Theoretical and experimental investigation of the magnetic properties of polyvinylidene fluoride and magnetite nanoparticles-based nanocomposites

Theoretical and experimental investigation of the magnetic properties of polyvinylidene fluoride... In the present study, the effect of size distribution of magnetite nanoparticles in a PVDF matrix on the magnetic properties of PVDF ? Fe O nanocomposites was experimentally and theoretically investigated. The size distribution of nanopar- 3 4 ticles in polymer matrix and morphology of the nanocomposites were studied by the means of scanning electron micro- scopy and atomic force microscopy. It was found that when the Fe O nanoparticles are introduced into the polymer 3 4 matrix, their coagulation takes place. The increase in the size of the particles depends on their concentration in the polymer matrix, the type of polymer (polar, non-polar, its viscosity, etc.), reaction temperatures, etc. In addition, when Fe O 3 4 nanoparticles are introduced into the polymer network, the oxidation of the surface layer of particles occurs and the magnetic size decreases. Consequently, the reduced magnetic properties may also be observed. The hysteresis loops have been recorded in small magnetic field range. It was found that the magnetic hysteresis parameters depend on the size and concentration of Fe O nanoparticles. Theoretical calculations were compared with experimental results obtained from 3 4 M(H) measurements. The reasons of differences between theoretical and experimental results have been explained. Keywords Magnetite  Nanocomposite  Polymer  Hysteresis  Polyvinylidene fluoride Introduction nanocomposites attract significant academic and industrial interest because of their relatively easy and low-cost pro- Magnetic nanomaterials are drawing increased attention ducing technology. due to their remarkable physical properties. Superparam- The formation of unique properties of polymer-based agnetic iron oxide nanoparticles, especially magnetite magnetic nanocomposites depends on many factors such as phase and nanocomposites based on Fe O nanoparticles, particles size and shape, degree of dispersion, 3 4 have attracted interest from research due to possible concentration. applications of such materials in various fields [1, 2]. The The determination of the size of the Fe O nanoparticles 3 4 combination of different materials allows to make com- before and after their introduction into the polymer matrix pletely new composite materials with a wide range of has been investigated in our early works [4]. The change in functional properties: mechanical, chemical, electrical, nanoparticle size depends on the type of polymer. magnetic, optical and many others [3]. Among these In the presented work, the dependence of the average nanomaterials, thermoplastic polymer-based magnetic size of Fe O nanoparticles in the polymer matrix on its 3 4 volume content and the dependence of the magnetic properties of the composites (saturation magnetization, residual magnetization, coercive force, etc.) on the size and & M. A. Ramazanov mamed_r50@mail.ru; nanomaterials@bsu.edu.az concentration of the filler have been investigated. Baku State University, Z. Khalilov Str. 23, AZ 1148 Baku, Azerbaijan Institute of Physics, National Academy of Sciences of Azerbaijan, Pr. H. Javid 131, Baku, Azerbaijan 123 Journal of Theoretical and Applied Physics The samples of nanocomposites were obtained by hot Experimental details pressing method at melting point of PVDF under 15 MPa pressure within 4 min on further cooling to room temper- Materials ature [2]. Polyvinylidene fluoride (PVDF) is a polar polymer that has a density of 1.78 g/cm at 25 C, melting point at the Results and discussion T = 177 C. Magnetite nanoparticles were obtained by co-precipita- Figure 1 shows SEM images of nanocomposites based on tion method in an alkaline medium. The average PVDF ? Fe O at various magnetite contents. As can be nanoparticle size is 7–15 nm [1, 2]. 3 4 seen from the figure, for 1 and 3% volume contents of the filler, the sizes of magnetite nanoparticles in matrix are Methods 13–21 nm and 29–40 nm, respectively. Using SEM ima- ges, approximately 100 particle sizes were taken for sta- Scanning electron microscopy (SEM) tistical parameters calculation. The values of parameters in Gaussian and lognormal The distribution of magnetite nanoparticles in the polymer distribution of the Fe O nanoparticles size in PVDF matrix has been studied by scanning electron microscopy 3 4 matrix are reported in Tables 1 and 2, respectively. (SEM, JEOL JSM-7600 F). Scanning was carried out in As can be seen from Table 2, the values of the standard SEI mode with an accelerating voltage of 15 kV and a deviation indicate a narrow lognormal particle size distri- working distance of 4.5 mm. bution. The values of the polydispersity index confirm the monodispersity PVDF ?Fe O nanocomposites system. AFM analysis 3 4 This shows that the size distribution of Fe O particles in 3 4 polymer matrix is fairly good and can be described by a The