Kinetics of free radical polymerization of spacerless dendronized macromonomers in supercritical carbon dioxide

Article abstract of DOI:10.1021/ma2002189

The kinetics of the free radical polymerization in supercritical carbon dioxide of third (G3) and fourth (G4) generation spacerless dendronized macromonomers, bearing a methacrylate group at the focal point, is experimentally investigated. Conversions up

Full text of DOI:10.1021/ma2002189

ARTICLE
pubs.acs.org/Macromolecules
Kinetics of Free Radical Polymerization of Spacerless Dendronized
Macromonomers in Supercritical Carbon Dioxide
L. I. Costa,† G. Storti,† M. Morbidelli,*,† X. Zhang,‡ B. Zhang,‡ E. Kas€emi,‡ and A. D. Schl€uter‡
†Institute for Chemical and Bioengineering, Swiss Federal Institute of Technology Z€urich, ETHZ, Wolfgang-Pauli-Strasse 10,
HCI F-129, 8093 Z€urich, Switzerland
‡Laboratory of Polymer Chemistry, Swiss Federal Institute of Technology Z€urich, ETHZ, Wolfgang-Pauli-Strasse 10, HCI J-541,
8093 Z€urich, Switzerland
S Supporting Information
b
ABSTRACT: The kinetics of the free radical polymerization in
supercritical carbon dioxide of third (G3) and fourth (G4)
generation spacerless dendronized macromonomers, bearing a
methacrylate group at the focal point, is experimentally inves-
tigated. Conversions up to 90% could be achieved in few hours
for both monomers, with degrees of polymerization on the
order of thousands of monomer units for G3 and 100ꢀ200 for
G4. Experimental data are interpreted using a conventional free radical kinetic scheme. Within this frame, chain termination is
dominated by chain transfer to monomer and the extremely high reactivity of the macromonomers when polymerized in
supercritical carbon dioxide is reflecting reduced termination rate at increasing dendron generation.
structural defects, even though high generation denpols with
large degree of polymerization can be produced. In the graft-to
approach, preformed dendrons of the final desired generation are
coupled to a linear polymer backbone. This way, all the pendant
dendrons are structurally perfect, an aspect that can be critical in
the graft-from approach, but high dendron coverage on the
backbone is difficult to achieve, especially for high generations.12
For example, according to the last previous citation, Frꢀechet-type
dendrons functionalized with an azide group in the focal point
were reacted with poly(vinyl acetylene) bearing pendant alkynes
on the repeating units, by an efficient Cu(I)-catalyzed azideꢀ
alkyne 1,3-dipolar cycloaddition. The authors could synthe-
size denpols with coverage >98% up to the third generation,
while the fourth generation dendron, G4, was not reacting at all.
A reasonable explanation is that, at high dendron generation, the
branches fold back hiding the focal point and hindering its
coupling with the acetylene units. The third route is the macro-
monomer one, which involves the direct polymerization of
dendrons of the desired generation functionalized with a poly-
merizable unit at the focal point (e.g., a vinyl group). This way,
fully covered denpols can be produced with structurally perfect
dendrons. On the other hand, a long reaction time is required to
achieve decent conversions (typically larger than 20 h), and the
degree of polymerization dramatically decreases at increasing
generation.16,17 The crowding effect is presumably the main
reason for this general trend: for higher generations, dendrons
1. INTRODUCTION
Dendronized polymers (denpols) are comb polymers in which
regularly branched dendrons are the chain substitutents.1ꢀ3 The
high steric demand of the peripheral branched units stretches and
stiffens the polymer backbone, forcing the resulting denpol to
uncoil and adopt a cylindrical shape characterized by a tunable
thickness, with a well-defined external surface dense of sites
available for functionalization.4,5 Backbone stiffening is more and
more pronounced as the generation of the attached dendrons,
and therefore the crowding effect on the conformation of the
resulting denpol, increases.4ꢀ8
Properly functionalized denpols allow unprecedented control
over self-assembly and hierarchical structure formation.8ꢀ10
Single chains may behave as glassy systems,11 can be visualized
and manipulated at the molecular level by atomic force micro-
scopes (AFM),12ꢀ14 and self-fold when negatively charged on
the peripheral groups, thus mimicking biomacromolecules.15 For
all these features, such molecules are promising materials for
nanotechnology applications. Nevertheless, the efficient synthe-
sis of high generation (i.e., from the third generation on)
dendronized polymers with high degree of polymerization still
constitutes an issue.
Three synthetic strategies are most commonly applied to
produce dendronized polymers: the “graft-from”, the “graft-to”,
and the “macromonomer” route.1ꢀ3 Each of them presents
specific advantages and disadvantages. In the graft-from ap-
proach, first generation dendrons are stepwise divergently
coupled onto a linear polymer backbone up to the desired
generation. This way a large number of synthetic and purification
steps are required, and the resulting polymers inevitably bear
Received: January 31, 2011
Revised:
April 15, 2011
Published: May 05, 2011
r
2011 American Chemical Society
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Scheme 1. Reagents and Conditions for the Synthesis of G4 Monomer (3b) from 1a and 2aa
a :Key: (a) HCl/dioxane, rt, 3 h (96%); (b) EDC HCl, DCM/DMF, ꢀ15 °C, 24 h (80%); (c) TEA, DMF/methanol, ꢀ20 °C, 24h (72%); (d) MAC,
3
TEA, DMAP, THF/DMF, 24 h (71%).
are compressed and forced away from the backbone,4 so the steric
repulsion thus generated may cause the dendrons close to the chain
end to bend outward, limiting the reacting site’s accessibility.
Recently, we found that the free radical polymerization of
dendronized macromonomers carried out in supercritical carbon
dioxide (scCO2) is superior to the conventional polymerization
in solution. Indeed, although neither the monomers nor the
forming polymers were soluble in scCO2, higher degrees of
polymerization were obtained compared to solution poly-
merization.18 In the same work, it has been demonstrated that
even a fifth generation macromonomer (G5) could be oligomer-
ized by the macromonomer approach. Driven by such promising
preliminary results, the polymerization kinetics of third (G3) and
fourth (G4) generation macromonomers in scCO2 is further
investigated in this work.
The selected dendrons are spacerless macromonomers bear-
ing a methacrylate group on the focal point. The chemical struc-
ture of G3 (molecular weight = 2625 g/mol) and its homologous
G4 monomer (molecular weight = 5428 g/mol) are shown in our
previous contribution18 and in Scheme 1 (compound 3b),
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respectively. Monomers, as well as their polymers were found to
be insoluble in the reaction medium.18 Therefore, the reactions
occur in a two-phase system, the scCO2 supercritical phase and
the CO2-swollen phase composed of monomer and forming
polymer. SEM images of the samples collected after the reaction
end suggest that the reaction temperature was above the glass
transition temperature of the monomer/polymer mixture,19 thus
supporting the assumption that polymerization occurred in a
highly viscous rubbery phase.
