Advertisement
No access
Article

Domain Shapes and Patterns: The Phenomenology of Modulated Phases

Science
27 Jan 1995
Vol 267, Issue 5197
pp. 476-483

Abstract

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.

Get full access to this article

View all available purchase options and get full access to this article.

References

ALERHAND, O.L., SPONTANEOUS FORMATION OF STRESS DOMAINS ON CRYSTAL-SURFACES, PHYSICAL REVIEW LETTERS 61: 1973 (1988).
ANDELMAN, D, MONOLAYER TRANSITIONS WITH POLAR-MOLECULES, COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II 301: 675 (1985).
ANDELMAN, D, EQUILIBRIUM SHAPE OF 2-COMPONENT UNILAMELLAR MEMBRANES AND VESICLES, EUROPHYSICS LETTERS 19: 57 (1992).
ANDELMAN, D, PHASE-TRANSITIONS IN LANGMUIR MONOLAYERS OF POLAR-MOLECULES, JOURNAL OF CHEMICAL PHYSICS 86: 3673 (1987).
ANDERSON, D.M., PERIODIC SURFACES OF PRESCRIBED MEAN-CURVATURE, ADVANCES IN CHEMICAL PHYSICS 77: 337 (1990).
BACRI, J.C., MAGNETIC LIQUIDS, ENDEAVOUR 12: 76 (1988).
BACRI, J.C., INSTABILITY OF FERROFLUID MAGNETIC DROPS UNDER MAGNETIC-FIELD, JOURNAL DE PHYSIQUE LETTRES 43: L649 (1982).
BAHIANA, M, CELL DYNAMIC SYSTEM APPROACH TO BLOCK COPOLYMERS, PHYSICAL REVIEW A 41: 6763 (1990).
BARKER, W.A., DIPOLAR FORCES AND STRIPE DOMAIN-STRUCTURE IN FERROMAGNETIC-PLATES NEAR THE PHASE-TRANSITION, JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 16: 6415 (1983).
BATES, F.S., BLOCK COPOLYMER THERMODYNAMICS - THEORY AND EXPERIMENT, ANNUAL REVIEW OF PHYSICAL CHEMISTRY 41: 525 (1990).
BENVEGNU, D.J., LINE TENSION BETWEEN LIQUID DOMAINS IN LIPID MONOLAYERS, JOURNAL OF PHYSICAL CHEMISTRY 96: 6820 (1992).
BERKOVSKY, B.M., TOPOLOGICAL INSTABILITY OF MAGNETIC FLUIDS, JOURNAL DE PHYSIQUE LETTRES 46: L483 (1985).
BODENSCHATZ, E, TRANSITIONS BETWEEN PATTERNS IN THERMAL-CONVECTION, PHYSICAL REVIEW LETTERS 67: 3078 (1991).
BORUE, V, A STATISTICAL-THEORY OF WEAKLY CHARGED POLY-ELECTROLYTES - FLUCTUATIONS, EQUATION OF STATE, AND MICROPHASE SEPARATION, MACROMOLECULES 21: 3240 (1988).
BRAZOVSKII, S. A., JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS 41: 85 (1975).
Brochard, F., Physics of Amphiphilic Layers (1987).
BROCHARDWYART, F, STABILITY OF A LIQUID RIBBON SPREAD ON A LIQUID SURFACE, COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II 311: 295 (1990).
CAPE, J.A., MAGNETIC SOMAIN STRUCTURES IN THIN UNIZAXIAL PLATES WITH PERPENDICULAR EASY AXIS, JOURNAL OF APPLIED PHYSICS 42: 5732 (1971).
Tsebers, A. O., Magnetohydrodynamics 16 2: 22 (1980).
