Lecture3 - Polymer Physics Chain Conformations Lecture 3 Dr...

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Unformatted text preview: Polymer Physics Chain Conformations Lecture 3 Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics – AB Brennan EMA 1 Agenda • • • • • • • • Rotational States Bond Rotational Energetics Spatial Relationships Characteristic Dimensions Freely Jointed Model Freely Rotating Model Hindered Rotation Random Flight Statistical Model EMA 6165 Polymer Physics – AB Brennan EMA 2 Polymer Structure -Property Behavior • chain chain thermodynamics thermodynamics • chain dimensions • chain environment • chain topography • mechanical mechanical behavior behavior EMA 6165 Polymer Physics – AB Brennan EMA 3 Chain Dimensions Chain Rotational Isomers Rotational Ref: Chem Draw Pro – ethane_conformers Ref: • Staggered conformation – Erot~ 0 kJ/mol, Φ = kJ/mol, 60, 180, 300 deg. 60, • Eclipsed - Erot~ 12 kJ/mol, Φ = 0/360, 120, 240 Eclipsed 12 deg. deg. • Staggered 0 kJ/mol < Erot < 0 kJ/mol, Staggered kJ/mol EMA 6165 Polymer Physics – AB Brennan EMA 4 Chain Dimensions Chain Ethanes Rotational Isomer Energies States Ethanes EMA 6165 Polymer Physics – AB Brennan EMA 5 Chain Dimensions Chain n-Butane Conformational States n-Butane Ref: Chem Draw Pro file – butane conformers EMA 6165 Polymer Physics – AB Brennan EMA 6 Chain Dimensions Chain Local Steric Repulsion Local EMA 6165 Polymer Physics – AB Brennan EMA 7 Chain Dimensions Chain Conformational States Conformational Number of Conformation States is: N = RIS n −1 RIS = Number of Rotational Isomeric States (Gauche+, Trans, Gauche-) n = number of sigma bonds in chain backbone N = 1 x 104770 for PE where Xn ~ 10,000 EMA 6165 Polymer Physics – AB Brennan EMA 8 Chain Dimensions Gaussian Chain • Random Chain Random Conformation Conformation • End-to-End End-to-End Distance <ro> Distance • Radius of Radius Gyration <rg> Gyration EMA 6165 Polymer Physics – AB Brennan EMA 9 Chain Dimensions • Gaussian Chain • End - to - end Gaussian End or random chain: distance and radius or of gyration : – Gaussian of Gaussian distribution of RIS, I.e., trans and gauche states states – characteristic characteristic dimensions based upon molar mass, chain structure and temperature temperature EMA 6165 Polymer Physics – AB Brennan EMA 10 Chain Dimensions Chain n r 2 = ∑mr i =1 n 2 ii ∑m i =1 s 2 i End to End Distance = r 2 6 Radius of Gyration m - mass of repeat unit (segment) r - vector form center of gravity to atom i EMA 6165 Polymer Physics – AB Brennan EMA 11 Chain Dimensions Chain Experimental Determination of Hydrodynamic Volume Experimental EMA 6165 Polymer Physics – AB Brennan EMA 12 Chain Dimensions Chain Experimental Methods Experimental • Scattering • Viscosity – Absolute method Absolute (Mw) (Mw) – Light – X-Ray – Neutron – Relative method (Mv) – Mark-Houwink EMA 6165 Polymer Physics – AB Brennan EMA 13 Chain Dimensions Scattering Function Kc 1 1 16 2 r 2θ = + π + 2 A2 c 2 sin Rθ MW MW 3 6λ 2 2 where: K - contrast factor c - concentration of scattering species Rθ - Rayleigh ratio (reduced intensity) r - distance from scattering center to detector. detector. I0 - incident wave intensity A2 - 2nd virial coefficient EMA 6165 Polymer Physics – AB Brennan EMA 14 Vertical Polarization Horizontal Polarization Unpolarized EMA 6165 Polymer Physics – AB Brennan EMA 15 Chain Dimensions Generation of a Zimm Plot limθ →0 Kc 1 = + 2 A2 c Rθ MW Kc 1 1 16 2 r 2θ = + π 2 sin Rθ MW MW 3 6λ 2 2 limc→0 EMA 6165 Polymer Physics – AB Brennan EMA 16 Chain Dimensions Chain Zimm Plot Zimm EMA 6165 Polymer Physics – AB Brennan EMA 17 Chain Dimensions Characteristic Dimensions r2 0 = Cnl 2 where: <r2>o - chain dimensions at Theta conditions C - Characteristic Chain Ratio nθ - number of segments l - segment dimension (length) EMA 6165 Polymer Physics – AB Brennan EMA 18 Summary • Chain bond rotational potential Chain energies dictate properties energies • Zimm Plots from scattering Zimm measurements give dimensions Mw measurements and rg separately, along with A2 and • Characteristic dimensions defined by Characteristic structure and environment structure EMA 6165 Polymer Physics – AB Brennan EMA 19 References • Introduction to Physical Polymer Science, 4th Edition, Lesley H. Sperling, Wiley Interscience (2006) ISBN 13 978-0-471-70606-9 ISBN • Principles of Polymer Chemistry, P.J. Flory (1953) Principles Cornell University Press, Inc., New York. Cornell • The Physics of Polymers, Gert Strobl (1996) The Springer-Verlag, New York. Springer-Verlag, • Figures were reproduced from Polymer Physics, Figures (1996) Ulf Gedde, Chapman & Hall, New York. (1996) EMA 6165 Polymer Physics – AB Brennan EMA 20 ...
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