Dynamic Coupling at Low Reynolds Number

Collective and emergent behaviors of active colloids provide useful insights into the statistical physics of out‐of‐equilibrium systems. Colloidal suspensions containing microscopic active swimmers have been intensively studied to understand the principles of energy transfer at low Reynolds number conditions. Studies on active enzymes and Ångström‐sized organometallic catalysts have demonstrated that energy can even be transferred by molecules to their surroundings, thereby influencing the overall dynamics of the systems substantially. By monitoring the diffusion of non‐reacting tracers in active solutions, it has been shown that the nature of energy transfer in systems containing different swimmers is surprisingly similar—irrespective of their size, modes of energy transduction, and propulsion strategies. This Review discusses research results obtained so far in this direction, highlighting the common features observed in the dynamic coupling of swimmers with their surroundings.     

Kinetics of Iron-catalyzed decomposition of hydrogen peroxide in alkaline solution

The decomposition of alkaline hydrogen peroxide solutions at 20°C has been studied in the presence of both supported iron catalysts and in systems with iron initially in solution. Studies with an iron-alumina supported catalyst showed the decomposition reaction was first order with respect to total peroxide concentration, while studies with alkaline Fe³⁺ produced more complex behavior. This has been attributed to the presence of at least two distinct catalytically active iron species. The first species is highly active and gives rise to high initial rates of reaction. A decrease in concentration of this species is observed together with an increase in concentration of a second, less active, iron species. The catalytic behavior of this “aged” iron species was found to be very similar to that of the supported iron catalyst.     

Mesoscopic model for diffusion-influenced reaction dynamics

A hybrid mesoscopic multiparticle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum, and energy so that hydrodynamic effects are fully taken into account. Reactive and nonreactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C <==> B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction phi of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.     

Polymerization of ethylene oxide with potassium-graphite inclusion compounds

The polymerization of ethylene oxide (EO) in tetrahydrofuran (THF) initiated by inclusion compounds of potassium in graphite (C₂₄K) at 50°C was studied. During the initial slow stage of the polymerization the catalyst efficiency increases, while during the second rapid stage the reaction proceeds at a constant concentration of the active centers. The influence of the catalyst and monomer concentrations on the concentration of the active centers and on the catalyst efficiency was studied. The existence of the slow stage is explained by diffusion of ethylene oxide between the graphite planes, where both initiation and initial chain growth take place. The diffusion of the growing chains from the catalyst into the solution brings about the formation of a necessary concentration of active centers in the solution, which ensures the rapid growth of the polymer chains under homogeneous conditions. An x-ray study of the catalyst after polymerization shows a strongly disturbed crystal structure of the graphite. Poly-(ethylene oxide) obtained at a higher degree of conversion, does not contain low molecular weight fractions.     

The Direct Electron Transfer of Iron‐containing Metal Organic Frameworks (Mil‐100) and Its Catalysis for the Oxygen Reduction Reaction in Room‐Temperature Alkaline Media on a Glass Carbon Electrode

The most common electrocatalysts for the oxygen reduction reaction (ORR) are platinum‐based ones. This work demonstrates the performance of iron‐containing metal organic frameworks (MOFs) as non‐platinum‐based nano‐electrocatalysts for ORR in an alkaline medium. As a new non‐platinum catalyst to achieve the active sites for the ORR, Mil‐100 (Fe) nanoparticles were used in aqueous KOH by the rotating‐disk electrode method. The main objectives of this study are the investigations on the electron transfer number (n ), Tafel slope, and catalytic performance. The particles size of the obtained powders is in the nanoscale range (approximately 25 nm). The electron transfer number for the ORR on the surface of iron‐containing catalyst is approximately 4, and the Tafel slope of diffusion‐corrected kinetic current density is ~50.7 mV per decade at low overpotential. This work might extend a new non‐precious‐metal catalyst structure for ORR for use in low‐temperature fuel cells.     

Retention and mass transfer characteristics in reversed-phase liquid chromatography using a tetrahydrofuran-water solution as the mobile phase.

The characteristics of the retention and the mass transfer kinetics in reversed-phase liquid chromatography (RPLC) were measured on a system consisting of a C18-silica gel and a tetrahydrofuran-water (50:50, v/v) solution. These parameters were derived from the first and the second moments of the elution peaks, respectively. Further information on the thermodynamic properties of this system was derived from the temperature dependence of these moments. Some correlations previously established were confirmed for this system, namely, an enthalpy-entropy compensation for both retention and surface diffusion and a linear free-energy relationship. These results are compared with those observed in other similar systems using methanol-water (70:30, v/v) and acetonitnile-water (70:30, v/v) solutions. The contribution of surface diffusion to intraparticle diffusion in C18-silica gel particles was shown to be important. The analysis of the thermodynamic properties of surface diffusion suggests that, in these three RPLC systems, its activation energy is lower than the isosteric heat of adsorption. The nature and the extent of the influence of the mobile phase composition on the parameters describing the retention and the mass transfer kinetics are different but the chromatographic mechanisms involved in RPLC systems appear similar, irrespective of the nature of the organic modifier in the mobile phase.     

