Supporting Information
Correlation
between
Polydispersities
of
Molecular
Weight
Distribution and Particle Size Distribution in RAFT Emulsion
Polymerization of Styrene
Kun Yan, Xiang Gao, Yingwu Luo
The State Key Laboratory of Chemical Engineering, College of Chemical and
Biological Engineering, Zhejiang University, 38 Zhe Da Road, Hangzhou 310027, PR
China
Correspondence to: Xiang Gao (E-mail: gaox@zju.edu.cn) or Yingwu Luo (E-mail:
yingwu.luo@zju.edu.cn)
Calculation of 𝑪𝑻,𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆
As referred to Scheme 1 in the main text, an active particle with a radical inside
would be deactivated mainly through two ways: (1) Exit of the radical. Due to the
chain transfer to monomer, a polymeric radical could transfer into a small monomeric
radical, which is able to diffuse out to the aqueous phase.1 With regular initiator
concentrations, this route could be negligible. However, in the cases of very low
initiator concentrations like in the current study, this radical exit route becomes
significant (as evidenced in Table S1, which the average radical number per particle
(𝑛̅) values are all blow 0.5). (2) Entry of new radical. The free radicals in the aqueous
phase could enter the growing particle and terminate with the existed propagating
radical immediately, assuming zero-one kinetic should be applied in the current case1.
For RAFT emulsion polymerization, Prescot2 proposed that the amphiphilic oligomer
radicals formed in water and then entered particles should likely exit out once capped
by RAFT groups and then being fragmented to explain the polymerization rate
retardation. However, such a hypothesis is inconsistent with experimental data3. So
referring to Scheme 1 of the main text, the particle deactivation rate coefficient could
be expressed:
𝑘𝑑𝑒𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒 = ρ + k
(1)
where ρ (s-1) is the rate coefficient of radical entry and k (s-1) is the rate coefficient
of radical exit from a particle.
The model for radical entry put forward by Morrison and colleagues4 has been well
accepted considering the aqueous phase propagation and termination of free radicals.
The equation is adopted for calculating the entry rate coefficient of initiator derived
radicals based on the initiator concentration. However, in the current cases, the
re-entry of the exit monomeric radical could be significant since the initiator
concentration is very low. So the total entry rate coefficient cannot be determined
only based on the initiator concentration.
According to the work of Gilbert1, an exited monomeric radical would most likely
result in re-entry into a particle and remain inside to propagate without re-exiting in
the case of emulsion polymerization of styrene. In the steady-state, Equation (2) has
been derived1
ρ = 2k𝑛̅2 /(1 − 2𝑛̅)
(2)
in which
k = 𝑘𝑑𝑀 𝑘𝑡𝑟,𝑀 /𝑘𝑃1
(3)
in which 𝑘𝑡𝑟,𝑀 is chain transfer to monomer rate coefficient, 0.0292 L/(mol s) at 70
℃, 𝑘𝑃1 is the growth rate coefficient for monomer radicals, 𝑘𝑃1 = 4𝑘𝑃 1.
The desorption rate coefficient of the monomeric radicals1
𝑘𝑑𝑀 = 3𝐷𝑤 [𝑀]𝑤 /(𝑟𝑆2 [𝑀]𝑃 )
(4)
in which 𝐷𝑤 is the diffusion coefficient of monomeric radical in aqueous phase,
1.5×10-9 m2/s for styrene at 70 ℃, 𝑟𝑠 is the swollen particle radius and [𝑀]𝑤 is the
concentration of monomer in the aqueous phase, 0.0056 mol/L at 70 ℃.1
Equation (2) allows us to estimate the rate coefficient of radical entry directly from
the experimental 𝑛̅ data.
𝑛̅ can be calculated from the kinetic curves (shown in Figure S1)
𝑛̅ = (𝑑𝑐𝑜𝑛𝑣/𝑑𝑡 × 𝑁𝐴 × [𝑀]0 )/(𝑘𝑃 × 𝑁𝑃 × [𝑀]𝑃 )
(5)
with 𝑑𝑐𝑜𝑛𝑣/𝑑𝑡 the slope value of conversion vs time curve during the steady state
(monomer conversion between 30%-65%, where the polymerization rate is constant
and the conversion versus time curve is almost a straight line), 𝑁𝐴 Avogadro’s
number, [𝑀]0 the initial molar concentration of monomer, [𝑀]𝑃 the concentration
of monomer in a particle, 5.8 mol/L at 70 ℃,
𝑘𝑃 the propagation rate constant of
styrene (480 L mol-1 s-1 at 70 ℃), respectively1.