DCM/DMF (400 mL/10 mL) at ꢀ15 °C. The reaction mixture was allowed
to warm up to room temperature and then was stirred for 24 h. After
washing by saturated NaHCO3 solution and then brine, the organic
phase was dried by MgSO4 and purified by column chromatography
(ethyl acetate/hexane 2:1) affording the product as a white solid (16.9 g,
80%). 1H NMR (300 MHz, CDCl3): δ = 1.42 (s, 36 H; tBu), 1.90ꢀ2.12
(m, 12 H; OCH2CH2CH2N), 2.88 (d, 4 H; COCH2CH2CO),
3.25ꢀ3.27 (m, 8 H; CH2NH), 3.60ꢀ3.62 (m, 4 H; CH2NH),
3.87ꢀ4.08 (m, 12 H; PhOCH2), 4.89 (br, 4 H; NH), 6.50 (s, 2 H;
Ph), 6.69 (d, 1 H; Ph), 6.88 (d, 4 H; Ph), 7.04 (br, 2 H; NH), 7.18 (d,
2 H; Ph) ppm. 13C NMR: δ = 25.68 (COCH2CH2CO), 28.42
(C(CH3)3), 28.86, 29.48 (OCH2CH2CH2N), 37.54, 37.77 (OCH2C-
H2CH2N), 65.85, 66.62 (OCH2CH2CH2N), 104.50, 105.66, 108.64, 108.76,
126.66, 136.68, 156.08 (Ar), 159.96 (NHCOO), 161.60, 167.41 (NHCO),
169.23 (NCOCH2) ppm. HRMS MALDI, m/z: calcd, 1288.6219 [M þ
Na]þ; found, 1288.6211 [M þ Na]þ. Anal. Calcd for C63H91N7O20: C,
59.75; H, 7.24; N, 7.74. Found: C, 59.80; H, 7.27; N, 7.54.
2. EXPERIMENTAL SECTION
2.1. Synthesis of the Macromonomers. All reagents were
purchased from Aldrich, Acros, or Fluka. Methacryloyl chloride
(MAC) was freshly distilled before use. Tetrahydrofuran (THF) and
triethylamine (TEA) were refluxed over Na with benzophenone as
indicator, dichloromethane (DCM) was dried by distillation over CaH2.
All other reagents and solvents were used as received. All reactions were
performed under nitrogen atmosphere. Silica gel 60 M (Macherey-
Nagel, 0.04ꢀ0.063 mm/230ꢀ400 mesh) was used as stationary phase
for column chromatography. Whenever possible, reactions were mon-
itored by thin-layer chromatography (TLC) using TLC silica gel coated
aluminum plates 60F254 (Merck). Compounds were detected by UV
light (254 or 366 nm) and/or by treatment with a solution of ninhydrin
in ethanol followed by heating. If not otherwise noted, 1H and 13C NMR
spectra were recorded on Bruker AM 300 (1H, 300 MHz; 13C, 75 MHz)
and AV 500 (1H, 500 MHz; 13C, 125 MHz) spectrometers at room
temperature. High-resolution mass spectral (HRMS) and ESIꢀMS
analyses were performed by the MS-service of the Laboratorium f€ur
Organische Chemie at ETH Z€urich. ESIMS and MALDIꢀMS were run
on an IonSpec Ultra instrument. In the case of MALDIꢀMS, 2,5-
dihydroxybenzoic acid (DHB), 2-[(2E)-(4-tertbutylphenyl)-2-methyl-
prop-2-enylidene]-malononitrile (DCTB) or 3-hydroxypyridine 2-car-
boxylic acid (3-HPA) served as the matrix. The FAB experiments were
carried out with 3-nitrobenzyl alcohol (MNBA)/CH2Cl2. Elemental
analyses were performed by the Mikrolabor of the Laboratorium f€ur
Organische Chemie, ETH Z€urich. The samples were dried rigorously
under vacuum prior to analysis to remove strongly adhering solvent
molecules.
3,5-Bis{3-[3,5-bis(3-{3,5-bis(3-[3,5-bis(3-tert-butoxycarbonylamino
propyl)benzoylamino]propyloxy)benzoylamino}propyloxy)benzoyl-
amino]propyloxy}benzyl Alcohol (3a). A solution of 1b (1.90 g,
2.12 mmol) and TEA (3.43 g, 34.0 mmol) in DMF/methanol (15 mL/
3 mL) was added dropwise to a solution of 2b (13.41 g, 10.06 mmol) in
DMF (120 mL) at ꢀ20 °C. The reaction mixture was allowed to warm
up to room temperature and then was stirred for 24 h. After washing with
KHSO4 solution (10%) and brine successively, the organic phase was
dried over MgSO4 and purified by column chromatography (ethyl
1
acetate/hexane 3:1) affording 3a as a white solid (8.17 g, 72%). H
NMR (300 MHz, DMSO-d6): δ = 1.35 (s, 144 H; tBu), 1.79ꢀ1.84 (m,
32 H; OCH2CH2CH2N), 1.96 (m, 28 H; OCH2CH2CH2N), 3.04ꢀ3.10
(m, 32 H; CH2NH), 3.38ꢀ3.40 (m, 28 H; CH2NH), 3.96ꢀ3.99 (m, 32
H; PhOCH2), 4.04 (m, 28 H; PhOCH2), 4.40 (d, 2 H; PhCH2O), 5.13
(t, 1 H; OH), 6.34 (s, 1 H; Ph), 6.47 (s, 2 H; Ph), 6.59 (s, 8 H; Ph), 6.62
(s, 6 H; Ph), 6.88 (br, 16 H, NH), 6.99 (m, 16 H; Ph), 7.03 (s, 8 H; Ph),
8.49 (m, 14 H; NH) ppm. 13C NMR (75 MHz, DMSO-d6): δ =
28.19 (C(CH3)3), 28.84, 29.16 (OCH2CH2CH2N), 36.36, 36.89
(OCH2CH2CH2N), 62.84 (OCH2), 65.51, 65.67 (OCH2CH2CH2N),
77.47 (C(CH3)3), 103.66, 104.51, 105.73, 136.49, 145.06, 159.57,
159.59 (Ar), 155.60 (NHCOO), 165.73, 165.76 (NHCO) ppm; HRMS
MALDIꢀTOF, m/z: calcd, 5379.8363 [M þ Na]þ; found, 5380.87
[M þ Na]þ. Anal. (%) Calcd for C275H402N30O77: C, 61.62; H, 7.56; N,
7.84. Found: C, 60.66; H, 7.53; N, 7.67.
The third generation monomer G3 and compounds 1a, and 2a
(Scheme 1) were synthesized according to literature methods.16,20,21 In
the following, the synthesis of the fourth generation monomer G4 (3b in
Scheme 1) from 1a and 2a is described.
