Surface area controlled heterogeneous nucleationBrian Steer, Boris Gorbunov, Jonathan Rowles, and David Green Citation: J. Chem. Phys. 136, 054704 (2012); doi: 10.1063/1.3681400 View online: http://dx.doi.org/10.1063/1.3681400 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v136/i5 Published by the American Institute of Physics. Related ArticlesImpacts of aerosols on available solar energy at Mbour, Senegal J. Renewable Sustainable Energy 4, 013105 (2012) Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensionalnumerical simulations J. Appl. Phys. 111, 014911 (2012) Sound absorption characteristics of aluminum foam with spherical cells J. Appl. Phys. 110, 113525 (2011) Quantification of impact energy dissipation capacity in metallic thin-walled hollow sphere foams using high speedphotography J. Appl. Phys. 110, 083516 (2011) Laser-supported ionization wave in under-dense gases and foams Phys. Plasmas 18, 103114 (2011) Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

THE JOURNAL OF CHEMICAL PHYSICS 136, 054704 (2012)

Surface area controlled heterogeneous nucleationBrian Steer,1,2 Boris Gorbunov,2,a) Jonathan Rowles,2 and David Green2

1University of Kent at Canterbury, Canterbury, United Kingdom2Naneum Limited, Canterbury Innovation Centre, University of Kent, Canterbury, United Kingdom

(Received 21 October 2011; accepted 13 January 2012; published online 6 February 2012)

Heterogeneous nucleation of liquid from a gas phase on nanoparticles has been studied under var-ious saturation ratios and nuclei size. The probability of liquid droplet nucleation, especially at alow degree of deviation from equilibrium, was measured for both atmospheric aerosol particles andengineered nanoparticles Cr2O3. The concept of a critical saturation ratio and the validity of theone-to-one relationship between the nuclei number and the number of droplets were examined. Atransient zone between no nucleation and established nucleation termed the surface area controllednucleation was observed. In this zone, the probability of stable phase formation is determined by thesurface area of nuclei. There are two distinctive features of the surface area controlled nucleation: thenucleation probability is much less than 1 and is proportional to the surface area of nuclei. For con-densation particle counters (CPCs) counting nanoparticles, these features mean that counts measuredare proportional to the surface area of nanoparticles and, therefore, the CPCs counts can be calibratedto measure the surface area. © 2012 American Institute of Physics. [doi:10.1063/1.3681400]

INTRODUCTION

Homogeneous and heterogeneous nucleation1, 2 are non-equilibrium processes of a stable phase formation from ametastable phase. Heterogeneous nucleation, where a stablephase is formed in contact with a foreign material, is morecommon.2 Heterogeneous nucleation of water in the atmo-sphere, such as ice,3 fog, snow and rain formation,4 as well asthe formation of secondary atmospheric aerosols5 and min-erals in the Earth’s crust due to solidification6 are examplesof heterogeneous nucleation. The foreign material stimulat-ing heterogeneous nucleation could be a cluster of ions7 ormolecules8 or (more often in nature and practical applica-tions) a surface of a solid particle.2–4 The deviation from equi-librium is crucial for the compensation of the work necessaryto form an embryo of the stable growing phase.2, 3, 9 The for-eign material reduces the work and increases the probabilityof nucleation. This explains why heterogeneous nucleation ismore common than homogeneous nucleation. The probabilityof nucleation is determined by the deviation of the metastablephase from the equilibrium state. For example; the nucle-ation of a liquid phase from gas is controlled by the ratio ofthe partial vapour pressure of the nucleating material p to itsequilibrium pressure pe and is known as the saturation ratio(S = p/pe).1–3 The saturation ratio, or similarly the supersat-uration (S − 1), are measures of the degree of deviation fromthe equilibrium condition (p = pe).

In addition to many atmospheric and geologicalprocesses, heterogeneous nucleation plays an importantrole in microelectronics,10, 11 occupational hygiene,12

nanotechnology,12, 13 metallurgy, etc. Heterogeneous nucle-ation is the basis for counting the number of nanoparticles

a)Author to whom correspondence should be addressed. Electronic mail:boris.gorbunov@naneum.com.

and other objects in the gas phase and it is widely employedin condensation particle counters (CPCs).14

CPCs based upon heterogeneous nucleation enable thenumber and the size (with a differential mobility technique)of nanoparticles10 to be measured. Another important char-acteristic of nanoparticles is the surface area that has to bemeasured because many nano-objects are not spherical andthe spherical approximation is far from reality.13 There isa vast body of experimental data showing that the surfaceis key to the toxicity of insoluble nanoparticles.14 The sur-face is an important characteristic for catalytic nano-powdersand any non-spherical nanoparticles such as agglomerates,nano-wires, carbon nano-tubes, and aggregates. The surfaceplays an important role in various physical-chemical pro-cesses where nano-objects are involved.

