Intrinsic Diffusion Coefficients Research Articles

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein’s displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.

Mixing behaviour of Ni–Al melt at 1873 K

ABSTRACTRegular associated solution model and quasi-lattice model have been employed to study the thermodynamic and microscopic properties of Ni–Al liquid alloy at 1873 K. In thermodynamic properties, we have estimated free energy of mixing (), enthalpy of mixing () and entropy of mixing (), and in microscopic structural properties, we have studied concentration fluctuation in long wave length limit () and Warren–Cowely short-range-order parameters (). Additionally, transport properties, such as ratio of mutual and intrinsic diffusion coefficients () and the viscosity of Ni–Al melt at 1873 K have been computed using different approaches.

The intrinsic diffusivities in multi component systems

The complete understanding of the phenomenological process related to the position of the Matano and Kirkendall plane in multicomponent system is still lacking. In this paper some aspects of Matano and lattice plane migration are studied by means of numerical simulations. New approach to calculate intrinsic diffusion coefficients in binary Ni–Au system and ternary Cu–Fe–Ni and Co–Fe–Ni is presented. Diffusivities were calculated using modified Boltzmann–Matano method. Self diffusion coefficients of the elements in diffusion couple must be known as well as position of the Kirkendall plane after the experiment to use this method. Diffusion profile was calculated using presented equations. Calculations compared with experimental data prove validity of the presented approach. This work proves that intrinsic diffusion coefficients should be given by the concentration function, not the exact value.

Hydrodynamic behavior of quaternized chitosan at acidic and neutral pH

The study is devoted to estimation of the effect of quaternization on the molecular properties of polysaccharide chitosan. Solution properties of quaternized chitosan derivative, N-[(2-hydroxy-3-trimethylammonium)propyl]chitosan, have been studied in comparison with the initial chitosan in 0.33М СН3СООН + 0.2М CH3СООNa. The averaged quaternization degree of the modified samples was (90 ± 5) %. Hydrodynamics methods, translation isothermal diffusion and viscometry, and static/dynamic light scattering were applied for characterization of two homologues series of chitosans. The equilibrium chain rigidity value and Mark–Kuhn–Houwink relationships for intrinsic viscosity and diffusion coefficient have been received for the both polysaccharides at pH 3.54 and high ionic strength value. A change of thermodynamic conditions in the same solvent was detected for the modified chitosan in relation to initial analog. Even though the side substituents length is longer for the modified polysaccharide, the hydrodynamic dimension of its molecules could be smaller than initial polysaccharide of the same polymerization degree due to nonequivalent contributions of thermodynamic/electrostatic interactions to the total chain rigidity. The hydrodynamic behavior of quaternized chitosan in 0.33М СН3СООН + 0.2М CH3СООNa has been compared to its behavior in 0.2 M NaCl. The influence of the secondary amino group protonation on hydrodynamic properties of modified chitosan molecules was detected at neutral pH. Solution properties of quaternized chitosan in 0.2 M NaCl were identified as the concentration dependent.

Extracting intrinsic dynamic parameters of biomolecular folding from single-molecule force spectroscopy experiments.

Single-molecule studies in which a mechanical force is transmitted to the molecule of interest and the molecular extension or position is monitored as a function of time are versatile tools for probing the dynamics of protein folding, stepping of molecular motors, and other biomolecular processes involving activated barrier crossing. One complication in interpreting such studies, however, is the fact that the typical size of a force probe (e.g., a dielectric bead in optical tweezers or the atomic force microscope tip/cantilever assembly) is much larger than the molecule itself, and so the observed molecular motion is affected by the hydrodynamic drag on the probe. This presents the experimenter with a nontrivial task of deconvolving the intrinsic molecular parameters, such as the intrinsic free energy barrier and the effective diffusion coefficient exhibited while crossing the barrier from the experimental signal. Here we focus on the dynamical aspect of this task and show how the intrinsic diffusion coefficient along the molecular reaction coordinate can be inferred from single-molecule measurements of the rates of biomolecular folding and unfolding. We show that the feasibility of accomplishing this task is strongly dependent on the relationship between the intrinsic molecular elasticity and that of the linker connecting the molecule to the force probe and identify the optimal range of instrumental parameters allowing determination of instrument-free molecular dynamics.