3,5-Bis{3-[3,5-bis(3-{3,5-bis(3-[3,5-bis(3-tert-butoxycarbonylamino
propyl)benzoylamino]propyloxy)benzoylamino}propyloxy)benzoyl-
amino]propyloxy}benzyl Methacrylate (3b). A solution of metha-
cryloyl chloride (MAC) (43 mg, 0.41 mmol) in dry THF (5 mL) was
added dropwise to a mixture of 3a (1.03 g, 0.193 mmol), TEA (115 mg,
1.14 mmol), and DMAP (8 mg) in dry THF/DMF (70 mL/15 mL) at
0 °C. After the reaction mixture had been stirred for 24 h at room
temperature, it was successively washed with saturated NaHCO3 solu-
tion and brine. The organic phase was dried over MgSO4. Evaporation of
the solvents in vacuo at room temperature followed by chromatographic
separation (DCM/methanol 15:1) yielded 3b as a white solid (0.74 g,
3,5-[Bis(3-{3,5-bis[3-aminopropylox-
y]benzoyl}amino)propyloxy]benzyl alcohol 4HCl (1b). A solution of
3
HCl in dioxane (12 mL, 4 mol/L) was added to 1a (2.6 g, 2.25 mmol) in
10 mL dioxane at room temperature. The reaction mixture was stirred at
rt for 3 h, until the product precipitated. The solvent was removed in
vacuo and the residue was washed 3 times with dioxane and dried over
high vacuum to yield 1b as a white solid (1.95 g, 96%). 1H NMR (300
MHz, D2O): δ = 2.03ꢀ2.19 (m, 12 H; OCH2CH2CH2N), 3.18ꢀ3.23
(m, 8 H; CH2NH), 3.50ꢀ3.54 (m, 4 H; CH2NH), 4.06ꢀ4.13 (m, 12 H;
PhOCH2), 4.48 (s, 2 H; PhCH2O), 6.34 (s, 1 H; Ph), 6.52 (d, 2 H; Ph),
6.74 (d, 2 H; Ph), 6.86 (d, 4 H; Ph) ppm; 13C NMR (75 MHz, D2O):
δ = 26.40, 27.74 (OCH2CH2CH2N), 37.34, 37.44 (OCH2CH2CH2N),
63.68 (OCH2), 65.85, 65.53 (OCH2CH2CH2N), 100.67, 104.96,
105.63, 105.96, 106.11, 135.95, 143.16, 143.24, 159.28, 159.31 (Ar),
169.47 (NHCO) ppm; HRMS MALDI: m/z: calcd: 755.4344 [M þ
H]þ; found: 755.4348 [M þ H]þ. Anal. calcd for C39H62N6O9Cl4: C
52.00, H 6.94, N 9.33; found: C 49.62, H 7.33, N 8.83.
1
t
71%). H NMR (300 MHz, DMSO-d6): δ = 1.35 (s, 144 H; Bu),
1.78ꢀ1.85 (m, 32 H; OCH2CH2CH2N), 1.87 (s, 3 H; CdCCH3), 1.95
(m, 28 H; OCH2CH2CH2N), 3.03ꢀ3.09 (m, 32 H; CH2NH),
3.38ꢀ3.40 (m, 28 H; CH2NH), 3.95ꢀ3.99 (m, 32 H; PhOCH2), 4.03
(m, 28 H; PhOCH2), 5.06 (s, 2 H; PhCH2O), 5.66 (m, 1 H; CdCH2),
6.04 (s, 1 H; CdCH2), 6.44 (s, 1 H; Ph), 6.51 (s, 2 H; Ph), 6.58 (s, 8 H;
Ph), 6.62 (s, 6 H; Ph), 6.85 (br, 16 H, NH), 6.98 (m, 16 H; Ph), 7.01 (s, 8
H; Ph), 8.48 (m, 14 H; NH) ppm. 13C NMR (75 MHz, DMSO-d6): δ =
18.44 (CdCCH3), 28.93 (C(CH3)3), 29.34, 29.65 (OCH2CH2CH2N),
36.90, 37.34 (OCH2CH2CH2N), 66.01, 66.86 (OCH2CH2CH2N),
66.17 (OCH2), 77.96 (C(CH3)3), 101.12, 104.15, 106.22, 106.49,
136.98, 138.85, 160.07, 160.29 (Ar), 126.56 (CH2dC), 136.20 (CH2dC),
2,5-Dioxopyrrolidin-1-yl 3,5-Bis(3-{3,5-bis[3-(tert-butyloxycarbo-
nylamino)propyloxy]benzoylamino}propyloxy)benzoate (2b). EDC
3
HCl (4.12 g, 20.0 mmol) was added to the solution of 2a (19.6 g,
16.7 mmol) and N-hydroxysuccinimide (2.10 g, 18.4 mmol) in dry
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The differences between the conversion values calculated by the
two equations were always less than 10% and average values were
considered.
AFM measurements were performed on a Nanoscope IIIa Multi
Mode Scanning probe microscope (Digital Instruments, San Diego, CA)
with an “E” scanner (10 μm ꢁ 10 μm) in the tapping mode at ambient
condition. Olympus silicon OMCL-AC160TS cantilevers (Atomic
Force F&E GmbH, Mannheim, Germany) were applied with a reso-
nance frequency in the range 200ꢀ400 kHz and a spring constant of
about 42 N/m. The samples were prepared by spin-coating (2000 rpm,
40 s) the polymer solution of PG3 or PG4 (∼10 mg/L in chloroform)
onto freshly cleaved mica (from PLANO W. Plannet GmbH, Wetzlar,
Germany).
Figure 1. Peak area vs sample concentration for solutions of G4
monomer (O) and PG4 polymer ()). Lines: linear fittings.
3. POLYMERIZATION KINETICS OF G3 AND G4 IN
SCCO2
156.10 (NHCOO), 166.23, 166.75 (NHCO) ppm. HRMS, m/z: calcd,
5449.86 [M þ Na]þ; found, 5449.94 [M þ Na]þ. Anal. Calcd for
C279H406N30O78: C, 61.73; H, 7.54; N, 7.74. Found: C, 60.70; H, 7.31; N, 7.62.
