Surface-enhanced Raman scattering has been proven a powerful means in the fast detection and recognition of chemicals at trace levels, while quantitative analysis especially the compositional analysis of trace chemical mixtures remains a challenge. We report here a "triangle-rule" based on the principal component analysis (PCA) of surface-enhanced Raman scattering spectra, to calculate the composition of individual component of ternary chemical mixtures at trace levels, which can be simplified into the "balance-rule" for binary mixtures. We demonstrated the validity of the triangle-rule and balance-rule in estimating the composition of ternary and binary mixtures of methyl orange, methylene blue, and crystal violet with different molecular structures, and the validity for ternary and binary mixtures of three isomers of monochlorobiphenyl with very similar molecular structures. This idea might be also applicable to mixtures of more components at the trace levels.
Keywords: Balance-rule; Compositional analysis; Principal component analysis; Surface-enhanced Raman scattering; Triangle-rule.