Publications

We revisit the important issues of polymorphism, structure, and nucleation of cholesterol·H2O using first-principles calculations based on dispersion-augmented density functional theory. For the lesser known monoclinic polymorph, we obtain a fully extended H-bonded network in a structure akin to that of hexagonal ice. We show that the energy of the monoclinic and triclinic polymorphs is similar, strongly suggesting that kinetic and environmental effects play a significant role in determining polymorph nucleation. Furthermore, we find evidence in support of various O–H···O bonding motifs in both polymorphs that may result in hydroxyl disorder. We have been able to explain, via computation, why a single cholesterol bilayer in hydrated membranes always crystallizes in the monoclinic polymorph. We rationalize what we believe is a single-crystal to single-crystal transformation of the monoclinic form on increased interlayer growth beyond that of a single cholesterol bilayer, interleaved by a water bilayer. We show that the ice-like structure is also relevant to the related cholestanol·2H2O and stigmasterol·H2O crystals. The structure of stigmasterol hydrate both as a trilayer film at the air–water interface and as a macroscopic crystal further assists us in understanding the polymorphic and thermal behavior of cholesterol·H2O. Finally, we posit a possible role for one of the sterol esters in the crystallization of cholesterol·H2O in pathological environments, based on a composite of a crystalline bilayer of cholesteryl palmitate bound epitaxially as a nucleating agent to the monoclinic cholesterol·H2O form.

The most widely used antimalarial drugs belong to the quinoline family. Their mode of action has not been characterized at the molecular level in vivo. We report the in vivo mode of action of a bromo analog of the drug chloroquine in rapidly frozen Plasmodium falciparum-infected red blood cells. The Plasmodium parasite digests hemoglobin, liberating the heme as a byproduct, toxic to the parasite. It is detoxified by crystallization into inert hemozoin within the parasitic digestive vacuole. By mapping such infected red blood cells with nondestructive X-ray microscopy, we observe that bromoquine caps hemozoin crystals. The measured crystal surface coverage is sufficient to inhibit further hemozoin crystal growth, thereby sabotaging heme detoxification. Moreover, we find that bromoquine accumulates in the digestive vacuole, reaching submillimolar concentration, 1,000-fold more than that of the drug in the culture medium. Such a dramatic increase in bromoquine concentration enhances the drug's efficiency in depriving heme from docking onto the hemozoin crystal surface. Based on direct observation of bromoquine distribution in the digestive vacuole and at its membrane surface, we deduce that the excess bromoquine forms a complex with the remaining heme deprived from crystallization. This complex is driven toward the digestive vacuole membrane, increasing the chances of membrane puncture and spillage of heme into the interior of the parasite.

Invited for this month's cover are the group of Prof. Lia Addadi at the Weizmann Institute of Science, Israel and collaborators at the Università Degli Studi di Milano, Italy, and the ALBA Synchrotron Light Source, Spain. The front cover shows how cholesterol crystals form in macrophage cells and in lipid bilayers of different compositions. Cholesterol monohydrate stable triclinic crystals form in vitro as rhomb-shaped plates, whereas the monoclinic crystals fold into tubular or helical shapes. Read the full text of the article at 10.1002/cplu.201800632.

The eyes of some aquatic animals form images through reflective optics. Shrimp, lobsters, crayfish, and prawns possess reflecting superposition compound eyes, composed of thousands of square-faceted eye units (ommatidia). Mirrors in the upper part of the eye (the distal mirror) reflect light collected from many ommatidia onto the photosensitive elements of the retina, the rhabdoms. A second reflector, the tapetum, underlying the retina, back-scatters dispersed light onto the rhabdoms. Using microCT and cryo-SEM imaging accompanied by in situ micro-X-ray diffraction and micro-Raman spectroscopy, we investigated the hierarchical organization and materials properties of the reflective systems at high resolution and under close-to-physiological conditions. We show that the distal mirror consists of three or four layers of plate-like nanocrystals. The tapetum is a diffuse reflector composed of hollow nanoparticles constructed from concentric lamellae of crystals. Isoxanthopterin, a pteridine analog of guanine, forms both the reflectors in the distal mirror and in the tapetum. The crystal structure of isoxanthopterin was determined from crystal-structure prediction calculations and verified by comparison with experimental X-ray diffraction. The extended hydrogen-bonded layers of the molecules result in an extremely high calculated refractive index in the H-bonded plane, n = 1.96, which makes isoxanthopterin crystals an ideal reflecting material. The crystal structure of isoxanthopterin, together with a detailed knowledge of the reflector superstructures, provide a rationalization of the reflective optics of the crustacean eye.

A key drug target for malaria has been the detoxification pathway of the iron-containing molecule heme, which is the toxic byproduct of hemoglobin digestion. The cornerstone of heme detoxification is its sequestration into hemozoin crystals, but how this occurs remains uncertain. We report new results of in vivo rate of heme crystallization in the malaria parasite, based on a new technique to measure element-specific concentrations at defined locations in cell ultrastructure. Specifically, a high resolution correlative combination of cryo soft X-ray tomography has been developed to obtain 3D parasite ultrastructure with cryo X-ray fluorescence microscopy to measure heme concentrations. Our results are consistent with a model for crystallization via the heme detoxification protein. Our measurements also demonstrate the presence of considerable amounts of non-crystalline heme in the digestive vacuole, which we show is most likely contained in hemoglobin. These results suggest a tight coupling between hemoglobin digestion and heme crystallization, highlighting a new link in the crystallization pathway for drug development.

This cooperative endeavour first describes early studies in chemical crystallography, encompassing molecular packing modes, characterization of weak hydrogen bonds, the engineering of functional crystals and monitoring of reaction pathways in molecular crystals by x-ray and neutron diffraction. With the design of 'tailor-made' auxiliary molecules, it became possible to correlate molecular enantiomerism and crystal enantiomorphism, to control the early stages of crystal nucleation, to resolve enantiomers by crystallization, induce the precipitation of metastable polymorphs, and shed light on the role played by solvent on crystal growth. With such auxiliaries, the structure of mixed crystals was revised and the ability to perform 'absolute' asymmetric synthesis in host centrosymmetric crystals demonstrated. With the introduction of grazing incidence synchrotron x-ray diffraction from liquid surfaces it also became possible to design and characterize crystalline thin film architectures at the air-water interface providing a general insight on the mechanism of crystal nucleation at the molecular level, in particular that of ice and cholesterol. Finally the collective knowhow from these studies were crucial for obtaining homochiral peptides prepared from the polymerization of racemates of amphiphilic amino acids dissolved in aqueous solution, and for experiments towards elucidating the pathological crystallization of cholesterol and the malaria pigment in Plasmodium-infected red blood cells.

Heme detoxification is a critical step in the life cycle of malariaca-using parasites, achieved by crystallization into physiologically insoluble hemozoin. The mode of nucleation has profound implications for understanding the mechanism of action of antimalarial drugs that inhibit hemozoin growth. Several lines of evidence point to involvement of acylglycerol lipids in the nucleation process. Hemozoin crystals have been reported to form within lipid nanospheres; alternatively, it has been found in vitro that they are nucleated at an acylglycerol lipid-water interface.We have applied cryogenic soft X-ray tomography and three-dimensional electron microscopy to address the location and orientation of hemozoin crystals within the digestive vacuole (DV), as a signature of their nucleation and growth processes. Cryogenic soft X-ray tomography in the "water window" is particularly advantageous because contrast generation is based inherently on atomic absorption. We find that hemozoin nucleation occurs at the DV inner membrane, with crystallization occurring in the aqueous rather than lipid phase. The crystal morphology indicates a common {100} orientation facing the membrane as expected of templated nucleation. This is consistent with conclusions reached by X-ray fluorescence and diffraction in a companion work. Uniform dark spheres observed in the parasite were identified as hemoglobin transport vesicles. Their analysis supports a model of hemozoin nucleation primarily in the DV. Modeling of the contrast at the DV membrane indicates a 4-nm thickness with patches about three times thicker, possibly implicated in the nucleation.

Malaria, an infectious disease once considered eradicated, has reemerged in recent years, primarily due to parasite resistance to commonly used synthetic antimalarial drugs. These drugs act by inhibiting crystallization of the malaria pigment, hemozoin (HZ). Thus, there is a vital need for understanding the process of HZ nucleation. In a companion paper, the pseudopolymorphic behavior of β-hematin, the synthetic form of HZ, has been characterized by X-ray diffraction (XRD) (Straasø, T.; Kapishnikov, S.; Kato, K.; Takata, M.; Als-Nielsen, J.; Leiserowitz, L.Cryst. Growth Des. 2011, 11, DOI: 10.1021/cg200410b). Here, we employ van der Waals (vdW)-corrected density functional theory (DFT) to study the two β-hematin crystal structures and their repeat unit, a heme dimer. We find that vdW interactions play a major role in the binding of the heme dimer and the β-hematin crystal. In addition, accounting for the periodic nature of the system is essential to obtaining the correct geometry of the heme dimer, which is affected by vdW interactions with adjacent dimers in the β-hematin crystal. The different stereoisomers of the heme dimer and their molecular crystals are close in energy, which is consistent with pseudopolymorphism in β-hematin, in agreement with recent XRD experiments. Finally, we use our results to comment on β-hematin crystallization mechanisms. This work demonstrates the viability of vdW-corrected DFT as a tool for gaining valuable insight into pertinent problems involving biological systems.

