# Mathematical Theory of Sedimentation Analysis

## 1st Edition

**Authors:**Hiroshi Fujita

**Editors:**Eric Hutchinson P. Van Rysselberghe

**eBook ISBN:**9781483274355

**Imprint:**Academic Press

**Published Date:**1st January 1962

**Page Count:**328

## Description

*Mathematical Theory of Sedimentation Analysis* deals with ultracentrifugal analysis. The book reviews flow equations for the ultracentrifuge, for two component systems, for multicomponent systems, and in chemically reacting systems. It explains the Svedberg equation and its extensions, and also the tests of the Onsager reciprocal relation. By employing a system consisting of two strong electrolytes and a solvent, the book illustrates that the sedimentation processes can be treated in terms of thermodynamics of irreversible processes. It also explains sedimentation-diffusion equilibrium and an approach to sedimentation equilibrium. It reviews the prediction of the time required to reach equilibrium, the estimates being made by Weaver (1926), and by Mason and Weaver (1924). The book employs sedimentation in a sector-shaped cell in a centrifugal field, of which the solutions of Mason and Weaver closely approximate the actual concentration distribution in the ultra-centrifuge cell. Other accurate solutions are by Fujita, Nazarian (1958), Yphantis, and Waugh. The book will prove valuable for mathematicians, physical chemists, biophysical chemists students, or professor of advanced mathematics.

## Table of Contents

Foreword

Preface

Introduction

Part I Transport

Chapter I Flow Equations for the Ultracentrifuge

1.1 Introduction

1.2 The Coordinate System

1.3 Definitions Of Flows

1.4 Phenomenological Equations and Coefficients

1.5 Flow Equations for Sedimentation in the Ultracentrifuge

1.6 The Svedberg Equation and its Extensions

1.7 The Differential Equations for the Ultracentrifuge

1.8 Electrolyte Solutions

1.9 Tests of the Onsager Reciprocal Relation

1.10 Systems of Reacting Components

Appendices

References

Chapter II Two-Component Systems

A. Basic Equations

2.1 Introduction

2.2 Initial and Boundary Conditions

B. The Case of Negligible Diffusion

2.3 General Considerations

2.4 Some Examples

C. Solutions of the Faxén Type

2.5 An Exact Solution Due to Faxén for the Infinite Cell

2.6 Asymptotic Expansions of Faxén's Solution

2.7 Practical Form of Faxén's Solution

2.8 An Approximate Solution of the Faxen Type Subject to the Initial Condition (2.1)

2.9 Concentration-Dependent Sedimentation

2.10 An Approximate Solution for a Concentration-Dependent Sedimentation in which s is a Linear Function of c

2.11 Sedimentation with a Differential Boundary

D. Solutions of the Archibald Type

2.12 The Exact Solution Due to Archibald

2.13 Approximate Solutions of the Archibald Type

2.14 Some Features of Solutions of the Archibald Type

2.15 A Solution for Small ε'τ Subject to the Exact Boundary Conditions

2.16 Evaluation of Sedimentation Coefficients for Systems with Large ε'

E. The Archibald Method for Molecular Weight Determination

2.17 Basic Equations

2.18 Practical Procedures

F. Pressure-Dependent Sedimentation

2.19 Introduction

2.20 The Extrapolation Procedures Due to Oth and Desreux

2.21 The Approximation of Wales

Appendices

References

Chapter III Muiticomponent Systems

A. Relation Between Refractive Index and Concentration

3.1 Paucidisperse and Polydisperse Systems

3.2 Expressions for the Refractive Index and its Gradient

B. Paucidisperse Systems

3.3 Basic Equations for Three-Component Systems

3.4 The Case of Independent Sedimentation and Diffusion

3.5 Evaluation of Weight Fractions

3.6 The Equivalent Boundary Position

3.7 The Johnston-Ogston Effect

3.8 Extension of the Archibald Method to Muiticomponent Systems

C. Polydisperse Systems

3.9 Distribution Functions

3.10 Refractive Index Gradient Curves for Polydisperse Solutions

3.11 The Case of Negligible Diffusion

3.12 An Extrapolation Procedure for Obtaining α(S)

3.13 An Analysis for Gaussian Distributions

3.14 Determination of D and P

3.15 Extrapolation to Infinite Dilution

3.16 Some Examples

Appendix

References

Chapter IV Chemically Reacting Systems

A. Basic Equations

4.1 Introduction

4.2 Continuity Equations for Chemically Reacting Solutes

4.3 Constituent Quantities

B. Polymerization

4.4 Methods for Determining Polymerization Constants

4.5 Determination of Mω as a Function of c

4.6 Integration of the Continuity Equations for Monomer-Polymer Systems

4.7 Features of the Gradient Curves for Systems Involving Monomer-Polymer Equilibria

4.8 The Case of Finite Rates of Association and Dissociation

C. Isomerization

4.9 Basic Equations

4.10 Some Boundary Features of Isomer Systems

D. Complex Formation

4.11 The Solution of Gilbert and Jenkins for a Reacting System of the Type A + B ⇄ AB

4.12 Average Number of Small Molecules Bound to a Macromolecule

Appendix

References

Part II Equilibrium

Chapter V Sedimentation-Diffusion Equilibrium

A. Introduction

5.1 Sedimentation Equilibrium

5.2 Basic Equations for the Sedimentation Equilibrium

B. Two-Component Systems

5.3 Integration of the Basic Differential Equation

5.4 Virial Expansion for Sedimentation Equilibrium

5.5 Corrections for Pressure

C. Three-Component Systems

5.6 Effects of Solvation

5.7 Sedimentation Equilibrium in a Density Gradient

D. Polymer Solutions

5.8 Basic Equations and Assumptions

5.9 Derivation of the Virial Expansion for Sedimentation Equilibrium

5.10 Actual Procedure for Determining Mω and BSD

5.11 Expressions with the Continuous Distribution of Molecular Weights

5.12 Thermodynamic Ideality and the Theta Temperature

E. Determination of the Molecular Weight Distribution

5.13 Previous Theories

5.14 Expressions for Average Molecular Weights

5.15 A Method for Average Molecular Weights and Molecular Weight Distribution

5.16 Average Molecular Weights

5.17 Determination of the Function q(λ)

F. Other Problems

5.18 Electrolyte Solutions

5.19 Fluctuation of the Rotor Speed

Appendices

References

Chapter VI Approach to Sedimentation Equilibrium

6.1 Introductory Remarks

6.2 Prediction of the Time Required to Reach Equilibrium

6.3 Measurement of the Diffusion Coefficient from the Rate of Approach to Equilibrium

6.4 Nazarian’s Approach to the Determination of D

6.5 Application of the Synthetic Boundary Cell

References

Author Index

Subject Index

## Details

- No. of pages:
- 328

- Language:
- English

- Copyright:
- © Academic Press 1962

- Published:
- 1st January 1962

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483274355