Degree of Polymerization

1
Degree of Polymerization

• Generally described as the number of repeating
  units in an average polymer chain

Degree of Polymerization (DP) Total MW of
Polymer / MW of repeat unit
Assume Homopolymer
Adapted from H.R. Allcock and F.W. Lampe.
Contemporary Polymer Chemistry. 2nd Ed.
Prentice-Hall, Inc. 1990.
2
What is the Degree of Polymerization of 6,6-
Nylon?
The molecular weight of the repeat unit is
the sum of the molecular weights of the monomers,
minus that of the two water molecules that are
evolved
M repeat unit 116 146 2(18) 226 g/mol
The degree of polymerization refers to the total
number of repeat units in the chain. The chain
contains 531 hexamethylene diamine and 531 adipic
acid molecules.

Freely Jointed Chain Length (or x) (DP)
(length of repeat unit)
3
AMP2 Polymers Lecture 4
Molecular Weight Distributions
Thermal Response of Polymers
Correction to HW 13B Using a SPECIFIC volume
vs Temeperature diagram . . .
4
Molecular Weight Hierarchy
Bulk Polymer
Monomer
Molecular Weight
Molecular Weight
Number Average
Weight Average
Degree of Polymerization
Polydispersity Index
5
Molecular Weights (M)
M W/N
W total sample weight
N number of moles in the sample

• Can be defined for polymers with a distribution
  of chain lengths (i.e. varying DP)
• MWs often depend on the synthesis mechanism
• Molecular weights can be related to various
  properties
• Determination methods
• direct estimates of MW (osmostic-pressure,
  ultra-centrifugation, end-group analysis)
• Indirect , calibrated by references (light
  scattering, viscometry, GPC)

6
Mn Number Average Molecular Weight
Suppose that you have a mixture of polymer
molecules with different molecular weights in
which the number of molecules having a particular
molecular weight, Mi, is given by Ni.
wi total sample weight x polymer Ni number of
moles of x polymer Mi molecular weight fraction
of x polymer

• The number average is the simple arithmetic mean,
  representing the total weight of the molecules
  present divided by the total number of molecules.
• Data from analytical technique yielding the
  number of moles present in the sample of known
  weight osmotic pressure, end group analysis,
  etc.

7
Mw Weight Average Molecular Weight
Rather than count the size of each polymer in a
mixture, it is possible to just define an average
in terms of weights of molecules present at each
size level.
wi total sample weight x polymer Ni number of
moles of x polymer Mi molecular weight fraction
of x polymer

• Data from analytical technique yielding the
  weight of molecules at a given size level result
  in the weight average molecular weight light
  scattering, gpc, ultra-centrifuge, etc.

8
Degree Polymerization and Molecular Mass

• Depending on the situation, it may be more
  convenient to represent the size of polymer
  molecules in terms of the degree of
  polymerization (DP) (or chain length), rather
  than M.

Mn M(xn)
Mw M(xw)
m molecular mass of repeat unit
m molecular mass of repeat unit
xw weight average degree of polymerization or
chain length
xn number average degree of polymerization or
chain length
9
Polydispersity Index (PDI)

• A measure of the breadth of of the molecular
  weight distribution.

PDI Mw/Mn xw/xn
Typically MwgtMn
Monodispersed Sample PDI 1, e.g. biopolymers
Typical breadth PDI 1.02 - (over)50
10
Classification of Polymers
Polymers
Temperature Based Classifications
Structure
11
Definitions based on Thermal Response
Elastomer
Thermoset
Thermoplastic
As temperature is raised, a point will be reached
where the secondary bonds holding the chains
together (neglecting physical entanglements)
become insignificant and the chains are free
slide past one another
As the temperature is raised above the
dissociation energy of the primary covalent
bonds, both main-chain and cross-link bonds fail
randomly, and the polymer degrades.
Response corresponds to thermoplastics
Depending on the extent of cross-links, flow can
be achieved, but an increase in temperature will
still result in polymer degradation
12
Thermal Response Polymers in a Solution

• When we are trying to dissolve solid polymers in
  a solvent, why do we often raise the temperature?

• Typical polymer-solvent system
• Low temperature Upper Critical Solution
  Temperature (UCST) 2 phase system
• solvent rich (dilute solution)
• polymer rich (swollen-polymer or gel)
• Above UCST and below LCST, homogenous solution
  can be formed.
• At high temperatures Lower Critical Solution
  Temperature (LCST) is difficult to observe.

LCST
UCST
13
General Rules of Solubility

• Like dissolves like.
• At a particular temperature, solubility will
  decrease with increasing molecular weight.
• A. Crosslinking eliminates solubility
• B. Crystallinity, can generally act like
  cross-linking. In some cases it is possible to
  find solvents to overcome the bond strength.
  Heating close to Tm allows solubility.
• 4. The rate of polymer solubility decreases with
  increasing molecular weight.

14
Thermodynamics of Polymer Solubility

• ?G is negative mixing is thermodynamically
  feasible
• T must be positive and ?S is generally positive
  molecules in solution are usually in a random
  state
• -T?S favors solubility
• ?H can be both positive or negative
• Positive does note prefer mixing, since the
  polymer in a lower energy state
• SOLUBILITY ?H lt T?S
• Negative prefers mixing, since only solvent is
  the lower energy state
• SOLUBILITY specific interactions, i.e. H-bonds
  are formed between solvent and polymer molecules

• Assume mixture of pure polymer and pure
  solvent at constant pressure and temperature to
  form a solution

15
The Solubility Parameter

• Assume Regular Solutions

?H?E ??????????)2 cal/cm3 soln

• ?E the change in internal energy per unit
  volume of solution
• ? volume fractions
• ?isolubility parameters

• Limitations of Solubility Parameter
• Shortcomings in practice
• Polymer solubility is too complex to be
  described as a single parameter

???CED1/2(?E?/?)1/2

• CEDcohesive energy density (measure of
  intramolecular strength)
• ?????molar change in internal energy on
  vaporization
• ?? molar volume of liquid

????????????(cal/cm3)???
Like dissolves like Rough Rule of Thumb for
Solubility
16
Free Volume and Temperature
Specific V vs T for Linear PP

• Tg-Glass Transition Molecular motions in the
  amorphous polymer mass
• Motions based on activitation energy kT
• Dependent on the rate of cooling or heating.
• Extrapolation of the linear regions in specific V
  vs T curves, can also use refractive index and
  DSC.
• Second-order thermodynamic transition
• Tm- Melting Point Typified by flow
• Only present in polymers with some crystallinity
• Not present in cross-linked polymers
• First-order thermodynamic transition

Tm 170ºC
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Tg -10ºC
17
Influences on Tg

• The free volume of the polymer (vf). The higher
  the vf, the more room the molecules will have to
  move around, and the lower the Tg.
• The attractive forces between the molecules. The
  more strongly they are bound together, the more
  thermal energy will be required to produce
  motion.
• E.g. linear PAN - Tg is higher than degradation
  temperature, although it is linear
• Internal mobility of chains to rotate about
  bonds.
• Functional groups-steric hinderance
• Stiffness of the chains.
• Chain length directly proportional to Tg.
• e.g. Use of plasticizers can soften polymer,
  thereby reducing its Tg

1/Tg w1/Tg1 w2/Tg2
Copolymerization and Tg
18
Mechanical Properties and Temperature
Glassy Region
Transition / Leathery Region
Rubbery Plateau
Flow
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