Molecular Mechanisms of Hematin Crystallization from Organic

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Molecular Mechanisms of Hematin Crystallization from Organic Solvent Katy N. Olafson,† Megan A. Ketchum,† Jeffrey D. Rimer,*,† and Peter G. Vekilov*,†,‡ †

Department of Chemical and Biomolecular Engineering and ‡Department of Chemistry, University of Houston, 4800 Calhoun Road, Houston, Texas 77204, United States ABSTRACT: Here, we employ n-octanol to elucidate the fundamental processes of hematin crystallization from an organic solvent, identify the operational mechanisms of growth, and determine the respective control parameters. The values of the enthalpy, entropy, and free energy of the crystal−solution equilibrium suggest that octanol may structure around the hematin solute molecules and along the crystal interface. Time-resolved in situ atomic force microscopy demonstrates that hematin crystal growth strictly follows classical layer growth mechanisms. Steps propagate by the attachment of solute molecules, described by a first-order chemical rate law. The molecules reach the steps via adsorption on the crystal surface, followed by surface diffusion, and the kinetic barriers of this pathway offer additional crystallization control strategies. Solute incorporation into steps from the adjacent lower and upper terraces is strongly asymmetric, with the lower terrace contributing the major solute amount. These findings provide a foundation for the rational design of hematin crystals that may find applications utilizing their high magnetic and optical anisotropy.

1. INTRODUCTION Solution-grown crystalline materials are implemented in numerous applications owing to their chemical, mechanical, optical, and electrical properties. Single crystals of inorganic salts or mixed organic−inorganic materials are used in nonlinear optics elements1 and for other electronic and optical-electronic applications. Chemical products and intermediates are precipitated as crystals in thousands-of-tons quantities.2 Many pharmaceuticals are crystals that are specifically designed to exhibit a slow crystal dissolution rate for the sustained release of medications over longer periods of time compared to their amorphous or soluble counterparts.3−7 The need for predictive control of the physical and chemical properties of crystals and of crystalline populations has driven research efforts to elucidate the fundamental processes of crystallization.8 Many challenges to the traditional understanding of crystal growth mechanisms and the respective control parameters remain. For numerous systems, quantitative information on the thermodynamics and kinetics of solute incorporation into crystals is still missing, and these gaps hamper the development of efficient, sophisticated methods to prepare new and improved crystalline materials.9 Crystals grow by classical or nonclassical mechanisms. Classical pathways of solution crystallization include layer-bylayer growth involving either two-dimensional (2D) nucleation of layers on the crystal terraces or steps emanating from screw dislocations that form hillocks.10−14 The unfinished layers spread on the surface through the attachment of single ions or molecules. In contrast, nonclassical pathways involve a diverse set of precursors that range in complexity from oligomeric species and primary particles to bulk amorphous phases and small crystallites. Nonclassical crystal growth can involve a © XXXX American Chemical Society

dynamic sequence of events that include precursor attachment and structural rearrangement,15 leading to the formation of crystals that often exhibit a markedly different habit than those formed via classical pathways.16−20 Studies of the classical crystallization pathways in aqueous solution have provided extensive insights into processes at all relevant length scales: macroscopic, mesoscopic, and molecular. At the macroscopic level, the transport of solute (and impurities) toward the crystal−solution interface, the relative significance of convection and diffusion, and their interactions with crystal surfaces are relatively well-understood.21−28 These insights have allowed control over the development of growth instabilities and defects,29−35,28,36−38 which can substantially alter the material properties. At the mesoscopic scale, crystal faceting is attributed to the high surface free energy of the crystal−solution interface, which explains the relative significance of the individual crystal faces in the equilibrium crystal shape through the surface free energy anisotropy. 39,40 Importantly, it is known that faceted crystals grow by generation and spreading of layers and the frequency of layer generation is regulated by the surface free energy of the layer edges.14,41 At the molecular length scale, the density of growth sites, kinks along steps (Figure 1a), on the crystal−solution interface has been identified as the main spatial characteristic that determines the rate of step propagation.14,39,40,42,43 In turn, the growth site density has been correlated to the balance between the crystal bond strength and the solute−solvent interaction Received: August 12, 2015 Revised: September 16, 2015

