Software POLAROGRAPH.com (former Polar) is virtual polarograph and general electrochemical simulator with data analysis. It analytically and digitally simulates voltammograms (polarograms) on virtually any mechanism (finite and semi-infinite diffusions, and absorption) at over 10 electrode geometries (planar, spherical, semi-spherical, cylindrical, semi-cylindrical, microdisc, thin film, and rotating electrodes) in over 10 techniques (linear sweep and CV, DC, normal pulse, differential pulse, square wave, additive square wave, and staircase voltammetries). It also simulates the effects to change over 20 parameters, e.g. charge current, resistance, noise, preconcentration time and potential, convection, pH, the reactant and product numbers, etc. User can type in his mechanism with any symbol. It also includes over 200 theoretical equations.

It plots and analyses any x,y data for detecting peak location, peak height, peak width, semi-derivative, derivative, integral, semi-integral, convolution, deconvolution, curve fitting, and separating overlapped peaks and background current.

It shows tip when the user put mouse cursor over a label. The program can separate overlapped voltammograms into individuals, and extract real peak from voltammogram with noise and baseline. It outputs the theoretical peak values, the peak current and potential and current-potential data, which can be imported into other program (e.g. Lotus 123). User can copy-and-paste the voltammogram into his document.

It has been successfully applied to fit experimental polarograms (voltammograms) of In(III), Cd(II), Pb(II), Tl(I), Cr(III), Zn(II), and binuclear copper complex in aqueous and non-aqueous media at mercury, solid metal and non-metal electrodes (specifically the dropping mercury, hanging mercury drop, gold, platinum and glassy carbon electrodes) by various electrochemical techniques (differential pulse, square wave, and pseudo-derivative normal pulse polarographies) [1-5].

It is available from the author or my Web site. If you have any question, please read FAQ in its document. For tutorial, please read the course practices in the rmit.htm file.

It is assumed that you agree the Shareware license that you should register by US$20 to author in 20 days or you should delete it.

<big>Chapter 2
Polarography and Voltammetry</big>

2.1 Introduction

Modern electrochemical methods offer the analytical chemist a wide variety of techniques to solve analytical problems. Voltammetry is one such method, in which the current is measured as a function of applied potential. Polarography is another method, which differs from voltammetry in that it employs a dropping mercury electrode (DME) to continuously renew the electrode surface.

In this chapter, the fundamental principles of popular electrochemical techniques, e.g. direct current polarography (DCP), alternating current polarography (ACP), square wave polarography (SWP), normal pulse polarography (NPP), differential pulse polarography (DPP), pseudo-derivative normal pulse polarography (PDNPP), Linear sweep voltammetry (LSV) and stripping voltammetry (SV), are reviewed. Much of this theory is also applicable to voltammetry. If you are familiar with polarography and voltammetry, they can move directly to the next chapter.

Fig. 1 Schematic presentation of some polarographic methods.

(a) Potential sequence of a polarogram.

(b) Potential sequence on a single drop (n current sampling).

(c) Current-potential curves for 1 mM Zn²⁺ in 1 M KNO₃.

DC: t = 2 s; NP: t = 2 s, t_p = 5 ms; DP: t = 2 s, t_p = 5 ms; DE_p = 20 mV;

SW: delay time = 4 s, DE_p = 20 mV, f = 100 Hz.

Beside techniques, theoretical equations also depend on mechanism and electrode geometry. E.g. for 7 techniques, 2 mechanisms and 10 electrode geometries, we need 7x2x10=140 theoretical equations. There are more than 200 theoretical equations for analytical simulation and theoretical peak current and potential in this software. You can calculate the peak or limiting current and potential from the theoretical equations by clicking on the Theoretical Peak submenu.

2.2 Direct Current Polarography

Heyrovsky invented the original polarographic method, conventional direct current polarography (DCP), and Heyrovsky and Shikata constructed the first polarograph in 1925 [6]. DCP involves the measurement of current flowing through the dropping mercury electrode (DME) as a function of applied potential. Under the influence of gravity, mercury drops grow from the end of a fine glass capillary until they detach. Then the process is allowed to repeat itself. Drops may be allowed to fall naturally or may be dislodged after a specified interval with the aid of a mechanical device. A major advantage of the DME is that a constantly renewed electrode surface is exposed to the test solution so that problems of electrode blockage are avoided. Another advantage of the DME is that it allows a number of electrode reduction processes to be monitored, which would otherwise be inaccessible, because a wide negative potential region is available on account of the high overpotential for water reduction.

If an electroactive species is capable of undergoing a redox process at the DME, then an S-shaped current-potential relation is usually observed. This is called a polarographic wave. Figure 1.1 illustrates the response obtained from a reduction reaction where the current (i) increases over a particular potential (E) range until it reaches a limiting value. The limiting current is the diffusion-controlled limiting current (i_d). This i_d is of interest in analytical measurements as it is proportional to the concentration of reactant. For a charge reaction

A + ne = B

Ilkovic [4] first put the measurement of this current on a theoretical basis, and his equation is [4-6]

i_d = (7/3)^1/2 (36 p)^1/6 r^2/3 nF D^1/2 m^2/3 t_d^1/6 C (2.1)

where r is the density of mercury, n is the number of electrons, F is Faraday's constant, D is the diffusion coefficient, m is the flow rate of mercury, t_d is the drop time, and C is the concentration of the electroactive species in the bulk solution.

For a planar electrode,

i_d = nFAD^1/2 C / (p t_d)^1/2 (2.2)

For a spherical electrode with radius r,

i_d = i_d(planar)+nFADC / r = nFAD^1/2 C (1/ (p t_d)^1/2 + D^1/2 / r) (2.3)

For a microelectrode, a steady-state current is

i_d = GnFA^1/2 DC (2.4)

where G is an electrode geometry constant, only depending on electrode geometry.

For a microdisc electrode, G=4/(p)^½

i_d =4/(p)^½nFA^1/2 DC = 4nFDC r

For a microsphere electrode, G=2p^½

i_d = 2p^½nFA^1/2 DC = 4pnFDC r

The half-wave potential E_1/2 is another important parameter of the DC polarogram. This is the potential at which the current reaches half of its limiting value (Figure 1.1). The value of half-wave potential is usually independent of concentration and is characteristic of the electroactive species. Therefore it can be used for qualitative characterization of the species, and is the foundation of qualitative analysis.

The shape of the DC polarogram is also very important to the overall characterization of the electrode process. If the reduction reaction is reversible and controlled by diffusion, the potential (E) is related to the concentrations of reactant and product by the Nernst equation [7]:

E = E° + (RT/nF) ln( C_O(0)/C_R(0) ) (2.5)

where E° is the standard redox potential, R is a gas constant, T is temperature, C_O(0) and C_R(0) are the surface concentrations of species Ox and Red, respectively. The shape of the DC polarographic wave is then derived by combining the Nernst and Ilkovic equations as follows [8, 9]

E = E_1/2 + (RT/nF) ln( (i_d- i)/i )

i = i_d / [1 + exp( (nF/RT) (E - E_1/2))] (2.6)

where

E_1/2 = E° + (RT/2nF) ln( D_R/D_O ) (2.7)

Since the diffusion coefficients of oxidized and reduced forms, D_O and D_R, are often almost equal, then E_1/2= E°. When i = i_d/2, then E = E_1/2.

Equation (2.6) is the Heyrovsky-Ilkovic equation, and is often used in investigations into the nature of electrode processes. However, an experimental DC polarogram also shows the oscillatory behavior of the current due to the growth and fall of the mercury drop, and this is superimposed on the DC behaviour. This invariably causes problems in the measurement of wave heights and/or half-wave potentials, and of course has deleterious effects on measures of analytical performance, especially sensitivity and resolution. Despite these problems, the DME remains popular because of its constantly renewed surface.

2.3 Linear Sweep Voltammetry and Cyclic Voltammetry

Linear sweep voltammetry (LSV) is performed by applying a linear potential ramp in the same manner as DCP. However, with LSV the potential scan rate is usually much faster than with DCP. When the reduction potential of the analyte is approached, the current begins to flow. The current increases in response to the increasing potential. However, as the reduction proceeds, a diffusion layer is formed and the rate of the electrode reduction becomes diffusion limited. At this point the current slowly declines. The result is the asymmetric peak-shaped I-E curve, as in Figure 1.3.

