Atomistic Structure of Bottlebrush Polymers - American Chemical Society

Aug 12, 2014 - Biology and Soft Matter Division, Neutron Sciences Directorate,. ‡. National Center for Computational Sciences, and. §. Center for. ...
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Atomistic Structure of Bottlebrush Polymers: Simulations and Neutron Scattering Studies Zhe Zhang,†,⊥ Jan-Michael Y. Carrillo,‡,⊥ Suk-kyun Ahn,§,⊥ Bin Wu,∥ Kunlun Hong,§ Gregory S. Smith,† and Changwoo Do*,† †

Biology and Soft Matter Division, Neutron Sciences Directorate, ‡National Center for Computational Sciences, and §Center for Nanophase Materials SciencesOak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Physics and Astronomy, Joint Institute for Neutron Science, University of Tennessee, Knoxville, Tennessee 37996, United States S Supporting Information *

ABSTRACT: We have used small angle neutron scattering (SANS) measurement and atomistic molecular dynamics (MD) simulations to investigate the conformation of bottlebrush polymers with poly(norbornene) (PNB) backbone and different sizes of poly(lactide) (PLA) side chains (PNB25g-PLA5, PNB25-g-PLA10, and PNB25-g-PLA19). At early stage of simulations, stretched side chains with visible spatialcorrelations of about 30 Å were observed. The experimentally measured SANS data, on the other hand, does not exhibit any correlation peaks in the corresponding length scale indicating a compact form rather than a stretched-hairy polymer conformation. As the simulation continued, the spatial correlations between side chains disappeared after about 40 ns of chain relaxation, and the scattering intensity calculated for the simulated structure becomes reasonably close to the measured one. Statistical approach is used to overcome the time scale limitation and search for optimal conformation space, which also provides a good agreement with the experimental data. Further coarse-grained simulation results suggest that the side chain conformation strongly depends on the solubility competition among side chain, backbone, and solvent. Significant changes of backbone dynamics due to the side chain encapsulation have been revealed and discussed. a flexible rod. The analysis based on this model showed excellent agreement with scattering experiments and provided useful physical quantities that characterizes the polymer.5,6,13,15 However, in typical bottlebrush polymers, the grafted side chain is often a single chain which stems from the backbone and not the star-shaped brushes in which multiple side chain stem from a single core molecule. Therefore, one can imagine that the realistic cross section of such a bottlebrush polymer may be different from a disk and rather like an anisotropic oval shape with random orientation. This may or may not be true depending on how the side chains interact with solvent molecules. While the scattering experiments can provide characteristic length scales for a given model, the detailed structure of side chains which needs to be understood in order to justify the applied model is inevitably smeared by the ensemble averaging process of the scattering measurements. Molecular dynamics (MD) simulation is a powerful tool to provide an atomistic scale understanding of the structure and dynamics of biomolecules,16,17 proteins,18,19 and polymers.20−23 Most simulation studies of polymeric systems are generally performed using coarse-grained (CG) schemes24−26 due to the

1. INTRODUCTION Bottlebrush polymers are a special class of comb-shaped macromolecules where relatively short polymeric side chains are densely grafted along the polymer backbone.1−3 In the melt state, the highly branched side chains substantially reduce the entanglement, which allows their rheological properties and solid-state self-assembly to be altered for potential applications in nano-, bio- and photonic materials.4 In the solution state, the excluded volume interaction from side chain leads polymer backbone to be extended, resulting in overall polymer conformation to adopt a cylindrical or an ellipsoidal conformation in dilute condition.3 The conformation of bottlebrush polymers can be manipulated by molecular parameters including sizes5,6 of backbone and side chain, grafting density7,8 as well as solvent quality.9−11 Small angle neutron scattering (SANS) has been utilized extensively to investigate the structure and conformation of bottlebrush polymers in the past decade. Various analysis methods5,12 have been developed along with experiments which lead to a general understanding that the stiffness of the polymers is closely related to the conformation of side chains, backbones, and their interactions.13,14 One of the well accepted models for bottlebrush polymers has been the flexible-cylinder approximation, where the cross section of the bottlebrush polymers has been approximated as a disk and the backbone as © 2014 American Chemical Society

Received: March 25, 2014 Revised: July 25, 2014 Published: August 12, 2014 5808

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and depending on the side chain conformation around the backbone, the overall shape may become more cylindrical. The simulation was performed with the AMBER simulation package.38 Within the AMBER framework, the polymer was created by (1) building norbornenyl end-functionalized PLA macromonomer (NB-PLA) followed by (2) repeating NB-PLA units for 25 times. The atomic partial charges were derived using the AM1/BCC method, and general amber force field is employed to account for interatomic interactions.39−41 After energy minimization and solvation into tetrahydrofuran (THF) in a cubic periodic box of 200 Å on a side to ensure that there are at least 20 Å between the outermost atoms of the polymer and the boundary of the simulation box, the whole system was brought to equilibrium by NPT simulation over 1 ns at 300 K and 1 bar. The largest system has total 451139 atoms which include a polymer (PNB25-g-PLA19) consisting of 5265 atoms and 34298 THF molecules. The simulation time step was set to 2 fs. Within less than 500 ps simulation time, the density of the system was equilibrated to approximately 0.95 g/cm3. After the density, temperature, and pressure are stabilized during the first 1 ns NPT run, an additional 1 ns NPT simulation was performed before going into a long NVT simulation42 for 60 ns. Trajectories of atoms’ coordinates were written every 100 ps for the analysis. The scattering intensity from the trajectories was calculated by

large system sizes and the limitations of computing power. By reducing computational load, CG models have been applied to show many self-assembly behaviors such as vesicle formation and fusion,27 lamellar phase transformations,28 and thermal degradation behavior on substrates.29 Atomistic simulation, on the other hand, has limited accessible time and length scales which can be achieved at a given computing power and time. Despite the limitations of atomistic simulation, it can provide a better understanding of structure and dynamics at the molecular level such as internal dynamics of polymers and their interactions with surrounding solvents,30,31 which cannot be studied by approximated potential forms often used in CG models. In addition, atomistic simulations can be used to provide more realistic CG model parameters by using inverted Monte Carlo schemes32,33 or force matching approaches.34 Here, we investigate the detailed structure of side chains and backbones of bottlebrush polymers consisted of poly(lactide) (PLA) side chains and poly(norbornene) (PNB) backbone. To our knowledge, this is first investigation of bottlebrush polymers combining atomistic MD simulation, CGMD simulation, and scattering experiment in order to gain detailed understanding of polymer structures and dynamics. In addition, we believe that this is a first simulation study of a bottlebrush polymer with a PNB backbone incorporating explicit solvent molecules to address their effect on the conformation.

1 I(q) = ⟨ V

2

N

∑ bme

−iq ⃗· rm⃗

⟩

m=1

where q⃗ is the wavevector, r ⃗ is the position of the atom, b is the coherent scattering length of atom m, V is the sample volume, and m is the index of atoms of the polymer which consists of N total atoms. The angular average over the wave vectors is performed to take into account the random orientations of the polymers in the solution. Neutron Scattering Experiment. SANS measurement was performed at the EQ-SANS instrument at the Spallation Neutron Source (SNS) located at Oak Ridge National Laboratory (ORNL) using 60 Hz operation. Two configurations of sample-to-detector distances of 2.5 and 5 m with wavelength bands of 2.5 Å < λ < 6 and 10 Å < λ < 13.5 Å, respectively, were used to cover the q range of 0.005 Å−1 < q < 0.3 Å−1 where q = (4π/λ) sin(θ/2) is the magnitude of the scattering vector, and θ is the scattering angle. The polymer solution of PNB25-g-PLA19 in THF was prepared at 10 mg/mL concentration, and measured in a 2 mm path length quartz cell at 25 °C. The measured scattering intensity was corrected for detector sensitivity and the background from the empty cell, and placed on an absolute scale using a calibrated standard.

