buffer: Calculating Buffered Chemical Activities

Description

Calculate values of activity or fugacity of basis species buffered by an assemblage of one or more species.

Usage

buffer(logK = NULL, ibasis = NULL, logact.basis = NULL, 
    is.buffer = NULL, balance = "PBB")
  mod.buffer(name, species = NULL, state = thermo$opt$state, 
    logact = -3)

Arguments

logK

list, equilibrium constants of formation reactions of species, or NULL, indicates to load the species present in the buffer.

ibasis

numeric, which of the basis species whose activities are being calculated.

logact.basis

list, logarithms of activities of the basis species.

is.buffer

numeric, rownumbers of the buffering species in thermo$species.

balance

character, balance on this (name/formula of basis species or PBB) in buffer reactions.

name

character, name of buffer to add to or find in thermo$buffers.

species

character, names or formulas of species in a buffer.

state

character, physical states of species in buffer.

logact

numeric, logarithms of activities of species in buffer.

Value

List of logarithms of chemical activities (or fugacities) of the basis species derived from chemical activities of the species in the buffer.

Details

A buffer is treated here as assemblage of one or more species whose presence constrains values of the chemical activity (or fugacity) of one or more basis species. To perform calculations for buffers, the user generally does not call buffer directly, but instead uses basis to associate the name of the buffer with one or more basis species. After this, calls to affinity will invoke the required calculations. The calculated values of the buffered activites can be retrieved by setting return.buffer to TRUE (in affinity). The maximum number of buffered chemical activities possible for any buffer is equal to the number of species in the buffer; however, the user may then elect to work with the values for only one or some of the basis species calculated with the buffer.

The identification of a conserved basis species (or other reaction balancing rule) is required in calculations for buffers of more than one species. For example, in the pyrite-pyrrhotite-magnetite buffer ($\mathrm{FeS_2}$-$\mathrm{FeS}$-$\mathrm{Fe_3O_4}$) a basis species common to each species is one representing $Fe$; hence, when writing reactions between the species in this buffer one may conserve $Fe$ while utilizing $\mathrm{H_2S}$ and $\mathrm{O2}$ as the variables of interest. The calculation for buffers attempts to determine which of the available basis species qualifies as a conserved quantity. This can be overriden with balance. The default value of balance is PBB, which instructs the function to use the protein backbone group as the conserved quantity in buffers consisting of proteins, but has no overriding effect on the computations for buffers without proteins.

In the calculation of the buffered activities the user calls affinity which first determines the affinities of formation of all the species of interest (including species in the buffers) using the current reference activities of the basis species. affinity then calls buffer to calculate buffered values of the activities of basis species; the affinities of formation of all the species of interest are regenerated using the new (buffered) activities of basis species and returned to the user.

To view the available buffers, print the thermo$buffer object. Buffer definitions can be added to this dataframe with mod.buffer. It is possible to set the logarithms of activities of the species in the buffer through the logact argument; if this is missing unit activity is assigned to crystalline species in buffer, otherwise (for aqueous species) the default value of activity is 10$^{-3}$. If name identifies an already defined buffer, this function modifies the logarithms of activities or states of species in that buffer, optionally restricted to only those species given in species.

It is possible to assign different buffers to different basis species, in which case the order of their calculation depends on their order in thermo$buffers. This function is compatible with systems of proteins, including ionized ones, but note that for buffers made of proteins the buffer calculations presently use whole protein formulas (instead of residue equivalents) and consider nonionized proteins only (i.e., calculating values of pH buffered by proteins is so far not implemented).

References

Garrels, R. M. (1960) Mineral Equilibria. Harper & Brothers, New York, 254 p. http://www.worldcat.org/oclc/552690

Schulte, M. D. and Shock, E. L. (1995) Thermodynamics of Strecker synthesis in hydrothermal systems. Orig. Life Evol. Biosph. 25, 161--173. http://dx.doi.org/10.1007/BF01581580

Examples

Run this code

data(thermo)
  ## list the buffers
  thermo$buffers
  # another way to do it, for a specific buffer
  print(mod.buffer("PPM"))
  
  ## buffer made of one species
  # calculate the activity of CO2 in equilibrium with
  # (a buffer made of) acetic acid at a given activity
  basis("CHNOS")
  basis("CO2","AC")
  # what activity of acetic acid are we using?
  print(mod.buffer("AC"))
  # return the activity of CO2
  affinity(return.buffer=TRUE)
  # as a function of oxygen fugacity
  affinity(O2=c(-85,-70,4),return.buffer=TRUE)
  # as a function of logfO2 and temperature
  affinity(O2=c(-85,-70,4),T=c(25,100,4),return.buffer=TRUE)
  # change the activity of species in the buffer
  mod.buffer("AC",logact=-10)
  affinity(O2=c(-85,-70,4),T=c(25,100,4),return.buffer=TRUE)
  # see longex('co2ac') for a different strategy using the
  # 'what' argument of diagram

