Two-Step Nucleation Rather than Self-Poisoning: An Unexpected

Article pubs.acs.org/crystal

Two-Step Nucleation Rather than Self-Poisoning: An Unexpected Mechanism of Asymmetrical Molecular Crystal Growth Philipp Ectors,† Jamshed Anwar,‡ and Dirk Zahn*,† †

Lehrstuhl für Theoretische Chemie/Computer Chemie Centrum, Friedrich-Alexander Universität Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany ‡ Chemical Theory and Computation, Faraday Building, Department of Chemistry, Lancaster University, Lancaster LA1 4YB, United Kingdom ABSTRACT: The identification of two step nucleation mechanisms considerably extended our understanding of crystal nucleation. Here, we report an analogous observation of a twostep mechanism but in 2-D for deposition of molecules to a growing crystal face. Using molecular dynamics simulations connected with the Kawska-Zahn approach, α-resorcinol precipitation from the vapor is treated at the low driving force regime. Growth at the faster growing (01̅1̅) face reveals the deposition of molecules to form a disordered liquid-like layer. Strikingly, this apparently divergent (nonepitaxial) molecular arrangement does not represent self-poisoning which would lower the growth rate of the (01̅1̅) face. On the contrary, more favorable attachment energy along with a disorder−order transition, akin to a two-step nucleation observed in 3-D systems, leads to growth rates that are about 20 times faster than the more standard mode association of molecules at the (011) face where the molecules readily align according to the crystal lattice.

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INTRODUCTION The classical view of crystal nucleation relies on the spontaneous formation of crystalline motifs from an elsewise disordered vapor, melt, or solution. This long-established view is challenged by recent observations of prenucleation species and multistage crystal nucleation processes and inspired the term “nonclassical” nucleation. Such phenomena call for extensions to classical nucleation theory, which relates the competition of favorable bulk energy (as a consequence of molecular packing) and unfavorable surface/interface energy terms (resulting from surface tension and from implementing an order−disorder interface) to terms that scale linearly with volume and surface area, respectively.1 In its simplest form, the thermodynamics of a two-step nucleation process may be rationalized by the help of two energy profiles, each stemming from classical nucleation theory but based on the formation of differently ordered nuclei. The scenario illustrated in Scheme 1 implies the primary nucleation event to be dictated by the lowest energy barrier to nucleation, here arising from relatively low interface energy but not from optimal molecular packing in the bulk. At later stages of crystallization the bulk term becomes increasingly dominant and structural reorganization of the forming nuclei may lower its free energy considerably. This transition is however bound to a secondary nucleation barrier, the dimensions of which eventually determining whether twostep nucleation takes place or if the forming crystal is kinetically trapped into one of its less stable polymorphs. © 2015 American Chemical Society

Scheme 1. Illustration of the Free Energy Profiles Underlying the Nucleation of a Polymorphic Crystala

a

Respective polymorph stability is a function of aggregate size (radius), and solid−solid transitions (red arrow) may lead to reorganization in favor of the most stable crystal structure. Such secondary nucleation may also play a role during the growth of crystal faces: newly attached molecules that are misaligned with respect to the crystal face underneath might hinder further growth (self-poisoning) or undergo surface reconstructions at later stages of ad-layer growth.

It is intuitive to expect competing nucleation mechanisms to also apply for the two-dimensional case of molecule deposition on a growing crystal face. The formation of surface steps and Received: July 29, 2015 Revised: September 15, 2015 Published: September 17, 2015 5118

