6044
J. Phys. Chem. 1984,88, 6044-6048
Effects of Composition on Cholesteric Behavior in the Lyotropic Mesophase System of Potassium N-Dodecanoyl-l-aianinate Alan S. Tracey* and Keith Radley Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A IS6 (Received: April 23, 1984; In Final Form: June 29, 1984)
Cholesteric behavior in the lyotropic liquid-crystalline system of potassium N-dodecanoyl-Z-alaninatehas been investigated by nuclear magnetic resonance spectroscopy and by laser diffraction. The effects of amphiphile, decanol, and electrolyte concentration have been investigated. It was found that increase in amphiphile concentration caused a marked increase in twist, while increase in decanol content caused the twist to decrease, a result also obtained for increase in electrolyte content. The head-group orientation, like the twist, was found to be very sensitive to composition. The relationship between these two parameters was, moreover, found to be a linear one except in the case of the lower decanol concentrations. It is suggested that the relationship between these parameters is a result of the occurrence of an optimum micellar size. A change in the amphiphilic or decanol concentration then causes the total number of micelles to vary. A change in composition modifies head group to head group interactions, causing a change in head-group orientation. This in turn causes a change in shape of the micelle, leading to a modification of intermicellar interactions and thus a different twist. Alkali ion quadrupole splittings were found to follow the head-group splittings, maintaining a constant proportionality between the various sets of data.
Introduction Since the pioneering work of Reinitzer in the late nineteenth century, cholesteric liquid-crystalline materials have been intensively investigated. Most of the work has focused on thermotropic liquid-crystalline materials for which there are now extensive applications in science, technology, and A second class of cholesteric materials, those prepared from aqueous solutions of chiral amphiphiles, has not been extensively investigated. Over the past decade some work in this area has been reported.*1° The mechanism for the generation of cholesteric behavior in lyotropic liquid-crystalline systems is not well understood. Two basic mechanisms for this behavior have been s ~ g g e s t e d .The ~~~ first mechanism involves pairwise interactions between chiral centers on adjacent micelles. This interaction model has been rejected by other workers in favor of the second suggestion that the presence of chiral centers in the micelle serves to distort the micelle into a chiral shape. Interactions between chiral micelles then lead to cholesteric behavior.’J1 Nuclear magnetic resonance (NMR) spectroscopy and laser diffraction in conjunction with microscopy provide excellent “tmls” for the investigation of cholesteric lyotropic liquid-crystalline materials. The cholesteric materials investigated here were prepared from potassium N-dodecanoyl-1-alaninate(I-KDDA). This is a particularly convenient mesophase to work with since dipolar couplings within the alanine head group are readily obtained from the N M R spectra, thus providing a monitor of the surfactant behavior when various changes are made in mesophase composition. The nematic range of this mesophase is also quite large so that studies of the effect of rather large changes in concentration of amphiphile and of additives such as salt and (1) Meier, G.; Sackmann, E.; Grabmaier, J. G. “Applicationsof Liquid Crystals”; Springer-Verlag: West Berlin, 1975. (2) Castellano, J. A. In “Liquid Crystals, The Fourth State of Matter”; Saeva, F. D., Ed.; Marcel Dekker: New York, 1979; p 439. (3) Tracey, A. S.; Diehl, P. FEBS Lett. 1975, 59, 131. (4) Radley, K.; Saupe, A. Mol. Phys. 1978, 35, 1405. (5) Yu,L. J.; Saupe, A. J . Am. Chem. SOC.1980, 102,4879. (6) Acimis, M.; Reeves, L. W. Can. J . Chem. 1980, 58, 1533. (7) Covello, P. S.; Forrest, B. J.; Marcondes Helene, M. E.;Reeves, L. W.; Vist, M. J . Phys. Chem. 1983, 87, 176. (8) Alcantara, M. R.; Marques Correia de Melo, M. V.; Paoli, V. R.; Vanin, J. A. J . Colloid Interface Sci. 1983, 93, 560. (9) Alcantara, M. R.; Marques Correia de Melo, M. V.; Paoli, V. R.; Vanin, J. A. Mol. Cryst. Liq. Crysf. 1983, 90, 335. (10) Lasic, D. D.; Marwndes Helene, M. E.; Reeves, L. W. Can. J. Chem. 1983, 61, 1921. (11) Radley, K.;Tracey, A. S . Can. J . Chem., in press.
