Biomedical Engineering Reference
In-Depth Information
Due to thermal activation effects, the coercivity of a nanoparticle is dependent
on the measuring time. Sharock [131] pointed out that the coercivity as function
of time
t
, where
t
is the time elapsed to cause switching half of the moments, can
be expressed as:
(
)
1
n
kT
KV
ft
⎩
⎭
⎡
⎢
⎤
⎥
B
0
Ht H
()=
1
−
ln
(16.11)
C
0
ln
2
u
It can be seen from Equation 16.11 that
H
C
(
t
) decreases with increasing
t
and
the smaller (
K
u
V
/
k
B
T
), the higher rate of
H
C
(
t
) decreases with increasing
t
.
16.4.2.4
Superparamagnetism in Co Nanoparticle System and
its Direct Investigation
According to Equation 16.9, when the energy barrier of the particle is decreased
to certain value, the magnetization of the particle is free to align with the fi eld at
a given temperature and certain measuring time window. This state is referred to
as “superparamagnetic” because the particle behaves similarly to the paramagnetic
spin but with a much larger magnetic moment. For example, if an arbitrary mea-
surement time is taken as be
= 100 s and
f
0
= 10
9
s
− 1
, then the condition for
τ
superparamagnetism is
KV
=
25
kT
(16.12)
u
B
However, if the particles of a certain size were cooled below a critical tempera-
ture, the spins of the particles would be blocked (they would not relax during the
time of measurement), and thus hysteresis would appear and superparamag-
netism disappear. This critical temperature is termed the “blocking temperature”
(
T
B
), and is defi ned as:
KV
k
u
T
(16.13)
=
25
B
B
The magnetization of a particle,
M
(
B
,
T
) is described by the Langevin function:
()
⎡
⎢
MTVH
kT
kT
MTVH
⎤
⎥
⎛
⎝
⎞
⎠
−
S
B
(
) =
MHT
,
M T
()
coth
S
()
B
S
MTL
MT
(
)
VH
⎛
⎝
⎞
⎠
S
()
=
(16.14)
S
k
B
where
M
S
(
T
) is the spontaneous magnetization with temperature. The magnetiza-
tion curves at different temperatures fall into a single function when the magne-
tization is plotted against the applied magnetic fi eld divided by temperature (
H
/
T
).
