Optical factors determined by the T-matrix method in turbidity measurement of absolute coagulation rate constants

Turbidity measurement for the absolute coagulation rate constants of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor in deriving the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed during aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology, as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion of the physical insight for using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed, because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the data of the optical factor calculated by the T-matrix method for a range of particle radii and incident light wavelengths are listed.     

Study on improving the turbidity measurement of the absolute coagulation rate constant

The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. When the size parameter alpha = 2pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy.     

Toward an understanding of the turbidity measurement of heterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed.     

Fast coagulation of gold sols. Rate constants for dimerization of nanoparticles

By using the generalized Mie theory, the extinction cross sections for dimers of 46-nm gold particles immersed in water have been calculated. It has been found that, in the region of high-energy plasmon resonance band, the maximum value of normalized extinction cross section Qext1 gradually decreases as particles approach each other. The greatest changes in Qext1 are observed when interparticle distance h decreases from 10 to 3 nm. At shorter distances, Q_ext1 weakly depends on h. At the same time, the band position varies in a complicated manner; however, at h < 2.5 nm, it coincides with that for individual particles. The revealed properties of the high-energy plasmon resonance band for dimers have been used to determine the absolute rate constant for dimerization of 46-nm gold particles k₁₁. By spectrophotometry, we have investigated salt-induced coagulation of gold sols and have measured the rates of the decrease in optical density. Experimental and calculation data allowed us to establish, at initial stages of fast coagulation, when the distance between the surfaces of 46-nm gold particles is 1.3–2.0 nm (Dolinnyi, A.I., Colloid J., 2015, vol.77, p. 600.), the average value of k₁₁ is (9.20 ± 1.34) × 10^–12 cm³/s for sols with particle concentrations of (0.4–2.6) × 10₁₀ cm^–3.     

Estimation of kinetic rate constants by turbidity and nephelometry techniques in a homocoagulation process with different model colloids

 In this work turbidimetric and nephelometric techniques have been used to study the homocoagulation of aqueous dispersions of uniform spherical particles of surfactant-free latexes. Cationic and anionic latexes of similar particle sizes (361 and 370 nm) and different surface charge densities (+16.4 and −3.6 μC/cm²) were used throughout. The kinetic constants which control the aggregation processes when the electrical repulsion disappears were estimated by both techniques at different particle concentration and wavelength in order to establish the experimental conditions which provided reliable and similar values for the coagulation rate constant. Both experimental techniques (turbidity and nephelometry) and two ways of fitting the data have been used with both latexes. For the first method, the initial slope of turbidity or total scattered intensity versus time curves were used to calculate the kinetic constants. In the second method, the whole turbidity or total scattered intensity versus time curves were fitted and the kinetic constants calculated. An unambiguous experimental value for the doublet rate constant in diffusion conditions is obtained by turbidity and nephelometry techniques. By nephelometry both data treatments have permitted a distinction between the doublet rate constant and the global rate constant in diffusion conditions. Received: 2 June 1997 Accepted: 14 August 1997     

Light extinction at agglomerates of spheres--a practical test on the submicroscale

Today's theories applied to the inversion of measurement data from optical measurement devices are restricted to single spherical particles. However, particles formed in industrial processes such as precipitation and crystallization are often nonspherical or agglomerates. Theoretical approaches to describe the optical behavior of such particle systems have already been proposed. The verification of these theories has mostly been done using microwave scattering experiments with agglomerates in the millimeter range. This paper provides a first but surely not all-embracing practical test for a general extension of the Mie theory to agglomerates of submicroscale spheres. For the sake of simplicity and from practical viewpoints of online-sensor development only light extinction of an agglomerated suspension has been examined. The required rigid agglomerates have been produced using a spray-drying method that generates particles with a much higher mechanical stability than can be obtained by the usual procedures. Subsequent fractionation of the suspension delivers systems with only a limited number of agglomerate configurations. Extinction measurements at multiple wavelengths using dynamic extinction spectroscopy have been conducted to determine the extinction cross section of the agglomerated dispersions. These data are compared with computations of agglomerates scattering.     

Photofragmentation of the fluorene cation: II. Determination of the H-loss energy-dependent rate constant

The hydrogen-loss channel, induced by sequential multiphoton absorption, of the vapor-phase fluorene cation was investigated using a pulsed supersonic molecular beam, a time-of-flight mass spectrometer, and pulsed nanosecond lasers. Our new method leads to the determination of the absolute absorption cross section. Its attenuation with the number of absorbed photons has been approximated by means of statistical models. A model-free determination of the evolution of the dissociation rate constant in a relatively large energy range was obtained by solving the set of coupled differential kinetic equations numerically. Particular attention was focused on the data analysis techniques. The free fit of these rate constants is close to the photothermodissociation statistical model, but shows a discrepancy with the Rice and Ramsperger and Kassel model mainly at high energy. The resulting activation energy is in agreement with both that deduced from the ab initio calculations and that from the tight-binding energy potential surface model.     

