Simple approximate analytic expression for the electrophoretic mobility of a spherical colloidal particle in a mixed solution of 1:1 and 2:1 electrolytes

Simple approximate analytic expressions are derived for the electrophoretic mobility of a spherical colloidal particle of radius a and zeta potential ζ in a mixed solution of 1:1 and 2:1 electrolytes with common anions on the basis of the general mobility expression previously derived by Ohshima (Colloids Surf A Physicochem Eng Asp 267:50, 2005). The obtained expressions, which are applicable for spheres of any ζ and large radii such that κa ≥ ca. 30 (where κ is the Debye-Hückel parameter), consist of Smoluchowski’s equation and the correction term taking into account the relaxation effect.     

Surface behaviour of some phenol para-derivatives adsorbed at the free surface of water

Comparison is made between two methods for the determination of the average orientation angle of molecules adsorbed at the free surface of water; one based on electric surface potential measurements, the other on second harmonic generation. Assuming that the model of energetics of adsorbed molecules is similar to that of a system of non-interacting permanent dipoles in an external homogeneous field, the parameters of the probability density function in the form exp[ —a cos(0-0_o)], a =w/kT, w, being the absolute orientational energy, have been calculated for phenol, p-methyl-, p-nitro-, and p-bromophenol.     

Approximate analytic expressions for the diffusiophoretic velocity of a spherical colloidal particle

The general expression is derived for the diffusiophoretic velocity of a spherical colloidal particle of radius a in a concentration gradient of symmetrical electrolyte. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct up to the order of 1/κa is derived, where κ is the Debye-Hückel parameter. It is found that the approximate expression correct to order unity can be applied for κa ≥ 50 with negligible errors, while the approximate expression correct to order 1/κa can be applied for κa ≥ 20 with negligible errors.     

Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer

A general expression is derived for the electrophoretic mobility of a spherical charged colloidal particle covered with an uncharged polymer layer in an electrolyte solution in an applied electric field for the case where the particle zeta potential is low. It is assumed that electrolyte ions as well as water molecules can penetrate the polymer layer. Approximate analytic expressions for the electrophoretic mobility of particles carrying low zeta potentials are derived for the two extreme cases in which the particle radius is very large or very small.     

Low-Zeta-Potential Analytic Solution for the Electrophoretic Mobility of a Spherical Colloidal Particle in an Oscillating Electric Field

The equations developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans. 88, 3567 (1992)) to calculate the electrophoretic mobility of a solid, spherical colloidal particle subjected to an oscillating electric field are solved analytically for low zeta potential, ζ, to obtain the electrophoretic mobility correct to (eζ/k_BT). Due to severe numerical cancellation of the exponential integrals, two forms of the analytic solution are presented which are numerically stable for different regions of κa (where a is the particle radius and κ^-1 is the Debye screening length). This low-ζ analytic solution is valid for all frequencies, particle sizes, and electrolyte concentrations, and agrees to at least two significant figures with the "exact" results obtained by Mangelsdorf and White at eζ/k_BT = 1 (ζ ≈ 25 mV). A program implementing this low-zeta analytic formula for the electrophoretic mobility is available from the authors.     

Temperature dependence and anisotropy of the hole drift mobility in monoclinic tetracyanoethylene

The tensor of the hole drift mobility is determined in monoclinic tetracyanoethylene by the transient photoconductivity technique. The principal tensor components amount to μ₁ = 0.21, μ₂ = 0.10 and μ₃ = 0.15 cm²/V s at room temperature. Above 250 K the mobility is a decreasing function of temperature and follows an exp(E/kT) dependence (E = 0.08 eV) which is inconsistent with both band and hopping models. Below 250 K the mobility is controlled by a hole trapping level of 0.28 eV deep. The photogeneration efficiency is found to be independent of temperature and proportional to the light intensity.     

