Can Mono Domain Polar Molecular Crystals Exist? - Crystal Growth

Article pubs.acs.org/crystal

Can Mono Domain Polar Molecular Crystals Exist? J. Hulliger,* T. Wüst, K. Brahimi, and J. C. Martinez Garcia Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, CH-3012 Berne, Switzerland ABSTRACT: The growth of polar molecular crystals (near thermodynamic equilibrium) is investigated by a stochastic growth model. Two types of growth are considered: (i) layer by layer growth and (ii) a kink attachment model within a square lattice. An analytical treatment is in qualitative agreement with Monte Carlo simulations. Essentially, a polar seed progresses along the unique axis to form a minor number of orientational defects in one direction, whereas in the opposite direction a “global” reversal of dipolar building blocks is predicted. Polarity reversal can start from a single orientational defect, undergoing continuation and growth in consecutive layers/attachments (kink), leading finally to complete reversal of all molecular dipoles. Eventually, this behavior results in crystals featuring two sectors of opposite average polarity. The number of growth steps upon dipole reversal depends on the intermolecular interactions. It is shown that for lateral coupling close to or smaller than estimated by the Onsager theory of a ferromagnetic transition in 2D (external field H = 0), there is only a small number of attachments needed to obtain reversal, whereas for strong parallel couplings, the number of grown layers before dipole reversal increases exponentially. Our analysis shows that molecular crystals (made of dipolar building blocks) nucleating into a polar seed are subject to a fundamental growth instability which is adverse to the formation of mono domain polar crystals in general.

1. INTRODUCTION Molecular crystals represented by a polar space group are of special interest because their point symmetry allows for a number of physical effects used in many real world applications (e.g., pyro- and piezoelectricity or nonlinear optical effects).1,2 These materials express polar symmetry also by their morphology, etching figures and by an anisotropy in the growth/dissolution speed, R, of faces involving the polar axis.3 For uniaxial groups it is often found that along one direction of the polar axis, growth is very slow as compared to the reverse direction. Examples from the literature reporting on effects of a polar axis on the growth of molecular crystals are listed in Table 1.4−24 Because of the particular symmetry, molecular to surface recognition is different at both ends of a unique axis. Consequently, the differences of attachment energies were discussed in the literature to explain an observed anisotropy in the growth speed R along opposite growth directions. Essentially two models were proposed and analyzed in detail: (i) For crystals growing from solutions,7,5,14 it was argued that solvent molecules due to their interaction with active sites of attachment can give rise to slow growth kinetics. As coordination at both sides of the unique axis is different, slow growth in only one direction is possible. (ii) Misaligned constituents of a growing crystal can cause slowing down of regular attachment. This effect is called self-poisoning25 of growing faces. Taking into account disorder of constituents at growing faces, there is a particular type of orientational disorder, namely, the 180° reversal of dipolar entities. In this paper we present © 2012 American Chemical Society

theoretical results on 180° orientational defect formation which may lead to kinetic hindrance along one direction of the polar axis. Different from previous theoretical work to explain slow growth, here a statistical mechanism is at the origin of dipole reversal, i.e., misaligned constituents promoting kinetic hindrance. For a detailed description and understanding of this statistical approach, we refer to previous work on stochastic polarity formation:26−29 The essential message of a theory accounting for the probability of a 180° misaligned entity is that after a number of attached new crystal planes such reverted dipoles can give rise to a significant change of the total polarity of a crystal. By this kind of a defect mechanism a centric seed can develop net polarity in symmetry related growth sectors, the symmetry groups being the point groups of the seed. Consequently, the building up of net polarity in one sector related, e.g., by a mirror plane (so in point group 2/m), will produce a corresponding sector of the same net polarity, but of opposite sign. In previous work this grown-in real structure was called a bipolar state. A general theoretical elaboration by Markov chain type calculations30−32 has led to a surprising conclusion: Irrespective of starting by a centric or a polar seed, the final growth state of a crystal undergoing significant 180° orientational disorder is always bipolar. The ergodic properties of Markov chain type processes make the final state Received: March 29, 2012 Revised: September 20, 2012 Published: September 24, 2012 5211

dx.doi.org/10.1021/cg300422c | Cryst. Growth Des. 2012, 12, 5211−5218

Crystal Growth & Design

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Table 1. Representative Literature Data on the Growth of Polar Crystals

independent of the original state. In chemistry this is wellknown: Starting from whatever initial composition, an equilibrium state is described by a single constant K(T). The final consequence of this fundamental finding is that irrespective of the structure of a seed, the final as grown state will represent a bipolar state and the sum over all dipole moments is zero.

