Selfassembly of surfactant liquid crystalline phases by Monte Carlo …tomas/MFCS/1A_JCPv91.pdf · 2011. 10. 24. · lae, cylinders, or spheroids. The asymmetric surfactant pro duced

Selfassembly of surfactant liquid crystalline phases by Monte CarlosimulationR. G. Larson Citation: J. Chem. Phys. 91, 2479 (1989); doi: 10.1063/1.457007 View online: http://dx.doi.org/10.1063/1.457007 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v91/i4 Published by the American Institute of Physics. Related ArticlesMega-electron-volt proton irradiation on supported and suspended graphene: A Raman spectroscopic layerdependent study J. Appl. Phys. 110, 084309 (2011) Gel formation and aging in weakly attractive nanocolloid suspensions at intermediate concentrations J. Chem. Phys. 135, 154903 (2011) Waiting time dependence of T2 of protons in water suspensions of iron-oxide nanoparticles: Measurements andsimulations J. Appl. Phys. 110, 073917 (2011) The effects of shape and flexibility on bio-engineered fd-virus suspensions J. Chem. Phys. 135, 144106 (2011) Quantitative measurement of scattering and extinction spectra of nanoparticles by darkfield microscopy Appl. Phys. Lett. 99, 131113 (2011) Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Self-assembly of surfactant liquid crystalline phases by Monte Carlo simulation

R. G. Larson AT&T Bell Laboratories, Murray Hill, New Jersey 07974

(Received 23 November 1988; accepted 3 May 1989)

Three-dimensional microstructures of surfactant-water-oil systems self-assemble in a Monte Carlo lattice model, as shown here. The microstructures that form depend on the volume ratios of oil, water, and surfactant, and on the length of the surfactant, and on the ratio R of the length of the oil-loving to the water-loving portion. For R = 1 we find lamellar phases when the surfactant is mixed with equal amounts of oil and water. The lamellar spacing increases as the surfactant concentration is lowered. In the presence of water only, as the surfactant concentration is lowered the microstructure evolves from lamellar to broken lamellar to cylinders to spheroids. This progression is found to be independent of lattice size for lattices as large as 40 X 40 X 40. For R = 3, the progression seems to be replaced by a progression from lamellae to regular bicontinuous structures to cylinders, although we are not yet confident that this latter progression is independent of lattice size effects. The Monte Carlo technique can be used to study a wide variety of interesting phenomena, from micelle size and shape transitions to packing transitions and phase behavior to interfacial properties in the presence of surfactant.

I. INTRODUCTION

The problem of predicting the microstructure of surfac-tant-containing fluids based on the shape and flexibility of the constituent molecules and the intermolecular forces between them is an outstanding problem towards which many theories-starting with that of Hartleyl in 1935-have been directed.2 Since these theories inevitably involve specification of allowed microstructures, we believe that di-rect computer simulation of microstructure of self-assembly, with no a priori limitations on which microstructures are to be allowed, will prove invaluable in testing and enhancing the theories. In such a computer technique, the molecules are allowed to self-select a microstructure based only on the molecular properties and intermolecular interactions. The simulations could serve as a test of the theories in a way not possible by experiment, since in the simulations the molecu-lar and intermolecular properties can be adjusted or simpli-fied at will, and the resulting microstructure can be exam-ined in all detail.

crostructures spontaneously self-assemble at low tempera-tures. In the previous paper we presented evidence for the appearance of lamellar, cylindrical, and spheroidal micro-structures3 for systems containing varying amounts of oil, water, and the surfactant H4 T 4 that contains four water-loving "head" units and four oil-loving "tail" units, and oc-cupies eight sites on the lattice. We tentatively suggested for this system the schematic phase diagram depicted in Fig. 1.

