Kinetics of Heterogeneous Nucleation in Supersaturated Vapor: Fundamental Limits to Neutral Particle Detection Revisited

We examine the nucleated (with barrier) activation of perfectly wetting (zero contact angle) particles ranging from essentially bulk size down to approximately 1-nm mass diameter. While similar studies trace back to the pioneering work of Fletcher, we present here a novel approach to the analysis based on general area constructions that enable key thermodynamic properties, including surface and bulk contributions to nucleation work, to be interpreted geometrically with reference to the Kelvin curve. The kinetics of activation are described in more detail in terms of the mean first passage time (MFPT) for barrier crossing. MFPT theory and benchmark calculations are used to develop and test a new approximate-but-simpler-to-use analytic expression for the barrier crossing rate. The present study is motivated by recent condensation particle counter (CPC) studies that appear to finally establish the long-predicted detection of “sub-Kelvin” particles in the nano-size regime. Corresponding states thermodynamic and kinetic scaling approaches are used to facilitate the correlation and selection of optimal CPC working fluids and operating conditions based on a new metric for heterogeneous nucleation, the signal-to-noise ratio, and physical and chemical properties.

Copyright 2012 American Association for Aerosol Research     

Surface Topology of the Ion-Induced Vapor Nucleation Rate

ABSTRACT

Ion-induced nucleation involves additional electrostatic interactions between vapor molecules (atoms) and ions. The electrostatic force helps to form the ion stabilized prenucleation embryos and lowers the free energy barrier for nucleation. The free energy for ion-induced critical embryos formation has been calculated using the Thomson's term in the framework of the classical theory of nucleation. Nucleation theory has made obvious progress, but the understanding of the nucleation phenomenon is far from complete. Some ideas for the identification of possible new directions to improve both homogeneous and heterogeneous nucleation theories can be found by analyzing the topology of nucleation rate surfaces. The creation of the ion-induced nucleation rate surfaces is based on the knowledge of phase state diagrams, experimental results on ion-induced nucleation, and a few plausible assumptions. In this article the surfaces of the ion-induced nucleation rates for metastable vapor nucleation will be constructed. Semiempirical rules are formulated for the ion-induced vapor nucleation based on both known experimental and theoretical results. By using surface topology analysis, problems in heterogeneous nucleation theory can be formulated more clearly, and future directions for improvements can be discussed. A point on the spinodal line was found by extrapolation of the logarithm of the actual vapor pressure for ion-induced and homogeneous nucleation at a constant nucleation rate as a function of inverse temperature. Nucleation rate scaling of the surface should yield a quantitative scale for the ion-induced nucleation rates. Phase diagrams need to be incorporated into the interpretation of experimental and theoretical results on ion-induced nucleation.     

Rheological behavior of cellulose/monohydrate of N-methylmorpholine N-oxide solutions. Part 2. Glass transition domain

Dynamic mechanical experiments performed with original conditions allowed the analysis of a solution containing 15% cellulose dissolved in a monohydrate of N-methylmorpholine N-oxide (NMMO) in the amorphous state. The glass transition zone is studied by dynamic tensile experiments, while dynamic torsion technique is used to determine the viscoelastic behavior in the glassy state. A master curve of the storage and loss modulus versus frequency can be deduced from the isochronal curves measured by both techniques. This work allows one to complete the corresponding master curve obtained for the ‘liquid’ state and presented in a previous work [Rheol. Acta 1998;37: 107]. The measurements below the glass transition temperature exhibit two secondary relaxations. A modeling of the overall viscoelastic behavior, using the Nowick and Berry approach and the quasi-point defect theory, is proposed. Physical parameters deduced from this modeling are then discussed.     

From the sigmoidal to the downward concave shape behavior during the hydration of grains: Effect of the initial moisture content on Adzuki beans (Vigna angularis)

This work studied the change of the hydration behavior of Adzuki beans (Vigna angularis) as a function of their initial moisture content. By studying the hydration kinetics at different initial moisture contents, it was demonstrated that the hydration behavior of this grain changes from the sigmoidal to the downward concave shape (DCS) when the initial moisture content is above ∼20% d.b. This change happens when the moisture content passes from zone II to zone III of the grain's adsorption isotherm. This was attributed to the transition from the glassy state to the rubbery state, especially the in seed coat components. The seed coat is impermeable when the moisture content of the grain is low, so the water ingress is only by way of the hilum. However, when the seed coat is above ∼20% d.b. the water enters not only via the hilum, but also by way of the seed coat. The hydration behavior of the grain was modeled using a sigmoidal mathematical model, whose parameters were evaluated as a function of the initial moisture content; the water absorption rate parameter demonstrated a sigmoidal increasing behavior. The time to reach the inflexion point of the curve, related to the lag phase, showed an exponential decay. The equilibrium moisture content was not affected. Finally, a general model, which was able to predict the moisture content as a function of the initial moisture content of the grain and the process time, was obtained.     