Examples we have experimentally analyzed in great detail are channel type inclusion compounds33−36 and single component molecular crystals.37 In the case of a molecular crystal such a 4chloro-4′-nitro-stilbene (CNS), the overall packing can be considered as being centric because of a nearly 50:50% up vs down occupation of sites. However, pyroelectric and nonlinear optical techniques have revealed polar sectors involving the b5212



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axis (2) of the crystal.37 The stochastic mechanism is thus breaking the symmetry m of 2/m in P21/c, as originally refined by X-ray crystallography. Therefore, a certain extent of net polarity is grown-in as predicted by our theory, leading to a bipolar state, but with = 0 (P: polarization; vol: volume; : thermal expectation value). In case growth starts by a polar seed, we encounter a particular situation: According to the statistical framework also here the final growth state has to be bipolar. However, this can only be achieved if one side of the polar axis undergoes complete reversal of dipoles. Because this entropically favored process is associated with building up of critical stress within the crystal packing, kinetic hindrance could be the result, which may lead to a suppression of the growth process. For a discussion on the analogy of a Schottky-type quasi equilibrium at growing crystal faces and 180° orientational disorder of dipolar molecules see ref 38. The present work will systematically elaborate on stochastic dipole reversal being a fundamental property of growing crystals here described within the frame of nearest neighbor interactions. In the next section we will define and introduce the model used in analytical and Monte Carlo (MC) calculations; see also refs 28, 29, and 43.

interactions42 is in preparation. It is important to notice that in all calculations thermal equilibrium is assumed for establishing normal or faulted orientations and progress in growth is described by (i) a layer by layer or (ii) a kink attachment model within a square lattice (see Figure 2). For conceptual and technical details, see refs 28, 29, and 43. In (i) the Monte Carlo procedure starts by a seeding layer onto which a first ad-layer is placed for achieving a thermalized state in regard to the up vs down state of dipoles. By admitting one layer after the other, growth is described. Implementation of (ii) assumes attachments only at a kink sites. The up vs down state is set by probabilities allowing for a preferred orientation. The layer by layer growth model is a very convenient one for setting up a theoretical model; however, it is not realistic enough to account for a real growth situation. Therefore, we have included the classical kink attachment type. It is important to notice that a comparison of the two models showed phenomenological agreement between them. Kinetic effects arising, e.g., at large driving forces (supersaturation, supercooling), are explicitly not addressed here. Dipole reversal is thus discussed in the limit of growth speed R → 0, i.e., Δμ → 0 (chemical potentials of the crystal and nutrient are almost the same). This is an important assumption as we do not want to describe effects being dominated by fast kinetics. In real growth experiments, where nucleation may take place at large supersaturation, early growth can be quite fast. For comparison with present theoretical results, growth in evacuated ampules exposed to a small thermal gradient of ∼1 K represent a reasonable approach, as growth under these conditions takes place near thermodynamic equilibrium. 2.1. The Origin and Fate of Single Orientational Defects. Let us assume that a cooperative process, called nucleation, has created a seed crystal representing a uniaxial polar point group (2, 3, 4, 6, mm2, 3m, 4mm, 6mm). This seed is supposed to develop (hkl) and (h̅kl̅ ̅) faces along both directions of the polar axis (2, 3, 4, and 6). Given by symmetry, growth along the + and − direction is subject to different effective coupling energies. This situation is schematically shown in Figure 2: For simplicity dipoles are indicated as parallel arrows, although they are allowed to be tilted. Attachments (ongoing growth) may be described by a (i) layer by layer (Figure 2a) or (ii) a kink (Figure 2b) process. Configurational entropy (associated with 180° orientational faults38) within this up vs down description allows lowering the free energy in both cases (i), (ii). At this point we are interested to know the ratio of the probabilities P to create an 180° orientational fault at either the + or the − side of the polar axis. In agreement with former work27,28 and notations therein, we call these probabilities PI and PII (see Figure 2). PI thus refers to the + direction, i.e., site I in Figure 2, accounting for a faulted interaction (PII correspondingly). Numerical values can be obtained from a Boltzmann factor involving the interaction of “incoming entity to surface”, divided by the state sum.27,28 In order to understand on which side (I) or (II) of Figure 2 dipoles reversal is most likely to take place, we simply ask for the ratio of these two error probabilities PI, PII given as

