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Spacer Chains Prevent the Intramolecular Complexation in Miktoarm Star Polymers Pascal Hebbeker, Tabea Greta Langen, Felix A. Plamper, and Stefanie Schneider J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01663 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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The Journal of Physical Chemistry

Spacer Chains Prevent the Intramolecular Complexation in Miktoarm Star Polymers ∗

Pascal Hebbeker, Tabea G. Langen, Felix A. Plamper, and Stefanie Schneider

Institute of Physical Chemistry, RWTH Aachen University, D-52074 Aachen, Germany

E-mail: [email protected]

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The Journal of Physical Chemistry 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

Abstract The inuence of spacer chains on the intramolecular complexation in star-shaped heteroarm (miktoarm) polymers is investigated. To overcome the mutual attraction of dierent polymeric components present in a miktoarm star with dierent homopolymeric arms, spacer chains of dierent length are attached to the core of the star at three dierent positions. In most of the investigated cases, this leads to diblock copolymer arms within the miktoarm star. Hereby, the inner spacer separates outer blocks from their attractively interacting homopolymeric arms. The eect on the intramolecular complexation and the structure of the star polymer is obtained by Monte Carlo simulations of a simple bead-spring model. Then, long spacers can completely prevent the complexation. Both, local shielding by the spacer chains and the increased distance between the complex-forming polymers due to the spacer chains inhibit the complex formation. For a range of spacer positions and lengths, an equilibrium between a system forming a complex and a complex free system is found. The spacer chains can be used as a tool to tune the intramolecular complexation.

Introduction The structure of polymers is often utilized to tailor material properties. 1 The polymer topology has an impact on the lubrication, 2 thermal transport 3 and self-assembly behavior 46 and other properties. Self-assembly can be induced by various interactions like solvent-specic interactions, 713 interpolyelectrolyte complexes 1417 and hydrogen bonding. 1820 Steinschulte et al. 21 introduced a new system in which poly(dimethylaminoethyl methacrylate) (PDMAEMA) and poly(propylene oxide) (PPO) are incorporated in one miktoarm star-shaped polymer. It was shown that these two polymers are compatible in polymer melt 22 indicating the presence of an attractive interaction between these polymers. The eective intramolecular attraction between PPO and PDMAEMA within the miktoarm star prevents aggregation, leading to unimolecular micelles. Understanding this intramolecular 2


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complexation helps to predict the properties of such systems. We believe that systems with short-range attractive interactions can lead to a new micellization scheme which utilizes complexation in addition to the segregation, which is the driving force in the classical micellization scheme. 23 We want to use molecular simulations to give some insight into the intramolecular complexation in systems with short ranged attractive interactions. Previous simulation studies show the eect of composition and topology within amphiphilic heteroarm star copolymers 2427 and amphiphilic diblock star copolymers. 28,29 The systems studied in these cases are based on arm segregation, leading to the classical micellization scheme by intermolecular aggregation. 10,30 Intramolecular complexation was previously reported for polyampholytes. 3133 As the long range interactions of polyelectrolytes dier strongly from the behavior expected for short-ranged interactions, we previously published simulations, where we have shown the eect of composition and topology on the intramolecular complexation in heteroarm star polymers, diblock copolymers and alternating copolymers. 34,35 Additionally, we have shown how the complexation behavior is aected by liquid-liquid interfaces. 36 Here, we will focus on the eect of non-interacting spacer chains on the intramolecular complexation. It has been shown that by introducing spacer chains to a polymer, many properties like binding at interfaces, 37 self assembly, 38,39 cluster formation, 40 liquid crystal formation 41 and the micellization behavior 42 can be inuenced. We have investigated how the intramolecular complexation can be prevented by incorporating spacer chains into the star polymer. Our goal is to predict the qualitative inuence of spacer chains on the complexation in attractive miktoarm star polymers, like e.g. the systems presented by Steinschulte et al. 21 The exact nature of the attractive interactions in this concrete system is still not known. As the polymers are uncharged at conditions, where complexation is observed, we assume that the interactions are not due to charge-charge interactions, but are rather short ranged. Therefore, we chose a generic attractive Lennard-Jones potential to model the 3



interactions. This allowed for a qualitative investigation of the system. Previously, we used the same approach to successfully describe the experimental observations qualitatively. 35 Our simulation results will help to guide target-oriented syntheses of star polymers with tunable complex formation. To address the eect of the spacer chains we performed Monte Carlo Simulations of a bead-spring model similar to the one used in our previous simulations. 34,35 By quantifying both the amount of complex which is formed and the size of the star polymer we gain insight into the mechanism of how the spacer chains aect the complexation. Three dierent positions of the spacer chain in the star polymer were investigated and compared.

