Các đặc trưng đốt nóng cảm ứng của chất lỏng hạt nano từ và các yếu tố ảnh hưởng tt tiếng anh

MINISTRY OF
EDUCATION AND TRAINING

VIETNAM ACADEMY OF
SCIENCE AND TECHNOLOGY

GRADATE UNIVERSIY OF SCIENCE AND TECHNOLOGY 

Luu Huu Nguyen

THE CHARACTERISTICS OF
MAGNETIC INDUCTIVE HEATING
AND THEIR IMPACTS BY
THE PARTICLE ANISOTROPY AND FERROFLUID VISCOSITY

Major: Electronic materials
Code: 9.44.01.23

SUMMARY OF DOCTORAL THESIS IN MATERIAL SCIENCE

Ha Noi - 2019


This thesis was done at:
Laboratory of Magnetism and Superconductivity, Institute of Materials and
Sciene, Vietnam Academy of Science and Technology.

Supervisor: Prof., Dr. Nguyen Xuan Phuc
Assoc. Prof., Dr. Pham Thanh Phong

Reviewer 1: ......................................................

Reviewer 2: ......................................................
Reviewer 3: ......................................................

The dissertation will be defended at Graduate University of Science and Technology, 18

Hoang Quoc Viet street, Hanoi.
Time: ...h..., .../.../2019

This thesis could be found at National Library of Vietnam, Library of Graduate
University of Science and Technology, Library of Institute of Materials and Science,
Library of Vietnam Academy of Science and Technology.


INTRODUCTION
In recent decades, nanotechnology and nanoscience have been of great interest so they are
considered as a revolution in the 21st century. Nanotechnology encompasses design, analysis, fabrication and
application of structures, devices or systems by controlling the shape, size on a nanometer scale. The subject
of these technologies is nanomaterialsNanomaterials with very small sizes (about 1-100 nm) exhibit exciting
properties that are different from those of the bulk materials. Based on their size effects, nanomaterials have
open new applications in electronics, mechanics, environmental remediation, especially in biomedicine.
For dielectric and magnetic materials, inductive heating is the physical phenomenon by which the
materials become thermo-seeds when they are irradiated by proper alternating electromagnetic field. In the
case of bulk magnetic materials, the Magnetic Inductive Heating (MIH) using alternative magnetic field
(AMF) relies on two mechanisms of energy dissipation, which are energy losses due to Joule heating and
energy losses associated with magnetic hysteresis. In nano scale, it is generally known that the energy losses
associated with magnetic properties such as hysteresis loss and relaxation loss mainly contribute to the
heating.
For biomedical applications, magnetic nanoparticles (MNPs) have to be dispersed in a solvable
solvent to create nano ferrofluids. MNPs are coated by a surfactant for preventing the nanoparticles from
aggregation and keeping them well dispersed for many years. So, the nano ferrofluids in fact consist of core,

shell and solvent. Various magnetic nanoparticles such as magnetic metal nanoparticles, magnetic alloy
nanoparticles or magnetic metal oxide nanoparticles have been used as the core of nanofluids. The shell
materials can be polymer, copolymer or an oxide material. The fabrication of a magnetic nanofluids may be
realized using water or other solvents such as benzyl ether, phenyl ether. It is generally known that there are
many methods such as co-precipitation, sol – gel, solvo-thermal, hydrothermal, thermal decomposition or
reverse micelle, normally used in synthesing MNPs . The size and size distribution or magnetic properties of
nanoparticles depend on the synthesis method. Therefore, it is difficult to experimentally study the effect of
one or more parameters of a nano ferrofluid on the physical phenomenon.
Besides, the nano ferrofluids must satisfy two main conditions: they should have large heating power
with minimum amount of nanoparticles, they should have good biocompatability. In order to achieve these
goals, the so far studies focused on improving the heating power of magnetic nanoferrofluids. Based on
previous works, the heating power depends on several physical and magnetic parameters of the particles
including: particle size (D) – size distribution, saturation magnetization (Ms), magnetic anisotropy constant
(K), viscosity of magnetic fluid (η) as well as the AMF frequency and amplitude. Because there are so many
parameters affecting the heating power, experimental studies of optimizing MIH effect are difficult to realize.
Therefore, theoretical studying the role of physical parameters of different nanomaterials could be a good
approach to provide guidelines for experimental works, becausetheoretical calculations in fact play the role
as a “Digital experiment”, which contributes to predicting experimental results. Based on these theoretical
results, the experimental parameters can be adjusted to search for suitable materials according to the
researchers' goals.
In Vietnam, the basic and application works associated with magnetic nano materials are concerned
by a number of research groups at Institute of Materials Science (IMS), Institute for Tropical Technology, Ho
Chi Minh city Institute of Physcis - Vietnam Academy of Science and Technology, Hanoi University of
Science and Technology, Faculty of Physics in Hanoi University of Science, etc. However, only the research
1


group of Prof., Dr. Nguyen Xuan Phuc at IMS permomed theoretical and experimental studies of MIH and
focus on both aspects: the synthesis method such as magnetic metal nanoparticles (Fe), magnetite
nanoparticles (Fe3O4), doped magneitc nanoparticles (Mn 0.3Zn0.7Fe2O4, Mn0.5Zn0.5Fe2O4, La0.7Sr0.3MnO3) or

core

–

shell

magnetic

nanoparticles

-

Fe 3O4@

poly(styrene-co-acrylic

acid),

Fe3O4@

poly

(Nisopropylacrylamide-co-acrylic acid) and the physical mechanism of MIH.
Up to now, the experimental results on MIH are abudant and diverse. These results indicated the
advantage of particular materials, which is used as a core, shell or solvent of biomedical nano ferrofluids.
Besides, the experimental results of studying physical parameters on MIH contributed to explain its physical
mechanism. However, the dependence of MIH on the ferrofluid physical parameters has not been detailly
mentioned in recent experimental works and systematically considered in theoretical reports. So, a series of
questions should have satisfactory answers in the research process. Firstly, the heating efficiency of MIH is
optimal at which critical size of each mangnetic nano materials? Secondly, the same question for saturation