2. METHODS Atomistic Simulation. The PLA bottlebrush polymer is chosen as a model system, where the PLA side chains are grafted to the PNB backbone, denoted as PNBm-g-PLAn (Figure 1). This polymer was

3. RESULTS AND DISCUSSION In Figure 2a, the calculated scattering intensities from the simulations are plotted along with the experimentally measured one from the EQ-SANS. For the calculation of I(q) at different times from the NVT simulation, 1 ns duration trajectories were averaged and are vertically shifted in Figure 2a for comparison purposes. The simulated scattering curves at 40 ns and above essentially overlap after the density, temperature, and pressure stabilization. From the scattering curves at early stages of the NVT simulation (t < 10 ns), one can immediately notice that the structure at small length scales such as surface morphology or cross sectional structure is very different from the experimentally measured polymer structure, since the simulated polymer scattering shows a distinctive peak-feature at around q ∼ 0.2 Å−1 while the measured scattering curve does not. This artificial scattering feature is a result of PLA side chains, whose correlation distance is around 30 Å. (Supporting Information) Since there is only one polymer simulated and no sampling is performed, this correlation distance clearly appears in the calculated scattering curve. Qualitatively, the scattering intensities after 40 ns agree with the measured SANS data

Figure 1. Initial atomistic models for (a) PNB25-g-PLA5, (b) PNB25-gPLA10, and (c) PNB25-g-PLA19. (d) Projected view of model polymers along the backbone. The chemical structure is shown in the inset.

prepared by grafting-through approach using ring-opening metathesis polymerization (ROMP)35−37 that ensures complete grafting of PLA side chains on the PNB backbone. For simulations, PNBm-g-PLAn having different degree of polymerization (DP) of side chain (n = 5, 10, and 19) at constant DP of PNB backbone (m = 25) have been used. Although artificial, the initial structure of PNBm-g-PLAn described in Figure 1 is worth mentioning. While the projected shapes along the backbone (Figure 1d) look like circular disks and may seem to be consistent with the flexible cylinder approximation, the cross section of individual units along the backbone is far from cylindrical in cross section. Therefore, when the side chains are stretched, approximating the cross section of the bottlebrush polymer as circular disks may not reflect realistic geometry. This is however only the initial configuration 5809

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Figure 3. (a) For individual trajectory frame, χ2 is estimated by comparing the calculated Isim(q) with measured scattering profile and plotted against the Rg. The gray area represents χ2 < 0.3. (b) Isim(q) of single best frame, single worst frame, selected average frames are plotted along with the experimental data. (c) Iso-density surface of carbon atoms at the end of brushes is shown with the snapshot structure of PNB25-g-PLA19 at 60 ns. The scale bar indicates 100 Å. The backbone and the side chains of the bottlebrush are shown with red and yellow beads, respectively. All other atoms (hydrogens and oxygens) are not shown for visual clarity. (d) Fittings of scattering intensities by using a rigid cylindrical model (solid red) and an ellipsoid model (dashed blue) SANS data.

Figure 2. (a) Scattering intensities calculated at different simulation times. I(q) at 40, 50, and 60 ns (green, orange, and red, respectively) overlaps with each other. I(q) from the experimental SANS measurement is shown with blue open circles. (b) Radius of gyration over the simulated time. (c) Snapshot of the simulated polymer at 60 ns (left, axial view; right, side view). Backbones are indicated with red and side chain carbons are shown with yellow for visual clarity.

much better than the scattering curves at earlier stages of simulation, which indicates that the simulated structure above 40 ns is close to the experimentally measured equilibrated one. The variation of Rg over simulated time in Figure 2b indicates that the structure has reached to a state where the motion of the polymer is slower than the simulation time scales. This opens a possibility that the structure may change again toward a bigger Rg, if the simulation is kept running over a longer time. The snapshot at 60 ns from the simulation (Figure 2c) shows the structure whose scattering intensity agrees well with the measured one. It looks more like a compact form rather than stretched hairy brush which is commonly known structural concept of brush polymers. Since atomistic MD simulations can only provide limited time scales, time, space, and number ensemble averages that are comparable to the experimental time scale and number of polymers cannot be achieved. This implies that any dynamic features or conformations of polymer that are above the time scale of our simulation may not be captured. However, the conformational space which is covered by the current simulation can be used without specific time stamp information in order to find better agreement between possible polymer structures and the scattering intensity. In order to examine the full conformation space, comparisons between the experimental and theoretical SANS profiles were performed for each frame of simulation using Pearson’s χ2:

fit is generally obtained from the trajectories with Rg ∼ 37 Å. By selecting the trajectories which satisfy χ2 < 0.3, statistically averaged structure is estimated which shows better agreement than the scattering curves from the single-frame analysis (Figure 3b). The mismatch at q > 0.2 Å−1 is likely to be due to the lack of the structured solvent consideration31 which has density different from bulk solvent. The space which is accessed by the carbon atoms at the end of the brushes are shown in Figure 3c with iso-density plot along with the snapshot at 60 ns. This volumetric representation shows the ensemble averaged shape of the polymer solutions, while the atomistic view is an instantaneous snapshot of one possible conformation. On the basis of the structure observed in Figure 2c and Figure 3c, particular form factors such as the cylindrical form factor and the ellipsoidal form factor6,15 rather than a flexible chain form factor, which is commonly used for long bottlebrush polymers, are chosen to approximately model the SANS data. Best fits with these form factors result in the diameter and the length of 54 and 98 Å for a rigid cylindrical model and minor and major axis of 31 and 106 Å for ellipsoid model, respectively. (Figure 3d) From the brush polymer trajectories between 40 and 60 ns, the moment of inertia tensor along the principal axis of constituting 1782 carbon atoms is calculated to be

2

2

χ =

∑

(Iexp(q) − Isim(q))

⎡1352759.7 ⎤ 0 0 ⎢ ⎥ 2 I=⎢ 0 1432941.2 0 ⎥ [Å ] ⎢⎣ 0 0 524540.3⎥⎦

Iexp(q)

where Iexp(q) is the measured SANS intensity, and Isim(q) is the calculated scattering intensity from the MD trajectories. The sum was taken over 72 data points within 0 Å−1 < q < 0.4 Å−1. The program SASSIE43 was used to perform the batch process. As a result of motions of the polymer during the simulation, various χ2 and Rg can be observed from the trajectories as shown in Figure 3a. The χ2 distribution indicates that the best

By equating this with the inertia tensors of an ellipsoid, corresponding dimensions from the simulated polymer trajectory is obtained. (see Supporting Information for the expression) Using the trajectories between 40 and 60 ns, major axis a and minor axes b, c of an ellipsoid are estimated to be a = 5810

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The difference in solubility’s as dictated in the force field would reflect in the size of the bottlebrush polymer. For WCA, ⟨Rg2⟩ is larger with a value of 35.2 ± 0.6 σ2 against 30.2 ± 0.7 σ2 for the HSP. Considering only the backbone monomers, ⟨Rg2⟩ is 20.0 ± 0.6 σ2 and 16.9 ± 0.8 σ2 for the WCA and HSP, respectively. Since the experimentally measured structural data showed reasonable agreement with the representative simulation result, it follows that we can try to understand the influence of different side chain lengths on the PNB-g-PLA conformation and dynamics from the series of simulation results. In parts a−d of Figure 5, the snapshots of the polymers at 60 ns are

111.6 Å, b = 55.4 Å, and c = 52.8 Å, respectively. This shows that the dimensions from both models for scattering data fitting reasonably agree with the dimensions of simulated brush polymer, while the scattering intensities at high-q cannot be fit perfectly by either model due to the mismatch of the exact shapes. In an attempt to understand the side chain conformation observed in the simulation, the solubility difference between the backbone and the chain is considered. We performed CGMD in which backbone and side chain monomers are represented as Lennard-Jones beads of diameter σ, and the polymer architecture is maintained via finite extensible nonlinear elastic (FENE) bonds. The simulations were carried out in the canonical ensemble (NVT) with implicit solvent and the temperature was maintained by coupling the system to a Langevin thermostat such that thermal energy, kBT is one. The relative strength of the pair-interactions between different types of beads (i.e., PNB−PNB, PLA−PLA, and PNB−PLA) was estimated based on the calculated Flory−Huggins interaction parameter, χ that was obtained by using Hansen solubility parameters (HSP).44 For details of the CGMD simulations we direct the reader to the Supporting Information (Figure S7, Table S.1 and S.2). It was determined that THF is a better solvent for PLA than for PNB. The value for PNB is in at the boundary between a good-bad solvent given the accuracy provided by HSP. In this CGMD simulation, a slightly bad solvent quality is specified for PNB-THF interaction, which results in the condensed shape of the bottlebrush polymer having a form factor similar to the atomistic simulation and experiment. (Figure 4, HSP) For comparison, a CGMD

Figure 5. MD simulation snapshots at 60 ns of (a) PNB25, (b) PNB25g-PLA5, (c) PNB25-g-PLA10, and (d) PNB25-g-PLA19. Black bars at the bottom indicate 50 Å. (e) Radius of gyrations averaged between 40 and 60 ns of simulations. (f) Time-averaged coordination number of last carbon atoms of side chains with respect to the backbones.

