Polyolefins formed by chain walking catalysis - a matter of branching

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Polyolefins formed by chain walking catalysis - a matter of branching density only? Ron Dockhorn, Laura Plüschke, Martin Geisler, Johanna Zessin, Peter Lindner, Robert Mundil, Jan Merna, Jens-Uwe Sommer, and Albena Lederer J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.9b06785 • Publication Date (Web): 23 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019

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Journal of the American Chemical Society

Polyolens formed by chain walking catalysis - a matter of branching density only? †,k

Ron Dockhorn,

Peter Lindner,

¶

Laura Plüschke,

Robert Mundil,

§

†,‡,k

Martin Geisler,

§

Jan Merna,

Albena Lederer

†Leibniz

†,‡

†,‡

Johanna Zessin,

Jens-Uwe Sommer,

∗,†,‡

and

∗,†,‡

Institute of Polymer Research Dresden, Hohe Strasse 6, 01069 Dresden, Germany

‡Technische ¶Institute §University

Universität Dresden, 01069 Dresden, Germany

Laue-Langevin (ILL), 6 Rue Jules Horowitz, 38042 Grenoble, France

of Chemistry and Technology Prague, Technická 5, 16628 Prague 6, Czech Republic

kBoth

authors contributed equally to this work

E-mail: [email protected]; [email protected]

Abstract Recently developed chain walking (CW) catalysis is an elegant approach to produce materials with controllable structure and properties. However, there is still a lack in understanding, how the reaction mechanism inuences the macromolecular structures. In this study, series of dendritic polyethylenes (PE) synthesized by Pd-αdiimine-complex through CW catalysis (CWPE) is investigated by means of theory and experiment. Thereby, the exceptional ability of in-situ tailoring polymer structure by varying synthesis parameters was exploited to tune the branching architecture which allowed to establish a precise relationship between synthesis, structure, and solution properties. The systematically produced polymers were characterized by state-of-the-art multidetector separation, neutron scattering experiments 1

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as well as atomic force microscopy to access molecular properties of CWPE. On a global scale, the CWPE appear in a worm-like conformation independently on the synthesis conditions. However, severe dierences in their contraction factors suggested that CWPE dier substantially in topology. These observations were veried by NMR studies that showed that CWPE possess constant total number of branches but varying branching distribution. SANS experiments gave access to structural characteristics from global to segmental scale and revealed the unique heterogeneity of CWPE which is predominantly based on dierences in their dendritic side chains. The experimental data were compared to theoretical CW structures modeled with dierent reaction-to-walking probabilities. Simple theoretical arguments predict a crossover from dendritic to linear topologies yielding a structural range from purely linear to dendritic chain growth. Yet, comparison of theoretical and empirical scattering curves gave rst evidence that actually a transition state to worm-like topologies is experimentally accessible. This cross-over regime is characterized by linear global features and dendritic local sub-structures contrary to randomly hyperbranched systems. Instead, the obtained CWPE systems have characteristics of disordered dendritic bottle brushes and can be adjusted by the walking rate/reaction probability of the catalyst.

Introduction The revolutionary concept of chain walking mechanism leading to dendritic type of branching was rst realized by Brookhart in 1995 merizing ethylene and

α-olens.

1

and by Guan in 1999

2

for poly-

Unlike before, polyethylene (PE) with high molar mass

and narrow dispersity was accessible through a one-pot reaction and, even more remarkable, the molecular properties of the products could be easily tuned by adjusting synthesis conditions, e.g. pressure and temperature. The key to controllability lies within the chain walking (CW) mechanism performed by the Pd(II)-α-diimine catalyst.

3

In there, the structure dening step is the competition between chain walking within the macromolecule and monomer insertion at potential reaction pathways, which can be manipulated through synthesis variation. Numerous studies focused on determining

2


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molecular properties of polyethylene obtained from CW catalysis (CWPE) using techniques such as size exclusion chromatography (SEC), nuclear magnetic resonance (NMR) spectroscopy, matrix assisted laser desorption ionization-time of ight-mass spectrometry (MALDI-TOF-MS) and small angle neutron scattering (SANS).

4

Furthermore, rheology

measurements were performed to investigate ow behavior of CWPE, which is indicative of macromolecular topology.

5

Based on early empirical data, three classes of CWPE have

been discussed that appear depending on dierent reaction conditions: linear, moderately branched and hyperbranched.

612

We note that randomly hyperbranched polymers based

on ABn -polymerization are a distinct universality class of branched polymers, which are qualitatively dierent from dendrimers in their properties. and Tomalia

14

13

Already in 2001, Fréchet

reconsidered Guan's explanation and used the term dendrigraft instead

of hyperbranched emphasizing a bottle-brush-like structure possibly obtained within CW catalysis. Nevertheless, it was a widely accepted assumption in the past that the CW-mechanism leads to structurally broadly dispersed polymer topologies ranging from linear to extensive branch-on-branch structures which were associated with randomly hyperbranched polymers rather than with dendrimers or dendrigrafts. routes of synthesis were elaborated,

15

rarely simulations

1618

2,4,15

While many

of that approach were per-

formed, and certainly not in correlation to analytical experiments. First simulations by Chen et al.

16

indicate a transition behavior from a linear to a globular dendritic structure

depending on the parameters of the catalysis. However the data do neither emphasize any intermediate regime nor a theoretical model is oered. Simulations by Michalek and Ziegler

17

proposed again a highly branched regime (called again hyperbranched) but

without precise denition of the structure. Patil et al.

18

found in their simulation, that

the size of the polymer grows logarithmically as a function of the molecular weight. Furthermore, they mentioned a cross-over to linear (ideal) chain statistics for other parameters. The transition region and the logarithmic growth (indicating dendritic structures) is rarely discussed and due to the lack of the solvent eect (excluded volume) in these simulations no direct comparison to experiments can be made. In this work, we combine state-of-the-art structural characterization using multi-

3



detector size exclusion chromatography

19

Page 4 of 29

(SEC-D4) including dierential refractive index

(dRI), multi-angle laser light scatterng (MALLS), dynamic light scattering (DLS) and solution viscosity detector (VISCO) detectors, small angle neutron scattering (SANS), and atomic force microscopy (AFM) of precisely synthesized CWPEs. Furthermore, we performe Monte Carlo simulations under good solvent conditions to generate theoretically modelled CW structures. Thus, this study aims for a rst time to experimentally validate theoretical considerations of the process which controls the formation of the topology, recties branching formation potential of CW catalysis and shines light onto the internal and global structure of this specic type of dendritic molecules. The main nding of our work is that CW catalysis ultimately leads to bottle-brush-like molecules for suciently long time of synthesis and for suciently high walking rates. Using theoretical concepts supported by extensive simulations we also clarify the topological classes which can emerge and we show that CW catalysis is a suitable method to obtain dendritic polymers.