magnetization, hydrodynamic diameter and especially in magnetic anisotropy (K). How the characteristic
parameters of MIH are affected in low K or high K magnetic nanofluids? In other words, how can we classify
materials based on this parameter or other physical factors in MIH? How the heating efficiency of MIH is
affected when the particle is not monodispersive or the viscosity changes? These answers will contribute to
optimizing the MIH in each materials and orienting the applicability of these materials. It is a challenge for
us and other groups.
Based on the above reasons, we chose the research project for thesis, namely: “The characteristics
of magnetic inductive heating and their impacts by the particle anisotropy and ferrofluid viscosity”.
Research targets of the thesis:
(i) To thereticallystudy the overall characteristics of MIH and their impacts based on theoretical
calculation
(ii) To carry out experiments on the influence of alternating magnetic field, particle size and
viscosity on specific loss power for CoFe 2O4 and MnFe2O4, chosen as representative of respectively high K
and low K magnetic nanoparticles; and to compare the experimental behavior with that obtained by
theroretical calculations.
Scientific and practical meaning of the thesis:
Applying Linear Respones Theory (LRT) to find the competition between the Néel and the Brownian
relaxation which helps to more clearly understand about the role of magnetic anisotropy for classifying
materials in MIH.
Research methodology:
The thesis was carried out by theoretical calculation based on LRT (using MATLAB software) and
practical experimentation combined with numerical data process. CoFe 2O4 and MnFe2O4 samples were
fabricated by hydrothermal synthesis at Laboratory of Magnetism and Superconductivity, Institute of
Materials and Sciene, Vietnam Academy of Science and Technology. Samples were characterized by electron
microscopes (FESEM). The viscosity of magnetic fluids was measured by Sine wave Vibro Viscometer SV
10. DLS was used to determine the hydrodynamic diameter of magnetic fluid. Magnetic properties of
materials were investigated by Vibrating-Sample Magnetometer (VSM), and were used to evaluate the
presence of functional groups on magnetic nanoparticles. Magnetic Induction Heating was carried out on
RDO-HFI-5 kW set up installed at Institute of Materials Science..
2

Research contents of the thesis:
(i)

Overview of Magnetic inductive heating for nano ferrofluids

(ii)

Investigating the effect of physical parameters on the specific loss power based on LRT

(iii)

Compare theoretical results with experimental results of the influence of alternating
magnetic field, particle size and viscosity on specific absorption rate power for CoFe 2O4 and
MnFe2O4 magnetic nanoparticles

Layout of the thesis:
The contents of thesis were presented in 3 chapters.
• Introduction
• Chapter 1. Magnetic inductive heating for nano ferrofluids
• Chapter 2. The theoretical results of the specific loss power based on Linear Respones Theory
• Chapter 3. Verifying theory by experimental results
• Conclusion
Research results of the thesis were published in 06 scientific reports including: 02 ISI reports, 03
national reports, 01 report in international scientific workshop.
CHAPTER 1
MAGNETIC INDUCTIVE HEATING FOR NANO FERROFLUID
1.1. Overview of Magnetic inductive heating
1.1.1. Magnetic nanoparticle and superparamagnetic particle: basic properties

1.1.1.1. Domain of magnetic nanoparticle
In a bulk magnetic material, the magnetic moments are uniformly oriented in regions of certain sizes,
which are called “magnetic domains” or “domains”. tIn the absence of external filed, the moments vary from
domain to domain to make total magnetization minimized to zero. When the size of bulk material decreases,
the domain size decreased and the domain structure, the width of the domain wall changes. When the particle
was smaller than a critical size, it could not consist of two domains separated by a domain wall and the
particle becomes a single domain particle. The critical size for single domain behavior depends on type of
magnetic materials.
1.1.1.2. Superparamagnetism
If single-domain nanoparticles become small enough, thermal energy is larger than anisotropy energy
so spontaneously reverse the magnetization of a particle from one easy direction to the other likes a single
spin in paramagnetic materials. The spin system can be rotated synchronously and the magnetic state of
small size and non-interacting nanoparticles is called “superparamagnetic”.
The temperature at which the transition between the superparamagnetic state and the blocked state
occurs is called the blocking temperature TB . The blocking temperature TB also depends on other factors
such as magnetic anisotropy, size and the measurement time (τm). So, the blocking temperature depends on
size andτm for each materials. While the critical size of single domain is determined by the balance of energy
forms, superparamagnetic behavior depends on the measurement time.
1.1.1.3. Dependence of magnetic anisotropy on particle size
The anisotropy energy is the energy required by the external magnetic field to move the magnetic
moment from easy to hard direction of magnetization. It is the internal magnetocrystalline energy if
saturation magnetization is not oriented towards easy axis. This energy, which is associated with
3


magnetocystalline anisotropy and the crystal symmetry of the material is called magnetocystalline anisotropy
energy.
For fine or thin flim magnetic nanoparticles, surface anisotropy contributes yet to magnetocystalline
anisotropy. The surface anisotropy is caused by the breaking of the symmetry and a reduction of the nearest
neighbour coordination. Surface effects in small magnetic nanoparticles are a major source of anisotropy.

The effective anisotropy energy per unit volume is given by:
K = K +6 K
eff
V
D S
1.1.2. Nano ferrofluid: synthesis and application

(1.8)

The magnetic nanoparticles coated by surfactants and suspended in liquid carrier are called
ferrofluids or magnetic fluids, which is a commonly concept in biomedical applications. The magnetic fluids
are distingnuished not only by magnetic properties of nanoparticles (core) but also properties of liquids. For
example, the Néel and Brownian relaxations mainly contribute towards MIH of ferrofluids based on
superparamagnetic nanoparticles. Therefore, the physical effects of ferrofluid are influenced by magnetic
nanoparticles in the core, the shell , the solvent and also the synthesis method used.
1.1.3. Magnetic inductive heating and application
Inductive Heating (IH) is the physical phenomenon by which electromagnetic materials become
thermal seeds when they are inserted in proper alternating electromagnetic field. In case of nanosized
magnetic materials, it is generally known that the energy losses associated with magnetic properties such as
hysteresis loss, relaxation loss, v…v. mainly contribute to the heating. The MIH has been of great interest
because of their potential applications such as (i) adsorbent material desorption, (ii) cell activation for insulin
regulation, (iii) to characterize the nanoparticle distribution in organs and in tissues, (iv) thawing of
cryopreserved biomaterials, (v) hyperthermia-based controlled drug delivery and (vi) hyperthermia-based
cancer treatment.
1.2. Magnetic inductive heating mechanisms
1.2.1. Contribution factors to thepower of magnetic inductive heating
MIH of magnetic nanoparticles is derived from the process of adsorbed energy from external
alternating magnetic field. The total absorbed energy includes surface Joule loss (PF), hysteresis loss (PH),
Néel (PN) and Brown (PB) relaxation losses. Because, most nano materials are of high electrical resistivity
and small size, this leads to very low eddy current loss. Thus the MIH of nanoparticles is mainly caused by

