X-rays from radiative electron capture of highly-charged heavy ions in an electron cooler

The x-ray spectra induced by spontaneous capture of free cooling electrons into bare and hydrogenlike heavy ions have been observed. Au⁷⁸⁺, Au⁷⁹⁺ and U⁹¹⁺ ions were stored in the storage ring ESR at velocities between 60% and 65% of the velocity of light and the x rays were measured in coincidence with stored particles having captured one electron in the electron cooler. The lines observed can be attributed to the direct transition of cooling electrons into theK shell of the projectile and to the characteristicL K transitions. The latter are mainly induced by capture into higher shells and subsequent cascade transitions. The measurements are compared to detailed calculations within the framework of presently available theories. Although the relative structure of the measured spectra is in fair agreement with the theoretical prediction, the total charge-changing rate in the electron cooler is about a factor of three smaller than expected.     

The decay of153Gd

The sum peak method has been applied to calculate electron capture probability changes to 97 keV and 103 keV levels in the decay of¹⁵³Gd in different environments, e.g., HClO₄ and HNO₃. The relative and absolute intensities of KX-rays and -rays have been measured using a HPGe detector. In addition to these, electron capture intensities and electron capture decay energies (Q _Ec) have also been calculated.     

Ab initio molecular treatment of electron capture processes in the B3++He collision

The potential energy curves and the coupling matrix elements of the¹¹ and¹ states involved in the collision of the B³⁺(1s ²) multicharged ion on a He target have been calculated by means of an ab initio method with configuration interaction. The total and partial capture cross-sections have been determined, using a semi-classical method. The results are in good agreement with experiment, exhibiting a strong influence of rotational coupling even at low energies.     

Particle behaviour in shear and electric fields

Summary The interactions between two equal rigid conducting spheres in a Newtonian dielectric liquid in combined shear and electric fields are analyzed. The forces and torques, the translational and rotational velocities, and the resulting trajectories of the spheres are calculated for various ratios of the electric field strength to shear rate.The conditions under which the spheres can capture one another are deduced from which capture cross-sections, capture frequencies, and capture efficiencies are calculated, leading to a second order rate equation for capture at low particle concentrations.It is demonstrated that on capture the spheres should come into physical contact in a finite time. However, it is conjectured from previous experiments that dielectric breakdown is apt to occur in the interparticle gap because of the high electric field intensification; when this occurs, complications may be expected which are different in static and alternating electric fields.Closely related to the two sphere problem is the interaction of a rigid conducting sphere with a rigid conducting plane wall; this is discussed in the Addendum.

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Zusammenfassung Die Wechselwirkungen in gleichzeitig angelegten Scherströmungen und elektrischen Feldern zwischen zwei kleinen, gleiche, festen, leitenden, und in einer Newtonschen Flussigkeit schwebenden Kugeln sind untersucht werden. Die Krafte und Drehmomente, die Translations- und Rotationsgeschwindigkeiten, und die resultierenden Trajektionen der Kugeln werden für verschiedene Verhaltnisse der elektrischen Feldstärke und Schergeschwindigkeit berechnet. Entwickelt werden die Kugelanlagerungsbedingungen, wovon sich die Anlagerungsquerschnitte, die Anlagerungsgeschwindigkeiten, und die Anlagerungseffektivwerte ableiten lassen; dies führt zu einer Anlagerungsgleichung zweiter Ordnung bei geringer Teilchenkonzentration. Es wird gezeigt, daß die Kugeln sich physisch berühren sollten nach Ablauf einer bestimmten (endlichen) Anlagerungszeit. Jedoch, wie es sich aus vorhergehenden Experimenten ergab, dielektrischer Kurzschluß erfolgt im Kugelzwischenraum auf Grund der hohen elektrischen Feldverstarkung; folgendermaBen konnen Komplikationen erwartet werden, die sich für statische Felder und Wechselfelder verschieden ausarten mussen. Die Wechselwirkung zwischen einer kleinen, festen, leitenden Kugel und einer festen, leitenden, flachen Wand ist ein Sonderfall des Zwei-Kugel-Problems; dies wird im Addendum beschrieben.

