1 Effect of Block Length and Side Chain Length Ratios on Determining

Subscriber access provided by University of Rochester | River Campus & Miner Libraries

B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Effect of Block Length and Side Chain Length Ratios on Determining Multicompartment Micelle Structure Connor P. Callaway, Seung Min Lee, Mackenzie Mallard, Benjamin Clark, and Seung Soon Jang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b02231 • Publication Date (Web): 13 May 2019 Downloaded from http://pubs.acs.org on May 18, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28 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

The Journal of Physical Chemistry

Effect of Block Length and Side Chain Length Ratios on Determining Multicompartment Micelle Structure

Connor P. Callaway1, Seung Min Lee1, Mackenzie Mallard1, Benjamin Clark1, and Seung Soon Jang1,2,3,4, *

1

Computational NanoBio Technology Laboratory, School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA 30332-0245, USA

2

Institute for Electronics and Nanotechnology, Georgia Institute of Technology, Atlanta, GA, USA

3

Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA, USA

4

Strategic Energy Institute, Georgia Institute of Technology, Atlanta, GA, 30332, USA

*

Corresponding author. Email address: [email protected] 1 ACS Paragon Plus Environment

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 Previous work has identified the importance of the lipophilic-fluorophilic block length ratio ℛ𝑙 in predicting the morphology of linear lipophilic-hydrophilic-fluorophilic (hereafter referred to as BAC) micelle systems. Here, a generalized form ℛ of this structural parameter is developed that makes no assumption of BAC triblock copolymer linearity, while still providing accurate predictions of micelle morphology. The morphologies of BAC micelles formed by triblock copolymers with ℛ𝑙 ≪ 1 or ℛ𝑙 ≫ 1 have similar features, with the only notable difference being an inversion of the lipophilic and fluorophilic regions. A destabilization of the single-core micelle structure occurs as ℛ approaches unity from either direction. Finally, the extent to which micelle morphology depends on polymer architecture instead of composition alone is examined, with decreased patchiness observed in BAC systems with very long block lengths. Through modification of both the ℛ-value and the polymer architecture, the micelle morphology can be effectively tuned for use in immobilized catalysis and nanoreactor applications.

2 ACS Paragon Plus Environment

Page 2 of 28

Page 3 of 28 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. INTRODUCTION Throughout recent decades of catalysis science, the development and potential applications of various implementations of immobilized catalysis have attracted no shortage of attention1-10. Of growing interest in more recent years is the possibility to harness the versatile morphologies of multicompartment micelles to create catalytic nanoreactors11-18. As is well known, the traditional micelle results from self-assembly of diblock copolymers consisting of hydrophilic heads and hydrophobic tails in aqueous conditions19-20. The multicompartment micelle (MCM) likewise results from polymers of three (or more) mutually immiscible blocks, each with different solvophilicity, self-assembling in solution into complex structures containing distinct regions or “compartments” of the species in the various copolymer blocks21-26. Because of their ability to control the flow of reactant and product species within a solution, MCM nanoreactors display a fortuitous combination of the high reaction rates and selectivity observed in homogeneous catalysis with the separability enjoyed by heterogeneous catalysis, all without the need for multiple successive reaction chambers27-38. These systems thus present an opportunity to engineer immobilized catalytic reactions at the nanoscale, enabling such desirable features as cascade reactions, tandem catalysis, and catalytic compartmentalization in systems with nonorthogonal reaction steps. Although several of these features are not unique to micelle structures, the MCM nanoreactor enables the ability to combine them into one system with a relatively straightforward synthesis process. Moreover, MCMs offer a wide range of control over the resultant morphologies through modification of the architecture of the constituent copolymer species. A particularly noteworthy advantage of these systems is the ability to “tune” the micelle morphology without modifying the species that comprise the blocks of the constituent copolymers, allowing the



copolymer species to be selected on the basis of the chemical character of the reactants and products present in the reaction. Indeed, the spectrum of morphologies achievable through modification of the polymer architecture has been well documented to date24-26, 39-44. Although micelles consisting of polymers with a hydrophilic-lipophilic-fluorophilic (often termed “ABC”) block sequence typically result in layered onion-like spheroids39-42, 45-51, a wider variety of morphologies have been observed when the copolymer block sequence is modified to lipophilic-hydrophilic-fluorophilic (“BAC”)25, 39, 52. Previously, it was demonstrated that purely linear (i.e., without side chains) triblock copolymers with BAC block sequence result in morphologies that can be effectively tuned by modifying the lipophilic-fluorophilic block length ratio (ℛ𝑙 )39. Because of the ease with which the block lengths may be modified during copolymer synthesis, the structural parameter ℛ𝑙 provides a direct avenue for the MCM morphology to be controlled in order to improve the catalytic performance of the MCM nanoreactor system. However, despite the accuracy of the ℛ𝑙 -parameter in predicting micelle morphology for triblock copolymer systems with (approximately) linear polymer architecture, its effectiveness is notably diminished for triblock copolymers which cannot be modeled as linear, including species with bulky side chains. This limitation can be problematic, since the principal consideration when selecting the constituent species of the triblock copolymer is the solvophilicity of each species. It is natural, then, to seek a more generalized structural parameter ℛ that does not require the assumption of linearity of the polymer architecture that limits the applicability of the ℛ𝑙 parameter. In this computational study, we employ the dissipative particle dynamics (DPD) simulation method53-56 to study the variation in MCM morphologies as a function of the lipophilicfluorophilic block length and side chain length ratios in order to explore the form of such a


Page 4 of 28

Page 5 of 28 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


generalized parameter. This study will also examine the extent to which the lipophilic and fluorophilic side chains have a similar effect on MCM morphology to that exhibited by the block lengths of these species. Finally, we will discuss the relative importance of the polymer architecture in comparison with the overall composition to remark upon the influence of linearity in deciding the final MCM morphology.

