Book contents
- Frontmatter
- Dedicatioin
- Contents
- Preface
- 1 Introduction
- 2 Chemical Synthesis of Aerogels from Monomeric Precursors
- 3 Chemical Synthesis of Aerogels from Polymeric Precursors
- 4 Gelation
- 5 Drying of Wet Gels
- 6 Morphology of Aerogels
- 7 Density: Models and Measures
- 8 Specific Surface Area
- 9 Pores and Pore Sizes
- 10 Diffusion in Aerogels
- 11 Permeability for Gases
- 12 Thermal Properties
- 13 Mechanical Properties of Aerogels
- 14 How to Cook Aerogels: Recipes and Procedures
- Appendix A Thermodynamics and Phase Separation in Immiscibles
- Appendix B Flory–Huggins Theory of Polymer Solutions
- Appendix C A Brief Review on Scattering
- Appendix D Mathematics of Polycondensation
- Appendix E Time-Dependent Heat Transfer through an Isolated Tube
- References
- Index
Appendix D - Mathematics of Polycondensation
Published online by Cambridge University Press: 03 December 2021
Book contents
- Frontmatter
- Dedicatioin
- Contents
- Preface
- 1 Introduction
- 2 Chemical Synthesis of Aerogels from Monomeric Precursors
- 3 Chemical Synthesis of Aerogels from Polymeric Precursors
- 4 Gelation
- 5 Drying of Wet Gels
- 6 Morphology of Aerogels
- 7 Density: Models and Measures
- 8 Specific Surface Area
- 9 Pores and Pore Sizes
- 10 Diffusion in Aerogels
- 11 Permeability for Gases
- 12 Thermal Properties
- 13 Mechanical Properties of Aerogels
- 14 How to Cook Aerogels: Recipes and Procedures
- Appendix A Thermodynamics and Phase Separation in Immiscibles
- Appendix B Flory–Huggins Theory of Polymer Solutions
- Appendix C A Brief Review on Scattering
- Appendix D Mathematics of Polycondensation
- Appendix E Time-Dependent Heat Transfer through an Isolated Tube
- References
- Index
Summary
Aerogels starting with monomeric solutions quite often from polymers by polycondensation reactions. We give in the appendix a model of polycondensation based on an approach made more than 100 years ago by Smoluchowski, and derive from that the standard equations, such as the Carothers one and the Flory–Schulz distribution. We also present a volume fraction of polymers and explain how it depends on the degree of polymerisation or time.
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- The Chemistry and Physics of AerogelsSynthesis, Processing, and Properties, pp. 424 - 431Publisher: Cambridge University PressPrint publication year: 2021