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processes occurring at macroscopic and mesoscopic length scales follow mechanisms similar to those found in aqueous solvents and can be understood by rescaling the solvent viscosity, solute and impurity diffusivities, and the surface free energy of the solution−crystal interface with those characteristic of the organic solution. However, the processes occurring at the molecular length scale will likely not abide by similar rescaling laws. The reason is the lack of three-dimensional networks of hydrogen bonds in organic solvents that would significantly modify all energetic and spatial parameters of crystallization and potentially alter the molecular mechanisms of crystallization.61 The investigations discussed in this article aim to provide deeper understanding of the molecular processes involved in crystallization from an organic solvent. Hematin, illustrated in Figure 2a, is a suitable model compound for the proposed

Figure 2. Structures of (a) hematin and (b) β-hematin crystals. In (b), the atoms in hematin molecules are color-coded: Fe3+ ions are green, oxygen atoms are red, nitrogen atoms are blue, and carbons are gray. Region I highlights the head-to-tail dimer, which is composed of two hematin molecules associated through coordination bonds (depicted in region II). Region III highlights the hydrogen bonds between the head-to-tail dimers.

Figure 1. Schematic of crystal growth mechanisms. (a) The surface structure of a crystal growing by the generation and spreading of layers. An unfinished top layer and associated step, terrace, and kinks are identified. (b) The direct incorporation mechanism. (c) The surface diffusion mechanism. (d) The free energy profile encountered by a molecule during direct incorporation into a step. i and ii are the kinetic barriers for incorporation and detachment of a molecule from a growth site, respectively. (e) The free energy profile along the trajectory of a molecule diffusing toward a step via the surface diffusion mechanism. i, ii, iii, and iv are the kinetic barriers for, respectively, adsorption, desorption, surface diffusion, and incorporation into steps from the surface.

studies. Both natural and synthetic hematin crystals are triclinic, possessing P1̅ symmetry (Figure 2b).62,63 The unit cell is composed of a head-to-tail hematin dimer that is associated by two coordination bonds between the Fe3+ atoms in the center of the protoporphyrin rings and the carboxyl groups, as highlighted in Figure 2b. Sufficiently large (20−50 μm) hematin crystals can be reproducibly grown from n-octanol saturated with acidified aqueous buffer.64 The crystals can be attached to a suitable substrate and monitored in situ by atomic force microscopy (AFM) to obtain time-resolved images at near-molecular resolution. Hematin crystals potentially exhibit interesting material properties; they have been shown to possess remarkable magnetic and optical anisotropy.66,67 These properties stem from the high magnetic moment of the hematin head-to-tail dimer, μ = 4.21.68 In turn, this high magnetic moment is due to the presence of high spin (S = 5/2) paramagnetic Fe3+ ions.69 Besides application to materials synthesis, detailed insight into hematin crystallization from organic solvents may have a potentially significant societal impact. Hematin crystallization is a part of the physiology of malaria parasites infecting human hosts.66,70,71 It is feasible that the fundamental understanding of hematin crystallization will provide insight into the physiology of malaria parasites.

energy.14,42−44 The structuring of water around the solute molecules and at the growth sites has been identified as a significant contributor to the kinetic barrier for incorporation of solute molecules into growth sites.39,45−49 The pathways that a solute molecule may take en route to a growth site (i.e., direct incorporation from the solution into kinks, Figure 1b, or adsorption on the terraces between steps, followed by surface diffusion and incorporation into the kinks, Figure 1c) have been elucidated for numerous crystals,14,39,40,50−55 and criteria for the selection between the two pathways have been formulated.48,54 In aqueous solvents, the fundamental property of water to form a three-dimensional network of hydrogen bonds, molded around solute molecules and along the crystal−solution interface, can have a pronounced impact on the pathways and rate of crystallization.56−59 In recent years, organic liquids have emerged as an alternative solvent for preparation of crystalline materials and separation or purification by crystallization, e.g., for high-value materials such as pharmaceuticals and fine chemicals.60 In contrast to crystallization from aqueous solvents, the level of understanding of the fundamental processes of crystal growth from organic liquids is severely limited. It is likely that the

2. THE THERMODYNAMICS OF HEMATIN CRYSTALLIZATION FROM CITRIC BUFFER SATURATED OCTANOL Solvent selection often determines the speciation of solute (monomers, dimers, oligomers, and complexes), the transport B