Results And Discussion Scaling of CW structures in good solvents To clarify the dierence between dendrimers, randomly hyperbranched (rHB) polymers, CW-structures and linear chains, we used computer simulations to calculate the radius of gyration

Rg

as function of the monomer units

N

of the polymers in athermal solvent and

under full excluded volume conditions. In Figure 1A, these calculations are summarized, rescaled by the average bond length

b.

The radius of gyration for linear chains scales as:

Rg ∼ N ν

with

ν ' 0.588 being Flory-exponent for linear chains in good solvent. 20

(1)

This is indicated

as a black dashed line in Figure 1A. For comparison, we also display results for regular trifunctional dendrimers with dierent spacer length between the branching points (S

4


=1

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or 2) showing a mixed logarithmic-power-law behavior, as predicted by mean-eld theory (Supporting Information (SI), Equation 17). This particular behavior of dendrimers

13,21

led to confusion if interpreted as a pure power-law and explains the occurrence of various apparent scaling exponents reported before

22

varying from

1/5; 1/3

the scaling behavior of rHB polymers is still debated in theory where power laws with exponents between eld model presented in a previous work

Rg ∼ N 2/5 ,

1/3

13

and

1/2

23,24

to

0.6.

Similarly,

and experiment,

25,26

have been reported. The mean-

predicts the relation for rHB polymers as

which is supported by simulation ndings (Figure 1A and SI, Figure S13).

Scattering experiments of starch consisting of highly branched amylopectin suggest values of

0.39 27

and

0.37 − 0.49 28 , and for dextran a value between 0.30 − 0.43 29 , which are close

to the proposed exponent of

2/5.

In contrast, the CW-structures generated by the simulation show fundamentally different behaviors as compared with rHB polymers. The essential parameter characterizing the reaction-walking process is the walking rate

w, which we dene as the inverse probabil-

ity to perform a reaction event if the catalyst is located at a reactive site of the molecule. The chain walking rate is proportional to the number of steps the catalyst is walking on the molecule without performing a new synthesis event. At high walking rate

w1

the structures show a mixed logarithmic-power-law behavior characteristic for a dendritic growth, which can be tted by SI Equation 17. In this case, the catalyst can reach any reactive site on the entire structure before adding a monomer. Thus, the growth of the structure corresponds to the addition of single monomers at random places and leads to isotropic growth formed by all reactive sites. As we have shown in our previous work,

13

this yields molecules, which can be considered as imperfect dendrimers containing defects in their structure, which explains the observed fractal dimension et al

16

> 3 in the work of Chen

This can be easily understood by considering a Bethe-lattice as the native space in

which the topology of a branched molecule is created. Adding monomers at any reactive site with the same probability leads to spherical growth on the Bethe-lattice and thus, exponential growth of the mass of the structure with respect to its molecular diameter. In contrast, at low walking rate

w '1

the CW algorithm forms structures with linear

5



Page 6 of 29

topology. This case can be explained as follows. The catalyst now performs unrestricted random walking on the Bethe-lattice regardless whether it reaches the boundary of the existing structure or not. This mechanism would result in a linear topology, except for short branching which results for immediate return events of the walking catalyst. In Figure 1A, we display the radius of gyration of the CW structures for various walking rates

w,

which we obtained from our simulations in a double-logarithmic repre-

sentation. For CW structures at to linear chains with

w = 1,

ν = 0.588.

it is clearly visible that their slope is equivalent

On the other hand, the structures for high walking

rates show the behavior of dendrimers. Snapshots of the simulated structures for various walking rates are displayed in the upper part of Figure 1. Obviously, the two limiting cases have to merge for intermediate values of low molecular weight molecules and moderate to high walking rate

w 1,

w.

For

the emerging

structure is small enough to be explored by the catalyst before adding the next monomer. In this case, the monomer can be attached on every position in the structure leading to isotropic dendritic growth.

At a characteristic length scale

the catalyst cannot explore the entire structure. typical thread-length of a dendritic blob.

ξ(w)

depending on

w,

This length scale is related with a

A detailed explanation is given in the SI.

This thread length corresponds to the average diusive path the catalyst takes between two successive reaction events.

The idea of the dendritic blob model is sketched in

Figure 2. If the degree of polymerization is much smaller then this path, the dendritic topology dominates. In Figure 1A, this behavior can be clearly seen for high

w,

where

the radius of gyration follows a dendritic behavior. As the degree of polymerization is equal to the size of the path, the catalyst cannot cross the full structure within

w

steps.

Following our argument above, the catalyst tends to form a linear topology, however, containing dendritic sub-structures due to large excursion on the existing structure. Accordingly, we obtain disordered, dendritic bottle-brush molecules, as is also supported by the simulation snapshots.

Since the degree of polymerization of the dendritic sub-

structure grows exponentially with

w,

(SI, Equation 21) the crossover towards a linear

object can be shifted to extremely high molar masses for high values of

6


w.

This is the

Page 7 of 29

CW w=2

CW w=5

CW w=10

CW w=13.33

dendrimer G9 S2 f3

CW w=100

rHB

2

10

⊗

⊗

⊗

⊗ 0

Rg [b]

10 1 10 1

10

⊗

❖ ❉ ★ ✖

2

10

4

⊗

⊗

10 ⊗ ⊗ ⊗

✖ ❖ ❉ ✖❖ ❉❉ ❖ ❉❖ ❖ ✖ ❉ ⊗ ❖ ❉ ★ ❖ ✖ ⊗ ❖ ❉❉ ★ ❖ ✖ ⊗ ❖ ❉❉ ★ ❖ ❉ ✖ ⊗ ★ ❖ ❉ ❖ ✖ ⊗ ❖ ❉❉ ★ ❉ ★ ⊗ ✖❖ ❖ ❉ ❖ ❉ ★ ❉ ✖★❖ 1/5 2/5 Rg~N ·[ln(N)]

Linear Chain CW w=1 CW w=2 CW w=3 CW w=5 CW w=6.66 CW w=10 CW w=13.33 CW w=20 CW w=100 CW w=1000 Dendrimer S=1 Dendrimer S=2 slope Rg~N

3

10

1/3

★

Linear Chain CW w=1 CW w=2 CW w=3 CW w=5 CW w=6.66 ★ CW w=10 CW w=13.33 CW w=20 CW w=100 CW w=1000 Dendrimer S=1 Dendrimer S=2

⊗

B -0.764

1

10

-1

10

⊗

-2

❖ ❉ ★ ✖

10

[η]·N

A

⊗ ⊗

increasing chain walking rate

rHB slope 2/5

slope Rg~N

⊗ ⊗⊗⊗ ⊗ ⊗ ⊗⊗ ⊗⊗ ⊗⊗ ⊗⊗ ⊗⊗ ⊗⊗ ✖ ❉ ❖ ❉✖ ★ ❖ ❖ ❉ ❉ ✖ ★❖ ❖ ❉ ❖ ★❉ ✖ ❖ ❉ ❖ ★❉ ✖ ❖ ❉ ❖ ❉ ✖ ★ ❖ ❉ ❖ rHB ❉ ✖ slope -0.564 ★ ❖ ❉

