Development of minimal models of the elastic properties of flexible and stiff polymer networks with permanent and thermoreversible cross-links

Lin, David C.; Douglas, Jack F.; Horkay, Ferenc

doi:10.1039/b925219n

Cited by 66 publications

(61 citation statements)

References 77 publications

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“…3 with G 0 * = 430 Pa, Δh = -140 000 J mol -1 , and Δs = -475 J mol -1 K -1 . As discussed by Lin, et al [20], this sigmoidal temperature dependence of G 0 has been observed in a variety of amorphous solid materials [22][23][24], including both glass and gel materials. Evidently, this relation is a phenomenological counterpart for material stiffness to the Vogel-FulcherTammann relation describing the temperature dependence of the viscosity and structural relaxation time found in both glass-forming and self-assembled gel materials (e.g., see Kumar and Douglas [25]).…”

Section: Discussionmentioning

confidence: 96%

“…As described by Lin, et al [20], an effective medium treatment of rigidity percolation theory motivates taking the shear modulus of a self-assembled system to be proportional to the fraction, Φ, of associating species in the self-assembled state: (2) where G 0 * is the limiting value of the shear modulus in the fully self-assembled state, i.e., normally this means low temperatures but some materials can assemble upon heating. The temperature dependence of self-assembly upon cooling can be approximated by a simplified twostate model for the order parameter for the extent of self-assembly, Φ [20,21]:…”

Section: Discussionmentioning

confidence: 99%

“…The temperature dependence of self-assembly upon cooling can be approximated by a simplified twostate model for the order parameter for the extent of self-assembly, Φ [20,21]:…”

Section: Discussionmentioning

confidence: 99%

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Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution

Erk

Douglas

2012

MRS Proc.

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The shear stress relaxation of a thermally reversible, physically associating solution formed from a triblock copolymer in solvent selective for the mid-block was found to be well described over a broad temperature range by a stretched exponential function with a temperature independent 'stretching exponent', ≈ 1/3. This same exponent value has been suggested to have particular significance in describing structural relaxation in a wide range of disordered viscoelastic materials ranging from associating polymer materials ('gels') to glass-forming liquids. We quantify the temperature dependence of the high frequency, or short time, shear modulus as function of temperature and find that this property also follows a variation often observed in gels and glass-forming materials.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

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Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution

Erk

Douglas

2012

MRS Proc.

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“…This expression has been employed previously to describe the large strain behavior of elastic, self-assembled triblock copolymer gels deformed in uniaxial compression 1 and shear 14 and equivalent functions have been applied to describe the non-linear elasticity of biological systems 33 and recently stiff polymer networks. 34 The physically associating solution is assumed to deform affinely, so that the local extension ratios We assume that strain energy is stored in deformed 'network strands' or 'bonds', which in our case correspond to bridging midblocks that span different endblock aggregates. In a dynamic system like the triblock solutions used in our experiments, molecules are constantly transforming from these load-bearing 'bridging' configurations to non-load-bearing 'looping' configurations, where both endblocks reside in the same aggregate.…”

Section: Constitutive Modelmentioning

confidence: 99%

Rate-Dependent Stiffening and Strain Localization in Physically Associating Solutions

Erk

Shull

2011

Macromolecules

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Model physically associating solutions of acrylic triblock copolymer molecules in a midblockselective solvent displayed nonlinear strain-stiffening behavior which transitioned to rapid strain softening during shear start-up experiments at reduced rates spanning almost 4 orders of magnitude. Softening was believed to result from the shear-induced formation of highly localized regions of deformation in the macromolecular network. This behavior was accurately captured by a model that incorporated the strain energy and relaxation behavior of individual network strands in the solution. Flow curves predicted from the model were nonmonotonic, consistent with the onset of flow instabilities at high shear rates. The nonlinear stress response reported here, coupled with the wide range of accessible relaxation times of these thermoreversible solutions, makes them ideal model systems for studies of failure-mode transitions in physically associating solutions and gels.

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“…While the mechanical behavior of semiflexible polymer networks with compliant and rigid crosslinks has been studied in detail both experimentally and theoretically [5][6][7][8][9][10] , the interplay between active mechanisms of stress generation through motor activity and passive strain hardening properties of crosslinks has only been considered very recently 4,7 . In this regard, reconstituted actin networks can be particularly useful, since the density of crosslinks and motors can be varied in a desired manner to gain insights into the mechanisms of strain hardening and nonlinear elastic response.…”

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confidence: 99%

Strain stiffening induced by molecular motors in active crosslinked biopolymer networks

Chen

Shenoy

2011

Soft Matter

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We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which in turn causes to the deformation of the filaments. With increasing applied strain, the filaments further deform leading to a stiffened elastic response. When the crosslinks are incompliant, the contractile forces due to motors do not alter the network morphology in a significant manner and hence only small stiffening is observed.The mechanical properties of plant and animal cells are governed by the cytoskeleton, a flexible and dynamic network of biopolymer fibers combined with a group of associated regulatory and crosslinking proteins 1,2 . One of the key aspects of the mechanical behaviour of these networks is their highly nonlinear elastic response to applied stresses 3 , in particular their ability to strain stiffen by orders of magnitude when subject to large stresses. Cells also employ molecular motors to convert chemical energy into mechanical work 1 . Motors generate internal stress in the networks even in the absence of external loading 1,4 . In this manner, cells can regulate their mechanical properties by using both active and passive components.While the mechanical behavior of semiflexible polymer networks with compliant and rigid crosslinks has been studied in detail both experimentally and theoretically 5-10 , the interplay between active mechanisms of stress generation through motor activity and passive strain hardening properties of crosslinks has only been considered very recently 4,7 . In this regard, reconstituted actin networks can be particularly useful, since the density of crosslinks and motors can be varied in a desired manner to gain insights into the mechanisms of strain hardening and nonlinear elastic response. Indeed, recent experiments on networks that consist of actin filaments crosslinked by filamin A (FLNa) and bipolar filaments of muscle myosin II show that in 0 * a School of Engineering, Brown University, Providence, RI 02912, USA. Email:Vivek Shenoy@brown.edu the absence of any applied loads 7 , the motors stiffen the network by about two orders of magnitude. The degree of stiffening was found to increase with increasing density of myosin motors. Another key observation from this study relates to the magnitude of stiffening caused by compliant and incompliant crosslinks. While FLNa is a large, highly flexible dimer that promotes orthogonal F-actin crosslinking, scruin is an incompliant crosslink. Interestingly, it was found that in distinct contrast to FLNa, scruin does not promote activ...

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Development of minimal models of the elastic properties of flexible and stiff polymer networks with permanent and thermoreversible cross-links

Cited by 66 publications

References 77 publications

Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution

Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution

Rate-Dependent Stiffening and Strain Localization in Physically Associating Solutions

Strain stiffening induced by molecular motors in active crosslinked biopolymer networks

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