A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

Steady-state and pulsed studies of the radiation-induced polymerization of methyl methacrylate

In order to quantify our fluorogenic molecular probe studies on the radiation-induced polymerization of methyl methacrylate (MMA), measurements have been made of the monomer conversion, C _M, and polymer molecular weight distribution as a function of dose for bulk MMA polymerized by steady-state (⁶⁰Co γ-rays) and nanosecond-pulsed (3 MeV electrons) radiation. In all cases, C _M was found to increase close to linearly with dose up to ca. 30%. Above this conversion, autoacceleration of polymerization (the gel or Trommsdorff effect) occurs in the γ-irradiated samples. From the low-conversion steady-state data, using dose-rates of 0.21 and 2.7 Gy/s, the parameter 〈k _p〉 ² G(R^.)/2〈k _t〉 = 0.011 and 0.015 lmol^-1 s^-1 (100 eV)^-1 respectively have been determined (with 〈k _p〉 and 〈k _t〉 the average rate coefficients for bimolecular propagation and termination respectively, and G(R^.) the yield of the chain-initiating free radicals per 100 eV (G = 1 (100 eV)^-1 0.1036 μ mol J^-1)). From the 5 Hz repetitive pulse data the value of 〈k _p〉 G(R^.) = 1700 lmol^-1 s^-1 (100 eV)^-1 has been determined. Taking 〈k _p〉 = 342 lmol^-1 s^-1 from the literature results in G(R^.) = 5.0 (100 eV)^-1 and 〈k _t〉 = 2.7 × 10⁷ lmol^-1 s^-1.     

Vibrational energy transfer in the two-channel 1,1-cyclopropane-d2 isomerization system. Krypton bath gas

The study of intermolecular energy transfer in the 1,1-cyclopropane-d₂ system has been repeated for the neat gas at 973 K and has been extended to krypton bath gas at 823 K and 973 K. The method of study is by the competitive collisional activation “spectroscopy” technique for this two-channel competitive isomerization system. Results at 823 K give the relative collisional efficiency of krypton as β ≈ 0.46, at k/k_∞ ≈ 0.02 and yield the average down-jump energy step as 〈ΔE〉 ≈ 1200 cm^?1 on the basis of a stepladder model for the distribution of down-step sizes. At 973 K and k/k_∞ = 0.02, β ≈ 0.07 and 〈ΔE〉 ≈ 500 cm^?8, for both an exponential and stepladder distribution of down-step sizes. Agreement with related earlier data for other bath gases and for neat cyclopropane is good and verifies again a decrease in energy transfer collisional efficiency, and a decrease in 〈ΔE〉, with rise of temperature, as previously reported for this system.     

Kinetics of methyl methacrylate and n‐butyl acrylate copolymerization mediated by 2‐cyanoprop‐2‐yl dithiobenzoate as a RAFT agent

The RAFT (co)polymerization kinetics of methyl methacrylate (MMA) and n‐butyl acrylate (BA) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was studied with various RAFT concentrations and monomer compositions. The homopolymerization of MMA gave the highest rate. Increasing the BA fraction f_BA dramatically decreased the copolymerization rate. The rate reached the lowest point at f_MMA ～ 0.2. This observation is in sharp contrast to the conventional RAFT‐free copolymerization, where BA homopolymerization gave the highest rate and the copolymerization rate decreased monotonously with increasing f_MMA. This peculiar phenomenon can be explained by the RAFT retardation effect. The RAFT copolymerization rate can be described by 〈R_p〉/〈R_p〉₀ = (1 + 2(〈k_c〉/〈k_t〉)〈K〉)[RAFT]₀)^?0.5, where 〈R_p〉₀ is the RAFT‐free copolymerization rate and 〈K〉 is the apparent addition–fragmentation equilibrium coefficient. A theoretical expression of 〈K〉 based on a terminal model of addition and fragmentation reactions was derived and successfully applied to predict the RAFT copolymerization kinetics with the rate parameters obtained from the homopolymerization systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3098–3111, 2007     

