Prediction of the handedness of the chiral domains of amphiphilic monolayers: monolayers of amino acid amphiphiles

Colloids and Surfaces A: Physicochemical and Engineering Aspects 198– 200 (2002) 207– 221 www.elsevier.com/locate/colsurfa

Prediction of the handedness of the chiral domains of amphiphilic monolayers: monolayers of amino acid amphiphiles N. Nandi, D. Vollhardt * Max-Planck-Institut fo¨r Kolloid- und Grenzfla¨chenforschung D-14424 Potsdam/Golm, Germany Received 29 August 2000; accepted 10 January 2001

Abstract The effect of chiral interaction on the morphology of the condensed phase domains of amino acid amphiphiles has been investigated theoretically in the present paper. The amphiphiles considered are N-palmitoyl aspartic acid, N-stearoyl serine methyl ester, N-palmitoyl-allo-threonine methyl ester and N-stearoyl-allo-threonine methyl ester. The domains of these amphiphiles show pronounced curvatures in the experiment, which are known to be driven by the chirality of the molecules concerned. We use the previously derived relations to calculate the intermolecular potential of a pair of chiral molecules of general shape, which is dependent on the intermolecular separation and the mutual orientation of the molecules. It is observed that the chiral interaction favors a mutual azimuthal orientation between the molecules in the unit cell for all amino acid amphiphiles considered. However, the azimuthal projections of the molecules within the domain are parallel as observed in the experiment. The energy to obtain parallel arrangement between the molecules is of the same order of the hydrogen bonding energy in the amino acid residues. Thus, it is suggested that the hydrogen bond cycles present among the molecules within the domain prevent the tendency of intermolecular twist due to chiral interaction. However, at the interface between the condensed phase and the fluid phase, the hydrogen bonding energy is not as strong as that within the domain as well as less direction specific. It is expected that the chiral interaction is dominating at the interface resulting the curved shape of the domain. The mutual orientation driven by chirality is cooperative in nature i.e. the mutual orientations at short and long axis of the unit cell occur in the same direction and does not oppose each other. The directions of the orientations of the molecules with respect to a reference molecule have the same senses (handedness) as those of the aggregates. The theoretically predicted senses of all four amino acid amphiphiles considered in the present study agree fairly well with the experimentally observed handedness using Brewster angle microscopy. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Chirality; Monolayer; Molecular orientation; Amino acid amphiphile; Effective pair potential



Part of the paper was presented at the 9th LB9 conference held on 28th August– Ist September at Potsdam. * Corrresponding author. Tel.: +49-30-6392-3150; fax: + 49-30-6392-3102. E-mail address: [email protected] (D. Vollhardt).

0927-7757/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 1 ) 0 0 9 3 3 - 5

208

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

1. Introduction It is now well known that the chirality has a pronounced effect on the structure of the condensed phase domains in monolayer when the constituent molecules are chiral [1– 21]. It is expected that the problem of understanding of chiral interaction in monolayer (a two-dimensional (2d) system) is relatively easier compared with that in three-dimensional systems due to reduction of one degree of freedom. Also, control over an external variable (pressure) enables one to vary the intermolecular separation and thereby tuning the chiral interaction is relatively easier in monolayers compared with the three dimensional systems like bulk solid or liquid which are less compressible. Besides there are many fundamental and technological reasons to study the effect of chirality on aggregate morphology [22– 26]. The domain formed by an enantiomeric amphiphile is characterized by its curved shape. The domain formed by the mirror image isomer has the opposite handedness. However, there is no completely general way to define the handedness of a chiral object [22]. It depends on how the observer looks at the object. On the other hand the conclusion that chirality drives the curvature amounts to say that one should, in principle, can correlate the mutual molecular orientation with the variation of the curvature of domains formed by molecules with respect to an observer. Once the criterion that how the observer look at the domain is selected, there remains no ambiguity in defining the handedness. A simple way to define the handedness in the monolayer is to refer as the direction of the progress of the longer direction starting from a nucleus and the direction of progress is always measured away from the observer. Thus, the handedness of the monolayer aggregate can be concluded from the kinetics of growth. Static images of the domain can only be useful for identifying that two handedness exist for two enantiomers and no more. The competition between the line tension and the electrostatic repulsion [1,28– 33] is known to be an important factor for the shape transition of nonchiral amphiphiles. The importance of anisotropically acting electrostatic force in develop-