For a reversible reaction at a planar electrode, the peak current is

I_p = 0.4463 AC (nF)³^/2 (vD/(RT))^1/2 (2.8)

The peak potential is

E_p = E_1/2 – 1.109 RT/(nF) = E_1/2 – 28.5/n (mV) at 25 °C (2.9)

The half-peak potential is

E_p/2 = E_1/2 + 1.09 RT/(nF) (2.10)

The difference between peak potential and half-peak potential, similar to the half-peak width, is

| E_p - E_p/2 | = 2.2 RT/(nF) = 56.5/n (mV) at 25 °C (2.11)

Cyclic voltammetry is similar to linear sweep voltammetry except for the potential scans from the starting potential to the end potential, then reverse from the end potential back to the starting potential. Cyclic voltammetry is perhaps the most widely used electrochemical technique, and is frequently used for the characterization of a redox system. It can provide information about the number of redox states, as well as qualitative information about the stability of these oxidation states and the electron transfer kinetics. There are also simple models that can be used to calculate the rate of electron transfer (represented by k_s) and the rate of chemical reactions coupled to the electron transfer for simple systems (those where the cyclic voltammetric behavior is controlled by only one of these parameters). However, these simple models cannot be used for more complicated systems, since the effects of, for example, slow electron transfer kinetics and a coupled chemical reaction cannot be readily separated. This simulation software can help quantitative studies (e.g., mechanistic investigations) in cyclic voltammetry, so it can be useful for investigating the electrochemical mechanisms of real redox systems. The difference between two peak potentials is

DE_p =| E_pa - E_pc | = 2.3 RT/(nF) = 58/n (mV) at 25 °C (2.12)

E_1/2 = (E_pa + E_pc )/2

For a non-reversible reaction, DE_p becomes larger.

For a microdisk electrode, its steady-state current is the same as the eq. (2.4). Cyclic voltammetric responses at a disk microelectrode can be approximated in simulation by using a hemispherical electrode of the appropriate radius r_h=2r_d/p, , where r_dis the radius of the disk microelectrode; the CV responses at a band electrode can be approximated using a hemicylindrical electrode of the appropriate radius r_h=w/4, where w is width of the band electrode.

2.4 Staircase Voltammetry

Staircase Voltammetry (SV) is similar to linear scan voltammetry. It scans by staircase potentials, instead of linear potential. When a potential step is very small, it is the almost same as linear scan voltammetry. But you have choice to change the sampling time.

2.5 Alternating Current Voltammetry

A number of modifications to DCP have improved its analytical performance. One of them is alternating current voltammetry (ACV). It is the result of superimposing a small amplitude sinusoidal potential (DE) with a fixed frequency (w) on a slowly scanning DC ramp, as (c) in Figure 1.2. The applied potential is then given by summing the AC and DC components. Finally, the alternating current (AC) is measured as a function of DC potential. In particular, the amplitude of the AC current vs. the DC potential is plotted, as (g) in Figure 1.2. The current-potential (I-E) curve for a reversible reaction follows the equation [6]

I = n²F² AC DE (wD)^1/2 sech² [(nF/2RT)(E - E_1/2)] /(4RT) (2.13)

At a peak, sech()=1, then the above equation reduces to

I_p = n²F² AC DE (wD)^1/2/(4RT) (2.14)

It may be deduced from this equation that the amplitude of the AC component of the Faradic current (I) is peak-shaped. Moreover, the peak current is a linear function of concentration and therefore may be used in analytical applications. Like the half-wave potential E_1/2 in DCP, the peak potential E_p in ACP is characteristic of the electroactive species. Also, the half-peak width (i.e. the width of the peak at half its height, W_1/2) is [6]

W_1/2 = 3.52 RT/(nF) = 90/n mV at 25 °C. (2.15)

2.6 Square Wave Voltammetry

Square wave voltammetry (SWV) uses a small amplitude square wave voltage in place of the sinusoidal one used in ACP. Its potential waveform is shown in (d) of Figure 1.2. The current is sampled near the end of each square wave half cycle, to minimize double-layer charging effects, and the I-E response is obtained by plotting the differences in current between successive half cycles. For reversible electrode processes, the I-E curve for SWP is similar to that in ACP [6], so its properties, including the half-peak width W_1/2 and resolution, are obviously akin to ACP.

2.7 Additive square Wave Voltammetry

Additive square wave polarography (ASWP) uses a small amplitude square wave voltage in the same as one used in SWP, but its total current is sum of the positive and negative pulses currents, instead of difference of the positive and negative pulses currents. Because its two charge currents by the positive and negative pulses are opposite, it is possible to select suitable sample time to make its charge currents offset to zero. A charge current by a positive pulse is

I_c(t1) = (E_j-1– E_j)exp(-t1/RC)= -(Es+Ep)exp(-t1/RC)

where t1 is a sampling time at a positive pulse, R is resistance, C is double layer capacitance, Es is potential step, Ep is pulse potential.

A charge current by a negative pulse is

I_c(t2) = (E_j – E_j+1)exp(-t2/RC)= Ep exp(-t2/RC)

Total charge current is

I_c = I_c (t1)+ I_c (t2)

By setting I_c =0, a solution for the sampling time is

t2 = t1 - RC ln(Es/Ep+1)

It can show in dimensionless sampling time by division of the pulse time tp:

T2 = T1 – RC/tp ln(Es/Ep+1)

According to this equation, select sampling time t2 different from t1 to offset charge current to zero.

2.8 Normal Pulse Voltammetry

The pulse voltammetries including normal pulse voltammetry (NPV) and differential pulse voltammetry (DPV) stem from Barker's original work on square wave voltammetry [6]. The increased sensitivity of these techniques over DCP arises from their ability to discriminate against the charging current by measuring the total current after the charging current has decayed to values substantially less than the Faradic current.

The potential-time waveform used in NPP is presented as (a) in Figure 1.2. At the beginning of the potential sweep, the electrode is held at an initial potential where no Faradic current flows. Potential pulses of increasing amplitude are then applied to the electrode at regular intervals. The potential pulses are about 50 ms in duration and the current is measured at a time near the end of each pulse. A potential pulse is ended by a return to the initial potential and the drop is dislodged. The whole process is repeated except a few millivolts are added to the potential pulse in next cycle. A normal pulse polarogram is shown as (e) of Figure 1.2. The shape of the normal pulse polarogram is sigmoidal, looking similar to the shape of a DC polarogram, and indeed it can be described by a current-potential equation similar to that in DCP [6].

For a planar electrode,

i_d = nFAD^1/2 C / (p t_p)^1/2 (2.16)

For a spherical electrode with radius r,

i_d = i_d(planar)+nFADC / r = nFAD^1/2 C (1/ (p t_p)^1/2 + D^1/2 /r ) (2.17)

2.9 Reserve Pulse Voltammetry

Reserve Pulse Voltammetry is similar to normal pulse voltammetry, but its start potential is negative and its pulse is positive as opposite to normal pulse voltammetry.

2.10 Differential Pulse Voltammetry

Normal pulse voltammetry gives improved sensitivity by avoiding most of the charging current by sampling the total current as late as possible after the application of each potential pulse. However, there still is the charging current to some extent. Another defect of NPP is poor resolution between neighbouring wave because of drawn-out sigmoidal I-E response. Differential pulse polarography (DPP) was designed to overcome these problems by arranging a charging current of smaller magnitude, and by producing a peak-shaped I-E curve.

The potential-time waveform used in DPV is shown as (b) of Figure 1.2. A voltage ramp is applied to the electrode as in the DCP, and a small amplitude potential pulse (DE) is added to the voltage towards the end of each drop's life. The currents are measured before applying the pulse and at the end of the pulse. When the difference between the two current samples is plotted as a function of the applied ramp voltage, a peak-shaped current response is shown as (f) in Figure 1.2.

The peak-shaped I-E curve allows polarographic responses in close proximity to each other to be more clearly resolved than in either DCP or NPV. The I-E curve for all values of the pulse amplitude is described by [6]

I = nFAC (D/ p t_p)^1/2 P (s²-1)/[(s+P)(1+Ps)] (2.18)

where

s = exp(nFDE/(2RT)) (2.19)

P = exp[(nF/(RT))(E - E_1/2 + DE/2)] (2.20)

At a peak, P=1, then the current equation reduces to

I_p = nFAC (D/ p t_p)^1/2 (s-1)/(1+s) (2.21)

E_p = E_1/2 - DE/2 (2.22)

The half-peak width is a very important parameter in resolution. The half-peak width W_1/2 is a function of the pulse amplitude as follows [6]

W_1/2 = 2RT/(nF) cosh^-1[2 + cosh(nFDE/(2RT))] (2.23)

For large values of |DE| (say |DE| > 200/n mV), W_1/2 approaches to |DE|, and for small values of |DE| (e.g. |DE| < 20/n mV), this equation reduces to equation (2.15).

Unfortunately, the above theoretical equations are derived by neglecting the DC effect in DPP, and although this is not a problem when the ratio of the drop time to the pulse time is larger than 50, the resulting distortion makes the theoretical treatment complicated, especially for a non-reversible reaction.

2.11 Pseudo-Derivative Normal Pulse Voltammetry

DPV is a very sensitive electroanalytical technique due to the effective discrimination against the charging current. However, DPV has two problems associated with the slowly increasing DC ramp. As the DC ramp progresses, filming may occur on the surface of the electrode if species form insoluble mercury compounds [6]. Since the characteristics of the electrode are changed by such a film, the current may not correspond to the simple theory. Another problem is that the theory itself is complicated by the effect of the DC ramp. NPP avoids these two problems. But the disadvantage of NPV is its poor resolution because of the sigmoidal wave. To overcome this shortcoming, NPV polarograms can be differentiated to produce peak-shaped responses, and thus combine the best features of both DPV and NPV while avoiding some of their limitations. This pseudo-derivative normal pulse polarography (PDNPV) nevertheless is not sensitive as DPV.

