Correlation between the microscopic and mesoscopic chirality in Langmuir monolayers

Thin Solid Films 433 (2003) 12–21

Correlation between the microscopic and mesoscopic chirality in Langmuir monolayers Nilashis Nandia,1, Dieter Vollhardtb,* a

Chemistry Department, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India b Max Planck Institute of Colloids and Interfaces, Potsdam D-14424, Germany

Abstract In this review, we briefly discuss the present status of the experimental information based on Brewster-angle microscopic studies of chiral monolayers and recent molecular theories on chiral amphiphilic systems. The theoretical results are compared with experimental information. Attention has been drawn to the fact that chirality present at the molecular level (at the microscopic length scale) is responsible for driving the chiral shape of the domains composed of such molecules which are of mesoscopic dimension. In some cases, strong influences of molecular chirality on the domain morphology are observed. While such correlations between chirality present at different levels of the structural hierarchy are known for many biological assemblies, the recent studies on biomimetic Langmuir monolayers conclusively provide a correlation between chirality present at different length scales of the molecular architecture. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Chirality; Monolayer; Brewster-angle microscopy; Effective pair potential theory

1. Introduction Chirality is a fundamental phenomenon of nature. Chiral objects lack symmetry. However, it is well known that chirality is present at macroscopic, molecular and even subatomic levels in nature. A chiral molecule is non-superimposable on its mirror image w1,2x and could be asymmetric. It is known that only one enantiomer of a drug is capable of curing diseases in many cases. The other enantiomer is either ineffective or produces adverse effects. Thus, understanding the absolute configuration seems to be essential for enantiomeric drug development technology w3x, which is a tremendously important industry. In many biological systems chirality is observed at lower and higher levels of structural hierarchy. Common examples are proteins and their constituent amino acids, and nucleic acids and their constituent sugars, as well as membranes and their constituent lipids and membrane proteins. In all cases, *Corresponding author. Tel.: q49-331-567-9258; fax: q49-331567-9202. E-mail addresses: [email protected] (D. Vollhardt), [email protected] (N. Nandi). 1 Fax: q91-1596-44183.

the fundamental subunits and higher-level structures composed of these subunits are chiral. However, it remained uncertain whether any correlation exists between microscopic and macroscopic chirality. It is known that chiral biological systems such as proteins and nucleic acids lose functionality when the chirality of the basic unit is altered. This strongly suggests a micro–macro correlation. This correlation is related to the well-known problem of homochiral evolution w4,5x. However, the molecular picture of such a possible correlation remained unclear. The structure and properties of several chiral surfactants were studied in recent years. Such studies were made in both bilayer and monolayer phases. Monolayer studies are simple because the system is two-dimensional. The reduction of a degree of freedom compared to a three-dimensional system made monolayer studies relatively easy. It is now well known that mesoscopic domains are formed in monolayers in the condensed phase, as detected by various optical techniques w6–9x. When the constituent amphiphiles are chiral and one enantiomer is present in excess, the domain shapes are asymmetric and hence chiral w8,9x. On the other hand, the domains composing a racemic mixture have sym-

0040-6090/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 3 . 0 0 2 9 8 - 0

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Fig. 1. Domains of N-tetradecyl-g,d-dihydroxy-pentanoic acid amide monolayers obtained by BAM.

