The purpose of this research project was to determine the feasibility of labelling a water-soluble polymer with a water-soluble dye and quencher. The water-soluble dye chosen was bis-(2,2-bipyridine)-ruthenium(II) -5-amino-1,10-phenanthroline hexafluorophosphate, RuNH2 , with a water solubility of 1×10^−3 mol/L. 3,5-Dinitrobenzyl alcohol was found to be an efficient quencher with a quenching rate constant of 2.7×10^9 M^−1 s^−1 as well as a water-solubility of 5×10^−3 mol/L. Both the dye and quencher were modified in a way such that they could be covalently linked to a polymer. RuNH2 was converted to bis-(2,2-bipyridine)-ruthenium(II)-5-isothiocyanato-1,10- phenanthroline hexafluoro-phosphate, RuNCS, using thiophosgene to yield an active isothiocyanate group. 3,5-Dinitrobenzylamine, DNB-NH2 , was synthesized via tritylamination of the commercially available 3,5-dinitrobenzyl chloride. A synthetic pathway has been established to covalently attach the dye and quencher to poly(N,N-dimethylacrylamide)(PDMA). Luminescence of this system was first characterized in N,N-dimethylformamide (DMF) rather than water to allow for future comparisons to be made between this water-soluble system and the previously established non-water-soluble system. Luminescence analysis of the RuNCS labelled polymers in DMF could be fitted with a sum of three exponentials with the strongest contribution being that of a 1000 ns long-lived species which is characteristic of the free dye. A luminescence decay of a polymer labelled with both RuNCS and DNB-NH2 was acquired and showed static quenching of the ruthenium dye by the quencher.

The purpose of this research project was to determine the feasibility of labelling a water-soluble polymer with a water-soluble dye and quencher. The water-soluble dye chosen was bis-(2,2-bipyridine)-ruthenium(II) -5-amino-1,10-phenanthroline hexafluorophosphate, RuNH2 , with a water solubility of 1×10^−3 mol/L. 3,5-Dinitrobenzyl alcohol was found to be an efficient quencher with a quenching rate constant of 2.7×10^9 M^−1 s^−1 as well as a water-solubility of 5×10^−3 mol/L. Both the dye and quencher were modified in a way such that they could be covalently linked to a polymer. RuNH2 was converted to bis-(2,2-bipyridine)-ruthenium(II)-5-isothiocyanato-1,10- phenanthroline hexafluoro-phosphate, RuNCS, using thiophosgene to yield an active isothiocyanate group. 3,5-Dinitrobenzylamine, DNB-NH2 , was synthesized via tritylamination of the commercially available 3,5-dinitrobenzyl chloride. A synthetic pathway has been established to covalently attach the dye and quencher to poly(N,N-dimethylacrylamide)(PDMA). Luminescence of this system was first characterized in N,N-dimethylformamide (DMF) rather than water to allow for future comparisons to be made between this water-soluble system and the previously established non-water-soluble system. Luminescence analysis of the RuNCS labelled polymers in DMF could be fitted with a sum of three exponentials with the strongest contribution being that of a 1000 ns long-lived species which is characteristic of the free dye. A luminescence decay of a polymer labelled with both RuNCS and DNB-NH2 was acquired and showed static quenching of the ruthenium dye by the quencher.

Spatial and temporal dynamics of polymer chains play critical roles in their rheological properties, which have a significant influence on polymer processing and fabrication of polymer-based (nano) materials. Many theoretical and experimental studies have aimed at understanding polymer dynamics at the molecular level that give rise to its bulk phase properties. While much progress has been made in the field over the past ~60 years, many aspects of polymers are still not understood, especially in complicated systems such as entangled fluids and polymers of different topologies. In addition, the physical properties of biological macromolecules, i.e. DNA, are expected to affect the spatial organization of chromosome in a cell, which has the potential impact on a broad epigenetics research. Here, we propose new methods for simultaneous visualization of diffusive motion and conformational dynamics of individual polymer chains, two most important factors that characterize polymer dynamics, based on a new single-molecule tracking technique, cumulative-area (CA) tracking method. We demonstrate the applicability of the CA tracking to the quantitative characterization of the motion and relaxation of individual topological polymer molecules under entangled conditions, which is possible only by using the newly-developed CA tracking, using fluorescently-labeled linear and cyclic dsDNA as model systems. We further extend the technique to multi-color CA tracking that allows for the direct visualization and characterization of motion and conformation of interacting molecules. We also develop a new imaging method based on recently developed 3D super-resolution fluorescence microscopy technique, which allows direct visualization of nanoscale motion and conformation of the single molecules that is not possible by any other methods. Using these techniques, we investigate spatial and temporal dynamics of polymers at the single-molecule level, with special emphasis on the effect of topological forms of the molecules and the confined geometry on their spatiotemporal dynamics. Our results demonstrate that the new methods developed in this thesis provide an experimental platform to address key questions in the entangled topological polymer dynamics. The research will provide a platform for developing new polymer-based materials and open the possibility of studying spatial organization of DNA in a confined geometry from physics point of view.