A Monte Carlo lattice technique that can simulate mi-crostructures of idealized surfactant-oil-water solutions was announced in an earlier publication.3 In this technique, oil and water molecules occupy single sites on the square or cubic lattice and surfactant molecules occupy a sequence of adjacent sites. By "adjacent" we here mean nearest neighbor or diagonal nearest neighbor sites. Thus each site has eight adjacent sites on the square lattice, 26 on the cubic lattice. The diagonal interactions are nonconventional, but speed up computations by allowing kink type motions to occur with the interchange of a single pair of units. The diagonal inter-actions also partially suppress the bias that exists in a regular lattice along the directions in which two sites can be adja-cent. 26 directions of adjacency is a better approximation to a continuum than is six, for example.

Starting at infinite temperature to randomize the molec-ular configuration, the system is slowly "cooled," and mi-

II. SIMULATION RESULTS

In this paper, we present additional simulations that qualitatively support the phase diagram for the symmetric surfactant H4T4 depicted in Fig. 1, and show the effects of molecular asymmetry by presenting some simulation results for H2T6 . The phase behavior depicted in Fig. I-which is

FIG. 1. Schematic phase diagram for H. T 4 on the cubic lattice.

J. Chern. Phys. 91 (4),15 August 1989 0021-9606/89/162479-10$02.10 @ 1989 American Institute of Physics 2479


2480 R. G. Larson: Surfactant liquid crystalline phases

consistent with the results of the simulations reported here-is simpler than, but nevertheless bears many similari-ties to phase diagrams typical of real systems. A schematic summary of the phase behavior found in real surfactants is reproduced in Fig. 2 from Davis et al.4

The simulation method is described earlier. The shortest runs presented here required two days on an Alliant FXl computer; the longest runs consumed five weeks of time on this machine. The compositions investigated can be grouped into two progressions. In progression I, the surfactant con-centration CA is systematically varied, holding the ratio of oil to water fixed at unity. Thus this progression runs down the center of the ternary diagram of Fig. 1. In progression II, the surfactant concentration is varied, with the oil concen-tration remaining at zero; this progression runs along the left side of the ternary diagram. Because of the symmetry of H4T4 and of the assumed intermolecular interactions, the microstructures along the right-hand side of the diagram for H4T4 are identical to those along the left-hand side.

The system is cooled from infinite temperature to in-verse dimensionless temperature w = 0.1538 in steps tabu-lated in Table I. The critical value of w for oil and water to form a single phase is w:::::0.09.

The numbers tabulated in Table I include failed at-tempts at movement. Progression I, which produces lamel-lar microstructures, requires fewer Monte Carlo steps than does progression II. The number of Monte Carlo steps re-

CYLINDRICAL MICELLa

e* SPHERICAL MICELLES

SURFACTANT

WATER

quired was determined empirically. Runs that are too short to equilibrate sufficiently produce irregular microstructures such as that depicted in Fig. 3. For the surfactants investigat-ed here, runs of sufficient length always produced a well defined microstructure: either lamellae, interrupted lamel-lae, cylinders, or spheroids. The asymmetric surfactant pro-duced a bicontinuous phase also. The large 30 X 30 X 30 or 40 X 40 X 40 systems require many more Monte Carlo steps than do the smaller lattices, both because the larger systems contain many more molecules, and because on the larger lattices molecules and structural information has to diffuse over larger distances. The quantity "T" in Table I, the num-ber of Monte Carlo steps at w = 0.1538 for large lattices, is given case by case in Figs. 7, 14, and 15.

A. Symmetric surfactant H4 T 4

Figures 4-6 show the microstructures that develop on 20 X 20 X 20 lattices for H4 T 4 in progression I; these micro-structures contain equal amounts of oil and water. In these and most subsequent figures, two orthogonal slices of the system are shown. The system can be readily visualized by imagining that the two images shown are abutting faces of a cube. The dashed line in Fig. 3 and following figures de-marks the volume actually simulated; the rest of the region is filled with periodic images of the simulated region. In Figs. 4-7, both tail and oil units are shown; in all other cases only

OIL INVERTED MICELLES

FIG. 2. Schematic diagram iIIustraing the phase behavior of real surfactant-oil-water systems. (from Davis et al., Ref. 4).

