The application of multiscale quasi 4D CT to the study of SrCrO4 distributions and the development of porous networks in epoxy-based primer coatings

Transport paths for inhibitor release within a model strontium chromate (SrCrO₄) inhibited/epoxy primer have been studied using a combination of tomography techniques. It has been found that the SrCrO₄ particles form independent clusters within the model primer. The clusters have a range of fractal dimensions with the largest clusters (a few hundred microns in size) having a fractal dimension of 2.36. Leaching of the SrCrO₄ from the primer appears to be initially through direct dissolution of particles in contact with the electrolyte but changes to diffusion through void pathways created by dissolution of the SrCrO₄ phase. No evidence was found for the diffusion of chromate ions through the epoxy. Transport through such clusters does not follow Fickian diffusion, which has traditionally been employed to describe inhibitor release dynamics. Release kinetics typically follow a t^m behaviour where t is time and m is an index which would be 0.5 for Fickian diffusion. Thus the overall release with time will evolve, being initially the result of direct dissolution, then at intermediate times, be dominated by transport through the fractal network and at the final stage go to zero since all the strontium chromate will be dissolved from the cluster connected to the surface. Clusters not connected to the surface remain undissolved and form additional reservoirs for further release in when local damage occurs in their vicinity. This new model of inhibitor transport creates new strategies for the development of self-healing properties for coatings.     

Small-angle neutron scattering of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers

Small-angle neutron scattering was used to characterize the structure of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers dissolved in methanol-d4 (CD₃OD). A radial density profile based on a power law functional form provided a good fit to the scattering data. While a model with homogeneous density profiles in the core and shell, respectively, and with a size distribution (a polydisperse core-shell model) also fits the data comparably well, the extra parameters required for this fit are difficult to justify on the basis of the data. In addition, unconstrained fits using the core-shell model failed to converge to values of the overall molecular size and molecular weight which agreed with values determined from independent light scattering measurements which leads to the conclusion that the power law model is a more appropriate function for describing the radial density function of these molecules. The density profile from either model showed that the polystyrene core of the molecules is not collapsed. Values of the second virial coefficient, A₂, have been calculated from Zimm plots and it was found that A₂ decreased as a function of generation to close to zero for the highest generation (i.e. highest molecular weight) polymers. Finally, it was found that the radius of gyration of the polymers increases with the molecular weight according to the scaling relationship, R_g∼M_w^v with v=0.24±0.04.     

Numerical simulations of transfer and transport properties inside packed beds of spherical particles

In this study, we investigate the transport and transfer properties inside packed beds of spherical particles by means of CFD simulations. Heat and mass transfer properties have been computed in packing configurations of increasing complexity at low to moderate Reynolds numbers (1<R_e<80). Only liquid-phase flows are studied (300<S_c<1000). The problem of contact points between particles, which is inherent to finite-volume numerical methods, is solved by applying a contraction of 2% on all the particles of the bed. We show that this treatment has very little influence on the results when analyzed with dimensionless numbers as N_u=f(R_e, P_r) or S_h=f(R_e, S_c). Finally, a very dense packing of spheres was built using a Discrete Element Method and used to represent the real granular media. Transfer predictions by the model are very realistic. Longitudinal and transverse dispersion coefficients are determined inside geometries containing hundreds of particles. Predictions of dispersion coefficients are consistent with literature, but a correction is applied to improve results, because the bed contraction leads to the underestimation of the transverse dispersion coefficient. The model is found to be very promising to study the “near wall channelling” phenomena inside small packed columns induced by the heterogeneity of the porosity profile close to the wall.     

Steady-state mass transfer in radial flow-through thin layer cells—I. Reversible metal systems

The convective diffusion model, prevailing in radial thin layer flow cells (thickness 2h ? 10^?2 cm) with central solution inlet at ultra-low flow rates J ? 10^?2 cm³ s^?1, has been investigated by numerical finite-difference techniques for the transport-controlled conversion of metal ions at a coulometric asymmetrical or symmetrical metal detector, mounted on one or on both sides of the thin layer, respectively. At symmetrical detectors, the concentration profiles and the conversion efficiency have been evaluated by assuming negligible radial diffusion and are in good agreement with previous eigenvalue solutions. At unsymmetrical detectors, the mass transfer study has been carried out in consideration of radial diffusion. The diffusional contribution to the radial flux becomes increasingly apparent in the concentration profiles and the conversion efficiency, as the internal detector boundary r₀ is shifted downstream at constant h and J, or as J and h are lowered proportionally at constant r₀. This effect can be diminished by choosing appropriate correlations between r₀, h and J, which are established together with the limiting conditions for coulometric detector operation.     

