Polymer Science and Engineering Quiz #1

Polymer

chain of monomers connected by covalent bonds

have a very large length scale and move slowly, don’t fully crystallize, and have large intermolecular forces

Homopolymers

1 monomer type in the polymer

Heteropolymers

>1 type of monomer in the polymer

Copolymers

macromolecules with >= 2 monomers making up the polymer

Isotactic

side chains are on the same side

Syndiotactic

side chains on alternating sides

Atactic/heterotactic

random placements of the side chains

harder to crystallize

Structural isomers

same formula, but different bonds

Geometrical isomers

same bonds, but different spacing

cis/trans isomers

Stereoisomers

non-superimposable images of each other

Mesoscopic structure (architecture)

linear, comb, star, ring, randomly branched, network (crosslinked)

strongly impacts the properties of the polymer

Number-average molecular weight (M_n)

sensitive to the largest number of molecules

Weight-average molecular weight (M_w)

sensitive to the species with the highest molecular weight

Dispersity

equal to the weight-average/number-average

always greater than or equal to 1

Dispersity of “perfect” DNA/RNA/proteins

1

Dispersity of “living”/monodisperse

<1.1

Dispersity of free radical

1.5-2

Dispersity of step-growth

2

Dispersity of Ziegler-Natta

>5

Dispersity of natural rubber/cellulose/chitins

>5

Functionality (f)

the number of bonds a molecule can form

Polycondensations

lose water or other small molecules during step-growth reactions of polymers

polyesters, polyamides

Polyurethanes/polyureas

no byproducts, but still a step-growth reaction of polymers

Principle of Equal Reactivity

a functional group’s reactivity is independent of molecular site/chain length (Flory) and allows us to treat step-growth kinetics more simply

Gelation

higher functionality will cause this to happen at a lower conversion (happens sooner)

Extent of reaction (p)

fraction of functional groups that have reacted at time t

can never actually equal 1

Carother’s Equation

X_n = N₀/N = 1/(1-p)

as p approaches 1, the degree of polymerization explodes (X_n) since the denominator is 1-p

you need p>0.99 to reach a useful degree of polymerization (X_n > 100)

assumes exact stoichiometry (r=1)

Generalized Carother’s

there is a stoichiometric imbalance

X_n = (1 + r)/(1 + r - 2rp)

an imbalance will always lower the degree of polymerization possible

Number-fraction

n_x = (1-p)²p^x-1

X_n = 1/(1-p)

Weight-fraction

w_x = x(1-p)²p^x-1

X_w = (1 + p)/(1 - p)

Dispersity with p

= 1 + p

1st moment of distribution

number-average molecular weight

2nd moment of distribution

weight-average molecular weight

3rd moment of distribution

z-average molecular weight

Partial moments of dispersity

viscosity-average molecular weight

Gel point

p_c = 2/f_av

Step-growth kinetics

catalyzed bimolecular reaction (2nd order) → C₀kt = [1/(1 - p)] -1

if self catalyzed: 3rd order → 2C₀²k”t = [1/(1 = p)²] - 1