It should be pointed out 𝑛̅ could be lowered by RAFT reaction in an RAFT emulsion
polymerization. The lowering effect is highly dependent on the RAFT equilibrium
and target molecular weight as suggested by a theoretical equation3
1
𝑛̅𝑅𝐴𝐹𝑇
= 𝑛̅
1
𝑏𝑙𝑎𝑛𝑘
+ 2𝐾[𝑅𝐴𝐹𝑇]
(6)
where 𝑛̅𝑅𝐴𝐹𝑇 is the average number of radical per particle in a RAFT emulsion
polymerization,
𝑛̅𝑏𝑙𝑎𝑛𝑘 is the average number of radical per particle in a RAFT free
emulsion polymerization and 𝐾 is the RAFT equilibrium constant.
A RAFT-free conversional emulsion polymerization of styrene was conducted with
sodium dodecyl sulfate (SDS) as surfactant (6×10-2 mol L-1). KPS was used as
initiator (1.46×10-2 mol L-1, same as Exp 9). The polymerization was carried out with
the same conditions as Exp 9. The final particle diameter is about 78 nm and 𝑛̅ is
estimated to be 0.43, which is very close to 0.4 in Exp 9. It is indicated that in the
current RAFT emulsion polymerization system, the used trithiocarbonate RAFT agent
should show little polymerization rate retardation effect.
With the values of ρ and k, the ratio of the rate of particle deactivation to particle
growth can be calculated as
𝐶𝑇,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 = 𝑘𝑑𝑒𝑎𝑐𝑡𝑖𝑣𝑎𝑡𝑒 /𝑘𝑃,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒
(7)
The growth rate of an active particle (supposing only a single radical should exist in
the particle)
𝑘𝑃,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 = 𝑘𝑃 [𝑀]𝑃
(8)
It should be noticed that the value of 𝐶𝑇,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 changes with monomer conversion
throughout the polymerization. In Table S1, we list the values of 𝐶𝑇,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 at
monomer conversion of 45% where the polymerizations are in steady state (interval II
of emulsion polymerization) and “zero-one” model is applicable1. As seen in Figure
S2, 𝐶𝑇,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 decreases in an accelerating rate when reducing the initiator
concentration, which indicates the activation/deactivation rate decreases sharply when
reducing the initiator concentration.
Table S1. Seeded RAFT Emulsion Polymerization of Styrene Mediated by
Macro-RAFT Agent with Different KPS Concentrations Post-Added
[KPS]/
[KPS] (×10-4
[RAFT]
mol 𝐋−𝟏
𝒍𝒂𝒕𝒆𝒙 ,
(total)
post-added)
9
1/5
10
𝒅𝒗
𝐥𝐨𝐠 𝑵𝑷 b
(nm)
(𝐋−𝟏
𝒍𝒂𝒕𝒆𝒙 )
14.4
71.1
1/20
3.51
11
1/80
12
13
Expa
a
𝑪𝑻,𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆 e
PDIMW
PDIPS
𝒏
̅c
𝑵𝑹𝑨𝑭𝑻 d
17.94
1.23
1.009
0.40
4575
4.90
72.7
17.92
1.28
1.019
0.31
4518
3.01
0.792
73.1
17.95
1.39
1.031
0.22
4830
2.24
1/320
0.113
72.8
17.95
1.55
1.059
0.15
4910
2.04
1/640
0
71.4
17.98
1.74
1.082
0.09
4850
1.92
(×105)
The same seed latex were used in Exp 10-11.Then conducted at 70 ℃ with 20%
solid content and molecular weight targeted at 30 kg mol-1; b Final number of particles
calculated according to Equation (1); c The average number of radicals per particle (𝑛̅)
was calculated by Equation (6) d The number of RAFT chains inside a particle was
calculated by Equation (4); e The ratio of the particle activation/deactivation and
particle growth rate coefficients is calculated by Equation (1) at the monomer
conversion of 45%.
Figure S1. Plot of conversion vs polymerization time in Exp 9-13 at 70 ℃ with 20%
solid content and targeted at 30 kg mol-1.
Figure S2. The influence of [KPS] on 𝐶𝑇,𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 in Exp 9-13 at 70 ℃.
References
1. R. G. Gilbert. Emulsion Polymerization: A Mechanistic Approach; Academic
Press: London, 1995.
2. S. W. Prescott, M. J. Ballard, E. Rizzardo, R. G. Gilbert. Macromol Theor Simul
2006, 15, 70-86.
3. Y. Luo, R. Wang, L. Yang, B. Yu, B. Li, S. Zhu. Macromolecules 2006, 39,
1328-1337.
4. I. A. Maxwell, B. R. Morrison, D. H. Napper, R. G. Gilbert. Macromolecules 1991,
24, 1629-1640.