G-Na+ + H+====G-H+ + Na+ 外部试液 a外 内部参比 a内 水化层 干玻璃 Ag+AgCl 电极构造： 球状玻璃膜(Na2SiO3，厚0.1mm)+[内参比电极(Ag/AgCl)+缓冲液] 膜电位产生机理： 当内外玻璃膜与水溶液接触时，Na2SiO3晶体骨架中的Na+与水中的H+发生交换： G-Na+ + H+====G-H+ + Na+ 因为平衡常数很大，因此，玻璃膜内外表层中的Na+的位置几乎全部被H+所占据，从而形成所谓的“水化层”。

Ag AgCl,[Cl-]=1.0M [H3O+] =ax 玻璃膜 [H3O+] =a,[Cl-]=1.0M, AgCl Ag 从图可见： 玻璃膜=水化层+干玻璃层+水化层 电极的相=内参比液相+内水化层+干玻璃相+外水化层+试液相 膜电位M= 外(外部试液与外水化层之间) +g(外水化层与干玻璃之间) -g’(干玻璃与内水化层之间) -内(内水化层与内部试液之间) 设膜内外表面结构相同(g=g’)，即 上式为pH 值溶液的膜电位表达式或采用玻璃电极进行pH 测定的理论依据！ 测定pH 值的电池组成表达式为： Ag AgCl,[Cl-]=1.0M [H3O+] =ax 玻璃膜 [H3O+] =a,[Cl-]=1.0M, AgCl Ag 玻璃电极(含内参比液） 待测液 外参比电极

11.4     直接电位法 将指示电极与参比电极构成原电池，通过测量电池电动热，进而求出指示电极电位，然后据Nernst 公式计算待测物浓度cx。但由于有不对称电位和液接电位，前述公式 因K0, 故不可从上式直接求出cx 一、标准曲线法 步骤： a) 待测物标准浓度cs系列的配制； b) 使用TISAB分别调节标准液和待测液的离子强度和酸度，以掩蔽干扰离子； c)  用同一电极体系测定各标准和待测液的电动势E； d) 以测得的各标准液电动势E对相应的浓度对数lgcs作图，得校正曲线； e) 通过测得的待测物的电动势，从标准曲线上查找待测物浓度。

二、标准加入法 步骤： a) 先测体积为Vx待测液的电动势： b) 于试液中加入体积为Vs(1%cx)、浓度为Cs(100cx)，再测其电动势： 其中 因加入待少量测物溶液，离子强度基本不变(x=x’)，常数K亦保持不变，故两式相减并作整理求得cx

滴定曲线：以pX(或电动势)对滴定体积作图所绘制的曲线，称为滴定曲线。发生电位突变时所对应的体积即为终点时所消耗的滴定剂体积。 微分曲线：对上述滴定曲线微分或以pX(或电动势)对E/V作图所绘制的曲线，称微分曲线。终点时出现的尖峰所对应的体积为滴定体积。滴定曲线进行多次微分而得到不同阶次的微分曲线，这些曲线均可用于滴定终点的指示。

VOLTAMMETRY A.) Comparison of Voltammetry to Other Electrochemical Methods 1.) Voltammetry: electrochemical method in which information about an analyte is obtained by measuring current (i) as a function of applied potential - only a small amount of sample (analyte) is used Instrumentation – Three electrodes in solution containing analyte Working electrode: microelectrode whose potential is varied with time Reference electrode: potential remains constant (Ag/AgCl electrode or calomel) Counter electrode: Hg or Pt that completes circuit, conducts e- from signal source through solution to the working electrode Supporting electrolyte: excess of nonreactive electrolyte (alkali metal) to conduct current

Apply Linear Potential with Time Observe Current Changes with Applied Potential 2.) Differences from Other Electrochemical Methods a) Potentiometry: measure potential of sample or system at or near zero current. voltammetry – measure current as a change in potential b) Coulometry: use up all of analyte in process of measurement at fixed current or potential voltammetry – use only small amount of analyte while vary potential

