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Thermal expansion study as a tool to understand the bending mechanism in a crystal Sumair A. Rather, and Binoy K. Saha Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00360 • Publication Date (Web): 16 Apr 2018 Downloaded from http://pubs.acs.org on April 16, 2018
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Crystal Growth & Design
Thermal Expansion Study as a Tool to Understand the Bending Mechanism in a Crystal Sumair A. Rather, and Binoy K. Saha* Department of Chemistry, Pondicherry University, Pondicherry 605014, India.
Supporting Information Placeholder ABSTRACT: Here for the first time thermal expansion study has been explored to understand the bending mechanism in crystals. Dimorphic 4-chlorobenzonitrile has been chosen to demonstrate it. We have postulated that some of the structural features of the concave and convex sides of the bent crystal would resemble thermally compressed and expanded crystal structures respectively in the expansion-contraction bending mechanism. In this mechanism it has been shown that the strain is proportional to the thickness of the crystal and inversely proportional to the radius of the curvature of the bent crystal. On the other hand, in the case of slip plane mechanism, the amount of sliding of a layer with respect to its neighbor at the two terminals of the crystal is proportional to the arc angle of the bent crystal and the distance between the two consecutive slip planes.
Owing to their enormous potential applications in materials science and biomedical field, during the last decade thermal expansion and flexible materials of small molecular crystals have gained some special attention among the re1-10 searchers. Thanks to some of the recent pioneering works by Desiraju, Naumov and Reddy in the field of bending crys9-23 tal. As a part of emerging field, new mechanisms and concepts are being postulated based on the structural features that are present in few crystal systems and then later on some of these are also being rejected or modified when not being followed in some other systems. For example, initially it was thought that bending needs weak interactions as a 20,21 prerequisite and plastic bending needs anisotropic inter13,20,21 actions as well as slip plane. However, some of the recent studies revealed that bending may even occur around 22,23 the strong hydrogen bonds and though anisotropy and slip planes are the two important parameters, they are not 4,15,24 essential for plastic bending . Some of these anomalies happen mainly due to the lack of supporting tools to prove the postulated mechanisms. Owing to the presence of mosaicity near the bent region, it is almost impossible to find out the structural changes that occur due to bending via single 12 crystal XRD and therefore, it is difficult to understand the actual mechanism through which the bending takes place. Only very recently Naumov et al. showed that Synchrotron Infrared Microscopy, coupled with theoretical calculation, could be used to understand the structural perturbation that 18 takes place at the bending site. Though there are reports where thermal expansion studies have been used to understand the anisotropy of expansion, 19,25-27 phase transformation and thermosalient effect, to the best of our knowledge, so far there is no such attempt to understand the bending mechanism in single crystals of the
small molecules. Bending in organic single crystal is generally an anisotropic phenomenon the crystal bends on a particular opposite pair of parallel faces along an axis and is brit9,13 tle on the other faces. Thermal expansion in crystals is also 5-7 anisotropic (except cubic systems). One of the parameters, useful for bending, is the presence of weak intermolecular 20,21 interaction in the crystal structure. The magnitude of thermal expansion also depends strongly on intermolecular interaction where weak interactions generally experience 26-29 larger thermal expansion. Bending mechanism relies on 10,12 molecular movement which is also the case that happens 30 during thermal expansion . Most importantly, it has been noticed that in many cases structural distortions caused by thermal and pressure treatment are similar and the directions of linear positive thermal expansion and positive linear 31 compressibility are same. Therefore, is it possible to correlate the bending property with thermal expansion? In other words, can thermal expansion study shed some light on the bending mechanism of a single crystal? With this aim, we have studied thermal expansion properties of a bending crystal, 4-chlorobenzonitrile. 4-chlorobenzonitrile is known as a dimorphic com32,33 pound. One of the forms crystallizes in a centrosymmetric space group, P21/c (Form-E) and the other form crystallizes in a noncentrosymmetric space group, Pc (Form-P). Desiraju and co-workers have mentioned the bending property of the 21 Form-P, though they did not perform any detail bending study on this form. Interestingly, in our study we have noticed that Form-E exhibits elastic bending whereas the FormP exhibits plastic bending. Here we have studied bending as well as thermal expansion properties of these two forms and then attempted to correlate these two properties. In Form-E (P21/c) there is only one molecule in the asymmetric unit and the molecular planes are parallel to each other and roughly parallel to the crystallographic (4 0 5) plane. The aromatic rings are stacked, with some offset, along the “a” axis and form an angle of ~62 with the “a” axis (Figure 1). The molecules form CNClC halogen bonds along the [1 0 1] direction and weak CHClC and CHNC interactions along the “b” axis. All these interactions are weak in nature and the bonding distances (268 K) are slightly longer than the sum of vdW radii of the two interacting atoms. Therefore, in terms of interaction strength, the structure is isotropic along all the directions. It has been previously proposed that isotropic interactions facilitate elas22 tic bending. Form-P crystallizes in a noncentrosymmetric space group, Pc, with one molecule in the asymmetric unit. A quick literature survey on reported bending crystals of achiral molecules suggests that 29% of the crystals crystallize in noncentrosymmetric space group (Supporting information, Table S1).