Approximate analytic expression for the dynamic electrophoretic mobility of a spherical colloidal particle in an oscillating electric field

An approximate analytic expression is derived for the dynamic electrophoretic mobility of a spherical charged colloidal particle in an electrolyte solution in an applied oscillating electric field. This expression, which takes into account the relaxation effects, is applicable for all values of zeta potential at large kappa a (kappa a > or = ca. 30) and omega/2pi < or = ca. 10 MHz, where kappa is the Debye-Hückel parameter, a is the particle radius, and omega is the frequency of the electric field. It is shown that the obtained mobility expression is in excellent agreement with the exact numerical results of Mangelsdorf and White (J. Chem. Soc., Faraday Trans. 1992, 88, 3567).     

Electroporation: A unified,quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes

We present a quantitative theory of electroporation of artificial planar lipid bilayer membranes. Assuming that aqueous pores are involved in electroporation, we describe the pore population of the membrane by the density function n (r, t), where n (r, t) dr is the number of pores with radius between r and r + dr at time t. We further assume that there is a minimum pore size r_min, that pores of radius r_min are created and destroyed by thermal fluctuations, and that the pore creation rate is proportional to exp(aΔφ_m²/kT, where a is a constant, Δφ_m is the membrane voltage, k is Boltzmann's constant, and T is the absolute temperature. We use a simple formula for the conductance of a pore as a function of radius, the expression for the pore energy previously derived by Pastushenko and Chizmadzhev, and a simple model of the external circuit. We solve the equations numerically and compare the solutions to the results of charge pulse experiments.In a charge-pulse experiment a membrane suffers one of four possible fates: (1) a slight increase in electrical conductance, (2) mechanical rupture, (3) incomplete reversible electrical breakdown, resulting in incomplete discharge of the membrane, or (4) reversible electrical breakdown (REB), resulting in complete discharge of the membrane. In agreement with experiment, this theory describes these four fates and predicts that the fate in any particular experiment is determined by the properties of the membrane and the duration and amplitude of the charging pulse.     

On the mechanism of conductivity of ammonium salts

The conductivities of HSO₄^?-doped (NH₄)₂SO₄ (AS) and NH₄H₂PO₄ (ADP) crystals are investigated in the temperature range 25°?180°C. The mobility of the charge carriers (protons) is thermally activated and is expressed in accordance with the relation μ = 0.16 exp(?0.49) eV/kT and μ = 0.80 exp(?0.54 eV/kT)cm² V^?1 sec^?1 for AS and ADP crystals, respectively. Three-stage mechanism of proton transport in the lattice of ammonium salt is suggested: (1) formation of the charge carrier NH₄⁺ + X^? → NH₃ + HX, (2) reorientation of the protonated anion HX → XH, and (3) proton jump to the neighbor anion XH + X^? → X^? + HX. The activation energy for mobility is close to that for dielectric relaxation process, i.e., the only thermally activated stage in the mobility process is reorientation of the protonated anion. This very stage is also the rate-determining in the mobility as it is seen from the comparison of the correlation time for proton diffusion and the dielectric relaxation time. These experimental results are in good agreement with the known proton dynamic data in KDP-type ferroelectric crystals.     

The hydrogen molecule ion in the old quantum theory

The ground state of the H ₂ ⁺ molecule is studied using the equations of classical mechanics and the Einstein quantum condition, J _ζ+J _μ = h, where J _ζ and J _μ are the action integrals over a complete cycle of the elliptic coordinates. Strong bonding is found, but the quantitative results are good only for R<0.05 and R>4a ₀. The greatest error comes at R _eq and results from the coalesence of two classically allowed regions where the electron can exist.     

Sur l'électrophorèse d'un ensemble de particules portant la même densité uniforme de charges

We consider the electrophoresis of solid particles embedded in a possibly non-uniform electric field E_t8. For particles admitting the same uniform zeta potential, the rigidbody motion of each particle is obtained without calculating the total electric field E within the electrolyte.     

Approximate expression for the electrophoretic mobility of a spherical colloidal particle covered with an ion-penetrable uncharged polymer Layer

An approximate analytic expression is derived for the electrophoretic mobility of a charged spherical colloidal particle covered with an ion-penetrable uncharged polymer layer in an electrolyte solution by taking into account the relaxation effects. This expression is applicable for all values of zeta potentials at large a(aca. 30), where is the Debye–Huckel parameter and a is the radius of the particle core. A simple expression for the ratio of the electrophoretic mobility of a polymer-coated particle to that of a bare particle without a polymer layer is also given.     

