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1. A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

   https://doi.org/10.1016/j.cma.2023.115982  

   Arunachala, Prajwal Kammardi ; Abrari Vajari, Sina ; Neuner, Matthias ; Linder, Christian ( May 2023 , Computer Methods in Applied Mechanics and Engineering)

   - (Ed.)

   Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system. 

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2. Transient Competitors to Modulate Dynamic Covalent Cross-Linking of Recombinant Hydrogels

   https://doi.org/10.1021/acs.chemmater.3c01575  

   Gilchrist, Aidan E. ; Liu, Yueming ; Klett, Katarina ; Liu, Yu-Chung ; Ceva, Sofía ; Heilshorn, Sarah C. ( November 2023 , Chemistry of Materials)

   Hydrogels cross-linked by dynamic covalent chemistry (DCC) are stiff and remodelable, making them ideal biomimetics for tissue engineering applications. Due to the reversibility of DCC cross-links, the opportunity exists to transiently control hydrogel network formation through the use of small molecule competitors. Specifically, we incorporate low molecular weight competitors that reversibly disrupt the formation of hydrazone cross-links as they diffuse through a recombinant hydrogel. Using complementary experimental, computational, and theoretical polymer physics approaches, we present a family of competitors that predictably alter hydrogel gelation time and mechanics. By changing the competitor chemistry, we connect key reaction parameters (forward and reverse reactions rates and thermodynamic equilibrium constants) to the delayed onset of a percolated network, increased hydrogel gelation time, and transient control of hydrogel stiffness. Using human intestinal organoids as a model system, we demonstrate the ability to tune gelation kinetics of a recombinant hydrogel for uniform encapsulation of individual, patient-derived stem cells and their proliferation into three-dimensional structures. Taken together, our data establish a validated framework to relate molecular-level parameters of transient competitors to predicted macromolecular-network properties. As interest in biomimetic, DCC-cross-linked hydrogels continues to grow, these results will enable the rationale design of bespoke, dynamic biomaterials for tissue engineering. 

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3. Effect of sticker clustering on the dynamics of associative networks

   https://doi.org/10.1039/D1SM00392E  

   Mahmad Rasid, Irina ; Do, Changwoo ; Holten-Andersen, Niels ; Olsen, Bradley D. ( October 2021 , Soft Matter)

   Recent experimental and theoretical work has shown that sticker clustering can be used to enhance properties such as toughness and creep resistance of polymer networks. While it is clear that the changes in properties are related to a change in network topology, the mechanistic relationship is still not well understood. In this work, the effect of sticker clustering was investigated by comparing the dynamics of random copolymers with those where the stickers are clustered at the ends of the chain in the unentangled regime using both linear mechanics and diffusion measurements. Copolymers of N , N -dimethyl acrylamide (DMA) and pendant histidine groups were synthesized using reversible addition–fragmentation chain transfer (RAFT) polymerization. The clustered polymers were synthesized using a bifunctional RAFT agent, such that the midblock consisted of PDMA and the two end blocks were random copolymers of DMA and the histidine-functionalized monomer. Upon addition of Ni ions, transient metal-coordinate crosslinks are formed as histidine–Ni complexes. Combined studies of rheology, neutron scattering and self-diffusion measurements using forced Rayleigh scattering revealed changes to the network topology and stress relaxation modes. The network topology is proposed to consist of aggregates of the histidine–Ni complexes bridged by the non-associative midblock. Therefore, stress relaxation requires the cooperative dissociation of multiple bonds, resulting in increased relaxation times. The increased relaxation times, however, were accompanied by faster diffusion. This is attributed to the presence of defects such as elastically inactive chain loops. This study demonstrates that the effects of cooperative sticker dissociation can be observed even in the presence of a significant fraction of loop defects which are known to alter the nonlinear properties of conventional telechelic polymers. 

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4. Statistical mechanics of chromosomes: in vivo and in silico approaches reveal high-level organization and structure arise exclusively through mechanical feedback between loop extruders and chromatin substrate properties

   https://doi.org/10.1093/nar/gkaa871  

   He, Yunyan ; Lawrimore, Josh ; Cook, Diana ; Van Gorder, Elizabeth Erin ; De Larimat, Solenn Claire ; Adalsteinsson, David ; Forest, M Gregory ; Bloom, Kerry ( October 2020 , Nucleic Acids Research)

   null (Ed.)

   Abstract The revolution in understanding higher order chromosome dynamics and organization derives from treating the chromosome as a chain polymer and adapting appropriate polymer-based physical principles. Using basic principles, such as entropic fluctuations and timescales of relaxation of Rouse polymer chains, one can recapitulate the dominant features of chromatin motion observed in vivo. An emerging challenge is to relate the mechanical properties of chromatin to more nuanced organizational principles such as ubiquitous DNA loops. Toward this goal, we introduce a real-time numerical simulation model of a long chain polymer in the presence of histones and condensin, encoding physical principles of chromosome dynamics with coupled histone and condensin sources of transient loop generation. An exact experimental correlate of the model was obtained through analysis of a model-matching fluorescently labeled circular chromosome in live yeast cells. We show that experimentally observed chromosome compaction and variance in compaction are reproduced only with tandem interactions between histone and condensin, not from either individually. The hierarchical loop structures that emerge upon incorporation of histone and condensin activities significantly impact the dynamic and structural properties of chromatin. Moreover, simulations reveal that tandem condensin–histone activity is responsible for higher order chromosomal structures, including recently observed Z-loops. 

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5. Increasing valence pushes DNA nanostar networks to the isostatic point

   https://doi.org/10.1073/pnas.1819683116  

   Conrad, Nathaniel ; Kennedy, Tynan ; Fygenson, Deborah K. ; Saleh, Omar A. ( March 2019 , Proceedings of the National Academy of Sciences)

   The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembled nanostructures that form thermoreversible equilibrium gels through base pair-controlled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel’s high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point$5<f_c\le 6$in agreement with the Maxwell prediction.

    

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