Supporting Information
Formation of Triblock Copolymers via a Tandem Enhanced Spin
Capturing – Nitroxide Mediated Polymerization (ESC-NMP)
Reaction Sequence
Thomas Junkers,*,1,2 Lin Zang,1 Edgar H. H. Wong,1,3Nico Dingenouts,4
Christopher Barner-Kowollik*,1
1
Preparative Macromolecular Chemistry, Institut für Technische Chemie und Polymerchemie,
Karlsruhe Institute of Technology (KIT), Engesserstrasse 18, 76128 Karlsruhe, Germany.
2
Institute for Materials Research, Universiteit Hasselt, Polymer Reaction Design Group,
Agoralaan, Gebouw D, B-3590 Diepenbeek, Belgium.
3
current address: Department of Chemical and Biomolecular Engineering, The University of
Melbourne, Parkville, Victoria 3010, Australia.
4
Polymeric Materials, Institut für Technische Chemie und Polymerchemie, Karlsruhe Institute
of Technology (KIT), Engesserstrasse 18, 76128 Karlsruhe, Germany
Correspondence to: C. Barner-Kowollik (E-mail: christopher.barner-kowollik@kit.edu), T.
Junkers (E-mail: thomas.junkers@uhasselt.be)
SAXS Measurements of the Block Copolymers
Small-angle s-ray scattering (SAXS) measurements were carried out using a high-flux smalland wide-angle X-ray scattering camera S3-Micro (Hecus X-Ray Systems, Graz, Austria)
equipped with a high-brilliance micro-beam delivery system, operating at a low power of 50
W (50 kV and 1 mA), with point-focus optics (FOX3D). The X-ray wavelength λ was 1.54 Å
and the SAXS-curves were recorded with a 1D-detector (PSD-50, Hecus X-ray Systems,
Graz, Austria). Contrasts were calculated out of density measurements performed with a
density meter DMA 5000 M from Anton Paar GmbH offering an accuracy of 510-6 g cm-³ for
the density of solution between 0.5 and 2.0 g cm-³.
(A) Density Measurement
To determine the specific volume v2’ of the polymer in the solvent, concentration series of
both block copolymers and the pure solvent (tetrahydrofuran) were measured. From the
regression of the density against the concentration one can calculate the density of the
polymer in the appropriate solvent.
Concentrations used
for density
measurements [g L-1]
Regression ρ(c)
Sample I
Sample II
0, 1.31, 3.43 and 5.077
0, 1.074, 3.135 and 4.967
0.887526 + 0.1709167  c
0,887549 + 0.1681032  c
0.8875
0.8875
1.0705
1.067
0.934
0.937
Density of solvent
[g/cm³]
(tetrahydrofuran)
Density polymer ρ
[g/cm³]
Specific volume v2
[cm³/g]
(B) Contrast Factor for Block Copolymers
The contrast factor KX,E in X-ray scattering is given as follows:
;
where NA is Avogadro’s constant and M the molecular weight. Δz2 accounts for the contrast
between solvent and polymer and is calculated according:
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M·z2 is the number of electrons in one molecule. For homopolymers z2 can be readily
calculated using MMono and the number of electrons ne,M from the monomer unit:
For block copolymers consisting of two blocks with different monomers – as in the present
case – z2 can be calculated via the same starting formula, yet the final result using both
monomer properties is more complicated (i.e. an average monomer unit will not lead to the
same result), thus
with
For a block copolymer, the contrast factor becomes a function of the composition ΦB1 of the
polymer which implies that additional information is required for the evaluation of the data.
Or – in other words – the scattering intensity can be expressed using a molecular-weight and
composition depending number Kx,M (M, ΦB1):
The final result of the scattering experiment for block copolymers is the above molecular
weight and composition depending factor. With additional information about the composition
or the molecular weight, it is possible to deduce absolute molecular weights (see below).
For the both block polymers under examination one obtains:
MMono
ne,M
Specific volume v2
[cm³/g]
Z2 (for composition
1:1)
KX,E (for
composition 1:1)
Block 1 (styrene)
104.15 g mol-1
56
Block 2 (tert-butylacrylate)
128.17 g mol-1
70
Sample I
Sample II
0.934
0.937
0.5419 mol g-1
0.5419 mol g-1
4.0410-3 mol g-²
3.89 10-3 mol g-²
(C) Calibration for Obtaining Absolute Scattering Intensities
The calculation of absolute intensities is carried out by measuring the primary beam with a
Ni-attenuator before and after each single measurement. Subsequently, one can calculate
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absolute scattering intensities
and sample adsorption.
[S1]
employing known values for the detector size, beam size
Additional recalibration of these intensities is carried out via the determination of the forward
scattering of standard liquids – here tetrahydrofuran – the solvent used for the scattering
measurements. Employing the measured density (0.8875 g cm-³) and the isothermal
compressibility[S2] κT (8,895E-04 MPa-1) of tetrahydrofuran at 25 °C, a forward scattering of
I(0)=318 nm-3 is obtained (I(0)=ρe2·kB·T·κT). With this value one can recalibrate the
calculated absolute intensities to achieve well defined absolute values for the scattering
intensity.
[S1]: S. Polizzi, N. Stribeck, H.G. Zachmann and R. Bordeianu; Coll. Polym. Sci. 267, 28191, (1989).