ment of spiral lipid domains was emphasized by Mo¨ hwald and coworkers [10,11]. To explain the curved shapes in chiral amphiphilic aggregates, McConnell and coworkers suggested that surrounding the chiral domain the line tension could be anisotropic or an intrinsic twisting force may be present within the molecules [1,27]. The origin of the intrinsic twisting force in bilayer was explained, for the first time on the molecular basis, based on an effective pair potential description [34]. It is also shown that the handedness of the helicity of the chiral bilayer structure can be predicted well from the theoretical consideration [35]. One may, thus, easily wonder whether the intrinsic twisting force is present in monolayers too, because the nature of the chiral interaction driving the morphology is expected not to be greatly different in monolayers and bilayers. Indeed, recently, the concept of effective pair potential has been used to understand the chirality-induced curvature of domains of phosphatidylcholine monolayers [36]. However, the domains formed by the amino acid amphiphiles are characterized by the absence of intermolecular twist. The azimuthal projections of the tails of the neighboring molecules remain parallel to each other within the domain. In a recent study we have shown that the underlying pair potentials of two amino acid amphiphiles (N-palmitoyl aspartic acid and Nstearoyl serine methyl ester) are orientation dependent and the minimal energy configurations of the pair of molecules favor a twist between them [37]. However, the energy to get back the parallel arrangement is of the same order as that of the intermolecular hydrogen bonding energy among the amino acid residues. It is suggested that the hydrogen bonding energy is less strong and less direction specific at the condensed phase/ fluid phase interface. As a result, the chiral interactions dominate at the interface and molecules orient gradually to form curved shapes as observed experimentally. In the present work we have calculated the pair potential of N-palmitoyl aspartic acid, N-stearoyl serine methyl ester, N-palmitoyl-allo-threonine methyl ester and N-stearoyl-allo-threonine methyl ester by varying the distance and mutual az-

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

imuthal orientation between them along the shorter as well as long axis of the unit cell. From the direction of the orientation of the other molecules, relative to the reference molecule, we attempted to correlate the handedness of the aggregate to the microscopic intermolecular orientation. In the next section we present the brief details of the theoretical calculation. In Section 3 we present the results, which is followed by discussion. We present the concluding remarks in Section 4.

2. Theoretical formulation

2.1. Calculation of the intermolecular pair potential The intermolecular interaction energy between two molecules is given in this work by a Lennard Jones potential and represents the short-range repulsion and long-range attraction over all nonbonded pairs of groups of the molecule:

     

U 4 = g(i %) kB T T

m g(i )g( j ) k

g( j )

×

s g(i )g( j ) | g(i )g( j )

− 12

−

s g(i )g( j ) | g(i )g( j )

 n −6

(1)

where, the sum runs over all groups of ‘i’th and ‘j’th molecules. The different groups are denoted as g(i ) or g( j ). The energy parameter m g(i )g( j ) is given by the Berthelot rule and is given by: m g(i )g( j ) =(m g(i )m g( j ))1/2 g(i )g( j )

(2)

Here, s is the separation between as g(i ) and g( j ). | g(i )g( j ) is the average Lennard Jones diameter of the corresponding groups. We consider the interface as a plane parallel to the air/water interface, which passes through the carbon atom where the alkyl chain of the amphiphile and the head group is joined. We denote these carbon atoms of ith and jth molecule as O(i ) and O( j ), respectively. We denote the groups, which compose the chain projected outward in air as t groups and the groups which compose the chain projected inwards the solvent region as h. In simple chiral molecules, as consid-

209

ered in the present calculation, side groups are attached with one or more h groups and these groups are denoted as a group Figs. 1 and 2. Next, we define the following distances and orientations:‘r’= intermolecular separation between O(i ) and O( j ). ‘t’ =magnitude of the t vector drawn from O to the center of the corresponding ‘t’ group. ‘h’ =magnitude of the h vector drawn from O to the center of the corresponding ‘h’ group. ‘a’= magnitude of the a vector drawn from the endpoint of the ‘h’ vector (to which the ‘a’ group is attached) to the center of the ‘a’ group. v= orientation of t with respect to the normal to the interface (Z). i=orientation of h t/h with respect to the normal to the interface. h i/j = orientation of the projection of t or h vector of the ith or jth molecule with respect to the intermolecular axis (r) on the interfacial plane. n=orientation of the a group with respect to the normal on the plane(Z%) drawn on a plane parallel to the interface. x =orientation of the a group with respect to the axis parallel to the intermolecular axis drawn on a plane parallel to the interface. With the above definitions, the distances between the groups of the molecules can be expressed as functions of ‘r’, the magnitude of the vectors related to the group and the related orientations. The explicit expressions are given in Appendix A. In the present calculation we consider the interaction between the molecules with respect to their chiral centers. In this case, ‘O’ coincides with the chiral center. With this choice, the t group can be represented as the group that is attached to the chiral center and directed towards air. For the rigid molecular geometry, the orientation of t is known from the average molecular tilt measured experimentally. The azimuthal projection is also known from the experiment and provides the estimate of the h orientations. The remaining orientations are known from the tetrahedral geometry around the chiral center for the molecules with single chiral center. In the case of molecules like palmitoyl-allothreonine methyl ester and stearoyl-allo-threonine methyl ester which contain two chiral centers, the minimization of pair potential is done according to the following procedure. We denote the chiral