Method Model To reduce complexity, the star polymers were modeled using a simple bead spring model. The systems investigated consist of beads of three dierent types: A, B and S beads. All star polymers are composed of one single B chain (of length nB ), and fA = 1, 3, 5 A chains (of length nA ). The A and B chains are connected by spacer chains (made up from S beads) of varying length nS . Three dierent architectures, which dier in the position of the spacer, are considered to investigate the inuence of the spacer location (a schematic representation is given in Fig. 1): 1.

Multiple Spacers :

fA spacer chains are attached to the rst bead of the B chain. One

A chain is attached at the other end of each spacer (Fig. 1a). 2.

Single Spacer :

One single spacer chain is attached to the rst bead of the B chain.

The fA A arms are attached to the nal bead of the spacer chain (Fig. 1b). 3.

Spacer as an Additional Arm :

All fA A arms and the B arm are attached to the rst

bead of a single arm. This additional arm has the same properties as the spacer chains 4


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in the other two topologies, therefore we call this arm a spacer as well (Fig. 1c). Note that for fA = 1 the case of the single spacer and the case of the multiple spacers are identical (see Fig. 1d). a)

b)

lB = 1

l B = nB c)

d)

Figure 1: Schematic representation of the simulated systems. The A beads are drawn in blue, the B beads in red and the S beads in green. The three dierent topologies are show. Multiple spacer (a), single spacer (b), and spacer as additional arm (c). In (d) a triblock copolymer resulting from the cases of single and multiple spacers, both at fA = 1. The numbering of the B segments is shown in (b). For clarity, the chains in this scheme are chosen much shorter than in the simulated systems. Each A and B chain is nA = nB = 100 beads long, while the length of the S chain nS varies between 1 and 484 beads. The total number of S beads NS equals nS in the case of a single spacer and for the spacer as an additional arm. For the case of the multiple spacers

NS = nS · fA . The simulations were carried out in the regime of innite dilution, meaning we simulate an isolated single polymer. Any intermolecular eects like aggregation are explicitly excluded to be able to study the intramolecular eects. To keep the model simple, only excluded volume interactions and an attractive potential to mimic the complexation

5



were used:

uij (rij ) =

   ∞

  4εij

σ rij

12

−

σ rij

6

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(rij ≤ σ )

(1)

(rij > σ )

where uij (rij ) is the potential between the beads i and j at distance rij and σ is the particle radius. The interactions are assumed to be pairwise additive. For bead type combinations of the type A-B (or B-A) the interaction parameter εij was set to εA-B (with εA-B = 0.0 to

1.2 kB T ). For all other bead combinations εij = 0.0 kB T . The bonds connecting the beads are modeled by a harmonic potential ubond

ubond = k/2(rij − r0 )2

(2)

with k = 16 kB T /σ 2 and r0 = 1.5 σ . As reference systems, single isolated linear chains with n = 4 to n = 484 were simulated. In these chains, the same parameters as for the star polymers were used, except that ε =

0.0 kB T for all particle-particle interactions. The results from these simulations can be found in the Section S1 in the supporting information.

The two main properties investigated are the mean squared radius of gyration Rg2

and the fraction of complexed B beads, hwB i. As in previous work, 35 we count a B to be complexed if it has a distance smaller than the cuto distance rcut = 1.6 σ to an A bead. This cuto distance was determined by locating the rst minimum in the radial

distribution function of the B-A distances at high εA-B . The position of this minima was found to converge to rcut = 1.6 σ with increasing εA-B for all investigated architectures. Using

rcut = 1.5 σ and rcut = 1.7 σ we obtained qualitatively similar results. We also present the fraction of complexation of individual segments hwB,l i as a function of the segment number

l. The segment numbering l starts with 1 at the segment with the shortest connection to the center (see Fig. 1b).