[S2]: A.K. Nain; Inversion of the Kirkwood–Buff Theory of Solutions: Application to
Tetrahydrofuran and Aromatic Hydrocarbon Binary Liquid Mixtures; J. Solution Chem. 2008,
37, 2008, 1541-1559.
(D) Scattering Intensity with a Concentration Series
Both block copolymers were measured at three concentrations and the scattering intensities
were corrected for absolute intensities (see (C), above). The following figure shows the
scattering intensity for the three measured concentrations and the solvent for the block
copolymer Sample II:
C3
C2
C1
THF
3
I(q) [e.u./nm ]
2000
1000
0
0.5
1.0
1.5
2.0
-1
q [nm ]
Figure S1. Scattering intensities of a concentration series (1.07, 3.14, 4,97 g L-1) of Sample II
in tetrahydrofuran. The concentration dependence can be readily identified at low scattering
vectors q. All concentrations and the solvent runs converge on a common value for high
scattering vectors are as expected.
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All scattering curves are corrected for solvent scattering. Subsequently, they can be used to
construct a Zimm-diagramm resulting in the molecular weight of the block copolymer.
(D) Molecular Weight Determination via a Zimm Diagramm
Using a theory similar to the one normally employed in static light scattering (also known as
Zimm-Expression) one can express the concentration dependence and q-dependence of the
scattering intensity for small scattering vectors q and small concentrations c with the
following formulas (Mw: weight average of the molecular weight; A2: second virial
coefficient; RG: Radius of gyration):
A graph of Kc/I(q) against q²+K1·c (K1 a arbitary constant) is known as Zimm-Diagram and
allows to perform both extrapolations in one diagram.
y(c->0)= 0.000605 *x + 2.648E-05
c -> 0
y(q->0)= 4.335E-05 *x + 2.570E-05
q² -> 0
c= 15.30 g/l
c= 10.00 g/l
c= 4.30 g/l
K  c / I(q) [mol/g]
0.00020
0.00015
0.00010
0.00005
0
0.5
1.0
2
1.5
-2
q + 0.100000  c [cm +g/l]
Figure S2. “Zimm-diagram” of Sample II in tetrahydrofuran. Using double extrapolation to
zero scattering angle and zero concentration as well as a regression of the extrapolated
intensities (see legend within figure), one obtains the molecular weight, the radius of gyration
and the second virial coefficient.
-5-
y(c->0)= 0.000344 *x + 4.898E-05
c -> 0
y(q->0)= 9.020E-05 *x + 4.866E-05
q² -> 0
c= 16.30 g/l
c= 11.30 g/l
c= 6.60 g/l
K  c / I(q) [mol/g]
0.00020
0.00015
0.00010
0.00005
0
0.4
0.8
2
-2
q + 0.050000  c [cm +g/l]
Figure S3. “Zimm-diagram” of Sample I in tetrahydrofuran. Using double extrapolation to
zero scattering angle and zero concentration and a regression of the extrapolated intensities
(see legend within figure), one obtains the molecular weight, the radius of gyration and the
second virial coefficient. Here the smoothed data is presented, resulting in a molecular weight
of 20500, the unsmoothed data gives 22000, on average 21300 g mol-1.
From the Zimm-diagrams one can calculate the following results:
Second Virial Coefficient
A2
Radius of Gyration
Mw (for composition 1:1)
Sample 1
Sample 2
2.25510-6 mol cm³ g-²
2,16710-3 mol cm³ g-²
4,6 nm
8,3 nm
86.11 g-1
149.3 g-1
21 300 g mol-1
38 300 g mol-1
(E) Molecular Weight Determination of the Block Copolymers
As already discussed in section (C), the contrast factor KX,E in X-ray scattering is, for
copolymers, a function of the composition of the polymer. From the Zimm diagram one
receives the product from this factor KX,E(B1) and the weight average molecular weight, Mw.
There are three possibilities for further evaluation:
1. Assuming a block copolymer composition of 1:1
2. Taking the composition from an alternative method
One possibility is the SEC measurement of the first block alone and of the whole
copolymer. Now one knows the composition B1 and therefore also the molecular
weight Mw. (Disadvantage: the calibration used for the SEC. If one employs only
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polystyrene standards, the results for the determined molecular weight and for the
composition can be unreliable).
3. Taking the molecular weight of the first block from an alternative method
In both samples under SAXS investigation, the first block of the copolymer was
polystyrene. Therefore, one has reliable SEC values for the first block. Subsequently
one can vary the composition until the Zimm-diagram delivers the same molecular
weight for the first block. In this case, one receives the composition and the total
molecular weight from the copolymer from the scattering data.
In the final table, the three methods are compared
Method
1
Assuming 1:1
composition
2
Composition
from SEC
3
MPS from
SEC
Mw (Sample I)
Results from SAXS
Assumption
Mw
MPS
B1
Assumption
Mw (Sample II)
Results from SAXS
Mw
MPS
B1
Composition
1:1
21 300
10650
-
Composition
1:1
38 300
19150
-
B1=0.4
20 867
8350
-
0.47
38 059
17 888
-
MPS= 8900
20 971
-
0.4244
MPS= 17900
38 062
-
0.4703
The best method appears to be method number 3, therefore these values are marked in bold.
For the block copolymers under consideration, it is evident that the influence of the
composition and therefore from the molecular weight is small and therefore all methods
deliver comparable results.
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