Synthesis and photochromic properties of novel spirooxazine

Summary Novel 1-[-(4-trifluromethyl benzoyloxy)ethyl]-3, 3-dimethyl-spiro[indoline-2, 3-[3H]-naphtho[2,1-b]-1,4-oxazine](III) was prepared and their photochromic properties were investigated in polystyrene (PS) films. It is shown that the kinetics of thermal decoloration was decreased with increasing concentration of III in PS films.     

Syntheses and characterizations of copolymers of dicyanoquinone methides with α-acetoxystyrenes

Summary 7,7-Dicyanoquinone methides (1a-b) copolymerized spontaneously with substituted -acetoxystyrenes (2a-b) in benzene at 60 °C to give alternating copolymers (poly(1a-b-co-2a-b)) with the molecular weights of 8–60×10⁴ in 42–66% yields. When these copolymers were heated under nitrogen, they eliminated acetic acid quantitatively at around 200 °C to be converted to the copolymers (poly(3a-d)) with olefinic bonds, which were characterized by infrared and nuclear magnetic resonance spectroscopy. Alternating copolymers and the corresponding copolymers with olefinic bonds were amorphous, and capable of being cast from their chloroform solutions into transparent, tough films.     

Synthesis,electrical and optical properties of multifunctional poly[2-(2-ethyl-hexyloxy)-1,4-phenylenevinylene]

Summary Branched monoalkoxy-substituted poly[2-(2-ethylhexyloxy)-1,4-phenylenevinylene] (EH-PPV) was prepared in thin films via the water-soluble precursor technique and solution elimination method. These precursor polymer films could be stretched up to 8 times, and the drawn films of the EH-PPV could be doped with I₂ and FeCl₃ to give conductivities of 5.28x10^-3 and 0.56 S/cm, respectively. The third-order nonlinear optical susceptibility of the polymer was determined by using third harmonic generation (THG) method at 1907 nm, fundamental wavelength. Measured ⁽³⁾(–3; ,,) value was 3.8x10^-12 esu. The maximum emission wavelength of EH-PPV film in photoluminescence spectrum was 560 nm, corresponding to the yellowish red color.     

Hyperbranched Poly(ferrocenylene)s Containing Groups 14 and 15 Elements: Syntheses,Optical and Thermal Properties,and Pyrolytic Transformations into Nanostructured Magnetoceramics

A series of hyperbranched poly(ferrocenylene)s containing elements (E) of groups 14 [E=Si (hb-1), Ge (hb-2)] and 15 [E=P (hb-3), Sb (hb-4)] are prepared in good isolation yields (up to 82wt%) by the salt-eliminative polycoupling of dilithioferrocene with tri-(RECl₃) or tetrachlorides of the elements (ECl₄). While the polymers with no or small R groups are insoluble or partially soluble, those with long alkyl chains (R=C_nH_2n+1 with n 8) are completely soluble and film forming. The polymers exhibit solution properties characteristic of hyperbranched macromolecules: e.g. hb-1(18) shows a low intrinsic viscosity ([]=0.02dL/g) despite its high absolute molecular weight (M_w=5 × 10⁵). Spectroscopic analyses reveal that the polymers possess rigid skeleton structures with extended conjugations, with their absorption spectra tailing into the infrared region (>700nm). The polymers show good thermal stability with T_d up to ~400°C and can be graphitized into iron-containing ceramics when pyrolyzed at high temperatures, with char yields up to ~60wt%. While calcinations of the Si-containing polymers (hb-1) at 1000°C under nitrogen give ceramics containing mostly -Fe nanoparticles, those of Ge-(hb-2) and Sb-containing polymers (hb-4) are completely transformed into their iron-alloys. The ceramics from the P-containing polymers (hb-3) show diffraction patterns of iron phosphides. Iron silicide nanocrystals of large sizes are obtained when the pyrolysis of hb-1 is conducted at a high temperature of 1200°C under argon. This ceramic is highly magnetizable (M_s up to ~51emu/g) and shows near-zero remanence and coercivity; in other words, it is an outstanding soft ferromagnet with a high magnetic susceptibility and practically nil hysteresis loss.     

