Statistical mechanical constitutive theory of polymer networks: The inextricable links between distribution, behavior, and ensemble

Buche, Michael R.; Silberstein, Meredith N.

doi:10.1103/physreve.102.012501

Cited by 23 publications

(32 citation statements)

References 39 publications

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“…This general form of the stress has been obtained previously (Buche and Silberstein, 2020), but the evolution of P A (ξ; t) is now more complicated here due to the breaking and reforming of chains.…”

Section: Constitutive Relationssupporting

confidence: 60%

“…( 26) and ( 27) show that each forward and reverse reaction rate coefficient function is completely determined by the single-chain model via the partition functions. These partition functions similarly determine the single-chain mechanical response and the equilibrium distribution of chain end-to-end vectors in the network (Buche and Silberstein, 2020).…”

Section: Transition State Theorymentioning

confidence: 99%

“…The equilibrium probabilities may be written using Eqs. ( 7) and ( 17) in the equilibrium system, or by using the ratio of partition functions (McQuarrie, 2000;Buche and Silberstein, 2020) as…”

Section: Transition State Theorymentioning

confidence: 99%

“…We will assume that the number of links in our chain N b remains high enough to utilize the Gibbs-Legendre method (Buche and Silberstein, 2020) to approximate ψ * A,con (γ), which in this case causes ϑ * A,con (γ) to be independent of N b . While the Gibbs-Legendre method is invalid under sufficiently small forces (Neumann, 1985), the regime of end-to-end lengths where this matters essentially vanishes with increasing N b (Manca et al, 2012(Manca et al, , 2014.…”

Section: The Ufjc Modelmentioning

confidence: 99%

“…This derivation will yield, from an arbitrary single-chain model Hamiltonian, (1) the single-chain mechanical response, (2) the equilibrium distribution of chains in the network, and (3) the mechanically-dependent kinetics of chain breaking and reforming. While the first two connections have previously been established (Buche and Silberstein, 2020), the force-dependent kinetics have not yet been directly connected to the statistical mechanics of the single-chain model. With limited additional assumptions, this statistical mechanical foundation will then be used to formulate macroscopic constitutive relations entirely informed by an arbitrary single-chain model.…”

Section: Introductionmentioning

confidence: 99%

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Chain breaking in the statistical mechanical constitutive theory of polymer networks

Buche,

Silberstein

2021

Preprint

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Elastomers are used in a wide range of applications because of their large strain to failure, low density, and tailorable stiffness and toughness. The mechanical behavior of elastomers derives mainly from the entropic elasticity of the underlying network of polymer chains. Elastomers under large deformation experience bonds breaking within the backbone chains that constitute the polymer network. This breaking of chains damages the network, can lead to material failure, and can be utilized as an energy dissipation mechanism. In the case of reversible bonds, broken chains may reform and heal the damage in the network. If the reversible bonds are dynamic, chains constantly break and reform and create a transient network. A fundamental constitutive theory is developed to model the mechanics of these polymer networks. A statistical mechanical derivation is conducted to yield a framework that takes in an arbitrary single-chain model (a Hamiltonian) and outputs the following: the single-chain mechanical response, the breaking and reforming kinetics, the equilibrium distribution of chains in the network, and the partial differential equations governing the deformationcoupled network evolution. This statistical mechanical framework is then brought into the continuum scale by using macroscopic thermodynamic constitutive theory to obtain a constitutive relation for the Cauchy stress. The potential-supplemented freely jointed chain (uFJC) model is introduced, and a parametric study of its mechanical response and breaking kinetics is provided. This single-chain model is then implemented within the constitutive framework, which we specialize and apply in two exemplary cases: the mechanical response and irreversible breakdown of a multinetwork elastomer, and the mechanical response of a dual crosslink gel. After providing a parametric study of the general constitutive model, we apply it to a hydrogel with reversible metal-coordination crosslinks. In several cases, we find that the breakdown of the network causes secondary physical mechanisms to become important and inhibit the accuracy of our model. We then discuss these mechanisms and indicate how our existing framework can be adjusted to incorporate them in the future.

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Section: Constitutive Relationssupporting

confidence: 60%

Section: Transition State Theorymentioning

confidence: 99%

Section: Transition State Theorymentioning

confidence: 99%

Section: The Ufjc Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chain breaking in the statistical mechanical constitutive theory of polymer networks

Buche,

Silberstein

2021

Preprint

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Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

2022

Small Science

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Figure 2. a,e) Experimental specimens of a regular Kagome lattice (a) and a topological Kagome lattice (e). b,f ) Isofrequency contours (first phaseconstant surface in the first Brillouin zone) of regular (b) and topological (f ) Kagome lattices calculated from FEA. c,g) Group velocity isofrequency contours (frequency increasing from dark red to bright yellow) highlighting symmetric or asymmetric directivity of regular (c) and topological (g) lattices. d,h) Snapshots of experimentally acquired wave fields in regular (d) and topological (h) lattices, confirming symmetric or asymmetric propagation. Colors denotes the magnitude of the scan point velocities, normalized by the largest value at the considered instants. a-h) Reproduced with permission. [40]

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Mechanics of interactions of F-actin and vimentin networks

López-Menéndez

2022

Mechanics of Fibrous Networks

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Statistical mechanical constitutive theory of polymer networks: The inextricable links between distribution, behavior, and ensemble

Cited by 23 publications

References 39 publications

Chain breaking in the statistical mechanical constitutive theory of polymer networks

Chain breaking in the statistical mechanical constitutive theory of polymer networks

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

Mechanics of interactions of F-actin and vimentin networks

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