2. MODELING AND SIMULATION METHODS In this study, dissipative particle dynamics (DPD) simulations are performed through Materials Studio57 to investigate the effects of modifying the block length ratio and the side chain length ratio between the lipophilic and fluorophilic blocks. As defined in our previous study, the lipophilic-fluorophilic block length ratio is given by ℛ𝑙 = 𝑏̃𝐿 ⁄𝑏̃𝐹 ,

(1a)

where 𝑏̃𝐿 and 𝑏̃𝐹 represent the reduced (i.e., coarse-grained) DPD block lengths corresponding to a real polymer of lipophilic and fluorophilic block lengths 𝑏𝐿 and 𝑏𝐹 , respectively39. It is worth noting that because the scaling factor should be very nearly identical for both the lipophilic and the fluorophilic blocks, the definition above may be alternatively written as ℛ𝑙 ≈ 𝑏𝐿 ⁄𝑏𝐹 .

(1b)

In a BAC micelle system composed of purely linear triblock copolymers, this expression also captures the composition ratio between the lipophilic and the fluorophilic blocks; when bulky side chains are present, however, it is only one component of the composition ratio. To capture the effect of side chains, we introduce an analogous parameter ℛ𝑠 : ℛ𝑠 = 𝑠̃𝐿 ⁄𝑠̃𝐹 ≈ 𝑠𝐿 ⁄𝑠𝐹 ,

(2)



Page 6 of 28

where 𝑠̃𝐿 and 𝑠̃𝐹 represent the reduced side chain lengths within the lipophilic and fluorophilic blocks, respectively. We note that, depending on the nature of the species in these blocks in a real polymer, the “true” side chain lengths 𝑠𝐿 and 𝑠𝐹 may or may not retain physical meaning. In cases where the side chain cannot be modeled as a series of repeating units, we recommend the use of standard estimates of statistical side chain dimension58 (〈𝑅 2 〉1⁄2 , 𝑅𝑔 , etc.) in place of 𝑠𝐿 and 𝑠𝐹 . Although the specific form of the generalized lipophilic-fluorophilic ratio parameter ℛ will be discussed later in this work, at this point it is instructive to highlight two major requirements for this quantity. First, it is expected that, in the absence of side chains (or in systems that can be modeled with linear polymers), it simplifies to the linear form ℛ𝑙 . Second, it is expected to serve as a reasonably good predictor of the micelle morphology based on the lipophilic and fluorophilic block and side chain lengths. In order to determine the form of the ℛ-parameter, the simulation systems were set to have 5% polymer and 95% water. Although this polymer concentration is larger than would be used in a real physical system, a larger concentration is employed in our simulations in order to ensure more intensive polymer-polymer interactions and thus to better study the self-assembly process. The simulation box size was defined as 30×30×30 with a grid spacing of 1.0 and a bead density of 3.0, enabling the use of the linear relationship between the DPD repulsion parameter 𝑎ij for species 𝑖 and 𝑗 and the corresponding Flory-Huggins 𝜒ij -parameter, as derived by Groot and Warren56: 𝑎ij = 25 + 3.5𝜒ij

(3)

Ensuring the physicality of the DPD simulations and of the micelle self-assembly process requires monitoring the simulation pressure and temperature as a function of time. Total simulation time was chosen in all cases as 𝛼𝑡𝑒 , where 𝑡𝑒 gives the minimum time required to achieve pressure equilibration (i.e., no monotonic change in pressure over time). The constant 𝛼, chosen arbitrarily 6 ACS Paragon Plus Environment

Page 7 of 28 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


here to be equal to 2.5, allows the simulation to proceed for a fixed amount of time after the equilibration stage is achieved in order to ensure a fully equilibrated state in the system. Using a time step of 0.05 reduced DPD unit, a total simulation time of 8.75×103 reduced units provided equilibrated results for all simulations. Reduced DPD unit time is taken as the duration necessary for a bead to diffuse a distance of its own radius due to thermal fluctuations55-56. Groot and Warren advise that the use of a time step greater than 0.05 reduced unit is discouraged due to the artificial (and unphysical) increase in system temperature that results from the use of larger time steps56. We note that the species A, B, and C used in this study are loosely based on the species displayed in Figure 1, which were selected for their spectrum of hydrophobicity. In order to obtain the repulsion parameters for this study, the corresponding 𝜒-values were first calculated via the COMputational Miscibility Analysis (COMMA) method previously developed by the authors59. These 𝜒-parameter values were then converted into repulsion parameters via equation (3) and slightly adjusted to improve distinct phase separation upon self-assembly; the 𝜒-parameters used in these DPD simulations therefore represent idealized values for model study. Table 1 summarizes the 𝑎ij -values for each pair of species used in this simulation system. Finally, in order to facilitate the communication of structural information for triblock copolymers, we here use a condensed notation such that 𝑋𝑏̃𝑋,𝑠̃𝑋 represents a block of species X with block length 𝑏̃𝑋 and side chain length 𝑠̃𝑋 . Figure 2 provides a visual representation of this notation for additional clarity. While branched triblock copolymers were indeed the focus of this study, simulations of several purely linear copolymers were also performed with compositions identical to select branched triblock copolymers. These linear copolymers were included in our study in order to probe the extent to which micelle morphology depends on polymer architecture.