Solid Polymer Electrolytes Based on Poly(1,3-diacetyl-4-imidazolin-2-one)

Summary Solid polymer electrolytes composed of a homopolymer (poly(AcIM)) of 1,3-diacetyl-1,4-imidazolin-2-one (AcIM) and lithium bis(trifluoromethanesulfonimide) (LiTFSI) or of copolymers (poly(AcIM/VC)) of AcIM with vinylene carbonate (VC) and LiTFSI were prepared and their ionic conductivities and thermal properties were investigated. For the polymer electrolyte of the poly(AcIM) with LiTFSI, the highest ionic conductivity was found at the [Li]/[O] ratio of 1/3 with the values of 8.5×10^-5 S/cm at 80 °C and 1.7×10^-6 S/cm at 30 °C, respectively. In the polymer electrolyte of poly(AcIM/VC) with LiTFSI at the [Li]/[O] ratio of 1/3, the ionic conductivity increased with increasing VC unit content in the copolymers, and the highest ionic conductivity was found at the AcIM/VC ratio of 39/61 (mol%) with the values of 7.0×10^-4 S/cm at 80 °C and 6.7×10^-5 S/cm at 30 °C, respectively. This copolymer electrolyte showed a linear relationship between the ionic conductivity and the reciprocal of the temperature, indicative of the system decoupled from the segmental motion of the polymer.     

Synthesis,electroconductivity and third-order nonlinear optical property of poly(2-isopropoxy-5-methoxy-1,4-phenylenevinylene)

Summary Asymmetrically disubstituted poly(2-isopropoxy-5-methoxy-1,4-phenylene-vinylene), PIMPV, was prepared in thin films via organic-soluble precursor polymer method. These polymer films could be easily stretched up to 7 times, and the drawn films of the PIMPV could be doped with FeCl₃ and I₂ to give conductivities of 26.9 and 11.3 Scm^-1, respectively. The third-order nonlinear optical susceptibility of the polymer was determined using third harmonic generation(THG) method at 1907 nm, fundamental wavelength. Measured ⁽³⁰⁾ (-3: , , ) value was 3.7x10^-12 esu.     

Bulk anionic ring opening polymerization of silacyclopent-3-enes

Summary Poly[1,1-diphenyl-1-sila-cis-pent-3-ene](I), poly[1,1-dimethyl-1-sila-cis-pent-3-ene](II), poly[1-methyl-1-phenyl-1-sila-cis-pent-3-ene](III), poly[1-methyl-sila-cis-pent-3-ene](IV), and poly[1-phenyl-1-sila-cis-pent-3-ene](V) were prepared by bulk anionic ring opening polymerization of the corresponding 1-silacyclopent-3-enes, at room temperature by use n-butyllithium or t-butyllithium and HMPA as co-catalysts. No solvent (THF or diethyl ether) was utilized.     

Synthesis, optical and electrochemical properties of luminescent polymers containing 1,2-diphenylmaleimide and thiophene segments

In an attempt to balance energy barriers of hole and electron injection we prepared and characterized homopolymer containing electron-transporting 1,2-diphenylmaleimide chromophores (P1) and copolymers consisting of 1,2-diphenylmaleimide and hole-transporting 2,5-thiophene moieties (P2, P3) via dehalogenation polycondensation. The copolymers are amorphous materials with decomposition temperature greater than 450 °C. Absorption and fluorescence spectra were employed to investigate their optical properties both in solution and film state. Photoluminescence maxima of P1, P2 and P3 films are 564, 559 and 558 nm, respectively. The HOMO and LUMO energy levels have been estimated from their cyclic voltammograms. The HOMO levels of P1, P2, and P3 were readily raised with increasing thiophene content (−5.99, −5.59, and −5.43 eV, respectively), whereas their LUMO levels were very similar (−3.61 to −3.65 eV). Double-layer light-emitting diodes (Al/PEDOT:PSS/P1-P3/ITO) were fabricated to evaluate their optoelectronic characteristics. Incorporation of thiophene units successfully reduced the turn-on electric field from 11.0×10⁵ to 2.9×10⁵ V/cm, but it decreased the luminescent efficiency and the maximum brightness.     

