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Mechanical Properties of Crystalline Materials

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Overview of Mechanical Properties

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Four mechanical properties of crystalline materials: shear strength, plasticity, elasticity, and brittleness. Information adapted from Saha et al. 2018.[1]
Designing a material with targeted mechanical properties requires command over complex structures across a range of length scales.

Designing a crystalline material with targeted properties requires an understanding of the material's molecular and crystal features in relation to its mechanical properties.[2] A mechanical property is the response of a material to an applied stress or load.[3] There are four mechanical properties of considerable interest for crystalline materials (plasticity, elasticity, brittleness, and shear strength), but soft organic crystals may demonstrate a range of such properties.[4] Mechanical properties can be defined by their macroscopic and microscopic characteristics from an engineering or chemical perspective.[4][5]

Origins of Mechanical Properties

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Intermolecular Interactions
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When a stress is applied to a material, molecules will be displaced from their equilibrium position, such process is controlled by the energy of the interactions within the lattice.[2] Additionally, during crystallization, structural motifs form according to the types, geometry, and electronics of intermolecular interactions present in the molecular system. Early work in crystal engineering recognized that manipulation of the intermolecular interaction network was a means for controlling bulk properties.[6] During crystallization, intermolecular interactions form according to an electrostatic hierarchy.[7] Strong hydrogen bonds are the primary director for crystal organization.[3][7][8] Weak halogen bonds are thought to be a secondary structural director.[9] There are conflicting reports about the organization directing potential of weak hydrogen bonds compared to strong halogen bonds.[9][10] Halogen bonds serve as a cohesive stabilizing force in self-assembling architectures because of the tunable strength, directionality, and stability in hydrophobic environments.[11] Strong halogen bonds ultimately lead to stronger self-assembling materials.[11] Pi-pi stacking in a crystal is another technique to influence bulk properties to be used when designing a molecular solid. Bulky substituents and heteroatoms influence the degree of pi-pi overlap between molecules in crystal structures.[12] Weak interactions, such as quadrupole-quadrupole and van der Waals, are crucial to maintaining structural adaptability.[13]

Crystal Architecture
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A. Slip planes associated with layered or columnar architectural features in crystalline materials. Red dotted and black dashed lines represent the direction of the weakest and strongest intermolecular interactions, respectively, which influences the slip plane. B. Example of the strongest (hydrogen bonds) and weakest (van der Waals) interactions in acetaminophen structure that influences the crystal structure.

As discussed above, identifying the crystal topography and architectural features is a strong indicator of a material’s ability to respond to an applied stress. A slip plane in a crystal structure is an area where molecular layers or columns move parallel to one another.[14] Typically, the strongest intermolecular interactions form the molecular layers or columns and the weakest intermolecular interactions form the slip plane.[15][16][17] For example, long chains or layers of acetaminophen molecules form due to the hydrogen bond donors and acceptors that flank the benzene ring. The weaker interactions between the chains or layers of acetaminophen required less energy to break than the hydrogen bonds. As a result, a slip plane is formed.

A supramolecular synthon is a pair of molecules that form relatively strong intermolecular interactions in the early phases of crystallization; these molecule pairs are the basic structural motif found in a crystal lattice.[18][19][20] Published in 2020, one study found that altering the crystal packing of probenecid and derivatives, a pharmaceutical ingredient, had a greater impact on plastic bending capabilities than exchanging the hydrogen bond donor groups.[3] Authors hypothesized that the more similar the molecular structure and hydrogen bond capabilities of the probenecid derivative are compared to unmodified probenecid, the more similar the observed mechanical properties will be.[3] On the contrary, the probenecid and probenecid hydrazide demonstrated plastic bending due to alike crystal packing and synthon structure. Probenecid amide, however, experiences brittleness in response to an applied load, despite the strong correlation of its molecular structure to probenecid. This study highlighted how crystal packing can dominate over molecular features in influencing the mechanical properties of a material.

Defects or Imperfections
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Lattice defects, such as point defects, tilt boundaries, or dislocations, create imperfections in crystal architecture and topology. Any disruption to the crystal structure alters the mechanism or degree of molecular movement, thereby changing the mechanical properties of the material.[21] Examples of point imperfections include vacancies, substitutional impurities, interstitial impurities, Frenkel’s defects, and Schottky’s defects.[22] Examples of line imperfections include edge and screw dislocations.[22]

Characterization Methods

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Instrumental techniques and methods used to assess mechanical properties and the crystal structure of crystalline materials is required for meaningful characterization. Information from these techniques is used to decipher the structure-property relationships for new crystalline materials. Crystal structure can be assessed using methods of crystallography, microscopy, Raman spectroscopy, and calorimetry.[22] Mechanical properties can be measured using methods of nanoindentation, Hirshfeld surfaces, and energy frameworks.[22]

Assessing Crystal Structure
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Crystallographic methods, such as X-ray diffraction, are used to elucidate the crystal structure of a material by quantifying distances between atoms.[22] The X-ray diffraction technique relies on a particular crystal structure creating a unique pattern after X-rays are diffracted through the crystal lattice. Microscopic methods, such as optical, electron, field ion, and scanning tunneling microscopy, can be used to visualize the microstructure, imperfections, or dislocations of a material.[22] Ultimately, these methods elaborate on the growth and assembly of crystallites during crystallization, which can be used to rationalize the movement of crystallites in response to an applied load.[23] Calorimetric methods, such as differential scanning calorimetry, use induce phase transitions in order to quantify the associated changes in enthalpy, entropy, and Gibb's free energy.[24] The melting and fusion phase transitions are dependent on the lattice energy of the crystalline material, which can be used to determine percent crystallinity of the sample. Raman spectroscopy is a method that uses light scattering to interact with bonds in a sample.[25] This technique provides information about chemical bonds, intermolecular interactions, and crystallinity.