Page 8 of 28

For all branched copolymers in this study, the total block length was constrained to 𝑏̃𝐿 + 𝑏̃𝐻 + 𝑏̃𝐹 = 30, while the total side chain length was constrained to 𝑠̃𝐿 + 𝑠̃𝐻 + 𝑠̃ 𝐹 = 8.

3. RESULTS AND DISCUSSION In order to probe the full spectrum of morphologies as a function of polymer architecture, simulations were performed for five ℛ𝑙 -values (ℛ𝑙 ≪ 1, ℛ𝑙 < 1, ℛ𝑙 = 1, ℛ𝑙 > 1, and ℛ𝑙 ≫ 1). At each of these ℛ𝑙 -values, five ℛ𝑠 -values were tested (with a range similar to the ℛ𝑙 -values), yielding a total of twenty-five architectures tested. It is important to note that, beyond a base length sufficient to ensure proper micelle coverage, the hydrophilic block length has been observed to have a minimal impact on the resultant morphology39, 52. The preliminary simulations indicated a similar trend in the impact of the hydrophilic side chain length. For these reasons, we here choose a constant hydrophilic block length of 𝑏̃𝐻 = 18 and hydrophilic side chain of 𝑠̃𝐻 = 4 in all cases. At this point, we introduce the generalized form of the structural lipophilic-fluorophilic ratio parameter as a multiplicative modifier to the linear parameter ℛ𝑙 : 𝑠̃ +1

𝑏̃ (𝑠̃ +1)

𝑏 (𝑠 +1)

ℛ = ℛ𝑙 (𝑠̃ 𝐿 +1) = 𝑏̃ 𝐿(𝑠̃ 𝐿 +1) ≈ 𝑏 𝐿(𝑠𝐿 +1) 𝐹

𝐹

𝐹

𝐹

𝐹

(4)

The reader may note that this form is essentially the composition ratio between the lipophilic and fluorophilic species. This is reasonable, given the reliability of the similar ℛ𝑙 -value in predicting the micelle morphology of purely linear systems. This form also simplifies to the simple ℛ𝑙 -value in systems without side chains (i.e., when 𝑠̃𝑋 = 0 for all species X), satisfying one of the major requirements set forth at the onset of this study. It must also be noted, however, that it is presently unknown whether the simple definition of ℛ as a compositional ratio between the lipophilic and fluorophilic blocks will hold for all polymer systems and, more specifically, all polymer architectures. Since the ABC block sequence is predominantly characterized by the formation of 8 ACS Paragon Plus Environment

Page 9 of 28 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


onion spheroids, the ℛ-value is of no utility in these systems; it is natural, then, to wonder whether its accuracy extends to other architectures that are significantly different from those studied here (e.g., ABC miktoarms). Thus, at present, while we do wish to highlight the intuitive connection of the ℛ-value to the lipophilic-fluorophilic compositional ratio in linear and branched BAC triblock copolymer systems, we stress that the functional form may vary quite widely in other architectures. As with the ℛ𝑙 -parameter, the generalized ℛ-parameter enables predictions of micelle morphology based on the block lengths and side chain lengths of the lipophilic and fluorophilic blocks. For systems where ℛ ≪ 1 or ℛ ≫ 1, the expected morphologies are quite similar: the micelles formed are spheroidal, largely preferring a single core composed of either the lipophilic or the fluorophilic species, whichever is in excess. The deficient species forms smaller patches surrounding the core, while the entire spheroid is covered with a layer of the hydrophilic species whose thickness is determined primarily by the hydrophilic block length. We continue the nomenclature wherein these morphologies represent regimes I (where ℛ ≪ 1) and III (ℛ ≫ 1). The intermediate regime II (where ℛ ≈ 1) is characterized by notably less spheroidal morphologies containing multiple cores of both lipophilic and fluorophilic species. 3.1. Micelle Morphologies with 𝓡𝒍 ≪ 𝟏 The first set of simulations was performed with a lipophilic block length of 𝑏̃𝐿 = 2 and a fluorophilic block length of 𝑏̃𝐹 = 10, representing the ℛ𝑙 ≪ 1 extreme of the horseshoe diagram. The results from these simulations are presented in Figure 3, along with the corresponding polymer architectures and ℛ-values; water visibility is disabled in all figures for visual clarity. When ℛ ≪ 1, as in the case of the B2,2A18,4C10,6 micelle, the system preferentially forms a characteristically spheroidal regime I morphology with a fluorophilic core and many small lipophilic patches.