the hysteresis loss, Néel and Brown relaxation losses.
The hysteresis loss refers to the loss due to irreversible magnetization process in AC field. This is the
mainly heat generation of ferrite or ferromagnetic multi – domain materials. For the superparamagnetic
nanoparticles, it is generally known that Néel and Brown relaxation losses mainly contribute to the MIH of
materials. The Néel relaxation loss is originated from relaxation effects of magnetization in magnetic field,
the Brown relaxation loss is due to the rotation of the nanoparticles as a whole in ferrofluid.
Nowadays, the theoretical models of MIH such as Rayleigh model, Stoner–Wohlfarth model based
theories (SWMBTs), and Linear Response Theory (LRT) depend on the applicable conditions. The
dimensionless parameter ξ to indicate the limit of validity of each theoretical model.
ξ = µ0 M SVH
(1.9)
k BT

4


When ξ < 1, nanoparticles show superparamagnetic behavior or H<and H can be approximated to a linear function. Therefore, the LRT can be applied. This model is based on
two mechanisms: Néel and Brown relaxation losses. In contrast, the hysteresis loss is the mainly heat
generation of ferrite or ferromagnetic multi – domain when the parameter ξ > 1. Thus Rayleigh and
SWMBTs models are applicable depending on field used.
1.2.2. Hysteresis loss
SW model is a theoretical model based on the hysteresis loss, which can be estimated from the area
of the hysteresis loop when the magnetization material is saturated. Note that the hysteresis loop changes
with the amplitude and frequency of the AMF.
For low AMF, Rayleigh model has been applied and it has been shown that the law SLP ∝ H3 could
describe the hysteresis losses. SWMBTs was built by the hypothesis: single domain ferromagnetic particles
with non interaction uniaxial anisotropy and orient randomly. According to the SWMBTs, the loss power was
equal to twice the anisotropic energy density. In fact, J. Carey et Al. found that it was equal to 1.92 the
anisotropic energy density.

1.2.3. Néel relaxation loss
For single domain particles, the anisotropy energy is smaller than thermal energy so that the particle
magnetic moment can rotate freely in the absence of an external magnetic field. Heating is accomplished by
rotating the magnetic moment of each particle against an energy barrier.
1.2.4. Brown relaxation loss
The Brown relaxation loss refers to the rotation of particle as a whole in magnetic fluid. This is
significant when the direction of the magnetic moment is tightly attached to particle (high magnetic
anisotropy) and low viscosity.
1.2.5. Linear Response Theory
LRT describes the ability of the magnetic moment to respond AMF. Based on theoretical results, J.
Carey et. al found that the condition of validity for the LRT is ξ < 1. So, LRT based on Néel and Brown
relaxation losses is suitable for superparamagnetic nanoparticles or H<Loss power of MIH based on relaxation losses is given by:

P
LRT

= µ πχ,, ( f ) H 2 f

(1.20.)

0

1. 3. Difficulties and challenges in experimental study of optimal MIH of nano ferrofluids
In biomedical applications, the preferred size of the nanoparticles (core) is typically around 10–50 nm,
nanoparticles have high saturation magnetization and must satisfy two main conditions: they should have
large heating power with minimum amount of nanoparticles and they should have good stability in
ferrofluids. Therefore, the major issue that is being investigated is optimal MIH.
Specific Loss Power – SLP or Specific Absorption Rate – SAR is commonly used to describe the
MIH capacitance or the ability to absorb energy from AMF of the magnetic nanopaerticles:

SLP / SAR = P

(1.23.)

ρ

1.3.1. Size particle and problem in controlling size and narrow size distribution
There are many magnetic nanoparticle synthesis methods such as co-precipitation, sol – gel, solvothermal, hydrothermal, thermal decomposition or reverse micelle. The size and size distribution or magnetic
properties of nanoparticles depend on the synthesis method. So, it is difficult to control size particle, size
distribution and material crystallization. For example, synthesizing magnetic fluids with a same medium size
5


but different size distribution or same size distribution with different medium size is not feasible. Therefore,
it is difficult to study of the effect of one or more parameters of nano ferrofluid on a physical phenomenon.
1.3.2. Saturation magnetization and attenuation from saturation magnetization by surface dead layer
The magnetization of a magnetic material is the sum of the magnetic moments per unit volume.
Surface effects and finite size effects are responsible for the difference between nanoparticle and bulk
material magnetization. The corresponding contributions of the two effects are opposite. The attenuation
from magnetic saturation of the nanoparticles is due to the existence of a dead layer or spin canting on the
particle surface.
1.3.3. Magnetic anisotropy of nanoparticle
For bulk magnetic materials, magnetic anisotropy depends on composition and crystal field of each
material. Because of the increased ratio of surface atoms to core atoms in nanoparticle, surface effects were
suggested to have significant role on the properties magnetic anisotropy of nanoparticle.
The magnetic anisotropy depends on shape and crystallization for nanoparticels with a same
ingredient. The magnetic anisotropy strongly depends on synthesis method and synthetic conditions of each
method. Thus, studying the dependence of MIH on the magnetic anisotropy by controlling the value of
magnetic anisotropy is impossible in experimental works
1.3.4. Viscosity of ferrofulids in applications