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Nomenclature a, b ^*,c, d, e, f ^*,g, b hydrodynamic force and torque coefficients - a ^* b sinb - b sphere radius - B, C; B₀, C₀; C^E trajectory constants whenf=0 (B0,C0); when 0<f< and 2 (B ₀ 0,C ₀ 0) ; whenf= and 2. - C^* orbit constant of a touching doublet - e _i particle fixed unit vectors,i=1, 2, 3, (fig. 1) - E;E ₀ local electric field strength; uniform field applied to the particle-free medium. Normal type designates scalar quantities - E ₃ ^* E _DB E/E ₀; dielectric breakdown strength of medium - f electrohydrodynamic parameter defined in [28] - f _c;f _c ^E collision frequency per unit volume; capture frequency per unit volume - f _i ^E ;f _i ^r ;f _i ^S ;f _i ^t force coefficients of a sphere near a wall due toE ₀; to rotation; to shear; to translation - f(), h() trajectory functions for f=0 defined in [1] and [2] - F _i;F _i ⁰ electric force coefficients (i =1 to 10) defined in [12] and [13] when spheres have potential Vj; when Vj=0. - F ^E ,F ^r ,F ^S ,F ^t forces acting on a sphere near a plane wall - F _i ^E (j) electric force component alongx _i ^' on spherej =1, 2. - g _i ^r ,g _i ^S ,g _i ^t torque coefficients on a sphere near wall - G shear rate - k capture rate constant defined in [44] - K dielectric constant of medium - n integer (n 0) - n ₀;n ₂ number concentration ofsuspension of single spheres; of captured doublets - P _ij coefficients of electric induction - P(r _p ) orientation function of a rigid conducting prolate spheroid - q ₂,q ₃ defined in [66] - Q _j ;Q _j ^* net charges on spherej = 1, 2; charges induced on spherej =1, 2 if as earthed - r;r _p centre-to-centre distance between spheres; axis ratio of spheroid - S _m () functions defined in [48]m = 1,2 - S _ij pure shear (deformation) tensor components - T period of rotation of doublet about ₁ axis whenf < 1 - T ^E ;T ^E ;T ^*E contact time of two spheres; a sphere and a wall; = (2₀ KE ₀ ² / 3)T ^E - T ^r ,T ^S ,T ^t torques on a sphere near a wall - u undistrurbed flow velocity - U;U(j) particle velocity of sphere near wall; of spherej - V _j electric potential of spherej - w _j ;W ₁ ^* dimensionless electric potential of spherej; of sphere 1 whenQ ₁ =0 - x _i ;x _i ;x ₃ ^* space-fixed coordinates defined in figure 1; particle-fixed coordinates alonge 1; = (2₀ KE ₀ ² /3G) ₃ - cos²₂ - Y _n ;Z _n functions defined in [17d]; in [17e] Script symbols A(),B(),L(),D(),E() functions defined in [23] - (F); (F ^(E ); (F ^(s ) general force-torque vector; in an electric field; in shear - L _i () velocity coefficients of two spheres in an electric field,i=1 to 4     

Mean squared slowing-down distance and age of americium-beryllium neutrons in perspex

The mean squared slowing-down distance, <r ²>, and the age to themal capture (Migration Area),M ², are direct measures of the slowing-down, and the spreading out, processes of neutrons in a medium. They also enter directly into reactor calculations. These parameters have been determined experimentally for Am-Be neutrons (mean energy 4.46 Me V), in a block of perpex, using the activities induced in thin indium foils from the¹¹⁵In(n,)¹¹⁶In reactions.     

