Specific Power Absorption & Intrinsic Loss Power Values

01 Dec Specific Power Absorption & Intrinsic Loss Power Values

One of the first steps when characterizing any sample of magnetic nanoparticles as a heating agent is to determine its capacity of absorbing power from the applied magnetic field. The parameter that measures this property is the Specific Power Absorption.

Magnetic heating refers to the process of increasing the temperature of a magnetic material by the application of an alternate magnetic field (AMF).

Many areas of nanotechnology include the phenomenon of magnetic heating of magnetic colloids through magnetic fields. The term “magnetic colloid” refers to a magnetic fluid made of ferromagnetic nanoparticles suspended in a non-magnetic carrier liquid.

This heating is produced by the transformation of the energy absorbed by the ferromagnetic nanoparticles into heat, when submitted to an alternate magnetic field of certain amplitude and frequencies, a process defined as Magnetic nanoHeating (MnH).

One way of characterizing the heating capability of the colloid is by means of the specific power absorption (SPA) or the intrinsic loss (ILP) values.

Calculation of Specific Power Absorption & Intrinsic Loss Power Values on Experiments of Magnetic Heating of Nanoparticles

Specific Power Absorption (SPA)

The capacity of a magnetic material to absorb energy from an alternating magnetic field is quantified by the SAR or SPA rate (Specific Absorption Rate // Specific Power Absorption)
SPA is defined as the amount of energy/power absorbed by the sample per mass unit (W/kg).

Equation for Specific Power Absorption

(Eq. 1)

where P is the absorbed power (in W) and mnp is the mass of nanoparticles in the sample (in kg).

The power absorbed by the magnetic colloid during a Magnetic nanoHeating experiment can also be defined as the amount of energy converted into heat per unit of time and mass

Equation of Specific Power Absorption depending on heat

(Eq. 2)

where Q is the heat (in Joules) generated by the MNPs within a time Dt (in seconds) by a mass mnp (in kg) of magnetic nanoparticles. This is an intensive property of the material.

For an adiabatic system, a calorimetric approach relates the heat dissipated (Q) by the nanoparticles in a colloid and the observed increase in temperature (DT) by:

(Eq. 3)

where mnp and ml are the mass of nanoparticles and the liquid carrier respectively, and cnp and cl are their specific heat capacities (in J/(K·kg)) which are intrinsic characteristics for each material.

Substituting the equation for Q in equation 2, the SPA is expressed as:

(Eq. 4)

Temperature increase with time is calculated by the temperature data obtained during the test. The value of increase in temperature with respect to time which is taken to calculate the SPA is the maximum value of the gradient of the temperature curve, which, in a test of Magnetic nanoHeating rate normally corresponds to its initial gradient (see Figure 1).

Temperature curve rate in magnetic nanoHeating test

Figure 1. Temperature Rate Curve of a magnetic colloid submitted to a Magnetic nanoHeating (MnH) test.

 

Thus, finally, the SPA value for a magnetic colloid submitted to an MnH test is calculated by the following expression:

(Eq. 5)

where the (δT/δt) is the maximum heating rate of the colloid submitted to an MnH test [K/s].

This equation can be further simplified assuming mnp·cnp << ml·cl and defining de sample concentration as j=mnp/Vl where Vl is the volume (in L) of colloid having a mass of nanoparticles mnp (in kg).

The SPA can be expressed as:

(Eq. 6)

 

Intrinsic Loss Power (ILP)

The intrinsic loss power parameter (ILP) was proposed1 to compare heating efficiency at different experimental conditions of amplitude and frequency of the magnetic field. It assumes al quadratic dependence with magnetic field (H) and linear dependence with frequency (f). Therefore, by normalizing the power absorption with these dependences as

(Eq. 7)

this parameter (in nH·m2/kg) allows a direct comparison of datafrom different laboratories or with different devices.

 

References

  1. Kallumadil, M.; Tada, M.; Nakagawa, T.; Abe, M.; Southern, P.; Pankhurst, Q. A., Suitability of commercial colloids for magnetic hyperthermia. Journal of Magnetism and Magnetic Materials 2009, 321 (10), 1509-1513.

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