DOI: 10.1021/acs.cgd.5b01082 Cryst. Growth Des. 2015, 15, 5118−5123

Crystal Growth & Design

Article

Chatchawalsaisin et al.12 specifically developed for accurately describing resorcinol. Shifted-force potentials were used in conjunction with a cutoff of 1 nm. To assess the nature of the individual resorcinol molecules during crystal growth, it is useful to employ a mobility criterion based on the maximum displacement of the molecular centerof-mass within a given period of time. In analogy to our previous investigation of crystal growth from the melt, we used the displacement within ±50 ps as a measure of molecular mobility.8

islands may impose the crossing of nucleation barriers, while individual molecules deposited on the growing surface might tend to misalign with respect to the beneath crystal. The persistence of such misalignment would lead to the “selfpoisoning” of crystal growth, akin to the formation of a lessstable polymorph during 3-D nucleation illustrated in Scheme 1. On the other hand, two-step crystal growth mechanisms have, to the best of our knowledge, not yet been reported. Here we have investigated the crystal growth of the surfaces bounding the polar axis of α-resorcinol from the vapor phase. The study reveals the remarkable feature of two-stage nucleation during the deposition of crystal layers for one of the faces. The interest in the molecular crystal α-resorcinol is due to relatively recent experiments which have revealed that certain polar crystals exhibit asymmetric crystal growth rates for the surfaces delineating the polar axis when grown from the vapor phase, with a particular case being α-resorcinol.2−7 This finding has challenged the earlier view that growth kinetics of these surfaces should be symmetric as the energy of layer attachment to the faces terminating the polar axis appear identical. We recently reported the mechanics of crystal growth of these surfaces from the melt based on molecular dynamics simulations and showed that there are no fundamental grounds for the growth kinetics to be symmetric given that crystal growth is determined by a variety of free energy barriers to crystal layer formation.8 Instead, asymmetric crystal growth from the melt was attributed to the slow-growing (011) face being less able to direct the correct alignment of the oncoming molecules, and the presence of an alternate resorcinol conformation that readily incorporates into the lattice at this surface, serving to poison and retard subsequent growth.

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RESULTS The most common approach to using molecular simulations for classifying the rates of crystal growth along different directions is to explore the association of an oncoming molecule to the respective face of the crystal, typically mimicked by ideal cuts from a single crystal model. It is educative to follow this strategy by calculating the related association energies in two steps: we first (i) placed the additional α-resorcinol molecule at positions matching lattice sites of the single crystal. This was performed for both crystallographic sites of α-resorcinol to effectively account for the association of a unit cell. As one would expect from simple symmetry considerations, association to either the (011) or (011̅ )̅ faces gives rise to identical gain in potential energy per molecule (Table 1). This however only Table 1. Resorcinol Deposition of Plain Cuts of the Single Crystala (011) (position a) unrelaxed average relaxed

METHODS

average

The α form of resorcinol crystals grows as capped prisms, with the {011} faces representing the fastest growing surfaces. The overall dipole moment of the crystal is directed along [001] and accounts for dissimilar growth rates of the (011)/(01̅1)and the (01̅1̅)/(011̅) faces. As starting points to investigating crystal growth of these faces a 4.3 × 4.6 × 5.6 nm3 sized slab was cut normal to the [011] direction from the single crystal of α-resorcinol (CSD refcode RESORA03, space group Pna21). Periodic boundary conditions were applied normal to [011] to model infinite (011) and (01̅1̅) surfaces, respectively. While the initial configurations for both growth runs hence reflect idealized cuts of the single crystal, the Kawska-Zahn method9−11 is used to overcome this limitation. Instead, (i) we mimic the diffusion of vapor molecules to the surface by placing the oncoming molecule at random orientation and relative position at a 0.7 nm distance from the surface. This distance was found to be a good compromise ensuring unbiased deposition even to rough surfaces and preventing excessive failed docking attempts due to vanishing intermolecular forces. Relaxation is then studied from (ii) steepest descent energy minimization first allowing only the oncoming molecule to move, and then (iii) full relaxation of the overall system from 0.1 ns molecular dynamics runs. The relaxation process represents the computationally most demanding part of our simulations and the above combination of procedures (i−iii) was found to provide rapid convergence of total energy (usually observed within 50 ps). Using this technique, 200 molecules were attached to the (011) and (01̅1̅) faces in independent simulation runs. For the chosen super cell model, a full (011)/(011̅ )̅ layer corresponds to 64 molecules, which implies that our analysis of crystal growth is based on the deposition of up to 3 layers. For the molecular dynamics simulations a time-step of 1 fs was chosen. The Nosé-Hoover thermostat was used to maintain a constant temperature of 300 K. Both intra- and intermolecular interactions are critical to describe the subtle energetics of resorcinol conformers and polymorphs which motivated the choice for the force-field of