DOI: 10.1021/acs.cgd.5b01157 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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of solute to the growth interfaces, and the mechanism of molecular incorporation at the growth sites. In aqueous solutions, hematin is known to form several dimers and higher oligomers, distinct from the head-to-tail dimer in the crystal structure: π−π dimers, in which two hematin monomers are in parallel positions, the two Fe atoms face outward, and the monomers are linked by overlapping π electron density; μ-oxo dimers, in which two parallel hematin monomers are bound by an O atom linking their facing Fe atoms; and larger oligomers, in which μ-oxo dimers catenate by π−π linkages.68 Recent evidence suggests that these dimers and larger oligomers may adsorb on the surface of crystals immersed in supersaturated aqueous solutions and prevent any further association of molecules and growth.65,72 These deleterious aggregates have not been observed in organic solvents, including n-octanol that we use as a solvent in the study reported here.73,74 Octanol is an amphiphilic molecule with an aliphatic tail of medium length and a polar head (−OH), which is smaller than the glycerol ester functional groups of the mono- and diglyceride lipids that form a distinct phase in physiological environments and serve as a putative medium for hematin crystallization.75,76 According to recent analyses, water is soluble in a biomimetic lipid mixture at 8.5 ± 0.5% weight, corresponding to 4.2 ± 0.3 mol kg−1. The water solubility in n-octanol, 2.70 mol kg−1, is lower than in the lipid mixture.77 Thus, to construct a biomimetic organic solvent for hematin crystallization, we used n-octanol saturated with citric buffer at pH 4.8 (within the physiological pH range),78,79 which we refer to as CBSO. A dependence of hematin solubility ce in CBSO on temperature is presented in Figure 3a. The data in Figure 3

(1)

where R is the universal gas constant. The slope of the ce data plotted in van ‘t Hoff coordinates ln ce(1/T) in Figure 3b yields ΔHocryst = −37 ± 8 kJ mol−1. The solubility data can also be used to determine the Gibbs free energy of crystallization ΔGocryst and the crystallization o o entropy ΔScryst . ΔGcryst is related to the crystallization equilibrium constant Kcryst as o ΔGcryst = −RT ln Kcryst = RT ln ce

(2)

Equation 2 yields ΔGocryst = −22 ± 3 kJ mol−1 at 25 °C. The difference between ΔHocryst and ΔGocryst provides an estimate for ΔSocryst o o o ΔScryst = (Hcryst − ΔGcryst )/T

ΔSocryst

(3) −1

−1

We obtain = −49 ± 7 J mol K . The crystallization entropy reflects the loss of translational and rotational degrees of freedom when a molecule from the solution incorporates into a crystalline lattice, partially balanced by the gain of vibrational degrees of freedom of the newly established crystal contacts. The molecular processes underlying ΔSocryst are similar to those during the entropy loss of a molecule binding to another molecule. Estimates of the latter process for molecules with sizes similar to that of hematin yield ΔSocryst in the range of −100 to −280 J mol−1 K−1.80,81 Thus, the magnitude of ΔSocryst for hematin is lower than the estimates for similarly sized molecules, which suggests a process leading to entropy increase during hematin incorporation into the growth sites on crystal surfaces. This process could possibly be the release of n-octanol molecules, which may be ordered at the crystal−solvent interface and surrounding hematin molecules in the solution.

3. HEMATIN CRYSTALS GROW BY A CLASSICAL MECHANISM Hematin crystals that form in physiological (hemozoin)82 and synthetic (β-hematin)64 processes are faceted with smooth faces oriented along crystallographic planes with low Miller indices and high density of molecules.83 Such faces typically follow the classical layer growth mechanism,58 wherein a new layer, typically one lattice spacing high, is deposited on the smooth surface of the underlying layer (Figure 1a). To elucidate the growth mechanism of hematin crystals, we employed time-resolved in situ AFM to image large crystals prepared as discussed in Olafson et al.65 In situ AFM has proven to be a valuable technique for clarifying structural and dynamic characteristics of classical and nonclassical crystallization mechanisms.17,44,84,85 AFM topographical images of the (1̅00) hematin face in Figure 4 reveal the presence of unfinished layers with heights h = 1.17 ± 0.07 nm, close to the unit cell dimension in the [100] direction, a = 1.22 nm.65 These images reveal that hematin crystals follow a classical mode of crystal growth, in which new layers are generated by 2D nucleation and spread to cover the entire facet. Straightforward geometrical considerations indicate that, in this growth mode, the growth rate R is the product of the step velocity ν and the step density, h/l, where l is the spacing between the steps

