Final Particle Number Research Articles

WIMPs without weakness: Generalized mass window with entropy injection

We study general freeze-out scenarios where an arbitrary number of initial and final dark matter particles participate in the number-changing freeze-out interaction. We consider a simple sector with two particle species undergoing such a thermal freeze-out; one of the relics is stable and gives rise to the dark matter today, while the other one decays to the Standard Model, injecting significant entropy into the thermal bath that dilutes the dark matter abundance. We show that this setup can lead to a stable relic population that reproduces the observed dark matter abundance without requiring weak scale masses or couplings. The final dark matter abundance is estimated analytically. We carry out this calculation for arbitrary temperature dependence in the freeze-out process and identify the viable dark matter mass and cross section ranges that explain the observed dark matter abundance. This setup can be used to open parameter space for both heavy (above the unitarity bound) or light (sub-GeV) dark matter candidates. We point out that the best strategy for probing most parts of our parameter space is to look for signatures of an early matter-dominant epoch.

Time dependence of adiabatic particle number

We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naively, this is not a well-defined notion for such a non-equilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and anti-particles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with non-trivial temporal sub-structure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, Spectral Function and Schrodinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.

Preparation of CdFe2O4-polymeric nanoparticles by inverse miniemulsion and its film properties

Abstract CdFe2O4-polymeric nanoparticles were prepared by inverse miniemulsion in order to achieve an acceptable grain size on the formed spin-coated film at a low calcination temperature. Sodium polyacrylate latex (PAANa) was synthesized by inverse miniemulsion polymerization using NaOH as a co-stabilizer. The effects of the NaOH content added to the inverse miniemulsion on the size and distribution of droplets and the latex particles were studied. The Cd-Fe salt droplets from the miniemulsion were absorbed by the PAANa latex particles, and the films formed by CdFe2O4-polymeric nanoparticles were characterized. The nucleation mechanism was characterized based on the ratio of the final number of latex particles to the initial number of droplets in a volume unit (Np/Nd). The increased NaOH dosage efficiently enhanced the stability of droplets, and Np/Nd approached 1. CdFe2O4-polymeric nanoparticles were formed using PAANa latex particles as a nano-reactor. The CdFe2O4-polymeric film prepared by inverse miniemulsion exhibits high reaction activity, as evidenced by the highly crystalline spinel structure formed at a low calcination temperature. The height of the film before and after calcination at 500 °C was 79 nm and 3.2 μm, respectively. The high reaction activity of CdFe2O4-polymeric nanoparticles can be successfully achieved by the inverse miniemulsion method.

Turkevich in New Robes: Key Questions Answered for the Most Common Gold Nanoparticle Synthesis.

This contribution provides a comprehensive mechanistic picture of the gold nanoparticle synthesis by citrate reduction of HAuCl4, known as Turkevich method, by addressing five key questions. The synthesis leads to monodisperse final particles as a result of a seed-mediated growth mechanism. In the initial phase of the synthesis, seed particles are formed onto which the residual gold is distributed during the course of reaction. It is shown that this mechanism is a fortunate coincidence created by a favorable interplay of several chemical and physicochemical processes which initiate but also terminate the formation of seed particles and prevent the formation of further particles at later stages of reaction. Since no further particles are formed after seed particle formation, the number of seeds defines the final total particle number and therefore the final size. The gained understanding allows illustrating the influence of reaction conditions on the growth process and thus the final size distribution.

A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range

Abstract. Multiple-charge inversion is an essential procedure to convert the raw mobility distributions recorded by mobility particle size spectrometers, such as the DMPS or SMPS (differential or scanning mobility particle sizers), into true particle number size distributions. In this work, we present a fast and easy-to-implement multiple-charge inversion algorithm with sufficient precision for atmospheric conditions, but extended functionality. The algorithm can incorporate size distribution information from sensors that measure beyond the upper sizing limit of the mobility spectrometer, such as an aerodynamic particle sizer (APS) or an optical particle counter (OPC). This feature can considerably improve the multiple-charge inversion result in the upper size range of the mobility spectrometer, for example, when substantial numbers of coarse particles are present. The program also yields a continuous size distribution from both sensors as an output. The algorithm is able to calculate the propagation of measurement errors, such as those based on counting statistics, into on the final particle number size distribution. As an additional aspect, the algorithm can perform all inversion steps under the assumption of non-spherical particle shape, including constant or size-dependent shape factors.

