Multiplication Algorithm for Combined Physical and Chemical Enhancement of X‑ray Effect by Nanomaterials

The total enhancement obtained from mixing silica-covered 90 nm gold nanoparticles and tetrakis (hydroxymethyl) phosphonium-covered 2 nm gold nanoparticles that individually under X-ray irradiation produced average physical enhancement and chemical enhancement respectively was studied experimentally and theoretically. The total or combined enhancement was shown to be the multiplication of the two individual enhancements, and this algorithm can be derived from the original definition of physical and chemical enhancement. The maximum total enhancement was 18-fold, whereas the maximum measured average physical enhancement was 7-fold and the derived chemical enhancement was 3.9-fold; all three maxima were achieved under different experimental conditions. The results of simulation using rate equations for the combined physical and chemical enhancement were obtained and were found to agree with the measured total enhancements.