The results of theoretical and experimental studies of the effect of the perturbation of magnetization of 
magnetic fluid in the initial part of magnetization curve, caused by thermal oscillations in the adiabatic 
sound wave are considered. The measurements were carried out on the magnetic colloid samples with dif-ferent viscosity of the dispersion medium within the frequency band of 20-60 kHz. In this frequency band, 
studied samples are characterized by the absence of thermal relaxation of the magnetization. The compari-son of the conclusions of the model of thermal relaxation of magnetization and the experimental results 
makes it possible to obtain information about the features of the rheology for the nearest molecular envi-ronment of a particle − nanorheology.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3635

Aref'ev, I.M.

Aref'eva, T.A.

Kazakov, Yu.B.

Korotkovskii, V.I.

Neruchev, Yu.A.

Polunin, V.M.

Ryapolov, P.A.

Storozhenko, A.M.

Tantsyura, A.O.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 6 No 3, 03056(4pp) (2014) Том 6 № 3, 03056(4cc) (2014) 
 
 
The article was reported at the International Conference «The Advanced Technology, Equipment and Analytical Systems for Materials», Kursk, 13-14 May, 2014 
2077-6772/2014/6(3)03056(4) 03056-1  2014 Sumy State University 
Features of the Rotational Kinetic of Magnetic Fluid Nanoparticles 
 
A.M. Storozhenko1,*, P.A. Ryapolov1, A.O. Tantsyura1, V.M. Polunin1, I.M. Aref'ev2, T.A. Aref'eva2, 
Yu.B. Kazakov2, Yu.A. Neruchev3, V.I. Korotkovskii3 
 
1 Southwest State University, Kursk, Russia 
2 Ivanovo State Power University named after V.I. Lenin, Ivanovo, Russia 
3 Kursk State University, Kursk, Russia 
 
(Received 19 May 2014; revised manuscript received 07 July 2014; published online 15 July 2014) 
 
The results of theoretical and experimental studies of the effect of the perturbation of magnetization of 
magnetic fluid in the initial part of magnetization curve, caused by thermal oscillations in the adiabatic 
sound wave are considered. The measurements were carried out on the magnetic colloid samples with dif-
ferent viscosity of the dispersion medium within the frequency band of 20-60 kHz. In this frequency band, 
studied samples are characterized by the absence of thermal relaxation of the magnetization. The compari-
son of the conclusions of the model of thermal relaxation of magnetization and the experimental results 
makes it possible to obtain information about the features of the rheology for the nearest molecular envi-
ronment of a particle − nanorheology. 
 
Keywords: Magnetic fluid, Acoustomagnetic effect, Relaxation of magnetization, Magnetic nanoparticle, 
Magnetization curve. 
 
 PACS numbers: 62.80. + f, 43.35. + d 
 
 
                                                                
* storogenko_s@mail.ru 
1. INTRODUCTION 
 
Magnetic fluids (MF) are stable systems of magnetic 
nanoparticles in a carrier liquid [1]. They are widely 
used in various branches of engineering [2-3]. Struc-
ture of real MF is studied by methods of acoustic spec-
troscopy [1, 4-6], Magneto-granulometric analysis [7], 
Magnetorelaxometry (MRX) [2], Acousto-granulometric 
analysis [8] and others. 
Data on the rheology of the nearest molecular envi-
ronment of magnetic fluid nanoparticle can be obtained 
by analyzing the initial part of the curve of acous-
tomagnetic effect (AME) [9]. AME curve is a depend-
ence of the relative amplitude of e.m.f. in the coil on the 
magnetic field voltage [1]. 
The aim of this paper is testing the proposed meth-
od on a series of MF-samples with different carrier liq-
uids. The subject of study is the effect of the perturba-
tion of the magnetization of a magnetic colloid caused 
by ultra-low thermal vibrations in the adiabatic sound 
wave, and its relaxation. 
 