2. THEORETICAL FRAMEWORK To set up a frame as general as possible we reduce crystal constituents (neutral, dipolar) to entities providing a structure as shown in Figure 1. A crystal is thus looked at as composed of

Figure 1. Scheme reflecting the polarity and topology of molecules to which the present analysis preferably may apply. A: electronic acceptor fragment. D: electronic donor fragment. π: delocalized π-electron system.

quasi particles, each featuring two orientational states (↓, ↑).To account for most contributing interactions with nearest neighbors, we introduce effective energy couplings EAA for A···A, EDD for D···D, and EAD for A···D contacts. These interactions are called longitudinal, referring to the “elongated” shape of typical organic molecules featuring an asymmetrical structure by parts representing acceptor (A) and donor (D) properties. The interaction parameters accounting in the lateral direction are Ep and Eap (p: ↑···↑; ap: ↓···↑). This topological reduction allows us to obtain a minimum set of free, effective energy parameters, i.e., ΔEA ≡ EAA − EAD, ΔED ≡ EDD − EAD, and ΔE⊥ ≡ Ep − Eap, being sufficient for a phenomenological description of growth induced polarity formation. Within our statistical approach these three parameters drive the system for orientational order/disorder at temperature T. Similar approaches based on nearest neighbors interactions were used to understand basics in crystal growth,39 surface roughening,40 and alloy formation including spinodal decomposition.41 A model taking into account long-range (force field type)

PdI PdII 5213

=

1 + e(ΔEA − ZΔE⊥)/ RT 1 + e(ΔED − ZΔE⊥)/ RT

(1)



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Figure 2. Graphical representation of the direction of dipoles in each domain after a certain number of attachments to a seed providing perfect polar ordering. Energies for defect formation at site I and II are different. + and − indicate the absolute direction of the polar axis. In the case of ΔEf < 0, reversal will take place at the −, II side as indicated. T: Temperature for thermalization.

where d means primary (single) 180° defect formation, and Z is the effective coordination number (Z = 4 for a square lattice in case of layer by layer growth, Z = 2 for kink attachment). Since we restrict ourselves to the positive sector for longitudinal coupling parameters, i.e., ΔEA, ΔED > 0, and ΔE⊥ < 0 (see also Figure 3) the exponential functions in eq 1 are much larger than 1, which allows us to simplify eq 1:

PdI PdII

Whatever polar crystal seed we consider being made of dipolar building blocks, dipole reversal is likely to occur in case there is a significant difference in EAA − EDD, i.e., Eatt(←···S) − Eatt(→ ···S) ≠ 0. For a positive sign of ΔEf dipole reversal will take place on faces preferably decorated by donor (D) moieties. Correspondingly, a negative sign will induce reversal for faces presenting acceptor (A) moieties to the nutrient (see Figures 1 and 2). A straightforward calculus allows us to say which side of the polar axis of an initial crystal should preferably undergo complete dipole reversal upon growth. To a good numerical approximation, the ratio of PI/PII is independent of the lateral coupling parameter ΔE⊥. The effect ΔE⊥ can have on the behavior of a system is elaborated in section 2.2. Here, we just conclude, that irrespective of the number of growth steps, one side of the polar axis is showing preferred reversal. How many attachments of layers are thus needed to effect reversal and how large does the density of single defects have to be, for starting the process? This shall be answered by MC simulations. 2.2. Results from Monte Carlo Simulations. We have performed extensive Monte Carlo simulations over the entire range of effective lateral energy couplings (favoring parallel over antiparallel alignments) to study the main features of growth induced polarity formation. Figure 3 summarizes the results assuming a layer by layer (a) and kink (b) growth model, respectively. For longitudinal interaction parameters, typical values were selected (for details, see caption of Figure 3). At zero lateral coupling, polarity is not vanishing as demonstrated by Markov chain theory.30−32 Here, xnet is a measure for net polarity, defined as xnet ≡ x(↓) − x(↑), x being the molar fraction of molecules pointing downward or upward in the sector involving the + direction. In both cases the system undergoes an antiferromagnetic-like ordering phase transition29 (visible as a bump in the xnet curves on the right side). Figure 3 represents a phenomenological summary of the general behavior of crystals undergoing 180° orientational disorder. To the right side we describe crystals being really

≈ eΔEf / RT (2)

with ΔEf ≡ ΔEA − ΔED = EAA − EDD. Equations 1 and 2 imply that defect formation with respect to sites I or II in Figure 2 can be significantly different and there is no dominant effect of the lateral interaction ΔE⊥. All depends on what makes growth induced polarity formation28,29 possible: EAA − EDD, i.e., in general, the longitudinal energy difference, if an acentric molecule is interacting with a crystal surface (S) by its “tip” or “back” (→···S vs ←···S). This representation of the interaction “molecule to surface” is more general, than parameters ΔEA, ΔED introduced above. However, as long as S···← is different from S···→, there is no conceptual contradiction. On the way to complete dipole reversal on one side of the polar axis, two consecutive processes are considered: c: continuation of defects in the next layer; and g: growth (enlargement of a defect); both succeeding primary defect (d) formation. The analytical treatment yields formally the same result for c and g processes as given by eq 1. Since we consider primary defect formation (d), continuation of a defect (c) and its enlargement (g) as being independent random processes driven by individual probabilities Pi (i = d, c, g), the total probability P to start and finally complete dipole reversal is described by the I,II I,II product of the three probabilities PI,II d , Pc , and Pg :

PI ≈ e3ΔEf / RT P II

(3) 5214



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ε=−

RTc 2.269

(5)

with R, gas constant. Below this value of ΔE⊥(Tc), the number of layers q needed to revert all dipoles is steeply increasing for the layer by layer growth model and may reach macroscopic size to accomplish reversal (Figure 4a). Closer to reality of growing surfaces we consider kink attachments (Figure 4b). Here, dipole reversal is obtained already by the first layer or after a few completed layers, depending on the value of ΔE⊥ < 0 (Figure 4b). In order to quantitatively determine the origin of dipole reversal (measured as the average number of completed layers, qswitching, before dipole reversal starts) we proceeded as follows: A Monte Carlo simulation runs until dipole reversal is entirely completed. Then all connected, reverted dipoles are detected by means of Hoshen−Kopelman cluster labeling anlysis.46 The minimum value of q for the largest such cluster marks the origin of dipole reversal. Figure 5 shows qswitching as a function of ΔE⊥ for various longitudinal energy couplings for layer by layer (a) and kink (b) growth, respectively. For the chosen energy parameters, an analytical approach predicts a linear law behavior, where the derivative m is given by:

|m| = 5Z /2RT

Indeed, the observed linear trend of the log-scale plots in Figure 5 is in good agreement with eq 6, both for layer by layer (Z = 4) and kink (Z = 2) growth. Surprisingly, a very low defect concentration (xnet ≤ 0.01) can give rise to reversal, whereas the counter side of the axis never underwent reversal along all our numerical calculations, even for a very large number of attached layers. This kind of stochastic twinning typically can start from a single defect (d) being continued (c) and enlarged (Figure 4) by further growth (g) of a crystal. There is no evidence from theory that this “kinetic” transition would need a critical size of a reverted cluster. There is also no evidence that dipole reversal should not take place below a certain ΔE⊥(Tc) value. The number of grown layers before the start of dipole reversal, however, increases exponentially (see eq 6) and might thus surpass the real length of a crystal, being thus a reason for obtaining monopolar crystals in real growth experiments.

