We propose a theoretical model for describing the electric-field-driven migration of rod-like biomolecules in nanofilters comprising a periodic array of shallow passages connecting deep wells. The electrophoretic migration of the biomolecules is modeled as transport of point-sized Brownian particles, with the orientational degree of freedom captured by an entropy term. Using appropriate projections, the formulation dimensionality is reduced to one physical dimension, requiring minimal computation and making it ideal for device design and optimization. Our formulation is used to assess the effect of slanted well walls on the energy landscape and resulting molecule mobility. Using this approach, we show that asymmetry in the well shape, such as a well with one slanted and one vertical wall, may be used for separation using low-frequency alternating-current fields because the mobility of a biomolecule is different in the two directions of travel. Our results show that, compared to methods using direct-current fields, the proposed method remains effective at higher field strengths and can achieve comparable separation using a significantly shorter device. 相似文献
Diffusive transport of particles or, more generally, small objects, is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions, transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro‐ and nanoscales must address both Brownian motion and entropic effects. Herein we report on recent advances in the theoretical and numerical investigation of stochastic transport occurring either in microsized geometries of varying cross sections or in narrow channels wherein the diffusing particles are hindered from passing each other (single‐file diffusion). For particles undergoing biased diffusion in static suspension media enclosed by confining geometries, transport exhibits intriguing features such as 1) a decrease in nonlinear mobility with increasing temperature or also 2) a broad excess peak of the effective diffusion above the free diffusion limit. These paradoxical aspects can be understood in terms of entropic contributions resulting from the restricted dynamics in phase space. If, in addition, the suspension medium is subjected to external, time‐dependent forcing, rectification or segregation of the diffusing Brownian particles becomes possible. Likewise, the diffusion in very narrow, spatially modulated channels is modified via contact particle–particle interactions, which induce anomalous sub‐diffusion. The effective sub‐diffusion constant for a driven single file also develops a resonance‐like structure as a function of the confining coupling constant. 相似文献
The operating properties of different-type Brownian photomotors have been compared in relation to the symmetry interplay between their moving (particle/molecule) and immovable (substrate) units. As found, essentially different symmetry constraints and hence different motor behavior are characteristic of molecules if their electron density redistribution on excitation involves only odd-order or only even-order multipole moments. The two respective types of molecules give rise to dipole and quadrupole photomotors. Purely dipole photomotors can operate only on substrates with symmetric charge distribution and their ensemble with random molecular orientations undergoes equidirectional diffusion rather than directed motion. Contrary to this, purely quadrupole photomotors need substrates with antisymmetric charge distribution for directed motion to occur and they can move directionally in an ensemble. Also, quadrupole photomotors provide much smaller velocities of directed motion than their dipole counterparts (as a result of the much weaker interaction of quadrupoles than dipoles with an electric field). The generic distinctions between the two photomotor types are exemplified by donor-acceptor-substituted stilbenoids (dipole molecules) and symmetric squaraines (quadrupole molecules). The model used affords the rational design of photomotors by the selection of promising moving molecules and by the continuous wide-range tuning of charge-distribution symmetry in substrates. 相似文献
The process of mass transport during hydrogen ion reduction in aqueous hydrochloric acid solutions is examined both with and without excess supporting electrolyte. The study of this process is based on a numerical solution to a system of equations of material balance and the movement of particles in solution under the influence of forces for diffusion, migration, and convection. The homogeneous chemical reaction of water dissociation is also taken into account. The results of calculations show that a diffusion layer forms near the electrode during the passage of current in these solutions and that the effective thickness of this layer is the same at any instant for all particles participating in mass transport in solution in spite of differences in their diffusion coefficients. The value of the diffusion coefficient measured in these multicomponent solutions by the methods of chronopotentiometry and rotating disk electrode should differ little from that of hydrogen ions in spite of the fact that other particles with different diffusion coefficients participate in the mass transport. 相似文献
A goal across multiple scientific fields (e.g. separations, polymer processing, and biomaterials) is to understand polymer dynamics at solid/liquid interfaces. In the last two decades, rapid developments in single-molecule techniques have revolutionized our ability to directly observe molecular behaviors with ultra-high spatial/temporal resolution and to decouple the elementary processes that were often veiled in ensemble experiments. This review provided an overview of principle and realization of two single-molecule fluorescence techniques that were often used to study the interfacial dynamics. In addition, this review updated recent progress in the discovery and understanding of dynamical anomalies of polymers at solid/liquid interfaces using these single-molecule techniques, emphasizing important elementary processes of diffusion, adsorption, and desorption. 相似文献
We have recently developed a new singularity‐free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro‐optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD‐simulations of the most common transient electro‐optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity‐free algorithm performs flawlessly. We find that, for these types of systems, the new singularity‐free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD‐algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single‐segment translational–rotational coupling, segment–segment fluid‐dynamic interactions and holonomic constraints.
Analytical solutions of the diffusion equations to obtain the diffusant concentrations in the macro- and micropores which constitute the pore system of a zeolite bed are presented. The parameter which determines the influence of each pore type on the evolution of the adsorbate/adsorbant system towards the equilibrium state is described. Examples are given to illustrate a qualitative and quantitative study based on the curves obtained from these equations. 相似文献
A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented. 相似文献
Gravitational instabilities and the conditions for the onset of convective motions in free diffusion boundaries are discussed for isothermal diffusion in ternary systems. It is shown that convective motion can grow even if the diffusion process does not promote density inversions inside the boundary. 相似文献