The value of viscosity changes from 1 to 4 mPa•s in biomedical applications or is equal infinite in
other applications such as adsorbent material desorption and thawing of cryopreserved biomaterials.
1.4. Review of magnetic inductive heating
1.4.1. Review of experimental works
Most of experimental studies have focused on the impact of insitric parameters of magnetic fluid (size
distribution, saturation magnetization, viscosity …) to loss power because of the limit of AMF in biomedical
applications.
There are some interesting experimental results such as the peak behavior of heating power versus
diameter, decrease of SLP with expanding size distribution or increasing the value of viscosity. As for the
tendencies of heating power decrease, there is the different behavior between the high-K and low-K magnetic
nanoparticles. However, the dependence of MIH on physical parameters has not been detailly and
systematically mentioned in recent experimental works because of difficulties in experimental study:
magnetic properties depend on size and shape of nano ferrofluids.
1.4.2. Review of theoretical works
The LRT is commonly used because of practical requirements in biomedical applications. Based on
LRT, the SLP exhibits a peak (SLPmax) at some critical diameter when the condition ωτ = 1 is satisfied and
this condition is compared with the experimental works. However, the value of Dcp, SLPmax and Dcp depend
on which physical parameters have not been mentioned.
The difference in the SLP(D) graph shape of nano ferrofluids is mentioned or used to explain the
different decrease of SLP with expanding size distribution of the γ-Fe2O3 and CoFe2O4. But, it is still an open
issue. In addition, the role of competition between Néel and Brown relaxation losses to MIH has not been
studied.
CHAPTER 2
THE THEORETICAL RESULTS OF THE SPECIFIC LOSS POWER
BASED ON LINEAR RESPONES THEORY
6


2.1. Characteristic of the specific loss power
2.1.1. The competition between Néel and Brown relaxation losses

It is indicated the existence of three particle diameter (D) regions that: the Néel relaxation dominates
in region I (D < DN), the Brownian relaxation dominates in region III (D > DB) and the two dissipation
mechanisms contribute simultaneously in region II (DB ≤ D ≤ DN).
2.1.2. The peak behavior of the specific loss power versus diameter
The peak behavior of the specific loss power versus diameter with the value of Dcp and SLPmax indicated
that SLP depends strongly on diameter. Parameter of full-width-half-maximum ∆Dcp is introduced to describe
these peaks. The vaule of ∆Dcp relates to decrease of SLPmax according to the deviation from Dcp.

2.1.3. Characteristics of optimal parameters in regions with different loss mechanisms
The difference in the SLP (D) graph shape of nano ferrofluids depends on the value of magnetic
anisotropy, specifically the low-K magnetic fluids such as FeCo, LSMO, MnFe2O4 and Fe3O4 or the high-K
magnetic fluids such as CoFe2O4 and FePt. These two groups are more or less of one rank the value of
magnetic anisotropy. We distinguish these nano ferrofluids into two groups: group A consists of low-K
magnetic fluids (FeCo, LSMO, MnFe2O4 and Fe3O4) (K < 10 kJ/m3) and group B consists of high-K
magnetic fluids (CoFe2O4 and FePt) (K > 100 kJ/m3).
For group A, the peak is narrow and small ∆Dcp. In contrast, the peak is bell-like with a large width
∆Dcp for group B. The cause of this phenomenon is due to the value of Dcp for each group. These values are
in regions I and II - group A, and, in region III - group B.
2.2. Effect of physical parameters on optimal parameters
2.2.1. The parameters of alternating magnetic field
a. Amplitude of alternating magnetic field
For nano ferrofluid with diameter of 4 nm, SLP depends on the amplitude of AMF as a quadratic form. SLP
is linearly dependent on H for nano ferrofluid with diameter of 36 nm. The cause of these different results is due
to H affecting SLP by H2 function and imaginary susceptibility χ’’. So, the dependence of SLP on H can be able
an exponential (first order, quadratic, or tertiary) function or a complex function.

Figure 2.5. Dependence of

SLPmax (H )

rate on H

SLPmax (H = 50(Oe))

for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt with Dcp
The value of SLPmax increases linearly with H for six ferrofluids. The heating power of the MIH
increases linearly with H at the critical diameter e even though the heat generation mechanism is Néel or
7


Brown relaxation loss. In addition, the optimal parameters Dcp and ∆Dcp do not depend on the the amplitude
of AMF.
b. Frequency of alternating magnetic field
The value of SLP reaches the maximum SLPmax at the critical size when this condition ωτ = 1 is
satisfied. The value of Dcp changes when the frequency changes. However, the impact of frequency on the
critical diameter is different for two groups (A and B).
For group A, the Dcp changes from 2.5 to 3.5 nm when the frequency changes from 100 kHz to 1
MHz. The Dcp changes from 4.5 to 5.5 nm when the frequency changes from 100 kHz to 1 MHz for CoFe 2O4
and FePt ferrofluids. While the Dcp of CoFe2O4 and FePt ferrofluids change 25% - 34%, the Dcp of group A
only changes ∼10% - ∼13%. However, the value of ∆Dcp do not depend on the the frequency of AMF.

( )

SLP f
(

)

100(kHz) rate on f

Figure 2.9. Dependence of SLP f

=

for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt with Dcp (f=100 kHz)
At the critical diameter (f = 100 kHz), the SLP increases linearly with frequency when the value of
frequency is smaller than ≤ 200 kHz – the condition ωτ ≈ 1 is satified. These values will be saturated in the
high frequency. The value of saturation SLP differs for magnetic fluids and is higher for low-K magnetic
nanofluids.
2.2.2. Saturation magnetization
Based on LRT, the value of SLP reaches the maximum SLPmax at the critical size when this condition
ωτ = 1 is satisfied. At the critical diameter, the value of SLPmax:

(PLRT ) max
SLPmax =

µ π Hf
≈

ρ

0

2ρ

(2.4.)

M S = A.MS

The value of SLPmax is an increasing linear function of MS. It can be explained by the independent

behavior of MS on the effective relaxation time.
Table 2.4. The slope ∆SLPmax / ∆M S for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 and FePt magnetic fluids
Magnetic fluid

∆SLP / ∆M

K
3

R2

FeCo
La0.7Sr0.3MnO3

(kJ/m )
1,5
2

2,39
2,37

1
1

MnFe2O4

3

2,39

1

Fe3O4

9

2,14

0,99729

max

8

S


CoFe2O4
FePt

180
206

1,05
1,77

0,99879
0.99985

However, the value of the slope ∆SLPmax / ∆M S for magnetic fluids depend on K. One can note again

that the materials having low and high K values behave differently. Namely, the slope of the materials with
K< 10 kJ/m3 changes very little with K ( ∆SLPmax / ∆M S ∼ 2.38 for FeCo, LSMO, MnFe2O4,), whereas that
of high K materialsis almost halved. The cause of this phenomenon is due to the value of Dcp for each group.
These values are in regions I and II - group A, and, in region III - group B. These results demonstrate the role
of magnetic anisotropy in explaining the physical mechanism of the MIH.
Two optimal parameters Dcp and ∆Dcp do not depend on the the frequency of AMF.
2.2.3. Viscosity of magnetic fluids
While all relaxation times depend on diameter, only the Brown relaxation time depends on the
viscosity of nano ferrofluids. The value of Dcp for group A is in regions I and II. The value of Dcp for group B
is in regions III – the Brown relaxation loss dominates. These are reasons that the optimal parameters change
when the viscosity of nano ferrofluids group B changes.