Influence of excluded volume on the conformational property of tail-like chain on the simple cubic lattice

The influence of excluded volume on the conformational property of linear tail-like chain with one end attached to a flat surface is investigated by means of dynamic Monte Carlo method. Conformational properties such as mean-square end-to-end distance 〈R²〉, mean-square radius of gyration 〈S²〉 and mean asphericity parameter 〈A〉 are calculated for random walking (RW) and self-avoiding walking (SAW) tail-like chains on the simple cubic lattice. We find that the EV has nearly the same effect on 〈R²〉 as on 〈S²〉: (1) 〈R²〉_SAW/〈R²〉_RW≈〈S²〉_SAW/〈S²〉_RW∝n^0.204±0.05, where n is the chain length, and (2) the limiting value of 〈R²〉/〈S²〉≈7.7 for both chains. The distribution P(R) of the SAW tail-like chain can be expressed as a R⁴ correction of that of the RW one. We find that the value 〈A〉 of the SAW tail-like chain is bigger than that of the RW tail-like chain for all chain lengths, and the limiting values are 0.446±0.006 and 0.403±0.005 respectively.     

Comparative study of monomer droplet nucleation in the seeded batch and semibatch miniemulsion polymerisation of styrene

Monomer droplet nucleation in the seeded miniemulsion polymerisation of styrene under monomer-flooded and monomer-starved conditions was studied. The miniemulsion feeds were added to the reactor either batchwise or semibatchwise. The droplets preserved longer under flooded conditions. As a result, the batch operation led to a larger number of particles (N_p) than the semibatch operation. For the miniemulsion droplets containing predissolved polymer, the final N_p was independent of the way that the feed was added to the reactor and was equivalent to the number of monomer droplets in the original miniemulsion feed. The size distribution of the final latexes, however, was influenced by the operation type. For the batch operation, the rate of polymerisation (R_p) with the miniemulsion feeds was higher than that with the conventional monomer emulsion feed because of the monomer droplet nucleation. But for the semibatch operation, the opposite was true because of R_p controlled by the rate of monomer diffusion from rather stable miniemulsion droplets to the growing polymer particles.     

Reorientation of hydrogen-bonded solvents around a large dipole

Using picosecond spectroscopy, we find rise times τ_R ? 20 ps for p-dimethylaminobenzonitrile S₂ → S₀ fluorescence in the weakly hydrogen-bound alcohols 2,2,2-trifluoroethanol and 2-fluoroethanol. Since we previously obtained τ_R ≈ 40 ps in methanol and ethanol, this provides evidence that hydrogen-bonding-retarded solvent reorientation largely governs the fluorescence in these solvents.     

Temperature dependence of limiting viscosity number and radius of gyration of cellulose diacetate in acetone

Acetone solutions of a cellulose diacetate fraction were studied by viscosity and light scattering methods over the range 12.6–50.3². The temperature dependences of the limiting viscosity number [η], the mean-square radius of gyration 〈s²〉, and the second virial coefficient A₂ were determined. The unperturbed mean-square radius of gyration 〈s²〉_o and the expansion factor α, were estimated by using theoretical relations to the interpenetration function. It was found that dln 〈s²〉_o/dT is ?6.4 × 10^?3 deg^?1, while α, is close to unity over the whole temperature range studied. The viscosity results are interpreted to show that the draining effect is not negligible and the Flory viscosity parameter Φ slightly increases with increasing temperature. It is finally concluded that the value of ?6.9 × 10^?3 deg^?1 for dln [η]/dT can be ascribable to the rapid decrease in 〈s²〉_o.     

