| Title: | Analysis of Differential Calorimetry Scans |
|---|---|
| Description: | It includes functions for applying methodologies utilized for single-process kinetic analysis of solid-state processes were recently summarized and described in the Recommendation of ICTAC Kinetic Committee. These methods work with the basic kinetic equation. The Methodologies included refers to Avrami, Friedman, Kissinger, Ozawa, OFM, Mo, Starink, isoconversional methodology (Vyazovkin) according to ICATAC Kinetics Committee recommendations as reported in Vyazovkin S, Chrissafis K, Di Lorenzo ML, et al. ICTAC Kinetics Committee recommendations for collecting experimental thermal analysis data for kinetic computations. Thermochim Acta. 2014; 590:1-23. <doi:10.1016/J.TCA.2014.05.036> . |
| Authors: | Serena Berretta [aut] and Giorgio Luciano [aut,cre], Kristian Hovde Liland [ctb] |
| Maintainer: | Serena Berretta <[email protected]> |
| License: | GPL-2 |
| Version: | 0.2.0 |
| Built: | 2025-03-09 03:25:47 UTC |
| Source: | https://github.com/sere3s/takos |
add to the thermogram the value of rate(s) for each cycle(s) as provided by the user
addRate(dat, lab_rate, lab_cycles)addRate(dat, lab_rate, lab_cycles)
dat |
matrix |
lab_rate |
rate that corresponds to the cycles of the analysis performed |
lab_cycles |
number of the cycles of the analysis performed |
the input matrix with one added column with the values of the rate of the cycles performed
performs analysis of the thermograms using the avrami method
avrami(mat)avrami(mat)
mat |
matrix of the all the thermograms checked using the functiom mat.check |
models "mod", datable "xy" for plot
1. Avrami M. Kinetics of Phase Change. I General Theory. J Chem Phys. 1939;7(12):1103-1112. doi:10.1063/1.1750380.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) avr<-avrami(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) avr<-avrami(ar)
Title checkmat
checkmat(dat, header = TRUE, selected = c(0, 1, 2, 0, 0, 0, 4, 0))checkmat(dat, header = TRUE, selected = c(0, 1, 2, 0, 0, 0, 4, 0))
dat |
MUST be a data.frame where each column represent a parameter of the thermogram you need to check |
header |
present or not in your data.frame |
selected |
a vector that include the coded position of the parameters present in the dataset. 0 equal not present, while if you insert a number its value will refer to the index of the column of the input matrix where the parameter is stored. the coding of the vector selected is the following 1. "time.minutes" 2. "time.seconds" 3."temperature.s" 4."temperature.r" 5."temperature.s.K" 6."temperature.r.K"7."heat.flow"8. "id" |
i.e. selected=c(1,0,2,0,0,0,3) means that your first column is time.seconds, the second column is the temperature of the sample and the this column is the heat flow. 0 represents the other column of your files that are not present in your dataset
Checked data frame
npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) x=seq(1,1000) x2=seq(200,500,length.out=1000) dat=data.frame(x,x2,y) colnames(dat) <- c("time.seconds", "temperature.s","heat.flow") cmat<- checkmat(dat,selected=c(1,0,2,0,0,0,3,0))npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) x=seq(1,1000) x2=seq(200,500,length.out=1000) dat=data.frame(x,x2,y) colnames(dat) <- c("time.seconds", "temperature.s","heat.flow") cmat<- checkmat(dat,selected=c(1,0,2,0,0,0,3,0))