CHEN, L.Q., DYNAMICS OF SIMULTANEOUS ORDERING AND PHASE-SEPARATION AND EFFECT OF LONG-RANGE COULOMB INTERACTIONS, PHYSICAL REVIEW LETTERS 70: 1477 (1993).
COWLEY, M.D., INTERFACIAL STABILITY OF A FERROMAGNETIC FLUID, JOURNAL OF FLUID MECHANICS 30: 671 (1967).
CROSS, M.C., PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM, REVIEWS OF MODERN PHYSICS 65: 851 (1993).
DELACRUZ, M.O., TRANSITIONS TO PERIODIC STRUCTURES IN BLOCK COPOLYMER MELTS, PHYSICAL REVIEW LETTERS 67: 85 (1991).
DEUTCH, J.M., THEORY OF SHAPE TRANSITIONS OF 2-DIMENSIONAL DOMAINS, JOURNAL OF PHYSICAL CHEMISTRY 96: 7097 (1992).
DICKSTEIN, A.J., LABYRINTHINE PATTERN-FORMATION IN MAGNETIC FLUIDS, SCIENCE 261: 1012 (1993).
DUFIET, V, NUMERICAL-STUDIES OF TURING PATTERNS SELECTION IN A 2-DIMENSIONAL SYSTEM, PHYSICA A 188: 158 (1992).
ELDER, K.R., DYNAMIC SCALING AND QUASI-ORDERED STATES IN THE 2-DIMENSIONAL SWIFT-HOHENBERG EQUATION, PHYSICAL REVIEW A 46: 7618 (1992).
ELDER, K.R., ORDERING DYNAMICS IN THE 2-DIMENSIONAL STOCHASTIC SWIFT-HOHENBERG EQUATION, PHYSICAL REVIEW LETTERS 68: 3024 (1992).
Eschenfelder, A. H., Magnetic Bubble Technology (1980).
FABER, T.E., THE INTERMEDIATE STATE IN SUPERCONDUCTING PLATES, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES 248: 460 (1958).
FISCHER, A, ON THE NATURE OF THE LIPID MONOLAYER PHASE-TRANSITION, JOURNAL DE PHYSIQUE LETTRES 45: L785 (1984).
FREDRICKSON, G.H., FLUCTUATION EFFECTS IN THE THEORY OF MICROPHASE SEPARATION IN BLOCK COPOLYMERS, JOURNAL OF CHEMICAL PHYSICS 87: 697 (1987).
GAREL, T, PHYS REV B 226: 325 (1982).
GAREL, T, PHYS REV B 226: 325 (1982).
GAUB, H.E., REVERSIBLE FORMATION OF PLASTIC TWO-DIMENSIONAL LIPID CRYSTALS, JOURNAL OF PHYSICAL CHEMISTRY 90: 1721 (1986).
GOLDSTEIN, R.E., DOMAIN SHAPE RELAXATION AND THE SPECTRUM OF THERMAL FLUCTUATIONS IN LANGMUIR MONOLAYERS, JOURNAL OF PHYSICAL CHEMISTRY 98: 9626 (1994).
HAENSSLER, F, STATICS AND DYNAMICS IN INTERMEDIATE STATE OF TYPE 1 SEMICONDUCTORS, HELVETICA PHYSICA ACTA 40: 659 (1967).
HASEGAWA, H, BICONTINUOUS MICRODOMAIN MORPHOLOGY OF BLOCK COPOLYMERS .1. TETRAPOD-NETWORK STRUCTURE OF POLYSTYRENE POLYISOPRENE DIBLOCK POLYMERS, MACROMOLECULES 20: 1651 (1987).
HASEGAWA, H, MORPHOLOGY OF BLOCK COPOLYMERS AND MIXTURES OF BLOCK COPOLYMERS AT FREE SURFACES, POLYMER 33: 475 (1992).
HASHIMOTO, T, UNIFORMITY OF MICRODOMAIN SIZE OF BLOCK POLYMERS AS COMPARED WITH UNIFORMITY OF THEIR MOLECULAR-WEIGHTS, MACROMOLECULES 18: 1864 (1985).
HECKL, W.M., A NARROW WINDOW FOR OBSERVATION OF SPIRAL LIPID CRYSTALS, BERICHTE DER BUNSEN-GESELLSCHAFT-PHYSICAL CHEMISTRY CHEMICAL PHYSICS 90: 1159 (1986).