1/3

-1

10 -3

10

-2

10

★

❖ ❉ ❖✖ ❉❖ ❉ ★

-3

-4

10

10

1

2

10

10

3

4

10

10

-2/5

[η]~N

increasing chain walking rate

2

10

❖ ❉ ✖ ❖ ❉ 6/5

·[ln(N)]

0

10 0 10

1

2

10

3

10

4

10

0

10

1

10

2

10

3

10

N

4

10

10

N

2

10

1

10

D r ea

n ai ch

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ★ ❖ ❖ ❖ ★ ❖ ❖ ★ ❖ ❖ ❖ ★ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ★ ✖ ❖ ❖★ ❖ ❖ ❖ ★ ❖ ✖❖ ❖ ❖ ★ ❖ ❖ ❖ ✖ ❖ ❖ ❖ ❖ ✖ ★ ❖ ❖ ❖ ★ ❖ ❖ ✖ ❖ ★ ❖ ❖ ★ ❖ ❖ ✖ ❖ ★ ❖ ❖ ★ ✖ ❖ ★ ❖ ✖ ★ ❖ ❖ ✖ ★ ❖ ★ ✖ ❖ ★ ❖ ✖ ★ ★ ✖ ★ ✖ ★ ★ ✖ ★ ★

-0.764

Rg [nm]

C

linear chain

lin

-2

10

[η]·M

CWPE1 CWPE2 CWPE3 CWPE4 ✖ CWPE5 CWPE6 CWPE7 ★ CWPE8 ❖ CWPE9 CWPEx

✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ✖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★ ★ ❖ ★ ★ ❖ ❖ ❖ ❖ ❖ ❖ ★ ★ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★ ★ ★ ★ ★ ★ ★ ★

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ er

CWPE1 CWPE2 CWPE3 CWPE4 ✖ CWPE5 CWPE6 CWPE7 ★ CWPE8 ❖ CWPE9 CWPEx

rim nd de

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-3

4

5

10

10

10

Figure 1: (A) Radius of gyration, rates

w

10

6

M [g/mol]

Rg ,

5

10

6

M [g/mol]

10

of CW-structures obtained by dierent walking

for various degree of polymerization

corresponding snapshots with

4

10

N = 3072

N

in computer simulations, see also the

above. Results for linear polymer chains, rHB,

and perfect dendrimers are plotted for comparison. (B) Predicted intrinsic viscosity, [η], rescaled by linear chain behavior, [ηL ∼ N −0.764 ], for CW-structures with excluded volume. Here we used the Flory-Fox equation (SI, Equation 19). The inset displays the results for randomly hyperbranched polymers. (C) (D) Rescaled

[η] as a function of M .

Rg

as a function of molar mass

M.

Experimental data (C, D) obtained by HT-SEC-D4.

7



reason why we do not observe linear structures for

Page 8 of 29

w > 10 in our simulations (Figure 1A).

We note that very dense dendritic bottle-brushes can be obtained for higher values of

w if

the reaction proceeds for suciently long time to form high molecular weight molecules. low walking rate linear chain

moderate walking rate disordered dendronized bottle-brush

high walking rate disordered dendrimer high generation

Figure 2: Sketch of the structures obtained by the chain walking mechanism at dierent chain walking rates

w

of the catalyst. For low walking rate/long reaction times a linear

structure emerges while on smaller time-scales walking dominates leading to dendritic topology. The resulting structure corresponds to a disordered dendronized bottle-brush becoming denser for higher chain walking rates

w. The scale in the dendritic blob model ξ , grows with the average number of

which characterizes the dendritic sub-structure,

walking steps between two successive reaction events.

Size and solution viscosity A library of ten samples has been prepared using the Pd-α-diimine catalyst (SI, Figure S1) with systematical variation of the reaction parameters pressure, temperature, time, and catalyst concentration (see Table 1).

The novel architecture of CWPE, which is

a result from the catalyst´s working principle, is characterized by a remarkably high branch-on-branch structure. ify in an amorphous state.

This specic architecture enables the molecules to solidTherefore, the polymers are soluble in common laboratory

solvents at moderate conditions, which clearly simplies the molecular characterization of CWPE, when compared to common polyolens. While THF was used for SEC and SANS experiments at room temperature (RT-SEC), high temperature SEC (HT-SEC-D4) was performed in 1,2,4-trichlorobenzene (TCB) allowing also for comparison to linear PE. Both solvents have been reported as good solvents for CWPE in the past.

8

Multi-detector

SEC is a standard analytical technique which gives an array of molecular properties resolved by the hydrodynamic volume of the analyte.

Classical triple detection implies

MALLS, VISCO and dRI instruments. Adding DLS detection has the advantage of simultaneous determination of three dierent radii, namely the radius of gyration,

8


Rg ,

the

Page 9 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


hydrodynamic radius,

RH , and the radius by intrinsic viscosity, Rη , in addition to the mo-

lar mass determination.

19

Molecular parameters obtained from multi-detector RT-SEC

in THF and quadruple-detector HT-SEC-D4 in TCB are listed in Table 1 and SI, Table S2, respectively. Unless stated otherwise, the characterization of CWPE on global scale refers to HT-SEC-D4 in TCB from this point. Table 1: Molecular properties of dendritic PEs determined by HT-SEC-D4 in TCB at a 150°C. Sample

p

[bar]

T

[°C]

t

[h]

CWPE1

7

0

20

CWPE2

7

0

7

CWPE3

7

0

3

CWPE4

7

10

20

CWPE5

0.14

0

7

CWPE6

0.14

0

20

CWPE7

0.14

10

20

CWPE8

0.14

35

20

CWPE9

0.05

0

20

CWPEx*

0.05

0

20

Mw [kg/mol] 173.0 ± 4.9 54.6 ± 2.4 23.9 ± 0.3 383.1 ± 7.9 68.0 ± 1.2 168.9 ± 0.7 383.5 ± 1.9 232.6 ± 1.9 157.0 ± 1.5 157.4 ± 2.4

Mw /Mn 1.05 1.10 1.09 1.12 1.03 1.08 1.18 1.38 1.03 1.12

Rg [nm]b 18.5 ± 0.2 10.5 ± 0.2 8.0 ± 0.3 30.4 ± 0.3 8.6 ± 0.6 12.9 ± 0.1 19.4 ± 0.1 15.1 ± 0.1 10.9 ± 0.1 11.5 ± 0.1

RH [nm]c Rη [nm]b [η] [mL/g]d 13.5 ± 0.7 16.1 ± 0.2 145.0 ± 3.3 excluded 8.3 ± 0.1 60.6 ± 0.3 excluded 5.1 ± 0.1 33.2 ± 0.3 21.9 ± 0.3 24.8 ± 0.1 227.1 ± 1.1 excluded 7.15 ± 0.1 32.8 ± 0.2 10.5 ± 0.1 11.5 ± 0.1 54.3 ± 0.2 16.2 ± 0.1 17.6 ± 0.1 78.9 ± 0.4 11.5 ± 0.1 13.4 ± 0.1 47.5 ± 0.4 9.3 ± 0.1 10 ± 0.1 39.0 ± 0.4 9.6 ± 0.1 10.3 ± 0.1 40.9 ± 0.5

a

b All averages and uncertainties calculated from triple determination. z-average values. c d Uncertainty weighted-average values. Weight-average values. *Catalyst concentration of CWPEx is

0.6mg/mL

in contast to CWPE1-9 (0.3 mg/mL).