2. THEORETICAL BASIS 
 
The equation of acoustomagnetic effect for low-
concentration MF is 
 
 
       
max 0
1 2 2
* 0
/ ( / )
1 / 1 / 1
S
T d H
M M M M
M M N M  

   
               
 (1) 
 
where ΔM / Mmax is relative increment in the amplitude 
of the magnetization, M0 is the magnetization of the me-
dium in the unperturbed state, MT is the temperature 
magnetization coefficient, MH is the magnetic suscepti-
bility, Nd is the dynamic demagnetization factor [10], 
γ*  qTc2/Cp, q is the thermal expansion coefficient, T is 
the absolute temperature, c is the sound speed in the 
MF, Cp is the specific heat capacitance at constant pres-
sure,  is the circular frequency of oscillation, 
  1(1 + NdMH) – 1 is the relaxation time of the magnetic 
moment. 
The initial part of AME curve is a linear dependence 
on magnetic field voltage [11-12]. Its angular coefficient is 
 
 
   
 

   




  
       
  
  
 
1 2
1
2
tg ( / ) 1 1
1
A S d
T
M k N
T
 (2) 
 
where χ is initial magnetic susceptibility of MF, 
k′  qc2/Cp. 
The expression (2) can be used for comparing with 
the experimental results in frequency band, which in-
cludes the area of thermal relaxation of the magnetiza-
tion. 
With respect to low-concentration MF in mono-
dispersed approximation it is possible to use a well-
known generalization of Langevin theory of paramag-
netism for superparamagnetics [3, 13]: 
 
 
2
0 * 0 *
0 03 3
SM m nm
k T k T
 
   , (3) 
 
where m* is the magnetic moment of a nanoparticle, n is 
the volume concentration, 0 is the magnetic constant, 
k0 is the Boltzmann constant.  
After the substitution of (3) for (2), we obtain 
 
 
2
0 *
2
0
1
( )
1 / 3
3 1 ( )
A
k
m ktg
k T






 

, (4) 
 
 A.M. STOROZHENKO, P.A. RYAPOLOV, ET AL. J. NANO- ELECTRON. PHYS. 6, 03056 (2014) 
 
 
03056-2 
where
2
0 * 0 *
0 0
d d SN nm N M mk
k T k T
 
   [14]. 
The obtained expression (4) contains the dependence 
of tgθА on the frequency of sound oscillations  and the 
thermal relaxation time of the particle magnetization . 
From the formula (4) we obtain tgθ2 which is the an-
gular coefficient of the initial part of AME-curve when 
Nd  0, k"  0 
 
 
2
0 *
2 2
0
1 ( )
3 1 ( )
m k
tg
k T
 


 
 

, (5) 
 
the expression for tgθ3 when (ωτ)20 
 
 0 * 0 *
3
0 0
1 1
3 1 / 3 3
m mk k
tg
k T k k T k
 

  
   
  
, (6) 
 
the expression for tgθ4 when (ωτ)21 
 
 0 *
4
03
m
tg
k T

  . (7) 
 
Henceforward, the conclusions of the model theory of 
thermal relaxation in the form of the formulas (4)-(7) 
will be we compared with the experimental results. 
 
3. DECRIPTION OF THE OBJECTS AND 
METHODS OF RESEARCH 
 
The samples of magnetic fluids on the high-
dispersive magnetite Fe3O4 basis stabilized with oleic 
acid С8Н17СНСН(СН2)7СО—О-Н+ in different carrier 
liquids were studied during the experiment: 
 Sample MF-1, the carrier is kerosene; 
 Sample MF-2, the carrier is Polyethylsiloxane-2; 
 Sample MF-3, the carrier is mineral hydrocarbon 
oil; 
 Sample MF-4, the carrier is Polyethylsiloxane-4; 
 Sample MF-5, the carrier is synthetic hydrocarbon 
oil. 
These samples were supplied by the scientific re-
search laboratory of Applied ferrohydrodynamics of 
Ivanovo State Power Engineering University. The sam-
ples have similar magnetic properties: saturation mag-
netization and initial magnetic susceptibility; these 
make it possible to determine the potential influence of 
the carrier liquid properties on time of thermal relaxa-
tion of the MF magnetization. 
The physical parameters of the MF samples are shown 
in Table 1. The following notations are used: density , 
volume concentration of the solid phase , volume con-
centration of the magnetic phase М, initial magnetic 
susceptibility χ, saturation magnetization MS, sound 
speed с in the ―MF-glass tube‖ system, thermal expan-
sion coefficient q, specific heat capacitance at constant 
pressure Ср, plastic viscosity . 
The parameters ρ, q and Cp were determined exper-
imentally in the laboratory of molecular acoustics of 
Kursk State University at the Department of General 
Physics [15]. 
For the MF test samples the time of the Brownian 
rotational diffusion of colloidal particles was determined 
according to B  3VηS0 / k0T, where V is the volume of 
the particle, ηS0 is the static shear viscosity of the carri-
er liquid. В for the samples is MF-1 τВ  2 s, MF-2 
τВ  6 s, MF-3 В  21 s, MF-4 τВ  26 s, MF-5 
τВ  46 s. 
The frequency-field dependence of the AME was 
studied using research facility in the Nanoscale acous-
tics laboratory of Southwest State University. The de-
tailed descriptions of the research facility block scheme 
and the experimental techniques are given in [8, 11]. 
Magnetic parameters χ and MS are calculated on the 
basis of the magnetization curves М(Н) obtained in the 
same laboratory using ballistic method [1]. 
 