Figure 3. General features of growth induced polarity formation in single component crystals. Curves: xnet vs lateral coupling ΔE⊥ for two different longitudinal couplings (solid/dashed), solid line: ΔEA = 5 kJ/ mol, ΔED = 2 kJ/mol, dashed line: ΔEA = 11 kJ/mol, ΔED = 2 kJ/mol, RT = 2.5 kJ/mol (T = 300 K; R, molar gas constant); error bars are too small to be shown. Shaded backgrounds and corresponding inset figures (showing typical cross sections of crystals growing along both directions upon a given seeding state; blue/red squares: down/upward oriented molecular dipoles) indicate regions of different phenomenological behavior of growth induced polarity formation. q represents the number of newly attached/accomplished layers. For ΔE⊥ < 0, the region boundary is given by the Onsager value (ΔE⊥ = −2.199 kJ/mol, eqs 4 and 5); for ΔE⊥ > 0, the boundary is defined by the value of ΔE⊥ where the second order transition takes place (here shown for the solid line). (a) Layer by layer growth; (b) kink growth.

3. DISCUSSION Present calculations demonstrate that a polar seed growing step by step (at very low driving force) will develop into a final state representing two polar domains of equal average polarization, but opposite in sign (bipolar macrostate; see Figure 3). Are there real crystals representing such an as-grown state? Structure types which allow for 180° orientational disorder because there is practically no stress associated with this state may serve for a comparison: For 4-chloro-4′-nitrostilbene (a system we have extensively investigated by X-ray diffraction,47 scanning pyroelectric microscopy48 and phase sensitive second harmonic microscopy49), on average a polar space group (P21) was found with significant deviation from a 50:50% population (↑ vs ↓) of dipoles. The microscopy techniques revealed a bipolar state for sectors involving the polar axis 2. However, for this and similar cases, we do not know the symmetry of the seed: (i) In case it started by being centric, a few layers of growth will produce the average polar order found by X-ray. (ii) In case it started by a polar seed, a few layers are needed and both sides of the polar

centric, i.e., showing almost no polarity by disorder. To the left side, crystals are almost perfectly polar, however, bearing a potential for reverting dipoles. In the mid zone we have the transition cases: at ΔE⊥ = 0 ideal inclusion systems are found, showing no lateral interaction. For values ΔE⊥ > ΔE⊥(Tc) (less negative) the tendency to revert dipoles on one side of the polar axis is strongly increasing and disorder on both sides of the axis is considerable. ΔE⊥(Tc) can be calculated from the Onsager theory on ferromagnetic ordering in the 2D Ising model (H = 0):44,45 ΔE⊥(Tc) = 2ε

(6)

(4)

In Onsager’s exact solution, the relation between Tc and ε reads as 5215



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Figure 4. Snapshots of growing crystals under dipole reversal. (a) Layer by layer growth; (b) kink growth. Colored domains indicate reversed dipoles with respect to the initial dipole orientation (empty space). Connected clusters of reversed dipoles have the same color. The chosen colors themselves have no physical meaning and only serve to better distinguish the various domains. q is the number of layers by which growth proceeds. ΔEA = 5 kJ/mol, ΔED = 2 kJ/mol, lateral interaction = −2.4 kJ/mol, RT = 2.5 kJ/mol (T = 300 K; R, molar gas constant). Here, a donor type substrate was used (ΔEf > 0).