Reduced efficacy of marine cloud brightening geoengineering due to in-plume aerosol coagulation: parameterization and global implications

Abstract. The intentional enhancement of cloud albedo via controlled sea-spray injection from ships (marine cloud brightening) has been proposed as a possible method to control anthropogenic global warming; however, there remains significant uncertainty in the efficacy of this method due to, amongst other factors, uncertainties in aerosol and cloud microphysics. A major assumption used in recent cloud- and climate-modeling studies is that all sea spray was emitted uniformly into some oceanic grid boxes, and thus these studies did not account for subgrid aerosol coagulation within the sea-spray plumes. We explore the evolution of these sea-salt plumes using a multi-shelled Gaussian plume model with size-resolved aerosol coagulation. We determine how the final number of particles depends on meteorological conditions, including wind speed and boundary-layer stability, as well as the emission rate and size distribution of aerosol emitted. Under previously proposed injection rates and typical marine conditions, we find that the number of aerosol particles is reduced by over 50%, but this reduction varies from under 10% to over 90% depending on the conditions. We provide a computationally efficient parameterization for cloud-resolving and global-scale models to account for subgrid-scale coagulation, and we implement this parameterization in a global-scale aerosol-climate model. While designed to address subgrid-scale coagulation of sea-salt particles, the parameterization is generally applicable for coagulation of subgrid-scale aerosol from point sources. We find that accounting for this subgrid-scale coagulation reduces cloud droplet number concentrations by 46% over emission regions, and reduces the global mean radiative flux perturbation from −1.5 W m−2 to −0.8 W m−2.

Preparation of polystyrene latex particles by miniemulsion polymerization using a predissolved fluorinated block copolymer as the sole co-stabilizer

The fluorinated block copolymer [P(St-b-DFM)] of styrene (St) and dodecafluoroheptyl methacrylate (DFM) was used as the sole co-stabilizer in St miniemulsion instead of the conventional co-stabilizers. The fluorinated block copolymer was prepared by atom transfer radical polymerization (ATRP). The fluorine content in P(St-b-DFM) was determined based on the relative number–average molecular weight of the macroinitiator and P(St-b-DFM). In St miniemulsion polymerization, the effects of the fluorine content in the block polymer on the size and number of the initial monomer droplets and latex particles were investigated. The ratio of the final number of latex particles to the initial number of monomer droplets was used to discuss the nucleation mechanism. The P(St-b-DFM) copolymers with 6% and 11% fluorine contents had a better effect on the stability of the monomer droplets, and monomer droplet nucleation almost dominated the process of St miniemulsion polymerization. The water contact angle on the surface of the polystyrene latex film demonstrated the surface hydrophobicity, and the surface tension was estimated according to Girifalco–Good–Fowkes–Young equation.

Self-Assembled Mesoporous Silica Nanoparticles in Controlled Patterns Produced by Soft-Lithography and Ink-Jet Printing

This study demonstrate assembly of mesoporous silica nanoparticles (MSNs) into various patterns by soft-lithography and ink-jet printing techniques. A clear suspension containing MSNs with a particle size around 58 nm is firstly synthesized. Then, soft-lithographic techniques (i.e., MIMIC, impression with PDMS) and an ink-jet printing technique are applied to create various patterns assembled by MSNs. The MIMIC method results in a high density of MSNs, but is limited to linear patterns due to the capillary principle. The impression method led to MSN colloids in various patterns, but the MSNs assembled in low density due to the lack of the colloidal supplements. The ink-jet technique can create various patterns more conveniently, and the final patterns are generated after a de-wetting process. During the de-wetting process, the MSN concentrations and the jetted times are related only to the final number of particles dispersed in patterns. Comparison of different patterning techniques will be helpful towards creation of patterned assembly with MSNs.

Linear-, Cyclic-, and Multiblock Amphiphilic Polyelectrolytes as Surfactants in Emulsion Polymerization: Role of Topological Structure