Biological membranes comprise thousands of different lipids, differing in their alkyl chains, headgroups, and degree of saturation. It is estimated that 5%of the genes in the human genome are responsible for regulating the lipid composition of cell membranes. Conceivably, the functional explanation for this diversity is found, at least in part, in the propensity of lipids to segregate into distinct domains, which are important for cell function. X-ray diffraction has been used increasingly to characterize the packing and phase behavior of lipids in membranes. Crystalline domains have been studied in synthetic membranes using wide- and small-angle X-ray scattering, and grazing incidence X-ray diffraction. Herein we summarize recent results obtained using the various X-ray methods, discuss the correlation between crystalline domains and liquid ordered domains studied with other techniques, and the relevance of crystalline domains to functional lipid domains in biological membranes.

A pulsed IR laser beam was used to align a peptide at the air-water interface. This peptide was designed to form a cyclic ß-strand dimer through Glu-Lys interactions in solution, which, when spread onto water, yielded a self-assembled ß-sheet bilayer (see picture) following solvent evaporation. During this process illumination with linearly polarized laser light induced formation of an aligned crystalline film, whereas circular polarization did not. (Figure Presented).

X-ray scattering experiments on mixed films of cholesterol and phospholipids at air-water and Si solid-water interfaces were undertaken to glean information on pathological crystallization of cholesterol bilayers. Grazing-incidence X-ray diffraction patterns at the air-water interface of various cholesterol:dipalmitoyl-phosphatidylcholine (Ch:DPPC) monolayer mixtures compressed beyond monolayer collapse yielded the established 10×7.5 Å2 Ch bilayer motif, for Ch:DPPC molar ratios higher than 2.5:1. Attempts to obtain a diffraction signal from various Ch:phospholipid film mixtures at the Si solid-water interface, indicative of the presence of the Ch bilayer motif, were unsuccessful. Only after removal of sufficient water from the cell was a weak diffraction signal obtained suggestive of a cholesterol film two bilayers thick. Off-specular X-ray reflectivity measurements made on a 1.75:1 mixture of Ch and bovine cardiac phosphatidylcholine (BCPC) deposited as a bilayer on a Si wafer and placed in a cell filled with water yielded positive results. The derived electron density profile showed the presence of a bilayer mixture consistent with a phase separation of cholesterol and BCPC, and possible formation of a crystalline cholesterol bilayer within the hydrated mixed bilayer, but not a proof thereof.

We investigated the fine structure of a self-assembled monolayer of dodecanethiol functionalized by α-quaterthiophene on gold (α-4TC₁₂H₂₄SH). The molecular orientation, quantified using polarization modulation infrared reflection-absorption spectroscopy, was studied as a function of the adsorption time. The α-4T moieties arrange in the upright position on the surface as the adsorption time increases, while the alkyl chain organization remains poor. Here we quantify the orientation of the self-assembled monolayer and, more significantly, reveal through surface X-ray diffraction that after a long incubation period (12 h) the α-4T on the gold surface adopts a 2D crystal structure.

Symmetry violation: Recent results by Tremel and co-workers on the phase selection of calcium carbonate through the chirality of adsorbed amino acids appear to provide a deterministic route to "mirror-symmetry breaking", which may have ramifications for the emergence of homochirality on Earth. In our view, however, the crystallization experiments violate basic rules of symmetry and we suspect the presence of chemical, biological, or other homochiral or achiral contaminants in the system.

Recent experimental and theoretical studies on functional self-assemblies formed at interfaces are presented and placed in perspective to earlier studies. The focus is on chiral and achiral systems that are at the boundary between two-dimensional and three-dimensional architectures and investigated at almost molecular level. More specifically, we present studies on: (i) self-organization of achiral molecules and separation of racemates into two-dimensional enantiomorphous domains at the air-water interface; (ii) molecular recognition between solute molecules and Langmuir films; (iii) the structural correlation between chiral morphology of mesoscopic architectures and the absolute configuration of the component molecules; (iv) polymerization of amphiphilic molecules at various interfaces and (v) the use of two-dimensional films as templates in three-dimensional crystallization, with relevance to biomineralization.

The morphology of micrometer-sized β-hematin crystals (synthetic malaria pigment) was determined by TEM images and diffraction, and by grazing incidence synchrotron X-ray diffraction at the air-water interface. The needle-like crystals are bounded by sharp {100} and {010} side faces, and capped by {011} and, to a lesser extent, by {001} end faces, in agreement with hemozoin (malaria pigment) crystals. The β-hematin crystals grown in the presence of 10% chloroquine or quinine took appreciably longer to precipitate and tended to be symmetrically tapered toward both ends of the needle, due to stereoselective additive binding to {001} or {011} ledges. Evidence, but marginal, is presented that additives reduce crystal mosaic domain size along the needle axis, based on X-ray powder diffraction data. Coherent grazing exit X-ray diffraction suggests that the mosaic domains are smaller and less structurally stable than in pure crystals. IR-ATR and Raman spectra indicate molecular based differences due to a modification of surface and bulk propionic acid groups, following additive binding and a molecular rearrangement in the environment of the bulk sites poisoned by occluded quinoline. These results provided incentive to examine computationally whether hemozoin may be a target of antimalarial drugs diethylamino-alkoxyxanthones and artemisinin. A variation in activity of the former as a function of the alkoxy chain length is correlated with computed binding energy to {001} and {011} faces of β-hematin. A model is proposed for artemisinin activity involving hemozoin nucleation inhibition via artemisinin-β-hematin adducts bound to the principal crystal faces. Regarding nucleation of hemozoin inside the digestive vacuole of the malaria parasite, nucleation via the vacuole's membranous surface is proposed, based on a reported hemozoin alignment. As a test, a dibehenoyl- phosphatidylcholine monolayer transferred onto OTS-Si wafer nucleated far more β-hematin crystals, albeit randomly oriented, than a reference OTS-Si.

In a recent paper, Srinivasan and Sherwood reported that α-resorcinol crystals grow unidirectionally at the {011} faces in the vapor phase and suggested that this phenomenon of unidirectional growth is intrinsic to polar crystals. Here, we present a molecular modeling study suggesting a plausible "self-poisoning" mechanism that may explain the unidirectional growth of α-resorcinol in the vapor phase, a process that does not exclude the inhibition of crystal growth by solvent.

Theories of prebiotic life suggest that homochirality emerged in Nature in abiotic times via deterministic or chance scenarios. This chapter deals with experiments demonstrating the feasibility of stochastic mirror symmetry breaking that occurs via autocatalytic processes involving the self-assembly of molecular clusters, 2-D and 3-D crystals, supramolecular organo-metallic catalysts, and polymeric helices and sheets. Once generated spontaneously by chance, chirality can be preserved and propagated to the environment provided that the symmetry breaking step is coupled with a sequential step of efficient amplification via self-replication reactions. Common features for the systems of relevance are that they take into consideration small fluctuations from the racemic state, and they display non-linear kinetic effects induced by diastereoisomeric supramolecular self-assemblies that exhibit different physical or chemical properties.

(Graph Presented) Crystallization of the thermodynamically metastable β glycine is explained on the basis of its growth at the opposite poles of the crystal (see graph) and by considering the structure of the relevant surfaces of the three polymorphs and their interactions with solvent molecules.

Cholesteryl-L-glutamate (CLG) thin films were investigated when deposited on pure water and on saturated solutions of water soluble amino acids, to test the capacity of the CLG monolayer to recognize and incorporate amino acids from the subphase. Analysis of grazing incidence X-ray diffraction measurements indicates that the hydrophobic amino acids, leucine, isoleucine, and valine, are adsorbed between the glutamate moieties, within the CLG crystalline monolayer, but also around their domains, forming, for L-Leu and D-Val, crystalline bilayers. The presence of Cu²⁺ ions in the aqueous subphase enhances the crystallinity of the CLG monolayer without overly affecting the lateral packing, by bridging glutamate moieties on neighbor molecules. When amino acids are injected in a Cu²⁺ containing solution, the domain size of the mixed monolayers formed with the CLG molecules and hydrophobic amino acids is drastically increased.

In this review, the delicate interplay between stereochemical control, monitoring at the subnanometer level, and an understanding of crystal nucleation is probed. Control of crystal nucleation may be achieved employing tailor-made auxiliaries, which are either nucleation inhibitors or promoters. The process may be monitored at an interface via grazing incidence X-ray diffraction (GIXD). By these means, we can glean experimental knowledge of crystal nucleation in various molecular systems. A hypothesis was invoked that supersaturated solutions containing molecular clusters adopt various arrangements and shapes, some of which resemble the crystals into which they develop. This hypothesis was taken advantage of for the design of tailored inhibitors in achieving kinetic resolution of enantiomers and induced precipitation of particular crystal polymorphs. The control and behavior of polymorphic crystallization may be understood at the molecular level through the interplay between inhibitor, solvent, solute, crystal and layer lattice energies, as well as surface layer structures. With respect to promotion of crystal nucleation, it may be achieved by Langmuir monolayers at the air-aqueous solution interface, acting as a templating agent. Determination of the monolayer crystal structure by GIXD yields the extent and nature of the complementary fit between nucleator and nucleant. Finally, GIXD was applied to monitor by a snapshot technique the layer-by-layer crystalline assembly of cholesterol molecules at the air-water interface, which involved changes in molecular packing as the film grew in thickness.

