Transferred Charge and Number of Electrons from Chronoamperogram

Evaluating transferred charge and the corresponding number of electrons from chronoamperogram related to electrochemical experiment, performed simultaneously with the EPR time series measurement or independently of the latter. To acquire charge, the input $I$ vs $time$ relation (coming from the data.at) is integrated by the pracma::cumtrapz function. Prior to integration a capacitive current correction must be done, especially if it is relatively high in comparison to faradaic one. Afterwards, the number of electrons is calculated by Faraday's law (see details). The output plot can be visualized either as $Q(N_{\text{e}})$ vs $t$ (time) or as $Q(N_{\text{e}})$ vs $E$ (potential, if available in the input data.at).

Usage

eval_ECh_QNe_chronoamp(
  data.at,
  time = "time_s",
  time.unit = "s",
  tlim = NULL,
  Current = "I_A",
  Current.unit = "A",
  E = NULL,
  E.unit = NULL,
  ref.electrode = NULL,
  Ne.output = TRUE,
  separate.plots = FALSE
)

Arguments

data.at: Data frame (table) object, including required columns like Time ($t$), Current ($I$). Even though an arbitrary column label can be used, the best option is to use labels such as time_s, I_uA or I_mA. Optionally, column related to potential ($E$) may be present as well for the transferred charge ($Q$) or number of electrons ($N_{\text{e}}$) vs $E$ visualization (see also the arguments E, E.unit and ref.electrode).
time: Character string, pointing to time-axis/column header in the original data.at. Default: time = "time_s" (time in seconds).
time.unit: Character string, pointing to time-quantity unit. There are following units available: time.unit = "s" (default), time.unit = "ms", time.unit = "us" (microseconds), time.unit = "ns" or time.unit = "min".
tlim: Numeric vector of the time-quantity lower and upper limit, e.g. xlim = c(5,400) (time in seconds. Default: tlim = NULL actually setting the entire time interval from the original dataset.
Current: Character string, indicating the Current($I$)-axis/column quantity name in the original data.at object. Default: Current = "I_A" (current in $\text{A}$).
Current.unit: Character string, pointing to Current quantity unit like Current.unit = "uA" (microamps) Current.unit = "A" (default), Current.unit = "mA" and Current.unit = "nA".
E: Character string, referring to $E$(potential) column name within the input data.at dataset. Default: E = NULL, corresponding to situation, when one doesn't want to visualize transferred charge (or number of electrons) vs $E$.
E.unit: Character string, setting the potential unit (see E argument), usually E.unit = "mV" or E.unit = "V". Default: E.unit = NULL, corresponding to situation, when one doesn't want to visualize transferred charge (or number of electrons) vs $E$.
ref.electrode: Character string, corresponding to reference electrode notiation/label, e.g. ref.electrode = "Ag-quasiref" or ref.electrode = "Fc/Fc+". Default: ref.electrode = NULL (displayed potential is not related to any ref.electrode).
Ne.output: Logical. Should be the number of transferred electrons (Ne) presented within the plot ? Default: Ne.output = TRUE.
separate.plots: Logical. By default, both relations: $Q(N_{\text{e}})$ vs $t,E$ (time or potential) are shown in one plot (separate.plots = FALSE). One can separate $N_{\text{e}}$ vs $t,E$ and $Q$ vs $t,E$ into individual plots setting up the separate.plots = TRUE.

Value

List containing the following elements, depending on separate.plots:

If separate.plots = FALSE
df

Original data.at data frame object with the following additional columns/variables: Q_C (charge in coulombs), Q_mC (charge in millicoulombs, if the maximum charge $\leq 0.099\,\text{C}$) and Ne (number of transferred electrons, if Ne.output = TRUE).

plot

Side-by-side plot object (list) of $N_{\text{e}}$ vs $t,E$ as well as $Q$ vs $t,E$.
If separate.plots = TRUE
df

Original data.at data frame object with the following additional columns/variables: Q_C (charge in coulombs), Q_mC (charge in millicoulombs, if the maximum charge $\leq 0.099\,\text{C}$) and Ne (number of transferred electrons, if Ne.output = TRUE).

plot.Ne

Plot object (list) of $N_{\text{e}}$ vs $t,E$.

plot.Q

Plot object (list) of $Q$ vs $t,E$.