J. Chern. Phys., Vol. 91, No.4, 15 August 1989


R. G. Larson: Surfactant liquid crystalline phases 2481

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CA 0.6

Co 0.0

FIG. 3. Perpendicular slices through 20X 20x 20 lattice containing 60% H. T., 0% oil, 40% water. Only the tail units are shown. For this system the run time was only 25% of that given in the third column of Table I. This was inadequate to obtain a regular structure. The result of a run four times as long as this is depicted in Fig. 10.

the tail units are shown. By symmetry the microstructures in progression I must be invariant to interchange of oil for wa-ter and (simultaneously) heads for tails. The only known regular microstructures that possess such symmetry are la-mellar and various bicontinuous structures. In the simula-tions we observe lamellar microstructures with the lamellar

TABLE I. Number of configurations sampled in each Monte Carlo run.

20 X 20 X 20 lattices

II

Y

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a

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x

. ... . .... . ... . .... . .... . ..... . .. . ... . · .... . . ..... . . ... . . ... . . ... . . .. . .... · .... ..... ..... ...... . .. . . .... .

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C A 0.8

Co 0.1

FIG. 4. 20X 20 X 20 lattice containing 80% H. T., 10% oil, 10% water. Tail units are designated by (0), oil units by (*).

spacing increasing as the surfactant concentration drops from 80% to 30%. As reported earlier, 3 the pattern takes an orientation on the lattice that allows it to fit the desired peri-odicity into the given lattice size. We expect that if the sur-factant concentration becomes low enough, the system will form three coexistent phases; see Fig. 1. Figure 7 shows,

w Progression I Progression II 30 X 30 X 30 or 40 X 40 X 40 lattices

0.0154 0.10T 0.0308 20000000 80000000 O.IOT 0.0462 O.IOT 0.0615 50000000 200000000 O.IOT 0.0769 0.25T 0.0923 50000000 200000000 0.25T 0.1077 0.5T 0.1231 100000 000 400000000 0.5T 0.1308 T 0.1385 200000000 800000000 T 0.1462 T 0.1538 200000000 800000000 T

total 620000 000 2480000000 5.9T




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x

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FIG. 5. 20X20X20 lattice containing 50% H.T., 25% oil, 25% water. Tail units are designated by (0), oil units by (*).

however, that lamellar structures are obtained when CA is as low as 30%, even on a 30 X 30 X 30 lattice.

It has been hypothesized that some surfactant systems ought to display irregular bicontinuous structures for oil! water ratios near unity when the surfactant concentration is reduced to values near those at which multiphases appear. 5

Lamellar phases in this region are to be expected when the surfactant-laden interface between water and oil domains of the microstructure is rigid and not susceptible to thermal distortions that would bend it enough to produce the curved surfaces required for bicontinuous structures. It is known empirically that the addition of "cosurfactants" -usually consisting of short surfactant or alcohol molecules-is re-quired in surfactant-oil-water mixtures if undesirable high-viscosity liquid crystalline structures, such as the lamellar phase observed in our simulations, are to be avoided. In fu-ture simulations, it is hoped that we can compute bending energies of surfactant-laden interfaces, and examine the ef-fects of added small amphiphiles such as HIT!.

Figures 8-13 show the microstructures of 20 X 20 X 20 systems containing H4T4 and water with no oil (progression II). As the concentration of surfactant decreases, the micro-structure evolves from broken lamellae at 80%-70% surfac-tant to arrays of cylinders at 60%-50% to arrays of spher-oids at 40%-30% surfactant. The spacing of the broken lamellae at 80% surfactant concentration in progression II is

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y Ii! H4 T•

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51

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X FIG. 7. 30X 30X 30 lattice containing 30% H.T., 35% oil, 35% water; Tin Table I equals 0.8 X 109 . Tail units are designated by (0), oil units by (*).