Electrochemical Parameters of Phenoxazine Derivatives in Solution and at Monolayer‐Modified Gold Electrodes

Electrochemical properties of β‐(10‐phenoxazinyl) propylamine (APPX) and β‐(10‐phenoxazinyl) propionic acid (PPX) have been studied in solution, and in immobilized state on gold electrodes modified with monolayers of cystamine and mercaptoundecanoic acid. A reversible diffusion‐controlled process of APPX and PPX was observed at a bare gold electrode. The electrochemical conversion of both compounds at modified gold electrodes was a quasi‐reversible diffusion‐controlled process. The redox potential of immobilized APPX (443 mV) was similar to the potential in solution, while the value of the immobilized PPX was 131 mV higher than in solution. The immobilized mediators were electrocatalytically active in the fungal peroxidase‐catalyzed hydrogen peroxide reduction.     

Overcoming Diffusion Limitation of Faradaic Processes: Property-Performance Relationships of 2D Conductive Metal-Organic Framework Cu3(HHTP)2 for Reversible Lithium-Ion Storage

Faradaic reactions including charge transfer are often accompanied with diffusion limitation inside the bulk. Conductive two-dimensional frameworks (2D MOFs) with a fast ion transport can combine both—charge transfer and fast diffusion inside their porous structure. To study remaining diffusion limitations caused by particle morphology, different synthesis routes of Cu-2,3,6,7,10,11-hexahydroxytriphenylene (Cu₃(HHTP)₂), a copper-based 2D MOF, are used to obtain flake- and rod-like MOF particles. Both morphologies are systematically characterized and evaluated for redox-active Li⁺ ion storage. The redox mechanism is investigated by means of X-ray absorption spectroscopy, FTIR spectroscopy and in situ XRD. Both types are compared regarding kinetic properties for Li⁺ ion storage via cyclic voltammetry and impedance spectroscopy. A significant influence of particle morphology for 2D MOFs on kinetic aspects of electrochemical Li⁺ ion storage can be observed. This study opens the path for optimization of redox active porous structures to overcome diffusion limitations of Faradaic processes.     

N<Subscript>2</Subscript>O catalytic decomposition — effect of pelleting pressure on activity of Co-Mn-Al mixed oxide catalysts

The effect of pelleting pressure (0–10 MPa) during the preparation of Co-Mn-Al mixed oxide catalyst on its texture and activity for N₂O catalytic decomposition was examined for small grain sizes used in laboratory experiments, and for model industry catalyst particles. Adsorption/desorption measurements of nitrogen, mercury porosimetry and helium pycnometry were used for detail characterization of porous structure. A volume of micropores of about 20 mm³ g⁻¹ was evaluated using modified BET equation. This value did practically not change with the increasing pelletization pressure except that of the sample formed at the pressure of 10 MPa. Although an increase of pelleting pressure caused an increase in bulk density and a decrease in pore size and pore volume of the prepared catalyst (resulting in lower values of N₂O effective diffusion coefficient), no direct correlation between pelleting pressure used and catalyst activity has been found. In contrary, estimation of the internal diffusion limitation according to the Weisz-Prater criterion indicated that even laboratory experimental data obtained for catalyst grains with particle size lower than 0.315 mm pelletized at higher pressures could be influenced by internal diffusion. Estimation of the internal mass transfer limitation in industrial catalyst particles described by the effectiveness factor showed that effectiveness factor of about 0.07 and 0.2 can be obtained for spheres with the radius of 1.5 mm and 0.5 mm, respectively, if pelleting pressure of about 6 MPa was used for the catalyst preparation. Presented at the 35th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 26–30 May 2008.     

A comparison of clay colloid and artificial microsphere transport in natural discrete fractures

Transport of monodispersed buoyant 1-mum latex microspheres, dense 1.34-microm montmorillonite particles, Li(+) and Br(-) was investigated in a naturally fractured chalk core with an average equivalent hydraulic aperture of 183 microm. Studied parameters were: tracer arrival time, C/C(0) values, mass recovery, size distribution and the impact of initial concentration. Breakthrough time of both colloidal tracers was faster than that of the soluble tracers. Significantly lower recovery and slightly slower breakthrough time were observed for the clay particles relative to the microspheres, apparently mainly due to the former's higher density, resulting in preferential gravitational settling of the clay particles. However, variable surface charge and nonuniform shape and size of the clay particles may also play a role in the observed differences. From the theoretical scale ratio, the time interval calculation seems to be a major factor in colloid recovery. Clay-particle size fractionation was observed (0.62 vs 1.34 microm at the outflow and inflow, respectively), and there was no significant influence of the initial concentration (100 and 500 mg/L) on transport properties. Our observations indicate that colloid density is a dominant property for their transport in fractures. This work emphasizes the need for caution when the results of studies in which buoyant colloids are used as tracers are extrapolated to natural systems in which clay colloids are present.     