HINSHAW, G.A., TRANSITIONS AND MODULATED PHASES IN CHIRAL TILTED SMECTIC LIQUID-CRYSTALS, PHYSICAL REVIEW A 39: 5914 (1989).
HINSHAW, G.A., MODULATED PHASES IN THIN FERROELECTRIC LIQUID-CRYSTAL FILMS, PHYSICAL REVIEW LETTERS 60: 1864 (1988).
HOHENBERG, P.C., EFFECTS OF ADDITIVE NOISE AT THE ONSET OF RAYLEIGH-BENARD CONVECTION, PHYSICAL REVIEW A 46: 4773 (1992).
Huebener, R. P., Magnetic Flux Structures in Superconductors (1979).
HURLEY, M.M., DOMAIN-ARRAY MELTING IN THE DIPOLAR LATTICE GAS, PHYSICAL REVIEW B 46: 5783 (1992).
JACKSON, D.P., HYDRODYNAMICS OF FINGERING INSTABILITIES IN DIPOLAR FLUIDS, PHYSICAL REVIEW E 50: 298 (1994).
JOANNY, J.F., WEAKLY CHARGED POLYELECTROLYTES IN A POOR SOLVENT, JOURNAL DE PHYSIQUE 51: 545 (1990).
KAWAKATSU, T, PHASE-TRANSITIONS AND SHAPES OF 2-COMPONENT MEMBRANES AND VESICLES .1. STRONG SEGREGATION LIMIT, JOURNAL DE PHYSIQUE II 3: 971 (1993).
KELLER, D.J., THEORY OF SUPERSTRUCTURES IN LIPID MONOLAYER PHASE-TRANSITIONS, JOURNAL OF PHYSICAL CHEMISTRY 90: 2311 (1986).
KHOKHLOV, A.R., COMPATIBILITY ENHANCEMENT AND MICRODOMAIN STRUCTURING IN WEAKLY CHARGED POLYELECTROLYTE MIXTURES, MACROMOLECULES 25: 1493 (1992).
KITTEL, C, THEORY OF THE STRUCTURE OF FERROMAGNETIC DOMAINS IN FILMS AND SMALL PARTICLES, PHYSICAL REVIEW 70: 965 (1946).
KITTEL, C, PHYSICAL THEORY OF FERROMAGNETIC DOMAINS, REVIEWS OF MODERN PHYSICS 21: 541 (1949).
KNOBLER, C.M., PHASE-TRANSITIONS IN MONOLAYERS, ANNUAL REVIEW OF PHYSICAL CHEMISTRY 43: 207 (1992).
KOOY, C, PHILIPS RESEARCH REPORTS 15: 7 (1960).
KWAK, B.S., STRAIN RELAXATION BY DOMAIN FORMATION IN EPITAXIAL FERROELECTRIC THIN-FILMS, PHYSICAL REVIEW LETTERS 68: 3733 (1992).
LANDAU, L, PHYS Z SOWJETUNION 8: 153 (1935).
Landau, L. D., Electrodynamics of Continuous Media (1980).
LANDAU, L.D., PHYS Z SOWJETUNION 11: 129 (1937).
LANDAU, L.D., PHYS Z SOWJETUNION 11: 129 (1937).
Landau, L. D., Statistical Physics (1980).
LANGER, S.A., TEXTURES IN A CHIRAL SMECTIC LIQUID-CRYSTAL FILM, PHYSICAL REVIEW A 34: 5035 (1986).
LANGER, S.A., DYNAMICS OF LABYRINTHINE PATTERN-FORMATION IN MAGNETIC FLUIDS, PHYSICAL REVIEW A 46: 4894 (1992).
LEIBLER, L, THEORY OF MICROPHASE SEPARATION IN BLOCK CO-POLYMERS, MACROMOLECULES 13: 1602 (1980).
LEIBLER, S, ORDERED AND CURVED MESO-STRUCTURES IN MEMBRANES AND AMPHIPHILIC FILMS, JOURNAL DE PHYSIQUE 48: 2013 (1987).
LOSCHE, M, IMPURITY CONTROLLED PHASE-TRANSITIONS OF PHOSPHOLIPID MONOLAYERS, EUROPEAN BIOPHYSICS JOURNAL WITH BIOPHYSICS LETTERS 11: 35 (1984).
