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Electronic theses and dissertations repository


Tesi etd-12072011-120258

Thesis type
Tesi di dottorato di ricerca
Microscopic Dynamics of Polymer Melts: Numerical Simulations with Coarse-Grained Models
Settore scientifico disciplinare
Corso di studi
tutor Prof. Leporini, Dino
Parole chiave
  • polymers
  • molecular dynamics
  • Glass transition
  • density-temperature scaling
  • Debye-Waller factor
  • cage correlations
Data inizio appello
Riassunto analitico
Every liquid in principle can transform into a glass if it is cooled or compressed fast enough. Glass<br>is one of the most important artificial materials utilized by man. Numerous applications of glass<br>materials and glass transition phenomenon include obtaining of the optimal wet-skid resistance by<br>using the tread rubber with high glass transition temperature, enhancement of the ballistic<br>penetration resistance of armor coatings obtained by energy dissipation associated with an impact induced<br>transition of the coating to the glassy state, the material selection for acoustic tiles on<br>submarines allowing to undergo the glass transition at the frequency of the active sonar at seawater<br>temperatures thus dampening the sonar, arterial walls restoring, preservation of food,<br>highly soluble pharmaceuticals. So, the study of glassy state tends to be one of the most promising<br>and interesting tasks in chemistry in our days. This fact was my main motivating factor to study the<br>structural and dynamical characteristics of the polymer melt approaching to glass transition from above<br>in group of Prof. Dino Leporini in Pisa University.<br>The particles(in this Thesis the word “particle” signifies the most elementary rigid part of the system<br>under investigation. In general, it can be either molecule for the system containing the rigid molecules,<br>or atom for the case of flexible molecules. As far, as in this Thesis the polymer melt is the system<br>that I am investigating, the word “particle” in context of my research signifies the monomer) spend<br>increasing periods of time, rattling in cages formed by their neighbors while the liquid, consisting of<br>these particles, approaches the glass transition. Finally, the particles are relaxed from their cages -<br>this process is called the structure relaxation. The main aim of this thesis is the investigation of the<br>microscopic dynamics of the particles trapped in these cages and the study of the possible ways to<br>connect this fast dynamics in cage to slow macroscopic dynamics associated with structure relaxation.<br>First direction of research is based on the density-temperature scaling of the one of the most important<br>characteristics of the cage dynamics - the Debye-Waller factor(that is the amplitude of the particle’s<br>rattling in the cage, see the section 1.2 for the details). The density-temperature scaling has become<br>very popular in the recent years due to the improvement of the technical equipment of the experiments,<br>that allowed to change both density and temperature of the system in simultaneous and prompt way.<br>The density-temperature scaling of the structure relaxation time for single and multi-component liquids<br>having different interaction potentials was introduced and investigated in this thesis from the different<br>points of view, including the pressure-energy correlations and potential energy landscapes with citations<br>of the correspondent sources (see the section 3.1). Recent research of the Prof. Leporini group has<br>presented the universal scaling between the structure relaxation time and Debye-Waller factor(see the<br>subsection 3.1.5). Nevertheless, the research of the density-temperature scaling of the Debye-Waller factor has been missing so far and I tried my best to improve this situation and to show that the<br>density-temperature scaling is valid for the microscopic processes, too. In the terms of the second<br>direction of investigation I studied several functions of cage correlation for the polymer melt. This<br>study should have allowed me to better understand the processes taking place in the cages or “shells”<br>surrounding the tagged particle and to discover the new types of connection between these microscopic<br>processes from one side and the macroscopic processes, like e.g. the structure relaxation, from another<br>side. Results of this study could help to develop the new ways of understanding of the universal scaling<br>between the structure relaxation time and Debye-Waller factor. Furthermore, it is interesting to study<br>the cage correlation functions of the polymer melt because the polymers have been never studied in<br>this way so far. Previous researches of the correlation functions dealt with the binary mixtures,<br>hard spheres and disks, etc. I also have to say that this study is based on introduction of different<br>correlation functions including the self-correlation functions of displacement that have not been studied<br>in context of the liquids state research so far.<br>As to the meaning of the results of the thesis, I may state the following:<br>• the density-temperature scaling of the Debye-Waller factor is evidenced(see the section 3.1 and<br>the Chapter number 4). The values of the scaling exponent γ are consistent with the predictions<br>from the study of Lennard-Jones liquids. Data of all the polymers in the study, that have different<br>molecular masses and interaction potential, collapse the straight lines of Debye-Waller factor vs<br>TV γ plot, where any straight line is uniquely defined by the molecular mass and parameters of<br>the interaction potential. These lines cross in one “universal” point.<br>• the cage correlation functions, describing the time evolution of the neighbor cage of the given<br>particle(see the subsection 3.2.1 and section 5.1) and following from the immediate physical interpretation,<br>represent the alternative but perfectly equivalent instrument for the description of<br>the structure relaxation, compared to the more rigorous intermediate scattering function.<br>• the analysis of the spatial correlation of displacement(see the subsection 3.2.2 and section 5.2)<br>evidences the link between the well-known static properties of the system and the dynamic properties,<br>represented by the direction and modulus correlation functions of displacement. Origin of<br>this correlation is not perfectly clear and needs further investigation.