Diffusiophoresis of a cylindrical colloidal particle oriented parallel to an electrolyte concentration gradient field

We derive the general expression for the diffusiophoretic mobility of a cylindrical particle oriented parallel to an applied electrolyte concentration gradient field in a symmetrical electrolyte solution. From the general mobility expression as combined with an approximate analytic expression with negligible error for the electric potential distribution around a cylinder, an accurate analytic mobility expression is obtained, which is applicable for arbitrary values of the particle zeta potential and the electrical double layer thickness. It is also found that the low zeta potential approximation is an excellent approximation for low-to-moderate values of the particle zeta potential.     

Sano-Tachiya-Noolandi-Hong versus Onsager modelling of charge photogeneration in organic solids

We have studied the electric field dependence of charge photogeneration efficiency in organic solids for various radial distribution functions (Dirac delta, Gaussian, exponential) of initial e-h pairs in the framework of Sano-Tachiya-Noolandi-Hong (STNH) theory assuming that the final recombination (capture reaction) proceeds on a sphere of finite radius (a) with a finite velocity (κ). We compare the STNH results with the conventional Onsager theory assuming a = 0. We show that charge photogeneration is more enhanced, especially in low-electric field range, for broader initial pair distributions and for smaller final recombination velocities. We compare theoretical results with experimental data taken from electromodulation of photoluminescence (EML) for two archetypical organic photoconductors, Alq₃ and Ir(ppy)₃, commonly used as emitters in organic LEDs. From analysis of our results we infer the lower limit of final recombination velocity, κ = 0.2-2 cm/s, in vacuum evaporated films of Alq₃ and Ir(ppy)₃ which compares favorably with an evaluation of this quantity in amorphous solids.     

Density dependence of electron mobility in dense gases

The density (N) dependence of electron mobility (μ) in various dense gases (H₂, N₂, O₂, CO₂ and rare gases) has been calculated using a multiple-scattering approach. Deviation of the high density gas from its perfect gas behaviour has been taken into account through the temperature-dependent second virial coefficient. Multiple scattering of electrons leads to shifts in their kinetic energy and it also changes their distribution functions. This unified approach predicts both positive and negative effects. The positive (negative) effect entails on increase (decrease) of μ withN. We have assessed the available data on momentum transfer cross-sections by comparing the mobility at very low densities (Nμ)₀ with experimental results. The density dependence is studied by comparing the calculated ratioNμ)/Nμ)₀ with the observed values and other theoretical work. The Legler model which assumes a constant cross-section is inadequate for predicting the observed density dependence. We obtain good agreement with available experimental work for all the atomic and molecular species studied here.     

The electrokinetic study on the deposition of polystyrene latex onto Nylon fiber

Theζ-potentials of anionic polystyrene latex particles and Nylon fiber were measured as a function of concentration of NaCl, Na₂SO₄, Na₃PO₄ and CaCl₂, and the deposition of the latex onto Nylon fiber was considered. In the range of ionic strength from 5×10^?4 to 5×10^?2 where the rate of deposition was measured, the increase of electrolyte concentration resulted in the slight increase due to the adsorption of negative ion in the negativeζ-potentials of the latex particles. However, the rate of deposition increased with increasing concentration of electrolyte because of the decrease due to compression of the electrical double layer in the negativeζ-potentials of Nylon fiber. This result was supported by the fact that the maximum repulsive energy between electrical double layers of a latex particle and Nylon fiber decreased, as predicted theoretically, with decreasing ratio of theζ-potential of the fiber to that of the latex particle.     

