Depletion forces induced by spherical depletion agents

Transcription

1 Depletion forces induced by spherical depletion agents Laurent Helden Jules Mikhael. Physikalisches Institut Universität Stuttgart Model system for hard core interactions accessible fortirm-measurements. Hard (purely entropic) spheres as depletion agent Charged spheres as depletion agent Comparison with charged polymers as depletion agent

2 Typical particle wall interaction potentials Potential for hard core interactions Potential [k B (a) (b) 65 nm 8 k B T 5 nm 8 k B T κ -1 = 3 nm κ -1 = 11 nm deep v.d.waals-minimum Distance z [µm] Superposition of gravity electrostatics van der Waals The range of interactions determines which force is dominant. Probe particle samples out about 8 k B T Metastable situation Φ els ( z) = Bexp( κ z) 1 κ = kt B πe ε 1 c salt Screen van der Waals!

3 Design of a system with hard core interactions screening of van der Waals attraction index-matching (good compatibility of DMF and SiO ) screening of electrostatics high salt stable and suitable probe particles Silica particles as indexmatched depletion agent. total internal reflection at glass-silica interface Solvent: dimethylformamid, (DMF) n~1,3 evanescent wave Salt: LiCl a=1.85µm PS-DVB n=1.59 glass substrate n=1,51

4 Potential [k B Screening of electrostatics (no depletion agent added) LiCl concentration mm.1 mm.5 mm 1 mm 5 mm 1 mm mm.m LiCl screen electrostatics very short ranged repulsion (solvation forces) no attractive parts (no v.d. Waals) System is good candidate to study purely entropic interactions Distance z [µm] Increasing salt concentration reduces screening length. Particle wall distance becomes smaller. Φ els ( z) = Bexp( κ z) κ = π e ε kt B c salt Potential [k B Distance z [µm]

5 Now add 86nm diameter silica spheres Solvent: dimethylformamid, (DMF) n~1,3 a=1.85µm PS-DVB n=1.59 evanescent wave Salt: LiCl glass substrate n=1,51

6 Potential (k B T) Bidisperse spheres, entropic, low densities 6 -,% exp. Fit repulsion,3% exp.,3% AO,3% exp.,3% AO = 1mM LiCl < 5% vol. d=r=86nm SiO spheres as depletion agent. Thanks to: M. Oversteegen, C. Vonk, H.N.W. Lekkerkerker (Utrecht) for clean, high density dispersion. a=3.7µm PS-DVB probe particle. Potential (k B T) Distance in (µm) 1mM LiCl, 5.6% vol Distance [µm] high aspect ratio a/r=3. Highest possible volumefraction 5.6% Average density of solvent and depletion agent matches probe particle density

7 Potential (k B T) Varying interactions: from entropic to charged systems 8.3% no salt.1 mm.5 mm 1 mm 5 mm 1 mm.1%, 1 mm Distance [σ], σ =86nm good approximation to entropic system Potential [k B 8 Lower salt concentrations. Larger Debye length. Stronger and longer ranged - electrostatic interactions. a More structure in -8-1 Compare hard spheres at higher, effective volume fractions - Depletion.% z agent - Interaction potential Deeper potential Distance wells z [µm].1% a= 185nm, 8.% r= 3nm, 11.% a/r= 3d 16.% d=r=86nm SiO spheres as depletion agent a=3.7µm PS-DVB probe particle high aspect ratio a/r=3 Thanks to: M. Oversteegen, C. Vonk, H.N.W. Lekkerkerker (Utrecht) Mapping on hard sphere system can explain some features, but wrong spacing choice of effective volumefraction remains empirical. it can not account for the shift in absolute particle wall distance.

8 Varying volumefraction at fixed salt concentration (5µM, κ -1 =13.nm) Potential [k B onset of replusion Volume fraction,7%,17%,35%,5% a = 3.7 µm r = nm κ 1 salt =13.nm ( 5 µm LiCl) Absolute distance [σ], σ = nm nm SiO spheres (Ludox TMA) as depletion agent 3.7µm PS-DVB probe particle, high aspect ratio a/r= 168

9 Varying volumefraction at low salt concentration / strong coupling Potential [k B Not sampled because of the height of the repulsion barrier Absolute distance [σ], σ =nm nm SiO spheres (Ludox TMA) as depletion agent 3.7µm PS-DVB probe particle high aspect ratio a/r= 168 ξ Volume fraction,3%,58%,98% 1,85% a = 3.7 µm r = nm κ 1 >nm The stronger the electrostatic interaction the more correlations and structure is in the potentials. Stronger effect and smaller spacing at higher volumefractions. Counterions reduce debye length Hidden potential wells near the surface Qualitative understanding of all trends, but no rigorous theory (so far).

10 Period of oscillation (nm) Volume fraction (%) Oscillation Period ξ no salt potentials 5 µm potentials 1 µm potentials Linear Fit F Close to bulk scaling found in some polymer depletion systems ξ c 1 3 Experimental scaling of correlation length with concentration/volumefraction Period of oscillation (nm) ξ 15 1 c.3±. no salt potentials 5 µm potentials 1 µm potentials Linear Fit Bulk spacing Volume fraction (%)

11 Comparison with charged polymer systems Oscillatory depletion forces for increasing concentration of Na PSS In charged systems many features appear to be general i.e independent of the detailed form of the depletion agent (spheres, polymers, rods...) Potential [k B Potential (k B T) % Not sampled because of the no salt height of the - repulsion barrier mm mm mm mm Absolute distance [σ], σ =nm 1 mm.1%, 1 mm Distance [σ], σ =86nm Compare also AFM: Piech, Walz J. Phys. Chem. B 18 () "The Oscillatory Packing and Depletion of Polyelectrolyte Molecules at an Oxide-Water Interface Biggs, Dagstine, Prieve, J. Phys. Chem. 16, ().

12 Summary bidisperse spheres Lower salt concentrations lead to larger screening length and stronger coupling / correlations. Higher volumefractions lead to stronger attraction and shorter length scale for oscillations. (Counterions also reduce screening length.) Mapping on entropic system with effective volume fraction does not work. Interesting similarities to depletion systems with charged polymers. However on a qualitative level all trends are well understood.