A grazing-incidence X-ray-diffraction (GIXD) study of the self-assembly, on water, of nonracemic γ-stearyl glutamic acid (pure or as a mixture with racemic or (S)-1,2 -dipalmitoyl-glycero-3-phosphoethanolamine (DPPE)) demonstrated a phase separation of the α-amino acid amphiphile into racemic and enantiomorphous two-dimensional crystallites within the phospholipid domains. The packing arrangements of the two α-amino acid crystalline phases were identical to those found in the absence of DPPE and have been determined, at almost atomic resolution, by X-ray structure-factor calculations. By contrast, racemic and nonracemic N^ε -stearoyllysine spontaneously segregated into two-dimensional enantiomorphous domains within the DPPE environment that induced a change in the tilt direction of the hydrocarbon chains of the α-amino acid molecules. Phase separation of nonracemic amphiphiles, originating from preferred lateral homochiral or heterochiral intermolecular interactions, is in agreement with the formation of enantiomerically pure or enriched homochiral oligopeptides in overrepresented amounts in the polycondensation of activated nonracemic amphiphilic α-amino acids on plain water or within phospholipid monolayers.

The advent of intense X-rays from synchrotron sources made possible to probe, at the molecular level, the structural aspects of self-assemblies generated at interfaces. Here we present the two-dimensional (2-D) packing arrangements of two-, three- and multi-component organo-metallic self-assemblies formed via interfacial reaction at the air-aqueous solution interface, as determined by grazing incidence X-ray diffraction (GIXD) and X-ray specular reflectivity techniques. GIXD yields structural information on the crystalline part of the Langmuir film, including the ions and counterions lateral order. Specular reflectivity yields the electron density profile of the film in the direction normal to the air-solution interface and, by modeling, gives independent information on the structure of both crystalline and amorphous parts of the film. In particular, we focus on the following systems: ordering of metal ions bound to the polar head groups of amphipilic molecules; use of bolaamphiphiles to generate oriented thin films with metal ions arranged in periodic layers; delineation of differences in the lateral organization of metal ions at interfaces as induced by racemates and enantiomerically pure amphiphiles; organization of ionophores in the presence of metal ions in membrane-like environment; self-assembly of 2×2 and 3×3 silver(I) grid-type complexes generated at the air-solution interface.

The feasibility of generating oligopeptides with homochiral sequence via lattice-controlled polymerization of racemic mixtures of precursor molecules that undergo spontaneous segregation into two-dimensional (2-D) enantiomorphous domains at the air-aqueous solution interface was analyzed. For model systems, we studied the polymerization reaction within 2-D crystalline domains of mixtures of (R,S)-N^εstearoyl-thio-lysine with ∼10% (R,S)-N^ε-stearoyl-lysine, and (R,S)-N^α-carboxyanhydride of N^ε-stearoyllysine. According to in situ grazing incidence X-ray diffraction (GIXD) measurements at the air-water interface, the molecules form 2-D crystallites packing by translation symmetry only. Oligopeptides 4-6 units long were obtained at the air-solution interface after injection of an appropriate catalyst into the subphase. The course of the chemical transformations was monitored by GIXD. The distribution of the diastereoisomeric oligopeptides was determined by matrix-assisted laser-desorption ionization time-offlight (MALDI-TOF MS) mass spectrometry on samples prepared from precursor molecules enantioselectively labeled with deuterium. The experimental relative abundance of oligopeptides with homochiral sequence was found to be larger than that calculated for a theoretical random process, yielding an excess by a factor of 2.5-3.5 for the tetra- to hexapeptides. The present studies may be relevant for probing the role that might have been played by ordered clusters at interfaces for the generation of homochiral oligopeptides under prebiotic conditions.

Hybrid organic/inorganic Langmuir-Blodgett (LB) films were prepared by the synthetic solid/gas reaction. Addition to the thiocarboxylic acid to the LB film stabilized the ordered phase.

Structural studies on two-dimensional films of chiral amphiphiles at the air-solution interface, as investigated in situ primarily by grazing incidence x-ray diffraction (GIXD) using synchrotron radiation, yielded the crystalline packing arrangement at almost the molecular level. Results regarding three different topics are described. (1) It has proven possible to establish whether racemic mixtures of amphiphiles spread on water self-organize into 2-D crystals in which the two enantiomers either form heterochiral domains or spontaneously separate into enantiomorphous islands composed of homochiral molecules. Diastereoisomeric acid-base interactions between two different chiral amphiphiles were also used to achieve spontaneous chiral separation in two dimensions. (2) Ordered binding of solute molecules to the chiral amphiphiles could be applied in order to study their enantioselective interactions with chiral solutes present in the aqueous subphase. (3) Crystalline multilayer films of supramolecular architecture composed of water-soluble and water-insoluble chiral components may be formed at the air-solution interface and their packing arrangement determined by GIXD.

Insertion of the 1,3-bis(ethynylene)benzene unit as a rigid spacer into a linear alkyl chain, thus separating the two resulting stems by 9 Å, induces chain folding at the air-water interface. These folded molecules self-assemble into crystalline monolayers at this interface, with the plane of the folding unit almost perpendicular to the water surface, as determined by synchrotron grazing-incidence X-ray diffraction. Three distinct molecular shapes, of the types U, inverted U, and M, were obtained in the two-dimensional crystal-line state, depending upon the number of spacer units, and the number and position of the hydrophilic groups in the molecule. The molecules form ribbons with a higher crystal coherence in the direction of stacking between the molecular ribbons, and a lower coherence along the ribbon direction. A similar molecule, but with a spacer unit that imposes a 5 Å separation between alkyl chains, yields the conventional herring-bone arrangement.

To provide more direct information on the role played by "tailor-made" auxiliary molecules in the early stages of crystal nucleation, the interplay between clusters of polar headgroups of monolayers of the copper complexes 5-Cu-S′ and S-Cu-R′ and water-soluble copper complexes S′-Cu-S′ and R′-Cu-R′ were investigated [where S represents enantiomerically pure (S)-palmitoyl-N^ε-lysine, and S′ and R′ represent chiral resolved (S) and (R) forms of alanine, serine, or valine]. The different monolayers were formed by spreading the amphiphilic (R) or (S) α-amino acid on an aqueous solution of copper acetate followed by injection of the water-soluble (S′) or (R′) α-amino acid into the subphase. The surface pressure-molecular area isotherms of the Langmuir monolayers of the two type of complexes (S-Cu-S′ and S-Cu-R′) are different, the former being substantially more expanded. The polar headgroups of the S-Cu-S′ and of the S-Cu-R′ monolayers transferred onto a solid support assume a trans and cis configuration, respectively, according to comparative X-ray photoelectron spectroscopy (XPS) studies with appropriate cis and trans three-dimensional (3-D) α-amino acid Cu complexes. A grazing incidence X-ray diffraction (GIXD) analysis demonstrated that the S-Cu-S′ and S-Cu-R′ monolayers have different 2-D crystal structures, in keeping with the XPS results. A model is presented suggesting that the water-soluble S′-Cu-S′ copper complexes are enantioselectively bound to the periphery of the domains of the cis S-Cu-S′ monolayers, but not to the domains of the trans S-Cu-R′ monolayers. By symmetry, the same principal holds for the monolayers and water soluble copper complexes of α-amino acids of the opposite handedness.

On studies of large scale optical resolution by crystallization, it was found that α-amino acid salts crystalline in the form of conglomerates. The conglomerates were composed of lamellar twins, hence are not amenable to large scale resolution. By conducting further studies, it was found that the occurrence of the lamellar twins can be prevented with the assistance of 'tailor-made' enantioselective crystal nucleation inhibitors that allow the resolution of hydrophobic racemic α-amino acids by kinetic crystallization.

Single crystals of benzamide which form hydrogen-bonded (001) bilayers are obtained from ethanol or 1-propanol solutions. The added presence of amide cosolvent such as X-CONH₂, X = CH₃ or CF₃, yields very thin (001) plates which are twinned. Grazing incidence X-ray diffraction (GIXD) measurements from the (001) surface of pure benzamide indicates that the surface almost exclusively exposes the phenyl substituents. The observed GIXD data from the (001) surface of the affected crystals revealed lamellar twinning. Structural modeling of the data showed that the top surface layer contains about 15% adsorbed amide cosolvent, all oriented with their -X moieties exposed to air. A simple structural model has been invoked to account for the solvent-induced twinning.

Model molecules, designed to simulate a chain fold, self-assemble into crystalline monolayers at the air - water interface, the structure of which has been determined, in situ, by synchrotron grazing-incidence X-ray diffraction. The two-dimensional packing arrangement in such monolayers is consistent with a structure composed of ribbons containing translationally related molecules adopting an inverted U-shape. The distance between these molecules along the ribbon is optimum for creating an additional chain fold, leading to the possibility that a polymeric molecule will undulate on the water surface.

The structure of mixed Langmuir films of the normal alkane C₃₂H₆₆ with different quantities of the normal alcohol C₃₁H₆₃OH or the diol HO(CH₂)₃₀OH on pure water were determined in situ by applying surface-sensitive methods that include grazing incidence X-ray diffraction (GIXD) and infrared reflection - absorption spectroscopy (IRRAS) and by induced freezing of water drops. Random solid solutions were formed between the alkane and C₃₁H₆₃OH. On the other hand, segregation of the two components was observed in the mixed systems of the alkane and HO(CH₂)₃₀OH. These findings suggest new ways for the design of hydrophobic surfaces bearing hydrophilic sites, which may be appropriate for epitaxial ice nucleation and cloud seeding purposes.

