Thank you for the valuable suggestion. I think there are only one truth in the world, and people from different disciplines offer different perspective in discussion will definitely help in unveiling the truth. I'd like to describe my understanding below.
Please image there are nano-particles of several tens to hunders of nanometer in diameter dispersed in some liquid, such as water or oil. We use a coarse-grained model to study the aggregation of nano-particles in the liquid, which allows us to treat the liquid as an uniform matrix regardless of different size.
As we known, van der Waals force (vdW) is a primary force on microscopic scale. vdW consists of three part of contribution, i.e. force between permanent dipoles, force between permanent dipole and induced dipole, and force between two instaneously induced dipoles. Lennard-Jones potential is used as approximate model for vdW as a function of distance in Molecular Dynamics simulation with cutoff distance (rc) of 2.5 σ , where σ represents diameter of particle size. This means vdW is operative over a range of 2.5 times size of the particles under study.
When we take a look at a plate capacitor. We'll expect minimal quantity of charges on the plates if the capacitor is filled with vacuum. But more and more charges are expected on the plates when we fill the space between the plates with matrices of higher dielectric constant. I believe this is also true between two nano-particles, as shown in the following picture.
With higher dielectric constant of the maxtix, there are more induced charges on neighbouring nano-particle, and I believe the two nano-particles will experience higher vdW force. So we can say the matrix propagates vdW force. This apparently will alter the aggregation behaviour of the nano-particles.
So here is my questions:
1. Does the vdW force is constant between two neighbouring nano-particles? If not, what factors will alter the intensity of vdW then?
2. Does matrix influences vdW of nano-particles as I depict above? Are there some Law or equation in physics on this? Keywords, papers, links, books, hints are all welcome.
3. If I'm wrong in theory or direction, please feel free to point out.