Statistics of aggregates

Aggregation phenomena of elementary particles into clusters has received considerable attention during the past few decades. We adopt here a stochastic approach for the modeling of these phenomena. More precisely, we formulate the problem in the following dynamical setup: given a population of n discernible atoms partitioned into p discernible (model 1) or indiscernible (model 2) groups, how does a new atom eventually connect to any of these p groups forming up a new partition of n+1 atoms into a certain amount of clusters? Nucleation is said to occur when the inserted atom does not connect (it nucleates), whereas aggregation takes place if it does (clusters coalesce). Depending on this local “logic” of pattern formation, the asymptotic structure of groups can be quite different, in the thermodynamic limit N→∞. These studies are the main purpose of this work. Understanding these aggregation phenomena requires first to derive the fragment size distributions (that is, the number P of fragments, or clusters, and the number n_m of size-m fragments with m fragments with constitutive atoms), as a function of the control parameter which is chosen here to be the average number of atoms 〈N〉. As 〈N〉 approaches infinity, we derive the study of these variables in the thermodynamic limit n → ∞. It is shown, making extensive use of combinatorics, that two regimes are to be distinguished: the one of weakly connected aggregates where nucleation dominates aggregation and the one of strongly connected aggregates where aggregation dominates nucleation. In the first (“diluted”) regime, the number of clusters P(n) always diverges as n → ∞, the asymptotic equivalent of which being under control in most cases. Large deviation results are shown to be available. Concerning N _m(n), distinct behaviours are observed in models 1 and 2. In the second (“condensed”) regime, the number of groups P(n) and size-m groups N _m(n) may converge in the thermodynamic limit, with a special role played by the geometric and Poisson distributions. The asymptotic variables become observable macroscopically. This work is therefore aimed toward a better understanding of the fundamentals involved in clusters' formation processes.     

Light-scattering of polyamide hydrazide solutions and conformational characteristics of its molecules

Light-scattering measurements have been carried out for 18 samples of polyamide hydrazide (PAH) in dimethylsulphoxide (DMS) with an over 10-fold variation in molecular weights. It was shown that the excluded volume effect in DMS does not appreciably affect the size of PAH molecules. The length of the Kuhn segment (A ≈ 240 · 10^?8 cm) was estimated from the experimental determinations of molecular weights $\text{M}{}_{\mathrm{w}}$ and the radii of gyration 〈R²〉_z. Viscometric determination of the rigidity of PAH chains yields the value of A ≈ 200 · 10^?8 cm and the hydrodynamic diameter d ≈ 5 · 10^?8 cm. The whole collection of data shows that PAH is a typical rigid-chain polymer; the extended conformation is due to the backbone rigidity tather than to the excluded volume effects.     

Effect of total degree of substitution on molecular parameters of cellulose acetate

An attempt was made to establish for cellulose acetate (CA) the relationship between the molecular properties, the total degree of substitution 〈〈F〉〉 and the degree of solvation. For this purpose, the comprehensive solution data for CA with 〈〈F〉〉 = 0.49-2.92 in previous papers were analyzed. In addition, the strength of the solvation was estimated from the chemical shift of O-acetyl- and hydroxyl-protons in NMR spectra and the number of the solvated solvent molecules at infinite dilution (s_o) was determined from the adiabatic compressibility. The strength of solvation and s_o increased with the dielectric constant ? of the solvent. The close correlation between s_o, the unperturbed chain dimension A and the free draining effect was demonstrated; these three quantities and the exponent a in the Mark-Houwink-Sakurada equation attained their maximum at $\text{〈〈F〉〉 ? 2.5}$, if CA is dissolved in dimethylacetamide. The characteristic variation of the chain rigidity, estimated from A, and of the draining effect with ? of the solvent and 〈〈F〉〉 can be reasonably explained by the solvation. The cellulose molecule dissolved in a hypothetical non-polar (? = 1) solvent was shown to be a freely rotating chain, by duplicated extrapolation A for CA to 〈〈F〉〉 = 0 and to ? = 1.     

