| dc.description.abstract | The thesis presents theoretical and computer simulation studies of dynamics in several complex systems, namely, electrolyte solutions, aqueous binary mixtures, nanoconfined binary mixtures, polymer dimerization, and non-equilibrium Fluorescence Resonance Energy Transfer (FRET). A unifying theme across the chapters of the thesis is dynamics in correlated systems, especially the role of interactions in determining transport and rate processes. Based on the phenomena studied, the thesis has been divided into five major parts:
I. Study of alkali metal ions in water-dimethyl sulfoxide (DMSO) binary mixtures.
II. Exploration of the hydrophobic interaction induced strengthening of hydrogen bond in water-dimethyl sulfoxide (DMSO) binary mixture.
III. Investigation of nano-confined binary mixture.
IV. Calculation of rate of non-equilibrium Fluorescence Resonance Energy Transfer (FRET).
V. Study of non-equilibrium dimerization of model polymer chains.
These five parts have been further divided into eleven chapters. Below, we briefly outline the contents of each chapter.
Part I consists of two chapters focusing on the structure and dynamics of ions in aqueous binary mixtures. In Chapter 1, we provide a brief overview of the ions’ motion in water. Here, we address the diffusion of ions and limiting laws of electrochemistry. This chapter also discusses continuum model theories of dielectric friction and ion solvation dynamics. Chapter 2 contains the results of our simulation study on the structure and dynamics of alkali metal ions (Li+, Na+, K+, RB+ and Cs+) in various compositions of water-dimethyl sulfoxide (DMSO) binary mixtures. We uncover a number of composition-dependent ion diffusion anomalies that can be traced back to the interplay between the size-dependent charge density of the ion and the resulting difference in the interactions of the ion with water and DMSO molecules. We observe that diffusion of each ion shows non-monotonic composition dependence, with a broad minimum of around 35%. This is found to be related to the maximum in the total viscosity. Further, we observe a breakdown of the Stokes-Einstein relation, particularly at the intermediate composition range, as we vary the DMSO concentration.
Part II delves into the analysis of the structure and dynamics of the hydrogen bond network in the water-DMSO binary mixture. This part again consists of two chapters. Chapter 3 provides an introduction to non-ideality often encountered in aqueous binary mixtures. We discuss different theoretical models for the treatment of binary mixtures. Chapter 4 explores the hydrophobic interaction-induced strengthening of the hydrogen bond in the water-DMSO binary mixture. Using computer simulations, we perform microscopic structural and dynamic analyses to find that these anomalies arise at least partly from an “action-at-a-distance” effect where the attraction between the hydrophobic methyl groups results in the self-aggregation of DMSO molecules that “cages” both rotational and linear motions of molecules involved, leading to the slowdown of bond breaking dynamics. The correlation is reflected in the observed strong correlation of the lifetime with the local coordination number of the associated methyl groups. The elongated water-DMSO hydrogen bond lifetime causes a slowdown of collective dynamics and affects the lifetime of the water-water hydrogen bond. This nonlinear feedback mechanism explains the strong composition dependence of viscosity and is anticipated to play a dominant role in many self-assemblies. Furthermore, the water-DMSO hydrogen bond-breaking mechanism changes from low to high DMSO concentration. We introduce a new order parameter-based investigation of the free energy surface of the bond-breaking pathway. A two-dimensional transition state rate theory (TSRT) calculation is performed for the lifetime of the water-DMSO hydrogen bond, which is found to be semi-quantitatively accurate.
In Part III, we explore transport properties in nanoconfined binary mixtures. This part comprises two chapters. In Chapter 5, we briefly discuss the anomalous behaviour of water under nanoconfinement. In Chapter 6, we study the nanoconfined aqueous ethanol solutions, where we find the long-distance rare but repetitive exchange of ethanol molecules between the two parallel graphene surfaces in nanoconfined aqueous ethanol solutions. We compute the rate of exchange as a function of the separation distance (d) between the two surfaces. We discover that the initiating (or, the launching) step in this exchange is the attainment of an instantaneous orientation of the carbon-oxygen bond vector relative to the graphene surface. This observation led us to construct a two-dimensional free energy surface for this exchange, with respect to two order parameters, namely, (i) the perpendicular distance of ethanol molecule from the graphene surfaces, z and (ii) the orientation of the O-C bond vector, θ of the tagged ethanol molecule. For d = 3 nm, the rate of exchange is found to be 0.44 ns-1 for the force field used. We use both the transition state theory and Kramers’ theory to calculate the rate. The calculated rate agrees well with the simulated value as mentioned above. We find that the rate of exchange phenomenon is sensitive to the interaction strength of graphene and the hydrophobic group of ethanol.
Part IV deals with non-equilibrium Fluorescence resonance energy transfer. This part also consists of two chapters. Chapter 7 provides a detailed derivation of Fӧrster rate expression for a non-radiative process of excitation energy transfer from a donor to an acceptor molecule and discusses the limitation of Fӧrster theory. This chapter highlights the potential application of the technique in understanding biological processes. In Chapter 8, we explore excitation energy transfer in a non-equilibrium regime. Vibrational relaxation can play an important role when the excitation energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor-to-acceptor energy transfer can occur from the excited vibrational states. Here, we develop Green’s function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the well-known Fӧrster’s expression leads to an overestimation of donor-acceptor separation distance.
The last part of the thesis, Part V, contains an account of the ongoing research that focuses on non-equilibrium polymer dimerization. This part also consists of two chapters. In Chapter 9, we carry out a brief survey of the existing theories of polymers in solution, and of polymer collapse. In Chapter 10, we present the preliminary results of the non-equilibrium polymer dimerization. We study the process by using computer simulations and analytical theory. We employ Langevin dynamics simulations with a coarse-grained model of the polymer to capture the dimerization process. We find that at separations much shorter than the length of the monomeric polymer, the dimerization could happen fast and irreversibly in the partly extended state itself. However, when the initial separation is larger than a critical distance, dc, the polymer collapse precedes dimerization, and a significant number of single polymers do not dimerize within the time scale of simulations. Further, we introduce several time-dependent order parameters: (i) a time-dependent radius of gyration of individual polymers describing the size of the protein, (ii) a centre of mass to centre of mass distance parameter, RMM¬(t), (iii) effective distance between the two polymeric monomers, we introduce another order parameter, RCP(t), and (iv) a time-dependent overlap function between the two monomeric polymers Q(t), mimicking contact order parameter of proteins. These functions evaluated by simulations display rich behaviour. Further, we conduct a theoretical analysis using the dynamical disorder model to capture the stochastic processes of collapse and dimerization.
In the concluding note, Chapter 11 summarises the outcome of the thesis and the scope of future work. The thesis contains one appendix where we discuss the Potential of Mean Force (PMF) calculation. | en_US |