Assessing Mechanical Properties
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Nanoindentation is a standard and widely-accepted method for measuring mechanical properties within the crystal engineering field.[4][26][27][28][29] This method quantifies hardness, elasticity, packing anisotropy, and polymorphism of a crystalline material.[4][26][27][28][29]

Hirshfeld surfaces are visual models of electron density at a specific isosurface that aid in visualizing and quantifying intermolecular interactions.[30][31][32] An advantage to using Hirshfeld surfaces in crystal engineering is that these surface maps are embedded with information about a molecular and its neighbors.[30] The insight into molecular neighbors can be applied to assessment or prediction of molecular properties.[26] An emerging method for topography and slip plane analysis using energy frameworks, which are models of crystal packing that depict interaction energies as pillars or beams.[3][26][29][33] One study found energy frameworks to be the most accurate method to identify slip planes within a crystalline material when compared to a visualization method and energetic analysis.[34] An accurate prediction method, however, needs to consider changes in energy due to movement from equilibrium position in a crystal. The main drawback of particular, methods such as energy frameworks or Hirshfeld surfaces, is that energy is calculated based on a static molecular position within the crystal structure.[26]  

Bibliography

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  4. ^ a b c d Saha, Subhankar; Mishra, Manish Kumar; Reddy, C. Malla; Desiraju, Gautam R. (2018-11-20). "From Molecules to Interactions to Crystal Engineering: Mechanical Properties of Organic Solids". Accounts of Chemical Research. 51 (11): 2957–2967. doi:10.1021/acs.accounts.8b00425. ISSN 0001-4842.
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  15. ^ Wang, Chenguang; Sun, Changquan Calvin (2019-04). "Computational Techniques for Predicting Mechanical Properties of Organic Crystals: A Systematic Evaluation". Molecular Pharmaceutics. 16 (4): 1732–1741. doi:10.1021/acs.molpharmaceut.9b00082. ISSN 1543-8384. {{cite journal}}: Check date values in: |date= (help)
  16. ^ Wang, Chenguang; Sun, Changquan Calvin (2018-03-07). "Identifying Slip Planes in Organic Polymorphs by Combined Energy Framework Calculations and Topology Analysis". Crystal Growth & Design. 18 (3): 1909–1916. doi:10.1021/acs.cgd.8b00202. ISSN 1528-7483.
  17. ^ Wang, Chenguang; Sun, Changquan Calvin (2019-04). "Computational Techniques for Predicting Mechanical Properties of Organic Crystals: A Systematic Evaluation". Molecular Pharmaceutics. 16 (4): 1732–1741. doi:10.1021/acs.molpharmaceut.9b00082. ISSN 1543-8384. {{cite journal}}: Check date values in: |date= (help)
  18. ^ Mukherjee, Arijit (2015-06-03). "Building upon Supramolecular Synthons: Some Aspects of Crystal Engineering". Crystal Growth & Design. 15 (6): 3076–3085. doi:10.1021/acs.cgd.5b00242. ISSN 1528-7483.
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  21. ^ Williams, J. O.; Thomas, J. M. (1967). "Lattice imperfections in organic solids. Part 1.—Anthracene". Trans. Faraday Soc. 63 (0): 1720–1729. doi:10.1039/TF9676301720. ISSN 0014-7672.
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  23. ^ Chow, Ernest H. H.; Bučar, Dejan-Krešimir; Jones, William (2012). "New opportunities in crystal engineering – the role of atomic force microscopy in studies of molecular crystals". Chemical Communications. 48 (74): 9210. doi:10.1039/c2cc32678g. ISSN 1359-7345.
  24. ^ Kong, Y.; Hay, J. N. (2002-06-01). "The measurement of the crystallinity of polymers by DSC". Polymer. 43 (14): 3873–3878. doi:10.1016/S0032-3861(02)00235-5. ISSN 0032-3861.
  25. ^ "Analysis of crystal polymorphism by Raman Spectroscopy for Medicine Development" (PDF). Jasco Application Note. Retrieved 23 February 2021.{{cite web}}: CS1 maint: url-status (link)
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  34. ^ Wang, Chenguang; Sun, Changquan Calvin (2018-03-07). "Identifying Slip Planes in Organic Polymorphs by Combined Energy Framework Calculations and Topology Analysis". Crystal Growth & Design. 18 (3): 1909–1916. doi:10.1021/acs.cgd.8b00202. ISSN 1528-7483.
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