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o .0 211 .. ... x

FIG. 8. 20X20X20latticecontaining 80% H.T., 0% oil, 20% water. This run was twice as long as the other runs of progression II for 20X20x20 systems.

the same as that of the lamellae at 80% surfactant concentra-tion in progression I; compare Figs. 4 and 8. As C A decreases in progression II, the spacing increases between broken la-mellae in Figs. 8 and 9, between cylinders in Figs. 10 and 11, and between spheres in Figs. 12 and 13. Although for the small systems studied here compromise structures such as the broken lamellae seen in Figs. 8 and 9 seem to be optimal, we suspect that bulk systems with surfactant concentrations in this range would form lamellae and cylinders in coexis-tence; this is indicated on Fig. I. The preference for cylindri-cal microstructures at intermediate concentration is con-firmed in Fig. 14, which shows the microstructure on 30 X 30 X 30 lattice for 50% surfactant. In Fig. 10 the cylin-ders are oriented parallel to the Z axis of the lattice, while in Fig. 11 they are parallel to a diagonal of the ZX face of the lattice, consistent with the reduced concentration of surfac-tant, and consequent wider spacing of the cylinders in the latter. On the 30X 30X 30 lattice of Fig. 14 they orient paral-lel to the diagonal of lattice cube itself. Thus in this latter case, to visualize the cylinders, we depict the YX face of the cube (Fig. 14, upper), and a cross section which is a plane perpendicular to the YZ face of the cube whose intersection with the yz face is a diagonal of the YZ face (lower). Al-though one would expect hexagonal packing of cylinders in macroscopic systems, for the 20 X 20 X 20 and 30 X 30 X 30 lattices simulated here, the cylinders pack in asymmetric

y

z

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I

. . · · · .. · ... ... . .... ::::. ::!. .... ..-

.::::. ··T, •• . .... ••••• •• I

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.0 . . ... · · . .:: .. . .... ..,

x

.... ..... ...... ..... ... . . .... ... . .. · .. . .. . . .. . . .. . . .. . . ...... . . .... . . ... . · ... . ..... ... ::::.

::::: . . ... ..... ... . .. · .. . .. . . .. . . .. . . .. . ........ . ..... ..... · .... ..... ... ... : · •• 0 .... ..... .... .... •• 0 • . .. . . .... . . ... . ..... .... .:::: . . .... .:::::: ...

••• 0 o · ... .... . .... .... .... .... .... . .... . . ... . . ... . .... .....

:::: : • •• 000 • . ..... ... ..

· . . . .. ... ..

· .. · .. . .. . .. ..

o:~

· .. .. . . . . . . . . .. .0 .0 . . . · . . · .. .0 .. . . . . .. .. .0

.0 . . . · . . ...

CA 0.7

Co 0.0

FIG. 9. 20X20X20 lattice containing 70% H.T., 0% oil, 30% water.

~ D •••••• ••••• 00 0 ••• 0000 . ..

0 •• 0 •• 0 .0. 0 •• 0 •• 0.0 • 0 • •• 0 •• 0 • 0 . ••••• 00 . .000 • 0 •• 0 o 0 ••• 0 . ... ... 00 .00 o •

II ...... •• 0 •• 0 •• 00 •• .00.00

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H4 T4 iii ----~-~!!!Z~----------1 0 •• 00 •• 00.000 • • 0 .. .. . • ::::= •• . ... ... . ....

CA 0.6 .. ::::::0 ..0 •• 0 . . ..0 •• 0 0 •• o ••• 0'0 .

0.0 •• i ... s ••• 000 • 0000 • Co 0.0 ...... .00000 DO •••• • 0 , . .

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2484

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• 0.0 D. • I D.O. D. 0

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a

o

....... ......... . ........ . ....... . · ...... . ..... . ....... . . ...... . .... .. . . ..... . ......... . ....... . .......... .. . .......... .

