Reactions and Interfacial Behaviors of the Water–Amorphous Silica System from Classical and Ab Initio Molecular Dynamics Simulations Page: 62
x, 214 pages : illustrationsView a full description of this dissertation.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
calculate the diffusion coefficient through the Einstein diffusion equation (Eq. 0-19)
which describes random-walk diffusion in a three-dimensional crystal [225]:
D =1lim-MSD Eq. 0-19
6 t->oo dt
The 1/6 coefficient removes the redundancy in the degrees of freedom since the MSD
data includes forward and backward movement in each of the three dimensions (x, y,
and z). The limit as time approaches infinity is critical as atoms will go through three
different diffusion stages. The first is the ballistic region, where the MSD is proportional
to time squared [226]. The next region is the cross over region, where the MSD is
independent of time [226]. The final region is the diffusion region, and occurs when the
MSD is proportional to time [226]. The difference in diffusion regions is particularly
apparent when the logarithm of the MSD with time is plotted. Representative plots of the
mean squared displacement (MSD) data with time is included in Figure 0-4 for hydrogen
atoms in water, to demonstrate the change in the diffusion regimes with time.
a).
0.8 .
0.6
0.2 -
U)
0.0 ' ' ' ' '
0 1 2 3 4 5 6 7
Time (ps)62
Upcoming Pages
Here’s what’s next.
Search Inside
This dissertation can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Dissertation.
Rimsza, Jessica M. Reactions and Interfacial Behaviors of the Water–Amorphous Silica System from Classical and Ab Initio Molecular Dynamics Simulations, dissertation, May 2016; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc849660/m1/73/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .