Two-Dimensional Crystal Growth from Undersaturated Solutions
Anne E. Murdaugh,† Mary Liddelow,‡ Anneliese M. Schmidt,§ and Srinivas Manne*,†
Department of Physics and Department of Materials Science & Engineering, UniVersity of Arizona,Tucson, Arizona 85721
ReceiVed December 7, 2006. In Final Form: March 21, 2007
The solubility of a substance is commonly understood as the minimum concentration necessary for the condensationof a solid phase from solution. Here we report the nucleation and growth of ionic compounds from aqueous concentrationson the order of 0.1 times the solubility. The condensation is catalyzed by a foreign substrate, and the new phase growsas a crystalline monolayer. Undersaturated growth is observed only in cases where the dissolved compound is isomorphicwith the substrate and the interaction strength between a dissolved-ion/substrate-ion pair exceeds that between thetwo dissolved ions. These results are consistent with a simple model in which favorable ion-surface interactions leadto ion enrichment and supersaturation in the two-dimensional interfacial zone.
A solid cluster nucleating from a metastable solution mustovercome a kinetic barrier arising from its unfavorable interfacialenergy, and the size of this barrier determines the degree ofsupersaturation required for condensation to occur within anexperimental time frame. If the solution is already in contactwith a crystal of the solute material, then the energy barrier iseliminated and any solute in excess of solubility begins tocondense immediately onto the crystal surface. A solution incontact with aforeign substrate is usually considered to be anintermediate system in which the interfacial energy barrier isreduced but not eliminated. Here,some supersaturation iscommonly considered to be a requirement for epitaxial growth,with the amount depending on the chemical and physicalcompatibility between the substrate and solute. This model hasbeen challenged by recent reports1,2of semiconductor films grownfrom undersaturatedsolutions on certain foreign substrates (Geon Si and Al0.8Ga0.2As on GaAs). These observations have sofar been indirect (via calorimetry) and limited to semiconductorfilms in metallic solvents at concentrations near (>0.8×) thesolubility. The results have been interpreted in terms of a globalreduction of interfacial energy,1 but the molecular-level drivingforces and the 2D growth mechanisms are not well understood.
Although semiconductor heterostructures drive the techno-logical interest in epitaxy, ionic crystals offer a scientificallyaccessible model system because they possess a wider varietyof well-known lattice structures and spacings and their aqueoussolution chemistry can be visualized at room temperature byatomic force microscopy (AFM).3-16 The adsorption of metal
ions on mineral lattices also plays an important role in geochemicalweathering models17,18 and can lead to new strategies forfreshwater remediation.19 Whereas previous AFM studies ofepitaxial growth have usually focused on individual overgrowth/substrate systems in supersaturated solutions, here we haveinvestigated a wide variety of systems in undersaturated solutions(Table 1) in an effort to find the general conditions for filmgrowth in subcritical environments. The substrates used wereperfectly cleavable, sparingly soluble minerals that resulted inwell-defined terrace-step structures on which growth could bemonitored on imaging time scales. The most reproducible resultswere obtained on celestite (SrSO4), barite (BaSO4), and calcite(CaCO3) substrates, although some experiments were alsoperformed on other carbonates and sulfates.20The aqueous solutecompounds were chosen across a range of parameters (e.g., latticesymmetry, spacing, and ion size) related to solute-substratecompatibility. Solutions of these sparingly soluble salts wereprepared by mixing aliquots of soluble salt solutions (chlorideor nitrate salts of the cation and sodium salts of the anion). Thedeparture from solubility was calculated using the parameterâ≡ [C][A]/ Ksp, with [C] and [A] being the molar cation and anionconcentrations, respectively, andKspbeing the known solubilityproduct. Carbonate solutions were handled differently becauseof the strong pH dependence of [CO3
2-], as described earlier;4
briefly, aliquots of the cation solutions were mixed with thoseof NaHCO3, the pH was adjusted using NaOH (usually in thepH range of 8.4 to 8.8), andâ was calculated using the
* Corresponding author. E-mail: [email protected].† Department of Physics.‡ Department of Materials Science & Engineering.§ Now at Antares Group, Inc., Landover, MD 20785.(1) Hansson, P. O.; Albrecht, M.; Dorsch, W.; Strunk, H. P.; Bauser, E.Phys.