metric features. In addition, chiral discriminating effects are observed. Such effects are manifested in the form of different shapes of the surface pressure–area (p–A) isotherms or the different-handedness exhibited by domains from different enantiomers w8–10x. It is interesting to obtain a molecular understanding of such chirality effects. For monolayers, being simpler biomimetic systems, it is expected that the molecular understanding of the chiral interaction in these chiral aggregates could shed light on the meso–micro relation of chirality in other biological assemblies. In the present review we discuss the recent experimental results obtained from Brewster-angle microscopic studies and theoretical results based on molecular theories concerning monolayers composed of chiral molecules. Chiral discrimination effects in monolayers are also mentioned, followed by the concluding remarks. 2. Brewster-angle microscopic studies on monolayers composed of chiral amphiphiles Brewster-angle microscopy (BAM) is based on the principles of reflection spectroscopy w11–15x. In this technique, direct visualization of the monolayer is possible and inferences can be made about the molecular orientation at the interface. The results are not influenced by any external perturbation, such as the presence of a probe, because no external probe is used in the BAM technique. Many chiral amphiphiles develop interesting mesoscopic domains, and the shape of a domain and the molecular orientation within it depend on the molecular chiral structure of the amphiphile. Achiral amphiphiles or racemic mixtures develop symmetric-shaped domains. Monolayers of achiral acid amide amphiphiles, such as

N-tetradecyl-b-hydroxy propionic acid amide w16x and N-alkyl-g-hydroxy butyric acid amide with various chain lengths (dodecyl and tetradecyl) w17x, form domains with a symmetric shape. This symmetric shape of the domains indicates an underlying molecular symmetry. We discuss the chirality-induced features of some amphiphiles in this section. BAM studies proved to be particularly useful when chiral effects were unobserved by other techniques, such as p–A isotherms. In many cases, mesoscopic chiral structures are observed for domains composed of enantiomers, but isotherm studies indicated no signature of chiral discrimination. It is known that chiral discrimination is apparent in the differences in the morphology or the physical behavior of a monolayer system as a function of its enantiomeric content. The discrimination is manifested in various ways, such as the characteristic features of the p–A isotherm, the shapes of the domains formed in the condensed phase, or the differences in the lattice structures of the enantiomer (or its mirror image) and the racemic mixture. It is important to note that both hetero- and homochirality are experimentally observed and it is still unclear why a particular interaction is dominant in an amphiphilic system. BAM studies of N-tetradecyl-g,d-dihydroxy pentanoic acid amide (TDHPA) showed the growth of dendriteshaped domains. The direction of the main growth axes bears a mirror-image relationship for the enantiomers w18x. The domains of the racemic mixture are quite similar; however, they have no mirror symmetry. BAM images of enantiomeric and racemic TDHPA are shown in Fig. 1. The p–A isotherms of the enantiomeric and racemic monolayers are nearly identical. Amphiphiles containing amino acid head groups show a wide variety of domain shapes w19–21x. In many

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Fig. 2. BAM images of the domains of N-stearoyl serine methyl ester monolayers spread on pH 3 water: (a) D-enantiomer; (b) L-enantiomer; (c,d) 1:1 DL-racemate. Image size 80=80 mm2.

cases the domains are curved and the curvature crucially depends on the chirality of the enantiomer. Explicitly, if D-enantiomeric domains curve in a left-handed way, the L-enantiomeric domain curves in a right-handed way. The domain shape of the 1:1 racemic mixture is usually different from the enantiomeric domains. In many cases, the single domain composed of a racemic mixture contains segments curved in a left- as well as a righthanded way. Condensed-phase domains of N-stearoylserine methyl ester monolayers (Fig. 2) show such features. The racemate domain shows curvature in both directions. This is indicative of chiral segregation. Explicitly, the enantiomeric-rich regions separate from the racemic mixture and the separated regions curve in opposite directions. Similarly, the domains of N-a-palmitoyl-threonine monolayers are spirally curved (Fig. 3). The sense of the curvature is opposite for opposite enantiomers. Racemic monolayers grow from a center in the opposite direction and the growth directions are opposite. Symmetric domain structures with opposite curvature grow from the center of a nucleus and suggest chiral segregation. The domains formed by amino acid amphiphiles show no inner anisotropy. The domains are uniformly

bright. This is indicative of the absence of mutual azimuthal orientation. However, inner structural features are observed in monoglycerol monolayers. In a small area of the p–A isotherm, small, clockwise curved spirals are formed in the S-enantiomeric monolayer of 1-O-hexadecyl-glycerol, whereas in the 1:1 racemic mixture, spirals are formed both clockwise and counterclockwise. In contrast to the faceted shapes of the condensed-phase domains of 1-O-hexadecyl-rac-glycerol, the domain shapes of 1monopalmitoyl-rac-glycerol have a disk-like shape. The domain structure of homologous 1-monostearoyl-rac glycerol monolayers resembles that observed in 1monopalmitoyl-rac-glycerol monolayers w22x. The bestdeveloped disk-shaped domains are subdivided into seven segments which meet in a center. The segments have different reflectivity and each segment is homogeneously reflecting. This clearly indicates a constant chain tilt. Cardioid-shaped domains are also observed (Figs. 4 and 5). The enantiomeric domains of 1-stearylamino-glycerol monolayers show the development of filigree-like domains w23x curved in opposite directions for the two different enantiomeric forms. The racemic mixture

Fig. 3. Chiral discrimination in the domain texture of N-a-palmitoyl-threonine monolayers observed by BAM: (a) D-enantiomer; (b) L-enantiomer; (c) 1:1 DL-racemate. Image size 350=350 mm2.

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Fig. 4. Chiral discrimination in 1-O-hexadecyl-glycerol domains, Ts 23 8C, Af0.3 nm2ymolecule: (a) racemic mixture with curvatures of the spirals in two opposite directions; and (b) S-enantiomer only clockwise curved spirals.

evolves fractal-like domains without any specific sense of curvature of the filigree (Fig. 6). Other than the monolayers of amino acid and glycerol head-group amphiphiles, those of phospholipids have been extensively investigated by optical techniques w6– 8,24–26x, including BAM and fluorescence spectroscopy. Dipalmitoyl phosphatidyl choline (DPPC) and dimyristoyl phosphatidyl ethanolamine (DMPE) have been studied in detail. The chirality of the mesoscopic domains is observed in the curvature of the defect lines

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inside the domains or the curvature of the domain arms (Fig. 7). The corresponding non-equilibrium structures show dendritic growth with curvature of the same sense. In the fractal-like structures the effect of chirality cannot be observed, because at the beginning the patterns are non-ordered (Fig. 8). In the corresponding racemic mixtures of different phospholipids, curvature is not formed; rather, straight dendritic arms or uncurved compact domains are formed. The comparison of the BAM images of the enantiomeric phospholipids LDMPE and L-DPPC monolayers reveals very different domain textures. In equilibrium, L-DMPE monolayers form compact domains with a different number of segments (five–eight) separated by chirally curved lines where the molecular orientation jumps. The lines join together in a center located inside the domain (the shape of the domain is circular) or in its edge (the shape of the domain is bean-shaped). The molecular orientation in the branched domains formed at high compression rates under non-equilibrium is similar to that in the compact domains. DPPC monolayers form in equilibrium triskelionshaped domains, the arms of which are curved oppositely for the two enantiomeric forms Fig. 9). The racemic mixture shows the development of straight arms. In

Fig. 5. BAM images of a round and cardioid domain of 1-monopalmitoyl-rac-glycerol monolayers and schematic presentation of the tilt direction of the alkyl chains in both domain forms.

Fig. 6. Fluorescence microscopy of the chiral discrimination in 1-stearylamine glycerol monolayers, Ts35 8C, ps5 mNym: (a) S-enantiomer; (b) R-enantiomer; (c) 1:1 racemate The star marks the chiral C-atom and the bar length is 100 mm.

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Fig. 7. Representative equilibrium domains of phospholipids. Left. Curved domain arms in D-DPPC monolayers. Middle. Curvature in the brightness change within the domains in L-DPP (Me)2E monolayers. Right. Curved defect lines in L-DPPE monolayers.