Effective Diffusivity of Electrolyte in Porous Structure Using a Three-Dimensional Random Pore Network Model

In Li-ion cell, electrochemical discharge and intercalation/deintercalation occur at length scales that differ by an order of magnitude1. Analysis of these processes has been conventionally done using the classical pseudo 2D-model2 that is based on the porous-electrode theory, which solves the volume-averaged species conservation in the electrolyte. However, the species conservation in solid active material is solved by using the intrinsic diffusion coefficient since the model uses a microstructure that is composed of a single spherical particle placed at each grid location in the electrode. Hence, this model is unable to account for the percolation network in real particle clusters. Therefore, to make volume averaging process applicable at each grid location in the electrode, it is necessary to estimate the effective diffusivity in both particle and electrolyte phases. In this work, a model has been used to predict the effective diffusivity in the porous structure. It is assumed that the micro-porous structure of an electrode in Li-ion battery can be approximate by 3-D random pore network model as shown in Fig. 1. In this model, a pore is assumed to be circular bond segment which connects any two nodes. To make the model more realistic, length and diameter of each pore segment are chosen with the circular diameter of each bond segment distributed using a Gaussian distribution. The length of the bond segment, which is the distance between the nodes placed randomly is also prescribed using a second Gaussian. The lengths and diameters of each pore segment are iteratively adjusted such that the total pore volume fraction generated is equal to the porosity. When a pore geometry of required porosity is attained, fixed concentration boundary conditions are prescribed at two faces (with zero-flux imposed on all other faces) and the steady-state Fick’s diffusion equation is solved in the electrolyte phase. By applying mass balance equation at each node of the lattice, the effective mass diffusivity can be calculated. The sensitivity of number of nodes (from 3 ᵡ 3 ᵡ 3 nodes to 50 ᵡ 50 ᵡ 50 nodes or more if necessary) over effective diffusivity for a range of electrode porosities will be studied to determine the optimum number of nodes over which the transport parameter becomes independent of the node number. At optimum node network, the calculated effective diffusivity will be compared with the existing theoretical models based on idealizations and simplifying assumptions such as Bruggeman, Weissberg and Maxwell correlation. So far, no electrochemical reaction or transport is assumed at solid-liquid interface to evaluate the effective diffusivity in electrolyte phase. Apart from effective diffusivity and conductivity in electrode, the interfacial electrochemical reaction rate is another homogenized quantity based on idealized spherical particle in pseudo 2D model. Now to estimation effective diffusivity in solid phase and electrochemical reaction flux, the corresponding microscopic transport equations, for ion concentration and electric potential in solid and liquid phase in steady state is to be solve. To solve the above transport equations, specifying the state variables value at opposite end of the cube as boundary condition (Dirichlet boundary condition). Finally, the solution of transport equations is used to calculate the localized electrochemical reaction flux along the interface based on Butler-Volmer equation. To evaluate the normalized overall reaction current density, the flux integrate over the entire interface and is divided by total interfacial area. All the transport equations are solved in steady state, because diffusion and conduction occur over a much smaller distance in cubic geometry (placed at each node) than in electrode.

Thermodynamic and structural properties of Bi-based liquid alloys

Thermodynamic and microscopic structural properties of two Bi-based liquid alloys, such as In–Bi at 900K and Tl–Bi at 750K have been studied employing the regular associated solution model. We have estimated the mole fractions of the complexes and the free monomers assuming the existence of complexes In2Bi in In–Bi melt and TlBi in Tl–Bi melt. The thermodynamic properties have been studied by computing the Gibbs free energy of mixing, enthalpy of mixing, entropy of mixing and activities of the monomers. The compositional contributions of the heat associated with the formation of complexes and the heat of mixing of the monomers to the net enthalpy change has also been studied. The structural properties of the liquid alloys have been studied by computing concentration fluctuation in the long-wavelength limit, chemical short-range order parameter and the ratio of mutual to intrinsic diffusion coefficients. For both of the alloy systems, the theoretical as well as the experimental values of SCC(0) are found to be lower than the corresponding ideal values over the whole composition range, indicating the hetero-coordinating nature of Bi–In and Bi–Tl alloy melts. All the interaction energy parameters are found to be negative and temperature dependent, and both the alloy systems are found to be weakly interacting.