Although the absolute range of molar mass is quite broad with

384 kg/mol

Mw

from 24 to

depending on the reaction time, the molar mass distribution is narrow with

polydispersity index

D = 1.03 − 1.38. This low value veries the nature of the living poly-

merization that is performed by the CW catalyst. The radii determined by SEC display dierent size ranges with

Rg = 8.0−30.4 nm, RH = 9.3−21.9 nm, and Rη = 5.1−24.8 nm.

It is noteworthy that samples CWPE2, CWPE3, and CWPE5 partly exceed the resolution limits of SEC-MALLS (>

10 nm)

but have only been excluded for

RH

due to high

statistical errors resulting from low intensities. The molar mass dependency of Figure 1C. The results for

RH

and

Rg Rη

is given by the double-logarithmic scaling plots in are displayed in SI, Figure S2. From the double

logarithmic representation a slope can be retrieved which is expressed as the power law exponent

ν,

see Equation 1.

We emphasize that many macromolecules, like CWPE,

do not show self-similarity and the local exponent varies with molar mass.

30

Hence,

the interpretation of the slope and its physical meaning has to be considered with care.

9



Experimentally obtained values for the apparent exponent

Page 10 of 29

ν determined from scaling plots

are summarized in SI, Table S3. Based on previous studies, CWPE is expected to display a high branching density from synthesis with low pressure and/or elevated temperature. Reaction pressure controls the ethylene concentration in the experimental setup.

2,5

Low

pressure (i.e., low ethylene concentration) shifts the equilibrium of the catalyst state strongly towards the chelate complex, which inhibits monomer trapping and consequently promotes a high chain walking rate

w.

Likewise, elevated reaction temperature promotes

chain propagation relative to ethylene trapping and insertion resulting in topologies with high branching, again related with a higher walking rate. In Figure 1D, the intrinsic viscosity

7

[η] in the Kuhn-Mark-Houwink-Sakurada (KMHS)

plot with respect to linear chain and dendrimer scaling is presented. The experimental data show two regimes depending on the pressure. While high pressure analytes follow linear chain behavior by displaying a constant plateau, CWPE from low pressure displays a decrease of

[η]

that is related to the progressive compactness of the growing polymer.

Although rather marginal, the trend in the KMHS plot is also present at high pressure systems. Interestingly, theoretical (1B) and experimental data (1D) show a good systematic agreement in the rescaled KMHS plot. All systems display the behavior simulated for CW structures, whereas high and low pressure CWPE correspond to a lower and higher walking rate. A rather minor inuence of reaction time and temperature is observed as no transition between dendritic and linear regime can be triggered for moderate chain walking rates.

Branching Dendritic polymers are typically characterized by their degree of branching (DB ), calculated by linear, dendritic and terminal units using NMR.

3133

This denotes the relative

number of branching points but disregards further correlation between branching points and is therefore only an incomplete measure with respect to the topology. As an example, we note that linear chains where each monomer is bearing one methyl-group lead to

DB = 0.5, but this structure is clearly dierent from rHB polymers although showing the

10


Page 11 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


same degree of branching. CW structures obtained in our simulations show a plateau-like behavior of the degree of branching as a function of number of monomers in the molecule (SI, Figure S15), where the plateau-value increases with the walking rate and reaches a maximum value of about of

CH3 -groups,

Figure S7).

0.8 for

walking

w > 4. 1 H -NMR

results on the relative number

show little variation depending on reaction conditions (Figure 3 and SI,

Further, based on the analyses of

13

C -NMR

observed for the distribution of short chain branches (≤

spectra, very little change is

C6)

per 1000C (SI, Table S4).

Most noteably, an increase of the CW probability causes a reduction of methyl branches but enhances the quantity of longer branches (C6+) and the ndings from previous NMR studies on CWPE. this indicates that walking rates below

8,9

sec-butyl units, which conrms

In comparison to the simulations,

w ' 3−4 do not occur during synthesis.

Moreover,

it demonstrates that topological properties are not solely determined by the number of branching points.

3437

Therefore, additional dierentiation between linear and branched

counterparts should be found. Zimm and Stockmayer

38

quantied the reduction of radius of branched macromoleculeRgBRA

to an equivalent linear chain

RgLIN

introducing the so called contraction factor

tion 7). Shortly after, this concept was transferred to

g0

(SI, Equation 8).

[η]

g (SI, Equa-

by Stockmayer et al.

Besides the requirement of a linear analogue,

g

and

39

g0

yielding

are valid

under the following terms: (1) chemical equality, (2) overlap of molar mass distribution (MMD) of both entities and (3) uniformity of the type of branching across the MMD. To determine contraction factors, theoretical models

41,42

40

were used as linear reference,

which have clear advantages over using a linear sample. Figure 3 and Table S3 show the contraction factors

g

and

g0

of CWPE. Naturally, both parameters show a molar mass

dependency and decrease with increasing the range between

0.15 − 0.48

and for

g0

Mw . 43,44

between

The weight-average value for

0.12 − 0.45,

g

is in

respectively. Unlike exper-

imentally obtained values, these data demonstrate that CWPE has extremely high compactness. For comparison, polystyrene stars with four to 18 arms exhibit and

g 0 = 0.76 − 0.35,

respectively.

contraction factors lower than

45

Hyperbranched polyesters with

g, g 0 = 0.3. 46

g = 0.63 − 0.23

DB = 0.50

display

However, none of these demonstrate such a

11



Page 12 of 29

pronounced contraction as CWPE. In fact, CWPE8 showing the lowest values of and

g 0 = 0.12,

reaches at high molar mass a contraction of more than

g = 0.15

90% relative to the

linear model. This compact topology is a result of the working principle of the CW catalyst. As previously discussed, distinct reaction conditions cause a scenario in which the trapping and insertion of ethylene is restricted resulting in enhanced chain walking. The walking distance between two monomer insertions increases and allows a statistically distributed translocation of the catalyst within the molecule. Compared to hyperbranched polymers, which are synthesized by step- or chain-growth approach, CWPE are superior as the CW catalyst is in principle able to insert new monomers at any position of the polymer (tertiary C-atoms excluded) due to the profound mobility. The moving pattern of the CW catalyst will create linear structures with dendritic sub-structures, as discussed above. For long reaction times and low pressure, this behavior will result in elongated CW structures with high number of dendritic sub-branches. The relation between synthesis conditions and

g, g 0

is given in Figure 3.

