Handbook of Solvents - George Wypych - ChemTech - Ventech!

792 Michelle L. Coote and Thomas P. Davis
tude of the Bootstrap effect is independent of the comonomer feed ratios. Hence in a bulk
copolymerization, the monomer partitioning may be represented by the following equilibrium
expression:
f
f
1
2
K f
=
f
⎛
⎜
⎝
1bulk
2bulk
⎞
⎟
⎠
The equilibrium constant K may be considered as a measure of the Bootstrap effect.
Using this expression to eliminate the effective monomer fractions (f 1 and f 2) from the terminal
model equations, replacing them with the measurable ‘bulk’ fractions (f 1bulk and f 2bulk),
the following equations for composition 43 and k p 118 may be derived.
F
F
k
1
2
p
Kf
=
f
1bulk
2bulk
rKf 1 1 + f2
rf + Kf
bulk bulk
2 2bulk 1bulk
2 2
1 rK 1 f1 + 2Kff+
r f
=
Kf + f rKf / k + r f / k
1bulk 2bulk
bulk 1bulk 2bulk 2
2 2bulk 1 1bulk 11 2 2bulk 22
Examining the composition and k p equations above, it is seen that the Bootstrap effect
K is always aliased with one of the monomer feed ratios (that is, both equations may be expressed
in terms of Kf 1 and f 2). It is also seen that once Kf 1 is taken as a single variable, the
composition equation has the same functional form as the terminal model composition
equation, but the k p equation does not. Hence it may seen that, for this version of the Bootstrap
effect, the effect is an implicit effect - causing deviation from the terminal model k p
equation only. It may also be noted that, if K is allowed to vary as a function of the monomer
feed ratios, the composition equation also will deviate from terminal model behavior - and
an explicit effect will result. Hence it may be seen that it is possible to formulate an implicit
Bootstrap model (that mimics the implicit penultimate model) but in order to do this, it must
be assumed that the Bootstrap effect K is constant as a function of monomer feed ratios.
It should be noted that the above equations are applicable to a bulk copolymerization.
When modelling solution copolymerization under the same conditions, the equations may
be used for predicting copolymer composition since it is only the relationship between bulk
and local monomer feed ratios that determines the effect on the composition and
microstructure of the resulting polymer. However, some additional information about the
net partitioning of monomer and solvent between the bulk and local phases is required before
k p can be modelled. It should be observed that in a low-conversion bulk
copolymerization, knowledge of the monomer feed ratios automatically implies knowledge
of the individual monomer concentrations since, as there are no other components in the
system, the sum of the monomer fractions is unity. However, in a solution copolymerization
there is a third component - the solvent - and the monomer concentrations depend not only
upon their feed ratio but also upon the solvent concentration. Modelling k p in a solution
copolymerization could be achieved by re-writing the above equilibrium expression in
terms of molar concentrations (rather than comonomer feed ratios), and including the solvent
concentration in this expression.