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Interestingly, this value is much higher than what is found among the overall small achiral organic compounds crystal34,35 lizes in noncentrosymmetric space groups (10 15%). Unlike Form-E, here the molecular axes are not parallel/antiparallel to each other, rather oriented in two different directions (Figure 2). One benzene ring is almost parallel to the (53 5) plane and the other ring is almost parallel to the (2 1 2) plane. If viewed down the “c” axis, the molecules are appeared to be in a zig-zag arrangement. Similar to Form-E, in this structure also the interactions are weak and none of the short contacts are within sum of vdW radii (268 K). Unlike Form-E, there is no CNClC halogen bond in the crystal structure of Form-P but the CHClC and CHNC weak contacts are present as usual. Therefore, the interac4,15 tions in this crystal structure are also isotropic in nature. (a)
(a)
(b)
Figure 2. View along the (a) “a” and (b) “c” axes of the crystal structure of Form-P. The plausible slip planes are shown in (a) and the hinge angle that changes with temperature has been shown in (b). Various CHNC and CHClC interactions are shown.
(b)
Figure 1. View along the (a) “a” and (b) “b” axes of the crystal structure of Form-E. Various CHNC, CHClC, CNClC and stacking interactions are shown. Face indexing experiment suggests that the crystals of both the forms grow (long axis of the crystal) along the crystallographic “a” direction and the wider side face of the crystals is 26 parallel to the (0 0 1) plane. The forceps-needle experiments on the single crystal of these two forms suggest that both the crystals bend on the (0 0 1) plane along the “a” axis and the bending is elastic in the case of Form-E but it is plastic in the case of Form-P (Figure 3).
Elastic bending causes shortening of the layers in the concave side and lengthening of the layers in the convex side (expansion-contraction mechanism). If the length of the straight crystal is L0, thickness T and the crystal forms a circular loop (Scheme 1) of radius R, then Lv L0 = 2[R + (T/2)] 2R = T and L0 – Lc = 2R 2[R (T/2)] = T (the length of the concave and convex sides of the loop are Lc and Lv respectively). The generated strain on the surface layers are (Lv L0)/L0 = (L0 Lc)/L0 = T/2R = T/2R, which depends upon the thickness as well as the radius of the loop but independent of the length of the crystal. Therefore, for a typical 10 mm long crystal with 0.2 mm thickness, the strain would be 0.06. That means, due to bending, the unit cell length along the bending axis has to be expanded by 6% in the convex side face and compressed by 6% in the concave side face which is in the order of thermal expansion when a crystal of typical small organic molecule is heated by ~150 C. Therefore, structural distortion occurs due to thermal expansion can be used to visualize some of the probable structural changes that occur due to bending. In the present case, as the bending is small (Figure 3a), the R is large and hence strain also would be small. On the other hand, if slip plane
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Crystal Growth & Design mechanism (generally occurs for plastic bending) works for bending, then Lv = L0 = Lc (Scheme 1). Sliding would be minimum at the middle of the crystal and maximum at the two edges of the crystal. Therefore, the amount of sliding at each end would be (Lv – Lc)/2 = [{R + (T/2)} {R (T/2)}]/2 = .T/2, where = angle in radian of the arc, a part of a circular loop of radius R (Scheme 1), made by the two edges of the bent crystal at the center of the circle and Lv is the length of the convex surface if there were no sliding. If the distance between the two consecutive slide planes is “S”, then the number of slide plane present within the thickness “T” is (T/S)-1 T/S (as T/S >> 1). Therefore, at the two edges of the crystal, the average amount of sliding by a plane with respect to its neighbor is (.T/2)/(T/S) = .S/2, which is independent of the thickness as well as the length of the crystal but depends upon the distance between the slide planes and the arc angle. Therefore, a higher bending or a longer distance between the two consecutive slip planes would require a larger sliding around the slip plane near the two edges of the crystal. It may be noted that the concave surface has larger arc angle than that of the convex surface in the case of sliding mechanism but the magnitudes are same in the case of expansion-contraction mechanism. For a bending crystal with a typical distance of 10 Å between the slip planes, the two consecutive planes around the slip plane have to slide with respect to each other by 31.4 Å or 15.7 Å near the two edges if the crystal forms a complete circular loop ( = 2 radian) or a semicircular arc ( = radian) respectively, which are quite long distances in the molecular level. Apart from these modifications, it may be noted that there is a third type of structural rearrangement that occurs due to bending at each plane, parallel to the bent surface, in both types of mechanisms.
