Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 32

Automatic dispenser

Syringe with
ligand solution

Stirrer

Macromolecular
solution

Solvent

Adiabatic jacket

Titration cell Reference cell

Figure 2.9

Schematic view of an ITC calorimeter.

are placed in an automated syringe and injected into the titration cell, which is maintained at
a constant temperature. Consecutive injections of small volumes (5

10 μL) are performed
and the heat exchange during the dilution is monitored. Experiments must be conducted
with very dilute solutions.
The system works with a power compensation method, accomplished by continuously
regulating the amount of heat applied to the titration cell, so as to drive the temperature
difference between the two cells towards the baseline, the steady-state value. The thermal
power required to return to the steady-state temperature differential as a function of time
is the quantity determined, and this is directly proportional to the heat of the reaction
(Freire et al., 1990 ). In the most sensitive instruments, very low heat exchanges, c.40 nW,
can be detected.
The basic equations for ITC are known from standard thermodynamics. The equili-
brium constant K eq which characterizes a molecular complex formation is related to the
Gibbs free energy change

-

Δ G:

e D G K eq ¼ ; ð 2 : 22 Þ

RT

where R is the gas constant and T the temperature in Kelvins (K). The equilibrium
constant for chemical reactions in solutions containing different species i is expressed as
a function of the activity a i of the solutes:
K eq ¼ ∏ i a i ν i

; ð 2 : 23 Þ

where cients.

When K eq is expressed in terms of concentrations instead of activities, it is called the

ν i are the stoichiometric coef

af nity constant, K a .