Hình 2.12. Dependence of SLP on D at various η for (a)CoFe2O4 and (b)FePt
For group B: the Brown relaxation loss dominates at the critical diameter. Thus, the critical diameter
depend on the viscosity:
− 2δ = A − 2δ
Dcp = 3 k BT
2
3
π fη
η

(2.5)

All optimal parameters SLPmax, Dcp and ∆Dcp change with changing the value of the viscosity of
magnetic fluids in gropu B. It is easy to see from the figure that the SLPmax of CoFe2O4 and FePt decreases
strongly (∼ 50% – ∼ 60%) and the characteristic parameters Dcp and ∆Dcp do insignificantly with increasing
the viscosity from 1 mPa•s to 2 mPa•s.

9

Hình 2.13. Dependence of SLPmax on MS at various η for (a)CoFe2O4 and (b)FePt
SLPmax was directly proportional to Ms depending not on the viscosity, meanwhile the slope of them
decreased with increasing of viscosity. The contrast results between group A and group B continue to confirm
that the MIH is primarily derived from the Brown relaxation loss for group B or from the Néel relaxation
loss for group A.
2.2.4. Size ditribution
With expanding the size distribution (the value of σ increases), the contribution of magnetic
nanoparticles with diameter around the value of Dcp is larger. Thus, the SLPmax decreases with increasing
standard diameter deviation σ of size distribution for all magnetic fluids. However, it has a difference
between two groups: A and B.
These results found the value of SLPmax of group A decreases stronger than group B with expanding
particle the size distribution from 0 (monodispersion) to 0.25. When the value of σ increases from 0.25 to
0.5, the value of SLPmax of group A decreases slower than group B.

Figure 2.15. Dependence of

SLPmax (σ ) rate on σ for FeCo, LSMO, MnFe2O4, Fe3O4, CoFe2O4 và FePt
(σ = 0)

SLP

max

The difference in ∆Dcp and heating mechanism between group A and B is the key to explain the
decrease of SLPmax with expanding the size distribution. The Néel and Brown relaxation losses are the main
heating mechanisms. Depdencce of the Néel relaxation loss on diameter is stronger than depdencce of the
Brown relaxation loss on diameter. So, the value of SLP decreases strongly with decreasing of diameter in
region I (D < DN). When diameter increases in region III (D > DB), SLP decreases slowly.

For group A, the contribution ratio of nanoparticles from region I is greater than region III when σ
increases from 0 to 0.25. So, the value of SLPmax decreases strongly. In constract, the value of SLPmax
decreases slowly because the contribution ratio of nanoparticles from region III is greater than region I when
σ increases from 0.25 to 0.5.
The value of Dc is near region I, the more obvious this phenomenon is. This explains that the fastest
increasing of ∆Dcp for FeCo magnetic fluid and the least increasing of corresponding value for Fe 3O4
magnetic fluid in group A.
In contrast, the value of SLPmax for group B decreases slowly because the contribution ratio of
nanoparticles from region III is greater than region I when σ increases from 0 to 0.25. The contribution of
nanoparticles from region I increase when σ increases from 0.25 to 0.5, resulting in a decrease in the value
of SLPmax for group B faster than group A.
10


The competition between Néel and Brown relaxation losses is a decisive role in this phenomenon.
2.3. The role of magnetic anisotropy on the competition between Néel and Brown relaxation losses
Two groups of magnetic fluids (group A and group B) exhibit different characteristics of the optimal
parameters of MIH. For group A, the value of SLPmax decreases strongly with expanding size distribution and
is independent on viscosity. For the B group, the SLPmax value decreases slowly with expanding size
distribution and was dependends on the viscosity. The cause of this phenomenon is due to the competition
between Néel and Brown relaxation losses. The Néel relaxation loss dominates for group A and the Brown
relaxation loss dominates for group B. These results show the important role of magnetic anisotropy with this
competition.

Figure 2.18. The plot of SLP(D) for Fe3O4 at various K khác nhau
The plot of SLP(D) for Fe3O4 changes from “sharp” to “bell” and the changing of peak is at 34 kJ/m 3.
All optimal parameters for Fe3O4 change with changing of K.
Table 2.11. The value of Dcp, ∆Dcp and SLPmax for Fe3O4
Magnetic anisotropy
Dcp

SLPmax
∆Dcp
(kJ/m3)
5
10

(nm)

(nm)

(W/g)

23
18,5

3
3

169,9
130,5

15

16,5

4

99,9

20

15

8,5

82,4

25

14

11,5

69,5

30

13,5

13,5

60

34

13

15

54,9

35

16

15

54,9

40

16

15,5

54,9

45

16

16

54,9

50

16

16

54,9

When the value of K increases from 5 kJ/m3 to 34 kJ/m3, the value of Dcp changes because the Néel
relaxation loss still affects this parameter. When the value of K for Fe3O4 is larger than 35 kJ/m3, Dcp and
SLPmax are not changed due to the domination of Brown relaxation loss. So, it changes abruptly at some
critical anisotropy KC = 35 kJ/m3.
11


For optimal parameter ∆Dcp, the width of peak of SLP does not changes abruptly at K = 35 kJ/ m3. It is
continuous process with beginning at the value of K = 15 kJ/ m3 and saturating at K = 35 kJ/ m3. The value
of KC is checked by this result: the SLPmax value decreases slowly with expanding size distribution for Fe 3O4
with K ≥ 35 kJ/m3 – the Brown relaxation loss dominates.