The potential-time waveform in PDNPV is as in NPV, but the current data of PDNPV are displayed in a difference mode. The current is subtracted from those for the following pulses, and the difference is plotted as a function of potential, as in DPV.

The theoretical treatment of PDNPV is simple and easy. The reversible current-potential equation is similar to that of DPV except for the DC term [6]. The half-peak width or resolution is akin to that of DPV.

2.12 Stripping Voltammetry

Stripping voltammetry involves three main steps: electrodeposition (preconcentration), equilibration, and stripping. The first step is to concentrate the analyte from the dilute test solution into or onto the electrode at negative reduction (or positive oxidation) potentials, usually accompanied by stirring. The second step is to leave the solution to settle down. The third step is then to strip the preconcentrated analyte from the electrode back into the solution by using one of the polarographic techniques described above. A major advantage of this method is its extremely sensitivity. This is because the concentration of the analyte on the electrode is 100-1000 times greater than that in the starting solution [6]. Stripping analysis is the most sensitive of all commonly used electroanalytical techniques. Analyses can be performed at the trace level and are applicable to solutions containing metal ions in the concentration range of 10^-6 - 10^-12 M. Other advantageous features of stripping voltammetry include the capability for simultaneous multielement determination and relatively inexpensive instrumentation compared to that required for the spectroscopic techniques.

Step 1. The electrodeposition step

The metal ions Mⁿ⁺ of interest are deposited (preconcentrated) electrochemically into or onto the surface of an electrode (usually a mercury film electrode or a hanging mercury-drop electrode), in the form of amalgam, M(Hg):

A short-time electrolysis (30 sec to 5 min) in a stirred solution and at a potential suitable for the reduction of the ions of interest (E -E_1/2 about -200 mV) may result under proper conditions in a fairly concentrated amalgam. This step is called the electrodeposition step. The concentration of the metal ion in the film depends on concentration of Mⁿ⁺ in solution, time of electrolysis and rate of stirring. Since the electrodeposition is carried out on small electrodes, the amount of material deposited into it usually does not change significantly the concentration of the metal ions Mⁿ⁺ in the solution. Step 1 is only an intermediate step and there is no need to know the concentration reached in the amalgam. However, it can be estimated.

The enrichment of the metal M in the amalgam in respect to the initial concentration of Mⁿ⁺, C_Mⁿ⁺, is estimated in stirred solutions, using Nernst simplified model.

For typical laboratory conditions the Nernstian layer thickness in well-stirred solutions is about 20 .

As a result of electrolysis for a time t, the concentration of M in the amalgam, C_M(Hg), is

where A and V are the area and the volume of the mercury electrode.

The enrichment of the metal in the amalgam, using D = 10^-5 cm²/s, is

The enrichment factor at HMDE

For a hanging mercury-drop electrode A/V = 3/r, and for r ~0.03 cm it is 100 cm^-1, thus

For a 100 s deposition time, the enrichment factor is 50.

The enrichment factor at TFME

The TFME consists of a thin mercury film coated on glassy carbon. A/V for this electrode depends solely on the thickness of the film. Typical dimensions for a thin-film mercury electrode are: A = 0.2 cm² and film thickness about 10^-5 cm. The value of A/V for TFME is 10⁵, which is 1000 times that of HMDE.

As a result of a 100 sec electrolysis, the concentration of the metal in the amalgam will be ~5·10⁴ times larger than that of the metal in the solution.

The enrichment factor for a hanging mercury-drop electrode is 1000 times smaller than that for a thin mercury film. Nevertheless, substantial increase in concentration is achieved also with this type of electrode for electrolysis time t larger than 100 sec.

The degree of decrease of concentration in solution as result of the electrodeposition step is calculated for a mercury film (A = 0.2 cm²; thickness = 10^-4 cm). The initial concentration of the metal ions in the solution C_Mⁿ⁺ = 10^-8 M. The volume of the tested solution is 10 ml (10^-10 mole Mⁿ⁺). The concentration of the metal in the film, reached at the end of the electrolysis step C_M(Hg) = 10^-5 M (2·10^-13 mole). Thus, the decrease of concentration of Mⁿ⁺ in solution after electrolysis is negligible.

Step 2. Rest period

After a predetermined time, the stirring of the solution is turned off. The solution is allowed to become quiescent and the concentration of the metal in the amalgam - to reach uniformity. The rest period extends for about 30 sec, during which the applied potential remains unchanged, thus ensuring that no reoxidation of the metal by traces of oxygen takes place. During the rest period the electrodeposition current decreases.

Step 3. Stripping

After the preconcentration step, the deposited metal M is oxidized ("stripped") from the mercury electrode back into the solution by oxidation to the ionic form under conditions of diffusion control, using one of the voltammetric methods:

The anodic diffusion current is used to determine the concentration of the metal in the amalgam, which is proportional to time of electrolysis, stirring rate and concentration of Mⁿ⁺ in solution.

<big>Chapter 3
Features

This software analytically and digitally simulates voltammograms (polarograms) on virtually any mechanism at 10 electrode geometries in 6 techniques, calculates their theoretical peak current and potential, retrieve parameters by curve fitting, and separate overlapped peaks and baseline. </big>

· Digital simulation
Flexible for any mechanism up to second-order chemical reaction and absorption. You can type your mechanism and chemical symbols. An implicit finite difference algorithm is used.

· Analytical simulation
No divergence problem in simulation. No overflow problem in simulation. Fast simulation.

· Over 10 techniques
Linear sweep, CV, DC, normal pulse, reverse normal pulse, differential pulse, square wave, additive square wave, staircase voltammetries. Multi-cyclic voltammetry, cyclic normal pulse, cyclic differential pulse, cyclic square wave, cyclic additive square wave, cyclic staircase voltammetries.

· Surface concentration
It shows what happen each species in the electrode surface, and checking accuracy of simulation.

· Over 200 theoretical equations
You can compare your data with theoretical peak values to see if your experimental conditions reach theoretical limit or not.

· Over 20 effect factors

It can simulate over 20 effect factors, e.g. noise, charge current, resistance, preconcentration time and potential, convection, pH, reactant number, product number, electron number, electrode geometries, electrode size, electrode rotating speed, scan rate, concentration, pulse height, pulse width, sampling time, scan direction, scan cycle, diffusion coefficient, drop time, standard redox potentials, rate of electron transfer, transfer coefficient, diffusion coefficient, forward and reverse chemical reaction rate constants, temperature, electrode area, and experimental parameters, etc.

· Separating overlapped peaks
It manually and auto separates overlapped peaks into individuals, and extract real peak from voltammogram with noise and baseline. So you can exactly determine peaks.

· Preconcentration
You can change preconcentration conditions for stripping voltammetry.

· Pre-equilibration

Calculate the concentration at equilibrium.

· Curve fitting
It manually and auto fits the simulated voltammograms into experimental data, and extracts kinetic parameters from experimental data.

· Import and export data
You can export simulated data into your favor program (e.g. MS Excel). You can copy-and-paste the voltammogram into your document.

· Data Analysis

Derivative, integral, semi-derivative, semi-integral, convolution, deconvolution, Tafel analysis, convolution analysis. Semi-derivative is useful for CV. It can change a shape of reversible CV into symmetric peak so easy to determine peak.

· Over 10 electrode geometries
The planar, spherical, semi-spherical, cylindrical, rotating cylindrical, band, microdisk, thin film, disk, rotating disk, rotating semi-spherical electrodes, ring electrode, and rotating ring electrode.

· Tips
It shows tips for help when you put mouse cursor over a label.