6


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Simulation Details The integrated Monte Carlo/molecular dynamics/Brownian dynamics simulation package Molsim, 43 with minor extensions by the authors, was used. The Metropolis Monte Carlo 44 (MC) simulations were carried out in the canonical ensemble in a cubic simulation box using periodic boundary conditions. To ensure that the polymer does not interact with its images, the box length is chosen to be larger than the contour length of the polymer. Single particle moves (99% of all moves) and pivot moves 45 (1% of all moves) were used. Automatically optimized maximal displacement parameters for the single particle moves were used. 46

Results Multiple Spacers To quantify the collapse of the A, B and S polymers, the radius of gyration was determined for all chain types as a function of εA-B . Some exemplary results are shown in Section S2 in the supporting information. As in previous work, 35 three distinct regions of εA-B with qualitatively dierent behavior of the radius of gyration can be observed:

• At εA-B = 0.0 kB T , there is no collapse of the polymer. This is the reference state of a star polymer without intramolecular attraction which in the following we call the case of

no complexation.

• At εA-B = 0.6 kB T , we observe the onset of the collapse of the polymers. While the radius of gyration of the spacer is similar to the reference system with εA-B = 0.0 kB T , we observe a large eect of the length of the spacer S, and of fA , on the radius of gyration of the A and B polymers. In the following we call this case weak complexation.

• At εA-B = 1.2 kB T , the intramolecular attraction leads to a strong collapse of the polymers, and the length of the spacer has no inuence on the radius of gyration 7



of the B polymer and only a small inuence on the A polymer. The inuence of the number of A arms (fA ) can be clearly seen, and shows the presence of dangling uncomplexed A beads in the system as discussed in previous work. 35 The spacer chain is now reduced in size as compared to the system with εA-B = 0.0 kB T . We call this the

strong complexation

case.

In the following, we will separately discuss the case of weak complexation and the case of strong complexation. We will, in each of the cases, look at the results for dierent systems and compare them with the reference case of no complexation.

Weak Complexation The collapse of the polymeric species is quantied by the radius of gyration. Focusing only on the case of weak complexation (εA-B = 0.6 kB T ) the eect of the spacer on the radius of gyration is shown in Fig. 2. The radius of gyration is normalized to the radius of gyration of the linear reference chain with the same number of beads. Considering the radius of gyration of the A polymers we see that for short spacers, the polymer is more extended when having more A arms. At εA-B = 0.0 kB T (open symbols) this is due to the increased excluded volume due to the increased number of A arms. At

εA-B = 0.6 kB T (and short spacers) the B polymer can only complex a limited number of A beads. Therefore, increasing fA leads to a higher number of free (extended) A chain segments. This leads to an overall larger radius of gyration of the A arms, as we have seen in previous studies on star polymers without spacer. 35 In the case of no complexation, increasing the spacer length nS diminishes the eect of the arm number and the radius of gyration of the A polymers takes the value found for the system with fA = 1. At high spacer length, the A polymers are well separated from each other and are only aected by the spacer chain which they are anchored to. Therefore, the environment that the polymers experience resembles the environment of the diblock copolymer (fA = 1). In the case of weak complexation, we observe that the collapse is reduced for all systems 8


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1 A arm

1.1

3 A arms

5 A arms

1.0 A arms

0.9 0.8 1.1 1.0

2 2 Rg / Rg,lin

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


B arm

0.9 0.8 0.7 1.1 1.0 0.9

S arms 1

10

nS

100

Figure 2: Mean squared radius of gyration of the A (top), the B (middle) and S polymer (bottom) as a function of the spacer length nS for the case of multiple spacers. The radius of gyration is normalized to the radius of gyration of a linear chain with the same number of beads. Spheres are for fA = 1 (orange), triangles for fA = 3 (violet) and squares for fA = 5 (turquoise). Solid lines (closed symbols) are for the system with weak complexation (εA-B = 0.6 kB T ) and dotted lines (open symbols) are the reference systems (εA-B = 0.0 kB T ).

