The effect of particle size distribution on the usage of the ac susceptibility in biosensors

Magnetic nanoparticles in a liquid have two relaxation times, Néel relaxation τN and Brownian relaxation τB. For particle size larger than 25nm, τN quickly becomes much larger than τB and can be ignored. τB has a relaxation period from 10−1to10−5s, and related to the particle’s hydrodynamic volume, which includes coatings and biomolecules attached to the magnetic nanoparticle cores. This causes the imaginary part of the ac magnetic susceptibility to display a maximum at a frequency f=1∕2πτB, and can be used to create a sensor capable of detecting biomolecules. Because this is based on particle size, a size distribution will broaden the curve and reduce the sensitivity. Although the magnetic nanoparticles may have a narrow size distribution, this may not be true once coatings have been added and biomolecules have bonded to the magnetic cores. Our group has examined the effects of normal and lognormal size distributions on the ac magnetic susceptibility using several theoretical measurements, and we have found that the effect of size distributions on the ability to use τB and the ac magnetic susceptibility as the basis of a biosensor is not significant.