0022-3654/84/2088-6044$01.50/0
TABLE I: Basic Mesophase Compositions Used for the Various Concentration Studies sample I-KDDA“.~ decanolb D20b A B
160 160
45 45
45OC 450d
I-KDDA refers to potassium N-dodecanoyl-Z-alaninate. Weights are given in mg of each component. CDzOcontains the following: LiCl, 0.6%; NaCI, 1.0%; RbC1, 1.0%;CsCI, 1.6%; d,l-alanine, 0.5%; l-alanine, 0.5% by weight. d D 2 0contains d,l-alanine and l-alanine 0.67% and 0.17% by weight, respectively. decanol can be made. Such studies are important for developing an understanding of cholesteric behavior in this system.
Experimental Section Potassium N-dodecanoyl-1-alaninate(1-KDDA) was prepared as previously described.” The liquid-crystalline samples were prepared by weighing the various components into test tubes constricted in the center. The tubes were sealed and the components mixed by repetitively warming and then centrifuging through the constriction. The homogeneous materials so formed were transferred to N M R tubes which were then sealed. Three concentration studies were made for which detergent, decanol, and electrolyte proportions were varied. The compositions of the samples used as starting points are given in Table I. For the detergent concentration studies the concentration given in A was varied between 140 and 240 mg in 10-mg steps. For the decanol concentration study the decanol content of entry A was changed in 3-mg steps from 35 to 50 mg. For the electrolyte concentration study the CsCl of solution B was varied from 20 to 64 mg in 4-mg steps. The extremes of either concentration represent the limits of mesophase stability at 30 OC. N M R spectra were obtained from a 400-MHz N M R spectrometer operating in the FT mode. The pitch of the induced helical axis was measured by laser diffraction as previously described.” All measurements were made at 30 OC. Results and Discussion The formation of a nematic lyotropic mesomorphic material is determined by the interactions between micelles. These interactive forces result in the generation of long-range order of the micelles with respect to each other. In the event that the micelles contain chiral additives or are formed from chiral amphiphiles, an asymmetry in the interactive forces is obtained. As a consequence, information concerning chirality is transmitted via the intermicellar forces and a twisted nematic (cholesteric) mesophase 0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 6045
Cholesteric Behavior of I-KDDA
TABLE Ik Various N M R Parameters Measured and Selected Ratios of Those Parameters Obtained as a Function of Potassium N-Dodecanoyl-l-alaninate( I -KDDA) Concentration
composition'
spectral parameters*
ratio of splittings
I-KDDA
AvD,O
AVCI
AVODd
022
DCH~
DCH,lD22
140 150 160 170 180 190 200 210 220 230 240
0.279 0.274 0.27 1 0.278 0.265 0.253 0.260 0.226 0.240 0.219 0.167
1.06 1.04 1.09 1.16 1.14 1.18 1.24 1.14 1.20 1.11 0.92
3.79 3.80 4.02 4.16 4.30 4.60 4.76 5.06 5.00 5.00 5.53
0.635 0.582 0.542 0.521 0.477 0.442 0.422 0.350 0.354 0.325 0.242
29.3c 28.1 28.2 28.1 26.1 24.1 24.4 20.9 21.0 18.8 14.1
46.1c 48.3 52.0 53.9 54.7 55.9 57.8 59.7 59.3 51.8 58.3
AyD20/D22
0.44 0.47 0.50 0.53 0.56 0.57 0.62 0.65 0.68 0.67 0.69
"Amount of 1-KDDA (in mg) contained in the mesophase. bAll splittings are given in kHz. DZ2is the CH3 dipolar coupling in I-KDDA while D C His~ the alanine methyl dipolar splitting. cMultiply by a factor of lo-'. dDecanoldeuterium quadrupole splitting. I
2.