4. RESULTS 
 
For getting the features of the rheology for the nearest 
molecular environment of a particle we compared theoret-
ical conclusions with the experimental data. For all the 
studied MF samples the dependence of the relative ampli-
tude of the AME on the value of the magnetic field within 
the frequency band of 20-60 kHz were obtained. 
We compared theoretical values of angular coeffi-
cients of initial parts of AME-curves with experimental 
results. Fig. 1 shows the plots, constructed using formu-
las (4)-(6), of the dependences of the tangent of the an-
gle of inclination of the initial parts of the AME curves 
on frequency (lines) and the corresponding experimental 
data (points). The line tgθ1 corresponds to formula (4), 
line tgθ2 has been constructed using formula (5) taking 
into account Nd  0, and line tgθ3 has been constructed 
using formula (6) under the condition (ωτ)2  0.  
Calculation using expression (7) within the limits of an 
infinitely large thermal relaxation time gives us the fol-
lowing numerical values of the tangent of the angles of 
inclination: 0.080, 0.072, 0.078, 0.075, and 0.070, respec-
tively, for samples MF-1, MF-2, MF-3, MF-4, and MF-5. 
The values of magnetic moments of the nanoparti-
cles m* were calculated according to expression (3). We 
also used values τВ and values of the dynamic demag-
netizing factor Nd which were obtained experimentally 
in the frequency band of 10-60 kHz in [10]. 
We can state that the dependence tgθ3(ν) corre-
sponds the most to the experimental data. In this case, 
the chief criterion is the inclination of the theoretical  
 
Table 1 – Physical properties of the samples under study 
 
 ρ, kg/m3 φ, % φМ, % χ 
Ms, 
kA/m 
c, m/sec q, 1/K 
Cp, 
J/kgК 
η 
(Pa·sec) 
MF-1 1252 10,6 8,5 2,8 35 937 0,00091 1489 0,012 
MF-2 1385 10,3 8,3 2,5 34 930 0,0007 1375 0,125 
MF-3 1282 10,3 8,2 2,6 34 1005 0,00082 1283 0, 368 
MF-4 1405 10,2 8,2 2,6 34 954 0,00069 1326 0, 630 
MF-5 1290 10,4 8,3 2,4 33 1024 0,00082 1284 1,110 
 
 
 
 FEATURES OF THE ROTATIONAL KINETIC OF MAGNETIC FLUID NANOPARTICLES J. NANO- ELECTRON. PHYS. 6, 03056 (2014) 
 
 
03056-3 
 
Fig. 1 – The theoretical and experimental values of tgθ: sample MF-1 (a); sample MF-2 (b); sample MF-3 (c); sample MF-4 (d); 
sample MF-5 (e) 
 
curve toward the frequency axis. As concerns a certain 
displacement of dependences tgθ3(ν) along the Y-axis 
relative to the trend of the experimental values, it may 
be the result of proximity of the parameter values enter-
ing into k' and k'', e.g., the m* values obtained from the 
single particle approximation. 
The correspondence between experimental data and 
theoretical results calculated according to the formula 
(6) indicates the absence of the thermal relaxation of 
the MFs magnetization in the initial part of the field 
dependence of AME in the frequency band of 10-60 kHz. 
The ―relaxation frequency‖ values of νR ≡ 1/2В for 
the samples MF-1, MF-2, MF-5, MF-3, and MF-4 are 
80 kHz, 27 kHz, 7.6 kHz, 6.1 kHz and 3.5 kHz respec-
tively. Therefore, if ωτВ ≈ 1 is considered as the criterion 
of the thermal relaxation of the magnetization, then for 
the MF test samples (except sample MF-1) in the fre-
quency band of 20-60 kHz this phenomenon should have 
been confirmed experimentally. 
Nevertheless, what experimentally confirmed is the 
hypothesis according to which thermal relaxation is 
absent in the studied colloids, which is "low-probable" 
from the viewpoint of notions on rotational Brownian 
particle diffusion in a Newtonian fluid. 
Thus, the fact of the absence of the thermal relaxa-
tion of the magnetization in relation to the values of the 
slope of the initial parts of the curves of the magnetiza-
tion and the acoustomagnetic effect was experimentally 
obtained. Consequently, the surrounding environment 
of the nanoparticle in this case exhibits the properties of 
non-Newtonian fluid, which is characterized by special 
relations between the strain rate and stress. 
The shearing strain of the medium, caused by the 
rotational oscillations of the nanoparticles, can be de-
scribed by the Maxwell model, which is well-known in 
the viscoelastic media theory [16, 17]. The Maxwell me-
chanical model consists of a series-connected spring and 
piston (Fig. 2). In this case, the medium strain in the 
neighborhood of a nanoparticle is composed of two 
parts. The first part is instantaneous elastic strain, 
which is characterized by the shear modulus G. The 
second part is retarded viscous strain caused by me di-
um flotation, characterized by the shearing viscosity . 
 