morphology of the nanocomposites was studied using lognormal distribution function: atomic force microscopy Integra Prima (NT-MDT, Zele- nograd). For the scan used special silicon cantilevers fab- ln x  ln x ricated by plasma etching method with the needle radius of pffiffiffiffiffiffi f ðxÞ¼  exp 2r 2pr  x curvature of 20 nm and the resonance frequency was 1–5 Hz. Scan area was 2 9 2 mm. The measurements It is also clear from the table that the nature of the were taken in the semi-contact microscopy mode in air; the distribution of the Fe O particles in the polymer matrix, as 3 4 amplitude of cantilever’s oscillation was fixed while a function of their concentration and time, does not change. determining the surface topography. The scanning speed Only the distribution parameters:ln x and r depend on the and the number of scanned lines of the image are 256 and concentration of the particles in the polymer matrix and on 1,969 Hz, respectively. the time. During coagulation, the dependence of the aver- age particle diameter on time is analogous to the depen- Method for studying magnetic properties dence of the average particle diameter on the number of particles (concentration), according to the theory [5]. Measurements: Magnetization curves acquired at 300 K Figure 2 shows the lognormal distribution of Fe O 3 4 (room temperature) by a Quantum Design SQUID mag- nanoparticles in PVDF matrix at different volume contents. netometer in the field range ± 50 kOe. The magnetization The dependence of the average size of Fe O nanopar- 3 4 is reported per gram of measured sample. ticles in PVDF matrix on their concentrations was studied. Figure 3a, b represents the dependence of the average Synthesis of nanocomposites particle sizes of Fe O nanoparticles in the polymer matrix 3 4 on volume content. The polymer nanocomposite materials were prepared as As can be seen from Fig. 3a, b, the dependence curve of follows: poly(vinylidene fluoride) was solved in the Fe O particles diameter on the concentration in PVDF 3 4 dimethylformamide (DMF) solvent, at the room tempera- matrix is complicated. At low concentrations, this depen- ture. Magnetite nanoparticles were added into the polymer dence for PVDF matrix is weak. This is due to the particle solution and stirred within 2 h in order to prepare a and polymer properties. Coagulation of particles also homogeneous mixture. In order to remove the solvent from depends on the viscosity of the polymer which it has during the mixture, it was evaporated within 1 day. the preparation of the composite. In a medium with a lower viscosity, the coagulation process will happen faster. As 123 Journal of Theoretical and Applied Physics Fig. 1 SEM images of nanocomposites based on PVDF ? Fe O . a PVDF ? 1%vol Fe O , b PVDF ? 3%vol Fe O 3 4 3 4 3 4 Table 1 Geometric values of the parameters (distribution interval, average value (d), standard deviation (r), asymmetry (as), excess (e) and polydispersity index (PDI)) of Fe O particles size distribution in PVDF matrix 3 4 Sample d - d (nm) r GA e PDI min max d (nm) pvdf ? 1% Fe O 13.2–57.2 23.83 1.403 1.547 2.264 1.789 3 4 pvdf ? 3% Fe O 17–54.2 27.92 1.196 1.22 1.453 1.421 3 4 Table 2 The logarithmic values of the parameters (distribution interval, average value (d), standard deviation (r), asymmetry (as), excess (e) and polydispersity index (PDI)) of Fe O particles size distribution 3 4 sample d - d (nm) r GA e PDI min max d (nm) pvdf ? 1%Fe O - 18.14–16.68 - 17.62 0.0516 0.6435 0.0103 1.00 3 4 pvdf ? 3% Fe O - 17.89–16.73 - 17.434 0.039 0.535 - 0.208 - 1.00 3 4 Fig. 2 The size distribution function of Fe O particles in 3 4 the PVDF polymer matrix: a PVDF ? 1% Fe O , 3 4 b PVDF ? 3% Fe O 3 4 the concentration of the filler in the matrix increases, the d ¼ 6:67 þ 5000:0  u ð1Þ Fe O 3 4 viscosity of the medium changes and the coagulation At high concentrations of the filler, the saturation condition changes as well. occurs, reaching at the maximum value of the coagulated The linear part of the d(u) dependence curve (low particle diameter, which can be described with an expo- concentration) can be described by using the following nential law (Fig. 3a). equations: 123 Journal of Theoretical and Applied Physics Fig. 3 Dependence of the diameter of Fe O nanoparticles 3 4 on their concentration in polymer PVDF matrix. a High content of the filler; b low content of the filler The theory of coagulation of nanoparticles in solutions mixture and the i-th component, and x is the fraction of the component in the medium. From the latter it is possible to at their low concentrations is known. According to this theory, the number of particles during coagulation determine the kinematic (further dynamic) viscosity of the mixture: decreases according to the law [6, 7] ! ! dn n ¼k  n m ¼ exp exp x lg lgðÞ m þ 0:6 mix i i dt i¼1 The value of r is defined as: The obtained results are consistent with AFM 8kT k ¼ ð2Þ illustrations. 