Figure 3. Characterization of the crystal−solution equilibrium from bulk crystallization experiments (yellow circles) and by in situ atomic force microscopy (blue squares). (a) The temperature dependence of hematin solubility in CBSO. (b) The solubility data in van ’t Hoff coordinates. The corresponding enthalpy and entropy of crystallization are ΔHocryst = −37 ± 8 kJ mol−1 and ΔSocryst = −49 ± 7 J mol−1 K−1, respectively.

reveal excellent agreement between the solubility measured by two separate techniques: bulk crystallization and in situ AFM. o To evaluate the standard enthalpy ΔHcryst of hematin crystallization in CBSO, we note that, in the crystallization equilibrium hematin(solution) ⇆ hematin(crystal), the product is a solid phase and has activity of one. We assume that the activity of the soluble hematin is equal to its concentration. This assumption is justified by the low values of the solubilities in Figure 3 that correspond to long intermolecular separations, at which the intermolecular interactions are weak and the activity coefficients are near unity. With this, the equilibrium constant for crystallization is Kcryst = ce−1 and the temperature T dependence of solubility ce(T) is given by the classical van ’t Hoff equation

R = (h / l )ν C

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Figure 4. In situ AFM observation of 2D island growth in a CBSO solution with hematin concentration cH = 0.28 mM. (a) Five islands marked with daggers were monitored as a function of time during continuous imaging. (b, c) Over 22 min, the islands grow and merge. The dashed line in (a) indicates the crystal edge.

The mean step density, h/l, is determined by the rate of 2D nucleation of new layers. The step velocity ν is determined by the rate of association of molecules to the kinks, the kink density, and the supply of molecules to the steps, which is a process that is heavily dependent on the competition with adjacent steps. In a previous paper,65 we discussed the mechanism of layer generation and the resulting step density. Here, we focus on the mechanisms of molecular attachment to the steps

Figure 5. Step velocity ν in the c ⃗ and b⃗ directions on the {100} hematin crystal faces as a function of hematin concentration cH. AFM measurements were performed at temperature T = 27.8 ± 0.1 °C, where the hematin solubility is ce = 0.16 mM. Step velocities were measured by tracking single steps (h = 1.2 nm) with interstep distances l ≥ 180 nm. The step kinetic coefficients for growth in the c ⃗ and b⃗ directions, βc⃗ and βb,⃗ are displayed in the plot.

4. INCORPORATION OF MOLECULES INTO STEPS DURING ISLAND GROWTH The edges of the generated layers grow by the association of hematin from the solution. In Figure 4, we report the evolution of five newly formed islands, highlighted in Figure 4a, on a (1̅00) hematin crystal face. Monitoring the island size revealed that the islands grow in both c ⃗ and b⃗ directions. During growth, the island shape transitions from circular to elliptical. The shape of islands with radius R ≈ Rcrit, (where Rcrit is the critical radius for layer nucleation) is thermodynamically controlled.65 The isometric shape of such islands indicates that the surface free energy of the layer edge γ possesses higher symmetry that that of the crystal face. This conclusion complies with the Curie principle, according to which the symmetry of a crystal property can be equal or higher (but cannot be lower) than the symmetry of the crystal. The transition to an elliptical shape is governed by the disparate rate of kinetics of layer advancement in the b⃗ and c ⃗ directions, as we discuss below. The velocity of advancing steps ν is a fundamental growth variable that was measured from sequential in situ AFM images, where step displacements along the b⃗ and c ⃗ directions were tracked with respect to a reference point. Two averages, νb⃗ and νc⃗, were calculated for each hematin concentration. The interstep distances l were also measured for each image along the b⃗ and c ⃗ directions. Figure 5 reveals that ν is a linear function of hematin concentration cH measured with steps separated from adjacent steps by more than 180 nm ν = β Ω(cH − ce)

0 μsolution = μsolution + kBT ln cH

(6)

and 0 eq μcrystal = μsolution = μsolution + kBT ln ce

(7)

We obtain Δμ/kBT = ln(cH /ce)

(8)