2.2. Polymerization Procedure. Batch reactions were carried
out in a mechanically stirred stainless steel autoclave (Premex Reactor
AG) equipped with inlet and outlet valves, pressure transducer and dip
tube with temperature sensor Pt-100. Defined amounts of AIBN
initiator (2,20-Azobis(2-methylproprionitrile), purity >98%, from Fluka,
used as received) and monomer (30ꢀ50 mg) were separately loaded
into two glass vials, which were then put into the high-pressure reactor.
The reactor was sealed and loaded/unloaded 8 times by carbon dioxide
up to a pressure of 20 bar at room temperature in order to fully remove
oxygen. The desired amount of CO2 (99.95% pure, from PanGas) was
injected by a high-pressure piston pump (NWA GmbH, Germany) into
the reactor, which was then heated to the reaction temperature by
immersion in a thermostatic oil bath. At the final reaction time, the
reactor was slowly vented, and the product was sampled from the vial
where the monomer was initially loaded.
3.1. Conversion. Recipe conditions and representative results
for the reactions carried out at T = 65 °C and P = 130 bar at
different initiator concentrations are reported in Table 1. The
conversion profiles measured at three different initiator concen-
trations are shown in Figure 2 and Figure 3 for the polymeriza-
tion of G3 and G4, respectively. At intermediate and low AIBN
content, significant induction times, τ, were observed for the
polymerization of G3, where shorter reaction times were used.
The observed inhibition might be attributed to traces of
impurities present in the monomer and acting as radical
scavengers. Such explanation is quite possible due to the very
large number of synthetic steps required to produce the
monomers; moreover, it will be assessed in more quantitative
way in section 5. The presence of some kind of inhibitors in
the original monomer could also explain why no polymer was
obtained when decreasing the initiator concentration to [I2] =
0.35 mM (Table 1, run 15); even though monomers of similar
chemical structure are known to give thermally induced
polymerization.22
Monomer conversion increased in all cases with time and
initiator concentration, reaching values as high as 90% for both
monomers. It is worth noting the extremely fast reaction rate
measured for the polymerization of G3, the conversion of which
was almost complete within few hours (cf. Table 1 runs 1 and 2).
A limiting conversion of about 90% was observed for the
polymerization of G3 monomer (Figure 2), presumably due to
depressed monomer mobility at the high concentration of
denpols reached in the reacting phase mixture.
The selected mass ratio between monomer and CO2 was always very
small (on the order of 10ꢀ3). For this reason, whatever the partition
coefficient of the initiator between the two phases, the concentration of
AIBN in the supercritical phase, [I2], was estimated as the ratio between
the charged moles of AIBN and the total reactor volume.
2.3. Polymer Characterization. The collected samples were dis-
solved in DMF (1ꢀ2 mg/mL), filtered by porous stainless steel frit (porosity
0.2 μm), and characterized by GPC, using a PL-GPC 220 apparatus (Polymer
Laboratories) equipped 2x PL-Gel Mix-B LS columns, refractive index
detector (RI), and viscosity detector. DMF þ 1gr/L LiBr, at 1 mL/min
flow rate, was used as eluent at T=45°C. GPC columns were calibrated using
PMMA standards, Mp = 2680 to 3 900 000 g/mol; Polymer Laboratories
Ltd., U.K. Sample molecular weights were calculated by universal calibration.
To estimate the monomer conversion, the response factors of monomers
(G) and polymers (PG) to the RI detector were first determined. For each pure
species, GPC elution profiles were collected using solutions at different con-
centrations. The peak areas, A, were plotted against the corresponding solution
concentrations, c, and the response factors, mG and mPG, were evaluated by
linear regression. An example of A vs c data for solutions of pure G4 and pure
PG4 is shown in Figure 1 along with the corresponding linear fittings.
When analyzing by GPC solutions of collected samples, the areas of
produced polymer (APG) and residual unreacted monomer (AG) were
both measured. From such values, the corresponding conversion is
readily calculated in two different ways:
The high value of monomer conversion to polymer was also
1
1
proved by H NMR. A representative H NMR spectrum of a
sample collected after the reaction of G4 monomer is shown in
Figure 4. A 1H NMR spectrum of the pure G4 monomer is shown
in Figure 5a for comparison. Arrows in Figure 4 indicate the
characteristic peaks of the monomer. The broadening of such
peaks after the reaction is a confirmation of the polymerization
occurrence. The peaks associated with the double bond, located
at δ = 5.6 ppm and δ = 6.1 ppm, almost disappeared after the
reaction, thus proving the almost complete conversion of the
monomer double bonds. Note the peak associated with dioxane
ꢀ
ꢁ
1
in the H NMR spectrum of the monomer (Figure 5a). Such
AG
X1% ¼ 100 1 ꢀ
ð1Þ
ð2Þ
solvent, residue from the G4 synthesis, could not be removed
despite monomer being subjected to several freeze-drying
cycles before polymerization. It was instead completely ex-
tracted by scCO2. Indeed, it was visible in the spectrum of
neither the polymerized sample spectrum (Figure 4), nor the
mGc
ꢀ
ꢁ
A
PG=mPG
X2% ¼ 100
A
PG=mPG þ AG=mG
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Table 1. Recipes and Results for the Polymerization of G3
a
and G4 in scCO2
run
monomer
time [h]
X %
Pn
Pw
PDI
[AIBN]0 = 8.6 mM
1
2
3
4
G3
G3
G3
G3
2.0
6.0
63
93
93
94
487
493
456
428
2354
3588
4653
4437
4.8
7.3
12.5
20.0
10.2
10.4
Figure 2. Conversion as a function of time for G3 polymerization at
[AIBN]0 = 8.6 mmol/L (2), 2.7 mmol/L (b), and 0.84 mmol/L (9).
Curves: calculated solving eqs 7ꢀ10 using R = 370 and inhibition time,
τ, as reported in Table 4.
[AIBN]0 = 2.7 mM
5
6
7
8
9
G3
G3
G3
G3
G3
1.5
4.0
-
19
71
90
90
540
630
512
352
1718
2766
3464
4356
3.2
4.4
7.5
12.3
21.0
6.8
12.4
[AIBN]0 = 0.84 mM
10
11
12
13
14
G3
G3
G3
G3
G3
2.0
6.0
-
-
11.5
16.0
20.0
41
43
79
451
406
448
2147
2094
5136
4.8
5.2
11.5
[AIBN]0 = 0.35 mM
20.0
[AIBN]0 = 16.3 mM
15
G3
-
Figure 3. Conversion as a function of time for G4 polymerization at
[AIBN]0 = 16.3 mmol/L ((), 8.0 mmol/L (2), and 2.6 mmol/L (b).