cut a region of a spectra and substitutes it with a sequence with initial value i.start and end valye i.end
cutSelect(x, i.start, i.end)cutSelect(x, i.start, i.end)
x |
x to be cut |
i.start |
index value of the starting point for the cut to be performed |
i.end |
index value of the ending point for the cut to be performed |
npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) ycut=cutValue(y,10,40,0.003,0.001) plot(y) lines(ycut,col="red")npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) ycut=cutValue(y,10,40,0.003,0.001) plot(y) lines(ycut,col="red")
cut a region of a spectra and substitutes it with a sequence with initial value i.start and end valye i.end
cutValue(x, i.start, i.end, value.start, value.end)cutValue(x, i.start, i.end, value.start, value.end)
x |
to be cut |
i.start |
index value of the starting point for the cut to be performed |
i.end |
index value of the ending point for the cut to be performed |
value.start |
desired value at point i.start |
value.end |
desired value at point i.end |
x after cut
npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) ycut=cutSelect(y,10,40) plot(y) lines(ycut,col="red")npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) ycut=cutSelect(y,10,40) plot(y) lines(ycut,col="red")
calculates the ratio of two differential according to the value of d.step
dadx(x, a, d.step = 2)dadx(x, a, d.step = 2)
x |
denominator variable for calculating da |
a |
numerator variable for calculating dt |
d.step |
step of differentiation |
ratio of two differential of the tw0 input variables
npoints=100 seed=42 x1=round(runif(npoints,0,1), 2) seed=1234 x2=round(runif(npoints,0,1), 2) xdiff <- dadx(x1,x2)npoints=100 seed=42 x1=round(runif(npoints,0,1), 2) seed=1234 x2=round(runif(npoints,0,1), 2) xdiff <- dadx(x1,x2)
performs analysis of the thermograms using Friedman method to calculate the activation energy (Ea)
FRI(mat, id = "rate", degree = seq(0.2, 0.8, by = 0.05))FRI(mat, id = "rate", degree = seq(0.2, 0.8, by = 0.05))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
id |
variable choosen for subsetting mat (default = "rate") |
degree |
selected degrees of cristallinity for performing the analysis |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degree
H.L. Friedman, Kinetics of thermal degradation of char-forming plastics from thermogravimetry, Appl. Phen. Plastic J. Polym. Sci. Part C: Polym. Symp. 6 (1964)
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) fri<-FRI(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) fri<-FRI(ar)
simulate a thermogram using JMA theory
JMA(A = exp(35), Ea = 120000, q = 50, T0 = -100, T.end = 300, npoints = 898, n = 2)JMA(A = exp(35), Ea = 120000, q = 50, T0 = -100, T.end = 300, npoints = 898, n = 2)
A |
pre exponential parameters (1/s) |
Ea |
Activation energy (J/mol) |
q |
= rate of analyis (K/min) |
T0 |
= starting temperature of the simulated thermogram expressed in K |
T.end |
= ending temperature of the simulated thermogram expressed in K |
npoints |
desired number of points of the simulate thermogram |
n |
numerical parameter required by JMA model |
T.C = temperature in Celsius
time.s = time in second
1. Vyazovkin S, Chrissafis K, Di Lorenzo ML, et al. ICTAC Kinetics Committee recommendations for collecting experimental thermal analysis data for kinetic computations. Thermochim Acta. 2014;590:1-23. doi:10.1016/j.tca.2014.05.036.