210

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

center closest to the alkyl tail as first chiral center and the next chiral center as second chiral center. Positions and orientations of the groups in the amino acid residue of the reference molecule are assumed to be the same as those at the minimal energy conformation of the corresponding amino acid molecule [38]. The bond joining the alkyl chain and amino acid residue is assumed to be in trans configuration with respect to the rest of the alkyl chain (which is assumed also to be in trans configuration). The vector representing the t group (for example NHC(O) (CH2)14CH3 in the case of palmitoyl-allo-threonine methyl ester) of the second molecule are rotated by 2y with respect to the same vector of the first molecule. Simultaneously, we rotate both the CH3 and OH groups attached to second chiral center by 2y in a plane parallel to the interface and by 2y in a plane normal to the interfacial plane with respect to the same groups of the first molecule. In the next section we describe the choice of parameters.

2.2. Details of the choice of parameters The necessary parameters for the calculations are the Lennard Jones parameters for different groups and their orientations as given by v,h,i,x etc. It is well known that the effective sizes of the alkyl groups increases linearly with their chain length [39]. The effective sizes of the groups are obtained from the group increments provided by Bondi [40] and the empirical relations provided by Ben Amotz and Herschbach [39]. Note that these values are remarkably accurate and insensitive to the deviation of the group shape from sphericity. It is also known that the Lennard Jones energy parameter is also linearly dependent on the size of the group. For 1 A, increase in the effective size of the group, the m/kB increases by  100 K. Here we take the m/kB values of the groups as proportional to their diameters. The parameters for smaller groups in the case of palmitoyl and stearoyl-allo-threonine methyl ester are taken from the OPLS (optimized potentials for liquid

Fig. 1. Schematic diagram of a pair of amphiphilic molecules at the interface. The laboratory fixed frame of reference is shown in the figure. The vectors drawn from a chosen center (O) to the centers of the different groups are also shown.

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

211

Fig. 2. The geometry of the different groups, t (tail), h (head) and a (attached to h). The orientations are explained in detail in the text.

simulations) parameter set [41]. Parameters used in the present calculation are shown in Table 1.

2.3. Prediction of the handedness In order to predict the handedness, we place a reference molecule in a corner of the unit cell. The azimuthal projection and the tilt from the normal of the reference molecule are taken from experimental data [21]. The experimental information about the average azimuthal projection and tilt from the normal are obtained from grazing incidence X-ray diffraction (GIXD) at HASYLAB, DESY, Hamburg, Germany. These data are used only for the reference molecule. Subsequently, we bring other molecules in the remaining three corners from an infinite separation (where the interaction with the reference molecule is essentially absent). Each molecule is oriented by 2y, relative to the reference molecule. We then observe the orientation of the three molecules with respect to the reference molecule when the intermolecular

interaction energy is minimum. If the azimuthal projection of the other molecules does not coincide with that of the reference molecule and the change in azimuthal projection occurs in an anticlock wise fashion (with respect to the reference molecule) then we can predict that the handedness of the aggregate would be left wise. In all cases we place the reference molecule away from the observed and the remaining molecules further away from the observer. The growth of the domain is observed by Brewster angle microscope (BAM). The experimentally observed handedness of the domain is concluded from the growth of the domain as observed by BAM. We discuss the theoretical results and compare with the experimental observations in the next section.

3. Results and discussion The orientation dependent pair potentials along the short axis and the long axis of the unit cell of

212

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

Table 1 Parameters of N-palmitoyl aspartic acid (abbreviated as PA), N-stearoyl serine methyl ester (abbreviated as SS), N-palmitoyl-allothreonine methyl ester (abbreviated as PT) and N-stearoyl-allo-threonine methyl ester (abbreviated as ST) used in the calculation Molecule

Group (with respect to C*)

LJ diameter in A°

m /k in K

v and k in degrees [21]

PA

t h a t h a t h(CH) [41] h(CH3) [41] a(COOCH3) [41] a(OH) [41] T h(CH) [41] h(CH3) [41] a(COOCH3) [41] a(OH) [41]

8.4 3.8 3.17 8.72 3.55 2.71 8.4 3.8 3.91 4.39 2.96 8.72 3.8 3.91 4.39 2.96

1068.33 376 317 1138.14 355 271 1068.33 40.23 81.82 439 105.59 1138.14 40.23 81.82 439 105.59

31°, 115.62°

SS

PT

ST

48°, 104.8°

53°, 106.61°

55°, 109.53°

Temperatures are 298.15 °K for PA, 297.15 °K for SS and 288.15 °K for PT and ST. The tilt from normal (v) and the lattice angle (g) used in the calculation refer to somewhat different surface pressures used in the experiment. Note that the fourth group attached to the chiral carbon (C*) is hydrogen and interaction with hydrogen is neglected, as common in literature [41].