−15.71 kJ/mol −20.24 kJ/mol −38.17 kJ/mol −39.44 kJ/mol

(011) (position b) −24.76 kJ/mol

−40.70 kJ/mol

(01̅1̅) (position a) −30.02 kJ/mol −20.24 kJ/mol −48.96 kJ/mol −42.53 kJ/mol

(01̅1̅) (position b) −10.45 kJ/mol

−36.10 kJ/mol

a Docking was first performed by placing the additional molecule at crystalline positions a and b (unrelaxed) leading to identical averages of the binding energy. However, when allowing the molecular arrangements to relax, association to the (01̅1̅) face of the crystal is favored by 3.1 kJ/mol.

applies to oncoming molecules which are fixed to lattice sites of the template crystal. When (ii) the system is allowed to freely relax by energy minimization, association to the (01̅1̅) face turns out to be favored by 3.1 kJmol−1 (see also Table 1). Using Boltzmann statistics the ratio of growth rates may be assessed from r(0 1̅ 1̅ ) r(011)

⎛ ΔE ⎞ = exp⎜ − association ⎟ kBT ⎝ ⎠

(1)

Using the energy difference as estimated above would thus imply that (011̅ )̅ growth outperforms (011) growth by a factor of about 3.5. This however only reflects a rough estimate based on a single association step which might not be representative for overall crystal growth. Indeed, when inspecting the molecular arrangements after relaxation a striking observation is that of structural misalignment of the molecules newly attached to the (01̅1̅) face, while growth of the (011) face appears rather epitaxial (Figure 1). This finding may be rationalized by the amphiphilic nature of resorcinol, comprising a weakly polar phenyl group and two OH groups. The outermost surface of the (011) face consists of phenyl groups which weakly interact with newly attached resorcinol molecules. 5119



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and leads to molecular arrangements that strongly divert from the crystalline lattice sites. In other terms, association to the (01̅1̅) face should lead to a divergent, nonepitaxial ad-layer, an intuitive interpretation of this being self-poisoning. In the long run one would hence expect the (01̅1̅) growth rate to quickly decline. This assumption, however, stands in contradiction to the experimentally confirmed preference of the (01̅1̅) face.2−7 Interestingly, previous simulation studies which employed the same interaction models, but relied on investigating the structure of plain crystal faces, suggested epitaxial growth of (01̅1̅) and self-poisoning of the opposite (011) face.13 The controversy of simulation studies can only be attributed to the different type of crystal surface models used. This is a clear indicator for resorcinol crystal growth from the vapor being too complex to allow rationalization by simple models such as plain cuts of single crystals or the attachment of a single unit cell to such surfaces. In what follows we therefore study the whole process of (011)/(01̅1̅) growth and provide a mechanistic analysis based on the evolution of the growth front at a molecule-by-molecule resolution. Within independent simulation runs, we employed the Kawska-Zahn approach performing 200 molecule association steps to the (011) and (01̅1̅) faces, respectively. These simulations mimic the regime of crystal growth at very low vapor pressures (low driving force). The mechanistic analysis was implemented in analogy to our previous study on resorcinol growth from the melt.8 Accordingly, immobilized molecules are identified on the basis of the maximum center-ofmass displacement encountered within a 100 ps time frame. Based on vibrations within the bulk crystal, a threshold of >0.69 Å was found best suited to discriminate mobile molecules. Using this measure, we plot the number of immobilized molecules as a function of the amount of deposited molecules in Figure 2. For the growth of the (011) face, we find a linear relation with a slope of 1 which nicely matches the rather

Figure 1. Illustration of the (011) and (01̅1̅) faces as cut from the single crystal structure including the preferred arrangements of additional molecules when individually deposited from the vapor. For comparison, the corresponding arrangements (two types of lattice sites indicated as a,b) in the crystal below are highlighted using the same color. The direction of the overall dipole field is indicated by the green arrow.