Curves: calculated solving eqs 7ꢀ10 using R = 60 and inhibition time, τ,
as reported in Table 4.
16
17
18
G4
G4
G4
12.0
20.0
30.0
61
85
89
56
58
56
106
99
1.9
1.7
2.0
109
solution polymerization only when using lower generation
monomers.16 To the best of our knowledge, there are no
publications reporting almost complete conversion and Pw on
the order of thousands monomer units obtained at the same time
using the macromonomer approach with high generation den-
dronized monomers. These results address the potential of
using CO2 as reacting medium to synthesize denpols by the
macromonomer route.
3.2. Number-Average Degree of Polymerization, Pn. In
addition to the very large values of final conversion and Pw
obtained, an even more surprising finding is the independence
of the number-average degrees of polymerization, Pn, upon
amount of initiator and conversion. This is clearly shown by
the Pn values for PG3 in Figure 6, as well as by the results
provided in Table 1 for PG4. Pn values are always in the range
of 450ꢀ630 monomer units for PG3, while Pn = 56ꢀ73 for
PG4. Even though the experimental values exhibit some
scatter, the independence of the molecular weight upon the
initiator concentration was proved in a fully convincing way
when comparing the GPC elution profiles at similar conver-
sions: they were almost superimposed for all samples whatever
the amount of initiator.19
On average, constant values of Pn = 500 monomer units for
PG3 and 65 for PG4 were obtained. If the polymerization
kinetics in scCO2 is somehow similar to that of the conven-
tional free radical polymerization in solution (see section 5),
constant Pn at different initiator concentrations and polym-
erization rates, would be considered a clear proof that chain
transfer to monomer is the dominant chain termination
mechanism. This is clear when considering the Mayo equa-
tion, for which the number-average degree of polymerization
[AIBN]0 = 8.0 mM
19
20
21
G4
G4
G4
12.7
20.0
30.3
24
53
73
78
65
70
120
98
1.5
1.5
1.7
116
[AIBN]0 = 2.6 mM
22b
23b
24
G4
G4
G4
19.8
20.3
30.5
14
10
14
73
109
1.5
a All reactions performed at T = 65 °C and P = 130ꢀ140 bar. Reported
initiator concentrations are average values over all corresponding
batches. b At such low conversion, polymer and monomer peak super-
position prevented reliable calculation of Pn and Pw.
monomer subjected to CO2 pressure (without adding any
initiator; Figure 5b). Comparison of the two spectra in
Figure 5 confirms the well-known ability of scCO2 of extract-
ing solvents and confirms the monomer structure is not
affected by high pressure CO2.
About the degrees of polymerization, PG3 samples exhibit
longer chains and larger values of the polydispersity index (PDI)
compared to PG4 samples (cf. Table 1). The number, Pn, and
weight-average, Pw, degrees of polymerization for PG3 samples
are plotted as a function of conversion in Figure 6 and the
corresponding PDI in Figure 7. Weight-average degrees of
polymerization, Pw, of the orders of thousands monomer units
for the third generation monomer were systematically obtained,
corresponding to molecular weights of several million g/mol.
Such extremely large Pw can be produced through conventional
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Figure 4. 1H NMR spectrum of crude reaction mixture for the polymerization of G4 (Table 1 run 17, X % = 85%) in DMSO-d6 at 80 °C. Arrows indicate
the peaks characteristics of the monomer G4 (cf. Figure 5). Note that that the peaks of the PG4 are broad, and the peaks at δ = 5.6 and 6.1 ppm,
corresponding to G4 double bond signal, are almost invisible (see the zoomed inset). / and // denote the signals of DMSO and water, respectively.
Figure 5. 1H NMR spectrum of G4 (a) before and (b) after treatment with scCO2 at T = 60 °C, P = 140 bar, for 8 h. The signal for residual dioxane
(Dox, δ = 3.57 ppm) in spectrum (a) disappeared after the treatment (b). / and // denote the signals of DMSO and water, respectively.
in the absence of chain transfer to solvent, initiator, or chain
transfer agents, is given by23,24
average values of CG = 1/500 and CG = 1/65 are estimated for
G3 and G4, respectively. We can exclude the chain transfer to
occur on the methacrylate group (which is also the reactive
site in our dendronized macromonomers) because methyl
methacrylate (MMA) exhibits negligible transfer to monomer
constant.25 Alternative sites for chain transfer to monomer to
occur by H abstraction could be (i) the CH bonds R to the
ether oxygen atoms and (ii) the benzylic hydrogen at the core
of the monomers. Let us consider case (i) first. The CH bonds
alpha to the ether oxygen atoms are also present at the dendritic
shell. Therefore, they are accessible as potential sites for chain
transfer to polymer reactions too, and the value of the chain
transfer to polymer constant should be close to the measured CG,
ꢀ
ꢁ
ktRp
k2p½Gꢂ
1
1 þ γ
¼
2 þ CG
ð3Þ
Pn
2
where Rp, [G], and CG are the rate of polymerization, the
monomer concentration and the transfer to monomer con-
stant, ratio between the rate constants of transfer to monomer
and propagation. In eq 3, kp and kt are propagation and radical
termination rate constants and the parameter γ is the ratio
between the rate constant of radical termination by dispro-
portionation and kt. From the experimental data in Table 1
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Figure 6. Number-average, Pn (open symbols) and weight-average Pw
(filled symbols) degrees of polymerization vs conversion, X %, for PG3
samples polymerized in scCO2 at [AIBN]0 = 8.6 mmol/L (2), 2.7
mmol/L (b), and 0.84 mmol/L (9). Lines are guides for the eye.
Figure 8. GPC elution profiles of crude PG3 samples at 2 h (continuous
line, Table 1 run 1), 6 h (dashed line, Table 1 run 2) and 12.5 h of
reaction time (dotted line, Table 1 run 3). Monomer peaks, visible at
largest retention time, are also shown.
Figure 7. Polydispersity index, PDI, vs conversion, X%, of PG3 samples
polymerized in scCO2 at [AIBN]0 = 8.6 mmol/L (2), 2.7 mmol/L (b),
and 0.84 mmol/L (9). The line is a guide for the eye.
Figure 9. GPC elution profiles of crude PG4 samples at 13 h
(continuous line, Table 1 run 19), 20 h (dashed line, Table 1 run 20),
and 30 h of reaction time (dotted line, Table 1 run 21). Monomer peaks,
visible at largest retention time, are also shown.
because the same reaction is involved. Such extremely large values of
chain transfer to polymer constants would have caused branching
reactions to occur at severe extent, and more for the polymerization of
G4 compared to the polymerization of G3 monomer. This was not
the case (cf. section 3.3) and therefore H abstraction by propagating
radicals at sites (i) can be tentatively excluded.
elution profiles in the high molecular weight region at increasing
conversion and reaction time was observed in all cases for both
monomers. Such broadening is evident in Figures 8 and 9, where
three elution profiles at different reaction time and constant
initial AIBN concentration are shown for PG3 and PG4 samples,
respectively.
