142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

Poly(macromonomers), Homo- and Copolymerization 165
R crit , S=S crit , q=q crit , and q D =q Dcrit . Since the particle number N remains constant
after this point, both R and S, at any subsequent conversion, can be described
by the expressions
(23a)
(23b)
where r 1 is the reactivity ratio in copolymerization of monomer (M 1) with macromonomer
(M 2). At low conversion, r 1 in this system is defined as
(24)
According to Paine [129], computer simulations using the multibin kinetic
model for the coalescence between the unstable moieties indicate that the particle
number (N) at the critical point is given by
(25)
where k p is the propagation rate constant (M –1 s –1 ), k t is the termination rate
constant (M –1 s –1 ), and k 2 is the diffusion-controlled rate constant for coalescence
between similar-sized particles (M –1 s –1 ). [I] is the initiator concentration
(mol/l), and f k d is the product of initiator efficiency and the decomposition rate
constant (s –1 ) of the initiator. From Eqs. (19) and (25), the q crit can be written as
Substituting Eqs. (19) and (26) into Eq. (23) yields the equations
(26)
(27)
(28)
In Eq. (27) one sees that the radius of latex particle follows simple scaling relationships
with the key parameters in the system being q 1/3 , [monomer] o 2/3 ,
[macromonomer] o –1/2 , [initiator]o –1/12 , where [ ]o means initial concentration.
These equations predict that the particle size and stabilization are determined
by the magnitude of r 1 . In addition, one sees in Eq. (28) that the surface area occupied
by a stabilizer chain follows q –1/3 in the case of azeotropic copolymeriza-