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Re: [ESPResSo] General Suitability of Espresso for Fine Particles

From: Burkhard Duenweg
Subject: Re: [ESPResSo] General Suitability of Espresso for Fine Particles
Date: Tue, 09 Oct 2007 14:28:12 +0200
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Lorenzo Isella wrote:

Dear All,
I think I now have a smattering of the basics of Espresso and I have
to start thinking how and if to use it for my research.
I have browsed the web and found espresso applications for polymers,
ions, proteins,  and so on, but my task is really to simulate the
Langevin dynamics of exhaust fine particles (think of them as
carbonaceous particles whose diameter ranges from 2 to 600 nanometers,
the larger ones created by the agglomeration of the small ones) to
investigate agglomeration.
These particles are typically suspended in air, there may or may not
be convection from a carrier flow.
People typically assume that their motion is ruled by a Langevin
equation, and that these particles stick when they collide, giving
rise to complicated structures I would like to investigate.

(1) First of all, am I right to say that the dynamics in the Langevin
thermostat as implemented in Espresso simulates stochastic particle
paths? This is my understanding of the Langevin thermostat in general,
but I am also obviously concerned about the implementation.

==> Yes. Actually, the diffusion is in momentum space.
    You should distinguish between a Langevin equation
    of the type:
    (d/(dt)) x = \mu f + noise
    (that would only live in real space)
    (d/(dt)) x = p / m
    (d/(dt)) p = F - \Gamma (p/m) + noise
    where the the noise couples to the momentum, and the
    particle starts to diffuse only on longer time scales
    t >> m / \Gamma .
    It is the latter case which is implemented in Espresso
    as the Langevin thermostat.

(2) Can e.g. the fene or the harmonic potential be twisted to simulate
this "sticking upon collision"?
Basically I need a strong binding potential with a short interaction
range, the interaction range being identified with the particle
radius. If not, is there any conceptual problem in tabulating it?

===> I think you should twist the LJ potential, and stochastically
     add a FENE bond once you (or your random generator) have decided
     that two particles stick. I don't know about implementational
     details, but I think in principle this should be doable.
     Likewise, tabulated potentials should be implementable.
     All this will probably require some coding, though.

(3)Back to the particle (stochastic) trajectories: the treatment of
the friction and noise terms is particularly delicate. In my case,
this noise stands for the effects of air molecules kicking the
particles. Depending on the air temperature, the air mean-free path
could be larger or smaller than the particle radius and this has to be
taken into account. Can I "tune" the noise term in Langevin equation?

==> Note that the temperature is a parameter in the simulation.
    Higher temperature means a larger means square noise amplitude.
    Therefore the effect which you mention should be automatically
    included. The air mean free path is irrelevant. It is rather
    important how much momentum is transferred onto the particle,
    and here the mass ratio between particle and air molecules is
    much more crucial.

    Let me add: If you think the convection of surrounding air
    is important, then you can do this via coupling to a lattice
    Boltzmann fluid. Then you also get the hydrodynamic correlations
    between the particles right. See P. Ahlrichs and B. Duenweg,
    Journal of Chemical Physics 111, 8225 (1999).

(4)Related to the previous questions: let us say you have a set of
single particles, each of them separately obeying a Langevin equation
with a certain noise.
After colliding and giving rise to a certain agglomerate, the noise
acting on the agglomerate will NOT in general be the sum of the noises
on the individual particles, due to shielding effects (inner particles
may be difficult to reach by air molecules). Can this be somehow
accounted for in Espresso?

===> You could, for example, use the DPD thermostat (see, e.g.
     T. Soddemann, B. Duenweg, and K. Kremer, Physical
     Review E 68, 046702 (2003), and then exploit that the
     friction is a pairwise property and can be different for
     each particle pair - as was done in
     Jacqueline Yaneva, Burkhard Duenweg and Andrey Milchev,
     Journal of Chemical Physics 122, 204105 (2005). In your case,
     you would reduce your friction as soon as the particle
     pair becomes bonded.

     Or you simulate with explicit air and the DPD thermostat.
     Then the effect which you mention would automatically be
     be included.

     Again I cannot tell how easily this is realized in Espresso.

You should however be warned that you leave the realm of
well-defined equlibrium statistical mechanics as soon as you
start to hook up particles irreversibly during the course
of the simulation. But you are probably simulating a non-
equilibrium system anyways.

Regards Burkhard.

| Burkhard Duenweg             e-mail: address@hidden   |
| Max-Planck-Institut          Phone:      +49-6131-379-198        |
|   fuer Polymerforschung      Fax:        +49-6131-379-340        |
| Ackermannweg 10              Home Phone: +49-6721-186221         |
| D-55128 Mainz                                                    |
| Germany                                                          |

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