Amperometric determination of live <Emphasis Type="Italic">Escherichia coli</Emphasis> using antibody-coated paramagnetic beads

Detecting and enumerating fecal coliforms, especially Escherichia coli, as indicators of fecal contamination, are essential for the quality control of supplied and recreational waters. We have developed a sensitive, inexpensive, and small-volume amperometric detection method for E. coli -galactosidase by bead-based immunoassay. The technique uses biotin-labeled capture antibodies (Ab) immobilized on paramagnetic microbeads that have been functionalized with streptavidin (bead–Ab). The bead–Ab conjugate captures E. coli from solution. The captured E. coli is incubated in Luria Bertani (LB) broth medium with the added inducer isopropyl -D-thiogalactopyranoside (IPTG). The induced -galactosidase converts p-aminophenyl -D-galactopyranoside (PAPG) into p-aminophenol (PAP), which is measured by amperometry using a gold rotating disc electrode. A good linear correlation (R²=0.989) was obtained between log cfu mL^–1 E. coli and the time necessary to product a specific concentration of PAP. Amperometric detection enabled determination of 2×10⁶ cfu mL^–1 E. coli within a 30 min incubation period, and the total analysis time was less than 1 h. It was also possible to determine as few as 20 cfu mL^–1 E. coli under optimized conditions within 6–7 h. This process may be easily adapted as an automated portable bioanalytical device for the rapid detection of live E. coli.     

Transfer Reactions of Rydberg (Quasi-Rydberg Molecular) Electrons in Condensed Media: IV. Large Proton Displacements upon Phosphorescence Quenching via Highly Excited Triplet States T* of Substituted Aromatic Solute Molecules in Solutions at 77 K

Intramolecular phosphorescence quenching via states T* in aromatic solute molecules containing N–H (diphenylamine (DPA) or carbazole), O–H (naphthol), etc. bonds was observed in methylcyclohexane at 77 K. The quantum yield of quenching measured for DPA increases with increasing the energy of the T* state. As in the case of external electron acceptors, the quenching and photodissociation are associated with the capture of excited * electrons onto polarized bonds N–H⁺, O–H⁺and with the formation of triplet complexes (for example, Ph₂N···H*, where H* is the excited hydrogen atom). The complexes can be deactivated via configurations with large proton displacement distances (Ph₂N^–···H⁺).     

Ion pair generation rates near planar3H and63Ni electron capture detector foils

The ion-pair generation rate (ionization topography) in plasmas from⁶³Ni and particularly Ti³H₄ foils, as used in electron capture detectors, was measured at room temperature using large, parallel plates of low backscattering ability in nitrogen gas of varying density. For one atmosphere pressure, the fall-off of ion pair formation as calculated from the exponential region equalsN ₀·e ^–0.19d for⁶³Ni andN ₀·e ^–1.4d for³H (whereN ₀ is the initial ionization rate immediately adjacent to the foil andd is the distance from the foil in mm). The experimentally measured half ranges (distances from the foil within which 50% of all possible ion pairs are created) are 2.7 mm for⁶³Ni and 0.27 mm for³H. The half ranges calculated from the exponential region where there is less interference from electron backscattering, are 3.7 and 0.5 mm, respectively. The latter values are considered closer to the true, unimpeded ionization topography near planar⁶³Ni and³H foils.Material taken from doctoral thesis     

1H NMR studies on intermolecular association of amphiphilic cationic polyelectrolyte micelles induced by hydrophobic counteranions in water

Interactions of a series of amphiphilic cationic polyelectrolytes with various kinds of organic counteranions have been investigated in water by one- and two-dimensional ¹H NMR spectroscopy at 20 °C. The cationic polyelectrolytes were prepared by micellar homopolymerization of tail-type cationic surface-active monomers with a cationic charge with -end, (ST–C_m–AB, m=5, 7, and 9, where ST is a styrenic group, C_m, an alkylene chain at the 4-position of styrene, and AB, alkyltrimethylammonium bromide). Aliphatic monosodium salt of maleic acid (MAS) and its stereoisomer, fumaric acid (FAS), sodium benzoate (NaB), potassium hydrogen phthalate (PHK), and sodium salicylate (NaSal) were added to a salt-free aqueous solution of the polyelectrolytes and ¹H NMR measurements were carried out. Amphiphilic P(ST–C_m–AB) polyelectrolytes act as efficient hosts to strongly capture the hydrophobic counteranions B^–, PH^–, and Sal^–, but not MA^– and FA^–. The ¹H NMR signals of these hydrophobic counteranions remarkably shift upfield and broaden in water in the presence of the amphiphilic polyelectrolytes. The nuclear Overhauser effect (NOE) signals between the cationic group of the polymer and aromatic benzoate counteranion protons are clearly observed to imply cation– interaction. The capturing of hydrophobic counterions by the polyelectrolytes is likely due to electrostatic, hydrophobic, and cation– interactions between them. The reduced viscosity, _sp/C_p, for the solution at [PHK]/[P(ST–C₇–AB)]=1.0 steeply increases with increasing polymer concentration (C_p) above ca. 0.9 g/dL to show pronounced viscoelasticity.     

