Nanostructuring Single-Molecule Polymeric Nanoparticles via

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Nanostructuring Single-molecule Polymeric Nanoparticles via Macromolecular Architecture Petra Ba#ová, Emmanouil Glynos, Spiros H Anastasiadis, and Vagelis Harmandaris ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b09374 • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 11, 2019

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Nanostructuring Single-Molecule Polymeric Nanoparticles via Macromolecular Architecture Petra Bačová,† Emmanouil Glynos,∗,‡ Spiros H. Anastasiadis,‡,¶ and Vagelis Harmandaris∗,†,§ †Institute of Applied and Computational Mathematics (IACM), Foundation for Research and Technology Hellas (FORTH), GR-70013 Heraklion, Crete, Greece ‡Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology Hellas (FORTH), GR-70013 Heraklion, Crete, Greece ¶Department of Chemistry, University of Crete, GR-71409 Heraklion, Crete, Greece §Department of Mathematics and Applied Mathematics, University of Crete, GR-71409 Heraklion, Crete, Greece E-mail: [email protected]; [email protected]

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Abstract Heterogeneous polymer-based nanoparticles comprise a very promising family of materials for a broad range of applications. Here we present a detailed study of structural heterogeneities in nanostructured single-molecule nanoparticles, in various environments, by means of atomistic molecular dynamics simulations. The nanoparticles consist of mikto-arm star copolymers with two types of chemically incompatible arms, namely poly(ethylene oxide), PEO, and polystyrene, PS, (PS)n (PEO)n , where n is the number of arms. The immiscibility between the two components gives rise to intramolecularly nanostructured particles. The nanostructured objects resemble either “Janus-like" or “patchy-like" particles, depending on the number and/or the length of the arms as well as the interaction with the surrounding medium. The degree of intramolecular heterogeneity increases with increasing number of arms and/or with decreasing affinity of star components to the polymer host. We provide a detailed analysis of the internal structure of the star-shaped particles, focusing on the intramolecular packing and the spatial arrangement of the arms. The results of our study can be used to design heterogeneous, internally nanostructured particles with two phases of distinct static properties for challenging specific applications of next generation materials.

Keywords: polymeric nanoparticles, mikto-arm copolymer stars, intramolecular nanosegregation, particle design, atomistic simulations

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Nowadays, there is an increasing interest in using nanoparticles of different shapes, composition, patterns, and functionalities as building blocks of mesoscale assemblies with particular targeted structures and morphologies. Such a hierarchical self-assembly offers a sophisticated bottom-up strategy for the synthesis of nanostructured complex materials. Typical examples of such building blocks include, but are not limited to, inorganic particles, 1,2 hairy particles, 3–9 macromolecules, 10–13 polymer micelles 14–17 and soft colloids. 18 Because of the enormous diversity of polymer species and architectures, polymer-based nanoparticles provide a versatile platform to tune intra- and interparticle interactions by the choice of polymer chemistry, surface functionalization, and medium. Such polymer-based nanoparticles are poised to become the ’atoms’ and ’molecules’ of next generation materials if they can be successfully self-assembled into useful (desired) structures. 19–21 Among the diverse family of polymer nanoparticles, nanostructured ones, composed of two or more chemically distinct components, have attracted considerable attention as they can be employed as the building blocks for the synthesis of multiphase nanostructured materials. To this end, grafting chemically distinct polymer chains to the surface of a solid or an organic nanoparticle, thus, forming mixed brush-grafted nanoparticles, has attracted considerable attention as a practical route to construct multi-compartment nanostructured particles. 8,9,22 In this case, when two immiscible polymers are grafted onto the nanoparticle they can phase separate into different domains at the nanoparticle surface due to the balance between maximizing chain entropy and minimizing unfavorable contacts between the immiscible polymer chains. Depending on the polymer chain lengths, the Flory interaction strength, the grafting density, and the size of the solid particle, the self-consistent mean field theory and the fluctuating dynamic mean-field theory have predicted the creation of a variety of surface patterns from Janus to multipatchy ones. 23–27 Such surface morphologies may be used as a direct way to empower specific interactions between nanoparticles and, consequently, direct their self-assembly behavior, as well as the mesoscopic morphology of the resulting material. Very recently, solid-state NMR measurements were used to deter-