Effect of an open tube in series with a packed capillary column on liquid chromatographic performance: The influence of particle diameter,temperature, and system pressure

A postcolumn reactor or a simple open tube connecting a capillary column to, for example, a mass spectrometer affects the performance of a capillary liquid chromatography system in two ways: stealing pressure from the column and adding band-spreading. This effect is especially intolerable in fast separations. Our calculations show that in the presence of a 25 μm radius postcolumn reactor, column (50 μm radius) efficiency (number of theoretical plates) is severely reduced by more than 75% with a t₀ of 10 s and a particle diameter from 1 to 5 μm for unretained solutes at room temperature. Therefore, it is necessary to minimize the reactor's effect and to improve the column efficiency by optimizing postcolumn conditions. We derived an equation that defines the observed number of theoretical plates (N_obs) taking into account the two effects stated above, which is a function of the maximum pressure P_m, the particle diameter d_p, the reactor radius a_r, the column radius a_c, the desired dead time t₀, the column temperature T and zone capacity factor k″. Poppe plots were obtained by calculations using this equation. The results show that for a t₀ shorter than 18 s, a P_m of 4000 psi, and a d_p of 1.7 μm, a 5 μm radius reactor has to be used. Such a small reactor is difficult to fabricate. Fortunately, high temperature helps to minimize the reactor effect so that reactors with manageable radius (larger than 12.5 μm) can be used in many practical conditions. Furthermore, solute retention diminishes the influence of a postcolumn reactor. Thus, a 12.5 μm reactor supersedes a 5 μm reactor for retained solutes even at a t₀ of 5 s (k″ > 3.8, or k′ > 2.0).     

Rhodium(I) complexes with κP coordinated ω-phosphinofunctionalized alkyl phenyl sulfide, sulfoxide and sulfone ligands and their reactions with sodium bis(trimethylsilyl)amide and Ag[BF4]

Reactions of ω-diphenylphosphinofunctionalized alkyl phenyl sulfides Ph₂P(CH₂)_nSPh (n = 1, 1a; 2, 2a; 3, 3a), sulfoxides Ph₂P(CH₂)_nS(O)Ph (n = 1, 1b; 2, 2b; 3, 3b) and sulfones Ph₂P(CH₂)_nS(O)₂Ph (n = 1, 1c; 2, 2c; 3, 3c) with dinuclear chlorido bridged rhodium(I) complexes [(RhL₂)₂(μ-Cl)₂] (L₂ = cycloocta-1.5-diene, cod, 4; bis(diphenylphosphino)ethane, dppe, 5) afforded mononuclear Rh(I) complexes of the type [RhCl{Ph₂P(CH₂)_nS(O)_xPh-κP}(cod)]¹ (n/x = 1/0, 6a; 1/1, 6b; 1/2, 6c; 2/0, 8a; 2/1, 8b; 2/2, 8c; 3/0, 10a; 3/1, 10b; 3/2, 10c) and [RhCl{Ph₂P(CH₂)_nS(O)_xPh-κP}(dppe)] (n/x = 1/0, 7a; 1/1, 7b; 1/2, 7c; 2/0, 9a; 2/1, 9b; 2/2, 9c; 3/0, 11a; 3/1, 11b; 3/2, 11c) having the P^S(O)_x ligands κP coordinated. Addition of Ag[BF₄] to complexes 6-11 in CH₂Cl₂ led with precipitation of AgCl to cationic rhodium complexes of the type [Rh{Ph₂P(CH₂)_nS(O)_xPh-κP,κS/O}L₂][BF₄] having bound the P^S(O)_x ligands bidentately in a κP,κS (13a-18a, 15b-18b) or a κP,κO (13b, 14b, 13c-18c) coordination mode. Unexpectedly, the addition of Ag[BF₄] to 6a in THF afforded the trinuclear cationic rhodium(I) complex [Rh₃(μ-Cl)(μ-Ph₂PCH₂SPh-κP:κS)₄][BF₄]₂·4THF (12·4THF) with a four-membered Rh₃Cl ring as basic framework. Addition of sodium bis(trimethylsilyl)amide to complexes 6-11 led to a selective deprotonation of the carbon atom neighbored to the S(O)_x group (α-C) yielding three different types of organorhodium complexes: a) Organorhodium intramolecular coordination compounds of the type [Rh{CH{S(O)_xPh}CH₂CH₂PPh₂-κC,κP}L₂] (22a-c, 23a-c), b) zwitterionic complexes [Rh{Ph₂PCHS(O)_xPh-κP,κS/O}L₂] having κP,κS (21a, 21b) and κP,κO (20b/c, 21c) coordinated anionic [Ph₂PCHS(O)_xPh] ligands, and c) the dinuclear rhodium(I) complex [{Rh{μ-CH(SPh)PPh₂-κC:κP}(cod)}₂] (19). All complexes were fully characterized spectroscopically and complexes 15b, 15c, 12·4THF and 19·THF additionally by X-ray diffraction analysis. DFT calculations of zwitterionic complexes gave insight into the coordination mode of the [Ph₂PCHS(O)Ph] ligand (κP,κS versus κP,κO).     