3g Morphology of the samples and the degree of dispersion where g is the viscosity of medium. of inorganic phase in the polymer matrix were investigated using atomic force microscopy (AFM) (Fig. 4). AFM By the definition u ¼ , where V , V is the volume of s s observation showed that the size of the dispersed phases solid phase and medium, respectively. Since V ¼ N  V s 0 N S increases with increasing filler content in the nanocom- and n ¼ ¼ , we rewrite the last differential equation in V V 0s posites. The sizes of Fe O nanoparticles are 22, 33 and 3 4 the following form: 45 nm for 1, 3 and 6% volume content of filler, respec- dV tively. These results were found to be consistent with the ¼k u dt results obtained from the theoretical calculations. The magnetic properties of PVDF ? Fe O -based The solution is V ¼ k  u þ V . In the latter expres- 0t 0 0 3 4 sion, if we substitute d ,we will get the following formula: nanocomposites were studied by experimental and theo- 0t retical investigation. Figure 6 illustrates the experimental 2k u t d ¼ d 1 þ 0t 0 hysteresis loops of magnetic polymer composite materials pd with different volume contents of the filler. The expression obtained is valid for low volume content M(H) magnetization versus magnetic field curves of of particle. As can be seen, the diameter of nanoparticles PVDF ? Fe O -based nanocomposites for different filler 3 4 aggregated is a linear function of concentration, which is concentrations have a similar shape (superimposable). In consistent with the previous results obtained (Fig. 3b). At this case, only the 0–50 KOe section of the M(H) curve is high concentration of the filler, the last expression should informative. The inset at the left panel demonstrates be rewritten with the help of such a function that the value M(H) magnetic curve of PVDF ? Fe O -based nanocom- 3 4 of the function should asymptotically approach to the fixed posites at low magnetic field. However, the whole value ‘‘d’’ when the value of the variable is high. m(H) curve of PVDF ? Fe O sample is coherent with a 3 4 The values of ‘‘k’’ were calculated with the help of (2. SPM behavior of this material. The inset on the left shows To determine the viscosity of the mixture, the Walter for- a small hysteresis loop close to H = 0 which is within the mula was used [7, 8]: margin of error (Table 3). n Figure 6a, b shows the theoretical magnetization versus lg lgðÞ m þ 0:8¼ x lg lgðÞ m þ 0:6 magnetic field curve and the magnetic susceptibility curve mixture i i i¼1 of a composite based on PVDF matrix and magnetite nanoparticles with size of 20 nm. Numerical differentiation where c and c are the kinematic viscosities of the mix i was carried out by the method [9, 10]. 123 Journal of Theoretical and Applied Physics Fig. 4 AFM image of PVDF ? Fe O nanocomposites. a PVDF ? 1 vol% Fe O , b PVDF ? 3 vol% Fe O and c PVDF ? 6 vol% Fe O 3 4 3 4 3 4 3 4 be seen from Figs. 5 and 6a, the magnetic field dependence Table 3 Results obtained from magnetic measurements of the magnetization obtained from the experiments and Sample Ms Mr calculated theoretically is close to each other for low PVDF ? 1 vol% Fe O 2.24 0.022 magnetic field. 3 4 PVDF ? 3 vol% Fe O 8.01 0.073 It is known that for dispersed systems, during the 3 4 PVDF ? 6 vol% Fe O 8.12 0.19 magnetization, the value of the saturation magnetization 3 4 can be given by the following equation: M ¼ u M ð3Þ s m As can be seen from Fig. 6a, b, the magnetization curves where M , M are the saturation magnetizations of the have the hysteresis loop. This is typical for particles which composite and the filler, respectively, and u is the volume have many magnetic domains. The hysteresis parameters of content of the filler. the nanocomposites (saturation magnetization, residual To explain this, suppose that the geometric sizes of the magnetization, coercive force, etc.) depend on the size and nanoparticles (dt) are not equal to the magnetic sizes of the concentration of Fe O particles. As the size and concen- 3 4 nanoparticles (dm). tration of Fe O particles increase, the number of magnetic 3 4 For comparison of magnetic sizes with the geometric domains increases in the both particle and medium. As can sizes of nanoparticles, we use the following equations: Fig. 5 M(H) Magnetization versus magnetic field curves of b Experimental magnetization versus magnetic field M(H) curves of PVDF ? Fe O -based nanocomposites. a (1) PVDF ? 1 vol% PVDF ? Fe O -based nanocomposites under low magnetic filed for 3 4 3 4 Fe O (2) PVDF ? 3 vol% Fe O (3) PVDF ? 6 vol% Fe O . PVDF ? 