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mine the patch fractions, the degree of phase separation, and the morphology of well-defined mixed brush-grafted nanoparticles consisting of ZrO2 nanocrystals with polystyrene (PS) and poly(ethylene oxide) (PEO) ligands. 28 Macromolecular architecture may serve also as an important tool to obtain complex multicompartment nanostructured all-polymer particles such as Janus 29–31 and patchy 32,33 particles. Experimentally, the challenge is the synthesis of monodispersed multi-compartment building blocks with programmable shape and spatial compositional anisotropy (e.g., patches). As an example, block copolymers with dissimilar segments are able to self-assemble into nanoparticles with defined compartmentalization that can be used to self-assemble at higher levels. 16,34–36 Soft Janus particles with a tunable Janus balance, with two phase-separated chemically different hemispheres, or patchy (e.g., soccer ball/raspberry) particles may be produced upon cross-linking of compartments within precisely defined multi-compartment micelles, which are formed by triblock copolymers. 29,37–39 An interesting scenario arises if one considers branched copolymers and in particular starlike architectures. In this case, star polymers with large number of arms (frequently expressed as a functionality, f ) have a behavior akin to soft colloids. 40–42 If one grafts together to a central core two chemically different kinds of arms, as in the case of mikto-arm star-shaped copolymers, then geometrical constraints arising from the macromolecular morphology will promote an intramolecular structuring of such systems. In particular, it is expected that the structure of the mikto-arm stars exhibits complex patterns, as a result of the interplay between entropic and enthalpic interactions of the different components within the same, single, macromolecule. To clarify such issues, molecular simulations have been proven to be a valuable tool, complementary to experiments. The structural properties of single-molecule copolymer stars have been studied by bead-spring models, through molecular dynamics or Monte Carlo simulations; the final morphology of the model mikto-arm star consisted of either freely-mixed arms, if favorable interactions between polymer blocks are assumed (e.g., miscible arms in a presence of a good solvent), or arms segregated into Janus-like

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particles, if incompatible blocks are considered. 43–45 More refined, patchy-like structures have been detected only in star-block copolymer architectures in which every arm is a diblock copolymer, i.e., it consists of two distinct blocks. 46 The diblock character of the arm led to a formation of fully-detached patches on the surface of the segregated star. It is important to point out that all the above simulation works use generic (bead-spring type) models, which are capable of providing qualitative information for a range of different interactions between components and solvent quality. However, these models neglect important chemical characteristics such as details at the monomeric level, bulkiness or polarity of the particular species, as well as specific interactions between the different components. Thus, they are not able to provide quantitative information about specific complex nanostructured materials. It is clear from the above discussion that a detailed investigation of realistic single molecule mikto-arm stars at the atomic level is still missing. Such an investigation is necessary for the design of nanostructured polymer nanoparticles, with the desired properties and morphologies, for the realization of next generation materials for emerging applications. For example, well-characterized single-molecule conformations have been proven to be essential for further prediction of the self-assembly behavior of the particles in selective solvents. 47–49 To this end, simulations accounting for the chemical details of the system could be a valuable tool to reveal important information. This is exactly the goal of the present work: to provide quantitative information about the structural behavior of mikto-arm star-shaped molecules using detailed atomistic molecular dynamics simulations. In more detail, we model miktoarm stars composed of poly(ethylene oxide), PEO, and polystyrene, PS, arms ((PS)n (PEO)n , where n is the number of the arms). Each arm consists of only one type of monomer (either ethylene oxide or styrene) and the arms are connected to the core alternately, a scenario that mimics standard and well-established synthetic procedures. 50 PEO and PS arms are thermodynamically immiscible. The unfavorable interactions between the two different star components lead to the formation of internally nanostructured particles, where the final morphology and the shape depend on the number and length of the arms as well as on the

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interaction of the components with the environment. Here, we simulate particles in three different environments, namely in vacuum, in an oligomeric PEO host (o-PEO) and in a polybutadiene (PB) host to examine the role of the interactions with the host on the final morphology of nanostructured polymer particles. PS- and PEO-based copolymers are of great importance for applications in energy storage systems, such as for the fabrication of solid polymer electrolytes for lithium-ion batteries. 20,51–56 For the latter, PEO provides solvation of ions and constitutes the conducting phase while PS constitutes the rigid phase providing the mechanical strength. Furthermore and very relevant to this work, it was recently shown, that the addition of (PS)30 (PEO)30 polymer nanoparticles to an oligomeric PEO electrolyte led to the development of nanostructured solid polymer electrolytes that exhibit a combination of high modulus and high ionic-conductivity at room temperature. 20 The final morphology in such systems is the result of balancing the intermolecular effective attraction between the PS arms, which promotes particle aggregation, and the athermal interactions between the PEO arms of the nanoparticles with the oligomeric PEO host, which drives particle dispersion. Such a morphology was recently observed also with atomistic simulations. 19