In a CPC under non-equilibrium conditions, a nanoparti-cle (a nucleus) produces a single micro-droplet of about 1 μmfrom a supersaturated gas. These micro-droplets are readilycounted by a laser optical counter.14 Normally every nanopar-ticle with a size greater than dpmin produces one droplet to becounted. The deviation of the supersaturated gas from equi-librium is chosen experimentally to achieve a state where aone-to-one relationship exists between the number ofnanoparticles and the number of droplets formed from thesupersaturated gas.14–16 For example, for nanoparticles withdpmin = 10 nm, the probability of heterogeneous nucleationP(dp), sometimes referred to as counting efficiency, is closeto 1 if dp > dpmin. However, for smaller particles with dp

< dpmin the probability of heterogeneous nucleation falls offsignificantly as the size of the particle is decreased. This be-haviour of the nucleation probability (P(dp) ∼ 1) is the basisfor nanoparticle counting. Many instruments for nanoparticlecounting and size measuring10 have been developed using thisconcept. These are essential tools widely used in atmosphericscience, nanotechnology,7 environmental science,12 aerosolscience,11 occupational health,6 etc.

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054704-2 Steer et al. J. Chem. Phys. 136, 054704 (2012)

It is generally accepted that for heterogeneous nucleationif the saturation ratio is greater than a certain critical valueS*, then every nanoparticle of sufficient size3, 9 greater thandpmin produces a stable phase formation (e.g., droplet or acrystal).3, 4 These are the two conditions of heterogeneous nu-cleation on nano-objects: the deviation from equilibrium andthe object size (S > S* and dp > dpmin). Under these con-ditions, a one-to-one relationship exists between the numberof nuclei and the number of stable phase pieces (droplets)formed. Thus, the heterogeneous nucleation either exists andthe new phase is formed or it does not and the new phasecannot be formed. This is the foundation for the concept of acritical saturation ratio.17

This concept came from experimental observations andtheoretical consideration of homogeneous nucleation of liq-uid from gas. Here, a stable phase formation can be achieved(e.g., droplets growth) without the need for seed nuclei of an-other material. Homogeneous nucleation is largely an all-or-nothing process: the formation of the new phase occurs withina narrow window of supersaturation, and a critical value S*can be associated with the onset of nucleation.15 The criticalsaturation ratio is influenced by the physical properties of thephases, the temperature of the system, and the interfacial sur-face between vapor and liquid.

The validity of this concept for heterogeneous nucleationhas not been fully understood. Here we study the effects ofthe nanoparticle size and the saturation ratio on the probabil-ity of new phase formation, with special attention to smalldeviations from the equilibrium state. The aim of this paperis to examine the validity of the one-to-one relationship forgas-to-liquid nucleation on both atmospheric aerosol particlesand engineered nanoparticles Cr2O3 in the range of supersat-uration between the well-developed heterogeneous nucleationand no-nucleation conditions.

EXPERIMENTAL

The experimental setup consists of a nanoparticle aerosolgenerator, a particle charger, a size fractioning device, asteady-state flow condensation chamber, and an optical parti-cle counter (Fig. 1). A commercial Cr2O3 nanoparticle gen-erator NG100 (PMS Inc.) was used to produce engineerednanoparticles in the size range from 20 nm to 100 nm at a flowrate 0.3 l/min and the aerosol particle number concentrationfrom 105 to 107 cm−3. In addition, atmospheric aerosols wereused for comparison. Test aerosols can be switched by a three-way valve. Initially generated polydisperse nanoparticles andatmospheric aerosols were positively charged with a unipo-lar Corona charger C2000 (PMS Inc.). Then, they were frac-tionated down to monodisperse particles of chosen sizes witha standard geometric deviation σ g = 1.04 (Ref. 16) using adifferential mobility analyser (PMC500 by PMS Inc.). Theseparticles were then used as nuclei for heterogeneous nucle-ation of dimethyl benzene-1,2-dicarboxylate (DBD) vapourin a flow nucleation chamber combined with a laser opticalcounter16, 18 (R-Net, PMS Inc.). DBD of high-performanceliquid chromatography grade was supplied by Sigma Aldrich.