 
Fig. 2 – The offered model 
 
The monomolecular layer of the stabilizer serves as 
an elastic component in the model under study, and the 
circumambient dispersion medium serves as a damper. 
Besides, neighboring particles of the disperse phase can 
retard the establishment of the equilibrium orientation 
of the magnetic moment of a particle. This occurs due to 
steric interaction. 
The isolation of the elastic properties of the stabi-
lizer coating has physicochemical nature: a molecule of 
the oleic acid on its polar end О-Н+ is attracted to the 
solid phase surface forming thereon a dense unimolecu-
lar film of δ ≈ 2 nm thickness. Relatively closely-packed 
molecular structure of the stabilizer causes predomi-
nantly elastic shear strain of the coating which is char-
acterized by short relaxation time. Considerable viscosi-
ty of the dispersion medium blocks the flotation pro-
cesses at low rotational oscillations of nanoparticles. 
―Instantaneous‖ shear strain of the stabilizer coating 
under ultra-low temperature oscillations provides sig-
nificant decrease of the values of the thermal relaxation 
time of the magnetization τ compared to the Brownian 
rotational relaxation time В. 
 
5. CONCLUSION 
 
The comparison of the conclusions of the model of 
thermal relaxation of magnetization and the experi-
mental results makes it possible to obtain information 
 
0 
0.01 
0.02 
0.03 
0.04 
0.05 
0.06 
10 20 30 40 50 60 70 
ν, кГц 
 
tgθ 
 tgθ1 
 
tgθ2 
 
tgθ3 
 
 
 
0 
0.01 
0.02 
0.03 
0.04 
0.05 
10 20 30 40 50 60 70 
ν, кГц 
 
tgθ 
 tgθ1 
 
tgθ2 
 
tgθ3 
 
 
a b c 
d e 
H 
G 
 
G 
 
Nanoparticle of MF Maxwell model 
 A.M. STOROZHENKO, P.A. RYAPOLOV, ET AL. J. NANO- ELECTRON. PHYS. 6, 03056 (2014) 
 
 
03056-4 
about the features of the rheology for the nearest mo-
lecular environment of a particle − nanorheology. 
The process of the magnetization perturbation of 
magnetic fluid caused by ultra-small thermal oscilla-
tions in a sound wave is largely determined by the rota-
tional mobility of magnetic nanoparticles; the last one is 
determined by the viscoelastic properties of the medi-
um. In this regard, the researches carried out in this 
direction are of great interest. 
However, from both the experimental and theoreti-
cal point of view there are problems with the reliability 
of the obtained results and their interpretation. In re-
spect to experiments the study of MF samples with low 
concentrations, as well as the displacement of the lower 
boundary of the magnetic force band to the area of small 
values are of great interest. From the theoretical per-
spective, there is a problem of developing a theoretical 
model which takes into account the polydispersity of the 
system and the interparticle interaction. 
 
ACKNOWLEDGMENT 
 
We are grateful for funding of this work via 
theGrant of the President of the Russian Federation for 
support of young researchers №14.Z56.14.5515-МК 
―The Development of an integrated methodology of 
acoustomagnetic researching of composition and struc-
tural parameters of magnetic nanoparticles in ferroflu-
ids and ferrosuspensions‖. 
 
