Heterogeneous Nucleation Theory Research Articles

Understanding condensation halo growth on superhydrophobic surfaces: Insights from a vapor diffusive model

Anti-icing technologies are vital across various sectors, from transportation to energy systems. In this study, we investigate the formation of condensation halos during the process of condensation–freezing on superhydrophobic surfaces. Experimental tests were conducted on metallic nanostructured superhydrophobic surfaces, where droplet icing was induced and observed under controlled conditions. The formation of condensation halos, characterized by the sudden appearance and subsequent vanishing of microdroplets around the freezing droplets, was captured and analyzed. A vapor diffusive model coupled with heterogeneous nucleation theory was developed to understand and quantify the growth of condensation halos. The model considers vapor diffusion around the icing droplet and the critical vapor pressure required for nucleation. Experimental observations and theoretical predictions demonstrated a strong dependence of condensation halo size on the icing droplet radius. The study sheds light on the mechanisms underlying condensation halo formation and provides insights into the intricate interplay between droplet size, surface properties, and environmental conditions in condensation–freezing phenomena, offering valuable perspectives for the development of effective anti-icing strategies.

Effect of multiple environmental conditions on the formation process and adhesion strength of ice on asphalt binder surface

Road icing caused by freezing rain significantly impacts driving safety. Since asphalt binder plays a pivotal role in pavement infrastructure, understanding the formation process and adhesion strength of ice on asphalt binder surfaces is crucial for assessing road icing risk. This work investigated the effect of different environmental conditions on asphalt-ice interface adhesion strength via a self-designed low-temperature adhesion testing system. In addition, the icing process on asphalt binder surfaces was observed to analyze the asphalt-ice adhesion strength formation mechanism. Results show that the completion time of water-ice phase transition signified the initial development of asphalt-ice adhesion strength. Moreover, as the internal structure of the ice evolved from transparent to needle-like fine lines to dense, the asphalt-ice adhesion strength gradually increased until it reached stability. At asphalt-ice adhesion began forming after 40 min and stabilized after 80 min, whereas at −8°C, adhesion strength started forming after 20 min and stabilized by 60 min. The growth rates of asphalt-ice adhesion strength for temperatures ranging from −2°C to −10°C were approximately 7.92 kPa/°C, 6.56 kPa/°C, 5.14 kPa/°C, 3.29 kPa/°C, and 1.49 kPa/°C, respectively, showing a positive correlation with temperature and a negative correlation with time. According to heterogeneous nucleation theory, the influence mechanism of temperature and water depth on the nucleation icing process and asphalt-ice adhesion strength is analyzed. lower temperatures lead to asphalt-ice adhesion strength increase originating from the larger supercooling, which reduces the critical nucleation energy and thus accelerates the ice nucleation rate. In addition, the increase in water depth promotes the formation of nucleation sites and further enhances the asphalt-ice adhesion strength. Finally, an asphalt-ice adhesion strength prediction model was developed, with PSO-SVM-G achieving over 90 % accuracy. These results provide insights for evaluating ice adhesion behavior on asphalt surfaces and designing anti-icing asphalt materials.

Origin and Nucleation Kinetics of Transcrystalline Layer in Bamboo fiber@nano‐TiO2/Polypropylene Composite

AbstractHerein origin and nucleation kinetics of transcrystalline layer (TCL) in bamboo fiber deposited with nano‐TiO2 (BF@TiO2)/polypropylene (PP) composite is studied. Firstly, the surface morphology, roughness, and energy, as well as crystalline structure (e. g., crystal face indices (hkl)) of BF@TiO2 are analyzed to clarify the origin of TCL in the composite. Subsequently, the nucleation kinetics of TCL in BF@TiO2/PP composite at different crystallization temperatures (Tc) are investigated through polarized optical microscopy. The results find that the surface roughness and energy of BF@TiO2 increase by 47.55 % and 2.41 % compared with untreated BF, respectively. Interestingly, the mismatch rates (MRs) of hkl(BF) vs. hkl(PP) are >320 %. In comparison, the MRs of (101)(BF@TiO2)TiO2 vs. (hkl)(PP) are dramatically decreased to <25 %, suggesting a similar crystal plane between BF@TiO2 and PP matrix. These results indicate that the TCL formation in the composite is more facile in BF@TiO2 than in the untreated BF. During isothermal crystallization, the nucleation and spherulite growth rates decrease as the Tc increases. The interface free energy difference (▵σ) between BF@TiO2 and PP is calculated based on the heterogeneous nucleation theory. The ▵σ is 1.54±0.11 J cm−2, highlighting that the BF@TiO2 strongly induces the PP nucleation.