ReV. Lett. 1994, 73, 444.(2) Jeganathan, K.; Qhalid Fareed, R. S.; Baskar, K.; Ramasamy, P.; Kumar,
J. J. Cryst. Growth2000, 212, 29.(3) Hillner, P. E.; Gratz, A. J.; Manne, S.; Hansma, P. K.Geology1992, 20,
359.(4) Hay, M. B.; Workman, R. K.; Manne, S.Langmuir2003, 19, 3727.(5) Dove, P. M.; Hochella, M. F.Geochim. Cosmochim. Acta1993, 57, 705.(6) Teng, H. H.; Dove, P. M.; Orme, C. A.; De Yoreo, J. J.Science1998, 282,
724.(7) Davis, K. J.; Dove, P. M.; De Yoreo, J. J.Science2000, 290, 1134.(8) Hoffmann, U.; Stipp, S. L. S.Geochim. Cosmochim. Acta2001, 65, 4131.(9) Liang, Y.; Baer, D. R.Surf. Sci.1997, 373, 275.(10) Lea, A. S.; Hurt, T. T.; El-Azab, A.; Amonette, J. E.; Baer, D. R.Surf.
Sci.2003, 524, 63.(11) Jun, Y. S.; Kendall, T. A.; Martin, S. T.; Friend, C. M.; Vlassak, J. J.
EnViron. Sci. Technol.2005, 39, 1239.
(12) Astilleros, J. M.; Pina, C. M.; Ferna´ndez-Dı´az, L.; Putnis, A.Geochim.Cosmochim. Acta2000, 64, 2965.
(13) Sanchez-Pastor, N.; Pina, C. M.; Astilleros, J. M.; Ferna´ndez-Dı´az, L.;Putnis, A.Surf. Sci.2005, 581, 225.
(14) Shtukenberg, A. G.; Astilleros, J. M.; Putnis, A.Surf. Sci.2005, 590, 212.(15) Pina, C. M.; Becker, U.; Risthaus, P.; Bosbach, D.; Putnis, A.Nature
1998, 395, 483.(16) Becker, U.; Gasharova, B.Phys. Chem. Miner.2001, 28, 545.(17) Krauskopf, K. B.Geochim. Cosmochim. Acta1956, 10, 1.(18) Brown, G. E.; Parks, G. A.Int. Geol. ReV. 2001, 43, 963.(19) Sturchio, N. C.; Antonio, M. R.; Soderholm, L.; Sutton, S. R.; Brannon,
J. C.Science1998, 281, 971.(20) Only clear and colorless natural crystals were chosen for experiments.
Crystals were cleaved using a sharp blade and a hammer and then glued to thesample puck and imaged in water within 1 h ofcleaving. (The water used in theseexperiments was distilled and deionized with a minimum resistivity of 17.8 MΩcm. All ionic salts were used as received from Sigma-Aldrich and had a minimumpurity of 99%.) Only surfaces showing broad terraces (>500 nm) and faceted,monomolecular steps were used for growth experiments. All AFM images werecaptured in static solutions at room temperature by a Digital Instruments AFM(Nanoscope III or Dimension 3000) using cantilever spring constants of∼0.6N/m, imaging forces of∼1-10 nN, and scan rates of 5-20 Hz at a scan angleof 90°. All images shown are unfiltered except for slope removal along each scanline.
corresponding value of [CO32-] for a solution equilibrated withthe atmosphere21 (Supporting Information). Each substratetypically was first imaged in water to check for normal dissolutionbehavior before exchanging the fluid cell volume (>10×) withthe foreign solution. Concentration effects were explored byexchanging dilute solutions with progressively higher concentra-tions, up to and including supersaturated solutions (â > 1). Eachsubstrate compound was also imaged in solutions of thesamecompound to confirm that homoepitaxial crystal growth begannearâ ) 1 as expected. The growth results for foreign overlayersare summarized in Table 1.
