I am calculating mechanical properties (Elastic modulus, adhesion and deformation) of soft polymers, I want to know either any relationship exist between elastic modulus and adhesion/deformation? any correlation between density and elastic modulus?
there is no physical relation between adhesion and Elastic modulus or between adhesion and deformation. The adhesion depends on the surface energy of the polymer itself and the surface energy of the surface it shall adhere to --> keyword: Young equation. A second contributor to adhesion is the adhesion built-up mechanism (physical: dipole interactions (e.g. van der Waals bonds) or chemical (hydrogen bonds, covalent bonds etc.)).
Elastic modulus and deformation can have a relationship depending on the polymer class (--> keyword: entropy elasticity) For more info please check a textbook on polymer physics.
The elastic modulus and deformation can have relation, but it is material specific, you can not have any generalized equation or relation. Adhesion and elastic modulus can find correlation , that too at the interface where it forms a layer,
Generally lower E-Modulus means higher deformability and higher deformability means that stresses (e.g. on adhesive joints) can be handled better which leads to better adhesive joint robustness. So this is an interesting relation to study. But of course you can only harvest any of those relations if the preconditions are possible in your application or research field.