Fig. 3. Plot of intermolecular potential for a pair of the same type of enantiomers of N-palmitoyl aspartic acid along the shorter axis of the unit cell. The pair potential is expressed in units of kBT (T =293.15 °K). The intermolecular separation is scaled by the diameter of the a group (indicated by |a ) and is expressed in a dimensionless unit. The mutual azimuthal orientation of the molecules (lat ) is varied from 0 to 360°. The relations used in the calculation of the pair potential are given in the text and in Appendix A. The necessary parameters are shown in Table 1.

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

213

Fig. 4. Plot of intermolecular potential for a pair of same type of enantiomers of N-palmitoyl aspartic acid along the longer axis of the unit cell. The pair potential is expressed in units of kBT (T =293.15 °K). The intermolecular separation is scaled by the diameter of the a group (indicated by |a ) and is expressed in a dimensionless unit. The mutual azimuthal orientation of the molecules (lat ) is varied from 0 to 360°. The relations used in calculation of the pair potential are given in the text and in Appendix A. The necessary parameters are shown in Table 1.

the D form of N-palmitoyl aspartic acid are shown in Figs. 3 and 4, respectively. The pair potential profiles along both directions show pronounced orientation dependence. Particularly, the minimum of the pair potential always occurs at a nonzero angle between the azimuthal orientations of the tail parts of the two amphiphiles. The energy to achieve parallel orientation is of the same order of the energy of the hydrogen bond cycle among the amino acid residues [42]. In order to predict the handedness of the curvature, we schematically depict the favored orientation of the three molecules in a unit cell with respect to the reference molecule whose azimuthal projection is fixed according to the experimental data [21]. This is schematically depicted in Figs. 5 and 6. The three dimensional structure of the molecule is schematically presented in Fig. 5. Fig. 6 schematically shows how the other molecules are oriented in an anticlockwise way with respect to the reference molecule, when their intermolecular energy with respect to the reference molecule is minimized. We show only the projection of the t group and the projection of the COOH group in Fig. 6. The

minimal energy configuration is at an arrangement when the azimuthal projections of the three molecules have a mutual orientation (measured anticlockwise) with respect to the reference molecule. This amounts to an anticlockwise twist for all three molecules. Thus, it is expected that the energy of the hydrogen bond cycle cannot drive the molecules to parallel arrangement at the interface between the condensed phase and the fluid phase. Consequently, the molecules at the interfacial region will have a twist between them. It is, thus, reasonable to predict that due to the anticlockwise nature of the intermolecular twist, the aggregate of D-palmitoyl aspartic acid will develop with left-handedness. The theoretically predicted handedness agrees with the experimentally observed handedness as shown in Table 2. The orientation dependent pair potentials along the short axis and the long axis of the unit cell of D form of N-stearoyl serine methyl ester are shown in Figs. 7 and 8, respectively. As in the case of palmitoyl aspartic acid, the pair potential profiles of stearoyl serine methyl ester show pronounced orientation dependence. The minima of the pair potentials occur at nonzero angle between

214

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

the azimuthal orientations of the tail parts of the two amphiphiles. We have schematically depicted the three dimensional structure of the molecule in Fig. 9. We show the projection of the t group and the projection of the CH2OH group in Fig. 10. As shown schematically in Fig. 10, the intermolecular energy is minimized when the azimuthal projection of the three molecules have a mutual orientation (measured anticlockwise) with respect to the reference molecule. This amounts to an anticlockwise twist for all three molecules. Thus, we predict that the aggregate will develop with left-handed curvature for D-stearoyl serine methyl ester. This conclusion agrees with the experimentally observed handedness as shown in Table 2. Both palmitoyl-allo-threonine methyl ester and stearoyl-allo-threonine methyl ester contain two

Fig. 6. The schematic representation of the molecules in a unit cell of palmitoyl aspartic acid. The bold-faced arrows indicate the projections of the groups shown in figure. The position of the reference molecule is indicated by filled circle in the unit cell. Blank circles denote the positions of the remaining three molecules. The dotted arrows indicate the initial orientations of the corresponding groups of the three molecules, which are parallel to those of the reference molecule. The collective direction of orientation of all three molecules is denoted by an arrow in the middle of the lattice. Table 2 Comparison of the theoretically predicted handedness and the experimentally observed handedness (using BAM, see text for details) of N-palmitoyl aspartic acid (abbreviated as PA), N-stearoyl serine methyl ester (abbreviated as SS), N-palmitoyl-allo-threonine methyl ester (abbreviated as PT) and Nstearoyl-allo-threonine methyl ester (abbreviated as ST) Molecule

Handedness predicted by theory

Handedness observed from experiment

D-PA D-SS D-ST D-PT

Left Left Left Left

Left Left Left Left

All enantiomers mentioned in the table have D-form. The mirror image isomers (L form) have the opposite handedness and are not mentioned in the table. Fig. 5. The three dimensional structure of N-palmitoyl aspartic acid. The projection formula is depicted at the top of the figure and the three dimensional structure of the molecule in the air/water interface is obtained in three successive steps. The segments of the molecule directed towards air and water are indicated by arrows.

