Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

The entanglement concept in polymer rheology

The molecular constitution of viscoelastic gels is customarily described in terms of networks, which may have a transient or permanent character. Such supermolecular structures are often observed in biological or macromolecular systems, but can even occur in dilute solutions of some detergents. Surfactant molecules in solution, under suitable conditions, assemble reversibly into large aggregates of rod-like geometry. Depending on the ionic strength of the solution, these particles may be completely stiff or semiflexible. At low concentrations, when the lengths of the rods are much smaller than their mean distance of separation, there exists a sol state which is highly sensitive to shear forces. At higher surfactant concentrations, where the lengths of the rod shaped micelles become comparable to their mean distance, one observes gel formation and the solutions exhibit pronounced elastic properties. In analogy to polymer systems, these elongated, rod shaped micelles are strongly entangled; this leads to co...

Viscoelastic surfactant solutions: model systems for rheological research

The classical linear theory of viscoelasticity was apparently first formulated by Boltzmann1 in 1874. His original presentation covered the three-dimensional case, but was restricted to isotropic materials. The extension of the theory to anisotropic materials is, however, almost immediately evident on reading Boltzmann’s paper, and the basic hypotheses of the theory have not changed since 1874. Since that date, much work has been done on the following aspects of linear viscoelasticity: solution of special boundary value problems,2a reformulation3,4 of the one-dimensional version of the theory in terms of new material functions (such as “creep functions” and frequency-dependent complex “impedances”) which appear to be directly accessible to measurement, experimental determination2b of the material functions for those materials for which the theory appears useful, prediction of the form of the material functions from molecular models, and, recently, axiomatization5,6 of the theory.

Foundations of Linear Viscoelasticity

Specific metal−ligand coordination between bis-Pd(II) and Pt(II) organometallic cross-linkers and poly(4-vinylpyridine) in DMSO defines a three-dimensional associative polymer network. Frequency-dependent dynamic mechanical moduli of a series of four different bulk materials, measured across several decades of oscillatory strain rates, are found to be quantitatively related through the pyridine exchange rates measured on model Pd(II) and Pt(II) complexes. Importantly, the mechanism of ligand exchange in the networks is found to be the same solvent-assisted pathway observed in the model complexes, and so the bulk mechanical properties are determined by relaxations that occur when the cross-links are dissociated from the polymer backbone. It is how often the cross-links dissociate, independently of how long they remain dissociated, that determines the bulk mechanical properties. The quantitative relationship between bulk materials properties and the kinetics and mechanisms observed in model compounds holds ...

A. S. Lodge

Papers

A network theory of flow birefringence and stress in concentrated polymer solutions