1% Fe O 3 4 3 4 3 4 3 4 123 Journal of Theoretical and Applied Physics Fig. 6 Theoretically calculated magnetic properties of PVDF ? Fe O 3 4 nanocomposites. a Magnezitation versus magnetic field M(H) b susceptibility versus magnetic field curvesv(H) where the size decreases (i.e., the oxidization of the surface V ¼ N  d t t layer is close to the lattice parameter of the particle, a = 0.839 nm). where u ; u and V can be given as below: t m m u ¼ V =V; u ¼ V =V and V ¼ N  d t m m m t m m p Conclusion ¼ N  ðÞ d  x m t It was found that when the Fe O particles are introduced 3 4 where V, V and V are the volumes of medium, solid and t m into the polymer matrix, their coagulation takes place. The magnetic phase, respectively. Then, by using the expres- increase in the particle size depends on their concentration sion for the concentration of the magnetic phase, we obtain in the polymer matrix, the type of polymer (polar, non- the relation between geometrical and magnetic phase: polar, viscosity, etc.), reaction temperatures, etc. When 3 Fe O particles are introduced into the polymer matrix, at 3 4 u =u ¼ d =ðd þ xÞ ¼ a t m t the same time with the coagulation, the oxidation of their After the manipulation of the last expression, we get the surface layer also occurs and the magnetic size decreases cubic equation: and hence the magnetic characteristics are reduced. It 3 2 2 3 becomes clear that the magnetic hysteresis parameters x  3  d x þ 3  d x ð1  aÞd ¼ 0 ð4Þ g g depend on the size and concentration of Fe O particles in 3 4 The last equation was solved by the Cardan method the polymer matrix. Theoretical calculations were com- [11]. Table 4 reports the results obtained from cubic pared with experimental results obtained from M(H) mea- equation. It should be noted that the magnetic properties of surements. At the same time, it was shown that the nanocomposites are independent on the type of the magnetic field dependence of the magnetization obtained polymer. from the experiments and calculated theoretically is close It can be concluded that the thickness of the polymer to each other for low magnetic field. With increasing layer around nanoparticle rises with the increasing size of nanoparticle size, the difference between theoretical and the nanoparticles and it also depends on the properties of experimental values increases. It is related to the fact that the medium (molecular weight, polarity, viscosity, etc.). unlike to the reality, theoretically the magnetite nanopar- It can also be seen from the table that in all cases the ticles are accepted to be single-domained. particle size increases, except for d = 20 nm, u = 0.03, Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creative Table 4 The result obtained from cubic Eq. (4) commons.org/licenses/by/4.0/), which permits unrestricted use, dis- tribution, and reproduction in any medium, provided you give d (nm) u u x (nm) t m appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were 20 0.01 0.371 46.7 made. 40 0.01 0.323 87.3 20 0.03 0.0254 - 1.07 30 0.03 1.33 76.9 References 30 0.06 1.35 55.4 1. Ramazanov, M.A., Hajiyeva, F.V., Maharramov, A.M., Di 40 0.07 1.35 Palma, L., Sannino, D., Makoto Takafuji, H.M., Mammadov, U., Hasanova, A., Shirinova, H.A., Bayramova, Z.A.: New magnetic 123 Journal of Theoretical and Applied Physics polymer nanocomposites on the basis of isotactic polypropylene 7. Evdokimov, I.N., Losev, A.P.: Absence of additivity of properties and magnetite nanoparticles for adsorption of ultra high fre- of petroleum mixtures. Drill. oil Technol. 1, 32–33 (2012) quency electromagnetic waves. Polym. Plast. Technol. Eng. 8. Ramazanov, M.A., Alizade, R.A., Maharramov, A.M., Hajiyeva, (2017). https://doi.org/10.1080/03602559.2017.1320721 F.V., Sultanova, J.R., Shirinova, H.A.: Theoretical and experi- 2. Shirinovaa, H., Di Palma, L., Sarasinib, F., Tirillo`b, J., Rama- mental study of the magnetic properties and size of distribution of zanov, M.A., Hajiyevaa, F., Sanninoc, D., Polichettid, M., Gal- PVDF ? Fe based nanocomposites. J. Inorg. Organomet. Polym. luzzid, A.: Synthesis and characterization of magnetic Mater. (2018). https://doi.org/10.1007/s10904-018-0863-2 nanocomposites for environmental remediation. Chem. Eng. 9. Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.M.: Numerical Trans. 47, 103–108 (2016) Methods. Nauka, Moscow (1975) 3. Stabik, J., Chrobak, A., Haneczok, G., Dybowska, A.: Magnetic 10. Krylov, V.I., Bobkov, V.V., Monostyrny, P.I.: Computational properties of polymer matrix composites filled with ferrite pow- Methods, vol. 2, p. 399. Nauka, Moscow (1977). (Russian) ders. Arch. Mater. Sci. Eng. 48(2), 97–102 (2011) 11. Mathematical Handbook for Scientists and Engineers: Defini- 4. Ali-zade, R.A., Ramazanov, M.A., Sadykhov, R.Z.: Size distri- tions, Theorems, and Formulas for Reference and Review (Dover bution of magnetite nanoparticles in a polymer matrix. Ukr. Civil and Mechanical Engineering) [Granino A. Korn, Theresa J. Funct. Mater. 16(2), 183–189 (2009) M. Korn], p. 832. Nauka, Moscow (1973) 5. Shchukin, E.D., Pertsov, A.V., Amelina, E.A., Zelenev, A.S.: Colloid and Surface Chemistry, vol. 12, p. 774. Elsevier Science, Amsterdam (2001) Publisher’s Note 6. Gerasimov, Y.I., Dreving, V.P., Eremin, E.N., Kiselev, A.V., Springer Nature remains neutral with regard to jurisdictional claims in Lebedev, V.P., Panchenkov, G.M., Shlygin, A.I.: Kursfizich- published maps and institutional affiliations. eskojhimii [Course in Physical Chemistry], vol. 2, p. 624. Khi- miya, Moscow (1973). (In Russian) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Theoretical and Applied Physics Springer Journals