The rates of first-order reversible chemical processes are proportional to [exp(Δμ/kBT) − 1].86,87 In turn, the definition of Δμ in eq 8 implies that [exp(Δμ/kBT) − 1] = (cH − ce)/ce. Thus, the correspondence of the ν(cH) data in Figure 5 to the trend predicted by eq 5 indicates that the attachment of molecules to steps is a first-order reversible chemical process. The step velocity ν may deviate from a linear dependence on cH owing to several factors: competition with adjacent steps for the supply of solute,14,39,88,89 insufficient kink density,44,90,91 impurity effects,92,93 and others. The competition for solute occurs at short step separations and is discussed in the next section. The agreement between experimental data in Figure 5, obtained with well-separated steps (l > 180 nm), and the rate expression in eq 5 indicates that the steps are rich in kinks and the effects of impurities are negligible. The data in Figure 5 indicate that βc⃗ = 4.3 ± 0.2 μm s−1 and βb⃗ = 1.6 ± 0.1 μm s−1. The ratio βc⃗/βb⃗ is approximately equal to 2.7, which is consistent with the average c/b aspect ratio of unfinished layers discussed above. The correspondence of these two ratios indicates that the anisotropy of the growing islands in Figure 4 is due to the anisotropic kinetics of step propagation. To understand why νc⃗ is faster than νb,⃗ we note that ν is determined by the free energy barrier for association of molecules to kink sites and the kink density.58 A kink density ratio of 2.7× would correspond to a dramatic difference is step structure, with long straight segments of the steps in the b⃗ direction, which is not observed in Figure 4.42,44,58 Hence, the likely reason for the faster growth along the c ⃗ direction is the lower barrier for incorporation in kinks along these steps than

(5)

In this expression, β is the step kinetic coefficient and Ω is the volume occupied by a hematin molecule in the crystal. To understand this linear relation, we note that the thermodynamic driving force for hematin crystallization is the excess of hematin chemical potential in the solution over that in the crystal, Δμ = μsolution − μcrystal. We again assume that the hematin molecules in the solution do not interact and the respective activity coefficient is equal to unity at concentrations cH of the experiments in Figures 4 and 5 and ce at equilibrium, so that D

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for incorporation into steps moving in the b⃗ direction. The b⃗ and c ⃗ directions are not related by a symmetry operation, and the respective incorporation barriers do not have to be equal. To understand how asymmetric incorporation barriers are compatible with relatively symmetric surface free energy γ, we note that γ reflects the rearrangement of a 2D island, during which molecules dissociate and incorporate into it. It is feasible that the asymmetry of the incorporation barriers is similar to that of the dissociation barriers, leading to a relatively symmetric thermodynamic energies. With this, we can determine the first-order rate constant k for attachment of molecules to kinks, defined as β = ak

(9)

where a is the projection of the molecular dimension on the direction of step growth. Using the above values of β, we obtain k ≅ 104 s−1.

Figure 6. Evidence for the surface diffusion mechanism. (a) Step velocity ν at cH = 0.19 mM in the c⃗ direction as a function of the interstep distance l. The step velocity ν slows down at l < 180 nm, highlighted by shading. (b) The same data in (a) is replotted using coordinates [σ/ν](1/l), where σ = (cH − ce)/ce. Shaded area corresponds to the one in (a). (c) In situ AFM image collected with a disabled vertical scan axis at hematin concentration cH = 0.26 mM. In this imaging mode, the vertical axis represents time. i and ii denote a lower and higher step, respectively; 1, 2, and 3 label the terraces adjacent to these two steps.