Effect of chain length distribution on thermal characteristics of model polytetrahydrofuran (PTHF) networks

A series of model polytetrahydrofuran (PTHF) networks were synthesized via end-linking reactions of α, ω-allyl PTHF oligomers with a stoichiometric tetrafunctional crosslinker. The telechelic PTHF oligomers were synthesized by living cationic ring-opening polymerization of tetrahydrofuran followed by a termination reaction with allyl alcohol. Networks thus prepared have well-controlled architecture in terms of the inter-crosslink chain length (M_c) and chain length distribution: resulting in unimodal, bimodal and clustered structures. Unimodal network was prepared by using polymer chains of same molecular weight, bimodal networks were synthesized by using two groups of polymer chains with different average molecular weights, and the clusters are prepared by incorporating clusters of networks with small molecular weight chains in a network matrix made of longer chains. Thermal characteristics of these model networks were investigated as a function of crosslink density, as well as inhomogeneities of crosslink distribution using DSC. We demonstrate that glass transition temperature (T_g) and crystallization behavior (melting temperature and crystallinity) of the networks are both strongly influenced by crosslink density (M_c). By comparing the unimodal, bimodal and clustered networks with similar average M_c, the effects of inhomogeneities in the crosslink distribution on the thermal properties were also investigated. Results show that inhomogeneities have trivial influence on T_g, but strongly affects the crystallization behavior. Moreover, the effects of the content ratio and length ratio between long and short chains, and the effects of cluster size and size distribution on the thermal characteristics were also studied.     

Evidence for C60 aggregation from solvent effects in [Ps-C60] molecular complex formation

Using a molecular probe positronium (Ps), Ps reaction rate constants (k) with C₆₀, a strong Ps acceptor, are determined for the formation of a donor-acceptor type molecular complex in solvents of varying surface tension (σ) and viscosity (η). Within the framework of Smoluchowski’s theory of diffusion, the calculated Stokes radius for C₆₀ in the different solvents deviated from the monomeric value, implying the existence of aggregated clusters in solution and using transmission electron microscopy, C₆₀ aggregation in carbon disulphide (CS₂) is observed with the formation of spherical fractal clusters of ∼90 nm size with aggregation number 1.7×10⁴ and a fractal dimension of 1.9 at a concentration of 0.5 mM. The fractal dimension of 1.9 revealed the mechanism of aggregation to proceed through a diffusion limited process with the estimated diffusion coefficient and the diffusion length of the aggregated cluster to be 2.27×10⁻⁶ cm²/s and 0.63 nm, respectively.     

Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Y-Faujasite Encapsulated Co Clusters: Synthesis, Characterization and Theoretical Model as Probe of the Methane Homologation

The adsorption of Co₂(CO)₈ onto the dehydrated Y-faujasite powder under an N₂ atmosphere and onto the tetrahydrofuran slurry of Y-faujasite under a mixed CO and H₂ atmosphere predominately yielded supported Co₄(CO)₁₂ and supported Co₆(CO)₁₆, respectively. The molecular cobalt-carbonyl clusters and their decarbonylated products have been structurally characterized by extended X-ray absorption fine structure (EXAFS). The decarbonylated sample a possesses a cluster of two Co atoms and the decarbonylated sample b has a cluster phase of three Co atoms. The decarbonylated sample a exhibited higher CH₄ conversion and C₂₊ selectivity (C₂₊ selectivity = ∑nC _n(n = 2–5)/∑nC _n (n = 1–5) * 100%) in comparison with the decarbonylated sample b in methane homologation. A density functional theory (DFT) model was employed to calculate Co clusters adsorbed on a silica substrate which simulates Y-faujasite encapsulated Co clusters. The structural geometries, net spin electronic charge densities, energies of the metal–silica and metal–metal interactions in stable geometries are discussed and used to interpret the cluster size dependence of the catalytic activity and selectivity to C ₂₊ hydrocarbons in the methane homologation.     