We develop a self-consistent field theory of polymer dynamics, based on a functional integral approach, which is analogous to the existing equilibrium self-consistent field theory for polymers. We apply a saddle-point approximation to the exact dynamical theory, which generates a set of mean-field equations for the time-dependent density and mean force field. We also develop a method of treating the single-chain dynamics exactly, subject to this mean-field, resulting in a functional Fokker-Planck equation that must be solved along with the mean-field equations in a self-consistent manner. To test the self-consistency, we apply the theory to the simple but non-trivial case of np Brownian particles in one dimension interacting via a short-range repulsion in a harmonic external potential. Results for the non-interacting case agree with the literature. The interacting case demonstrates physically sensible interaction-dependent dynamics, such as an increased broadening of the density field when the repulsion is increased. We also examine the dynamics of a binary system with two distinct particle species. We calculate the center-of-mass trajectories for colliding distributions of species A and B, and observe that when the difference of repulsion strengths between like and unlike species chi is greater than a threshold value (between chi = 0.3 and chi = 0.4), the two species do not mix (indicating the onset of phase segregation).

This thesis investigates DNA dynamics and translocation through nanopores using Brownian dynamics (BD) simulations, offering insights into sequencing technologies, DNA marker detection, and accurate barcoding utilizing solid-state nanopore platforms. First, we in silico study the intricate process of capture and translocation in a single nanopore. Our simulation reveals a high probability of hairpin loop formation during the capture process. However, attaching a charged tag to one end of DNA improves multi-scan rates and enhances unidirectional translocations. We use modulating voltage biases to multi-scan a lambda-phage dsDNA with oligonucleotide flap markers (tags) through a single and double nanopore system. Our study shows that the bulkier tags introduce velocity variations along the chain length that lead to potential inaccuracies in genetic distance (barcode) estimations. We introduce an interpolation scheme that incorporates both the tag velocities and the average velocity of the chain to improve barcode precision. Subsequently, we include bead and side-chain tags to explain asymmetric dwell time distributions as observed in double nanopore experiments. Our findings indicate that local charge interactions between tags and the nanopore's electric field introduce dwell time asymmetries that can be used for discriminating tags based on their net charges. Finally, we obtain the current blockades of the molecular motifs attached to a dsDNA using electrokinetic Brownian dynamics (EKBD) simulation. Our simulation demonstrates that divalent salt reduces the translocation speed, facilitating precise measurement of the motif's dwell time. Finally, we formulate a volumetric ansatz to construct current blockade diagrams from the ordinary BD simulation in a computationally efficient way and show that using simple scale factors, these volumetric blockades can be mapped accurately to the ionic current blockades obtained from more expensive EKBD simulation. Our studies present comprehensive explorations of DNA translocation and barcoding methods in solid-state nanopores, demonstrating their utility in nanopore sequencing and nanobiotechnology

This thesis contains several contributions to the theoretical description and interpretation of biophysical single-molecule measurements: (i) For semiflexible polymers, we derive an efficient formulation of their local transverse dynamics in terms of a Generalized Langevin Equation. The elastic and frictional properties of the polymer are condensed into a memory kernel that is a function of the polymer\'s length and stiffness, the level of backbone tension, the position of the force probe along the polymer backbone and the boundary conditions at the polymer ends. At short times, the memory kernel attains a universal limiting form that depends neither on the polymer length nor on the boundary conditions; we obtain analytical results that accurately describe this regime. We discuss how to quickly and reliably evaluate the memory kernel for arbitrary times using a spectral decomposition method, and use an extensive body of numerical data to obtain analytical approximations to the memory kernel that cover the complementary long-time limit wherein polymer friction can be subsumed under a renormalized drag coefficient. (ii) Based on a systematic nonequilibrium treatment of an overdamped, one-dimensional stochastic escape process driven by external force, we develop a theory of Dynamic Force Spectroscopy (DFS) that generalizes previously available DFS theories to the high loading rates realized in novel experimental assays and in computer simulations. (iii) Extrapolating to future DFS experiments that may operate at far higher time resolution than presently achievable, we discuss the fast nonequilibrium relaxation of a semiflexible linker after bond rupture. Based on a rigorous theory of tension propagation in semiflexible polymers, we predict the relaxation of force within the force actuator, show that this relaxation is dominated by linker contraction, and demonstrate quantitative agreement of our predictions with experimental data obtained by a collaborating experimentalist group.

