10: Electrosta7cs in solu7on

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1 Nanomanufacturing University of Michigan ME Winter : Electrosta7cs in solu7on February 15, 2010 John Hart hdp:// A.J. Hart 1

2 Announcements Video assignment discussion/quesmons Example: hdp://vimeo.com/ PS2 due next Monday (Feb/22) 2010 A.J. Hart 2

3 Recap: small- scale flows Wall fricmon grows nonlinearly as flow scale (e.g., pipe diameter) decreases However, when wall fricmon dominates, we must consider the nature of molecule- wall interacmons, called slip We define flow regimes by Knudsen number, Kn Kn = λ / L Gases, l = mean free path = b / L o o Liquids, b = slip length Q i, s dp = π dz 4 R + 8µ 3 sr 2µ We can superimpose slip upon a no- slip model 2010 A.J. Hart 3

4 What s the molecular origin of slip? Fluid- fluid interacmons are stronger than fluid- wall interacmons (e.g., hydrophobicity). Surface roughness traps gas molecules dissolved in the liquid, creamng a lubricamon layer at the wall. Here, what happens at high Re? Molecules hop between minimum- energy sites in the wall ladce; therefore slip is a rate process and slip length depends on temperature. Squires and Quate, Rev Mod Phys 77:977, Lichter et al., Phys Rev LeD 98:226001, A.J. Hart 4

5 Measuring gas flows in microchannels Arkilic et al., J MEMS 6(2):167, A.J. Hart 5

6 They measured kg/s 10-4 cm 3 /s Arkilic et al., J MEMS 6(2):167, A.J. Hart 6

7 Arkilic et al., J MEMS 6(2):167, A.J. Hart 7

8 Flow through CNTs Holt et al., Science 312: , A.J. Hart 8

9 Flow through CNTs Holt et al., Science 312: , A.J. Hart 9

10 Extreme slip flow through CNTs Majumder et al., Nature 438:44, A.J. Hart 10

11 Importance of gas damping in MEMS: DMD micromirrors 2010 A.J. Hart 11

12 Mirror dynamics at various ambient pressures Karniadakis and Beskok A.J. Hart 12

13 Today s agenda How surfaces become charged in solumon Modeling the electrical double layer CompeMMon between electrostamc repulsion and VDW adracmon forces (DLVO theory) à stability vs. coagulamon Nanofluidic transistors Electrophoresis 2010 A.J. Hart 13

14 Today s readings (ctools) Nominal: Hiemenz and Rajagopalan, excerpt on The electrical double layer and double- layer interacmons, from Principles of Colloid and Surface Chemistry Karnik et al., ElectrostaMc control of ions and molecules in nanofluidic transistors Extras: Israelachvili, excerpt on ElectrostaMc forces between surfaces in liquids, from Intermolecular and Surface Forces à same topics as Hiemenz above Bouzigues et al., Nanofluidics in the Debye layer at hydrophilic and hydrophobic surfaces à measurements of slip length on charged surfaces 2010 A.J. Hart 14

15 Surfaces become charged in solu7on WHY? IonizaMon or dissociamon of surface groups, e.g., - COOH à - COO - + H + AdsorpMon of ions from solumon à Charged surfaces are balanced by counterions in solumon, so electrical neutrality is preserved à Some counterions adsorb to the surface, and others are distributed near the surface within the double layer à This is very important for interac7ons between nanostructures in solu7on 2010 A.J. Hart 15

16 Ion concentra7on profiles Israelachvili, Mulvaney A.J. Hart 16

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23 Effect of electrolyte concentra7on and valence (Debye- Huckel approxima7on) Hiemenz and Rajagopalan A.J. Hart 23

24 Comparison of double layer models Large Ψ 0 Exact solumon (Gouy- Chapman) Debye- Huckel approximamon 0.01M solumon of 1:1 electrolyte Hiemenz and Rajagopalan A.J. Hart 24

25 Limi7ng solu7ons for small (spherical) and large (locally planar) par7cles Hiemenz and Rajagopalan A.J. Hart 25

26 Repulsion between overlapping layers Hiemenz and Rajagopalan A.J. Hart 26

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30 Stabiliza7on of colloids: DLVO theory Mulvaney A.J. Hart 30

31 Net interac7on energy governs stability Israelachvili A.J. Hart 31

32 a) Strong long- range repulsion, fully dispersed - highly- charged surface in dilute electrolyte; long Debye length b) KineMcally stable at secondary minimum or fully dispersed - higher electrolyte concentramon than (a) c) Slow aggregamon - low surface charge density d) Rapid coagulamon e) EffecMvely no repulsion Israelachvili A.J. Hart 32

33 Example: interac7on between a pair of Au par7cles Mulvaney A.J. Hart 33

34 Example: interac7on between a pair of Au par7cles Mulvaney A.J. Hart 34

35 Diffuse layer and Stern layer Zeta potenmal is typically measured Think about slip.. Hiemenz and Rajagopalan A.J. Hart 35

36 Overlapping double layers in a nanogap Oh et al., IEEE MEMS A.J. Hart 36

37 Nanofluidic transistors Karnik et al., Nano LeDers 5(5): , A.J. Hart 37

Electrophoresis: placing par7cles in gaps MoMon is diffusive (Brownian) far from gap Substrate- parmcle repulsion dominates at low V Spherical DEP

38 Electrophoresis: placing par7cles in gaps MoMon is diffusive (Brownian) far from gap Substrate- parmcle repulsion dominates at low V Spherical DEP region grows and dominates at high V EP- induced oscillamon only important at low frequencies Barsod et al., Small 3(3):488, A.J. Hart 38

39 V = 1.5 V à 2V à 3V g = 30 nm à 80 nm à 125 nm Barsod et al., Small 3(3):488, A.J. Hart 39

40 Dielectrophoresis for posi7oning CNTs Vijayaraghavan et al., Nano Le*, V.7 No. 6, , A.J. Hart 40

41 Electric field- directed growth of CNTs à Alignment force vs. thermal vibramon Zhang et al., Applied Physics LeDers 79, A.J. Hart 41

42 Zhang et al Appl Phys Le* 79, 2001 Homma et al Appl Phys Le* 88, A.J. Hart 42

07: Intermolecular and surface forces

Nanomanufacturing University of Michigan ME599-002 Winter 2010 07: Intermolecular and surface forces February 3, 2010 John Hart ajohnh@umich.edu hfp://www.umich.edu/~ajohnh 2010 A.J. Hart 1 Announcements