Table 1 Feature

Version	Shareware	Student	Teacher	Academics	Professional	Competitor 2.0
Digital simulation	y	y	y	y	y	y
Analytical simulation	y	y	y	y	y	n
Theoretical peak	y	y	y	y	y	n
Multi-electron reaction	y	y	y	y	y	n
Surface concentration	y	y	y	y	y	n
Any species symbol	y	y	y	y	y	n
Tips	y	y	y	y	y	n
Import and export data	n	n	y	y	y	y
Show pulse current	n	y	y	y	y	n
Techniques:
LSV and CV	y	y	y	y	y	y
DC	y	y	y	y	y	n
Normal pulse	n	y	y	y	y	n
Reserve pulse	n	y	y	y	y	n
Differential pulse	n	y	y	y	y	n
Cyclic diff. pulse	n	y	y	y	y	n
Square wave	n	y	y	y	y	n
Cyclic square wave	n	y	y	y	y	n
Additive square wave	n	n	y	y	y	n
Cyclic additive square wave	n	n	y	y	y	n
Staircase	n	n	n	n	y	n
Cyclic staircase	n	n	n	n	y	n
Effect:
Absorption	y	y	y	y	y	n
Convection	y	y	y	y	y	n
Noise	y	y	y	y	y	y
Charge current	y	y	y	y	y	y
Resistance	y	y	y	y	y	y
Reactant number	y	y	y	y	y	n
Product number	y	y	y	y	y	n
Preconcentration time	y	y	y	y	y	n
Preconcentration potential	y	y	y	y	y	n
Pre-equilibration	y	y	y	y	y	y
pH	y	y	y	y	y	n
Electron number	y	y	y	y	y	n
Pulse height	y	y	y	y	y	n
Pulse width	y	y	y	y	y	n
First sampling time	n	n	n	n	y	n
Second sampling time	n	n	n	n	y	n
No. Of Second order chemical reaction	0	2	4	8	12	y
Analysis:
Differentiate	y	y	y	y	y	n
Integrate	y	y	y	y	y	n
Semi-differentiate	y	y	y	y	y	n
Semi-integrate	y	y	y	y	y	n
Manual fit	y	y	y	y	y	n
Auto fit	n	n	n	y	y	y
Manual separate	y	n	y	y	y	n
Auto separate	n	n	n	y	y	n
Electrode:
Planar	y	y	y	y	y	y
(Micro) spherical	y	y	y	y	y	y
(Micro) hemispherical	y	y	y	y	y	y
(Micro) cylindrical	y	y	y	y	y	y
Rotating cylindrical	y	y	y	y	y	n
Rotating hemispherical	y	y	y	y	y	n
Microdisc	y	y	y	y	y	n
Band	y	y	y	y	y	n
Thin film	y	y	y	y	y	n
Rotating disc	y	y	y	y	y	n
Ring	y	y	y	y	y	n
Rotating ring	y	y	y	y	y	n

Note: y = yes, n = no. Feature may be changed without notice.

<big>Chapter 4
Menu</big>

File menu

· Open Parameter submenu

Open a file of parameters and read parameters back. You can continue your work of last time. The Plot window title will show the file name.

· Save Parameter submenu
Save experimental parameters into a text file.

· Open Data submenu
Read data from a file and shows curves. The Plot window title will show the file name.

· Save Data submenu
Save data as a text file. e.g. if you save data as the .csv file, you can load it into MS Excel by double-clicking the .csv file.

· Copy To Clipboard submenu
Copy graph into clipboard, so you can paste graph into your document.

· Print submenu
Print graph.

· Exit submenu

Input menu

· Technique submenu

Select one of 7 techniques. The default technique is LSV and CV.

· Instrument submenu

Change instrument parameters. You can use the default values without any change.

· Mechanism submenu

Input your mechanism and species symbol in Digital simulation, or choose predefined mechanisms in Analytical simulation. The default mechanism is Fe³⁺ + e = Fe²⁺.

· Kinetics submenu

Change kinetic parameters. You can use the default values without any change.

· Concentration submenu

Change concentration, diffusion coefficient, absorption coefficient and maximum absorption amount of species.

Run menu

· Simulate submenu
Run simulation, and show curves on a Plot window. You can click on any point of curve to get the x and y values.

· Manual Fit submenu
Fit the simulated curve into experimental curve as you manually change parameter values.

· Auto Fit submenu
Auto fit the simulated curve into experimental data.

· Manual Separate submenu
Separate the overlapped peaks into individuals as you manually change parameter values.

· Auto Separate submenu
Auto separate the overlapped peaks into individuals.

Plot menu

· i vs. E submenu
Plot current i vs. potential E without run simulation.

· i pulse vs. E submenu
Plot the pulse currents vs. potential E without run simulation. It only available for pulse techniques.

· C0 vs. E submenu
Plot surface concentration C0 vs. potential E without run simulation.

· E vs. t submenu
Plot potential E vs. time t, which is imposed to electrodes in the technique.

· Convert submenu

Convert current into the surface concentration or the surface concentration into current.

· Convert i to C0 submenu

· Convert Co0 and Cr0 to i submenu

Convert surface concentrations of both oxidized and reduced species into current.

· Convert i1 to C0 for E mechanism 1 submenu

Convert current to surface concentration of oxidized and reduced species for simple charge reaction mechanism 1 in the Analytical Simulation panel.

· Convert Co0 to i1 for E mechanism 1 submenu

Convert a surface concentration of oxidized species into current for simple charge reaction mechanism 1 in the Analytical Simulation panel.

· Convert Cr0 to i1 for E mechanism 1 submenu

Convert a surface concentration reduced species into current for simple charge reaction mechanism 1 in the Analytical Simulation panel.

· Convert i8 to C0 for E mechanism 8 submenu

Convert current to surface concentration of oxidized and reduced species for catalytic reaction mechanism 8 in the Analytical Simulation panel.

· Convert Co0 to i8 for E mechanism 8 submenu

Convert a surface concentration of oxidized species into current for catalytic reaction mechanism 8 in the Analytical Simulation panel.

· Convert Cr0 to i8 for E mechanism 8 submenu

Convert a surface concentration reduced species into current for catalytic reaction mechanism 8 in the Analytical Simulation panel.

· Semi- dy/dt submenu

Semi-differentiate the y data with time t. Semi-differentiation is the same as deconvolution of current with 1/ Ö(pt). Since version 4.7, it changes to semi-differentiate with time t.

· Semi-integrate submenu

Semi-integrate the y data with time t. Semi-integrate is the same as convolution of current with the 1/ Ö(pt). Since version 4.7, it changes to semi-differentiate with time t.

· dy/dt submenu

Differentiate the y data with time, dy/dt. Since version 4.7, it changes to differentiate with time t, dy/dt.

· Integrate submenu

Integrate y data with time t. Since version 4.7, it changes to integrate with time t.

· Smooth submenu

Smooth y data.

· Log((i lim 1 - i)/(i – i lim 2)) submenu

Tafel plot. It converts S-shape of curve to a linear line. E.g. it converts DC voltamogram, convolution of CV into linear lines.

· X Data submenu

Multiply 0.001, 0.1, 10, or 1000 on X data. If your experimental potential data is not in Volt unit, you should convert to Volt unit by this submenu.

· X data reverse submenu

Reverse the order of data.

· Y Data submenu

Multiply 0.001, 0.1, 10, or 1000 on Y data. If your experimental current data is not in Amp unit, you should convert to Amp unit by this submenu.

· Option submenu
It is to change plot options, color, line style, etc.

Analyze menu

· Find Peak submenu

Find the peak current and potential of curves of the peak shape.

· Find Halfwave E submenu

Find the half wave potential and limiting current of curves of the S shape.

· Theoretical Peak submenu

Calculate the theoretical limiting current, peak current and potential from theoretical equations. You select a mechanism from Analytical Simulation in the Mechanism window. This submenu is active for Analytical Simulation only.

· Curve Number submenu
Shows current curve number. So you can analyze this curve.

· Next Curve Number submenu
Shows next curve number. So you can analyze this curve.

· Time submenu

Display the simulation time and curve-fitting results.

Help menu

· Logon submenu
You logon to activate menus by input of password.

· Manual submenu
Display this manual.

· Home Page submenu

· About submenu

Show version number and ID of this software.

Some menus will be activated only after you click the Simulate submenu or load data because they require data.

<big>Chapter 5
Input</big>

5.1 Techniques Window

1) Linear sweep, cyclic voltammetry, multi cyclic voltammetry
2) DC voltammetry
3) Normal pulse voltammetry and reverse normal pulse voltammetry
4) Differential pulse voltammetry and cyclic differential pulse voltammetry
5) Square wave voltammetry and cyclic square wave voltammetry

6) Additive square wave voltammetry and cyclic Additive square wave voltammetry

7) Staircase voltammetry and cyclic Staircase voltammetry

5.2 Instrument Window

This Instrument window is used to define the parameters of the instrument in experiment, which are as follows:

The potential range of the experiment (Estart, and Eend).
The scan rate (v).
The number of potential scan Cycles.
Solution resistance (R u) and double layer capacitance (C d).
The electrode Geometry (e.g., planar, spherical) and surface Area.

Instrumental Parameters Section:

E start: starting potential (V).
E end: ending potential (V).
E step: step potential (V).
v: scan rate (V/s). For square wave voltammetry, v=E _step/t _pulse.
E pulse: pulse potential (V).
T: temperature (°C).
t pulse: pulse time or pulse width for pulse voltammetry (s).
t drop: mercury dropping time or pulse length in pulse voltammetry (s).
Noise: noise signal (A).

ts1: first dimensionless sampling time, value is from 0.1 to 1. For square wave pulse, it is sampled in first pulse during of first half square wave. For different pulse, it is sampled in during before pulse. For normal pulse, it is sampled in pulse during. For staircase, it is sampled in a staircase during. It is not used for LS and CV. For digital simulation, you should set the Time Grid Factor in the Digital Simulation Model section to about 10 before you change the sampling time less than 1.

ts2: second dimensionless sampling time, value is from 0.1 to 1. For square wave pulse, it is for second opposite pulse of second half square wave. For different pulse, it is sampled in pulse during. It is not used for other techniques. For digital simulation, you should set the Time Grid Factor in the Digital Simulation Model section to about 10 before you change the sampling time less than 1.