Figure 4. Conformation of coarse-grained PNB-g-PLA bottlebrush polymer for a system using solvent qualities derived from Hansen solubility parameters (HSP, top left) and for a system that is good solvent for both PLA and PNB (WCA, bottom left). Form factor of the WCA and HSP conformation (right). The values for the P(q) of WCA set was shifted by 10× for clarity.

summarized. It should be noted that the snapshot of atomistic MD simulation cannot capture any dynamics or conformations that is outside the simulated time scale. The carbon atoms in the backbone and the side chains are indicated in red and yellow, respectively. All other atoms are not shown for visual clarity. PNB25 homopolymer with no side chains exhibits typical Gaussian coil motions and shape. As the length of the side chain increases from PLA5 to PLA19, the shape of polymer changes from a chain-like to a compact form, i.e. with the presence of long side chain, the polymers are densely packed rather than being hairy. The size of polymers in terms of radius of gyrations is compared in Figure 5e. Overall, the Rg increases with increasing PLA chain length. The growth rate of backbone, however, seems to be smaller, possibly due to the free space restriction imposed by the side chains. As expected, the Rg with side chains is slightly bigger than Rg of pure backbones and the difference keeps increasing as the side chain length increases. The Rg of PNB25-g-PLA5 shows distinctively increased size

simulation was performed where good solvent quality was specified for all interactions (Weeks−Chandler−Andersen, WCA potential) resulting in a correlation peak at high-q (q = 1.67 σ−1 which is r = 3.76 σ) similar to what was observed in the early stages of the atomistic MD simulation. (Figure 4, WCA) This correlation peak is absent in the HSP simulation. The HSP simulation is qualitatively in agreement with the results of the SANS experiment and equilibrated atomistic MD simulation where the conformation of the brush follows a more condensed shape while that of the WCA follows the conformation of the unequilibrated atomistic simulation (t < 10 ns) where there is a correlation between the distances of the side-chains. However, when 50 simulation frames were used for averaging, such correlation peaks disappear mostly (Figure S8). 5811

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previously reported.15 In addition, the Rg of backbone seems to be influenced by the side chains in both atomistic MD simulation and CGMD. The CGMD backbone adopts a stretched conformation and its extent of stretching increases with the side chain length but saturates at Nsc ≈ Nb/2 similar to what was observed by Rathgeber et al.,46 where Nsc is the number of monomers of the side chain and Nb is that of backbone. Structural arrest by the side chain not only influences the overall shape of the polymer but also changes the chain dynamics dramatically, especially the dynamics of the backbones. The incoherent intermediate scattering functions, estimated from the atomistic MD trajectories of the backbone, are shown in Figure 7a for selected q values for visual clarity.

compared to its neighbors, which is comparable with the size of PNB25-g-PLA19. (Figure 5e) It should be noted that this does not indicate the structural details of two polymers are the same. In Figure 5f, the coordination number of the last carbon atoms of side chains with respect to the backbone chain is estimated and averaged over the simulation time. As expected, the peak shifts toward longer distance with increasing side chain length. However, the coordination number of PNB25-g-PLA5 decays much slower and extends to the distance comparable to others. The distinct shape of the coordination number profile of PNB25-g-PLA5 should be attributed to the stretched backbone. Since the individual side chain length is very short for PNB25-gPLA5, the coordination number at long distance tale (>30 Å) should mainly come from different side chains and reflects the conformation of the backbone directly. Therefore, the backbone has to be stretched more in order to have finite coordination number at long distances. One can speculate to explain the nonmonotonic behavior of Rg from the atomistic simulation. The added short side chains prevent coiling motions of backbones due to excluded volume effect, which results in more stretched conformation (Figure 5b). When the length of PLA becomes longer, the relative solubility difference discussed before with CGMD can drive the PLA side chains to encapsulate the PNB backbones leading to a compact shape with smaller radius of gyration (Figure 5c). However, with bigger side chains (PLA19) the free volume available for the polymers to compact is hindered by PLA’s own volume and therefore, the radius of gyration increases again (Figure 5d). This implies that solubility and the side chain length play important roles in determining the conformation of bottlebrush polymers.45 It is interesting to note that such nonmonotonic relation between the side chain length and the size of the bottlebrush polymer was also found from Figure 4 and 5 in ref 6, although the polymer is different. In CGMD with HSP potential, however, Rg showed monotonic changes with increase side chain length. (Figure 6) It is not completely ruled

