Applicability of Statistical Theories of Network Formation

Dusˇek, Karel

doi:10.1002/masy.200751002

Cited by 7 publications

(3 citation statements)

References 42 publications

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“…To study how the formation of a network chain determines the tensile and thermodynamic properties, a number of theoretical analyses [1][2][3][4][5][6] and numerical simulations [7][8][9][10][11][12][13] have investigated the length or molecular weight of the monomer chains and the topology of networks. The two main theoretical models used to describe elastomer thermodynamics are affine [12] and phantom network models [13].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Simple quantification of elastomers’ deformation-induced entropy changes through maxwell relation implementation

2023

Phys. Scr.

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An upper division experimental method to determine the configurational entropy change using an approximated Maxwell relation for short fiber reinforced polymers is presented. This approach mainly integrates two regression models in data analysis, respectively being the phenomenological Mooney-Rivlin model and the linear tension-temperature relation; the former simulates the tensile performance under various isothermal conditions, while the latter is used to measure the partial differential value (∂S/∂l)_Tin the Maxwell relation. To further correct tensile data to accurately measure the minute configurational entropy change in loading, a linear-form segmented compensation function was used to correct the dynamic fatigue effect in repetitive tensile testing. With corrected Mooney-Rivlin fits under various temperature conditions graphed, one may focus on a fixed strain and investigate its corresponding linear tension-temperature relation to establish the numerical value of (∂S/∂l)_T. In this way, the remaining unknown variable in the Maxwell relation is entropy, thereby enabling its mathematical determination. Such a simple experimental design serves as a convenient method to measure configurational entropy change with strain for basic research.

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Section: Introduction 1motivationmentioning

confidence: 99%

Simple quantification of elastomers’ deformation-induced entropy changes through maxwell relation implementation

2023

Phys. Scr.

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“…Chemical reactions not only affect the property of network chain, but also affect the network topology. To study the effect of chemical reactions on the formation of a network chain, a lot of theoretical analyses − and numerical simulations ,− have paid the main attention to the length or molecular weight of the chains and the topology of networks. Here, we focus on the effects of chemical reactions on the property of average network chains.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Model of Polymer Network Chain Formation under Strain

Yan

et al. 2018

ACS Omega

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In this article, the polymer network chain formation through cross-linking and scission under n strain stages is studied based on the thermal fluctuation principle. The aim is to clarify the effects of chemical reactions, especially the network chain cross-linking, dangling chain cross-linking, cross-link scission, and network chain scission, on the free energy of network chain to generalize the classical two-network model. In our model, the free energy change for a chain formation is associated with the reaction sequences, except network chain cross-linking or cross-link scission reactions under the same strain stage. A new constitutive expression for network chain formed under two strain stages is derived according to affine deformation theory in which independent network hypothesis and stress-transfer function are not required. Comparison between our model and previous experimental data about recovered stretch ratio of γ-irradiated silicone elastomer validates that our model can give more precise result than previous two-network model.

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“…In some other cases, the difference does not exceed experimental uncertainty, but in some stage of the process the difference can be important. The “combined method” was designed in which some stages are described by kinetic method and the formed structures (superspecies) are linked by the statistical method. − However, which of the processes are statistically fully independent must be carefully analyzed. , The statistical build-up is essentially a Markov process and it is imperative that the transition probabilities, identical with linking probabilities, be determined by chemical kinetics…”

Section: Introductionmentioning

confidence: 99%

Polymer Networks from Preformed Precursors Having Molecular Weight and Group Reactivity Distributions. Theory and Application

Dušek

Dušková‐Smrčková

Huybrechts³

et al. 2013

Macromolecules

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High-performance cross-linked polymeric materials are now prepared from preformed precursors typical by distributions of molecular weights, number and reactivities of functional groups, and specific architectures. This makes theoretical treatment of networks evolution and their final structure difficult. This paper describes kinetically controlled cross-linking of a precursor formed from polyfunctional cores by arm extension by which molecular weight distribution develops and new groups of different reactivity are formed. These precursors are then cross-linked with a polyfunctional cross-linker. If the precursor groups react independently, a random (binomial) distribution of reactive groups results and the gel point conversion and other network parameters are independent of the differences in reactivity the groups with the cross-linker. If the condition of random (binomial) distribution is not met (fixed numbers of groups or substitution effect in the precursor molecules), this independence does not exist. Relations for molecular weight averages prior to gelation and gel fraction and concentration of elastically active network chains in the postgel state are derived. This general treatment applies to precursors obtained by a wide variety of chain extension chemistries and any of the family of cross–linking reactions of A + B type. In the second part, the general form of the theory was adapted to describe polyether precursors prepared by addition of an epoxy ester (glycidyl pivalate) to multifunctional polyols and their curing with a tri-isocyanate. Some of the primary OH groups of the core are chain–extended to form a polyether chain terminated by a secondary OH group. The distributions are altered by additional reactions – transesterification and alcoholysis. The branching theory was modified and the results compared with experiments. Gel point conversions were affected by these additional reactions, but the concentration of elastically active network chains (EANCs) (calculated from equilibrium elastic modulus) did not change much. The fraction of formed bonds wasted in cycles amounted to 12–22%.

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Applicability of Statistical Theories of Network Formation

Cited by 7 publications

References 42 publications

Simple quantification of elastomers’ deformation-induced entropy changes through maxwell relation implementation

Simple quantification of elastomers’ deformation-induced entropy changes through maxwell relation implementation

Theoretical Model of Polymer Network Chain Formation under Strain

Polymer Networks from Preformed Precursors Having Molecular Weight and Group Reactivity Distributions. Theory and Application

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