Single-molecule study on polymer diffusion in a melt state: effect of chain topology

Fluorescence Resonance Energy Transfer Measurements in Polymer Science: A Review

Fluorescence resonance energy transfer (FRET) is a non-invasive characterization method for studying molecular structures and dynamics, providing high spatial resolution at nanometer scale. Over the past decades, FRET-based measurements are developed and widely implemented in synthetic polymer systems for understanding and detecting a variety of nanoscale phenomena, enabling significant advances in polymer science. In this review, the basic principles of fluorescence and FRET are briefly discussed. Several representative research areas are highlighted, where FRET spectroscopy and imaging can be employed to reveal polymer morphology and kinetics. These examples include understanding polymer micelle formation and stability, detecting guest molecule release from polymer host, characterizing supramolecular assembly, imaging composite interfaces, and determining polymer chain conformations and their diffusion kinetics. Finally, a perspective on the opportunities of FRET-based measurements is provided for further allowing their greater contributions in this exciting area.

Blending Linear and Cyclic Block Copolymers to Manipulate Nanolithographic Feature Dimensions

Block copolymers (BCPs) consist of two or more covalently bound chemically distinct homopolymer blocks. These macromolecules have emerging applications in photonics, membrane separations, and nanolithography stemming from their self-assembly into regular nanoscale structures. Theory suggests that cyclic BCPs should form features up to 40% smaller than their linear analogs while also exhibiting superior thin-film stability and assembly dynamics. However, the complex syntheses required to produce cyclic polymers mean that a need for pure cyclic BCPs would present a challenge to large-scale manufacturing. Here, we employ dissipative particle dynamics simulations to probe the self-assembly behavior of cyclic/linear BCP blends, focusing on nanofeature size and interfacial width as these qualities are critical to nanopatterning applications. We find that for mixtures of symmetric cyclic and linear polymers with equivalent lengths, up to 10% synthetic impurity has a minimal impact on cyclic BCP feature dimensions and interfacial roughness. On the other hand, blending with cyclic BCPs provides a route to "fine-tune" linear BCP feature sizes. We analyze simulated blend domain spacings within the context of strong segregation theory and find significant deviations between simulation and theory that arise from molecular-level packing motifs not included in theory. These insights into blend self-assembly will assist experimentalists in rationally designing BCP materials for advanced nanolithography applications.

Spatially and Temporally Resolved Heterogeneities in a Miscible Polymer Blend

Mapping the spatial and temporal heterogeneities in miscible polymer blends is critical for understanding and further improving their material properties. However, a complete picture on the heterogeneous dynamics is often obscured in ensemble measurements. Herein, the spatial and temporal heterogeneities in fully miscible polystyrene/oligostyrene blend films are investigated by monitoring the rotational diffusion of embedded individual probe molecules using defocused wide-field fluorescence microscopy. In the same blend film, three significantly different types of dynamical behaviors (referred to as modes) of the probe molecules can be observed at the same time, namely, immobile, continuously rotating, and intermittently rotating probe molecules. This reveals a prominent spatial heterogeneity in local dynamics at the nanometer scale. In addition to that, temporal heterogeneity is uncovered by the nonexponential characteristic of the rotational autocorrelation functions of single-molecule probes. Moreover, the occurrence probabilities of these different modes strongly depend on the polystyrene: oligostyrene ratios in the blend films. Remarkably, some probe molecules switch between the continuous and intermittent rotational modes at elevated temperature, indicating a possible alteration in local dynamics that is triggered by the dynamic heterogeneity in the blends. Although some of these findings can be discussed by the self-concentration model and the results provided by ensemble averaging techniques (e.g., dielectric spectroscopy), there are implications that go beyond current models of blend dynamics.

Entangled polymer dynamics beyond reptation

Macroscopic properties of polymers arise from microscopic entanglement of polymer chains. Entangled polymer dynamics have been described theoretically by time- and space-averaged relaxation modes of single chains occurring at different time and length scales. However, theoretical and experimental studies along this framework provide oversimplified picture of spatiotemporally heterogeneous polymer dynamics. Characterization of entangled polymer dynamics beyond this paradigm requires a method that enables to capture motion and relaxation occurring in real space at different length and time scales. Here we develop new single-molecule characterization platform by combining super-resolution fluorescence imaging and recently developed single-molecule tracking method, cumulative-area tracking, which enables to quantify the chain motion in the length and time scale of nanometres to micrometres and milliseconds to minutes. Using linear and cyclic dsDNA molecules as model systems, our new method reveals chain-position-dependent motion of the entangled linear chains, which is beyond the scope of current theoretical framework.

Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods

We propose a novel approach to analyze random walks in heterogeneous medium using a hybrid machine-learning method based on a gamma mixture and a hidden Markov model. A gamma mixture and a hidden Markov model respectively provide the number and the most probable sequence of diffusive states from the time series position data of particles/molecules obtained by single-particle/molecule tracking (SPT/SMT) method. We evaluate the performance of our proposed method for numerically generated trajectories. It is shown that our proposed method can correctly extract the number of diffusive states when each trajectory is long enough to be frame averaged. We also indicate that our method can provide an indicator whether the assumption of a medium consisting of discrete diffusive states is appropriate or not based on the available amount of trajectory data. Then, we demonstrate an application of our method to the analysis of experimentally obtained SPT data.

Macrocyclic poly(p-phenylenevinylene)s by ring expansion metathesis polymerisation and their characterisation by single-molecule spectroscopy

Ring expansion metathesis polymerisation (REMP) has proven to be a viable approach to prepare high purity macrocyclic phenylenevinylene polymers.

Ring expansion metathesis polymerisation (REMP) has proven to be a viable approach to prepare high purity cyclic polymers. Macrocyclic polymers with a fully conjugated defect free backbone are of particular interest as these polymers have no end groups that can act as charge traps. In this work soluble macrocyclic poly(p-phenylenevinylene)s (cPPVs) have been prepared directly via the REMP of substituted paracyclophanedienes. Single-molecule spectroscopy of the two topological forms of PPV i.e., linear (lPPV) and cyclic (cPPV) revealed that lPPV exists in an extended conformation whereas the cPPV adopts a restricted ring-like conformation. Despite such large differences in the chain conformation, the spectral properties of the two compounds are unexpectedly very similar, and are dominated by torsional deformations in relatively short conjugated segments.

Quantitative Characterization of the Membrane Dynamics of Newly Delivered TGF-β Receptors by Single-Molecule Imaging

The dynamics and stoichiometry of receptors newly delivered on the plasma membrane play a vital role in cell signal transduction, yet knowledge of this process is limited because of the lack of suitable analytical methods. Here we developed a new strategy that combines single-molecule imaging (SMI) and fluorescence recovery after photobleaching (FRAP), named FRAP-SMI, to monitor and quantify individual newly delivered and inserted transmembrane receptors on plasma membranes of living cells. Transforming-growth-factor-β type II receptor (TβRII), a typical serine/threoninekinase receptor, was studied with this method. We first eliminated the fluorescence signals from the pre-existing EGFP-labeled TβRII molecules on the plasma membrane, and then we recorded the individual newly appeared TβRII-GFP by total-internal-reflection fluorescence imaging. The fluorescence-intensity distributions, photobleaching steps, and diffusion rates of the single TβRII-GFP molecules were analyzed. We reported, for the first time, that TβRII was transported to the plasma membrane mainly in the monomeric form in both resting and TGF-β1stimulated cells. This strongly supported our former discovery that TβRII could exist as a monomer on the cell membrane. We also found that ligand stimulation resulted in enhanced delivery rates and prolonged membrane-association times for the TβRII molecules. On the basis of these observations, we proposed a mechanism of TGF-β1-induced TβRII dimerization for receptor activation. Our method provides a useful tool for the real-time quantification of the spatial arrangement, mobility, and oligomerization of cell-surface proteins in living cells, thus providing a better understanding of cell signaling.

Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses

Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots.

What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers?

Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6 . 2 × 10 - 7 N l 2 / 3 obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement ( g 3 ( t ) ) curves for the crossing simulations are consistent with the Rouse model; we find g 3 ( t ) = 6 D r t . Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer.

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

We demonstrate a method for the synthesis of cyclic polymers and a protocol for characterizing their diffusive motion in a melt state at the single molecule level. An electrostatic self-assembly and covalent fixation (ESA-CF) process is used for the synthesis of the cyclic poly(tetrahydrofuran) (poly(THF)). The diffusive motion of individual cyclic polymer chains in a melt state is visualized using single molecule fluorescence imaging by incorporating a fluorophore unit in the cyclic chains. The diffusive motion of the chains is quantitatively characterized by means of a combination of mean-squared displacement (MSD) analysis and a cumulative distribution function (CDF) analysis. The cyclic polymer exhibits multiple-mode diffusion which is distinct from its linear counterpart. The results demonstrate that the diffusional heterogeneity of polymers that is often hidden behind ensemble averaging can be revealed by the efficient synthesis of the cyclic polymers using the ESA-CF process and the quantitative analysis of the diffusive motion at the single molecule level using the MSD and CDF analyses.

