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thermodynamic isotope effect The effect thermosphere Atmospheric shell extending
of isotopic or substitution on an equilibrium con- from the top sof the mesosphere to outer space.
stant is referred to as a thermodynamic (or equi- It is a region of more or less steadily increasing
librium) isotope effect. For example, the effect temperature with height, starting at 70 or 80 km.
of isotopic substitution in reactant A that partici- It includes the exosphere and most or all of the
pates in the equilibrium: ionosphere (not the D region).
←−
A + B −→ C
threshold energy, E E E 0 0 0 Potential energy gap
h
1
is the ratio K /K of the equilibrium constant for between reactants and the transition state, some-
the reaction in which A contains the light isotope times involving the zero point energies, but
to that in which it contains the heavy isotope. The usually not.
ratio can be expressed asthe equilibrium constant
for the isotopic exchange reaction
threshold phenomenon For a linearly sta-
1 h ←− h 1 ble fixed point in a system of ordinary differ-
A + C −→ A + C
ential equations, returning to the fixed point is
in which reactants such as B that are not isotopi- monotonic for small perturbations. But for per-
cally substituted do not appear. turbations greater than a threshold, the dynamic
The potential energy surfaces of isotopic variables can undergo large excursion before
molecules are identical to a high degree returning to the fixed point (see excitability).
of approximation, so thermodynamic isotope
effects can only arise from the effect of isotopic
tight constraint Same as active constraint,
mass on the nuclear motions of the reactants and but some authors exclude the redundant case,
products, and can be expressed quantitatively in
where an inequality constraint happens to hold
terms of partition function ratios and for nuclear
with equality, but it is not binding.
motion:
)
K 1 (Q 1 nuc /Q h nuc C time constant (of a detector), τ τ τ If the
= 1 . c c c
K h (Q /Q h ) output of a detector changes exponentially with
nuc nuc A
time, the time required for it to change from its
Although the nuclear partition function is a prod-
initial value by the fraction [1 − exp(−t/τ )]
uct of the translational, rotational, and vibra- c
(for t = τ ) of the final value, is called the time
tional partition functions, the isotope effect is c
determined almost entirely by the last named, constant.
specifically by vibrational modes involving
motion of isotopically different atoms. In the time-staged A model with a discrete time
case of light atoms (i.e., protium vs. deuterium parameter, t = 1, ..., T , as in dynamic program-
or tritium) at moderate temperatures, the isotope ming, but the solution technique need not use the
effect is dominated by zero-point energy differ- DP recursion. The number of time periods (T) is
ences. called the planning horizon.
thermodynamic motif A conserved pattern
tint The edge coloring corresponding to the
of changes in the thermodynamic quantities
type of biochemical relationship between two
G, H, or S for a set of reactions. See also
nodes of the biochemical network.
biochemical, chemical, dynamical, functional,
kinetic, mechanistic, phylogenetic, regulatory, Comment: The three fundamental relation-
ships are sinistralateral, dextralateral, and
and topological motives.
catalyst. The sum of the sinistralateral and dex-
thermolysis The uncatalyzed cleavage of tralateral relationships is the reactant relation-
one or more covalent bonds resulting from expo- ship. These relationships are directly specified in
sure of a compound to a raised temperature, or the database. Note that tint is not a proper edge
a process in which such cleavage is an essential coloring as two adjacent edges can have identical
part. colors.

© 2003 by CRC Press LLC
© 2003 by CRC Press LLC