Single-file diffusion near channel boundaries

Molecular transport under the conditions of single-file diffusion was investigated near the channel boundaries by using dynamic Monte Carlo and molecular dynamics simulations of tracer exchange between single-file channels and their surroundings. The boundary effect reported in our recent papers (Vasenkov S.; K?rger, J. Phys. Rev. E 2002, 66, 052601. Schüring, A.; Vasenkov S.; Fritzsche, S. J. Phys. Chem. B 2005, 109, 16711) was studied in detail. This boundary effect is characterized by deviations of the intrachannel concentration profiles of tracer molecules observed in the case of single-file diffusion near the channel boundaries from the corresponding profiles typical for normal diffusion. It has been shown in our previous studies that these deviations occur under the conditions when the potential-energy difference inside and outside of single-file channels was both comparable and much larger than the activation energy of intrachannel diffusion. Here, we report a quantitative model describing the boundary effect. According to this model, an occurrence of the boundary effect is related to a complex character of diffusion in finite single-file systems. Such diffusion can be described by the following two types of movements occurring in parallel: (i) correlated displacements of all molecules in any particular channel and (ii) fast displacements of single molecules, which are uncorrelated with the displacements of all other molecules in the same channel. The latter displacements are restricted to a certain length interval that depends on the channel length and the channel occupancy. This length interval is shown to determine the extensions of the channel margins where the boundary effect is observed.     

Enhanced flow in smooth single-file channel

We investigate the flux of particles in a smooth single-file channel where particles cannot cross each other as well as in wider channels of varying cross section where particles execute normal diffusion. All the channels are connected to an infinite reservoir at one end and the flux of particles is measured at the other open end. We perform random walk Monte Carlo simulation using lattice model. The flux decreases monotonically as the channel cross section is increased from single-file channel to wider channel and finally reaches a constant value for a sufficiently wide channel. The observation of enhanced flux in single-file channel as compared to a wider channel can be tested for efficient separation of particles through smooth nanochannels.     

The effect of rotational and translational energy exchange on tracer diffusion in rough hard sphere fluids

A study is presented of tracer diffusion in a rough hard sphere fluid. Unlike smooth hard spheres, collisions between rough hard spheres can exchange rotational and translational energy and momentum. It is expected that as tracer particles become larger, their diffusion constants will tend toward the Stokes-Einstein hydrodynamic result. It has already been shown that in this limit, smooth hard spheres adopt "slip" boundary conditions. The current results show that rough hard spheres adopt boundary conditions proportional to the degree of translational-rotational energy exchange. Spheres for which this exchange is the largest adopt "stick" boundary conditions while those with more intermediate exchange adopt values between the "slip" and "stick" limits. This dependence is found to be almost linear. As well, changes in the diffusion constants as a function of this exchange are examined and it is found that the dependence is stronger than that suggested by the low-density, Boltzmann result. Compared with smooth hard spheres, real molecules undergo inelastic collisions and have attractive wells. Rough hard spheres model the effect of inelasticity and show that even without the presence of attractive forces, the boundary conditions for large particles can deviate from "slip" and approach "stick."     

Direct quantification of intraparticle protein diffusion in chromatographic media

Diffusion coefficients of proteins in chromatographic media are important parameters for the rational design of stationary phases and purification schemes. In contrast to free diffusion, intraparticle diffusion is hindered by the porous structure of the media. Direct intraparticle diffusion analysis (IDA) is a novel approach for the determination of intraparticle protein diffusion coefficients. IDA is based on the evaluation of spatially and temporally resolved intraparticle concentration profiles. To prevent adsorption and to study diffusion only, the chromatographic media are investigated in underivatized form. With IDA, intraparticle concentration profiles are measured in a microcolumn by confocal laser scanning microscopy (CLSM). From this dynamic data, the diffusion coefficients are determined by parameter estimation, using a spheric diffusion model. The boundary condition is given by the measured protein concentration in the bulk phase. IDA is applied to determine intraparticle diffusion coefficients of seven different proteins in Sepharose 6 FF. The results show excellent congruence of experimental data and simulation results. Moreover, the determined diffusion coefficients lie well within the range of data published in the literature. Given that the material in question allows optical analysis, IDA is a general approach for studying protein diffusion in porous particles and is easily adapted to different proteins, solution conditions and stationary phases.     