However, as Figure 3 demonstrates, increasing the ℛ𝑠 -value of the constituent polymers (and, by extension, increasing the ℛ-value) leads to the development of a smaller number of larger patches. In particular, a clear morphological difference can be observed between the morphologies of the B2,2A18,4C10,6 and the B2,6A18,4C10,2 micelles: while the latter retains a fluorophilic core, it nonetheless displays a morphology intermediate in character to regimes I and II. These morphologies are well reflected by the difference in the corresponding ℛ-values (ℛ = 0.086 and ℛ = 0.467, respectively). The lack of morphologies in the regime II-III range is also explained by the range of ℛ-values surveyed, as ℛ < 1 for all architectures studied. 3.2. Micelle Morphologies with 𝓡𝒍 < 𝟏 The second set of simulations was performed with 𝑏̃𝐿 = 4 and 𝑏̃𝐹 = 8, representing the ℛ𝑙 < 1 region of the horseshoe diagram. Several features of these simulations are of note. As shown in Figure 4, the first polymer architecture tested (B4,2A18,4C8,6) results in a nearly identical morphology to that of the B2,4A18,4C10,4 architecture in Figure 3, as predicted by their ℛ-values (ℛ = 0.214 and ℛ = 0.2, respectively). Since the regime II morphologies dominate around ℛ~1, it would be expected that the B4,6A18,4C8,2 micelle (ℛ = 1.167) would disfavor a spheroidal singlecored morphology; indeed, Figure 4 confirms this, with this architecture instead forming a more segmented morphology. 3.3. Micelle Morphologies with 𝓡𝒍 ~𝟏 Simulations in the ℛ𝑙 ~1 region of the horseshoe diagram were performed with 𝑏̃𝐿 = 6 and 𝑏̃𝐹 = 6. For these simulations, the architectures tested span a range of 0.429 < ℛ < 2.333, providing an effective representation of the tunability possible in BAC micelle systems. Although regimes I and III are not fully accessible based on the ℛ𝑙 - and ℛ𝑠 -values chosen, as Figure 5 demonstrates, the micelles at either end of the spectrum still display the characteristic similarity 10 ACS Paragon Plus Environment

Page 10 of 28

Page 11 of 28 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


predicted based on their 𝑅 -values: the B6,2A18,4C6,6 and B6,6A18,4C6,2 micelles both exhibit a spheroidal structure with the core composed of the species in excess and a small number of larger patches composed of the deficient species. Likewise, as the micelles’ ℛ-values approach unity from either direction, the regions of the deficient species grow large enough to rival the regions of the dominant species, leading to a destabilization of the single-cored structure as expected. 3.4. Micelle Morphologies with 𝓡𝒍 > 𝟏 The set of simulations performed with 𝑏̃𝐿 = 8 and 𝑏̃𝐹 = 4 represent the ℛ𝑙 > 1 region of the horseshoe diagram, with the resultant morphologies shown in Figure 6. Notably, the horseshoe diagram associated with these simulations mirrors the diagram displayed in Figure 4. In particular, the B8,6A18,4C4,2 architecture (ℛ = 4.667) forms a morphology that is essentially an inversion of the B4,2A18,4C8,6 architecture (ℛ = 4.667−1 ). Both the B8,2A18,4C4,6 and the B8,3A18,4C4,5 micelles form similar morphologies, as both polymer architectures display ℛ-values near unity (ℛ = 0.857 and ℛ = 1.333, respectively). However, as the ℛ𝑠 - and ℛ-values increase, the lipophilic core grows, leading to the system favoring spheroidal morphologies in the regime III limit. 3.5. Micelle Morphologies with 𝓡𝒍 ≫ 𝟏 In a similar vein, Figure 7 displays the set of simulations which studies the ℛ𝑙 ≫ 1 extreme of the horseshoe diagram, with lipophilic and fluorophilic block lengths of 𝑏̃𝐿 = 10 and 𝑏̃𝐹 = 2, respectively. The spectrum of morphologies generated from these polymer architectures in turn mirrors the diagram shown in Figure 3. When ℛ ≫ 1, as in the case of the B10,6A18,4C2,2 micelle, the system exhibits the characteristic regime III morphology with a single lipophilic core and several smaller fluorophilic patches. This morphology is, in essence, an inversion of the B2,2A18,4C10,6 micelle in Figure 3, as expected from the ℛ-values of each micelle (ℛ = 11.667 and ℛ = 11.667−1, respectively). As the ℛ-value is decreased toward unity, the fluorophilic patches 11 ACS Paragon Plus Environment


grow in size and approach the non-spheroidal morphologies found in regime II; however, regime I remains fully inaccessible for the given micelles because ℛ > 1 for all copolymer architectures. 3.6. Comparison of Branched Architecture to Linear Architecture Finally, in order to further study the effect of polymer architecture on micelle morphology in comparison to that of composition alone, simulations were performed with compositions identical to those studied previously, but with purely linear architectures instead of architectures with side chains. Figure 8 shows a side-by-side comparison between each branched architecture and the corresponding linear architecture with identical composition and ℛ-value. As can be seen from Figure 8, a few morphologies are in agreement between the branched and linear architectures; in particular, for ℛ-values of 0.086, 0.429, and 2.143, the linear and branched micelles display similar morphologies. However, in other cases, the linear architectures result in a markedly lower extent of patchiness in comparison with the branched architecture. We ascribe this result primarily to chain entanglement occurring in cases with much larger block lengths, as well as the difficulty of forming small patches surrounding the core when the mean end-to-end distance of the polymer chains are larger than the characteristic patch size associated with the corresponding ℛ-value. These simulation results highlight an important limitation of the ℛ-value: while it has been demonstrated that this parameter enables reliable prediction of multicompartment micelle structure for a particular family of polymer architectures, significant discrepancies may arise when comparing micelles composed of polymer species from different architectural families (e.g., purely linear, branched, miktoarm, etc.). In other words, while the ℛ-value can describe a considerable amount of tunability based on compositional variation, the polymer architecture plays an important role in determining micelle morphology that currently lies beyond the scope of the ℛ-value. We intend to expand this parameter in future studies by mapping micelle morphology as a function of