For most substrate/solute combinations, the condensation ofa solute film occurred only in supersaturated solutions, if at all.However, for two cases, SrSO4 on BaSO4 (Figure 1) and PbSO4on BaSO4 (Figure 2), film growth was observed at concentrationsfar below the solubility.22 Both systems showed wetting growthat very low threshold concentrations (â ) 0.03 for SrSO4 andâ ) 0.06 for PbSO4), beginning at steps on the BaSO4 substrate.The speed of the growing step increased with concentration,with the PbSO4 growth exhibiting much faster step speeds thanthe SrSO4.23At higher concentrations, step flow was accompaniedby the nucleation and spread of islands on substrate terraces,
beginning atâ ) 0.2 for PbSO4 solutions (still undersaturated)andâ ≈ 2 for SrSO4 solutions. For both compounds, step flowand/or island spread continued until the substrate was coveredby a single molecular layer. This 2D overgrowth was perfectlyautophobic, never advancing over a lower terrace of the samematerial and never nucleating a second layer in undersaturatedsolutions (Figures 1C and 2C). Atomic scans (not shown) revealedno statistically significant differences between the film andsubstrate lattices. After the 2D film was complete, additionallayers could be grown only at high supersaturations (â > ∼30),in agreement with previous work.13
We now consider how a solute film can grow over aforeignsubstrate (where it must overcome lattice strain) under conditionswhere the solute fails to grow over itsowncrystal lattice. Twotrends are noteworthy here (Table 1). First, undersaturated growthis never observed unless the substrate and solute are isomorphic.Second, among isomorphic cases, undersaturated growth isobserved only in cases where the association of an aqueous ionand its substrate counterion is more favorable than that betweenthe two aqueous species themselves. For instance, in the case ofthe SrSO4 solute on the BaSO4 substrate, the dissociation freeenergy of the aqueous SO4
2- species and the substrate Ba2+
species (9.43× 10-20J) exceeds that of the two dissolved species(6.12× 10-20 J). These trends are also broadly consistent withprevious semiconductor results (Table 1). In the undersaturatedgrowth of Ge on Si, for example, the solute lattice is alsoisomorphic with the substrate, and the Ge-Si bond strength(5.00× 10-19 J) exceeds that of Ge-Ge (4.54× 10-19 J).
(21) Stumm, W.; Morgan, J. J.Aquatic Chemistry: An Introduction EmphasizingChemical Equilibria in Natural Waters; John Wiley & Sons: New York, 1981.
(22) These observations survived several control experiments. Each case ofundersaturated growth was repeated over at least four independent experimentsusing different substrates, cantilevers, and stock solutions. Simultaneous lateralforce microscopy (shown in Figures 1D and 2D) confirmed that the growing filmswere chemically distinct from the substrate. Conversely, we also confirmed thatthe correspondinghomoepitaxial systems, namely, SrSO4 on SrSO4 and BaSO4on BaSO4, showedno film growth in undersaturated solutions. We minimizedtip scanning effects on the growing film by using low imaging forces, and wealso confirmed the similarity in images between scanned and previously unscannedareas.
(23) For a given sample and step orientation, measured step speeds rangedfrom ∼0.3 nm/s atâ ) 0.06 to∼0.8 nm/s atâ ) 0.2 for PbSO4 and from∼0.02nm/s atâ ) 0.03 to∼0.1 nm/s atâ ) 1.9 for SrSO4. Step speeds varied somewhatbetween samples and depended strongly on step orientation.