n
0
O
r
Oo0
O I
0.16
I
I
0.20
I
I
0.24
I g Figure 1. The behavior of the twist (0)and the differencein alignment of the d- and Lalanines (@) as the proportion of amphiphile is increased. [DETERGENT
is obtained. The mechanism giving rise to the helical structure of the cholesteric material is not well understood. Pairwise interactions from chiral centers on one micelle to those in another do not appear to account satisfactorily for observed results.lOJ1 It has been suggested that the individual micelles are distorted into a chiral shape and that the chiral micelles then aggregate to form domains, the structure of which is characterized by the helical axis generated." There are various procedures available which allow the interactive forces between micelles to be modified. These involve changing characteristics of the micellar surface by changing the amount of detergent present or by using an achiral diluent such as decanol. The characteristics of the aqueous region can be changed by altering salt concentration. Figure 1 shows that the twist (the inverse pitch) increases in a near-linear fashion as the proportion of chiral amphiphile is increased while all the other variables, water, salt, decanol, and d,l-alanine, are kept constant. With a 71% increase in the amount of amphiphile present the twist rises by a factor of 6.4. The NMR spectrum of d,l-alanine provides a convenient monitor of the contact interaction between the chiral centers of the micellar surface and those of d- and 1-alanine. With the 640% increase in twist only a 38% increase in the difference between the alignment of the methyl groups of the two alanines was observed. Concurrent with the increase in twist there is a substantial decrease in alignment of the head groups as determined from dipolar couplings within the C H C H 3 moiety as well as from deuterium quadrupole splittings from the amido deuteron. There are two components contained in this mesophase which should provide quadrupole splittings essentially, although probably not completely, independent of the head-group alignment. These components are the C1- ion and the hydroxyl deuterium of the decanol. Table I1 gives the quadrupole splittings observed for these two species as the amphiphile concentration is changed. It is seen that the C1- splitting remains essentially constant throughout the range of concentrations while the deuterium splitting shows a significant increase. It is apparent that the marked decrease in head-group methyl splitting, D22, does not derive from a corresponding decrease in alignment of the micelles. All the remaining components in the mesophase, the alkali ions, the water, and the alanine, undergo specific interactions with the
,
1000 H z
,
Figure 2. 'H NMR spectrum showing the head-group dipolar couplings and the alanine spectrum (inset).
head group. As a consequence of this, it is expected that to an extent there should be a correlation between the splittings from the above species and those from the head group. It is clear from Table I1 that such a correlation is obtained both for the deuterated water and for the alanine. The splittings from these compounds decrease almost linearly with the head-group splitting. It seems clear that the decrease in head-group alignment as the amphiphile proportion is increased is a result of changes in head-group packing within the interface of the micelle. Large conformational changes within the head group itself can be ruled out since such a conformational change should be reflected in large relative changes in the quadrupole and dipole splittings from the head group. As can be seen from Table 11, the various ratios are essentially constant. Although there is apparently a consistent trend, this could result from incorrect spectral analysis caused by the broad transitions from which the splittings were obtained. The broadness is a result of the overlap of many transitions originating from dipolar couplings between the protons of the n-alkyl hydrocarbon chain and the head group. A typical spectrum is shown in Figure 2. With regard to head-group alignment it should be noted that head-group, alkali ion, and water splittings remain constant when the racemic amphiphile is replaced in a stepwise manner with the I-amphiphile." Such constant values are not expected since for a random distribution in the racemate, d,l interactions prevail. For I-amphiphiles only interactions of the 1 to 1 variety occur. Since presumably the 1,l (d,d) and d,l interactions are different in energy, it seems possible that in the racemic mixture there is a distribution of amphiphiles into regions of high 1-amphiphile concentrations and other regions of high d-amphiphile concentrations. It is even possible that some micelles are predominantly
6046
Tracey and Radley
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984