Optimization for field emission from carbon nanotubes array in hexagon

In order to investigate the influence of the arrangement of the carbon nanotubes (CNTs) array on the field emission, the more practical model in hexagon was proposed. From the calculation with the image floated sphere model, the results showed that the arrangement has little influence on the field emission and the intertube distance R of CNTs array critically affects the field emission from the CNTs array, which accords with the results from the numerical simulations and experiments. When R is less than the height of tube h, the enhancement factor decreases rapidly with R. Considering the field emission current density, the field emission can be optimized when R is comparable with h, which accorded with the results from experiments. Furthermore, the influence of the anode–cathode distance d on the field emission from CNTs array was also discussed, which proved that d has little effect on the field emission from CNTs array. For the fixed field strength E for the certain materials in filed emission, we can reduce the threshold voltage to some extent by decreasing d in the case of R > 2h.     

Image Analysis and Computer Simulation of Nanoparticle Clustering in Combustion Systems

The current work presents a new method to model and characterize the formation and growth of nanoparticles clusters which includes the three dimensional geometric properties of the clusters, such as aspect ratios, main chain length, radius of gyration, fractal dimension and fractal prefactor. In the model, semi-stochastic mathematics is used to represent varying levels of Coulomb and van der Waals forces during clustering of monodisperse particles. Parametric studies of the relative particle interactions are conducted to evaluate the effects on cluster geometry. Radius of gyration and main chain length were identified as the geometric properties with the greatest sensitivity to changes in the interparticle forces. To demonstrate the analytical capability of the approach, clusters of combustion-generated tin dioxide (SnO₂) nanoparticles were imaged and evaluated to identify the dominant forces controlling cluster morphology. The results show the geometry of the SnO₂ clusters is a result of strong Coulomb interactions.     

Distribution analyses of multi-modal dynamic light scattering data

A method of data analysis for dynamic light scattering is proposed to evaluate the weight fraction, w(R_h), of a small amount of large aggregates in a dilute solution, where R_h is the hydrodynamic radius. We examined the time-correlation function of scattering intensity for model multi-modal systems, i.e., mixtures of latex solutions having different particle sizes and of polystyrene standard solutions having different molecular weights, by properly taking into account the unknown fractions, w(R_h), and scattering intensities of individual components. We derived an equation to evaluate the weight fractions of the components. The validity of this method was verified by successfully reconstructing the observed correlation functions having fast and slow modes. As a demonstration, the fraction of aggregates in a thermosensitive polymer solution in water was evaluated as a function of temperature.     

Characterization of poly(1,4-phenyleneterephthalamide) in concentrated sulphuric acid. 2: Determination of molecular weight distributions

By combining static and dynamic properties (M_w, A₂, k_dR_g and R_h) of poly(1,4-phenyleneterephthalamide), PPTA (commercially known as Kevlar), with a detailed analysis of measured time correlation functions at different scattering angles in dilute solution, we have been able to estimate the molecular weight dependence of the radius of gyration, R_g(M), the persistence length ? ($\text{≈ 290}\text{A}\text{?}$), and the molecular weight distribution (M_z:M_w:M_n ≈ 6.2:1.8:1) using an unfractionated PPTA sample (M_w = 4.3 × 10⁴ g/mole). Laplace inversion of the time correlation function was accomplished independently by means of two different algorithms: the singular value decomposition technique with discrete multi-exponentials to approximate the normalized characteristic linewidth distribution function G(г) and the method of regularization whereby a linearized smoothing operator was used. The non-intrusive laser light scattering technique permits us to characterize, for the first time, the molecular weight distribution of PPTA which has been difficult to perform by means of other more established methods, such as size exclusion chromatography, because of the corrosive nature of solvents used in preparing PPTA solutions.     

