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#' @title Harkins-Jura Isotherm Non-Linear Analysis
#' @name harkinsjuraanalysis
#' @description A model that assumes the possibility of multilayer adsorption
#' on the surface of absorbents having heterogenous pore distribution
#' @param Ce the numerical value for the equilibrium capacity
#' @param Qe the numerical value for the adsorbed capacity
#' @import nls2
#' @import Metrics
#' @import stats
#' @import ggplot2
#' @return the nonlinear regression, parameters for the Harkins-Jura 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 harkinsjuraanalysis(Ce, Qe)
#' @author Paul Angelo C. Manlapaz
#' @author Chester C. Deocaris
#' @references Harkins, W. D., and Jura, G. (1944) <doi:10.1021/ja01236a048> Surfaces of solids. XIII.
#' A vapor adsorption method for the determination of the area of a solid without
#' the assumption of a molecular area, and the areas occupied by nitrogen and other
#' molecules on the surface of a solid. Journal of the American Chemical Society,
#' 66(8), 1366-1373.
#' @export
# Building the Harkins-Jura isotherm nonlinear form
harkinsjuraanalysis <- function(Ce, Qe){
x <- Ce
y <- Qe
data <- data.frame(x,y)
# Harkins-Jura isotherm nonlinear equation
fit1 <- y ~ (A/(b-log(x)))^1/2
# Setting of starting values
start1 <- data.frame(A = c(1, 100), b = c(1, 100))
# Fitting of the Harkins-Jura isotherm via nls2
fit2 <- nls2::nls2(fit1, start = start1, data=data,
control = nls.control(maxiter = 100 , warnOnly = TRUE),
algorithm = "port")
print("Harkins-Jura Isotherm Nonlinear Analysis")
print(summary(fit2))
print("Akaike Information Criterion")
print(AIC(fit2))
print("Bayesian Information Criterion")
print(BIC(fit2))
# Error analysis of the Harkins-Jura isotherm model
errors <- function(y) {
rmse <- Metrics::rmse(y, predict(fit2))
mae <- Metrics::mae(y, predict(fit2))
mse <- Metrics::mse(y, predict(fit2))
rae <- Metrics::rae(y, predict(fit2))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit2))^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)
rsqq <- lm(Qe~predict(fit2))
print(summary(rsqq))
# Graphical representation of the Harkins-Jura isotherm model
### Predicted parameter values
parsharkj <- as.vector(coefficients(fit2))
pars_A <- parsharkj[1L];
pars_b <- parsharkj[2L]
rhs <- function(x) {(pars_A/(pars_b-log(x)))^1/2}
#### 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_function(color = "#D35400", fun = rhs ) +
ggplot2::labs(x = "Ce",
y = "Qe",
title = "Harkins-Jura Isotherm Nonlinear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
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