Modeling and experimental evaluation of an aerosol generator for very high number currents based on a free turbulent jet

In this paper we report on theoretical and experimental work on aerosol formation in a free turbulent jet. A hot DEHS vapor issues through a circular nozzle into slowly moving cold air. Vapor concentration and temperatures are such that particles are formed via homogeneous nucleation close to the nozzle upon mixing with the surrounding air. The vapor is completely quenched in the nucleation regime so that further particle growth is controlled by coagulation. A simple growth dynamics model is presented and the theory is used to design a generation system that produces liquid aerosols at a very high number current [up to 10¹² particles (s)]. The aerosol properties can be controlled by two easily adjustable parameters. The aerosol properties are related to these parameters by simple scaling laws. The results of measurements of the number current and the average particle size support these scaling laws.     

Interface-based crystal particle autoselection via membrane crystallization: From scaling to process control

Accurate crystallization control is an essential aspect for chemical engineering and separation processes. Herein, we demonstrated the novelty of membrane crystallization (MCr) on the interfacial based-crystal particle autoselection aimed for nucleation regulation and process control. With the proposed model based on a van der Waals-friction-hydrodynamic force field and classical nucleation theory, the motion mechanisms of heterogeneously induced nucleation were illustrated. The defined particle detachment criterion K revealed the control mechanism of the crystal particle motion behavior: temporary adherence, detachment, and perpetual adherence (scaling) at the membrane interface. For the first time, the function region of MCr (nucleation detection, scaling control, and crystallization regulation) was systematically illustrated and validated with the directly observed laboratory demonstration. These findings also demonstrate the potential applications of the uniform size distribution, morphology modified particle manufacture, and in situ nucleation detection. © 2018 American Institute of Chemical Engineers AIChE J, 65: 723–733, 2019     

The anomalous melting behavior of water in aqueous PVME solutions

The Wertheim lattice thermodynamic perturbation theory is used to predict the liquid-liquid and solid-liquid coexistence data for a model polymer solution. The theory predicts bimodal LCST phase behavior and an unusual step with composition in the solid-liquid equilibrium of the solvent.The theoretical solid-liquid equilibrium calculations are used to interpret experimental data obtained for aqueous solutions of poly(vinyl methyl ether) (PVME), which is known to show bimodal LCST phase behavior. An experimental method is proposed, employing Fourier transform infrared (FTIR) spectroscopy to determine the equilibrium melting line of water in the presence of PVME. In addition, the complete melting line of water is obtained by partial integration of the melting endotherm observed using modulated temperature differential scanning calorimetry (MTDSC). Both, the FTIR and MTDSC methods are in good agreement, experimentally confirming the predicted step with composition in the solid-liquid equilibrium. This peculiar concentration dependence of the melting curve of ice provides a new explanation for the inhibited crystallization of water in aqueous PVME solutions, since the actual supercooling (at high polymer concentration) is smaller than it could be anticipated for a conventional course of the melting curve. Hence, the vicinity of the glass transition region in these highly concentrated polymer mixtures leads to a dramatic slowing down of the nucleation rate and thus the subsequent crystallization. Moreover, the atypical shape of the equilibrium melting line also provides a new explanation for the double melting endotherm observed in (MT)DSC experiments, which is conventionally attributed to the melting at different temperatures of bound and free water.     

Underpotential—overpotential transition phenomena in metal deposition processes

The transition phenomena in metal deposition processes have been studied in the system Ag(hkl)/Pb²⁺ by potentiostatic pulse experiments from the underpotential to the overpotential range. The analysis of the current-time transients indicates a model of progressive nucleation and hemispherical diffusion to the growing 3-D crystallites. An important influence of the initial state in the underpotential range on the nucleation rate has been found. Furthermore, the nucleation rate strongly depends on the overvoltage and on the substrate nature. All experimental results are explained by a stepwise bulk phase formation process including rearrangement of adatoms in the 2-D adsorbed layer, formation of critical clusters and further rearrangement and growth forming epitaxially orientated 3-D crystallites. The nucleation process must be treated by an atomistic model due to the derived low number of atoms in the critical cluster.     