Gas permeation in thin films of “high free-volume” glassy perfluoropolymers: Part I. Physical aging

Physical aging of both thick and thin films of “high free-volume” glassy perfluoropolymers was studied by monitoring changes in pure gas permeability of O₂, N₂ and CH₄. All permeability measurements were done at a fixed temperature of 35 °C for more than 1000 h of aging. Two grades of perfluoropolymers, Teflon AF and Hyflon AD, having different comonomer structures but with similar comonomer ratios were studied to understand the effect of comonomer type and content on the aging behavior. The effect of casting process (solution vs. spin coating) and solvent type (vapor pressure and boiling point) had a significant effect on the absolute permeability of both thick and thin films; however, the aging rates were more affected by thickness and solvent type rather than the casting process for similar thicknesses. After 1000 h of aging, the relative permeability for thin films of Teflon AF 2400 was decreased by 27% compared to only 10% for thick films prepared from Novec 7500 solvent. Teflon AF, which has a higher fractional free volume (FFV) than Hyflon AD, is believed to undergo significant aging well before the initial permeability measurement could be made (after ∼ 1 h of aging) and, therefore, Teflon AF materials showed a lower decrease in relative permeability compared to Hyflon AD for the same aging time. The comonomer type and content has a significant effect on the permeability; the initial absolute oxygen permeability for AF 2400 was an order of magnitude higher compared to AD 60. The physical aging of thin films of the various glassy perfluoropolymers was also tracked by recording changes in the refractive index and thickness with time by ellipsometry. The ellipsometry data also confirmed higher aging rates in Hyflon AD compared to Teflon AF materials. The volumetric aging rate, obtained from the change in the refractive index using the Lorentz–Lorenz equation, and the permeability reduction rate from the (P_1000h/P_1h) ratio showed an excellent linear correlation. The (P_1000h/P_1h) ratio also showed a stronger correlation with (T_g−35) °C than with FFV.     

A Study of Ozone Generation by Negative Corona Discharge Through Different Plasma Chemistry Models

The Steady radial distribution of chemical species in a wire‐to‐cylinder ozone generator filled with pure oxygen has been computed by applying four different plasma chemistry models of increasing complexity. The most complete model considers ten species (e, O₂ ⁺, O₂ ^?, O₃ ^?, O^?, O₂, O₂(¹Δ_g), O₂(¹∑_g ⁺), O and O₃) and 79 reactions, including ionization by electron impact, electron attachment and detachment, electron-ion recombination, charge transfer, etc. The chemical model is coupled with the electrical model through Poisson's equation. The spatially averaged ozone density has been computed as a function of the current intensity and compared with the experimental values obtained by UV spectroscopy.     

Water-Soluble Chalcogenide W6-Clusters: On the Way to Biomedical Applications

Despite the great potential of octahedral tungsten cluster complexes in fields of biomedical applications such as X-ray computed tomography or angiography, there is only one example of a water-soluble W₆Q₈-cluster that has been reported in the literature. Herein we present the synthesis and a detailed characterization including X-ray structural analysis, NMR, IR, UV–Vis spectroscopies, HR-MS spectrometry, and the electrochemical behavior of two new cluster complexes of the general formula W₆Q₈L₆ with phosphine ligands containing a hydrophilic carboxylic group, which makes the complexes soluble in an aqueous medium. The hydrolytic stability of the clusters’ aqueous solutions allows us to investigate for the first time the influence of W₆-clusters on cell viability. The results obtained clearly demonstrate their very low cytotoxicity, comparable to the least-toxic clusters presented in the literature.     

The structure of hydrated complexes of o-hydroxybenzoic acid in water-modified supercritical carbon dioxide: The Car-Parrinello molecular dynamics simulation

The study of the o-hydroxybenzoic acid (o-HBA)–water molecular structures formed in supercritical carbon dioxide (T = 318 K, ρ = 0.7 g/cm³) by Car-Parrinello molecular dynamics method has been performed. Atom–atom radial distribution functions, coordination numbers, average hydrogen bond (HB) numbers, and vibrational densities of states have been calculated from molecular trajectories saved during simulation procedure. It has been shown that, despite of the high co-solvent polarity, the hydroxyl group of the o-HBA preferably forms an intramolecular HB, whereas o-HBA–water hydrogen bonding involves only acid carboxyl group. The formed o-HBA–(H₂O)₂ complex and remaining water molecules compose a labile hydrogen-bonded cluster. The average HB number per water molecule is equal to 1.93, 26.4% out of the total amount of HBs formed by water molecules being water–o-HBA HBs, and the rest being water–water HBs. Evolution of hydrogen-bonded clusters has been analyzed, using instantaneous structures saved during the simulation. It was shown that water–water HBs are less stable than water–o-HBA ones.     

