ) in ML was calculated by the technique given in [33]: we used formula t b  = L 20 /<D>, where <D> = (1/N)∑k B T/[3πη(d i  + 2δ)] is the average diffusion coefficient; L 0 = k B T/[<V NCPM> (<ρ NCPM> − ρ lc)g] is the average hypsometric height; η is the dynamic viscosity, determined for the concentrated ML by a laboratory viscometer (the time of leakage of the fluid through a glass capillar with diameter of 0.2 mm was ≈300 s); the value η of diluted ML, according to experimental data [18], was calculated by Einstein formula: η/η 0 = 1 + 5φ/2, where η 0 is the dynamic viscosity of the liquid carrier (η 0 of PS is approximately equal to 0.890 mPa s at the temperature of 25 °C). The estimated values t b in ML1–3 are nine years and more. The experimental value of L for ML3 is L exp = 2.4 ± 8 % cm.

Using the found parameters of Fe3O4/HA/DOX/Na ol./PEG nanostructure in composition of magnetic liquid, the dependencies of hypsometric height (Fig. 8, curve 1) and specific surface area of DR (curve 2) on thickness h 3 of DOX layer were plotted for the model magnetic liquid of ML3 type, in which Fe3O4/HA/DOX/Na ol./PEG NC was characterized by the fixed size of the core and layers of hydroxyapatite and combined stabilizer (d Fe3O4 NP = 10.8 nm, h 2 = 3.5 nm, h 4 = 3.4 nm). Calculation dependence L(h 3) was built by formula (8), S sp (h 3)—(9):

$$S_{\text{sp}} = \frac{6}{{\rho_{\text{NCPM}} (d + 2\delta )}}$$
(9)
Fig. 8
figure 8

Calculation dependences: hypsometric height L (curve 1) and specific surface area Ssp of DR (curve 2) on the thickness h3 of DOX layer for the model magnetic liquid of ML3 type, in which Fe3O4/HA/DOX/Na ol./PEG NC is characterized by the fixed size of the core and layers of hydroxyapatite and combined stabilizer (dFe3O4 NP = 10.8 nm, h 2 = 3.5 nm, h 4 = 3.4 nm)

Full size image

The value <ρ NCPM> was obtained by the formulas (5.1–5.3).

Dependence L(h 3), shown in Fig. 8, curve 1, is typical for the colloidal systems [37]. The experimental value of L for ML3 (L exp = 2.4 ± 8 % cm) corresponds to h 3 = 2.2 ± 8 % nm.

Dependence S sp(h 3) given in Fig. 8 (curve 2) has a maximum caused by that S sp is a complex function of ρ NCPM and (d + 2δ). Its position (h 3cr) can be found analytically by equating to zero the expression dS sp/dδ (the criterion for finding thickness of the shell, which corresponds to the maximal specific surface area of the core–shell structure S sp). Ordinate corresponding to the experimental value S expsp  = 120 ± 3 % for DR3 (Table 5), twice crosses the calculated dependence S sp with abscissas h 3 = 1.94 nm and h 3 = 5.0 nm. The value h 3 = 5.0 nm contradicts the data of magnetic measurements (Table 5) and the value obtained by L exp (Fig. 8, curve 1).

So, using three independent experimental methods for measurement of σ s , L, S sp, we obtained three values of the thickness of doxorubicin layer h 3 in the structure of Fe3O4/HA/DOX nanocomposite: 2.0 nm (Table 5), 2.2 nm (Fig. 8, curve 1), 1.94 nm (Fig. 8, curve 2), respectively. The found values h 3 are rather close, which shows their reliability.

We note that analysis of the sizes of superparamagnetic iron oxide nanoparticles coated with a layer of carboxydextran, which are applied as contrast agents in magnetic resonance imaging (a commercial product Resovist and SH U555C) using a magnetization curve and images of ensembles of particles, obtained by transmission electron microscopy, has been performed in [38].

The results of experimental investigations and calculations given in this paper, their testing by different ways and comparison suggest that using ensembles of magnetic carriers as a superparamagnetic probe and Langevin’s paramagnetism theory, one can evaluate the sizes of the components of complex shell structure of nanocomposites. The obtained data may be useful in optimizing chemical composition, structure and properties of new magnetic liquids and adsorbents containing magnetosensitive nanocomposites with complex construction of shell [39, 40].

Conclusions

The processes of DOX adsorption on Fe3O4/HA NC surface from solution in physiologic liquid were studied. It was determined that an increase in equilibrium concentration of DOX within the studied concentration range does not lead to adsorption saturation of the surface of Fe3O4/HA adsorbent. It was revealed that release of DOX into saline decreases with growing of its quantity on NC surface.

Magnetosensitive Fe3O4/HA/DOX NC were synthesized. It has been determined that cytotoxic influence and antiproliferative activity of NC with respect to S. cerevisiae cells are typical for interaction of these cells with a free form of doxorubicin.

Magnetic liquids containing Fe3O4/HA/DOX NC stabilized by sodium oleate and polyethylene glycol were produced and investigated. Using the ensemble of Fe3O4 carriers as a superparamagnetic probe, Langevin’s paramagnetism theory, the values of density of nanocomposite constituents, the size parameters of their shell were evaluated, which was corroborated by independent measurements of specific surface area of nanostructures and kinetic stability of the corresponding magnetic liquids. The obtained results may be used for the development of novel forms of magnetocarried medical remedies for targeted delivery and adsorbents based on nanocomposites of superparamagnetic core–shell type with multilevel nanoarchitecture, as well as for determination, control, and optimization of the size parameters of its components.