Table 1. Summary of Ionic Crystal Growth Resultsa
substrate solute (∆Gi-s - ∆Gi-i)/kTundersaturated
growth?description of
observed growth
AnisomorphicCaCO3 BaCO3 -0.26 no 3D growth at steps atâ ) 950
CaC2O4‚H2O -0.37 no wetting growth atâ ) 2.9CaF2 +0.46 no no growth up toâ ) 3.1CaMoO4 +1.47 no no growth up toâ ) 6800CaSO4‚2H2O +9.14 no wetting growth atâ ) 15CaWO4 +0.95 no no growth up toâ ) 14 000SrCO3 -1.79 no wetting growth atâ ) 7.9
SrSO4 CaSO4‚2H2O +4.51 no no growth up toâ ) 320SrC2O4‚H2O -0.77 no no growth up toâ ) 2.4
BaSO4 BaMoO4 +5.79 no no growth up toâ ) 110BaC2O4‚H2O +5.36 no no growth up toâ ) 63BaCO3 +3.17 no no growth up toâ ) 12
IsomorphicCaCO3 CdCO3 -8.12 no wetting growth atâ ) 5.4
MnCO3 -5.01 no wetting growth atâ ) 380SrSO4 BaSO4 -8.07 no 3d growth at steps atâ ) 93
Si Ge (+12.2)b yes film growth at∼80% of solubilityGaAs Al0.8Ga0.2As (+14.6)b,c yes film growth at slightly
undersaturated conditions
a Results are divided into the anisomorphic and isomorphic cases.∆Gi-i is the dissociation free energy of the two solute ions, and∆Gi-s is thedissociation free energy of the common ion (ion common to substrate and solute) and its complimentary substrate ion.∆G values are determinedfrom ∆G ) -ln Ksp, whereKsp values are taken from ref 27. (The compound forms were assumed to be those most favorable to form under aqueousconditions.) For the observed cases of undersaturated growth, the soluteKsp values were also checked against primary references.37,38 Note thatanisomorphic systems never exhibit undersaturated growth, and isomorphic systems exhibit undersaturated growth only when∆Gi-s > ∆Gi-i. b Forthese cases, because theKsp values are not known in the particular liquid metal solvents used in the experiments, bond strengths in vacuum (alsofrom ref 27) were used for comparison. When corrected for the presence of the solvent, the dissociation free energy values will decrease.c For thiscase, the average bond strengths were determined by weighting the interactions according to the reported stoichiometry.2 (See Supporting Information.)
Letters Langmuir, Vol. 23, No. 11, 20075853
We propose that a strong interaction between a substrate speciesand a solubilized species creates a surface excess of the latter,leading to a local supersaturation that drives 2D condensation(Figure 3). This model is consistent with several observations.First, previous experiments have shown that conventional crystalgrowth (e.g., SrSO4 on SrSO4)24 occurs by step flow at lowsupersaturations, followed by island nucleation at higher super-saturations. This is exactly the growth progression observed herefor the epitaxial films (at much lower bulk concentrations),suggesting that theinterfacial solution layer is similarlysupersaturated in both cases. Second, the observed autophobicityof the growing film is consistent with the comparatively weakattraction between solute ions and their own solid phase, leadingto a smaller adsorption density over the film region. Thus, whereasa supercritical 2D solution above the substrate “feeds” the initialmonolayer film, the 2D solution above the growing film remainssubcritical, preventing the nucleation of further layers (compareleft vs right halves of Figure 3B). Third, lateral force microscopy(LFM, Figures 1D and 2D) shows that the imaging tip experiencessignificantly lower friction over the growing film, which isconsistent with the expected lower concentrations and weakerbinding of adsorbed ions on top of the film region. The frictioncontrast is especially revealing here because in previous epitaxialsystems requiringsupersaturatedsolutions4 the overgrowth hasalways exhibitedhigherfriction than the substrate (an observationthen attributed to strain-induced defects in the overlayer).
The above model is also consistent with two separate controlexperiments. Whereas SrSO4 solutions on the BaSO4 substrateshowed undersaturated growth atâ ) 0.03, the reverse system(BaSO4 solution on a SrSO4 substrate, Figure 4) showed nogrowth at all until high supersaturation (â ) 93). Here, thecommon anion (SO42-) has alessfavorable interaction with thesubstrate counterion (Sr2+) than with the dissolved counterion(Ba2+), so no interfacial enrichment is expected. Moreover, whena BaSO4 substrate with pregrown SrSO4 islands was exposed toPbSO4 solution (result not shown), undersaturated growth of aPbSO4 monolayer was observedonlyover the substrate (BaSO4)region, where interfacial enrichment is expected, and not overthe SrSO4 islands.