LUBENSKY, T.C., THEORY OF RIPPLE PHASES OF LIPID BILAYERS, PHYSICAL REVIEW LETTERS 71: 1565 (1993).
MACLENNAN, J, NOVEL STRIPE TEXTURES IN NONCHIRAL HEXATIC LIQUID-CRYSTAL FILMS, PHYSICAL REVIEW LETTERS 69: 2082 (1992).
MACLENNAN, J, CORRECTION, PHYSICAL REVIEW LETTERS 69: 3267 (1992).
MACLENNAN, J.E., TEXTURES IN HEXATIC FILMS OF NONCHIRAL LIQUID-CRYSTALS - SYMMETRY-BREAKING AND MODULATED PHASES, PHYSICAL REVIEW E 49: 3207 (1994).
Manneville, M., Dissipative Structures and Weak Turbulence (1990).
MARDER, M, THEORY OF THE INTERMEDIATE RIPPLED PHASE OF PHOSPHOLIPID-BILAYERS, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES 81: 6559 (1984).
MARKO, J.F., MICROPHASE SEPARATION OF CHARGED DIBLOCK COPOLYMERS - MELTS AND SOLUTIONS, MACROMOLECULES 25: 1503 (1992).
MARKO, J.F., PHASE-SEPARATION IN A GRAFTED POLYMER LAYER, PHYSICAL REVIEW LETTERS 66: 1541 (1991).
MATSEN, M.W., STABLE AND UNSTABLE PHASES OF A DIBLOCK COPOLYMER MELT, PHYSICAL REVIEW LETTERS 72: 2660 (1994).
MCCONNELL, H.M., STRUCTURES AND TRANSITIONS IN LIPID MONOLAYERS AT THE AIR-WATER-INTERFACE, ANNUAL REVIEW OF PHYSICAL CHEMISTRY 42: 171 (1991).
MITSUI, T, DOMAIN STRUCTURE OF ROCHELLE SALT AND KH2PO4, PHYSICAL REVIEW 90: 193 (1953).
MOHWALD, H, PHOSPHOLIPID AND PHOSPHOLIPID-PROTEIN MONOLAYERS AT THE AIR/WATER INTERFACE, ANNUAL REVIEW OF PHYSICAL CHEMISTRY 41: 441 (1990).
MOLHO, P, IRREVERSIBLE EVOLUTION IN THE TOPOLOGY OF MAGNETIC DOMAINS, JOURNAL OF APPLIED PHYSICS 61: 4188 (1987).
MULLER, P, SHAPE ANISOTROPY OF FERROELECTRIC DOMAINS IN A LANGMUIR MONOLAYER, JOURNAL OF PHYSICAL CHEMISTRY 95: 3257 (1991).
MULLER, P, 1ST MEASUREMENT OF THE LIQUID-SOLID LINE ENERGY IN A LANGMUIR MONOLAYER, PHYSICAL REVIEW LETTERS 67: 1106 (1991).
O'Dell, T. H., Reports on Progress in Physics 49: 589 (1983).
OHTA, T, EQUILIBRIUM MORPHOLOGY OF BLOCK COPOLYMER MELTS, MACROMOLECULES 19: 2621 (1986).
OUYANG, Q, CHAOS 1: 411 (1991).
OUYANG, Q, TRANSITION FROM A UNIFORM STATE TO HEXAGONAL AND STRIPED TURING PATTERNS, NATURE 352: 610 (1991).
PROST, J, STRUCTURES IN COLLOIDAL PHYSICAL-CHEMISTRY, NATURE 350: 11 (1991).
RASENAT, S, EXPERIMENTAL STUDIES OF DEFECT DYNAMICS AND INTERACTION IN ELECTROHYDRODYNAMIC CONVECTION, PHYSICAL REVIEW A 42: 5998 (1990).
REHBERG, I, PATTERN-FORMATION IN A LIQUID-CRYSTAL, FESTKORPERPROBLEME-ADVANCES IN SOLID STATE PHYICS 29: 35 (1989).
Roland, C., Physical Review B 42: 6658 (1990).
Rosensweig, R. E., Ferrohydrodynamics: CH7 (1985).
ROSENSWEIG, R.E., LABYRINTHINE INSTABILITY IN MAGNETIC AND DIELECTRIC FLUIDS, JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 39: 127 (1983).