Direct numerical simulations of microlayer formation during heterogeneous bubble nucleation

In this article, we present direct numerical simulation results for the expansion of spherical cap bubbles attached to a rigid wall due to a sudden drop in the ambient pressure. The critical pressure drop beyond which the bubble growth becomes unstable is found to match well with the predictions from classical theory of heterogeneous nucleation imposing a quasi-static bubble evolution. When the pressure drop is significantly higher than the critical value, a liquid microlayer appears between the bubble and the wall. In this regime, the interface outside the microlayer grows at an asymptotic velocity that can be predicted from the Rayleigh–Plesset equation, while the contact line evolves with another asymptotic velocity that scales with a visco-capillary velocity that obeys the Cox–Voinov law. In general, three distinctive regions can be distinguished: the region very close to the contact line where dynamics is governed by visco-capillary effects, an intermediate region controlled by inertio-viscous effects away from the contact line yet inside the viscous boundary layer, and the region outside the boundary layer dominated by inertial effects. The microlayer forms in a regime where the capillary effects are confined in a region much smaller than the viscous boundary layer thickness. In this regime, the global capillary number takes values much larger then the critical capillary number for bubble nucleation, and the microlayer height is controlled by viscous effects and not surface tension.

A universal and accurate LPMI method for calculating mismatch in heterogeneous ice nucleation.

The interfacial correlation factor f(m,x), where m refers to the interaction among ice, water and the substrate and x refers to the ratio of the critical nucleation size to the surface topography characteristic size of the substrate, plays a crucial role in the classical theory of heterogeneous ice nucleation as it significantly impacts the energy of nucleation. Generally, a smaller value of f(m,x) indicates a higher propensity for ice nucleation. The degree of structural compatibility between ice and the substrate greatly influences f(m,x), particularly on specific substrates. Several approaches have been proposed to calculate the lattice matching based on this idea, which allows whether a surface is favorable for nucleation to be determined. However, none of these methods adequately correlates the mismatch index with ice growth phenomena. In this paper, we embarked on a new attempt to calculate the mismatch index by combining the lattice parameter and Miller index (LPMI). Droplet freezing experiments have been carried out on α-Al2O3 and silicon surfaces with different Miller indices to verify the rationality of the LPMI method. Furthermore, we validated the LPMI method extensively against other works and further demonstrated its readiness, accuracy and universality for freezing problems. The results consistently show that δd = 2|di - ds|/(di + ds) with interplanar spacing more accurately predicts heterogeneous ice nucleation rates across a wide range of substrates than δ1 = (ai - as)/ai with the lattice parameter of ice and the substrate and is more generally applicable than δ2D = (di - di)/di with the distances between two adjacent and congener atoms on the same plane. We believe that the proposed approach will aid in the selection of substrates for promoting or inhibiting heterogeneous nucleation on a specific substrate.

The smallest nanodrop describable via macroscopic interfacial concepts: Testing classical heterogeneous nucleation theory with perfect wetting down to 3 nm

HypothesisThe smallest nanodrop tractable with macroscopic notions such as the interfacial energy could be determined by comparing heterogeneous nucleation observations and capillary theory predictions at decreasing drop diameters dp. AnalysisThis is done here for the condensation of n-butanol vapors on polyethylene glycol nano-globules (3 nm ≤ dp ≤ 9 nm). We use published activation probability measurements P(w,dp), where w is the accurately controlled saturation ratio of n-butanol vapor in a gas stream exiting a saturator. The maximal saturation ratio achieved in the nucleation region by cooling this gas-vapor stream in the apparatus of Gallar et al. satisfies Smax = Cw. The key unknown constant C and the preexponential term K governing the nucleation rate are determined by assuming that classical theory applies to the largest particles used. This yields P(Smax,dp) data, directly comparable with capillary theory with perfect wetting. FindingsExcellent agreement is found above 5 nm for the critical dependence Smax(dp) resulting from the constraint P(Smax,dp) = 0.5. The entire P(Smax,dp) curves also agree closely between 5 and 7 nm. Smaller particles depart only slightly from theory, even at dp = 3 nm. Capillary theory hence describes accurately the heterogeneous nucleation process above 3–5 nm, provides a reliable method to determine Smax, and yields experimentally the nucleation rate constant K.

