I want to define the simplest theoretical way of describing the water affinity property of the nanoparticles.
Well, you can estimate the dispersion coefficients or Hamaker constants of your material either by DFT or by the Lifshitz theory for which you "only" need to know their dielectric functions. However, the resulting value gives you only an idea, the resulting value may deviate more or less from the theoretical prediction. A good introduction can e.g. be found in this book:
https://onlinelibrary.wiley.com/doi/book/10.1002/3527602313
However, nothing replaces an actual experiment and contact angle measurements are definitely faster than a high-level DFT calculation or measuring the full dielectric functions of your nanoparticles.
I do not understand if you need to calculate it only or you just need to do it practicaly fast even with using experiment. It is possioble get this infomation also by AFM. Try to find keywords such as hydrophobicity and AFM. There is some paper for example: Article Measurement of Surface Hydrophobicity of Engineered Nanopart...
where is also shown relation betwen adhesion force hydrophobicity.
One of the ways is to know the surface free energy of the material. If it is low then you expect higher contact angle. Further the surface roughness is another important parameter, which you should know. You can use a nano-profilometer to measure the same. The bottomline is that you may not be able to accurately predict the contact angle as your particle is too small.
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