Transfer Reactions of Rydberg (Quasi-Rydberg Molecular) Electrons in Condensed Media: V. Large Proton Displacement in the N–H Bond upon Photoionization of Diphenylamine via Highly Excited Triplet State T* in Methanol at 77 K

The mechanism of large proton displacements in polarized R–H⁺ bonds, which involves the formation of a triplet complex R···H* (H* is the excited hydrogen atom) in the T* state upon the capture of an excited * electron onto the p, d, and f quasi-Rydberg proton orbitals in H⁺ (part IV) is further substantiated. It is assumed that the proton displaced upon photoionization of added diphenylamine molecules (Ph₂NH) via the complex Ph₂N···H* in methanol at 77 K can be fixed by the polarization of the medium in the vicinity of the diphenylaminyl radical (Ph₂N···H⁺ _sol) formed. When the solution is thawed up to 106 K, the protons returns to Ph₂N to afford the radical cation Ph₂NH⁺.     

Particle behaviour in shear and electric fields

Summary Observations of the pair interactions of rigid, conducting spheres suspended in a Newtonian dielectric fluid are described for experiments in which the fluid was subjected to combined simple shear of rateG and uniform electric fields of strengthE ₀ where behaviour is predicted to depend on a parameterf proportional toEsk₀/² G. Agreement with theory was excellent for touching spheres which oriented themselves with calculable rates inE ₀ alone and rotated with calculable periods of rotation in subcritical fields (f<1); in supercritical fields(f1) the doublets assumed their stable predicted orientations.The trajectories of separated spheres were found to be in good agreement with theory, with capture observed as predicted provided an experimentally determined minimum value,f _min, was exceeded whose value appeared to depend on the surface roughness of the spheres and on their behaviour during dielectric breakdown of the medium when the spheres were close together. After capture spheres appeared to make physical contact.The capture cross-sections were measured and agreed with the theoretical values except belowf _min.The significance of the phenomena and the possibilities of employing them for measuring physical properties of dielectric liquids are discussed.

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Zusammenfassung Die beobachteten Wechselwirkungen zwischen zwei kleinen, festen, leitenden und in einer dielektrischen (isolierenden) Newtonschen Flüssigkeit schwebenden Kugeln werden für einige Versuche beschrieben, in denen die Flüssigkeit gleichzeitig einer einfachen Scherströmung (mit SchergeschwindigkeitG) und einem gleichmäßigen elektrischen Feld (mit Feldstärke E₀) ausgesetzt wird. Es läßt sich für eine solche Versuchsanordnung erwarten, daß die Wechselwirkungen mit einem definierbaren Parameterf (proportionalE ₀ ² G) in einem direkten Verhältnis stehen sollen. Die Obereinstimmung mit der Theorie war ausgezeichnet für zwei sich berührende Kugeln, die mit errechneter Orientierungsgeschwindigkeit inE ₀ E ₀ (f = ) ausgerichtet wurden und in unterkritischen Feldern (f<1) mit errechneten Rotationszeiten gedreht wurden; die Kugelpaare stellten sich in überkritischen Feldern (f1) auf die erwarteten stabilen Achsenrichtungen genau ein. Die Bewegungsbahnen getrennter Kugeln stimmten gut mit der Theorie überein, sofern ein experimentell bestimmbares,f _minüberschritten wurde, dessen Wert von der Kugeloberflächenrauheit und vom dielektrischen Kurzschlußverhalten bei engstem Kugelabstand abhing. Elektrische Anlagerung wurde mit nachweisbarem physikalischem Kontakt abgeschlossen. Gemessene Anlagerungsquerschnitte entsprachen den von der Theorie abgeleiteten Formen und Größen ausgenommen fürff _min Die Bedeutung dieser Beobachtungen und deren Anwendungsmöglichkeiten zur Messung physikalischer Eigenschaften von dielektrischen Flüssigkeiten wird erläutert.

