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

164 K. Ito, S. Kawaguchi
solvent. (2) Accompanied by the decomposition of the initiator, linear oligomers,
polymers, and graft copolymers are all produced by polymerization in the
continuous phase. The solubility of these polymers is a function of their MW
and the composition of the graft copolymer. Polymers with a MW larger than a
certain critical value precipitate and begin to coagulate to form unstable particles.
(3) These particles coagulate on contact, and the coagulation among them
continues until sterically stabilized particles form. (4) This point is referred to
as the critical point, and it occurs when all of the particles of interest contain sufficient
stabilizer polymer chains on the surface to provide colloidal stability
[112–114].
After this point, particles grow both by diffusive capture of oligomers and coagulation
of very small yet unstable particles (nuclei, precursors) produced in
the continuous phase and by polymerization of the monomer occluded within
the particle. The total number of such sterically-stabilized particles remains
constant so that their size is only a function of amount of polymers produced.
The particle size is determined at the critical point by the amount of polymers
produced at that point. In the discussion that follows, one uses the term q to describe
the fractional conversion of monomer to polymer (0�q�1), and q D to describe
the corresponding conversion of macromonomer. The weight (W M in g/l)
of the monomer polymerized at any point in the reaction is defined as
(19)
Here, W Mo is the weight of monomer in the reactants; R is the radius (cm) of
the particle occupied by the polymer chains only, N is the total number of particles
per liter, and r is their density.
The surface area per sterically-stabilized particle is determined by the surface
area (S) occupied by a macromonomer chain times the number (n') of these
chains grafted onto the surface.
(20)
(21)
W Do is the weight (in g/l) of macromonomer in the reactants, N A is
Avogadro's number, and M D is the molecular weight of the macromonomer.
From Eqs. (19)–(21), one can obtain a universal relationship between the particle
radius and the extent of polymerization for sterically stabilized particles:
(22)
At the critical point, sterically stabilized particles are formed, and coalescence
between similar-sized particles is terminated. At this point one has R=