Studies show that dynamical properties of ultra-thin polymer films deviate from those of bulk materials. Despite some controversial issues, there is growing evidence indicating that the interfacial properties play a key role for observed dynamical anomalies. However, how and how much the interfacial properties affect the average dynamics of the nanometer scale systems are still elusive. In this work, we developed several novel techniques to investigate near-free-surface dynamics of thin polymer films. We studied surface dynamics of glassy i-PMMA films using a nano surface hole relaxation technique: a strong substrate property dependence and an unexpected molecular weight dependence were observed; we found that a local Tg of ~40K below bulk Tg could be assigned to the surface region. We used nano gold particle embedding to study PS surface dynamics: enhanced surface dynamics and weak temperature dependence were observed for the surface region; a depth profile with the nm resolution was observed; viscous liquid-like and soft solid-like properties were observed in the first 5.5nm and next 3.3 nm regions in PS films; no molecualr weight dependence was found in glassy PS films. We built a low level noise measurement system to study the thermal polarization noise in PVAc films: cooperative rearranging dynamics were evidenced; the noise power spectral density (PSD) is found to fluctuate around a certain average level without discernable peak shift; we observed some relatively big jumps or fluctuations in successive integrated PSD’s, which indicate some energy exchange between different microscopic domains in glassy polymer systems. We developed a novel nano rheology AFM technique to study the near-free-surface dynamics of thin polymer films: enhanced near-free-surface dynamics with weak temperature dependence are observed for PVAc films, which is similar with the PS case.

Studies show that dynamical properties of ultra-thin polymer films deviate from those of bulk materials. Despite some controversial issues, there is growing evidence indicating that the interfacial properties play a key role for observed dynamical anomalies. However, how and how much the interfacial properties affect the average dynamics of the nanometer scale systems are still elusive. In this work, we developed several novel techniques to investigate near-free-surface dynamics of thin polymer films. We studied surface dynamics of glassy i-PMMA films using a nano surface hole relaxation technique: a strong substrate property dependence and an unexpected molecular weight dependence were observed; we found that a local Tg of ~40K below bulk Tg could be assigned to the surface region. We used nano gold particle embedding to study PS surface dynamics: enhanced surface dynamics and weak temperature dependence were observed for the surface region; a depth profile with the nm resolution was observed; viscous liquid-like and soft solid-like properties were observed in the first 5.5nm and next 3.3 nm regions in PS films; no molecualr weight dependence was found in glassy PS films. We built a low level noise measurement system to study the thermal polarization noise in PVAc films: cooperative rearranging dynamics were evidenced; the noise power spectral density (PSD) is found to fluctuate around a certain average level without discernable peak shift; we observed some relatively big jumps or fluctuations in successive integrated PSD’s, which indicate some energy exchange between different microscopic domains in glassy polymer systems. We developed a novel nano rheology AFM technique to study the near-free-surface dynamics of thin polymer films: enhanced near-free-surface dynamics with weak temperature dependence are observed for PVAc films, which is similar with the PS case.

For polymers near the glass transition, the dynamics in some regions can be orders of magnitude different compared with the dynamics in other regions only a few nanometers away, so called spatial heterogeneity [1]. In this thesis, single molecule fluorescence microscopy as a powerful tool, was applied to study the spatially heterogeneous dynamics, both orientational and translational, within the polymer matrix near the glass transition temperature. With our total internal reflection fluorescence microscopy (TIRFM) methods, many individual fluorescent dye molecules embedded in the poly (isopropyl acrylate) (PIPA) thin films can be simultaneously excited. Their emission patterns are analyzed using our orientation determination methods [2] to give the true 3D orientational trajectories of the individual molecules. At Tg < T < 1.2 Tg, single molecule tracking was used to study the dye molecules translational diffusion. Results show that, below 1.1 Tg, the probe molecules are in the confined flow region [3]; at T > 1.1 Tg, the diffusion follows normal diffusion model; at T = 1.2 Tg, although the statistical results shows that normal random walk behavior is followed, the individual molecules still show different diffusion behaviors, clear evidence of the spatial heterogeneity that still exists at this temperature. The second part of this thesis is a development of the 3-detector method to determine the 3D orientation of single molecules [4]. This method is based on the work proposed by Fourkas [4] in 2001. Results utilizing this experimental setup are compared with our emission pattern fitting methods. The results show that, with a little bit higher error range (10º in θ, 20º in φ), the 3-detector method can give agreeable orientation fittings, further more, with higher time resolution of < 10 ms. This 3-detector method is useful and can be applied to study the fast orientation dynamics in different systems.

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