Figure 3: Contraction factors

g

(pink squares),

(black circles), apparent segmental density

dAPP

g0

ε NBr

(red squares), drainage exponent

(blue triangles), branching number

(green pentagon) and long-chain branching (orange triangles) of CWPE as a function of synthesis conditions. All results are weight-average values determined by HT-SEC-D4 in 1 1,2,4-TCB at 150°C. NBr was obtained from H -NMR.

12


Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


As already observed in the behavior of

[η],

high pressure demonstrate clear dierence.

0.15 (g 0 = 0.12) CWPE9 (p

and CWPE1 with

= 0.05 bar)

the structures obtained from low and

The two extrema are CWPE8 with

g = 0.42 (g 0 = 0.45).

g =

It should be noted, that

does not show the highest contraction but CWPE8, a system

obtained from low pressure and high temperature. Both parameters contribute oppositely to topological properties of the resulting molecule. While with increasing temperature, the catalyst's walking is enhanced (also the propagation rate), increasing the pressure promotes the insertion of ethylene.

4,7

Combining low pressure and high temperature

leads to the formation of CWPE with the highest branching density. The contraction factors are correlated by the drainage exponent From theory,

ε

is limited to

0.5 − 1.5. 39,47

or molecules with low amount of branching.

Values with

ε ∼ 1.0

ε dened as: g 0 = g ε .

ε ∼ 0.5

correspond to stars

are found for statistically branched

polymers. Comb-shaped macromolecules and other densely branched systems display

ε∼

1.5. 48

For

In previous work,

44,49

we found that

CWPE, the contraction factors while

ε

g

and

does not (see Figure 3).

g0

ε correlates with the degree of branching.

show a strong dependency on synthesis variation

This demonstrates that synthesis variation in CW

catalysis interferes with the branching topology rather than with the number of branching. Additionally,

NBr conrms this conclusion showing similar trend as ε.

Thereby, dierences

in the branching quality refers mainly to long chain branching (LCB) and branch-onbranch units on the linear backbone leading to bottle-brush molecules. While the latter can be determined to a certain extent using

13

C-NMR (SI, Table S4), analysis of LCB

can be performed by SEC-MALLS using the approach of Zimm & Stockmayer. molar mass dependency of LCB per

1000C

38,39

The

atoms is given in the SI, Figure S7 and displays

evidently the pronounced dierences of CWPE produced from dierent CW probabilities. Additionally, we suggest an alternative approach by comparing the apparent density

dAPP

(SI, Equation 12) of CWPE. In our calculation of

dAPP , we assume that the polymer

chain in solution occupies the volume of a sphere. SI, Figure S6 displays the apparent density calculated from dierent as a function of the

g0.

Rg

(SANS in dTHF, SEC in THF, HT-SEC in TCB)

For dierently determined

13

Rg , dAPP


decreases with increasing


g0

demonstrating the close correlation between topology and molecular density.

This

concept can be further transferred to correlate with synthesis variation (see Figure 3). Here, both LCB and observe that

dAPP

dAPP

are depicted as a function of synthesis conditions. First, we

of CWPE can be well-controlled through pressure, temperature, time

and catalyst concentration. Moreover, we demonstrate that the respective contraction or expansion of CW structures directly correlates with the number of LCB. With regard to the temperature dependence, the weight average LCB does not support this hypothesis, which results from various chain propagation rates at the selected temperature points. However, at given molar mass, it can be validated that an increase of reaction temperature provokes a higher quantity of LCB (SI, Figure S8). Combined with the ndings from

13

C-NMR, we are able to substantiate our proposition that the synthesis variation

within CW catalysis aects the branching quality, namely the number of long chain and secondary branches. These alterations cause a severe change in the branching density. Furthermore, the molecular compactness is in very good agreement with the simulation results and the theoretical expectations from the idea of catalysts walking unconstrained and diusive on the molecular structure.

Molecular shape 1.6 1.5

linear chain high pressure CWPE

1.4 1.3

ρ=Rg/RH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 29

❖ ★ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ★★★★★★★★★★★★★ ★★ ★ ★ ❖ ★ ★ ★ ★ ★ ★ ❖ ★ ★ ★ ★ ★ ★ ❖ ★ ★ ★ ★ ★ ★ ❖ ★ ★ ★ ★ ★ ★ ★ ❖ ★ ★ ★ ★ ★ ★ ❖ ★ ★ ❖ ★★★★★★★ ❖ ❖❖❖❖❖❖❖❖❖

1.2

★

❖ ❖ ❖❖❖❖❖❖

1.1

❖ ❖

❖❖

1.0

CWPE1 CWPE4 CWPE6 CWPE7 ★ CWPE8 ❖ CWPE9 CWPEx

low pressure CWPE

0.9 0.8

hard sphere

0.7

5

10

Figure 4: Structure ratio

ρ

6

10

M [g/mol]

as function of molar mass of CWPE obtained by HT-SEC.

The marked region corresponds to the conformation of all CWPE at high molar masses which is proposed to be dendritic bottle-brush architecture.

Multi-detector HT-SEC gives access to the ratios

14

ρ =


Rg and RH

κ =

Rη , which mirRg

Page 15 of 29

ror the sensitivity to changes in macromolecular structure and can give insights into the shape of the polymer. Both ratios give the relation of sions of the macromolecule but in a dierent way. diusion coecient while experimental results of

κ = 1.3)

ρ

Rη

RH

Rg

to the hydrodynamic dimen-

is governed by the translational

is aected by the uid viscosity. In Figure 4 we display the

for CWPE. Here, the limiting cases of hard spheres (ρ

and linear random coils (ρ

= 1.5 − 1.8, κ = 0.5 − 0.8)

molar masses, the values for CWPEs approaches the range of

ρ ' 1.25

lower boundary as reported for randomly HB polymers before (ρ structural change marked by

ρ

and

κ

= 0.778,

are marked. For large which is on the

= 1.2 − 1.5). 19,45,50

The

(SI, Figure S4) is in agreement with our observa-

tions of the contraction factors of CWPE. As we discussed above, at higher contraction (lower

g0

values) pronounced globular structures are observed. This observation is further

conrmed by the contraction factor dependency of the Flory-Fox parameter S5).

Φ (SI, Figure

44

a.u. B

A

C

45 nm

180 nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


w=1000

w=6.66

Figure 5: AFM images of CWPE8 on HOPG substrate in (A) amplitude and (B) height mode. (C) Density distribution of CW structures for at

w = 6.66

and

w = 1000.

N = 1024 obtained from simulation

The CW structures have been stretched along the longest

path revealing the dense branching of dendritic side-chains.