Scan:
Single: single scan.
Cycles: cyclic scan, e.g. cyclic voltammetry (CV).
2 Cycles: 2-cycle scan.

3 Cycles: 3-cycle scan.

Electrode Section:

Planar: planar electrode.
(Micro) Spherical: spherical electrode or micro spherical electrode.
(Micro) Hemispherical: hemispherical electrode or micro hemispherical electrode.
(Micro) Cylindrical: cylindrical electrode or micro cylindrical electrode.
Microdisc: microdisc electrode, radius <1e-4 cm.

Polymer film: polymer film electrode. Its diffusion is definite.
Mercury film: thin film electrode, or thin layer cell. Its diffusion is definite.
(Rotating) Disc: rotating disc electrode with convection and a disk electrode.
(Rotating) Hemispherical: rotating hemispherical electrode with convection or a hemispherical electrode.
(Rotating) Cylindrical: rotating cylindrical electrode with convection or a cylindrical electrode.

(Rotating) Ring: rotating ring electrode with convection or a ring electrode.

Band: band electrode.
Area: electrode area (cm²). When you change the value of area, the value of radius is changed automatically.
Radius: electrode radius (cm). When you change the value of radius, the value of area is changed automatically.
Length: electrode length for cylindrical electrode or micro cylindrical electrode (cm).

Ring Radius 2: inner radius of ring electrode (cm).

Ring Radius 3: outer radius of ring electrode (cm).

Thickness: thickness of the polymer or mercury film electrode (cm).

Rotation: electrode rotation rate (rpm). For stationary electrodes, set this value to 0.

Preconcentration Section:

E pre: preconcentration potential (V).
R stir: stirring rate (rpm). Stirring solution.
t pre: preconcentration time (s).
t pre const: preconcentration time constant (/s).

Baseline section:

C dl: double layer capacitor for charge current (F).
R: resistance (Ohm).

I start: a starting current (A).

I end: an ending current (A).

Digital Simulation Model section:
Space Grid Factor: space expanding grid factor. Its value is from 0.001 to 0.9. The smaller value it is, the more accuracy simulation is, but the longer computer time. Default value is 0.5.

Time Grid Factor: the number of time grid in one pulse for normal pulse technique, or in one half pulse for square wave technique, or one potential step for other techniques. Its value is from 1 to 100. The larger value it is, the more accuracy simulation is, but the longer computer time. Default value is 1. It depends on techniques. The suggestion value is 5 for DC, and normal pulse techniques, 10 for staircase, differential pulse, and square wave techniques.

This section factors are used for digital simulation only, not for analytical simulation.

The most important three parameters are the Space grid factor, the Time Grid Factor and the Potential steps, which specify the resolution of the space and time grids, respectively, that are used in the simulation. Entering lower values for the Expanding grid factor and the Potential steps parameter or higher value for the Time Grid Factor will increase the resolution of the grid, which may increase the accuracy of the simulation. However, there is a point beyond which further increases in resolution will have no effect. Increasing the grid resolution will also increase the time required for the calculation, but this is generally no longer an issue with the speed of PCs now available. There are two occasions when decreasing the Space Expanding grid factor is useful, and these are discussed in later chapter (see Chapter 7 How Do You Know It is Right?).

5.3 Mechanism Window

You can type in your mechanism in the Digital Simulation section with any symbol. In order to faster computation, you should type in reactants only without products if chemical reaction is irreversible.

Uncheck the Digital Simulation checkbox, you will see the Analytical Simulation section. In the Analytical Simulation section, you choose a predefined mechanism. Although the electron number, and reactant and product numbers are inside the Digital Simulation section, they are for both Digital and Analytical Simulations.

A+ne = B charge reaction

A+ne <-> B reversible charge reaction

A(a)+ne = B(a) Langmuir absorption reaction

A(a)+ne <-> B(a) reversible Langmuir absorption reaction

5.4 Kinetics Window

This section is used to enter thermodynamic and kinetic parameters for the reactions involved in the mechanism. The following must be defined for each (Heterogeneous) electron transfer reaction:

The redox potential (E°).
The transfer coefficient (a).
The electron transfer rate constant (k_s).

Heterogeneous Reaction Section:

ks: heterogeneous standard rate constant (cm/s).
a: electron transfer coefficient.
E°: standard electrode potential (V).

Three parameters are required for each chemical (Homogeneous) reaction: the equilibrium constant (Keq), and the rates of the forward and reverse reaction (kf and kb). Only two parameters kf and kb can be defined by the user, since Keq = kf/ kb.

Homogeneous Reaction Section:

kf: forward chemical reaction rate constant. Its unit is /s for the first order reactions, or /sM for second order reactions.
kb: backward chemical reaction rate constant.
Keq: chemical equilibrium constant, Keq = k_f/ k_b.

Solution Section:

Electrolyte: electrolyte in solution.

C: concentration of electrolyte (M).

pH: the pH value of solution. The default value is 7.

Vis: viscosity of solution (cm /s).

Vol s: solution volume (ml).

5.5 Concentration Window

The Species Parameters are also entered in this dialog box. These are the diffusion coefficients (D) and concentrations of all the species involved in the redox mechanism. Two concentrations are shown here. The user enter the analytical concentrations (Canal), which are corresponding to the bulk concentrations that in the solution. The initial concentrations (Cinit) are the equilibrium concentrations at the electrode surface, and are determined by Estart, all Eo values, all Keq values, and all Canal values. It is the Cinit values rather than the Canal values that are used in the simulation. The calculation of the Cinit values can be switched off by disabling the Pre-Equilibration in its checkbox. If the calculation of Cinit is disabled, the Canal values are the same as Cinit.

Species Section:

D: diffusion coefficient (cm²/s). The default value is 10^-5.
C anal: analytical concentration (M).
C init: initial concentration at equilibrium (M). This concentration is used for simulation and theoretical calculation.
C fitted: fitted value of concentration (M).
C min: minimum concentration for fitting (M).
C max: maximum concentration for fitting (M).

b: Absorption coefficient (/M). The default value is 10^4. For non-absorptive species, set this value to 0.

G_m: Maximum absorption amount (mol/cm²). The default value is 10^-8.

Pre-equilibration checkbox:

When this option is enabled, it automatically assumes that all the chemical and electrochemical reactions in the vicinity of the electrode surface are in equilibrium as determined by the thermodynamic parameters: chemical equilibrium constant Keq, the standard potential E°, and by the starting electrode potential E_start. Then, the entered values of analytical concentrations are not identical to the corresponding initial concentrations.

It is a good idea to keep the pre-equilibration option enabled. When the pre-equilibrated and analytical concentrations are different significantly, the initial condition for the experiment and the simulation may not be what was expected. The degree, to which the pre-equilibrated concentrations may be considered to be the bulk concentrations, will depend upon time of pre-equilibration (i.e., the time between setting the starting potential and initiating the potential scan), the operative kinetics, and the geometry. The value of the initial concentrations will act as if they are the bulk concentrations. A reasonable assumption only if the electrode geometry does not produce steady-state diffusion and if the pre-equilibration time is much longer than the duration of experiment.

When the pre-equilibration is not selected, the pre-equilibrated and analytical concentrations are the same.

<big>Chapter 6
Playing Around</big>

6.1 Simulating over 20 Factors

A simplest way to run simulation is just to click the Run menu and then the Simulate submenu. It uses the default values to simulate a linear sweep voltammogram. You can change technique under the Technique menu, or change mechanism in the Mechanism window under the Mechanism menu, or change instrumental parameters in the Instrument windows under the Instrument menu, kinetic parameters in the Kinetic window under the Kinetic menu, or concentration and coefficients parameters in the Concentration window under the Concentration menu. You have choice for digital or analytical simulation by clicking the Digital Simulation checkbox in the Mechanism window. The analytical simulation is fast, and useful for comparison of digital simulation.

Notice that some menu (e.g. the Plot menu and the Analyze menu) will be activated only after run simulation or load data because they require data.

This software can simulates the effects to changing over 20 factors, e.g. charge current, resistance, noise, preconcentration time, preconcentration potential, convection, pH, the reactant number, and product numbers, standard redox potentials, rate of electron transfer, transfer coefficient, concentration, diffusion coefficient, forward and reverse chemical reaction rate constants, temperature, electrode area, and experimental parameters, etc.

6.1.1 Effect of pH

Click the Mechanism menu to open a Mechanism window, tick the “pH effect” checkbox, change the number of H⁺ in the charge reaction, and then click the OK button to close the Mechanism window. Click the Kinetics menu to open a Kinetics window, change the pH value in the Solution section, and then click the OK button to close the window. Run the simulation. You should see the peaks shift when pH is larger or less than 7. As the pH value increases, the peak shifts to more negative potential. For a charge reaction

a A + h H⁺ + ne = b B

where a is the reactant number, b is the product numbers, h is the number of H⁺, and n is the electron number. The relationship of the peak position with the pH value usually is linear:

E_p = k1 - k2 pH

Where k1 and k2 are constants. k2 depends on the electron number, the number of H⁺, the numbers of reactant and product, etc. For a=h=n=b=1, it becomes

E_p = k1- 0.059 pH

It shows that the peak position shifts to 59 mV more negative potential per pH. This relationship agrees with the theoretical equation (2.5).

