Relaksaciona svojstva modela subdifuzivnog gasa na trougaonoj rešetki
Relaxation properties of subdiffusive gas model on a triangular lattice
Author
Šćepanović, Julija R.Mentor
Vrhovac, SlobodanCommittee members
Knežević, MilanElezović-Hadžić, Sunčica
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Show full item recordAbstract
Predmet ove doktorske disertacije obuhvata proučavanje transportnih svojstava
razuređenih sistema kao što su porozni materijali, staklasti sistemi i granularni materijali. U ovom radu korišćene su numeričke simulacije modelnih gasova na dvo-
dimenzionalnim rešetkama koje su bazirane na konceptu geometrijske frustracije. Osnovni ciljevi rada vezani su za bolje razumevanje fenomena anomalne difuzije u sistemima kao što su mikro-porozni materijali i super-ohlađene tečnosti. Subdifuzivni
transport karakteriše sublinearna zavisnost srednjeg kvadratnog pomeraja čestica od
vremena. Razvijen je model subdifuzivnog gasa na triangularnoj rešetki koji ima
translacione i rotacione stepene slobode. Taj model je uspešno reprodukovao neka
važna svojstva staklastih sistema. Pre svega, izučavanjem Van Hove-ove korelacione
funkcije pokazano je prisustvo dinamičkih heterogenosti u sistemu. Pokazano je da
supresija rotacionih stepeni slobode ima važnu ulogu za pojavu subdifuzivnog režima
transporta. Potpu...no ukidanje rotacije omogućilo je proučavanje poroznih sistema koje
karakteriše pojava ”single-file” difuzije (difuzija duž kanala u kome ne može doći do
mimoilaženja čestica). Relaksaciona vremena u sistemu su određivana praćenjem vre-
menske zavisnosti korelacione funkcije rasejanja (self-intermediate scattering function).
U skladu sa predikcijama teorije spregnutih moda dobijena je stepena divergencija vremena relaksacije korelacione funkcije rasejanja i inverznog difuzionog koeficijenta, sa
istim eksponentom u oba sluˇcaja. U sluˇcaju objekata koji su linearni segmenti (k-meri)
nije primećena pojava strukturne zarobljenosti u sistemu. Model je generalizovan tako
da objekti mogu biti složene samonepresecajuće šetnje na triangularnoj rešetki, što je
omogućilo analizu uticaja veličine i simetrije objekata na subdifuzivni transport, pre
svega u super-ohlađenim tečnostima. Osim toga, proučavana su perkolaciona svojstva
modela slučajne sekvencijalne adsorpcije složenih objekata na triangularnoj rešetki
sa ciljem da ona budu dovedena u vezu sa subdifuzivnom dinamikom odgovarajućeg
gasa na rešetki. Dobijeni rezultati ukazali su na to da za razne objekte iste dužine,
prag za perkolacije kompaktnih objekata ima veću vrednost od praga koji odgovara
izduženim, anizotropnim objektima. Nađeno je da u blizini praga za perkolacije, korelacione funkcije rasejanja iščezavaju kao stepena funkcija, za dovoljno male talasne
vektore. Ispod praga za perkolacije, korelacione funkcije za velika vremena opadaju u
skladu sa Kohlrausch-Williams-Watts zakonom. Za svaki proučavani objekat, vreme
relaksacije sistema (gasa na rešetki) divergira kada gustina sistema teži odgovarajućoj
kritičnoj gustini. Kritična gustina zavisi od geometrijskih svojstava objekta i uvek je
viša od vrednosti perkolacionog praga za taj objekat. Za sve objekte, osim k-mera,
kritična gustina ima vrednost manju od vrednosti gustine zagušenja (jamming den-
sity), što ukazuje na postojanje strukturne zarobljenosti sistema. Prethodno navedena
dinamička svojstva sistema su u skladu sa rezulatatima dobijenim u raznim modelima
koji se bave formiranjem gelova.
The subject of this dissertation includes the study of transport properties of disor-
dered systems such as porous materials, glassy systems and granular materials. In this
thesis, we used the numerical simulations of the model of gases on two-dimensional
lattice that are based on a concept of geometrical frustration. The main objectives of
the work are related to better understanding of the phenomenon of anomalous diffu-
sion in systems such as micro-porous materials and super-cooled liquid. Subdiffusive
transport is characterized by sublinear dependence of the mean square displacement
of the particles of the time. We developed the model of the subdiffusive gas on tri-
angular lattice which has translational and rotational degrees of freedom. This model
has successfully reproduced some important properties of glassy systems. First of all,
by investigating Van Hove’s correlation function, it is shown the presence of dynamic
heterogeneity in the system. Also, it has been shown that supp...ression of rotational
degrees of freedom has an important role in the occurrence of subdiffusive transport.
Complete surpression of the rotation is enabled study of the porous system that char-
acterizes the phenomenon of ”single-file” diffusion (diffusion along the channel where
it is not possible to reach the passing particles). Relaxation times in the system are
determined by examining the time dependence of the self-intermediate scattering func-
tion. In accordance with the predictions of the mode coupling theory we obtained the
power law divergence of the relaxation time and of the inverse value of the diffusion
coefficient, with the same exponent in both cases. In the case of objects that are linear
segments (k-mer) we haven’t observed the structural arrest of the system. The model is
generalized so that objects can be complex self-avoiding walks on the triangular lattice,
enabling the analysis of the size effects and symmetry of the objects on subdiffusive
transport, especially in super-cooled liquids. In addition, we studied the percolation
properties of the model of a random sequential adsorption of the complex objects on
triangular lattice with the aim of it being correlated with subdifusive dynamics rel-
evant to the gas on lattice. Results have shown that for a variety of objects of the
same length, percolation threshold for the compact object has a greater value than
the threshold corresponding to elongated, anisotropic structures. It has been found
that near the percolation threshold, correlation function vanishes via power law for
small enough wave vectors. Below the percolation threshold, the correlation function
for large times, decreases in accordance with the Kohlrausch-Williams-Watts law. For
each studied object, relaxation time of the system (gas on the lattice) diverges when
the density of the system approaches the adequate critical density. Critical density
depends on the geometrical properties of the object and its value is always higher than
value of the percolation threshold for the object. For all objects, except k-mers, the
critical density has a value lower than the jamming density, which indicates the ex-
istence of structural arrest of the system. The mentioned dynamic properties of the
system are consistent with the results obtained in a variety of models that deal with
the formation of gels.