Molecular Diffusion Theory Research Articles

Microscopic self-healing of multi-walled carbon nanotube-modified asphalt based on the dual diffusion-energy theory

To investigate the self-healing performance of multi-walled carbon nanotube-modified asphalt and its influencing mechanism, the asphalt molecular self-healing models were established by the molecular dynamics method. The results were analyzed based on molecular diffusion theory and surface energy repair theory. Based on the Arrhenius model, two theories were combined, and a new index healing factor was proposed to evaluate the self-healing performance by considering the diffusion characteristics and energy changes of asphalt molecules. The results show that multi-walled carbon nanotubes can accelerate the diffusion behavior of molecules in the temperature of 278--318 K to improve the self-healing properties of asphalt. Based on the proposed surface free energy equation, the self-healing properties are reasonably evaluated; the enthalpy change can be used as an index for judging the self-healing performance. The transformation model of the diffusion coefficient and cohesive work and the new index can reflect the self-healing performance more comprehensively.

Molecular Diffusion in Nanoreactors' Pore Channel System: Measurement Techniques, Structural Regulation, and Catalytic Effects.

Nanoreactors, as a new class of materials with highly enriched and ordered pore channel structures, can achieve special catalytic effects by precisely identifying and controlling the molecular diffusion behavior within the ordered pore channel system. Nanoreactors-driven molecular diffusion within the ordered pore channels can be highly dependent on the local microenvironment in the nanoreactors' pore channel system. Although the diffusion process of molecules within the ordered pore channels of nanoreactors is crucial for the regulation of catalytic behaviors, it has not yet been as clearly elucidated as it deserves to be in this study. In this review, fundamental theory and measurement techniques for molecular diffusion in the pore channel system of nanoreactors are presented, structural regulation strategies of pore channel parameters for controlling molecular diffusion are discussed, and the effects of molecular diffusion in the pore channel system on catalytic reactivity and selectivity are further analyzed. This article attempts to further develop the underlying theory of molecular diffusion within the theoretical framework of nanoreactor-driven catalysis, and the proposed perspectives may contribute to the rational design of advanced catalytic materials and the precise control of complex catalytic kinetics.

Single-molecule FRET and molecular diffusion analysis characterize stable oligomers of amyloid-β 42 of extremely low population

AbstractSoluble oligomers produced during protein aggregation have been thought to be toxic species causing various diseases. Characterization of these oligomers is difficult because oligomers are a heterogeneous mixture, which is not readily separable, and may appear transiently during aggregation. Single-molecule spectroscopy can provide valuable information by detecting individual oligomers, but there have been various problems in determining the size and concentration of oligomers. In this work, we develop and use a method that analyzes single-molecule fluorescence burst data of freely diffusing molecules in solution based on molecular diffusion theory and maximum likelihood method. We demonstrate that the photon count rate, diffusion time, population, and Förster resonance energy transfer (FRET) efficiency can be accurately determined from simulated data and the experimental data of a known oligomerization system, the tetramerization domain of p53. We used this method to characterize the oligomers of the 42-residue amyloid-β (Aβ42) peptide. Combining peptide incubation in a plate reader and single-molecule free-diffusion experiments allows for the detection of stable oligomers appearing at various stages of aggregation. We find that the average size of these oligomers is 70-mer and their overall population is very low, less than 1 nM, in the early and middle stages of aggregation of 1 µM Aβ42 peptide. Based on their average size and long diffusion time, we predict the oligomers have a highly elongated rod-like shape.

Influence of Temperature Control of Coke Oven on Life Cycle of Refractories

Different stages of the oven drying are analyzed by the theory of molecular diffusion and crystal change in oven drying process. It’s pointed that in order to ensure uniform expansion and gray seam integrity, the speed of spreading to the outside about within water should be in accordance with the speed of evaporation about surface moisture in the drying period, heating up too quickly will easily lead to extending drying period and destroying masonry rigor. The expansion of silica brick is mainly from the volume effect form with the transition between the allotrope in the expansion period, the heating rate of crystal transformation point must be strictly controlled. At the same time, quartz content should be higher, lesser residual quartz content will be better. The hot state engineering period is consistent with the construction schedule, the construction sequence can’t be reversed, and it is not recommended at this stage to extend the construction period. Effective control of the heating rate of the three stages above lays a solid foundation to extend the oven life.