Figure 2.20. Dependence of

SLPmax (σ ) on σ for Fe3O4
SLP
max

(σ = 0)

Bảng 2.14. The value of KC at various viscosity or frequency
f (kHz)
10
100

η = 1mPa•s
2

20

η = 2mPa•s
6
33

KC (kJ/m3)
η = 3mPa•s
9
47

250

50

63

85

119

143

500

59

112

163

>180

>180

750

100

153

>180

>180

>180

1000

102

>180

>180

>180

>180

η = 4mPa•s

11
60

η = 5mPa•s
14
72

It can be seen, that the anisotropy boundary of the transition from Néel to Brown domination
changes with changing the frequency of AMF, depending yet on the viscosity of the magnetic fluids

(

Figure 2.22. The plots of KC versus (a) f with fitting function K C ( f ) = A1 1 − e− B1 ×

(f−f )
0

)

or (b) η with fitting function K C (η ) = A2 + B2 ×η
The shift from the main contribution by the Néel relaxation loss to the Brown relaxation loss can occur for
nanoparticle fluids with depending on the choice of f and η suitable the value of given K. For example,

12


the Néel relaxation loss dominates when f is equal 250 kHz and η is equal 1 mPa•s for magnetic fluid Fe 3O4
(K = 40 kJ/m3). For this magnetic fluid, the Brown relaxation loss dominates when f is larger than 400 kHz
and η is larger than 4 mPa•s. It is confirm that the role of magnetic anisotropy on the competition between
Néel and Brown relaxation losses.

2.4. Some orientations for experimental study
The synthesis requirement for group A is indicated so that the error between size and critical size
within 2 nm and the standard deviation of size distribution is smaller than 0.25. For group B, the error
between size and critical size can be up to 5 nm and the standard deviation of size distribution is smaller than
0.4.
These results showed that a behavior to analyzing the competition of contribution between Néel and
Brown relaxation losses: the different of dependence of SLP on viscosity on two groups A and B. If SLP
depends on viscosity, the main heating generation is the Brown relaxation loss. In contrast, the main heating
generation mechanism is Néel relaxation loss with independence of SLP on viscosity.
Based on the value of K, the shift from the main contribution by the Néel relaxation loss to the Brown
relaxation loss can occur for nanoparticle fluids by changing frequency or viscosity. For example, the main
heating generation is the Brown relaxation loss at f ≤ 200 kHz for magnetic fluid with K = 50 kJ/m3.
However, the main heating generation mechanism is Néel relaxation loss for this magnetic fluid when f is
larger than 400 kHz.
CHAPTER 3
VERIFYING THEORY BY EXPERIMENTAL RESULTS
3.1. Fabrication of CoFe2O4 and MnFe2O4 magnetic fluids
3.1.1. Chemicals and equipment
Synthesis of CoFe2O4 and MnFe2O4 nanoparticles by hydrothermal method was conducted at
Laboratory of Magnetism and Superconductivity, Institute of Materials and Science. The chemicals used
include CoCl2.6H2O (99.99%), MnCl2.4H2O (99.99%), FeCl3.6H2O (99.99%), and solid NaOH (99.99%) of
Merck (Germany), HCl and acetone are of Chinese industrial chemicals with purity of 98.9%.
3.1.2. Process of synthesizing nano particles
CoFe2O4 and MnFe2O4 nanoparticles were fabricated by hydrothermal method described in the
following diagram (Figure 3.2.)

Figure 3.2. Process of synthesizing CoFe 2O4 and MnFe2O4 nano particles
3.1.3. Fabrication of magnetic fluids
13

CoFe2O4 and MnFe2O4 magnetic fluids were formed according to the following process: the magnetic
nanoparticles were removed from the thermos flask - it was still in NaOH solution. Then the magnetic
nanoparticles were washed several times by pure water. Magnetic nanoparticles were dispersed into solvents
by ultrasonic vibrations (2 hours) into magnetic fluids.
3.2. Structure and magnetic property
3.2.1. Structure

Figure 3.4. X-ray diffraction of samples: (a) MnFe2O4 and (b) CoFe2O4
The diffraction peaks at the planes of (220), (311), (222), (400), (422), (511), and (440) confirm the
presence of single-phase face-centered cubic structure. The patterns in (a) and (b) are in good agreement with
their corresponding standard patterns of CoFe2O4 (cubic, space group: Fd3m, Z = 8; ICDD PDF: 22–1086)
and MnFe2O4 (cubic, space group: Fd3m, Z = 8; ICDD PDF: 73–1964), respectively. The broad peaks in Co
and Mn ferrite indicate fine nanocrystalline nature of samples.
For MFO sample, the obtained a = 8.39 Å was smaller than that of bulk counterparts (8.51 Å).
Oxidation of Mn2+ to Mn3+ and different cation distributions of Mn ferrite nanoparticles could lead to
decrease in the lattice constant. In bulk Mn ferrite, cation distribution is demonstrated as
(Mn0.82+Fe0.23+)A(Mn0.22+Fe1.83+)B, where A and B denote the tetrahedral and octahedral sites in spinel
structure, respectively. Oxidation of Mn∼2+ (0,81 Å) to Mn3+ (0.72 Å) reduces the lattice parameter.
Aslibeiki and Kameli obtained a = 8.34 Å for 6.5 nm MnFe2O4 nanoparticles prepared by a thermal
decomposition method. They explained this result by discussing the difference in the cation distribution
between nanoparticles and bulk manganese ferrite. For CFO sample, a = 8,39 Å is approximately equal to
the lattice constants obtained from bulk (a = 8.38 Å).
Table 3.2. The value of DXRD and aexp
Sample
Mean szie
lattice constant
DXRD (nm)
16
18

DFESEM (nm)
19
21

aexp (Å)
8.39
8.39

aLT (Å)

MFT100
MFT120
MFT140

20

22

8.40

8.51

MFT160

23

26

8.40

MFT180

29

31

8.41

CFT100

18

20

8.39

CFT120

21

23

8.39

14

8,38

CFT140
CFT160

24
28

27
32

8.39
8.41

CFT180

34

38

8.42

3.2.2. Magnetic properti of CoFe2O4 and MnFe2O4
Fig. 3.7 and Fig 3.9. show the typical room-temperature hysteresis loops for two samples. The
enlarged view of M-H in the inset of Fig. 3.7 confirms this superparamagnetic behavior

Figure 3.7. Magnetic hysteresis loops at T=300 K of MnFe2O4 nanoparticles
SPM

Table 3.3. The value of MS, Keff and D
for MnFe2O4 nanoparticles
Sample

MS (emu/g)
Keff (erg/cm3)
DSPM (nm)
4
MFT100
55
41
2.77 ×10
4
MFT120
59.9
40
3.01 ×10
4
MFT140
63.1
40
3.18 ×10
4
MFT160
65.4
39
3.29 ×10
4
MFT180
68.1
39
3.29 ×10
Different from the magnetic nanoparticles MnFe 2O4 that all showed the pure superparamagnetism
behavior, the CoFe2O4 nanoparticles exhibit significant coercivity. As the particle size increases, the

coercivity of these particle systems increases from 1200 to 2650 Oe (Table 3.4). The HC values of CoFe2O4
magnetic nanoparticles were used to determine the value of effective magnetic anisotropy.