Page 12 of 28

Page 13 of 28 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


coordinates within ℛ -space, including the consideration of the architectural component of morphology. It is worth noting that while the architectural effect is not yet fully understood, when comparisons are made within a single architectural class, the ℛ-value retains its ability to make robust morphological predictions. Considering only the linear architectures in Figure 8, a trend is still observed in the micelle morphologies as a function of ℛ (which is functionally equivalent to ℛ𝑙 in this case). When ℛ ≪ 1, spheroidal fluorophilic-cored micelles result, albeit with relatively fewer and larger lipophilic patches than in the corresponding branched case of equal ℛ. The characteristic lipophilic-fluorophilic inversion is observed in this architectural family as well, with the ℛ ≫ 1 micelles displaying spheroidal lipophilic-cored micelles with fluorophilic patches. Within the ℛ~1 region, the preferred morphologies are split-cored spheroids, in contrast to the segmented morphologies formed by branched architectures and linear architectures with short block lengths39. Thus, although there are significant differences between the trends observed for branched, short-block linear, and long-block linear architectures, in all cases the trends themselves are well mapped by the ℛ-value. The morphological differences observed between the branched and linear architectures are not necessarily detrimental; indeed, the range of morphologies generated between the branched and linear architectures for some ℛ-values establishes an additional layer of tunability even at constant ℛ. Because the patches surrounding the core represent distinct catalytic regions and can serve as entry points for reactants or exit points for products, it is useful to consider all avenues of structural tunability when designing a multicompartment micelle system for nanoreactor applications. These avenues may therefore include modification of the ℛ𝑙 - or ℛ𝑠 -values as well as complete modification of polymer architecture.



4. CONCLUSIONS In this computational study, we have identified a generalized form ℛ of the lipophilicfluorophilic structural parameter ℛ𝑙 for linear triblock copolymers introduced previously by the authors. The generalized ℛ-value makes no assumption of polymer linearity while still allowing accurate predictions of the resultant aqueous BAC micelle morphology, although the effectiveness of this parameter is diminished slightly in cases with overlong block lengths. In addition, the ℛvalue collapses into the ℛ𝑙 -value in cases where no side chains are present, as expected. Thus, the generalized ℛ-value meets all requirements set forth for this parameter. The morphologies formed by branched BAC triblock copolymers are highly consistent with those formed by linear BAC triblock copolymers. For ℛ ≪ 1 or ℛ ≫ 1, these copolymers preferentially form spheroidal morphologies with a single core composed of either the lipophilic or the fluorophilic species, whichever is in excess, while the deficient species forms patches surrounding the core. By contrast, copolymers with ℛ~1 instead form non-spheroidal micelles with multiple “cores” of both lipophilic and fluorophilic species. In all cases, patchiness is noticeably decreased for copolymers with very long block lengths when compared to branched copolymers of the same composition and ℛ-value. While this phenomenological study has provided quite satisfactory insights into the dependence of multicompartment BAC micelle morphologies on polymer architecture (and, by extension, the structural tunability of these systems), deeper mechanistic analysis is still required to understand the reason for the morphological trends observed in these systems. Moreover, a freeenergy analysis may uncover heretofore unobserved morphologies of interest in immobilized catalysis applications. Through coarse-grained molecular mechanics calculations (e.g., approaches


Page 14 of 28

Page 15 of 28 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


based on mean-field theory or free energy perturbation), the energetic contributions leading to the stability of patchy spheroids (regimes I and III) and multi-core agglomerates (regime II) may be identified. These contributions will provide essential insights into the morphological diversity of multicompartment BAC micelle systems, allowing for finer structural control than ever before.

5. ACKNOWLEDGEMENTS This research was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award DE‐ FG02‐ 03ER15459.

6. REFERENCES 1. Madhavan, N.; Jones, C. W.; Weck, M. Rational Approach to Polymer-Supported Catalysts: Synergy between Catalytic Reaction Mechanism and Polymer Design. Acc. Chem. Res. 2008, 41, 1153-1165. 2. Weck, M.; Jones, C. W. Mizoroki−Heck Coupling Using Immobilized Molecular Precatalysts: Leaching Active Species from Pd Pincers, Entrapped Pd Salts, and Pd Nhc Complexes. Inorg. Chem. 2007, 46, 1865-1875. 3. Long, W. Designing Immobilized Catalysts for Chemical Transformations: New Platforms to Tune the Accessibility of Active Sites. Dissertation, Georgia Institute of Technology, Atlanta, 2012. 4. End, N.; Schöning, K.-U. Immobilized Catalysts in Industrial Research and Application. In Immobilized Catalysts: Solid Phases, Immobilization and Applications, Kirschning, A., Ed. Springer-Verlag: Berlin, 2004; Vol. 242. 5. Trapp, O.; Troendlin, J. Studies of Immobilized Catalysts. In Molecular Catalysts: Structure and Functional Design, Gade, L. H.; Hofmann, P., Eds. Wiley-VCH: 2014. 6. Hübner, S.; de Vries, J. G.; Farina, V. Why Does Industry Not Use Immobilized Transition Metal Complexes as Catalysts? Adv. Synth. Catal. 2016, 358, 3-25. 7. Cozzi, F. Immobilization of Organic Catalysts: When, Why, and How. Adv. Synth. Catal. 2006, 348, 1367-1390. 8. Sabater, S.; Mata, J. A.; Peris, E. Catalyst Enhancement and Recyclability by Immobilization of Metal Complexes onto Graphene Surface by Noncovalent Interactions. ACS Catal. 2014, 4, 2038-2047. 9. Huang, H.; Denard, C. A.; Alamillo, R.; Crisci, A. J.; Miao, Y.; Dumesic, J. A.; Scott, S. L.; Zhao, H. Tandem Catalytic Conversion of Glucose to 5-Hydroxymethylfurfural with an Immobilized Enzyme and a Solid Acid. ACS Catal. 2014, 4, 2165-2168. 10. Lohr, T. L.; Marks, T. J. Orthogonal Tandem Catalysis. Nat. Chem. 2015, 7, 477.