Tuning the growth of intermetallic compounds at Sn-0.7Cu solder/Cu substrate interface by adding small amounts of indium

The void defect in intermetallic compounds (IMCs) layer at the joints caused by inhomogeneous atomic diffusion is one of the most important factors limiting the further development of Sn-based solders. In this work, the thermodynamic stability of IMCs (high-temperature η-Cu6Sn5 and o-Cu3Sn phases) was improved by adding small amounts of indium (In), and the IMCs layers with moderate thickness, low defect concentrations and stable interface bonding were successfully obtained. The formation order of compounds and the interfacial orientation relationships in IMCs layers, the atomic diffusion mechanism, and the growth tuning mechanism of In on η-Cu6Sn5 and Cu3Sn, after In adding, were discussed comprehensively by combining calculations and experiments. It is the first time that the classic heterogeneous nucleation theory and CALPHAD data were used to obtain the critical nucleus radius of η-Cu6Sn5 and Cu3Sn, and to explain in detail the main factors affecting the formation order and location of IMCs at joints during the welding process. A novel and systematic growth model about IMCs layers in the case of doping with alloying elements was proposed. The growth tuning mechanism of In doping on η-Cu6Sn5 and Cu3Sn was further clarified based on the proposed model using first-principles calculations. The growth model used in this study can provide insights into the development and design of multielement Sn-based solders.

Deposition freezing, pore condensation freezing and adsorption: three processes, one description?

Abstract. Heterogeneous ice nucleation impacts the hydrological cycle and climate through affecting cloud microphysical state and radiative properties. Despite decades of research, a quantitative description and understanding of heterogeneous ice nucleation remains elusive. Parameterizations are either fully empirical or heavily rely on classical nucleation theory (CNT), which does not consider molecular-level properties of the ice-nucleating particles – which can alter ice nucleation rates by orders of magnitude through impacting pre-critical stages of ice nucleation. The adsorption nucleation theory (ANT) of heterogeneous droplet nucleation has the potential to remedy this fundamental limitation and provide quantitative expressions in particular for heterogeneous freezing in the deposition mode (the existence of which has even been questioned recently). In this paper we use molecular simulations to understand the mechanism of deposition freezing and compare it with pore condensation freezing and adsorption. Based on the results of our case study, we put forward the plausibility of extending the ANT framework to ice nucleation (using black carbon as a case study) based on the following findings: (i) the quasi-liquid layer at the free surface of the adsorbed droplet remains practically intact throughout the entire adsorption and freezing process; therefore, the attachment of further water vapor to the growing ice particles occurs through a disordered phase, similar to liquid water adsorption. (ii) The interaction energies that determine the input parameters of ANT (the parameters of the adsorption isotherm) are not strongly impacted by the phase state of the adsorbed phase. Thus, not only is the extension of ANT to the treatment of ice nucleation possible, but the input parameters are also potentially transferable across phase states of the nucleating phase at least for the case of the graphite/water model system.

Lattice Boltzmann model for predicting frosting process on surfaces considering wettability.

The process of frosting is a multiscale problem, which leads to challenges of proposing accurate numerical methods. In this study, a lattice Boltzmann model for predicting frost formation and growth on surfaces of various wettabilities is proposed based on the heterogeneous nucleation and dendrite growth theories. Three lattice Boltzmann equations are used to calculate the velocity, humidity, and temperature distributions. Furthermore, the heterogeneous nucleation theory and dendrite growth theory are used to construct the equations that govern ice production during the frosting process, so that the surface wettability can be considered. After experimental validation, the model was used in the analysis of frosting behaviors on plates and in microchannels with different wettabilities. The effects of the intrinsic contact angles and roughness on the frost layer properties were evaluated. This study will likely facilitate a better understanding of frosting on the mesoscopic level.