Figure 3. Elastic (a) and plastic (b) bending of Form-E and Form-P single crystals respectively. Thermal expansion studies have been performed on FormE in the range of 163 – 283 K (Supporting information, Table S2). The major thermal expansion principal axis (X3) is roughly parallel to the “a” axis (Supporting information, Table S4) and it has been found that it is almost perpendicular to the molecular plane. Generally, planar molecules vibrate more strongly perpendicular to the plane rather than along 27 the plane. Apart from this vibrational expansion, there is a sliding of the stacked molecules along the “a” axis. Combination of these two effects causes the major thermal expansion principal axis (X3) to be aligned approximately along the “a” axis. Therefore, compared to the other directions, along the “a” axis the molecular packing can be easily distorted upon the application of heat. As the temperature
increases, the offset value of the stacking also increases due to sliding of the molecules along the “a” axis, which in turn increases the inclination angle of the molecule with respect to the “c” axis and also increases the length of the “a” axis (Figure 1b).
Scheme 1. Schematic representation of the straight and bent crystals, neutral planes (dotted lines), arc angle ( radian), concave and convex surfaces, and radius (R) of the circle made of the bent crystals. In the case of expansion-contraction mechanism, the length of the concave (Lc) and convex (Lv) surfaces differ, but is same. This is vice versa in the case of slip plane mechanism. When a crystal bends upon the application of some stress, the pressure is increased in the concave side whereas it is decreased in the convex side of the bending region of the crystal. Therefore, the molecular arrangement in these two sides also would be different. It is known that pressure and temperature has inverse relationship but causes similar types 31 of structural changes. Therefore, we postulate that at the convex side of the bent crystal the molecular arrangement resembles thermally expanded molecular arrangement (high temperature structure), whereas at the concave side of the crystal the molecular arrangement resembles thermally contracted molecular arrangement (low temperature structure). The molecules slide in such a way that in the concave side they are stacked with a smaller offset and in the convex side they are stacked with a larger offset. This causes shortening of the “a” axis in the concave side and lengthening of the same axis in the convex side (Scheme 2). Previously Hayashi et al. proposed this type of sliding mechanism for the bend9 ing of 4,7-Dibromo-2,1,3-benzothiadiazole crystal. As a result of this type of rearrangement, the close packing is still maintained throughout the crystal except some small mosai12 city near the bending region. In the present case, during sliding on the surface of another molecule, the negatively polarized equatorial region of the Cl atom of one molecule encounters another negatively polarized equatorial region of the Cl atom at one end (when offset decreases) and negatively polarized N atom at the other end (when offset increases) of the other molecule. In between these two extreme ends, the Cl atom can slide on the surface of the aromatic ring only with small difference in energy and therefore, the crystal shows an elastic bending. In this way it is possible to expand the “a” axis by 40% which is much higher than what is actually required in this case. The crystal of Form-P was heated in the range of 163 – 283 K (Supporting information, Table S3) and structural changes were analyzed. Similar to Form-E, the major thermal expan-
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sion principal axis (X3) was found almost parallel to the “a” axis (Supporting information, Table S4) that is approximately along the resultant of the normal of the two rings planes. Therefore, in this crystal also the molecular movement is more prominent along the “a” direction under thermal treatment. In the structure, we found a plausible slip plane which is parallel to the (0 0 1) plane as well as the wider side face of the crystal that bends plastically. The molecules around the slip plane slide along the “a” axis which is the major thermal expansion axis (X3) and also the long axis of the crystal. The “a” axis is just ~4 Å and therefore, during sliding along this axis, an atom always slides on the surface of the same type of atom. During the sliding process the interaction angles change continuously. As the interactions across the slip plane are only of weakly directional CHNC and CHClC type, there is not much compromise in terms of energy.