Synthesis and Properties of Novel Eugenol–Based Polymers

Summary This work deals with the synthesis and characterization of novel eugenol–based polymers. The polymerization of 2–methoxy–4-propenyl–1-prop–2–ynyloxybenzene (1) with Rh, Mo, and W catalysts gave the corresponding polyacetylene [poly(1)], while that using BF₃ catalyst gave poly(1), without affecting the triple bond. A novel cross–linked polyacetylene was synthesized from poly (1) with [(nbd)RhC1]₂–Et₃N catalyst.     

The mechanism of copper powder formation in potentiostatic deposition

A mechanism for copper powder formation in potentiostatic deposition is proposed, and the critical overpotential of copper powder formation is determined. A good agreement between theoretical and experimental results has been obtained.List of symbols C ₀ bulk concentration (mol cm^–3) - D diffusion coefficient (cm² s^–1) - F Faraday's constant (C mol^–1) - h height of protrusion (cm) - h _c height at which dendrites crack (cm) - h _i height (cm) - h ₀ initial height of protrusion (cm) - h _j,t elevation at pointj and timet (cm) - h _j,0 initial elevation at pointj (cm) - I limiting diffusion current (A) - I ₀ initial limiting diffusion current (A) - i limiting current density (A cm^–2) - i _d current density on the tip of dendrite of height h (A cm^–2) - i _t total current (A cm^–2) - j number - k proportionality factor [cm (mol cm^–3)^m] - k constant - M number of dendrites - m number - N number of elevated points - n number of electrons - p concentration exponent - Q _c quantity of electricity (C) - R gas constant (J mol^–1 K^–1) - S electrode surface area (cm²) - T temperature (K) - t time (s) - t _a longest time in which approximation h is valid (s) - t _i induction time (s) - V molar volume (cm³ mol^–1) - surface tension (J cm^–2) - thickness of diffusion layer (cm) - overpotential (V) - _c,p critical overpotential of powder formation (V) - fraction of flat surface - apparent induction time (s)     

Orange to black electrochromic behaviour in poly(2-(2-thienyl)-1H-pyrrole) thin films

We have studied an electrochromic precursor, 2-(2-thienyl)-1H-pyrrole (1), using two improved procedures of the Trofimov reaction. Optimised stereochemical calculations at the B3LYP/6-311G* level showed almost equal s-cis and s-trans conformational populations in 1 with marked out-of-plane deviations of ca. 30°. Model calculations suggest that the predominant rotational conformation in undoped poly(1) would be s-trans with the essential out-of-plane deviations around the all three interheterocyclic bonds of ca. 25-30°. Monomer 1 exhibited two irreversible oxidation processes at +0.86 and +1.3 V corresponding to the oxidation of the pyrrole and thiophene rings, respectively. Orange to black electrochromic behaviour was found in ClO₄⁻ doped poly(1) thin films with colouring and bleaching times of 1.8 and 1.3 s, respectively. The colouration efficiency during the bleaching process was 233 cm²/C. The optical contrast at 450 nm was 19% and in the near-IR was 36%. The band-gap of poly(1) (1.6-1.7 eV) was found to be significantly lower than that of polypyrrole (2.85 eV) and polythiophene (2.3 eV) as a consequence of increased electron delocalisation in the system. Important differences in the morphology of doped and dedoped poly(1) films were observed by atomic-force microscopy (AFM). Doped poly(1) films showed a granular morphology with primary particles of 45-60 nm in size and an average surface roughness of 3.5 nm. On the other hand, dedoped poly(1) films showed interconnected aggregates of 65-90 nm in size as a consequence of particle fusion, with a surface roughness of 9.2 nm. In summary, poly(1) is a promising material for emerging flexible electrochromic devices such as displays and variable optical attenuators.     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