Differently, the benzylic CꢀH bond (case (ii)) is susceptible
of hydrogen abstraction but the same hydrogen would unlikely
be accessible for chain transfer to polymer reactions. In fact, the
benzylic CꢀH bond is weaker than the aliphatic CꢀH bond23
due to the stabilization imparted to the radical resulting from the
abstraction by the benzene ring. On the other hand the same
CꢀH group is very close to the backbone of the polymer chain
after a monomer is polymerized, and therefore not easily
accessible to propagating radicals for the chain transfer to
polymer reaction. It is thus interesting to compare the chain
transfer constants per number of benzylic hydrogens, n, of the
macromonomers used in this work, with that of a quite similar
but undendronized system. CG/n for the chain transfer reaction
of MMA to dibenzyl ether (DBE) is 2.5 ꢁ 10ꢀ4 (at T = 60 °C),26
Such broadening is especially evident for PG3 samples, where
much broader distributions were measured: PDI values up to 12
for PG3 samples while maximum PDI values around 2 were
found for PG4 samples. The evolution of Pw and PDI for PG3
samples shown in Figures 6 and 7, indicate that Pw and PDI
increased slightly with conversion for X% smaller than 80%, with
PDI ranging from 3 to 5, and then sharply at larger conversions.
Let us consider first the lower conversion range. PDI values
ranging from 3 to 5 are not unusual for the free radical
polymerization of the herein considered monomers even when
chain transfer to polymer is not occurring at severe extent.16,27
Indeed, chain transfer to polymer is more likely to occur at the
dendritic shell rather than at the sterically hindered backbone. In
this case, larger PDI values would have been observed for the
PG4 samples due to the large number of potential sites available
for hydrogen abstraction compared to the PG3 homologue.
Instead, this was not the case and polydispersity values for
PG4 were always smaller. On the other hand, the very sharp
PDI increase at high conversion (higher than 80%) suggests that
chain transfer to polymer may become important at least at such
conditions (large values of the polymer to monomer ratio in the
reacting mixture). Notably, even when the limiting monomer
conversion was reached, PDI went on increasing with time (cf. in
while for G3 and G4 we estimated 1 ꢁ 10ꢀ3 and 7.7 ꢁ 10ꢀ3
,
respectively. The agreement between the values of CG/n for G3
and MMA/DBE supports a chain termination dominated by
chain transfer to monomer. On the other hand, the increasing
value of CG/n from a conventional system (MMA/DBE), to G3
and to G4, suggests that the focal point conformation of the
monomers, or of the propagating radicals, favors hydrogen
abstraction rather than propagation to the double bond at
increasing dendronization.
3.3. Polydispersity Index and Branching. With respect to
the time evolution of polydispersity, a broadening of the GPC
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Figure 10. Representative AFM phase images of (a) PG3 and (b) PG4 after spin-coating the polymer solutions on mica.
Table 1 run 2 with run 3 and run 8 with run 9). A possible
explanation is that when only few percents of unreacted mono-
mer are left, their propagation is hindered by diffusion limitations
in the highly viscous denpol-crowded environment. At such
condition, the primary radicals produced by the initiator decom-
position (half-life time for AIBN at T = 65 °C in scCO2 is 25 h)28
start reacting with the polymer chains via transfer to polymer
reaction, thus creating branched denpols of very high molecular
weight and increasing the broadness of the molecular weight
distribution.
Such mechanistic picture could be validated looking for
branched macromolecules in the final product. The quantitative
assessment of branching for dendronized polymers is difficult,
but a rough estimation can be derived by AFM image analysis.27
Two representative images of PG3 and PG4 samples are shown
in Figure 10, parts a and b, respectively. Note that, more than to
confirm larger Pw and PDI for PG3 compared to PG4, Figure 10a
is shown here to evidence that polymer aggregates are formed by
spin-coating on mica (such as in the right-upper part of the
figure). In similar cases, it is difficult to clearly discriminate if the
polymer chains were actually branched or just entangled: there-
fore, all the detected branched-entangled chains were counted as
branched points, thus overestimating the extent of branching.
Nevertheless, the extent of branching was found to be quite
limited: for samples with PDI larger than 10, a maximum of 0.32
to 0.57 average number of branches per chain was estimated by
phase and height image analysis of several chains per sample.
Therefore, even though chain branching occurred, only at minor
extent at conversion exceeding 80%, such limited interchain connec-
tions is enough to produce a major PDI increase, most probably
because of the large size of the involved macromolecules.
Table 2. Effect of Pressure for the Polymerization of G3 and
G4 in scCO2
a
run monomer AIBN [mM] P [bar] time [h] X% Pn
Pw
PDI
10.4
1
2
3
4
5
6
7
G3
G3
G3
G3
G3
G4
G4
8.3
8.6
135
185
267
138
190
130
280
20
20
20
20
20
20
20
94 428 4437
93 660 8328 þ gel 12.6
94 736 3630 þ gel 4.9
8.5
0.83
0.89
8.2
79 448 5136
11.5
77 516 7222 þ gel 14.0
53 65 98
1.5
1.7
8.3
31 115 200
a All reactions performed at T = 65 °C and 20 h reaction time.
average polymerization degrees reported in Table 2 runs 2, 3,
and 5, characterize only the soluble fraction of the polymer, being
the small amount of insoluble polymer (defined “gel” in Table 2;
about 10 to 40% of the produced polymer) removed by filtration
prior to injection into the GPC instrument. Unfortunately, the
exact nature of the insoluble fraction could not be assessed, but it
is reasonably due to cross-linked high molecular weight denpol
chains: such finding supports the role of chain-connecting
reactions mentioned above.
About the polymerization of the fourth generation G4 mono-
mer, larger pressures slowed down the reaction and favorably
affected the degree of polymerization: Pw almost doubled when
increasing the pressure from 130 to 280 bar (Table 2, run 7).
In general, a pressure increase favors the dissolution of low
molecular weight species in the scCO2 phase.29 This effect can
explain the reduced conversion at larger pressures due to AIBN
preferential partitioning into the supercritical phase, thus redu-
cing its amount in the polymer-rich phase. The same reason
cannot explain the increased degree of polymerization, which, as
shown above, is independent upon the initiator concentration.
