Sample questions: Short answer

1. Complete hydrogenation of a polybutadiene with a microstructure that is 50% 1,4-trans, 40-% 1,4-cis, and 10% 1,2-vinyl gives a polymer that can be considered to be the copolymer of which two 1-alkenes?

2. A Hooke's law spring with force constant k connects two masses, m₁ and m₂. The vibrational energy of the first excited state, in terms of k, m₁, and m₂, is:

3. Write the equation that defines the energy levels of a harmonic oscillator. Define all terms.

4. Explain how the backbone CH₂ protons can be used to determine the tacticity of a sample of PMMA.

5. Toluene and polystyrene absorb at 260 nm and emit at 280 nm. Dilute solutions of polystyrene (but not toluene) also show emission at 340 nm. Why does polystyrene show the 340 nm band, but toluene does not?

6. When dilute solutions of toluene and polystyrene in cyclohexane are excited at 255 nm, do their emission spectra contain the same number of bands? Explain

7. Arrange these molecular processes in polystyrene in order of increasing times
   • Absorbance of a photon at 255 nm
   • Lifetime of a singlet excited state
   • One vibration of a C-C bond
   • One vibration of a C-H bond

8. Arrange the following fouir processes in polystyrene in order of increasing energy
   • Energy of excimer emission
   • Energy of "monomer" emission
   • Energy required to excite the electrons in the ring
   • Energy required to excite the vibrations in the ring

9. Which spectroscopic technique (CD, Fluorscence, IR, NMR, UV) is best suited to each task?
   • Does atactic poly(methyl methacrylate) obey Bernoullian statistics?
   • How rapidly do micelles of polystyrene-block-polyoxyethylene exchange chains, using samples labelled with naphthalene and pyrene?
   • Is a helix left- or right-handed?
   • Is there intimate mixing of poly(vinyl alcohol) and poly(methyl methacrylate) in a blend?

10. Define linear infrared dichroism. Then explain how it can be used to distinguish between two polymorphs of poly(L-alanine).

11. Define a first-order phase transition and state an example that was discussed in the text.

12. According to the random flight model, what is the ratio of the number of bonds in a linear chain (n_l) and the number of bonds in a three-armed star-branched molecule (n_s) with arms of the same length (n_s/3) if both macromolecules have the same mean square radius of gyration?

13. How do the conformational properties of n-butane and n-pentane affect the assumption of independent bonds in polyethylene?

14. Define the two parameters in the worm-like chain model. How should these parameters be assigned for a flexible chain? How should they be assigned for a rigid rod?

15. For very long unperturbed chains, the log of the probability of r = 0 vs. log M yields a straight line. Why? What is the slope of this line?

16. Explain the connection between the following equation and the mean square dimensions of macromolecules. (3f - 2)/f²

17. The 3.6₁₃ helix of poly(L-alanine) is more popularly known as the ______ helix and is _____-handed.

18. For a polyethylene of molecular weight 10⁶, arrange the following in order of increasing size:
    • Length when all internal C-C bonds are in trans state
    • Maximum dimension of the unit cell for the crystal
    • Root-mean-square end-to-end distance under Theta conditions
    • Span of a mature spherulite
    • Thickness of a single crystal grown from solution

19. Explain how a density arguement can be used to show that a pure switchboard model, with chains running perpendicular to the surface, is unlikely to be physically accessible.

20. In an osmotic pressure experiment, how does one write:
    • The effect of the solute on the chemical potential of the solvent?
    • The effect of pressure on the chemical potential of the solvent?
    • Which effect is larger at equilibrium?

21. Identify the parts of the expression i ~ alpha²I₀N(1 + cos² theta)/lambda⁴r²V for scattering from gases that arise from
    • Concentration dependence
    • Incident beam
    • Instrument geometry
    • Molecular property of the gas

22. If a sample of a polymer has different eta_sp/c vs. c in two good solvents, will it
    • Have different slopes of pi/c vs. c in these solvents?
    • Have different intercepts of pi/c vs. c in these solvents?

23. Write the Bragg equation for the relationship between the scattering angle and the spacing of places. Define all terms in the equation.

24. Explain why beta sheets have unit cells in which two dimensions are nearly independent of the type of amino acid, but the third dimension depends strongly on the type of amino acid.

25. If you are limited to glycine and L-proline as your monomer units, how would you arrange them in a copolymer in order to produce a triple helix? Explain

26. Write a single short paragraph that describes the relationship between IF, NIF, and "thinning" for a monodisperse polyethylene of an appropriate molecular weight.

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