9



due to the spacer chains, which hinder the complexation. When the spacer is suciently long to prevent any complexation, the radius of gyration of the A polymer converges to the value found in the system with no complexation as the eect of εA-B becomes negligible. Turning to the B polymer, we see the excluded volume eect of the A-containing diblock copolymer chains extending the B polymers with increasing fA in the case of no complexation (open symbols). For the case of the weak complexation (lled symbols) we observe that the collapse is increasing when fA is increasing. This can be explained by the enhanced complexation due to the star topology, as shown in previous work. 34 For short spacers the radius of gyration of the B arm is decreasing with the number of arms, which is the opposite of the behavior of the A arms. In the case of no complexation, increasing the spacer length has no eect on the radius of gyration of the B arm. The excluded volume of the A arms acting on the B arm in the case of a short spacer is replaced by the excluded volume eect of the S arms acting on the B arm. In the case of the weak complexation, increasing the spacer length again reduces the complexation and therefore the B arm collapses less. Again, we observe that in the case of very long spacers the properties from the weakly complexing system converges to the properties of the non complexing system, as the complexation is hindered. For the S polymers no data for nS = 1 is given, because the radius of gyration of a single particle is zero by denition. In the systems with no complexation and the weakly complexing systems, we see that the radius of gyration is increasing with the number of A arms, again, showing the excluded volume eect. At all spacer lengths the S polymer is smaller in the case of the weakly complexing systems compared to the corresponding systems with no complexation showing that the spacer is folded by the complex formation. To additionally analyze the complexation, we present the fraction of the complexed B beads hwB i in Fig. 3a. We see that the fraction of complexation decreases as the radius of gyration of B increases (with increasing nS ), showing that the collapse and the complexation go hand in hand. As seen for the radius of gyration, we see here that with increasing 10


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a)

1 A arm

3 A arms

5 A arms

0.3 hwB i

0.2 0.1 0.0

1

10

100

nS

b) 1 0.6

10 1 A arm

nS

100

3 A arms

5 A arms

0.4

wB,l

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


0.2 0.0

1

50 lB

100 1

50 lB

100 1

50 lB

100

Figure 3: Fraction of complexed B beads at εA-B = 0.6 kB T for the case of multiple spacers. (a) Fraction of complexed B beads hwB i as a function of the spacer length nS . The spheres are for fA = 1 (orange), the triangles for fA = 3 (violet) and the squares for fA = 5 (turquoise). (b) Fraction of complexation hwB,l i of each segment lB along the B chain for fA = 1 (left), fA = 3 (center) and fA = 5 (right).

11



spacer length the complexation is hindered. A rather long spacer (nS ≈ 50) is needed to reduce the complexation of a star polymer with fA = 5 arms to the fraction of complexation in a diblock without spacer. The fraction of complexed A beads (see Section S3 in the supporting information) shows a qualitatively similar behavior: The fraction of complexed beads is generally decreasing with increasing spacer length. To further illustrate the eect of the spacer on the complexation, the fraction of complexation of each segment along the B chain hwB,l i is investigated. It is the ensemble averaged fraction of complexation of each individual segment lB along the chain. Segments with lB = 1 and with lB = 100 are at the center or at the outermost part of the star, respectively. The results are given in Fig. 3b . When the spacer is only one bead long, the innermost beads are the most complexed beads. When increasing the length of the spacer, the complexation of the inner segments is more eectively suppressed by the spacer than the complexation of the outer segments. We assume that there are two relevant eects: Firstly, the spacer beads shield the B arm from the A beads by its excluded volume. This eect is local and can only act on the innermost segments which are in the direct vicinity of the spacer. This interpretation is supported by simulations in which the spacer beads exert no excluded volume interactions with the A and B beads. In these simulations the sharp reduction of the rate of complexation of the innermost segments cannot be observed (see Section S4 in the supporting information). Secondly, the spacer increases the average distance between the B and the A beads, making the complexation less favorable. This reduces the fraction of complexation of all B beads. We have shown that at εA-B = 0.6 kB T introducing multiple spacer chains from the center of the star polymer towards the A arms reduces complexation as illustrated in Fig. 4. We see that the spacer extension is reduced so that the A and B polymers can form a complex. Without a spacer, the innermost B segments are the most complexed beads, and introducing a short spacer mainly reduces the complexation of these innermost B segments. To eectively overcome the complexation, long spacer chains (nS > 50) are needed. 12


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a)

b)

c)

Figure 4: Snapshots of star polymers with fA = 3 at εA-B = 0.6 kB T for the case of multiple spacers. All beads which form a complex are drawn with the diameter of 1 σ , while the uncomplexed beads are drawn with a diameter of 0.5 σ to emphasize the complexed beads. The snapshots are at a spacer length of nS = 1 (a), of nS = 16 (b) and of nS = 225 (c).