Results and Discussion Intramolecular nanosegregation in vacuum: In the first part of our study, we provide a detailed investigation concerning the effect of functionality (f or 2n) and the degree of polymerization of the arms on the structure of single (PS)n (PEO)n mikto-arm stars. We start by modeling single-molecule nanoparticles in vacuum (i.e., a bad solvent environment for both PEO and PS components) through atomistic simulations, thus providing direct information on the internal, intramolecular nanosegregation in the star-shaped copolymers, driven by balancing the entropy and the unfavorable enthalpic interactions among arms only. The effect of a different environment (as for exam-

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ple, an explicit polymer host) is examined in the next section. Mikto-arm stars are labeled in the text as f /m with f denoting the functionality and m the number of monomers per arm of a specific kind of polymer. Note that the star-shaped copolymers under investigation have the same number (n) of PEO and PS arms (n = f /2) and the same number of monomers per arm. For comparison, we run simulations of homopolymer stars with different functionalities, which are denoted as f PEO or f PS and always contain 40 monomers per arm. In Fig. 1 characteristic simulation snapshots are shown as a function of the functionality and the degree of polymerization of each arm for the (PS)n (PEO)n mikto-arm star systems studied here. All systems exhibit collapsed conformations and nearly spherical nanostructured particles are formed as a result of the bad solvent environment (vacuum) for both components. To check the overall shape, we have further calculated the asphericity; 19 in all cases, its value is very close to 0, denoting an almost spherical particle (data not shown here). Due to the immiscibility of PEO and PS, the two components separate into domains to reduce the number of unfavorable PEO:PS contacts; the intramolecular nanostructuring is the result of a complex interplay between the entropic effects (entropy decreases with segregation) acting against the gain in enthalpy by nano-phase separation. It should be noted that the tendency of the arms to nanosegregate in the closest vicinity of the star core is obstructed by their connectivity to the core atoms, more specifically by the fact that they are bonded alternately to the carbons belonging to the last generation of the dendritic core structure (see Fig. S1 in the Supporting Information). In Fig. 1, the PEO arms are painted in red and the PS arms in blue. It is clear that an increase in star functionality results in an increase in the number of nanosegregated regions (patches) of the mikto-arm star. While the stars with functionalities lower than 16 seem to nanosegregate into two main regions, resembling a structure akin to Janus particles, the 32-arm stars clearly consist of 3 or more regions. This observation is consistent with the notion that the intramolecular

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structural complexity increases with functionality, as it has been also observed by beadspring molecular simulations. 45 The PEO region in the Janus-like particles is smaller than the PS region despite the fact that both PS and PEO arms have the same number of arms and number of monomers per arm. This is due to the significant difference in the monomeric volume of the PEO and PS units, owing to the bulky side group (phenyl ring) of PS. It is important to point out that our additional simulations revealed that, if the PS and PEO arms were placed by construction in a Janus-like arrangement at the core (i.e., in the limiting case of a 32-arm star with all PEO arms attached on one side and all PS arms attached on the other side of the molecule), the internal morphology of the polymer nanoparticle remained Janus-like (data not shown here).

Figure 1: Scheme of nanosegregated mikto-arm star particles in vacuum at 400K. The gray central region represents the star core, PEO arms are painted in red and PS arms in blue. The atoms of PS monomers are transparent for a better visibility of PEO block segregation.