Rosensweig, R. E., Scientific American 247:136 (1982).
SAGUI, C, KINETICS OF PHASE-SEPARATION IN 2-DIMENSIONAL SYSTEMS WITH COMPETING INTERACTIONS, PHYSICAL REVIEW E 49: 2225 (1994).
SAGUI, C, KINETICS OF TOPOLOGICAL DEFECTS IN SYSTEMS WITH COMPETING INTERACTIONS, PHYSICAL REVIEW LETTERS 71: 3995 (1993).
SEDDON, J.M., CUBIC PHASES OF SELF-ASSEMBLED AMPHIPHILIC AGGREGATES, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 344: 377 (1993).
SELINGER, J.V., CHIRAL SYMMETRY-BREAKING IN LANGMUIR MONOLAYERS AND SMECTIC FILMS, PHYSICAL REVIEW LETTERS 70: 1139 (1993).
Selke, W., Phase Transitions and Critical Phenomena 15 (1992).
SEMENOV, A. N., JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS 61: 733 (1985).
SESHADRI, R, STATISTICAL-MECHANICS OF MAGNETIC-BUBBLE ARRAYS .1. TOPOLOGY AND THERMALIZATION, PHYSICAL REVIEW B 46: 5142 (1992).
SESHADRI, R, STATISTICAL-MECHANICS OF MAGNETIC-BUBBLE ARRAYS .2. OBSERVATIONS OF 2-DIMENSIONAL MELTING, PHYSICAL REVIEW B 46: 5150 (1992).
SESHADRI, R, COLLECTIVE TRANSPORT AND SHEAR-FLOW OF MAGNETIC-BUBBLE ARRAYS, PHYSICAL REVIEW B 47: 8620 (1993).
Seshadri, R., Physical Review Letters 66: 2774 (1991).
SESHADRI, R, FORCED SHEAR-FLOW OF MAGNETIC-BUBBLE ARRAYS, PHYSICAL REVIEW LETTERS 70: 234 (1993).
SEUL, M, DYNAMICS OF DOMAIN SHAPE RELAXATION IN LANGMUIR FILMS, JOURNAL OF PHYSICAL CHEMISTRY 97: 2941 (1993).
SEUL, M, PATTERN-ANALYSIS OF MAGNETIC STRIPE DOMAINS - MORPHOLOGY AND TOPOLOGICAL DEFECTS IN THE DISORDERED STATE, PHILOSOPHICAL MAGAZINE B-PHYSICS OF CONDENSED MATTER STATISTICAL MECHANICS ELECTRONIC OPTICAL AND MAGNETIC PROPERTIES 66: 471 (1992).
SEUL, M, EVOLUTION OF DISORDER IN MAGNETIC STRIPE DOMAINS .1. TRANSVERSE INSTABILITIES AND DISCLINATION UNBINDING IN LAMELLAR PATTERNS, PHYSICAL REVIEW A 46: 7519 (1992).
SEUL, M, EVOLUTION OF DISORDER IN MAGNETIC STRIPE DOMAINS .2. HAIRPINS AND LABYRINTH PATTERNS VERSUS BRANCHES AND COMB PATTERNS FORMED BY GROWING MINORITY COMPONENT, PHYSICAL REVIEW A 46: 7534 (1992).
SEUL, M, COMPETING INTERACTIONS AND DOMAIN-SHAPE INSTABILITIES IN A MONOMOLECULAR FILM AT AN AIR-WATER-INTERFACE, PHYSICAL REVIEW LETTERS 64: 1903 (1990).
SEUL, M, EVOLUTION OF DISORDER IN 2-DIMENSIONAL STRIPE PATTERNS - SMECTIC INSTABILITIES AND DISCLINATION UNBINDING, PHYSICAL REVIEW LETTERS 68: 2460 (1992).
SEUL, M, ISOTROPIC AND ALIGNED STRIPE PHASES IN A MONOMOLECULAR ORGANIC FILM, PHYSICAL REVIEW LETTERS 70: 1658 (1993).