We present a study of two-dimensional (2D) crystallites of cholesterol formed at the air-water interface. Grazing-incidence X-ray diffraction (GIXD) measurements performed along the surface pressure-area isotherm revealed a transition from a monolayer to a highly crystalline rectangular phase, about two layers thick. This variation in the film thickness was confirmed by ellipsometry measurements. Films transferred onto solid support by the Langmuir-Blodgett technique were seen by atomic force microscopy (AFM) to display elongated and faceted crystallites about 10 layers thick. The effect of the phospholipid dipalmitoylphosphatidylcholine (DPPC) on the 2D crystallization of cholesterol was studied by GIXD and AFM with three cholesterol:DPPC mixtures in molar ratios 1:1, 2:1, and 5:1. The phospholipid additive reduced the crystallinity of the cholesterol in the 5:1 and 2:1 mixtures, totally suppressing it in the 1:1 mixture.

A direct relationship between the structures of two-dimensional (2-D) crystallites of 4-octadecyloxy-E-cinnamic acid and 4-octadecyloxy-E- cinnamamide amphiphiles at the air-water interface and their photochemical behavior, is presented. The detailed packing arrangements of the monolayers were determined, close to the atomic level, from the diffraction pattern measured, in situ on the water surface, by the grazing incidence X-ray diffraction (GID) technique using synchrotron radiation. The products of the photochemical reaction, performed by irradiating the monolayer films directly on the water surface, were collected and analyzed. While the acid crystallites yield a β-truxinic acid product together with the cis-isomer, the amide undergoes only trans-cis isomerisation, in full agreement with the 2-D crystalline packing arrangements of the two amphiphiles on the water surface.

Monolayers of the long-chain alcohols on water promote nucleation of ice. In order to determine the minimum size of crystalline alcohol monolayer domains that induce ice nucleation, we reduced their size in two distinct ways. One approach encompassed embedding the pure hydrocarbon alcohol, C_nH_2n+1OH(n = 20, 31), into a matrix of an immiscible monolayer of perfluoro alcohol C₁₀F₂₁C₂H₄OH, which is inert as an ice nucleator. The second set of experiments involved the introduction of random defects into the monolayer crystalline domains of C₂₉H₅₉OH through the use of the fully miscible guest alcohol molecule, C₃₁H₆₃OH, as additive. By these methods we estimated that ∼450 water molecules are necessary to form a stable ice cluster at the onset of induced ice nucleation at a temperature just below 0°C.

The formation of Langmuir monolayers at the air water interface has long been believed to be limited to amphiphilic molecules containing a hydrophobic chain and a hydrophilic headgroup. Here we report the formation of crystalline mono- and multilayer self-assemblies of oligothiophenes, a class of aromatic nonamphiphilic molecules, self-aggregated at the air water interface. As model systems we have examined the de position of quaterthiophene (S₄), quinquethiophene (S₅), and sexithiophene (S₆) from chloroform solutions on tile water surface. The structures of the films were determined by surface pressure area isotherms, by scanning force microscopy (SFM after transfer of the films onto atomically smooth mica, by cryo-transmission electron microscopy (Cryo-TEM) on vitreous ice, and by grazing incidence synchrotron X-ray diffraction (GII) directly on the water surface. S₄ forms two polymorphic crystalline multilayers. In polymorph χ, of structure very similar to that of the three-dimensional solid, the molecules are aligned with their long molecular axis tilted by about 23 from the normal to the water surface. In polymorph β the long molecular axis is perpendicular to the water surface. S⁵ self-aggregates at tile water surface to form mixtures of monolayers and bilayers of the β polymorph: S₆, forms primarily crystalline monolayers of both χ and β forms. The crystalline assemblies preserve their integrity during transfer from the water surface onto solid supports. The relevance of the present results for the understanding of the early stages of crystal nucleation is presented.

A correlation is presented between the crystalline structure of monolayers and multilayers of α,ω-alkanediols HO-(CH₂)_n-OH (n = 16, 18, 19, 21, 22, 23, 24, 30) at the air-water interface and their function as ice nucleators. Structural elucidation was carried out by the following methods: grazing incidence X-ray diffraction, scanning force microscopy, cryo-transmission electron microscopy and external reflection Fourier transform-infrared spectroscopy.

Grazing incidence synchrotron X-ray diffraction measurements were made on an uncompressed monolayer of 1:1 triacontanoic acid (C₂₉H₅₉COOH) and nonacosylamine (C₂₉H₅₉NH₂), spread on pure water and on aqueous ZnCl₂ solution. The measured diffraction data of the mixed monolayer on water provides clear evidence of a complete mixing of the acid and amine molecules into a two-dimensional crystal where the hydrocarbon chains pack in a herringbone motif. A model has been proposed in which the ionized acid and amine moieties are ordered and form a continuous hydrogen-bonded array.

Keywords: Engineering, Multidisciplinary; Materials Science, Multidisciplinary

The induced formation of multilayer crystallites at liquid interfaces provides a direct means of monitoring the dynamics of crystal nucleation and of elucidating the effect of molecular inhibitors on polymorphism and crystal growth. The spontaneous formation of crystalline multilayers of n‐alkanes spread from solution onto the water interface are described and X‐ray structural investigations discussed which indicate that the full crystal symmetry is present even in layers that are only a few unit cells thick.

Tailor-made auxiliaries for the control of nucleation and growth of molecular crystals may be classified into two broad categories: inhibitors and promoters. Tailor-made inhibitors of crystal growth can be used for a variety of purposes, which include morphological engineering and etching, reduction of crystal symmetry, assignment of absolute structure of chiral molecules and polar crystals, elucidation of the effect of solvent on crystal growth, and crystallization of a desired polymorph. As for crystal growth promoters, monolayers of amphiphilic molecules on water have been used to induce the growth of a variety of three-dimensional crystals at the monolayer-solution interface by means of structural match, molecular complementarity or electrostatic interaction. A particular focus is made on the induced nucleation of ice by monolayers of water-insoluble aliphatic alcohols. The two-dimensional crystalline structures of such monolayers have been studied by grazing incidence X-ray diffraction. It has become possible to monitor, by this method, the growth, dissolution and structure of self-aggregated crystalline nonolayers, and indeed multilayers, affected by the interaction of solvent molecules in the aqueous. suphase with the amphiphilic headgroups, and by the use of tailor-made amphiphilic additives.

Crystals formed in biological tissues often adopt remarkable morphologies that are thought to be determined mainly by the shapes of the confined spaces in which they grow. Another possible way of controlling crystal shape, demonstrated only in vitro, is by means of specialized proteins preferentially interacting with certain crystal faces. In so doing, they reduce the rate of growth in these directions and consequently change the overall crystal shape. In an X-ray diffraction study of the distribution of defects within the lattice of calcite crystals produced by certain sponges, we show that a remarkable correlation exists between the defect patterns or crystal texture and the macroscopic morphology of the spicules. This was observed in two cases in which proteins are present within the spicule crystal, but not in a third case where such intracrystalline proteins are absent. Furthermore, one of the spicules exhibited marked differences in texture even within families of structurally identical crystal planes, demonstrating that the organisms exert exquisite control over the microenvironment in which crystals grow. We conclude that highly controlled intercalation of specialized proteins inside the crystals is an additional means by which organisms control spicule growth.

We enjoyed reading the article by Ron Dagani (C&EN, Aug. 29, 1994, page 28) on the current field of catenanes. We were dismayed by his reference to "a chemist" who synthesized the first catenane in 1960. That pioneering study was performed by Ed Wasserman, who is considered as the originator of this field of science. Wasserman not only synthesized the first catenane, but also elaborated on the topological aspects of this class of materials. Wasserman, who is well known for his original contributions in pure and applied chemistry, is currently at DuPont Experimental Station, Wilmington, Del. [1st paragraph]

The spontaneous aggregation of the bolaamphiphile α,ω‐docosanediol into embryonic three‐dimensional crystallites at the air‐water interface can be inhibited by additives. A study with the aim of determining the necessary properties of such supplements is reported, which uses additives with molecular recognition properties and methods such as X‐ray reflectivity, cryotransmission electron microscopy, and atomic force microscopy in order to detect structural changes at the nanometer level.

Crystallization of R,S-alanine in the presence of small amounts of other resolved α-amino acids results in the precipitation of the racemic compound as twinned crystals displaying a propeller-like morphology of 222 symmetry, in contrast to needlelike crystals of mm2 symmetry when grown from pure aqueous solution. This unusual twinning is explained by assuming that the supersaturated solutions contain ordered clusters of structures akin to the mature crystals of (R,S)-, (R)-, and (S)-alanine. The resolved α-amino acid additive, e.g., R′, stereospecifically inhibits growth of the R,S and R nuclei but not of the S nuclei. The latter serve as a template onto which the (R,S) crystals nucleate and grow. A model which takes into consideration the structural similarity between the racemic and chiral resolved forms of alanine to explain the twinning is presented. An X-ray diffraction analysis of a twinned crystal specimen is in agreement with a gradual change in structure, from a chiral crystal of space group P2₁2₁2₁ to the racemic compound of space group Pna2₁. To substantiate the model, crystals of alanine were grown from optically enriched solutions containing excess of one of the alanine enantiomers, which also induce the twinning phenomenon and an overall reduction in crystal symmetry. The relevance of these observations to the early stages of crystal nucleation is discussed.

Spreading of the bolaamphiphile alpha,omega-docosanediol, HO(CH2)(22)OH, on water results in spontaneous aggregation into embryonic 3-D crystallites. These crystallites have been analyzed by cryo-transmission electron microscopy, scanning force microscopy, X-ray reflectivity, and external reflection Fourier transform infrared spectroscopy. The molecules are aligned in an almost perpendicular fashion in a rectangular cell, and the crystallites are about five molecular layers thick.