Synthesis and Properties of Soluble and Light-Colored Poly(amide-imide-imide)s Based on Tetraimide-Dicarboxylic Acid Condensed from 4,4'-Oxydiphthalic Anhydride, 2,2-Bis[4-(4-aminophenoxy)phenyl]sulfone, and m-Aminobenzoic Acid, and Various Aromatic Diamines

A new-type of tetraimide-dicarboxylic acid (I) was synthesized starting from the ring-opening addition of m-aminobenzoic acid (m-ABA), 4,4'-oxydiphthalic anhydride (ODPA), and 2,2-bis[4-(4-aminophenoxy)phenyl]sulfone (BAPS) at a 2:2:1 molar ratio in N-methyl-2-pyrrolidone (NMP), followed by cyclodehydration to the diacid I. A series of soluble and light-colored poly(amide-imide-imide)s (III _a-j) was prepared by triphenyl phosphite-activated polycondensation from the tetraimide-diacid I with various aromatic diamines (II _a-j). All films cast from DMAc had cutoff wavelengths shorter than 390 nm (379–390 nm) and had b ^* values between 24.17–35.50; these polymers were much lighter in color than those of the alternating trimellitimide series. All of the polymers were readily soluble in a variety of organic solvents such as NMP, N,N-dimethyl acetamide, N,N-dimethylformamide, dimethyl sulfoxide, and even in less polar m-cresol and pyridine. Polymers III _a-j afforded tough, transparent, and flexible films, which had a strength at break ranging from 93 to 118 MPa, elongation at break from 8 to 11%, and initial modulus from 2.2 to 2.8 GPa, and some films showed yield points in the range of 95–111 MPa at stress–strain curves. The glass transition temperature of the polymers was recorded at 240–268°C. They had 10% weight loss at a temperature above 540°C and left more than 55% residue even at 800°C in nitrogen.     

Laser flash photolysis of poly(silylenes) in dilute solution. Generation of ionic species

Radical cations are generated via monophotonic processes upon irradiation of poly(methylphenyl silylene) (PMPSi), poly(biphenylmethyl silylene) (PBMSi), poly(dihexyl silylene) (PDHeSi), and poly(hexylmethyl silylene) (PHeMSi) in dilute tetrahydrofuran solution with 15- or 20-ns flashes of 266- or 347-nm light, respectively. This was inferred from electrical conductivity measurements. Typical quantum yields (ion) are as follows: for PBMSi, 4×10² (_inc=266nm) and 3×10³ (_inc=347nm); and for PDHeSi, 8×10³ (_inc=266nm) and 9×10⁴ (_inc=347nm). In all cases, a significant portion of the transient absorption spectrum recorded at the end of the flash is attributed to the spectrum of the radical cation. The latter strongly overlaps the spectra of other intermediates (presumably silyl radical and silylene).     

Synthesis and electro-optical properties of helical polyacetylenes carrying carbazole and triphenylamine moieties

Novel chiral acetylene monomers bearing carbazole and triphenylamine groups, namely, (S)-3-butyn-2-yl 2-(9-carbazolyl)ethyl carbonate (1) and (S)-3-butyn-2-yl 4-(diphenylamino)benzoate (2) were synthesized, and polymerized with Rh⁺(nbd)[η⁶-C₆H₅B⁻(C₆H₅)₃] catalyst to give the corresponding polymers with moderate molecular weights (M_n 13.0 × 10³ and 15.5 × 10³) in good yields (86% and 88%). CD spectroscopic studies revealed that poly(1) and poly(2) took predominantly one-handed helical structure in CHCl₃. The helical structures of poly(1) and poly(2) were very stable against heating and addition of MeOH. The solution of poly(1) and poly(2) emitted fluorescence in 0.52% and 7.2% quantum yields, which were lower than those of the corresponding monomers 1 and 2 (22.5% and 76.5%). The cyclic voltammograms of the polymers indicated that the oxidation potentials of the polymers were lower than those of the monomers. The polymers showed electrochromism and changed the color from pale yellow to pale blue by application of voltage, presumably caused by the formation of polaron at the carbazole and triphenylamine moieties. The onset temperatures of weight loss of poly(1) and poly(2) were 225 and 270 °C under air.     

