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#' @title Elovich Isotherm Linear Analysis
#' @name elovich.LM
#' @description Elovich isotherm model is based on kinetic principle which
#' assumes that the adsorption sites would exponentially increase with chemical
#' reactions responsible for adsorption. It is suited for describing the behavior
#' of adsorption concurring with the nature of chemisorption.
#' @param Ce the numerical value for the equilibrium capacity
#' @param Qe the numerical value for the adsorbed capacity
#' @import Metrics
#' @import stats
#' @import ggplot2
#' @return the linear regression, parameters for Elovich isotherm, and model
#' error analysis
#' @examples Ce <- c(0.01353, 0.04648, 0.13239, 0.27714, 0.41600, 0.63607, 0.80435, 1.10327, 1.58223)
#' @examples Qe <- c(0.03409, 0.06025, 0.10622, 0.12842, 0.15299, 0.15379, 0.15735, 0.15735, 0.16607)
#' @examples elovich.LM(Ce,Qe)
#' @author Jemimah Christine L. Mesias
#' @author Chester C. Deocaris
#' @references Zeldowitsch, J. (1934). "Uber Den Mechanismus der Katalytischen
#' Oxidation Von CO a MnO2," URSS, Acta Physiochim, Vol. 1, No. 2, 1934, pp. 364-449.
#' @references Foo, K. Y., and Hameed, B. H. (2009, September 13).
#' <doi:10.1016/j.cej.2009.09.013> Insights into the modeling of adsorption isotherm
#' systems. Chemical Engineering Journal.
#' @export
# Building the Elovich isotherm linear form
elovich.LM <- function(Ce,Qe){
x <- Qe
y <- log(Qe/Ce)
data <- data.frame(x, y)
# Fitting of the Elovich isotherm linear form
rhs <- function(x, KE, Qmax){
log(KE*Qmax)-(x/Qmax)
}
fit1 <- lm(y~x)
print("Elovich Analysis")
print(summary(fit1))
### y = a + bx
c <- summary(fit1)
a <- c$coefficients[1]
b <- c$coefficients[2]
### Parameter values calculation
Qmax <- -1/b
print("Qmax")
print(Qmax)
KE <- exp(a)/Qmax
print("KE")
print(KE)
# ---------------------------------
print("Akaike Information Criterion")
print(AIC(fit1))
print("Bayesian Information Criterion")
print(BIC(fit1))
# Error analysis of the Elovich iostherm model
errors <- function(y) {
rmse <- Metrics::rmse(y, predict(fit1))
mae <- Metrics::mae(y, predict(fit1))
mse <- Metrics::mse(y, predict(fit1))
rae <- Metrics::rae(y, predict(fit1))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit1))^2)/(N-2))
colnames(y) <- rownames(y) <- colnames(y)
list("Root Mean Squared Error" = rmse,
"Mean Absolute Error" = mae,
"Mean Squared Error" = mse,
"Relative Absolute Error" = rae,
"Standard Error of the Regression S" = SE)
}
a <- errors(y)
print(a)
# Graphical representation of the Elovich isotherm linear model
#### Plot details
ggplot2::theme_set(ggplot2::theme_bw(10))
ggplot2::ggplot(data, ggplot2::aes(x = x, y = y)) + ggplot2::geom_point(color ="#3498DB" ) +
ggplot2::geom_smooth(formula = y ~ x, method = "lm", se = F, color = "#D35400" ) +
ggplot2::labs(x = "Qe",
y = "ln(Qe/Ce)",
title = "Elovich Isotherm Linear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
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