Finally, G4 polymerizations were carried out at increasing
temperature to check whether or not the G4 polymerization rate
could be enhanced while producing denpols of decent degree of
polymerization. Recipes and results are listed in Table 3 to be
compared with reference reactions carried out at T = 65 °C. A
strong effect of temperature on the reaction rate was observed:
increasing the temperature, the reaction time could be decreased
of almost 20ꢀ30 times, with final conversion increasing of a
factor from 1.7 (Table 3, run 1 and 3) to almost 4 (Table 3, run 4
and 5). Therefore, also the fourth generation monomer was
4. ROLE OF PRESSURE AND TEMPERATURE
Finally, a few more reactions were performed to assess the
effect of pressure and temperature on kinetics and degree of
polymerization. Recipes and characterization results for reactions
carried out at T = 65 °C and 20 h of reaction time are provided in
Table 2. The polymerization of the third generation monomer
(G3) was still almost complete producing samples at extremely
high molecular weight and large values of the polydispersity
index. Quite interestingly, while samples polymerized at a
pressure of about 130 bar were completely soluble in DMF,
denpols obtained at higher pressures were not. Clearly, the
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Table 3. Effect of Temperature on the Polymerization of G4
in scCO2
Table 4. Calculated Inhibition Times and Inhibitor/Mono-
mer Ratiosa
a
run
AIBN [mM]
T [°C]
time [h]
X %
Pn
Pw
PDI
Polymerization of G3
[AIBN]0 [mM]
τ [h]
[Z]0/[G]0
1
2
3
4
5
8.2
8.3
8.1
2.6
2.7
65
75
83
65
85
20
53
92
88
14
41
65
51
46
73
58
98
94
1.5
1.9
1.7
1.5
1.9
1.7 ꢁ 10ꢀ4
4.0 ꢁ 10ꢀ4
3.3 ꢁ 10ꢀ4
5.1
1.3
30.5
1.3
8.6
0.33
2.5
80
2.7
109
110
0.84
7.0
a All reactions performed at P = 130 ( 10 bar.
Polymerization of G4
[AIBN]0 [mM]
τ [h]
[Z]0/[G]0
polymerized up to almost complete conversion within few hours
(Table 3 run 3) and, most important, no appreciable effects on
the degree of polymerization were observed.
16.3
8.0
2.0
7.0
4.0 ꢁ 10ꢀ3
6.4 ꢁ 10ꢀ3
4.2 ꢁ 10ꢀ3
2.6
16.0
a Inhibition time, τ, for reactions in Table 1, with kd = 7.76 ꢁ 10ꢀ6/s.
The moles of inhibitor per moles of monomer, [Z]0/[G]0, are estimated
through eq 11 using 2fKI2 = 1, [G3]0 = 0.457 M, and [G4]0 = 0.221 M.
5. DISCUSSION
In general, the polymerization of dendronized monomers may
exhibit features which are not involved in the conventional free
radical schemes. Two mechanistic pictures are frequently dis-
cussed, as shortly illustrated by the following examples.
consumption starts. At such conditions, the monomer and
initiator consumption rates (up to the limiting conversion) can
be expressed as:
It has been observed that both conversion and degree of
polymerization are depressed by high monomer to solvent ratios
(i.e., monomer concentration larger than about 53%) in solution
polymerization.30 Similar results have been reported for non-
dendronized macromonomers.31 Such experimental evidence
can be attributed to hindered polymerization reaction either
because of limited monomer mobility at high viscosity of the
reaction medium, or because of encapsulation and consequent
inaccessibility of the active center of the propagating denpol.
Other authors have shown that dendrons may self-assemble
and form supramolecular reactors with larger concentration of
polymerizable groups (the focal point double bonds).32ꢀ34 In
such a case, Percec et al.34 found enhanced reaction rate and
larger degrees of polymerization in the presence of self-assembly
compared to conventional solution polymerization, and referred
to this case as “self-encapsulated self-accelerated polymerization”.
The better conditions established in scCO2 (fast reaction
rate and large degrees of polymerization) demonstrate that the
active radical as well as the monomer double bond are always
more “accessible” in such reaction medium than in solution.18
On the other hand, no study has been reported focused on
conformation and/or self-assembly behavior of dendrons similar
to those under examination in supercritical carbon dioxide.
Therefore, as first step of a critical evaluation of the different
mechanistic pictures, it makes sense to verify whether or not the
kinetics follows a conventional free radical polymerization
scheme, and an explanation alternative to self-assembly can be
found to justify the enhanced kinetics in scCO2 compared to
solution polymerization. This is done in the following.
d½Gꢂ
¼ 0 at t < τ
ð4Þ
ð5Þ
ð6Þ
dt
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d½Gꢂ
dt
2fkdKI2½I2ꢂ
¼ ꢀ kp½Gꢂ
at t g τ
kt
d½I2ꢂ
dt
¼ ꢀ kd½I2ꢂ
where f is the initiator efficiency in the monomer/polymer phase,
kd is the dissociation rate constant (the same value is assumed in
both phases) and KI2 is the initiator partition coefficient. By
integrating eqs 4-6, the following relation between fractional
conversion, X, and reaction time is obtained at t > τ:
FðXÞ ¼ RFðtÞ
ð7Þ
where:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
1
ð8Þ
ð9Þ
FðXÞ ¼ ln
ð1 ꢀ XÞ ½I2ꢂ0 expð ꢀ kdτÞ
FðtÞ ¼ ½1 ꢀ eꢀðk =2Þðt ꢀ τÞꢂ
and the dimensionless constant R is given by
d
rffiffiffiffiffiffiffiffiffiffi
kp
pffiffiffi
kt
8fKI2
R ¼
ð10Þ
kd
As anticipated, the examined monomers are insoluble in
scCO2 and the reaction volume is composed by the scCO2
phase and by the amorphous monomer/polymer-rich phase
swollen by CO2. At monomer concentrations equal to zero
(i.e., in the supercritical phase), the efficiency of the initiator
becomes negligible.35 It can thus be assumed that all the active
radicals are actually produced by dissociation of the initiator
present in the monomer/polymer phase. Moreover, it is assumed
that AIBN partitioning between the two phases is at thermo-
dynamic equilibrium, and that any inhibiting impurity is com-
pletely consumed at reaction time τ, after which monomer
According to eq 7, F(X) is a linear function of F(t) whatever the
initial initiator concentration, [I2]0, provided that constant value
of R applies (and therefore not after the limiting conversion has
been reached). The values of both the functions are readily
estimated using the experimental data in Table 1, a value of
decomposition rate constant, kd, of 7.76 ꢁ 10ꢀ6 s
,
ꢀ1 28 and the
different values of inhibition time as given in Table 4. The values
of τ were first estimated from an analysis of each kinetic profile
and then optimized to improve the linear fit of eq 7. The resulting
F(X) values are plotted against F(t) in Figure 11 for both
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pffiffiffiffiffiffiffiffiffiffiffi
kp
pffiffiffi
kt
G4 :
. 0:066 1 þ γ
ð15Þ
Note that parameter γ is ranging between 0 and 1: therefore, the
square root term does not affect our estimation at a significant
extent.