Polymer Complexes. XLIII. EPR, Spectra, and Stereochemical Versatility of Novel Copper(II)Polymer Complexes

Copper(II) polymer complexes of empirical formula [Cu(ligand)₂X₂] (where X = Cl, Br, I, NO₃, and SO₄) and [Cu(ligand)(CH₃COO)₂] have been prepared with poly(3-phenylacrylidine semicarbazone). All the polymer complexes prepared have been characterized by elemental analysis, magnetic moment, conductance, IR, electronic, ¹H-NMR, and electronic paramagnetic resonance spectral studies. The polymer complexes [Cu(ligand)₂X₂] and [Cu(ligand) (CH₃COO)₂] may have tetragonal symmetry while the [Cu(ligand)₂( SO₄)₂] may be five-coordinate trigonal bipyramidal in structure. All complexes exhibit normal magnetic moments corresponding to one unpaired electron except [Cu(ligand)(CH₃COO)₂] which shows a subnormal magnetic moment. EPR spectra of the polymer complexes have been studied with a view to assigning their stereochemistries. Various EPR parameters have been calculated. The g, A, G values for all the polymer complexes are consistent with a tetragonal 1–5 and trigonal bipyramidal 6 stereochemistry in the Cu(II) polymer complexes of homopolymer.     

Calculations on the effect of gas evolution on the current-overpotential relation and current distribution in electrolytic cells

Gas evolution during electrode reactions has several effects on the electrode behaviour. One of these effects is the nonuniform increase of the resistivity of the electrolyte with the resultant increase of IR drop through the solution and the distortion of current distribution. Calculations of these effects are presented for an electrode built of vertical blades. This geometry has the peculiarity that it allows the inclusion of linear polarization and gas effects in the treatment, without the necessity to use numerical or approximate solutions of the differential equations. It is shown that the system parameters can be combined into a single dimensionless parameter to describe those aspects of the electrode behaviour which depend on the gas evolution. The parameters examined include the geometry of the electrode, the polarization resistance, gas bubble rise velocity, and solution resistivity. Expressions are given for optimization of the electrode geometry to achieve minimum overpotential.Nomenclature b Polarization resistance ( cm²) - C Constant, =RT( + t)/lPtFs (A^–1cm) - E(x) Potential of the solution at pointx (V) - f _av Average volume fraction of gas (dimensionless) - (fy) Volume fraction of gas at heighty (dimensionless) - f(Y) Volume fraction of gas at reduced heightY (dimensionless) - F Faraday number (coulomb mol^–1) - h Height of the electrode (cm) - i Nominal current density of the electrode =I _T/hw (A cm^–2) - i(y) Local electrode current density at heighty (A cm^–2) - i(Y) Local electrode current density at reduced heightY (A cm^–2) - i _f(x) Faradaic current density at pointx (A cm^–2) - i _f(X) Faradaic current density at reduced lengthX (A cm^–2) - i _f,av Average faradaic current density in the slot=I _s/2hl(Acm^–2) - I _s Total current entering one slot (A) - I _T Total current flowing to the electrode (A) - I(x) Current flowing in the solution phase of one slot at pointx (A) - k Constant, = (2/b)^1/2 (cm^–1) - K Dimensionless parameter =hRT(2/b)^1/2/4lPzFs, or = 1–(1–iCh)^1/4 - l Horizontal length of the slot (cm) - n Number of slots on the electrode (dimensionless) - p Pressure of gas liberated on the electrode (assumed to be independent of height) (atm) - R Universal gas constant (cm³ atm K^–1 mol^–1) - s Bubble rise velocity (cm s^–1) - t Thickness of the blades (cm) - T Temperature of the gas (K) - dV(y) Volume of gas present in a volume element of the slot (cm³) - w Width of the electrode (cm) - x Horizontal distance from the back plate (cm) - X Reduced horizontal distance =x/l (dimensionless) - y Vertical distance from the bottom of the electrode (cm) - Y Reduced vertical distance =y/h (dimensionless) - z Number of Faradays needed to produce one mole of gas (mol^–1) - Width of a slot (blade spacing) (cm) - Measured overpotential of the electrode =(l)(V) - (x) Overpotential at pointx (V) - Resistivity of gas free electrolyte ( cm) - (y) Resistivity of gas filled electrolyte at, heighty ( cm).     

