## A rheological and structural study of polymer networksContents of this doctoral dissertation include: primary polymer molecules with a mondisperse distribution of the molecular weights, crosslinks of any functionality, primary polymer molecules with a disperse distribution of the molecular weights, the sol fraction, number and weight average degrees of polymerization, Schulz-Zimm distribution, fractions of ideal networks and dangling ends, molar masses between the crosslinks |

### From inside the book

Page 11

In general other pairs of more convenient quantities are used, but always

to the phase-lag and the amplitude ratio. '' Accordingly, for the two convenient

dynamic moduli it follows that: G' = ^-cos5 (1.9) and G' = ^sin<5 (1.10) Hence the

elastic modulus multiplied with the strain amplitude represents the amplitude of

the stress component that is in phase with the strain, whereas the product of the

viscous modulus and the strain amplitude is the amplitude of the stress

component ...

In general other pairs of more convenient quantities are used, but always

**related**to the phase-lag and the amplitude ratio. '' Accordingly, for the two convenient

dynamic moduli it follows that: G' = ^-cos5 (1.9) and G' = ^sin<5 (1.10) Hence the

elastic modulus multiplied with the strain amplitude represents the amplitude of

the stress component that is in phase with the strain, whereas the product of the

viscous modulus and the strain amplitude is the amplitude of the stress

component ...

Page 56

and for the weight average degree of polymerisation: xw = x,fi(2-a) = xwfi(l-±a) (

2.101) where Jw 0 is the weight average degree of polymerisation at the onset of

the polymerisation ( a= 0 ) and is at that instant

degree of polymerisation by: D0=^-=2 (2.102) '0 ~ — x. n.O When for a system the

polydispersity index (D = Mw/Mn ) is known then the monomer conversion, a, can

be calculated through the combination of equation (2.100) and (2.101). To find an

...

and for the weight average degree of polymerisation: xw = x,fi(2-a) = xwfi(l-±a) (

2.101) where Jw 0 is the weight average degree of polymerisation at the onset of

the polymerisation ( a= 0 ) and is at that instant

**related**to the number averagedegree of polymerisation by: D0=^-=2 (2.102) '0 ~ — x. n.O When for a system the

polydispersity index (D = Mw/Mn ) is known then the monomer conversion, a, can

be calculated through the combination of equation (2.100) and (2.101). To find an

...

Page 57

The number and weight average degrees of polymerisation at the start of the

polymerisation are, for polymer molecules that are prepared by a free radical

batch polymerisation with combination as the termination process,

=^ = 1.5 Xn,0 (2.105) By substituting equation (2.95) into (2.59) and (2.54) the

number average degree of polymerisation in the network fraction is now given by:

'51 a - 4 + Asni ( 1 - w}f-' ) 4( 1 -a )+ASFIi ( 1 -a f ( 1 - h^-' ) 2+^15(l-w//-') 2 + ^,, (!-«)

( I-w/'-') 2 ...

The number and weight average degrees of polymerisation at the start of the

polymerisation are, for polymer molecules that are prepared by a free radical

batch polymerisation with combination as the termination process,

**related**by: D0=^ = 1.5 Xn,0 (2.105) By substituting equation (2.95) into (2.59) and (2.54) the

number average degree of polymerisation in the network fraction is now given by:

'51 a - 4 + Asni ( 1 - w}f-' ) 4( 1 -a )+ASFIi ( 1 -a f ( 1 - h^-' ) 2+^15(l-w//-') 2 + ^,, (!-«)

( I-w/'-') 2 ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

_t A Rheological and Structural Study of Polymer Networks | 1 |

Modelling of Polymer Networks | 18 |

Simulations of Polymer Networks | 74 |

Copyright | |

3 other sections not shown

### Common terms and phrases

active network chains average crosslinking index average molar mass average molecular weight calculated complex formation enthalpies constant crosslink functionality crosslinked system crosslinks per unit curves cycle rank dangling ends decrease deformation degree of polymerisation discotic side chain discotic side-chain polymers disperse distribution dynamic elastically active network equilibrium shear modulus figure Flory fraction of dangling fraction of ideal frequency high shear rates hypothetical crosslinking process increase kg/mol mijn molecular weight distribution monodisperse distribution network fraction network of polymer network parameters Nijenhuis number and weight number average degree number average molecular number of crosslinks physical network polydispersity index polymer in 1,1,2-trichloroethane polymeric polyvinyl chloride primary polymer molecules relationship rheological measurements Schulz-Flory distribution Schulz-Zimm distribution side chain polymer sol fraction solubility parameter solution of discotic solvent storage modulus strain structure substituting equation temperature tetrafunctional crosslinking total number unit volume values viscoelastic viscosity w/w solution weight average crosslinking weight average molecular yield stress zijn