11. Lal, M.; Kumar, N. D.; Joshi, M. P.; Prasad, P. N. Polymerization in a Reverse Micelle Nanoreactor: Preparation of Processable Poly(P-Phenylenevinylene) with Controlled Conjugation Length. Chem. Mater. 1998, 10, 1065-1068. 12. Vriezema, D. M.; Comellas Aragonès, M.; Elemans, J. A. A. W.; Cornelissen, J. J. L. M.; Rowan, A. E.; Nolte, R. J. M. Self-Assembled Nanoreactors. Chem. Rev. 2005, 105, 1445-1490. 13. Peters, R. J. R. W.; Louzao, I.; van Hest, J. C. M. From Polymeric Nanoreactors to Artificial Organelles. Chem. Sci. 2012, 3, 335-342. 14. Adıgüzel, R.; Taşcıoğlu, S. Micelle Nano-Reactors as Mediators of Water-Insoluble Ligand Complexation with Cu(Ii) Ions in Aqueous Medium. Chem. Pap. 2013, 67, 456-463. 15. Boucher-Jacobs, C.; Rabnawaz, M.; Katz, J. S.; Even, R.; Guironnet, D. Encapsulation of Catalyst in Block Copolymer Micelles for the Polymerization of Ethylene in Aqueous Medium. Nat. Commun. 2018, 9, 841. 16. Marguet, M.; Bonduelle, C.; Lecommandoux, S. Multicompartmentalized Polymeric Systems: Towards Biomimetic Cellular Structure and Function. Chem. Soc. Rev. 2013, 42, 512529. 17. Fischlechner, M.; Schaerli, Y.; Mohamed, M. F.; Patil, S.; Abell, C.; Hollfelder, F. Evolution of Enzyme Catalysts Caged in Biomimetic Gel-Shell Beads. Nat. Chem. 2014, 6, 791. 18. Longstreet, A. R.; McQuade, D. T. Organic Reaction Systems: Using Microcapsules and Microreactors to Perform Chemical Synthesis. Acc. Chem. Res. 2013, 46, 327-338. 19. Hartley, G. S. Aqueous Solutions of Paraffin-Chain Salts; a Study in Micelle Formation; Hermann & Cie: Paris, 1936. 20. Slomkowski, S., et al. Terminology of Polymers and Polymerization Processes in Dispersed Systems. Pure Appl. Chem. 2011, 83, 2229. 21. Laschewsky, A. Polymerized Micelles with Compartments. Curr. Opin. Colloid Interface Sci. 2003, 8, 274-281. 22. Lutz, J. F.; Laschewsky, A. Multicompartment Micelles: Has the Long‐ Standing Dream Become a Reality? Macromol. Chem. Phys. 2005, 206, 813-817. 23. Kubowicz, S.; Baussard, J. F.; Lutz, J. F.; Thünemann, A. F.; von Berlepsch, H.; Laschewsky, A. Multicompartment Micelles Formed by Self‐ Assembly of Linear Abc Triblock Copolymers in Aqueous Medium. Angew. Chem. Int. Ed. 2005, 44, 5262-5265. 24. Li, Z.; Kesselman, E.; Talmon, Y.; Hillmyer, M. A.; Lodge, T. P. Multicompartment Micelles from Abc Miktoarm Stars in Water. Science 2004, 306, 98-101. 25. Moughton, A. O.; Hillmyer, M. A.; Lodge, T. P. Multicompartment Block Polymer Micelles. Macromolecules 2012, 45, 2-19. 26. Moughton, A. O.; Sagawa, T.; Yin, L.; Lodge, T. P.; Hillmyer, M. A. Multicompartment Micelles by Aqueous Self-Assembly of Μ-a(Bc)N Miktobrush Terpolymers. ACS Omega 2016, 1, 1027-1033. 27. Rosser, T. E.; Reisner, E. Understanding Immobilized Molecular Catalysts for FuelForming Reactions through Uv/Vis Spectroelectrochemistry. ACS Catal. 2017, 7, 3131-3141. 28. Bullock, R. M.; Das, A. K.; Appel, A. M. Surface Immobilization of Molecular Electrocatalysts for Energy Conversion. Chem. Eur. J 2017, 23, 7626-7641. 29. Song, C. E.; Yang, J. W.; Roh, E. J.; Lee, S. g.; Ahn, J. H.; Han, H. Heterogeneous Pd‐ Catalyzed Asymmetric Allylic Substitution Using Resin‐ Supported Trost‐ Type Bisphosphane Ligands. Angew. Chem. Int. Ed. 2002, 41, 3852-3854.