Combining atom transfer radical polymerization (ATRP) and “click” chemistry, a set of well-defined amphiphilic block copolymers poly(n-butyl acrylate)-b-poly(acrylic acid) (PnBA20-PAA85) with a similar chemical component, but different topological structures, i.e., linear-, cyclic-, and multiblock structures, were successfully prepared, characterized (size exclusion chromatography (SEC), FT-IR and 1H NMR), and used as surfactants in emulsion polymerization. Our further transmission electron microscopy (TEM) and laser light scattering (LLS) characterization of the resultant latex particles demonstrates all the surfactants with different topologies can effectively stabilize the latex particles but no significant difference among the solids contents was observed. Moreover, we have, for the first time, experimentally established the quantitative relation between the final number of latex particles (Np) and the concentration of polymeric surfactant with different topologies (C), i.e., Np = kCα, and the order of our measured exponent α is as follows: αmulti(1.10) > αlinear(0.81) ≥ αcyclic(0.73), indicating cyclic surfactant molecules behave more like small-molecule surfactants attributed to its strongest unimers extraction and diffusion ability; in contrast, multiblock surfactant molecules can act as seeds to directly nucleate to create latex particles. In addition, Np,multi > Np,linear ≥ Np,cyclic at higher concentration, and Np,linear > Np,cyclic ≥ Np,multi at lower concentration was observed. Similar results (αmulti(1.02) > αlinear(0.65) ≥ αcyclic(0.58)) were also observed when polystyrene-b-poly(acrylic acid) (PS9–PAA60) copolymers were used as surfactants. Further aqueous SEC characterization shows the broad size distribution of our micellar solution has no effect on obtaining narrowly distributed latex particles. Finally, interfacial tension measurement of the micellar solution indicates, compared to multiblock structure, the rate of adsorption at a hydrophobic interface is much faster for linear and cyclic-block structures, agreeing with our observed order of exponent α.

The SISCone jet algorithm optimised for low particle multiplicities

The SISCone jet algorithm is a seedless infrared-safe cone jet algorithm. There exists an implementation which is highly optimised for a large number of final state particles. However, in fixed-order perturbative calculations with a small number of final state particles, it turns out that the computer time needed for the jet clustering of this implementation is comparable to the computer time of the matrix elements. This article reports on an implementation of the SISCone algorithm optimised for low particle multiplicities. Program summary Program title: siscone_parton Catalogue identifier: AELF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELF_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 1588 No. of bytes in distributed program, including test data, etc.: 41 164 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: All RAM: Negligible for low parton multiplicities. Classification: 11.9 Nature of problem: Clustering of particles into jets. Solution method: Infrared-safe cone algorithm. Restrictions: Hard-coded restriction to 64 final state particles on 64-bit machines, but recommended to be used only for configurations with up to 10 final state particles. Running time: Depending on the number of final state particles, O ( μs ) for configurations up to 5 final state particles.

Classicalization of gravitons and Goldstones

We establish a close parallel between classicalization of gravitons and derivatively-coupled Nambu-Goldstone-type scalars. We show, that black hole formation in high energy scattering process represents classicalization with the classicalization radius given by Schwarzschild radius of center of mass energy, and with the precursor of black hole entropy being given by number of soft quanta composing this classical configuration. Such an entropy-equivalent is defined for scalar classicalons also and is responsible for exponential suppression of their decay into small number of final particles. This parallel works in both ways. For optimists that are willing to hypothesize that gravity may indeed self-unitarize at high energies via black hole formation, it illustrates that the Goldstones may not be much different in this respect, and they classicalize essentially by similar dynamics as gravitons. In the other direction, it may serve as an useful de-mystifier of via-black-hole-unitarization process and of the role of entropy in it, as it illustrates, that much more prosaic scalar theories essentially do the same. Finally, it illustrates that in both cases classicalization is the defining property for unitarization, and that it sets-in before one can talk about accompanying properties, such as entropy and thermality of static classicalons (black holes). These properties are by-products of classicalization, and their equivalents can be defined for non-gravitational cases of classicalization.

Real-Time Monitoring of Copolymer Stabilized Growing Gold Nanoparticles

A great challenge in the production of nanoparticles with defined sizes and properties is to control their growth in situ. We developed a dedicated combined small-angle X-ray scattering (SAXS) and X-ray absorption spectroscopy (XAS) setup to monitor nanoparticle formation in solution. The capabilities of simultaneously deriving particle sizes and oxidation states of atoms/ions are illustrated for the formation of spherical gold nanoparticles by the reduction of hydrogen tetrachloroaureate (HAuCl(4)). Particles with initial radii of 4.60 +/- 0.10 nm and final radii of 5.67 +/- 0.10 nm were produced in a levitated droplet with a volume of 4 microL. An ethylene oxide/propylene oxide triblock copolymer PEO-PPO-PEO (Pluronic F-127) functions as reducing agent and colloidal stabilizer. XANES shows in situ how the gold was reduced in the droplet from Au(III) to Au(0), and simultaneously SAXS recorded the size distribution of the formed nanoparticles. It is shown that the final particle number is reached quickly. Thereafter, only the particles' sizes increase. Comparison of XANES and SAXS shows that the quantity of Au(0) is higher than the quantity of gold located in the nanoparticles while the particles are growing. Finally, all the Au(0) is found in the nanoparticles. We tentatively attribute this finding to the pseudo crown ether effect of the polymer surfactant that kinetically stabilizes gold atoms when formed from gold ions within their protecting cavity. A simple "burst" mechanism for the gold nanoparticle formation is the consequence. The possibility of an inhomogeneous particles structure with an enhanced density near the particle surface is discussed.