Fig. 8. Representative non-equilibrium domains of phospholipids. Left. L-and DL-DPPE monolayer not so far from equilibrium with dendritic (ordered) growth with chiral influence; curved axes and arms for enantiomeric monolayers (L-DPPE), straight axes and arms for racemic monolayers (DL-DPPE). Right. L-DPPC monolayer far from equilibrium with fractal-like (disordered) growth without chiral influence.

Fig. 9. Chiral discrimination in DPPC monolayers. The two enantiomeric triskelions are curved in opposite directions, clockwise for D-DPPC (left) and counterclockwise for L-DPPC (middle). The arms of the racemic DL-DPPC are straight. Image size 500=500 mm.

enantiomeric DPPC domains, the orientation changes gradually within each arm of the triskelions w24–26x. Early epifluorescence microscopic studies on DPPC also indicated the decisive role of chirality on the domain shapes w27x. BAM studies showed the development of feather-like dendrites in enantiomeric monolayers of dodecyl mannonamide w28x. Side arms develop from these featherlike shapes preferentially in one direction along the main

axis. The enantiomeric domains show this development in one direction, and in the case of racemic monolayers, the side arms are evolved in both directions. This is suggestive of chiral segregation and an example of homochiral preference exhibited by chiral amphiphiles. In summary, recent BAM studies indicated that the underlying chiral molecular structure drives many asymmetric mesoscopic aggregates in the condensed phase. Experimental observations clearly indicate a correlation

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between chirality present at the meso and micro levels. However, theoretical interpretations are needed to understand this correlation. In the following we discuss the available theories on chiral monolayers that have been used for this purpose. 3. Microscopic monolayers

studies

on

chiral

amphiphilic

Different versions of the continuum theory are proposed for chiral monolayers. Many such theories consider the Ginzburg–Landau-type free energy functions. These theories neglect the molecular structure. Consequently, it is not possible to include a realistic molecular structure, other than considering the average direction of the tail. Such theories cannot start from first principles and cannot explain how one enantiomer gives rise to a particular handedness, etc. Molecular theories are most promising for explaining the chirality-induced features of chiral monolayers. In the previous section we have seen how different molecules with subtle differences in the chemical structure or configuration lead to different domain morphology. Thus, theories are required to understand the underlying causes of the correlation between the molecular structure and mesoscopic shape. However, it is difficult to develop a complete firstprinciple molecular theory due to several factors, such as the complete absence of molecular symmetry, a lack of detailed knowledge of the structural details of the interface of the condensed-phase domains at the molecular level and the molecular arrangement in the underlying subphase, the heterogeneity of the system and the large number of molecules present in a domain. It is also difficult to carry out an atomistic simulation for the same reason. However, theoretical studies and simulations focus in this direction based on some simple ideas, as discussed below. A general theory of the shape transition of finite lipid monolayer domains, which can deal with chiral systems, was developed by McConnell and coworkers w7,29,33– 43x. An exact closed-form solution of the shape transition problem is now available w44,45x which is based on McConnell’s theoretical framework. Based on this theory, it could be concluded that surrounding the chiral domain the line tension could be anisotropic, and thus molecules at the solidyfluid interface are subjected to local forces causing them to twist. Similar twist is also observed in three-dimensional systems such as bilayers w46,47x. This twist may propagate in the bulk to give rise to the chiral shape. Another possibility suggested in McConnell’s theory is that an intrinsic twisting force may be present, which can develop an intermolecular orientation. This mutual orientation may propagate in the bulk to give rise to the chiral shape. Spiral lipid domain growth is also considered in models for which a tendency to curvature is assumed in the free energy

Fig. 10. Schematic representation of the model of chiral amphiphilic molecule in EPP model. The molecular segments of the molecule are shown, present in air and aqueous subphase. Interactions between all possible pairs of groups are considered.

