etd@IISc Collection:
http://hdl.handle.net/2005/42
Wed, 13 Apr 2016 17:19:08 GMT2016-04-13T17:19:08ZStudies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional Systems
http://hdl.handle.net/2005/2480
Title: Studies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional Systems
Authors: Sahoo, Shaon
Abstract: This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems.
Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry.
In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique.
Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally.
In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states.
The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.Thu, 03 Sep 2015 18:30:00 GMThttp://hdl.handle.net/2005/24802015-09-03T18:30:00ZElasticity And Structural Phase Transitions Of Nanoscale Objects
http://hdl.handle.net/2005/2498
Title: Elasticity And Structural Phase Transitions Of Nanoscale Objects
Authors: Mogurampelly, Santosh
Abstract: Elastic properties of carbon nanotubes (CNT), boron nitride nanotubes (BNNT), double stranded DNA (dsDNA), paranemic-juxtapose crossover (PX-JX) DNA and dendrimer bound DNA are discussed in this thesis. Structural phase transitions of nucleic acids induced by external force, carbon nanotubes and graphene substrate are also studied extensively. Electrostatic interactions have a strong effect on the elastic properties of BNNTs due to large partial atomic charges on boron and nitrogen atoms. We have computed Young’s modulus (Y ) and shear modulus (G) of BNNT and CNT as a function of the nanotube radius and partial atomic charges on boron and nitrogen atoms using molecular mechanics calculation. Our calculation shows that Young’s modulus of BNNTs increases with increase in magnitude of the partial atomic charges on B and N atoms and can be larger than the Young’s modulus of CNTs of same radius. Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charges and is always less than the shear modulus of the CNT. The values obtained for Young’s modulus and shear modulus are in excellent agreement with the available experimental results. We also study the elasticity of dsDNA using equilibrium fluctuation methods as well as nonequilibrium stretching simulations. The results obtained from both methods quantitatively agree with each other. The end-to-end length distribution P(ρ) and angle distribution P(θ) of the dsDNA has a Gaussian form which gives stretch modulus (γ1) to be 708 pN and persistence length (Lp) to be 42 nm, respectively. When dsDNA is stretched along its helix axis, it undergoes a large conformational change and elongates about 1.7 times its initial contour length at a critical force. Applying a force perpendicular to the DNA helix axis, dsDNA gets unzipped and separated into two single-stranded DNA (ssDNA). DNA unzipping is a fundamental process in DNA replication. As the force at one end of the DNA is increased the DNA starts melting above a critical force depending on the pulling direction. The critical force fm , at which dsDNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the dsDNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base-pairs. Similar force-extension curve has also been observed when crossover DNA molecules are stretched along the helix axis. In the presence of mono-valent Na+ counterions, we find that the stretch modulus (γ1 ) of the paranemic crossover (PX) and its topoisomer juxtapose (JX) DNA structure is significantly higher (30 %) compared to normal B-DNA of the same sequence and length. When the DNA motif is surrounded by a solvent of divalent Mg2+ counterions, we find an enhanced rigidity compared to in Na+ environment due to the electrostatic screening effects arising from the divalent nature of Mg2+ counterions. This is the first direct determination of the mechanical strength of these crossover motifs which can be useful for the design of suitable DNA motifs for DNA based nanostructures and nanomechanical devices with improved structural rigidity. Negatively charged DNA can be compacted by positively charged dendrimer and the degree of compaction is a delicate balance between the strength of the electrostatic interaction and the elasticity of DNA. When the dsDNA is compacted by dendrimer, the stretch modulus, γ1 and persistence length, Lp decreases dramatically due to backbone charge neutralization of dsDNA by dendrimer. We also study the effect of CNT and graphene substrate on the elastic as well as adsorption properties of small interfering RNA (siRNA) and dsDNA. Our results show that siRNA strongly binds to CNT and graphene surface via unzipping its base-pairs and the propensity of unzipping increases with the increase in the diameter of the CNTs and is maximum on graphene. The unzipping and subsequent wrapping events are initiated and driven by van der Waals interactions between the aromatic rings of siRNA nucleobases and the CNT/graphene surface. However, dsDNA of the same sequence undergoes much less unzipping and wrapping on the CNT/graphene due to smaller interaction energy of thymidine of dsDNA with the CNT/graphene compared to that of uridine of siRNA. Unzipping probability distributions fitted to single exponential function give unzipping time (τ) of the order of few nanoseconds which decrease exponentially with temperature. From the temperature variation of unzipping time we estimate the free energy barrier to unzipping. We have also investigated the binding of siRNA to CNT by translocating siRNA inside CNT and find that siRNA spontaneously translocates inside CNT of various diameters and chiralities. Free en- ergy profiles show that siRNA gains free energy while translocating inside CNT and the barrier for siRNA exit from CNT ranges from 40 to 110 kcal/mol depending on CNT chirality and salt concentration. The translocation time τ decreases with the increase of CNT diameter having a critical diameter of 24 A for the translocation. After the optimal binding of siRNA to CNT/graphene, the complex is very stable which can serve as siRNA delivery agent for biomedical applications. Since siRNA has to undergo unwinding process in the presence of RNA-induced silencing complex, our proposed delivery mechanism by single wall CNT possesses potential advantages in achieving RNA interference (RNAi).Sun, 13 Dec 2015 18:30:00 GMThttp://hdl.handle.net/2005/24982015-12-13T18:30:00ZSlow Dynamics In Complex Fluids : Confined Polymers And Soft Colloids
http://hdl.handle.net/2005/2459
Title: Slow Dynamics In Complex Fluids : Confined Polymers And Soft Colloids
Authors: Kandar, Ajoy Kumar
Abstract: The thesis describes the study of slow dynamics of confined polymers and
soft colloids. We study the finite size effect on the dynamics of glassy polymers
using newly developed interfacial microrheology technique. Systematic
measurement have been performed to address the issue of reduction of glass
transition under confinements. Slow and heterogeneous dynamics are the underlined observed behavior for dynamics in confined glassy polymers. The slow relaxation dynamics and dynamical heterogeneity in polymer grafted nanoparticles (PGNPs) systems were studied using advanced X - ray photon correlation spectroscopy (XPCS) techniques. Our studies presented in this thesis on dynamics of polymer grafted nanoparticle systems in melts and solution are the first attempt to study them experimentally. Thus our work shed the light about new technique to study confined system more accurately and explore new soft colloidal system to study fascinating dynamics and interesting phase behavior.