Figure 7. (a) Incoherent intermediate scattering function of PNB backbone at q = 0.1 Å−1 (solid line) and q = 0.2 Å−1 (dashed). (b) Relaxation times from the stretched exponential fitting. Error bars are omitted because they are smaller than the size of markers. (black, PNB25; red, PNB25-g-PLA5; green, PNB25-g-PLA10; blue, PNB25-gPLA19).

Since only incoherent scattering part is considered, self-motions of monomer segments dominate the relaxation process within 10 ns. Both PNB25-g-PLA10 and PNB25-g-PLA19 seem to show very slow backbone dynamics compared to the PNB25-g-PLA5 or PNB25 homopolymer. A simple estimation of the relaxation time scale by fitting a stretched exponential form (S(q,t) ∼ exp(−(t/τ))β) show that the relaxation time scale for all qranges of PNB25-g-PLA5 is about 1 order of magnitude faster than the other two polymers, but still significantly slower than the PNB homopolymer. (Figure 7b) The slow chain dynamics can be attributed to the compact structure, where the PLA side chains form shells encapsulating the PNB backbones. (Figure 5c,d) This shows an excellent example how the dynamics of polymer backbones is related with the structure of the bottlebrush polymers and the length of the side chains. More details of data and fitted parameters can be found in the Supporting Information.

Figure 6. Radius of gyrations from the CGMD with HSP potential along with the number of monomers of the side chain (NSC). (black, all beads; blue, backbone beads only).

4. CONCLUSION We have investigated structure and dynamics of PLA bottlebrush polymers (PNB-g-PLA) using atomistic MD and CGMD simulations as well as neutron scattering experiment. The scattering intensities calculated at longer simulation time (t > 40 ns) matched well with that from experimental SANS measurement, even though the simulation time was shorter than the longest relaxation time scale of the PNB25-g-PLA19. This agreement implies that the configurations from MD trajectories are reliable to interpret the SANS data for structural understanding. With increasing side chain length, the structure of the bottlebrush polymer is found to change from a flexible

out that the nonmonotonic relationship between side chain length and the bottlebrush polymer size from the full atomistic MD simulation comes from (1) force field oriented artifact or (2) short simulation time scale coverage, and it is currently under investigation with different partial charge methods and force-field as well as experimental efforts to synthesize bottlebrushes with different side chain lengths. Regardless of this discrepancy, MD results suggest that the high relative ratio between the length of backbone and side chain is a critical parameter for bottlebrush polymers to be highly extended as 5812

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chain to a compact form. It was also found that the resulting structures influence on the dynamic properties of the polymers suggesting close relation between the structure and the dynamics properties of bottlebrush polymers. Addition of even a short side chain slowed down the motion of backbones approximately 1 order of magnitude. The dynamics of backbone motion is found to be saturated once the side chains start to encapsulate the backbones.

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ASSOCIATED CONTENT

S Supporting Information *

Materials, details of atomistic simulation procedure, scattering models, and CGMD methods. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(C.D.) E-mail: [email protected]. Author Contributions ⊥

These authors have equally contributed to this work. The manuscript was written through contributions of all authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research at Oak Ridge National Laboratory’s Spallation Neutron Source and Center for Nanophase Materials Sciences was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Research presented in this work is also supported by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Energy Division. This research used resources of the Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22725 with UT-Battelle, LLC. J -M.C.’s contribution was sponsored by the Office of Advanced Scientific Computing Research; U.S. Department of Energy and performed at the Oak Ridge National Laboratory, which is managed by UTBattelle, LLC under Contract No. DE-AC05-00OR22725. The authors thank Dr. Joseph Curtis for a discussion and guide on SASSIE and Dr. Wei-Ren Chen for scientific discussions. This work benefitted from CCP-SAS software developed through a joint EPSRC (EP/K039121/1) and NSF (CHE-1265821) grant.

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