Studies of the development of fibrillar structure in nylon 6

Very thin films of poly(vinyl alcohol) could be prepared by utilizing the adsorption of polymer molecules at air/water interface from the aqueous solutions of the poly(vinyl alcohol) derived from vinyl trifluoroacetate. The films prepared by the bubble method were thinner than those obtained by the frame method. The minimum thickness of the former films was 260 Å and that of the latter was 1800 Å. These very thin films resisted water at temperatures below 55°C. The maximum Young's modulus of the drawn/annealed films prepared from these samples was 30 GPa. The permeability of water, J_w/δP, was 2–6 × 10^?3 cm · s^?1 atm^?1 (0–55°C) for the untreated film (thickness: 1800 Å) prepared by the frame method and 0.8–2.2 × 10^?2cm · s^?1 · atm^?1 (5–55°C) for the untreated film (360 Å) prepared by the bubble method, and depended on the thickness of film.     

High strength and high modulus fibers of poly(p-xylylene)

Summary High strength and high modulus fibers of poly(p-xylylene) (PPX) were obtained by drawing of as-polymerized films (molecular weight 5×10⁵) at 420 °C in the conformationally disordered ₂ phase. Fibers of PPX have been obtained having a tensile strength at break of 3.0 GPa, a Young's modulus of 102 GPa and a strain at break of 3 %. The theoretical strength of PPX was calculated to be 23 GPa.     

Mass transfer enhancement by suspensions in a shear flow

Electrochemical measurement of mass transfer enhancement in a dilute suspension of particles, due to particle rotation in the presence of a shear flow, has been studied with a Couette cell. An effective diffusivityD _e involving the Peclet numberPe of the particles and the molecular diffusivityD of the solute was obtained for low particle volume fraction asD _e=D(1+3.5Pe ^1/2). From steady-state and transient data, it was shown that aggregation may occur with alumina particles and that inertial effects due to centrifugation reveal a marginal layer free of particles near the rotating inner cylinder.Notation a particle radius (cm) - c _o initial concentration of the solute (mole cm^–3) - c(x, t) solute concentration at timet and locationx (mole cm^–3) - D molecular diffusivity of the solute (cm² s^–1) - D _e effective diffusivity of the solute (cm² s^–1) - e gap thickness (cm) - I(t) time dependent current (A) - I steady-state value of the current (A) - J mass flux (mol cm^–2 s^–1) - J ₀,J ₁ Bessel functions of the first kind - K coefficient in Equation 11 - r radial coordinate Equation 3 (cm) - R ₁,R ₂ inner and outer radii of the Couette cell (cm) - S wall velocity gradient (s^–1) - t time (s) - v local velocity around each particle (cm s^–1) - V ₀ linear velocity of the mobile plane in the plane Couette cell (Fig. 1) (cm s^–1) - x, y, z Cartesian coordinate system - Y ₀,Y ₁ Bessel functions of the second kind Greek symbols _n roots of Equation 10 - , exponents in Equation 11 - , diffusion layer thickness (Equation 12) (cm) - v kinematic viscosity (cm² s^–1) - particles volume fraction (%) - angular velocity of particles (rad s^–1) This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.