iMechanica - Comments for "Surface Energies? Continuum Molecular Dynamics?"
https://imechanica.org/node/4129
Comments for "Surface Energies? Continuum Molecular Dynamics?"enDefinitely helps.
https://imechanica.org/comment/9052#comment-9052
<a id="comment-9052"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/9049#comment-9049">A little explanation</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Thanks for your reply, it does help. I am getting Israelachvili's book, which hopefully will answer my questions.
</p>
<p>
I have learned a lot trying to understand this sort of modeling. I was naïvely hoping for a while there was a simple answer for me to understand the different surface energy forms for different materials, but in a way it is enough of an answer to know that there are no strong rules for choosing such forms.
</p>
<p>
You remark that "Continuum equations derived from these potentials are tricky to<br />
construct and this constitutes a vigorous research area in itself." I am curious if you have any references or further explanation on this issue. I could find virtually no information on the Continuum L-J model, let alone any others, and Attard does not provide a reference. This seems like an extremely interesting (though irrelevant to my interests in the matter) part of this research.
</p>
<p>
</p>
<p>
Thanks again,
</p>
<p>
Mike
</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/4129%23comment-form">Log in</a> or <a href="/user/register?destination=node/4129%23comment-form">register</a> to post comments</span></li>
</ul>Thu, 30 Oct 2008 02:46:54 +0000Mike Grahamcomment 9052 at https://imechanica.orgA little explanation
https://imechanica.org/comment/9049#comment-9049
<a id="comment-9049"></a>
<p><em>In reply to <a href="https://imechanica.org/node/4129">Surface Energies? Continuum Molecular Dynamics?</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>
I hope this helps a little. The Lennard-Jone (L-J) potential is not a continuum potential but rather a model of interaction between particles, so it is therefore only appropriate for particle methods, especially molecular dynamics (MD), or, depending on your frame of reference, meshless Lagrangian methods at the atomic length scale. L-J a specific progeny from a larger family of vein Mie potentials, where the attractive part (z^-6) corresponds to the van der Waals (vdW) equation of state and the repulsive part (z^-12) is adopted purely for mathematical convenience.
</p>
<p>
L-J is appropriate when considering atoms or small molecules and is the typical choice for first principles MD simulations; however, the number of particles required for systems of engineering interest are often prohibitively expensive to evaluate computationally (I am not an expert on this but I believe the current state-of-the-art limits using the largest clusters is still restricted to the low billions of atoms). Instead, you need larger representative elements, and other contact laws need to be used in that case.
</p>
<p>
Continuum equations derived from these potentials are tricky to construct and this constitutes a vigorous research area in itself. Often, a combined experimental and simulation approach is used where carefully constructed MD simulations are used to are combined with experimentally-derived parameters to develop these continuum (constitutive) equations. For many situations, though, analytically derived contact laws can suffice. The contact laws you mentioned in the post (JKR and DMT) are derived from analytical consideration of several particles in specific agglomerated geometries (spheres and planes) evaluated using vdW to determine constitutive equations for the pairwise agglomerate interaction and are therefore appropriate for modeling larger adhesive bodies (>nm). Strictly Hertzian contact is appropriate only for larger aggregates (>100's microns) where adhesion is not a significant influence.
</p>
<p>
A good overview of surface interactions at the scale level you are referring to can be found in Israelachvili's "Intermolecular and Surface Forces"
</p>
</div></div></div><ul class="links inline"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/4129%23comment-form">Log in</a> or <a href="/user/register?destination=node/4129%23comment-form">register</a> to post comments</span></li>
</ul>Wed, 29 Oct 2008 18:32:33 +0000Scott Johnsoncomment 9049 at https://imechanica.org