data <- JMA(A = exp(35),Ea = 120000,q = 50,T0 = -100,T.end = 300,npoints=898,n=2) require(data.table) #choose the rates for the simulation of the thermograms rates=c(0.5,1,2,5,10,20,50) #first serie of thermograms for all the chosen rate a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) #setup column names a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s, a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) #create a plot using the function thermo amaxH <- max(sapply(a, function(x) max(x$heat.flow))) # calculate the max plot(c(0,300),c(0,amaxH),mytitle="dataset A 120/60 0.66/0.33", ylab="ExothermicHeatFlow", xlab="Temperature") lapply(a, function(x) lines(x$temperature.s,x$heat.flow,lwd=3))data <- JMA(A = exp(35),Ea = 120000,q = 50,T0 = -100,T.end = 300,npoints=898,n=2) require(data.table) #choose the rates for the simulation of the thermograms rates=c(0.5,1,2,5,10,20,50) #first serie of thermograms for all the chosen rate a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) #setup column names a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s, a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) #create a plot using the function thermo amaxH <- max(sapply(a, function(x) max(x$heat.flow))) # calculate the max plot(c(0,300),c(0,amaxH),mytitle="dataset A 120/60 0.66/0.33", ylab="ExothermicHeatFlow", xlab="Temperature") lapply(a, function(x) lines(x$temperature.s,x$heat.flow,lwd=3))
performs analysis of the thermograms using Kissinger-Akahira-Sunose (KAS) method
KAS(mat, degree = seq(0.2, 0.8, by = 0.05))KAS(mat, degree = seq(0.2, 0.8, by = 0.05))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
degree |
selected degrees of cristallinity for performing the analysis |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
1. Akahira, T. Sunose T. Method of determining activation deterioration constant of electrical insulating materials. Res Rep Chiba Inst Technol (Sci Technol). 1971. 2. Kissinger HE. Reaction Kinetics in Differential Thermal Analysis. Anal Chem. 1957;29(11):1702-1706. doi:10.1021/ac60131a045. 3. Starink M. The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods. Thermochim Acta. 2003;404(1-2):163-176. doi:10.1016/S0040-6031(03)00144-8.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) kas<-KAS(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) kas<-KAS(ar)
performs analysis of the thermograms using Kissinger method to calculate the activation energy (Ea)
Kiss(mat)Kiss(mat)
mat |
matrix of the all the thermograms checked using the functiom mat.check |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
1. Avrami M. Kinetics of Phase Change. I General Theory. J Chem Phys. 1939;7(12):1103-1112. doi:10.1063/1.1750380. 2. Kissinger HE. Reaction Kinetics in Differential Thermal Analysis. Anal Chem. 1957;29(11):1702-1706. doi:10.1021/ac60131a045.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) kiss<-Kiss(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) kiss<-Kiss(ar)
performs analysis of the thermograms using the linearized avrami method in the interval of Xc selected by the user
lavrami(mat, up = 0.9999, low = 1e-04)lavrami(mat, up = 0.9999, low = 1e-04)
mat |
matrix of the all the thermograms checked using the functiom mat.check |
up |
max degree of the interval for applying the linearized model default 0.9999 |
low |
min degree of the interval for applying the linearized model default 0.0001 |
models "mod", datable "xy" for plot
1. Avrami M. Kinetics of Phase Change. I General Theory. J Chem Phys. 1939;7(12):1103-1112. doi:10.1063/1.1750380.
zeroes time (in seconds) according to peak given by the user
matzero(mat, spks = 1, x = mat$time.seconds.zero, colname = "v.check", myby = "id_cycle")matzero(mat, spks = 1, x = mat$time.seconds.zero, colname = "v.check", myby = "id_cycle")
mat |
matrix of spectra |
spks |
number of the peak selected as the starting point |
x |
variable to be reset according to the position of the selected peak |
colname |
name of the selected column |
myby |
varialbe selected for subsetting the matrix |
performs analysis of the thermograms using Mo method
MO(mat, degree = seq(0.2, 0.8, by = 0.2))MO(mat, degree = seq(0.2, 0.8, by = 0.2))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
degree |
selected degrees of cristallinity for performing the analysis |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