Improved orthokinetic coagulation model for fractal colloids: Aggregation and breakup

An improved discretized population balance equation (PBE) is proposed in this study. This improved discretized PBE has new probability distribution functions for aggregates produced in non-uniform discrete coagulation modeling. The authors extended an improved particle coagulation model previously developed to an adjustable geometric size interval (q), where q is a volume ratio of class k+1 particles to class k particles (υ_k+1/υ_k=q). This model was compared with exact numerical solutions of continuous (uniform discretized) PBEs and applied to simulate the particle aggregation and breakup with fractal dimensions lower than 3. Further, comparisons were made using the fractal aggregate collision mechanisms of orthokinetic coagulation with the inclusion of flow induced breakup.In the course of the investigation the new algorithm was found to be a substantial improvement in terms of numerical accuracy, stability, and computational efficiency over the continuous model. This new algorithm makes it possible to solve fractal particle aggregation and breakup problems with high accuracy, perfect mass conservation, and exceptional computational efficiency, thus the new model can be used to develop predictive simulation techniques for the coupled coagulation using computational fluid dynamics (CFD) and chemical reaction modeling.     

An extended two-state model for grain growth during gas phase production of powders

We have investigated a Monte-Carlo treatment of particle-growth by evaporation–condensation based on a combination of a two-state Potts, or Ising, model with the Metropolis algorithm for the acceptance/rejection of simulated growth steps. The effects of initial size-distribution and lattice occupancy on particle-growth through Ostwald ripening via evaporation–condensation have been explored and the sensitivity of the results to model-parameters, such as interaction energy, temperature and second-nearest-neighbour weightings has been investigated.From an initial random distribution of particles, the predicted growth follows a square root dependence on time, consistent with well known analytical treatments. When the temperature parameter was examined, a critical temperature T_c was found. Below T_c the rate of particle-growth increased with increasing T; but above T_c the growth-rate decreased with increase in T. The correspondence, in the absence of second-nearest-neighbour interactions, of the computed T_c with the analytically determined value demonstrates the robustness of our procedures.The effects of evaporation–condensation on the size-distribution, characterized by a mean size 〈R〉 and r.m.s. deviation δ, have received particular consideration. It is predicted that, for three different initial particle size distributions, with the same initial mean size, growth by evaporation–condensation will lead to convergence of the normalized δ/〈R〉 versus time or δ/〈R〉 versus 〈R〉 curves. Counter-intuitively, a narrow initial size-distribution is not maintained by particles growing by evaporation–condensation.Finally, we have developed a simple technique for incorporating diffusive phenomena into this model by incorporating distance dependence into the probability of migration. This has reduced the necessary computational time and enabled us to compare the dependence of the δ/〈R〉 versus 〈R〉 relationship for different values of the characteristic distance. Remarkably and somewhat unexpectedly, we find that for a wide range of model-parameters the normalized deviation is effectively independent of this characteristic distance.     

Effect of zinc concentration on the microstructure and relaxation frequency of Mn–Zn ferrites synthesized by solid state reaction

Mn3Zn polycrystalline ferrites with Mn_1−xZn_xFe₂O₄ stoichiometry (x=0.59, 0.61, 0.65) were prepared by solid state reaction. These ferrites were heated at different temperatures. The cubic structure with space group Fd3m (O_h⁷) No. 227 was confirmed by the refinement of x-ray diffraction (XRD) powders through Rietveld´s method using fullprof. Scanning electron microscopy (SEM) results revealed for all compounds a non-homogeneous grain size and shape distribution, with a mean grain size of 9 μm. The Curie temperature T_c was found to decrease as the Zn concentration increases. The magnetic domain relaxation was investigated by inductance spectroscopy (IS). The relaxation frequency f_r shows an increase with the increase of the grain size while the initial permeability µ_i decreased. We propose an R_pL_p parallel arm equivalent circuit to model the IS results. The theoretical approximation is in agreement with the experimental results. We found that Mn–Zn ferrites with zinc concentration at x=0.59 and heated to 1300 °C during 6 h show a slight improvement of the homogeneous microstructure and a relatively higher relaxation frequency without the abrupt degradation of their permeability. This result suggests that ferrites treated in the manner presented in this paper are good candidates for high frequency applications.