An official website of the United States government
Slide-ring gels are polymer networks with cross-links that can slide along the chains. In contrast to conventional unentangled networks with cross-links fixed along the chains, the slide-ring networks are strain-softening and distribute tension much more uniformly between their strands due to the so-called “pulley effect”. The sliding of cross-links also reduces the elastic modulus in comparison with the modulus of conventional networks with the same number density of cross-links and elastic strands. We develop a single-chain model to account for the redistribution of monomers between network strands of a primary chain. This model takes into account both the pulley effect and fluctuations in the number of monomers per network strand. The pulley effect leads to modulus reduction and uniform tension redistribution between network strands, while fluctuations in the number of strand monomers dominate the strain-softening, the magnitude of which decreases upon network swelling and increases upon deswelling.
more »
« less
Foundation of Network Forensics
We develop a forensic-like framework for network structural characterization based on an analysis of their nonlinear response to mechanical deformation. For model networks, this methodology provides information about the strand degree of polymerization between cross-links, the effective cross-link functionality, the contribution of loops and entanglements to network elasticity, as well as the fraction of stress-supporting strands. For networks with trapped entanglements, we identify a transition from cross-link-controlled to entanglement-controlled network elasticity with increasing degree of polymerization of network strands between cross-links and show how specific features of this transition are manifested in changes of entanglement and structural shear moduli characterizing different modes of network deformation. In particular, this cross-link-to-entanglement transition results in saturation of the network shear modulus at small deformations and renormalization of the degree of polymerization of the effective network strands determining nonlinear elastic response in the strongly entangled networks. The developed approach enables the classification of networks according to their topology and effectiveness of stress distribution between network strands.
more »
« less
- Award ID(s):
- 2049518
- PAR ID:
- 10565341
- Publisher / Repository:
- ACS
- Date Published:
- Journal Name:
- Macromolecules
- Volume:
- 56
- Issue:
- 22
- ISSN:
- 0024-9297
- Page Range / eLocation ID:
- 9289 to 9296
- Subject(s) / Keyword(s):
- polymer networks, nonlinear elasticity
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen.These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.more » « less
-
null (Ed.)Cells dynamically control their material properties through remodeling of the actin cytoskeleton, an assembly of cross-linked networks and bundles formed from the biopolymer actin. We recently found that cross-linked networks of actin filaments reconstituted in vitro can exhibit adaptive behavior and thus serve as a model system to understand the underlying mechanisms of mechanical adaptation of the cytoskeleton. In these networks, training, in the form of applied shear stress, can induce asymmetry in the nonlinear elasticity. Here, we explore control over this mechanical hysteresis by tuning the concentration and mechanical properties of cross-linking proteins in both experimental and simulated networks. We find that this effect depends on two conditions: the initial network must exhibit nonlinear strain stiffening, and filaments in the network must be able to reorient during training. Hysteresis depends strongly and non-monotonically on cross-linker concentration, with a peak at moderate concentrations. In contrast, at low concentrations, where the network does not strain stiffen, or at high concentrations, where filaments are less able to rearrange, there is little response to training. Additionally, we investigate the effect of changing cross-linker properties and find that longer or more flexible cross-linkers enhance hysteresis. Remarkably plotting hysteresis against alignment after training yields a single curve regardless of the physical properties or concentration of the cross-linkers.more » « less
-
Merks, Roeland M.H. (Ed.)Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.more » « less
-
Hemmer, Philip R.; Migdall, Alan L. (Ed.)We study a quantum switch that creates shared end-to-end entangled quantum states to multiple sets of users that are connected to it. Each user is connected to the switch via an optical link across which bipartite Bell-state entangled states are generated in each time-slot with certain probabilities, and the switch merges entanglements of links to create end-to-end entanglements for users. One qubit of an entanglement of a link is stored at the switch and the other qubit of the entanglement is stored at the user corresponding to the link. Assuming that qubits of entanglements of links decipher after one time-slot, we characterize the capacity region, which is defined as the set of arrival rates of requests for end-to-end entanglements for which there exists a scheduling policy that stabilizes the switch. We propose a Max-Weight scheduling policy and show that it stabilizes the switch for all arrival rates that lie in the capacity region. We also provide numerical results to support our analysis.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acs.macromol.3c00612
