Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 33

nity
constant K a is the ratio of the molar concentration of the complex [ML] to the product of
the molar concentrations of the species [M] and [L]:
For the reaction M

For a bimolecular interaction between a macromolecule M and a ligand L, the af

þ L , ML

½ ML

K a ¼

½ :

ð 2 : 24 Þ

½ M L

Knowledge of the af nity constant does not, in itself, establish the association mecha-

nism; such interactions are better characterized by separating the enthalpic and entropic
contributions:

D G ¼ D H T D S : ð 2 : 25 Þ

Δ

The enthalpy term H is related to the difference in energy required to create and to break

the bonds between L, M and the solvent during the complex formation. The entropic term
characterizes the number of accessible states or microscopic con gurations which, in

aqueous solution, are generally dominated by rearrangements of the water molecules.

G,
being a combination of these two, may make either a net additive or subtractive contribution.
Isothermal titration calorimetry measures the binding af

Δ

nity K a , enthalpy change Δ H,

binding stoichiometry (n) and the entropy change S simultaneously from a single

experiment involving a macromolecule and a ligand. When substances bind, heat is
either generated or absorbed. An example of a titration curve is shown in Figure 2.10 ,
which also shows, albeit under ideal conditions, the experimental procedure.
ITC allows the direct measurement of the temperature dependence of

Δ

Δ H and the

variation of the heat capacity of the solution:

δðD H Þ

¼ D C p : ð 2 : 26 Þ

δ

T

The latter is related, for instance, to changes of the polar surfaces accessible to the solvent
during complex formation.

2.4 Microscopy of gel networks

Traditionally, studies of physical gels have used optical or electron microscopy. The
various techniques of transmission electron microscopy (TEM) have been quite widely
employed. Scanning electron microscopy (SEM) has also been used, but images tend not
to be very revealing. More recently, atomic force microscopy has been employed. Many
of the published images have proved informative but, as with TEM, there are always
caveats, since the gel sample under study is no longer in its native state.

2.4.1 Transmission electron microscopy (TEM)

The assumption that polymers in the gel state are interconnected throughout the liquid
phase is one of the major arguments for the origin of elasticity in gels. The ability of gels