Calculate *dP/dT* and temperature of phase transitions; scale logarithms of activity to a desired total activity.

1 2 3 4 |

`ispecies` |
numeric, species index of a mineral phase |

`P` |
numeric, pressure (bar) |

`dPdT` |
numeric, values of ( |

`Htr` |
numeric, enthalpy(ies) of transition (cal/mol) |

`logact` |
numeric, logarithms of activity |

`length` |
numeric, numbers of residues |

`logact.tot` |
numeric, logarithm of total activity |

`dPdTtr`

returns values of *(dP/dT)Ttr*, where *Ttr* represents the transition temperature, of the phase transition at the high-*T* stability limit of the `ispecies`

in `thermo$obigt`

(no checking is done to verify that the species represents in fact one phase of a mineral with phase transitions).
`dPdTtr`

takes account of the Clapeyron equation, *(dP/dT)Ttr*=*DS/DV*, where *DS* and *DV* represent the changes in entropy and volume of phase transition, and are calculated using `subcrt`

at Ttr from the standard molal entropies and volumes of the two phases involved.
Using values of `dPdT`

calculated using `dPdTtr`

or supplied in the arguments, `Ttr`

returns as a function of `P`

values of the upper transition temperature of the mineral phase represented by `ispecies`

.

`GHS_Tr`

can be used to calculate values of G, H, and S at Tr for the cr2, cr3, and cr4 phases in the database.
It combines the given `Htr`

(enthalpies of transition) with the database values of GHS @ Tr only for the phase that is stable at 298.15 K (cr1) and the transition temperatures and Cp coefficients for higher-temperature phases, to calculate the GHS @ Tr (i.e. low-temperature metastable conditions) of the phases that are stable at higher temperatures.

`unitize`

scales the logarithms of activities given in `logact`

so that the logarithm of total activity of residues is equal to zero (i.e. total activity of residues is one), or to some other value set in `logact.tot`

.
`length`

indicates the number of residues in each species.
If `logact`

is NULL, the function takes the logarithms of activities from the current species definition.
If any of those species are proteins, the function gets their lengths using `protein.length`

.

Numeric returns are made by `dPdTtr`

, `Ttr`

, `spearman`

, `mod.obigt`

Functions with no (or unspecified) returns are `thermo.plot.new`

, `thermo.postscript`

, `label.plot`

and `water.lines`

.

Alberty, R. A. (2003) *Thermodynamics of Biochemical Reactions*, John Wiley & Sons, Hoboken, New Jersey, 397 p. http://www.worldcat.org/oclc/51242181

For some of the functions on which these utilities depend or were modeled, see `paste`

, `substr`

, `tolower`

, `par`

and `text`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ```
## properties of phase transitions
si <- info("enstatite")
# (dP/dT) of transitions
dPdTtr(si) # first transition
dPdTtr(si+1) # second transition
# temperature of transitions (Ttr) as a function of P
Ttr(si,P=c(1,10,100,1000))
Ttr(si,P=c(1,10,100,1000))
# calculate the GHS at Tr for the high-temperature phases of iron
# using transition enthalpies from the SUPCRT92 database (sprons92.dat)
Htr <- c(326.0, 215.0, 165.0)
iiron <- info("iron")
GHS_Tr(iiron, Htr)
# the results calculated above are stored in the database ...
info(1:3 + iiron)[, c("G", "H", "S")]
# ... meaning that we can recalculate the transition enthalpies using subcrt()
sapply(info(0:2 + iiron)$T, function(T) {
# a very small T increment around the transition temperature
T <- convert(c(T-0.01, T), "C")
# use suppressMessages to make the output less crowded
substuff <- suppressMessages(subcrt("iron", T=T, P=1))
diff(substuff$out$iron$H)
})
## scale logarithms of activity
# suppose we have two proteins whose lengths are 100 and
# 200; what are the logarithms of activity of the proteins
# that are equal to each other and that give a total
# activity of residues equal to unity?
logact <- c(-3,-3) # could be any two equal numbers
length <- c(100,200)
logact.tot <- 0
loga <- unitize(logact,length,logact.tot)
# the proteins have equal activity
stopifnot(identical(loga[1],loga[2]))
# the sum of activity of the residues is unity
stopifnot(isTRUE(all.equal(sum(10^loga * length),1)))
## now, what if the activity of protein 2 is ten
## times that of protein 1?
logact <- c(-3,-2)
loga <- unitize(logact,length,logact.tot)
# the proteins have unequal activity
stopifnot(isTRUE(all.equal(loga[2]-loga[1],1)))
# but the activities of residues still add up to one
stopifnot(isTRUE(all.equal(sum(10^loga * length),1)))
``` |

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