@joyphys 2015-07-06T14:06:06.000000Z 字数 3010 阅读 1665

# 胶体电荷重整化 Colloidal Charge Renormalization

note

## Cell Model, Poisson-Boltzmann Theory, Alexander’s Prescription

2ϕ(r)=κ2ressinhϕ(r)(1)

nϕ(r)|r=a=ZλBa2

nϕ(r)|r=R=0

2ϕ(r)=2(ϕ(r)ϕR)=2ϕ˜(r)

κ2ressinhϕ(r)=κ2res[sinhϕR+coshϕR(ϕ(r)ϕR)]=κ2rescoshϕR[tanhϕR+ϕ˜(r)]=κ2rescoshϕR[γ0+ϕ˜(r)]=κ2PB[γ0+ϕ˜(r)](2)

2ϕ˜(r)=1r2ddr[r2ddrϕ˜(r)]=κ2PB[γ0+ϕ˜(r)](3)

ϕ˜(r)|r=R=0

nϕ˜(r)|r=R=0

ϕ˜(r)=γ0[1+κPB+12κPBeκPBReκPBrr+κPB12κPBeκPBReκPBrr]

dϕ˜(r)drr=a=ZeffλBa2

Zeff=γ0λBκPB{(κ2PBaR1)sinh[κPB(Ra)]+κPB(Ra)cosh[κPB(Ra)]}(4)

1. 解方程($\ref{eq:PB}$)，得ϕR$\phi_R$
2. 计算κ2PB=κ2rescoshϕR$\kappa_{PB}^2=\kappa_{res}^2\cosh\phi_R$
3. 带入方程($\ref{eq:Zeff}$)，计算Zeff$Z_{eff}$

## Renormalized jellium model

- PHYSICAL REVIEW E 69, 031403 (2004)
- THE JOURNAL OF CHEMICAL PHYSICS 126, 014702 (2007)
- THE JOURNAL OF CHEMICAL PHYSICS 133, 234105 (2010)

2ϕ(r)=4πλBZbackρ+κ2ressinhϕ(r)(5)

κ2res=8πλBsinhϕ()

nϕ(r)|r=a=ZλBa2

nϕ(r)|r==0

4πλBZbackρ+κ2ressinhϕ()=0

## RJ reformulated

- THE JOURNAL OF CHEMICAL PHYSICS 133, 216101 (2010)
- PHYSICAL REVIEW E 83, 041401 (2011)

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