SEUL, M, DOMAIN COARSENING IN A 2-DIMENSIONAL BINARY MIXTURE - GROWTH DYNAMICS AND SPATIAL CORRELATIONS, PHYSICAL REVIEW LETTERS 73: 2284 (1994).
SEUL, M, DOMAIN-WALL FLUCTUATIONS AND INSTABILITIES IN MONOMOLECULAR FILMS, PHYSICA A 168: 198 (1990).
SEUL, M, MORPHOLOGY AND LOCAL-STRUCTURE IN LABYRINTHINE STRIPE DOMAIN PHASE, SCIENCE 254: 1616 (1991).
SEUL, M, unpublished data.
SINGER, S.J., LAYER BUCKLING IN SMECTIC-A-LIQUID CRYSTALS AND 2-DIMENSIONAL STRIPE PHASES, PHYSICAL REVIEW E 48: 2796 (1993).
SORNETTE, D, UNDULATION INSTABILITY IN STRIPE DOMAIN-STRUCTURES OF BUBBLE MATERIAL, JOURNAL DE PHYSIQUE 48: 151 (1987).
SORNETTE, D, STRIPE MAGNETIC DOMAINS AND LYOTROPIC LIQUID-CRYSTALS, JOURNAL DE PHYSIQUE 48: 1413 (1987).
SRAJER, G, FIELD-INDUCED 1ST-ORDER PHASE-TRANSITION AND SPINODAL POINT IN NEMATIC LIQUID-CRYSTALS, PHYSICAL REVIEW LETTERS 67: 1102 (1991).
STINE, K.J., BUCKLING INSTABILITY IN MONOLAYER NETWORK STRUCTURES, PHYSICAL REVIEW LETTERS 65: 1004 (1990).
SWIFT, J, HYDRODYNAMIC FLUCTUATIONS AT CONVECTIVE INSTABILITY, PHYSICAL REVIEW A 15: 319 (1977).
TANIGUCHI, T, PHASE-TRANSITIONS AND SHAPES OF 2-COMPONENT MEMBRANES AND VESICLES .2. WEAK SEGREGATION LIMIT, JOURNAL DE PHYSIQUE II 4: 1333 (1994).
TER HAAR, D, LANDAU COLLECTED PAPERS 18 (1965).
TER HAAR, D, LANDAU COLLECTED PAPERS 30 (1965).
THIELE, A.A., THEORY OF CYLINDRICAL MAGNETIC DOMAINS, BELL SYSTEM TECHNICAL JOURNAL 48: 3287 (1969).
THIELE, A.A., THEORY OF STATIC STABILITY OF CYLINDRICAL DOMAINS IN UNIAXIAL PLATELETS, JOURNAL OF APPLIED PHYSICS 41: 1139 (1970).
Thomas, E. L., Nature 334:598 (1988).
THOMAS, E.N., PHYS TODAY 21: 27 (1990).
VANDERBILT, D, PHASE SEGREGATION AND WORK-FUNCTION VARIATIONS ON METAL-SURFACES - SPONTANEOUS FORMATION OF PERIODIC DOMAIN-STRUCTURES, SURFACE SCIENCE 268: L300 (1992).
VANDERLICK, T.K., MODE SELECTION AND SHAPE TRANSITIONS OF PHOSPHOLIPID MONOLAYER DOMAINS, JOURNAL OF PHYSICAL CHEMISTRY 94: 886 (1990).
WEBER, A, DEFECTS IN CONTINUOUS MEDIA, ADVANCED MATERIALS 3: 191 (1991).
WEIS, R.M., CHOLESTEROL STABILIZES THE CRYSTAL LIQUID INTERFACE IN PHOSPHOLIPID MONOLAYERS, JOURNAL OF PHYSICAL CHEMISTRY 89: 4453 (1985).
WEIS, R.M., TWO-DIMENSIONAL CHIRAL CRYSTALS OF PHOSPHOLIPID, NATURE 310: 47 (1984).
ZASADZINSKI, JAN, RIPPLE WAVELENGTH, AMPLITUDE, AND CONFIGURATION IN LYOTROPIC LIQUID-CRYSTALS AS A FUNCTION OF EFFECTIVE HEADGROUP SIZE, JOURNAL DE PHYSIQUE 48: 2001 (1987).
ZEPPENFELD, P, SIZE RELATION FOR SURFACE SYSTEMS WITH LONG-RANGE INTERACTIONS, PHYSICAL REVIEW LETTERS 72: 2737 (1994).
ZIMMERMANN, W, MRS BULLETIN 16: 46 (1991).