chiral centers. As mentioned in the theoretical section, we varied the orientation of the t group (attached to the first chiral center, as defined previously) as well as the orientation of the

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

groups attached to the second chiral center of the second molecule and find the minimum energy configuration. We have plotted the variation of

215

energy with variation of the molecular separation and the twist between the azimuthal projections of the t group. In this plot the difference in angle (a

Fig. 7. Plot of intermolecular potential for a pair of the same type of enantiomers of N-stearoyl serine methyl ester along the shorter axis of the unit cell. The energy is expressed in units of kBT (T= 291.15 °K). The intermolecular separation is scaled by the diameter of the a group (indicated by |a) and is expressed in a dimensionless unit. The mutual azimuthal orientation of the molecules (lht ) is varied from 0 to 360°. The relations used for the calculation of the pair potential are given in the text and in the Appendix A. The necessary parameters are shown in Table 1.

Fig. 8. Plot of intermolecular potential for a pair of same type of enantiomers of N-stearoyl serine methyl ester along the longer axis of the unit cell. The energy is expressed in units of kBT (T =291.15 °K). The intermolecular separation is scaled by the diameter of a group (indicated by |a) and is expressed in dimensionless unit. The mutual azimuthal orientation of the molecules (lht) is varied from 0 to 360°. The relations used in calculation of the pair potential are given in the text and in Appendix A. The necessary parameters are shown in Table 1.

216

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

over which the energy can be minimized compared with the monochiral amphiphile. We have schematically depicted the three dimensional structure of the molecule in Fig. 13. We show the projection of the t group and the projection of the COOCH3 group in Fig. 14. As shown schematically, the intermolecular energy is minimized when the azimuthal projection of the tail parts of the three molecules have a mutual orientation (measured anticlockwise) with respect to the reference molecule. This amounts to an anticlockwise twist for all three molecules. Thus, we predict that the aggregate will develop with left-handed curvature for D-palmitoyl-allo-threonine methyl ester. The molecular structure and lattice parameters of N-stearoyl-allo-threonine methyl ester are not largely different from the N-palmitoyl-allothreonine methyl ester. Explicitly, the t group differs by two methylene units and this difference is expected not to affect the chiral interaction

Fig. 9. The three dimensional structure of N-stearoyl serine methyl ester. The projection formula is depicted at the top of the figure and the three dimensional structure of the molecule at the air/water interface is obtained in three successive steps. The parts of the molecule directed towards air and water are indicated by arrows.

twist angle) between the groups attached to the second chiral center of the reference molecule and the second molecule is kept the same as the same twist angle obtained at the minimal energy state (obtained by varying all degrees of freedom as described in the theoretical section). The pair potential profiles of palmitoyl-allo-threonine methyl ester along the shorter and longer axes are shown in Figs. 11 and 12, respectively. The pair potential profiles of the molecule along both axes are distinctly different from those of the monochiral amphiphiles like palmitoyl aspartic acid and palmitoyl serine methyl ester. In the multichiral amphiphile, the energy of interaction is expected to be favorable over a broader orientational space due to the availability of more degrees of freedom

Fig. 10. The schematic representation of the molecules in a unit cell of N-stearoyl serine methyl ester. The bold-faced arrows indicate the projections of the groups shown in figure. The position of the reference molecule in an unit cell is indicated by filled circle. Blank circles denote the positions of the remaining three molecules. The dotted arrows indicate the initial orientations of the corresponding groups of the three molecules, which are parallel to those of the reference molecule. The collective direction of orientation of all three molecules is denoted by an arrow at the middle of the lattice.

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

217

Fig. 11. Plot of intermolecular potential for a pair of same type of enantiomers of N-palmitoyl-allo-threonine methyl ester along the shorter axis of the unit cell. The pair potential is expressed in units of kBT (T =288.15 °K). The intermolecular separation is scaled by the diameter of the a group (indicated by |a ) and is expressed in a dimensionless unit. The mutual azimuthal orientation of the molecules (lht ) is varied from 0 to 360°. The relations used in calculation of the pair potential are given in the text and in Appendix A. The necessary parameters are shown in Table 1.

Fig. 12. Plot of intermolecular potential for a pair of same type of enantiomers of N-palmitoyl-allo-threonine methyl ester along the longer axis of the unit cell. The pair potential is expressed in units of kBT (T= 288.15 °K). The intermolecular separation is scaled by the diameter of the a group (indicated by |a) and is expressed in a dimensionless unit. The mutual azimuthal orientation of the molecules (lht ) is varied from 0 to 360°. The relations used in calculation .of the pair potential are given in the text and in Appendix A The necessary parameters are shown in Table 1.

