Non-entropic theory of rubber elasticity: Flexible chains grafted on a rigid surface

Drozdov, Aleksey D.

doi:10.1016/j.ijengsci.2005.03.010

Cited by 9 publications

(7 citation statements)

References 27 publications

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“…In the non-entropic model developed by Drozdov (Drozdov, 2005) for an ensemble of non-interacting chains grafted on a rigid plane, the constitutive function can be written as…”

Section: Examples Of Constitutive Equationsmentioning

confidence: 99%

Atomic Force Microscopy of Polymer Brushes: Insights into Controversies

2022

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Atomic force microscopes (AFM) and nanoindenters have been used for decades to evaluate mechanical properties of thin films at the nanoscale. It is argued that the elastic solutions to the indentation problem, which are most often associated with the names of Galin or Sneddon, may be used for extracting elastic contact modulus of bulk samples and continual films, while their application to contact between an AFM probe and a polymer brush is a priori questionable. This is because the character of compression of a polymer brush is drastically different from the response of an elastic half-space to indentation. In the present paper, a number of controversial issues related to the interpretation of the AFM data obtained for polymer brushes tested with a rigid probe are studied. In particular, a correct relation has been established between the constitutive equation for a single polymer brush in compression with a bare rigid surface and the constitutive equation for two identical polymer brushes in compression under the assumption of lack of interpenetration of compressed brushes. It is shown that the so-called apparent elastic modulus of a polymer brush introduced based on the Hertzian force-displacement relation depends on the indenter radius and, thus, may not serve as a characteristic of polymer brush. Also, the Derjaguin’s approximation-based method of identifying the point of initial contact is given in opposition to controversial methods, which are broadly based on the Hertzian contact mechanics.

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“…In the non-entropic model developed by Drozdov (Drozdov, 2005) for an ensemble of non-interacting chains grafted on a rigid plane, the constitutive function can be written as…”

Section: Examples Of Constitutive Equationsmentioning

confidence: 99%

Atomic Force Microscopy of Polymer Brushes: Insights into Controversies

2022

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“…The physical interpretation of these parameters is often unclear [3]. On the other hand, some models are based on statistics of molecular chains network which are also been proposed with idealized assumptions [10,11]. Moreover, Eremeyev and Naumenko [12] developed a relationship between effective work adhesion and peel force for thin hyperelastic films undergoing large deformation.…”

Section: Introductionmentioning

confidence: 99%

Peridynamic model for visco-hyperelastic material deformation in different strain rates

Huang

Oterkus

et al. 2019

Continuum Mech. Thermodyn.

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This study presents a peridynamic (PD) constitutive model for visco-hyperelastic materials under homogenous deformation. The constitutive visco-hyperelastic model is developed in terms of Yeoh strain energy density function and Prony series. The material parameters in the model are identified by optimizing the classical stress–strain relation and tension test data for different strain rates. The peridynamic visco-hyperelastic force density function is proposed in terms of the peridynamic integral and the Yeoh strain energy density. The time-dependent behaviour for different strain rates is captured by numerical time integration representing the material parameters. The explicit form of peridynamic equation of motion is then constructed to analyse the deformation of visco-hyperelastic membranes. The numerical results concern the deformation and damage prediction for a polyurea membrane and membrane-type acoustic metamaterial with inclusions under homogenous loading. Different surface defects are considered in the simulation. The peridynamic predictions are verified by comparing with finite element analysis results.

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“…Moreover, a different choice of solvent allows one to modify the wetting properties of a polymercovered surface, 8,9 as well as affect the rheology of polymeric colloids used as lubricants or delivery materials. 10 The result of applying an external force, either via perpendicular compression, lateral shear, or by injection into a narrow cavity, [11][12][13][14][15][16][17] depends on the type of polymer layer and its surface density. For example, the full coverage of a surface by a polystyrene brush has been estimated to reduce friction by a factor of two.…”

Section: Introductionmentioning

confidence: 99%

“…5 Here, we seek to cast light into the microscopic behaviour of polymer brushes under compression and decompression. Whereas the deformation of a single polymer mushroom by an applied force is relatively well understood, [14][15][16][19][20][21][22][23] the mechanisms underlying the distinct responses uniquely related to the surface coverage are still unclear. For example, lateral forces can induce compression and tilting in grafted polymers, possibly leading to the formation of a ''nematic liquid-crystal phase'' 24 (i.e., a first-order transition whereby an isotropically swollen brush becomes a nematically-ordered one).…”

Section: Introductionmentioning

confidence: 99%

Brownian dynamics of a compressed polymer brush model. Off-equilibrium response as a function of surface coverage and compression rate

Carlsson

Kamerlin

Arteca

et al. 2011

Phys. Chem. Chem. Phys.

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We study the compressive behaviour of a polymer-covered surface (i.e., a "polymer brush") using Brownian dynamics simulations. The model consists of grafted chains with variable flexibility, variable intra- and inter-chain interactions, as well as different surface coverage. We discuss the polymer brush response to confinement by considering variable rates of compression under a hard plane. Our results show a small degree of inter-chain entanglement, regardless of whether the interaction is attractive or merely excluded volume. We observe that the molecular shape depends strongly on the surface coverage. Dense brushes exhibit a limited degree of lateral deformation under compression; instead, chains undergo a transition that produces a local patch with near-solid packing. This effect due to surface density can be undone partially by increasing the attractive nature of the chain interaction, by modulating the rate of compression, or by allowing "soft anchoring", i.e., the possible Brownian drift of the grafting bead on the surface. We have also studied the polymer brush relaxation while maintaining the compressing plane, as well as after its sudden removal. We find evidence that also the relaxation depends on surface density; dense brushes appear to be configurationally frustrated at high compression and are unable to undergo swelling, regardless of the pressure applied.

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Non-entropic theory of rubber elasticity: Flexible chains grafted on a rigid surface

Cited by 9 publications

References 27 publications

Atomic Force Microscopy of Polymer Brushes: Insights into Controversies

Atomic Force Microscopy of Polymer Brushes: Insights into Controversies

Peridynamic model for visco-hyperelastic material deformation in different strain rates

Brownian dynamics of a compressed polymer brush model. Off-equilibrium response as a function of surface coverage and compression rate

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