Measurements of particle size distribution parameters in ferrofluids

Abstract

A method is presented by means of which (for a ferrofluid with a lognormal distribution of particle size) it is possible to determine the standard deviation (σ) and median particle diameter (D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</inf> ) from the room temperature magnetisation curve. The method has been applied to several commercial ferrofluids, containing ferrite particles, and to fluids consisting of cobalt particles in toluene prepared by the method of Hess and Parker. The particle size distributions have also been measured by using an electron microscope. It has been found that the magnetic data gives estimates of the 'magnetic size distribution' parameters D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vm</inf> and σ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> , which differed from the 'physical size distribution' parameters D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vp</inf> and σ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> obtained from electron microscope data. It is found that D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vp</inf> > D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vm</inf> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sigma_{p} &lt; \sigma_{m}</tex> . These observations are consistent with the results of Kaiser and Miskolczy and Granqvist and Buhrman.