TABLE 111: Various NMR Parameters Measured and Selected Ratios of Those Parameters Obtained as a Function of Potassium N-Dodecanoyl-l-alaninate(I-KDDA) Concentration composition" spectral parameters* ratio of splittings I-KDDA AVND D12 022 h i AvNa Avcs AvND/D12 AvNDfD22 DIZIDZZ Av~iID22 AVNalD22 140 150 160 170 180 190 200 210 220 230 240
21.5 19.2 17.8 16.8 15.2 13.7 13.0 11.0 10.8 9.4 7.2
0.289 0.263 0.242 0.234 0.225 0.195 0.185 0.152 0.151 0.137 0.098
0.635 0.582 0.542 0.521 0.477 0.442 0.422 0.350 0.354 0.325 0.242
0.556 0.513 0.488 0.472 0.436 0.410 0.393 0.343 0.336 0.287 0.219
6.29 5.72 5.43 5.25 4.80 4.40 4.24 3.63 3.57 2.99 2.29
0.301 0.272 0.260 0.252 0.230 0.215 0.190 0.175 0.172 0.150 0.115
74.4 73.0 73.8 71.8 67.4 70.5 70.5 72.4 71.5 68.7 73.4
33.8 33.0 32.9 32.2 31.8 31.1 30.9 31.4 30.5 28.9 29.7
0.45 0.45 0.45 0.45 0.47 0.44 0.44 0.43 0.43 0.42 0.40
0.88 0.88 0.90 0.91 0.91 0.93 0.93 0.98 0.95 0.88 0.90
9.91 9.82 10.0 10.1 10.1 9.95 10.0 10.4 10.1 9.2 9.5
AVCSIDZZ 0.47 0.47 0.48 0.48 0.48 0.52 0.45 0.50 0.49 0.46 0.48
OArnount (in mg) of I-KDDA present in mesophase A of Table I. bAll splittings are given in kHz. DI2is the H to CH3 dipolar coupling in I-KDDA while Dz2is the CH, dipolar coupling. TABLE I V Various NMR Parameters Measured and Selected Ratios of Those Parameters Obtained as a Function of Decanol Concentration composition' spectral parametersb ratio of splittings
47 44 41 38 35c
19.1 17.4 14.2 12.0 7.6
0.247 0.234 0.197 0.160 0.147
0.574 0.541 0.448 0.370 0.345
0.527 0.472 0.396 0.326 0.202
5.88 5.42 4.36 3.58 2.23
0.281 0.259 0.210 0.172 0.108
1.18 1.16 0.91 0.77 0.50
77.3 74.4 72.1 75.0 51.7
33.3 32.2 31.7 32.4 22.0
0.43 0.43 0.44 0.43 0.42
0.92 0.87 0.88 0.88 0.59
10.2 10.0 9.7 9.7 6.5
0.49 0.48 0.47 0.46 0.3 1
'Amount (in mg) of decanol (DeOH) in mesophase A of Table I. bAll splittings are given in kHz. D12is the H to CH, dipolar coupling in I-KDDA while DZ2is the corresponding CHpcoupling. 'This mesophase is very near a phase transition region. 1 in character while others are predominantly d. If such a spontaneous separation does occur, then the constancy in the measured parameters is to be expected. From Table I11 it can be seen that the measured splittings from the head group decreased by a factor of 3 over the composition range studied. The quadrupole splittings from the alkali ions, Li+, Na+, and Cs+, decreased by the same amount. As can be seen in Table 11, the ratio of splittings is essentially constant. The constant ratio between the sets of data indicates that the quadrupole splitting from the alkali ions derives mainly from binding interactions to the carboxylate group of the amphiphile as has been found for potassium dodecanoate.l* The results from this study of the effect of amphiphile concentration suggest that the micelle size is not significantly affected by increasing surfactant concentration so therefore the number of micelles must be increased. The increasing surfactant concentration also induces a change in head-group orientation with a concurrent increase in twisting power of the mesophase. The increase in twist cannot simply be caused by the higher concentration of micelles since it has been shown that the twist increases as the water content of the liquid-crystalline material is increased.' Consequently, the increase in twisting power with increase in amphiphile concentration must be associated with the observed change in orientation of the head group and is therefore a measure of the distortion induced in the micelle by the chiral center. This distortion is apparently determined by the proximity of neighboring head groups. If this conclusion is sound, it is reasonable to expect that if the concentration of head groups in the micellar surface is diluted, an opposite behavior should be observed. It is possible to achieve such a dilution by varying the amount of decanol contained in the micelle. When the decanol is incorporated into the micelle, its hydroxyl group becomes an integral part of the micellar surface. It is then to be expected that with increase in decanol concentration the pitch will decrease and that the alaninate splittings, both dipolar (CHCH3) and quadrupolar (N-D), will increase. A decrease in the difference of alignment of the d- and 1-alanines would also be expected. Figure 3 shows the decrease expected for the pitch and for the d,l-alanine alignment differences. Table (12)
Tracey, A. S.;Boivin, T. L. J. Phys. Chem. 1984, 88, 1017.
r
0 0
'i
I
0
I
I
0.04
0.05 [DECANOLI g
Figure 3. The behavior of the twist (0)and the difference in alignment of the d- and I-alanines ( 0 )as the proportion of decanol is increased.
1 0.028
,
,
.
0.044 [SALT CsCIl g
01060 '
Figure 4. The behavior of the twist (0)and the difference in alignment of the d- and I-alanines ( 0 )as the proportion of CsCl in the mesophase is increased.