Single-file diffusion through inhomogeneous nanopores

Strict one-dimensional diffusion, due to geometrical confinement in a nanopore, of an assembly of particles forbids overtaking by each other, giving rise to single-file diffusion (SFD). Smooth carbon nanotube is the epitome of SFD. However, natural nanoporous materials are far from smooth; morphologically, the nanopores' inner surface may provide an inhomogeneous environment for diffusion to occur, giving rise to subnormal diffusion even for an isolated particle diffusing through this fractal landscape. The realm of fractional diffusion (FD) falls under this paradigm. In order to understand the characteristics of SFD through inhomogeneous nanopores, here, we introduce a fractional SFD (FSFD) formalism that deals with a combination of these two phenomena, namely, SFD of particles, each of which are moving subdiffusively in one dimension. For an infinite system, we obtain the mean square displacement (MSD) of the combined entity and our analysis is based on FD equation for particles moving in concert where the single-file correlation is established through reflection principle. For a finite system, we calculate the transport probabilities based on continuous time random walk model. While both the diffusion mechanisms (SFD and FD) acting separately are responsible for slow dynamics at long times, their combined effect leads to ultraslow diffusion. For example, while the long time asymptote of MSD of SFD scales as sqr rt of t, that for FSFD is sqr rt of t(alpha), where alpha is the measure of the extent of inhomogeneity. These findings, which are believed to occur in a natural inhomogeneous nanopore, is also important for design and fabrication of nanofluidic devices through which the fluid delivery can be engineered.     

Toward observation of single-file diffusion using the tracer zero-length column method

The tracer zero-length column (ZLC) method has been employed to study the diffusion of toluene in one-dimensional ZSM-12 and SAPO-5 zeolites. A significant deviation in the shape of the measured tracer exchange curves from monoexponential behavior was observed for toluene diffusion in both adsorbents in the limit of long-time asymptotes. In contrast, water/ZSM-12 and acetylene/SAPO-5 systems exhibit tracer exchange curves that are close to monoexponential behavior. Monoexponential curves are usually observed for systems obeying normal (Fickian) diffusion. Such diffusion is expected for the latter two systems because the diameters of both sorbates are less than the radii of their corresponding host channels. The differences in the shape of the tracer exchange curves for large and small sorbates can be explained by assuming the occurrence of anomalous, single-file diffusion for large sorbates in narrow, one-dimensional channels.     

Statics and dynamics of ethane molecules in AlPO(4)-5: a molecular dynamics simulation study.

From an experimental perspective, there has been disagreement among researchers on whether ethane would display single-file or normal diffusive behavior in the channels of AlPO(4)-5. Pulsed field gradient nuclear magnetic resonance measurements implied single-file diffusion, while quasielastic neutron scattering showed normal diffusion. In this paper we present the results of extensive classical molecular dynamics simulations of the diffusion of ethane molecules adsorbed in AlPO(4)-5. Our aim is to provide microscopic details of the static and dynamic properties of the adsorbed molecules in order to verify whether the conditions for the single-file regime can be achieved in a nondefective AlPO(4)-5 crystal structure.     