B.) Theory of Voltammetry 3.) Voltammetry first reported in 1922 by Czech Chemist Jaroslav Heyrovsky (polarography). Later given Nobel Prize for method. B.) Theory of Voltammetry 1.) Excitation Source: potential set by instrument (working electrode) - establishes concentration of Reduced and Oxidized Species at electrode based on Nernst Equation: - reaction at the surface of the electrode 0.0592 (aR)r(aS)s … Eelectrode = E0 - log n (aP)p(aQ)q … Apply Potential

Current is just measure of rate at which species can be brought to electrode surface Two methods: Stirred - hydrodynamic voltammetry Unstirred - polarography (dropping Hg electrode) Three transport mechanisms: (i) migration – movement of ions through solution by electrostatic attraction to charged electrode (ii) convection – mechanical motion of the solution as a result of stirring or flow (iii) diffusion – motion of a species caused by a concentration gradient

Voltammetric analysis Analyte selectivity is provided by the applied potential on the working electrode. Electroactive species in the sample solution are drawn towards the working electrode where a half-cell redox reaction takes place. Another corresponding half-cell redox reaction will also take place at the counter electrode to complete the electron flow. The resultant current flowing through the electrochemical cell reflects the activity (i.e.  concentration) of the electroactive species involved Pt working electrode at -1.0 V vs SCE Ag counter electrode at 0.0 V AgCl Ag + Cl- Pb2+ + 2e- Pb EO = -0.13 V vs. NHE K+ + e- K EO = -2.93 V vs. NHE SCE X M of PbCl2 0.1M KCl

Pb2+ + 2e- Pb -1.0 V vs SCE Concentration gradient created between the surrounding of the electrode and the bulk solution K+ K+ Pb2+ Pb2+ Pb2+ K+ Pb2+ Pb2+ K+ K+ K+ K+ K+ Pb2+ K+ Pb2+ K+ Pb2+ Pb2+ K+ Pb2+ K+ K+ K+ Pb2+ K+ K+ K+ Pb2+ Pb2+ Pb2+ K+ Pb2+ migrate to the electrode via diffusion K+ Pb2+ K+ Pb2+ Pb2+ K+ Pb2+ Pb2+ K+ Pb2+ Pb2+ K+ K+ K+ K+ Layers of K+ build up around the electrode stop the migration of Pb2+ via coulombic attraction

Mox + e- » Mred If Eappl = Eo: 0 = log ˆ [Mox]s = [Mred]s At Electrodes Surface: Eappl = Eo - log Mox + e- » Mred 0.0592 [Mred]s at surface of electrode n [Mox]s Applied potential If Eappl = Eo: 0 = log ˆ [Mox]s = [Mred]s 0.0592 [Mred]s n [Mox]s

ˆ [Mred]s >> [Mox]s Apply Potential E << Eo If Eappl << Eo: Eappl = E0 - log ˆ [Mred]s >> [Mox]s 0.0592 [Mred]s n [Mox]s

2.) Current generated at electrode by this process is proportional to concentration at surface, which in turn is equal to the bulk concentration For a planar electrode: measured current (i) = nFADA( ) where: n = number of electrons in ½ cell reaction F = Faraday’s constant A = electrode area (cm2) D = diffusion coefficient (cm2/s) of A (oxidant) = slope of curve between CMox,bulk and CMox,s dCA dx dCA dx dCA dx

As time increases, push banding further and further out. Results in a decrease in current with time until reach point where convection of analyte takes over and diffusion no longer a rate-limiting process.