Influence of operating temperatures on long-duration wax deposition in flow lines

Operating temperatures have major impacts on wax deposition. Although significant research efforts have been expended on this topic, no satisfactory agreement has been achieved in the available literature. In the present work, we conducted cold-flow flow-loop wax deposition experiments using a waxy condensate with 9.5% wax content to investigate the influence of operating temperatures on wax deposition. To achieve a closer representation of field operation, we varied the oil temperature while keeping the initial wall temperature constant and conducted the tests up to 72 h. It was observed that the deposit forms more slowly but contains higher wax content as the difference between oil temperature and wall temperature increases, and these trends hold at both 48 and 72 h. Moreover, we calculated the diffusive mass flux at different operating conditions using the prevailing theory of molecular diffusion and found that the predicted trends are opposite to experimental observations. These results, along with findings from recent publications, collectively suggest that the long-standing modeling approach based on molecular diffusion is insufficient to completely describe wax deposition phenomenon, and that wax deposit morphology and other deposition mechanisms deserve further attention to close this knowledge gap.

Vertical Sediment Concentration Distribution in High-Concentrated Flows: An Analytical Solution Using Homotopy Analysis Method

Transport of suspended sediment in open channel flow has an enormous impact on real life situations, viz. control and management of reservoir sedimentation, geomorphic evolution such as dunes, rivers, and coastlines etc. Transport entails advection and diffusion. Turbulent diffusion is governed by the concept of Fick’s law, which is based on the molecular diffusion theory, and the equation that represents the distribution of sediment concentration is the advection-diffusion equation. The study uses the existing governing equation which considers different phases for solid and fluid, and then couples the two phases. To deal with high-concentrated flow, sediment and turbulent diffusion coefficients are taken to be different from each other. The effect of hindered settling on sediment particles is incorporated in the governing equation, which makes the equation highly non-linear. This study derives an explicit closed-form analytical solution to the generalized one-dimensional diffusion equation representing the vertical sediment concentration distribution with an arbitrary turbulent diffusion coefficient profile. The solution is obtained by Homotopy Analysis Method, which does not rely on the small parameters present in the equation. Finally, the solution is validated by comparing it with the implicit solution and the numerical solution. A relevant set of laboratory data is selected to check the applicability of the model, and a close agreement shows the potential of the model in the context of application to high-concentrated sediment-laden open channel flow.

Diffusion of carbon and nitrogen in TC4 titanium alloy plasma electrolytic saturation

The study aims at deriving an equation for the temperature field of the specimen- vapour-gaseous envelope (VGE) – electrolyte three-phase system, followed by the calculation of the temperature distribution expression. The diffusion mechanism of carbon and nitrogen, in light of the theory of molecular diffusion, and the mechanism behind the plasma electrolytic saturation, is also discussed. In the PES process, the diffusion of carbon and nitrogen is affected by the strengthening voltage and processing time, which in turn affects the thickness and element distribution of the diffusion layer. Carbon, of which the diffusion depth ranges from 0.5 μm to 2.5 μm, is mainly distributed into the outermost layer. While the nitrogen is able to distribute throughout the diffusion layer as indicated by its several tens microns of diffusion depth. Further, the influence of process parameters on the diffusion of atoms during the strengthening process is verified experimentally.

ChemInform Abstract: Transient Free Radicals in Viscous Solvents

AbstractReview: 72 refs.

Transient free radicals in viscous solvents

The majority of free radicals are highly reactive species which participate in bimolecular reactions with each other. Validation of the theory of molecular diffusion and reactivity in the liquid state requires knowledge of rate constants of radical–radical reactions (recombination, disproportionation) and their viscosity dependencies. An accurate comparison of theory and experiment has become available due to experimentally measured diffusion coefficients of reactive radicals by transient grating technique. Initial distribution of radicals in solution can be not random but pair-wise as in photo- or thermoinitiation of free radical polymerization reactions. Probability of a radical escape of a partner (cage escape) characterizes the initiator efficiency. Despite decades of measurement of cage effect values, cage effect dynamics with free radicals have only been investigated quite recently. The present tutorial review considers the effect of viscosity of Newtonian liquid on two types of recombination—in the solvent bulk and in a cage. Further, since radicals are paramagnetic species, external magnetic field affects probability of their reactions in pairs. These effects are also observed in viscous liquids, and reasons for such observations are explained. The recently discovered low magnetic field effect is also observed on radical pairs in viscous liquids.