Motif of the three-layered close packing of cluster anions in [RhPy<Subscript>4</Subscript>Cl<Subscript>2</Subscript>]<Subscript>4</Subscript>[Re<Subscript>6</Subscript>S<Subscript>8</Subscript>(CN)<Subscript>6</Subscript>]·1.5H<Subscript>2</Subscript>O

[RhPy₄Cl₂]₄[Re₆S₈(CN)₆]·1.5H₂O (Py is pyridine) was investigated by X-ray analysis. In the cluster anion, the Re-Re distances vary from 2.6063(2) Å to 2.6125(2) Å. For two crystallographically independent complex cations, the distances are 〈Rh-N〉 2.060 Å and 〈Rh-Cl〉 2.336 Å. The motif of the three-layered close packing was found; the [Re₆S₈(CN)₆]^4? anions follow the vertices of a rhombohedron with the parameters a _c ≈ 15.5 Å and α_c ≈ 61°.     

Phase separation, cation ordering and nano-structural complexities in Nd2/3−xLi3xTiO3 with x=0.14

Transmission electron microscopy (TEM) investigations on Nd_2/3−xLi_3xTiO₃ with x=0.14 reveal a rich variety of structural features in the samples prepared under different conditions, such as superstructures, anti-phase domains, and nano-chessboard structures. Our careful analysis shows that these structural phenomena can be fundamentally understood as the combination of structural effects of (Nd, Li)-ordering along the 〈001〉_p direction and the spinodal decomposition along the 〈100〉_p/〈010〉_p direction. The coexistence of phase separation and cation ordering can lead to visible nano-structural complexities in many crystals, as the typical results, the regular lamella structure, nano-chessboard structures and anti-phase boundaries have been extensively studied.     

Determination of orientational order parameters in oriented lipid membrane systems by angle-resolved fluorescence depolarization experiments

Angle-resolved fluorescence depolarization experiments have been performed on some lipid membrane systems in order to test the validity of a recently developed theory describing this type of experiments. Good agreement between theory and experiment was found. The experiments yield the order parameters 〈P₂〉 and 〈P₄〉 and a rotational correlation time τ_c. On applying an information-theoretic form of the orientational distribution function. 〈P₂〉 and 〈P₄〉 were used to estimate the degree of order in the systems studied. Knowledge of 〈P₄〉 proved useful to get more detailed information on the orientational order. Another finding was that the angle between the absorption and emission moment of the used fluorescent probe, diphenyl-hexatriene, depends on the membrane system in which it is incorporated. Finally, the experimental results point to the fact that for some membrane systems the molecular motion is inadequately described by the simple strong-collision model.     

Unseeded semibatch emulsion polymerization of butyl acrylate: Bimodal particle size distribution

Unseeded semibatch emulsion polymerization of butyl acrylate (BA) using sodium lauryl sulfate as emulsifier and potassium persulfate as initiator was carried out at the conditions where secondary nucleation was probable. This was achieved by using no emulsifier in the initial reactor charge. The effects of changes in monomer emulsion feed rate, initiator concentration and distribution, emulsifier concentration in the feed, and temperature on the evolution of particle size averages and distribution were investigated. Bimodal particle size distributions (PSD) were obtained for most of the latexes. Inhibition effects were found to be important in the development of PSD. Primary particle formation occurred through micellar nucleation, whereas secondary nucleation probably occurred through homogenous nucleation. The polydispersity index (PDI) of the latexes increased with the decreasing monomer emulsion feed rate. The application of a larger amount of initiator to the reactor charge or using a higher temperature, reduced the formation of secondary particles and resulted in a formation of an unimodal PSD. The overall steady‐state rate of polymerization was found to approach the rate of monomer addition (R_p ≈ R_a ), if the emulsifier concentration in the aqueous phase was appreciable. This is different from the correlation 1/R_p = 1/K + 1/R_a obtained for the BA semibatch process with neat monomer feed. This suggests that different rate expressions can be used for BA semibatch emulsion polymerization at different conditions. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 528–545, 2000     

The C—H⋯O hydrogen bond. An ab initio study of nitrosomethane and its hydrogen bonded dimer