Rough estimates of ion concentrations lend additional supportto the interfacial enrichment model. Assuming Boltzmannstatistics, the surface concentration of an adsorbed ion is inverselyproportional to its desorption probability e-∆G/kT, where∆G isthe free energy cost of desorption,k is the Boltzmann constantandT is the temperature. We define the surface excessS of adissolved ion as the ratio of its interfacial concentration on aforeign (f) substrate to that on a hypothetical reference (r) substrateof the solute crystal (e.g., for the cation,SC ≡ [C]f/[C]r ≈e(∆Gf-∆Gr)/kT, where∆Gf and∆Gr are the dissociation free energieson the two substrates). Thus the interfacial concentration productis âf ≡ [C]f[A]f/Ksp) SCSAâ, whereSC andSA are the cation andanion surface excesses, respectively. For the SrSO4 solute on theBaSO4substrate, the surface excessesSSO4
2- ≈e(∆GBaSO4-∆GSrSO4)/kT
≈ 3000 andSSr2+ ≈ 1 (because Sr2+ interacts with the same ionicspecies in solution and at the surface), yieldingâf ≈ 3000â.Thus, at the observed onset of 2D growth of SrSO4 on BaSO4(24) Pina, C. M.; Enders, M.; Putnis, A.Chem. Geol.2000, 168, 195.
Figure 1. AFM images of SrSO4 monolayer growth on a BaSO4(001) cleavage plane. (All images show the same area.) (A) BaSO4substrate in water. (B) Sample 68 min after exchanging withundersaturated SrSO4 solution atâ ) 0.03. A crystalline monolayerof SrSO4 grows outward from the step edges at a rate of∼0.02 nm/s.The measured step height (∼0.4 nm) is half the SrSO4 unit cellheight, consistent with the known spacing of near-equivalent (002)planes.15,39 (C) Height and (D) LFM images of a sample 168 minafter exchanging with SrSO4 solution atâ ) 1.9. The step speedincreases to∼0.1 nm/s, and island nucleation begins with a perimetergrowth rate of∼0.3 nm/s. Note that islands growing near step edgesnever advance over the previously grown SrSO4 layer, indicatingthat the film is autophobic. No dissolution of the substrate wasobserved on the time scale of the experiment.
Figure 2. AFM images of PbSO4 monolayer growth on a BaSO4(001) cleavage plane. (All images show the same area.) (A) BaSO4substrate in water. (B) Sample 22 min after exchanging withundersaturated PbSO4 solution atâ ) 0.06. A crystalline monolayerof PbSO4 grows outward from the step edges at a rate of∼0.3 nm/s.The PbSO4 step height (∼0.3 nm) is half a unit cell height, as inFigure 1.15,39 (C) Height and (D) LFM images of a sample 11 minafter exchanging with PbSO4 solution atâ ) 0.2. The step speedincreases to∼0.8 nm/s, and island nucleation begins with a perimetergrowth rate of∼3.8 nm/s. Note that islands growing near step edgesnever advance over the previously grown PbSO4 layer, indicatingthat the film is autophobic. No dissolution of the substrate wasobserved on the time scale of the experiment.
5854 Langmuir, Vol. 23, No. 11, 2007 Letters
(Figure 1B),â ) 0.03w âf ≈ 90. Similar calculations yieldâf
≈ 230â for PbSO4 on BaSO4, giving âf ≈ 14 at the onset of 2Dgrowth for this case. In both cases, the condition for 2D nucleation(âf >1) is fulfilled in undersaturated solutions as long as theinterfacial liquid is understood to be a unique region with its owndistinct ion concentrations. (A more realistic calculation forâf
would take into account electrostatic interactions within theadsorbed layer. However, this will not drastically changeâf
because whereas electrostatic repulsion within the anion layerwould tend toreduce the anion surface excess, electrostaticattraction would tend toincreasethe cation excess to a similardegree.)
