Analytical ultracentrifugation of polymers and nanoparticles

Analytical ultracentrifugation (AUC) is a powerful method for the characterization of polymers, biopolymers, polyelectrolytes, nanoparticles, dispersions, and other colloidal systems. The method is able to determine the molar mass, the particle size, the particle density and interaction parameters like virial coefficients and association constants. Because AUC is also a fractionation method, the determination of the molar mass distribution, the particle size distribution, and the particle density distribution is possible. A special technique, the density gradient method, allows fractionating heterogeneous samples according to their chemical nature that means being able to detect chemical heterogeneity. The book is divided into chapters concerning instrumentation, sedimentation velocity runs, density gradient runs, application examples and future developments. In particular, the detailed application chapter demonstrates the versatility and power of AUC by means of many interesting and important industrial examples. Thus the book concentrates on practical aspects rather than details of centrifugation theory.

Both authors have many years of experience in an industrial AUC research laboratory of a world leading chemical company.

1 Introduction	p. 1
1.1 Historic Examples of Ultracentrifugation	p. 2
1.1.1 Investigations on Gold Colloids in 1924	p. 3
1.1.2 Investigations on the Structure of DNA in 1957	p. 5
1.2 Basic Theory of Ultracentrifugation	p. 7
1.2.1 Svedberg's Simplified Theory	p. 8
1.2.2 Derivation of Lamm's Equation	p. 10
1.3 Basic Experiment Types of Ultracentrifugation	p. 12
1.3.1 Sedimentation Velocity Experiment	p. 12
1.3.2 Synthetic Boundary Experiment	p. 13
1.3.3 Sedimentation Equilibrium	p. 13
1.3.4 Density Gradient	p. 14
1.3.5 Approach-to-Equilibrium (or Archibald) Method	p. 15
1.4 Closing Remarks	p. 15
References	p. 16
2 Analytical Ultracentrifugation, Instrumentation	p. 17
2.1 Ultracentrifuges	p. 18
2.1.1 The Beckman-Coulter Optima XL-A/I	p. 19
2.1.2 User-Made Centrifuges	p. 21
2.2 Rotors	p. 25
2.3 Measuring Cells	p. 26
2.4 Detectors	p. 29
2.4.1 Absorption Optics	p. 31
2.4.2 Interference Optics	p. 34
2.4.3 Schlieren Optics	p. 37
2.4.4 Other Detectors	p. 38
2.5 Multiplexer	p. 43
2.6 Auxiliary Measurements	p. 43
2.6.1 Measurement of the Solvent Density and the Partial Specific Volume	p. 43
2.6.2 Measurement of the Refractive Index and the Specific Refractive Index Increment	p. 45
References	p. 46
3 Sedimentation Velocity	p. 47
3.1 Introduction	p. 47
3.2 Basic Example of Sedimentation Velocity	p. 47
3.2.1 Determination of s	p. 50
3.2.2 Standard Conditions for s Estimation	p. 51
3.2.3 Radial Dilution and Thickening	p. 52
3.2.4 Concentration Dependence	p. 53
3.3 Advanced Theory of Sedimentation Velocity Runs	p. 54
3.3.1 Johnston-Ogston Effect	p. 54
3.3.2 Self-Sharpening of Boundarie	p. 55
3.3.3 Pressure Dependence	p. 55
3.3.4 Speed Dependence	p. 56
3.3.5 Charge Effects	p. 57
3.3.6 Separation of Sedimentation and Diffusion	p. 58
3.3.7 Test of Homogeneity	p. 61
3.4 Sedimentation Velocity Runs of Macromolecules to Measure Average M and MMD	p. 62
3.4.1 Evaluation of the Average Molar Mass M by Sedimentation Velocity Runs via Scaling Laws	p. 62
3.4.2 Evaluation of Molar Mass Distributions (MMD) by Sedimentation Velocity Runs via Scaling Laws	p. 64
3.5 Sedimentation Velocity Runs on Particles to Measure Average d[subscript p] and PSD	p. 69
3.5.1 Particle Size Distribution via AUC Turbidity Detector and Mie Theory	p. 70
3.5.2 Coupling Technique to Measure very Broad PSD	p. 77
3.5.3 H[subscript 2]0-D[subscript 2]0 Density Variation Method to Measure Particle Densities via Sedimentation Velocity Runs	p. 80
3.5.4 PSD Measurement of very Small Platinum Clusters Using UV Optics	p. 84
3.6 Synthetic Boundary Experiments	p. 86
3.6.1 Synthetic Boundary Crystallization Ultracentrifugation	p. 93
References	p. 95
4 Density Gradients	p. 97
4.1 Introduction	p. 98
4.2 Static Density Gradients	p. 101
4.2.1 Theory of Static Density Gradients	p. 102
4.2.2 Gradient Materials	p. 115
4.2.3 Experimental Procedure	p. 117
4.2.4 Examples	p. 118
4.3 Dynamic Density Gradients	p. 120
4.4 Other Types of Density Gradients	p. 125
4.4.1 Percoll Density Gradient	p. 125
References	p. 129
5 Sedimentation Equilibrium	p. 131
5.1 Introduction	p. 131
5.2 Experimental Procedure	p. 133
5.3 Data Analysis	p. 138
5.3.1 Basic Equations for Molar Mass Averages - Classical Evaluation of AUC Equilibrium Runs	p. 138
5.3.2 Basic Equations for Molar Mass Distributions - Nonlinear Regression Evaluation (Lechner Method)	p. 141
5.3.3 Application of the Basic Equations - Classical and Nonlinear Regression Evaluation	p. 144
5.3.4 M-STAR, a Special Data Analysis to obtain M[subscript w]	p. 149
5.4 Examples	p. 151
5.4.1 Absorption Optics Examples of a Polyelectrolyte and Calibration Polystyrene NBS 706	p. 152
5.4.2 Association Equilibrium Example and AUC Buoyant Density Method to Determine [Characters not reproducible]	p. 155
5.4.3 The New Fluorescence Detector of Laue Used for Green Fluorescent Protein	p. 158
5.5 Further AUC Methods to Measure Molar Masses	p. 159
References	p. 162
6 Practical Examples of Combination of Methods	p. 163
6.1 Combination of Different AUC Methods	p. 163
6.1.1 Core/Shell Particles	p. 163
6.1.2 Characterization of Microgels and Nanogels	p. 170
6.1.3 Ion Exchange in Carboxylated Latices	p. 179
6.2 Combination of AUC with Other Techniques	p. 189
6.2.1 AUC and SFFF	p. 190
6.2.2 AUC and EM	p. 198
6.3 Literature Examples: AUC and Nanoparticles	p. 212
References	p. 212
7 Recent Developments and Future Outlook	p. 215
7.1 New AUC Instrumentation and Detectors	p. 216
7.2 New AUC Methods	p. 222
7.3 New AUC Data Analysis	p. 228
References	p. 233
8 Subject Index	p. 235

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