Thesis Colloquium: Theoretical Studies of Dynamics in Complex Systems: Liquids, Polymer Dimerization and Non-Equilibrium FRET 

Theoretical and experimental studies of the structure and dynamics of complex systems, such as nanoconfined liquids, electrolyte solutions, binary mixtures,and polymer dimerization, are of great interest to both fundamental and applied sciences. Understanding these intricate dynamics, including molecular interactions, composition-based anomalies, confinement effects, molecular aggregations, and non-equilibrium energy relaxation, provides valuable insights into the complex behaviours of materials at small lengths and time scales. It offers crucial knowledge for the advancement of various fields, such as physical, chemical, and biological sciences.[1,2]

In the first part, we employ molecular dynamics simulations and theoretical analyses to explore the structure and dynamics of various complex binary liquids.[4-6]. Within this context, we delve into nanoconfined aqueous ethanol solutions, where we find the remarkable phenomenon of long-distance, rare, but repetitive exchange of ethanol molecules between two parallel graphene surfaces. We carry out a detailed study to understand the mechanisms, and we use both the transition state theory and Kramers’ theory to calculate the rate. [4]   Next, we explore the structural and dynamical properties of alkali metal ions in water-dimethyl sulfoxide (DMSO) solutions, revealing composition-dependent anomalies. We observe that anomalies stem from the interplay between ion size-dependent charge density and their interactions with water and DMSO molecules. Additionally, the research delves into the analysis of the hydrogen bond network in the Water-DMSO Binary mixture.[5]We observe anomalies to arise due to the  hydrophobic interaction between the methyl groups that “cages” both rotational and linear motions of molecules involved in hydrogen bonding. Subsequently, we use a two-dimensional transition state theory to obtain the rate of hydrogen bond breaking and obtain a semi-quantitative agreement.[6]

In the second part of the thesis, we investigate non-equilibrium polymer dimerization. We employ Langevin dynamics simulations with a coarse-grained model of the polymer to capture the essence of the dimerization process. Further, we conduct a theoretical analysis using a dynamical disorder model to capture the stochastic processes of collapse and dimerization. [7,8]

In the third part of the thesis, we study non-equilibrium Forster resonance energy transfer (FRET). 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 Forster’s expression might lead to an overestimation of donor-acceptor separation distance. [2,3].

References:

[1] B. Bagchi, Non-equilibrium Statistical Mechanics: An Introduction with Applications (CRC Press, 2023).

[2]  B. Bagchi, Molecular Relaxation in Liquids (Oxford University Press, 2012).

[3] S. Mondal, S. Mondal, K. Seki, B. Bagchi, J Chem. Phys, 154, 134104(2021).

[4] S. Mondal, S. Acharya, S. Mondal, B. Bagchi, J Chem. Phys,157, 194703 (2022).

[5] S. Mondal, B. Bagchi, J Chem. Phys.160,114505 (2024).

[6]S. Mondal, B. Bagchi,Synergy between hydrogen bond and hydrophobic attractions enhance the stability of aggregates: A quantitative view,J Chem. Phys, (2024) (under review) [arXiv preprint arXiv:2404.13001].

[7] S. Mondal, B. Bagchi, Journal of Innovative Materials in Extreme Conditions,(2024) (in press)

[8] S. Mondal, V. Mahajan, B. Bagchi, Nonequilibrium Dimerization of Model Polymer Chains(under preparation)

[9] S. Mondal, B. Bagchi, A stochastic approach to Maxwell velocity distribution via Central limit theorem and Boltzmann’s entropy formula, (2022)[arXiv preprint arXiv:2206.05180]