Polimerleşme ve jelleşme süreçlerinin bilgisayar benzetim deneyleriyle modellenmesi
Modeling of polymerization and gelation processes via computer simulation
Yazar: ALPTEKİN YILDIZ
Danışman: PROF. DR. YAŞAR YILMAZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering ; Polimer Bilim ve Teknolojisi = Polymer Science and Technology
Dizin: Ağ benzetimi = Network simulation ; Monte Carlo benzetimi = Monte Carlo simulation ; Radikal polimerleşme = Radical polymerization ; İstatistiksel fizik = Statistical physics

Özet:
Hayatımızın önemli bir parçası haline gelen polimerler, her geçen gün birçok sektördeki yerine daha da arttırmaya devam etmektir. Kişilerin her geçen gün artan ihtiyaç ve beklentileri, bunları karşılamak isteyen polimer sektörünü, her seferinde farklı bir ürün geliştirmek için çalışmaya sevk etmektedir. Bu gelişmenin sağlanabilmesi adına, en temel aşama olan polimerleşme kinematiklerinin iyi bilinmesi hatta kontrol edilebilmesi gerekmektedir. Yapılan tez çalışması, bahsedilen bu kinematiklerin incelendiği, polimerleşme ve jelleşme süreçlerini temel almaktadır.
Son yıllarda gittikçe gelişen bilgisayar teknolojileri, birçok alanda, yakın zamana kadar hayal bile edilemeyecek gelişmeleri de beraberinde getirdi. Özellikle bu konuda en şanslı taraf biliminsanları oldu.  Yapılan bilgisayar benzetimleri ve kullanılan oldukça kaslı bilgisayarlar ile yeni bir çağın ilk adımları çoktan atıldı. Deneysel gözlemlerini ve kurdukları teorileri, yazdıkları benzetimler ile sınayan biliminsanları, bilim ve teknolojinin gelişmenin ciddi anlamda ivmelenmesini sağladı.
Yapılan tez çalışmasında, bilgisayar teknolojisinin bu faydaları göz önüne alınarak, polimerleşme ve jelleşme süreçleri ile ilgili benzetimler ele alınmıştır. Moleküler dinamiğe girmeden, istatistiksel yöntemlerle yapılan bu benzetimlerde, polimerleşme ve jelleşme kinematikleri incelenmiştir. Bu konuda en temel teori olan sızma (perkolasyon) teorisi, kullanılan basit ve kolay anlaşılabilir yöntemlerle yazılan benzetimle çalışılmış ve buradan kazanılan tecrübelerle daha farklı ve gelişmiş benzetim yöntemlerine kapı açılmıştır.  
Ayrıca tez kapsamında, polimerleşme ve jelleşme süreçlerinin deneysel olarak gözlemlenmesine kullanılan, bir floresans aktif molekül olan piranin (Py) molekülü üzerine de çalışmalar yapılmıştır. Polimerleşme sırasında polimer zincirlerine tutunarak floresans özelliği değişen Py molekülünün, bahsedilen bu zincirlere tutunma mekanizması, tarafımızdan teorik olarak modellenmiş ve yapılan benzetim çalışmalarıyla bu model ayrıntılı bir şekilde incelenmiştir. Ardından deneysel gözlemleri ile sonuçlar kıyaslanmıştır.
Yapılan tüm çalışmaların sonucunda, bilgisayar benzetimleri sayesinde, polimerleşme ve jelleşme süreçlerinin, pratik ve verimli bir biçimde incelenebileceği, alınan sonuçlar ve yapılan tartışmalarla açık bir şekilde ortaya konmuştur.

Abstract:
Polymers, which are used in many parts in our daily life, also are vital materials in industry with their various applications. With increasing demands and necessities of end users, manufacturers pushed themselves to develop new products which have to meet customers' desires and expectations.
In order to achieve these targets, it was necessary to learn and even control the polymerization kinetics, which constitutes the basics of all. This thesis covers the kinetics, polymerization and also gelation processes of polymers.
Continuous development in computer technology of late years, has led to extraordinary innovations in many relevant fields which could not be possibly imagined even a decade ago. The scientists are the leading major group which took advantage of these innovations the most in the asserting new theories and solutions to certain problems.
Scientists have made progress by testing their experimental results using computer simulations, which turned out to be an inevitable tool in the field of science and technology. In this thesis, simulations of polymerization and gelation processes are discussed by using the improvements in computer technology.