To further examine the intramolecular structure and the degree of nanosegregation we 8


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calculated the probability distribution functions for the pair distances r between the centersof-mass of monomers belonging to different arms (inter-arm) for both PS and PEO components; data are shown in Fig. 2 for stars with f = 4, 8, 16, 32 and arm length of 40 monomers. This analysis is very similar to the standard procedure used for the radial distribution function, 57 however, our data have been normalized in a way that the integral of the distribution function equals to 1; for simplicity we denote the distribution g(r). The inter-arm probability distribution functions, g(r), (data shown in Fig. 2 for PEO:PEO, PS:PS and PS:PEO correlations) are directly related to the position and arrangement of segregated regions. The peaks appearing at short distances in PEO:PEO and PS:PS pair distributions show the characteristic distance of first inter-arm neighbors within a segregated domain. Notice that the intensity of the first peak is significantly higher in PEO:PEO (Fig. 2a) than in PS:PS 9


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(Fig. 2b) correlations. Clearly the PEO monomers are closely packed together and their local environment is mostly homogeneous, i.e., it involves predominantly neighbors of the same polymer. As the functionality increases, the preferred PEO:PEO pair distances shift to higher values arising as a second or a third peak, indicating multi-arm aggregation and a more complex ordering of the arms. The same tendency is also observed for stars with longer arms when comparing stars with different functionality. In contrast, the shapes of PS:PS and PEO:PS pair distributions are comparable for all systems studied here (i.e., for different f and arm lengths), exhibiting a more heterogeneous local environment for the PS units. In mikto-arm stars with f = 32, a small but distinct shoulder emerges in the PEO:PEO distribution at r ≈ 4 nm, confirming the presence of numerous PEO domains separated by PS-rich domains, as previously presented in Fig. 1. A more pronounced shoulder at distance r ≈ 5 nm is also observed for 32-arm stars with longer arms (32/80 and 32/160 ones); see Fig. 2(d). In contrast to the PEO:PEO probability distribution function, there is no evidence of a shoulder in the g(r) of PS:PS pairs. This observation is associated with the big difference in monomeric volumes of PS and PEO; PS arms occupy most of the particle’s volume and form an interconnected phase and thus the decay of the g(r) at large r is smooth, with no evidence of fully-segregated PS patchy domains. To corroborate the origin of the shoulder at large distances in the probability distance distribution function of PEO:PEO pairs, we compare the g(r) of 32/40 mikto-arm stars with their homopolymer star analogues, namely with the homopolymer star systems containing either the same number of PEO arms (16PEO) or having the same functionality (32PEO). The results are plotted in Fig. S2 (a,b) of Supporting Information. At longer distances, the g(r) of homopolymer PEO stars exhibit a smooth decay without a shoulder, indicating that the shoulder is a characteristic feature of patchy-like nanostructured particles. The g(r) for PS:PS pairs in the 32/40 mikto-arm system and in the corresponding homopolymer PS star analogues are very similar (Fig. S2(b)), further supporting the prior statement about

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the interconnected phase of PS monomers. Seemingly, the intramolecular structure of PS monomers is not significantly altered by the presence of the chemically incompatible, flexible PEO arms. In order to quantify the transition from "Janus-like" to "patchy-like" nanostructured nanoparticles with increasing number of arms, we present in Fig. 3 the distance between the centers-of-mass of PEO and PS components (i.e., all monomers of each polymer type are taken into account), cmP EO -cmP S , normalized by the radius of gyration of the star Rg. The quantity reaches the highest values at low functionalities (i.e., for f = 4 and f = 8), which is in agreement with the observation in Fig. 1 where the arms are fully segregated into "Janus-like" particle. The normalized distance between the PEO and PS component drops at f = 16 and attains its lowest value for f = 32, as the arms nanosegregate into more than one domain of each polymer type and thus the position of the center-of-mass of both PEO and PS components approaches the position of the center-of-mass of the molecule. For f = 16 the drop is much stronger for the stars with 80 monomers per arm than for those with 40 monomers per arm highlighting the fact that both the increase of the arm length and of the functionality can contribute to the formation of a patchy-like morphology. To further investigate the patchy-like character of the nanoparticles, we measured the 1.2 1 (cmPEO-cmPS)/Rg

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angles between all end-to-end vectors of PEO arms (i.e., the vectors pointing from the middle core carbon towards the terminal arm monomer) in a way that is illustrated in Fig. 4(a). This geometrical analysis allows us to estimate the most probable spatial arrangement of the PEO arms during the simulation. The data can be found in Fig. 4(b). The angle distribution for the 32/40 system is bimodal, with two broad, but well-separated peaks. The peak at small angles comes from the arms aligned close to each other, i.e., arms in a segregated region (e.g., arms at angle α in Fig. 4(a)). The peak at larger angles suggests a presence of distant regions (e.g., arms forming the β angle in Fig. 4(a)). Comparing the intensities of the two peaks, it is twice as likely to find segregated arms (i.e., forming an angle around 100 degrees) than arms next to each other (i.e., angle around 50 degrees), indicating that there are 2 or more patchy regions positioned at similar mutual angle. The angle distributions for 32/80 and 32/160 stars display less pronounced maxima at various (more than 2) angles. The lower intensity of the peaks for stars with longer arms is closely connected to the fact that each patchy region is formed by fewer arms and the multiple maxima are a result of the arrangement of the arms into numerous patchy regions. The higher number of patchy regions is a consequence of the decreased ability of efficient packing of longer arms, which we verified 32/40, PEO 32/80, PEO 32/160, PEO

