Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 28

flow through the disc into
both pans. Under steady-state conditions (when no reactions and no transitions occur),
the differential signal

When the furnace is heated, the same amount of heat should

Δ T - normally an electric potential difference - provides a baseline

for heat flow due to differences in heat capacity between the sample and the reference.

When a transition occurs, the steady-state equilibrium is disturbed and a differential
signal is generated which is proportional to the difference in heat

flow rates to the sample

and to the reference.
Measured heat

ow rates ϕ m are proportional to temperature differences:

furnace!sample - furnace!reference ≈ -D T ð 2 : 14 Þ

m ≈ K m D T ð 2 : 15a Þ

true ¼ K m: ð 2 : 15b Þ

Measured flow rates are obtained by the manufacturer by careful

calibration with reference materials (to determine the parameters K m and K ϕ ). The heat

ϕ m and true ϕ true heat

flux is expressed in μW or mW (power units).
The enthalpy difference

Δ H in a phase transition, being the change in a state variable,

is a well-de ned parameter. This enthalpy is always a function of pressure p, temperature

T and composition

, which is, in turn, related to structural changes.
The heat capacity C p, χ (T) at constant pressure and constant

χ

' structural ' composition of

the sample is

p ; χ :

Þ¼ ∂

H

C p ; χ ð T ð 2 : 16 Þ

∂

T

The enthalpy change H of the sample at constant temperature and pressure, due to a

phase transition, a chemical reaction or a mixing effect associated with changes of
composition

Δ

χ , is given by

T ; p :

∂ H

∂χ

D ¼ ð 2 : 17 Þ

H

DSC experiments measure the rate of change of the heat (or heat flux) through the sample

during a temperature ramp, dQ m /dt:

dQ m
dt

m ¼ : ð 2 : 18 Þ

At constant pressure and in the absence of any external energy perturbation, the total heat

flux is related to the enthalpy changes arising from the two contributions shown in ( 2.17 )
and ( 2.18 ). Differentiating these equations with respect to time,

∂ dt ;

dT
dt þ

H
∂χ

d

m ð T ; p ; χÞ¼ C p ; χ ð T Þ ð 2 : 19 Þ

p ; T

where dT/dt is the rate of change of the temperature (in general taken as constant). The
heat capacity C p, χ (T) is proportional to the sample mass m, while c p, χ (T) =C p, χ (T)/m is
the heat capacity per unit mass.