difference between the relaxation modulus and the dynamic modulus is small, due to
the fast dynamics of the transient crosslinks with Zn
2+ .
In order to make a connection with the large strain behaviors discussed in the next
section, let us check the strain dependence of the stress relaxation in shear. A shear
stress relaxation was carried out for different imposed strains (1, 10, and 20%), and
results are shown in Fig. 5b for the P(AAm-co-VIm)-Zn
2+ gel. The relaxation
modulus of the P(AAm-co-VIm)-Zn
2+ gel decreases with increasing strain,
suggesting that the slower relaxation did not satisfy the separability between the
strain- and time-dependent terms of the stress. This point is further discussed in the
next section.
3.4 Intermediate Strain Tensile Cyclic Tests
At intermediate deformations, we carried out a series of loading and unloading
cycles up to λ ¼ 2 at seven different stretch rates (0.0003, 0.01, 0.003, 0.01, 0.03,
0.1, and 0.3 s
À1 ) on both types of dual crosslink gels to investigate the strain
dependence of the modulus as well as the hysteresis (Fig. 6a, c). These gel samples
were not stretched to rupture, and the same sample was stretched repeatedly at
different stretch rates after a sufficiently large recovery time of 30 min between
each cycle.
Both initial modulus and hysteresis show a strong stretch rate dependence for the
P(AAm-co-VIm)-Ni
2+ gel, while for the P(AAm-co-VIm)-Zn
2+ gel the dependence
is weaker. At the end of the unloading cycle, we observed a small residual deformation increasing with stretch rate due to the bending of the sample. This residual
deformation disappears during the recovery period.
This large strain behavior is now analyzed in terms of separability between the
strain-dependent and time-dependent component of the tensile stress. In a previous
publication [18], we showed that for a similar system, the reduced stress f
Ã
¼ σ/(λ À
λ
À2 ) measured at different stretch rates, plotted as a function of time, formed a master
curve. For these gels, for λ < 2, the stress could be separated into a strain-dependent
term (neo-Hookean contribution) and a time-dependent term f
à (dynamics of the
physical crosslinks). By using the loading part of the data of Fig. 6a, c, we plotted the
reduced stress f
à as a function of time in Fig. 6b, d, and a reasonable master curve
was obtained for both dual crosslink gels with Ni
2+ and Zn
2+ , demonstrating the
approximate separability into a strain-dependent neo-Hookean term, and a timedependent term f
à in that range of intermediate strain where only softening is
observed (see Fig. 2).
Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .
11
the fast dynamics of the transient crosslinks with Zn
2+ .
In order to make a connection with the large strain behaviors discussed in the next
section, let us check the strain dependence of the stress relaxation in shear. A shear
stress relaxation was carried out for different imposed strains (1, 10, and 20%), and
results are shown in Fig. 5b for the P(AAm-co-VIm)-Zn
2+ gel. The relaxation
modulus of the P(AAm-co-VIm)-Zn
2+ gel decreases with increasing strain,
suggesting that the slower relaxation did not satisfy the separability between the
strain- and time-dependent terms of the stress. This point is further discussed in the
next section.
3.4 Intermediate Strain Tensile Cyclic Tests
At intermediate deformations, we carried out a series of loading and unloading
cycles up to λ ¼ 2 at seven different stretch rates (0.0003, 0.01, 0.003, 0.01, 0.03,
0.1, and 0.3 s
À1 ) on both types of dual crosslink gels to investigate the strain
dependence of the modulus as well as the hysteresis (Fig. 6a, c). These gel samples
were not stretched to rupture, and the same sample was stretched repeatedly at
different stretch rates after a sufficiently large recovery time of 30 min between
each cycle.
Both initial modulus and hysteresis show a strong stretch rate dependence for the
P(AAm-co-VIm)-Ni
2+ gel, while for the P(AAm-co-VIm)-Zn
2+ gel the dependence
is weaker. At the end of the unloading cycle, we observed a small residual deformation increasing with stretch rate due to the bending of the sample. This residual
deformation disappears during the recovery period.
This large strain behavior is now analyzed in terms of separability between the
strain-dependent and time-dependent component of the tensile stress. In a previous
publication [18], we showed that for a similar system, the reduced stress f
Ã
¼ σ/(λ À
λ
À2 ) measured at different stretch rates, plotted as a function of time, formed a master
curve. For these gels, for λ < 2, the stress could be separated into a strain-dependent
term (neo-Hookean contribution) and a time-dependent term f
à (dynamics of the
physical crosslinks). By using the loading part of the data of Fig. 6a, c, we plotted the
reduced stress f
à as a function of time in Fig. 6b, d, and a reasonable master curve
was obtained for both dual crosslink gels with Ni
2+ and Zn
2+ , demonstrating the
approximate separability into a strain-dependent neo-Hookean term, and a timedependent term f
à in that range of intermediate strain where only softening is
observed (see Fig. 2).
Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .
11