In Chapter 1, we provide the theoretical background along with brief review of the literature for understanding the results presented in this thesis. The details of the experimental set up and their operating principle along with the details of the experimental conditions are provided in Chapter 2. In Chapter 3 we present our newly developed technique (interfacial microrhelogy) and its consequences to study the complex fluids at interface. Chapter 4 discusses the concentration and temperature dependent glassy dynamics in confined glassy
polymers. In Chapter 5 we provide the structural and dynamical study of polymer
grafted nanoparticles in melts and solutions. We provide the summary of
our result and the future prospective of the work in Chapter 6.
Chapter-1 provides the ground work and theoretical aspects for understanding
the results presented in this thesis. It starts with the discussion about
the slow dynamics of complex fluids and transit to dynamic behavior of polymer
in confinement, glassy dynamics in confinements . This also discusses
the basic aspects of studying viscoelastic properties using rheology, interface
rheology, microrheology, interface microrheology techinques. In continuation it
discusses structure and dynamics of different soft colloids investigated for last decade and then theoretical aspects of XPCS is discussed. Towards the end
of this Chapter, we discuss the procedure to explain and understand systems
dynamical heterogeneity near glass like phase transition.
Chapter-2 contains the details of the experimental techniques which has been used for the study of confined polymers and soft colloids. Brief introduction to basic principles of the measurements followed by details of the material and
methods have been provided.
Chapter-3 we discuss the interafacial microrheology of different complex fluids and advantages of the techniques is discussed in Chapter 3. This includes
discussion about the technique sensitivity at the surface using quantum dots
(QDs) as a probe and about the configuration of the QDs at/on monolayer. Later
on establishment of the technique has been demonstrated through easurements on arachidic acid, poly(methylmethacrylate) (PMMA), poly(vinylacetate) (PVAc), poly(methylacrylate) (PMA) monolayers. The extracted subdiffusive nature of QDs in on monolayers through mean square displacement has been explained using fractional Brownian motion model. Towards the end of the chapter we discuss about the extraction of real and imaginary elastic modulus from mean square displacement data using generalized Stokes-Einstein relation for the quasi two dimensional systems and explains about the possible viscoelastic transition in the different monolayers.
The concentration and temperature dependent glassy dynamics of confined polymers (PMMA) are discussed in Chapter-4. We demonstrate the microscopic nature of spatio-temporal variation of dynamics of glassy polymers confined to a monolayer of 2 3 nm thickness as a function of surface density and temperature. It illustrates the systems dynamical heterogeneity and explain the observed large reduction of glass transition temperature in confined system through finite size effect.
In Chapter 5 we discuss the result based on systematic studies of dynamics of PGNPs in melts and solutions. In addition it also illustrates the structural anisotropy and anomalous dynamical transitions in binary mixture of PGNPs and homopolymers in good solvent condition. It provides temperature
and wave vector dependent XPCS measurements on polymer grafted nanoparticles with the variation of functionality. The functionality ( f ) dependent nonmonotonic relaxation in melts of PGNPs and solvent quality dependent non monotonic relaxation of PGNPs system have been elaborated in the continuation.
We present possible phase behavior of PGNPs system in good solvent with addition of homopolymer of two different molecular weight.
Chapter 6 contains the summary and the future perspective of the work presented.Tue, 04 Aug 2015 18:30:00 GMThttp://hdl.handle.net/2005/24592015-08-04T18:30:00ZConfinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding Systems
http://hdl.handle.net/2005/2502
Title: Confinement, Coarsening And Nonequilibrium Fluctuations In Glassy And Yielding Systems
Authors: Nandi, Saroj Kumar
Abstract: One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking.
Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion
of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis.
In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding.
In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters.
The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents.
In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases.
The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid.
When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials).
We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory.
In the final chapter, we summarize the problems studied in this thesis and point out some future directions.Tue, 16 Feb 2016 18:30:00 GMThttp://hdl.handle.net/2005/25022016-02-16T18:30:00Z