Theoretical and experimental investigation of the magnetic properties of polyvinylidene fluoride and magnetite nanoparticles-based nanocomposites

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Abstract

In the present study, the effect of size distribution of magnetite nanoparticles in a PVDF matrix on the magnetic properties of PVDF ? Fe O nanocomposites was experimentally and theoretically investigated. The size distribution of nanopar- 3 4 ticles in polymer matrix and morphology of the nanocomposites were studied by the means of scanning electron micro- scopy and atomic force microscopy. It was found that when the Fe O nanoparticles are introduced into the polymer 3 4 matrix, their coagulation takes place. The increase in the size of the particles depends on their concentration in the polymer matrix, the type of polymer (polar, non-polar, its viscosity, etc.), reaction temperatures, etc. In addition, when Fe O 3 4 nanoparticles are introduced into the polymer network, the oxidation of the surface layer of particles occurs and the magnetic size decreases. Consequently, the reduced magnetic properties may also be observed. The hysteresis loops have been recorded in small magnetic field range. It was found that the magnetic hysteresis parameters depend on the size and concentration of Fe O nanoparticles. Theoretical calculations were compared with experimental results obtained from 3 4 M(H) measurements. The reasons of differences between theoretical and experimental results have been explained. Keywords Magnetite  Nanocomposite  Polymer  Hysteresis  Polyvinylidene fluoride Introduction nanocomposites attract significant academic and industrial interest because of their relatively easy and low-cost pro- Magnetic nanomaterials are drawing increased attention ducing technology. due to their remarkable physical properties. Superparam- The formation of unique properties of polymer-based agnetic iron oxide nanoparticles, especially magnetite magnetic nanocomposites depends on many factors such as phase and nanocomposites based on Fe O nanoparticles, particles size and shape, degree of dispersion, 3 4 have attracted interest from research due to possible concentration. applications of such materials in various fields [1, 2]. The The determination of the size of the Fe O nanoparticles 3 4 combination of different materials allows to make com- before and after their introduction into the polymer matrix pletely new composite materials with a wide range of has been investigated in our early works [4]. The change in functional properties: mechanical, chemical, electrical, nanoparticle size depends on the type of polymer. magnetic, optical and many others [3]. Among these In the presented work, the dependence of the average nanomaterials, thermoplastic polymer-based magnetic size of Fe O nanoparticles in the polymer matrix on its 3 4 volume content and the dependence of the magnetic properties of the composites (saturation magnetization, residual magnetization, coercive force, etc.) on the size and & M. A. Ramazanov mamed_r50@mail.ru; nanomaterials@bsu.edu.az concentration of the filler have been investigated. Baku State University, Z. Khalilov Str. 23, AZ 1148 Baku, Azerbaijan Institute of Physics, National Academy of Sciences of Azerbaijan, Pr. H. Javid 131, Baku, Azerbaijan 123 Journal of Theoretical and Applied Physics The samples of nanocomposites were obtained by hot Experimental details pressing method at melting point of PVDF under 15 MPa pressure within 4 min on further cooling to room temper- Materials ature [2]. Polyvinylidene fluoride (PVDF) is a polar polymer that has a density of 1.78 g/cm at 25 C, melting point at the Results and discussion T = 177 C. Magnetite nanoparticles were obtained by co-precipita- Figure 1 shows SEM images of nanocomposites based on tion method in an alkaline medium. The average PVDF ? Fe O at various magnetite contents. As can be nanoparticle size is 7–15 nm [1, 2]. 3 4 seen from the figure, for 1 and 3% volume contents of the filler, the sizes of magnetite nanoparticles in matrix are Methods 13–21 nm and 29–40 nm, respectively. Using SEM ima- ges, approximately 100 particle sizes were taken for sta- Scanning electron microscopy (SEM) tistical parameters calculation. The values of parameters in Gaussian and lognormal The distribution of magnetite nanoparticles in the polymer distribution of the Fe O nanoparticles size in PVDF matrix has been studied by scanning electron microscopy 3 4 matrix are reported in Tables 1 and 2, respectively. (SEM, JEOL JSM-7600 F). Scanning was carried out in As can be seen from Table 2, the values of the standard SEI mode with an accelerating voltage of 15 kV and a deviation indicate a narrow lognormal particle size distri- working distance of 4.5 mm. bution. The values of the polydispersity index confirm the monodispersity PVDF ?Fe O nanocomposites system. AFM analysis 3 4 This shows that the size distribution of Fe O particles in 3 4 polymer matrix is fairly good and can be described by a The morphology of the nanocomposites was studied using lognormal