Engineering Heterogeneous Nucleation during Solidification of Multiphase Cast Alloys: An Overview

The theory of heterogeneous nucleation was initially developed as a part of condensed matter physics, and later it was used as an important engineering tool to design metallurgical processes. This success has led to wide applications of the theory in metallurgical practice. For example, engineering heterogeneous nucleation in ductile iron has been used to reduce shrinkage defects, suppress cementite formation, and modify the size and shape of microstructural constituencies. This demonstrates how theoretical knowledge could benefit industry practice. This overview aims to summarize the authors’ published studies in co-authorship with colleagues and students, which covers different aspects of engineering heterogeneous nucleation in multiphase cast alloys. Several approaches for engineering heterogeneous nucleation using thermodynamic simulation as well as practical methods for improving efficiency of nucleation using the co-precipitation technique and a local transient melt supersaturation are suggested. Automated scanning electron microscopy/energy-dispersive X-ray (SEM/EDX) analysis and high-resolution transmission electron microscopy (TEM) were used to verify the simulation predictions. Practical examples of controlling microporosity shrinkage in cast irons with spheroidal graphite are presented to illustrate the power of engineering heterogenous nucleation.

Thermodynamic Analyses of the Two-Step Method of CsPbBr3 Crystal Growth for Inorganic Perovskite Solar Cells

We conducted integrated thermodynamic analyses for the two-step method of CsPbBr3 growth. Deriving from Gibbs free energy and heterogeneous nucleation theory, a thermodynamic reaction model equation was proposed and verified, from which we could find that the grainsizes of the CsPbBr3 can be precisely controlled by the CsBr concentration. The impact of temperature of the solvent was also studied. Finally, a best cell was fabricated showing a power conversion efficiency of 4.75%, with open circuit voltage of 1.13 V, short circuit current of 6.68 mA/cm2 and fill factor of 63%. Our results will help other researchers to determine the appropriate condition of the growth of CsPbBr3 by the two-step method.

The microscopic contact morphology of ice crystal on substrate and its effect on heterogeneous nucleation/icing

As one of the long-standing crucial theoretical assumptions of the heterogeneous nucleation and substrate icing theory, the tiny shape of an ice tip on the substrate commands further detailed experimental observation. In this paper, the morphology and growth processes of ice on different near-thermal insulation surfaces at a low supercooling degree were observed by microscope. Experimental results show that the contact angles of the dendritic ice tip on the substrates are all obtuse under a lower supercooling degree, and decrease with temperature as a Sigmoid function. Moreover, the analysis of ice growth on different substrates reveals that the surface property can affect substrate icing by altering the ice tip; that is, as the ice contact angle increases, the radius will increase and the influence of the thermal conduction of substrate on the ice tip will decrease, ultimately leading to a slower growth rate. Significantly, heterogeneous nucleation experiments illustrate that the obtained ice contact angle is close to the ice nucleus contact angle. Consequently, compared with previous theories, the temperature-dependent ice contact angle could be used to accurately predict the nucleation rate and ice growth.

Heterogeneous Nucleation in Protein Crystallization.

Protein crystallization was first discovered in the nineteenth century and has been studied for nearly 200 years. Protein crystallization technology has recently been widely used in many fields, such as drug purification and protein structure analysis. The key to successful crystallization of proteins is the nucleation in the protein solution, which can be influenced by many factors, such as the precipitating agent, temperature, solution concentration, pH, etc., among which the role of the precipitating agent is extremely important. In this regard, we summarize the nucleation theory of protein crystallization, including classical nucleation theory, two-step nucleation theory, and heterogeneous nucleation theory. We focus on a variety of efficient heterogeneous nucleating agents and crystallization methods as well. The application of protein crystals in crystallography and biopharmaceutical fields is further discussed. Finally, the bottleneck of protein crystallization and the prospect of future technology development are reviewed.

Enhanced heterogeneous nucleation of Al6(Fe,Mn) compound in Al alloys by interfacial segregation of Mn on TiB2 particles surface

In this study, the composition templating theory for heterogeneous nucleation was applied to achieve TiB2 particles with Mn segregation on the surface, which supplied the initial composition for the heterogeneous nucleation. The interfacial segregation of added alloy element Mn and the other common impurities, such as Fe and Si, was investigated with scanning transmission electron microscopy (STEM). The modified TiB2 particles was applied in Al-2.0Mn-1.0Fe alloys to test its effects on grain refinement of Al6(Fe,Mn) compound. The interfaces between Al6(Fe,Mn) particles and the engulfed TiB2 particles were examined with TEM observation.

