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Long-chain branching in polymers

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Macroconformation of Polymers

Part of the book series: Advances in Polymer Science ((POLYMER,volume 18))

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Abbreviations

A 2 :

Second virial coefficient of osmotic pressure

a1, a2:

Coefficients in the expansion of α 2 (6.1)

b1, b2:

Coefficients in expansion relating to A 2 (6.6)

Ctm, Ctp:

Chain transfer coefficients with monomer and polymer

g:

〈s 2〉br/〈s 2〉lin

g 0 :

g for molecules of unperturbed dimensions

{ie3-1}:

g at T=Θ

g′:

[η]br/[η]lin

h:

Rbr/Rlin

M:

Molecular weight

{ie}:

Number and weight average DP

n b :

Number of branches per polymer molecule

{ie}:

Number and weight average DP

R:

Hydrodynamic radius (4.7)

S 0 :

Sedimentation constant at zero concentration

〈s 2〉:

Mean square molecular radius

〈s 20 〉:

〈s 2〉 for molecules of unperturbed dimensions

〈{ie3-2}〉:

〈s 2〉 at T=Θ

x:

Exponent in g′=g x; DP in Beasley's equation (7.3)

Zx, Zc:

Number of chain atoms at cross-over point for melt viscosity and at break point in log viscosity plot for linear polymers

α:

Flory's coil expansion factor (3.2)

β:

Excluded volume per pair of polymer segments; Beasley's branching parameter (7.3)

η, η 0 :

Viscosity; viscosity at zero rate of shear

[η]:

Intrinsic viscosity

Θ:

Flory's theta temperature (6.9)

Θ {ie3-3}:

Temperature at which A 2=0

{ie3-4}:

Temperature at which α=1

λ:

Fraction of material in backbone of comb-shaped molecule; number of branches per MW unit

ξ:

Degree of conversion in polymerization reaction

ϱ:

Number of branches per monomer unit

ψ 1 :

Coefficient in expression for excess chemical potential (6.9)

br, lin:

Subscripts denoting branched and linear molecules

LCB:

Long-chain branching

DP:

Degree of polymerization

MW, MWD:

Molecular weight; molecular weight distribution

LDPE:

Low-density polyethylene

HDPE:

High-density polyethylene

PVAc:

Poly(vinyl acetate)

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  1. Department of Chemistry, University of Manchester, England

    Percy A. Small

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Small, P.A. (1975). Long-chain branching in polymers. In: Macroconformation of Polymers. Advances in Polymer Science, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07252-7_1

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  • DOI: https://doi.org/10.1007/3-540-07252-7_1

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  • Print ISBN: 978-3-540-07252-2

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