As expected, the ratio kp/kt0.5 decreases upon increasing
dendron generation, but, quite surprisingly, its order of magni-
tude is in any case larger, or in the worse case (G4) comparable,
to that typically observed for the solution polymerization of
MMA, that is on the order of 0.1.23,36 Because of the crowding
nature and large molecular size of the used monomers, the
absolute values of both propagation and termination rate
constants are expected to be smaller than those typical of
MMA. This means that the reduction of kt due to dendroniza-
tion is larger than that of kp and, as a result, G3 exhibits larger
value of kp/kt0.5 compared to MMA. On the other hand,
moving from the third to the fourth generation, the value of
the ratio kp/kt0.5 decreases, thus indicating that the decrease
of kp becomes more important at higher crowding of the
monomer.
Figure 11. F(X) (eq 8) vs F(t) (eq 9) evaluated through the experi-
mental data in Table 1. Symbols: polymerization of G3 at [AIBN]0 =
8.6 mmol/L (2), 2.7 mmol/L (b), and 0.84 mmol/L (9); polymer-
ization of G4 at [AIBN]0 = 16.3 mmol/L ()), 8.0 mmol/L (Δ), and
2.6 mmol/L (O).
monomers: a remarkably nice linearity is found in all cases, thus
providing constant values of the slope R equal to 370 Mꢀ0.5 for
G3 and 60 Mꢀ0.5 for G4.
To check the compatibility of the estimated τ values with the
presence of some inhibitor, here indicated by Z, the ratio between
the moles of inhibitor and the initial moles of monomer is
expressed as:
6. CONCLUSIONS
½Zꢂ
2fKI2½I2ꢂ0ð1 ꢀ expðꢀkdτÞÞ
½Gꢂ0
Third (G3) and fourth (G4) generation spacerless dendro-
nized macromonomers, bearing a methacrylate group at the focal
point, were polymerized in supercritical carbon dioxide using
AIBN as initiator. Conversion values as high as 90% could be
achieved for both monomers within a few hours. A limiting
conversion of about 90% was observed for the reaction of G3,
attributed to hindered monomer mobility when most of the
reacting phase is made of polymerized denpol chains. Weight-
average degrees of polymerizations were on the order of thou-
sands monomer units for PG3 samples, and in the range
100ꢀ200 for PG4 samples.
½Gꢂ00
¼
ð11Þ
Assuming equipartition of the initiator between the two phases
(KI2 = 1) and a value of 2f equal to one, the [Z]0/[G]0 values
reported in Table 4 are estimated. The absolute values are
quite small and compatible with the very large number of
synthetic steps required to synthesize the monomers. More-
over, comparable values are found for each set of data at
constant generation: therefore, the assumption of inhibiting
impurities entering the system with the monomers seems
reasonable.
Data collected at constant temperature and different initiator
contents were analyzed in the frame of a conventional free radical
kinetic scheme. This analysis suggests that chain termination is
dominated by transfer to monomer, presumably occurring on the
weak benzylic hydrogens. Such finding is especially promising
because it implies that even larger degrees of polymerization
could be achieved when using monomers not containing weakly
bonded hydrogen atoms. Reaction kinetics up to limiting con-
version are consistent with a simple kinetic scheme accounting
for inhibition due to traces of impurities in the initial monomers.
Within this frame, kp/kt0.5 ratios larger than that typical of MMA
are needed to explain the observed high reactivity of the
monomers. Since the propagation rate constants of these macro-
monomers are expected to be depressed by the crowding effect,
this result implies an even stronger reduction of the termination
rate when running the polymerization in supercritical carbon
dioxide.
A reliable absolute value of kp/kt0.5 could not be determined
from the estimated values of R because of the unknown initiator
efficiency (in the monomer/polymer-rich phase) and partition
coefficient (cf. eq 10). On the other hand, a reasonable lower
bound of the same ratio can be determined as follows.
With chain termination occurring predominantly by chain
transfer to monomer, the first term on the right-hand side of eq 3
must be much smaller than CG:
ꢀ
ꢁ
ktRp
k2p½Gꢂ
1 þ γ
, CG
ð12Þ
2
2
Making explicit kp/kt0.5 from eq 10 and plugging it into eq 12, the
inequality is rearranged and the upper bound value for the
product fKI2 is found:
ꢀ
ꢁ
R½GꢂCG
2
pffiffiffiffiffiffi
fKI2
,
ð13Þ
1 þ γ
4
½I2ꢂ
’ ASSOCIATED CONTENT
Using the initial values for [G] ([G3]0 = 0.457 M and [G4]0 =
0.221 M), and [I2], eq 13 provides fKI2 , 1.82/(1 þ γ) for G3
and fKI2 , 0.8/(1 þ γ) for G4. Using these values, the lower
bounds of the ratio kp/kt0.5 are finally estimated from eq 10 as
S
Supporting Information. Discussion of the physical state
b
of the monomer/polymer mixture, including SEM images of G3
monomer before polymerization and of G3/PG3 crude mixture
after polymerization, and representative GPC elution profiles of
PG3 and PG4 samples. This material is available free of charge via
the Internet at http://pubs.acs.org.
pffiffiffiffiffiffiffiffiffiffiffi
kp
pffiffiffi
G3 :
. 0:27 1 þ γ
ð14Þ
kt
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’ AUTHOR INFORMATION
(29) Brantley, N. H.; Bush, D.; Kazarian, S. G.; Eckert, C. A. J. Phys.
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(30) Shu, L.; Schl€uter, A. D. Macromol. Chem. Phys. 2000,
201, 239–245.
(31) Tsukahara, Y.; Tsutsumi, K.; Yamashita, Y.; Shimada, S. Macro-
molecules 1990, 23, 5201–5208.
Corresponding Author
*E-mail massimo.morbidelli@chem.ethz.ch. Telephone: þ41-
44-6323034. Fax: þ41-44-6321082.
(32) Percec, V.; Ahn, C.-H.; Ungar, G.; Yeardley, D. J. P.; M€oller, M.;
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(34) Percec, V.; Ahn, C.-H.; Barboiu, B. J. Am. Chem. Soc. 1997,
119, 12978–12979.
’ ACKNOWLEDGMENT
We gratefully thank Thomas-B. Schweizer (ETHZ) for valu-
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