The quantitative difference between SrSO4 and PbSO4 growthrates probably reflects differences in compatibility with the BaSO4
substrate. The Pb2+ ion (118 pm) is closer in size to the Ba2+
ion (136 pm) than is the Sr2+ ion (113 pm),25 and the rectangularPbSO4 unit cell on the cleavage plane (0.847 nm× 0.539 nm)is a closer match to BaSO4 (0.887 nm× 0.545 nm) than is SrSO4(0.838 nm× 0.537 nm).26 Similarly, ∆GPbSO4(17.5kT) is closerto ∆GBaSO4(22.9kT) than is∆GSrSO4(14.9kT).27 The unit cell andion size comparisons suggest that PbSO4 should be morecompatible with the substrate than SrSO4, consistent with theobservations of faster step speeds for PbSO4 and smallerâf atthe onset of PbSO4 nucleation. The free-energy comparisonsindicate that the interfacial enrichment effect will be smaller for
PbSO4 and that 2D growth will start at a slightly higherbulkconcentration than for SrSO4, exactly as observed.
Whereasâf >1 is necessary for undersaturated growth, it isnot a sufficient condition, as evidenced by several anisomorphicsystems showing no undersaturated growth despite favorableion-substrate interactions (Table 1). In the case of BaMoO4 onBaSO4, for example, the attraction between Ba2+ (aq) and SO42-
(substrate) ions should lead to an interfacial product ofâf ≈330â, yet epitaxial growth of BaMoO4 was never observed forany concentration tested up toâ ) 110. Lattice strain likelyplaces an additional constraint on growth, especially foranisomorphic systems, where steric constraints prevent the low-energy planes of the film lattice from adopting the same symmetryas the substrate lattice. Although strain is difficult to quantifyfor anisomorphic lattices, rough estimates for isomorphic latticesshow that the twosystemsexhibitingundersaturatedgrowthsatisfythe energy requirement for spontaneous wetting growth.28
The above analysis assumes that the 2D condensate inundersaturated growth is a pure phase of the original solutematerial. Although mixed phases (containing significant fractionsof substrate Ba2+ ions) cannot be ruled out, several observationsindicate that a pure phase is far likelier. First, the observeddissolution of the BaSO4 substrate was infinitesimal even inpure water, as reported previously.29 We estimate an upper limitof ∼10-5 monolayers of BaSO4 solubilized in the first 10 minof exposure, yielding a [Ba2+]/[Sr2+,Pb2+] ratio of at most∼10-7
in the fluid cell volume before the onset of 2D undersaturatedgrowth. Second, these tiny BaSO4 dissolution rates observed inwater are likely further suppressed by the presence of Sr2+ orPb2+ ions in the growth solution because these ions adsorbpreferentially to substrate steps (Figures 1 and 2), where
(25) Marcus, Y.Biophys. Chem.1994, 51, 111.(26) Klein, C.; Hurlbut, C. S.Manual of Mineralogy, 20th ed.; John Wiley &
Sons: New York, 1977; pp 349-350.(27)Lange’s Handbook of Chemistry, 16th ed.; Speight, J. G., Ed.; McGraw
Hill: New York, 2005.
(28) A 2D film forms spontaneously when (γfilm + γstrain) < γsubstrate, whereγfilm andγsubstrateare the aqueous interfacial tensions of the film and substratematerials, respectively, andγstrainis the lattice strain energy per unit area. Assumingthat the strain is limited to the film lattice (which distorts to match the substratelattice), the strain energy in vacuumγvac is B∆V/A ) Bh(∆A/A), whereB is thebulk modulus of the film material,∆V is the volume change in the unit cell,his the height of the film, and∆A/A is the fractional area change of the film lattice.This energy cost originates from Coulomb interactions between ions, which inan aqueous environment are reduced by the dielectric constantε of water, givingγstrain) (Bh/ε)(∆A/A). Using published values (sources below) gives the followingestimates: for SrSO4 on BaSO4, γfilm ) 87 mJ/m2, γstrain) 8.4 mJ/m2, andγsubstrate
) 140 mJ/m2; for PbSO4 on BaSO4, γfilm ) 100 mJ/m2, γstrain ) 24 mJ/m2, andγsubstrate) 140 mJ/m2. In both cases (γfilm + γstrain) < γsubstrate, consistent with theobservation of wetting growth. (Sources: Klein, C.; Hurlbut, C. S.Manual ofMineralogy, 20th ed.; John Wiley & Sons: New York, 1977; pp 349-350.SmithellsMetals Reference Book,6th ed.; Brandes, E., Ed.; Butterworths: London, 1983.Sohnel, O.J. Cryst. Growth1982, 57, 101.)