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Nomenclature d gap distance between Couette cylinders or flat electrodes - E ₀ ^f uniform electric field for forming doublets - f _min minimum (or critical) value off for capture - F _t(j) hydrodynamic forces alongx _i acting on spherej = 1,2 - G _c critical (minimum) shear rate to cause doublet separation - V electric potential difference acrossd Greek symbols error symbol - b size of surface asperities of spheres - _DB ;_min critical gap distance between spheres on dielectric breakdown; minimum gap distance of spheres travelling along trajectories given byB andC = 0 in ([1, 2])¹) whenf = 0 - ₂ ⁱ , ₂ ^f initial and final ₂ before and after applyingE ₀ whenG = 0 - density of suspending liquid With 6 figures and 9 tables     

The microrheology of colloidal dispersions VII. Orthokinetic doublet formation of spheres

Summary A theory is developed for the rate of doublet formation in dilute dispersions of spheres subjected to a simple shear flow of gradient G when Brownian motion can be neglected but taking account of both hydrodynamic and interparticle interactions. When Coulombic repulsive forces are negligible, the capture frequency is found to be approximately proportional toG ^0.82; when they dominate the van der Waals attractive forces, the capture frequency is zero. When both attractive and repulsive forces are important no simple relationship exists, but the capture frequency can be calculated numerically. Experiments are described which are in qualitative agreement with the theory. Hamaker constants for polystyrene in water calculated from the measured doublet formation agree with those calculated by means of the present theory from experimental data of other workers, but are somewhat higher than those obtained from perikinetic coagulation rates.

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Zusammenfassung Eine Theorie für Doppelkugelformationen in verdünnten Dispersionen, welche einer einfachen Scherströmung mit dem GradientenG ausgesetzt sind, bei dem die Brown'sche Molekularbewegung vernachlässigt werden kann, unter Berücksichtigung aber von hydrodynamischen und Zwischenkörper-Kräften, wird entwickelt. Wenn Coulomb'sche Abstoßungskräfte vernachlässigt werden können, ergibt sich die Einfanghäufigkeit mit ca.G ^0.82; wenn deren Größe aber die der Van der Waals Kräfte überschreitet, ist die Einfanghäufigkeit null. Bei Auftreten von anziehenden und abstoßenden Kräften existiert keine einfache Beziehung, sondern es kann nur eine numerische Berechnung durchgeführt werden.Experimente werden beschrieben, die in qualitativer Übereinstimmung mit der Theorie sind. HamakerKonstanten für Polystyrol in Wasser, errechnet von den gemessenen Doppelkugelformationen, stimmen mit den, mit Hilfe der bestehenden Theorie von anderen Forschungsergebnissen errechneten Werte überein, sind aber etwas höher als jene, die von perikinetischen Koagulationsmaßen erhalten wurden.

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List of Symbols A Hamaker constant - A(r*), B(r*), C(r*) functions introduced in [7] - b sphere radius - c, c _t volumefraction ofsingle spheres, total volume fraction - C _A ,C _R ratio of attractive and repulsive forces to hydrodynamic forces, resp. - d distance between top and bottom of tube - function introduced in [7] - F _attr,F _rep attractive and repulsive forces, resp - G, G _c shear rate, critical value - J; J ₈ capture frequency per particle; according toSmoluchowski - K dielectric constant of suspending medium - l; l* semi-axis ofcapture crosssection inX ₂-direction;l/b - N _o ;N _t number concentration of particles att=0; at timet - p (r* - 2)r - r;r* distance between sphere centers;r/b - R, R _o radial distance from tube center, tube radius - S;S ₁; S₂ ratio of singlets to doublets; at top of tube; at bottom of tube - t,t*;t* real and dimensionless time (Gt); average ofGt - u ₃ undisturbed fluid velocity in X₃-direction - x _i ;X _i ;X _i Cartesian coordinates;xi/b; coordinate axes - Z(x ₂);Z* (x ₂) boundary of capture crosssection; dimensionless value (Z(x ₂)/b) - ₀ orthokinetic capture efficiency, defined in [6] - o permittivity of free space - n suspending fluid viscosity - 0, polar coordinates - x reciprocal double layer thickness - ; xxx London wavelength; /2b - ratio of capture to collision cross-section - ; _c ratio of sphere radius and double layer thickness; critical value - ₀; ₀ ^c surface potential of sphere; critical value     