distribution function: atomic force microscopy Integra Prima (NT-MDT, Zele- nograd). For the scan used special silicon cantilevers fab- ln x  ln x ricated by plasma etching method with the needle radius of pffiffiffiffiffiffi f ðxÞ¼  exp 2r 2pr  x curvature of 20 nm and the resonance frequency was 1–5 Hz. Scan area was 2 9 2 mm. The measurements It is also clear from the table that the nature of the were taken in the semi-contact microscopy mode in air; the distribution of the Fe O particles in the polymer matrix, as 3 4 amplitude of cantilever’s oscillation was fixed while a function of their concentration and time, does not change. determining the surface topography. The scanning speed Only the distribution parameters:ln x and r depend on the and the number of scanned lines of the image are 256 and concentration of the particles in the polymer matrix and on 1,969 Hz, respectively. the time. During coagulation, the dependence of the aver- age particle diameter on time is analogous to the depen- Method for studying magnetic properties dence of the average particle diameter on the number of particles (concentration), according to the theory [5]. Measurements: Magnetization curves acquired at 300 K Figure 2 shows the lognormal distribution of Fe O 3 4 (room temperature) by a Quantum Design SQUID mag- nanoparticles in PVDF matrix at different volume contents. netometer in the field range ± 50 kOe. The magnetization The dependence of the average size of Fe O nanopar- 3 4 is reported per gram of measured sample. ticles in PVDF matrix on their concentrations was studied. Figure 3a, b represents the dependence of the average Synthesis of nanocomposites particle sizes of Fe O nanoparticles in the polymer matrix 3 4 on volume content. The polymer nanocomposite materials were prepared as As can be seen from Fig. 3a, b, the dependence curve of follows: poly(vinylidene fluoride) was solved in the Fe O particles diameter on the concentration in PVDF 3 4 dimethylformamide (DMF) solvent, at the room tempera- matrix is complicated. At low concentrations, this depen- ture. Magnetite nanoparticles were added into the polymer dence for PVDF matrix is weak. This is due to the particle solution and stirred within 2 h in order to prepare a and polymer properties. Coagulation of particles also homogeneous mixture. In order to remove the solvent from depends on the viscosity of the polymer which it has during the mixture, it was evaporated within 1 day. the preparation of the composite. In a medium with a lower viscosity, the coagulation process will happen faster. As 123 Journal of Theoretical and Applied Physics Fig. 1 SEM images of nanocomposites based on PVDF ? Fe O . a PVDF ? 1%vol Fe O , b PVDF ? 3%vol Fe O 3 4 3 4 3 4 Table 1 Geometric values of the parameters (distribution interval, average value (d), standard deviation (r), asymmetry (as), excess (e) and polydispersity index (PDI)) of Fe O particles size distribution in PVDF matrix 3 4 Sample d - d (nm) r GA e PDI min max d (nm) pvdf ? 1% Fe O 13.2–57.2 23.83 1.403 1.547 2.264 1.789 3 4 pvdf ? 3% Fe O 17–54.2 27.92 1.196 1.22 1.453 1.421 3 4 Table 2 The logarithmic values of the parameters (distribution interval, average value (d), standard deviation (r), asymmetry (as), excess (e) and polydispersity index (PDI)) of Fe O particles size distribution 3 4 sample d - d (nm) r GA e PDI min max d (nm) pvdf ? 1%Fe O - 18.14–16.68 - 17.62 0.0516 0.6435 0.0103 1.00 3 4 pvdf ? 3% Fe O - 17.89–16.73 - 17.434 0.039 0.535 - 0.208 - 1.00 3 4 Fig. 2 The size distribution function of Fe O particles in 3 4 the PVDF polymer matrix: a PVDF ? 1% Fe O , 3 4 b PVDF ? 3% Fe O 3 4 the concentration of the filler in the matrix increases, the d ¼ 6:67 þ 5000:0  u ð1Þ Fe O 3 4 viscosity of the medium changes and the coagulation At high concentrations of the filler, the saturation condition changes as well. occurs, reaching at the maximum value of the coagulated The linear part of the d(u) dependence curve (low particle diameter, which can be described with an expo- concentration) can be described by using the following nential law (Fig. 3a). equations: 123 Journal of Theoretical and Applied Physics Fig. 3 Dependence of the diameter of Fe O nanoparticles 3 4 on their concentration in polymer PVDF matrix. a High content of the filler; b low content of the filler The theory of coagulation of nanoparticles in solutions mixture and the i-th component, and x is the fraction of the component in the medium. From the latter it is possible to at their low concentrations is known. According to this theory, the number of particles during coagulation determine the kinematic (further dynamic) viscosity of the mixture: decreases according to the law [6, 7] ! ! dn n ¼k  n m ¼ exp exp x lg lgðÞ m þ 0:6 mix i i dt i¼1 The value of r is defined as: The obtained results are consistent with AFM 8kT k ¼ ð2Þ illustrations. 