In summary, we have shown that one of the dimorphic forms of 4-chlorobenzonitrile exhibits elastic bending and the other form exhibits plastic bending. We have performed thermal expansion studies on these two systems to analyze the structural changes that occur at high and at low temperatures and then used these structural changes to explain plausible bending mechanism. In these cases, the long axis of the crystal that bends also is the direction of the major principal thermal expansion axis. We postulated that the rearrangement of the molecules at the concave side of the bent crystal resembles some of the structural features that are obtained at low temperature, whereas the rearrangement of the molecules at the convex side corresponds to some of the structural features that are obtained at high temperature. We also have shown that the presence of non-centrosymmetric space group among the bending crystals is quite high. Noncentrosymmetric space group generally causes loose packing and in most of the cases bending also rely on the weak interactions. Therefore, though it would be too early to draw any conclusion at this moment based on this less number of data, the possibility of correlation between noncentrosymmetry and bending cannot be ignored. We anticipate that in many cases thermal expansion study can be used as an effective tool, though indirect one, to understand the mechanism of bending of molecular single crystals. ASSOCIATED CONTENT
Scheme 2. Schematic representation of the expansioncontraction mechanism that occurs during the elastic bending of Form-E. It shows how the length of the “a” axis decreases or increases due to decrease (concave side) or increase (convex side) in the of offset of the stacking but still maintains close packing. There are few recent reports that suggest that slip plane is 15,23 not essential for plastic bending. In this case also it is possible to explain the bending phenomenon via expansioncontraction mechanism. It has been noticed during the variable temperature experiments that the hinge angle, (Figure 2b) decreases with increasing temperature which causes scissor like motion and lengthening of the “a” axis. Colossal thermal expansion/contraction in some systems due to scis31,36 sor like motion have been reported in the literature. This types of structural modification, caused by the bending, has also been postulated in the literature and supported by ex1 pensive synchrotron X-ray diffraction study or without any 22,37 supporting study . Here, we have used very simple thermal expansion study to understand the mechanisms. Therefore, at the concave side of the bent crystal, the hinge angle increases (corresponds to low temperature crystal structure) and at the convex side it decreases (corresponds to high temperature crystal structure) during bending. In this crystal structure the hinge angle () is ~115. The relationship between and a can be given as a2 /a1 cos(2/2)/cos(1/2), where a1 and a2 are the lengths of the “a” axis when the hinge angles are 1 and 2 respectively. Therefore, if the hinge angle changes only by 4 then the length of the “a” axis changes by ~ 5%. It has been noticed that after breaking near the bent region, the two broken parts of the crystal become 13,14 straight. Hence, even if slip plane mechanism exits, involvement of expansion-contraction mechanism also cannot be ignored.
Supporting Information Crystallization, list of reported achiral compounds with space groups that showed bending, the coefficient of thermal expansion along the principal axes, crystallographic data table and crystallographic data in cif format for the structures with CCDC 1824166 1824182, are all available in the supporting information for the article. This material is available free of charge via the Internet at http://pubs.acs.org.” AUTHOR INFORMATION
Corresponding Author Dr. Binoy K. Saha, Assistant Professor, Department of Chemistry, Pondicherry University, Puducherry, India, 605014.
[email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT B.K.S. thanks DST-FIST for single crystal X-ray Diffractometer and Council of Scientific and Industrial Research, India (No. 01(2908)/17/EMR-II) for research funding. S.A.R. thanks Pondicherry University for research fellowship. REFERENCES (1) Worthy, A.; Grosjean, A.; Pfrunder, M. C.; Xu, Y.; Yan, C.; Edwards, G.; Clegg, J. K.; McMurtrie, J. C. Atomic Resolution of Structural Changes in Elastic Crystals of Copper(II) Acetylacetonate. Nat. Chem. 2018, 10, 6569. (2) Boldyreva, E. Mechanochemistry of Inorganic and Organic Systems: What is Similar, What is Different? Chem. Soc. Rev. 2013, 42, 77197738.
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For Table of Contents Use Only Thermal Expansion Study as a Tool to Understand the Bending Mechanism in a Crystal Sumair A. Rather, and Binoy K. Saha*
Thermal expansion study has been used to understand the bending mechanism in a crystal. The convex side expands and hence resembles thermally expanded crystal structure, whereas the concave side contracts and hence resembles thermally contracted crystal structure.
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