A comparative study of temperature dependence of induction time and oscillatory frequency in polymer‐immobilized and free catalyst Belousov‐Zhabotinsky reactions

Environment‐sensitive poly(N‐isopropylacrylamide) (PNIPAM) microgel particles with covalently bonded ruthenium(4‐vinyl‐4′‐methyl‐2,2′‐bipyridine) bis (2,2′‐bipyridine) [Ru(vmbipy)(bipy)₂] display periodic size changes when placed in Belousov‐Zhabotinsky (BZ) reaction substrates. The temperature dependency of the induction time and oscillatory frequency of the BZ reaction in this polymer‐immobilized catalyst system were compared to the bulk BZ reaction with the catalyst in the solution phase. Prolonged induction times are observed for the immobilized catalyst, compared with free catalyst, while little difference is observed on the oscillation frequency. The Arrhenius frequency factor calculated using the induction time for the immobilized catalyst BZ reaction is about seven times smaller than that for the free catalyst Ru(bipy) case. On the other hand, the Arrhenius frequency factors calculated using the oscillatory frequency are almost the same, showing similar reaction kinetics during the BZ oscillations. The tunability of the induction time using a polymer matrix, as we observed here, while maintaining similar oscillatory behavior, should provide a new dimension to control the self‐assembling of BZ active particles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 847–854, 2009     

Sorption and Diffusion of Propylene and Ethylene in Heterophasic Polypropylene Copolymers

Summary: Sorption experiments of ethylene and propylene in different polypropylene powder samples, both homopolymer and heterophasic copolymers with different rubber content, have been carried out in a high-pressure magnetic suspension balance at 10 bars pressure and 70 °C. The gross solubilities measured can be well correlated with the rubber content of the polymer samples. Solubility of ethylene and propylene in the rubber phase differ from solubility in the amorphous fraction of the homopolymer, especially the concentration ratio of propylene to ethylene differs significantly between rubber phase and amorphous fraction of the homopolymer. From the slope of monomer uptake, information on kinetics of mass-transfer can be gained. No significant differences were observed in terms of mass-transfer for ethylene and propylene. With increasing rubber content, effective diffusion coefficients increased slightly. By combined sorption studies with powder samples and compressed films, information about both effective diffusion coefficients and the effective length scale of diffusion could be gained. It could be shown, that the particle radius is not the characteristic length of diffusion in the studied powder samples. Mass transfer of nearly all samples could be described by a constant diffusion length of 120 to 130 µm, independently on particle size. This indicates that the effective scale of diffusion in polymer particles is in between microparticle and macroparticle scale used in classical particle modeling.     

苯乙烯Ziegler-Natta聚合扩散控制动力学研究

本文研究苯乙烯在TiCl_3-Al(C_2H_5)_3催化下于甲苯、正庚烷或甲苯-正庚烷混合物介质中的聚合动力学。提出了一个含催化剂球形聚合物颗粒中发生单体扩散控制聚合的模型,导出的式子统一解释了不同介质中扩散阻力造成的不同程度的速率表减,定量说明了在聚笨乙烯良溶剂中聚合时扩散阻力小于在不良溶剂中时。     

Electrooxidation of Methanol on Platinum–Ruthenium Catalysts Applied to a Cation-Exchange Membrane

Possibilities for production of active Pt–Ru electrodes for the direct methanol fuel cell with a decreased content of platinum-group metals in them are studied. Platinum and ruthenium are electrodeposited on a thin layer of carbon black applied to a Nafion 117 membrane. The deposition potential effect on the specific surface area of the catalyst and its electrochemical activity in the methanol oxidation is studied. The oxidation currents are related to unit true surface area or unit catalyst mass. The dependence of activity on the Pt : Ru ratio in the plating solution and in the deposit is studied. The effect of the catalyst amount deposited and the particle size on the activity is studied. It is shown that the catalytic activity decreases at the average diameter of Pt–Ru particles less than 4 nm. The results are compared with the size effects observed earlier.     

