We usually tend to use Newton's second law for finding equations relating the forces being applied on the (not rotating) rigid body located at a plane surface and then calculate "Normal force" by extracting its value from the value of other present forces. And also we always say that the "Normal force" just depends on the surface's intrinsic properties.
Now my question is:
Can we describe/define "Normal force" as a function of surface's intrinsic physical and chemical properties such as its material type, intermolecular interactions, etc? And if we can what is the formula of this function?
By talking more with the people answered me it turned out that the "Question statement" is actually wrong.
The conclusion of our conversation is as follows:
"Normal force" in general isn't a function of Body's and Surface's intrinsic properties and just equals to the opposite force the "Body" is exerting on the surface and vice-versa for the force the "Surface" is exerting on the body.
If the Body and Surface are rigid(in its ideal sense), there is no limit to the "Normal force" they are exerting on each other since the body/surface couldn't deform and as they havn't any elastic properties, we could just say the "Normal force" is generated merely for body/surface to resist deformation.
If the Body and Surface are elastic materials, still the normal force they are exerting to each other is equal to the opposite force exerted on both of them. But now there could be a maximum limit for "Normal force". The "Maximum Normal force" is defined the "Normal force" exerted on the body/surface when the body/surface couldn't resist deformation/peneteration anymore. Now this new quantity(Maximum normal force) is a function of both elastic body's and elastic surface's intrinsic properties. These properties are quantities we define in "Theory of elasticity", "Continuum mechanics" and "Fluid mechanics" and the function would be so complicated and will be possibly different at different situations.
So all of the following answers are correct.
For further information, see the discussion took place into the comments.