IV gives the effect on quadrupole splittings as the decanol content is increased. The deuterium quadrupole splitting and the dipolar couplings from the head group show the expected increases in magnitude. It is also clear from this table that, as found for changes in detergent concentration, the alkali ion splittings follow the head-group splitting very closely. Since the alkali ion quadrupole splittings are apparently highly dependent on the head-group alignment, it might be possible that this alignment is affected by electrolyte concentrations. Furthermore, as the electrolyte concentration is increased, it would be expected that because of the salting out effect, d- and l-alanine should show an increasing difference in their alignment as the
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 6047
Cholesteric Behavior of 1-KDDA
TABLE V Various NMR Parameters Measured and Selected Ratios of Their Values Obtained as a Function of Cesium Chloride Concentration composition" spectral parametersb ratio of splittings
CsCl 20 24 28 32 36 40 44 48 52 56 60 64
AVND
Dl2
D22
AVK
AVCS
nuel
19.4 18.9 18.4 17.9 17.4 16.2 17.1 15.0 15.5 14.1 12.9 13.2
0.275 0.270 0.254 0.255 0.242 0.237 0.239 0.207 0.213 0.194 0.176 0.178
0.607 0.598 0.583 0.568 0.542 0.531 0.534 0.469 0.581 0.442 0.403 0.408
5.44
0.234 0.234 0.239 0.238 0.241 0.237 0.255 0.233 0.252 0.232 0.229 0.239
1.84 1.86 1.80 1.77 1.69 1.64 1.54 1.55 1.37 1.40 1.24 1.11
5.57 5.60 5.88 5.74 5.20
AvND/D12
70.5 70.0 72.4 70.2 71.9 68.4 71.5 72.5 72.8 72.7 73.3 74.2
AvNDfD22
O12/O22
32.0 31.6 31.5 31.5 32.1 30.5 32.0 32.0 32.2 31.9 32.0 32.4
0.45 0.45 0.44 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.44 0.44
'Amount (in mg) of CsCl present in mesophase B of Table I. bAll splittings are given in kHz. DI2is the H to CH3 dipolar coupling in I-KDDA while D22is the corresponding methyl group coupling.
I
6000
level result in the formation of smaller sized micelles. Increasing or decreasing amphiphile concentration results in a corresponding increase or decrease in the number of micelles present. The electrolyte concentrations may have its major impact by determining the optimum micelle size.
.
'O,
O
Conclusions
a A>ND
16 KHi!
24
Figure 5. The twist (1/P) of the helical axis of the cholesteric mesophase
plotted against the deuterium quadrupole splitting from the amido group of the potassium N-dodecanoyl-I-alaninateand obtained as a function of component concentration: ( O ) , amphiphile concentration; (e),decanol concentration; (+), CsCl concentration. contact interactions are increased. Figure 4 shows the behavior of the measured twist and the difference in alignment of the alanines as a function of cesium chloride concentration. It is seen that a threefold increase in salt concentration caused a relatively small decrease in twist. The alanine splittings showed the expected increase in their difference. Table V shows that there is large increase in head-group splitting with increase in CsCl concentration. Unlike the previous results, no correlation between alkali ion and head-group splittings is apparent. This is expected since with added ions, there is not a proportionate increase in the number of sites available for binding and the observed splitting is an average for the binding and nonbinding ions. Both the C1- and water (zH, 170)quadrupole splittings increase with added salt content. Here as found for the change in amphiphile and decanol content there is a constant proportionality between the deuterium quadrupole splitting of the amido deuterium and the dipolar couplings of the CHCH, group. Since consistent proportionality constants between the dipole and quadrupole splittings for the head-group and the quadrupole splittings from the alkali ions (except for the case of changing electrolyte concentration) are observed, it is possible that a correlation exists between head-group splitting and the twist of the mesophase itself. Figure 5 shows the results of plotting the twist against the deuterium quadrupole splitting of the N-D group. The figure reveals that there is a linear relationship between the head-group alignment and the macroscopic twist as the amphiphile concentration is varied. This linear relationship is preserved at the higher decanol concentrations but not at the lower ones. Unfortunately, the results from changing the electrolyte concentration are not as definitive. The curve obtained appears to cross the previous one obtained from the amphiphile/decanol results. The observations encompassed by Figure 5 suggest that several conclusions about mesophase behavior can be made. The first is that, in the nematic medium, micelles have a maximum size. At concentrations above a threshold value increasing the amount of decanol or amphiphile results in an increase in the number of micelles present. Concentrations of decanol below the threshold
