PHILADELPHIA UNIVERSITY

 Dr. Mark Liff                                             M.S. in Materials                                                  

                                  POLYMER AND FIBER PHYSICS

office: Search Hall, R#320, ph. 951-2879

This course will introduce you to the physical properties of polymers and the investigation of the structure-property relationships in polymers by physical methods. The focus will be on the mechanical, thermodynamical and dielectric behavior of polymers. The statistical description of an isolated chain will be followed by the theories of rubber elasticity and viscoelasticity. The theory of the glass-rubber transition and the behavior of glasses, rubbers and melts will be discussed. Molecular motion and its manifestation in the mechanical, dielectric and NMR experiments constitute an important part of this class. The molecular structure of textile fibers, including natural protein fibers (silk, wool) will be discussed as well.

Listing of Topics.

• 1. Types of polymer structure: linear, branched, networked. Most common polymers and their end-use properties. Introductory ideas about structure-property relationship.
• 2. Rotational isomerism in small molecules. Ethane, n-butane. Trans and gauche positions. The energy dependence on rotational angle. Conformational state of a polymeric molecule. Number of conformations in a polymer.
• 3. Brownian motion in liquids, gases and solids. Correlation time and frequency. Specifics of molecular motion in polymers. Local, segmental and large scale motion in polymers and orders of the correlation time.
• 5. Average end-to-end distance for a flexible chain (average over time, average over ensemble) Substitution of a real chain by a model. Random walk, random flight. Freely jointed chain. Average end-to-end distance for a freely jointed chain. Comparison to a real chain. The idea of a statistic segment. The probability of finding two ends at a given distance. Elasticity. Entropic nature of rubber elasticity.
• 6. Ordered chain conformation. Polyethyleneterephthalate, nylon. Bulky substituents, polytetrafluoroethelene. Stereoregularity and microtacticity. Helical structures generated by succession of trans and gauche conformations.
• 7. Glass transition. Free volume theory. The equation of William-Landels -Ferry. Incremental method for the determination of Tg. Dependence of Tg on molecular weight.
• 8. Crystal structures. Lamella, micelle, fibril, spherulites. Crystallization from solution and from melt.. The changes in properties on crystallization. Dependence of melting on distribution of molecular weight. Dependence on branching.  A mesomorphic state.
• 9. Fibers. Orientation. The basic scheme of fiber spinning. Typical force-length diagrams. Young modulus. Breaking tenacity. Length -temperature relationship. Shrinkage (contractility). Protein fibers. Typical structure of proteins (alpha-helix, beta- sheet). Silk. Wool.
• 10. Molecular weight, M (number average, weight average). Light scattering and M determination. Raleigh ratio, its dependence on M and directional angle. Additivity of scattering from a solute and a solvent. The schematic of light scattering instrumentation. The asymmetry of light scattering when a wavelength is comparable to molecular dimensions. Zimm's double extrapolation for obtaining M.
• 11. Centrifugation. The principle of M determination by ultracentrifugation. Method of sedimentation velocity. The Svedberg factor and the diffusion factor. Svedberg equation. Sedimentation equilibrium.
• 12. Molecular weight and viscosity. Viscosity and Stokes law. Capillary viscometry and time of flow. Relative, specific, reduced and characteristic viscosity. Mark-Howink equation for dependence of viscosity on M.
• 13. Mechanical properties of polymers. Dependence of correlation time and viscosity on temperature. Activation energy barrier. Temperature dependence of modulus: correlation with glass and melt transitions. Dependence of stress on time upon application and removal of a constant force at different states: glass, rubber, melt, viscoelastic polymer. Stress-strain diagrams: initial and secant modulus, yield point, breaking tenacity. Instruments with a constant rate of elongation and loading: Instron, chainomatic method, inclined plane method.  Work of rupture and its measurement.  Elastic recovery for crystals, plastics, rubber networks, melts.   Time effects during recovery.
• 14. Models of viscoelastic behavior. Springs and pistons. Parallel and in series connections. Examination of relaxation and creep on Kelvin and Maxwell models. Dynamic testing. Diagram of force versus elongation for a spring and a piston. Energy losses. Quantities E', E'', A, tan d and their dependence on frequency of testing and molecular motion. Shear modulus. Poisson ratio.  Four- parameters models. Accounting for distibutions of relaxation and retardation times.
• 15. Thermal analysis. Principles and applications. Differential thermal analysis. Differential scanning calorimetry. Thermomechanical analysis. Thermogravimetric analysis. Dynamic mechanical thermal analysis. Dielectric thermal analysis.
• 16. Electrical properties. Measurements of conductivity, influence of moisture. Conductivity of fibers (volume or surface, ionic or electronic?). Static charges in fibers. Triboelectricity. Piezoelectricity.
• 17. Application of Nuclear Magnetic Resonance to some problems of Polymer Science: molecular weight determination, microtacticity, molecular motions.

Texts for FB12:

Painter, P & Coleman, M. Fundamentals of Polymer Science, 1997 (available in the bookstore).

Eisele, U., Introduction to Polymer Physics, Springer Verlag, Berlin, 1990.

Mark, J., E., et al. Physical Properties of Polymers, ACS, Washington, DC, 1993

Cowie, J. M. G. Polymers. Chapman and Hall, any edition.

Grading

Tests (min 2 and max 4, as needed) ............. 50 %

Comprehensive final.......................................................... 40 %

Review of 2 articles ......................................................... 10 %.

Time for the tests will be announced one week in advance.

Points Grade

85-100 A

71-84 B

61-70 C

51-60 D

If you are 1-2 points short of A, B, C, you will be graded A-, B- or C-, correspondingly. If you are in B or C limits and 3-4 points short of getting a higher grade, you will be graded B+ and C+, accordingly.

Special bonus for a successful final exam.

If you get A or B for your final all your other grades that are lower than the grade for the final will be disregarded and substituted by that higher grade. To qualify for this bonus your reviews should be turned in on time and graded no less than C+ and you must take all in-class tests.

Make-ups. The percentage of the missed test automatically goes into the final. The final exam is mandatory. There will be no individualized make-ups.