The fact that

ρ approximates a value of ∼ 1.25 with increasing molar mass for CWPE

(and suciently low pressure) indicates a universal shape of the molecules for long reaction time. Unlike pressure and temperature, reaction time is not a parameter that aects the walking-to-insertion ratio of the CW catalyst. In fact, it clearly inuences the global conformation of CWPE as synthesis time is proportional to chain growth. Intriguingly, CWPE obtained at lower pressures display a crossover from lower values of

ρ

(compact)

to the plateau behavior. This is consistent with a continuous shift from dendritic to linear

15



Page 16 of 29

shape as we expected from theoretical arguments given above and from the simulations merging in disordered dendritic bottle-brushes. We visualized the shape of CWPE8 by AFM imaging. To this end, the polymer was deposited by spin-coating on highly-oriented pyrolitic graphite (HOPG). The resulting images are displayed in Figure 5.

Unlike previous AFM studies,

9

we do not observe

spherical nano-objects but rather dendronized or bottle-brush structures. A slight wedgeshape of the structures occurs from the smooth cross-over from the rather spherical and compact shape of the disordered dendrimers at short reaction time towards the elongated bottle-brush structures at progressing synthesis duration. However, the barrier between polymer and substrate should be considered as rather smooth than sharp due to potential interactions between the AFM cantilever and the deposited material.

As a result of

spin-coating, the polymer chains are elongated and preferentially aligned at the atomic layer edges of HOPG substrate. We found that the macromolecular chain length ranges between

300−500 nm.

The height prole revealed a thickness of approximately

8−10 nm.

These sizes correspond to approximately 400 CH2 units along the backbone (assuming C-C bond length of 1.25 nm) and an average of 20 CH2 units in the dendritic side chains (for the CWPE8

Mn ∼ 116 kg/mol).

This is supported by simulations in Figure 5C. To

mimic the elongation ow during spin casting, we have stretched the longest thread of the simulated molecule and averaged over a short time series of conformations. All structures have a spanning path (linear backbone) across the molecule with dense branching of dendritic side-chains in common. The thickness correlates with the number of generations in the side-chains (dendritic blob) and is controlled by

w.

These observations give a direct

evidence that CWPE possess a wormlike conformation even though it is very densely branched on a local level.

Scattering behavior Small angle scattering experiments give access to a broad spectrum of structural properties including global attributes, such as size, conformation, and topology as well as characteristics on segmental scale e.g.

the persistence length.

16


5153

In terms of CWPE,

Page 17 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


using SANS experiments expands the aimed structure-property correlation towards the sub-nanometer dimension and supports the understanding of the synthesis mechanism. After raw data treatment, the general scattering function

I(q)

vs.

q

is the starting

point of any analytical procedure. Applying Zimm model (SI, Equation 26) gives access to general parameters such

Rg , Mw

and second virial coecient

A2 . 54

The respective values

of CWPEs are collected in SI, Table S2. The obtained values from SANS measurements for

Rg

are in good agreement with the results from light scattering experiments (Table

1). The log-log-plot of

I(q)

vs.

q

(SI, Figure S9) enables the extraction of shape related

information. According to Porod´s law,

I(q) approaches an asymptote at high momentum

transfer. In the scattering pattern, the so called Porod-region is marked by power law behavior with a negative slope The exponent dimension

χ

I(q) ∼ q −χ

in the double-logarithmic representation.

denotes the Porod exponent, which can be associated with the fractal

df = 1/ν

for self-similar structures (SI, Equation 20). The value of

for several macromolecular conformations including rigid rods (χ chains (χ (χ

' 1.70),

Gaussian chains (χ

= 2),

hard spheres (χ

= 1),

= 3) 45

χ is known

excluded volume

and rHB structures

' 2.5). 13 To shed light on the internal structure of the CW-molecules we discuss rst the simu-

lation data of the scattering function in Figure 6A. Additionally, we present rHB polymers and perfect dendrimers for comparison. The shape of the scattering function for perfect dendrimers is unique due to the central maximum as well as the number of secondary extrema as stronger as higher the generation (SI, Figure S16). These ndings are well supported by experimental ndings for PAMAM dendrimers with dierent generations. For rHB polymers, on the contrary, no secondary peaks occur.

Instead the scattering

curves show the expected power-law from Porod's law with scaling exponent of (SI, Equation 18). Only on short length scales (high

q -values),

55

χrHB =

5 2

an exponent indicating

linear structure can be found indicating short linear subbranches in the rHB structure, also (SI, Figure S16).

23,27,28

The simulation data of CW structures in the limiting case of a high walking rate

w = 100

(low pressure, high temperature in experiments), correspond to disordered

17



Page 18 of 29

dendrimers, which behave similarly to perfect dendrimers (compare also Figures S16 and S17). Their maxima occur in the same regime as for dendrimers and appear more pronounced at higher polymerization degrees / molar masses. Higher order maxima are less distinct as the CW mechanism leads to imperfect dendrimers containing structural defects. Interestingly, the scattering curves suggest linear subbranches for high decreasing the walking rate towards the region with linear growth

q -region

By

w ' 1, the overall shape

of the scattering function changes towards linear chain scattering with The maximum vanishes and the low

q , too.

ν =

1 χ

' 0.588.

is similar to the excluded volume chain

behavior corresponding to the linear backbone. The experimental results resemble the scattering behavior of the simulated samples for low and intermediate walking rates. By formally tting the intermediate a power law, values of the Porod-exponent between

q -values with

χ = 1.38 and 2.28 can be obtained for

high and low pressures, respectively (SI, Table S2). The broad range of

χ implies a broad

structural spectrum from semi-exible chains to compact structures. Also the value of is sensitive to changes in synthesis temperature e.g.

χ = 1.96 → 2.22 (T = 0°C → 35°C)

for CWPE6 to CWPE8 and polymerization time e.g.

χ = 1.58 → 1.38 (t = 3h → 20h)

for CWPE3 to CWPE1. By comparing the experimental and simulated values of found that CWPE experimentally reaches walking rates up to count that approximately

5

χ

w = 6.

χ,

we

Taking into ac-

chemical monomer units correspond to one coarse-grained

BFM-unit, we conclude that the catalyst will perform on average up to

30 − 35

walking

steps prior to inserting the next monomer at low reaction pressure/ethylene concentration. As mentioned in the above section Branching, we know that the total number of branching

NBr

is nearly independent on the synthesis scenario. Based on the associated

simulation data (SI, Figure S15), we deduce a lower estimate CW structures.

w∼3

for synthesizing the

Hence, CW structures with less then approximately

15

walking steps

between successive synthesis events are unlikely to be generated experimentally. The various topological regimes and transitions between them can be best identied in the modied Kratky representation function.

