Report

Capillary Interactions between Anisotropic Particles Kathleen J Stebe Chemical and Biomolecular Engineering University of Pennsylvania Acknowledgements • • • • • • • Eric Lewandowski-experiment, analysis Marcello Cavallaro-curvature gradients, confinement Lorenzo Botto-simulation, analysis Valeria Garbin-(Crocker)-interferometry Lu Yao-crowded surfaces, registry, repulsion Jorge Bernate-surface evolver Alice Tseng- environmental SEM MRSEC facilities at JHU/PENN; NSF On the attraction of floating particles W. A. Gifford and L. E. Scriven Chem. Eng. Sci. 1971, 26, 287. Received 8 August 1970; accepted 17 August 1970. Capillary attraction between floating particles, a phenomenon of everyday experience as well as technological importance, is caused by interfacial tension and buoyancy forces ... Bo grp 2 Finite Bo: sphere or infinite cylinder • • • • Nicolson Proc Camb Phil Soc 45 (1949) Gifford and Scriven Chem. Eng. Sci., 26, 287 (1971) Chan et al J. Colloid Interface Sci. 79 (1981) Singh and Joseph Journal Fluid Mech. 530 (2005) sphere or disk Slope Area Finite weight particles ga 2 Bo small h Bo h 2 h aK o ( ALV 1 A r lcap ) b A ln(r ) r lcap h h dA ~ Aplane Aexcess 2 Small slope; superposn h h (hh) h 2 h Ep Ep 2 hA hB dA Particles move in potential energy gradient created by their neighbor (or by a boundary) A h h 2 A n ds B S E p hAo h 2 B n ds Like beads on a strong- slide to low potential energy site Nicolson 1949; Chan et al 1981 S hAo Ep Fz 2 Bubbles, cheerios, froth flotation, .. Bo 0? Particles at free-surfaces • Particle-stabilized emulsions Ramsden (1904); Pickering (1907) • Bubbles Nicolson Proc Camb Phil Soc 45 (1949) • Current interest using microparticles: BINKS Special edition PCCP 2008 • Froth flotation Gifford and L. E. Scriven (1971) Chan et al (1981) Singh and Joseph (2005) Cheerios effect Capillary interactions-thin films Kralchevsky, Nagayama and collaborators 1990sWasan: argues not formed by capillary attraction nuclei Whitten, Deegan, Dupont: coffee rings... Negligible Bond number- capillary interactions Lucassen, Colloids and Surfaces 1992 Stamou et al: long range qp deflections Phys. Rev. E 2000 Dietrich, Oettel, and collaborators-ellipsoids Kralchevsky and collaborators-weakly non-spherical shapes Binks and collaborators Ellipsoids Hilgenfeldt Europhys.Lett. 72, 671 (2005) Loudet* et al. Phys. Rev. Lett. 2005, 2006, 2009 Lehle et al Eur Phys Lett 2008 Vermant, Fuller, Furst-assembly and rheology Complex shapes Whitesides: Bowden et al. Functionalized mm-particles Science 1997, Langmuir 2001+~20 more Rennie (2000); Fournier (2002): bi-metal microparticlesform qp Lewandowski et al Langmuir 2008, Soft Matter 2009 Interfacial deflections created by particle 2 H gh recast in non d form; L c rp Stamou, PRE 62, 2000 Quadrupolar deflection: long range perturbation 2 H Bo h Bo grp 2 small slope, small Bond number 2h 0 A hlong range 22 cos(2 2 r h(r , ) A0 ln r Ak r k cos(k k ) k 1 tds 0 Stamou, Duschl, Johannsmann, PRE 2000 Kralchevsky et al Langmuir 2001 Far field interactions h h Stamou, PRE 62, 2000 A 1 dS ~ A 2 LV Aexcess AAB plane S h h dA 2 2 hAhB n A d r12 Superposition approx. CA 2hB : curvature tensor of B at A Interaction Energy Force of Attraction Aexcess A weighted integral particle A's deformation Stamou E12 Aexcess F12 rp 2 12 H p cos 2(1 2 ) r12 4 dAexcess dr12 r 2 1 p 48 H p cos 2(1 2 )rp r12 1 2 5 Excess area drives interactions but no preferred orientation Undulated contact lines: pronounced for non-spherical particles interferograms Micro-Ellipsoids: Loudet and Yodh . 