Nondestructive testing of defects in adhesive joints

where Qt and Q∞ are the mol% increase in sorption at time t and equilibrium respectively. The
type of diffusion mechanism has been analysed in terms of the empirical relation
Q
log
Q
t
∞
= logk + n log t
………….. (2)
k and n have been determined from a least square fit of log Qt / Q∞ versus log T. Constant k
depends on the structural features of the polymer system and its interaction with the solvent
used [17]. The polarity and the size of the solvent along with the polar and non-polar segments
in the block copolymer determine the value of k parameter. n is the diffusional exponent, which
indicate the transport mechanism. If n =0.5, the mechanism of sorption is termed as Fickian,
where the rate of polymer chain relaxation is higher than the diffusion rate of the penetrant.
When n = 1, the mechanism is said to be non – Fickian where the chain relaxation is slower
than the solvent diffusion. If the value lies between 0.5 and 1, then the mechanism follows
anomalous transport where the polymer chain relaxation rates and the solvent diffusion rates
are similar. By regression analysis, the values of n and k are obtained as slope and intercept and
are consolidated in Table III. The correlation coefficient values are found to be 0.999. The
values of n range from 0.42 to 0.61, which indicates that the mechanism of sorption follows
Fickian mode in samples with lower NCO/OH ratios while the mechanism shifts to anomalous
mode with a bias to non – Fickian mode in the samples with higher NCO/OH ratios. In the
present study the k values do not show a regular trend.
Sorption kinetics
Sorption of liquid through polymer samples cause structural rearrangement, which induces
kinetic behaviour that in turn are affected by the total free volume and its distribution in the
polymer system. We have analysed the sorption data in terms of the first - order kinetic model.
The first – order rate constant k1 for the polymer – solvent system was obtained using the first –
order equation [20]
dc/dt = k1 (C∞ - Ct) ………………… (3)
where C∞ and Ct are the concentration of the penetrant at equilibrium and time t respectively.
C∞ and Ct are equivalent to the equilibrium swelling Q∞ and swelling at time t, which is Qt.
Integration of equation (3) gives
k1t = 2.303 log [C∞ / (C∞ - Ct)] ………(4)
Typical plots of log (C∞ - Ct ) versus time is given in Figure 2 and the estimated rate constants
for the penetrant are given in Table IV. A negative slope was observed and the values are found
to range form 3.29 x 10 3 min -1 to 19.30 x 10 3 min -1 .
Transport coefficients
Diffusion in polymer is complex and depends strongly on the concentration, degree of swelling,
solvent size and size of the voids in the polymer. From the slope θ of the linear portion of the
sorption curve, the diffusion coefficient D has been calculated using [21]