Application of ultrasound spectroscopy for nanoparticle sizing in high concentration suspensions: A factor analysis on the effects of concentration and frequency

Ultrasound is an attractive technique for nanoparticle sizing as it offers non-invasive, suitable for highly turbid and concentrated samples, and potentially no sample dilution needed features. This paper presents a factor analysis method for the determination of the concentration range and frequency domain for the use of ultrasound techniques for particle sizing when ECAH (Epstein, Carhart, Allegra and Hawley) model is applied. The advantage of using this method is by dealing with experimental data, some practically useful information, which the current theory cannot be employed to produce, may be identified, for instance, the critical volume concentration of particles below which sound attenuation is linearly dependent on particle concentration and the frequency domain in which frequencies have higher contribution to the attenuation than those outside the domain. 

To use this method, each data matrix is constructed by ultrasound attenuation data with frequency as variables and concentration as observations. Attenuation data are obtained with the measurements of ultrasound spectroscopy of oil/water emulsions and solid/water suspensions at different concentrations. 

As a result of the factor analysis, for emulsions up to 40%vol concentration, the linear dependence of attenuation on concentration and a same level contribution of frequency ranging from 1 to 120 MHz are found. However, for solid suspensions, attenuation appears to be nonlinearly related to solid concentration and the critical concentration value at which attenuation is turning into nonlinear from a linear trend can also be calculated. It is also found that in solid suspensions, frequencies less than 10 MHz have less contribution to attenuation than that of higher than 10 MHz. Therefore, for ultrasound particle sizing using ECAH model, before the inversion of attenuation to particle size distribution takes place, using this method the range of concentration and frequency to which the use of ECAH model is valid can be determined.