Unexpectedly low translational mobility of methane and tetrafluoromethane in the large-pore molecular sieve VPI-5

Molecular diffusion of methane and tetrafluoromethane in the microporous material VPI-5 was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and NMR exchange experiments. The translational mobility of both molecules in VPI-5 was found to be at least two orders of magnitude smaller than in ZSM-5. This is surprising since the channels in VPI-5 are about two times as wide as those in ZSM-5. The surprisingly small translational mobility in VPI-5 could be caused by a more complete stabilization effect or by single-file diffusion. The intracrystalline mean life time of methane in VPI-5 directly measured in the NMR tracer exchange experiments was found to be in satisfactory agreement with the value estimated on the basis of the PFG NMR data on translational mobility for ordinary intracrystalline diffusion. It must be ruled out, therefore, that molecular transportation over length scales of the order of the crystallite dimensions is controlled by single-file diffusion.     

Bursts in single-file motion mediated conduction

We present a cellular automaton (CA) model of particles in a single-file motion with free particle exchange at the boundaries of a one-dimensional channel connected to two infinite reservoirs in order to study the self-transmission of particles with excluded mutual passage. The parallel, local and homogeneous rule sets of the CA algorithm consider two different interactions of varying strength between particles, without any specific particle-channel interaction. CA model results suggest that one hallmark of single-file motion is the conduction bursts at a particular time scale, which have thus far only been discovered for hydrogen bond networked water translocation. The cumulative transport probabilities of particles through single-file channels of different length follow a single profile, which can be obtained through proper scaling of time. The universal features of our results suggest new experiments in single-file channel with fluids other than water.     

Microanalytical investigations on optical phase gratings in K(TiO)PO4 single crystals

The Rb/K ion exchange in micro-structured K(TiO)PO₄ single crystals in contact with Rb containing nitrate melts results in ion-exchanged zones with enlarged refractive index which works as an optical phase grating. The knowledge of the diffusion behavior was the prerequisite for the generation of optimum refractive index profiles. Therefore, the local Rb/K concentration of ion-exchanged single crystals was determined with an electron probe microanalyzer (EPMA). The observed degree of ion exchange and the calculated Rb/K counterdiffusion coefficients were used to estimate the optimum ion exchange conditions. The diffusion-generated optical phase gratings show very narrow and deep ion-exchanged zones. The ratio of the ion penetration depths results in an extreme diffusion anisotropy D_Rb/K(c):D_Rb/K(b) ≈ 500:1.

     

Topochemical aspects of elementary reactions of the emulsion polymerization of acrylonitrile

A combination of statistic and kinetic methods of analysis is used to collect quantitative data on the kinetics of elementary reactions of growth and termination of kinetic chains in each phase of a heterophase system as well as on interfacial mass exchange at the quasistationary stage of radiation-induced emulsion polymerization of acrylonitrile. It is found that, in the system, a steady-state concentration of polymer—monomer particles is attained, and these particles are able to increase their dimensions with an increase in monomer conversion. Activation of particles and chain termination on particles are due to the entrapment of macroradicals from water. As a result of a gradual increase in the dimensions of polymer-monomer particles and a decrease in the monomer concentration in the aqueous phase, the adsorption layer of acrylonitrile becomes so thin that, at the final stage, monomolecular layers lose integrity and the conditions of quasi-stationarity are violated.     

Single species transport and self diffusion in wide single-walled carbon nanotubes

We model and simulate gas flow through nanopores using a single-walled carbon nanotube model. Efficient protocols for the simulation of methane molecules in nanotubes are developed and validated for both the self-diffusivity, following a pulse perturbation, and for the transport diffusivity in an imposed concentration gradient. The former is found to be at least an order of magnitude lower than the latter, and to decline with increasing initial pressure, while the latter increases as the pressure gradient increases until it reaches an asymptotic value. Our previous analytic model, developed for single-file diffusion in narrow pores, is extended to wider pores for the case of single species transport. The model, which predicts the observed numerical results invokes four regimes of transport. The dominant transport is by ballistic motion near the wall in not too wide nanotubes when a pressure gradient or concentration is imposed; this mode is absent in the case of self-diffusion due to periodic boundary conditions. We also present results from systematic comparisons of flexible versus rigid tubes and explicit atom versus effective atomic potentials.     