Uncompressed arachidic acid films spread over 10⁻³ M cadmium chloride solution (pH 8.8 adjusted with ammonia) spontaneously form two-dimensional (2-D) crystalline clusters with coherence lengths of ≈1000 Å at 9 °C. Ten distinct low-order in-plane diffraction peaks and three high-order peaks were observed with grazing incidence X-ray diffraction (GID) using synchrotron radiation. Seven low-order peaks were attributed to scattering only from a crystalline cadmium layer and the remaining peaks to scattering primarily from the arachidate layer. The molecules in the arachidate layer arrange in a pseudorectangular unit cell with dimensions a = 4.60 Å and b = 8.37 Å and γ = 93.4° with the chains tilted 11° along the b axis. The chains of the two crystallographically independent molecules in the unit cell are related by pseudoglide symmetry along the b axis yielding the herringbone motif. The reflections from the cadmium layer were indexed according to a supercell a₈ = 2a, b₈ = 3(-a + b)/2. Analysis of X-ray specular reflectivity measurements and the GID data indicated that the counterionic layer consists of a CdOH⁺ species, bound to the arachidate layer in a stoichometry close to 1:1. The probable formation of a cadmium-ammonia complex at the high pH = 8.8 was strongly suggested by the X-ray reflectivity measurements employing CH₃NH₂, (CH₃)₂NH, and (CH₃)₃N as alternative counterions. The arrangements of the arachidate chains and of the Cd ions were each determined to near atomic resolution by fitting the GID data, but the relative offset between the arachidate and Cd “lattices” was difficult to ascertain.

The induced freezing of drops of supercooled water covered by uncompressed monolayers of the aliphatic alcohols C_nH_2n+1OH, n = 16-31 was investigated. The ice-nucleation temperatures were found to depend on the length of the hydrocarbon chain and the parity of the number of carbon atoms in the chain. A gradual increase of the freezing point from -14 °C leveling off to a plateau at -7.5 °C from n= 22 onward was observed for the even series. Alcohols with n odd raised the freezing temperature from -11 to-1 °Cforn= 17-31. Fatty acids (C_nH_2n+1+1COOH) or alcohols bearing a fluorocarbon chain or a steroidal backbone as the hydrophobic part induced nucleation of ice at much lower temperatures. Powder X-ray diffraction measurements showed that the monolayer C₃₁H₆₃OH induced formation of hexagonal ice with its (001) face parallel to the monolayer surface. Grazing incidence X-ray diffraction (GID) studies of uncompressed monolayers of C_nH_2n+1OH with n = 16, 20, 23, 30, 31 on water at 5 °C revealed two-dimensional (2D) crysalline self assembly and yielded their packing arrangements to near atomic resolution.¹ The extent of 2D crystalline order (i.e. coherence length) and the amount of crystalline material were less for monolayers with n = 16 and 20 than for monolayers with n = 23, 30, 31 according to a GID analysis, the latter property being independently confirmed by FT-IR. The best lattice match to ice was for n = 30 and 31, the lattice match to ice being poorer for n = 20 and 16, in terms of area per molecule, correlating with their less efficient ice-nucleation behavior. The packing arrangements of the hydrocarbon chains of monolayers C₃₀H₆₃OH and C₃₁H₆₃OH are very similar, but for the orientation of their CH₂OH moieties, which are different, resulting in different ice-nucleation behavior. Further evidence for the role played by the orientation of the C-OH group is the ice-nucleating properties of alcohols CH₃(CH₂)_nCOX(CH₂)_mOH (X = O, NH). In these systems the freezing point was found to depend on the parity of m but not on n. The 2D crystal structures of two ester-alcohols n = 19, m = 9, 10 on water were determined by GID and lattice energy calculations.¹Finally, mixtures of aliphatic alcohols with different chain lengths (by up to four CH₂ groups) substantially reduced the ice-nucleation temperature, implying drastic reduction in the lateral order of the 2D nets of alcohol OH groups. On the other hand, up to 50% fluorocarbon alcohol in a mixture with hydrocarbon alcohol did not reduce the freezing temperature of ice, indicating phase separation of crystalline domains.

The structure of an uncompressed monolayer of C₃₁H₆₃OH, which induces freezing of supercooled water drops at ∼-2°C, was studied by grazing incidence X-ray diffraction in the temperature range +6°C to freezing of the water subphase. As the water was cooled, the hydrocarbon chains underwent a change in tilt angle. The monolayer preserved its structure on the epitaxially-grown surface of hexagonal ice (after freezing) and, after the ice was melted, subsequent to the temperature being raised above 0°C. The coherence length of the observed ice crystallites parallel to the interface was about 25 Å, which is in agreement with the extent of match between the lattice of the monolayer and the ab lattice of ice. This yields some information on the critical size of the ice nucleus bound to the monolayer, just below 0°C.

Tailor-made molecular auxiliaries for the control of nucleatiw and growth of molecular crystals may be classified into two broad categories: Inhibitors and promoters, Tailor-made inhibitors of crystal growth can be used for a variety of purposes which include morphological engineering, reduction of crystal symmetry, assignment of absolute structure of polar crystals, elucidation of the effect of solvent on crystal growth and crystallization of a desired polymorph. As for crystal growth promoters, Langmuir monolayers on water have been used to induce growth of 3D crystals at the monolayer-solution interface by means of structural match, molecular complementarity or an electrostatic interaction. The 2D crystalline structures of these monolayers have been studied by grazing-incidence x-ray diffraction (gixd). It has become possible to monitor, by gixd, the growth and dissolution of self-aggregated crystalline monolayers affected by the interaction of solvent molecules in the aqueous subphase with the monolayer headgroups.

The spontaneous formation of highly crystalline two-dimensional films of uncompressed long chain amide and carboxylic acid amphiphiles spread on formamide has been demonstrated by grazing incidence X-ray diffraction. These results were compared to those found for the same amphiphiles on water. The observed diffraction data Of C29H59CONH2 over both water and formamide and those Of C29H59CO2H over formamide are strikingly similar, while those Of C29H59CO2H over water are different. Arachidamide (CH19H39CONH2) over water subphase forms a unimolecular layer with the molecules tilted by 18-degrees. Over formamide, the crystallites are made up, at least in part, of three molecular layers, with the molecules standing vertically. This was confirmed by X-ray specular reflectivity. These results are analogous to the well known, but as yet unexplained, influence which solvent may have on the growth of polymorphic modifications of three-dimensional crystals.

A unique set of proteins extracted from a variety of invertebrate calcitic mineralized tissues is able to selectively interact in vitro with certain crystal faces and not others. This was previously demonstrated by observing changes in morphology of crystals grown in the presence of proteins as compared to those grown in the absence of proteins. Following interaction, the proteins are overgrown by the crystal and are subsequently occluded within the crystal itself. Here we address the fundamental question of whether or not the proteins also alter the crystal texture in an anisotropic manner. For this purpose we used high-resolution synchrotron X-ray diffraction to monitor changes in coherence length and angular spread. We studied the interactions of proteins extracted from the mineralized skeletal hard parts of sea urchins and mollusks, with crystals of two calcium dicarboxylic acids, calcium fumarate and calcium malonate, as well as the polymorph of CaCO₃ calcite. For the calcium dicarboxylate crystals, we did demonstrate that the coherence lengths are reduced in the directions perpendicular to the planes onto which the proteins preferentially adsorb. In contrast the calcite crystals grown in the presence of the proteins exhibited an increase in angular spread compared to the controls, but no anisotropic effect in coherence length was detected. A biologically produced calcite crystal, on the other hand, showed a preferential reduction in coherence length in the direction of the c axis. Clearly in the case of calcite, the processes controlling crystal texture in the biological environment are more sophisticated than those in vitro. The detection of a reduction in coherence length in the directions perpendicular to the planes onto which the proteins preferentially adsorbed represents one of very few direct demonstrations that an additive that is able to selectively alter crystal morphology also affects crystal texture in an anisotropically specific manner. An understanding of this phenomenon may, in the future, improve our ability to control crystal texture in synthetic materials.

Principles are outlined for symmetry lowering of a mixed crystal composed of host and tailor-made additive molecules, based on selective occlusion of the latter through a subset of surface sites of the growing crystal, the symmetry of the surface generally being lower than that of the bulk. A survey is given of the various methods and approaches used to detect the reduction in symmetry. These include changes in crystal morphology, detection of enantiomeric segregation of chiral additives in 'centrosymmetric' crystals, generation of second-harmonic optical signals, optical birefringence, asymmetric photoreactions in the crystalline state and X-ray and neutron diffraction. The last two methods are applied to mixed crystals of cinnamamide (host) and thienylacrylamide (additive). The diffraction analysis demonstrated that the mixed crystals are composed of six sectors of reduced symmetry, from monoclinic centrosymmetric P2₁/c to triclinic P1 in four sectors and possibly Pc in the remaining two. The X-ray diffraction data were not sufficiently accurate to permit assignment of the absolute structures of the P1 sectors with the use of anomalous X-ray scattering. Thus, by this method one could not ascertain the absolute orientation of the guest molecules on the surface sites through which they were selectively occluded. This ambiguity was resolved by assignment of the absolute configuration of the chiral heterophotodimers, between host and guest, in enantiomeric excess in the P1 sectors, after irradiation with UV light. These results led to the definite conclusion that the selective occlusion of thienylacrylamide arises from a replacement of attractive C-H⋯π (electron) interactions between host molecules by repulsive sulfur (lone-pair electron)⋯π (electron) interactions between guest and host at the crystal surfaces.