Details

When quantitative EPR is carried out along with electrochemistry simultaneously, one can easily compare the number of radicals with the number of transferred electrons. Number of radicals ($N_{\text{R}}$) are evaluated from quantitative measurements (see also quantify_EPR_Abs), whereas number of transferred electrons ($N_{\text{e}}$) is related to charge ($Q$), according to: $$N_{\text{e}} = (Q\,N_{\text{A}})/F$$ where $N_{\text{A}}$ stands for the Avogadro's number and $F$ for the Faraday's constants. Both obtained by constans::syms$na and constants::syms$f, respectively, using the constants package (see syms). If both numbers match ($N_{\text{R}} = N_{\text{e}}$), it reveals the presence of one-electron oxidation/reduction, while different numbers may point to a more complex mechanism (such as comproportionation, follow-up reactions, multiple electron transfer).

References

Bard AJ, Faulkner LR, White HS (2022). Electrochemical methods: Fundamentals and Applications, 3rd edition, John Wiley and Sons, Inc., ISBN 978-1-119-33405-7, https://www.wiley.com/en-us/9781119334064.

Pingarrón JM, Labuda J, Barek J, Brett CMA, Camões MF, Fojta M, Hibbert DB (2020). “Terminology of Electrochemical Methods of Analysis (IUPAC Recommendations 2019).” Pure Appl. Chem., 92(4), 641–694, https://doi.org/10.1515/pac-2018-0109.

Neudeck A, Petr A, Dunsch L (1999). “The redox mechanism of Polyaniline Studied by Simultaneous ESR–UV–vis Spectroelectrochemistry.” Synth. Met., 107(3), 143–158, https://doi.org/10.1016/S0379-6779(99)00135-6.

Hans W. Borchers (2023). pracma: Practical Numerical Math Functions. R package version 2.4.4, https://cran.r-project.org/web/packages/pracma/index.html.

Examples

## loading package built-in example file =>
## `.txt` file generated by the IVIUM potentiostat software
triarylamine.path.cv <-
load_data_example(file = "Triarylamine_ECh_CV_ivium.txt")
## the data frame contains following variables:
## time, desired potential, current and the actual/applied
## potential
triarylamine.data.cv <-
  data.table::fread(file = triarylamine.path.cv,
    skip = 2,
    col.names = c("time_s",
                  "E_V_des", # desired potential
                  "I_A",
                  "E_V_app") # applied potential
  )
#
## simple chronoamperogram plot
plot_ECh_VoC_amperogram(data.vat = triarylamine.data.cv,
  x = "time_s",
  x.unit = "s",
  Current = "I_A",
  Current.unit = "A",
  ticks = "in"
 )

#
## transferred charge and the number of electrons
## with default parameters
triarylamine.data.QNe <-
  eval_ECh_QNe_chronoamp(data.at = triarylamine.data.cv)
#
## data frame preview
triarylamine.data.QNe$df
#>      time_s E_V_des          I_A      E_V_app           Q_C          Q_mC
#>       <num>   <num>        <num>        <num>         <num>         <num>
#>   1:    0.0  0.0000 -3.95429e-08 -0.000251648 1.0036104e-07 1.0036104e-04
#>   2:    0.5  0.0025 -3.35184e-08  0.002265060 8.2095711e-08 8.2095711e-05
#>   3:    1.0  0.0050 -2.92210e-08  0.004787570 6.6410861e-08 6.6410861e-05
#>   4:    1.5  0.0075 -2.54160e-08  0.007305210 5.2751611e-08 5.2751611e-05
#>   5:    2.0  0.0100 -2.19019e-08  0.009820580 4.0922136e-08 4.0922136e-05
#>  ---                                                                     
#> 794:  396.5  0.0125 -4.48087e-07  0.012252300 2.0162832e-04 2.0162832e-01
#> 795:  397.0  0.0100 -4.49558e-07  0.009752980 2.0140391e-04 2.0140391e-01
#> 796:  397.5  0.0075 -4.51201e-07  0.007249400 2.0117872e-04 2.0117872e-01
#> 797:  398.0  0.0050 -4.52992e-07  0.004751440 2.0095267e-04 2.0095267e-01
#> 798:  398.5  0.0025 -4.54648e-07  0.002258640 2.0072576e-04 2.0072576e-01
#>                 Ne
#>              <num>
#>   1: 6.2640432e+11
#>   2: 5.1240113e+11
#>   3: 4.1450399e+11
#>   4: 3.2924966e+11
#>   5: 2.5541589e+11
#>  ---              
#> 794: 1.2584650e+15
#> 795: 1.2570643e+15
#> 796: 1.2556588e+15
#> 797: 1.2542479e+15
#> 798: 1.2528316e+15
#
## graphical representation
triarylamine.data.QNe$plot