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X

R. G. Larson: Surfactant liquid crystalline phases

C A 0.5

Co 0.0

y

Z

~

Ii

Iil

!l

~

Ii

Iil

. · 0: • .:. .. . . ... . .. .... . ... ...... . ..... ....... .0 ••••• ......... ......... .......... . ......... ........... .::::::::: . • ••••••• 0 ....... . ........ . ::: . .. ....... . .. . . F----------------i----- · .:. . .. · .. .. ... . .. .... .... ...... . ..... ....... ....... ......... ......... .......... . ......... ........... . .......... ......... . ........

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, , . ' .

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.. :: .. · ·

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o 00.0 ___ ::0

10 ""

x

... ... ... . ..

0 ••• 0.00 · .. . ... ...

JO 40

H4 T4

C A 0.3

Co 0.0

FIG. 13. 20X20X20 lattice containing 30% H.T., 0% oil, 70% water. FIG. 11. 20X20X20 lattice contining 50% H.T., 0% oil, 50% water.

y

z

II

iii

a

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:::.... ~:: .... ••••• -:a ••••

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. . ... . ..... .:::: .. :

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Ii

........ ........ ......... :::::::: ..... .. .

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a

........ . ....... . ......... . ....... . ........ . ....... . ........ . ...... . •••• • .0 ••• .. . .. . ... . . ........ ......... .......... . .... ........ . ....... . .......... . ...... . ........ ... :::: .... . .. :::: ... . . .... .....

10

. .::::. 10

X

i

40

C A 0.4

Co 0.0

staggered arrays (Figs. 10 and 11) or in square arrays (Fig. 14). Apparently these lattices are too small to yield the pack-ings that we expect for bulk systems. For low concentrations we obtain spheroids, not only on the 20 X 20 X 20 lattices of Figs. 12 and 13, but also on 30X30X30 and 4OX40X40 lattices. On the 20X 20X 20 lattices the spheres pack in regu-lar arrays, a face centered cubic (fcc) packing appears in Fig. 12 and bOdy-centered cubic (bcc) in Fig. 13. These lat-tices are so small that they contain only one unit cell of the crystalline structure, and so one should not expect these symmetries to typify the bulk. Figure 15 shows that for larg-er 30 X 30 X 30 and 40 X 40 X 40 lattices, the 30% system forms positionally disordered spheres. It is not known whether these larger systems require longer runs to organize equilibrium crystal structures, or whether the disordered spheres of Fig. 15 represent the true eqUilibrium behavior of this system. Recent and forthcoming increases in computer power may allow runs long enough to resolve this uncertain-ty.


Within the volume of the 40 X 40 X 40 lattice in Fig. 15 there are 27 spheroidal micelles with aggregation numbers ranging from a low of 63 to a high of 113. The mean aggrega-tion number is 88 and the standard deviation about this mean is 14. Thus the distribution of micelle sizes is relatively narrow. In addition to these micelles there are ten unaggre-gated singlet surfactant molecules and one dimer. There are no aggregates with sizes in the range 3-62. A more detailed study of the micelle distribution function of this and other systems is in progress.




i

it

Ii

Y 1i1

H.T.

CA = 0.6 iii

Co = 0.0

!!

i

it

Ii

Z Ii

iii

!!

0 10 20 III ... so eo X

FIG. 14. 30x30x 30 lattice containing 50% H.T., 0% oil, 50% water; Tin Table I equals 3.2 X 109• In this depiction the lower image is not a face ofthe cubic lattice, but is a diagonal slice defined by the condition Z + Y = 61.

Because lamellae are infinite in two directions, there are two angles through which a lamellar microstructure can ro-tate to fit on a finite three-dimensional lattice. Thus we be-lieve that even with the small lattices considered here we have obtained lamellar crystalline order typical of the bulk. There is only one angle through which a cylindrical crystal-line microstructure can rotate, so the correct symmetry is less likely to be obtained on small lattices. Unless the lattice size is by chance commensurate with the equilibrium size of the unit cell, spheroidal packings such as bcc or fcc cannot fit on a finite lattice without defects or distortions. Thus for these latter systems, simulations on very large lattices (per-haps lOOX lOOX 1(0) will be required if one is to have any confidence that the crystal symmetry represents that of bulk material.

