- / An amorphous system can be viewed as a point in con guration space spending most
of its time vibrating about local minima of the energy hypersurface. Transitions to adjacent
minima, which correspond to elementary events of structural rearrangement, are
rare, since the vibrational energy of the system is not high enough to overcome the surrounding
energy barriers. Therefore, molecular dynamics simulations, which can track
a system's behavior over at most a few nanoseconds, fail to give us information about
the atomistic nature and characteristics of such minimum-to-minimum transitions.
In this work we try a di erent approach: we construct molecular con gurations
of an amorphous Lennard-Jones solid, which, for given values of the temperature and
stress/pressure, constitute local minima of the free energy under the quasi-harmonic
approximation (QHA). From the volumetric behavior of these con gurations for various
values of the temperature and/or pressure we conclude that the QHA is very reasonable
for our system and we calculate the values of the isothermal compressibility and of the
elastic constants. We then identify representative paths in con guration space leading
from one free energy minimum to an adjacent one at xed temperature and pressure.
For each of these transitions or elementary structural relaxation events we determine
the corresponding rate constant using the principles of multidimensional transitionstate
theory. The distribution of free energy barriers is found to be strongly asymmetric
and extremely broad, whereas the corresponding distribution of activation entropies is
narrow. There is a strong positive correlation between the volume change and the
free energy change accompanying each of these elementary transitions, as would be
expected from observed volume relaxation phenomena in glasses.
The physical phenomenon of physical ageing can be described as a sequence of
elementary relaxation events. Therefore, our next step is the analysis of sequential
minimum-to-minimum transitions. This analysis is performed via a novel kinetic
Monte-Carlo simulation method, which we call quasi-MD. The quasi-MD method tracks
di erent stable initial con gurations "escape" through one of the transition states surrounding
their current minimum and get trapped inside a neighboring one, which
becomes the new current state for the system. Each of the observed transition events
is associated with a characteristic time related to the randomly chosen escape route,
integrating-out the vibration inside the minimum. This way, it is possible to follow
the time-dependence of the system's properties during the relaxation process. One
of the most characteristic such properties for the phenomenon of physical ageing is
the self-part of the intermediate scattering function Ss(q; t). Calculation of the timedependence
of Ss(q; t) for the glassy Lennard-Jones using quasi-MD clearly shows the
three known characteristic regions: a) initial rapid decay which corresponds to local
motion of the particles within their "cage", b) the slowly decaying plateau region corresponding
to relaxation of the "cage", called the -relaxation, and c) the nal decay
which corresponds to the breakup of the "cage" and escape of the particles, designated
as the -relaxation.
The glassy Lennard-Jones system used so far is an ideal system for the development
of novel simulation methods and the analysis of the validity of di erent approaches.
However, more complex systems are interesting from a technological point of view.
Therefore, our nal step is the analysis of a glassy polymer. We focus on the validity
of the QHA in glassy atactic polypropylene. Following the same procedure as in the
case of Lennard-Jones spheres, we construct di erent stable amorphous con gurations
for a series of temperatures and pressures. Using these con gurations we calculate the
values of the thermal expansion coefficient and isothermal compressibility, which agree
reasonably well with available experimental data. Finally, the amorphous polypropylene
con gurations get uniaxially strained leading to the estimation of the value of
Young modulus.
| Identifer | oai:union.ndltd.org:upatras.gr/oai:nemertes:10889/1457 |
| Date | 10 March 2009 |
| Creators | Κοψιάς, Νικόλαος |
| Contributors | Δώρος, Θεόδωρος, Δώρος, Θεόδωρος |
| Source Sets | University of Patras |
| Language | gr |
| Detected Language | English |
| Type | Thesis |
| Rights | 0 |
| Relation | Η ΒΥΠ διαθέτει αντίτυπο της διατριβής σε έντυπη μορφή στο βιβλιοστάσιο διδακτορικών διατριβών που βρίσκεται στο ισόγειο του κτιρίου της. |
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