REFERENCES 
 
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magnetic fluids (M.: FIZMATLIT: 2012). 
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3. S. Chikazumi, Physics of Ferromagnetism (Oxford 
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4. J. Kúdelčík, P. Bury, V. Závišová, M. Timko, 
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5. B. Zieliński, A. Skumiel, A. Józefczak, E. Vandeweert, 
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9. V.M. Polunin, Akusticheskii Zhurnal 29 No 6, 820 (1983). 
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180 (2012). 
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G.V. Karpova, V.M. Polunin, M.M. Tan, Magnetohydrody-
namics 47 No 4, 345 (2011). 
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of molecular acoustics (M: Nauka: 1964). 
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English

Features of the Rotational Kinetic of Magnetic Fluid Nanoparticles

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 6 No 3, 03056(4pp) (2014) Том 6 № 3, 03056(4cc) (2014)   The article was reported at the International Conference «The Advanced Technology, Equipment and Analytical Systems for Materials», Kursk, 13-14 May, 2014 2077-6772/2014/6(3)03056(4) 03056-1  2014 Sumy State University Features of the Rotational Kinetic of Magnetic Fluid Nanoparticles  A.M. Storozhenko1,*, P.A. Ryapolov1, A.O. Tantsyura1, V.M. Polunin1, I.M. Aref'ev2, T.A. Aref'eva2, Yu.B. Kazakov2, Yu.A. Neruchev3, V.I. Korotkovskii3  1 Southwest State University, Kursk, Russia 2 Ivanovo State Power University named after V.I. Lenin, Ivanovo, Russia 3 Kursk State University, Kursk, Russia  (Received 19 May 2014; revised manuscript received 07 July 2014; published online 15 July 2014)  The results of theoretical and experimental studies of the effect of the perturbation of magnetization of magnetic fluid in the initial part of magnetization curve, caused by thermal oscillations in the adiabatic sound wave are considered. The measurements were carried out on the magnetic colloid samples with dif-ferent viscosity of the dispersion medium within the frequency band of 20-60 kHz. In this frequency band, studied samples are characterized by the absence of thermal relaxation of the magnetization. The compari-son of the conclusions of the model of thermal relaxation of magnetization and the experimental results makes it possible to obtain information about the features of the rheology for the nearest molecular envi-ronment of a particle − nanorheology.  Keywords: Magnetic fluid, Acoustomagnetic effect, Relaxation of magnetization, Magnetic nanoparticle, Magnetization curve.   PACS numbers: 62.80. + f, 43.35. + d                                                                   * storogenko_s@mail.ru 1. INTRODUCTION  Magnetic fluids (MF) are stable systems of magnetic nanoparticles in a carrier liquid [1]. They are widely used in various branches of engineering [2-3]. Struc-ture of real MF is studied by methods of acoustic spec-troscopy [1, 4-6], Magneto-granulometric analysis [7], Magnetorelaxometry (MRX) [2], Acousto-granulometric analysis [8] and others. Data on the rheology of the nearest molecular envi-ronment of magnetic fluid nanoparticle can be obtained by analyzing the initial part of the curve of acous-tomagnetic effect (AME) [9]. AME curve is a depend-ence of the relative amplitude of e.m.f. in the coil on the magnetic field voltage [1]. The aim of this paper is testing the proposed meth-od on a series of MF-samples with different carrier liq-uids. The subject of study is the effect of the perturba-tion of the magnetization of a magnetic colloid caused by ultra-low thermal vibrations in the adiabatic sound wave, and its relaxation.  