218

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

largely. This is because, the chiral center being located in the head group region, the chiral interaction is expected not to be largely affected by the small changes in the structure of the tail part. The pair potential of stearoyl-allo-threonine methyl ester is indeed remarkably similar to that of the palmitoyl compound (not shown here). In the line of argument presented for palmitoyl compound we can conclude that the handedness of the stearoyl compound would be left wise. The theo-

Fig. 14. Schematic representation of the molecules in a unit cell of N-palmitoyl-allo-threonine methyl ester. The bold-faced arrows indicate the projections of the groups shown in the figure. The position of the reference molecule in the unit cell is indicated by filled circle. Blank circles denote the positions of the remaining three molecules. The dotted arrows indicate the initial orientations of the corresponding groups of the three molecules, which are parallel to those of the reference molecule. The collective direction of orientation of all three molecules is denoted by an arrow in the middle of the lattice.

Fig. 13. The three dimensional structure of N-palmitoyl-allothreonine methyl ester. The projection formula is depicted at the top of the figure and the three dimensional structure of the molecule as observed at the air/water interface is obtained in three successive steps. The parts of the molecule directed towards air and water are indicated by arrows.

retically predicted handedness of both palmitoyl and stearoyl-allo-threonine methyl ester agree with the experimentally observed handedness as shown in Table 2. The present study indicates that the chiral molecules show cooperative tendency to have a mutual orientation between themselves, which is arising from the chiral interaction. It would be interesting to include the effect of anisotropic dipolar interaction in the model, because the later may exaggerate or diminish the twisting tendency favored by the chiral interaction [10,11] depending on the dipolar orientation. It is also interesting to investigate the molecular orientation at the interface between the condensed phase and the fluid phase by experimental methods. This may provide useful information about the details of the molecular structure of the interface between the condensed phase and the fluid phase. Further studies in these directions may be useful.

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

4. Conclusions To summarize, we have used previously derived relations to calculate the intermolecular pair potential of chiral molecules of general shape to calculate the pair potential of chiral amino acid amphiphiles. The calculation is carried out based on an effective pair potential description of the groups attached to the chiral center. It is observed that the intermolecular interaction is favorable at a twist between the azimuthal orientation of the same type of enantiomeric molecule and energy of this twisted configuration is nearly of the same order as the intermolecular hydrogen bonding energy of the amino acid head groups. Thus, the observed curved shapes of the domains of amino acid amphiphiles could be due to a twist at the interface between the condensed phase and the

219

fluid phase, where the hydrogen bonding energy cannot drive the molecules to a parallel arrangement. We considered the direction of mutual azimuthal orientation with respect to a reference one and the direction of mutual orientation has been used as a guide to the handedness of aggregate. In all cases, the handedness of the orientation of other molecules in a unit cell with respect to the reference molecule (closest to the observer) is the same as the handedness of the aggregate, which can be determined by the growth kinetics.

Acknowledgements The present work is supported by Alexander von Humboldt foundation. We thank Professor H. Mo¨ hwald for pointing out [10,11].

Appendix A Here we give the detailed expressions of the orientation dependent distance between t, h and a groups. The separation between the pair of t-groups of ith and jth molecule is given by: S t(i )t( j ) = [{r 2 + t(i )2sin2 v(i ) + t( j )2sin2 v( j )− 2rt( j )sin v( j )cos h t( j ) + 2t(i ) sin v(i ) cos(h t(i ) +w1) (r 2 + t( j )2sin2 v( j ) − 2rt( j )sin v( j )cos h t( j ))1/2} + {t(i )cos v(i ) − t( j )cos v( j )}2]1/2



where,

n

{r − t( j )sin v( j )cos h t( j )} {r +t( j ) sin2 v( j ) −2rt( j )sin v( j )cos h t( j )}1/2

61= cos − 1

!

(A1)

2

2

"

(A2)

The separation between the pair of t-group and h-group of ith and jth molecule is given by: S t(i )h( j ) =

t(i )2cos2 v(i ) + (t(i )2cos2 v(i )X 21 (h( j )cos i( j ) + t(i )cos v(i ))2)

+

!

1/2

(1 − t(i )cos v(i ))2X 21 (h( j )cos i( j ) +t(i )cos v(i ))2)+ h( j )2cos2 i( j )

"

1/2

(A3)

where, X1 ={r 2 + t(i )2sin2 v(i ) + h( j )2sin2 i( j )−2rh( j )sin i( j )cos h h( j ) + 2t(i )sin v(i )(r 2 +h( j )2sin2 i( j ) − 2rh( j )sin i( j )cos h h( j ))1/2cos (h t(i )+ w2)}1/2 and, w2 =cos − 1



{r − h( j )sin i( j )cos h( j )} {r +h( j ) sin2 i( j ) − 2rh( j )sin i( j )cos h h( j )}1/2 2

2

n

The separation between the pair of h-group of ith and t-group of jth molecule is given by:

(A4)

(A5)