3g Morphology of the samples and the degree of dispersion where g is the viscosity of medium. of inorganic phase in the polymer matrix were investigated using atomic force microscopy (AFM) (Fig. 4). AFM By the definition u ¼ , where V , V is the volume of s s observation showed that the size of the dispersed phases solid phase and medium, respectively. Since V ¼ N  V s 0 N S increases with increasing filler content in the nanocom- and n ¼ ¼ , we rewrite the last differential equation in V V 0s posites. The sizes of Fe O nanoparticles are 22, 33 and 3 4 the following form: 45 nm for 1, 3 and 6% volume content of filler, respec- dV tively. These results were found to be consistent with the ¼k u dt results obtained from the theoretical calculations. The magnetic properties of PVDF ? Fe O -based The solution is V ¼ k  u þ V . In the latter expres- 0t 0 0 3 4 sion, if we substitute d ,we will get the following formula: nanocomposites were studied by experimental and theo- 0t retical investigation. Figure 6 illustrates the experimental 2k u t d ¼ d 1 þ 0t 0 hysteresis loops of magnetic polymer composite materials pd with different volume contents of the filler. The expression obtained is valid for low volume content M(H) magnetization versus magnetic field curves of of particle. As can be seen, the diameter of nanoparticles PVDF ? Fe O -based nanocomposites for different filler 3 4 aggregated is a linear function of concentration, which is concentrations have a similar shape (superimposable). In consistent with the previous results obtained (Fig. 3b). At this case, only the 0–50 KOe section of the M(H) curve is high concentration of the filler, the last expression should informative. The inset at the left panel demonstrates be rewritten with the help of such a function that the value M(H) magnetic curve of PVDF ? Fe O -based nanocom- 3 4 of the function should asymptotically approach to the fixed posites at low magnetic field. However, the whole value ‘‘d’’ when the value of the variable is high. m(H) curve of PVDF ? Fe O sample is coherent with a 3 4 The values of ‘‘k’’ were calculated with the help of (2. SPM behavior of this material. The inset on the left shows To determine the viscosity of the mixture, the Walter for- a small hysteresis loop close to H = 0 which is within the mula was used [7, 8]: margin of error (Table 3). n Figure 6a, b shows the theoretical magnetization versus lg lgðÞ m þ 0:8¼ x lg lgðÞ m þ 0:6 magnetic field curve and the magnetic susceptibility curve mixture i i i¼1 of a composite based on PVDF matrix and magnetite nanoparticles with size of 20 nm. Numerical differentiation where c and c are the kinematic viscosities of the mix i was carried out by the method [9, 10]. 123 Journal of Theoretical and Applied Physics Fig. 4 AFM image of PVDF ? Fe O nanocomposites. a PVDF ? 1 vol% Fe O , b PVDF ? 3 vol% Fe O and c PVDF ? 6 vol% Fe O 3 4 3 4 3 4 3 4 be seen from Figs. 5 and 6a, the magnetic field dependence Table 3 Results obtained from magnetic measurements of the magnetization obtained from the experiments and Sample Ms Mr calculated theoretically is close to each other for low PVDF ? 1 vol% Fe O 2.24 0.022 magnetic field. 3 4 PVDF ? 3 vol% Fe O 8.01 0.073 It is known that for dispersed systems, during the 3 4 PVDF ? 6 vol% Fe O 8.12 0.19 magnetization, the value of the saturation magnetization 3 4 can be given by the following equation: M ¼ u M ð3Þ s m As can be seen from Fig. 6a, b, the magnetization curves where M , M are the saturation magnetizations of the have the hysteresis loop. This is typical for particles which composite and the filler, respectively, and u is the volume have many magnetic domains. The hysteresis parameters of content of the filler. the nanocomposites (saturation magnetization, residual To explain this, suppose that the geometric sizes of the magnetization, coercive force, etc.) depend on the size and nanoparticles (dt) are not equal to the magnetic sizes of the concentration of Fe O particles. As the size and concen- 3 4 nanoparticles (dm). tration of Fe O particles increase, the number of magnetic 3 4 For comparison of magnetic sizes with the geometric domains increases in the both particle and medium. As can sizes of nanoparticles, we use the following equations: Fig. 5 M(H) Magnetization versus magnetic field curves of b Experimental magnetization versus magnetic field M(H) curves of PVDF ? Fe O -based nanocomposites. a (1) PVDF ? 1 vol% PVDF ? Fe O -based nanocomposites under low magnetic filed for 3 4 3 4 Fe O (2) PVDF ? 3 vol% Fe O (3) PVDF ? 6 vol% Fe O . PVDF ? 