Excitation Energy Transfer In Donor-Acceptor Systems Involving Metal Nanoparticles, And In Conjugated Polymers
This thesis consists of two parts and nine chapters. The first part (Part I) presents theoretical studies on non-radiative mode of excitation energy transfer (EET) in donor-acceptor (D-A) systems involving metal nanoparticles. Part I contains four chapters and describes EET in following different D-A systems: (i) dye and a spherical metal nanoparticle of different sizes, (ii) two spherical metal nanoparticles, and (iii) two prolate shaped metal nanoparticles at different relative orientations. Part II provides a detailed study on the origin of photochemical funneling of excitation energy in conjugated polymers like poly-[phenylenevinylene] (PPV) and consists of three chapters. The ninth chapter provides a concluding note. The thesis begins with a basic introduction on Forster resonance energy transfer(FRET), presented in chapter 1. This chapter provides a detail derivation of Forster’s rate expression for a non-radiative process of EET from a donor to an acceptor molecule and discusses the limitations of Forster theory. The chapter highlights the huge success of FRET technique in understanding biological processes assisted by changes in conformations of biopolymers under conditions where Frster theory is valid. The chapter also discusses practical limitations of FRET technique such as use of pre-averaged value of orientation factor and photobleaching of dye molecules. Part I starts with chapter 2 which explains the advantages of using metal nanoparticles over dye molecules in D-A systems. The chapter discusses recent experimental re-ports of excitation energy transfer to nanoparticles, now commonly referred to as nanoparticle surface energy transfer (NSET). Theories describing the process of EET from a dye molecule (dye molecule is assumed to be a point dipole) to a planar metallic surface are discussed. In the case of energy transfer from a donor dye molecule to a planar metallic surface, the distance dependence of the rate of EET is found to vary as 1/d4 where dis a distance from the center of a dye molecule to the metallic surface. This is unlike conven-tional FRET where rate of EET follows 1/R6 distance dependence with R as a distance between the centers of D and A. Also, a recent experimental study by Yun et al [J. Am. Chem. Soc. 127, 3115 (2005)] on energy transfer from a dye molecule to a spherical gold nanoparticle reports that the rate of EET follows 1/d4 distance dependence. The remaining chapters of this part focus on understanding this deviation from the Forster theory in different D-A systems. Chapter 3 describes quantized electro-hydrodynamic approach used to model the plasmonic excitations in metal nanoparticles. The optical absorption frequencies of nanoparticles computed here are subsequently used in chapters 4 and 5 for the calculation of the rate of EET. The chapter discusses the merits and de-merits of electro-hydrodynamic approach in comparison to other available techniques. The electro-hydrodynamic method of calculating the absorption frequencies provide a physically appealing, mathematically simple and numerically tractable approach to the problem and is also at the same time, semi-quantitatively reliable. The optical frequencies obtained as a function of size and aspect ratio of metal nanoparticles are found to be in good agreement with physical predictions. Chapter 4 studies the distance dependence of rate of EET for a D-A system similar to one studied by Yun et al [J. Am. Chem. Soc. 127, 3115 (2005)]. The chapter contains the relevant derivations of the quantities required for computing the interaction matrix elements. The dependence of the rate of EET on R is found surprisingly to be in agreement with Forster theory even at intermediate distances compared to the size of spherical nanoparticles (a). However, the dependence of rate of EET on d is found to vary as 1/dσwith σ=3 - 4 at intermediate distances which is in good agreement with the experimental results of Yun et al. At large values of d, the distance dependence of rate is found to vary as 1/d6 . The chapter discusses the physical basis behind these results. The theory predicts a non-trivial dependence of rate on the size of a nanoparticle which ultimately attains the asymptotic a3 size dependence. The rate of EET is also studied for different orientations of dye molecule. Chapter 5 studies surface plasmon mediated EET between two metal nanoparticles. The rate of EET between two prolate and spherical shaped silver nanoparticles is studied as a function of Rand d. d, in present chapter denotes surface-to-surface separation distance between two nanoparticles. In case of EET between two non-spherical nanoparticles, even at separations larger than the size of the nanoparticle, a significant deviation from 1/R6 dependence is obtained. However, 1/R6 distance dependence of EET rate is found to be robust for spherical nanoparticles over an entire range of separations. The deviation of rate from 1/R6 distance dependence becomes more pronounced with in-crease in the aspect ratio of the nanoparticle. The relative orientation of the nanoparticles is found to markedly influence the R-dependence of EET rate. Interestingly, the relative orientation of nanoparticles effect the d-distance dependence of the rate to a lesser extend in comparison to the R-dependence of the rate. Therefore, we predict that for non-spherical nanoparticles studying EET rate as a function of will provide more conclusive results. The chapter also discusses the size dependence of rate of EET for this particular D-A system. In Part II, excitation energy transfer (EET) in a conjugated polymer is studied. To start with, chapter 6 provides a brief introduction to photophysics of conjugated polymers. The chapter discusses the nature of photoexcitations in these systems and stresses on the influence of polymer’s morphology on the optical properties of conjugated polymers. Chapter 7 describes the theory used for modeling conjugated polymer chain. A polymer chain consists of number of spectroscopic units (chromophores) of varying lengths. The average length of chromophores in conjugated polymer depends on defect concentration. In the present study we treat an excitation generated on each chromophore within “particle-in-a-box” formalism but one that takes into account the electron-hole interactions. The transition dipole moments and the radiative rates are computed for different lengths of chromophores with parameters appropriate for PPV chain. These quantities are used in chapter 8 for calculating the absorption and emission spectra of conjugated polymer chains at different defect concentrations. The main aim of Chapter 8 is to understand the origin of photochemical funneling of excitation energy in conjugated polymers. PPV chain is modeled as a polymer with the length distribution of chromophores given either by a Gaussian or by a Poissonian distribution. We observe that the Poissonian distribution of length segments explains the optical spectra of PPV rather well than the Gaussian distribution. The Pauli’s master equation is employed to describe the excitation energy transfer among different chromophores. The rate of energy transfer is assumed to be given here, as a first approximation, by the well-known Forster expression. The observed excitation population dynamics confirm the photochemical funneling of excitation energy from shorter to longer chromophores of the polymer chain. The calculations show that even in steady state more than one type of chromophore contribute towards the emission spectrum. The observed difference between the calculated emission spectra at equilibrium and in steady state indicates the existence of local domains in a polymer chain within which the non-radiative excitation energy transfer from shorter to longer chromophores take place. These results are found to be in agreement with recent experimental reports. The concluding chapter 9 gives a brief summary of the outcome of the thesis and ends up with suggestion of a few future problems which in current scenario are of great interest.
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