Design Features of a Prompt Gamma Neutron Activation Analysis System at HANARO

The design features are described of a prompt gamma neutron activation analysis system at HANARO, a 30 MW research reactor in the Korea Atomic Energy Research Institute. The beam consists of polychromatic thermal neutrons diffracted by a set of pyrolytic graphite crystals at orders n in the range 1n6 at a Bragg angle of 45° on a horizontal beam line. A neutron flux of 1.0·10⁸ n·cm^–2·s^–1 is calculated at the sample position from the reflectivity of the crystal which has been confirmed in a measurement of a diffracted neutron spectrum using a time-of-flight spectrometer and gold-wire activation. The fast neutron and gamma backgrounds will be low due to the use of a diffracted beam and a tapered collimator. The detection system comprises a 30% n-type HPGe detector, signal electronics and a fast ADC. The first application of this system will be the analysis of boron concentration in biological samples for neutron capture therapy. Construction of the beam line and the arrangement of the detection system is proceeding.     

Simultaneous electron capture and target ion excitation in collisions of C4+ and N5+ on He

Cross sections for simultaneous electron capture and target ion excitation have been measured for impact of slow He-like C⁴⁺ and N⁵⁺ ions on He. The energy of the primary ion beams has been varied over more than two orders of magnitude: 0.05–7 keV/amu. The results are discussed on basis of a slightly modified version of the dynamic classical over-barrier model for multiple electron capture. The differences in the energy dependences of the experimental results of C⁴⁺ and N⁵⁺ — He can be explained qualitatively by assuming that for N⁵⁺ binding energy sharing between the two participating electrons is of importance, particularly at the lower impact energies.     

Reactor production and processing of therapeutic radioisotopes for applications in nuclear medicine

In this paper the reactor production of a variety of therapeutic radionuclides of current clinical interest are discussed. Examples include radioisotopes produced by single neutron capture and those which are available from –/decay of reactor-produced parent radioisotopes. Two examples of generator parents produced by double neutron capture of targets are also discussed. One key example in this category is¹⁸⁸W, produced from irradiation of enriched¹⁸⁶W. The production of¹⁸⁸W in the ORNL High Flux Isotope Reactor and the fabrication and performance of the first production level large-scale clinical prototype¹⁸⁸W/¹⁸⁸Re generators are also described.     

Curium isotopes in Chernobyl fallout

In nuclear reactors plutonium and transplutonium isotopes are produced by multiple neutron capture of uranium and plutonium and are important for the energy production and their composition reflects the core burnout. Under normal operation these elements are not released to the environment in significant amounts. There are accordingly very few areas or source terms where exotic transplutonium elements, such as curium isotopes, can be studied in the environment. The Chernobyl accident provided a complex spectrum of fission and activation products in fallout while the relative amounts, compared to the core inventory, of refractory elements such as transuranium and transplutonium elements were small. The major alpha-activity consisted of ²⁴²Cm (T _1/2 = 163 d) that would have decayed after a few years. In this study we have demonstrated the presence of so called supported ²⁴²Cm from the long-lived ²⁴²Am^m (T _1/2 = 141 a) in environmental samples, following fallout from the Chernobyl accident. It has also been possible to assess the core burn up by using the data obtained for the Cm isotopes. The curium isotopes ²⁴³Cm (T _1/2 = 29.1 a) and ²⁴⁴Cm (T _1/2 = 18.1 a) cannot be resolved by conventional alpha-spectrometry. The assessment of these isotopes in environmental samples contaminated from the Chernobyl accident has been made by studying the effective half-life of the mixture of the isotopes. The data are compared with those previously obtained by high-resolution alpha-spectrometry and spectral deconvolution.     