Liu T, Mo Z, Wang S, Zhang H. Nonisothermal melt and cold crystallization kinetics of poly(aryl ether ether ketone ketone). Polym Eng Sci. 1997;37(3):568-575. doi:10.1002/pen.11700.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) mo<-MO(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) mo<-MO(ar)
performs analysis of the thermograms using Ozawa-Flynn and Wall method
OFW(mat, degree = seq(0.2, 0.8, by = 0.05))OFW(mat, degree = seq(0.2, 0.8, by = 0.05))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
degree |
selected degrees of cristallinity for performing the analysis |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
1. Flynn J, Wall L. Res natl bur standards. Phys Chem. 1966;70:487-492.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) ofw<-OFW(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) ofw<-OFW(ar)
performs analysis of the thermograms using Ozawa method
OZ(mat, n.step = 1, spks = 1, eps = 0.001)OZ(mat, n.step = 1, spks = 1, eps = 0.001)
mat |
matrix of the all the thermograms checked using the functiom mat.check |
n.step |
number of steps for selecting temperature ranges |
spks |
id of the peaks selected for applying the method |
eps |
tollerance for the selection process |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
1. Ozawa T. Kinetics of non-isothermal crystallization. Polymer (Guildf). 1971;12(3):150-158. doi:10.1016/0032-3861(71)90041-3.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) oz<-OZ(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) oz<-OZ(ar)
template for plotting results from avrami function
plot_avrami(out, skip = 2)plot_avrami(out, skip = 2)
out |
output from avrami function |
skip |
plot symbols every nth points |
template for plotting results from friedman function
plot_fri(out)plot_fri(out)
out |
from friedman function |
template for plotting results from avrami function
plot_lavrami(out, skip = 2)plot_lavrami(out, skip = 2)
out |
output from lavrami function |
skip |
plot symbols every nth points |
template for plotting results from Mo function
plot_mo(out)plot_mo(out)
out |
from mo function |
template for plotting results from avrami function
plot_ozawa(out)plot_ozawa(out)
out |
from ozawa function |
calculate the running integral for the selected peak
ri(x, y, pks, TAP = FALSE, linear = FALSE, ...)ri(x, y, pks, TAP = FALSE, linear = FALSE, ...)
x |
x axis for the intergration |
y |
y axis for the intergration |
pks |
selected peak |
TAP |
if TRUE will apply a baseline using tangent area proportional (default=FALSE) |
linear |
if TRUE will apply a linear baseline (default=FALSE) |
... |
parameters in TAPPA function |
ds data frame containing original x and y given as input
ri running integral
b.tap baseline calculate if the switch TAP is TRUE
y.tap = y - b.tap
#' require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) a.dt <-lapply(seq(1,length(a)), function(x) data.table(data.frame(a.check[[x]]))) a<-rbindlist(a.dt) a$rate<-a$id a.peaks <- a[,.(res.list = list(findpeaks(heat.flow,sortstr=TRUE,npeaks=2))),by=id] a.peaks$rate<-a.peaks$id ref.peak=1 a.peaks <- data.table(data.table(a.peaks$rate),rbindlist((lapply(a.peaks$res.list, function(x) data.table(t(x[ref.peak,])))))) colnames(a.peaks)<- c("rate","peak.value","ind.max","left.lim","right.lim") a.mat<- lapply(unique(a$rate),function(x) ri(a[a$rate==x]$time.seconds,a[a$rate==x]$heat.flow,a.peaks[rate==x]))#' require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) a.dt <-lapply(seq(1,length(a)), function(x) data.table(data.frame(a.check[[x]]))) a<-rbindlist(a.dt) a$rate<-a$id a.peaks <- a[,.(res.list = list(findpeaks(heat.flow,sortstr=TRUE,npeaks=2))),by=id] a.peaks$rate<-a.peaks$id ref.peak=1 a.peaks <- data.table(data.table(a.peaks$rate),rbindlist((lapply(a.peaks$res.list, function(x) data.table(t(x[ref.peak,])))))) colnames(a.peaks)<- c("rate","peak.value","ind.max","left.lim","right.lim") a.mat<- lapply(unique(a$rate),function(x) ri(a[a$rate==x]$time.seconds,a[a$rate==x]$heat.flow,a.peaks[rate==x]))
calculates the running integral for customer input
runningIntegral(x, y, integrate.step = 1)runningIntegral(x, y, integrate.step = 1)
x |
variable x use for integration process |
y |
variable y use for integration process |
integrate.step |
= the step used for calculating the integrale the default value is 1 |
npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) runningIntegral(x,y)npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) runningIntegral(x,y)
Title
select_degree(mat, degree = seq(0.01, 0.99, by = 0.01))select_degree(mat, degree = seq(0.01, 0.99, by = 0.01))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
degree |
selected degrees of cristallinity for performing the analysis |
"DT" built with the values of mat according to the specified degrees
create a simulated spectra with gaussian shape
simG(vlen, i.start, gheight, shift = 0, wd = 30)simG(vlen, i.start, gheight, shift = 0, wd = 30)
vlen |
desired length of the spectra |
i.start |
starting value for the peak |
gheight |
height value |
shift |
shift from 0 |
wd |
width of the gaussian curve |
y=(simG(500,35,1,0,w=20)) plot(y)y=(simG(500,35,1,0,w=20)) plot(y)
a wrapper for the loess function included in the R base system
smooth.loess(x, y, safe.start = 5, safe.end = 5, myspan = 0.28)smooth.loess(x, y, safe.start = 5, safe.end = 5, myspan = 0.28)
x |
variable x |
y |
variable y |
safe.start |
exclude a the n-th first values from calculation |
safe.end |
exclude a the n-th end values from calculation |
myspan |
span parameter for loess function |
npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) y.smooth=smooth.loess(x,y) plot(x,y)npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) y.smooth=smooth.loess(x,y) plot(x,y)
performs analysis of the thermograms using Starink method
Starink(mat, degree = seq(0.2, 0.8, by = 0.05))Starink(mat, degree = seq(0.2, 0.8, by = 0.05))
mat |
matrix of the all the thermograms checked using the functiom mat.check |
degree |
selected degrees of cristallinity for performing the analysis |
models "mod", datable "xy" for plot, "Ea" list of value, datatable "DT" built with the values of mat according to the specified degrees
Starink MJ. A new method for the derivation of activation energies from experiments performed at constant heating rate. Thermochim Acta. 1996;288(1-2):97-104. doi:10.1016/S0040-6031(96)03053-5.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) star<-Starink(ar)require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) ar<-testMat(a) star<-Starink(ar)
examples of functions for presenting the results obtained with different methods Title summaryTable A
summaryTableA(mat.mod)summaryTableA(mat.mod)
mat.mod |
output matrix from avrami function |
table with the summary of result of applying the avrami function on the selected thermograms
Title summaryTableF
summaryTableFri(mat.mod)summaryTableFri(mat.mod)
mat.mod |
output matrix from friedman function |
table with the summary of result of applying the friedman function on the selected thermograms
Title summaryTableK
summaryTableKiss(mat.mod)summaryTableKiss(mat.mod)
mat.mod |
output matrix from Starink function |
table with the summary of result of applying the starink function on the selected thermograms
Title summaryTable Mo
summaryTableMo(mat.mod)summaryTableMo(mat.mod)
mat.mod |
output matrix from Mo function |
table with the summary of result of applying the ozawwa function on the selected thermograms
Title summaryTableOz
summaryTableOz(mat.mod)summaryTableOz(mat.mod)
mat.mod |
output matrix from ozawa function |
table with the summary of result of applying the ozawwa function on the selected thermograms
a wrapper for the baseline.rdfbaseline function in the package baseline in order to have the output in the same format as the input
t_baseline(y)t_baseline(y)
y |
baseline correction on y |
y.baseline returns the corrected y
y.baseline <- t_baseline(y)y.baseline <- t_baseline(y)
calculates the background of a thermogram according to Tangent-area-proportional method
TAPPA(T, dAlpha, interval = 10, tol = 0.001)TAPPA(T, dAlpha, interval = 10, tol = 0.001)
T |
temperature |
dAlpha |
the da/dt values |
interval |
number of points to use for interpolating the two lines that will merge according to the area of the peak |
tol |
tollerance for the iterative process |
B baseline values
1. Svoboda R. Tangential area-proportional baseline interpolation for complex-process DSC data - Yes or no? Thermochim Acta. 2017;658:55-62. doi:10.1016/J.TCA.2017.10.011.2. Svoboda R. Linear baseline interpolation for single-process DSC data-Yes or no? Thermochim Acta. 2017;655:242-250. doi:10.1016/J.TCA.2017.07.008.
