# izraz za struju anodizacije iz clanka:
# R. Jin, et al., A capacitor circuit model for theoretical derivation of anodizing current, Electrochim. Acta (2016),
# http://dx.doi.org/10.1016/j.electacta.2016.11.066
#' j_anod_jin(t, k1, k2, k3, k4, k5, t0 = 0, U0 = 60, d = 0.005)
#' @author K. Juraic
#' @description Theoretical expresion for anodisation current as a function of time.
#' Equation is adopted from publication:
#' R. Jin, et al., A capacitor circuit model for theoretical derivation of anodizing current, Electrochim. Acta (2016), http://dx.doi.org/10.1016/j.electacta.2016.11.066
#' For detailed description of the model and used parameters check
#' R. Jin publication
#' @param t time variable (usualy given in seconds)
#' @param k1 model parameter (see R. Jin)
#' @param k2 model parameter (see R. Jin)
#' @param k3 model parameter (see R. Jin)
#' @param k4 model parameter (see R. Jin)
#' @param k5 model parameter (see R. Jin)
#' @param t0 model parameter (see R. Jin) Starting moment of experiment (voltage switched on)
#' @param U0 model parameter (see R. Jin) anodisation voltage
#' @param d model parameter (see R. Jin) distance between electrodes
#' @return j(t) for given set of parameters
#' @export
#' @importFrom forcats %>%
#' @importFrom ggplot2 ggplot geom_line theme_linedraw
#' @examples
#' library(ggplot2)
#' k1 <- 55.556
#' k2 <- 9.086
#' k3 <- 6.5734
#' k4 <- 0.047
#' k5 <- 5# 6.6772
#' t0 <- 0
#' U0 <- 60
#' d <- 0.005
#' t <- 0:900
#' j1 <- U0 / k2 * exp(-(t - t0) / k1) / (1 - exp(-(t - t0) / k3))
#' j2 <- k4 / sqrt(d) * (U0 * (1 - exp(-(t - t0) / k1)) - k5 * log(t - t0))
#' anod_sim <- data.frame(
#' t = t,
#' struja = j_anod_jin(t = t, t0 = t0, k1 = k1, k2 = k2, k3 = k3, k4 = k4, k5 = k5),
#' j1 = j1,
#' j2 = j2,
#' j_uk = j1 + j2
#' )
#' head(anod_sim)
#' ggplot2::ggplot(data = anod_sim) +
#' geom_line(mapping = aes(x = t, y = struja), color = "red") +
#' geom_line(data = anod_sim, mapping = aes(x = t, y = j1), color = "blue") +
#' geom_line(data = anod_sim, mapping = aes(x = t, y = j2), color = "green") +
#' geom_line(data = anod_sim, mapping = aes(x = t, y = j_uk), color = "purple") +
#' theme_linedraw(base_size = 20)
j_anod_jin <- function(t, k1, k2, k3, k4, k5, t0 = 0, U0 = 60, d = 0.005) {
exp_k1 <- exp(-(t - t0) / k1)
exp_k3 <- exp(-(t - t0) / k3)
janod <- U0 / k2 * exp_k1 / (1 - exp_k3) + k4 / sqrt(d) * (U0 * (1 - exp_k1) - k5 * log(t - t0))
janod
}
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