6.1.2 Effect of Reactant And Product Number

For a charge reaction

a A + ne = b B

where a is the reactant number, b is the product numbers, and n is the electron number.

If you change the reactant and/or product number of charge reactions in Digital Simulation section, you should see the peak shape change. But for the charge reaction 2A+2e=2B, its current should be the same as the current for the charge reaction A+e=B, because the first reaction becomes to the second reaction by division of the first reaction by 2. This agrees with the eq. (2.5). For the reaction 2A+e=2B, it is the same as the reaction A+0.5e=B. By linear sweep technique at a planar electrode, its peak becomes lower and broader. Its peak current is 3e-5 A, which agrees with the theoretical value in the eq. (2.8). This is 0.5^1.5=0.35 lower than the peak current in the one-electron reaction. Its peak potential Ep= E_1/2-0.06 V, which is agree with the theoretical eq. (2.9). This is double of the peak movement to more negative in the one-electron reaction. Its half peak width |E_p/2 – Ep|=0.11 V, which agrees with the theoretical value in the eq. (2.11). This is double of the half peak width 0.055 V in the one-electron reaction.

6.1.3 Effect of Electron Number

If you change the electron number of charge reactions in Digital Simulation section for both Digital and Analytical Simulation, you should see that peak height increases and peak width decreases as the electron number increases. For LS technique at a planar electrode, its peak current increases, which agrees with the eq. (2.8), its peak potential shifts to more negative, which agrees with the eq. (2.9), and its half peak width decreases, which agrees with the eq. (2.11). If you change sign of electron number to negative, then reactant A becomes a reduced species, product B becomes an oxidized species, and the reaction becomes oxidation.

6.1.4 Effect of Electrode Geometry

Currents at different electrode geometries are different as their diffusion models are different. By keeping the same area of the electrodes, the peak current at the cylindrical electrode is larger than the peak current at the planar electrode. The peak current at the spherical electrode is larger than the peak current at the cylindrical electrode. These agree with theoretical equations.

6.1.5 Effect of Electrode Size

The peak current increases linearly with the electrode area for planar electrodes, or with square of the electrode radius for planar disk electrodes. But it increases linearly with square root of the electrode area or with the electrode radius for microelectrodes, regardless of electrode geometry, spherical or disk electrodes. It agrees with theoretical equations.

Not only the electrode geometry has effects on shape of current, but also the electrode size does. When the electrode size is very small, e.g. electrode radius is 1e-4 cm, its current becomes the S-shape from the peak shape, and steady-state current at the spherical electrode in LS technique is 1.2e-9 A, which agrees with the eq. (2.4). The steady-state current at the micro disc electrode in LS technique is 3.86e-10 A, which agrees with the eq. (2.4). A shape of linear scan voltammogram at spherical electrodes is changed from peak shape to S-shape. When the products of scan rate and radius, v r > 10^-5, the shape is peak. When v r < 10^-7, the shape is wave. The steady-state current is independence of the time factors, e.g. the scan rate, the electrode-rotating rate, the pulse time, the drop time, or the sampling time.

Note that the planar electrode geometry is not available for microelectrodes because the planar electrode has not edge effect of microelectrodes.

6.1.6 Effect of Electrode Rotating Speed

For the rotating electrodes, current increases as the electrode rotating speed increases, which agree with theoretical equations. When the ratio of rotating speed to scan rate, w/v < 1, the shape is peak. When high-speed w/v > 10³, the shape becomes S-shape wave. If you set the rotation speed to 0, the current should be the same as one without rotation.

6.1.7 Effect of Scan Rate

For LS and CV techniques at a planar electrode in a simple reversible and irreversible charge reactions, the peak current increases linearly as square root of scan rate increases, which agrees with the eq. (2.8). In absorption reaction, the peak current increases linearly with scan rate. But in quasi-reversible reaction, these relationships are not linear anymore. In catalytic reaction, the limit current is independent of scan rate. For reversible charge and absorption reactions, the peak location and the width at half peak are independent of scan rate. For irreversible charge and absorption reactions, the peak widths at half peak are still independent of scan rate, but the peak locations are not. The reduction peak location shifts linearly to more negative potential and the oxidized peak location shifts linearly to more positive potential as log of scan rate increases. Therefore the separation between the reduced and oxidized peaks becomes larger as scan rate increases. These agree with theoretical equations.

For square wave and additive square wave techniques, the peak current increases linearly as square root of frequency increases.

At a microelectrode in a simple charge reaction, the steady-state currents are independent of the time factors (e.g. the scan rate, the electrode-rotating rate, the drop time, the pulse time, or the sampling time) for all LS, DC, and normal pulse techniques, which agree with the theoretical equations.

6.1.8 Effect of Preconcentration Time

For anode stripping voltammetry, set the start potential to –0.3 V and the end potential to 0.3 V. Select the Preconcentration checkbox in the Instrument window. Change the preconcentration time in the t pre field. The preconcentration time usually is a number of minutes. If you increase the preconcentration time, e.g. from 600 second to 1000 second, the peak current increases, but the peak current will have a limit. If you set the preconcentration time to 0, you should see that the peak current is the same as one without preconcentration. You should enter your mercury film thickness into the Length field in the Electrode section of the Instrument window if you use a planar mercury film electrode.

6.1.9 Effect of Preconcentration Potential

Select the Preconcentration checkbox in the Instrument window. Change the preconcentration potential value in the E pre field. If you increase the preconcentration potential, e.g. from 0 to –0.3 V for the standard electrode potential of 0.1 V, the peak current increases, but the peak current will have a limit. It reaches the limit when the preconcentration potential value usually is -0.2/n V to species’ standard electrode potential for anode stripping or 0.2/n V for cathode stripping. E.g. you further increase the preconcentration potential, e.g. from –0.3 to –0.4 V, the current will not increase anymore.

6.1.10 Effect of Concentration

For a simple charge reaction, as the bulk concentration of reactant increases, the peak currents increase linearly, which agrees with the theoretical equations. But for absorption reaction, the peak current increases linearly in lower concentration, then increase slow nonlinearly, finally reach a limit at high concentration.

6.1.11 Effect of Pulse Height

In pulse voltammetries, for small pulse, the peak currents increase linearly with pulse height, which agrees with the theoretical equations. For large pulse, the peak currents increase, but not linearly anymore. But resolutions become poor as pulse height increases.

6.1.12 Effect of Pulse Width

In pulse voltammetries, as the pulse width increases, the peak or limiting current decreases, which agrees with the theoretical equations.

For normal pulse and different pulse techniques, the limiting or peak current decreases linearly as square root of pulse time increases, which agrees with the eq. (2.2).

6.1.13 Effect of Sampling Time

As the sampling time decreases, the peak or limiting current increases and the charge current increases as well, which agrees with the theoretical equations. In Staircase Voltammetry, the peak potentials shift to positive potential as well. You can change the first sampling time different from the second sampling time to offset charge current to zero. But the sampling time has not effect for steady-state current at the microelectrode.

6.1.14 Effect of Techniques

From current shape point of view, techniques are divided into three types. The first type is S-shape. The shapes of DC and normal pulse polarogram are S-shape. The second type is peak shape. The shapes of differential pulse and square wave voltammograms are peak-shape. But there is effect of the DC term on differential pulse voltammogram. When you check the Pulse Current checkbox in the Options window, you will see these pulse current and DC current. The third type is the peak tailor shape. For LS, CV, additive square wave, and staircase techniques, their current shapes usually are the peak tailor shape, but depend on scan rate, electrode geometry, electrode size, reaction mechanism, etc. The pulse currents in square wave technique are the same as the current in the staircase technique when pulses become zero, which agree with theory.

6.1.15 Effect of Scan Direction

For a reduction reaction, the scan direction is from positive to negative, i.e. the start potential is large than the ending potential, so the current is positive. For an oxidation reaction, the scan direction is from negative to positive, i.e. the start potential is less than the ending potential, so the current is negative.

6.1.16 Effect of Scan Cycle

For CV, current in second cycle is different from current in first cycle. But the current in third cycle is close to the current in second cycle. So third cycle is enough.

6.1.17 Effect of Diffusion Coefficient

For CV in reversible simple charge reaction, the potential shift of the CV associated with a change in the ratio of diffusion coefficient D_A/D_B. It shows that the peak potential shifts to more positive as the ratio increases. This agrees with theoretical equation dE/d ln(D_A/D_B) = RT/(2nF). However, the height of the reverse peak almost does not change, although a very small change occurs because of the changing relative position of E_end and E_peak.

6.1.18 Effect of Catalytic Mechanism

For catalytic mechanism

A+e=B, C+B->A

Assume that its charge reaction is reversible, chemical reaction is irreversible, the concentration of species C is much larger than the concentration of species A, and chemical reaction rate is very large. The currents in LS, CV, staircase, and additive square wave techniques become S-shape from peak-shape. The limiting current increases linearly with square root of the concentration of species C and chemical reaction rate, but is independence of the time factors, e.g. the scan rate, the electrode rotating rate, the drop time, the pulse time, or the sampling time. It is similar to the steady-state current. This agrees with the theoretical equations. For digital simulation, if you set both chemical reaction rates kf=0 and kb=0, it becomes the same as one in a simple charge reaction without catalytic mechanism.