Page 16 of 28

Page 17 of 28 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


30. Annis, D. A.; Jacobsen, E. N. Polymer-Supported Chiral Co(Salen) Complexes: Synthetic Applications and Mechanistic Investigations in the Hydrolytic Kinetic Resolution of Terminal Epoxides. J. Am. Chem. Soc. 1999, 121, 4147-4154. 31. Peukert, S.; Jacobsen, E. N. Enantioselective Parallel Synthesis Using Polymer-Supported Chiral Co(Salen) Complexes. Org. Lett. 1999, 1, 1245-1248. 32. Chapuis, C.; Barthe, M.; de Saint Laumer, J. Y. Synthesis of Citronellal by Rhi‐ Catalysed Asymmetric Isomerization of N,N‐ Diethyl‐ Substituted Geranyl‐ and Nerylamines or Geraniol and Nerol in the Presence of Chiral Diphosphino Ligands, under Homogeneous and Supported Conditions. Helv. Chim. Acta 2001, 84, 230-242. 33. Lu, J.; Dimroth, J.; Weck, M. Compartmentalization of Incompatible Catalytic Transformations for Tandem Catalysis. J. Am. Chem. Soc. 2015, 137, 12984-12989. 34. Hopwood, D. A.; Sherman, D. H. Molecular Genetics of Polyketides and Its Comparison to Fatty Acid Biosynthesis. Annu. Rev. Genet 1990, 24, 37-62. 35. Arigoni, D.; Sagner, S.; Latzel, C.; Eisenreich, W.; Bacher, A.; Zenk, M. H. Terpenoid Biosynthesis from 1-Deoxy-D-Xylulose in Higher Plants by Intramolecular Skeletal Rearrangement. Proc. Natl. Acad. Sci. U.S.A 1997, 94, 10600-10605. 36. Agapakis, C. M.; Boyle, P. M.; Silver, P. A. Natural Strategies for the Spatial Optimization of Metabolism in Synthetic Biology. Nat. Chem. Biol. 2012, 8, 527. 37. Shi, J.; Zhang, L.; Jiang, Z. Facile Construction of Multicompartment Multienzyme System through Layer-by-Layer Self-Assembly and Biomimetic Mineralization. ACS Appl. Mater. Interfaces 2011, 3, 881-889. 38. Miller, A. L., II; Bowden, N. B. A Materials Approach to the Dual‐ Site Isolation of Catalysts Bonded to Linear Polymers and Small, Ionic Molecules for Use in One‐ Pot Cascade Reactions. Adv. Mater. 2008, 20, 4195-4199. 39. Callaway, C. P.; Bond, N.; Hendrickson, K.; Lee, S. M.; Jang, S. S. Structural Tunability of Multicompartment Micelles as a Function of Lipophilic–Fluorophilic Block Length Ratio. The Journal of Physical Chemistry B 2018, 122, 12164-12172. 40. Chou, S.-H.; Tsao, H.-K.; Sheng, Y.-J. Morphologies of Multicompartment Micelles Formed by Triblock Copolymers. J. Chem. Phys. 2006, 125, 194903. 41. Zhao, Y.; Liu, Y.-T.; Lu, Z.-Y.; Sun, C.-C. Effect of Molecular Architecture on the Morphology Diversity of the Multicompartment Micelles: A Dissipative Particle Dynamics Simulation Study. Polymer 2008, 49, 4899-4909. 42. Marsat, J.-N.; Heydenreich, M.; Kleinpeter, E.; von Berlepsch, H.; Böttcher, C.; Laschewsky, A. Self-Assembly into Multicompartment Micelles and Selective Solubilization by Hydrophilic−Lipophilic−Fluorophilic Block Copolymers. Macromolecules 2011, 44, 2092-2105. 43. Gröschel, A. H.; Schacher, F. H.; Schmalz, H.; Borisov, O. V.; Zhulina, E. B.; Walther, A.; Müller, A. H. E. Precise Hierarchical Self-Assembly of Multicompartment Micelles. Nat. Commun. 2012, 3. 44. Wang, L.; Lin, J. Discovering Multicore Micelles: Insights into the Self-Assembly of Linear Abc Terpolymers in Midblock-Selective Solvents. Soft Matter 2011, 7, 3383-3391. 45. Zhong, C.; Liu, D. Understanding Multicompartment Micelles Using Dissipative Particle Dynamics Simulation. Macromol. Theory Simul. 2007, 16, 141-157. 46. Xia, J.; Zhong, C. Dissipative Particle Dynamics Study of the Formation of Multicompartment Micelles from Abc Star Triblock Copolymers in Water. Macromol. Rapid Commun. 2006, 27, 1110-1114.