Modeling batch crystallization processes: Assumption verification and improvement of the parameter estimation quality through empirical experiment design

In this work, experimental data of different batches was used for estimation of the kinetic parameters for the secondary nucleation framework of Gahn and Mersmann [Gahn, C. and Mersmann, A., 1999. Brittle fracture in crystallization processes. Chem. Eng. Sci. 54, 1273–1292].An empirical experiment design procedure was used to design an informative batch experiment through optimization of the seed quality, size and mass and process conditions at seeding. The parameters estimated using the data of the designed experiment showed smaller magnitudes of the confidence ellipsoids and standard deviations as compared to those obtained by using the data of conventional (un)seeded batch experiments. It was shown that the designed experiment allowed reducing uncertainty in the initial conditions, namely, the mass and crystal size distribution of the initial population of crystals and the initial supersaturation.It was also demonstrated that the main reason for the model/process mismatch was the origin of nuclei. Dynamic experimental data could be described better if the state of the crystals forming the crystallization system corresponded to the assumptions of the used kinetic model. Differences in the crystal surface properties, shape, and strain content could be responsible for a divergent nucleation and growth behavior in batches that were initiated either by primary nucleation, seeding with small ground seeds or seeding with coarse crystals from the product of the previous batch.     

Change in the critical nucleation radius and its impact on cell stability during polymeric foaming processes

The critical radius of cell nucleation is a function of the thermodynamic state that is uniquely determined by the system temperature, system pressure, and the dissolved gas concentration in the polymer/gas solution. Because these state variables change continuously during the foaming process, the critical radius varies simultaneously despite the traditional concept that it is a fixed thermodynamic property for a given initial state. According to classical nucleation theory, the critical radius determines the fate of the bubbles. Therefore, the change in the critical radius during foaming has a strong impact on the stability of foamed cells, especially in the production of microcellular or nanocellular foams. In this study, the continuous change in the critical radius is theoretically demonstrated under atmospheric pressure while bubbles are generated and expanded by the decomposition of a chemical blowing agent. The experimental results observed from the visualization cell are used to support the theoretically derived concept. Sustainability of the nucleated bubbles is also discussed by comparing the bubble size to the critical radius.     

Substrate effect on the crystallization of isotactic polypropylene

The evolution of storage modulus measured by a rotational rheometer shows that the isothermal crystallization of isotactic polypropylene (iPP) melts in contact with aluminum plates (PP-Al) are considerably faster than that with stainless-steel plates (PP-SS). The difference is bigger at higher temperatures, and this behavior is opposite to that expected by our numerical simulation considering uniform bulk phase transition and substrate's ability to remove the latent heat. Polarized optical observations and surface energy evaluations via contact angle measurement indicate that surface energy of the substrates, including the effects of submicrometer morphology and roughness, should be the key factor to affect the crystallization of iPP. Transcrystallization zones, in which the nucleation density is controlled by the surface energy of substrates, were observed to grow toward the bulk with the thickness of about 0.2 mm for iPP to affect the global crystallization behavior. The critical value of surface energy of substrate to promote the interfacial crystallization of a polymer melt is derived, in terms of which the aluminum and stainless steel as well as optical glass, promote the surface nucleation with respect to the bulk nucleation of iPP. As a consequence, the conventional differential scanning calorimetry measurement mainly gives the heat fluxes of interfacial crystallization rather than the bulk crystallization due to the large surface-to-volume ratio of the specimen and the aluminum pan used which is a high surface energy substrate. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Mixing induced by buoyancy‐driven flows in porous media

A theoretical model for fluid mixing in steady and transient buoyancy‐driven flows induced by laminar natural convection in porous layers is presented. This problem follows a highly nonlinear dynamics and its accurate modeling poses numerical challenges. Based on the Taylor dispersion theory, a one‐dimensional analytical model is developed for steady and transient velocity fields. To investigate steady‐state mixing, a unicellular steady velocity field is established by maintaining a thermal gradient across a porous layer of finite thickness. A passive tracer is then introduced into the flow field and the mixing process is studied. In the case of transient flows, as the convective flow grows and decays with time the behavior of the dispersion coefficient is characterized by a four‐parameter Weibull function. The simple analytical model developed here can recover scaling relations that have been reported in the literature to characterize the mixing process in steady and transient buoyancy‐driven flows. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1378–1389, 2013     

Prediction of adsorption rate constants of activated carbon for various vapors

In the past decade, a theoretical calculation of the adsorption properties of activated carbon has successfully been used to predict the adsorption capacity for untested vapors after initial characterization of the carbon with a reference vapor. However, using this theoretical approach, it has not been possible to predict the second fundamental property of carbons, namely its adsorption rate constant, and therefore only a family of curves for adsorption performance could be calculated. A new extension of the present theory is proposed which would permit prediction of the adsorption rate constant of vapors, after initial characterization of the carbon with a reference vapor, so that a curve of adsorption performance can be calculated for any vapor needed.     