Figure 3.9. Magnetic hysteresis loops at T=300 K of CoFe2O4 nanoparticles
Table 3.4. The value of MS, HC, MR and Keff for CoFe2O4 nanoparticles
Sample
CFT100

MS (emu/g)
53.8

HC (Oe)
1200
15

MR (emu/g)
17.5

Keff (erg/cm3)
6

1.07 ×10


1.33 ×106

CFT120

57.6

1400

24

CFT140

61.1

2300

29.5

CFT160

63.9

2400

32

2.46 ×106

CFT180

73

2650

37

3.09 ×106

The value of

magnetic anisotropy

(

)

2.3 ×106

of CoFe2O4 nanoparticles is range form 1.02 ×106 to

3.09 ×10 6 erg / cm3 .
3.3. Hydrodyamic diameter and viscosity of magnetic fluid
3.3.1. Hydrodyamic diameter of nano particles
The hydrodyamic diameter of the two nanofluids, CFO and MFO nanoparticles, were measured using
a dynamic light scattering (DLS) system.
Table 3.5. Distributions of the hydrodynamic diameter
Sample
Size distribution
σ

MFT100
MFT120

DH (nm)
21
23

0.18
0.18

MFT140

24

0.21

MFT160

27

0.17

MFT180

37

0.1

CFT100

25

0.18

CFT120

27

0.12

CFT140

29

0.1

CFT160

38

0.25

CFT180

43

0.27

3.3.2. Viscosity of magnetic fluid
Rheological characterization of nanofluids was performed by a Sine wave Vibro Viscometer SV 10,
featuring the vibrating tuning fork measurement method. It measures viscosity by detecting the driving
electric current necessary to resonate two sensor plates at constant frequency of 30 Hz and amplitude of less
than 1 mm. The temperature dependence of the viscosity was measured at room temperature.
3.4. Magnetic Inductive Heating
Magnetic Inductive Heating was carried out on RDO-HFI-5 kW. The Specific Absorption Rate – SAR
is given by:

SAR = C

m ∆T
s

mi ∆t

3.5. Some experimental results for verifying theoretical results
3.5.1. Dependence of MIH on alternating magnetic field
For ferrite nanofluids, eddy current losses are almost negligible because it has low conductivity. For
MFT100, the major heating contribution is relaxation loss because magnetic nanoparticles are
superparamagnetic. For CFT100, the mainly heating contribution is also relaxation loss because the value of
H is smaller than the coercivity (1200 Oe - Table 3.4.
Table 3.6. SAR for MFT100 and CFT100 nanofluids
H (Oe)
SAR (MFT100) (W/g) SAR (CFT100) (W/g)
50

8.8
16

6.9


60
70

13.4
20

9.2
13.8

80

31.7

21.3

Figure 3.15 shows that SAR depends on the amplitude of AMF as a quadratic form. This experimental
result is in good agreement with results of M. Cobianchi, P. M. A. Caeteno and B. B Lahiri. It confirmed that
the LRT is suitable for the MIH at low magnetic fields.
As can be seen from figure 3.15, SAR does not depends on the amplitude of AMF as a quadratic form
at H = 80 Oe. In other words, LRT is inaccurate with the amplitude of AMF lager than 80 Oe. The value of
parameter ξ for MFT100 and CFT100 are 0.85 and 1.24 when H is equal to 80 Oe. While the value of
parameter ξ for MFT100 is is the intersection between the two models: SWMBTs and LRT, the value of
parameter ξ for CFT100 indicated that the heating contributions are relaxation loss and hysteresis loss.
Therefore, to accurately compare the experimental results and the LRT, the SAR value of these two systems
is subtracted from the heating contribution from the hysteresis loss. This is method that P. H. Nam and
colleagues used in their work.

Figure 3.15. Depenedence of SAR on the amplitude of AMF for MFT100 and CFT100.
The solid lines represent the fitting curve assuming the quadratic function
The dependences of SAR on f are shown in Fig. 3.15, which can be fitted very well by a linear
relationship for CFT100 and MFT100. These experimental results are in good agreement with results of M.
Cobianchi, Kishimoto and Fortin
Table 3.7. The value of SAR for MFT100 và CFT100
f (kHz)
SAR (MFT100)
SAR (CFT100)

(W/g)
(W/g)
166
178

10.5
16.9

2.6
8.2

236

31.7

21.3

The dependences of SAR on AMF indicated that the LRT is suitable for the MIH at low AMF for
CFT100 and MFT100.

17


Figure 3.17. The dependences of SAR on f
The solid lines represent the fitting curve assuming the linear function
3.5.2. Dependence of MIH power on particle size
The particle size of sample was changed by changing the synthesis temperature from 100 oC to
180oC. The values of size of samples are in range from 21 nm to 43 nm.
The existence of critical particle size was found in many theoretical studies. Surprisingly, not much
experimental work is reported on the influence of particle size. It is known that these were previously

published only in two experimental works by Deatsch et al. and Krishnan et al. for Fe 3O4 nanoparticles.
Krishnan et al. found that the values of Dcp approximately equal to 16 nm at 170 Oe, 376 kHz. By
performing data from eight different references, Deatsch et al. indicated that SAR maximized at Dcp ∼ 15-18
nm.

Figure 3.19. The value of SLP/MS and SAR/MS for MnFe2O4 magnetic fluids
As can be seen Fig. 6, the value of SAR/MS maximized for a range of about 25-30 nm. It is
interesting that both calculated SLP/MS and experimental SAR/MS of MFO exhibits a peak at Dcp of about 27
nm (MFT160). The experimental data are in good agreement with those data from theory.

