Network structure, kinematics of deformation and constitutive equations of rubber elasticity

1974 ◽  
Vol 252 (10) ◽  
pp. 767-783 ◽  
Author(s):  
Andrzej Ziabicki
Keyword(s):  
Network Structure ◽  
Constitutive Equations ◽  
Rubber Elasticity

Rubber elasticity and network structure

1986 ◽  
Vol 264 (1) ◽  
pp. 9-18 ◽  
Author(s):  
H. G. Kilian ◽  
K. Unseld
Keyword(s):  
Network Structure ◽  
Rubber Elasticity

Rubber Elasticity

1982 ◽  
Vol 55 (4) ◽  
pp. 1123-1136 ◽  
Author(s):  
J. E. Mark
Keyword(s):  
Network Structure ◽  
Glassy State ◽  
Crystalline Polymer ◽  
Spatial Arrangement ◽  
High Viscosity ◽  
Rubber Elasticity ◽  
Polymer Chains ◽  
Chain Extension ◽  
Chain Molecule ◽  
High Degree

Abstract Rubber elasticity may be operationally defined as very large deformability with essentially complete recoverability. In order for a material to exhibit this type of elasticity, three molecular conditions must be met: (1) the material must consist of polymeric chains, (2) the chains must be joined into a network structure, and (3) the chains must have a high degree of flexibility. The first requirement arises from the fact that the molecules in a rubber or elastomeric material must be able to alter their arrangements and extensions in space dramatically in response to an imposed stress, and only a long-chain molecule has the required very large number of spatial arrangements of very different extensions. This versatility is illustrated in Figure 1, which depicts a random spatial arrangement of a relatively short polymer chain. In this random arrangement, the chain extension (as measured by the end-to-end separation) is quite small. For even such a short chain, the extension could be increased approximately fourfold by simple rotations about skeletal bonds, without any need for distortions of bond angles or bond lengths. The second characteristic cited is required in order to obtain the elastomeric recoverability. It is obtained by joining together or “crosslinking” pairs of segments, approximately one out of a hundred, thereby preventing the extended polymer chains from irreversibly sliding by one another. The resulting network structure is illustrated in Figure 2, in which the crosslinks are represented by dots. These crosslinks may be either chemical bonds [as would occur in sulfur-vulcanized natural rubber' or physical aggregates (for example the small crystallites in a partially crystalline polymer or the glassy domains in a multiphase block copolymer). The last characteristic specifies that the different spatial arrangements be accessible, i.e., changes in these arrangements should not be hindered by constraints as might result from inherent rigidity of the chains, extensive chain crystallization, or the very high viscosity characteristic of the glassy state.

NEW INSIGHTS INTO RUBBER NETWORK STRUCTURE BY A COMBINATION OF EXPERIMENTAL TECHNIQUES

2017 ◽  
Vol 90 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Beatriz Basterra-Beroiz ◽  
Robert Rommel ◽  
Francois Kayser ◽  
Stephan Westermann ◽  
Juan López Valentín ◽  
...  
Keyword(s):  
Network Structure ◽  
Uniaxial Stress ◽  
Industrial Applications ◽  
Rubber Elasticity ◽  
Experimental Techniques ◽  
Multiple Quantum ◽  
Physically Based ◽  
Complementary Techniques ◽  
The Individual ◽  
The Impact

ABSTRACT Robust quantitative cross-link density characterization becomes necessary for the complete understanding of the structure and optimization of final properties of rubber compounds for industrial applications. A combination of different experimental techniques have been used to establish the quantitative consistency on the correlations between the results obtained by the individual methods within a reliable unique (physically based) platform reclined on the concept of rubber elasticity that considers the impact of entanglements in technical rubbers. The contribution of cross-links and elastically active entanglements to mechanical properties has been quantified by the analysis of uniaxial stress–strain measurements by means of the extended tube model of rubber elasticity. In a complementary manner, rubber network structure has also been investigated by state-of-the-art multiple-quantum low-field NMR experiments and classical T1 and T2 relaxation measurements. In addition, equilibrium swelling data were analyzed by the classical phantom and Flory–Rehner limits as well as by applying the theoretical approach proposed by Helmis, Heinrich, and Straube that takes into account topological constraints during swelling. Correlations among these complementary techniques have been reported, and the interpretation of the obtained differences is addressed. The baseline study focuses on unfilled NR, setting the basis for the investigation of unfilled SBR matrices and filled rubbers.

