# Theory of Electric Polarization

### Dielectrics in Static Fields

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Theory of Electric Polarization: Dielectrics in Static Fields: Second Edition concerns the theory of the static behavior of dielectrics. The book reviews electric moment, electric dipoles, some concepts of, and problems of electrostatics. One problem concerns the phenomena of a conducting sphere in a homogeneous external field which was resolved using Laplace's equation. The text also discusses the work required to assemble a charge distribution, the energy of a dialectric or an induced dipole in an external field, and the electrostatic interaction of two particles. The book explores the reaction field of a polarizable or non-polarizable point dipole, the reaction field in an ellipsoidal cavity, the reaction field of an eccentric dipole in a spherical cavity, and the contribution of the permanent dipoles to the cohesion energy of a liquid. The text tackles the Onsager equation, the Debye equation, a correction to the Clausius-Mossotti equation, and the Kirkwood correlation factor. The book explains normal and anomalous saturation, electrostriction, as well as the non-linear effect due to the anisotropy of polarizability and hyperpolarizabilities. The text can prove beneficial for researchers, investigators or scientists whose work involve organic chemistry, analytical chemistry, physical chemistry, and inorganic chemistry.

## Table of Contents

Foreword

Preface to the Second Edition

Important Symbols

Historical Introduction

References

Chapter I. Electric Dipoles and Multipoles

1. Electric Moment and Electric Dipoles

2. The Electric Field of an Ideal Dipole in vacuo

3. Non-Ideal Dipoles. The Description of Potentials with the Aid of Legendre Functions

4. Axial Multipoles

5. General Multipoles

References

Chapter II. Some Concepts and Problems of Electrostatics

6. The Vector Fields Ε and D

7. The Electric Polarization

8. The Relation Between Ε and Ρ

9. Some Electrostatical Problems

10. The Polarizability α

References

Chapter III. Polarization and Energy

11. The Relation Between Potential and Energy

12. The Work Required to Assemble a Charge Distribution

13. The Work of Assembly as a Thermodynamic Quantity

14. The Energy of a Dielectric in an External Field

15. The Energy of an Induced Dipole in an External Field

16. The Electrostatic Interaction of Two Particles

References

Chapter IV. The Reaction Field

17. Introduction

18. The Reaction Field of a Non-Polarizable Point Dipole

19. The Reaction Field of a Polarizable Point Dipole

20. The Reaction Field in an Ellipsoidal Cavity

21. Reaction Field and Energy

22. The Average Reaction Field of an Arbitrary Charge Distribution in an Ellipsoidal Cavity

23. The Reaction Field of an Eccentric Dipole in a Spherical Cavity

24. The Contribution of the Permanent Dipoles to the Cohesion Energy of a Liquid

References

Chapter V. The Dielectric Constant in the Continuum Approach to the Environment of the Molecule

25. Introduction

26. The Dependence of the Polarization on the Internal and the Directing Field

27. The Internal Field for Non-Polar Dielectrics

28. The Internal and the Directing Fields for Polar Dielectrics

29. The Onsager Equation

30. The Generalization of the Onsager Equation for Ellipsoidal Molecules

31. The Debye Equation

32. A Correction to the Clausius-Mossotti Equation

33. The Correction to the Clausius-Mossotti Equation for Ellipsoidal Molecules

34. Mixtures of Non-Polar Compounds

References

Chapter VI. Statistical-Mechanical Theories of the Dielectric Constant

35. Introduction

36. The 3N-Dimensional Vectors and Tensors

37. The Clausius-Mossotti Equation

38. The Dielectric Virial Coefficients of Gases

39. The Dielectric Constant of Pure Dipole Liquids

40. The Kirk Wood Correlation Factor

References

Chapter VII. Non-Linear Effects

41. Introduction

42. Normal Saturation

43. Anomalous Saturation

44. Non-Linear Effects Due to the Anisotropy of the Polarizability and to the Hyperpolarizabilities

45. Electrostriction

References

Appendix I. Some Applications of Vector and Tensor Calculus

1. Differentiation of Scalar and Vector Fields

2. Some Vector-Analytic Equations

3. Integration of Scalar and Vector Fields

4. Spherical Coordinates

5. The Nabla Operator in Spherical Coordinates

6. Tensors and Matrix Representations of Tensors

7. Transformations and Invariants of Symmetric Matrices

References

Appendix II. The Solution of Laplace's and Poisson's Equations

1. Laplace's Equation

2. The General Solution of Laplace's Equation in Spherical Coordinates for the Case of Axial Symmetry

3. The Three-Dimensional δ-Function

4. Poisson's Equation

References

Appendix III. Some Properties of the Legendre Polynomials

1. The Generating Function and Recursion Formulas

2. Legendre's Differential Equation

3. The Solution of Legendre's Equation

4. A Table of the Legendre Polynomials

5. Orthogonality of the Legendre Polynomials

Reference

Author Index

Subject Index

Chemical Name Index

## Product details

- Language: English
- Copyright: © Elsevier Science 1973
- Published: January 1, 1973
- Imprint: Elsevier Science
- eBook ISBN: 9780444600066

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