Does dielectric constant influences van der Waals interaction?

[aktuon]

Hi, all

 

I'm in polymer science and trying to use molecular dynamics simulation (MD) to study the aggregation behaviour of electrically neutral nano-particles in polymer melts.

 

The short-range interaction of two neighbouring particles are represented by a Lennard-Jones potential function. Presume the two neighbouring particles are immersed in some uniform matrix with different dielectric constant, how does the interaction change with the dielectric constant of the matrix? Is it related to the depth of the potential well of potential function? Any suggestion is highly appreciated.

Edited October 22, 2012 by aktuon

[Enthalpy]

I can't easily make a mental picture of this.

 

Van der Waals forces have a range of one atom or less, and the "uniform dielectric matrix" is made of atoms that will pull the nano-particles at least one atom away from each other, meaning the nano-particles don't interact directly any more.

 

It must be possible that the matrix propagates some VdW forces say if a hydrogen bond deforms the orbital of an oxygen or nitrogen, changing its appetite for one hydrogen more, but a dielectric constant must be far too coarse to model that.

 

The dielectric constant is used to model the effect of a solvent on ions, and such a model is already brutal - but at least a ion acts over several molecules distance, and you have half a dozen solvent molecules to apply a macroscopic value (permittivity) to! VdW forces being so more local, I hardly imagine using a macroscopic value for one or two atoms of a molecule.

 

Beware I'm no expert in this field.

[aktuon]

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 (r_c) 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.

Edited October 24, 2012 by aktuon

[Enthalpy]

These are electrostatic forces, for which some established models to consider the solvent as a fine-grained (as if it didn't consist of atoms!) dielectric medium.

For all other forces, such a model can't be adequate, to my opinion, because their range is smaller than one molecule, so the "fine-grained" trick can't possibly work.

[aktuon]

It looks like importing electrostatic forces is a good choice in my system. Thank a lot.