13



Strong Complexation In case of multiple spacers, we will again look at the radius of gyration and the rate of complexation to characterize the case of the strong complexation (εA-B = 1.2 kB T ). In previous work, we found that in the case of the strong complexation the A and B segments form a dense homogeneous globular structure, decorated with uncomplexed, dangling A segments. Furthermore, we have already seen that the topology (number of A arms; fA ) has no inuence on the complexation, but the system is only aected by the composition (ratio of B to A beads). 35 1 A arm 1.0

3 A arms

5 A arms

A arms

0.8 0.6 0.4 0.2

2 2 Rg / Rg,lin

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

1.0 0.8

B arm

0.6 0.4 0.2 1.0

S arms

0.8 0.6

1

10

nS

100

Figure 5: Mean squared radius of gyration of the A (top), the B (middle) and S polymer (bottom) as a function of the spacer length nS for the case of multiple spacers. The radius of gyration is normalized to the radius of gyration of a linear chain with the same number of beads. The spheres are for fA = 1 (orange), the triangles for fA = 3 (violet) and the squares for fA = 5 (turquoise). Solid lines (closed symbols) are for the system with strong complexation (εA-B = 1.2 kB T ) and dotted lines (open symbols) are the reference systems (εA-B = 0.0 kB T ). The eect of the spacer length on the radius of gyration in the case of the strong complexation is shown in Fig. 5. Again, the radius of gyration is normalized to the radius of gyration of the linear reference chain with the same number of beads. It can be seen, that the spacer has no inuence on the radius of gyration of the A and B arm and is not able 14


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to prevent the complexation. For the A arm, we see that with increasing fA the individual arms collapse less. The origin of the increased radius of gyration is not due to a change in the complexation but rather due to the increasing amount of uncomplexed dangling A segments. 35 For the B beads, the small change in the radius, when comparing the diblock (fA = 1) and star polymers (fA = 3, 5), is also due to the change in the composition of the polymer. As slightly more A beads are present in the complex, the dense globular region of the complex is slightly enlarged. Therefore, the radius of gyration of the B arm, which is incorporated in the dense structure, is increasing. The relative size of the spacer (S) decreases with the spacer length due to back-folding and increases with the number of A arms. 1 A arm

7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0

3 A arms

5 A arms

2 2 Ree /Rg

a)

1

10

nS

100

b) 0.6

1

10 1 A arm

nS

100

3 A arms

5 A arms

0.4

P R2ee /R2g

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


0.2 0.0

0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 R2ee /R2g R2ee /R2g R2ee /R2g

2 Figure 6: Shape ratio ( Ree /Rg2 ) of the spacer chains in the case of strong complexation (εA-B = 1.2 kB T ) for the case of multiple spacer chains as a function of the spacer length nS . (a) The average shape ratio of the spacer. Spheres denote fA = 1, triangles fA = 3 and the squares fA = 5. (b) Probability density of the shape ratio for fA = 1 (left), fA = 3 (center) and fA = 5 (right). The color denotes the spacer length. Note that the systems with a spacer length of nS = 1 and 4 are not shown as for such short chains the shape ratio diers from the shape ratio of longer chains (confer Section S1 in the supporting information). To obtain an in-depth view of the conformation of the spacer chain we analyze the shape of the polymer. We dene the shape ratio as the ratio of the squared end-to-end distance 15



2 and the squared radius of gyration Ree /Rg2 . 4750 For an ideal chain we expect the ratio to