<br>• analysis of the time correlations of displacement (see the section 5.3) shows that the directionality<br>of motion rather than the displacement modulus seems to connect the fast microscopic and slow<br>macroscopic dynamics. The direction of the displacement of a particle at the time scales of cage<br>regime determines in general the direction of the particle’s motion even at much longer times.<br>As far, as the outlook of the Thesis is concerned, I have to point out that the further investigation,<br>generalization and improvement of these results could be useful. The results of current Thesis allow to<br>construct only several very narrow and rickety bridges between the fast microscopic and slow macroscopic<br>dynamics. These narrow links should be united with the other existing ones and with those that<br>will be created in future, thus forming the new theories, methods and approaches. Among the possible<br>ways of developing of the results of this Thesis I can point to either the prospect of the study of the<br>influence of TV γ on the behavior of the cage correlation functions, uniting the two main directions of<br>research of this thesis, could be the most promising direction of further study, or to the aforementioned<br>possible research of the reasons of the correlation between the static and dynamic(represented by the<br>direction and modulus correlation functions of displacement) properties of the system. Results and<br>outlook of the Thesis are discussed in the Conclusions in more detailed way.<br>My thesis consists of five chapters. First chapter of my PhD thesis presents the introduction to glass<br>transition phenomenon (section 1.1); covers the information about the static structure and relaxation in<br>liquids and introduces the functions that describe these processes (section 1.2); and describes the glass<br>transition in polymers with particular attention to the similarities and differences of the glass transition<br>processes in simple liquids and polymers(section 1.3), thus explaining why the polymers usually are the<br>good glass-formers.<br>Then, in the second chapter, covering the methods of the computer simulations of polymers, there<br>follow:<br>• the review of numerous methods of molecular dynamics and (a bit) of monte-carlo simulations of<br>the glass-forming polymers(section 2.1), allowing to better understand the future ways of development<br>of the simulation studies of the polymers and to enrich the arsenal of a modern scientist<br>with new powerful computational methods enabling the simulations to become more quick and<br>effective<br>• separate section (2.2) describing the numerical methods and MD model (developed by Cristiano<br>De Michele, a former member of the Leporini group) used in the MD simulations runs during the<br>work over the fourth and fifth chapters<br>Third chapter contains the theoretical background for the fourth and fifth chapters.<br>• the theoretical introduction to the popular aspect of density-temperature scaling of the relaxation<br>time in numerous classes of simple liquids and polymers (section 3.1). Theoretical basis of the<br>scaling and its connection to the inverse power law is discussed in the subsection 3.1.1, the numerous<br>ways of approximation of the scaling exponent γ are presented in the subsection 3.1.2. The<br>speculations upon the relation between the density-temperature scaling and the pressure-energy<br>correlations in liquids are presented in the subsection 3.1.3; the connection of the temperaturedensity<br>scaling to the fragility and potential energy landscapes is discussed in the subsection 3.1.4.<br>Section ends with results of Leporini group (subsection 3.1.5) obtained just before beginning of<br>my work over the PhD thesis. These results allowed to ascertain the universal scaling between the<br>fast microscopic and the slow macroscopic dynamics and also urged me to explore the possibility<br>of temperature-density scaling not only of the slow macroscopic dynamics reflected in such macroscopic<br>parameter as the relaxation time, but also of the microscopic dynamics closely connected<br>to the Debye-Waller factor.<br>• section 3.2, consisting of the introduction to the functions regarding the cages surrounding the<br>tagged atom (subsection 3.2.1) and the basic theoretical information about the spatial correlation<br>functions (subsection 3.2.2)<br>The original results of the research of temperature-density scaling of the Debye-Waller factor are<br>presented into the fourth chapter.<br>The fifth chapter reports an original investigation of the correlation functions of supercooled polymeric<br>melt. The peculiarities of motion of the atoms in the supercooled liquid, especially when it<br>approaches the glass transition, are always of great interest and importance, because the understanding<br>of the laws of this motion could be crucial for prediction of various properties of materials close to their<br>glass transition. The correlation functions give us a rather detailed picture of the motion of the atoms.<br>In the section 5.1 I explored the correlation functions regarding the cages surrounding the tagged atom.<br>The description of the program, calculating the neighbor list and cage correlation functions (already<br>introduced in subsection 5.4.1), follows in subsection 5.1.1. The results of the run of this program using<br>the input data from the simulations of our MD model, already described in section 2.2, are presented in<br>subsection 5.1.2. In section 5.2 there follows the research of the spatial correlation functions. The structure<br>of this subsection is similar to the previous one with the introductory part of the corresponding<br>functions being presented in subsection 3.2.2, program description in subsection 5.2.1 and the results of<br>the run in subsection 5.2.2. In the section 5.3 I introduced the original self-correlation functions of displacement<br>in subsection 5.3.1. The program, calculating these functions, is described in the subsection<br>5.3.2, the results of run - in the subsection 5.3.3.<br>Finally there follow the conclusions, appendix and bibliography.