Point of Zero Charge
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H |
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Ka |
− Kb |
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Q = 0 = qN0 |
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S |
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S |
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1 |
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K |
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b |
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+ 2 |
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+ 2 |
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pH |
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Ka Kb = H |
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S |
H |
B |
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Ka =10− pKa , Kb =10− pKb
ID
pzc = pKa + pKb
2
pKa = −2, pKb = 6
For SiO2
Self-consistent surface charge
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H |
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Ka |
− Kb |
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Q( pH ) = qN0 |
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S |
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S |
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1 |
+ K |
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S |
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Q =QDL +QMOS
~QDL =Q0 exp zqψ0
kBTL
ψ |
0 |
= kBTL ln Q Q |
pH |
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zq |
0 |
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[H+ ]S =[H+ ]Be−qψ0 /kBT
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δQ |
≡ −qβint |
Intrinsic buffer capacity |
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δ (pHs ) |
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Aside: Surface potential and Buffer capacity
[H+ ]S =[H+ ]Be−qψ0 /kBT
pH
pHs = pHB + qψ0 
2.3kBT
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δψ0 |
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δψ0 |
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δ pHs |
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δ (pHB )+δ (qψ0 |
2.3kBT ) |
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δψ0 |
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δψ0 |
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δQ |
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1 |
×(−qβint ) |
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δ (pHs ) |
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δ pHs |
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δQ |
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CDL |
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δψ0 |
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−1 |
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= −2.3 kT |
1+ |
2.3kBTCDL |
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δ pHB |
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q |
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q2 βint |
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12
Outline
1)How to calculate pH
2)pH and surface charge
–Surface binding model
3)Nernst Limit of an ISFET
4)Conclusions
Alam, Principles of Nanobiosensors, 2013 |
13 |
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