  ## buffer made of three species
  ## Pyrite-Pyrrhotite-Magnetite (PPM)
  # specify basis species and initial activities
  basis(c("FeS2","H2S","O2","H2O"),c(0,-10,-50,0))
  # note that the affinity of formation of pyrite,
  # which corresponds to FeS2 in the basis, is zero
  species(c("pyrite","pyrrhotite","magnetite"))
  affinity(T=c(200,400,11),P=2000)$values
  # attach basis species H2S and O2 to the PPM buffer
  basis(c("FeS2","H2S","O2","H2O"),c(0,"PPM","PPM",0))
  # inspect values of H2S activity and O2 fugacity
  affinity(T=c(200,400,11),P=2000,return.buffer=TRUE)
  # now, the affinities of formation reactions of 
  # species in the buffer are all equal to zero
  print(a <- affinity(T=c(200,400,11),P=2000)$values)
  for(i in 1:length(a)) stopifnot(isTRUE(
    all.equal(as.numeric(a[[i]]),rep(0,length(a[[i]])))))
  ## buffer made of one species: show values of logfO2 on an 
  ## Eh-pH diagram; after Garrels, 1960, Figure 6
  basis("CHNOSe")
  # here we will buffer the activity of the electron by O2
  mod.buffer("O2","O2","gas",999)
  basis("e-","O2")
  # start our plot, then loop over values of logfO2
  thermo.plot.new(xlim=c(0,14),ylim=c(-0.8,1.2),
    xlab="pH",ylab=axis.label("Eh"))
  # the upper and lower lines correspond to the upper
  # and lower stability limits of water
  logfO2 <- c(0,-20,-40,-60,-83.1)
  for(i in 1:5) {
    # update the logarithm of fugacity (logact) of O2 in the buffer
    mod.buffer("O2","O2","gas",logfO2[i])
    # get the values of the logarithm of activity of the electron
    a <- affinity(pH=c(0,14,15),return.buffer=TRUE)
    # convert values of pe (-logact of the electron) to Eh
    Eh <- convert(-as.numeric(a[[1]]),"Eh")
    lines(seq(0,14,length.out=15),Eh)
    # add some labels
    text(seq(0,14,length.out=15)[i*2+2],Eh[i*2+2],
      paste("logfO2=",logfO2[i],sep=""))
  }
  title(main=paste("Relation between logfO2(g), Eh and pH at\n",
    "25 degC and 1 bar. After Garrels, 1960"))

  ## buffer made of two species
  # conditions for metastable equilibrium among 
  # CO2 and acetic acid. note their starting activities:
  print(mod.buffer("CO2-AC")) 
  basis("CHNOS")
  basis("O2","CO2-AC")
  affinity(return.buffer=TRUE)  # logfO2 = -75.94248
  basis("CO2",123)  # what the buffer reactions are balanced on
  affinity(return.buffer=TRUE)  # unchanged
  # consider more oxidizing conditions
  mod.buffer("CO2-AC",logact=c(0,-10))
  affinity(return.buffer=TRUE)
  
  ## log fH2 - temperature diagram for mineral buffers
  ## and for given activities of aqueous CH2O and HCN
  ## After Schulte and Shock, 1995, Fig. 6: 
  ## 300 bars, log fCO2=1, log fN2=0, log aH2O=0
  # the mineral buffers FeFeO, QFM, PPM and HM are already
  # included in the thermo$buffers table so let's plot them.
  basis.logacts <- c(999,1,0,0,999,999,999)
  basis(c("Fe","CO2","H2O","nitrogen","hydrogen",
    "H2S","SiO2"),basis.logacts)
  basis(c("CO2","N2"),"gas")
  # initialize the plot
  xlim <- c(0,350)
  thermo.plot.new(xlim=xlim,ylim=c(-4,4),
    xlab=axis.label("T"),ylab=axis.label("H2"))
  res <- 50
  Tseq <- seq(xlim[1],xlim[2],length.out=res) 
  # a function to plot the log fH2 of buffers and label the lines
  logfH2plot <- function(buffer,lty,where) {
    basis("H2",buffer)
    a <- as.numeric(affinity(T=c(xlim,res),P=300,return.buffer=TRUE)$H2)
    lines(Tseq,a,lty=lty)
    # "where" is the percent distance along the x-axis to plot the label
    wherethis <- seq(xlim[1],xlim[2],length.out=100)[where]
    if(length(grep("_",buffer)) > 0) tt <- 
      thermo$buffers$logact[thermo$buffers$name==buffer] else tt <- buffer
    text(wherethis,splinefun(Tseq,a)(wherethis),tt)
  }
  # plot log fH2 of each mineral buffer
  logfH2plot("FeFeO",1,16)
  logfH2plot("QFM",1,30)
  logfH2plot("PPM",1,80)
  logfH2plot("HM",1,40)
  anotherplotfunction <- function(mybuff,lty,logact,where) {
    for(i in 1:length(logact)) {
      # update the species activity
      mod.buffer(mybuff,logact=logact[i])
      logfH2plot(mybuff,lty,where[i])
    }
  }
  # add and plot new buffers (formaldehyde and HCN)
  mod.buffer("mybuffer_1","formaldehyde","aq")
  logact <- c(-6,-10,-15); where <- c(10,10,25)
  anotherplotfunction("mybuffer_1",3,logact,where)
  mod.buffer("mybuffer_2","HCN","aq")
  where <- c(20,73,50)
  anotherplotfunction("mybuffer_2",2,logact,where)
  # title
  title(main=paste("Mineral buffers (solid), HCN (dashed), formaldehyde",
    "(dotted)\n",describe(thermo$basis[c(2,4),],T=NULL,P=300),
    "After Schulte and Shock, 1995"),cex.main=0.9)

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