The necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers. This is accomplished by use of the concept of the submolecule, a portion of polymer chain long enough for the separation of its ends to approximate a Gaussian probability distribution. The configuration of a submolecule is specified in terms of the vector which corresponds to its end‐to‐end separation. The configuration of a molecule which contains N submolecules is described by the corresponding set of N vectors. The action of a velocity gradient disturbs the distribution of configurations of the polymer molecules away from its equilibrium form, storing free energy in the system. The coordinated thermal motions of the segments cause the configurations to drift toward their equilibrium distribution. The coordination is taken into account by the mathematical requirement that motions of the atom which joins two submolecules change the configurations of both submolecules. By means of an orthogonal transformation of coordinates, the coordination of all the motions of the parts of a molecule is resolved into a series of modes. Each mode has a characteristic relaxation time. The theory produces equations by means of which the relaxation times, the components of the complex viscosity, and the components of the complex rigidity can be calculated from the steady flowviscosities of the solution and the solvent, the molecular weight and concentration of the polymer, and the absolute temperature. Limitations of the theory may arise from the exclusion from consideration of (1) very rapid relaxation processes involving segments shorter than the submolecule and (2) the obstruction of the motion of a segment by other segments with which it happens to be in contact. Another possible cause of disagreement between the theory and experimental data is the polydispersity of any actual polymer; this factor is important because the calculated relaxation times increase rapidly with increasing molecular weight.

/pdf/a-theory-of-the-linear-viscoelastic-properties-of-dilute-mrv4nglavh.pdf

A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers

The Classical Field Theories

A method of determining the stress-strain relation of materials when stresses are applied for times of the order of 20 microseconds is described. The apparatus employed was a modification of the Hopkinson pressure bar, and detonators were used to produce large transient stresses. Thin specimens of rubbers, plastics and metals were investigated and the compressions produced were as high as 20% with the softer materials. It was found that whilst Perspex recovered almost as soon as the stress was removed, rubbers and polythene showed delayed recovery, and copper and lead showed irrecoverable flow. The phenomenon of delayed recovery is discussed in terms of the theory of mechanical relaxation and memory effects in the material.

https://iopscience.iop.org/article/10.1088/0370-1301/62/11/302/pdf

An Investigation of the Mechanical Properties of Materials at very High Rates of Loading

A set of 61 ion polarizabilities has been derived from the dielectric constants of 129 oxides and 25 fluorides using a least squares refinement technique in conjunction with the Clausius–Mosotti equation. These polarizabilities can be used to estimate mean dielectric constants of ‘‘well‐behaved’’ compounds. They should be particularly useful in calculation of mean dielectric constants of compounds whose dielectric constants have not been determined. They can also be used as a framework for distinguishing unusual dielectric behavior from normal dielectric behavior where deviations can frequently be attributed to piezo‐ or ferroelectricity, conductivity (ionic or electronic), ‘‘rattling’’ or ‘‘compressed’’ cations with correspondingly high or low polarizabilities, or the presence of dipolar impurities. Deviations observed from calculated dielectric constants can be used to search for unusual physical behavior.

Dielectric polarizabilities of ions in oxides and fluorides

Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

/pdf/the-rock-physics-handbook-tools-for-seismic-analysis-of-58lw74s1oi.pdf

The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

Piezoelectric crystals and their application to ultrasonics , Piezoelectric crystals and their application to ultrasonics , دانشگاه تهران

Piezoelectric Crystals and Their Applications to Ultrasonics

Physical Acoustics: Principles and Methods

Electromechanical transducers and wave filters

The techniques of physical acoustics have been applied in determining the elastic properties and internal friction of polycrystal and single crystal metals, glasses, nonmetallic crystals, high polymer materials, and ceramics. They have been used as tools in investigating such solid state phenomena as grain and domain boundary effects in metals and ferromagnetic and ferroelectric materials, in the diffusion of atoms, molecules and vacancies through a solid, in the motion of imperfections such as dislocations and have even detected an interaction between the lattice sound vibrations and free electrons in metals at low temperatures.These effects are studied by techniques varying from the vibrations of torsional pendulums at frequencies below 1 cy to frequencies as high as 300 Mc by ultrasonic pulsing methods and have employed strain values from 10−8 to 10−2. Four examples of these techniques are discussed in the present paper. These include diffusions of nitrogen and carbon atoms in iron, the motion of domai...

Warren P. Mason

Papers

Piezoelectric Crystals and Their Applications to Ultrasonics

Physical Acoustics: Principles and Methods

Electromechanical transducers and wave filters

Physical acoustics and the properties of solids

Physical Acoustics and the Properties of Solids