A class of polar compounds we did not address so far is molecular based ferroelectrics of neutral molecules.51−55 By lowering the temperature below Tc some centric materials undergo a solid to solid transition into a polar and switchable (E ≠ 0, electrical field) state. Here, the probability to form polar domains is equal for all symmetry equivalent directions in the native lattice. Because of this degeneracy a mono domain is in principle not to be expected, although it can be found experimentally for reasons of processing (e.g., anisotropic cooling). A further class of molecular crystals made of centric molecules crystallizing in a polar space group needs some comments: Here we have to distinguish between geometrically polar and physically polar. The present model is based on “molecule-to-surface-interactions” excluding a center of symmetry. In case we have a symmetrical molecule, the “moleculeto-surface-geometry” is still acentric, but reversal of the molecule will yield the same attachment energy. Because of Eatt(→···S) ≠ Eatt(←···S) being the basic ingredient of the present theory and argumentation, we cannot account for these types of crystals, however, showing very weak macroscopic effects of polarity as known.

axis will again adopt an equal level of opposite average polarity, after reversing very early. In any case, a bipolar macrostructure is obtained, being experimentally confirmed. For clarity we have to add here a comment on the length scale of different experimental techniques: X-ray is averaging over the volume radiation is passing, typically on the order of 300 μm. Scanning pyroelectric microscopy48 is resolving a few micrometers at best. Second harmonic generation49 is limited to the order of the ground wave (∼1 μm). A modern technique allowing for a nanometer resolution is scanning piezoelectric microscopy.48 The general situation in crystals where dipole reversal is associated with the building up of significant stress is certainly different. Consequently, we argue that the statistical demand for reversal in crystals where this twinning process is leading to a critical amount of stress, growth may exceed kinetic hindrance up to a complete stop. In case we would rigorously apply the result of the kink model to real growth, crystals will develop into an 180° orientational polar twin upon the first layer of attachment (ΔE⊥ ≳ −4 kJ/mol, T = 300 K). In reality, however, the real mechanism leading to attachment of a building block may lead to a few layers necessary. Under these more realistic conditions kinetic control, i.e., slowing down growth by faulted orientations, is likely. There is another form of twinning which can macroscopically cancel polarity: lamellar twinning. In 4-iodo-4′-nitrobiphenyl for example,50 the planes (containing the polar axis 2) undergo 180° orientational disorder to form stacks of nanometer thickness, producing a nonpolar morphology, although individual lamellae show mm2 symmetry. However, here a twinning plane exists, which does not raise large barriers for growth under reversal.

4. CONCLUSIONS In summary we are about to answer the key question in the following way: By results of the present stochastic theory a centric or polar seed made of dipolar molecules (growing in the high vacuum at very low driving force) is expected to develop into a bipolar macroscopically nonpolar total state (see Figures 2, 3, and 4). Because of a stochastic mechanism of twinning, reversal upon single 180° orientational faults may lead to kinetic hindrance for one of the polar growth directions. As a result, a quasi mono 5216



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found in real growth experiments are considered as a result of (i) kinetic control or (ii) low probability in view of a stochastic need for dipole reversal. Although we argue by kinetic control (i) as previous work in this field (see references in Table 1), the mechanism behind it is a different one. As present calculations are based on nearest neighbor interactions, MC studies involving long-range coupling will be performed. However, because nearest neighbor (mean field) models are generally able to reproduce basic features of solid state phenomena, we expect to reproduce dipolar reversal as well, however at altered numerical measure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the Swiss National Science Foundation, Project No. 200021-129472/1. REFERENCES

