Low Frequency Vibrations and Diffusion in Disordered Polymers Bearing an Intrinsic Microporosity as Revealed by Neutron Scattering

The microscopic diffusion and the low frequency density of states (VDOS) of PIM-EA-TB(CH3) are investigated by inelastic and quasi-elastic neutron scattering where also the demethylated counterpart of PIM-EA-TB(H2) is considered. These intrinsic microporous polymers are characterized by large BET surface area values of several hundred m2/g and pore sizes between 0.5 and 2 nm. Detailed comparison is made to the archetype of polymers of intrinsic microporosity, PIM-1, and polynorbornenes also bearing a microporosity. Due to the wavelength of neutrons, the diffusion and vibrations can be addressed on microscopic length and time scales. From the inelastic neutron scattering experiments the low frequency density of states (VDOS) is estimated which shows excess contributions to the Debye-type VDOS known as Boson peak. It was found that the maximum frequency of the Boson peak decreases with increasing microporosity characterized by the BET surface area. However, besides the BET surface area, additional factors such as the backbone stiffness govern the maximum frequency of the Boson peak. Further the mean squared displacement related to microscopic motions was estimated from elastic fixed window scans. At temperatures above 175 K, the mean squared displacement PIM-EA-TB(CH3) is higher than that for the demethylated counterpart PIM-EA-TB(H2). The additional contribution found for PIM-EA-TB(CH3) is ascribed to the rotation of the methyl group in this polymer because the only difference between the two structures is that PIM-EA-TB(CH3) has methyl groups where PIM-EA-TB(H2) has none. A detailed comparison of the molecular dynamics is also made to that of PIM-1 and the microporous polynorbornene PTCNSi1. The manuscript focuses on the importance of vibrations and the localized molecular mobility characterized by the microscopic diffusion on the gas transport in polymeric separation membranes. In the frame of the random gate model localized fluctuations can open or close bottlenecks between pores to enable the diffusion of gas molecules.

A Practical Guide to Analyzing and Reporting the Movement of Nanoscale Swimmers

The recent invention of nanoswimmers– synthetic, powered objects with characteristic lengths in the range of 10-500 nm - has sparked widespread interest among scientists and the general public. As more researchers from different backgrounds enter the field, the study of nanoswimmers gains new opportunities but also significant experimental and theoretical challenges. In particulr, the accurate characterization of nanoswimmers is often hindered by strong Brownian motion and the lack of a clear way to visualize them. When coupled with improper experimental design and imprecise practices in data analysis, these issues can translate to results and conclusions that are inconsistent and poorly reproducible. In light of the increasing popularity of nanoswimmer research and its challenges, we here offer suggestions of best practices for reporting and analyzing their movement. A particular emphasis is on the calculation and analysis of mean squared displacement, the key method for quantifying the mobility of a nanoswimmer. When applied carefully and systematically, the suggested practices can significantly improve the reliability of analyses and prevent embarrassing mistakes

Characterizing persistence and pause dynamical behaviors in biological systems

This paper analyzed motion that randomly switches between the persistent motion runs and pause periods. A two-state continuous-time Markov chain is used to model the motion, which led to a system with coupled differential equations. Using a combined Fourier–Laplace transform, an analytical expression for calculating the mean-squared displacement is derived. The overall motion is investigated and identified from the obtained mean-squared displacement. The mean-squared displacement is a nonlinear function in time that is dependent on the phase transition rate, the direction switching rate, the average speed, and the initial state. It decays and grows with increasing the direction switching and average speed, respectively. The effective diffusivity descents exponentially in short times and remains constant in long times. The waiting time in each phase decayed exponentially. The probability density function for the position of a particle at a given time tends to be Gaussian in long times. The motion can be interpreted as a super-diffusion in short times and a standard diffusion in long times with a diffusion coefficient dependent on the phase transition rates, the direction switching rate and the average speed. Persistence influences the dynamical behavior for short times while for long times diffusive behavior is exhibited.

