these additional bonds may reduce local stress concentration, delaying the rupture of
the chemical networks [12]. As reversible bonds, various non-covalent and dynamic
covalent bonds can be employed, and there have been many examples reported in the
literature [3, 5, 13, 14]. It should be noted that hydrogels with only physical
crosslinks (and possibly entanglements) may irreversibly plastically flow at long
time scales if the longest characteristic relaxation time is comparable to or shorter
than the inverse of the strain rate. Adding a small amount of chemical crosslinks to
prevent the terminal flow and keep the reference state of deformation is a practical
solution as employed in the certain number of the systems reported in the literature,
especially for the networks with short-lived reversible bonds [15–17].
Creton, Narita, and their coworkers have reported an intriguing example of such
“dual crosslink” hydrogels, having a small amount of permanent crosslinks and a
large amount of transient crosslinks [18–21]. Based on polyvinyl alcohol, PVA,
permanently crosslinked by glutaraldehyde and transiently crosslinked by borate
ions (by dynamic covalent bond), their PVA dual crosslink gels exhibit timedependent elasticity. Prepared by a simple procedure, consisting of incorporating
physical crosslinks by diffusion of borate ions into a previously prepared chemical
gel, some unique rheological features of the PVA dual crosslink gel have been
experimentally and theoretically characterized with the corresponding chemical gel
as reference [18, 20–26]. The chemical and physical crosslinks contribute to the
viscoelasticity independently, and the moduli of the dual crosslink gels can be
decomposed into the contribution of the chemical bonds (the same as that of the
reference chemical gel) and that of the physical bonds (not identical to a
corresponding physical gel due to the suppression of the terminal flow by the
chemical crosslinks) (additivity) [22, 25]. The stretch-rate-dependent stress can be
then separated into the product of a time-dependent term (equivalent to a relaxation
modulus) and a strain-dependent term (expressed as a neo-Hookean model)
[22]. This behavior can be quantitatively described by a constitutive model combining large strain elasticity and time-dependent sticker dynamics [19, 23, 24], and
using only four physically based parameters is sufficient to fit both tensile and
torsion tests results.
The systematic studies of the mechanical properties of the PVA dual crosslink
gels over a wide range of time scales and strain rates indicate the importance to study
the properties at different characteristic bond breaking rates as well as at very high
extension [22, 25]. Does the dual crosslink gel behave similarly to the chemical gel
at time scales much longer than its transient bond breaking time? Or can the strain
rate be normalized by a characteristic time measurable in linear rheology to obtain a
universal law for the time-dependent properties? In order to answer these questions,
it is important to investigate the mechanical properties of dual crosslink gels having a
short characteristic time and/or at very slow stretch rate. The relaxation time of the
PVA dual crosslink gel is relatively long (of the order of 1 s), and it is difficult to tune
it in a physicochemical manner. It is also experimentally difficult to perform timeconsuming mechanical tests at very slow stretch rates, due to problems of drying or
poroelastic relaxation.
Metal-ligand coordination bonds can be a promising option as tunable transient
crosslinks: by changing metal ion, species dynamics can be tuned. Various physical
Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .
3
the chemical networks [12]. As reversible bonds, various non-covalent and dynamic
covalent bonds can be employed, and there have been many examples reported in the
literature [3, 5, 13, 14]. It should be noted that hydrogels with only physical
crosslinks (and possibly entanglements) may irreversibly plastically flow at long
time scales if the longest characteristic relaxation time is comparable to or shorter
than the inverse of the strain rate. Adding a small amount of chemical crosslinks to
prevent the terminal flow and keep the reference state of deformation is a practical
solution as employed in the certain number of the systems reported in the literature,
especially for the networks with short-lived reversible bonds [15–17].
Creton, Narita, and their coworkers have reported an intriguing example of such
“dual crosslink” hydrogels, having a small amount of permanent crosslinks and a
large amount of transient crosslinks [18–21]. Based on polyvinyl alcohol, PVA,
permanently crosslinked by glutaraldehyde and transiently crosslinked by borate
ions (by dynamic covalent bond), their PVA dual crosslink gels exhibit timedependent elasticity. Prepared by a simple procedure, consisting of incorporating
physical crosslinks by diffusion of borate ions into a previously prepared chemical
gel, some unique rheological features of the PVA dual crosslink gel have been
experimentally and theoretically characterized with the corresponding chemical gel
as reference [18, 20–26]. The chemical and physical crosslinks contribute to the
viscoelasticity independently, and the moduli of the dual crosslink gels can be
decomposed into the contribution of the chemical bonds (the same as that of the
reference chemical gel) and that of the physical bonds (not identical to a
corresponding physical gel due to the suppression of the terminal flow by the
chemical crosslinks) (additivity) [22, 25]. The stretch-rate-dependent stress can be
then separated into the product of a time-dependent term (equivalent to a relaxation
modulus) and a strain-dependent term (expressed as a neo-Hookean model)
[22]. This behavior can be quantitatively described by a constitutive model combining large strain elasticity and time-dependent sticker dynamics [19, 23, 24], and
using only four physically based parameters is sufficient to fit both tensile and
torsion tests results.
The systematic studies of the mechanical properties of the PVA dual crosslink
gels over a wide range of time scales and strain rates indicate the importance to study
the properties at different characteristic bond breaking rates as well as at very high
extension [22, 25]. Does the dual crosslink gel behave similarly to the chemical gel
at time scales much longer than its transient bond breaking time? Or can the strain
rate be normalized by a characteristic time measurable in linear rheology to obtain a
universal law for the time-dependent properties? In order to answer these questions,
it is important to investigate the mechanical properties of dual crosslink gels having a
short characteristic time and/or at very slow stretch rate. The relaxation time of the
PVA dual crosslink gel is relatively long (of the order of 1 s), and it is difficult to tune
it in a physicochemical manner. It is also experimentally difficult to perform timeconsuming mechanical tests at very slow stretch rates, due to problems of drying or
poroelastic relaxation.
Metal-ligand coordination bonds can be a promising option as tunable transient
crosslinks: by changing metal ion, species dynamics can be tuned. Various physical
Dual Crosslink Hydrogels with Metal-Ligand Coordination Bonds: Tunable Dynamics. . .
3