B. Asymmetric surfactant H2 T 8

The changes in microstructure from lamellar to cylin-drical to spheroidal that occur as one decrease CAin progres-sion I are driven by volumetric constraints. Since the surfac-tant H4 T 4 is symmetric, it would prefer to reside at uncurved interfaces. As CA is reduced however with the oil concentra-tion held at zero, the oil-loving component (tails only) be-comes more and more in the minority volumetrically. The system therefore chooses to pack the tails into confined cy-

i ... . . iI ~.4 ~.4

y "" -"" -Ii ---------~------ H.T. . ~.4!~.4 CA = 0.3 iii Co = 0.0 . , . "4t -1"4t .,.

z

x

FIG. 15. 4OX40X40latticecontaining30% H.T., 0% oil, 70% water; Tin Table I equals 1.6x 109 •

lindrical or spheroidal regions to make room for the majority water-loving material (heads and water). It is of interest to counter this tendency by mixing an asymmetric surfactant H2 T 6-that prefers to reside at interfaces curved towards the water-loving side-with water and no oil. For such mix-tures, the volumetric constraints are opposed by the curva-ture tendencies inherent in the surfactant. Thus consider a system containing 20% H2 T 6 in water. Since for this surfac-tant the ratio R ofthe length of oil-loving portion to water-loving portion is 3, the volume of oil-loving material in this system is 15%-the same as a system containing 30% H4 T 4 in water. If the volumetric constraint controlled the micro-structure, 20% H2 T 6 should then form spheroids, and look comparable to Fig. 12 or 13. The surfactant, however, does not want to reside at an interface curved toward the long tails. A compromise is struck, therefore, and the simulation produces a cylindrical morphology; see Fig. 16. Likewise 50% H2 T 6' which has volumetrically the same amount of oil-loving material as 75% ofH4T4, forms lamellae in Fig. 17 instead of the broken lamellae formed by H4 T 4 in Figs. 8 and 9. A 40% concentration of H2 T 6 yields the most interesting microstructure of all. Figure 18 shows successive slices through this system arranged in a clockwise progression. It is bicontinuous and is topologically equivalent to the Schwarz surface depicted in Fig. 19. The system size here is too small for one to be at all confident that this result is




Ii ....... . ....... . :: •••• 00 •••• .... 000 • .. :::::::0 · .. .

II

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:: 0:::.::::: · ·::·:1 !!

. : .0000 ID

0 ••• 0l1li

-,'

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000.001

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D ••••

•• 20 X

..

•••• 0 ...... ....... •••• 0

• ••• 0 ••• 00 ...

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0 ••••• 0 ••• 0 •

000 •• ..... ...

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•••• 00 •••• 00 •• 0000

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00000 0.000

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000000 000 •• . ::::

••• 000 •• 0000 000000

0000 00000

0000 0000

00000 00000

a 0000 00000

0000

H2T8

CA= 0.2

Co = 0.0

FIG. 16. 20X20X20 lattice containing 20% H2T •• 0% oil. 80% water.

typical of the bulk: only one unit cell is generated on the 20X20X201attice. On the 4OX40X40 lattice with Tin Ta-ble I equal to 3.2X 109 , this system again yields a bicontin-uous microstructure, but it is not a regular one. It does, how-ever, show a cellular structure with a cell size that is comparable to that found on the 20 X 20 X 20 lattice. This compositon on the 30X30X30 lattice with T= 3.2X 109

gives a lamellar structure rather than bicontinuous, appar-andy because the preferred cell size of the bicontinuous structure is not commensurate with the 30 X 30 X 30 lattice. We believe that it is significant that regular bicontinuous structures appear only for the asymmetric H2 T 6 and are not generated by the symmetric surfactant H4 T 4' at the composi-tions investigated here. Scriven et al.4•5 have speculated that bicontinuous microstructures might appear in surfactant-water mixtures.

