# ChE541_Basic Principles of Polymer Molecular Weights

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### Text of ChE541_Basic Principles of Polymer Molecular Weights

• BASIC PRINCIPLES OF POLYMER MOLECULAR WEIGHTS

z Polymers are mixtures of molecules of different

molecular weight. Why? z A typical polymer sample contains a multitude of

individual molecular chains, many of which may have widely differing molecular weights.

z To distinguish between different samples of the

same polymer, need an average MW.

• z Mechanical properties and processing behaviour depend on the average size and the distribution of sizes of macromolecules in the sample. The influence depends on both the property and on the nature of the polymer (e.g. effect of MW on viscosity and modulus of amorphous polymers).

z Average MW and breadth of the MWD are

determined by the polymerization process. The control of MW is essential for the practical application of a polymerization process.

z Successful market competition of a plastic

depends on the ability to control MW during the reaction (Reaction Engineering) and the understanding of how MW influences final application properties (Polymer Science and Polymer Processing).

• MWD AND MW AVERAGES Peebles (1971); Billingham (1977) z Basic concepts from small particle statistics z Ni indicates the number of molecules with a MW

equal to Mi

• Definitions z Number average MW ( NM )

z Weight average MW ( WM )

z Arithmetic means of the number and weight

distributions of molecular weights z NM and WM may be measured directly but it is

usually necessary to measure the detailed distribution to estimate higher averages

N M N = M

i

iiN

C M C = M

i

iiW

• z MW averages of a discrete distribution of molecular weights can be defined by the generalized expression:

where the parameter '' is a weighting factor

= 1 ===> MN

= 2 ===> MW

= 3 ===> MZ

= 4 ===> MZ+1

M N M N = M

i1 -

i

ii

• Example: Consider a polymer sample for which 99% of the weight is composed of material with MW=20,000 and the remaining 1% of MW = 109 Then:

MN = 20,200

MW = 107

MZ = 109 z Obviously, MW and MZ must be used with care in

such an instance z High MW portion ===> microgel z MW and MZ emphasize the high MW portion of the

distribution to a greater extent than does MN

• z A more useful definition is in terms of the moments of the distribution:

where

j = j-th moment of the MWD

Mi = molecular weight of i-th species

qi = quantity of polymer with mol. weight Mi per unit volume of the sample (e.g. Ni, xi, Ci, wi)

z Generalization beyond two averages; facilitate the

estimation of parameters related to the breadth and the symmetry of the distribution

M q = ij

ij

• M M M ZWN

MM = PDI

N

W

Breadth Of The MWD z z The equality occurs only if all the species have

the same MW (monodisperse polymer) z Polydispersity index : z Not a sound statistical measure of the distribution

1 - MM = PDI

N

W

• z Correct measure of distribution breadth:

z If distribution is monodisperse, then:

and

and

1 - MM =

M NW

N2

n2

1 - MM =

M WZ

W2

w2

0 = = w2

n2

M = M = M ZWN

1 = PDI

• z Highly branched polymers have a PDI of 20 or more

z Most polymers have a PDI in the range 2-20 z Condensation polymers:

PDI = 2 Most probable distribution z Anionic polystyrenes:

PDI = 1.04

assumed monodisperse; calibration standards

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