The Visco-elastic Properties of Network Structure I. General Formalism
05 Apr 1956-Journal of the Physical Society of Japan (The Physical Society of Japan)-Vol. 11, Iss: 4, pp 413-421
TL;DR: In this article, the authors derived the stress-strain-time (S − S − T )relation at each instance of macroscopic observations by using the statistical mechanical considerations of equilibrium states.
Abstract: Many kinds of amorphous high polymer substances show the non-ideal rheological behaviours even in the “static” observations. In this paper, the general stress-strain-time relation and energy of dissipation of these systems are treated by adopting the modified rubber-like network model in which the junctions connecting the polymer chains break up and reform continually. The probability of the breakage of the junction, namely the breakage of the chain, per unit time is not a constant but a functions of both the number of segments which construct the chain and the end-to-end distance of the chain. It is assumed that the velocities of deformation of the system and of the change of the situation of network structure are extremely slower than those of the micro-Brownian movements of polymer segments. Therefore the statistical mechanical considerations of equilibrium states may be used to derive the stress-strain-time ( S – S – T )relation at each “instance” of macroscopic observations. From our general expressi...
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01 Jan 1974
1,090 citations
TL;DR: In this paper, a constitutive equation is derived from a Lodge-Yamamoto type of network theory for polymeric fluids, where the network junctions are not assumed to move strictly as points of the continuum but allowed a certain "effective slip".
Abstract: A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.
1,066 citations
TL;DR: The use of polymer modified asphalts for waterproofing and in road pavement has been continually increasing worldwide, because a relatively small quantity of added polymer can significantly enhance performance and durability as mentioned in this paper.
Abstract: The use of polymer modified asphalts for waterproofing and in road pavement has been continually increasing worldwide, because a relatively small quantity of added polymer can significantly enhance performance and durability. The knowledge of the morphological structure of such materials is still incomplete and controversial, mainly because of the compositional complexity. In practice, rheology is one of the most useful tools for the study of polymer modified asphalt. Particularly, nonlinear rheology may give unique information that helps to interpret how the polymer organizes when it is blended with asphalt. In this paper, besides a brief description of linear rheological properties and modeling, particular attention is paid to the most recent studies on the structure and to material functions, such as shear viscosity and relaxation modulus in the nonlinear viscoelastic region. The correlation of nonlinear behavior with polymer characteristics and with the architecture established when polymers are blended with asphalts is then described.
286 citations
238 citations
TL;DR: In this article, constitutive equations based on the network models of Yamamoto, Lodge, and Kaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum.
Abstract: In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by alternative assumptions concerning the creation and loss of network segments, and the theory is extended to non-Gaussian networks.Kayes theory is extended to allow for the presence of entanglement junctions of different complexities.
211 citations
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TL;DR: In this article, the second law of thermodynamics is used to define dissipation of energy at constant temperature and explicit expressions for dissipation energy for any strain history are obtained, inasmuch as relaxation during straining causes an essential reorganization of structure which is in fact the cause of dissipation.
Abstract: A molecular theory of relaxing media is presented which gives an expression for the stress in terms of the strain history. At any given time the strain history produces a distribution in internal strains which for mechanical properties can be characterized by a limited number of internal strain parameters. The second law of thermodynamics is used to define dissipation of energy at constant temperature and explicit expressions for dissipation of energy for any strain history are obtained. Inasmuch as relaxation during straining causes an essential reorganization of structure which is in fact the cause of dissipation, the kinetic theory of elasticity is extended to non‐isotropic polymeric networks. A tensor expression for the stress‐strain‐time relations is thereby developed.
766 citations
TL;DR: In this article, a chemical kinetic interpretation of the rheological behavior of high polymers has been proposed, in which the polar force of segments locks the adjacent segments in neighboring molecules in a similar way to crosslinking in vulcanized rubber.
Abstract: A chemical kinetic interpretation of the rheological behavior of high polymers has been proposed, in which the polar force of segments locks the adjacent segments in neighboring molecules in a similar way to crosslinking in vulcanized rubber. The change of such a crosslink caused by the thermal motion of segments and by external stress on the sample gives rise to rheological phenomena, such as the relaxation of stress or strain. The elasticity or viscosity of high polymers is related to the equilibrium crosslinkage which is affected not only by the temperature change but also by external stress. The structural viscosity, the yield point, or the effect of solvent on elasticity or on viscosity can also be understood according to this interpretation. The theoretical treatment gives many equations previously found in experiments: the equation for relaxation of deformation or stress, i.e., the four-element-model equation, the Dienes' equation with respect to the temperature dependence of elasticity of polyvinyl chloride, or Rabinovitch's equation for structural viscosity.
16 citations