This study of the potassium N-dodecznoyl-I-alaninate/decanol/electrolyte/water mesomorphic system has provided information concerning the development of cholesteric behavior. This behavior derives from the chiral center contained in the head group of the amphiphile. The alaninate head group
contains both an amido and a carboxylate functionality. The N M R spectrum provides three splittings, a deuterium quadrupole splitting from the N-D and H to CH3 and CH3 dipolar couplings. These couplings may be used to characterize the alignment of the head group. The fact that the head group contains a center of optical activity means that the three splittings are not sufficient to completely specify alignment. Furthermore, there is the possibility of internal rotation. It was however found that despite large changes in composition of the mesophase the three splittings maintained a constant proportionality to each other. Furthermore, it was also found that the alkali ions, which are associated with the carboxylate group, also maintained their proportionality of splitting both with themselves and with the head-group splittings. This behavior is like that expected for a rigid entity moving about a director. The director alignment then scales the splittings by the term 1/2(3 cosz 8 - l), where 8 is the angle between the head-group director and the director for the micelles. Upon changing the mesophase composition by increasing amphiphile concentration, it was found that the splittings decreased in magnitude. Associated with this decrease was a large increase in twist induced by the chiral center. It was found that the twist was linear with the N-D deuterium quadrupole splitting but of negative slope so that for a decrease in deuterium splitting an increase in twist was obtained. This clearly establishes that the head-group orientation and twist are closely related. In contrast to the amphiphile, an increase in decanol content serves to decrease both the twist and the head-group splittings. It was, however, found that linearity between splittings and twist was maintained with variation in decanol content but only at the higher concentrations. It may be that, at the lower concentrations of decanol, micelles of the optimum size can no longer be obtained so that linearity is lost because of the change in micelle size. Optimum micelle size is otherwise maintained simply by increasing or decreasing the micelle concentration. The major role of the electrolyte may be that of determining the optimum size for the micelles.
6048
J. Phys. Chem. 1984, 88, 6048-6052
The dominant factor in obtaining a large twist in the mesophase is that of high detergent concentration. High concentration increases head groups to head group interactions, leading to their reorientation in the micellar surface. This reorientation in turn results in an increased distortion of the individual micelles. The change in intermicellar interactions between the chiral micelles provides the increase observed for the macroscopic twist. An increase in the decanol content weakens head-group interactions
which in turn provide less distorted micelles and a resultant smaller twist.
Acknowledgment. Thanks are gratefully extended to the Natural Sciences and Engineering Research Council of Canada for its financial support of this work. Registry No. I-KDDA, 76402-41-0; decanol, 112-30-1.
Monte Carlo Calculation of the Molecular Structure of Surfactant Bilayers Brian Owenson and Lawrence R. Pratt* Department of Chemistry, University of California, Berkeley, California 94720 (Received: May 7, 1984; In Final Form: July 12, 1984)
A simple primitive molecular model of bilayers composed of single-chain surfactant molecules is studied by Monte Carlo computer simulation. The results provide numerically exact data with which to test recent statistical mechanical theories of similarly primitive model surfactant bilayers. In addition, the numerical results emphasize several qualitative physical features of the molecular structure of surfactant bilayers which deserve particular theoretical attention. These include the molecular scale flexibility and roughness of these bilayer surfaces and differences between chain packing in monolayers and bilayers. Finally, on the basis of the present results we discuss the physical explanation for the well-known increase in chain ordering near the bilayer surface.