The advent of well‐collimated, high‐intensity synchrotron X‐ray sources and the consequent development of surface‐specific X‐ray diffraction and fluorescence techniques have recently revolutionized the study of Langmuir monolayers at the air–liquid interface. These methods allowed for the first time the determination of the in‐plane and vertical structure of such monolayers with a resolution approaching the atomic level. We briefly describe these methods, including grazing incidence X‐ray diffraction, specular reflectivity, Bragg rods, standing waves, and surface fluorescence techniques, and review recent results obtained from them for Langmuir films. The methods have been successfully applied in the elucidation of the structure of crystalline aggregates of amphiphilic molecules such as alcohols, carboxylic acids and their salts, α‐amino acids, and phospholipids at the water surface. In addition, it became possible to monitor by diffraction the growth and dissolution of the crystalline self‐aggregates as well as structural changes occurring by phase transitions. Furthermore, the surface X‐ray methods shed new light on the structure of the underlying ionic layer of attached solvent or solute species. Examples are given where singly or doubly charged ions bound to the two‐dimensional (2D) crystal form either an ordered or diffuse counterionic layer. Finally, the surface diffraction methods provide data on transfer of structural information from 2D clusters to 3D single crystals, which had been successfully accomplished by epitaxial‐like crystallization both in organic and inorganic crystals.

Different growth rates on the opposite hemihedral faces of polar, platelike crystals of N-n-octyl-D-gluconamide were observed. One face is hydrophobic and the other hydrophilic, in keeping with contact angles of various solvents on these faces which were measured. It was found that the different growth rates can be explained by the hydrophilicity and hydrophobicity of the crystal surfaces.

A general approach is presented toward the determination at near atomic resolution of two-dimensional (2-D) crystalline structures of amphiphilic molecules at the air-water interface. It involves fitting of grazing incidence X-ray diffraction (GID) data from the 2-D crystal using molecular models, complemented by lattice energy calculations. In this way, one may eliminate ambiguities associated with assignment of the 2-D crystal symmetry, the molecular conformation, and the packing arrangement. The method was applied to the elucidation of the low temperature (5°C) structure of an uncompressed monolayer of triacontanoic acid C₂₉H₅₉CO₂H. We deduced a packing of the molecules in a rectangular unit cell in plane group pg. The molecular chain axes are tilted from the vertical by 27° along the short 5.53-Å axis of the unit cell and oriented so as to form the orthogonal O_⊥ packing type. The CO₂H groups are not directly interlinked by O-H⋯O hydrogen bonds. A distinct improvement of the agreement between observed and calculated GID data was achieved by partial relaxation of the glide plane symmetry. The observed Bragg peaks suggested very anisotropic shapes for the crystallites. This anisotropy was correlated with the energy of attachment of a molecule to a specific crystallite facet.

X‐ray diffraction methods for Langmuir films on the surface of water are briefly presented, together with recent results for docosanoic acid monolayers on pure water and for eicosanoic acid monolayers on an ionic subphase.

Monolayers of aliphatic long chain alcohols (C_nH_2n+1OH) were found to induce nucleation of ice at temperatures approaching O°C in contrast to water‐soluble alcohols which are efficient antifreeze agents. The corresponding fatty acids and alcohols with bulky hydrophobic groups, induce ice nucleation at temperatures lower by as much as 12°C. The freezing point induced by the amphiphilic alcohols was found to be sensitive not only to area per molecule but also to chain length and parity, reaching higher temperatures for monolayers with n odd. Grazing incidence X‐ray diffraction studies performed on some of these alcohols at the air/water interface (at 5°C and at zero pressure), demonstrated the formation of crystalline two‐dimensional clusters with a distorted hexagonal cell whose dimensions resemble those of hexagonal ice. The catalysis of ice nucleation by these alcohol monolayers may be rationalized in terms of the structural match between the monolayer domains and the ab layer of hexagonal ice.

Nucleation, growth, and dissolution of crystals have been studied by stereochemical approach involving molecular recognition at interfaces. A methodology is described for using "tailor-made" additives designed to interact stereospecifically with crystal surfaces during growth and dissolution. This procedure was instrumental in controlling crystal morphology and in revising the concept of the structure and symmetry of solid solutions. Consequently, it was applied to the transformation of centrosymmetric single crystals into solid solutions with polar arrangement displaying second-harmonic generation and to the performance of asymmetric synthesis of guest molecules inside centrosymmetric host crystals. The method has led to a discovery of a new "relay" mechanism explaining the effect of solvent on crystal growth. Finally, it allowed for the design of auxiliary molecules that act as promoters or inhibitors of crystal nucleation that can be used to resolve enantiomers and crystallize desired polymorphs.

Sea urchin skeletal elements are composed of single crystals of calcite. Unlike their synthetic counterparts, these crystals do not have well-developed cleavage and are consequently much more resistant to fracture. This phenomenon is due in part to the presence of acidic glycoproteins occluded within the crystals. By means of x-ray diffraction with synchrotron radiation, it is shown that the presence of the protein in synthetic calcite only slightly decreases the coherence length but significantly increases the angular spread of perfect domains of the crystals. In biogenic calcite, the coherence length is 1/3 to 1/4 as much as that in synthetic calcite and the angular spread is 20 to 50 times as wide. It is proposed that the presence of macromolecules concentrated at mosaic boundaries that are oblique to cleavage planes is responsible for the change in fracture properties. These results may be important in the material sciences, because of the unusual nature of this material, namely, a composite based on the controlled intercalation of macromolecules inside single-crystal lattices.

A new series of amphiphilic molecules bearing two amide groups along the hydrocarbon chain form head-to-tail Z-type (polar) multilayers by the Langmuir-Blodgett (LB) technique, in contrast with the common amphiphiles that tend to deposit in the head-to-head, tail-to-tail Y-type fashion. Molecules with one amide group along the chain form Y-type or Z-type structures, depending on the location of the amide along the chain. p-Nitroaniline or merocyanine groups could be aligned in a polar sense, by attaching them covalently to such amphiphiles, to yield multilayers displaying second-harmonic generation (SHG). These films were characterized by ellipsometric, X-ray diffraction, IR, UV, and SHG measurements. The Z-type deposition correlates with the observed low water contact angles of the films, indicating formation of porous structures in which water may penetrate. This behavior is rationalized in terms of the hydrophilic nature of the amide groups that retain water by hydrogen bonding. In keeping with this mechanism, it was anticipated that amphiphiles bearing other polar groups, such as hydroxyls along the hydrocarbon chain, also form Z-type LB films.

The formation of two-dimensional ordered aggregates of water-soluble hydrophobic α-amino acids at the air-solution interface has been demonstrated through the induced epitaxial nucleation of α-glycine crystals at these interfaces. This crystallization method, albeit indirect, has been found to be very sensitive to small changes in the structure of the presumed aggregates. The hydrophobic-amino acids used were divided into two classes: The first, including valine, leucine, phenylalanine, norleucine, isoleucine, and n-aminooctanoic acid, induced fast oriented crystallization of α-glycine, at the solution surface, whereas the second class, tert-butylglycine, neopentylglycine, and hexafluorovaline, did not. The comparison between the packing arrangement of the α-glycine crystalline face attached at the interface and that of various hydrophobic α-amino acid crystals, complemented by surface tension measurements, brought evidence in favor of the formation of structured domains which must carry precise enantioselective information to generate the oriented crystallization process. These results may be relevant to any process involving structural self-aggregation.

Monolayers of PFA, a fluorinated surfactant, on water were studied using synchrotron X-ray grazing incidence diffraction (GID) and reflectivity measurements (XR). The uncompressed monolayer is found to self-assemble into crystalline domains giving a strong GID peak. Upon compression and decompression a surface pressure driven solid-solid phase transition takes place. A hexagonal lattice with vertical molecules at high pressure undergoes a distortion due to a rigid molecular tilt as the pressure is decreased. Bragg rod scans provide conclusive evidence for a tilt of about 20 " at 10 mN/m and show the tilt to be towards nearest neighbours. The uncompressed monolayer has a molecular tilt of about 25 '.

Crystal nucleation of glycine and sodium chloride has been studied under floating Langmuir monolayers at air/solution interfaces, and at glass slides coated with Langmuir-Blodgett films. The packing arrangements of the polar head groups of the monolayers were varied in a controlled manner by introducing different groups in the hydrophobic tails. The structures of some of these monolayers were independently elucidated by grazing incidence X-ray diffraction and reflectivity measurements using synchrotron light. It was found that the crystals nucleated at the interface exposed a top layer of molecules with an arrangement similar or complementary to that of the polar head groups of the monolayer. These results imply that the packing of the polar head groups determines the morphology and the nucleation rate of the attached crystal.

We have demonstrated, for the first time by diffraction methods, that a solid solution composed of host and guest molecules can exhibit a crystal symmetry lower than that of the host. The study proves that the symmetry of a solid solution is dependent not only upon the host crystal structure and the guest molecular structure but also upon the surface structure and symmetry of the host crystal. The crystal structures of (S)-asparagine monohydrate [D₂NCOCH₂CH(ND₃)CO₂.D₂O] and of the solid solution (0.848:0.152) (S)-asparagine/(S)-aspartic acid [DO₂CCD₂CD(ND₃)CO2] monohydrate were refined by using neutron diffraction data obtained at 15 K. The space group of the pure host crystal is P2₁2₁2₁(Z = 4), whereas that of the host/guest crystal is monoclinic P12₁1 with two molecular sites per asymmetric unit. The ratios of guest/host occupancies of the two independent sites are 0.173:0.827 and 0.132:0.868. The reduction in symmetry is in accordance with the preferred adsorption of guest aspartic acid on the (010) crystal face at half of the orthorhombic, symmetry-related surface sites. Aspartic acid mimics, at the preferred (010) surface sites, molecular asparagine, participating in all hydrogen bonds. At the less-favored (010) surface sites a “normal” N-H.O(host) hydrogen bond is replaced by O(hydroxyl).O(host) repulsion between lone-pair electrons.

