The combined use of natural ECM components and synthetic materials offers an attractive alternative to fabricate hydrogel-based tissue engineering scaffolds to study cell-matrix interactions in three-dimensions (3D). A facile method was developed to modify gelatin with cysteine via a bifunctional PEG linker, thus introducing free thiol groups to gelatin chains. A covalently crosslinked gelatin hydrogel was fabricated using thiolated gelatin and poly(ethylene glycol) diacrylate (PEGdA) via thiol-ene reaction. Unmodified gelatin was physically incorporated in a PEGdA-only matrix for comparison. We sought to understand the effect of crosslinking modality on hydrogel physicochemical properties and the impact on 3D cell entrapment. Compared to physically incorporated gelatin hydrogels, covalently crosslinked gelatin hydrogels displayed higher maximum weight swelling ratio (Qmax), higher water content, significantly lower cumulative gelatin dissolution up to 7 days, and lower gel stiffness. Furthermore, fibroblasts encapsulated within covalently crosslinked gelatin hydrogels showed extensive cytoplasmic spreading and the formation of cellular networks over 28 days. In contrast, fibroblasts encapsulated in the physically incorporated gelatin hydrogels remained spheroidal. Hence, crosslinking ECM protein with synthetic matrix creates a stable scaffold with tunable mechanical properties and with long-term cell anchorage points, thus supporting cell attachment and growth in the 3D environment.

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We examine the simplest relevant molecular model for large-amplitude shear (LAOS) flow of a polymeric liquid: the suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response. We include a detailed comparison of these predictions with the corresponding results for the simplest relevant continuum model: the corotational Maxwell model. We find that the responses of both models are qualitatively similar. The rigid dumbbell model relies entirely on the dumbbell orientation to explain the viscoelastic response of the polymeric liquid, including the higher harmonics in large-amplitude oscillatory shear flow. Our analysis employs the general method of Bird and Armstrong ["Time-dependent flows of dilute solutions of rodlike macromolecules," J. Chem. Phys. 56, 3680 (1972)] for analyzing the behavior of the rigid dumbbell model in any unsteady shear flow. We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the "paren functions," we use these for evaluating the shear stress for LAOS flow. We find the shapes of the shear stress versus shear rate loops predicted to be reasonable.

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When polymeric liquids undergo large‐amplitude shearing oscillations, the shear stress responds as a Fourier series, the higher harmonics of which are caused by fluid nonlinearity. Previous work on large‐amplitude oscillatory shear flow has produced analytical solutions for the first few harmonics of a Fourier series for the shear stress response (none beyond the fifth) or for the normal stress difference responses (none beyond the fourth) [JNNFM, 166, 1081 (2011)], but this growing subdiscipline of macromolecular physics has yet to produce an exact solution. Here, we derive what we believe to be the first exact analytical solution for the response of the extra stress tensor in large‐amplitude oscillatory shear flow. Our solution, unique and in closed form, includes both the normal stress differences and the shear stress for both startup and alternance. We solve the corotational Maxwell model as a pair of nonlinear‐coupled ordinary differential equations, simultaneously. We choose the corotational Maxwell model because this two‐parameter model (η0 and λ) is the simplest constitutive model relevant to large‐amplitude oscillatory shear flow, and because it has previously been found to be accurate for molten plastics (when multiple relaxation times are used). By relevant we mean that the model predicts higher harmonics. We find good agreement between the first few harmonics of our exact solution, and of our previous approximate expressions (obtained using the Goddard integral transform). Our exact solution agrees closely with the measured behavior for molten plastics, not only at alternance, but also in startup.