Contents xiii 7.4 Osm tic Pressure… 258 7.4.1 Osmotic Pressure:General Case .259 7.4.1.1 Number-Average Molecular Weight......... .261 7.4.2 Osmotic Pressure:Flory-Huggins Theory263 7.5 Phase Behavior of Polymer Solutions............ 264 7.5.1 Overview of the Phase Diagram............... .265 7.5.2 Finding the Binodal ............. .268 7.5.3 Finding the Spinodal............. .269 7.5.4 Finding the Critical Point............ .270 7.5.5 Phase Diagram from Flory-Huggins Theory.. .271 7.6 What's in x?........ 275 7.6.1 X from Regular Solution Theory.... .275 7.6.2 from Experiment........... .276 7.6.3 Further Approaches to x........ .278 7.7 Excluded Volume and Chains in a Good Solvent 280 7.8 Chapter Summary .. .283 Problems… .284 References..... ,287 Further Readings..... 288 8 Light Scattering by Polymer Solutions..289 8.1 Introduction:Light Waves............... 289 8.2 Basic Concepts of Scattering............ .291 8.2.1 Scattering from Randomly Placed Objects.......................292 8.2.2 Scattering from a Perfect Crystal.292 8.2.3 Origins of Incoherent and Coherent Scattering.............................293 8.2.4 Bragg's Law and the Scattering Vector........ 294 8.3 Scattering by an Isolated Small Molecule.......... ,296 8.4 Scattering from a Dilute Polymer Solution..... ,298 8.5 The Form Factor and the Zimm Equation..... .304 8.5.1 Mathematical Expression for the Form Factor.. .305 8.5.2 Form Factor for Isotropic Solutions.... ..306 8.5.3 Form Factor as qRg→0.… .307 8.5.4 Zimm Equation........ .307 8.5.5 Zimm Plot...... ..308 8.6 Scattering Regimes and Particular Form Factors..... ,312 8.7 Experimental Aspects of Light Scattering. 314 8.7.1 Instrumentation. 316 8.7.2 Calibration...… 317 8.7.3 Samples and Solutions.............. 319 8.7.4 Refractive Index Increment.......... .319 8.8 Chapter Summary. 320 Problems 321 References. 325 Further Readings.… 325 9 Dynamics of Dilute Polymer Solutions.. .327 9.1 Introduction:Friction and Viscosity.... ,327 9.2 Stokes'Law and Einstein's Law. 3307.4 Osmotic Pressure ......................................................................................................... 258 7.4.1 Osmotic Pressure: General Case .....................................................................259 7.4.1.1 Number-Average Molecular Weight...............................................261 7.4.2 Osmotic Pressure: Flory–Huggins Theory ......................................................263 7.5 Phase Behavior of Polymer Solutions......................................................................... 264 7.5.1 Overview of the Phase Diagram......................................................................265 7.5.2 Finding the Binodal .........................................................................................268 7.5.3 Finding the Spinodal........................................................................................269 7.5.4 Finding the Critical Point ................................................................................270 7.5.5 Phase Diagram from Flory–Huggins Theory..................................................271 7.6 What’s in x?................................................................................................................. 275 7.6.1 x from Regular Solution Theory .....................................................................275 7.6.2 x from Experiment...........................................................................................276 7.6.3 Further Approaches to x..................................................................................278 7.7 Excluded Volume and Chains in a Good Solvent ...................................................... 280 7.8 Chapter Summary ........................................................................................................ 283 Problems ................................................................................................................................ 284 References.............................................................................................................................. 287 Further Readings.................................................................................................................... 288 8 Light Scattering by Polymer Solutions...................................................289 8.1 Introduction: Light Waves........................................................................................... 289 8.2 Basic Concepts of Scattering....................................................................................... 291 8.2.1 Scattering from Randomly Placed Objects .....................................................292 8.2.2 Scattering from a Perfect Crystal ....................................................................292 8.2.3 Origins of Incoherent and Coherent Scattering ..............................................293 8.2.4 Bragg’s Law and the Scattering Vector ..........................................................294 8.3 Scattering by an Isolated Small Molecule .................................................................. 296 8.4 Scattering from a Dilute Polymer Solution................................................................. 298 8.5 The Form Factor and the Zimm Equation .................................................................. 304 8.5.1 Mathematical Expression for the Form Factor ...............................................305 8.5.2 Form Factor for Isotropic Solutions................................................................306 8.5.3 Form Factor as qRg!0....................................................................................307 8.5.4 Zimm Equation ................................................................................................307 8.5.5 Zimm Plot ........................................................................................................308 8.6 Scattering Regimes and Particular Form Factors........................................................ 312 8.7 Experimental Aspects of Light Scattering .................................................................. 314 8.7.1 Instrumentation ................................................................................................316 8.7.2 Calibration........................................................................................................317 8.7.3 Samples and Solutions.....................................................................................319 8.7.4 Refractive Index Increment .............................................................................319 8.8 Chapter Summary ........................................................................................................ 320 Problems ................................................................................................................................ 321 References.............................................................................................................................. 325 Further Readings.................................................................................................................... 325 9 Dynamics of Dilute Polymer Solutions ...................................................327 9.1 Introduction: Friction and Viscosity............................................................................ 327 9.2 Stokes’ Law and Einstein’s Law................................................................................. 330 Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C000 Final Proof page xiii 5.11.2007 8:20pm Compositor Name: JGanesan Contents xiii