Quantification of nanoparticle dispersion within polymer matrix using gap statistics

This study was prompted by the inadequacy of most dispersion quantification techniques to address issues pertaining to scalability, implementation complexity, accuracy/error, uncertainty factors and versatility. Therefore, a method for quantifying dispersion based on gap statistics was developed. A dispersion quantity ( D ) was formulated from a Gap factor Particle spacing dispersity ( PSD ₁) and Particle size dispersity ( PSD ₂) factors. The summation of the factors resulted in the dispersion parameter ( D _p) which must be equal to one for an ideal or uniformly distributed condition. The state of dispersion increases as D → 100%. The concept was tested with simulated models having uniform dispersion, random dispersion, small aggregate, three large aggregate and one large aggregate were successfully quantified to show 99.34%, 82.42%, 34.17%, 8.95% and 3.65% respectively. For validation of concept, the state of dispersion when samples with (scenario 1) and without (scenario 4) silane treatment were quantified as 32,02% and 7.72% respectively. The concepts were then validated using real microscopy images. This approach is robust, versatile and easy to implement.