Table 1.

Overview of Viscoelastic Hydrogel Systems Relevant to Tissue Engineering and Regeneration, and Their Stress Relaxation Behavior

Material system	Cross-linking strategy	Stress relaxation behavior
		Qualitative features	Quantitative features
Alg11	Ionic cross-linking	Stress relaxation tuned by varying molecular weights of alginate leading to decreasing network connectivity and increasing chain mobility	τ½: ∼2 × 102 s to ∼5 × 103 s Quantified using compression test at a fixed strain of 15% with an initial deformation rate of 1 mm/min
Alg-PEG11,28	Ionic cross-linking	Hydrogels made of alginate grafted with increasing PEG concentrations exhibited faster stress relaxation	τ½: 102–103 s Quantified using compression stress relaxation test at strain of 20% at a deformation rate of 1 mm/min
Click-functionalized alginate and fibrillar collagen type I30	Sequential ionic and covalent cross-linking	Combination of alginate polymers, each with covalently conjugated click partner, underwent ionic cross-linking of constituent G-blocks followed by collagen self-assembly and covalent cross-linking of spatially confined click groups	τ½: ∼3 × 103 s to 1.0 × 104 s Quantified using oscillatory shear rheology (1 Hz, 1% strain at 25°C and at 37°C) with cone-plate geometry
PEO-based triblock co-polymer39	Hydrophobic interactions	Viscoelasticity tuned by changes in the length of hydrophobic end-blocks (alkyl side-chains)	τ½: 10−1–105 s Quantified using oscillatory shear rheology at 5% strain at 25°C
PEG-hydrophobic DFA40	Hydrophobic interactions	Viscoelasticity tuned by adding surfactant SDS or urea	τ½: 47–270 s Quantified using oscillatory shear rheology at 0.1% strain, 25°C
8-Arm PEG star macromers end-functionalized with thiols (PEG-8SH)44	Dynamic covalent bonding based on thioester exchange	Viscoelasticity tuned with varying concentration of thiols and pH (ranging from 6.0 to 9.0) Stress relaxation increased upon alteration of cross-linker structure by uncaging of thioester exchange catalyst MPAA	τ: 1.1 × 104 s to 6.5 × 106 s (calculated values) Quantified using oscillatory shear rheology at 1 Hz, 1% strain at 1 Hz followed by 10% strain over 5 s and monitoring over 20 s
HA-collagen27	Dynamic covalent hydrazone cross-linking	Stress relaxation tuned by modulating HA cross-linker affinity, molecular weight of HA, or HA concentration	τ½: ∼2.3 × 102 s to 1.8 × 104 s Quantified using oscillatory shear rheology at 1 Hz, 10% strain, 37°C with cone-plate geometry
PEG45	Dynamic covalent bonding with hydrazone bonds	Viscoelasticity tuned by changing the relative percentage of aHz bHz cross-links	τ½: 4 × 103 s (h) to 2.78 × 106 s (months) Quantified using oscillatory shear rheology with 10% shear strain applied over a 10 s ramp at 37°C
cis-1,2-diols functionalized octa-arm PEGs117	Dynamic covalent bonding with adaptable boronate bonds	Viscoelasticity tuned using different boronic acid derivates (Wulff-type-like boronic acid, m-boroxole, 2-fluorophenyl boronic acid)	τ½: tuned on the order of 1 s or below Relaxation dynamics characterized by frequency sweep instead of direct relaxation tests (inferred from G′-G″ cross over frequency)
UPy-functionalized PEG chains37	Hierarchical assembly of supramolecular fibers based on hydrogen bonding	Viscoelastic behavior of the hydrogels tuned by altering the ratio of UPy-based building blocks used	τ½: ∼5 s to >10 min Quantified using oscillatory shear rheology at a fixed strain of 1%
Colloidal hydrogels assembled from gelatin nanoparticles31	Attractive colloidal particles aggregate and form an arrested network of percolated particles	Viscoelascity modulated via interparticle interactions	τ½: 10−1–102 s Quantified using oscillatory shear rheology with step strain and subsequent relaxation within 10 min at 25°C

τ_1/2: Half relaxation time (defined as time taken for relaxing half of the initial stress value generated under a constant deformation). τ: Calculated mean relaxation time (calculated by fitting the normalized stress curves using a method reported by Brown et al.⁴⁴).

aHz, alkyl-hydrazone; Alg, alginate; bHz, benzyl-hydrazone; DFA, dimer fatty acid; HA, hyaluronic acid; MPAA, 4-mercaptophenylacetic acid; PEG, poly(ethylene glycol); PEO, poly(ethylene oxide); SDS, sodium dodecyl sulfate; UPy, ureido-pyrimidinone.