- largest slope (highest current) will occur if: Thickness of Diffusion Layer (d): i = (cox, bulk – cox,s) - largest slope (highest current) will occur if: Eappl << Eo (cox,s . 0) then i = (cox, bulk – 0) where: k = so: i = kcox,bulk therefore: current is proportional to bulk concentration - also, as solution is stirred, d decreases and i increases nFADox d nFADox d nFADox d

Potential applied on the working electrode is usually swept over (i. e Potential applied on the working electrode is usually swept over (i.e. scan) a pre-defined range of applied potential 0.001 M Cd2+ in 0.1 M KNO3 supporting electrolyte Electrode become more and more reducing and capable of reducing Cd2+ Cd2+ + 2e- Cd Current starts to be registered at the electrode Current at the working electrode continue to rise as the electrode become more reducing and more Cd2+ around the electrode are being reduced. Diffusion of Cd2+ does not limit the current yet All Cd2+ around the electrode has already been reduced. Current at the electrode becomes limited by the diffusion rate of Cd2+ from the bulk solution to the electrode. Thus, current stops rising and levels off at a plateau i (A) E½ Working electrode is no yet capable of reducing Cd2+  only small residual current flow through the electrode id Base line of residual current -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 V vs SCE

E½ at ½ i Limiting current Related to concentration 3.) Combining Potential and Current Together Limiting current Related to concentration E½ at ½ i Half-wave potential : E1/2 = -0.5 . E0 - Eref E0 = -0.5+SCE for Mn+ + me- » M(n-m)+

current varies as drop grows then falls off 4.) Types of Voltammetry a) Polarography 1) first type of Voltammetry 2) controlled by diffusion, eliminates convection 3) uses dropping Hg electrode (DME) as working electrode current varies as drop grows then falls off

4) Advantages of Hg drop Electrode a) high overpotential for reduction of H+ 2H+ + 2e- » H2 (g) allows use of Hg electrode at lower potentials than indicated from thermodynamic potentials eg. Zn2+ and Cd2+ can be reduced in acidic solutions even though Eo’s vs. SHE = -0.403 (Cd2+/Cd) & -0.763 (Zn2+/Zn) b) new electrode surface is continuously generated - independent of past samples or absorbed impurities c) reproducible currents quickly produced

5) Disadvantages of Hg drop Electrode a) Ease of Hg0 oxidation Hg0 » Hg+ + e- E0 = +0.4V ˆ can not use above this potential Occurs at even lower potentials in presence of ions that complex Hg+ ex. Cl-: 2Hg + 2Cl- » Hg2Cl2 (s) + 2 e- starts at .0V b) Non-Faradaic (charging) current - limits the sensitivity to ~ 10-5 M - residual current is > diffusion current at lower concentrations c) cumbersome to use - tends to clog causing malfunction - causes non-uniform potential maxima d) Hg disposal problems

A Mn+ + ne- +Hg » M(Hg) amalgam i max i avg The ripples are caused by the constant forming and dropping of the mercury electrode Half-wave potential Residual current 6) Classic Polarography a) ½ wave potential (E½) characteristic of Mn+ E0 b) height of either average current maxima (i avg) or top current max (i max) is ~ analyte concentration c) size of i max is governed by rate of growth of DME -> drop time (t, sec) rate of mercury flow (m, mg/s) diffusion coefficient of analyte (D, cm2/s) number of electrons in process (n) analyte concentration (c, mol/ml) Ilkovic equation: (id)max = 706nD1/2m2/3t1/6c (id)avg = 607nD1/2m2/3t1/6c A

d) necessary to do experiment with sample and blank to see analyte signal vs. residual current - residual current due to impurities and charging (nonfaradaic) currents e) can use method to quantitate or identify elements in sample down to ~ 10-5 M f) can also use method to study reactions involving Mn+ as long as reaction is reversible ex. Mn+ + ne- +Hg » M0(Hg) amalgam plus reaction: Mn+ + xA- » MAx(n-x)+ (E1/2)with complex – (E1/2)without complex = -0.0592/n log Kf – 0.0592x/n log [A-] ˆ plot of (E1/2)with complex – (E1/2)without complex vs. log[A-] gives slope and intercept that can be used to give Kf and x Kf