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

220

S h(i )t( j ) = {(X2 −X3)2 +(t( j )cos v( j ))2}1/2 + {X 23 + {h(i )cos i(i ))2}1/2

(A6)

where, X2 = {(h(i )sin i (i )sin h h(i ))2 +y12 + (t( j )sin v( j )sin h t( j )) 2 + 2(h(i )sin i (i )cos h h(i )+ Y2)Y1 + (h(i )sin i (i )cos h h(i ) + Y2) 2 + 2h(i )sin i (i )sin h h(i )t( j )sin v(j)sin h t( j )}1/2 X2 h(i )cos i(i ) (t( j )cos v( j ) + h(i )cos i(i )) t( j )sin v(j)sin (h t( j ))(r +h(i )sin i (i )cos h h(i )− t( j )sin v( j )cos h t( j )) Y1 = (h(i )sin i(i )sin h h(i )+ t( j )sin v( j )sin h t( j )) X3 =

Y2 = r − Y1 −t( j )sin v( j )cos h t( j )

(A7) (A8) (A9) (A10)

The separation between the pair of a-group of ith and h group of jth molecule is given by: S a(i )h( j ) = {(a(i )cos n(i ))2 + (r%2 − (h(i )cos i(i )− h( j )cos i ( j )) 2) + 2a(i )cos n(i )(r%2 − (h(i )cos i (i )− h( j )cos i ( j )) 2)1/2cos 63 + x(i)) + (a(i )sin x(i ) − h(i )cos i(i )+ h( j )cos i( j ))2}1/2

(A11)

h(i )h( j )

In general, r% is equal to S when the rotations are considered on a plane containing groups other than the chiral center(for example, CH2 groups at the end of the alkyl chain of the neighboring amphiphiles), where, a(i ) is attached at the end of h(i ) as explained in the text. When r passes through the two chiral centers, r% coincides with r. 63



{r%2 −(h(i )cos i(i ) − h( j )cos i( j ))2)− (h(i )sin i(i )sin h h(i )− h( j )cos i( j )sin h h( j ))2}1/2 {r%2 −(h(i )cos i(i )− h( j )cos i( j ))2}1/2 × (A12)

= cos − 1

n

The separation between the pair of h-group of ith and a-group of jth molecule is given by: S

h(i )a( j )

= {r%2 −(h(i )cos i(i ) − h( j )cos i( j )) 2 + (a( j )cos n( j ))2 + 2(r%2 − (h(i )cosi(i ) − h( j )cosi( j ))2)1/2a( j )cos n( j ) sin (x(i )+ 63) + (a( j )sin n( j ) + h(i )cos i (i )−h( j )cos i( j )) 2}

(A13)

S a(i )t( j ) and S t(i )a( j ) can be calculated by replacing the appropriate parameters for t groups in Eqs. (A11), (A12) and (A13). The separation between the pair of a-groups of ith and jth molecule is given by: S a(i )a( j ) = {(a(i )cos n(i ))2 +(a( j )cos n( j ))2 + r%2 −(a(i )sin n(i ) +a( j )sin n( j ) +h(i )cos i(i )− h( j )cos i( j ))2 +2(r%2 −h(i )cos i(i ) −h( j )cos i( j ))2)1/2a( j )cos n( j )sin (x(i )+63) + 2a( j )cos n( j )((r%)2 −h(i )cos i(i )− h( j )cos i( j ))1/2 + 2(r%2 −(h(i )cos i(i ) − h( j )cos i( j ))2)1/2a( j )cos n( j )sin(x(i )+ 63))cos64 + (a( j )cosn( j ) − a(i )cosn(i ) + h(i )cos i(i )− h( j )cos i( j ))2}1/2 64 =x(i ) + cos

(A14)

[{r% −(h(i )cos i(i ) − h( j )cos i(j)) )

−1

2

2

− (h(i )sin i(i )sin x(i ) −h( j )cos i( j ) sin x( j ))2}1/2/{r%2 − (h(i )cos i (i )− h( j )cos i( j ))2}1/2] + cos − 1[{r%2 −(h(i )cos i(i ) −h( j )cos i( j ))2)− (h(i )sin i(i )sin x(i )− h( j )cos i( j ) sin x ( j ))2}1/2 × /{r%2 −(h(i )cos i(i ) − h( j )cos i( j ))2}1/2]

(A15)