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by measuring the intra-arm g(r) (data not shown). It is important to point out that despite the fact that the arms are attached to the dendritic core in a strictly regular, alternating way (see Fig. S1 in the Supporting Information), the final arrangement of the segregated regions in our particles is anisotropic, i.e., the addition of the unit vectors gives a non-zero vector with a length of approximately 4 times the size of the unit vector for the 32-arm stars. Please note that for isotropic nanoparticles, narrower peaks at well-defined angles would be formed in the angle distribution function while the geometric addition of the normalized endto-end vectors (i.e., unit vectors with the same direction as the end-to-end vectors) should be a zero vector, or a vector of a negligible size. The spatially anisotropic arrangement of the patches was also found in spherical nanoparticles, which were uniformly grafted with chemically incompatible polymer chains. 58,59 More specifically, for small number of grafts and ligands, it was shown that the inter-particle potential had a strong orientational dependence. The orientational dependence turned out to be the essence in reproducing the anisotropic assembly observed for this type of nanoparticles. 4,60–62 Still, a direct comparison with those systems and a consecutive prediction of the self-assembling behavior can not be made, since the nanoparticles in our study are soft and the patches are formed intramolecularly. Influence of environment in the intramolecular segregation: We now turn our attention to the structural properties of mikto-arm stars in various explicit polymer hosts. We studied the intramolecular structure of mikto-arm stars with the arm length of 40 monomers and different functionalities embedded either in oligomeric poly(ethylene oxide) or polybutadiene (PB) linear polymer matrix. The temperature was kept the same as in the vacuum simulations, i.e., 400K. The oligomeric PEO host (o-PEO) is a selective (athermal) environment (solvent) for the PEO component and a bad one for the PS arms. The o-PEO was previously used with (PS)n (PEO)n mikto-arm stars for the synthesis of high ionic conductivity solid polymer electrolytes for energy storage applications. 20 Cis 1,4-polybutadiene has been chosen for its importance in the rubber industry in connection with polystyrene. It is a non-polar polymer, generally hardly miscible with

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PEO. 63 The compatibility of PS and PB has been widely studied and it is worth mentioning that a phase separation of PS/PB linear mixtures has been reported for lower temperatures and higher molecular weights than those in our study. 64–66

Figure 5: Scheme presenting randomly selected snapshots of mikto-arm stars with arm length of 40 mers in different media (see the label on the left side). The gray central region represents the star core, PEO arms are painted in red and PS arms in blue. The atoms belonging to PS monomers are transparent. The polymer host was omitted for clarity.

In Fig. 5 we present characteristic snapshots of mikto-arm stars in the different polymer host (o-PEO or PB) together with the corresponding systems in vacuum. At first sight, it is apparent that the mikto-arm stars embedded in the polymer host are less compact compared to the systems in vacuum (compare top and middle snapshots with the bottom ones in Fig. 5). Stars with high functionalities f ≥ 8 are fairly spherical (i.e., the asphericity parameter is 14