2. THEORETICAL BASIS  The equation of acoustomagnetic effect for low-concentration MF is          max 01 2 2* 0/ ( / )1 / 1 / 1ST d HM M M MM M N M                     (1)  where ΔM / Mmax is relative increment in the amplitude of the magnetization, M0 is the magnetization of the me-dium in the unperturbed state, MT is the temperature magnetization coefficient, MH is the magnetic suscepti-bility, Nd is the dynamic demagnetization factor [10], γ*  qTc2/Cp, q is the thermal expansion coefficient, T is the absolute temperature, c is the sound speed in the MF, Cp is the specific heat capacitance at constant pres-sure,  is the circular frequency of oscillation,   1(1 + NdMH) – 1 is the relaxation time of the magnetic moment. The initial part of AME curve is a linear dependence on magnetic field voltage [11-12]. Its angular coefficient is                        1 212tg ( / ) 1 11A S dTM k NT (2)  where χ is initial magnetic susceptibility of MF, k′  qc2/Cp. The expression (2) can be used for comparing with the experimental results in frequency band, which in-cludes the area of thermal relaxation of the magnetiza-tion. With respect to low-concentration MF in mono-dispersed approximation it is possible to use a well-known generalization of Langevin theory of paramag-netism for superparamagnetics [3, 13]:   20 * 0 *0 03 3SM m nmk T k T    , (3)  where m* is the magnetic moment of a nanoparticle, n is the volume concentration, 0 is the magnetic constant, k0 is the Boltzmann constant.  After the substitution of (3) for (2), we obtain   20 *201( )1 / 33 1 ( )Akm ktgk T , (4)   A.M. STOROZHENKO, P.A. RYAPOLOV, ET AL. J. NANO- ELECTRON. PHYS. 6, 03056 (2014)   03056-2 where20 * 0 *0 0d d SN nm N M mkk T k T    [14]. The obtained expression (4) contains the dependence of tgθА on the frequency of sound oscillations  and the thermal relaxation time of the particle magnetization . From the formula (4) we obtain tgθ2 which is the an-gular coefficient of the initial part of AME-curve when Nd  0, k"  0   20 *2 201 ( )3 1 ( )m ktgk T   , (5)  the expression for tgθ3 when (ωτ)20   0 * 0 *30 01 13 1 / 3 3m mk ktgk T k k T k        , (6)  the expression for tgθ4 when (ωτ)21   0 *403mtgk T  . (7)  Henceforward, the conclusions of the model theory of thermal relaxation in the form of the formulas (4)-(7) will be we compared with the experimental results.  3. DECRIPTION OF THE OBJECTS AND METHODS OF RESEARCH  The samples of magnetic fluids on the high-dispersive magnetite Fe3O4 basis stabilized with oleic acid С8Н17СНСН(СН2)7СО—О-Н+ in different carrier liquids were studied during the experiment:  Sample MF-1, the carrier is kerosene;  Sample MF-2, the carrier is Polyethylsiloxane-2;  Sample MF-3, the carrier is mineral hydrocarbon oil;  Sample MF-4, the carrier is Polyethylsiloxane-4;  Sample MF-5, the carrier is synthetic hydrocarbon oil. These samples were supplied by the scientific re-search laboratory of Applied ferrohydrodynamics of Ivanovo State Power Engineering University. The sam-ples have similar magnetic properties: saturation mag-netization and initial magnetic susceptibility; these make it possible to determine the potential influence of the carrier liquid properties on time of thermal relaxa-tion of the MF magnetization. The physical parameters of the MF samples are shown in Table 1. The following notations are used: density , volume concentration of the solid phase , volume con-centration of the magnetic phase М, initial magnetic susceptibility χ, saturation magnetization MS, sound speed с in the ―MF-glass tube‖ system, thermal expan-sion coefficient q, specific heat capacitance at constant pressure Ср, plastic viscosity . The parameters ρ, q and Cp were determined exper-imentally in the laboratory of molecular acoustics of Kursk State University at the Department of General Physics [15]. For the MF test samples the time of the Brownian rotational diffusion of colloidal particles was determined according to B  3VηS0 / k0T, where V is the volume of the particle, ηS0 is the static shear viscosity of the carri-er liquid. В for the samples is MF-1 τВ  2 s, MF-2 τВ  6 s, MF-3 В  21 s, MF-4 τВ  26 s, MF-5 τВ  46 s. The frequency-field dependence of the AME was studied using research facility in the Nanoscale acous-tics laboratory of Southwest State University. The de-tailed descriptions of the research facility block scheme and the experimental techniques are given in [8, 11]. Magnetic parameters χ and MS are calculated on the basis of the magnetization curves М(Н) obtained in the same laboratory using ballistic method [1].  4. RESULTS  For getting the features of the rheology for the nearest molecular environment of a particle we compared theoret-ical conclusions with the experimental data. For all the studied MF samples the dependence of the relative ampli-tude of the AME on the value of the magnetic field within the frequency band of 20-60 kHz were obtained. We compared theoretical values of angular coeffi-cients of initial parts of AME-curves with experimental results. Fig. 1 shows the plots, constructed using formu-las (4)-(6), of the dependences of the tangent of the an-gle of inclination of the initial parts of the AME curves on frequency (lines) and the corresponding experimental data (points). The line tgθ1 corresponds to formula (4), line tgθ2 has been constructed using formula (5) taking into account Nd  0, and line tgθ3 has been constructed using formula (6) under the condition (ωτ)2  0.  