As a consequence, association is not driven by local hydrogen bonding, but instead follows the electric dipole field of the overall molecular crystal. This gives rise to almost epitaxial growth, indicated by much smaller molecular rearrangements during (011) growth as compared to the (011̅ )̅ face. In contrast to this, the OH moieties at the (01̅1̅) surface tend to act as hydrogen bonding donor/acceptors, thus adding specific shortranged interaction features to the overall electric field (which is of equal strength at both faces). The identified differences in association energies and the observed structures shown in Figure 1 clearly show that local hydrogen bonding at the (01̅1̅) outperforms the more global electric dipole field of the crystal

Figure 2. Number of immobilized molecules in the course of molecule deposition to the (011) and (01̅1̅) faces of α-resorcinol. While resorcinol molecules attached to (011) are almost ideally arranged at crystalline lattice sites (which would correspond to the dashed line), the (01̅1̅) face exhibits a more complex growth mechanism. The dots indicate the snapshots shown in Figures 3 and 4 5120



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Figure 3. Snapshots of molecule-by-molecule deposition and relaxation on the (011) face. Epitaxial growth is observed with only a few molecules temporarily deviating from immediate immobilization. Root-mean-square deviations of the center-of-mass positions are indicated by a color code.

Figure 4. Snapshots of molecule-by-molecule deposition and relaxation on the (01̅1̅) face. The outermost ad-layer exhibits a liquid character. Molecular immobilization instead occurs as a secondary liquid→solid transformation. Note that both solid−liquid and liquid−vapor interfaces propagate during crystal growth giving rise to a constant thickness of the liquid domain. Analogous to Figure 3, root-mean-square deviation of the center-of-mass positions are indicated by a color code.

epitaxial growth mechanism illustrated in Figure 3. On the other hand, the (01̅1̅) growth front exhibits significant retardation of ad-layer solidification (Figure 4). To facilitate visual inspection, we use a color code for highlighting the beforehand described measure of molecular mobility. The detailed molecule-by-molecule growth study indeed shows the structural features already indicated for the association of single molecules (Figure 1). Figure 4 illustrates the formation of a liquid-like ad-layer at the (01̅1̅) face which is best explained by a dynamical interplay of hydrogen bonding (short-ranged electric multipole field acting only locally) and the electric dipole field of the crystal. The thickness of the liquid-like domain is however rather limited, and upon further molecule deposition, we observe propagation of the (01̅1̅) growth front accompanied by crystallization beneath the liquid−vapor interface. This indicates that different molecular arrangements at the (01̅1̅) face should not be seen as self-poisoning, but instead reflect a two-step mechanism for crystal growth.

The situation thus appears similar to the observation of twostep nucleation processes1,14,15 in which the early stage of aggregate formation involves structural motifs different from that of the final crystal. In many cases this size-induced phase transformation is subject to considerable energy barriers or only weak thermodynamic favoring such that the secondary nucleation step occurs at late stages of nuclei growth (e.g., beyond the 10 nm scale).14,15 To validate this concept, it is educational to analyze the different evolution of potential energy in the course of molecule association and relaxation of the (011) and the (01̅1̅) faces, respectively. Strikingly, our detailed surface growth simulations confirm a continuous favoring of resorcinol association to the liquid-like layer at the (01̅1̅) face during crystal growth. The energetic preference over resorcinol attachment to the (011) face is subject to considerable fluctuations, but on average (assessed from crystal growth by 1−200 molecules) amounts to 7.5 kJ/mol and thus tends to be even larger than estimated from the simple considerations based on plain crystal faces. After the estimated 5121



