R/afmYoungModulus.R

In afmToolkit: Functions for Atomic Force Microscope Force-Distance Curves Analysis

#' @title afmYoungModulus
#'   
#' @description This function computes the Young's Modulus of the sample from the approach
#'   curve using Hertz's  contact model  for a pyramidal tip.
#' @usage afmYoungModulus(afmdata, thickness = NULL, model = "Hertz", geometry =
#'   c("pyramid","paraboloid"), silent = TRUE, params)
#' @param afmdata An \code{afmdata} object. It should be a valid afmdata object upon which
#'   the Contact Point, the baseline correction and the Zero Force Point and the 
#'   Indentation must have been calculated first (using functions 
#'   \code{afmContactPoint()}, \code{afmBaselineCorrection()}, \code{afmZeroPointSlope()},
#'   and \code{afmIndentation()})
#' @param thickness Thickness (in m) of the surface. The Force - Indentation fit will be 
#'   done for values of the Indentation variable smaller than the thickness. If no value 
#'   is given, it will be done for all values in the curve for which the Indentation is 
#'   negative.
#' @param model Contact mechanics model to be used. Currently only Hertz's pure elastic 
#'   model is available.
#' @param geometry Geometry of the tip. Currently only pyramidal (default) and paraboloid
#'   geometries are implemented.
#' @param silent Logical value. If FALSE it prints the fit model summary (via 
#'   \code{summary.lm()}). Default value is TRUE
#' @param params A list containing different parameters of the model: e.g. nu (Poisson's 
#'   ratio) or alpha (internal angle, in degrees, of the pyramidal tip) or R (tip radius, 
#'   in the paraboloid geometry)
#' @return An \code{afmdata} class variable which will consist on the original input 
#'   \code{afmdata} variable plus a new list named \code{YoungModulus} with the following 
#'   fields:
#'   
#'   \code{YoungModulus} The Young's modulus value (in Pa).
#'   
#'   \code{fitYM} The Force vs Indentation^2 fit as an \code{lm} object.
#'   
#'   \code{fitdata} The subset of the data used in the fit.
#' @examples 
#' data <- afmReadJPK("force-save-JPK-2h.txt.gz", path = path.package("afmToolkit"))
#' data <- afmContactPoint(data, width = 20, mul1 = 1, mul2 = 20)
#' data <- afmDetachPoint(data, width = 40, mul1 = 3, mul2 = 40)
#' data <- afmBaselineCorrection(data)
#' data <- afmZeroPointSlope(data, segment = "approach")
#' data <- afmIndentation(data)
#' data <- afmYoungModulus(data, thickness = 1e-8, params = list(alpha = 22),
#'                         silent = TRUE)
#' print(data$YoungModulus$YoungModulus)
#' @importFrom stats coef lm predict
#' @export


afmYoungModulus <-
  function(afmdata,
           thickness = NULL,
           model = "Hertz",
           geometry = c("pyramid","paraboloid"),
           silent = TRUE,
           params) {
    Segment <- Indentation <- ForceCorrected <- NULL
    if (is.afmexperiment(afmdata)) {
      afmexperiment <-
        lapply(afmdata, function(x){
          if(!is.null(x$params$curvename)){
            print(paste("Processing curve: ",x$params$curvename), sep = " ")
          }
          afmYoungModulus(
            x,
            thickness = thickness,
            model = model,
            geometry = geometry,
            params = params,
            silent = silent)
          })
      return(afmexperiment(afmexperiment))
    } else if (is.afmdata(afmdata)) {
      if (!("ForceCorrected" %in% names(afmdata$data))) {
        stop("Baseline correction should be done first!")
      }
      if (!any ("Slopes" %in% names(afmdata))) {
        stop("Zero Point Force should be found first (run afmSlopes)!")
      }
      if (!afmdata$params$SpringConstant > 0) {
        stop("The cantilever spring constant should be provided!")
      }
      if (!("Indentation" %in% names(afmdata$data))) {
        stop("Indentation should be computed first(run afmIndentation)!")
      }
      if (is.null(thickness)) {
        fitdata <-
          subset(afmdata$data,
                 Segment == "approach" & Indentation <= 0)
      } else{
        fitdata <-
          subset(
            afmdata$data,
            Segment == "approach" & Indentation <= 0 &
              abs(Indentation) < thickness
          )
      }
      #  fitdata$Indentation <- -fitdata$Indentation
      fitdata$Indentation <-
        fitdata$Indentation - fitdata$Indentation[1]
      fitdata$ForceCorrected <-
        fitdata$ForceCorrected - fitdata$ForceCorrected[1]
      geometry <- match.arg(geometry)
      if (geometry == "pyramid"){
      fitYM <- lm(ForceCorrected ~ I(Indentation ^ 2) - 1, data = fitdata)
   
      predYM <-  predict(fitYM, newdata =
                           data.frame(Indentation = fitdata$Indentation))
      
      slope <- coef(fitYM)
      if (!silent) {
        print(summary(fitYM))
      }
      if (is.null(params$nu)) {
        params$nu <- 0.5
      }
      YM <-
        as.numeric(slope * sqrt(2) * (1 - params$nu ^ 2) / tan(params$alpha * pi /
                                                                 180))
      }else {
        fitdata$Indentation <- -fitdata$Indentation
        fitdata <- subset(fitdata, Indentation>=0)
        fitYM <- lm(ForceCorrected ~ I(Indentation ^ 1.5) - 1, data = fitdata)
        
        predYM <-  predict(fitYM, newdata =
                             data.frame(Indentation = fitdata$Indentation))
        
        slope <- coef(fitYM)
        if (!silent) {
          print(summary(fitYM))
        }
        if (is.null(params$nu)) {
          params$nu <- 0.5
        }
        YM <-
          as.numeric(slope * 0.75 * (1 - params$nu ^ 2) / sqrt(params$R))
      }
      YoungModulus <- list(YoungModulus = YM,
                           fitYM = fitYM,
                           fitdata = subset(fitdata, 
                                            select = c(Indentation,ForceCorrected))) 
      return(append.afmdata(afmdata,YoungModulus))
    } else {
      stop("Error: input is not a valid afmdata or afmexperiment.")
    }
  }