Determination of the singlet state lifetime of dissolved nitrous oxide from high field relaxation measurements

Longitudinal spin relaxation due to modulation of dipolar interactions often limits the development of hyperpolarized magnetic tracers. Recently, it has been demonstrated that transferring spin order to a singlet state significantly increases the polarization lifetimes in systems where nitrous oxide is dissolved in a liquid solvent. Additionally, previous studies have suggested that the longitudinal relaxation of nitrous oxide is largely dominated by the spin-rotation interaction. Models of spin-relaxation under Brownian motion nai?vely predict the angular momentum reorienting correlation time of the spin rotation interaction to be inversely proportional to the viscosity of the solution. This dependence implies the singlet lifetime can be lengthened by increasing the dissolving solvent's viscosity-an extension which is not observed. Our work formulates a model which describes the relaxation of nitrous oxide dissolved in various solvents. We investigate the effect of altering the temperature of the solvent, as well as the effect of varying solute-solvent interactions on the singlet state as well as the longitudinal polarization lifetime. We predict the singlet lifetime for nitrous oxide dissolved in several solvents by fitting rotational and angular momentum correlation times measured at high magnetic field, and relate singlet relaxation to translational diffusion constants.     

Classical differential cross sections and rotational energy transfer distributions for realistic ion—molecule potentials in the CPST limit

Classical differential cross sections, rotational energy transfer distributions at specified scattering angles and the first moments of the rotational energy transfer distributions are calculated for two ion—molecule systems: K⁺ ?CSCl and Li⁺ ?CO. The deflection angles and change in angular momentum are calculated using classical perturbation scattering theory (CPST). Monte Carlo techniques are then used to calculate the orientation averaged total differential cross sections and the rotational energy transfer distributions. Results are compared with experiment and agreement is found to be satisfactory. These two systems represent two extremes in anisotropy. For Li⁺ ?CO a strong classical rainbow peak is still seen in the differential cross section, while in the K⁺ ?CSCl system the rainbow is complete quenched. In the rotational energy transfer distributions of both systems, rotational rainbow peaks are clearly observed. The calculations also predict a leveling off of the first moment of the rotational energy transfer distribution at high angles, corresponding to the transition to repulsive scattering. On the basis of these results some comments are made on the nature of classical rainbow scattering for anisotropic systems.     

Piece by Piece—Electrochemical Synthesis of Individual Nanoparticles and their Performance in ORR Electrocatalysis

The impact of individual HAuCl₄ nanoreactors is measured electrochemically, which provides operando insights and precise control over the modification of electrodes with functional nanoparticles of well‐defined size. Uniformly sized micelles are loaded with a dissolved metal salt. These solution‐phase precursor entities are then reduced electrochemically—one by one—to form nanoparticles (NPs). The charge transferred during the reduction of each micelle is measured individually and allows operando sizing of each of the formed nanoparticles. Thus, particles of known number and sizes can be deposited homogenously even on nonplanar electrodes. This is demonstrated for the decoration of cylindrical carbon fibre electrodes with 25±7 nm sized Au particles from HAuCl₄‐filled micelles. These Au NP‐decorated electrodes show great catalyst performance for ORR (oxygen reduction reaction) already at low catalyst loadings. Hence, collisions of individual precursor‐filled nanocontainers are presented as a new route to nanoparticle‐modified electrodes with high catalyst utilization.     

Heterogenous catalysis in fine chemistry: the Heck reaction on Pd/SiO<Subscript>2</Subscript> catalysts

The preparation conditions to obtain a Pd/SiO₂ catalyst effective in the Heck reaction between para-substituted halogenobenzene and alkylacrylate have been studied. The impregnation of SiO₂, functionalised with a thiourea derivative, with a Pd(CH₃COO)₂ solution resulted in an active, but unstable catalyst. The catalyst became stable after calcination, but its activity appeared to be strongly dependent on the calcination temperature. IR spectra of adsorbed CO indicated that such a dependence should result from differences in the surface structure of the supported particles.     

Calculating a Characteristic Bulk Current Density in the Cathode of a Hydrogen-Oxygen Fuel Cell with a Solid Polymer Electrolyte

The magnitude of currents of electrodes in hydrogen-oxygen fuel cells of all types is shown to be fully determined by values of the effective coefficient of gas diffusion, the effective coefficient of ionic conduction, and the characteristic bulk current density. The characteristic bulk current density is estimated in two versions for cathodes with Nafion: the catalyst is distributed in the bulk of substrate grains or at their external surface. The currents commensurate with those observed in experiments are given only by the second version. Means of computer-aided simulation are used to imitate the formation of fractal films composed of the catalyst particles on the surface substrate grains. The simulation means made it possible to link the magnitude of the specific surface area of platinum particles with its weight content in substrate grains. Electrochemical characteristics of the cathode with Nafion-the potential dependence of the optimum magnitude of the overall current and the thicknesses of the active layer and the weight of platinum in it, as well as the magnitudes of the optimum current generated by a unit weight of platinum—are calculated. A notion of “ norm” is introduced for the characteristic bulk current density of the cathode. 1 × 10^?3 A cm^?3 is the electrochemical-process intensity, which the technology of preparation of active layers of cathodes can provide at this stage in the development of fuel cells with a solid polymer electrolyte.