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barrier) oras demonstrated by the present workmore rapid growth of specific crystal faces. While the mechanistic concepts described above are intuitive, we point out that most of the simulation studies on resorcinol growth were based on idealized surface/interface arrangements originally cut from a single crystal. Regardless of how accurately the interaction energies are being calculated, using such models implies the risk of oversimplifying what could be a manifold of structures (kinks, islands, steps, etc.) relevant to crystal growth. Indeed, for the modeling studies on resorcinol so far, only one explicitly looked into molecule-by-molecule growth.8 In the present work, we followed this track of exploring resorcinol growth from its vapor by employing a recently developed method for explicit simulation of crystal nucleation and growth. The Kawska-Zahn approach combines molecule-by-molecule association with molecular dynamics simulations of structural relaxation as a function of aggregate size, and thus appears particularly suited for in-depth mechanistic analyses of both crystal nucleation9−11 and growth.17

difference in association energy in eq 1 is replaced by this more reliable average, the ratio of (01̅1̅)/(011) growth rates is predicted to be 20.2. It is important to note that the difference in potential energy discussed above only refers to the association of molecules from the vapor. The total change in potential energy upon crystal growth at either the (011) or (01̅1̅) face must be identical, as identical solid-state structures are formed. Indeed, we observe potential energy of the overall models to evolve practically identically for crystal growth of both faces. As an average over the last 100 resorcinol deposition steps, we even found a slight disfavoring of the (01̅1̅) face by ∼1 kJ/mol. While at the edge of our model accuracy,16 such slight disfavoring in potential energy of the overall solid could be attributed to a weak hysteresis in the secondary nucleation process of the liquid→ crystal transformation beneath the outermost layer of the (01̅1̅) growth front. Another striking observation is the diminishing role of βconformers which were found to account for self-poisoning of α-resorcinol growth from the melt.8 For crystal growth from the vapor, we identified the β-conformer to only temporarily occur at the edges of forming ad-layers. β-Conformer transformation is enhanced at the interface to vapor (note that in the vapor β-conformers are favored by 0.8 kJ/mol, while in the melt α-conformers are preferred by 2.3 kJ/mol8). As a consequence, only a few β-conformers are found in the liquidlike domain, and none appear in the crystal. Indeed, the average lifetime of β-conformers on both of the growing crystal faces along the polar axis was found as 1.5 ns, while for the bulk melt the β → α transition was found within about 5 ns.8

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Zahn, D. Thermodynamics and kinetics of pre-nucleation clusters, classical and non-classical nucleation. ChemPhysChem 2015, 16, 2069−2075. (2) Wells, A. F. Abnormal and modified crystal growth. Discuss. Faraday Soc. 1949, 5, 197. (3) Wireko, F. C.; Shimon, L. J. W.; Frolow, F.; Berkovitchyellin, Z.; Lahav, M.; Leiserowitz, L. Effect of solvent on the growth of organic crystals 1. The riddle of alpha-resorcinol. J. Phys. Chem. 1987, 91, 472−481. (4) Davey, R. J.; Milisavljevic, B.; Bourne, J. R. Solvent interactions at crystal surfaces − the kinetic story of alpha-resorcinol. J. Phys. Chem. 1988, 92, 2032−2036. (5) Khoshkhoo, S.; Anwar, J. Study of the effect of solvent on the morphology of crystals using molecular simulation: Application to alpha-resorcinol and N-n-octyl-D-gluconamide. J. Chem. Soc., Faraday Trans. 1996, 92, 1023−1025. (6) Hussain, M.; Anwar, J. The riddle of resorcinol crystal growth revisited: Molecular dynamics simulations of alpha-resorcinol crystalwater interface. J. Am. Chem. Soc. 1999, 121, 8583−8591. (7) Srinivasan, K.; Sherwood, J. N. Asymmetric Growth of alphaResorcinol Crystals: Comparison of Growth from the Vapor Phase and from Aqueous Solution. Cryst. Growth Des. 2005, 5, 1359−1370. (8) Ectors, P.; Sae-Tang, W.; Chatchawalsaisin, J.; Zahn, D.; Anwar, J. The molecular mechanism of α-resorcinol’s asymmetric crystal growth from the melt. Cryst. Growth Des. 2015, 15, 4026−4031. (9) Kawska, A.; Brickmann, J.; Kniep, R.; Hochrein, O.; Zahn, D. An Atomistic Simulation Scheme for Modeling Crystal Formation from Solution. J. Chem. Phys. 2006, 124, 24513. (10) Anwar, J.; Zahn, D. Uncovering Molecular Processes in Crystal Nucleation using Molecular Simulation. Angew. Chem., Int. Ed. 2011, 50, 1996−2014. (11) Milek, T.; Duchstein, P.; Seifert, G.; Zahn, D. Motif Reconstruction in Clusters and Layers: Benchmarks for the KawskaZahn Approach to model Crystal Formation. ChemPhysChem 2010, 11, 847−852. (12) Chatchawalsaisin, J.; Kendrick, J.; Tuble, S. C.; Anwar, J. An optimized force field for crystalline phases of resorcinol. CrystEngComm 2008, 10, 437−445.