6.1.19 Effect of Drop Time

For charge reaction in DC, NPV and DPV techniques, the limiting or peak currents decrease linearly as square root of the drop time increases, which agrees with the eq. (2.2).

6.1.20 Effect of Chemical Reaction Rate

For a reaction A+e=B, B->C, a reverse peak in CV decreases as the chemical reaction rate increases. You can change the rate up to 10^20.

6.1.21 Effect Of Heterogeneous Standard Rate Constant

If the heterogeneous standard rate constant ks is very large e.g. 10^4, then the charge reaction is reversible, and the heterogeneous standard rate constant has not any effect. If the heterogeneous standard rate constant is very small, e.g. 10^-4, then the charge reaction is irreversible, and the heterogeneous standard rate constant has effect on the peak position only, as the standard potential.

6.1.22 Effect Of Absorption Reaction

The adsorptive system assumes that the adsorption obeys Langmuir isotherm.

For reversible absorption reaction, the forward and reverse currents are symmetric peaks in the same location and same height. The reverse current looks like mirror of forward current.

For non-reversible absorption reduction reaction, the forward and reverse currents are not symmetric peaks in the same location anymore. The forward current peak moves to negative direction, while its reserve current peak moves to positive direction. The peak separation becomes larger as the rate ks becomes smaller. This agrees with theoretical equations.

6.1.23 Effect Of Absorption Coefficient

For reversible absorption reaction, when absorption coefficient of product is larger than absorption coefficient of reactant, then peak move to positive direction. When absorption coefficient of product is smaller than absorption coefficient of reactant, then peak moves to negative direction.

For irreversible absorption reduction reaction, forward peak location is independent of absorption coefficients.

6.2 Surface Concentration

After run simulation, click the Plot menu, then click the C0 vs E submenu to show surface concentrations. The concentrations at the electrode surface are useful for checking accuracy of simulation.

For a reduction reaction A+e=B, the concentration of reactant decreases and the concentration of product increases as potential moves to more negative since scan. The concentration of reactant decreases to zero and the concentration of product increases to the same as initial concentration of reactant at the end of scan. Because all amount of species A becomes the same amount of B at the end of scan. Their concentrations cross at the half wave potential. These agree with the theoretical eq. (2.5).

For a reduction reaction A+e=2B, the concentration of reactant decreases to zero and the concentration of product increases to double of initial concentration of reactant at the end of scan, which agrees with theory because one molecular of species A produces two molecular of species B.

For a reduction reaction 2A+e=B, the concentration of reactant decreases to zero and the concentration of product increases to half of initial concentration of reactant at the end of scan, which agrees with theory because two molecular of species A produces one molecular of species B.

For EE reactions A+e=2B, B+e=2C, the maximum surface concentration of the species C is double of the species B, and the maximum concentration of the species B is double of the species A, which agrees with theory, because one molecular of species A produces two molecules of species B and two molecules of species B produces four molecules of species C.

For EE reaction 2A+e=B, 2B+e=C, it is opposite to the above reaction.

The surface concentrations look like the same in reversible simple reaction, regardless of scan rate, electrode size, electrode geometry, and techniques if pulse height is zero, digital simulation, and analytical simulation. For NPV and DPV, the surface concentrations move the pulse potential. For square wave and additive square wave techniques, the surface concentrations move half the pulse potential.

6.3 Comparing Curves

After run first simulation, click the Plot menu, and then the Option submenu. Select the Overlap checkbox, and then run second simulation. You can change color and line styles for individual curves. This software can compare up to six curves.

6.4 Analyzing Data

This software can analyze the x,y data for peak location, peak height, peak width, convolution, deconvolution, semi-derivative, derivative, integral, semi-integral, curve fitting, and separating overlapped peaks. Semi-derivative is useful for CV. It can change the asymmetric peak shape of CV into the symmetric peak for easy measurement.

6.5 Calculating Theoretical Limiting Current

Click the Analyze menu and then the Theoretical Peak submenu to calculate the theoretical values of limiting current, peak current, peak location, and peak width. Select a mechanism from the Analytical Simulation section in the Mechanism window. The theoretical limiting values are good both for checking simulation accuracy and for seeing if your experiments reach the theoretical limit or not.

6.6 Extracting Parameters by Curve Fitting

The difficult part of a voltammetric experiment is extracting the chemical information from the current-voltage curve. Apart from very simplistic analysis, the measured current cannot be directly interpreted. This software can extract the chemical information from the whole current-voltage curve. It helps to get parameter values and mechanisms.

6.6.1 Fitting to Simulation Curve

In order to extract kinetic parameters, you can fit a simulation curve to another simulated or experimental curve. It can retrieve any of 30 parameters (e.g. concentration C, standard electrode potential E°, and the heterogeneous standard rate constant ks) from voltammogram by curve fitting. Select parameters that you want to fit, input the minimum and maximum values of the parameters. e.g. after run simulation with all default values, select a concentration, then change the C value from 1e-3 to 2e-3 in the Species section, click the Auto Fit menu. You will see the fitted value of 0.001 in the C fitted field next to the C text field. Notice that when you auto fit, you should not click on the OK button on the Chemicals window to close the Chemicals window, otherwise you will get the “Runtime error 6: overflow”. This bug is fixed since version 4.6.

You should manual fit before auto fit. The manual fit shows how well your initial guesses values work. If it diverged, you should change their initial values, then try again. By the manual fit, you should change the initial values every time of run.

6.6.2 Fitting to Experimental Curve

One of the key functions of this software is a fitting routine that optimizes selected simulation parameters to provide the best fit between the experimental and simulated voltammograms. Data is text file formats without header. There are a number of important points to note:

The data must be arranged as potential-current couples.
The potential and current values within a data couple must be separated using a comma.
The potential step must be constant.

It should also be stressed that the potential step (i.e., the difference between adjacent potential values) must be constant throughout the data set. We have observed that variation of the potential step value can cause considerable problems with the fitting routine.

It is similar to fit simulated curves. Click the File menu, the Open submenu, the Data submenu to select your data file. But you should input your experimental values of E_start, E_end, E_step, etc. into the Experimental section. This software requires that data are in SI unit and first peak is positive value. If your experimental data are not, please convert your experimental data to in SI unit. E.g. click the Analyze menu, and then the 0.001Y submenu to convert current from mA to A. After the experimental data (text) files are selected and loaded into this software, the mechanism and parameter values are then entered, and the parameters to be varied are selected. A parameter of start current in Baseline section should be zero. Once these have been done, you can start fitting operation by clicking the Fit menu.

It is important to note that any given voltammogram may be accurately simulated by more than one mechanism and/or set of parameter values. Experimental measurements should therefore be made over a wide range of parameter values. The most common variables are scan rate and technique, although variation of concentration and/or temperature can also be used. If one set of parameter values can provide a good match between the experimental and simulated voltammograms measured over a wide range of scan rates (and/or techniques), then this is good evidence that these parameter values are correct. However, it does not prove that the correct mechanism and parameter values have been selected. It is up to the user to determine whether the selected mechanism and parameter values are chemically and electrochemically reasonable (i.e., are they consistent with the results of electrochemical studies on similar systems?). The sensitivity of the fit to variations in the parameters values must also be investigated.

It should noted that for irreversible charge reactions, you cannot fit both the heterogeneous standard rate constant and the standard electrode potential in the same time because they become dependent each other.

6.7 Separating Overlapped Peaks

For multi charge reactions, overlapped peaks are usually observed. There are errors in determination of peak height and position in each reaction as the overlapped peaks. It is necessary to separate overlapped peaks into individual peaks. If you click the Manual Separate submenu under the Run menu, you will see individual peaks. Click the Find Peak submenu under the Analyze menu, and then it will give out individual peak heights and positions.

6.8 Separating Faradic Current From Background Current

Because double layer capacitor and resistance, there is background current such as charge current. This software provides two ways to separate Faradic current from background current.

1. To simulate current with background current, click the Input menu, the Instrument submenu, change the value of C_d to 0.0001 and the value of resistance R to 10000 in the Baseline section, and run simulation. You should see current with baseline. When click the Manual Separate menu, you should see third curve for the Faradic current without background current.

2. To simulate background current, click the Input menu, the Instrument submenu, change the value of C_d to 0.0001, the value of resistance R to 10000 in the Baseline section and the value of the concentration C to 0 in the Concentration window, and run simulation. You should see background current. Then, select the Overlap checkbox in the Option window, change the value of the concentration C to 1e-3 in the Concentration window, and run simulation. You should see second curve for current with background current. Finally, click the Plot menu, the Y Data submenu, and the Y2-Y1 submenu. You should see third curve for the Faradic current without background current.

<big></big>Chapter 7
How Do You Know It Is Right?

