Derivation of Young’s Equation
V
S
A
G
= |
πR3 |
(1−cosθ)2 |
(2 |
+cosθ) |
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θ |
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= 2πR2 (1−cosθ) |
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R θ |
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=π(R sinθ)2 |
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G =γLV S +γSL A +γSV (A∞ − A) |
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9πV 2 |
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1/3 |
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= |
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(2γLV −a(1+cosθ)) |
(1−cosθ)(2 +cosθ) |
2 |
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where, a =γSV −γSL
Energy minimization: dG |
= 0 gives, cosθE = (γSV −γSL )/ γLV |
dθ |
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Alam, Principles of Nanobiosensors, 2013
Corrugation improves hydrophobicity
Flat surface
cosθE = (γSV |
−γSL )/ γLV |
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γLV cosθE |
=1×(γSV −γSL ) |
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With corrugation |
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Top view |
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γLV cosθ* =φ(γSV −γSL ) −(1−φ)γLV |
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φ = fractional area covered by the pillars |
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θ* = contact angle of new droplet |
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Determine periodicity φ to make the surface hydrophobic, Because we have weakened the influence of the substrate
Alam, Principles of Nanobiosensors, 2013
Droplet evaporation enhances sensitivity
A
B
B’
A’
A- A’ B- B’
| Z(t1) |
LCR meter time↑ » ρ ↑ » Vpp =10 mV
|Z|↓
| Z(t2 ) |
• Several data-points in one measurement cycle: Not an endpoint measurement
• Better resolution is achieved upon evaporation
Geometry of diffusion & phase space of biosensors
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Ns2 |
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1 |
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ts ~ |
Ns a |
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ts ~ |
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D |
2 |
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D ρ0 |
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ρ0 |
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