The nucleation chamber contains a condenser and a sat-urator (Fig. 1). The condenser was made of a 150 mm long

FIG. 1. Schematic of the experimental setup. DMA is differential mobilityanalyser. AF is an aerosol filter STERAPORE (Mitsubishi). MFM is a massflow meter (Honeywell). OPC is an optical particle counter.

stainless steel tube, with a 6.7 mm ID. The temperature ofthe condenser was control by a fan (not shown). Porous sil-ica (pore diameter 2.5 μm) soaked with DBD was heated inthe saturator by an electrical heater (not shown). The cham-ber was equipped with two inlets: one for aerosol samplesand another for clean air. The flow rate of the sample aerosolwas calculated as a difference between the total flow rate(0.3 l/min) and the flow rate of the clean filtered air measuredwith a mass flow meter. The aerosol flow rate was 15% of thetotal flow. The proportion of the aerosol sample was set by avalve. The two-inlet system enables all aerosol particles to bein the centre of the saturated flow and, therefore, all particleswere exposed to the same supersaturation. The sizing accu-racy of the DMA was 3%. The uncertainties of the concentra-tion measurements were within 20%. The temperature of theambient air and the saturator was measured with thermistorswith an accuracy of ±0.2 ◦C.

The deviation from equilibrium (supersaturation ofDBD) was controlled by varying the temperature of the sat-urator of the nucleation chamber. The number of monodis-perse nanoparticles was measured with a CPC (from Grimm).The probability of heterogeneous nucleation was calculatedas the ratio of the counts measured with the flow nucleationchamber to the number of nanoparticles measured with theGrimm CPC. The supersaturation was calculated using the fi-nite element Multi-Physics software COMSOL. The physicalproperties of DBD were taken from a reference source.19

RESULTS OBTAINED

The supersaturation field in the condenser of the nucle-ation chamber was calculated using COMSOL software. Cou-pled steady-state Navie-Stokes, heat transfer, and diffusionequations were solved for the geometry of the condenser. Amulti-stage approach to avoid the need for stabilisation of thenonlinear Navie-Stokes equation was adopted. The supersat-uration field in the height-radius (z, r) co-ordinate had a dis-tinctive wing shape (Figure 2). The maximum of S (68.7) wasin the centre of the flow (r = 0) at z = 90 mm. At this height,supersaturation decreases towards the edges of the condenser(Figure 3). The airflow trajectories in the condenser have beencalculated (Figure 4). The condenser is cylindrical and the ra-dial position from the centre is shown in millimetres along

054704-3 Surface nucleation J. Chem. Phys. 136, 054704 (2012)

FIG. 2. Saturation ratio field in the axial symmetry condenser of radius3.35 mm and 0.150 m height. Atmospheric pressure – 101 325 Pa; Radiusof aerosol inlet – 1.35 mm. Temperature of the ambient air – 20 ◦C; Temper-ature of the saturator – 100 ◦C. The colour coding saturation ratio varies from1 (dark blue) to 68.7 (dark red). The white peninsulla at the bottom of the plotbetween 1.35 mm and 1.7 mm is the top of the aerosol inlet separating theaerosol flow and the flow of the working fluid.

the abscissa. Nuclei are exposed to a relatively narrow rangeof S because they enter the condenser in the central part of theflow in a separate inlet (0 < r < 1.5 mm). The rest of the inletflow (2 < r < 3.5mm) is made up of clean air supersaturatedwith DBD. It was assumed that nuclei follow the air trajec-tories. Inertial forces for particles below 200 nm are weak.It can be seen that the air flow trajectories move close to thecentre. Therefore, nuclei that initially enter the central partof the condenser move close to the centre along the height ofthe condenser. Finally when the flow is established, nuclei oc-cupy the central part of the flow from 0 to 0.6 mm (Figure 4).

FIG. 3. Saturation ratio (S = c/ceq) profile across the flow at the saturationratio maximum (the radius on x axis is in arbitrary units) for the conditionsof Figure 2. Here, c/ceq is the saturation ratio S.

FIG. 4. Air flow trajectory calculated for the conditions of Figure 2.

Thus, the nuclei are exposed to a narrow range of saturationratios. The saturation ratio at the point S(r,z) = S(0.6 mm,90 mm) = 66.7. This gives the uncertainty in the maximumsaturation ratio that particles are exposed to be about 3%;(68.7 − 66.7)/68.7 = 0.029. There may be other uncertaintiesin the calculation of the saturation ratio; however, we assumethat they affect mainly the value of S but not significantly theshape of the function.

