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Network formation in curing of epoxy resins

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Epoxy Resins and Composites III

Part of the book series: Advances in Polymer Science ((POLYMER,volume 78))

Abstract

The build-up of branched and crosslinked structures from polyepoxides and curing agents is investigated theoretically and experimentally. The basis of crosslinking theories and their application to curing of epoxy resins are reviewed and analyzed. The network build-up is dependent on the functionality of the monomers, reactivity of functional groups and reaction paths as a function of conversion of the reactive groups. The knowledge of the reaction mechanism is a necessary input information of the branching theory and it also determines which of the available methods (e.g. statistical or kinetic theory) is to be used. The curing of polyepoxides with polyamines, polycarboxylic polyacids and cyclic anhydrides is treated in more detail. The theoretical treatment of polyetherification (polymerization) of epoxy groups is outlined. Results obtained on simple polyamine-diepoxide systems agree well with the theory, acid curing still requires refinement of the theoretical treatment and especially much more experimental studies. The problems of the theoretical treatment of the network build-up in important epoxy resincuring agent formulations, to which the branching theory has not yet been applied, are briefly discussed The problems of homogeneity or inhomogeneity of cured epoxy resins and of the diffusion control are also analyzed.

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Abbreviations

aP :

fraction of primary amine units

as :

fraction of secondary amine units

at :

fraction of tertiary amine units

ai :

fraction of diamine units with i reacted hydrogens (Fig. 7)

cx :

concentration of molecules composed of x monomer units

cx, 1 :

concentration of molecules composed of x monomer units and bearing 1 unreacted functional groups

cg :

constant in the Williams-Landell-Ferry equation

cg :

concentration of unreacted functional groups in the gel

f, fX :

functionality of the monomer (X)

fe :

number-average functionality of an active branch point, Eq. (73)

fX(z):

probability generating function

g(z):

generating function for the number fraction distribution

i:

concentration of the initiator, i0 initial value

k, ki :

rate constants

k1 :

rate constant for the reaction of a primary amine group with epoxide group

k2 :

rate constant for the reaction of a secondary amine group with an epoxide group

kI :

rate constant of initiation

kP :

rate constant of propagation

k +1 :

=k1/2

1:

number of unreacted functional groups in a molecule

mX :

weight (mass) fraction of monomer X

m:

molar concentration of the monomer

nX :

molar (number) fraction of component X

pi :

probability of finding a unit with i reacted functional groups

rA :

initial molar ratio of amine hydrogens to epoxy groups=2[A]0/[E]0

t:

time

ti :

coefficient of the pgf T(z)

u, ui :

variable in the cascade substitution, Eqs. (52–53)

v, vi :

extinction probability

v2 :

volume fraction of the monomer (polymer) in mixture with a diluent

wi :

weight fraction of i-mer

wg :

weight fraction of gel

ws :

weight fraction of sol

x:

number of monomer units in a molecule

z, zx, zxy :

auxiliary variable in a probability generating function

A:

front factor in the rubber elasticity theory

Aph :

front factor for a phantom network

[A]:

concentration of amine groups

[A]0 :

initial concentration of amine groups

C1, C2 :

Mooney-Rivlin constants

E:

activation energy

[E0]:

concentration of unreacted epoxy groups

[E]0 :

initial concentration of epoxy groups

F(z) FX(z):

probability generating function for the number of bonds issuing from a unit

F(N):

value of F(z) for z=N

F′(N):

value of ∂F(z)/∂z for z=N

F″(N):

value of ∂2F(z)/∂z2 für z=N

F YOX :

value of ∂FOX(z)/∂zY for z=1

F YX :

value of ∂FX(z)/∂zY for z=1

F YZXY :

value of ∂FXY(z)/∂zYX for z=1

Ge :

equilibrium shear modulus; Ge, c chemical, Ge, ent trapped entanglement contributions

M:

molecular weight

Mn :

number-average molecular weight

Mw :

weight-average molecular weight

Mz :

z-average molecular weight

\(\bar M\) :

number average molecular weight of monomers

MX :

molecular weight of component X

Ne :

number of elastically active network chains (EANC) per monomer unit

P:

degree of polymerization

Pn :

number-average degree of polymerization

Pw :

weight-average degree of polymerization

R:

gas constant

RE :

=([E]0−2[A]0)/[A]0

T:

temperature in K

Tg :

glass transition temperature

Tgo :

glass transition temperature of the system before curing

Tg∞ :

glass transition temperature at full cure

Te, Teg :

trapping factor in the trapped entanglement theory related to the whole system and to the gel, respectively

T(z), TX(z):

probability generation function for the number of bonds with infinite continuation issuing from a unit

W(z):

weight-fraction generating function

α:

conversion of functional groups

αX :

conversion of functionalities (functional groups) of type X

α1, α2 :

probabilities defined by Eq. (103)

αETH :

etherification conversion of excess epoxy groups, Eq. (81)

〈α 20 〉:

dilation factor in the rubber elasticity theory

δ klij :

Kronecker delta equal to 1 for ij=kl and zero otherwise

ε:

proportionality constant in Ge, ent

ε1, ε2 :

probabilities, Eq. (104)

ϰ:

=k1/kP

υe, υeg :

concentration of elastically active network chains in the whole system and in the gel, respectively

ϱ:

=k2/k1, ration of rate constant for the reaction of secondary and primary amine group with epoxide group

τ:

=kt

fsse:

first-shell substitution effect

gf:

generating function

pgf:

probability generating function

wfgf:

weight-fraction generating function

A:

amine

C:

carboxyl

E:

epoxide

AH2 :

primary amine

HAE(OH):

adduct of one epoxy and one amine group

A(E(OH))2 :

adduct of two epoxy groups and one amine group

DDA:

dodecylamine

DDM:

4,4′-diaminodiphenylmethane

DDS:

4,4′-diaminodiphenylsulfone

DGA:

N,N-diglycidylaniline

DGEBA:

diglycidyl ether of Bisphenol A

DGER:

diglycidyl ether of resorcine

EANC:

elastically active network chain

HMD:

hexamethylenediamine

PGE:

phenyl glycidyl ether

TGDDM:

N,N,N′,N′-tetraglycidyl-4,4′-diaminodiphenylmethane

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  1. Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 16206, Prague 6, Czechoslovakia

    Karel Dušek

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Dušek, K. (1986). Network formation in curing of epoxy resins. In: Dušek, K. (eds) Epoxy Resins and Composites III. Advances in Polymer Science, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035356

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