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equal or smaller than 0.1) while the stars with f = 4 are better described by a prolate shape (i.e., the values of the prolateness parameter are close to 1). 19 The PEO arms in o-PEO are protruding within the polymer matrix, while the PS arms are collapsed to minimize the number of unfavorable contacts with o-PEO matrix. As a result an octopus-like structure is formed, where the segregated PS region forms a “head" and the PEO arms represent the “tentacles". Nanoparticles in the PB host behave in a different manner. The PEO arms nanosegregate and arrange into isolated regions to avoid the contact with the PS arms and PB polymer host. The PS arms look more extended in PB than in o-PEO or vacuum, indicating some degree of affinity of PS towards this medium. This could be explained in terms of the low molecular weight of the PS arms and PB host along with the relatively high temperature of the simulated system. 64–66 More interestingly, the organization of PEO arms in different domains is similar to the pattern previously observed in vacuum systems: a single segregated PEO region in the stars with functionality f ≤ 16 and an appearance of patches for f = 32. Recently, mean field theory studies revealed that mixed-brushed nanoparticles with a radius of nanoparticle, Rp, smaller than the radius of gyration of the grafted ligands, Rgl , form Janus-like surface patterns in solution. This Janus-like surface patterns remain even with the introduction of defects (nonuniform grafting) and fluctuations. 26 To this end, mikto-arm stars under consideration may be seen as the limiting case of mixed-brushed nanoparticles with Rp/Rgl going to zero. Interestingly, our atomistic simulations, which, in contrast to the mean-field theory approach, fully capture local structural heterogeneities in such systems, show that mikto-arm stars with f = 32 the arm length of 40 mers form patchy-like particles. Our data indicate that the use of mikto-arm stars may offer a way for controlling the nanoparticle morphologies where the patchy domains do not localize only on the surface of the particle, as in mixed-brushed nanoparticles or self-assembled monolayer coated nanoparticles, 67–70 but are also internally interconnected. To examine the intramolecular structural heterogeneities in the mikto-arm stars with

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Figure 6: Normalized distribution function of the arm centers-of-mass distances for the segregated regions in 32/40 stars in different media. Inset: a semi-log plot of the same data.

f = 32, we calculated the distribution function of the inter-arm distances, focusing on the distances between the centers-of-mass of the given arms. Choosing the arm center-of-mass instead of the monomer center-of-mass as a reference point for the calculation of the distribution function worsens the statistics but it facilitates the assessment of the shoulder in the distribution, characteristic for the patchy regions. The normalized distributions garm (r) for the nanosegregated components in all three media are presented in Fig. 6. More specifically, the distribution function of PEO arms in the PB host (green dashed curve in Fig. 6) exhibits a very weak peak around r ≈ 4.5 nm, more visible in the semi-log representation (inset in Fig. 6), similarly to the vacuum systems (blue dotdash curve in Fig. 6). In the PB host, which acts as a bad solvent for PEO arms, the PEO monomers intend to pack closely together, but this tendency is hindered by stiffer and bulkier PS regions. This interplay between specific interactions and entropy is the driving force of the observed intramolecular segregation and the final morphology of the nanoparticles. On the other hand, the distribution of the PS:PS distances in o-PEO matrix shows a long tail at longer distances. In this case, no clearly separated shoulder can be identified. To visualize the packing ability of monomers in each system we construct contact maps

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Figure 7: Contact maps for segregated domains of (a) PS monomers in o-PEO host and segregated domains of PEO monomers in (b) PB host and (c) vacuum. The c denotes the number of contacts of the same monomer type in a spherical shell with a radius 0.7 nm for PEO:PEO contacts and 0.8 nm for PS:PS contacts averaged over the whole simulation. The colorful beads represent the monomeric units of each polymer type and the black beads correspond to the core atoms.

of monomers of the same polymer type within the star molecule. The number of contacts for each monomer was obtained in the following way: for each simulation frame and for each monomer the number of monomers of the same kind was counted within a sphere of a radius, which corresponds to the closest neighbors shell. The radius equals to the distance r of the first minima in Fig. 2, r = 0.7 nm for PEO:PEO and r = 0.8 nm for PS:PS. The data 17


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were, then, averaged over the whole simulation window. In Fig. 7 we use randomly selected snapshots of mikto-arm stars to schematically project the average number of contacts for each monomer. This visualization is a much more detailed, spatial representation of the number of the closest neighbors contributing to PEO:PEO and PS:PS pairs in overall (intraand inter-arm) g(r) function. The probability of finding regions with a high number of PS:PS neighbors in o-PEO matrix increases with increasing f (Fig. 7(a)). This observation is closely related to the fact that the monomer density around the star core increases with the increasing functionality. 40,71 More interestingly, the PS regions with the highest number of contacts appear to be slightly separated (notice the tiny gap between the dark blue regions for 32/40 star in Fig.7(a)), suggesting a tendency of the PS arms to segregate into more than one domain. Comparing the contact maps for PEO monomers in the PB host and vacuum (Fig. 7 (b) and (c), respectively), there are fewer regions with a low number of PEO:PEO contacts in the systems with PB matrix, indicating the ability of PEO arms to pack closer together. PS arms are less compact than in vacuum, leaving more space for PEO arms to approach. This is also apparent in Fig. 6, where the garm for the PEO arms in the PB matrix exceeds at very small distances (r < 0.5nm) the one for the PEO arms in vacuum (compare the blue and green line in Fig. 6). As a result, fewer regions but with more contacts per monomer are formed in the PB matrix in comparison to the systems in vacuum. 2

miktoarm stars in o-PEO, arm 40 miktoarm stars in PB, arm 40

1.8 (cmPEO-cmPS)/Rg

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1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 4