The application of an enhanced salinity-gradient solar pond with nucleation matrix in lithium extraction from Zabuye salt lake in Tibet

The utilization of salinity-gradient solar ponds (SGSPs) to extract lithium from salt lake brine is one of the most direct and effective uses of solar energy. The Qinghai-Tibet Plateau in China is rich in unique solar energy resources, as well as various types of salt lakes with abundant lithium resources. Among them, Zabuye salt lake in Tibet is a typical lithium-rich carbonate salt lake, and it has successfully realized the industrialization of lithium extraction from brine for the first time by using the SGSP. In recent years, with the continuous improvement of lithium resource market, the demand for lithium has further grown. There are some bottleneck problems restricting the lithium carbonate production in the lithium extraction technology with traditional SGSPs, which must be overcome, such as the slower heating rate, smaller heating amplitude, longer production cycle, lower crystallization efficiency and so on. From the angle of green environmental protection and high-efficiency technology, this research focused on the temperature field and salinity field distribution of the traditional SGSP and the special crystallization behavior of lithium carbonate, and carried out experimental research on process optimization in Zabuye mining area. Based on the heterogeneous nucleation theory, the use of an enhanced SGSP with a nucleation matrix for assisting the crystallization of lithium carbonate was proposed. The change of crystallization behavior of lithium carbonate, the influence of matrix materials and the spatial distribution on the crystallization effect were investigated. The results show that the enhanced SGSP with the nucleation matrix has a significant effect of increasing the production of lithium carbonate, and the lithium mixed salt attached to the nucleation matrix is of a higher grade and a lower moisture content. The yield per unit area of lithium carbonate on the nucleation matrix made of the gauze and plastic net is equivalent to that on the slope and bottom of the solar pond, and the grade of lithium carbonate approaches 80 %. The yield per unit area of lithium carbonate on the nucleation matrix made of tumbleweed is about four times as much as is achieved with other materials and the crystallization exceeds expectations. It is concluded that the application of the enhanced SGSP with the nucleation matrix can improve the crystallization efficiency, the output and the grade of lithium carbonate to a certain extent and this optimization technique will provide an important theoretical basis and application support for green, efficient development of lithium resources from salt lake brine.

Effect of plasma treatment on nucleation of Au nanoparticles

Nucleation is a basic issue in film science and technology, and it plays a vital role in the field of functional devices characterized in ultra-thin and continuous thin films. In this paper, Au clusters were deposited on three different substrates (BOPP, Si (100) and carton support film) by means of magnetron sputtering with or without air plasma pretreatment. The results show that plasma treatment conducted on BOPP substrate decreased the water contact angle significantly, indicating an enhanced surface energy of BOPP substrate. The introduction of polar groups (C–O/C–N, C=O/N–C=O and O–C=O) as well as a modified topology were responsible for the improvement of hydrophilicity. Au nanoparticles prepared on untreated substrates exhibited a non-uniform topology independent of substrate type. After plasma treatment, Au nucleation densities were increased greatly, and the nucleus sizes were much smaller. Based on the thermodynamics theory of heterogeneous nucleation, by means of plasma treatment, the substrate surface energy was enhanced and the film-substrate interfacial energy was decreased simultaneously, and both of them contributed to the higher nucleation density and smaller cluster size.

Al – Ti – B master alloys: structure formation in modified alloys

This paper provides an overview of existing grain refinement mechanisms and describes the solidification kinetics typical of alloys modified with the Al – Ti – B system. Of practical interest are intermetallic compounds of the binary Al – Ti system, the state diagram of which requires further study. It was found that, with titanium concentrations being low, the behaviour of the system is influenced by peritectic reaction leading to α-grains of aluminium forming on titanium aluminide particles (TiAl3). A unique feature of the Al – Ti system is that, compared with other alloys, it has the highest limited growth rate Q, which explains the high grain refinement performance. Microparticles of titanium diboride (TiB2) that form in the liquid state of the Al – Ti – B system act as nucleation centres for the intermediate phase of TiAl3. At the same time, TiAl3 was found to display metastable properties and it dissolves as aluminium solidifies. The classical crystallization theory defines the importance of heterogeneous substrates that help grain nucleation by lowering the threshold energy. According to the heterogeneous nucleation theory, supercooling tends to increase dramatically during grain nucleation as the discrepancy rises between the crystal lattice of the solid body and that of the substrate. In terms of constitutional supercooling, it takes lower supercooling for grain nucleation on a particle. The contributing factors include a lower rate of latent heat release and low grain growth rates. As the master alloy was introduced in the melt, the authors observed reduced modification efficiency (with the concentration >1.5 %) and dropped solubility of Ti in the presence of Si. Long soaking times would lead to the master alloy gradually lose its effect. The authors also considered how the properties of master alloys can be enhanced. Thus, they looked at breaking up TiAl3 by means of plastic deformation and deagglomerating TiB2 particles by contactless mixing.