I(q) · q 1/ν

vs.

q

(with

ν = 0.588)

of the scattering

The data obtained by simulation is depicted in Figure 6B. Linear topology

18


Page 19 of 29

10

1★ ✖ ❉ ✖❉ ❖★ ★ ✖⊗ ⊗ ❖ ★ ❉ ✖★ ❖ ✖ ❉ ⊗★ ❖ ✖❉ ❖ ★ ⊗ ✖★ ❉ ✖⊗ ❖ ★ ✖ ❉ ❖⊗ ★ ✖ -1.70 ❉ ❖⊗ I(q)~q ★ ✖ 0.1 ⊗ -5/2

⊗

❉ ❖ ★ ✖

❖❖ ❉ ❉ ★★ ✖✖

⊗ ⊗

✖ ❖ ❉ ✖ ★ ★

0.0001 -1 10

-4

⊗

0

10

2

★ ✖ ❖ ❉ ⊗ ★ ✖ ❖ ❉ ★ ✖

I(q)~q

I(q)~q

⊗ ⊗ CW w=1 χ=1.68

-4

❖

0

10

CW w=2 χ=1.73 CW w=3 χ=1.79 CW w=5 χ=2.05 CW w=6.66 χ=2.30 CW w=10 χ=2.79 CW w=13.33 χ=3.20 CW w=20 χ=3.86 ❖ CW w=100 χ=6.32 ❉ CW w=1000 χ=6.61 ★ Dendrimer S=1 χ=8.11 ✖ Dendrimer S=2 χ=7.92 rHB χ=2.20

2

3

10

q·Rg

10

✖ ✖ ✖ ✖

✖ ❖

❖

❖ ❖❖ ❖

✖ ✖✖ ❖❖ ❖ ❖ ❖

❖❖

❖ ❖

10

1/ν

✖ ✖ ✖✖ ✖✖

✖

CWPE1 (7bar, 0°C, 20h) CWPE4 (7bar, 10°C, 20h) CWPE6 (0.14bar, 0°C, 20h) CWPE7 (0.14bar, 10°C, 20h) ★ ★ CWPE8 (0.14bar, 35°C, 20h)

D (qRg) ·I(q) [a.u.]

✖

0.1

0

10

q·Rg

1

★

❖

★

1

0.1

2

10

10

★ ★★ ★★ ★★

0

10

100

★ ★★ ★

T

❖

q·Rg

★ ★ ★

★

1

2

10

10

100 CWPE1 (7bar, 0°C, 20h) CWPE2 (7bar, 0°C, 7h) CWPE3 (7bar, 0°C, 3h) ✖ ✖ CWPE5 (0.14bar, 0°C, 7h) CWPE6 (0.14bar, 0°C, 20h)

10

❖ ❖ CWPE9 (0.05bar, 0°C, 20h, 0.3mg/mL) CWPEx (0.05bar, 0°C, 20h, 0.6mg/mL)

F (qRg) ·I(q) [a.u.]

E

-5/2

100

✖

1

✖ ★ ❖ ❉ ★ ✖ ★ ❖ ★★ ★ ❉ ❖✖ ❉ ❖✖ ★ ★ ★ ★❉ ❖ ❖ ❖❉ ✖ ❉ ✖❉ ✖ ✖✖✖

❉ ❖ ✖ ★

★ ❖ ❉ ✖ ⊗

0.001 -1 10

10

CWPE2 (7bar, 0°C, 7h) ✖ ✖ CWPE5 (0.14bar, 0°C, 7h) CWPE1 (7bar, 0°C, 20h) CWPE6 (0.14bar, 0°C, 20h) ❖ ❖ CWPE9 (0.05bar, 0°C, 20h) CWPE4 (7bar, 10°C, 20h) CWPE7 (0.14bar, 10°C, 20h)

1/ν

(qRg) ·I(q) [a.u.]

10

scattering

❖⊗ ⊗❉ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ★ ❖✖ ❉ ★❉ ★ ⊗ ✖ ❖ ★ ❉ ❖ ★ ❖ ❉ ✖ ✖ ★ ★✖ ★ ⊗ ❖ ✖ ✖ ❉ ❖ ❉ ★ ✖ ⊗ ❖ ❉ ★ ✖

0.1

⊗ monomer

dendr i tic side chains

❉ ★ ✖

100

C

linear backbone

-1.70

0.01

3

10

q·Rg

I(q)~q 1

⊗ ❖✖ ❉ ★✖ ⊗ ❖✖ ❉ ❖✖ ❉ ❉ ❖ ✖ ★ ★ ✖ ❉ ❖⊗ ❖ ✖❉ ⊗ ⊗ ⊗ ✖ ★ ★ ❖ ❉ ✖★ ⊗ ❖✖ ❖ ✖❉ ❉ ★ ★★★

0.001

I(q)~q

B

CW w=2 χ=1.73 CW w=3 χ=1.79 CW w=5 χ=2.05 CW w=6.66 χ=2.30 CW w=10 χ=2.79 CW w=13.33 χ=3.20 CW w=20 χ=3.86 CW w=100 χ=6.32 CW w=1000 χ=6.61 Dendrimer S=1 χ=8.11 Dendrimer S=2 χ=7.92 rHB N3072 χ=2.20

1/ν

I(q)~q

⊗ ⊗ CW w=1 χ=1.68

(qRg) ·I(q)/I0

I(q)/I0 [a.u.]

A

10

❖

1/ν

t

1/ν

(qRg) ·I(q) [a.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 ✖

✖ ✖ ✖✖ ✖✖

✖

✖ ✖ ✖ ✖

✖

❖

❖❖ ❖

cat

❖ ❖❖ ❖❖ ❖

❖ ❖

❖ ❖

❖

❖ 1

✖ ✖✖

✖ 0.1

0

10

q·Rg

1

2

10

0.1

10

0

10

q·Rg

1

Figure 6: (A) Calculated scattering intensity as a function of momentum transfer CW structures (N

= 3072),

2

10

10

q

for

randomly hyperbranched molecules (rHB, N = 3072), and

perfect trifunctional dendrimers with

S = 1

(N = 3070) and

S = 2

(N = 3067).

The

orange solid line indicates the expected slope for a linear chain, whereas the green stroked line corresponds to the mean-eld prediction for rHB molecules. (B) Calculated modied Kratky-plot of CW structures with dierent walking rate. Experimental, modied Kratky plots of CWPE with varying synthesis pressure (C), temperature (D), polymerization time (E), and catalyst concentration (F). Data are shifted along the ordinate to match plateau region. Most of the symbols are omitted for clarity.

19



Page 20 of 29

appears here as horizontal lines. A power-law behavior of rHB structures is indicated in the plot too. In agreement with our analysis from the radius of gyration, none of the CW structures show characteristics of randomly hyperbranched macromolecules, but a transition from linear topology to dendrimers is observed. Right after reaching the maximum at

qRg ' 1,

the modied Kratky-plots of CW structures display a horizontal behavior

indicating the linear topology on large scales.