function w48x. This theory is capable of harmonic shape transition. However, theories of this class do not start with an explicit molecular structure and the molecular chirality is only considered through macroscopic parameters in the free energy function. To understand the monolayer structure, the tripodal model was used to analyze the chiral molecular structure in detail for the first time w49–51x. The molecule is considered to be composed of a chiral carbon to which four groups are attached. The tail points towards the air, away from the airywater interface, and the other three groups form a tripod towards the interface. The theory predicts a preferred heterochiral behavior for van der Waals’ interactions and homochiral behavior for the electrostatic interactions. Andelman and coworkers carried out a Monte Carlo simulation to study the chiral discrimination of D- and L-alanine. Homochiral preference was observed, which the authors suggested was due to short-range steric interactions. In the rigid tetrahedral model, heterochiral preference is observed for the Lennard–Jones (LJ) potential. Chiral preference is dependent on the intermolecular separation. At short separation homochirality is favored, while at greater distances heterochirality is favored. This conclusion draws attention to the non-trivial nature of chiral interaction. The effective pair potential theory (EPP theory) was also used to attempt to calculate the chiral interaction in Langmuir monolayers w19,20,46,47,52–54x. The EPP is calculated from the consideration of the molecular chiral structure (Fig. 10), which may be considered in atomistic detail or after coarse graining. However, the groups attached to the chiral center must be minimally considered. Note that when only four groups attached

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to chiral center are considered in the EPP model, the description is similar to the rigid tetrahedral model considered in the tripodal model. However, there are differences between the tripodal model and the EPP model. In the tripodal model, tail–tail interactions are neglected. In addition, the realistic orientations of the tails and head groups are neglected in the tripodal model and only selected mutual interactions between the pair of molecules are considered. However, in the EPP model, all realistic details of molecular configuration and arrangement in space can be considered. It is pointed out that the subtle stereogenicity at the chiral center of a molecule is the driving force for the chiral features (such as specific curvature or handedness) in the shape of the aggregate composed of the molecules. The EPP minimally depends on the distance and orientation between the groups of neighboring chiral molecules. While the EPP includes the essential stereochemical features of the neighboring chiral molecules, it is necessarily a reduced interaction obtained after summing over many detailed interactions. By varying the distance and orientation between the groups, the minimal energy arrangement can be obtained from this EPP. As the molecules within the domains are in a close packed state, both attractive and repulsive forces are important and a Lennard–Jones 6–12-type interaction can be a suitable choice to represent the intermolecular potential. The EPP theory has been applied to chiral amphiphiles containing amino acid head groups. The orientationdependent EPP of the molecule pair of N-palmitoyl aspartic acid and N-stearoylserine methyl ester was calculated w19x. It was observed that the minimum EPP corresponds to a mutual orientation between the pair of amphiphiles. However, BAM studies indicated that, despite the curvature of the domain, there is no change in the azimuthal projection of the molecule within a domain, but the overall shape of the domain is curved. Thus, at the condensed-phase domainyfluid phase interface, curvature is present that is due to mutual intermolecular orientation between successive neighbors. Consequently, the favored intermolecular mutual orientation is in competition with an interaction that favors parallel arrangement between the molecules within the domain. In amino acid amphiphiles, cycles of hydrogen bonding are present between neighboring molecules and these bonds could supply the energy needed for the parallel arrangement. A fascinating aspect of domains composed of chiral molecules is that the handedness (or sense) of their curvature is highly specific to the chirality of the molecule concerned. If the D-enantiomer gives the righthandedness of the aggregate, the L-enantiomer will give left-handedness and vice versa. Continuum theories completely fail to predict this handedness. It is essential to know how the molecules are arranged in the aggre-