"Anti-Condensation" Aluminum Superhydrophobic Surface by Smaller Nanostructures.

According to classical heterogeneous nucleation theory, the free energy barrier (ΔGc) of heterogeneous nucleation of vapor condensation ascends dramatically as the substrate nanostructure diameter (Rs) decreases. Based on this idea, we fabricated two types of superhydrophobic surfaces (SHSs) on an aluminum substrate by different roughening processes and the same fluorization treatment. Water vapor condensation trials by optical microscope and ESEM confirmed that on SHSs with submicron rectangle structures, a typical self-propelled motion of condensates or jumping condensation occurred. However, on SHS with coral-like micro/nano-structures, vapor nucleation occurred tardily, randomly, and sparsely, and the subsequent condensation preferentially occurred on the nuclei formed earlier, e.g., the condensation on such SHS typically followed the Matthew effect. Higher vapor-liquid nucleation energy barrier caused by smaller fluorinated nanostructures should be responsible for such a unique “anti-condensation” property. This study would be helpful in designing new SHSs and moving their application in anti-icing, anti-fogging, air humidity control, and so on.

Anti‐icing polyimide thin film with microcolumns fabricated by RIE with cooling and PCVD

Anti-icing polyimide (PI) thin films are a promising anti-icing technology for aircraft. A processing method combining reactive ion etching with cooling and plasma chemical vapour deposition is proposed to fabricate anti-icing PI thin films with microcolumns (PI-M). The anti-icing performance of PI-M was examined. The apparent contact angle (APCA) was 153° ± 1.4°, and the APCA hysteresis was 8.5° ± 0.5°. The calculated Weber number was high, and a droplet on PI-M rebounded within 2.56 s, whereas rebounding occurred more slowly on a smooth PI surface (PI-S). The freezing time of droplets on PI-M was 70% longer than that on PI-S. The average ice adhesion force on PI-M was 42% smaller than that on PI-S. Repeated measurements of the ice adhesion force on PI-M demonstrated that it was stable (deviation: ±1 N). The APCA showed that PI-M is superhydrophobic, which indicates that droplets on PI-M were in the Cassie state. The droplet bouncing behaviour was explained in terms of horizontal force equilibrium at the interface. The anti-icing mechanism of PI-M was modelled using heterogeneous nucleation theory and a contact area model. The results explained the good anti-icing performance and suggested that PI-M may have excellent potential for anti-icing applications.

Cluster activation studies with a diffusive condensation particle counter: Effect of chemical composition

We use KanomaxFMT's Fast Condensation Particle Counter (CPC) to study the growth (activation) of purified singly charged cluster ions of several salts by condensation of n-butanol vapor. Salts investigated include 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (EMI-FAP), and four tetra-alkylammonium bromides (CpH2p+1)4N+-Br-, with p = 4, 6, 7, 12. The clusters studied contained up to 20 salt molecules, which were formed via a bipolar electrospray source, and were size-selected with a differential mobility analyzer. The CPC is operated at variable condenser and fixed saturator temperatures, Tc, Ts. It uses 75% sheath gas, such that most aerosol-containing fluid streamlines are near the channel center, and experience very similar maximal saturation ratios. This results in a steep initial dependence of the activation probability on Ts for selected particles. Therefore, a well-defined activation onset temperature Ts∗ is determined as a function of cluster composition, polarity (±), and mobility diameter (dp). Notwithstanding a modest material dependence found for the inferred Tc∗(dp) curves (±0.25 nm), the steepness of the activation curves measured permits determining particle size distributions for aerosols of known composition. There is some ambiguity in the precise temperature profile in the CPC channel. Nevertheless, using our best estimate, the onset condition for all but one of the seed particles studied agrees well with predictions from classical heterogeneous nucleation theory (Fletcher, 1962) when the pre-exponential term K in the nucleation rate is chosen appropriately. This enables the incorporation of materials properties into the sizing process in terms of only this single parameter K. This finding also provides a method to determine K experimentally, suggesting that the material dependence of the activation probability is due to the different interaction potentials between the clusters and the vapor. Tetraheptylammonium bromide is peculiar in that its cluster anions fit classical theory very much as all other materials studied, but its cluster cations do not.