1% Fe O 3 4 3 4 3 4 3 4 123 Journal of Theoretical and Applied Physics Fig. 6 Theoretically calculated magnetic properties of PVDF ? Fe O 3 4 nanocomposites. a Magnezitation versus magnetic field M(H) b susceptibility versus magnetic field curvesv(H) where the size decreases (i.e., the oxidization of the surface V ¼ N  d t t layer is close to the lattice parameter of the particle, a = 0.839 nm). where u ; u and V can be given as below: t m m u ¼ V =V; u ¼ V =V and V ¼ N  d t m m m t m m p Conclusion ¼ N  ðÞ d  x m t It was found that when the Fe O particles are introduced 3 4 where V, V and V are the volumes of medium, solid and t m into the polymer matrix, their coagulation takes place. The magnetic phase, respectively. Then, by using the expres- increase in the particle size depends on their concentration sion for the concentration of the magnetic phase, we obtain in the polymer matrix, the type of polymer (polar, non- the relation between geometrical and magnetic phase: polar, viscosity, etc.), reaction temperatures, etc. When 3 Fe O particles are introduced into the polymer matrix, at 3 4 u =u ¼ d =ðd þ xÞ ¼ a t m t the same time with the coagulation, the oxidation of their After the manipulation of the last expression, we get the surface layer also occurs and the magnetic size decreases cubic equation: and hence the magnetic characteristics are reduced. It 3 2 2 3 becomes clear that the magnetic hysteresis parameters x  3  d x þ 3  d x ð1  aÞd ¼ 0 ð4Þ g g depend on the size and concentration of Fe O particles in 3 4 The last equation was solved by the Cardan method the polymer matrix. Theoretical calculations were com- [11]. Table 4 reports the results obtained from cubic pared with experimental results obtained from M(H) mea- equation. It should be noted that the magnetic properties of surements. At the same time, it was shown that the nanocomposites are independent on the type of the magnetic field dependence of the magnetization obtained polymer. from the experiments and calculated theoretically is close It can be concluded that the thickness of the polymer to each other for low magnetic field. With increasing layer around nanoparticle rises with the increasing size of nanoparticle size, the difference between theoretical and the nanoparticles and it also depends on the properties of experimental values increases. It is related to the fact that the medium (molecular weight, polarity, viscosity, etc.). unlike to the reality, theoretically the magnetite nanopar- It can also be seen from the table that in all cases the ticles are accepted to be single-domained. particle size increases, except for d = 20 nm, u = 0.03, Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creative Table 4 The result obtained from cubic Eq. (4) commons.org/licenses/by/4.0/), which permits unrestricted use, dis- tribution, and reproduction in any medium, provided you give d (nm) u u x (nm) t m appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were 20 0.01 0.371 46.7 made. 40 0.01 0.323 87.3 20 0.03 0.0254 - 1.07 30 0.03 1.33 76.9 References 30 0.06 1.35 55.4 1. Ramazanov, M.A., Hajiyeva, F.V., Maharramov, A.M., Di 40 0.07 1.35 Palma, L., Sannino, D., Makoto Takafuji, H.M., Mammadov, U., Hasanova, A., Shirinova, H.A., Bayramova, Z.A.: New magnetic 123 Journal of Theoretical and Applied Physics polymer nanocomposites on the basis of isotactic polypropylene 7. Evdokimov, I.N., Losev, A.P.: Absence of additivity of properties and magnetite nanoparticles for adsorption of ultra high fre- of petroleum mixtures. Drill. oil Technol. 1, 32–33 (2012) quency electromagnetic waves. Polym. Plast. Technol. Eng. 8. Ramazanov, M.A., Alizade, R.A., Maharramov, A.M., Hajiyeva, (2017). https://doi.org/10.1080/03602559.2017.1320721 F.V., Sultanova, J.R., Shirinova, H.A.: Theoretical and experi- 2. Shirinovaa, H., Di Palma, L., Sarasinib, F., Tirillo`b, J., Rama- mental study of the magnetic properties and size of distribution of zanov, M.A., Hajiyevaa, F., Sanninoc, D., Polichettid, M., Gal- PVDF ? Fe based nanocomposites. J. Inorg. Organomet. Polym. luzzid, A.: Synthesis and characterization of magnetic Mater. (2018). https://doi.org/10.1007/s10904-018-0863-2 nanocomposites for environmental remediation. Chem. Eng. 9. Bakhvalov, N.S., Zhidkov, N.P., Kobelkov, G.M.: Numerical Trans. 47, 103–108 (2016) Methods. Nauka, Moscow (1975) 3. Stabik, J., Chrobak, A., Haneczok, G., Dybowska, A.: Magnetic 10. Krylov, V.I., Bobkov, V.V., Monostyrny, P.I.: Computational properties of polymer matrix composites filled with ferrite pow- Methods, vol. 2, p. 399. Nauka, Moscow (1977). (Russian) ders. Arch. Mater. Sci. Eng. 48(2), 97–102 (2011) 11. Mathematical Handbook for Scientists and Engineers: Defini- 4. Ali-zade, R.A., Ramazanov, M.A., Sadykhov, R.Z.: Size distri- tions, Theorems, and Formulas for Reference and Review (Dover bution of magnetite nanoparticles in a polymer matrix. Ukr. Civil and Mechanical Engineering) [Granino A. Korn, Theresa J. Funct. Mater. 16(2), 183–189 (2009) M. Korn], p. 832. Nauka, Moscow (1973) 5. Shchukin, E.D., Pertsov, A.V., Amelina, E.A., Zelenev, A.S.: Colloid and Surface Chemistry, vol. 12, p. 774. Elsevier Science, Amsterdam (2001) Publisher’s Note 6. Gerasimov, Y.I., Dreving, V.P., Eremin, E.N., Kiselev, A.V., Springer Nature remains neutral with regard to jurisdictional claims in Lebedev, V.P., Panchenkov, G.M., Shlygin, A.I.: Kursfizich- published maps and institutional affiliations. eskojhimii [Course in Physical Chemistry], vol. 2, p. 624. Khi- miya, Moscow (1973). (In Russian)

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Journal of Theoretical and Applied PhysicsSpringer Journals

Published: May 28, 2018

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