8

functionality

16

32

Figure 8: Distance of centers-of-mass of the PS and PEO components (including all the monomers of the given type) divided by the molecular radius of gyration Rg as a function of functionality.

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In Fig. 8 the normalized distance of the centers-of-mass of the PS and PEO components for the stars in selective polymer matrices as a function of the star functionality is presented. As in the case of vacuum (Fig. 3), the function reaches the lowest value for f = 32; however, the overall shape is different. While the data for the systems in o-PEO matrix decay monotonically with increasing functionality, the function exhibits a non-monotonic behavior with f in PB matrix, reaching a maximum at f = 8. The different trends at low functionalities might be related to the fact that the overall shape of the particles in polymer matrices with f ≤ 8 is more prolate in comparison to the almost perfectly spherical nanoparticles in vacuum. The more spherical the particle, the more relevant the use of the molecular radius of gyration as the characteristic measure of the particle’s size and, thus, as a normalizing factor. In Fig. 9(a) the distributions of the angles between PEO arms, calculated in the same way as the data in Fig. 4, for the mikto-arm stars in the PB host are shown. For stars with f < 32 there is one main peak at small angles, in agreement with the previously observed Janus-like arrangement and the tendency of PEO arms to pack efficiently close to each other in these systems (see also Fig. 7(b)). More specifically, the probability of finding two arms with mutual angle less than 90 degrees during the simulation reaches 80% for 4/40 star and 4/40, PEO arm in PB 8/40, PEO arm in PB 16/40, PEO arm in PB 32/40, PEO arm in PB

(a)

0.016 0.012 0.008

32/40, PEO arm in vacuum 32/40, PEO arm in o-PEO 32/40, PEO arm in PB

(b) 0.012 Probability

Probability

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0.008

0.004

0.004 0

0 0

30

60

90 120 angle [deg]

150

180

0

30

60

90 120 angle [deg]

150

180

Figure 9: Distributions of the angles between the end-to-end vectors for (a) PEO arms stars with different functionality in PB matrix; (b) PEO arms in 32/40 star in three different media. See Fig. 4(a) for more details about the procedure of measuring the angles.

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90% for 8/40 and 16/40 star in PB host. In contrast, the angle distribution for the 32/40 star shows a bimodal character, confirming a patchy-like structure of the nanoparticle. In Fig. 9(b) we compare the PEO arms angle distributions for 32/40 mikto-arm stars in the three different media under investigation. In o-PEO a very broad distribution with no characteristic peaks is detected, indicating no preferential orientation of the PEO end-toend vectors, as expected for the arms with an affinity with the polymer matrix. On the contrary, the distributions for PEO arms in the PB host and vacuum are bimodal, however, with different peak positions and intensities. In particular, the first peak corresponding to the PEO arms in PB matrix is higher and shifted to smaller angles compared to the vacuum system, pointing out to a presence of more compact, more populated patchy regions in PB host. The second main peak is much smaller than the one in vacuum and its maximum is positioned at higher values of the characteristic angle. In other words, the probability of finding a distant, segregated PEO region is higher in vacuum (i.e., there are more patches in vacuum); however, the regions in PB matrix are more isolated, as can also be identified for 32/40 stars by the differences in the positions of the two main red regions in Fig.7(b) and the various smaller red regions in Fig.7(c).