5. THE MOLECULAR TRAJECTORY TO A STEP AND STEP−STEP INTERACTIONS There are two possible routes for molecular incorporation into steps: the solute molecules may directly attach to growth sites (e.g., kinks or steps) or they may first adsorb on terraces between steps and diffuse along the surface to incorporate into the growth sites.50−55 These two pathways and the respective energy landscapes are illustrated in Figure 1 b−e. The trajectory for direct incorporation, illustrated in Figure 1b involves a single energy barrier (i) that takes into account multiple factors, including the orientation of the molecule, the geometry of the site, and the displacement of solvent as the molecule docks in the growth site. The surface diffusion pathway, illustrated in Figure 1c, involves several energy barriers: for adsorption on a terrace (i), desorption (ii), diffusion along the surface toward a step (iii), and, finally, for attachment to a growth site (iv). Note that the energy barrier for the latter stage (iv) differs from that for direct incorporation from solution.48 Clearly, the surface diffusion pathway has a richer set of governing parameters that offer varied mechanisms to inhibit the growth process. To discriminate between the two possible mechanisms of molecule incorporation into steps, we used data on the dependence of step velocity on interstep distance l.51,52,54,55,94 During direct incorporation into steps, the solute supply fields are three-dimensional, extending into the bulk solution, and the competition for supply has a marginal effect on the velocity of closely spaced steps.51,94 For the surface diffusion pathway, closely spaced steps compete for supply from a 2D space of the terrace between them and exhibit a strong dependence of step velocity on interstep distance.51,52,54,55 Observations of growing steps on hematin crystals revealed that groups of closely spaced steps move significantly slower than well-separated steps (Figure 6a). The strong interaction between the steps suggests that the molecules enter the steps by way of the crystal surface. An analytical expression for the dependence of step velocity on supersaturation, step spacing, and rate of diffusion through the solution boundary layer for the case of crystal growth from solution was derived by Cabrera and co-workers.88 In the case where diffusion of solute from bulk solution toward the crystal interface is not a limiting factor for step motion, the step velocity can be expressed as51,52 ν=

−1 ⎡Λ 1 l ⎤ λ ΩD (cH − ce)⎢ s + coth ⎥ ⎣ λ h Λ 2 2λ ⎦

where λ is the characteristic length of surface diffusion and D is the diffusivity of the hematin molecules in the solution. Besides λ, the other important kinetic parameters in eq 10 are Λ and Λs. Λ is the resistance, measured as length, for adsorption from bulk solution to the crystal surface; the kinetic coefficient for adsorption is βad = D/Λ. Λs is the resistance for incorporation into kinks from the surface, also measured as length, and, similarly to Λ, it is linked to the kinetic coefficient βsurf for incorporation from the terraces as βsurf = Ds/Λs, where Ds is the surface diffusivity. The Einstein relation for diffusion along the crystal surface is λ2 = 4Dsτ, where τ is the residence time of an adsorbed molecule on the surface. Equation 10 can be simplified under two conditions: when l ≫ 2λ, we have coth(l/2λ) ≅ 1, and when l ≪ 2λ, we have coth(l/2λ) ≅ 2λ/l. We define σ ≡ [exp(Δμ/kBT ) − 1] = (cH − ce)/ce

(11)

and rewrite eq 10 with new coordinates, [σ/ν](1/l), and get for these two limiting cases hΛ ⎡ Λs 1⎤ 1 σ , for l ≫ 2λ = + ⎥= ⎢⎣ 2 ⎦ Ωceβ ν λ ΩceD λ

(12)

and h ΛΛ σ Λ h = 2 s + , for l ≪ 2λ v ΩceD l λ ΩceD

(13)

Equation 12 indicates a constant segment in the [σ/ν](1/l) dependence at high values of l. Comparing this relation with the definition of β in eq 5 yields the second equality in eq 12. According to eq 13, if the surface diffusion mechanism operates, σ/ν should increase linearly with 1/l at low values of l. The data for hematin in Figure 6b comply with both trends and present a second argument in favor of the surface diffusion growth pathway. The value of l at which the straight lines representing eqs 12 and 13 cross is l = 2λ. From here, we evaluate the