Synthesis and characterization of Ru/Au,Pd/Au,Pd/2Au,Pt/2Au and Cu/2Au heterometallic complexes of cyclodiphosphazane cis-{(o-MeOC6H4O)P(μ-NBu)}2

Mononuclear complexes of cyclodiphosphazane with an uncoordinated phosphorus centre [RuCl₂(η⁶-cymene){l-κP}] (1a) (L = cis-{(o-MeOC₆H₄O)P(μ-N^tBu)}₂) and [PdCl₂(PEt₃){l-κP}] (1b) react with 1 equiv. of [AuCl(SMe₂)] to afford Ru^II/Au^I and Pd^II/Au^I heterodinuclear complexes [RuCl₂(η⁶-cymene){μ-l-κP,κP}AuCl] (2) and [PdCl₂(PEt₃){μ-l-κP,κP}AuCl] (3), respectively. Heterotrinuclear complexes [PdCl₂{μ-l-κP,κP}₂(AuCl)₂] (4), [PtCl₂{μ-l-κP,κP}₂(AuCl)₂] (5) and [CuI{μ-l-κP,κP}₂(AuCl)₂] (6) containing Pd^II/2Au^I, Pt^II/2Au^I and Cu^I/2Au^I metal centers have been synthesized from the reactions of trans-[PdCl₂{l-κP}₂] (1c), cis-[PtCl₂{l-κP}₂] (1d) and [CuI{{l-κP}₂] (1f) respectively, with 2 equiv. of [AuCl(SMe₂)]. Molecular structures of complexes 2, 3 and 4 were established by single crystal X-ray diffraction studies.     

Ruthenium(II) and iron(II) complexes of N-pyridyl substituted imidazolin-2-ylidenes

N-mesityl-N′-pyridyl-imidazolium chloride 1a and the corresponding bromide salt 1b have been deprotonated with NaH in THF giving the free N-heterocyclic carbene N-mesityl-N′-pyridyl-imidazolin-2-ylidene 2 in 80% yield (starting from 1a). Imidazolium salt 1a reacts with RuCl₃ · xH₂O to give a racemic mixture of dinuclear di-μ-chloro bridged ruthenium complexes [(κ²-2)₂Ru(μ-Cl)₂Ru(κ²-2)₂]²⁺ [3a]²⁺. The carbene carbon atoms as well as the halides are arranged in cis-positions to each other whereas the nitrogen atoms adopt a trans-configuration. The di-μ-bromo bridged derivative [(κ²-2)₂Ru(μ-Br)₂Ru(κ²-2)₂]²⁺ [3b]²⁺ was obtained from RuCl₃ · xH₂O and 1b. The bridging halide ligands can be removed by the reaction with silver or sodium salts of bidentate Lewis acids. Complex [3a]²⁺ reacts with silver pyridylcarboxylate to give a racemic mixture of the mononuclear complex [4]⁺. Reaction of [3a]²⁺ with the sodium salt of l-proline resulted in a diastereomeric mixture of complexes [5]⁺. The free N-heterocyclic carbene 2 reacts with [FeCl₂(PPh₃)₂] to give after anion exchange with NaBPh₄ cis/cis/trans coordinated [Fe(κ²-2)₂(MeCN)₂](BPh₄)₂ [6](BPh₄)₂. The molecular structures of [3b](PF₆)₂, [4]PF₆ and [6](BPh₄)₂ · H₂O are reported.