Air bubble formation and dissolution in dispensing nanoimprint lithography

We report an experimental and theoretical study of two most critical yet stillto-be-answered issues in dispensing-based nanoimprint lithography (D-NIL): air bubbleformation and absorption, and discuss their impact on NIL yield and throughput. Usingreal-time observation via video, we found two different mechanisms for air bubble formation(feature pinning and multi-droplet encircling), and studied the dynamic behaviour of theair absorption and air bubble shrinking under different conditions. Furthermore, wedeveloped theoretical models and simulation programs of the air absorption and bubbleshrinking based on molecular diffusion theory and hydrodynamics. We compared thesemodels with experiments, and found excellent agreement. Our study shows that the keyfactors that affect the air dissolution time (and hence the air bubble shrinkingtime) are air bubble initial size, imprinting pressure, air solubility, and resistresidue layer thickness. One of our key conclusions from the study, which hassignificant practical importance, is that although the air in a bubble can be completelydissolved in a resist liquid as long as the bubble is smaller than a certain size,the air absorption time might be too long for the dispensing-NIL operating inatmosphere or poor vacuum to have a necessary throughput in mass manufacturing.

Freeze drying of pharmaceuticals in vials: Influence of freezing protocol and sample configuration on ice morphology and freeze-dried cake texture

In pharmaceutical freeze-drying processes, the freezing step is a key-step because it fixes the morphology of the frozen material and, by the way, the final morphology of the freeze-dried material. It is the most difficult step to control, as it concerns the nucleation processes and it is also a damaging step with respect to the biological activity loss of pharmaceutical proteins. In this paper, we have reported original data obtained with a BSA (bovine serum albumin) based formulation used to stabilize pharmaceutical proteins during their freeze-drying process. Morphological characteristics of the ice crystals just after the freezing step were determined for different freezing protocols. Mean diameters and size distributions of the ice crystals have been determined by a direct optical microscopy method in cold chamber for different freezing parameters: size and type of vials (moulded or tubing), height of filling, vial right sectional surface area, shelf loading temperature. It was observed that the ice crystals sizes distributions depended not only on the freezing rates (well known result) but also on the vial size and type and also on the filling height. It was observed that moulded vials or higher values of filling height reduced the morphology heterogeneities resulting from large supercooling degrees and gave more homogeneous ice crystal size distributions. This behaviour was explained by the decrease of the supercooling effects which generally led to larger and non-homogenous distributions. Moreover, a convenient annealing treatment could homogenize and increase notably the mean ice crystals sizes. Water vapour mass transfer resistances data during the sublimation step were also determined and correlated to the experimental values of the mean ice crystals diameters which affected directly the dried layer permeability. These data were interpreted by the mass transfer laws of molecular diffusion theory (Knudsen regime).

Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime

The transport of small particles in the free-molecule regime is investigated on the basis of gas kinetic theory. Drag force formulations were derived in two limiting collision models-namely, specular and diffuse scattering-by considering the potential force of interactions between the particle and fluid molecules. A parametrized drag coefficient equation is proposed and accounts for the transition from specular to diffuse scattering as particle size exceeds a critical value. The resulting formulations are shown to be consistent with the Chapman-Enskog theory of molecular diffusion. In the limit of rigid-body interactions, these formulations can be simplified also to Epstein's solutions [P. S. Epstein, Phys. Rev. 23, 710 (1924)].

Investigation of Paraffin Deposition During Multiphase Flow in Pipelines and Wellbores—Part 2: Modeling

A Joint Industry Project to investigate paraffin deposition in multiphase flowlines and wellbores was initiated at The University of Tulsa in May 1995. As part of this JIP, a computer program, based on the molecular diffusion theory, was developed for prediction of wax deposition during multiphase flow in pipelines and wellbores. The program is modular in structure and assumes a steady-state, one-dimensional flow, energy conservation principle. This paper will describe the simulator developed for predicting paraffin deposition during multiphase flow that includes coupling of multiphase fluid flow, solid-liquid-vapor thermodynamics, multiphase heat transfer, and flow pattern-dependent paraffin deposition. Predictions of the simulator are compared and tuned to the experimental data by adjusting the film heat transfer and diffusion coefficients and the thermal conductivity of the wax deposit.