be 6. 51 When both chain ends meet (the polymer forms a loop), the shape ratio becomes close to zero. Note that we are not presenting the ratio of the averages, but the average of the ratios of the dierent radii. This allows us to evaluate the distribution of the shape. The shape ratio of the S arm is given in Fig. 6. It can be observed that with increasing spacer length, the shape ratio of the spacer is continuously decreasing. The spacer loops back so that both ends are attached to the structure formed by the complex of the A and B beads resulting in a very low end-to-end distance while the radius of gyration is increasing with the spacer length. The distribution of the shape ratio shows that the tendency to form a loop is decreasing with fA . In the case of the star with fA = 5 we see a higher fraction of extended chains, and for nS = 225 we observe a bimodal distribution of the spacer shape. As not all A segments are complexed it is possible that one or several of the A arms do take part in the complex if the other A arms counterbalance the complexation. We observe the presence of extended A chains in the distribution of the shape ratio of the star polymers with fA = 5. The shape of the spacer, in the case of multiple spacers and weak complexation, is not discussed in the main part, but the data for the shape ratio for the case of multiple spacers and weak complexation can be found in Section S5A in the supporting information. The fraction of complexation in the case of strong complexation is not aected by the spacer, as shown in Section S5B in the supporting information. As a conclusion: We have shown that in the case of strong complexation (εA-B = 1.2 kB T ) introducing multiple spacer chains from the center of the star polymer towards the A arms has little eect on the complexation as illustrated in Fig. 7. The spacers do not take part in the complex and form loops.

Single Spacer Positioning a single spacer chain between the center of the star and the B arm leads to qualitatively similar eects as in the case of multiple spacers. Therefore, we will only focus 16


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a)

b)

c)

Figure 7: Snapshots of star polymers with fA = 3 at εA-B = 1.2 kB T for the case of multiple spacers. All beads which form a complex are drawn with the diameter of 1 σ , while the uncomplexed beads are drawn with a diameter of 0.5 σ to emphasize the complexed beads. The snapshots are at a spacer length of nS = 1 (a), of nS = 16 (b) and of nS = 225 (c).

17



on one eect that strongly diers compared to the case of multiple spacers: the spacer is looping in the case of weak complexation. A detailed description of the complexation rate and the radius of gyration for the case of weak and strong complexation, as well as snapshots illustrating the chain looping, can be found in Section S6 in the supporting information. a)

1 A arm

3 A arms

5 A arms

2 2 Ree /Rg

6.0 5.0 4.0

1

10

nS

100

b) 0.3

1

10 1 A arm

nS

100

3 A arms

5 A arms

0.2

P R2ee /R2g

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

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0.1 0.0

0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 R2ee /R2g R2ee /R2g R2ee /R2g

2 /Rg2 ) of the spacer chain in the case of the weak complexation Figure 8: Shape ratio ( Ree (εA-B = 0.6 kB T ) for the case of a single spacer as a function of the spacer length nS . (a) The average shape ratio of the spacer. Spheres (solid lines) denote fA = 1, triangles fA = 3 and the squares fA = 5. (b) Probability density of the shape ratio for fA = 1 (left), fA = 3 (center) and fA = 5 (right). The color denotes the spacer length. Note that the systems with a spacer length of nS = 1 and 4 are not shown as for such short chains the shape ratio is diers from the shape ratio of longer chains (confer Section S1 in the supporting information). To characterize the looping of the spacer for the case of weak complexation, we investigate

2 the shape ratio ( Ree /Rg2 ) given in Fig. 8. It can be seen for intermediate spacer length

(nS ≈ 150)and fA ≥ 3 there is an tendency for the spacer to form loops, which was not found

for the case of multiple spacers and weak complexation. A rough estimation (presented in Section S7 in the supporting information) shows that the free energy gained by forming the complex is in the same order of magnitude as the free energy penalty for forming a loop 18


Page 19 of 30 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


in the case of long spacers. When the spacer length increases above a certain threshold

nS ≈ 200, looping of the spacer becomes too unfavorable and the shape ratio of the spacer is increasing again. In the distribution of the spacer shape ratio (given in Fig. 8b) we observe a bimodal distribution of the shape ratio for fA = 3, 5 and high spacer length. This shows that there is an equilibrium between the state of a looped spacer (resulting in high fraction of complexation) and a state with an extended spacer (and no complexation). This equilibrium shifts towards the state with an extended spacer, with increasing spacer length. Note that such a bimodal distribution was not found for the case of multiple spacers and weak complexation (see Section S5A in the supporting information).

Spacer as an Additional Arm Finally, we briey present the results from the systems where the spacer is attached to the center of the star as an additional arm. The results are given in detail in Section S8 in the supporting information. For both the case of weak and strong complexation we nd that the spacer has only very little eect on the complexation. This shows that the assumption we made in previous work, 23,34,35 that a single non-interacting arm does not aect the complexation, is valid. Furthermore, this shows that the synthetic route used by Steinschulte et al., 52 which incorporates a non-interacting arm in the miktoarm star polymers with two complex-forming polymers, does not aect the intramolecular complexation.