npoints=1000 x=seq(1,npoints) y=(dnorm(seq(1,npoints), mean=npoints/2, sd=npoints/10)) #simulated peak y2=y+(dnorm(seq(1,npoints), mean=npoints, sd=npoints/10)) #secondary simulated peak y2[seq(npoints*0.735,npoints)]=y2[763] #flat the curve at the end of first peak ytap=TAPPA(x,y2) plot(x,y2) lines(x,ytap,col="red")npoints=1000 x=seq(1,npoints) y=(dnorm(seq(1,npoints), mean=npoints/2, sd=npoints/10)) #simulated peak y2=y+(dnorm(seq(1,npoints), mean=npoints, sd=npoints/10)) #secondary simulated peak y2[seq(npoints*0.735,npoints)]=y2[763] #flat the curve at the end of first peak ytap=TAPPA(x,y2) plot(x,y2) lines(x,ytap,col="red")
Title testMat
testMat(a, l.lim = 1, r.lim = NULL, toselect = c(0, 1, 2, 0, 0, 0, 3, 4))testMat(a, l.lim = 1, r.lim = NULL, toselect = c(0, 1, 2, 0, 0, 0, 3, 4))
a |
list of data tables of the checked thermograms using checkmat , obtained at different rates to change lines |
l.lim |
left lim of running integral |
r.lim |
rigth lim of running integral |
toselect |
vector |
data table ready to be used by all the methods for kinetic analysis included in the package
require(data.table) npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) x=seq(1,1000) x2=seq(200,500,length.out=1000) dat=data.frame(x,x2,y) colnames(dat) <- c("time.seconds", "temperature.s","heat.flow") dat=data.table(dat) dat2=dat dat$rates=20 dat2$rates=50 toTest=list(dat,dat2) tested=testMat(toTest)require(data.table) npoints=1000 x=seq(1,npoints) y=(dnorm(x, mean=npoints/2, sd=npoints/10)) x=seq(1,1000) x2=seq(200,500,length.out=1000) dat=data.frame(x,x2,y) colnames(dat) <- c("time.seconds", "temperature.s","heat.flow") dat=data.table(dat) dat2=dat dat$rates=20 dat2$rates=50 toTest=list(dat,dat2) tested=testMat(toTest)
performs analysis of the thermograms using Vyazovkin isoconversional method to calculate the activation energy (Ea)
VY(T, bet, Ea)VY(T, bet, Ea)
T |
temperature |
bet |
rate |
Ea |
estimated Ea to use as a first guess for the iterative process |
VYAZOVKIN, S. Advanced isoconversional method. Journal of thermal analysis, 1997, 49.3: 1493-1499.
require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) as<-select_degree(ar) vy<-as[, optimize(function(x) VY(temperature.s.K,rate,x), lower=50,upper=250),by=rit]require(data.table) require(MASS) rates=c(0.5,1,2,5,10,20,50) a<-lapply(rates, function(x) JMA(A=exp(35),Ea=120000,T0=0,T.end=300,q=x,npoints=5000,n=2)) a<-lapply(seq(1,length(a)), function(x) data.table(a[[x]]$time.s,a[[x]]$T.C, a[[x]]$dadT, rates[[x]])) lapply(seq(1,length(a)), function(x) setnames(a[[x]], c("time.seconds","temperature.s","heat.flow","rates") ) ) as<-select_degree(ar) vy<-as[, optimize(function(x) VY(temperature.s.K,rate,x), lower=50,upper=250),by=rit]