Production of large metallic clusters by thermal evaporation

Cluster beam evaporation has been used to produce metallic and semiconductor thin films for microelectronic applications. Previous work showed that the deposition of large clusters of antimony (>Sb 2000) onto silicon substrates and carbon films can be performed by thermal evaporation through a nozzle orifice and has been modelled using molecular diffusion theory. The results here show that the model can be extended to include other metals (e.g., Ag). TEM shows that cluster sizes in the case of Ag are much smaller than for Sb, having a di-similar statistical spread. Photoluminescence of Mg, Sb and Ag films show decreasing PL intensity with temperature which correlates with the expected concentration of clusters.

Modelling Modified Atmosphere Storage of Fresh Cauliflower Using Diffusion Channels

Abstract The storage of cauliflower under modified atmosphere (MA) was studied experimentally. The composition of oxygen in the storage chambers was regulated through the diffusion of oxygen in narrow channels. Fresh cauliflower was stored at 2·5°C in laboratory chambers equipped with channels of internal diameter 2mm and of different lengths. This technique was shown to be capable of maintaining different steady-state MA compositions (O 2 from 1·5 to 18·0%, depending on the length of the diffusion channels and the mass of the product; CO 2 ≈0%, with the help of a chemical adsorbent) for long periods of time. The steady-state compositions were stable under fluctuations in the cold room temperature. A model based on the molecular diffusion theory was developed to represent the observed phenomena. This model includes the effect of the mass of the produce and of the length and cross-sectional area of the diffusion channel, on the final gas composition in the chamber. Predictions of the diffusion model greatly underestimated the results obtained by experiment (i.e. 90% difference on the estimated channel length for an oxygen molar fraction of 0·03). Another model which takes into account convection in addition to pure diffusion, was found to be more appropriate to represent the experimental data (i.e. 10% difference on estimated length for the same conditions as above).

Stable Isotope Composition of Molecular Oxygen in Soil Gas and Groundwater: A Potentially Robust Tracer for Diffusion and Oxygen Consumption Processes

We have measured the concentration and isotopic composition of molecular oxygen in soil gas and groundwater. At a site near Lincoln, Nebraska, USA, soil gas oxygen concentrations ranged from 13.8 to 17.6% at depths of 3–4 m and the δ18O values ranged mostly from 24.0 to 27.2‰ (SMOW). The concentration of dissolved oxygen in a perched aquifer in the Texas Panhandle (depth to water ∼76 m) was about 5 mg/L and the δ18O values were 21.2–22.9‰. The δ18O of soil gas oxygen in our study are higher and those of dissolved oxygen are lower than the δ18O of atmospheric oxygen (23.5‰). A model for the oxygen concentration and isotopic composition in soil gas was developed using the molecular diffusion theory. The higher δ18O values in soil gas at the Nebraska site can be explained by the effects of diffusion and soil respiration (plant root and bacterial) on the isotopic composition of molecular oxygen. The lower δ18O of dissolved oxygen at the Texas site indicates that oxygen consumption below the root zone in the relatively thick unsaturated zone here may have occurred with a different fractionation factor (either due to inorganic consumption or due to low respiration rates) than that observed for the dominant pathways of plant root and bacterial respiration. It is concluded that the use of the concentration and isotopic composition of soil gas and dissolved oxygen should provide a robust tool for studying the subsurface gaseous diffusion and oxygen consumption processes.

Silica cycling within marine snow

The silica cycle within particles of marine snow from coastal waters off central California was examined. The ratios of biogenic silica to particulate organic nitrogen and to particulate org.anic carbon in aggregates were significantly greater than Redfield ratios, suggesting a large detrital silica component within the particles. Silicic acid concentrations within aggregates were ∼10‐fold greater on average than those in the surrounding seawater, with interstitial concentrations up to 305 µM Si(OH)4. Silica production rates within aggregates were sufficient to deplete the interstitial silicic acid in 0.3–4.0 h, suggesting rapid cycling of Si within the aggregates. Efflux of Si(OH)4 from the aggregates predicted from molecular diffusion theory was 20‐fold greater than the known maximum possible rates of silica dissolution could support. Congruence between efflux rates predicted by diffusion theory and dissolution kinetics requires the diffusion coefficient for Si(OH)4 in marine snow to be 2 orders of magnitude less than in pure seawater. Experimental determination of the concentration dependence of silicic acid use by diatoms in aggregates and by those in the surrounding seawater indicated that assemblages from both environments would experience Si‐replete conditions within marine snow. Aggregation of diatoms following silicic acid depletion at the end of blooms may provide Si‐replete microhabitats suitable for the formation of the heavily silicified resting spores that are central to the life‐history of many species.