gate, as well as the orientation of the molecule with respect to a given external axis. Then the molecular arrangement (and the concomitant curvature of the aggregate) can be understood using the customary rule that the handedness is observed as the curvature of the aggregate moves away from the observer. However, there is no completely general way to define the handedness of a chiral object; this depends on how the observer looks at the object. On the other hand, the conclusion that chirality drives the curvature amounts to saying that we can, in principle, correlate the mutual molecular orientation with the variation of the curvature of domains formed by molecules with respect to an observer. The handedness of the monolayer aggregate can be concluded from the growth kinetics. Static images of the domain can only be useful in identifying that two-handedness exists for two enantiomers and no more. EPP theory is applied to monolayers of amino acid amphiphiles, such as N-palmitoyl aspartic acid, N-stearoyl serine methyl ester, N-palmitoyl-allo-threonine methyl ester and N-stearoyl-allo-threonine methyl ester, to predict the handedness of domains composed of these molecules w20x. The intermolecular pair potential is calculated between groups of neighboring amphiphiles using the LJ potential. The potential is dependent on the orientation-dependent distance between groups of neighboring amphiphiles. The results of the theoretical prediction of the EPP-based theory and the experimentally observed handedness are in complete agreement for all monolayer systems considered w20x. Molecular chiral interaction in DPPC monolayers w52x was calculated using the EPP theory using a coarsegrained description of the molecular structure. In the coarse-grained description, the tails and the heads of the molecule are represented by an array of collinear spherical groups. While atomistic details are neglected in the calculation, the average orientation of the groups with respect to the chiral center is considered over a reasonably small length scale. The domain shape of enantiomeric DPPC monolayers is triskelion-shaped with arms curved in a specific direction. The domain curvature is specific for enantiomers and no curvature is observed for racemates. BAM studies suggested that neighboring molecular directors are in a mutually oriented state along the width and length of the arms of the triskelions. From the minima of the pair potential, the preferred orientation of a pair of aggregating molecules can be obtained. The mutual orientation between a pair of molecules provides information about the domain handedness of the aggregate in the condensed state in which the molecules are aligned in a next-to-next order. It is important to note that in the condensed state of the domains, the molecules are at close separation and chiral interactions are dominant. The effect of the orientational distribution of the head group in the aqueous subphase

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on the chiral shape of the aggregate was also investigated. The EPP calculation indicates that the molecule segments have a large favorable energy when they all are oriented in a right-handed way with respect to the tail, which is closest to the observer in aggregates composed of D-enantiomers. This mutual orientation is cooperative in the sense that all segments favor the tendency to have a right-handed turn with respect to the reference at the minima of the pair potential. In all cases, a high-energy barrier separates the minimum of the EPP, which favors the opposite handedness (left-handedness). The favorable mutual azimuthal orientation gradually moves to a parallel arrangement with increasing molecular separation. In addition, the EPP becomes increasingly shallow with increasing temperature. All these results are in excellent agreement with the known experimental data. It was also shown that the effect of chirality is not destroyed even if a distribution of the orientation of the head groups exists in the aqueous subphase. Simulation studies of the DPPC monolayer structure are available that considered the EPP concept w53x. The theory considers the chiral pair potential, in addition to the dipolar repulsion and line tension at the domain boundary. The results of the simulation show that incorporation of an EPP that favors mutual molecular orientation originating from chiral molecular structure is necessary to understand the interactions. Recently, chiral discrimination energy in domains composed of chiral amphiphilic monolayers has been theoretically studied w54x. First, calculations on simpler model systems were carried out, which show that the depth of the pair potential is well dependent on the extent of coarse graining of the molecular structure. However, systematic coarse-graining of model systems shows that the consistent use of a set of parameters can correctly predict the chiral preference (homo- or heterochirality). The model calculation further suggests that, with a gradual loss of chirality of the model molecule, chiral interaction is diminished. Calculations of the chiral discriminating pair potential of three chiral compounds, N-stearoyl serine methyl ester, N-palmitoyl aspartic acid and N-tetradecyl-g,d-dihydroxypentanoic acid amide, indicate a homochiral preference. The preference is observed in both the packing of a pair of molecules and the pair potential energy profile. The enantiomeric pairs are closely packed and have a lower minimum pair potential compared to the racemic pairs. The homochiral preference corroborates the domain features observed by BAM. The growth in both directions observed in racemic domains is suggestive of breakage of the local chiral symmetry, which is possible in the case of a preferred homochiral interaction. The results of calculation of the discrimination energy by the present approach and the results of the tripodal model were compared. While the basic conclusions of

