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3 Dilute Solution Thermodynamics, Molecular Weights, and Sizes 71 3.1 Introduction / 71

3 Dilute Solution Thermodynamics, Molecular Weights, and Sizes 71 3.1 Introduction / 71 3.2 The Solubility Parameter / 73 3.3 Thermodynamics of Mixing / 79 3.4 Molecular Weight Averages / 85 3.5 Determination of the Number-Average Molecular Weight / 87

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3 Dilute Solution Thermodynamics, Molecular Weights, and Sizes 71 3.1 Introduction / 71

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  1. 3 Dilute Solution Thermodynamics, Molecular Weights, and Sizes 71 3.1 Introduction / 71 3.2 The Solubility Parameter / 73 3.3 Thermodynamics of Mixing / 79 3.4 Molecular Weight Averages / 85 3.5 Determination of the Number-Average Molecular Weight / 87 3.6 Weight-Average Molecular Weights and Radii of Gyration / 91 3.7 Molecular Weights of Polymers / 103 3.8 Intrinsic Viscosity / 110 3.9 Gel Permeation Chromatography / 117 3.10 Mass Spectrometry / 130 3.11 Instrumentation for Molecular Weight Determination / 134 3.12 Solution Thermodynamics and Molecular Weights / 135 4 Concentrated Solutions, Phase Separation Behavior, and Diffusion 145 4.1 Phase Separation and Fractionation / 145 4.2 Regions of the Polymer–Solvent Phase Diagram / 150 4.3 Polymer–Polymer Phase Separation / 153 4.4 Diffusion and Permeability in Polymers / 172 4.5 Latexes and Suspensions / 184 4.6 Multicomponent and Multiphase Materials / 186 References /

  2. Polymer Solutions

  3. Solubility parameter Regular solutions – heat of mixing (Hilderbrand and Scott 1949) V is total volume, DE is energy of vaporization, f volume fraction Before mixing After mixing If we assume that there is no specific interactions (hydrogen bonding etc.) , we ca assume that interaction e12 is some average from e11 and e22 Example geometrical mean (small numbers are more weighted) e11 represents how molecules 1 interact with itself – i.e. Cohesive energy or energy of vaporization energy of vaporization per volume

  4. General rule: polymer will dissolve if solubility parameters (solvent and polymer) are close to each other (1) If there are specific interactions (like hydrogen bonding...) then polymer can dissolve even if the solubility parameter difference is large.. Like poly(ethylene oxide) and water..

  5. 3.2.2 Experimental determination Crosslinked polymers: Best solvent gives the maximum swelling Non-crosslinked polymers: Best solvent (best solvent = similar solubility parameter) – polymer coil conformation is most expanded  instric viscosity largest

  6. Theoretical calculation ,where G is group molar attraction constant, r polymer density and M is repeat unit molar mass Example polystyrene: 133 28 735 Example polyethylene:

  7. Phase diagrams Small molecule mixtures:

  8. Binodaali – coexistence curve

  9. Special case – symmetric composition: Binodal – coexistence curve

  10. Phase separation kinetics T

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