Comparing the Spacer Locations When comparing the spacer locations, we focus on the cases of single spacer and multiple spacers, as we have seen that the spacer as an additional arm has no eect on the complexation. Additionally, we only discuss the case of weak complexation, as we have found that in the case of strong complexation the spacer chains do not inuence the complexation in the range of spacer lengths investigated in this work. 19



1 A arm

3 A arms

5 A arms

2 2 Rg (B) / Rg,lin

1.0 0.9 0.8 0.7

0.3 0.2

hwB i

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

0.1 0.0

1

10

NS

100

Figure 9: The mean squared radius of gyration of the B arm, normalized by the squared radius of gyration of a plain linear polymer with the same number of beads (top) and the fraction of complexed B beads hwB i (bottom) as a function of the total number of spacer beads NS at εA-B = 0.6 kB T . Spheres (orange), triangles (violet) and squares (turquoise) denote fA = 1, 3, 5 respectively. Filled symbols (solid lines) represent the systems with multiple spacers, empty symbols (dashed lines) represent the systems with a single spacer.

20


Page 20 of 30

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To compare the eect of the spacer locations on the conformation of the B arm, the radius of gyration and the fraction of complexed B beads (hwB i) is given as the total number of S beads NS = fS · nS in Fig. 9 for the case of a single spacer and the case of multiple spacers. Note that in the previous gures the spacer length nS was given. The radii of gyration of the B arm agree well with each other for low spacer lengths. For very long spacers, we observe that the systems with multiple spacers exhibit slightly more extended B arms (the eect increases with fA ). This is due to the increased excluded volume at the center of the arm (where the B arm is located in the case of multiple spacers) compared to the periphery of the star (where the B arm is situated in the case of a single spacer). For the fraction of complexed B beads, the dierence between the two spacer locations is increasing with the number of A arms. At intermediate numbers of spacer beads (NS ≈ 80) a higher fraction of complexed B beads is found in the case of a single spacer. Therefore, the multiple spacers towards the A arm are more eective in preventing the complexation compared to the single long spacer towards the B arm. We believe that the reason is both the increased shielding of the B arm due to the multiple attached spacer chains and the reduced local concentration of A beads when they are separated by the multiple spacers. In the systems with in total NS ≈ 500 spacer beads, we observe that for fA = 3 the single spacer towards the B arm prevents the complexation more strongly than the multiple spacers towards the A arms. We believe that the reason is that in that case it is more feasible to loop one of the multiple shorter spacers (leading to some complexation) than to loop the single longer spacer (which is required to have some complexation).

Conclusions We have shown how the introduction of spacer chains into a miktoarm star polymer inuences the intramolecular complexation. Depending on the spacer position, we observe dierent behavior. When the spacer simply is bound to the center of the star, the complexation is

21



Page 22 of 30

not aected by the spacer. In contrast, when positioning a single spacer towards the B arm or multiple spacers towards the A arms the complexation can be inhibited by the spacer in the case of weakly complexing polymers. To completely hinder the complexation a rather long spacer is needed (> 100 beads). We have shown indications that the complexation is reduced by two mechanisms: (i) there is a local shielding of the segments directly attached to the spacer and (ii) the complexing partners are separated spatially by the spacer, thus preventing the complex formation. In the case of strongly complexing polymers, the spacer was unable to aect the complexation independent of the spacer location or the spacer length investigated. These insights help future development of intramolecular complex-forming star polymers. We claried how the spacer inuences the complexation and the results can direct the synthesis, when aiming for specic properties. By using a spacer chain which can be switched by an external stimuli (e.g. temperature or pH), one might obtain a system with responsive complexation. Finally, the formation of a polymeric loop described here could assist the synthesis of cyclic polymers.

Acknowledgement We thank Walter Richtering, and Per Linse for fruitful discussions. Further, the funding by Fonds der Chemischen Industrie (FCI) for a scholarship (P.H., F.P.) and by the German Research Foundation DFG (grant PL 571/3-2) is gratefully acknowledged.

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Graphical TOC Entry ⇌ To complex, or not to complex

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