Any simulation procedure has its stability and accuracy limitations. This software provides four ways to check for accuracy of simulation.

The first approach is to compare simulated voltammograms with theoretical values. Uncheck the Digital Simulation checkbox to Analytical Simulation, select your mechanism, then click the Theoretical Peak submenu from the Analyze menu, it calculates out the theoretical peak or limiting current and peak potential.

The second method is to compare digital simulated voltammograms with analytical simulation voltammograms. However, there is no guarantee that mechanisms proposed in the program are yours.

The third approach is to change the computational parameters. The exponential time and space grids used by the implicit finite difference computation are characterized by t and x. Although these parameters are not defined explicitly in the user interface, changing the potential steps, and the space expanding grid factor in the Instrument window respectively can alter their values. Decreasing the values of these parameters almost always improves the accuracy of a given simulation, but the computation time is also increased. This software sets default values for these parameters that will produce acceptable accuracy (e.g. better than 0.5%) in most cases. However, there are instances where the particular set of the used parameter values causes computational problems. Decreasing the values of one or both of these Model Parameters can eliminate this problem. It is possible to obtain a simulated voltammogram that looks reasonable but is still inaccurate. It is good practice to run any simulation using different values for the expanding grid factor and the potential steps to check for accuracy. A significant difference in the results indicates that the default values are inadequate for accurate simulation. Because the smaller values of the potential step and/or space expanding grid factor will effect a noticeably longer computation time, we should use the possible largest values, which retain acceptable accuracy.

The fourth method is to check the concentration at the electrode surface. See Section 2.6 Surface Concentration.

<big></big>Chapter 8
Frequently Asked Questions (FAQ)

Q: Which platforms can Polar run on?
A: Its 32-bit version Polar runs on IBM PC under Windows 95/98/NT while its 16-bit version Polar runs under Windows 3/3.1/3.11/95/98/NT.

The 32-bit version needs Microsoft Visual Basic 6 runtime DLL files (e.g. msvbvm60.dll, comdlg32.ocx) in the same directory as Polar or in the directory \windows\system for Windows 3.11 or 95, or in the directory \winnt\system32 for Windows NT.

The 16-bit version needs Microsoft Visual Basic 4 runtime DLL files (e.g. vb40016.dll and oc25.dll) in the same directory as Polar or in the directory \windows\system for Windows 3.1, or in the directory \winnt\system for Windows NT.

Q: I cannot save a file.

A: You miss the Microsoft Visual Basic 6 runtime DLL file comdlg32.ocx.

Q: Where can I download these dll?

A: Microsoft Visual Basic 6 runtime DLL files are from http://www.simtel.net/simtel.net/win95/dll.html, where msvbvm60.dll is inside simvb6-5.zip. Microsoft Visual Basic 4 16-bit runtime DLL files are from http://www.simtel.net/simtel.net/win3/dll.html.

Q: When I click the Simulate menu, I got error: “No data”, or "Run-time error 13”, with the message: "Type mismatch".

A: I guess you are running it under non-English version of Windows. Please change language setting to English in the Regional Setting of the Control Panel, and restart Polar. Or try it under English version of Windows. Some non-English versions of Windows have problem to run English version program.

Q: When I installed to run setup.exe, an error occurred:
while registering the file
>c:\windows\system\MSRD2x35.dll
Shall I (Abort, Retry, Ignore)?
A: Ignore. Do not worry about MSRD2x35.dll. Running Polar did not use it, setup.exe check it only.

Q: Still have install problem?
A: You should close all programs (include Office, Mail) before install Polar. If you still have problem, try to register file msvbvm60.dll by double click or type following command in DOS:

Cd \windows\system
Regsvr32 msvbvm60.dll
then start Polar.

Q: Why are some menus inactive?
A: Some menus will be activated only after you click the Simulate menu or load data because they need data.

Q: I cannot see any chemical reaction in Shareware version. Is this part of the program not finished yet or is it only available in the registered version?
A: It is only available in the registered versions. You can change chemical reaction rate k_f up to 10²⁵. The registered versions simulate virtually any mechanisms.

Q: Does it include my mechanism?
A: If your mechanism is missing, please send your requirement into author. Author may add your mechanism into new version special for you.

Q: Can it fit data by curve fitting?
A: Yes. Click to select a parameter that you want to fit, and then click the Auto Fit menu.

Q: Can I change graph into other program Lotus 123 or Excel?
A: Yes. You export data in text file, and then read data into Lotus 123 or Excel.

Q: Some submenus semi-derivative, semi-integral, derivative, and integral, seem to not work sometime. How can I do?
A: You should first click the Next submenu under the Plot menu, then try semi-derivative submenu.

Q: How much does registration cost?
A: From $99.

Q: How can I get registered version?
A: You will receive it if you pay author register fee.

Q: What are differences among Shareware, Student, Teacher, Academics and Professional versions?
A: The Shareware version is for try before you buy, the Student version is for students, the Teacher version is for teachers, the Academic version is for academics, and the Professional version is for professionals. Please see Table 1 Feature for details.

Q: When I run the SWV with default conditions as a digital simulation, it does not appear to give the correct curve. Why?
Because default conditions are for linear sweep and CV only. For SWV, DC, NPV and DPV, you should change scan rate v to 0.01. For SWV you should calculate correct scan rate by v=E step/t pulse before run digital simulation.

Q: Is it possible to click on a point and then have displayed both the current and potential for the point?

A: Yes, since version 4.7.

Q: How to simulate oxidation reaction?

A: change the scan potential to the E_start < the E_end in the Instrument window.

Q: When I click on the Auto Fit menu, I got “Runtime error 6: Overflow”. Why? How to fix it?

A: Because you close the Chemicals window. When you auto fit, you should not click on the OK button on the Chemicals window to close the Chemicals window, otherwise you will get the “Runtime error 6: overflow”. It has been fixed since version 4.6.

Q: Is it licensed for user or machine?

A: Software is like hardware. If you want to use different PC, you had to buy different machines. Can you just buy a single machine in order to use different PC? Many users can share one machine. It is the same as many users can share one copy of software. Therefore, software license is for machine, not for user. One copy of software is for one machine. If you want to use software for different PC, you should buy more copies of software, and you will get discount.

Q: What happen when I upgrade machine?

A: When you upgrade the hardware of machine, you can change motherboard, CPU, RAM, add hard disk, but it is suggested that you should keep your old hard disk, so your software ID does not change, it will work.

Q: What data format can be imported?

A: The x-y pairs of text data. Please see Chapter 6.6.2 Fitting to Experimental Curve.

Q: How does it compare to competitors?
A: Polar has advantages over competitors (see details on the feature table in Chapter 2 Features):

1. Competitor only digitally simulates a single technique CV at 5 electrode geometries, while Polar analytically and digitally simulates over 10 techniques at over 10 electrode geometries.

2. Competitor cannot simulate absorption while Polar can.

3. Competitor cannot simulate reactions with reactant or product number, e.g. 2A+e=B, while Polar can.

4. Competitor cannot separate overlapped peaks, while Polar can.

5. Competitor does not support Windows 95 features, e.g. long filename, while Polar does.

6. Competitor cannot simulate effect of pH, while Polar simulates over 20 effect factors.

7. Competitor cannot calculate any theoretical value, while Polar includes over 200 theoretical equations.

8. Competitor cannot analyze data, while Polar can.

9. Competitor cannot check simulation accuracy by surface concentration, while Polar can.

10. You download and try Polar free.

11. Polar is much cheaper and more powerful.

12. You do not worry about if you lose the Dongle. Competitor is copy-protected by the Dongle, but Polar is not.

Q: I still have questions.

A: Please post your questions to Electrochemistry Forum in website www.electrochem.net.

<big>Chapter 9
References</big>

[1] W. Huang, T. Henderson, A.M. Bond and K.B. Oldham, Curve fitting to resolve overlapping voltammetric peaks: model and examples, Anal. Chim. Acta, 1995, 304, 1-15.

[2] W. Huang and B. Hibbert, Computers & Chem., 1995, 19(4), 433.

[3] W. Huang and B. Hibbert, Computers & Chem., 1995, 19(4), 435.

[4] W. Huang and B. Hibbert, Polar 2.0 for Windows: simulator of voltammogram, Chem. in Aus., 1996, 131.

[5] J. Mo, P. Cai, W. Huang and F. Yun, Theory and application on multiple semidifferential electrochemical stripping analysis with thin mercury film formed in situ, Acta Chimica Sinica, 1984, 42(6), 556-561, [CA 101: 162712].

[6] A. J. Bard and L. R. Faulkner, Electrochemical Methods, John Wiley & Sons, New York, 1980.

[7] D. Britz, Digital Simulation in Electrochemistry, Springer-Verlag, Berlin, 1988.

[8] Roy Lowry, Polar, Physical Science Educational Review, 2002, Nov., 3(2), 26-27, http://dbweb.liv.ac.uk/ltsnpsc/swrevs/5polar.htm.

Contents

<big>Chapter 1 Introduction</big>

<big>Chapter 2 Polarography and Voltammetry</big>