Role of the Molar Volume on Estimated Diffusion Coefficients

The role of the molar volume on the estimated diffusion parameters has been speculated for decades. The Matano–Boltzmann method was the first to be developed for the estimation of the variation of the interdiffusion coefficients with composition. However, this could be used only when the molar volume varies ideally or remains constant. Although there are no such systems, this method is still being used to consider the ideal variation. More efficient methods were developed by Sauer–Freise, Den Broeder, and Wagner to tackle this problem. However, there is a lack of research indicating the most efficient method. We have shown that Wagner’s method is the most suitable one when the molar volume deviates from the ideal value. Similarly, there are two methods for the estimation of the ratio of intrinsic diffusion coefficients at the Kirkendall marker plane proposed by Heumann and van Loo. The Heumann method, like the Matano–Boltzmann method, is suitable to use only when the molar volume varies more or less ideally or remains constant. In most of the real systems, where molar volume deviates from the ideality, it is safe to use the van Loo method. We have shown that the Heumann method introduces large errors even for a very small deviation of the molar volume from the ideal value. On the other hand, the van Loo method is relatively less sensitive to it. Overall, the estimation of the intrinsic diffusion coefficient is more sensitive than the interdiffusion coefficient.

Intermetallic formation and interdiffusion in diffusion couples made of uranium and single crystal iron

We studied the interfacial phase formation and diffusion kinetics in uranium–iron diffusion couples. A comparison was made between polycrystalline uranium (U) bonded with polycrystalline iron (FeP) and polycrystalline uranium bonded with single crystalline Fe (FeSC). After thermal annealing at 575 °C, 600 °C, 625 °C and 650 °C, respectively, diffusion and microstructures at the interface were characterized by scanning electron microscopy and transmission electron miscopy. The presence of grain boundaries in iron has a significant influence on interface reactions. In comparison with U–FeP system, interdiffusion coefficients of the U–FeSC system are significantly lower and were governed by much higher activation energies. Integrated interdiffusion coefficients and intrinsic diffusion coefficients were obtained. The intrinsic diffusion coefficients show faster diffusion of iron atoms in both U6Fe and UFe2 intermetallic phases than uranium.

Statistical calculations of tracer and intrinsic diffusion coefficients in concentrated alloys and estimates of microscopic parameters of diffusion from experimental data

The earlier-developed statistical theory of diffusion in concentrated alloys based on the master equation approach is generalized to treat tracer diffusion in binary alloys. The theory developed is used to describe concentration dependencies of both tracer and intrinsic diffusion coefficients and to estimate microscopic parameters of diffusion in alloys CuNi, CuZn and AgCd for which necessary experimental data are available. We show that all main features of strong and peculiar concentration dependencies of diffusion coefficients observed in these alloys are naturally explained by the theory. Signs and scales of interatomic interactions important for diffusion in these alloys are found to strongly depend on the ratio of atomic sizes of alloy components, and types of these dependencies agree with simple physical considerations. We also discuss physical reasons for sharp concentration dependencies of diffusion coefficients characteristic of real alloys.

Separation of ethanol from water by pervaporation using mixed matrix copolymer membranes

Several ethanol selective mixed matrix membranes were prepared from the copolymer of butyl acrylate and styrene and an organophilic nano size clay filler. The clay was incorporated in the polymer during its synthesis from the butyl acrylate and styrene monomer by emulsion polymerization in water. These membranes were characterized and used for the separation of 2.5–15wt% ethanols from water by pervaporation. The mixed matrix copolymer membrane containing 2% (wt% of total polymer) clay was observed to yield the best result, i.e., a flux of 0.34kg/m2h and an ethanol selectivity of 26.4 at 30°C for 5wt% ethanol in water. The permeability, intrinsic membrane selectivity and concentration average diffusion coefficients of the solvents were also determined.