THE FORMATION AND PROPERTIES OF THREE-DIMENSIONAL POLYMERS: III. THE EFFECT OF NETWORK STRUCTURE ON ELASTIC PROPERTIES

1949 ◽  
Vol 27b (2) ◽  
pp. 139-150 ◽  
Author(s):  
J. Bardwell ◽  
C. A. Winkler
Keyword(s):  
Molecular Weight ◽  
Statistical Mechanics ◽  
Elastic Properties ◽  
Network Structure ◽  
Three Dimensional ◽  
Butyl Rubber ◽  
Rubber Elasticity ◽  
Cross Linking

The tension exerted by stretched rubber at a given temperature and elongation is determined by the initial molecular weight and the concentration of cross-linkages. With the copolymer of butadiene and styrene (GR-S) the effect of molecular weight on elastic properties is identical with that found by Flory for butyl rubber and arises from the inactivity of terminal chains. When the molecular weight is fixed, the retractive force is approximately linear with the degree of cross-linking, in agreement with the statistical mechanics of rubber elasticity.

The Effect of Network Structure in the Equation of Rubber Elasticity

1976 ◽  
Vol 49 (5) ◽  
pp. 1232-1237 ◽  
Author(s):  
E. M. Valles ◽  
C. W. Macosko
Keyword(s):  
Shear Modulus ◽  
Temperature Dependence ◽  
Network Structure ◽  
Mechanical Response ◽  
Structural Features ◽  
Model System ◽  
Rubber Elasticity ◽  
Stress Strain ◽  
Good Agreement

Abstract Though the stress, strain, and temperature dependence for an ideal rubber is fairly well established, the relation between network structural features like crosslinks, dangling ends, and entanglements and mechanical response is uncertain. The modulus-structure relations recently derived by Miller and Macosko for several types of networks are tested here with a model system: the hydrosilation crosslinking of vinyl-terminated polydimethylsiloxane chains with a tetra-functional silane. Results of shear modulus as a function of extent of reaction and of stoichiometric imbalance are in good agreement with the theory.

Dependence of Elastic Properties of Vulcanized Rubber on the Degree of Cross-Linking

1950 ◽  
Vol 23 (1) ◽  
pp. 9-26
Author(s):  
Paul J. Flory ◽  
Norman Rabjohn ◽  
Marcia C. Shaffer
Keyword(s):  
Statistical Theory ◽  
Network Structure ◽  
Short Circuit ◽  
Elastic Equilibrium ◽  
Butyl Rubber ◽  
Rubber Elasticity ◽  
Cross Linking ◽  
Substantial Part ◽  
Vulcanized Rubber ◽  
Low Degrees

Abstract The results reported above demonstrate a progressive increase in the force of retraction τ at fixed elongation with increase in the fraction p of the structural units which are cross-linked from ρ=0.10×10−2 to 3.0×10−2. Over this range, τ at 100 per cent elongation increases about thirteenfold. Swelling measurements indicate that the increase in τ with ρ continues over an additional tenfold range in ρ. Previous assertions that the modulus of elasticity of soft gum rubber vulcanizates depends largely on chain interaction and entanglements other than those imposed by the cross-linkages, and that the modulus is, therefore, not directly related to the degree of cross-linking, are without foundation. The statistical theory of rubber elasticity expresses the force of retraction as a function of the temperature, vulcanizate structure and elongation; no arbitrary constants are involved. The magnitudes of τ for α=2 are in remarkably close agreement with the predictions of the theory over most of the range in ρ. This fact is of the utmost significance in confirmation of the statistical theory of rubber elasticity and of the analysis of the network structure of vulcanized rubber. On the other hand, τ increases less rapidly with ρ than the direct proportionality prescribed by theory. Forces of retraction are higher than the theory predicts at low degrees of cross-linking, and an opposite deviation is observed for values of ρ greater than about 1×10−2. Previous observations on Butyl rubber, vulcanized to p values from about 0.16×10−2 to 0.28×10−2 indicated forces of retraction (for infinite molecular weight M) which exceed by about threefold those predicted from the theory. This deviation is decidedly larger than has been observed here in the same range for ρ. A substantial part of the discrepancy observed for Butyl rubber may have arisen from failure to secure elastic equilibrium, however. Deviations in the values of τ from theory probably originate largely from oversimplifications in the treatment of the network structure. Entanglements of the sort previously discussed tend to enhance the restraints imposed on the chains when the rubber is elongated. Their percentage effect should be greatest for low degrees of cross-linking, hence the observed τ values are higher than theory at low degrees of cross-linking. “Intramolecular” cross-linkages, yielding short-circuit structures contributing nothing to the elastic reaction of the network, should become increasingly important at higher degrees of cross linking. Such wastage of cross-linkages may account for the low values of τ obtained for higher ρ values.

An alter-centric perspective on employee innovation: The importance of alters’ creative self-efficacy and network structure.

2017 ◽  
Vol 102 (9) ◽  
pp. 1360-1374 ◽  
Author(s):  
Travis J. Grosser ◽  
Vijaya Venkataramani ◽  
Giuseppe (Joe) Labianca
Keyword(s):  
Network Structure ◽  
Self Efficacy ◽  
Creative Self
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