Examining dynamics in a polymer matrix by single molecule fluorescence probes of different sizes

Rotational motion of single fluorescence probes with different sizes doped inside films of polyvinylacetate is investigated by defocused single molecule fluorescence microscopy. Discrete vibration modes in the rotational motion of individual probes are clearly exposed in the power spectra of the rotation trajectories, reflecting multiple relaxation dynamics and also the difference in dynamics among separate locations. The power spectra show a strong dependence on the probe size and temperature. By sampling the rotation of a large number of probes, the averaged power spectra show that the activated rotation of the probes falls into the frequency range of the α-relaxation and data analysis shows that activation of the vibration modes with all probes corresponds to the maximum population of rotating probes, and this made the comparison between single molecule data and the ensemble data meaningful (differential scanning calorimetry, as an example). Such an analysis shows a coincidence between the temperature of a significant occurrence of glass transition and the activation of rotational motion of all probes with one specific size, indicating that such a dimension correlates with the size of the cooperative rearrangement region - a volume of approximately 1.0 nm(3).

Faster Convergence of Diffusion Anisotropy Detection by Three-Step Relation of Single-Particle Trajectory

We focus on the issue of limited number of samples in the single particle tracking (SPT) when trying to extract the diffusion anisotropy that originates from the particle asymmetry. We propose a novel evaluation technique of SPT making use of the relation of the consecutive three steps. More specifically, the trend of the angle comprised of the three positions and the displacements are plotted on a scatter diagram. The particle anisotropy dependence of the shape of the scatter diagram is examined through the data from the standard numerical model of anisotropic two-dimensional Brownian motion. Comparison with the existing method reveals the faster convergence in the evaluation. In particular, our proposed method realizes the detection of diffusion anisotropy under the conditions of not only less number of data but also larger time steps. This is of practical importance not only when the abundant data is hard to achieve but also when the rotational diffusion is fast compared to the frame rate of the camera equipment, which tends to be more common for smaller particles or molecules of interest.

Celebrating Soft Matter's 10th Anniversary: Topology matters: structure and dynamics of ring polymers

Considering topology among all polymer architectures polymer rings are unique, as they are the simplest closed structures without ends. In this review we present recent experimental advances addressing the structure and dynamics of rings. We focus mainly on neutron scattering results that reveal experimental insight on a molecular scale. We first briefly reflect on the progress in ring chemistry that made the experimental access possible. Structural investigations characterizing rings as compact objects in the melts are put into theoretical context. In contrast to the plateau regime common for all other high molecular weight polymer systems, the dynamic modulus of pure ring systems is characterized by a power law decay, while the viscosity displays a much weaker molecular weight dependence as a corresponding linear melt. The dynamics of ring melts is uniquely addressed by neutron spin-echo spectroscopy. The sub-diffusive center of mass motion at short times agrees well with simulation as well as theoretical concepts. In the internal dynamics the basic length scale of the ring molecule, the loop size, manifests itself clearly. The experiments reveal strong evidence for loop motions and call for further theoretical work describing them. Finally, small fractions of ring molecules in linear melts turn out to be very sensitive probes in order to scrutinize the dynamics of the host with the potential to reveal fundamental aspects of the dynamics of branched polymer systems.

Cyclic polymers revealing topology effects upon self-assemblies, dynamics and responses

A variety of single- and multicyclic polymers having programmed chemical structures with guaranteed purity have now become obtainable owing to a number of synthetic breakthroughs achieved in recent years. Accordingly, a broadening range of studies has been undertaken to gain updated insights on fundamental polymer properties of cyclic polymers in either solution or bulk, in either static or dynamic states, and in self-assemblies, leading to unusual properties and functions of polymer materials based on their cyclic topologies. In this article, we review recent studies aiming to achieve distinctive properties and functions by cyclic polymers unattainable by their linear or branched counterparts. We focus, in particular, on selected examples of unprecedented topology effects of cyclic polymers upon self-assemblies, dynamics and responses, to highlight current progress in Topological Polymer Chemistry.

Ferroelectric Polymer Matrix for Probing Molecular Organization in Perylene Diimides

Ferroelectric films of poly(vinylidene fluoride-co-trifluoroethylene) (PVDF-TrFE) provide a controlled environment to study the aggregation tendency of functional molecules such as perylene diimides (PDIs). The local electric field and free volume confinement parameters offered by the matrix are tailored to study the organizational and assembly characteritics of molecular acceptors. The optical properties of planar and nonplanar PDIs in the ferroelectric polymer matrix were studied systematically over a wide range that encompassed the ferroelectric transition temperature. This approach provides valuable insight into the properties of molecular materials used in applications ranging from bulk heterostructure-based photovoltaics to nonlinear optical materials.