Effect of dopants on the epitaxial growth and oxygen diffusion behaviors of CeO2−δ buffer layer for coated conductors

Ti, Zr and Hf doped CeO2−δ films with (00l) preferred orientation have been prepared on Ni–W substrates by chemical solution deposition method. The influence of ionic radii of dopants on the epitaxial growth process and oxygen diffusion behavior of Ce0.8M0.2O2−δ (M = Ti, Zr, Hf) films were explored by X-ray diffraction and atomic force microscopy. Since the ionic radii of doping cations of Ti, Zr and Hf are smaller than that of Ce and the lattice parameter of Ni–W substrate is smaller than that of CeO2−δ film, the compressive strain exists primarily in the doped film. The doping cation with small radius leads to the small lattice parameter of CeO2−δ film and small lattice mismatch between Ni–W substrate and epitaxial film. The compressive strain decreases resulting from the elastically lattice deformation in the films, while the compressive strain leads to the increase of the growth rate for CeO2−δ grains. The results show that the doping cation with smaller ionic radius has important influence on the surface roughness and the out-of-plane texture. Moreover, binding energy of dopants and oxygen vacancies, oxygen migration energies and vacancy formation energies are related to the intrinsic oxygen diffusion coefficient of buffer layers. Ionic radius has significant effect on the migration energies of oxygen ions. The Ti doped film shows severe oxygen diffusion due to steric effects. Therefore, the selection of suitable dopants would benefit the improvement of texture and surface morphology as well as the ability against oxygen diffusion of buffer layer.

Estimation of intrinsic diffusion coefficients in a pseudo-binary diffusion couple

Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in multi-component systems is developed utilizing the concept of a pseudo-binary approach. This is explained with the help of experimentally developed diffusion profiles in the Cu(Sn, Ga) and Cu(Sn, Si) solid solutions.

Pervaporative recovery of acetone from water using mixed matrix blend membranes

Several organophilic blend membranes were prepared by solution blending of polyvinyl chloride (PVC) and polystyrene (PS). Mixed matrix membranes were also prepared from PVC and PS by incorporating organophilic clay in these blends. These filled (mixed matrix) and unfilled blend membranes were characterized and used for pervaporative recovery of 5–25wt.% acetone from water. The filled blend membrane containing 2wt.% clay was observed to yield the best result, i.e., a flux of 0.042kg/m2h and acetone selectivity of 10.6 at 30°C for 5wt.% acetone in water. The permeability, intrinsic membrane selectivity and concentration average diffusion coefficients of the solvents were also determined.

Thermodynamic and structural behaviour of Tl-Na liquid alloy

In this work we intend to study the thermodynamic and microscopic structural properties of Tl-Na liquid alloy at 673 K on the basis of regular associated solution model. We have estimated the mole fractions of the complex and the free monomers assuming the complex TlNα as energetically favoured in the initial melt. In thermodynamic properties, we have computed free energy of mixing (GM), enthalpy of mixing (GM), entropy of mixing (SM) and activities of the monomers (αTl and αNα). The compositional contributions of the heat of mixing and the heat of formation of the complex to the net enthalpy change have also been studied. The microscopic structural properties of the alloy have been studied by computing concentration fluctuation in the long wavelength limit (SCC(O)), chemical short range order parameter (α1) and the ratio of mutual to intrinsic diffusion coefficients (DM/Did). Both the theoretical and the experimental values of SCC(O) are found to be less than the ideal values at all compositions which indicates the ordering nature of Tl-Na liquid alloy at 673 K. All the interaction energy parameters are found to be negative and temperature dependent. The liquid system is found to be moderately interacting.DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11784BIBECHANA 12 (2015) 20-29

Vanadium Pentoxide‐Based Cathode Materials for Lithium‐Ion Batteries: Morphology Control, Carbon Hybridization, and Cation Doping

Vanadium pentoxide (V2O5) is a promising cathode material for high‐performance lithium‐ion batteries (LIBs) because of its high specific capacity, low cost, and abundant source. However, the practical application of V2O5 in commercial LIBs is still hindered by its intrinsic low ionic diffusion coefficient and moderate electrical conductivity. In the past decades, progressive accomplishments have been achieved that rely on the synthesis of nanostructured materials, carbon hybridization, and cation doping. Generally, fabrication of nanostructured electrode materials can effectively decrease the ion and electron transport distances while carbon hybridization and cation doping are able to significantly increase the electrical conductivity and diffusion coefficient of Li+. Implementation of these strategies addresses the problems that are related to the ionic and electronic conductivity of V2O5. Accordingly, the electrochemical performances of V2O5‐based cathodes are significantly improved in terms of discharge capacity, cycling stability, and rate capability. In this review, the recent advances in the synthesis of V2O5‐based cathode materials are highlighted that focus on the fabrication of nanostructured materials, carbon hybridization, and cation doping.