Heterogeneous nucleation probability was measured ac-cording to the schematic shown in Figure 1 at various S calcu-lated with COMSOL. First, DBD nucleation probability wasrecorded at a higher deviation from equilibrium (S = 68.7). Atthis saturation ratio, the behaviour of the nucleation probabil-ity was identical to the common perception of heterogeneousnucleation, see the curve marked with triangles in Figure 5.For particles with 20 nm < dp < 450 nm, P(dp) is close to1. Decreasing particle size for particles dp < 10 nm leads toa steep drop in the probability. The 50% probability that cor-responds to dpmin was 10 nm. This was an example of all-or-nothing nucleation where a one-to-one relationship enablesthe number of nanoparticles to be evaluated from the numberof droplets formed in the nucleation chamber for particles ofsizes greater than dpmin.

In the second set of experiments, P(dp) was measured atlower deviations from equilibrium (S = 44.0). At this lowersaturation ratio, the relationship between the particle size andnucleation probability was found to be different. This canbe seen for atmospheric aerosol as shown by the squares inFig. 5. When S = 44.0, the probability P(dp) was not equalto 1 as it was at S = 68.7 but P(dp) � 1. The most impor-tant observation is that it steadily grows with the size of at-mospheric nanoparticles. The linearity of the P(dp) functionwith double logarithmic co-ordinates reveals a slope close to2. For example, for Cr2O3, P(22.5 nm) = 0.020 and P(101 nm)= 0.370. These data points show a slope of 1.94 (asolid line marked by circles and diamonds). Thus, in thisregime of lower supersaturation, the nucleation probability is

054704-4 Steer et al. J. Chem. Phys. 136, 054704 (2012)

FIG. 5. The probability of heterogeneous nucleation P(dp) vs. aerosol parti-cle size dp for DBD on atmospheric aerosol in the common regime (fully de-veloped heterogeneous nucleation where the saturation ratio is 68.7) is shownwith triangles and dashed line. The probability of heterogeneous nucleationof DBD vs. dp is shown for Cr2O3 (circles and diamonds) and atmosphericaerosol (squares) under the conditions corresponding to the surface controlledregime at a saturation ratio equal to 44.0.

proportional to the surface area of the nanoparticle nucleiP(dp) ∼ dp

2. The circles and diamonds correspond to the sameaerosol but different experimental runs: increasing sizes (cir-cles) and decreasing sizes (diamonds).

It is important to notice that the P(dp) functions foundfor the atmospheric aerosol and for Cr2O3 are different(Figure 5). At every size, P(dp) for atmospheric aerosol isabout ten times smaller than P(dp) for Cr2O3. This showsthe effect of surface properties on heterogeneous nucleationat smaller deviations from equilibrium.

This phenomenon is not fully understood. It can be spec-ulated that for the surface area controlled nucleation, the crit-ical embryo radius is much smaller than the radius of the nu-clei. Therefore, the change of the size of nuclei does not in-fluence the free energy of embryo formation. This means thatthe nucleation rate per unit surface area should not depend onthe nuclei size. The probability of droplet formation in thiscase can be influenced only by the surface area of nuclei. Thisassumption helps to explain the results observed.

This relationship between dp and the nucleation proba-bility indicates that new phase formation is proportional tothe surface area of nanoparticles. To distinguish this fromthe common developed heterogeneous nucleation, we referto it as the surface area controlled nucleation. Surface areacontrolled nucleation, which occurs at lower deviations fromequilibrium, takes place over a narrower range of conditionsthan developed heterogeneous nucleation (see Figure 6). Thedeviation of a system from equilibrium is greater for homoge-neous nucleation – zone A. Here a droplet is formed withoutseed nuclei. When the deviation (e.g., supersaturation for gasmedia or supercooling for liquid media) is decreased, hetero-geneous nucleation takes over with a well-developed nucle-ation (corresponding to a one-to-one relationship in CPCs) –zone B. With a further decrease in deviation from equilibrium,the surface area controlled nucleation appears – zone C. Fur-

FIG. 6. Schematic of nucleation zones at various deviations fromequilibrium.

ther reduction in the deviation stops nucleation completely –zone D.

