Two‐Dimensional Model Networks

Rehage, Heinz; Veyssié, M.

doi:10.1002/anie.199004393

Cited by 27 publications

(20 citation statements)

References 41 publications

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“…This relation reduces to τ = G c [λ ‐ 1/λ] in high dimensions and to an expression applicable to the elasticity rubbery membranes (e.g., polymerized Langmuir films) when take d = 2 in Eq. . Note that the LM implies that chain entanglement certainly exist in 2 dimensions.…”

Section: Application Of the Localization Model To The Elasticity Of Dmentioning

confidence: 96%

Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description

Douglas

2013

Macromolecular Symposia

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Summary Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of ‘classical’ model of rubber elasticity, the elasticity of the deformed network derives from the entropic changes that arise from a deformation of the network junction positions. The shortcoming of this approach is evident from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to the exploration of their local tube‐like molecular environments along their chain contours. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how the local molecular packing constraints become modified under deformation and the impact of these changes in chain confinement on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult many‐body problem. The present paper focuses on the simple ‘localization model’ (LM) of rubber elasticity of Gaylord and Douglas (GD), which provides a simple minimal model for the network elasticity of rubbery materials in the dense polymer state. Particular emphasis in the present paper is given to the implications of this model for describing how network elasticity changes with solvent swelling, a phenomenon for which large deviations from classical elasticity have been observed and a situation highly relevant to numerous applications that involve rubbery materials. We also discuss the physical nature of ‘entanglement’ based on the same molecular packing picture and deduce general conditions for entanglement in terms of molecular parameters. Our predictions accord rather well with experimental correlations relating chain molecular structure to the entanglement molecular mass, changing elasticity with swelling, etc.

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Section: Application Of the Localization Model To The Elasticity Of Dmentioning

confidence: 96%

Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description

Douglas

2013

Macromolecular Symposia

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“…The reduced stress in the LM model can be generalized to d‐dimensions: which reduces to the classical–like expression τ = G c [ λ − λ −1 ] in high dimensions24 and an expression applicable to the elasticity of membranes (e.g., polymerized Langmuir films) for d = 2 25…”

Section: The Elasticity Of Dry Rubbersmentioning

confidence: 99%

The Localization Model of Rubber Elasticity

Douglas

2010

Macromolecular Symposia

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Summary: While the unusual elastic properties of rubbery polymer materials have been studied for literally centuries, a quantitative theoretical description of these properties in terms of molecular structural parameters remains a challenging task. Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of model, the elasticity of the deformed network derives from the entropic changes in this idealized network arising from a deformation of the network junction positions. The shortcoming of this approach is clear from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to an exploration of their local molecular environments. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how local molecular packing constraints become modified under deformation and the impact of these changes on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult problem, but we focus on the simple 'localization model' of rubber elasticity introduced by Gaylord and Douglas (GD), which provides an attractive and mathematically simple minimal model for the network elasticity of rubbers having strong intermolecular interactions in the dense polymer state. GD assume that the network chain segments are localized at the network junctions, as in classical elasticity theory, but they also consider the chains to be localized along their contours by a local harmonic potential arising from inter-particle packing interactions, as in atoms in a simple harmonic crystal. This is the familiar Edwards-De Gennes 'tube' model of polymers in the condensed state. The existence of the tube means that the entropy of the network chains is reduced relative to chains without this constraint, but the crucial problem is how this entropy change becomes modified as the material becomes deformed. GD approach this problem by first observing that both the volume of the material and the network chains are essentially invariant under deformation so they require that the dimensions of the confining tube to also be a deformation invariant where this constraint is applied at a segmental level. The properties of the resulting 'localization model' of elasticity of dry and swollen rubbers are summarized and some extensions of the model to describe chain finite extensibility and stiff polymer networks are briefly summarized.

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“…This has been experimentally confirmed from surface rheology studies of 2D network materials by Veyssie and co-workers, [43,44] and more recently by Rehage. [45,46] Miyano and Veysié [43] assumed that close to p c , the number of connected bonds is proportional to the reaction time so that the shear modulus m is related to time, t, by a relationship similar to m $ (t À t c ) x where t c is the observed onset of gelation.…”

Section: Surface Compressional Modulusmentioning

confidence: 99%

“…Rehage [46] cited several of these factors, including diffusion and relaxation phenomena and the formation of ring structures. However, in the case of OTMS, the most important factor could be perhaps that p is not proportional to t and that at the gel point, a good fraction of the monomers are associated with dangling chain ends.…”

Section: Surface Compressional Modulusmentioning

confidence: 99%

Interfacial Behavior of a Reacting Alkoxysilane Monolayer System

Carino

Duran

2004

Macro Chemistry & Physics

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Summary: We report here the results on the investigations of the dynamic interfacial behavior of a trifunctional alkoxysilane, octadecyltrimethoxysilane (OTMS) as it is reacting at the air‐water interface. We have investigated both the Π‐A isotherms and A(t) isobars of OTMS at acidic subphases. An attempt to analyze the kinetics of the reaction in the monolayer was limited to the early stages of the reactions and only describes the kinetics of hydrolysis. We also confirmed by rheological measurements that this system does indeed form a network inefficiently and the resulting structure most likely consists of extensive linear segments as has been suggested in earlier reports. The general rheological characteristic indicates the product to have high molecular weight. The product also exhibited a 2D sol‐gel transition that has general features of a percolating network. However, the scaling behavior does not follow exactly that predicted; several reasons for this are discussed.A(t) isobars of OTMS at various subphase pHmagnified imageA(t) isobars of OTMS at various subphase pH

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Two‐Dimensional Model Networks

Cited by 27 publications

References 41 publications

Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description

Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description

The Localization Model of Rubber Elasticity

Interfacial Behavior of a Reacting Alkoxysilane Monolayer System

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