Home > Articles > Engineering

  • Print
  • + Share This
This chapter is from the book

Problems

1.1 A polymer sample combines five different molecular-weight fractions of equal weight. The molecular weights of these fractions increase from 20,000 to 100,000 in increments of 20,000. Calculate m-dash-n.jpg, m-dash-w.jpg, and m-dash-z.jpg Based upon these results, comment on whether this sample has a broad or narrow molecular-weight distribution compared to typical commercial polymer samples.

1.2 A 50-g polymer sample was fractionated into six samples of different weights given in the table below. The viscosity-average molecular weight, m-dash-v.jpg, of each was determined and is included in the table. Estimate the number-average and weight-average molecular weights of the original sample. For these calculations, assume that the molecular-weight distribution of each fraction is extremely narrow and can be considered to be monodisperse. Would you classify the molecular-weight distribution of the original sample as narrow or broad?

Fraction

Weight (g)

m-bar.jpg

1

1.0

1500

2

5.0

35,000

3

21.0

75,000

4

15.0

150,000

5

6.5

400,000

6

1.5

850,000

1.3 The Schultz–Zimm 11 molecular-weight-distribution function can be written as

023equ01.jpg

where a and b are adjustable parameters (b is a positive real number) and Γ is the gamma function (see Appendix E) that is used to normalize the weight fraction.

(a) Using this relationship, obtain expressions for m-dash-n.jpg and m-dash-w.jpg in terms of a and b and an expression for Mmax, the molecular weight at the peak of the W(M) curve, in terms of m-dash-n.jpg.

(b) Derive an expression for Mmax, the molecular weight at the peak of the W(M) curve, in terms of m-dash-n.jpg.

(c) Show how the value of b affects the molecular-weight distribution by graphing W(M) versus M on the same plot for b = 0.1, 1, and 10 given that m-dash-n.jpg = 10,000 for the three distributions.

Hint: 023equ02.jpg (if n is a positive integer).

1.4 The following requested calculations refer to Examples 1.1, 1.2, and 1.3 in the text:

(a) Calculate the z-average molecular weight, m-dash-z.jpg, of the discrete molecular weight distribution described in Example 1.1.

(b) Calculate the z-average molecular weight, m-dash-z.jpg, of the continuous molecular-weight distribution shown in Example 1.2.

(c) Obtain an expression for the z-average degree of polymerization, x-dash-z.jpg, for the Flory distribution described in Example 1.3.

  • + Share This
  • 🔖 Save To Your Account

Related Resources

There are currently no related titles. Please check back later.