COLLOIDAL SELF ASSEMBLY I: INTERACTIONS & PACMEN

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Lizbeth Floyd
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1 COLLOIDAL SELF ASSEMBLY I: INTERACTIONS & PACMEN David Pine Department of Physics New York University 2012 Boulder Summer School 24 July 2012 Boulder, Colorado

2 Outline of lectures on colloids Lecture 1: Today Overview of colloids (sizes, materials) Selfassembly of colloids: (colloidal liquids, crystals, & glasses) photonic crystals (& the diamond lattice) need for directional interactions van der Waals interactions (fluctuating electric dipoles) Electrostatic interaction: PoissonBoltzmann & DebyeHückel, DLVO Depletion interaction DNA hybridization Lecture II: Tomorrow Lock & key colloids Colloids with valence Colloidal molecules: to infinity and beyond

3 What are colloids? Small particles suspended in a liquid Brownian motion is important COLLOIDS: Diameters ~ 5 nm to 5 μm suspended thermally Materials plastic (PS, PMMA,...) inorganic (SiO2, TiO2,...) semiconductor (CdSe,...) metal (Au, Ag,...) Stabilized against aggregation by charge surfactants polymer brushes

4 Self assembly of charged colloids Electrically charged colloids spontaneously form ordered structures charged polystyrene spheres in methanol (90%) water (10%) (d = 91 nm) glass BF BCC FCC liquid Crystallization driven by repulsive interactions Sirota et al. PRL 62, 1524 (1989)

$5% 74% max packing fraction Crystallization driven by entropy colloidal crystal with lattice constant$

5 Selfassembly of hard spheres liquid fcc xtal Hardsphere phase diagram (athermal) a~λ 49.4% 54.5% 74% max packing fraction Crystallization driven by entropy colloidal crystal with lattice constant ~ 0.5 µm

from Australia Natural opals consist of tiny FCC ordered glass spheres (~200

6 Interesting optical properties Bragg scattering from different crystalline planes produce different colors Bragg scattering of light Gem quality opal from Australia Natural opals consist of tiny FCC ordered glass spheres (~200 nm) These structures (FCC, BCC) are nice but we would like to make others, such as...

7 Diamond crystal structure Photonic band structure for diamond light out band gap light in! = ck waveguide with sharp turns Ho et al. PRL 65, 3152 (1990) Twenty years and counting: No one can make this 3d structure on the nm length scale.

8 Why is assembling the diamond structure so hard? BCC 68% FCC 74% (densest sphere packing) diamond need directional interactions 34%

9 I believe that if we can learn to make structures from colloids with the control available to make molecules, that is, if we can design and control the structure of materials on the nm scale, it will have enormous practical applications... in photonics, optics, electronics, solar cells, and many other technologies. One key will be to develop colloids with directional interactions that can mimic atoms with valence... CO2 CH4 SO2

10 Intro to colloidal interactions Van der Waals (fluctuation electric dipoles) Screened Coulomb (DebyeHückel) Polymer brush ( steric repulsion) Depletion attraction } DLVO* * Derjaguin Landau Verway Overbeek ssdna hybridization

11 van der Waals: fluctuating electric dipoles p 2 p 1 r U(r) = p 1 p 2 E(r) = 1 3(p ˆr)ˆr 4 0 r 3 3(p 1 ˆr)(p 2 ˆr) r 3 p p 2 = 2 E 1 (r) induced dipole U(r) = p1 2 E 1 (r) 3(p 1 ˆr)( 2 E 1 (r) ˆr) r r 6

12 van der Waals interaction U(r) ' A Ham 2 Z V A Z V B 1 r 6 dv AdV B (fluctuating induced dipole) A Ham ' 3k BT 2 X! A m A m B m B m Ret(l) visible light travels 0.5 μm in one period (indexmatching reduces vdw interaction) A m B l (!) =1 X j a j 1 i! j X j b j (! j 2! 2 ) i j! U pp p 1p 2 r 3 p 2 E 1 (r) 1 r 3 relaxation times resonance frequencies damping rates ) U pp 1 r 6 contributions greatest near optical/uv frequencies

13 U(r) 2 U(r) ' van der Waals interaction A Ham 2 U(r) = A Ham 6 ' A Ham 12 ' 16A Ham 9 1 h = 1 r Z (between two spheres) V A Z V B 1 r 6 dv AdV B apple 2 (r/a) (r/a) 2 ln a h, for h a 2a a 6 r 6, for r a 1 r 6 (fluctuating induced dipole) 1 4 (r/a) 2 a h 3 r/a h = r 2a or weaker For 1 micron spheres at contact: r U(2a) visible light travels 0.5 μm in one period a 10 3 k B T

14 Screened Coulomb U(r) screened Coulomb DLVO 2 ' l B k B T e applea 2 Z 2 e appler 1applea r 3 r/a Bjerrum length l B = e 2 r k B T Debye screening length apple 1 = s r 0 k B T P i z2 i e2 c 0 i

15 Screened Coulomb van der Waals (DLVO theory) k B T for stability U(r) 2 screened Coulomb DLVO van der Waals ' l B k B T e applea 2 Z 2 e appler 1applea r 3 r/a Bjerrum length l B = e 2 r k B T Debye screening length apple 1 = s r 0 k B T P i z2 i e2 c 0 i

16 Screened Coulomb van der Waals (DLVO theory) brush k B T for stability U(r) 2 screened Coulomb DLVO van der Waals ' l B k B T e applea 2 Z 2 e appler 1applea r 3 r/a Bjerrum length l B = e 2 r k B T Debye screening length apple 1 = s r 0 k B T P i z2 i e2 c 0 i

17 Depletion interaction Solvent Asakura & Oosawa, J. Chem. Phys. 22, 1255 (1954).

18 Citation time line for original paper on the depletion interaction Asakura & Oosawa, J. Chem. Phys. 22, 1255 (1954). Total citations = 1399

19 singlestranded DNA (ssdna) doublestranded DNA 5 sticky ssdna ends closeup of sticky ends G T C C A A G C T C T A G G A T biotinstreptavidin anchor 4 DNA bases Thymine Adenine } TA (WC pair) sticky ends melt (come apart) near Tm = 40 C Tm depends on number (and kind) of base pairs specificity only complementary strands link: can program sticky ends by sequence of bases recognition Guanine Cytosine } GC (WC pair)

20 DNAcoated colloids singlestranded sticky ends ~10 bases doublestranded DNA (50 bases 20 nm) flexible PEG linker strand biotinstreptavidinbiotin link surfactant (PEOPPOPEO Pluronic F127) ~1 μm diameter polystyrene sphere (colloid)

21 DNA hybridization interaction interaction energy U TOTAL U brush U vdwaals B 2L A particle separation 2L ~1 μm diameter polystyrene sphere (colloid) U DNA

22 Tomorrow Colloids with directional interactions Pacman particles Colloids with valence

Complete and precise descriptions based on quantum mechanics exist for the Coulombic/Electrostatic force. These are used to describe materials.

Complete and precise descriptions based on quantum mechanics exist for the Coulombic/Electrostatic force. These are used to describe materials. The forces of nature: 1. Strong forces hold protons and neutrons together (exchange of mesons) 2. Weak interactions are involved in some kinds of radioactive decay (β-decay) 3. Coulombic or electrostatic