Effects of frequency change on vibronically induced resonance raman scattering

Frequency change effects on vibronically induced resonance Raman scattering (VIRRS) have been theoretically studied. It is shown that the excitation energy profile consists of a succession of doublets. The Raman spectrum of pyrazine resonant to the S₁ state has been calculated using the derived analytical expressions for the cross section.     

Stability of dispersions of colloidal hematite/yttrium oxide core-shell particles

The colloidal stability of suspensions of hematite/yttria core/shell particles is investigated in this work and compared with that of the pure hematite cores. The different electrical surface characteristics of yttrium and iron oxides, as well as the diameters of both types of spherical particles, dominate the overall process of particle aggregation. The aggregation kinetics of the suspensions was followed by measuring their optical absorbance as a function of time. By previously calculating the extinction cross section of particle doublets, it was demonstrated that for both core and core/shell particles the turbidity of the suspensions should increase on aggregation. Such an increase was in fact found in the systems in spite of the ever-present tendency of the particles to settle under gravity. The authors used the initial slope of the turbidity increment time plots as a measure of the ease of aggregation between particles. Thus, they found that the essential role played by pH on the charge generation on the two oxides and the shift of one pH unit between the isoelectric points of hematite and yttria manifest in two features: (i) the stability decreases on approaching the isoelectric point from either the acid or basic side and (ii) the maximum instability is found for hematite at pH 7 and for hematite/yttria at pH 8, that is, close to the isoelectric points of alpha-Fe(2)O(3) and Y(2)O(3), respectively. The role of added electrolyte is simply to yield the suspensions of either type more unstable. Using the surface free energy of the particles, the authors could estimate their Hamaker constants in water. From these and their zeta potentials, the DLVO theory of stability was used to quantitatively explain their results.     

A database of 660 peptide ion cross sections: Use of intrinsic size parameters for bona fide predictions of cross sections

An ion trap/ion mobility/time-of-flight mass spectrometry technique has been used to measure collision cross sections for 660 peptide ions generated by tryptic digestion of 34 common proteins. Measured cross sections have been compiled into a database that contains peptide molecular weight and sequence information. The database is used to generate average intrinsic contributions to cross section (size parameters) for different amino acid residues by solving systems of equations that relate the unknown contributions of individual residues to the sequences and cross sections of database peptides. Size parameters are combined with information about amino acid composition to calculate cross sections for database peptides. Bona fide cross section predictions (made prior to measurement) for peptides observed in tryptic digests of sperm whale myoglobin and yeast enolase are made. Eight of 10 predicted cross sections are within 2% of the experimental values and all 10 are within 3.2%. The utility of size parameters for cross section prediction is explored and discussed.     

Electron loss from multiply protonated lysozyme ions in high energy collisions with molecular oxygen

We report on the electron loss from multiply protonated lysozyme ions Lys-Hn(n)+ (n = 7 - 17) and the concomitant formation of Lys-Hn(n+1)+. in high-energy collisions with molecular oxygen (laboratory kinetic energy = 50 x n keV). The cross section for electron loss increases with the charge state of the precursor from n = 7 to n = 11 and then remains constant when n increases further. The absolute size of the cross section ranges from 100 to 200 A2. The electron loss is modeled as an electron transfer process between lysozyme cations and molecular oxygen.     

ZnS微粒子的光学截面及红外发射率光谱的计算

应用微粒子Ｍｉｅ散射理论，计算了ＺｎＳ粒子的散射、吸收和消化截面，并计算了相应粒子的红外发射率光谱，讨论了ＺｎＳ粒子在４．０－１０．０μｍ红外波段上的振荡吸收现象。     

Oxidation of hydrocarbons in the presence of added hydroperoxide. On the determination of rate constants by the hydroperoxide method

Oxidation of tetralin in the presence of tert-butyl hydroperoxide and tetralyl hydroperoxide, initiated with azobisisobutyronitrile, was studied at 60°C in order to examine the complications involved in the hydroperoxide method devised by Howard and Ingold. From literature data on absolute rate constants and our rates of oxidation, cross termination rate constants and contributions of each elementary propagation and termination step were computed. It was confirmed that this method was quite useful in determining the cross propagation rate constant, but it was also demonstrated that the rate of oxidation should be measured at very low conversion and with quite high concentrations of hydroperoxide, especially when the peroxy radical derived from the added hydroperoxide has a much lower termination rate constant than that from the oxidizing substrate.     

Enhanced viscoelastic focusing of particle in microchannel

A novel method is reported to enhance the focusing of microparticle in the viscoelastic fluid. Gradually contracted geometry is designed in microchannel, which changes the distribution of the elastic lift force on the cross section. Additionally, it induces the viscous drag force and the Saffman lift force in the lateral direction. Under the combined effect of these forces, microparticles fast migrate to the center of the channel. In comparison to the channel with constant cross section, the present channel significantly enhances the particle's lateral migration, leading to efficient viscoelastic particle focusing in a short channel length. The influence of flow rate, channel length, particle size and fluid property on the particle focusing is also investigated. With simple structure, small footprint and perfect particle focusing performance, the present device has great potential in the particle focusing processes in various lab-on-a-chip applications.     

