Physical Sciences and Mathematics Commons^™

Using An Expectation‐Maximization Algorithm To Obtain Dielectric Relaxation Time Spectra Ofaqueous Montmorillonite Clay Suspensions, Stephen E. Bialkowski, Lynn Dudley, Dani Or

Stephen E. Bialkowski

Determination of relaxation-time distributions from dielectric spectra of complex impedance or dielectric permittivity remains a challenge. This problem is one of a wider class of ill-posed inverse problems where the measurement is a superposition or convolution of functions containing the sought-after information. An expectation-maximization (EM) algorithm is shown to be useful for obtaining dielectric relaxation-time distributions from impedance data. This algorithm is stable and converges to realistic relaxation-time spectra without the need for constraints or initial values. The implementation used herein updates expectations in an iterative multiplication step. The models and basic assumptions of impedance spectroscopy are outlined in the …