Sample questions: Numerical answer

Include units where appropriate

1. If the molar extinction coefficient for a phenyl ring in a polymer is 200 cm²/mmol, the concentration of this chromophore that should be used in order to obtain an absorbance of 0.5 with a cell having a path length of 1 cm is:

2. If we want a transmittance of 50% for a solution of a chromophore that has a molar extinction coefficient of 1000 cm²/mmol, using a cell with a light path of 1 cm, the concentration of the chromophore should be:

3. If a polyethylene chain with a molecular weight of 10,000 adopts the planar zig-zag conformation, what are its end-to-end distance and radius of gyration? The length of a C-C bond is 153 pm, and the C-C-C bond angle is 112^o?

4. Calculate, to three significant figures, M_w and the polydispersity index for a sample composed of 90 molecules with M = 10,000 and 10 molecules with M = 90,000.

5. If a vinyl polymer with Bernoullian statistics has 0.1 as the probability for an isotactic triad, the probabilities of heterotactic and syndiotactic triads are:

6. If chromophores A and B are separated by 5.0 nm, and their Forster radius is 2.5 nm, the efficiency of nonradiative singlet energy transfer is:

7. The values of the LJ parameters epsilon/k and sigma are 8.6 K and 0.281 nm for H, and 257.2 K and 0.354 nm for Br. Calculate the maximum attraction between H and Br, and the separation at which the interaction changes from repulsive to attractive.

8. What is the radius of gyration of a uniform sphere of radius 10 nm?

9. What is the radius of gyration of a uniform thin rod of length 100 nm?

10. The height of the barrier in the torsion potential energy function for the C-C bond in ethane is:

11. For a flexible homopolymer in the limit as n becomes infinite, the value of x in <r²>₀ = x<s²>₀, where s denotes the radius of gyration, is x = :

12. Calculate the limiting value for C for a simple chain in which all bonds are of the same length, all bond angles are 110^o, and each bond has four equally probably torsional angles, which are 45, -45, 135, and -135^o.

13. A monodisperse polybutadiene fraction with M = 50,000 has a root-mean-square radius of gyration of 6.8 nm. The lengths of the C-C and C=C bonds are 153 and 134 pm, respectively. The numerical value of the characteristic ratio is:

14. What are the mean square unperturbed radius of gyration and mean square unperturbed end-to-end distance for a linear polyethylene with M = 10⁶ at 140^o C, where the characteristic ratio is 6.7?

15. When long chains are represented by a string of n connected, self-avoiding beads on a cubic lattice, the root-mean-square dimensions of the chain depend on n^a, and a depends on the energy, e, of the interaction of a bead with unoccupied nearest-neighbor sites such that
    • a = ____________ if e << 0.
    • a = ____________ if e >> 0.

16. For a long chain, the exponent a in <r²>^1/2 ~ n^a has values of _____ in a good solvent, _____ in a Theta solvent, and _____ in a poor solvent.

17. For a long chain, the exponent a in <s²> ~ n^2a has values of _____ in a good solvent, _____ in a Theta solvent, and _____ in a poor solvent. a

18. If a linear poly(1,4-cis-butadiene) chain has a root-mean-square radius of gyration of 50 nm in dilute solution in a Theta solvent, estimate the root-mean-square end-to-end distance in the bulk polymer, in the absence of solvent:

19. The alpha helix has a translation of 150 pm per residue, and 3.6 residues per turn. Its pitch is:

20. The typical length of the shortest dimension of a single solution-grown crystal of polyethylene is:

21. The exponent a in the Mark-Houwink-Sakurada equation is _____ in a poor solvent, _____ in a Theta solvent, and _____ in a good solvent.

22. If SAXS finds a thickness of 10 nm for the lamella of a crystalline alkane, and the tilt angle is 35^o, LAM would find that the length of the crystalline stem is ______ nm.

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