47. Procházka, K.; Martin, T. J.; Webber, S. E.; Munk, P. Onion-Type Micelles in Aqueous Media. Macromolecules 1996, 29, 6526-6530. 48. Talingting, M. R.; Munk, P.; Webber, S. E.; Tuzar, Z. Onion-Type Micelles from Polystyrene-Block-Poly(2-Vinylpyridine) and Poly(2-Vinylpyridine)-Block-Poly(Ethylene Oxide). Macromolecules 1999, 32, 1593-1601. 49. Pleštil, J.; Kříž, J.; Tuzar, Z.; Procházka, K.; Melnichenko, Y. B.; Wignall, G. D.; Talingting, M. R.; Munk, P.; Webber, S. E. Small‐ Angle Neutron Scattering Study of Onion‐ Type Micelles. Macromol. Chem. Phys. 2001, 202, 553-563. 50. Read, E. S.; Armes, S. P. Recent Advances in Shell Cross-Linked Micelles. ChemComm 2007, 3021-3035. 51. Synatschke, C. V., et al. Multicompartment Micelles with Adjustable Poly(Ethylene Glycol) Shell for Efficient in Vivo Photodynamic Therapy. ACS Nano 2014, 8, 1161-1172. 52. Wang, X.; Gao, J.; Wang, Z.; Xu, J.; Li, C.; Sun, S.; Hu, S. Dissipative Particle Dynamics Simulation on the Self-Assembly and Disassembly of Ph-Sensitive Polymeric Micelle with Coating Repair Agent. Chem. Phys. Lett. 2017, 685, 328-337. 53. Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics. EPL 1992, 19, 155. 54. Koelman, J. M. V. A.; Hoogerbrugge, P. J. Dynamic Simulations of Hard-Sphere Suspensions under Steady Shear. EPL 1993, 21, 363. 55. Español, P.; Warren, P. B. Statistical Mechanics of Dissipative Particle Dynamics. EPL 1995, 30, 191. 56. Groot, R. D.; Warren, P. B. Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423-4435. 57. Materials Studio, 5.0; Accelrys, Inc.: San Diego, 2009. 58. Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. 59. Callaway, C. P.; Hendrickson, K.; Bond, N.; Lee, S. M.; Sood, P.; Jang, S. S. Molecular Modeling Approach to Determine the Flory‐ Huggins Interaction Parameter for Polymer Miscibility Analysis. ChemPhysChem 2018.


Page 18 of 28

Page 19 of 28 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


Table 1. Repulsion parameters 𝑎ij between each pair of species in the DPD simulation system. Note that 𝑎ii = 25.0 by definition56 [see equation (3)]. Values in shaded cells are implied by other cells due to the fact that 𝑎ij = 𝑎ji . Block A

Block B

Block C

Water

Block A

25.0

40.0

45.0

27.5

Block B

40.0

25.0

40.0

47.5

Block C

45.0

40.0

25.0

60.0

Water

27.5

47.5

60.0

25.0



Figure 1. Chemical structures of blocks exhibiting (a) hydrophilic, (b) lipophilic, and (c) fluorophilic characteristics. Preliminary simulations were performed on these species to determine representative 𝜒ij -values, which were then adjusted to ensure microphase separation between all species present in the DPD simulations.


Page 20 of 28

Page 21 of 28 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


Figure 2. (a) A visual representation of the notation convention followed in this work, wherein 𝑋𝑏̃𝑋,𝑠̃𝑋 represents a block of species X with reduced block and side chain lengths in DPD of 𝑏̃𝑋 and 𝑠̃𝑋 , respectively. Following this convention, the triblock copolymer presented in (b) is represented as B2,6A18,4C10,2.



Figure 3. A horseshoe diagram demonstrating the structural variation of strongly fluorophilic-rich (ℛ𝑙 ≪ 1) BAC micelles as a function of the generalized structural predictor ℛ. Despite a constant ℛ𝑙 -value in all cases, tunability from regime I to near regime II is observed, highlighting the importance of ℛ as a governing structural parameter. Water visibility is disabled for clarity.


Page 22 of 28

Page 23 of 28 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


Figure 4. A horseshoe diagram demonstrating the structural variation of weakly fluorophilic-rich (ℛ𝑙 < 1) BAC micelles as a function of the generalized structural predictor ℛ. Despite a constant ℛ𝑙 -value in all cases, tunability between regimes I and II is observed, highlighting the importance of ℛ as a governing structural parameter. Water visibility is disabled for clarity.



Figure 5. A horseshoe diagram demonstrating the structural variation of balanced (ℛ𝑙 ~1) BAC micelles as a function of the generalized structural predictor ℛ. Despite a constant ℛ𝑙 -value in all cases, slight tunability across all regimes is observed. Water visibility is disabled for clarity.


Page 24 of 28

Page 25 of 28 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


Figure 6. A horseshoe diagram demonstrating the structural variation of weakly lipophilic-rich (ℛ𝑙 > 1) BAC micelles as a function of the generalized structural predictor ℛ. Despite a constant ℛ𝑙 -value in all cases, tunability between regimes II and III is observed. Water visibility is disabled for clarity.



Figure 7. A horseshoe diagram demonstrating the structural variation of strongly lipophilic-rich (ℛ𝑙 ≫ 1) BAC micelles as a function of the generalized predictor ℛ. Despite a constant ℛ𝑙 -value in all cases, tunability from near regime II to regime III is observed. Water visibility is disabled for clarity.


Page 26 of 28

Page 27 of 28 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


Figure 8. A comparison between the micelle morphologies resulting from branched and linear polymer architectures of identical ℛ -value. Although select architectures ( ℛ = 0.086 , ℛ = 0.429 , and ℛ = 2.143 ) preferentially form similar morphologies, a noticeable structural divergence between the two architectures even for identical ℛ-values suggests a dependence not only on composition, but on architecture as well.



Table of Content Graphics


Page 28 of 28

1 Effect of Block Length and Side Chain Length Ratios on Determining

Recommend Documents