Single-molecule imaging reveals topological isomer-dependent diffusion by 4-armed star and dicyclic 8-shaped polymers

The diffusion modes of the fluorophore incorporated 4-armed star and dicyclic 8-shaped polymers were investigated at the molecular level by means of single-molecule fluorescence imaging.

1,7-Bis-(N,N-dialkylamino)perylene Bisimides: Facile Synthesis and Characterization as Near-Infrared Fluorescent Dyes

Three symmetric alkylamino-substituted perylene bisimides with different n-alkyl chain lengths (n = 6, 12, or 18), 1,7-bis-(N,N-dialkylamino)perylene bisimides (1a–1c), were synthesized under mild condition and were characterized by ¹H NMR, ¹³C NMR and high resolution mass spectroscopy. Their optical and electrochemical properties were measured using UV-Vis and emission spectroscopic techniques as well as cyclic voltammetry (CV). These compounds show deep green color in both solution and solid state, and are highly soluble in dichloromethane and even in nonpolar solvents such as hexane. The shapes of the absorption spectra of 1a–1c in the solution and solid state were found to be almost the same, indicating that the long alkyl chains could efficiently prevent intermolecular contact and aggregation. They show a unique charge transfer emission in the near-infrared region, of which the peak wavelengths exhibit strong solvatochromism. The dipole moments of the molecules have been estimated using the Lippert–Mataga equation, and upon excitation, they show larger dipole moment changes than that of 1,7-diaminoperylene bisimide (2). Moreover, all the dyes exhibit two irreversible one-electron oxidations and two quasi-reversible one-electron reductions in dichloromethane at modest potentials. Complementary density functional theory calculations performed on these chromophores are reported in order to rationalize their electronic structure and optical properties.

Single-molecule diffusion and conformational dynamics by spatial integration of temporal fluctuations

Single-molecule localization and tracking has been used to translate spatiotemporal information of individual molecules to map their diffusion behaviours. However, accurate analysis of diffusion behaviours and including other parameters, such as the conformation and size of molecules, remain as limitations to the method. Here, we report a method that addresses the limitations of existing single-molecular localization methods. The method is based on temporal tracking of the cumulative area occupied by molecules. These temporal fluctuations are tied to molecular size, rates of diffusion and conformational changes. By analysing fluorescent nanospheres and double-stranded DNA molecules of different lengths and topological forms, we demonstrate that our cumulative-area method surpasses the conventional single-molecule localization method in terms of the accuracy of determined diffusion coefficients. Furthermore, the cumulative-area method provides conformational relaxation times of structurally flexible chains along with diffusion coefficients, which together are relevant to work in a wide spectrum of scientific fields.

Single-molecule localization and tracking technique is widely used to visualize molecular dynamics in life science, yet it fails to detect molecular conformation. Serag et al. address this limitation via spatial quantization of temporal fluctuations in the cumulative area occupied by molecules.

Green Perylene Bisimide Dyes: Synthesis, Photophysical and Electrochemical Properties

Three asymmetric amino-substituted perylene bisimide dyes with different n-alkyl chain lengths (n = 6, 12, or 18), 1-(N,N-dialkylamino)perylene bisimides (1a-1c), were synthesized under mild condition in high yields and were characterized by ¹H NMR, ¹³C NMR (nuclear magnetic resonance), HRMS (High Resolution Mass Spectrometer), UV-Vis and fluorescence spectra, as well as cyclic voltammetry (CV). These molecules show intense green color in both solution and solid state and are highly soluble in dichloromethane and even in nonpolar solvents, such as hexane. The shapes of the absorption spectra of 1a-1c in solid state and in solution were found to be virtually the same, indicating that the long alkyl chains could efficiently prevent aggregation. They exhibit a unique charge transfer emission in the near-infrared region, of which the peak wavelengths show strong solvatochromism. The dipole moments of the compounds have been estimated using the Lippert-Mataga equation, and upon excitation, they show larger dipole moment changes than that of 1-aminoperylene bisimide (2). Furthermore, all of the compounds exhibit two quasi-reversible one-electron oxidations and two quasi-reversible one-electron reductions in dichloromethane at modest potentials. Complementary density functional theory (DFT) calculations performed on these dyes are reported in order to rationalize their molecular structures and electronic properties.

SN2 regioselectivity in the esterification of 5- and 7-membered azacycloalkane quaternary salts: a DFT study to reveal the transition state ring conformation prevailing over the ground state ring strain

S_N2 regioselectivity in 5- and 7-membered azacycloalkanes quaternary salts is directed by the transition state ring conformation.