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the present and other models agree, the present model reveals non-trivial distance and orientation dependence of the discrimination energy. The results were shown to be insensitive to the choice of parameters. In Fig. 11, we have compared the EPP of enantiomeric and racemic pair potentials of N-stearoyl-serine methyl ester. Clear chiral discrimination is observed. The insensitivity of the result to parameters is shown by the similarity in EPP profiles generated by a variation of parameters as shown in Fig. 11 and the EPP profile previously obtained for enantiomeric systems (Fig. 7 in w20x). Due to the wide variety of molecular structures of chiral amphiphiles, more theoretical studies based on molecular approaches are necessary to provide a clear understanding of the diverse chirality effects observed in monolayers. 4. Concluding remarks The monolayer domain morphologies from chiral amphihiles are so diverse that the importance of understanding such shapes as a physical problem can hardly be ignored. Observation of a discrimination effect added a further challenge to this already complex problem. Recent experimental information on the monolayer morphology of a wide variety of amphiphiles, such as amino acid amphiphiles, lipids, amphiphilic monoglycerols, acid amide and other tailored amphiphiles, has shown that the domain shapes observed are different from one molecular system to another. The diversity is in terms of both the inner structure within the domain, which ˚ and the outer shape, which spans over a few 10s of A, is often mm-sized. The specific handedness of the domains formed by enantiomeric amphiphiles indicates the crucial influence of chirality on the domain morphology in such monolayers. The clear role of molecular chirality on the mesoscopic domain shape has only become apparent in recent years after the advent of precise optical and X-ray diffraction technologies and theoretical methods. Brewster-angle microscopy played an important role in determining the role of chirality in many cases when such conclusions cannot be drawn from measurements of the p–A isotherms. Again, this points to the important fact that revelation of the chiral effect at various levels of the structural hierarchy could be very different. Chirality in biological structures has recently been drawing much attention w55x. As indicated in Section 1, the results reviewed here with reference to a biomimetic system could be helpful in understanding the macro– micro relation of chirality in biological systems. Detailed information on such structural correlations might be useful in other biological systems, for example understanding the protein folding process or the principle involved in building up of the tertiary structure from the primary structure and the physical properties of

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Fig. 11. Effective pair potentials for pairs of molecules of enantiomeric and racemic N-stearoyl serine methyl ester (SSME). The enantiomeric and racemic pair potentials are marked as shown in the legend. The mutual orientation between pair of molecules is expressed in degrees and ˚ In generating the graphs, only representative values of parameters varied from 08 to 3608. The intermolecular separation is expressed as r (in A). were used to show the insensitivity of the calculation to the choice of parameters. Energy parameters necessary for calculation (´ykB ) are doubled compared to those used in calculation of EPP of enantiomeric pair in Ref. w20x. For details see the text. Temperature is 297.15 K.

DNA and RNA. In these systems, chirality may play a significant role in structure and function, which has yet to be explored in detail. Only a few theories are proposed that aim to understand the relation between the individual molecular structure and the features of domains composed of such molecules. The theories developed on the basis of molecular models and effective interactions seem promising in this direction. Initial theories seem promising as they can predict the outer shape of the domain (and handedness) and the inner structural features. Attempts have been made to develop theories for chiral discrimination. The results of such theories are also promising. However, these theories must include all possible factors, such as hydrogen bonding, line tension and electrostatic interactions, that may act in concert with or in opposition to the chiral interaction. These interactions may thus act favorably or unfavorably with the chiral interaction and can tune the shape of the aggregate. Detailed quantitative studies are required for better understanding of the interplay between hydrogen bonding systems and chiral interactions. The understanding of such correlations is of biological significance because hydrogen bonding is omnipresent in biological structures.

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