Thermo-physical properties of Al–Fe melt

The thermodynamic properties, such as free energy of mixing, heat of mixing, entropy of mixing, activity and microscopic properties, such as concentration fluctuation in long wavelength limit, chemical short range order parameter, ratio of mutual and intrinsic diffusion coefficients of Al–Fe in liquid state at 1873 K have been studied on the basis of regular associated solution model. The complex Al3Fe is supposed to be energetically favoured in the liquid solution which is evident from the phase diagram of Al–Fe alloys. Thus the liquid mixture is treated as the ternary solution of complex and unassociated components. The concentrations of the complex Al3Fe and unassociated atoms have also been estimated. The concentration fluctuation in long wavelength limit is less than ideal values in whole range of concentration indicating that the system is ordered at all compositions. Our theoretical analysis suggests that the melt is strongly interacting hetero-coordinating system. The interaction energy parameters...

Physics‐based proxy modelling of solvent transport in VAPEX process

VAPEX (vapour extraction) is a non‐thermal process that has significant potential to provide a more environmentally friendly and energy‐efficient alternative to steam injection. While numerical modelling techniques are available for simulating mass transfer in VAPEX process, computational constraints often preclude detailed numerical solution of the flow and transport differential equations, as is often implemented in traditional flow simulators. Efficient alternatives that are based on analytical solutions could be employed to assess the transport physics. In this paper, a novel physical‐based proxy is developed to model solvent transport in VAPEX at isothermal conditions, in a way analogous to the SAGD model described by Butler (Butler, J. Can. Petrol. Technol. 1985, 24, 42). Detailed analytical formulations are derived and implemented in a calculation procedure to advance the solvent–bitumen interface and to estimate producing oil rate with time. In our approach, solvent concentration and intrinsic diffusion coefficient are introduced in the model instead of temperature and thermal diffusivity in SAGD. A new mass penetration parameter is introduced and its change with time is modelled. Growth of solvent chamber and oil drainage rate predicted from the proxy model are in good agreement with Hele‐Shaw experimental data available in the literature. Results predicted by proxy model also match well with scaled‐up flow rates for a field case described by Das and Butler (Das and Butler, J. Can. Petrol. Technol. 1994, 33, 39).

Competition between Kirkendall and Frenkel effects during multicomponent interdiffusion process

In this work the competition between Kirkendall effect caused by intrinsic diffusion coefficients and vacancy generation and evolution is discussed. The proposed approach is based on the bi-velocity (Darken) approach which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity at non-equilibrium. The model is formulated for arbitrary systems however for discussion only the binary system is presented. The distributions of (1) components, (2) vacancy and (3) voids radius over the distance are presented.

Role of different factors affecting interdiffusion in Cu(Ga) and Cu(Si) solid solutions

A detailed diffusion study was carried out on Cu(Ga) and Cu(Si) solid solutions in order to assess the role of different factors in the behaviour of the diffusing components. The faster diffusing species in the two systems, interdiffusion, intrinsic and impurity diffusion coefficients, are determined to facilitate the discussion. It was found that Cu was more mobile in the Cu–Si system, whereas Ga was the faster diffusing species in the Cu–Ga system. In both systems, the interdiffusion coefficients increased with increasing amount of solute (e.g. Si or Ga) in the matrix (Cu). Impurity diffusion coefficients for Si and Ga in Cu, found out by extrapolating interdiffusion coefficient data to zero composition of the solute, were both higher than the Cu tracer diffusion coefficient. These observed trends in diffusion behaviour could be rationalized by considering: (i) formation energies and concentration of vacancies, (ii) elastic moduli (indicating bond strengths) of the elements and (iii) the interaction parameters and the related thermodynamic factors. In summary, we have shown here that all the factors introduced in this paper should be considered simultaneously to understand interdiffusion in solid solutions. Otherwise, some of the aspects may look unusual or even impossible to explain.