Because of the small size of the lattices, any conclusions that we draw about liquid crystalline phase behavior must be somewhat tentative. However, it is noteworthy that the to-pology of the microstructure (spheres, cylinders, lamellae, or bicontinuous) obtained for 20X20X20 lattices always persisted when larger lattices were considered. The regular crystal symmetries (fcc, bcc) seen on 20X20X20 systems never persisted on the larger lattices, however. This could mean either that the regularity found on 20 X 20 X 20 lattices is an artifact of the smallness of the lattice and the artificial constraint of the periodic boundary conditions, or that the J>ig lattices would have shown regularity if only the runs had been longer. If, as we think likely, the fonner possibility is

Y

l

!I

II

iii

!!

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•• 00::::::00 l 00.0::::::··

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000000

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o 000lI0

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: 0:0::::

!! r: :::::::

••

00.0 0 o D ••• o 0000

000000

.:0:::0 0::::::0

X

..

0000.00

: 00:::

o •• 0 · .. ::::: .0 •• 0 000.0 .0.0

• 000 a 0.0 00 .. · .. 00000 00000

00.000

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00

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a a ••• o ••• · .. ::::: 00 ••• •• 0 •• .000 . ...

o 000 .000 · .. 00.00

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H2 T8

C A = 0.0 Co = 0.0

FIG. 17. 20X20X20 lattice containing 50% H2TM 0% oil. 50% water.

the correct one, then perhaps ordering transitions to regular symmetries occur in these systems at temperatures lower than those considered here.

III. PROSPECTS

There are many interesting issues that can be addressed by a computer technique of the kind presented here.

One can seek the minimum length that a symmetric am-phiphile must be to fonn a given liquid crystalline micro-structure as a function of temperature. Preliminary results indicate that at w = 0.1538 H4T4 is the shortest amphiphile that fonns cylinders and H3 T 3 is the shortest that fonns la-mellae. H2T2 can be made to fonn lamellae if the inverse temperature w is increased to 0.20. The transition from a disordered phase to lamellae or any other ordered phase is first order. The thennodynamic properties of these transi-tions bear examination.

It will be worthwhile to examine the behavior at amphi-phile concentrations above the critical micelle concentration but below the concentration at which any crystalline order appears. Indications from the results presented here are that H4T4 fonns spheroids in this regime and H2T6 fonns cylin-ders. It would be interesting to detennine the ratio of the length of head group to the length of tail group at which the transition from spheres to cylinders in this concentration regime occurs.6 Also, the distribution of micelle aggregation number in this regime would be worth exploring.



II

a

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. ..... ...... ....... ...... ....... • 0.0 •• .... ...

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• 000 •••• •• 0.0

. . • • • • • •• . .. . . .

R. G. Larson: Surfactant liquid crystalline phases

.. .. I D. 00 • • 0.0 • 0000 •

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10 40 0

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iii P----------------------]

•• I O.

a

••• I ODD •••••• 0+0000.

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· · ·

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10 zo 10

10 40

2487

FIG. 18. Successive slices through a 20 X 20 X 20 lattice containing 40% H2 T 6,0% oil, 60% water. Every fourth layer of the lattice is shown above with the sucessive layers arranged in a clockwise progression.

It will be fascinating to study larger systems containing oil, water, surfactant, and possibly cosurfactant (such as HI T I) in regions of the phase diagram where one expects transitions to random bicontinuous phases of the kind postu-lated by Scriven5 and modeled by Talmon and Prager'? Wi-

FIG. 19. Schwarz surface suggested as a model for regular bicontinuous structures of surfactant-containing phases (taken from Scriven, Ref. 5).

dom,s and others.9 For symmetric surfactants, such transi-tions are most likely to occur at compositions just above the large three-phase triangle in Fig. 2.

