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#' @title Langmuir Isotherm Third Linear Form Analysis
#' @name langmuir3.LM
#' @description The Langmuir adsorption isotherm is used to
#' describe the equilibrium between adsorbate and adsorbent
#' system, where the adsorbate adsorption is limited to one
#' molecular layer at or before a relative pressure of unity is reached.
#' @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 parameters for the Langmuir isotherm (third form), model error analysis,
#' and linear regression 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 langmuir3.LM(Ce,Qe)
#' @author Keith T. Ostan
#' @author Chester C. Deocaris
#' @references Langmuir, I. (1918). <doi:/10.1021/ja01269a066> The adsorption of
#' gases on plane surfaces of glass, mics and platinum. Journal of the American
#' Chemical Society, 1361-1403.
#' @references Chen, X. (2015) <doi:/10.3390/info6010014> Modeling of Experimental
#' Adsorption Isotherm Data. 14-22.
#' @export
# Building the Langmuir isotherm linear form
langmuir3.LM <- function (Ce,Qe) {
x <- Qe/Ce
y <- Qe
data <- data.frame(x,y)
rhs <- function(x, Kl, Qmax) {
Qmax - (1/Kl)*x
}
# Fitting of the Langmuir isotherm linear form
fit1 <- lm(y ~ x)
print("Langmuir Isotherm Third Linear Form Analysis")
print(summary(fit1))
a <- (summary(fit1))
### Parameter values calculation
qmax <- a$coefficients[1]
print("Qmax")
print(qmax)
kl <- -(1/a$coefficients[2])
print("Kl")
print(kl)
# -------------------------------------------
print("Aikake Information Criterion")
print(AIC(fit1))
print("Bayesian Information Criterion")
print(BIC(fit1))
# Error analysis of the Langmuir isotherm 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 <- 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 for the Regression S" = SE)
}
a <- errors(y)
print(a)
# Graphical representation of the Langmuir isotherm 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/Ce",
y = "Qe",
title = "Langmuir Isotherm Linear Model",
subtitle = "Third Linear Form",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5),
plot.subtitle = ggplot2::element_text(hjust = 0.5))
}
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