2005, 2006 Floating poppy seed ~1mm (Hinsch, 82) Rennie: curved particles Micro-Cylinders: Stebe lab Lithographic Fabrication of Particles SU-8 photoresist Silicon Wafer UV light Mask SU-8 photoresist Expose resist through mask Silicon Wafer Develop photoresist SU-8 Particles Silicon Wafer Sonicate in EtOH to free particles Cylinders at fluid interfaces: Two mechanically stable states End On Bo grp 2 negligible Preferred orientation: GCP Compare SiAi for each state Side On Orientation of partially wet cylinders Side On End On Analytical assume -Flat interface along cylindrical body -Ends fully wet or de-wet - Neglect excess L/V area Minimum surface energy - Surface Evolver, contact angle L/V interface approximation - Equate holes in interface 2rL sin r 2 2L 1 x r sin Neglect Gravity Bo 1; (P L ) L Bo 1 Phase diagram Lewandowski, et al JPC B 2006; Langmuir in press x=1.2, =80o,r=3.5mm x=0.2, =110o,r=150nm x=1.3, =80o, r=3.5mm x=2.8, =110o,r=150nm End-to-end chaining of cylinders Undulated contact line owing to particle shape r12init ~ 180mm L/D ~ 2.5 50μm Lewandowski et al, Soft Matter, 5, 2009 Shape of interface around isolated cylinder =80o Interface topology satisfying contact angle not unique Surface evolver simulation, const P, Neumann conditions far field Minimum surface energy configuration Environmental SEM Interferometric Measurement of Interface: V. Garbin, J. Crocker, interferometry Far field: Quadrupolar Attraction r12 C t tc F12 Fdrag dr12 r12 ~ dt dt ~ r125 dr12 5 dr12 Cd 6 Rcyl m dt r12 C t tc 1 1 2 6 E (r12 ) r ELLIPSOIDS: C. Loudet et al, PRL, 018301, 2005 Extract magnitude of far field interaction energy Viscous dissipation i E Drag 6m R v (r ')dr ' 2.16 0.65 x105 kT CD rf r 0.6E Drag 2.24 0.67 x 105 kT CD=1.73 for L=3 Heiss and Coull Youngren and Acrivos Cylinder~ 60% immersed Capillary interaction energy ( L / D 1)2 4 1 1 5 E 12 H 1 R 0.985x10 kT 2 4 4 ( L / D 1) r12, f r12,i Asymptotic exp 2 p predicted Isoheight contours around cylinder a 2L Divide deformation field into 2 domains: exterior: elliptical quadrupolar deformation: 2-3 radii outside of ellipse circumscribing cylinder – (very) far field: cylindrical polar qp b 2D excess area map Elliptical quadrupolar deformation L:2R=5 near field: large area concentration at ends Quadrupoles in Elliptical Coordinates: End-to-end until nr contact Trajectory computed as: t E x 6m RfT x n φA n n 1 t E 8m R3 f R n φA+φB n (used experimentally measured drag coeffs ft & fr) Angle x n 1 Black line: simulation Colored symbols: experiment φB Dynamic simulation and experiment Time (secs) Simulation Experiment Rotation: very local; decays steeply Not in real time (slowed down X4) Lewandowski et al Langmuir 2010 Quadrupoles in Elliptical Coordinates: Side-to-Side on close approach Charged? Ellipsoids: Loudet Vermant uncharged Our analysis (ellip qps): Tip-to-tip preferred for separations >major axis Side-to-side preferred for separations < major axis EQP not full story Interface near contact gradient magnitude cylinder 1 cylinder 2 in-plane bending capillary bridge Lorenzo Botto, KJS, in prep Critical torque and yielding PREDICTIONS: yield torque Tc Constant torque experiment T>Tc strain softening (stress) critical bending moment should break chain f (strain) cylinder should snap to side-to-side Surfactant Mediated Arrest and Recovery of Capillary Interactions PDA on pH 2: Insoluble Surfactant Brewster Angle Microscopy Nguyen et al. PRL 1992, 4, 419 1. PDA creates a tangential immobile surface 2. NaOH deprotonates PDA (increased solubility) 3. SU-8 rods form ordered assemblies Lewandowski et al Soft Matter 2009 Magnet integrated into chain With Yao LU; w R LEHENY, unpublished Microstructure: rod-like particles cylinders ellipsoids “Polygonal” networks “Bamboo ” “Wormy ” chains- Jan Vermant Private commun vs. sphero-cylinders Rectangular arrays no deformation no interactions Other shapes: Fourier modes • Lucassen Colloids and Surfaces 65, 1992 – Interaction between sinusoidal contact lines – liquid-vapor surface area minimized f Frequency Amplitude In phase – Particles end face registry Particle Recognition f 0 Complex Shapes: Registry Far field interactions Quadrupolar in nature b = -3.75 Complex Shapes: Registry Interfacial deflections around cylinder n t nparticle t sin h h dS S 2 Aexcess 1/2 L flat L curve hcurved Lcurved ~ h flat L flat Steepest slope always on shortest face AEXCESScurve ~ AEXCESSflat Aspect ratio dictates preferred location: shortest face preferred L flat Preferred alignment