Calculation using expression (7) within the limits of an infinitely large thermal relaxation time gives us the fol-lowing numerical values of the tangent of the angles of inclination: 0.080, 0.072, 0.078, 0.075, and 0.070, respec-tively, for samples MF-1, MF-2, MF-3, MF-4, and MF-5. The values of magnetic moments of the nanoparti-cles m* were calculated according to expression (3). We also used values τВ and values of the dynamic demag-netizing factor Nd which were obtained experimentally in the frequency band of 10-60 kHz in [10]. We can state that the dependence tgθ3(ν) corre-sponds the most to the experimental data. In this case, the chief criterion is the inclination of the theoretical   Table 1 – Physical properties of the samples under study   ρ, kg/m3 φ, % φМ, % χ Ms, kA/m c, m/sec q, 1/K Cp, J/kgК η (Pa·sec) MF-1 1252 10,6 8,5 2,8 35 937 0,00091 1489 0,012 MF-2 1385 10,3 8,3 2,5 34 930 0,0007 1375 0,125 MF-3 1282 10,3 8,2 2,6 34 1005 0,00082 1283 0, 368 MF-4 1405 10,2 8,2 2,6 34 954 0,00069 1326 0, 630 MF-5 1290 10,4 8,3 2,4 33 1024 0,00082 1284 1,110     FEATURES OF THE ROTATIONAL KINETIC OF MAGNETIC FLUID NANOPARTICLES J. NANO- ELECTRON. PHYS. 6, 03056 (2014)   03056-3  Fig. 1 – The theoretical and experimental values of tgθ: sample MF-1 (a); sample MF-2 (b); sample MF-3 (c); sample MF-4 (d); sample MF-5 (e)  curve toward the frequency axis. As concerns a certain displacement of dependences tgθ3(ν) along the Y-axis relative to the trend of the experimental values, it may be the result of proximity of the parameter values enter-ing into k' and k'', e.g., the m* values obtained from the single particle approximation. The correspondence between experimental data and theoretical results calculated according to the formula (6) indicates the absence of the thermal relaxation of the MFs magnetization in the initial part of the field dependence of AME in the frequency band of 10-60 kHz. The ―relaxation frequency‖ values of νR ≡ 1/2В for the samples MF-1, MF-2, MF-5, MF-3, and MF-4 are 80 kHz, 27 kHz, 7.6 kHz, 6.1 kHz and 3.5 kHz respec-tively. Therefore, if ωτВ ≈ 1 is considered as the criterion of the thermal relaxation of the magnetization, then for the MF test samples (except sample MF-1) in the fre-quency band of 20-60 kHz this phenomenon should have been confirmed experimentally. Nevertheless, what experimentally confirmed is the hypothesis according to which thermal relaxation is absent in the studied colloids, which is "low-probable" from the viewpoint of notions on rotational Brownian particle diffusion in a Newtonian fluid. Thus, the fact of the absence of the thermal relaxa-tion of the magnetization in relation to the values of the slope of the initial parts of the curves of the magnetiza-tion and the acoustomagnetic effect was experimentally obtained. Consequently, the surrounding environment of the nanoparticle in this case exhibits the properties of non-Newtonian fluid, which is characterized by special relations between the strain rate and stress. The shearing strain of the medium, caused by the rotational oscillations of the nanoparticles, can be de-scribed by the Maxwell model, which is well-known in the viscoelastic media theory [16, 17]. The Maxwell me-chanical model consists of a series-connected spring and piston (Fig. 2). In this case, the medium strain in the neighborhood of a nanoparticle is composed of two parts. The first part is instantaneous elastic strain, which is characterized by the shear modulus G. The second part is retarded viscous strain caused by me di-um flotation, characterized by the shearing viscosity .   