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CONCLUSION The mechanisms of asymmetric crystal growth of resorcinol along its polar axis show an inspiring diversity. In both cases, the (01̅1̅) face is growing faster, but for quite different reasons. While self-poisoning by β-conformers was found to be of crucial importance for crystal growth from the melt, it appears insignificant for crystal growth from the vapor. Using moleculeby-molecule deposition, here we elaborate a two-step mechanism akin to nonclassical nucleation processes.1 While the (011) face grows by epitaxial association of molecules immediately arranged according to the crystal lattice, we identified the formation of a liquid ad-layer at the faster growing (01̅1̅) face. The common interpretation of such (mis)ordering would be self-poisoning and thus a decline in the growth rate. This however only applies if the divergent ordering is persistent. On the contrary, resorcinol growth from the vapor shows ongoing liquid→solid transformation upon molecule deposition and thus continuous propagation of the vapor− liquid-crystal interfaces. While this secondary reorganization step prevents the self-poisoning of crystal growth, faster growth along [01̅1̅] results from more favorable attachment of vapor molecules to the liquid layer on top of the corresponding crystal face. In more general terms, for both crystal nucleation and later stages of surface growth the fate of divergent ordering depends on the nature of secondary processes.1 Large barriers to reorganization would lead to self-poisoning (during crystal growth) or precipitation of less-favored polymorphic forms (if encountered during nucleation). On the other hand, small barriers to reorganization may lead to substantially faster crystal nucleation (via intermediate structures of lower nucleation 5122



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(13) Anwar, J.; Chatchawalsaisin, J.; Kendrick, J. Asymmetric crystal growth of alpha-resorcinol from the vapor phase: Surface reconstruction and conformational change are the culprits. Angew. Chem., Int. Ed. 2007, 46, 5537−5540. (14) Vekilov, P. The two-step mechanism of nucleation of crystals in solution. Nanoscale 2010, 2, 2346−2357. (15) Gebauer, D.; Coelfen, H. Prenucleation Clusters and Nonclassical Nucleation. Nano Today 2011, 6, 564−584. (16) Please note that we do not claim 1 kJ/mol accuracy for the absolute numbers of association energies (which are surely less accurate), but instead refer to the average energy difference assessed from analogously generated simulation models. (17) Milek, T.; Duchstein, P.; Zahn, D. Molecular modeling of (1 0 −1 0) and (0 0 0 −1) zinc oxide surface growth from solution: islands, ridges and growth-controlling additives. CrystEngComm 2015, 17, 6890−6894.

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Two-Step Nucleation Rather than Self-Poisoning: An Unexpected

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