Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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120 • Chapter 4 / Polymer Structures

resistant to dissolution and softening by heat. Some of these properties are discussed

in subsequent chapters.

Concept Check 4.5

(a)Compare the crystalline state in metals and polymers.(b)Compare the noncrys-

talline state as it applies to polymers and ceramic glasses.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]

EXAMPLE PROBLEM 4.2

Computations of the Density and Percent Crystallinity

of Polyethylene

(a)Compute the density of totally crystalline polyethylene. The orthorhombic

unit cell for polyethylene is shown in Figure 4.10; also, the equivalent of

two ethylene repeat units is contained within each unit cell.

(b)Using the answer to part (a), calculate the percent crystallinity of a branched

polyethylene that has a density of 0.925 g/cm^3. The density for the totally

amorphous material is 0.870 g/cm^3.

Solution

(a)Equation 3.5, utilized in Chapter 3 to determine densities for metals, also

applies to polymeric materials and is used to solve this problem. It takes

the same form, viz.

ρ=

nA

VCNA

wherenrepresents the number of repeat units within the unit cell (for

polyethylenen=2) andAis the repeat unit molecular weight, which for

polyethylene is

A=2(AC)+4(AH)

=(2)(12.01 g/mol)+(4)(1.008 g/mol)= 28 .05 g/mol

Also,VCis the unit cell volume, which is just the product of the three unit

cell edge lengths in Figure 4.10, or

VC=(0.741 nm)(0.494 nm)(0.255 nm)

=(7. 41 × 10 −^8 cm)(4. 94 × 10 −^8 cm)(2. 55 × 10 −^8 cm)

= 9. 33 × 10 −^23 cm^3 /unit cell

Now, substitution into Equation 3.5 of this value, values fornandAcited

above, as well asNA, leads to

ρ=

nA

VCNA

=

(2 repeat units/unit cell)(28.05 g/mol)

(9. 33 × 10 −^23 cm^3 /unit cell)(6. 023 × 1023 repeat units/mol)

=0.998 g/cm^3