N. Nandi, D. Vollhardt / Colloids and Surfaces A: Physicochem. Eng. Aspects 198–200 (2002) 207–221

References [1] H.M. McConnell, Annu. Rev. Phys. Chem. 42 (1991) 171. [2] D. Vollhardt, G. Emrich, V. Melzer, G. Weidemann, U. Gehlert, Short and Long Chains at Interfaces, in: J. Daillant, P. Guenoun, C. Marques, P. Muller (Eds.), Proceedings of the XXXth Rencontres De Moriond, J. Van Thanh Tran., Frontiers, Cedex, 1995. [3] V.M. Kaganer, H. Mo¨ hwald, P. Dutta, Rev. Mod. Phys. 71 (1999) 779. [4] E. Scalas, G. Brezesinski, V.M. Kaganer, H. Mo¨ hwald, Phys. Rev. A 58 (2B) (1998) 2172. [5] R. Rietz, W. Rettig, G. Brezesinski, W.G. Bouwman, K. Kjaer, H. Mo¨ hwald, Thin Solid Films 285 (1996) 211. [6] R. Rietz, W. Rettig, G. Brezesinski, H. Mo¨ hwald, Pharmazie 52 (1997) 701. [7] U. Gehlert, D. Vollhardt, G. Brezesinski, H. Mo¨ hwald, Langmuir 12 (1996) 4892. [8] F. Bringezu, G. Brezesinski, P. Nuhn, H. Mo¨ hwald, Biophys. J. 70 (1996) 1789. [9] H. Mo¨ hwald, A. Dietrich, C. Bohm, G. Brezesinski, M. Thoma, Mol. Membr. Biol. 12 (1995) 29. [10] W.M. Heckl, M. Lo¨ sche, D.A. Cadenhead, H. Mo¨ hwald, Eur. Biophys. J. 14 (1986) 11. [11] W.M. Heckl, H. Mo¨ hwald, Ber. Bunsenges Phys. Chem. 90 (1986) 1159. [12] D. Vollhardt, G. Emrich, T. Gutberlet, J.H. Fuhrhop, Langmuir 12 (1996) 5659. [13] V. Neumann, A. Gericke, H. Huhnerfuss, Langmuir 11 (1995) 2206. [14] J.G. Heath, E.M. Arnett, J. Am. Chem. Soc. 114 (1992) 4500. [15] D. Andelman, H. Orland, J.Am.Chem.Soc 115 (1993) 12322. [16] D. Andelman, J. Am. Chem. Soc 111 (1989) 6536. [17] A. Pelizzola, M. Pretti, E. Scalas, J. Chem. Phys. 112 (2000) 8126. [18] D.P. Parazak, J.Y.J. Uang, B. Turner, K.J. Stine, Langmuir 10 (1994) 3787.

221

[19] P. Nassoy, M. Goldmann, F. Rondelez, Phys. Rev. Lett. 75 (1995) 457. [20] J.V. Selinger, Z.G. Wang, R.F. Bruinsma, C.M. Knobler, Phys. Rev. Lett. 70 (1993) 1139. [21] D. Vollhardt, Unpublished work. [22] A.B. Harris, R.D. Kamien, T.C. Lubensky, Rev. Mod. Phys. 71 (1999) 1745. [23] S.F. Mason, Molecular Optical Activity and Chiral Discriminations, Cambridge University Press, Cambridge, UK, 1982. [24] S.F. Mason, Chemical Evolution, Clarendon Press, Oxford, UK, 1991 Chapter 14. [25] E.M. Arnett, N.G. Harvey, P.L. Rose, Acc. Chem. Res. 22 (1989) 131. [26] S.C. Stinson, Chem. Eng. News 28 (2000) 59. [27] H.M. McConnell, V.T. Moy, J. Phys. Chem. 92 (1988) 4520. [28] D.J. Keller, J.P. Korb, H.M. McConnell, J. Phys. Chem. 91 (1987) 6417. [29] H.M. McConnell, J. Phys. Chem. 94 (1990) 4728. [30] H.M. McConnell, R. de Koker, J. Phys. Chem. 96 (1992) 7101. [31] T.K. Vanderlick, H. Mo¨ hwald, J. Phys. Chem. 94 (1990) 886. [32] J.M. Deutch, F.E. Low, J. Phys. Chem. 96 (1992) 7097. [33] J.A. Miranda, J. Phys. Chem. B 103 (1999) 1303. [34] N. Nandi, B. Bagchi, J. Am. Chem. Soc 118 (1996) 11208. [35] N. Nandi, B. Bagchi, J. Phys. Chem. 101 (1997) 1343. [36] P. Kru¨ ger, M Lo¨ sche, Phys. Rev. E, 183 – 185 (2001) 67. [37] N. Nandi, D. Vollhardt, Colloid and Surfaces A 62 (2000) 7031. [38] F.A. Momany, R.F. McGuire, A.W. Burgess, H.A. Scheraga, J. Phys. Chem. 79 (1975) 2361. [39] D. Ben Amotz, D.R. Herschbach, J. Phys.Chem 94 (1990) 1038. [40] A. Bondi, J. Phys. Chem 68 (1964) 441. [41] W.L. Jorgensen, J. Tirado-Rives, J. Am. Chem. Soc 110 (1988) 1657. [42] G.A. Jeffrey, W. Saenger, Hydrogen bonding in Biological Structures, Springer Verlag, Berlin, 1991.