We have determined the packing arrangement of a floating monolayer of palmitoyl-(R)-lysine at the air-water interface by grazing incidence X-ray diffraction and reflection measurements. These techniques utilize the unique properties of synchrotron radiation: high intensity within a small natural collimation. In the grazing angle diffraction experiment two peaks were detected in the "twodimensional powder" pattern from a monolayer of palmitoyl-(R)-lysine. Their widths indicated coherence lengths of 500 J~. The positions and intensities of these peaks allowed us to choose between various models and to determine the monolayer structure. The packing arrangement of the Qt-amino acid headgroups in the model proved to be very similar to that found in the crystal structures of the 0t form of glycine and several hydrophobic at-amino acids, thus providing a simple explanation for the oriented crystallization of 0t-glycine at monolayer-solution interfaces. The tilt of the molecule calculated from the model is consistent with the results from reflectivity measurements and X-ray powder diffraction data of the crystalline powder material. Reflectivity measurements indicate that at surface pressures as high as 30 mN m- 1 the monolayer covers only about 90% of the surface. Reflectivity measurements of the monolayer over water and over solutions of 29/o (S)-glutamine showed significant differences, indicating binding of the solute molecules to the monolayer.

A measurement and interpretation on a molecular level of a phase transition in an ordered Langmuir monolayer is reported. The diagram of surface pressure (π) versus molecular area of a monolayer of chiral (S)-[CF3-(CF2)9-(CH2)2-OCO-CH2-CH (NH3+)CO2-] over water shows a change in slope at about πs= 25 millinewtons per meter. Grazing-incidence x-ray diffraction and specular reflectivity measurements indicate a solid-solid phase transition at πs. The diffraction pattren at low pressures reveals two diffraction peaks of equal intensities, with lattice spacings d of 5.11 and 5.00 angstroms; these coalesce for π ≥πs. Structural models that fit the diffraction data show that at π> πs the molecules pack in a two-dimensional crystal with the molecules aligned vertically. At π

The structures of the partially reacted crystals of the two complexes (5:2) deoxycholic acid (DCA)-acetophenone and (8:3) DCA-p-fluoroacetophenone were determined by low-temperature (-170 °C) X-ray diffraction. the structure analyses indicated that both independent guest acetophenone molecules G′ and G in DCA-acetophenone react and that in DCA-p-fluoroacetophenone the guest molecule G′ reacts whereas the other guest molecule G remains unreacted because of packing of G and G′ molecules along the channel. the observed guest photoconversion in DCA-acetophenone is 40%; the maximum value according to packing considerations is 50%. In DCA-p-fluoroacetophenone the observed guest photoconversion is 35%, very close to the maximum theoretical yield of 33% based on packing considerations. the analysis demonstrated that during the course of photoconversion there is minimal motion of the (guest) phenyl ring, pronounced rotation of the acetyl group about the exocyclic C-C bond, and displacement of unreacted and reacted molecules. Atom-atom potential energy calculations showed that in DCA-acetophenone a guest ketyl radical with a pyramidal geometry may rotate by a full 180° without inducing prohibitively short intermolecular contacts.

The two inclusion complexes of guest acetophenone and m, chloro-acetophenone with host deoxycholic acid (DCA) each yielded on UV irradiation a single diastereomeric photoaddition product at steroid atom C5, of configuration S at the generated stereogenic centre (DCAOHCH₃C₆H₄). Comparison of the host-guest arrangement at the sites of reaction with the S configuration at the new chiral atom C of the photoproducts indicates a net rotation of 180° by the guest acetyl group prior to C-C bond formation since the guest molecules expose their Re faces to the C5-H5 steroid bonds¹. To elucidate this rotation, photochemical and crystallographic studies were performed on four DCA complexes with engineered guest ketone arrangements. The guests were p-fluoroacetophenone and (p-substituted) propiophenones (XC₆H₄CO₂C₂H₅, X=H, F, Cl). The crystal structures of two isolated photoproducts are also reported. The channels of DCA-fluoroacetophenone contain two independent guest molecules G' and G, respectively exposing their Re and Si faces to the steroid C5-H5 bond vectors at the potential sites of reaction. Only one diastereomeric photoproduct was obtained with addition at atom C5, with absolute configuration S at the generated stereogenic centre, akin to that of the DCA-acetophenone complexes. The reaction is interpreted in terms of a 180° rotation of the acetyl group of the G' molecule; the absence of the R diastereomer is explained by a preclusion of photoaddition of guest G to DCA because of guest packing along the channel. The guest arrangements in the two complexes DCA-propiophenone and DCA-p-fluoropropiophenone are almost isomorphous. There are two independent guest molecules G and Ḡ related by a pseudo centre of inversion. Each of the two guest molecules exposes its Re face to a steroid C5-H5 bond at a site of reaction. Thus photoaddition takes place with and without 180° rotation of the propionyl group since the two complexes each yield the two diastereomeric photoproducts at C5. DCA-p-chloropropiophenone yields only one diastereomeric photoproduct at C5, with absolute configuration R about the new stereogenic centre. The crystal structure analysis suggests three independent guest molecules G, G' ana Ḡ; G and G' are related by pseudo two fold screw symmetry along the channel axis; Ḡ is related to G and G' by pseudo centre of inversion; once again the guests G, G' and Ḡ appear to expose their Re faces to the C5-H5 bonds at the sites of reaction.

Photochemical reactions in crystals proceed under control of the structure, including absolute configuration, of the bulk, unless preceeded by energy transfer, in which case defects may be important. The reaction may be followed by phase separation. Two-phase systems allow wider scope for reactant selection. The presence during growth of additives, matched stereochemically to the crystal, modifies habit and growth-rate, with far-reaching consequences. Some partially ordered systems are considered.

This chapter contains sections titled: Introduction; Statement of the Problem; The Bijvoet Method; A Bridge Between Crystal Structure, Crystal Morphology, and Molecular Chirality; Absolute Configuration from Chemical Reactivity in Polar and Enantiopolar Crystals; The Solvent Effect; Pyroelectricity, Piezoelectricity, and Optical Activity in Crystals; Determination of Absolute Configuration by Electron Microscopy; Conclusions

When crystals of organic compounds are grown in the presence of growth inhibitors, there is a change in crystal morphology. A stereochemical correlation exists between the crystal structure, its modified morphology, and the molecular structure of the inhibitor. This correlation has been successfully exploited for the efficient resolution of conglomerates, the engineering of organic crystals with desired morphologies, the direct and relative assignment of the absolute configurations of chiral molecules and crystals, and for the design of a new model for the spontaneous generation of optical activity. In an analogous way dissolution of organic crystals in the presence of these growth inhibitors induces etch pits at preselected faces. The effect of solvent on crystal growth has been analyzed in some model systems. The experimental results are complemented by atom‐atom potential energy calculations.

A general method for the controlled modification of the morphology of organic crystals is described. The method comprises stereospecific inhibition of growth of preselected faces with the assistance of "tailor-made" growth inhibitors. The change in crystal habit is explained by a mechanism which takes into consideration a stereochemical correlation between the molecular structure of the additive, the crystal structure of the substrate, and the affected growth directions. The method has been successfully applied to primary amides ((E)-cinnamide, benzamide, p-toluamide, and p-clorobenzamide), carboxylic acids ((E)-cinnamic acid and benzoic acid), and steroids (androsterone and epiandrosterone). Dramatic changes in habit were induced by replacement, at the crystal surface, of a substrate N-H ..,0 bond by an Q...Q repulsion, by replacement of an attractive C-H ..,0 interaction by a C-H ..,H or C-Cl..,0 repulsion, or by insertion of a methyl or chlorine substituent instead of hydrogen, etc. The induced morphological modifications were used to obtain information on molecular interactions and conformations of the adsorbed inhibitor at the crystal surface. Thus, we could show that adsorbed additives benzamide and picolinamide assume twisted and planar conformations, respectively, on the affected faces of host benzoic acid, which is planar in the solid. In contradistinction, p-aminobenzoic acid tends to be planar when interacting with the growing faces of the nonplanar p-aminobenzamide. The additive (E)-cinnamide assumes a syn-planar C=C-C=O conformation on the affected surface of host (E)-cinnamic acid, which tends to assume an antiplanar C=C-C=O conformation. The effect of various additives on crystal habit is accounted for and quantitatively evaluated by atom-atom potential energy calculations.

