Electricity: measuring and testing – Magnetic – Fluid material examination
Reexamination Certificate
2002-12-30
2004-11-30
Patidar, Jay (Department: 2862)
Electricity: measuring and testing
Magnetic
Fluid material examination
C324S233000, C324S226000, C436S526000, C204S557000, C422S068100
Reexamination Certificate
active
06825655
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to an arrangement for detecting changes of a magnetic response with at least one magnetic particle provided with an external layer in a carrier fluid, thus the method comprises using a measuring method comprising measuring the characteristic rotation time of said magnetic particle with respect to said external layer, which measuring method involves measuring Brownian relaxation in said carrier fluid under the influence of an external alternating magnetic field.
BACKGROUND
Magnetic spherical particles with a diameter of less than about 20 nm are magnetic mono domains both in a magnetic field and in the zero field. A particle being a magnetic mono domain means that the particle only contains one magnetization direction.
Depending on the size, geometry, temperature, measurement time, magnetic field and material of the particles, they can either be thermally blocked or super paramagnetic. The direction of the magnetization for thermally blocked particles are oriented in a specific direction in the magnetic particle in proportion to the crystallographic orientation of the particle, and “locked” to this direction, meanwhile studying the particle system. Under influence of an external magnetic field, the entire particle physical rotates so that their magnetization directions gradually partly coincide with the direction of the external added field.
Small magnetic particles can be manufactured in a number of materials, for example magnetite (Fe
3
O
4
), maghemite (&ggr;-Fe
2
O
4
), cobalt doped iron oxide or cobalt iron oxide (CoFe
2
O
4
). Other magnetic materials, especially (but not exclusively) rare earth metals (for example ytterbium or neodymium), their alloys or compounds containing rare earth metals, or doped magnetic (element) substances can also be possible. The sizes of the particles that can be produced from about 3 nm to about 30 nm. The final size in this process depends on a number of different parameters during manufacturing.
Magnetization in small particles can relax in two different ways, via Néelian relaxation or on the other hand via Brownian relaxation. These relaxation phenomena are related to particles with a magnetic arranged structure. They should not be mistaken for nuclear magnetic (NMR) resonance phenomenon's, the latter describes resonances within the atomic nucleus. The latter resonance phenomena have resonance frequencies typically within the GHz-range unlike resonance frequencies for the phenomenon considered in this patent, which are in the range of a few Hz to several MHz.
Néelian Relaxation
In Néelian relaxation the magnetization in the particle relax without the particle physical rotating (no thermal blocking). The relaxation period for this kind of relaxation strongly depends on size, temperature, material and (at high particle concentrations) on the magnetic interaction between the particles. For this relaxation being available the magnetization direction in the particle has to change direction fast in time, the particles have to be super-paramagnetic. Néelian relaxation period in the zero field can be described according the equation below:
τ
N
=
τ
0
ⅇ
KV
kT
wherein &tgr;
0
is a characteristic relaxation period, K is the magnetic anisotropic constant, V magnetic particle volume, k is Boltzman's constant and T temperature.
Brownian Relaxation
In the Brownian relaxation, the magnetization-direction rotates when the particle physically rotates. For this relaxation being available the magnetization has to be locked in a specific direction in the particle, and the particle has to be thermal blocked. The relaxation period for Brownian relaxation depends on hydrodynamic particle volume, viscosity of the carrier fluid in which the particles are dispersed in, contact between the surface of the particle and the fluid layer nearest it's surface (Hydrophobic and hydrophilic respectively). The Brownian relaxation can approximately be described according to the equation below:
τ
B
=
3
V
H
η
kT
wherein V
H
is the hydrodynamic volume for the total particle (inclusive of the polymer layer), &eegr; viscosity for the surrounding carrier fluid, k is Boltzmann's constant and T is the temperature. The above derivation assumes a perfect wetting (hydrophilic) has been assumed and a constant rotation speed (the initial approximation has been neglected).
The Brownian relaxation period accordingly depends on the (effective) size of the particle and the environmental effect on the particle. To discern if a particle shows Brownian relaxation or Néelian relaxation you can among other things study whether external influences (for example a different fluid viscosity, temperature changes, applied static magnetic field) changes the relaxation period.
You can also study the phenomenon in the frequency domain, which involves determining the resonance frequencies regarding the particle system. These can be obtained for example by means of AC-susceptometry (for Brownian relaxation some Hz till kHz region and for Néelian relaxation typically in the MHz region).
As is apparent from the above, a Brownian movement (Brownian relaxation) depends, among other things on the volume of the particle: the lager particle the longer relaxation period that is and the smaller the movement of the particle gets. Relaxations periods for particles lager than about 1 &mgr;m are much longer than 1 second, which in practice means a negligible movement. Even these particles, though can be used at detection. Larger particles can, however, show other types of relaxations wherein the inertia of the particles and visco-elastic characteristics of the carrier fluid must be included for a sufficient data interpretation.
Frequency Susceptibility
The magnetization for a particle system in an alternating magnetic field can be described according to:
M=&khgr;H
=(&khgr;′−
j
&khgr;″)
H
wherein M is the magnetization, H the alternating external magnetic field, &khgr; is the frequency dependent complex susceptibility consisting of an in phase component (real part), &khgr;′, and one out of phase component (imaginary part), &khgr;″. The in phase and the out of phase components for a magnetic particle system can approximately be described as:
χ
′
=
χ
0
1
+
(
2
π
f
τ
)
2
χ
′′
=
χ
0
(
2
π
f
τ
)
1
+
(
2
π
f
τ
)
2
wherein &khgr;
0
is the DC value of the susceptibility and &tgr; is the relaxation period for magnetic relaxation.
Assuming a particle system with varying particle sizes wherein some of the particles go through Brownian relaxation (the larger particles) and some Néelian relaxation (the smaller particles) you obtain a magnetic response contribution from both the relaxation processes depending on the frequency range AC field.
FIG. 1
shows schematically the total magnetic response as a function of the frequency for the particle system that shows both Brownian and Néelian relaxation. The upper curve (dashed line) in the figure is the real part of the susceptibility and the lower curve (continuous line) is the imaginary part of the susceptibility. The maximum for the imaginary part at lower frequencies is from the Brownian relaxation and the maximum at high frequencies is from the Néelian relaxation. The total magnetic response is the sum of the contributions from both the processes for both real and imaginary part of the susceptibility.
For this application only the Brownian relation is interesting, therefore the discussion is concentrated at these lower frequencies.
For a particle system with particles showing Brownian relaxation with only one hydrodynamic volume you obtain a maximum in the out of phase component (&khgr;″, the imaginary part of the complex susceptibility) at a frequency according to:
f
max
=
1
2
πτ
B
=
kT
6
π
&
Astalan Andrea P.
Johansson Christer
Krozer Anatol
Lagerwall-Larsson Kerstin
Minchole Ana
Imego AB
Patidar Jay
Sterne Kessler Goldstein & Fox PLLC
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