S
1
Control of
Grafting Density
and Distribution
in
Graft
Polymers
by Living Ring
-
Opening Metathesis Copolymerization
Tzu
-
Pin Lin,
†
Alice B. Chang,
†
Hsiang
-
Yun Chen,
†
Allegra L. Liberman
-
Martin,
†
Christopher M.
Bates,
‡
,
⊥
Matthew
J.
Voegtle,
§
Christina A. Bauer,
§
and Robert H. Grubbs
*,†
†
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125,
United States
‡
Materials Department
and
⊥
Department
of Chemical Engineering
, University of California, Santa Barbara,
California 93106, United States
§
Department of Chemistry, Whittier College, Whittier, California 90608, United States
SUPPORTING INFORMATION
S
2
Figure
S1.
1
H
NMR spectr
um
of
PS
in CD
Cl
3
.
S
3
Figure S
2
.
1
H
NMR spectr
um
of
PLA
in CDCl
3
.
S
4
Figure S
3
.
1
H
NMR spectr
um
of
PDMS
in CDCl
3
.
S
5
Figure S
4
.
1
H
NMR spectr
um
of
DME
in CDCl
3
.
S
6
Figure S
5
.
1
H
NMR spectr
um
of
DEE
in CDCl
3
.
S
7
Figure S6
.
1
H
NMR
spectr
um
of
DBE
in CDCl
3
.
S
8
Figure S7
.
SEC traces of
PS
(
Ɖ
= 1.04),
PLA
(
Ɖ
=
1.0
5
), and
PDMS
(
Ɖ
=
1.03
) macromonomers.
Note that the
retention time do not reflect the actual molar masses of the macromonomers due to different interactions
between
the
macromonomers and
the mobile phase (THF). The molar masses of the macromonomers were determined by
1
H NMR spectroscopy.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
15
16
17
18
19
Normalized dRI
Time (min)
PS
PDMS
PLA
S
9
Figure S
8
.
Selected
1
H NMR spectra
(solvent:
CDCl
3
)
obtained from the copolymerization reaction of
PS
with
D
B
E
(1:1)
as an example,
showing the depletion of the olefinic resonances which could be integrated against the
aromatic polystyrene resonances.
PS aromatic
PS
olefinic
DBE
olefinic
t
= 1 min
t
=
3
min
t
= 5 min
t
=
7
min
t
= 9 min
t
= 12 min
S
10
Figure S
9
.
Non
-
linear least
-
square curve fitting for the co
-
polymerization of
PS
(0.0
7
5 M) and
D
B
E
(0.0
2
5 M) in
CH
2
Cl
2
at 298 K. [
G3
]
0
= 0.5 mM. Calculated fits (solid lines) show close agreement with the measured values
(points). In
(b)
, the dashed lines indicate random copolymerization (
r
1
=
r
2
= 1).
S
11
Figure S
10
.
Differential scanning calorimetry (DSC) data for
PS
100
,
DBE
100
, and two copolymers thereof:
(PS
100
-
b
-
DBE
100
)
, a block copolymer with one fully grafted block and one ungrafted block, synthesized by sequential
addition of
PS
and
DBE
; and
(PS
0.5
-
ran
-
DBE
0.5
)
200
, a random bottlebrush copolymer with 50% grafting density,
s
ynthesized by copolymerizing
PS
and
DBE
in a
1:1 feed ratio as discussed in the text. The data were collected on
the second heating cycle using a 10 °C/min ramp rate, and glass transition temperatures (
T
g
, open circles
) were
identified from the co
rresponding derivative curves.
Both copolymers exhibit a single
T
g
between the
T
g
s
of the
pure components
,
indicating successful incorporation of both
PS
and
DBE
. The
T
g
of
PS
100
-
b
-
DBE
100
(which has a
guaranteed blocky sequence due to sequential addition and complete consumption of each block) differs from the
T
g
of (
PS
0.5
-
ran
-
DBE
0.5
)
200
in terms of both position and shape, suggesting that (
PS
0.5
-
ran
-
DBE
0.5
)
200
is not blocky
and likely ran
dom as desired.
S
12
Table S1.