As alluded to earlier, we would like to study the proper-ties of single surfactant layers between oil and water regions. Special box shapes and boundary conditions can be imag-ined that would facilitate this computer study. II Interfacial tension and bending constants, and the effects on these of addition of "cosurfactants" such as HI T I' could hopefully be calculated.

In principle, the phase behavior of mixtures of surfac-tant, oil, and water can be calculated since we can both in-spect the simulations visually for the presence of multiple phases, and can also compute free energies. In practice, this is very expensive computationally, since large systems are needed so that bulk quantities of all coexisting phases can be present simultaneously. Some preliminary work along this line was presented earlier,3 however, and more is currently under way for HITI. To compute phase behavior, a grand canonical ensemble I I (where chemical potential rather than composition is fixed) is better than the canonical ensemble used in all simulations to date. The canonical ensemble is useful for computing interfacial tensions, however, as illus-trated in Ref. 3.

In this paper we have begun to probe the effects of sur-factant asymmetry, that is asymmetry in the length of hydro-

J. Chern. Phys., Vol. 91 , No.4, 15 August 1989



philic and lyophilic parts. Asymmetry in the interactions, e.g., between head and tail vis a vis water and oil, are also well worth studying, since such asymmetries are characteris-tic of real systems. A small step in this direction was reported earlier. 10 One could also introduce longer range interactions than those considered here, although the artificiality of the lattice model would limit the significance of such an exten-sion of the basic model. Of course, moving the simulation off the lattice into continuous space would be a major step towards realism, but would entail vastly more computa-tional effort, if one is to remain true to the intention of allow-ing microstructure to self-assemble.

Finally, it may be possible to use this type of computer program to investigate the behavior of polymer amphiphiles such as block copolymers, or random copolymers. 12 There is a similarity between the microstructural transitions that oc-cur for diblock polymeric amphiphiles and those for surfac-tant amphiphiles as we have earlier noted.3 Of course, simu-lation of polymeric systems with molecular weight comparable to those used in typical experiments is currently out of the question.

The scope and diversity of the possibilities beckon new efforts and energies in this area.

ACKNOWLEDGMENTS

I wish to acknowledge helpful discussions with David Huse and Daniel Blankschtein.

IG. S. Hartley, Aqueous Solutions of Paraffin Chain Salts, Hermann, Paris, 1936).

2Physicsof Amphiphilic Layers, edited by J. Meunier, D. Langevin, and N. Boccara (Springer, New York, 1987).

3R. G. Larson, J. Chern. Phys. 89, 1642 (1988). 4H. T. Davis, J. F. Bodet, L. E. Scriven, and W. G. Miller (unpublished). 'L. E. Scriven in Micellization, Solubilization, and Microemu/sions, edited by K. L. Mittal (Plenum, New York 1977). ~his idea was stimulated by discussions with Daniel Blankschtein. 7y. Talmon and S. Prager, J. Chern. Phys. 69, 2984 (1978). 8B. Widom, J. Chern. Phys. 84, 6943 (1986). ·P. G. de Gennes and C. Taupin, J. Phys. Chern. 86, 2294 (1982). lOR. G. Larson, L. E. Scriven, and H. T. Davis, J. Chern. Phys. 83, 2411

(1985); R. G. Larson, Ph. D. thesis, University of Minnesota, 1980. 11K. Binder and D. Stauffer in Applications of the Monte Carlo Method in

Statistical Physics, edited by K. Binder (Springer, New York, 1984), pp. 1-36.

12L. Leibler has suggested simulating systems of random or regular alter-nating copolymers.



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Selfassembly of surfactant liquid crystalline phases by Monte Carlo …tomas/MFCS/1A_JCPv91.pdf · 2011. 10. 24. · lae, cylinders, or spheroids. The asymmetric surfactant pro duced