Introduction The molecular description of the structure of surfactant bilayers is a topic of great importance in both physical and biological Recently a very helpful molecular theory has been proposed for the molecular structure of these amphiphilic mesophase^.^ This theory is based on a lattice model of chain molecule condensed phases and a physical analogy between surfactant bilayers and interphase regions separating lamellar crystallites from adjoining amorphous regions of semicrystalline polymers. In this paper we present Monte Carlo computer experimental results on a similar underlying model. These results allow us to stringently test the physical approximations adopted in developing the consequences of the molecular theory. One of the chief advantages of computer simulation of condensed phases is that theories which have been developed only to the point of treating simplified models can be meticulously tested without necessarily simultaneously judging the accuracy with which the simplified model represents the physical systems of ultimate interest. In fact, it is clear that the simplified models which have been the basis of recent theoretical work3s4do faithfully represent, in a generic way, some of the molecular complications presented by real surfactant bilayers. Thus, the results obtained here also allow us to identify those complicating molecular features which deserve special physical consideration. The most important such feature is the molecular scale thermal roughness and flexibility of the bilayer surfaces. In many of the previous treatments of these systems, the bilayer surfaces have been assumed to be smooth and rigid.3,5-7 Some computer simulation work on fairly sophisticated (1) Israelachvilli, J. N.; Marcelja, S.; Horn, R. G. Q. Reu. Biophys. 1980, 13, 121. (2) Tanford, C. “The Hydrophobic Effect: The Formation of Micelles and Biological Membranes”,Wiley: New York, 1980; 2nd ed. (3) Dill, K. A.; Flory, P. L. Proc., Natl. Acad. Sci. U.S.A. 1980,77,3115. 1981,78,676. Dill, K. A.; J . Phys. Chem. 1982,86, 1498. (b) Dill, K. A.: Cantor, R. S. Macromolecules 1984,17,380. 1984,17, 384. (4) Haan, S. W.; Pratt, L. R. Chem. Phys. Lett. 1981,79,436.1981,81, 386. Owenson, B.; Pratt, L. R. J . Phys. Chem. 1984,88,2905. (5) Gruen, D. W. R.; de Lacey, E. H.B. In “Proceedings of the International Symposium on Surfactants in Solution“; Plenum: New York, 1982; Gruen, D. W. R. Chem. Phys. Lipids 1982,30, 105. (6) Cotterill, R. M. J. Biochem. Biophys. Acta 1976,433,264. Pink, D. A.; Lookman, T.; MacDonald, A. L.; Zuckerman, M. J.; Jan, N. Biochem. Biophys. Acta 1982,687,42. Lookman, T.; Pink, D. A,; Grundke, E. W.; Zuckerman, M. J.; deverteuil, F. Biochemistry 1983,21,5593.
model systems has incorporated an external field to pin the surfactant head groups to a smooth interfacial region of narrow defined On the basis of the results presented here, these important assumptions should be considered physically restrictive and unjustified. The present results, together with experimental data on the surface tensions of aqueous alkyl sulfate solutions, emphasize that these bilayer surfaces should be recognized as low-tension surfaces. Of course, structural fluctuations of membranes and proteins are generally necessary for their proper functioning; for some proteins, structural fluctuations have been the subject of specialized theoretical studies.I0 An additional important physical feature involves the relation between chain ordering in bilayers and in surfactant monolayers formed by ionic surfactants adsorbed on the interfaces between aqueous solutions and hydrocarbon liquids. Some previous treatments have assumed that the molecular structures of these layers are similar enough that the bilayer can be viewed as merely two separate monolayer^.^^^^^*^ Our results show some interesting consequences of the interactions of chains associated with opposite sides of the bilayer. A final interesting physical issue has to do with the explanation of the well-known disorder gradient in bilayers, Le., the increased ordering characteristic of chain segments near the bilayer surface compared to that near the bilayer midplane. One explanation of this disorder gradient is that the chains are cooperatively tilted with respect to the bilayer normal direction. Strong short-ranged orientational correlations between chains are just as likely in bilayers as in molecular liquids, and such correlations were clearly present in previous molecular dynamics calculations on model bilayersa8 However, it has been argued that correlated tilting over macroscopic distances is ~ n l i k e l y ;it~ is not found under the conditions of the present calculation. A second explanation assumes that the chains can always be viewed as essentially parallel (7) Scott, H. L., Jr. Biochem. Biophys. Acta 1977,469,264. J . Chem. Phvs. 1984. 80. 2197. i 8 ) Kox, A.’J.; Michels, J. P. J.; Wiegel, F. W. Nature (London) 1980, 287,319. van der Ploeg, P.; Berendsen, H. J. C. J . Chem. Phys. 1982,76, 3271. (9) Kox, A. J.; Weigel, F. W. Physica 1978,92.4, 466. (10) Case, D. A,; Karplus, M. J. Mol.Bioi. 1979,132,343. McCammon, J. A.; Karplus, M. Acc. Chem. Res. 1982,16, 187. Szabo, A,; Shoup, D.; Northrup, S. H.; McCammon, J. A. J . Chem. Phys. 1982, 77, 4484. McCammon, J. A.; Karplus, M. Annu. Rev. Phys. Chem. 1980, 31, 29.
0022-3654/84/2088-6048$01.50/00 1984 American Chemical Society
