You can try to communicate with a manufacturer.

Do HRTEM and look for lattice fringes. Try to match them with the expected materials from the literature.

 Thank you all for response.

The paper ”Nanomaterials in consumer products: a challenging analytical problem” presents analytical techniques suitable for the detection, characterization and quantification of NPs in food and cosmetics products.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4527077/

 Thank you Florian Glodeanu for the literature.

This requires a complete characterization, as its composition is completely unknown.

As you have mentioned that you want to find the nanomaterials and their size. The following procedure will help for the same.

Dry the toothpaste and grind. Do SEM, TEM, EDX. These characterizations will give an idea of the size and elemental composition.

Do XRD for identifying the crystalline part of it. EDX will help in this. Further, XPS will help in identifying the oxidation state of the elements.

Correlate all these results for confirming the size and composition.

Thank you Chandra Das for the recommendations.

Concise: suspend in water, dilute, apply DLScattering with Zetasizer or similar. In between apply separation methods: extraction of organics, sedimentation of bigger particles, acid dissolution of carbonates etc.etc. Just apply your imagination :-)

I suggests ICP-MS to identify the metals present in the toothpaste first. From that metal data can uses to go forward.

 Thank you Dimitar Mitev and Suresh Thangudu for the suggestions.

You can go for optical characterization techniques like Raman and PL for determining the presence.