Rheology and thermal behavior of polyamide reinforced with alumina whiskers

Alumina whiskers were melt‐mixed with polyamide 12 to obtain new composites with high performance properties and similar processability of neat polyamide. Three kinds of alumina whiskers were used to prepare composites (purified fibers, ribbon‐shaped fibers and silica‐coated fibers). The rheology, morphology and thermal behavior of composites were evaluated as function of the type of whisker and its amount in the samples. In terms of rheological properties, modulus and viscosity were enhanced as function of the amount of filler added. Good dispersion of alumina whiskers in PA12 and an optimal filler‐matrix interface were observed in morphological tests independently of the kind of fiber used. Studies on crystallization behavior indicated the nucleation action of whiskers, although the most important changes in crystalline state of PA12 were observed with ribbon‐shaped and silica‐coated fibers. Whiskers improved significantly the thermal stability of polyamide. But kinetics of degradation process studied using Coats‐Redfern method indicates that the best behavior wasobtained principally with ribbon‐shaped and silica‐coated whiskers. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Piezoresistive behavior of epoxy matrix‐carbon fiber composites with different reinforcement arrangements

In this work, the self‐monitoring capability of epoxy matrix‐carbon fiber composites has been studied. Different concentrations and arrangements of reinforcements were used, including random chopped, unidirectional and bi‐directional continuous carbon fibers, weaved and nonweaved. Mechanical properties were determined by uniaxial tensile tests. The composite electric to mechanical behavior was established by determining its electrical resistivity variation as a function of the stress‐strain curve. It was observed that the composites electrical resistance increased during tensile tests, a trend that indicates piezoresistive behavior. The increase was linear for the chopped reinforced composites, while it exhibits different slopes in the continuous reinforced composites. The initial smaller slope corresponds mainly to separation of the 90° oriented fibers and/or transversal cracking of the matrix, whereas the latter higher slope is caused by fiber fracture. The results demonstrated how each reinforcement configuration exhibited a unique and typical electrical response depending on the specific reinforcement, which might be appropriate either for strain‐monitoring or damage‐monitoring. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Bulk crystallization of poly(aryl ether ether ketone) (PEEK)

Concurrent measurements of transmitted polarized light intensity and recording of the phenomenon of crystallization through polarized optical microscopy have resolved some of the controversies on the bulk crystallization behavior of poly(aryl ether ether ketone) (PEEK). The process of bulk crystallization was studied through the separation of the nucleation and growth steps. Avrami plots have shown three characteristic ranges. It was observed that a first slope at low crystallization times is associated with massive heterogeneous nucleation and/or local-order-promoted primary nucleation of spherulitic crystals. A second gradual decrement in intensity follows, showing a logarithmic tendency. It represents a mixture of at least three parallel mechanisms. These are associated with the end of the process of crystallization of the primary spherulites and in large proportion the nucleation and growth, at lower rates, of sporadically nucleated spherulites. In addition, there is some contribution from secondary crystallization to the transmitted light emerging. The whole group of nucleated spherulites continue growing up to the point of impingement, which loosely marks the beginning of the third region. This last region with lower slope than the first one and an exponential tendency reflects secondary crystallization at long times. The general characteristics of the processes of nucleation and growth are discussed.     

Role of thermal history on quiescent cold crystallization of PET

The cold crystallization of poly(ethylene terephthalate) (PET) has been studied as a function of the initial structure of the glass using density, microhardness, wide angle X-ray scattering, small angle X-ray scattering and DSC measurements. Glassy PET samples varying from slightly crystalline to completely amorphous phase were investigated. Results reveal that differences in the inner structure of the starting glassy material induce different crystallization rates from the glassy amorphous state. Thus, it is observed that crystallization rate decreases with the increasing cooling rate used to quench the samples. Results have been analyzed using the Kolmogroff-Avrami-Evans theory. A good agreement between theoretical and experimental data is obtained providing accurate values for kinetic constants. The different crystallization rates obtained are explained in terms of differences in nucleation density.     

Crystallization regimes and reptation in polypropylene molecular weight fractions

Crystal growth rate data based on the kinetic nucleation theory of chain folding and the effect of reptation, have been used to predict the rate of crystal growth at moderate to high supercoolings in iPP molecular weight fractions. Growth rate data obtained for the fractions seem to be in agreement with the theoretical predictions of the regime theory. However, an extension of the gambler ruin treatment to the iPP data has not been successful with regard to the dominant morphology in regime II. The variable cluster model suggested as the morphology for polyethylene in regime II does not appear to be evident from this study. The effect of polydispersity, molecular weight, and tacticity on the crystallization behavior of iPP fractions have also been studied and correlated with the structure of polymer samples investigated. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 579–584, 1999     

Investigation of alternating-flow mixing in microchannels

A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe^-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe^-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.