Miniemulsion Polymerization of Styrene Initiated by Tween-surfinit

The sterically-stabilized miniemulsion polymerization of styrene initiated by peroxide-containing Tweens (Twper, surfinit) was investigated. The conversion curves for miniemulsion emulsion polymerization are concave downward throughout the polymerization and the observed limiting conversions are much below 100% conversion. The polymerization rate vs conversion curve is described by a curve with two rate intervals and rate maximum located at low conversion. The consumption of peroxide groups in Tween (Twper), including their immobilization and accumulation into micelles, leads to the dead-end polymerization. The maximal polymerization rate increases with increasing the emulsifier and peroxide concentrations. The particle size decreases and the number of particles increases with increasing the concentration of emulsifier, Twper and reducing agent. The increased stability of the polymer dispersions is attributed to the chemically bound moieties of Twper to the particle surface. The values of the ratio of the final number of polymer particles to the initial number of monomer droplets (N p /N d) favor the mixed mode of particle nucleation.

Particle formation and growth in ab initio emulsifier-free emulsion polymerisation under monomer-starved conditions

Particle formation and growth in the monomer-starved emulsifier-free emulsion polymerisation of monomers with different water solubility including methyl acrylate (MA), methyl methacrylate (MMA), and vinyl acetate (VA) were studied. The rate of formation of precursor particles, via homogenous nucleation, is proportional to the monomer concentration in the water phase. One may think that the maximum number of particles will be obtained when the water phase is saturated with the monomer. The number of PMA particles showed a maximum when the water phase was starved with the monomer. The number of PVA particles did not show any sensitivity to the monomer concentration in the water phase. More unexpectedly the final number of PMMA particles showed a minimum when the water phase was just saturated with the monomer. The minimum in the final number of PMMA particles was correlated with the enhanced rate of particle growth due to the gel effect. Under monomer-starved conditions, the number of particles produced was in the order of water solubility of the monomers; MA>VA>MMA. A reverse order was produced under monomer-saturated conditions as particle coagulation became progressively more important for some of the monomers.

Kinetics and mechanism of seeded dispersion polymerization

AbstractThe kinetics and mechanism of seeded dispersion polymerization of methyl methacrylate (MMA) was studied by applying both micron and submicron PMMA seeds. Using a 1.7 μm PMMA seed (Np = 1 × 1012/L) and a monomer polymer ratio (M/P) of 28/1, secondary nucleation was found to occur and the number of new particles exceeded that produced in a parallel ab initio dispersion polymerization. This was explained by the paradoxical initiator concentration effect seen in dispersion polymerizations where the number of particles decreases with increasing initiator concentration. In contrast, using 194 nm (Np = 26 × 1012/L; M/P = 833/1) and 317 nm (Np = 5.6 × 1012/L; M/P = 714/1) submicron seeds, it was found that the final particle number was similar to (or less in a few cases) the initial seed number over a relatively wide range of initiator concentrations. With increasing initiator concentration, the initial reaction rate increased but the maximum reaction rate decreased slightly. This was explained by increased radical termination particularly in unstable nuclei, leading to a reduced radical entry rate. The reaction rate was found to be moderately dependent on the number of seed particles, but was independent of the seed surface area. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Seeding as a means of controlling particle size in dispersion polymerization

AbstractTwo distinctively different seeded dispersion polymerization processes employing micron and submicron size seed particles, respectively, have been used to gain a better mechanistic understanding of the dispersion polymerization process. Using monodisperse micron‐size PMMA particles as seed, it was found that when low monomer/polymer ratios (M/P < 2.50) were used in methyl methacrylate (MMA) seeded dispersion polymerizations, particle growth dominates and the number of particles remains unchanged (i.e., narrow distributions are preserved). However, when higher M/P ratios (>2.50) were applied, bimodal or trimodal particle size distributions were produced, which is considered to result from the competition between particle growth and secondary nucleation. When small amounts of submicron seeds were used with the initial intention of gaining a better understanding of the nucleation process, it was surprisingly found that the final number of micron size particles was nearly the same as the initial number of submicron seed particles over a relatively wide range of reaction conditions, including seed, initiator, stabilizer, and monomer concentrations, and the medium composition. These results indicate that within certain limits seeded dispersion polymerization can be a more robust means of controlling particle size than ab initio dispersion polymerization in terms of reproducibly producing a target particle size. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008

