Isotropic Droplets in Thin Free Standing Smectic FilmsHeidrun Schu¨ring and Ralf Stannarius*Universita¨t Leipzig, Institut fu¨r Experimentalphysik I, Linne´str. 5, D-04103 LeipzigReceived June 7, 2002. In Final Form: September 17, 2002Isotropicliquiddropletsareformedbydifferentmechanismsnearthesmectic-isotropicphasetransitionin smectic freely suspended films. Because of the layered structure of the smectic films, the interplay oftensions that determines the droplet geometry is essentially different from that of liquid droplets on solidor isotropic liquid surfaces. By means of interferometric measurements, the three-dimensional dropletgeometryisdetermined.Amodelisproposedthatdescribesthedropletshapes,andtherelevantparametersare discussedon the basisof experimental data.We derive surfaceand interface tensionsof low molecularmass and polymeric mesogens and provide a molecular interpretation. In particular, the small differencebetweensurfacetensionsinthesmecticandisotropicphasesisaccessiblewiththemethod;itcanberelatedto the structure of the isotropic liquid to air interface of smectogens. Capillary forces causing a lateralmotion of droplets in inhomogeneously thick films are discussed. A trapping mechanism is described thatlines up the droplets at film thickness steps.1. IntroductionSmecticfree-standingfilmsrepresentthinorderedfluidlayers that can be prepared with macroscopic lateraldimensions (up to several square centimeters film area),and a thickness between two and more than thousandmolecularlayers.ThesmecticAphaseischaracterizedbya two-dimensional isotropic liquid disorder within thelayers, where the preferred orientation of the mesogensis normal to the free-standing film plane.In particular, these films are well suited to studyinfluences of decreasing dimensionality on phase transi-tionsandsurfacepropertiesofliquidandliquidcrystallinematerials. At the phase transition to the nematic orisotropic phase, the smectic layer order melts, and undercertain conditions, one can observe the formation ofnematicorisotropicliquidinclusionsinthefilm.Althoughthesedropletsdonotnecessarilyrepresentthermodynamicequilibrium structures, their lifetimes between severalminutes and hours allow us to study their shape anddynamics,whichprovidesvaluableinformationonsurfaceand interface tensions of the involved liquid and liquidcrystallinephases.Thestratified structure of the smecticfilms has important consequences for the geometricalappearance of the droplets.Equilibrium shapes of droplets in various liquid crys-talline bulk phases, including the “inverse” problem ofsmectic droplets in an isotropic liquid bulk, and theirrelations to surface and interface tensions have beenstudied theoretically as well as experimentally (e.g., seerefs 1-7). Similar to colloids, the isotropic droplets caninteract and self-organize themselves to ordered struc-tures.Whereasithasbeenshownthatdropletsofisotropicliquids embedded in a nematic bulk phase interact vialong-range but comparably weak elastic forces of thenematic director field,8-10the much stronger long-rangeforcesonparticles(orliquidinclusionsasconsideredhere)orbetweentheminthinfree-standingfilmsareprimarilyof capillary origin. We will show that they provide atrapping mechanism that pins the droplets to filmthickness steps. Because the dynamics of droplet motionis mainly determined by the supporting film and not bytheir inner structure, there is a direct relation to forceson solid particles suspended in liquid films, which havebeen described and measured, e.g., by Sur et al.11Interactions and self-organization of particles on thinorganic films have been discussed in the context ofbiologicalmembranes,12whereinteractionsofmembraneinclusions are mediated via deformations of the mem-brane.The high stability and well-defined discrete thicknessof smectic membranes makes them ideal model systemsfor quantitative studies of the involved viscous andcapillaryforces.Theformationofliquiddropletsinsmecticfilmshasbeenobservedearlier,13-15buttheiractualthree-dimensionalgeometryandtheinterplayofforcesbalancingthe stationary droplet shape have been disregarded sofar. We will show that, from their shapes and theirarrangement on thin smectic films, surface and interfacetensions are accessible.The paper is organized as follows: After a descriptionof the preparation and experimental setup, we presentexperimental data of isotropic droplets for differentmesogenic materials and analyze them qualitatively.Section 4 introduces models for the droplet shape, whichareevaluated onthe basisof theexperimental results.Inthe fifth section, the arrangement of droplets on filmswithdiscrete,inhomogeneousthicknessisdescribed,andtheroleofcapillaryforcesforthemotionofdropletsinthefilmplaneisdiscussed.Thefinalsectiongivesamolecular* To whom correspondence should be addressed.(1) Friedel, G.; Grandjean, F. Bull. Soc. Mineral 1910, 33, 409.(2) Oswald, P. J. Phys. France 1988, 49, 1083.(3) Oswald,P.;Melo, F.;Germain,C.J. Phys. France 1989,50, 3527.(4) Fournier, J.; Durand, G. J. Phys. France II 1991, 1, 845.(5) Buka, A.; Toth-Katona, T.; Kramer, L. Phys. Rev. E 1994, 49,5271.(6) Sallen, L.; Oswald, P.; Ge´minard, J. C.; Maltheˆte, J. J. Phys.France II 1995, 5, 937.(7) Blanc, C. Phys. Rev. E 2001, 64, 011702.(8) Poulin, P.; et al. Science 1997, 275, 1770.(9) Poulin, P.; Weitz, D. A. Phys. Rev. E 1998, 57, 626.(10) Stark, H. Phys. Rep. 2001, 351, 387.(11) Sur, J.; Pak, H. K. Phys. Rev. Lett. 2001, 86, 4326.(12) Schiller, P. Phys. Rev. E 2000, 62, 918.(13) Cluzeau, P.; Dolganov, V.; Poulin, P.; Joly, G.; Nguyen, H. T.Mol. Cryst. Liq. Cryst. 2001, 364, 381. Dolganov, V. K.; Demikhov, E.I.; Fouret, R.; Gors, C. Phys. Lett. A 1996, 220, 242.(14) Najjar, R.; Galerne, Y. Mol. Cryst. Liq. Cryst. 2001, 367, 475.(15) Pankratz, S.; Johnson, P. M.; Paulson, A.; Huang, C. C. Phys.Rev. E 2000, 61, 6689.9735Langmuir 2002, 18, 9735-974310.1021/la0260436 CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 11/13/2002interpretation of the measured surface tensions andsummarizes the results.2. Sample Preparation and ExperimentTheprimaryaspectfortheselectionofthemesogenicmaterialswasthedirectsmecticAtoisotropictransition.Thisrestrictsthenumber of suitable mesogens. Several low molecular massmesogens with different chemical structures have been inves-tigated. The formation of isotropic droplets near the clearingpoint has been observed without exceptions, and
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