One enantiomer of an initially racemic mixture of α-amino acids can be preferentially removed from solution by selective incorporation into the opposite enantiotopic faces of growing centrosymmetric crystals of the α-form of glycine^1,16. We report here that oriented growth of crystals of the α form of glycine has been achieved under chiral Langmuir monolayers comprising amphiphilic α-amino acids, by virtue of a structural match between the monolayer and the ac surface layer of the attached growing glycine crystals. Such monolayers of α-amino acid of R configuration, containing long hydrocarbon chains, induce glycine to crystallize with its (010) face attached to the monolayer, and by symmetry the corresponding S amino-acid monolayers induce attachment of the (0&1macr;0) face of glycine. Replacement of the hydrocarbon by a fluorocarbon chain induces analogous crystallizations, albeit, with only a partial degree of orientation, whereas monolayers of a resolved amino acid bearing a cholestanoyl moiety do not promote crystallization of glycine. Monolayers of the R, S-amino acids induce attachment of both (010) and (0&1macr;0) faces of glycine. These results on oriented crystal growth provide a new route for efficient amplification of optical activity of amino acids present in solution, through the enantioselective occlusion into the growing crystals of glycine¹ at water-air interfaces covered by a monolayer.

Doubly vs. singly hydrogen-bonded arrangements in crystalline N-acylated amino acids R-CONH-CHR′-C02H are examined by energy calculations. The O(amide) is a significantly stronger proton acceptor than the O(carboxyl). Thus in one-third of the crystal structures the molecules form doubly hydrogen-bonded systems O-H-O(amide) and N-H-O(amide), despite the general preference for the maximum number of proton acceptor sites to participate in hydrogen bonds, dictated by molecular packing and conformation. The energy results are consistent with the tendency for the molecules to be interlinked via single hydrogen bonds O-H-O(amide) and N-H-O(carboxyl), rather than the reverse, and the total absence of the doubly hydrogen-bonded systems O-H-O(carboxyl) and N H-(carboxyl).

Information contained in electron density distributions, derived from X-ray diffraction data, was exploited to improve the electrostatic parameters of atom-atom potential functions of the carboxyl group and thus to obtain a better estimate of the Coulomb intermolecular energies. The proton affinities of the carbonyl oxygen atom of the amide and carboxyl groups were compared in terms of electrostatic potential energy around these atoms and correlated with hydrogen-bonding properties. Energy calculations were undertaken to account for various characteristic packing motifs of carboxylic acid molecules, including the geometry of the catemer motif, order-disorder of the carboxyl dimer, preferred stacking of carboxyl dimers, the role played by C-H⋯O(carbonyl) interactions in stabilizing overall packing, characteristic packing of substituted benzoic acids, and the stability of the observed crystal structures of oxalic acid and formic acid, via the generation and analysis of ensembles of alternative crystal structures.

The ability of molecules, chiral by virtue of the presence of an s-butyl group, to display conformational polymorphism has been exploited for the performance of asymmetric syntheses of either sense on the same chiral molecule; this phenomenon is illustrated for the asymmetric solid-state polymerization of the monomer (R)-(–)-(1).

A molecular model which accounts for stereoselective interactions within the series of chiral secondary amides RCONHCH(CH₃)Ar is proposed. It assumes that a guest molecule intercalates between two host molecules in their 5-Å translation H-bonded array to form diastereomeric arrangements for the two enantiomers, differing in stability. The model explains various aspects of chiral recognition: (1) the gas chromatographic separation of enantiomers achieved with N-acyl-α-arylethylamines as chiral phases; (2) the difference in solubility of (R)- and (S)-N-trifluoroacetyl-α-(1-naphthyl)ethylamine in solid (R)-N-lauroyl-α-(1-naphthyl)ethylamine. The packing arrangement of certain diamide molecules was examined in order to reinforce the assumptions on which the explanation of the stereoselective effects was based. Energy computations support the stability relationships which follow from the model.

Resolved 1-phenylpropyl and 1-phenylbutyl 9-anthroates, when crystallised from n-hexane, form 6:1 inclusion molecular complexes which are isostructural; X-ray analysis of the propyl derivative demonstrates the formation of a channel structure by the anthracenes, in which the n-hexane is included.

NA

The crystal structures of the α- and β-forms of tetrolic acid have been determined from X-ray diffractometer data. Crystals of the α-form are triclinic, space group P1, Z = 2, a = 7.320, b = 5.099, c = 7.226 Å α = 83.97, β = 117.46, γ = 112.00°. The structure was refined to R 0.07 for 985 reflections. The molecules form hydrogen-bonded cyclic dimers (O ⋯ O 2.649 Å) in which the C-O bond lengths are almost equal (1.252, 1.265 Å). 'Half hydrogens' were attached to each oxygen, their parameters refined, and their presence substantiated by a difference-Fourier synthesis. The methyl hydrogen atoms were located. The structure of the monoclinic β-modification [a = 7.887, b = 7.121, c = 3.937 Å, β = 100.18°, Z = 2, P2₁] was refined from counter data to R 0.04 (687 reflections). The methyl hydrogen atoms were located. The bond lengths within the carboxylic group are distinct: C=O 1.204, C-O 1.310 Å; the hydroxy-hydrogen was clearly evident. The molecules form a continuous array of O-H ⋯ O= hydrogen bonds (O ⋯ O 2.655 Å) between molecules related by a two-fold screw axis similar to the arrangement in the structure of formic and acetic acids. The carbon - carbon bond lengths of the α- and β-forms are: H₃C-C 1.458, 1.455, C≡C 1.182, 1.178, and C-CO₂H 1.441, 1.441 Å.

The crystal structure of the title compound has ben solved from X-ray diffractometer data by direct methods and refined by least-squares to R 0·038 for 1182 independent reflections. Crystals are monoclinic, space group P21, with Z= 2 in a unit cell of dimensions: a= 7·367(1), b= 9·041(1), c= 3·742(1)Å, β= 99·39(1)°. The mean σ for bond lengths not involving hydrogen is 0·002 Å.

The hydrogen-bond network is two-dimensional. The amide and carboxy-groups of molecules related by translation form cyclic hydrogen-bonded (asymmetric) pairs (OH ⋯ O, 2·660; NH ⋯ O, 2·838 Å) generating chains which are interlinked, along the 21 axis, by NH ⋯ O (2·935 Å) bonds. The conformations of the groups C:C·C(NH2):O and C:C·C(OH):O are syn-planar, in contrast to the antiplanar C:C·C:O arrangements in the α- and β-forms of fumaric acid.

The bond lengths are: C[double bond, length half m-dash]C 1·320, C(OH)–C 1·497, C(NH2)–C 1·486, C(OH)[double bond, length as m-dash]O 1·209, C(NH2)[double bond, length as m-dash]O 1·247, C–OH 1·310, and C–NH2 1·323 Å.

The title compound crystallises in space group Pca2₁ with two molecules in the asymmetric unit, the cell having dimensions a = 8.060, b = 4.195, c = 25.433 Å. The phases were determined from a diffractometer data by a multi-solution method and the structure refined by a least-squares procedure to R 0.067 for 968 independent reflections. The bond lengths are C≡C 1.175, 1.179; ≡C-C 1.455, 1.453; C-CO₂H 1.484, 1.506; C=O 1.221, 1.214; C-OH 1.307, 1.259 Å. The C(:O)·O·C⋮C system is syn-planar. The molecules are hydrogen-bonded (O-H ⋯ O 2.69 and 2.65 Å) in pseudo-centrosymmetric pairs. In the crystal there are no intermolecular ethynyl-H ⋯ O=C interactions: rather, the acetylenic C-H bond points at the C≡C triple bond, [H ⋯ C⋮C(midpoint) 3.0 Å]. The C(sp³)-H ⋯ bond is directed towards the carbonyl oxygen (C-H ⋯ O 3.45, and H ⋯ O 2.6 Å). But-3-ynoic acid also appears in a pseudo-orthorhombic form showing order-disorder. The relationship of the two forms is discussed.

Die Kristallstruktur der Titelverbindung wurde mit Hilfe der SEARCH‐Methode gelöst und aufgrund von 4050 (einschließlich 1484 „unbeobachteten”) Reflexen (sin Θ/λ ≤ 0.66) und 150 starken Reflexen im Bereich 0.66 Kα‐Strahlung (Differenz‐Filter‐Methode) auf einem mit Lochstreifen gesteuerten Siemens‐Diffraktometer gemessen worden waren. Die Standardabweichung der kristallographisch unabhängigen Längen der Dreifachbindung (1.192 Å) sowie der exocyclischen (1.434 Å) und endocyclischen Bindungen der Benzolkerne (mit Symmetrie m statt 6) beträgt 0.003 Å. Die Abweichung der Kohlenstoffatome der Dreifachbindungen aus den Ebenen ihrer Benzolringe (maximal 0.103 Å) ist signifikant, da die Ringatome selbst durchschnittlich nur 0.004, maximal 0.010 Å außerhalb dieser Ebenen liegen. Die Konformation des Moleküls entspricht eher der Symmetrie m als ō m 2, wofür Packungseffekte verantwortlich gemacht werden. „Overcrowding” der dreifach‐gebundenen ortho‐Kohlenstoffatome ist nicht klar erkenntlich. Die beobachteten Schwankungen der aromatischen Bindungslängen und ‐winkel werden durch Hybridisierungsunterschiede der mit C oder H substituierten Ringkohlenstoffatome erklärt.

The crystal structure of trans,trans-sorbamide has been solved from 1380 three-dimensional counter data (Cu K_α radiation), corrected for absorption, and refined by a least-squares method with anisotropic temperature factors of all but the hydrogen atoms. The "final" agreement factors were r = 0.009, R = 0.046 and 0.045, including and excluding |F_c| > kF_t, respectively. The e.s.d. of heavy-atom and hydrogen co-ordinates are estimated as 0.002 and 0.03 Å, respectively. A rigid-body analysis of the molecule has been carried out, and the bond lengths have been corrected accordingly. The molecular dimensions and the packing arrangement are discussed.