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Utrecht-LMC-July052
Stabilizing colloids against van der Waals
1. Charge Stabilization
DLVO potential (1940’s)
Derjaguin
Landau
Verwij
Overbeekpicture1968
Utrecht-LMC-July053
Stabilizing colloids against van der Waals
1. Charge Stabilization
2. Steric Stabilization
3. Nano-halo Stabilization?
Utrecht-LMC-July054
V. Tohver, J. Lewis et al. (2001) Proc. Natl. Acad. Sci. USA 98, 8950-8954
Nano-particle halo stabilization?
depletion
v.d. Waals
3 n
m n
an
opart
icle
s
285 nm colloids
Utrecht-LMC-July055
V. Tohver, J. Lewis et al. (2001) Proc. Natl. Acad. Sci. USA 98, 8950-8954
Nano-particle halo stabilization?
1. Uncharged colloids
2. Charged nano-particles
3. Extreme size-ratios
4. Re-entrant attraction
5. Low surface coverage
Featuresdepletion
v.d. Waals
3 n
m n
an
opart
icle
s
285 nm colloids
Utrecht-LMC-July056
Today’s Questions: Do these experiments show a new kind of stabilization? Are the features universal? Can this be used more broadly?
(this talk hopes to inspire experimentalists)
Nano-particle halo stabilization?
Outline of talk:
1. Intro to the experiments
2. Calculating effective interactions beyond simple depletion
3 Features of the nano-particle halo mechanism
4. Conclusion: answers to questions above: yes
Utrecht-LMC-July057
• Veff(r) depends on Vss(r), Vbs(r),
• Total potential: V(r) = Vbb(r) + Veff(r)
Vss(r) =0, Vbs(r) = VHS(r) gives Asakura Oosawa model depletion (A. Vrij 1976 – also in Utrecht)
Calculating effective potentials beyond simple depletion
€
ρs
Utrecht-LMC-July058
• Veff(r) depends on Vss(r), Vbs(r),
• Total potential: V(r) = Vbb(r) + Veff(r)
•HS + Yukawa is flexible
Calculating effective potentials beyond simple depletion: HS + Yukawa model
€
ρs€
Vbs(r) = VbsHS (r) +
ε bsσ bsr
exp −(r −σ bs)
λ bs
⎡
⎣ ⎢
⎤
⎦ ⎥
Vss(r) = VssHS (r) +
ε ssσ ssr
exp −(r −σ ss)
λ ss
⎡
⎣ ⎢
⎤
⎦ ⎥
Utrecht-LMC-July059
Two strategies for repulsive potentials
Simple depletion:
€
q =σ sσ b
= 0.2
Simulations for
Utrecht-LMC-July0510
Two strategies for repulsive potentials
1. Small-small repulsion
€
q =σ sσ b
= 0.2
€
q =σ sσ b
= 0.2
Simulations for
Utrecht-LMC-July0511
Two strategies for repulsive potentials
2. big-small attraction
€
q =σ sσ b
= 0.2
€
q =σ sσ b
= 0.2
Simulations for
Utrecht-LMC-July0512
Flexible ways to calculate Veff(r)?
Great many parameters
Needs a flexible method: simulations too slow
We finally settled on HNC integral equations
• Works well for soft repulsions
• Works well for low density
• Flexible and fast
Utrecht-LMC-July0513
Accuracy of HNC integral equations
€
q =σ sσ b
=1
5= 0.2
βε ss = 3
λ ss = 0.33σ ssλ bs = 0.8σ ss
φs =π
6ρsσ ss
3 = 0.1
HNC works well for soft repulsions
small-small repulsion
Utrecht-LMC-July0514
Accuracy of HNC integral equations
Conclusion: HNC works well for low densities and extreme size-ratios q trustworthy for qualitative effects
pure HS
q=0.01
Utrecht-LMC-July0515
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
€
q =σ sσ b
=1
100
βε ss = 6
λ ss = 5σ ss
φs =π
6ρsσ ss
3
small particle packing fraction is varied
Utrecht-LMC-July0516
using strategy 1 (small-small repulsion)
€
q =σ sσ b
=1
100
βε ss = 6
λ ss = 5σ ss
φs =π
6ρsσ ss
3
small particle packing fraction is varied
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Utrecht-LMC-July0517
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
€
q =σ sσ b
=1
100
βε ss = 6
λ ss = 5σ ss
φs =π
6ρsσ ss
3
small particle packing fraction is varied
Stabilization?
Utrecht-LMC-July0518
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Stabilization?
Utrecht-LMC-July0519
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Utrecht-LMC-July0520
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Utrecht-LMC-July0521
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Utrecht-LMC-July0522
using strategy 1 (small-small repulsion)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
Correlation attraction: (not depletion!)
€
∝φ2
Utrecht-LMC-July0523
Bridging
We can engineer almost any potential shape we want!
using strategy 2 (big-small attraction)
S. Karanikas and AAL, Phys. Rev. Lett. 93, 248303 (2004)
€
λbs = λ ss
€
λbs = 3λ ss
Utrecht-LMC-July0524
using strategy 2 (big-small attraction)
J. Liu and E. Luijten , Phys. Rev. Lett. 93, 247802 (2004)
q=0.01
Utrecht-LMC-July0525
using strategy 2 (big-small attraction)
J. Liu and E. Luijten , Phys. Rev. Lett. 93, 247802 (2004)
It’s amazing HNC works so well!
metastability reminiscent of DLVO?
Utrecht-LMC-July0527
Properties of the “nano-particle halo”
•halo = average accumulation at surface
•halos are very dilute
•Stabilisation does not correlate with detailed halo properties
•halos are fluctuating or “dynamic”
For same set of parameters 2d packing is almost same
but stabilization window is not!
Utrecht-LMC-July0529
Will stabilization persist in non-equilibrium?
Smaller particles (larger diffusion coefficients) will be better.
Large stabilization windows will be more robust
For more on hydrodynamics +Brownian forces see
poster P11.6 with Johan PaddingQuickTime™ and a
YUV420 codec decompressorare needed to see this picture.
Utrecht-LMC-July0530
Stabilization by nano-particle halos?: yes! Conclusions:
•Nano-particle halo mechanism is fundamentally different from previous steric and charge stabilisation.
•Adding nanoparticles helps engineer potentials:
•Depletion attraction
•Accumulation repulsion (can be re-entrant) (negative non-addivity)
•Correlation attraction
•Bridging
•Repulsive effects seen in large swathes of parameter space
•Works best for smaller added particles and large screening length, but q=0.2 is also possible
•Should be widely applicable in colloid science and biology
•GO TRY IT (Experiments needed)!
•Contact us at: www-louis.ch.cam.ac.uk