(0)eLetters

eLetters is a forum for ongoing peer review. eLetters are not edited, proofread, or indexed, but they are screened. eLetters should provide substantive and scholarly commentary on the article. Embedded figures cannot be submitted, and we discourage the use of figures within eLetters in general. If a figure is essential, please include a link to the figure within the text of the eLetter. Please read our Terms of Service before submitting an eLetter.

Log In to Submit a Response

No eLetters have been published for this article yet.

Information & Authors

Information

Published In

Science
Volume 267 | Issue 5197
27 January 1995

Submission history

Published in print: 27 January 1995

Permissions

Request permissions for this article.

Authors

Affiliations

Michael Seul
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
David Andelman
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel. Also at Section de Physique et Chimie, Institut Curie 11, rue Pierre et Marie Curie, 75231 Paris Cedex 05, France

Metrics & Citations

Metrics

Article Usage

Altmetrics

Citations

Cite as

Export citation

Select the format you want to export the citation of this publication.

Cited by

  1. Growth of self-integrated atomic quantum wires and junctions of a Mott semiconductor, Science Advances, 9, 18, (2023)./doi/10.1126/sciadv.abq5561
    Abstract
  2. Spontaneous evolution of equilibrium morphology in phospholipid-cholesterol monolayers, Science Advances, 8, 14, (2022)./doi/10.1126/sciadv.abl9152
    Abstract
  3. Helical Nanofilament Phases, Science, 325, 5939, (456-460), (2021)./doi/10.1126/science.1170027
    Abstract
  4. All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes, Science Advances, 6, 31, (2020)./doi/10.1126/sciadv.aba2331
    Abstract
  5. Phase and Morphology Changes in Lipid Monolayers Induced by SP-B Protein and Its Amino-Terminal Peptide, Science, 273, 5279, (1196-1199), (1996)./doi/10.1126/science.273.5279.1196
    Abstract
  6. Nanoscale Magnetic Domains in Mesoscopic Magnets, Science, 272, 5269, (1782-1785), (1996)./doi/10.1126/science.272.5269.1782
    Abstract
  7. Nonequilibrium Structures in Condensed Systems, Science, 272, 5268, (1596-1597), (1996)./doi/10.1126/science.272.5268.1596
    Abstract
Loading...

View Options

Check Access

Log in to view the full text

AAAS ID LOGIN

AAAS login provides access to Science for AAAS Members, and access to other journals in the Science family to users who have purchased individual subscriptions.

Log in via OpenAthens.
Log in via Shibboleth.

More options

Purchase digital access to this article

Download and print this article for your personal scholarly, research, and educational use.

Purchase this issue in print

Buy a single issue of Science for just $15 USD.

View options

PDF format

Download this article as a PDF file

Download PDF

Media

Figures

Multimedia

Tables

Share

Share

Share article link

Share on social media