Optical determination of the pitch-dependent diffusion constant in a cholesteric liquid crystal

The concentration profile of a cholesteric compound diffusing into a nematic liquid crystal is observed with optical methods. We propose new experimental initial and boundary conditions which allow a more accurate mathematical solution of the differential equation involved. A numerical approach is applied to compute the concentration profiles with a concentration dependent diffusion constant. Diffusion is found to decrease with the shorter pitch length.     

Diffusiophoresis in suspensions of highly charged soft particles

Diffusiophoresis phenomenon of aoft particles suspended in binary electrolyte solutions is explored theoretically in this study based on the spherical cell model, focusing on the chemiphoresis component in absence of diffusion potential. Both the electrostatic and hydrodynamic aspects of the boundary confinement, or steric effect, due to the presence of neighboring particles are examined extensively under various electrokinetic conditions. Significant local extrema are found in mobility profiles expressed as functions of the Debye length in general, synchronized with the strength of the motion-inducing double layer polarization. Moreover, a seemingly peculiar phenomenon is observed that the soft particles may move faster in more concentrated suspensions. The competition between the simultaneous enhancement of the motion-inducing electric driving force and the motion-retarding hydrodynamic drag force from the boundary confinement effect of the neighboring particles is found to be responsible for it. The above findings are also demonstrated experimentally in a very recent study on the diffusiophoretic motion of soft particles through porous collagen hydrogels. The results presented here are useful in various practical applications of soft particles like drug delivery.     

Fast grain boundary diffusion and surface exchange reactions at active surface sites of polycrystalline materials

Analytical solutions to the diffusion equations for fast grain boundary diffusion and surface exchange reactions at active surface sites are derived. The microstructure of the polycrystalline sample of finite thickness is modelled by parallel grain boundaries. The ratio between the surface exchange coefficient and the diffusion coefficient for the grain boundaries is assumed to be greater than or equal to that for the bulk. The analytical solutions allow the calculation of diffusion profiles for thin films. Special emphasis is laid on a detailed analysis of the time dependence of the total amount of diffusant exchanged between the constant diffusion source (e.g. gas phase) and the polycrystalline sample (e.g. oxide ceramics) which corresponds to relaxation curves obtained from, e.g., oxygen exchange measurements. The calculated relaxation curves refer to Harrison's type-A kinetics where homogeneous medium solutions are satisfactorily applicable, introducing effective kinetic parameters. Apart from expressions for the effective diffusion coefficient analogous relations for the effective surface exchange coefficient are proposed, depending on the microstructure of the polycrystalline material and the corresponding kinetic parameters of bulk and grain boundary regions, respectively.     

Using (18)O/(16)O exchange to probe an equilibrium space-charge layer at the surface of a crystalline oxide: method and application

The use of an (18)O/(16)O exchange experiment as a means for probing surface space-charge layers in oxides is examined theoretically and experimentally. On the basis of a theoretical treatment, isotope penetration profiles are calculated for (18)O/(16)O exchange across a gas-solid interface and subsequent diffusion of the labelled isotope through an equilibrium space-charge layer depleted of mobile oxygen vacancies and into a homogeneous bulk phase. Profiles calculated for a range of conditions all have a characteristic shape: a sharp drop in isotope fraction close to the surface followed by a normal bulk diffusion profile. Experimental (18)O profiles in an exchanged (001) oriented single crystal of Fe-doped SrTiO(3) were measured by time-of-flight secondary ion mass spectrometry (ToF-SIMS). By extracting the space-charge potential from such profiles, we demonstrate that this method allows the spatially resolved characterization of space-charge layers at the surfaces of crystalline oxides under thermodynamically well-defined conditions.     