(1) Weber, M. J., Ed. Handbook of Laser Science and Technology, Supplement 2: Optical Materials; CRC Press: Boca Raton, 1995. (2) Nalwa, H. S.; Miyata, S. Nonlinear Optics of Organic Molecules and Polymers; CRC Press: Boca Raton, 1997. (3) Curtin, D. Y.; Paul, I. C. Chem. Rev. 1981, 81, 525. (4) Ryu, G.; Yoon, C. S. J. Cryst. Growth 1998, 191, 190. (5) Cang, H. X.; Huang, W. D.; Zhou, Y. H. J. Cryst. Growth 1998, 192, 236. (6) Valluvan, R.; Selvaraju, K.; Kumararaman, S. Mater. Lett. 2005, 59, 1173. (7) Srinivasan, K.; Kanimozhi, S. Cryst. Res. Technol. 2010, 45, 611. (8) Buguo, W.; Weizhuo, Z.; Cheng, Y.; Erwei, S.; Zhiwen, Y. J. Cryst. Growth 1996, 160, 375. (9) Youping, H.; Genbo, S.; Feng, P.; Bochang, W.; Rihong, J. J. Cryst. Growth 1991, 113, 157. (10) Shekunov, B. Y.; Shepherd, E. E. A.; Sherwood, J. N.; Simpson, G. S. J. Phys. Chem. 1995, 99, 7130. (11) Brezina, B.; Hulliger, J. J. Cryst. Res. Technol. 1991, 26, 155. (12) Shepherd, E. E. A.; Sherwood, J. N.; Simpson, G. S.; Yoon, C. S. J. Cryst. Growth 1991, 113, 360. (13) Srinivasan, K.; Biravaganesh, R.; Gandhimathi, R.; Ramasamy, P. J. Cryst. Growth 2002, 236, 381. (14) Srinivasan, K.; Gandhimathi, R.; Biravaganesh, R.; Ramasamy, P. Mater. Sci. Eng. 2001, B84, 237. (15) Chen, B. D.; Garside, J.; Davey, R. J.; Maginn, S. J.; Matsuoka, M. J. Phy. Chem. 1994, 98, 3215. (16) Chen, B. D.; Garside, J. Phys. D: Appl. Phys. 1991, 24, 131. (17) Srinivasan, K.; Sherwood, J. N. Cryst. Growth Des. 2005, 5, 1359. (18) Shimon, I. J.; Wireko, F. C.; Wolf, J; Weissbuck, I.; Addadi, L.; Berkovitch-Yellin, Z.; Lahav, M.; Leiserowitz, L. Mol. Cryst. Liq. Cryst. 1986, 137, 67. (19) Wireko, F. C.; Shimon, L. J. W.; Frolow, F.; Berkovitch-Yellin, Z.; Lahav, M.; Leiserowitz, L. J. Phys. Chem. 1987, 91, 472. (20) Davey, R. J.; Milisavljevic, B.; Bourne, J. R. J. Phys. Chem. 1988, 92, 2032. (21) Anwar, J.; Chatchawalsaisin, J.; Kendric, J. Angew. Chem., Int. Ed. 2007, 46, 5537. (22) Han, G.; Poornachary, S. K.; Chow, P. S.; Tan, R. B. H. Cryst. Growth Des. 2010, 10, 4883. (23) Martin, S. A.; Dhas, B.; Natarajan, S. Mater. Lett. 2008, 62, 2633. (24) Moolya, B. N.; Jayarama, A.; Sureshkumar, M. R.; Dharmaprakash, S. M. J. Cryst. Growth 2005, 280, 581. (25) Gervais, C.; Hulliger, J. Cryst. Growth Des. 2007, 7, 1925.

Figure 5. Dipole reversal (qswitching) as a function of ΔE⊥ for several combinations of ΔEA and ΔED, respectively, from Monte Carlo simulations. (a) Layer by layer growth, average of 20 independent simulations. (b) Kink growth, average of 200 independent simulations. qswitching denotes the number of completed layers at the start of dipole reversal. RT = 2.5 kJ/mol (T = 300 K; R, molar gas constant). All energies in [kJ/mol].

domain crystal object may be obtained. In case a structure can accommodate a continuous increase of 180° orientational faults (no critical stress), the object may develop into a bipolar state upon a certain number of growth steps. Following strictly the kink growth model, a crystal may develop into a bipolar state upon the first few layers. In case the probability for dipole reversal is very low, the real length of a crystal may not be sufficient to achieve reversal and thus a monopolar object is obtained. The present study provides a completely new perspective of crystal growth of molecular materials made of polar building blocks. So far, theoretical approaches involving force-field based structure prediction or molecular dynamics based surface calculations did not take into account the statistical role of single defects along the process of growth and its final state. Analytical reasoning on the fate of single orientational defects, confirmed by Monte Carlo simulations, however, has revealed the crucial effect of a low number of primary orientational defects, becoming active for reversal only on one side of a polar axis. Consequently, mono domain polar molecular crystals 5217



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Can Mono Domain Polar Molecular Crystals Exist? - Crystal Growth

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