How To Calculate Degree Of Polymerization

Number of monomeric units in a macromolecule or polymer

The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule.^{[1] [two] [3]}

For a homopolymer, in that location is only one type of monomeric unit and the number-average degree of polymerization is given by ${\displaystyle DP_{due north}\equiv X_{n}={\frac {M_{n}}{M_{0}}}}$ , where M_n is the number-average molecular weight and One thousand₀ is the molecular weight of the monomer unit. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. This number does not reflect the variation in molecule size of the polymer that typically occurs, it only represents the mean number of monomeric units.

Some authors, however, define DP as the number of echo units, where for copolymers the echo unit may not be identical to the monomeric unit.^{[4] [5]} For instance, in nylon-vi,6, the repeat unit contains the ii monomeric units —NH(CH₂)_half-dozenNH— and —OC(CH_two)₄CO—, so that a chain of 1000 monomeric units corresponds to 500 repeat units. The degree of polymerization or chain length is so 1000 by the beginning (IUPAC) definition, only 500 by the 2d.

Step-growth and chain-growth polymerization [edit]

In stride-growth polymerization, in order to reach a loftier degree of polymerization (and hence molecular weight), X _north, a high fractional monomer conversion, p, is required, according to Carothers' equation^{[vi] [7]} ${\displaystyle {\bar {X}}_{northward}={\frac {1}{1-p}}}$ For instance, a monomer conversion of p = 99% would exist required to achieve X _n = 100.

For chain-growth complimentary radical polymerization, however, Carothers' equation does not employ. Instead long chains are formed from the beginning of the reaction. Long reaction times increase the polymer yield, but have niggling effect on the average molecular weight.^[viii] The degree of polymerization is related to the kinetic chain length, which is the boilerplate number of monomer molecules polymerized per chain initiated.^[9] However information technology often differs from the kinetic concatenation length for several reasons:

• chain termination may occur wholly or partly by recombination of two chain radicals, which doubles the degree of polymerization^[x]
• chain transfer to monomer starts a new macromolecule for the same kinetic chain (of reaction steps), corresponding to a decrease of the degree of polymerization
• chain transfer to solvent or to another solute (a modifier or regulator besides decreases the degree of polymerization ^{[11] [12]}

Correlation with physical backdrop [edit]

Relationship between degree of polymerization and melting temperature for polyethylene. Data from Flory and Vrij (1963).

Polymers with identical composition but different molecular weights may showroom unlike physical properties. In general, increasing degree of polymerization correlates with higher melting temperature ^[13] and higher mechanical strength.

Number-boilerplate and weight-boilerplate [edit]

Synthetic polymers invariably consist of a mixture of macromolecular species with different degrees of polymerization and therefore of dissimilar molecular weights. There are different types of boilerplate polymer molecular weight, which can be measured in different experiments. The two most important are the number average (Ten_n) and the weight average (Ten_w).^[4]

The number-average caste of polymerization is a weighted mean of the degrees of polymerization of polymer species, weighted by the mole fractions (or the number of molecules) of the species. It is typically determined past measurements of the osmotic pressure of the polymer.

The weight-average degree of polymerization is a weighted mean of the degrees of polymerization, weighted past the weight fractions (or the overall weight of the molecules) of the species. Information technology is typically determined by measurements of Rayleigh low-cal scattering by the polymer.

See also [edit]

• Anhydroglucose unit

References [edit]

1. ^ IUPAC Definition in Compendium of Chemical Terminology (IUPAC Gold Book)
2. ^ Cowie J.Grand.Thousand. Polymers: Chemistry and Physics of Modern Materials (2d ed. Blackie 1991), p.ten ISBN 0-216-92980-six
3. ^ Allcock H.R., Lampe F.W. and Mark J.P. Gimmicky Polymer Chemistry (third ed. Pearson Prentice-Hall 2003), p.316 ISBN 0-13-065056-0
4. ^ ^{a b} Fried J.R. "Polymer Science and Engineering science" (Pearson Prentice-Hall, 2nd edn 2003), p.27 ISBN 0-13-018168-4
5. ^ Rudin, Alfred "Elements of Polymer Science and Engineering" (Bookish Press 1982), p.seven ISBN 0-12-601680-1
6. ^ Rudin, p.171
7. ^ Cowie p.29
8. ^ Cowie, p.81
9. ^ Allcock, Lampe and Mark, p.345
10. ^ Allcock, Lampe and Mark, p.346
11. ^ Allcock, Lampe and Marking, p.352-vii
12. ^ Cowie p.63-64
13. ^ Flory, P.J. and Vrij, A. J. Am. Chem. Soc.; 1963; 85(22) pp3548-3553 Melting Points of Linear-Concatenation Homologs. The Normal Methane series Hydrocarbons.|doi=10.1021/ja00905a004|url=http://pubs.acs.org/doi/abs/10.1021/ja00905a004

Source: https://en.wikipedia.org/wiki/Degree_of_polymerization

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