Diffusion of small molecules in a chitosan/water gel determined by proton localized NMR spectroscopy

Proton localized NMR spectroscopy (MRS) has been applied to study the diffusion of three small molecules, caffeine, theophylline and caprolactam, in chitosan gels with different concentration of water. This technique allows the non-destructive monitorization of diffusant concentration as a function of time and location. Concentration profiles were compared with theoretical curves based on solutions of Fick's diffusion equation for the best fitting, with the appropriate boundary conditions. The measured concentration profiles show a good agreement with the Fickian law. Values of the diffusion coefficients D ranging from 6.1×10(-6) to 3.4×10(-6)cm(2)s(-1) depending on chitosan concentration and type of diffusant molecule were determined. In addition, measurements of diffusion coefficients at equilibrium conditions with proton pulsed field gradient NMR methods supported the observed Fickian behavior and showed values of D in excellent agreement with those determined by proton MRS. All these facts demonstrate that proton MRS is an appropriate method for investigating diffusion process in complex systems, such as polymer gels.     

Flow-induced translocation of polymers through a fluidic channel: a dissipative particle dynamics simulation study

The dynamics of flow-induced translocation of polymers through a fluidic channel has been studied by dissipative particle dynamics (DPD) approach. Unlike implicit solvent models, the many-body energetic and hydrodynamic interactions are preserved naturally by incorporating explicit solvent particles in this approach. The no-slip wall boundary and the adaptive boundary conditions have been implemented in the modified DPD approach to model the hydrodynamic flow within a specific wall structure of fluidic channel and control the particles' density fluctuations. The results show that the average translocation time versus polymer chain length satisfies a power-law scaling of τ ～N(1.152). The conformational changes and translocation dynamics of polymers through the fluidic channel have also been investigated in our simulations, and two different translocation processes, i.e., the single-file and double-folded translocation events, have been observed in detail. These findings may be helpful in understanding the conformational and dynamic behaviors of such polymer and/or DNA molecules during the translocation processes.     

Optical determination of the pitch-dependent diffusion constant in a cholesteric liquid crystal

Abstract

The concentration profile of a cholesteric compound diffusing into a nematic liquid crystal is observed with optical methods. We propose new experimental initial and boundary conditions which allow a more accurate mathematical solution of the differential equation involved. A numerical approach is applied to compute the concentration profiles with a concentration dependent diffusion constant. Diffusion is found to decrease with the shorter pitch length.     

Pulsed field gradient NMR study of phenol binding and exchange in dispersions of hollow polyelectrolyte capsules

The distribution and exchange dynamics of phenol molecules in colloidal dispersions of submicron hollow polymeric capsules is investigated by pulsed field gradient NMR (PFG-NMR). The capsules are prepared by layer-by-layer assembly of polyelectrolyte multilayers on silica particles, followed by dissolution of the silica core. In capsule dispersion, (1)H PFG echo decays of phenol are single exponentials, implying fast exchange of phenol between a free site and a capsule-bound site. However, apparent diffusion coefficients extracted from the echo decays depend on the diffusion time, which is typically not the case for the fast exchange limit. We attribute this to a particular regime, where apparent diffusion coefficients are observed, which arise from the signal of free phenol only but are influenced by exchange with molecules bound to the capsule, which exhibit a very fast spin relaxation. Indeed, relaxation rates of phenol are strongly enhanced in the presence of capsules, indicating binding to the capsule wall rather than encapsulation in the interior. We present a quantitative analysis in terms of a combined diffusion-relaxation model, where exchange times can be determined from diffusion and spin relaxation experiments even in this particular regime, where the bound site acts as a relaxation sink. The result of the analysis yields exchange times between free phenol and phenol bound to the capsule wall, which are on the order of 30 ms and thus slower than the diffusion controlled limit. From bound and free fractions an adsorption isotherm of phenol to the capsule wall is extracted. The binding mechanism and the exchange mechanism are discussed. The introduction of the global analysis of diffusion as well as relaxation echo decays presented here is of large relevance for adsorption dynamics in colloidal systems or other systems, where the standard diffusion echo decay analysis is complicated by rapidly relaxing boundary conditions.