(10) E

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characteristic length of surface diffusion λ ≅ 90 nm. The constant σ/ν = 3.3 s nm−1 ratio at high l’s yields β = 4.3 μm s−1, in good agreement with the value determined from the data for νc⃗ in Figure 5. To further validate the surface diffusion mechanism, we monitored with in situ AFM the behavior of steps separated by several nanometers. To improve the time resolution, we disabled the vertical scan axis so that the AFM tip continuously probed a single line parallel to the c ⃗ crystallographic direction. As shown in Figure 6c, the vertical axis in the collected AFM image represents time. The image presents the displacement in the c ⃗ direction of two steps on a (1̅00) hematin crystal surface. The height of each step is ∼1.2 nm, consistent with the lattice parameter in the [100] direction.63 This step pair is separated from other steps by about 200 nm in both the positive and negative c ⃗ directions (i.e., outside the imaging area). Figure 6c demonstrates that, during 52 s of imaging, the lower step, labeled as i, advances by about 5 nm, corresponding to ν ≅ 0.1 nm s−1. During this time, the step velocity is relatively steady, with inevitable fluctuations, despite the increasing separation from the higher step ii. The independence of the step velocity from the width of the higher terrace, labeled 2, indicates that its supply of solute from the side of terrace 2 is insignificant. Furthermore, the velocity of this step is in good agreement with the data for the same cH = 0.26 mM in Figure 5, which were collected with steps separated from their neighbors on both sides by more than 180 nm. This agreement suggests that step i receives a complete supply of molecules from the side of terrace 3, where a competing step is at a distance of about 200 nm. In contrast, step ii exhibits only fluctuations in its position and negligible net growth. This behavior indicates equilibrium with the source of molecules. Importantly, step ii does not grow even though it is separated from its competing step on terrace 1 by about 200 nm, suggesting that molecular incorporation from the side of the higher terrace is prohibitively slow. These collective observations reveal strong asymmetry in the incorporation of molecules into steps from the sides of the two adjacent terraces. Such asymmetry is impossible if molecules reach the steps directly from the solution. On the other hand, asymmetric incorporation is often observed during step growth via adsorption on the terraces and surface diffusion;95 it is referred to as the Ehrlich−Schwoebel effect.96,97 The observed asymmetric incorporation strongly supports surface diffusion as the mechanism of step growth. In situ AFM has provided valuable insight of the pathway for molecular incorporation into steps; however, several questions regarding the mechanism of surface diffusion remain unanswered. One is the existence and potential role of solvent structuring at the crystal surface. Amphiphilic solvents, such as n-octanol, may self-assemble into ordered structures at solid− solvent interfaces. Evidence for solvent ordering on hematin crystal surfaces comes from the determination of the crystallization entropy, ΔSocryst, discussed above. To what degree this ordering, if any, affects surface diffusion is not wellunderstood. Moreover, the solvent may influence the propensity of an adsorbed hematin molecule to “jump” from one terrace to another and influence the value of the Ehrlich− Schwoebel barrier; however, the exact pathways of molecular diffusion on crystal terraces are unknown. Lastly, diffusion constrained between closely spaced steps may follow kinetic laws different from those for Brownian motion in unlimited 2D or 3D spaces.

6. CONCLUSIONS Crystallization is a continually growing field that impacts a myriad of applications spanning energy and electronics to medicine. Fundamental knowledge of crystal growth mechanisms can be used to develop novel and more efficient methods of tailoring material properties (e.g., size and habit) for improved performance in commercial processes. The results presented here demonstrate that, during crystallization from an organic solvent, hematin follows a classical mechanism, whereby new crystal layers spread by molecule attachment to steps. Our findings reveal that molecular attachment to steps strictly follows first-order kinetics. We provide evidence for surface diffusion as a dominant pathway over direct incorporation, which, to our knowledge, is the first indication of the significance of surface diffusion as a mechanism of crystallization in organic media. These insights into the mechanism of hematin crystallization may potentially facilitate the judicious selection of synthesis parameters to modify the rates of crystallization, and hence the optical, magnetic, tensile, and other material properties of bulk crystals. Future studies to assess the impact of solvent selection and the potential roles of solvent structuring may lead to advancements in crystal engineering and our understanding of natural processes, such as malaria pathogenesis. 7. EXPERIMENTAL SECTION Materials. The following reagents were purchased from SigmaAldrich (St. Louis, MO): n-octanol (anhydrous, ≥ 99%), citric acid (anhydrous), sodium hydroxide (anhydrous reagent grade pellets, ≥98%), and porcine hematin. All materials were used as received unless otherwise noted. Deionized (DI) water was produced by a Millipore reverse osmosis−ion exchange system (RiOs-8 Proguard 2 − Milli-Q Q-guard). Preparation of Citric Buffer-Saturated Octanol. For detailed methods see Olafson et al.64 In brief, we prepared citric buffer at pH 4.80 using 50 mM citric acid titrated with 0.10 M NaOH. To citric buffer, we added n-octanol to prepare the initial citric buffer-saturated solution. The resulting two-phase solution was allowed to equilibrate at 23 °C for 30 min. The upper layer, consisting of CBSO, was removed with a pipet far from the interface. Fresh CBSO solutions were prepared before every crystal synthesis and in situ AFM experiment. Preparation of Hematin Supersaturated Solutions in CBSO. We placed CBSO and hematin powder (directly from Sigma-Aldrich) by weight that was sufficient to make a 6 mM solution. The solution was maintained at 39.5 ± 0.2 °C. After achieving the desired hematin concentration, the solution was filtered through a 0.22 μm PVDF membrane. The hematin concentration was measured spectrophotometrically using a previously determined extinction coefficient of ε = 3.1 ± 0.3 cm−1 mM−1 at λ = 594 nm.98 Concentrations of the working solutions were adjusted to a chosen value between 0.1−0.3 mM with the addition of CBSO. The solutions were used in AFM experiments within 3 h of preparation. Hematin Crystal Preparation. We grew hematin crystals (10−30 μm in length) by placing 2 mM hematin powder in direct contact with freshly prepared CBSO. The solution was held at T = 66.4 ± 0.5 °C for two consecutive days followed by a one-day incubation at T = 22.6 ± 0.2 °C. For AFM, hematin crystals were grown on 12 mm round glass coverslips (Ted Pella, Redding, CA). The coverslip was scratched near the center and placed in the vial containing hematin powder and CBSO. The coverslip was removed after synthesis, rinsed with DI water and ethanol, and dried under air. All prepared crystals were used within 1−2 days of drying. In Situ Atomic Force Microscopy. We employed a Multimode atomic force microscope (Nanoscope IV) from Digital Instruments (Santa Barbara, CA) for in situ AFM. We used Olympus TR800PSA F