At higher q-values, a minimum follows,

which becomes more pronounced for higher walking rates and which can be related to the dendritic-like structure on smaller scales. Eventually, for very large walking rates the horizontal part disappears which indicates dendritic structure across all molecular scales, see also the snaphots in Fig.1. Modied Kratky plots of CW structures obtained from simulation and experiment show a high degree of conformity. The experimental data are depicted in Figure 6C-F and shifted along the ordinate to match the plateau region in the modied Kratky plot. The experiments are grouped as sets where only one synthesis parameter diers while all others are kept constant to determine the impact of the respective factor change on the CW structure. For CWPE obtained from low pressure (Figure 6C), we observe a maximum at low

qRg

followed by a minimum and an increase of the scattering intensity at high

qRg .

Con-

trary, CWPE from high pressure (CWPE1, CWPE2, CWPE4) demonstrate a plateau, typically obtained for excluded volume chains since the walking of the catalyst is highly suppressed and the propagation occurs rapidly. As stated in the literature by Brookhart

1

2

and Guan , the walking-to-insertion ratio of the catalyst is strongly inuenced by ethylene pressure, which relates to the actual monomer concentration. Lowering the pressure facilitates chain walking and exploration of the structure by the catalyst introducing subbranches along the backbone.

As the dierence of the logarithmic scattering intensity

between maximum and minimum

∆ ln I(q) · q 1/ν

is a direct indication for branching

(dendritic substructures), all lower pressure samples (CWPE5-CWPE9, CWPEx) display the characteristic minimum. At the same time, the pressure has nearly no inuence on

Mw

at equal

T

and

t

(see Table 1).

The evidence for the transition between lin-

20


Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ear and bottle-brush-like topologies can be clearly seen for samples CWPE2→CWPE5, CWPE1→CWPE6→CWPE9, and CWPE4→CWPE7 in the shortening of the plateau and appearance of the minimum in full agreement with the simulation results. Changing the temperature as control parameter results in ambiguous behavior. Both, insertion and walking of the catalyst is enhanced by increasing temperature, as reported in the literature.

4,7

As it can be seen in Figure 6D for samples CWPE1→CWPE4 and

CWPE6→CWPE7→CWPE8, the eect on higher walking rate seems to dominate, as a slight shift towards more dendritic structures appears. temperature results in an increased molar mass

35°C

Mw .

Additionally, increasing the

Obviously, sample CWPE8 (T

) shows the eect of beginning catalyst deactivation as the molar mass

=

Mw decreases,

but the branching degree is the highest as a result of extensive walking. In Figure 6E, the inuence of polymerization time on the scattering function of CWPE is depicted. Under equal the molar mass

Mw .

p

and

T,

a longer reaction time corresponds to an increase in

Theoretically, one would expect a transition from purely dendritic

to bottle-brush-like behavior at low pressures if the reaction time (and molar mass) increases.

The data for CWPE5 and CWPE6 give an indication for this transition.

Here, smaller macromolecules t to the behaviour of dendritic structures while the larger macromolecules display almost horizontal slope typical for the linear backbone.

If the

branching density along the backbone is not aected, only linear behaviour is observed independently on the molar mass increase as depicted by CWPE3→CWPE2→CWPE1. This is in agreement with our ndings from simulation for variation of

N

at xed

w

showing exactly the same intensity dierence in the bottle-brush transition region (see Figure S17). Within our investigation, we also focus on the correlation between polymer structure and catalyst concentration, an eect which was found to be negligible in previous studies at moderate pressures.

6

In Figure 6F, the scattering data for dierent catalyst concen-

tration at low pressure is depicted.

A lower pressure results additionally in a reduced

ethylene concentration and in a competition between the insertion and the availability of ethylene. As the consumption can not be increased, both samples CWPE9→CWPEx

21



Page 22 of 29

show similar molar mass under equal reaction conditions. The unavailability of ethylene results in an extended walking before insertion for higher catalyst concentration (CWPEx) leading to extended branching in comparison to lower catalyst concentration (CWPE9). Hence, modulating the catalyst concentration gives the possibility to synthesize a more dendritic topology at low pressure. Again we emphasize that scattering data of CWPE do neither indicate any characteristics of randomly hyperbranched structures nor show pure dendrimer behavior under the investigated reaction condition. Only the transition between linear chain and disordered dendritic bottle-brushes has been observed.

Conclusions Our combined study of theory, simulations and experiment reveals the impact of the CW mechanism on the structural properties of the polymer architecture.

Simulations

indicate a transition from dendritic behavior to elongated bottle-brush-like structures due to a limited walking capability of the catalyst as the polymers increase in size. At high walking rates, the catalyst explores the entire molecule and the attachment introduces isotropic dendritic growth.

Low walking rates cause successive insertion of

monomers yielding structures with linear behavior. This can be explained by visualizing the growing molecular structure on a Bethe-lattice. For low walking rates, the catalyst performs nearly unrestricted random walking on the lattice, which denotes the synthesized macromolecule. This corresponds to a linear structure. At a certain point, both regimes merge and the underlying structure exhibits both characteristics: a linear backbone and a dendritic substructure which jointly yield disordered dendritic bottle-brush structures on global scale. A similar transient behavior has been mathematically proven for so-called Bernoulli Growth Random Walks

56

which bear strong similarities to the CW structures.

We validate our predictions with systematically synthesized CW analytes produced via living coordination polymerization using Pd(II)-α-diimine catalyst. By applying stateof-the-art analytical tools including light and neutron scattering techniques as well as AFM imaging we conrm the unique structural properties on both global and segmental

22


Page 23 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


length scale. Moreover, we succeeded to establish an unequaled, detailed summary of the relation between synthesis, structure, and property of CW structures. We underline the dierence between CW structures from randomly hyperbranched macromolecules as often misinterpreted in the literature.

Our results demonstrate the possibility to synthesize

dendritic bottle-brush polymers based on generic properties of the chain-walking concept, thus, unlocking the opportunity for novel architectures and applications, where controlled aspect ratio of branched macromolecules is of special interest.

Acknowledgement We express our graditute to Dr.

Hartmut Komber for performing NMR spectroscopy.

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under the contract number LE 1424/7, SO 277/13 and Czech Science Foundation (15-15887J). We thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for generous allocations of CPU time.

Supporting Information Available Detailed experimental procedures and simulation details of the CW structures, theoretical background, unscaled SANS data of polymers in dilute solutions, unscaled KMHS plots, CP from factors

g0,

g

RH

and

and

g0,

Rη , theoretical models for calculation of contraction factors, contraction branching index

Flory-Fox parameter

Φ

vs.

g0,

ε,

ratios

ρ

and

κ

vs.

g0,

segmental densities

dAPP

vs.

molecular properties of CWPE in dierent solvents,

scaling exponents.

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For Table of Contents only

Figure 7

29


Polyolefins formed by chain walking catalysis - a matter of branching

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