Analytical solution (ρT > ρMP)
Each probe captures at most 1 target particle
∂ρ |
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ρ − |
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spherical probes |
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ρs = 0
N (t)= 4πDa0 ρt
R1 = N(t)
t = 4πDa0 ρ Per MP
R = 4πDa0 ρρMP ≡ ρ
τ
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τ = |
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4πDa |
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MP |
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Analytical solution: transient solution
∂ρ |
= D 2 |
ρ − |
ρ |
τ ≡ |
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∂t |
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r2 |
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ρ(r,t)= At−3/ |
2e−t /τ e |
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4Dt |
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S (t)= |
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∞∫ρ(r,t)4πr2dr |
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e |
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∞∫ρ(r,t = 0)4πr2dr |
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0 |
Alam, Principles of Nanobiosensors, 2013 |
11 |
Analytical solution for barcode sensor
Eq. 1b
ts ρMP−1
Eq. 1a |
ts ρT−1 |
Alam, Principles of Nanobiosensors, 2013 |
12 |
A ‘Mendeleev table’ for biosensors
aM |
fM |
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pM |
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nM |
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Biobarcode sensors ‘beat’ the diffusion limit by fragmenting the space
Alam, Principles of Nanobiosensors, 2013 |
13 |