Transport of finite chains with free ends through thin channels

We describe the transport of a finite chain of [Formula: see text] identical particles in a thermal bath, through thin channels that forbid any crossing with a conceptually and technically simple method, that is neither restricted to the thermodynamic limit (infinite systems with finite density) nor to overdamped systems. We obtain analytically the mean squared displacement of each particle. Regardless of the damping, we identify a correlated regime for which chain transport is dominated by the correlations between individual particles. At large damping, the mean squared displacement evidences the typical single file behavior, with a time dependence that scales as [Formula: see text]. At small damping, the correlated regime is rather described by a diffusion-like behavior, with a diffusivity which is neither the individual particle diffusivity nor the Fickian diffusivity of the chain as a whole. We emphasize that, for a chain with free ends, the fluctuations of the chain ends are larger by a factor two than the fluctuations of its center. This effect is observed whatever the damping [Formula: see text], but the duration of this fluctuations enhancement is found to scale as [Formula: see text] for low damping and as [Formula: see text] for high damping. We discuss the relevance of this model to the transport of actual systems in confined geometries.

3D trajectories and diffusion of single ceria particles near a glass surface and their removal

We extend our recent 2D trajectory (x–y plane) and diffusion coefficient data of ceria particles near a glass surface obtained at pH 3, 5, and 7 using evanescent wave microscopy and video imaging to 3D trajectories by analyzing the separation distance between the particles and the glass surface in the vertical z‐direction. Mean squared displacement (MSD3D) of ceria particles was calculated to quantify 3D trajectories. Three‐dimensional diffusion coefficients were obtained from the MSD3D curves and were compared with two‐dimensional diffusion coefficients. By analyzing the MSD curves, we found that ceria particles exhibited only confined motion at pH 3 and 5, while both confined and Brownian motion were showed at pH 7. We also evaluated the cleaning ability of DI water adjusted to pH 10 and 12 to remove ceria particles from glass surfaces and related the results to the calculated trajectory, diffusion coefficient, and interaction potential data.

A Flexible Laboratory Exercise Introducing Practical Aspects of Mean Squared Displacement

ABSTRACT Mean squared displacement is a standard biophysical tool for characterizing the motion of particles in a thermally dominated environment, yet it is rarely formally introduced or discussed in undergraduate curriculum. Here, we provide a flexible and adaptable experimental or computational lab activity that provides a practical introduction to mean squared displacement and anomalous diffusion that includes optional experimental protocols and computational simulation techniques for data collection and discusses a variety of analysis techniques. This lab activity has been implemented both face-to-face and completely online and provides crucial experience in important research techniques, helping to bridge traditional undergraduate curriculum and modern biophysics research.

Mechanistic Understanding of Surface Migration Dynamics with DNA Walkers

<p>Dynamic DNA walkers can move cargoes on a surface through various mechanisms including enzymatic reactions and strand displacement. While they have demonstrated high processivity and speed, their motion dynamics are not well understood. Here, we utilize an enzyme-powered DNA walker as a model system and adopt a random walk model to provide new insight on migration dynamics. Four distinct migration modes (ballistic, Lévy, self-avoiding, and diffusive motions) are identified. Each mode shows unique step time and velocity distributions which are related to mean squared displacement (MSD) scaling. Experimental results are in excellent agreement with the theoretical predictions. With a better understanding of the dynamics, we performed a mechanistic study, elucidating the effects of cargo types and sizes, walker sequence designs, and environmental conditions. Finally, this study provides a set of design principles for tuning the behaviors of DNA walkers. The DNA walkers from this work could serve as a versatile platform for mathematical studies and open new opportunities for bioengineering.</p>

Mechanistic Understanding of Surface Migration Dynamics with DNA Walkers

<p>Dynamic DNA walkers can move cargoes on a surface through various mechanisms including enzymatic reactions and strand displacement. While they have demonstrated high processivity and speed, their motion dynamics are not well understood. Here, we utilize an enzyme-powered DNA walker as a model system and adopt a random walk model to provide new insight on migration dynamics. Four distinct migration modes (ballistic, Lévy, self-avoiding, and diffusive motions) are identified. Each mode shows unique step time and velocity distributions which are related to mean squared displacement (MSD) scaling. Experimental results are in excellent agreement with the theoretical predictions. With a better understanding of the dynamics, we performed a mechanistic study, elucidating the effects of cargo types and sizes, walker sequence designs, and environmental conditions. Finally, this study provides a set of design principles for tuning the behaviors of DNA walkers. The DNA walkers from this work could serve as a versatile platform for mathematical studies and open new opportunities for bioengineering.</p>