Pionic X-ray intensity ratios in chromium compounds

Pionic X-ray intensity ratios in chromium compounds were compared with those from muonic X-rays. The ratios were found depending on the ^– capture ratio as on ^– capture. The difference of the ratios between Cr/H₂O/₆Cl₃ and CrCl₃ was attributed to the formation of pseudoneutron ^– by interaction of hydrogenic protons during passage of a pion in the hydrated compound.     

Structural aspects of the radiation modification of the dielectric properties of polyolefins

The effects of crystallization conditions and supermolecular structure on the processes of radical formation and changes in the dielectric (tan; ) and strength (E _st) properties of LDPE, HDPE, and PP under exposure to -radiation were studied. It was found that polyolefin specimens with a high crystallinity exhibited an enhanced electric strength, radiation stability, and a high yield of quasi-stable radicals at 293 K. It was assumed that a possible mechanism of the electric strengthening of PE and PP by their radiation modification (at radiation doses of 30–50 and to 5–6 Mrad, respectively) consists in a reaction of the type R^· + e^– R^–, the capture of trapped electrons by quasi-stable radicals.__________Translated from Khimiya Vysokikh Energii, Vol. 39, No. 3, 2005, pp. 176–182.Original Russian Text Copyright © 2005 by Magerramov, Dashdamirov.     

The microrheology of colloidal dispersions

Summary A theory of doublet formation, the first step in coagulation of dilute monodisperse spherical sols subjected to shearing motion, in which Brownian motion dominates the effects of shear is presented. Contrary to Smoluchowski's predictions, it is found that the increase in the rate of coagulation due to shear is not proportional to the shear rateG, but toG _1/2 with the proportionality constant depending on the perikinetic capture efficiency, the translational diffusion constant and sphere radius. With non-spherical particles the increase rate due to shear also varies with G_1/2 and depends, in addition, on particle size and shape.

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Zusammenfassung Eine Theoriefür Doppelkugelformationen als der erste Schritt in der Koagulation von verdünnten, monodispersen, kugelförmigen Solen wird präsentiert. Die Sole sind -einer Scherströmung ausgesetzt, in der die Brownsche Molekularbewegung über die Effekte der Scherbeanspruchung dominiert. Im Gegensatz zu Smoluchowskis Voraussagen wurde gefunden, daß die Steigung im Ausmaß der Koagulation, hervorgerufen durch die Scherung, nicht einfach dem GeschwindigkeitsgradientenG, sondernG _1/2 proportional ist. Die Proportionalitätskonstante hängt vom perikinetischen Einfangwirkungsgrad, der translatorischen Diffusionskonstanten und dem Kugelradius ab. Mit nicht-kugeligen Teilchen variiert das Koagulationsausmaß auch mitG _l/2, hängt aber zusätzlich von Teilchengröße und Gestalt ab.

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List of Symbols ai constant of integration - d distance at whichf _t changes sign - diffusion tensor - D ,D functions describing radial and tangential components of diffusion - function defined in [39] - f(r ^*),f (r ^*) function representing radial part ofn, belonging to eigen value - g(, ) function representing tangential part ofn - i –1 - J, J _B,J _S flux, due to Brownian motion, due to shear - k Boltzmann constant - k _i constant of integration - K(r ^*) function defined in [28] - l, m integers - n, normalized number concentration, value in outer expansion - N; N ₀ number concentration of single particles; at infinity - O (r ^*) of orderr ^* - P operator defined in [14] - P ^|m|(cos) associated Legendre polynomials - Q constant defined in [34] - Pe _t ^1/2 r^* - R radius of imaginary sphere around reference sphere - operator defined in [13] - T absolute temperature - U velocity vector - Pe _{t 1/2}x _i - z _l function defined in [22] - ; ^* defined in [20 a] ; + - _p; _{p p} ^* perikinetic capture efficiency(/2); _p ^*/2 - _l, ₂ collision efficiencies - ₃ 2₂/3x03C0; - ; ^* constant defined in [39b]; 2 - constant defined in [27] - gamma function - percentage increase in capture frequency due to shear - arbitrarily small distance - eigen value - differential operatorM With 3 figuresThis work was supported by Grant MA-4012 of the Medical Research Council of Canada