I know there are volumes of International Colour Index (homepage, wiki, paper), but I can't really extract from there for example what red colorants are compatible with both silk and polyester, etc.

This paper mentions that such compatibility can be estimated using numerical methods:

"Metropolis Monte Carlo methods have been used to determine the surface interaction or binding energy for dyes to cellulose." [ref]

  1. Is there a comprehensive database for this?
  2. Is there an analytical way to determine/predict/estimate such compatibility?

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