Fig. 2 – The offered model  The monomolecular layer of the stabilizer serves as an elastic component in the model under study, and the circumambient dispersion medium serves as a damper. Besides, neighboring particles of the disperse phase can retard the establishment of the equilibrium orientation of the magnetic moment of a particle. This occurs due to steric interaction. The isolation of the elastic properties of the stabi-lizer coating has physicochemical nature: a molecule of the oleic acid on its polar end О-Н+ is attracted to the solid phase surface forming thereon a dense unimolecu-lar film of δ ≈ 2 nm thickness. Relatively closely-packed molecular structure of the stabilizer causes predomi-nantly elastic shear strain of the coating which is char-acterized by short relaxation time. Considerable viscosi-ty of the dispersion medium blocks the flotation pro-cesses at low rotational oscillations of nanoparticles. ―Instantaneous‖ shear strain of the stabilizer coating under ultra-low temperature oscillations provides sig-nificant decrease of the values of the thermal relaxation time of the magnetization τ compared to the Brownian rotational relaxation time В.  5. CONCLUSION  The comparison of the conclusions of the model of thermal relaxation of magnetization and the experi-mental results makes it possible to obtain information  0 0.01 0.02 0.03 0.04 0.05 0.06 10 20 30 40 50 60 70 ν, кГц  tgθ  tgθ1  tgθ2  tgθ3    0 0.01 0.02 0.03 0.04 0.05 10 20 30 40 50 60 70 ν, кГц  tgθ  tgθ1  tgθ2  tgθ3   a b c d e H G  G  Nanoparticle of MF Maxwell model  A.M. STOROZHENKO, P.A. RYAPOLOV, ET AL. J. NANO- ELECTRON. PHYS. 6, 03056 (2014)   03056-4 about the features of the rheology for the nearest mo-lecular environment of a particle − nanorheology. The process of the magnetization perturbation of magnetic fluid caused by ultra-small thermal oscilla-tions in a sound wave is largely determined by the rota-tional mobility of magnetic nanoparticles; the last one is determined by the viscoelastic properties of the medi-um. In this regard, the researches carried out in this direction are of great interest. However, from both the experimental and theoreti-cal point of view there are problems with the reliability of the obtained results and their interpretation. In re-spect to experiments the study of MF samples with low concentrations, as well as the displacement of the lower boundary of the magnetic force band to the area of small values are of great interest. From the theoretical per-spective, there is a problem of developing a theoretical model which takes into account the polydispersity of the system and the interparticle interaction.  ACKNOWLEDGMENT  We are grateful for funding of this work via theGrant of the President of the Russian Federation for support of young researchers №14.Z56.14.5515-МК ―The Development of an integrated methodology of acoustomagnetic researching of composition and struc-tural parameters of magnetic nanoparticles in ferroflu-ids and ferrosuspensions‖.  REFERENCES  1. V.M. Polunin, Acoustic properties of nanodispersed magnetic fluids (M.: FIZMATLIT: 2012). 2. S. Odenbach, Colloidal Magnetic Fluids: Basics, Development and Application of Ferrofluids (Berlin: Springer: 2009). 3. S. Chikazumi, Physics of Ferromagnetism (Oxford University Press: 1997). 4. J. Kúdelčík, P. Bury, V. Závišová, M. Timko, P. Kopčanský, Acta Electrotechnica et Informatica 10 No3, 90 (2010). 5. B. Zieliński, A. Skumiel, A. Józefczak, E. Vandeweert, Molecular and Quantum Acoustics 26, 309 (2005) 6. T. Sawada, H. Nishiyama, T. Tabata, J. Magn. Magn. Mater. 252 186 (2002). 7. A.F. Pshenichnikov, V.V. Mekhonoshin, A.V. Lebedev, J. Magn. Magn. Mater.161, 94 (1996). 8. S.G. Emelyanov, G.V. Karpova, V.M. Paukov, V.M. Polunin, P.A. Ryapolov, Acoustical Phys. 56 No 3, 283 (2010). 9. V.M. Polunin, Akusticheskii Zhurnal 29 No 6, 820 (1983). 10. V.M. Polunin, A.O. Tantsyura, A.M. Storozhenko, P.A. Ryapolov, Acoustical Phys. 59 No 6, 662 (2013). 11. V.M. Polunin, A.M. Storozhenko, Acoustical Phys. 58 No 2, 180 (2012). 12. V.M. Polunin, A.M. Storozhenko, P.A. Ryapolov, Russ. Phys. J. 55 No 5, 536 (2012). 13. M.I. Shliomis Usp. Fiz. Nauk 112 No 3, 427 (1974). 14. A.M. Storozhenko, A.O. Tantsyura, P.A. Ryapolov, G.V. Karpova, V.M. Polunin, M.M. Tan, Magnetohydrody-namics 47 No 4, 345 (2011). 15. Y.A. Neruchev, O.S. Ryshkova, V.I. Korotkovsky, Method of experimental determination of the isobaric heat capacity of organic liquids using a differential scanning calorime-ter, (M: Standartinform: 2012). 16. I.G. Mikhaylov, V.A. Solov’ev, Yu.P. Cyrnikov The basics of molecular acoustics (M: Nauka: 1964). 17. A.A. Tager Physico-chemistry of polymers (M: Scientific World: 2007).  

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