Characterizations of
graft polymers
(PLA
x
-
ran
-
DME
1
-
x
)
n
with various grafting densities (x = 1,
0.75, 0.5, 0.25) and backbone degrees of polymerization (n = 167, 133, 100, 67, 33)
Grafting density
(x)
Targeted
b
ackbone DP
(
n
)
Expected
M
n
(
kg/mol
)
Measured
M
n
a
(
kg/mol
)
Difference
between the
expected and
measured
M
n
Molar mass
dispersity
(
Ɖ
a
)
100%
167
539
548
1.7%
1.025
133
431
432
0.1%
1.014
100
323
335
3.7%
1.008
67
216
227
5.3%
1.009
33
108
109
1.0%
1.017
75
%
167
413
404
-
2.2
%
1.033
133
330
337
1.9
%
1.029
100
248
250
0.8
%
1.029
67
165
169
2.2
%
1.019
33
82.6
81.1
-
1.8
%
1.023
50%
167
287
296
3.3
%
1.026
133
230
234
1.7
%
1.015
100
172
179
3.9
%
1.010
67
115
119
3.4
%
1.008
33
57.4
60.1
4.7
%
1.019
25%
167
161
161
0.2
%
1.009
133
129
126
-
2.6
%
1.014
100
96.6
97.4
0.8
%
1.013
67
64.4
66.1
2.6
%
1.014
33
32.2
32.3
0.2
%
1.021
a
As determined by SEC differential refractive index detector.
The
SE
C analyses were performed on the ether vinyl
ether quenched reaction mixtures without
further workup or purification.
S
13
Instructions
for copolymerization kinetics fitting
This model fits the copolymerization of two monomers (M
1
and M
2
) with independently determined
homopolymerization rate constants
k
11
and
k
22
(refer to the experimental section in the main text for details). The
initial concentrations M
1
C
i
(M
1
*, M
1
propagating species) and M
2
C
i
(M
2
*, M
2
propagating species) are arbitrarily
given as long as the sum of M
1
C
i
and M
2
C
i
equals C
i
(G3 concentration). To use the codes
,
1.
Use MATLAB to save the following
documents
(see below)
FitKinData.m
,
odeSolver.m
, and
model.m
,
as .m files
under
the same folde
r.
2.
Use MATLAB to save the following array of kinetic data
with time
(first column, unit: s)
, M
1
(t)
(second
column, unit: M)
, and M
2
(t)
(third column, unit: M)
. Note that the concentrations at time zero
are
not
included.
To s
ave the data as .mat file
,
copy and paste the following
example
in the command window of
MATLAB
(under the same folder)
:
KinDataTimePS_DBE31 = [60.0000 0.0660 0.0210
120.0000 0.0566 0.0176
180.0000 0.0495 0.0150
240.0000 0.0435 0.0127
300.0000 0
.0375 0.0109
420.0000 0.0289 0.0079
540.0000 0.0221 0.0056
720.0000 0.0150 0.0034];
save ExampleData
3.
Open FitKinData.m file, follow comments line by line to setup the .mat file name, the array name,
k
11
,
k
22
,
initial concentrati
ons, as well as the boundary of the fitting parameters for
k
12
and
k
21
.
4.
Run the FitKinData.m file to find solutions for
k
12
and
k
21
.
S
14
MATLAB codes for copolymerization kinetics fitting
FitKinData.m
%Codes reported in TPL, ABC, HYC, and RHG, JACS 2017,
DOI: 10.1021/jacs.7b00791
.