In order to study the short C—H?O contact which has been found in several nitroso compounds, a series of ab initio calculations have been performed on nitrosomethane and it's cyclic “hydrogen bonded” dimer. A potential function for the C—H?O contact has been found and the effect of this contact upon the NO and CN bonds has been studied. The potential is shallow with a minimum of only ?2.65 kcal mol^?1 for each contact and the equilibrium C?O distance is 3.524, A. These results indicate that the C—H?O bond is better described as a van der Waal's type contact than a hydrogen bond. The equilibrium length of the NO bond (R_NO) changes in a regular manner with variations in the C?O (R_HYD) distance, i.e. when R_HYD becomes shorter R_NO becomes longer. However, the variations in the CN bond lengths, which in the nitrosomethane monomer molecule is a long and weak bond, are anomalous.     

Conformation study of poly(p‐dioxanone) fibers by polarized Raman spectroscopy,X‐ray diffraction,and conformation analysis

The molecular orientation distribution of poly(p‐dioxanone) (PPDX) uniaxially oriented commercial fibers was determined by polarized Raman spectroscopy and X‐ray diffraction. The order parameters 〈P₂₀₀〉 and 〈P₄₀₀〉 of the orientation distribution function were determined by polarized Raman spectroscopy. For the C?O stretching band, the values of 〈P₂₀₀〉 and 〈P₄₀₀〉 obtained are equal to ?0.40 ± 0.04 and 0.28 ± 0.04, respectively. These results clearly indicate that the carbonyl groups are highly oriented perpendicular to the fiber axis. X‐ray diffraction led to a fiber repeat value of 0.628 nm for these samples, and to 〈P₂₀₀〉 and 〈P₄₀₀〉 values of 0.93 and 0.82, respectively, for the c‐axis orientation, indicating a high orientation in the draw direction of the fibers. A Monte‐Carlo conformational search led to 20 low‐energy conformations, but only one of these was found compatible with both the fiber repeat and the angle between the C?O bond and the fiber axis. This conformation, a 2₁ helix with a tg^?ttg^? succession of torsion angles, is proposed as the existing conformation in the crystalline state. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 406–417, 2008     

A study of homogeneous nucleation of ibuprofen in a flow chamber. Determination of the surface tension of critical nuclei

Homogeneous nucleation of ibuprofen vapor is studied in a nucleation flow chamber, a horizontal quartz tube equipped with an external heater. The area of the chamber where the nucleation proceeds most efficiently is determined, and the volume of this area is estimated. The temperature and supersaturation are determined and the homogeneous nucleation rate is calculated for this area. Saturation vapor pressure over liquid ibuprofen is measured in a temperature range of 353–383 K. Using an exact formula that has recently been derived for the nucleation rate based on the works by Kusaka, Reiss, as well as the Frenkel liquid-kinetics theory, surface tension and the radius of surface of tension of a critical nucleus σ= 25.9 mN/m and R _s = 1.6 nm, respectively, are calculated at 318 K. The measurement of the surface tension of an ibuprofen planar surface shows that, at 318 K, σ_∞ = 24.38 mN/m; i.e., σ is higher than σ_∞ by 6%. A critical nucleus is established as containing nearly 36 ibuprofen molecules.     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

Covalence reduction factors of four-coordinated pseudo-tetrahedral paramagnetic compounds inD 2d symmetry

Theoretical expressions for the covalence reduction factors of orbital angular momentum and spin-orbit coupling in pseudo-tetrahedral four-coordinated paramagnetic complexes withD _2d symmetry, denoted ask's andR's respectively, have been derived. p ]The mixing coefficients in the antibonding MO's for the CuCl ₄ ^2- ion in three complexes are estimated using suitable approximations. It is shown thatk's must be less thanR's in Tinkham's approximation. Certain misconceptions existing in the literature regarding the value of the integral 〈p _u |???u|s〉 have been clarified.