Fractionation of soil gases by diffusion of water vapor, gravitational settling, and thermal diffusion

Air sampled from the moist unsaturated zone in a sand dune exhibits depletion in the heavy isotopes of N 2 and O 2. We propose that the depletion is caused by a diffusive flux of water vapor out of the dune, which sweeps out the other gases, forcing them to diffuse back into the dune. The heavy isotopes of N 2 and O 2 diffuse back more slowly, resulting in a steady-state depletion of the heavy isotopes in the dune interior. We predict the effect's magnitude with molecular diffusion theory and reproduce it in a laboratory simulation, finding good agreement between field, theory, and lab. The magnitude of the effect is governed by the ratio of the binary diffusivities against water vapor of a pair of gases, and increases ~linearly with the difference between the water vapor mole fraction of the site and the advectively mixed reservoir with which it is in diffusive contact (in most cases the atmosphere). The steady-state effect is given by δ i = [ i / j i o / j o − 1 ] 10 3 ‰ ≅ [ ( 1 − x H 2 O 1 − x H 2 O 0 ) ( D j − H 2 O / D i − H 2 O ) − 1 − 1 ] 10 3 ‰ , where δ i is the fractional deviation in permil of the gas i/gas j ratio from the advectively mixed reservoir, x H 2O and x H 2O 0 are respectively the mole fractions of water vapor at the site and in the advectively mixed reservoir, and D i−H 2O is the binary diffusion coefficient of gas i with water vapor. The effect is independent of scale at steady state, but approaches steady state with the time constant of diffusion set by the length scale. Exploiting the mechanism, we make an experimental estimate of the relative diffusivities of O 2 and N 2 against water vapor, finding that O 2 diffuses 3.6 ± 0.3% faster than N 2 despite its greater mass. We also confirm in the study dune the presence of two additional known processes: gravitational fractionation, heretofore seen only in the unconsolidated firn of polar ice sheets, and thermal diffusion, well described in laboratory studies but not seen previously in nature. We predict that soil gases in general will exhibit the three effects described here, the water vapor flux fractionation effect, gravitational fractionation, and thermal diffusion. However, our analysis neglects Knudsen diffusion and thus may be inapplicable to fine-grained soils.

The group theory of molecular diffusion and chemical reactions in the liquid state of matter

Abstract By assuming that the ensemble average of statistical mechanics reduces according to group theory several new results are obtained concerning the nature of time cross correlation functions (c.c.f.′s) in the isotropic liquid state of matter. In the laboratory frame (X, Y, Z) group theory allows the possibility for several time c.c.f′s between transport processes of appropriate symmetry. These provide new Green Kubo coefficients that can be investigated in principle by computer simulation and observed experimentally. The rule governing time cross correlation between translational, rotational, and vibrational dynamical variables of a diffusing molecule are deduced both in frame (X, Y, Z) and in the molecule fixed frame (x, y, z) of the point group character tables. The rules are valid for all molecular point groups. The group theoretical considerations are extended to cross correlations between physical properties of different molecules, on preparation for considering by group theory the symmetry of a chemical reaction in solution.

Irrotational and vortex fields in the theory of molecular dynamics

Abstract The theory of molecular diffusion is extended to include consideration of the position vector r of the centre of mass of each molecule in the ensemble. This implies automatically that the interaction of rotation and translation must be considered in the treatment of non inertial accelerations in the molecular ensemble. This leads to a consideration of vortex and irrotational fields in the theory of molecular dynamics in the laboratory frame (x,y,z) and in the moving frame (1,2,3) defined by the frame of the principal molecular moments of inertia. Computer simulations of supercooled liquid water are used to determine the nature of the time dependence of some of these autocorrelation functions involved in the development of the theory. This in turn might lead to a method of linking the ideas of molecular dynamics and hydrodynamics in the theory of fluids.