Chem-To-Math的博客

泊松-玻尔兹曼Poisson–Boltzmann方程的提出1.简要历史回顾1.1 基本原理1.2 方程推导1.简要历史回顾泊松-玻尔兹曼方程是用来计算电解质溶液中离子浓度和电荷密度分布的一个微分方程，其基本形式为∇2ϕ(r)=−4πϵ∑ici0ziqe−βziqϕ(r)(1)\nabla^2\phi(\textbf r)=-\frac{4\pi}{\epsilon}\sum_{i} c_i^0z_iqe^{-\beta z_iq\phi(\textbf r)} \tag{1}∇2ϕ(r)=−ϵ4π​i

An electrochemical double layer (EDL) can be described by Gouy-Chapman-Stern (GCS) model.The EDL is composed of a compact layer between the metal surface and the Helmholtz plane (HP), and a diffuse layer stretching toward the solution bulkThe HP layer ha

Test conditionNo stirring;Fast kineticsStep to an arbitrary potential suddenlyCottrell-like experimentHalf reaction:(1)O+ne⇌RO+ne{\rightleftharpoons} R \tag{1}O+ne⇌R(1)In the case of Nerstian...

Test condition: 1. No stirring; 2. The concentration of reactant at the electrode surface is always 0. Half reaction: O+ne→R(a)(a)O+ne→RO+ne\rightarrow R \tag{a} The equation of the limiting cur...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT](1)(1)i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\bet...

Kinetics analysis of the CO electrooxidation by Bulter-Volmer equationBulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT](1)(1)i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0...

交换电流Exchange Current 从Bulter-Volmer 方程看出，在平衡状态下，净电流为零，即正逆反应速率相等，电流而相互抵消，这时候的正逆向电流绝对值被称作交换电流Exchange current，i0。 i0=|ia|=|ic|i0=|ia|=|ic|i_0=|i_a|=|i_c|交换电流表达式为 i0=FAk0c∗Oexp−βF(Eeq−E0')RT=FAk0c...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT](1)(1)i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\bet...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT](1)(1)i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\bet...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT]i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\beta F(E-...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT]i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\beta F(E-...

Bulter-Volmer 方程：i=ic−ia=FAk0[cO(0,t)exp−βF(E−E0′)RT−cR(0,t)exp(1−β)F(E−E0′)RT]i=ic−ia=FAk0[cO(0,t)exp⁡−βF(E−E0′)RT−cR(0,t)exp⁡(1−β)F(E−E0′)RT]i=i_c-i_a=FAk^0 \left [c_O(0,t) \exp \dfrac{-\beta F(E-...

巴特勒 - 沃尔默方程推导Derivation of Butler-Volmer Equation阿伦尼乌斯Svante Arrhenius在1889年通过实验经验提出了化学反应速率常数Reaction Constant与活化能Activation Energy 和温度的关系： k=Aexp−EaRT(1)(1)k=Aexp⁡−EaRTk=A\exp\dfrac {-E_a}{...

电化学势【Electrochemical Potential】定义以及推导在电场中，带电微粒从一种环境变化到另外一种环境的过程中不仅受到化学势的驱使，同时也受到电势的驱使。那么电势如何作用于带电微粒呢？还得从无电场的热力学状态出发，推导出电势对于带电微粒的作用。 在热力学的简单系统中，内能(Internal energy, U)被描述为广度量（extensive variable） 熵(En...