18


Figure 3.20. The value of SLP/MS and SAR/MS for CoFe2O4 magnetic fluids
For the CoFe2O4 magnetic fluids, the value of size of samples are quite far above the optimal size
(Dcp = 16 nm) by calculated based on the LRT (Fig. 3.20). Although most experimental measurement points
(CFT 120, CFT140, CFT160 and CFT180) have same tendency with theoretical curve when size is larger
than theoretical Dcp (SAR or SLP decreases with increasing of diameter), the experimental data is not enough
to comment on the existence of the peak of SLP or SAR.
Besides, we now focus our attention on the large difference in the measured and calculated values.
This discrepancy might be due to the following reasons: firstly, the hydrodynamic volume is not a well
defined parameter because in colloidal dispersions the particles are coated with dispersants by forming
multiple layers on the surface. Secondly, there are magnetic interactions in the samples while non-interacting
nanoparticles are assumed in the calculation. In a recent work, Serantes et al. have numerically studied the
effect of magnetic interactions in MNPs on the magnitude of SAR. They found that in ferromagnetic MNPs
having dipolar interactions, SAR is enhanced (reduced) at low (high) field and is saturated at a higher field
than independent MNPs.
3.5.3. Analyze the contribution of Néel and Brown relaxation losses
The SLP value of MFT100 is almost unchanged with the viscosity of the magnetic fluid: this value
decreases from 65 W/g to 63.7 W/g when the viscosity increases from 1 to 2 mPa•s. The changing is very

small, accounting for only 2% of the SLP value of MFT100 in pure water. In contrast, the changing for
CFT100 is account for more than 34% (17 times more than MFT100). Therefore, it is evident that SLP of
two ferrites differently respond to viscosity.
Table 3.10. SLP and SAR for CFT100 and MFT100
Sample

CFT100

η
(mPa•s)

SAR
(W/g)

SLP
(W/g)

η
(mPa•s)

SAR
(W/g)

SLP
(W/g)

1.37
1.56

38.7

19.9

72
63.6

1
1.2

12
10.6

65
64.7

1.74

16.7

57.3

1.4

11.3

64.4

1.97

11.5

51.8

1.6

10.9

64.1

2.12

9.1

47.3

1.8

11

63.9

2

10

63.7

Sample

MFT100

It is interesting that both SLP (theoretical results) and (experimental results) SAR of CFT100 are
greatly influenced by the surrounding viscosity while those of MFT100 are almost unaffected.

19


Figure 3.22. Dependence of SAR on viscosity for (a) MnFe 2O4 and (b) CoFe2O4.
The red lines represent the theoretical results based on LRT.
In case of CFT100 nanofluids, SLP is influenced by the viscosity because due to its higher magnetic
anisotropy the “Brown relaxation loss” dominated heating power. In contrast to Co-nanofluid, both the SLP
and measured SAR of Mn-nanofluid were independent of the viscosity. This result implies that the nanofluid
is soft ferrite in which the “Néel relaxation loss power” dominated.
CONCLUSION
The theoretical results of MIH based on LRT deduce the following conclusions:
1.

It is indicated the existence of three particle diameter (D) regions that: the Néel relaxation dominates

in region I (D < DN), the Brownian relaxation dominates in region III (D > DB) and the two dissipation
mechanisms contribute simultaneously in region II (DB ≤ D ≤ DN).
2. The peak behavior of heating power (SLP) versus D is characteristic differently in the two different
groups of magnetic nanoparticles depending on their anisotropy (K). (i) For group A (K < KC) the peak is
narrow (small width ∆Dcp), the value of SLPmax decreases strongly with expanding size distribution and is
independent on viscosity. The Néel relaxation dominates totally when K << KC. Then, the contribution of
Brownian relaxation became stronger with magnetic anisotropy increasing up to the transition value K = KC.
For the B group (K >KC), the peak is bell-like with a large width ∆Dcp, the SLPmax value decreases slowly
with expanding size distribution and was dependends on the viscosity. The Brownian relaxation dominates
definitely for nanoparticles in the group B.
3. The values of KC depend on the frequency of AMF as exponential function and the viscosity of
magnetic fluids as a linear function.

The experimental results of the influence of alternating magnetic field, particle size and
viscosity on specific loss power for CoFe 2O4 and MnFe2O4 magnetic nanoparticles indicated that:
4.

The Linear Response Theory (LRT) is in good agreement with the experimental results when ξ <1.

The experimental values of SLP depended linearly on frequency and by quadratic function on the magnetic
field. The dependence of SLP on the particle diameter exhibited a peak at Dcp around 27 nm for MnFe 2O4
fluid, which is consistent with that obtained by LRT-based calculations. The various experimental results for
CoFe2O4 and MnFe2O4 confirmed the different behavior between the high-K and low-K magnetic
nanoparticles groups.

20


PUBLISHED REPORTS USED IN THIS THESIS
1.

P. T. Phong, L. H. Nguyen, L. T. H. Phong, P. H. Nam, D. H. Manh, I. –J. Lee, N. X. Phuc, “Study of
specific loss power of magnetic fluids with various viscosities”, Journal of Magnetism and Magnetic
Materials 428 (2017) 36

2.

P. T. Phong, L. H. Nguyen, I. –J. Lee, N. X. Phuc, “Computer Simulations of Contributions of Néel
and Brown Relaxation to Specific Loss Power of Magnetic Fluids in Hyperthermia”, Journal of
Electronic Materials 46 (2017) 2393.

3.

L. H. Nguyen, P. T. Phong, D. H. Manh, N. X. Phuc, “Tính toán công suất đốt từ phụ thuộc vào kích

4.

thước của các hệ hạt nano từ cấu trúc spinel MFe 2O4 (M=Fe, Mn, Co)”, Tạp chí Khoa học và Công
nghệ 52(3B) (2014) 74.
L. H. Nguyen, P. Q. Thong, P. H. Nam, L. T. H. Phong, P. T. Phong, N. X. Phuc, “Influence of

5.

saturation magnetization and viscosity on specific loss power for CoFe 2O4 and MnFe2O4 magnetic
nanoparticles”, Vietnam Journal of Science and Technology 54(1A) (2016) 33.
L. H. Nguyen, P. T. Phong, P. H. Nam, D. H. Manh, N. X. Phuc, “Influence of particle size
distribution on specific loss power of magnetic nanoparticle”, Vietnam Journal of Science and
Technology 56(1A) (2018) 79.

6.

L. H. Nguyen, P. T. Phong, P. H. Nam, D. H. Manh, N. T. K. Thanh, L. D. Tung, N. X. Phuc, “How to
distinguish a domination of Néel or Brown relaxation contribution to loss power of magnetic inductive
heating?”, Proceedings of MSSM2018 (07-10 Aug 2018, UWS, Paisley, UK), ISBN 9781903978634,
pp. 188-193.

21