A study of electrolytic coagulation of gold sols by the method of localized surface plasmon resonance spectroscopy

Surface plasmon resonance spectroscopy has been employed to study the aggregation of gold sols with average nanoparticle sizes of 15–35 nm under the action of an indifferent electrolyte (NaCl). The structure of resulting aggregates has been established as depending on the coagulation regime. In the regime of fast coagulation, anisotropic aggregates with branched structure are initially formed; then, they are transformed into denser aggregates with a lower degree of anisotropy. The change of the aggregate structure accelerates with an increase in hydrosol concentration. At the same time, slow coagulation obviously yields denser aggregates, the structure of which is independent of the sol concentration and particle size. A procedure has been proposed for estimating the critical coagulation concentration of gold hydrosols based on the analysis of variations in their extinction. It has been found that the critical coagulation concentration increases with a reduction in the sol concentration and gold nanoparticle size.     

Effect of Interaction Potential on Laser-assisted e-Ar Scattering

The interaction potentials between electron and atom play an important role in electron-atom scattering. Using three potential models, the absolute differential cross section has been calculated by the second Born approximation theory. Results show that these model potentials are successful in the laser-assisted e-Ar scattering system. The influence of static potential, exchange potential and polarization potential on the absolute differential cross section is also analyzed and discussed.     

Numerical Investigation of Brownian,Gradient, and Turbulent Coagulation Under Moving Vehicle Conditions in an Underground Garage

Particle coagulation behavior can affect particle formation and dispersion in vehicle plumes. An Eulerian particle transport model combining a Realizable k–? model, Brownian, gradient, and turbulent coagulation has been developed to analyze particle coagulation behavior in an underground garage under moving-vehicle conditions. The results show that prominent coagulation of nanoparticles occurs within a limited region, which is at a distance of less than 0.2 m in the vertical direction and no more than 0.4 m in the exhaust direction from a given vehicle. The coagulation of small particles with diameters of less than 130 nm is dominated by Brownian motion, while gradient and turbulent coagulation significantly affect the coagulation of particles with median diameters of 420 nm and larger diameters of 600–950 nm, respectively. The influence of turbulent coagulation increases as vehicle speed and particle size increase. The half-time due to coagulation is approximately two times and 10–20 times larger than the corresponding value due to dilution in the regions less than 0.2 and 1.5 m along the tailpipe centerline, respectively. It is demonstrated that coagulation has considerable influence on particle dispersion in the region less than 0.2 m from the tailpipe, compared with dilution.     

凝并和成核机理下颗粒尺度分布的Monte Carlo求解

颗粒的凝并和成核现象影响其尺度分布,现有的MonteCarlo方法描述颗粒尺度分布的时间演变过程存在若干困难.提出了一种新的多重MonteCarlo(MMC)算法,基于时间驱动,利用加权的虚拟颗粒的思想,在模拟过程中保持虚拟颗粒总数不变和计算区域体积不变.利用该算法对“常凝并核,一阶成核”的情况下颗粒尺度分布的时间演变过程进行了数值求解,所得结果与数值解相符,表明MMC算法具有高且稳定的计算精度.另外,MMC算法由于跟踪比实际颗粒数目少得多的虚拟颗粒而具有较低的计算代价.     

Direct images of the virtual source in a supersonic expansion

Direct images of the virtual source in a supersonic expansion of helium are presented. The images were obtained using a Fresnel zone plate with free-standing zones, 540 microm in diameter and with an outermost zone width of 50 nm. The general method can be extended to other beams, including seeded beams. Measurements were carried out at absolute source pressures ranging from 11 to 171 bar using a 10 microm nozzle with a source temperature of 320 K. The size of the virtual source was found to be strongly dependent on pressure, changing from a diameter of 67+/-6 microm at an absolute nozzle pressure of 11 bar to 180+/-9 microm at 171 bar. The virtual-source brightness displays a maximum at an absolute nozzle pressure of around 30 bar. This phenomenon occurs because of two competing effects: As the pressure increases, the total flux also increases, but at the same time the virtual source broadens. We modeled the expansion process by calculating the velocity distribution with solutions from the Boltzmann equation to estimate the location of the quitting surface where the frequency of interatomic collisions is assumed negligible. Realistic potentials have been used to calculate the cross section for atomic collisions and, for the velocity distribution perpendicular to the center streamline, a proper scaling with distance derived from the continuum expansion model has been introduced. A good agreement between experiments and model has been found and we discuss its approximation limits. For instance, backscattering effects are not included in the calculations and at present we cannot exclude that they also contribute to a broadening of the virtual-source size for the highest pressure regime. The results presented here are important for improving the understanding of the supersonic expansion process. The experimental method might eventually be used as a new way to test molecular and atomic interaction potentials.