Exploring the Limits of Emulsion Polymerization of Styrene for the Synthesis of Polymer Nanoparticles

Suspensions of polymer nanoparticles in water (latices) with average particle diameters between 20 and 80 nm were synthesized by batch emulsion polymerization of styrene using sodium dodecyl sulphate (SDS) as surfactant and potassium persulphate (KPS) as initiator. The influence of surfactant concentration, initiator concentration, monomer concentration, and reaction temperature on the final average particle diameters and size distributions of the latices were studied. The number of particles generated was proportional to the 0.56 power of the emulsifier concentration and to the 0.37 power of the initiator concentration in the whole concentration range which was observed. Furthermore, the final number of particles was dependant on the reaction temperature to the 2.06 power. With these correlations the average particle number as well as the average particle size could be estimated, and the results were in good agreement (±6%) with the experimental values. A reduction of the monomer/water ratio from 1:5 to 1:20 yielded smaller particle diameters, while leaving the particle number unaffected. The lower particle size limits for monomer ratios of 1:10 and 1:15 were estimated with diameters of about 18 and 16 nm.

On the Distribution of the Number of Final Particles in a Branching Process with Transformations and Pairwise Interactions

A Markov continuous time branching process with two types of particles $T_1$ and $T_2$ is considered. Particles of the two types appear either as the offspring of a particle of type $T_1$, or as a result of interaction of two particles of type $T_1$. Under certain restrictions on the distribution of the number of new particles the asymptotic behavior of the expectation and variance of the number of particles of the two types are investigated and the asymptotic normality of the distribution of the number of final particles of type $T_2$ is established when the initial number of particles of type $T_1$ is large.

Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation

The present study provides a comprehensive investigation on the solution of the dynamic population balance equation (PBE) for particulate processes undergoing simultaneous particle nucleation, growth and aggregation. The general PBE was numerically solved in both the continuous and its equivalent discrete form using the orthogonal collocation on finite elements and the discretized PBE method, respectively. A detailed investigation on the effect of particle nucleation rate on the calculated particle size distribution (PSD) was carried out over a wide range of variation of dimensionless aggregation, nucleation and growth times. The performance (i.e., accuracy and stability) of the two numerical methods was assessed by a direct comparison of predicted PSDs and/or their respective moments to available analytical solutions. For combined aggregation and nucleation problems, the numerical error scaled with the product of the dimensionless aggregation and nucleation times. On the other hand, for combined growth and nucleation problems, the numerical error scaled only with the dimensionless growth time. For particulate systems with minimal particle growth, constant particle nucleation rate and Brownian aggregation, the total particle number approached a “steady-state” value characterized by the equilibrium of particle aggregation and nucleation rates. When the particle nucleation rate followed a pulse-like function, the PSD converged to a self-similar distribution after the end of particle nucleation. Moreover, for particulate systems exhibiting a constant particle nucleation rate and a Brownian-type particle aggregation kernel, an increase in the particle growth rate resulted in a decrease in the final total number of particles. On the other hand, for a constant particle nucleation rate and an electrostatically stabilized Brownian aggregation kernel, an increase in the particle growth rate can lead to an increase in the final total number of particles.

Synthesis by RAFT of Amphiphilic Block and Comblike Cationic Copolymers and Their Use in Emulsion Polymerization for the Electrosteric Stabilization of Latexes

A series of diblock and comblike copolymers based on styrene and 4-vinylbenzyl chloride were synthesized by reversible addition fragmentation transfer (RAFT) using benzyl dithiobenzoate as a control agent. After quaternization of the well-defined hydrophobic precursors with triethylamine, the micellar aggregates, formed by the cationic amphiphilic diblock copolymer when dissolved in water, were investigated by static and dynamic light scattering. The spherical shape of the micelles was established in salted water. Then, the poly(styrene)-b-poly(vinylbenzyltriethylammonium chloride) cationic diblock copolymers were used as a stabilizer for the emulsion polymerization of styrene and appeared to display very good stabilization properties. The ratio between the initial number of micelles and the final number of latex particles was particularly high, as a characteristic of the high mobility of the copolymer chains. Finally, we underlined the strong influence of salt on the nucleation step of the emulsion polym...