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On the influence of distribution functions on the after-effect function of ferrofluids

The after-effect function, F(t), or magnetization decay of a ferrofluid sample may be determined from frequency-dependent complex relative magnetic susceptibility data of the sample. Here we report on the effect that two distribution functions, namely the magnetic analogues of the Cole-Cole and Frohlich distribution functions, have on the after-effect function of three ferrofluid samples. The samples chosen were those for which good alternating current susceptibility data, chi '( omega ) and xi ( omega ), were available, namely in the lower frequency range in which the frequency of the maximum of xi "( omega ), fmax, is indicative of the presence of aggregates. However, because of a lack of knowledge of the sizes of these aggregates it was not possible to generate a distribution function. By fitting the Cole-Cole and Frohlich distribution functions to the susceptibility data it is shown that the after-effect function is very sensitive to the distribution used, illustrating the difficulty of determining accurate after-effect functions without an adequate knowledge of the distribution function. It is shown that, in all cases, the use of the Frohlich distribution function results in a decay function with the fastest initial rate of decay.