close
all
%close all figure windows
clc
%clear command window
clear
all
%clear all workspace
load
ExampleData
%Load .mat file
%KinDataTimePS_DBE31 is the
array name containing data time, M1t, M2t
data=KinDataTimePS_DBE31;
%KinDataTimePS_DBE31_fit is fitting results containing [time M1t M2t M1C M2C]
FittingResultName=
'KinDataTimePS_DBE31_fit'
;
%Self
-
propagation rate constants obtained from homopol
ymerization of M1 and M2
k11=4.18;
%rate constant (M
-
1s
-
1) determined by homopolymerization of M1
k22=6.9;
%rate constant (M
-
1s
-
1) determined by homopolymerization of M2
%Initial conditions for the copolymerization
M1i=0.075;
%initial concentration
of M1 (M)
M2i=0.025;
%initial concentration of M2 (M)
M1Ci=0.00025;
%arbitrary initial concentration of M1C (M)
M2Ci=0.00025;
%arbitrary initial concentration of M1C (M). M1Ci+M2Ci = Ci
%fitting parameters for k12 and k21: [LowerBound InitialValue
UpperBound]
k12=[0 5 20];
k21=[0 5 20];
%%%%%the following part should not be modified%%%%%
Mi=[M1i M2i M1Ci M2Ci];
%save initial concentrations as Mi
C=[k11 k22];
%save k11 and k22 as C
%save Mi and C as constants.mat file in the current folder
save(
'constants'
,
'Mi'
,
'C'
)
data=[0 M1i M2i;data];
%add initial M1 and M2 concentration to the data
time=data(:,1);
M1M2=data(:,2:3);
P_lb=[k12(1) k21(1)];
P0 = [k12(2) k21(2)];
P_ub=[k12(3) k21(3)];
%fitting kinetic data with lsqcurvefit function.
It will call odeSolver.m file
%P0 = initial parameters for k12 and k21
%time = time points used to generate the analytical solution and the fit
%M1M2 = Experimentally determined M1 and M2 concentrations at different time points
%P_result = [k12 k21]
from the best fit
[P_result,resnorm] = lsqcurvefit(@odeSolver,P0,time,M1M2,P_lb,P_ub);
%use the k12 and k21 obtained from the best fit to simulate the reaction profile
odeSolver(P_result, [0 time(end)*1.3]);
load
AllResult
%load the reaction profil
e generated by odeSolver code
eval([FittingResultName
'= [time_ode Y];'
]);
r1Mr2=k11*k22/P_result(1)/P_result(2);
%calculate r1 x r2
S
15
plot(data(:,1),data(:,2),
'.b'
,data(:,1),data(:,3),
'.r'
,
'markers'
,12)
hold
plot(time_ode,Y(:,1),
'b'
,time_ode,Y(:,2),
'r'
,time_ode,Y(:,3),
'm'
,time_ode,Y(:,4),
'k'
)
%set legends, x
-
, y
-
label, x
-
axis limit. Report fitting parameters
legend(
'M_1 exp'
,
'M_2 exp'
,
'M_1 fit'
,
'M_2 fit'
,
'M_1* fit'
,
'M_2* fit'
)
xlabel(
'Time (s)'
)
ylabel(
'[M](t) (M)'
)
xlim([0 time(end)*1.3])
title({s
trjoin({
'k_1_1 = '
,num2str(k11),
' M^
-
^1s^
-
^1, k_2_2 = '
,num2str(k22),
' M^
-
^1s^
-
^1'
}),
...
strjoin({
'k_1_2 = '
,num2str(P_result(1),
'%.2f'
),
' M^
-
^1s^
-
^1, k_2_1 =
'
,num2str(P_result(2),
'%.2f'
),
' M^
-
^1s^
-
^1'
}),
...
strjoin({
'r_1 = '
,num2str(k11/P_result(1),
'%.2f'
),
', r_2 =
'
,num2str(k22/P_result(2),
'%.2f'
),
', r_1
\
timesr_2 = '
,num2str(r1Mr2,
'%.2f'
)}),
...
'TPL, RHG, JACS 2017'
})
hold
off
clear
k11
k12
k21
k22
M1Ci
M1i
M1M2
M2Ci
M2i
Mi
P0
P_lb
P_ub
r1Mr2
resnorm
time
C
P_result
data
ans
FittingResultName
time_ode
Y
S
16
odeSolver.m
%Codes reported in TPL, ABC, HYC, and RHG, JACS 2017,
DOI: 10.1021/jacs.7b00791
.
function
y = odeSolver(k, time)
load
constants
[t,Y]=ode45(@(t,Y) model(t,Y,k), time, Mi);
y=Y(:,1:2);
time_ode=t;
save(
'AllResult'
,
'Y'
,
'time_ode'
)