One problem with data detection in normal polarography is that i varies over lifetime of drop, giving variation on i over curve. One simple way to avoid this is to sample only current at particular time of drop life. Near end of drop = current sampled polarography Sample i at same time interval Easier to determine iavg, etc but limit of detection only slightly smaller (~3x)

7) Pulse Polarography a) Instead of linear change in Eappl with time use step changes (pulses in Eappl) with time b) Measure two potentials at each cycle - S1 before pulse S2 at end of pulse - plot Di vs. E (Di = ES2 – ES1) - peak height ~ concentration - for reversible reaction, peak potential -> standard potential for ½ reaction c) derivative-type polarogram d) Advantages: - can detect peak maxima differing by as mucha as 0.044 – 0.05 V < 0.2V peak separatioin for normal polarography < can do more elements per run - decrease limits of detection by 100-1000x compared to normal polarography

‚ approaches zero near the end of the life of a drop e) Reasons for Decrease in Limits of Detection - increase Faradaic current < surge of current that lowers reactant concentration demanded by new potential ‚ not seen in classic polarography ‚ timescale of measurments is long compared to lifetime of momentary surge < current decays to a level just sufficient to counteract diffusion < total current >> diffusion current ‚ reducing surface layer to concentration demanded by Nernst equation - decrease in non-Faradaic current < surge of non-Faradaic current also occurs as charge on drop increases ‚ current decays exponentially with time ‚ approaches zero near the end of the life of a drop < measure current at end of drop lifetime significantly reduces non- Faradaic current < signal-to-noise increases f) Can do differential pulse and square wave polarography on other types of electrodes - called differential or square wave voltammetry

Electrochemistry can be Fun!

b) Cyclic Voltammetry 1) Method used to look at mechanisms of redox reactions in solution 2) Looks at i vs. E response of small, stationary electrode in unstirred solution using triangular waveform for excitation Cyclic voltammogram

‚ ipc – cathodic peak current Start at E >> E0 Mox + ne- » Mred - in forward scan, as E approaches E0 get current due to Mox + ne- » Mred < driven by Nernst equation ‚ concentrations made to meet Nernst equation at surface < eventually reach i max < solution not stirred, so d grows with time and see decrease in i max - in reverse scan see less current as potential increases until reduction no longer occurs < then reverse reaction takes place (if reversible reaction) < important parameters ‚ Epc – cathodic peak potential ‚ Epa – anodic peak potential ‚ ipc – cathodic peak current ‚ ipa – anodic peak potential < ipc . ipa < d(Epa – Epc) = 0.0592/n, where n = number of electrons in reaction < E0 = midpoint of Epa  Epc

Mechanistic Studies Cyclic voltammetry is very a useful tool to study kinetic processes.

Electrochemistry of Enzyme Enzyme-based Electrochemical Biosensors Applications Electrochemistry of Enzyme Enzyme-based Electrochemical Biosensors

Diffusional mediators

Tethered mediators

Tethered mediators

Direct electrochemistry Mb-agarose/EPG (b) Hb-agarose/EPG (c) HRP-agarose/EPG (d) Cat-agarose/EPG (e) agarose/EPG

Cytochrome c Myoglobin

Horseradish Peroxidase Hemoglobin Horseradish Peroxidase

Ferric HRP + H2O2  Compound I + H2O Compound I + H+ + e- Compound II Catalytical reduction of hydrogen peroxide Ferric HRP + H2O2  Compound I + H2O Compound I + H+ + e- Compound II Compound II + H+ +e- Ferric HRP

思考题 说明CV用于判断电极反应的可逆性。 举例说明CV用于描述反应机理。

电极过程可逆性判断

电极反应机理研究

实验 循环伏安法判断电极过程 张剑荣等编，仪器分析实验，科学出版社，1999，P158 作业1： 电位法和伏安法的原理、仪器构成和应用。 电位法与伏安法的比较。