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Ureditvena stanja ograjenega nematskega linearnega polimera v kontinuumskem opisu s tenzorsko vezjo
Vidaković, Danijel (Author), Svenšek, Daniel (Mentor) More about this mentor... This link opens in a new window

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Abstract
V tem delu predstavim tipe stacionarnih ureditev linearnih nematskih polimernih verig, omejenih znotraj krogelne kapside (lupine). Pri tem uporabim poln tenzorski opis problema. Sestavim gostoto proste energije in numerično rešim sistem Euler-Lagrangeovih enačb za številsko gostoto polimernih segmentov in nematski ureditveni tenzor. Obe količini sta zaradi zveznosti polimernih verig povezani s kontinuumsko tenzorsko vezjo. Slednjo vključim v gostoto proste energije po ustreznem kazenskem potencialu. Najdene tipe ureditev prikažem na faznem grafu. V zadnjem delu naloge se ukvarjam še s problemom mehčanja DNA molekul. V modelu zamenjam kazenski potencial izvorov tenzorske vezi 2. reda s kazenskim potencialom 4. reda. Pri tem preverim stabilnost modela in se dotaknem nekaterih perečih vprašanj, kot so lokalno taljenje polimernih verig in prihodnja pričakovanja ter ideje o uporabi modela.

Language:Slovenian
Keywords:tenzorska vez, linearni polimeri, liotropni tekoči kristali, nematski tekoči kristali, ureditveni parameter, kontinuumski modeli, nematski ureditveni tenzor, omejeni tekoči kristali, "mehčanje" DNA molekul, stacionarna ureditev, defekti
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2020
COBISS.SI-ID:32296963 This link opens in a new window
Views:271
Downloads:65
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Secondary language

Language:English
Title:Ordering states of confined nematic linear polymers in continuum description with tensorial constraint
Abstract:
In this work I present types of stationary configurations of nematic polymer chains confined inside a spherical capsid. In this problem I use the complete tensor description of nematic ordering. The solutions are acquired by formulating the free energy density and solving the system Euler-Lagrange equations for number density of polymer segments and nematic order tensor. Due to the connectivity of polymer chains, both variables are connected by a continuity constraint. This constraint is integrated into free energy density functional via an appropriate penalty potential. The obtained types of polymer configurations are presented in a phase diagram. In the last part of this work the problem of DNA "softening" \, is addressed. The previous penalty potential of second order is replaced with the penalty potential of fourth order in the sources of the continuity constraint. I check the stability of this modified model and touch on some burning issues such as local melting of polymer chains, future expectations and ideas for the use of this model.

Keywords:tensor continuity constraint, linear polymers, lyotropic liquid crystals, nematic liquid crystals, order parameter, continuum models, nematic order tensor, confined liquid crystals, DNA "softening", stationary states, defects

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