Conclusions Here we present a detailed atomistic simulation study of the structural properties of miktoarm stars with varying functionality f and arm length in different environments. By means of molecular dynamics simulations, we design stars consisting of f = 4 up to 32 immiscible equally long poly(ethylene oxide) (PEO) and polystyrene (PS) arms. The higher the functionality of the mikto-arm star and the lower the affinity of its components to the media, the more the shape of the nanoparticle resembles a collapsed globule. The nanoparticles embedded in o-PEO host exhibit “octopus-like" shape, with PS monomers segregated into one “head" region and the PEO arms stretched toward the o-PEO matrix like “tentacles". In

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vacuum and in the PB matrix, the mikto-arm stars nanosegregate into “Janus-like" particles for f < 32 and into “patchy-like" objects for f = 32. We found a clear “fingerprint" of the “patchy-like" intramolecular nanosegregation by comparing the probability distributions of pair inter-arm monomer distances. The analysis of the spatial orientation of the angles formed by the arm end-to-end vectors revealed a higher number of patchy regions for the stars in vacuum than for those in the PB host. In the case of the mikto-arm stars in vacuum, the longer the arm length the higher the number of the detected segregated PEO regions. In addition, the patchy-like regions are distributed anisotropically in space. The results reported in this work introduce an interesting scenario in order to design structurally heterogeneous nanoparticles by building incompatible polymers in a mikto-arm architecture. We believe that the information collected from the current simulation methodology could be used for the computational design and testing of hybrid heterogeneous polymeric nanoparticles for various applications. Indeed, understanding the effect of polymer architecture as well as characterization of these nanoparticles on the intra-particle scale could, in principle, be used as a straightforward way to control interactions between nanoparticles, their self-assembly behavior, and the mesoscopic morphology of polymer nanocomposites with heterogeneous nanoparticles.

Method All the simulations were performed with the Gromacs simulation package 72 and the TRAPPE united-atom force field 73–76 at T=400K. Nanoparticles in vacuum: Each model system contains one star in vacuum, similar to the experimental conditions of a diluted star solution in a bad solvent. The absence of explicit solvent in the first part of our study allows us to fully focus only on the factors related to the structure of the nanoparticle. We vary the functionality, i.e., the number of arms, as well as the arm length to explore the effect of these structural features on the nanosegregation

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of the star particle. The arms are either built by PEO or PS monomers, whereas each arm is homopolymeric (i.e., it consists of monomers of only one type of polymer). We simulated mikto-arm stars, with both PEO and PS arms that are connected alternately to the core (see Fig. S1 in the Supporting Information), mimicking the most probable conformation during polymer synthesis. In addition, reference systems of homopolymer stars containing only one type of polymer, either PEO or PS, have been simulated. A table containing all details about the system compositions as well as a description of the equilibration procedure are included in the Supporting Information. The systems were simulated without periodic boundary conditions, in the NVT ensemble, in a box several times bigger than the actual size of each star. Langevin dynamics was used with a friction constant of 100 ps−1 . The cut-off Coulomb potential was applied with a cut-off of 2.0 nm. The same cut-off distance was used for the Lennard-Jones potential as well. The equations of motion in the production run were integrated with a time step of 1 fs. The length of the production runs is typically around 50-70 ns. Nanoparticles in explicit polymer host: Each system contains one star with the arm length of 40 monomers (i.e., f /40 systems) embedded in a polymer host. Two types of polymer hosts were simulated, an oligomeric poly(ethylene oxide) (o-PEO) consisting of 10 monomeric units per chain and polybutadiene (PB) with a length of 30 monomeric units. The number of chains in the box was adjusted to achieve a weight percentage of 11% of the 32/40 star in the PB host and 15% in all the other systems. The preparation and equilibration of the systems are described in the Supporting Information. In contrast to the vacuum systems, periodic boundary conditions were applied in the simulations of the stars in specific polymer host and Newton’s equations of motion were integrated with a time step of 1 fs. The production run was performed for about 50 ns, in NPT ensemble, using the particle-mesh Ewald (PME) method for the electrostatics. The pressure of 1 atm was maintained by the Parrinello-Rahman barostat and the temperature was controlled by the Nose-Hoover thermostat.

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Acknowledgments P. Bačová and E. Glynos acknowledge the financial support of the Stavros Niarchos Foundation within the framework of the project ARCHERS ("Advancing Young Researchers’ Human Capital in Cutting Edge Technologies in the Preservation of Cultural Heritage and the Tackling of Societal Challenges"). P. Bačová thanks G. Kritikos for his help with PB model and A. Giuliani and H. Mas for their help with the TOC picture.

Supporting Information Additional figures S1-S2 together with the description of the systems and equilibration method. This material is available free of charge via the Internet at http://pubs.acs.org.

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75. Fischer, J.;

Paschek, D.;

Geiger, A.;

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