Lcurve ALVcurve ~ ALVflat Curved side to curved side L flat Lcurve 1 L flat 4 L curve AEXCESS curve 1 AEXCESS flat L flat Lcurve 1 Flat side to flat side AEXCESS curve 1 AEXCESS flat Preferred location is shortest face L flat 0.66 L curve Surface Evolver Results: Confirm Slope Argument Steepest slope always on shortest face h 1 0.66 2.0 4.0 d Langmuir 2008 Glass Walls Glass Walls Cylinder alignment on curved interfaces Cylinder alignment on curved interfaces ALV depends on cylinder alignment ALV for a quadrupole on curved interface in small slope limit ALV C ALV o cos 2 4 Tcyl LV dALV LV C cos sin d Torque Two mechanical equilibria: 0 perpendicular to wall /2 parallel to wall Stable state: depends on sign of C d 2 ALV C cos 2 2 d C 4 rp 2 Hp R in agreement with experiment Alignment of ‘biscotti’ shaped particles A saddle on a saddle Alignment as a function of particle size E / kT -Background curvature 103 times particle radius Lewandowski et al. Langmuir 2008 Rparticles=3.5mm Cylinder assembly on curved interfaces 1 2 3 5 6 weak curvature 1 4 Strong curvature 1 2 3 In summary,the particle contribution to the total energy is 1 1 E p hcm Fz S Txy h0 ( x p ) : Π 2 2 This form reveals a structure that is very familiar in the study of electrostatics. •The force "interacts" with the height, • the torque "interacts" with the slope, •The quadrupole moment "interacts" with the curvature tensor. The first term is leading order for heavy isotropic particles, and corresponds to that derived by Nicholson. The second term is important for anisotropic particles acted upon by an external torque. For an anisotropic force- and torque-free particle, the first two terms are identically zero and the particle contribution to the energy becomes Ep h0 ( x p ) : Π Botto Conclusions • Ellipsoids vs. cylinders Cylinders: hierachy of interactions- elliptical quadrupolar/near field • Chaining: cemented by near field interactions • Preferred orientation: f(aspect ratio of particle) • Curvature gradients: Motion and alignment • Complex shapes: Registry of end-face features Cylinders on water drop in oil shapes with corners Current work: • complex particles • repulsion • crowded surfaces-gels • docking sites • mechanics of assemblies • scale Open issues: gels, networks, rheology, dense packings Charged Ellipsoids -percolating networks -open flower like structures -elastic, brittle interfaces Jan Vermant, Gerry Fuller at water-decane interface, -becomes denser with time on a water drop in oil Cylinders -rectangular lattices -ropes of chains -open networks at air water interface, spread, compressed to collapse compression isotherms, rheology, role of charge Other shapes at air water interface, with DPPC spread, compressed on a water drop in oil Far field: cylindrical polar quadrupolar mode Extract Fourier modes from numerical solution: r > 9Rcyl Hp r2 2 0 h(r , ) cos 2 d r ~ 9Rcyl At r ~ 9Rcyl , higher modes 5% contribution 4 L 6 R L L 2R Rate of approach: far field Fixed Aspect Ratio Varied Aspect Ratio L (t(t-t c) c-t) Faster approach as L increases: consistent with Hp increase Interactions of elliptical quadrupoles vs. r12 r12 2L Solid line ends at tip-to-tip contact end-to-end alignment favored r12/R Torque enforces end to end alignment Steric effects Steric effects imposed by anisotropic hard core repulsion Potential= Ellip Quadrupoles+ Repulsion preventing contact x 2/ y 2/ F 1 0 b a 0 superellipses cylinder surface of revolution =0.2 Asymptotics of interaction energy L/D Expansion in powers of 1/r12 : Eside to side 4 L / D 12 L2 R L / D 12 R 2 1 2 1 40 H 12H p 1 2 r p 2 12 L / D 1 D L / D 1 r12 Eend toend L / D 12 L2 L / D 12 R R 2 1 2 1 40 H 12H 1 2 r p 2 12 L / D 1 D L / D 1 r12 E 6 ~ 1 / r12 Torque ~ 6 2 4 6 2 p Torque decays faster (as 1/r6) than force (1/r5) Torque has strong aspect ratio (L=L/D) dependence T ~ 80 2 He R2 L(L 1) R 2 r L 1 12 2 3 6 Anisotropic pair potential after contact before contact Tip contact 104 kT H p2 ~ R 2 ~ 107 kT End-to-end favored until tip-to-tip contact (Langmuir 2010)