For example, if we characterise deviation from equilib-rium by the saturation ratio, then for DBD heterogeneous nu-cleation on Cr2O3 nanoparticles the homogeneous nucleation(zone A in Figure 2) occurs at S > 75. The developed het-erogeneous nucleation with a one-to-one relationship betweenthe number of nuclei and the droplets (zone B) takes place inthe range of saturation ratios: 46 < S < 75. The surface con-trolled heterogeneous nucleation (zone C) exists in a narrowrange: 41 < S < 46. If the saturation ratio is lower, S < 41,then the nucleation probability is equal to 0 or too low to bemeasured. This corresponds to zone D. The width of the sur-face controlled zone is only 5 points in the saturation ratiofrom 41 to 46 (11%) but the common heterogeneous nucle-ation zone spreads over 29 points from 46 to 75 (39%). Thismight explain why this type of nucleation was not reportedearlier.

The range of conditions for the surface area controllednucleation is much narrower than the range of conditions forthe fully developed heterogeneous nucleation but this doesnot lessen the importance of this phenomenon. In nature andin industry, nucleation normally starts when the system en-ters the first nucleation zone C from the no-nucleation zone D(Figure 6) due to an increasing deviation from equilibrium. Inthis path, the system inevitably spends some time in zone C.In this zone, the number of first created formations of the newphase will be small and proportional to the surface area ofthe nuclei. It is well known in nucleation that the first creatednew phase formations affect the deviation from equilibriumdue to depletion of the metastable phase and, therefore, thewhole phase transition process.3, 4 In solidification, it will af-fect the properties of the minerals or metals (in the case ofmetallurgy); in atmospheric physics, it will influence the pre-cipitation pattern. It is worth considering the importance ofthe surface area controlled nucleation on nucleation in vari-ous systems.

In practice, to find the surface controlled zone one has togradually increase or reduce the deviation from equilibrium.Inevitably at some point, the surface area controlled nucle-ation will be found. For example, for counting particles in acondensation particle counter the surface controlled zone (C)exists at a lower S than the saturation ratio required for parti-cle counting (B), see Figure 6.

In nature, the deviation from equilibrium is normallychangeable; for example, in the atmosphere due to coolingof the air mass or in the case of solidification during cooling

054704-5 Surface nucleation J. Chem. Phys. 136, 054704 (2012)

of lava. Inevitably any system is going to get into the zone ofthe surface area controlled nucleation C from zone D. Surfacearea controlled nucleation appears first before the fully devel-oped heterogeneous nucleation starts. Therefore, the surfacearea controlled nucleation is likely to be a wide spread phe-nomenon that can be identified as different sort of heteroge-neous phase transitions of the first kind.

One important and practical use of nucleation is theheterogeneous nucleation of liquids from gas on airbornenanoparticles and other nano-objects. In the surface area con-trolled nucleation zone, the number of droplets formed onnanoparticles can be used as a measure of the surface areaof nanoparticles. For CPCs, this means that counts measuredare proportional to the surface area of particles and, therefore,the CPCs counts can be calibrated to evaluate the surface.

The calibration coefficient k was determined from thedata obtained for Cr2O3 nanoparticles. For the conditions ofFigure 2 with a suitably lowered supersaturation, the coeffi-cient was found to be 0.063 (k = 0.063 μm2). The surfacearea of nanoparticles Snp then can be found from the num-ber of counts measured in the surface controlled mode NSCM

according to: Snp = kNSCM. This provides a method for evalu-ation of the surface area of nanoparticles. This method shouldbe applicable to other nano-objects such as carbon nanotubes,nano-wires, and fractal aggregates.

CONCLUSIONS

Surface area controlled nucleation has been observed inexperiments with gas to liquid heterogeneous nucleation. Un-der the conditions where this type of nucleation occurs, theprobability of stable phase formation is determined by the sur-face area of nuclei. For a plurality of substrates, e.g., nanopar-ticles in the air, the number of droplets is proportional to thetotal surface area of nanoparticles.

In the surface area controlled nucleation zone, the proba-bility of nucleation is smaller than 1: P < 1 and P(dp) ∼ dp

2.These are two distinctive features of surface area controllednucleation and have been demonstrated to hold true for at-mospheric aerosols as well as for some engineered nanopar-ticles. For CPCs counting nanoparticles these features meanthat counts measured are proportional to the surface area ofparticles and, therefore, the CPCs counts can be calibrated to

measure the surface area. This can be applied in various in-dustries. It also can help in understanding the heterogeneousphase transitions in nature, especially at low deviations fromequilibrium.

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