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probes (silicon nitride, Cr/Au coated, with spring constant 0.15 N/m). We collected images in height and amplitude (or deflection) modes with scan rates between 2 and 2.5 s−1 and 256 scan lines per image. Contact mode images were used in select cases to help visualize surface features; however, all in situ measurements were performed in tapping mode to minimize the possibility of disturbing solute attachment to crystal surfaces. Tapping mode images were collected at a tapping frequency of 32 kHz. For the scans with disabled vertical axis, we used BioLever Mini cantilever (silicon probe with k = 0.25 N/ m) at a scan rate of 4.93 Hz in tapping mode. All in situ AFM experiments were conducted after the fluid cell was flooded with hematin CBSO solutions and equilibrated for 15−30 min. Working solutions were renewed at 30 min intervals to maintain steady solute concentrations. The temperature of the growth solution within the AFM fluid cell during in situ crystal growth monitoring was measured with a copperconstantan thermocouple, connected to a temperature controller (SE5010, Marlow Industries Inc.) and calibrated using a crushed ice/ DI water bath. The thermocouple was embedded in a brass disk positioned right under the AFM sample. The liquid cell was sealed with a silicon O-ring and loaded with CBSO. To replicate the experimental conditions, we continuously imaged for 3 h a 2 × 2 μm2 area at a scanning rate 2.52 s−1. The temperature in the fluid cell reached a steady value of 27.8 ± 0.1 °C within 15 min of imaging. AFM Image Processing. All AFM height, amplitude, and deflection images were corrected by first or third order flattening or by plane fitting. Select images with sizes below 1 μm were processed with a 2D fast Fourier transform filter to remove periodic noise. No lowpass or median filters were applied to the AFM images. Image Analysis for Experimental Measurements. Step velocity ν was determined from time-resolved sequences of in situ AFM height mode images. Using a larger scanning area, we identified the crystal edge defined by the intersection of the studied (10̅ 0) surface and either of the adjacent {010} faces. The crystallographic b⃗ and c⃗ directions are, respectively, at 90.2° and 0° relative to this crystal edge. Lateral drift was accounted for by offsetting the coordinates between sequential images using a reference point on each image. For statistical analysis, a minimum of three steps and as many as 10 steps were tracked in an image sequence. Only single steps, which exhibit a measured step height of 1.17 ± 0.07 nm, were considered. In each image, the step displacements along the b⃗ and c ⃗ directions with respect to the reference point were measured.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (P.G.V.). *E-mail: [email protected] (J.D.R.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Bart Kahr, Leslie Leiserowitz, and David Sullivan for thoughtful discussions of hematin crystallization. This work was supported by NASA (NNX14AD68G and NNX14AE79G), NSF (Grant MCB-1244568), and The Welch Foundation (Grant E-1794).

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