(29) Higgins, S. R.; Jordan, G.; Eggleston, C. M.; Knauss, K. G.Langmuir1998, 14, 4967.
Figure 3. Schematic of proposed interfacial enrichment at a foreignsubstrate. (Arrows signify the surface diffusion of adsorbed ions.)(A) Adsorption of Sr2+ and SO4
2- onto a (hypothetical) referenceSrSO4 substrate. When the solution is undersaturated, the interfacialconcentration of Sr2+ and SO4
2- ions is insufficient for crystal growth.(B) Adsorption of Sr2+ and SO4
2- onto a foreign BaSO4 substrate.The strong attraction between solution SO4
2- and substrate Ba2+
species increases the interfacial concentration of SO42-. Even in
undersaturated solution, the interfacial concentration product of SO42-
and Sr2+ exceeds theKsp, leading to the condensation and growthof a monolayer step (right half). (A similar mechanism holds forPb2+ PbSO4 condensation.)
Figure 4. AFM deflection images of BaSO4 growth on a SrSO4(001) cleavage plane. (Both images show the same area.) (A) SrSO4substrate in water. (B) Sample 14 min after exchanging withsupersaturated SrSO4 solution atâ ) 93. BaSO4 overgrowth ispebblelike and anchored at step edges. Unlike the reverse system(Figure 1), here the overgrowth is nonwetting, and the SrSO4substratecontinues to dissolve throughout the experiment, as seen by themovement of steps 1 and 2.
Letters Langmuir, Vol. 23, No. 11, 20075855
dissolution normally occurs. Third, we observed no undersaturatedgrowth in the reverse system of BaSO4 on the SrSO4 substrate(Figure 4), where the substrate dissolved continuously, creatinga significant source of Sr2+ coexisting in solution with the originalBa2+ and SO4
2- species. In this case, even an impurity molefraction of order 1 (estimated Sr2+/Ba2+) did not result in 2Dfilm condensation until high supersaturations of BaSO4 werereached (∼10×). It therefore seems unlikely that solid solutionscould account for 2D condensation from highly undersaturatedsolutions of SrSO4 in Figure 1. These observations are alsoconsistent with the known rarity of Sr-Ba-SO4 solid solutionsin natural crystals and with the strong compositional zoning ofartificially cocrystallized samples observed previously.30
The current results on undersaturated film growth complimentother reports of subcritical condensation observed in markedlydifferent interfacial systems. For example, surfactant solutionsin contact with a solid surface can exhibit quasi-2D lyotropicphases of close-packed micelles at solution concentrations farbelow the 3D mesophase transition.31-33These interfacial phasesoccur either when a hydrophobic surface interacts with surfactanttails via hydrophobic interaction31or when a polar surface interactswith surfactant heads via electrostatic interactions.32,33Anotherexample of subcritical condensation is the underpotentialdeposition (UPD) of foreign metals on an electrode surface34
(i.e., the condensation of an initial 2D monolayer at electrodepotentials positive of the bulk electroplating potential). Although
the mechanism is not completely understood, results35,36 haveshown that strong anion-electrode interactions play a central(and sometimes decisive) role in the occurrence of UPD. Takentogether, thesephenomenasuggest thata2D liquid layermediatingbetween a surface and the bulk solution is a feature common toall immersed solids and that favorable substrate-solute interac-tions can create supercritical interfacial zones in subcriticalsolutions. The simple guidelines for undersaturated growthreported here can serve as a useful starting point in the designof organic interfaces for biomimetic materials synthesis or forthe sequestering of metal ions from aqueous systems.
Acknowledgment. This research is based upon work sup-ported by the National Science Foundation under grant no.0094385 and University of Arizona TRIF Program funding.
Supporting Information Available: Calculations of theinteraction strength andâ values. pH calculations and a plot of the ioniccomposition of pure water in equilibrium with atmospheric CO2 as afunction of pH. Glossary of terms. This material is available free ofcharge via the Internet at http://pub.acs.org