A single polymer chain consists of monomers having relatively small molecular weights, which are connected by covalent bonding. Thanks to the binding mechanism, the number of monomers of this polymer chain could be increase to ten million or more. Chromosome is maybe one of the most appropriate examples of such a polymer, by having hundreds of millions of monomers.
Gels simply can be defined as cross-linked polymer networks which can swell and shrink isotropically and surrounding its environment from one end to another. Gels are classified according to type of their determining parameters like monomers, solvent, mechanism of crosslinking.
The process of reacting monomer molecules in a chemical reaction to form polymer chains or three-dimensional networks is called as polymerization. One of the crucial constraints for observing such a reaction is, for a monomer, to be connected to at least two or more monomers, which is also called as monomers' functionality. Considering this fact, one can easily claim that there are plenty of chemical reaction types as well as reacting monomers, which affects the polymerization.
Concept of gelation is a compelling and challenging issue for many scientists. The first sensational work could be attributed to Flory in 1941 and Stockmayer in 1943.
Today the study known as "Classical Theory" or "Mean Field Theory" focuses on estimating the gel point and the molecular weight distribution in a solvent. Following the Classical Theory, one of the most important contribution to gelation theory has been made by Stauffer and De Gennes. This theory defining gelation on a periodic lattice is known as Percolation Theory.
Percolation theory which originally established by Broadbent and Hammersley more primitively, includes the enclosed circles naturally and handles this problem easily which was a challenging issue for Classical Theory.
This thesis primarily focused on percolation theory by using simulation techniques. In this study, polymerization and gelation kinetics have been discussed by these simulations which are created by statistical methods, without dealing with molecular dynamics. Percolation theory, which is considered as a very basic theory regarding this topic is studied with simple and comprehensive methods. The obtained results and gained skills about basics of this simulation, played an important role of being able to create more complex and challenging simulations.
Critical exponents, which are discussed in detail under the topic of percolation theory, are composing the basics of polymerization and phase transitions. It is very useful and gives relying outcomes that verifying the values of the critical exponents by making controlled experiments in addition to relevant mathematical approaches and computer simulations. During an experiment one should be very sensitive about not intervening the system physically or chemically. Observing a quick response and preventing that response to be using in an appropriate manner is also another issue to deal with.
In many studies it is shown that fluorescent spectroscopy is a very informative tool for determining the critical exponents. In this sense, fluorescent spectroscopy is discussed accordingly.
In computer simulations, various examinations exist about binding mechanisms of pyranine molecule. Before introducing this mechanism, it is briefly discussed the spectroscopic properties of pyranine molecule. The fluorescent spectrums of pyranine in distilled water and DMSO will be discussed. In these two different media, some characteristic properties such as pH, concentration, viscosity and polymerization are examined to see their effects on fluorescent characteristics.
Pyranine molecule bind the PAAm strands in two different ways. Pyranine molecule can be either an initiator or a terminator. At the very early stages of the reaction, pyranine becomes an initiator by interacting with the actual initiator molecule of APS and catalyzes the chain growth. Secondly, especially when the reaction comes to saturation meaning that the reaction speed is relatively low, pyranine molecules bind to the chain end by activating from environmental factors, which results a terminating characteristics of pyranine.
Considering these two characteristic properties of pyranine, it is clearly modelled of binding mechanism for pyranine molecule to PAAm chains in a statistical manner.
Third chapter of this thesis is dedicated to examine the simulations in a detailed way which constitutes the background of this study. In this sense random numbers, which are the most critical variable of whole simulation is studied.
The random number generator used, in this study is the Mersenne Twister (MT) generator which is developed by Makoto Matsumoto and Takuji Nishimura. In addition to its ease of utilization and quick response, MT also has a very long period (Around $2^{19937}-1$). The selected random number generator, has been compared with a random number generator belonging the library of C++ programming language. This computer program has generated random numbers between 0--100 and 0--1000 for $10^8$ times with both generators. After then, the results used for the histograms to compare these generators.
A special algorithm is designed for managing a reliable random walk along the grid which is used in simulation studies. Following this random walk a detailed explanation has been made about its advantages. Later on, critical exponents for sol-gel transition is determined and percolation simulations are run with this developed method.
Thanks to gained experimentation and ability of simulation skills, it was possible to move a step forward model smart chains. This technique led us to simulate polymerization and gelation processes with better methods. By using these smart chains, a model of binding mechanism for pyranine molecule is also simulated.
In order to verify the model that is asserted from study, collected results have been compared with an equation that is established by us too. For finalizing the study, the model for binding mechanism of pyranine molecule is tested in laboratory by using experimental techniques. The results obtained from both simulations and experiments are discussed to show the consistency of whole study.