Quantitative 3D determination of self-assembled structures on nanoparticles using small angle neutron scattering

The ligand shell (LS) determines a number of nanoparticles’ properties. Nanoparticles’ cores can be accurately characterized; yet the structure of the LS, when composed of mixture of molecules, can be described only qualitatively (e.g., patchy, Janus, and random). Here we show that quantitative description of the LS’ morphology of monodisperse nanoparticles can be obtained using small-angle neutron scattering (SANS), measured at multiple contrasts, achieved by either ligand or solvent deuteration. Three-dimensional models of the nanoparticles’ core and LS are generated using an ab initio reconstruction method. Characteristic length scales extracted from the models are compared with simulations. We also characterize the evolution of the LS upon thermal annealing, and investigate the LS morphology of mixed-ligand copper and silver nanoparticles as well as gold nanoparticles coated with ternary mixtures. Our results suggest that SANS combined with multiphase modeling is a versatile approach for the characterization of nanoparticles’ LS.


Supplementary Note 1. FTIR measurements of PET-DDT nanoparticles
In order to prove that the deuteration does not affect the ligand ratio on the nanoparticles, we used FTIR to measure the PET-DDT and PET-dDDT samples. As shown below, the FTIR spectra of a mixture of DDT and dDDT homoligand nanoparticles were recorded at varying molar ratios of the nanoparticles, Figure S3A. The ratio of the intensity of the CH2 and CD2 stretching peaks was then calculated and plotted against the molar ratio of the nanoparticles in order to build a calibration curve, Figure S3B. Then the FTIR spectra of PET-DDT and PET-dDDT nanoparticles were recorded, Figure S3C. The CD2 peak intensity of the PET-dDDT nanoparticles was then converted to the corresponding CH2 intensity using the calibration curve discussed above. The ratio of between the intensity of the aromatic CH stretching and the aliphatic CH2 stretching was then calculated for both the PET-DDT and PET-dDDT nanoparticles. For the former it was found to be 0.14 and for the latter it was found to be 0.13. We believe that these two values are within error one to each other indicating that the two particles have the same composition. We notice that these ratios do not indicated the stoichiometry on the ligand shell as they have not been corrected for the relative intensity of the two types of the peaks.

Supplementary Note 2. Description of MONSA fitting method
Scattering intensity from a dilute monodisperse solution is an average of scattering from all possible orientations of the particle, determined by I(q)=Σ Ω (A 2 (q)), where q=(4πsinθ)/λ, is the scattering vector, while 2θ is scattering angle and λ is the wavelength of neutron or Xray beam. In a SANS measurement, selective deuteration could be employed to highlight specific components. The scattering intensity thus becomes I(q)=Σ i n (Δρ i V i ) 2 P i (q), where Δρ i =ρ i-ρ s , is the contrast of component i against solvent and P i (q) is the form factor of each component. The partial amplitudes from the volume occupied by the k-th phase in a DAM are rapidly evaluated from the bead positions using spherical harmonics.
Starting from a random configuration, simulated annealing (SA) is employed to search for a model composed by interconnected compact phases, which simultaneously fits multiple scattering curves from the constructs to minimize overall discrepancy: Here the index k runs over the scattering curves, N k are the numbers of experimental points, c k are scaling factors and I calc (q j ) and σ(q j ) are the intensities calculated from the subsets of the beads belonging to the appropriate phases and the experimental errors at the momentum transfer q j , respectively.

Supplementary Note 3. Test of the Robustness of the Approach
To test the robustness of the proposed Monte-Carlo fitting method, different input parameters were used to fit the same data described above. Figure S7A shows the resulted model when the input volume fraction of PET-DDT was changed by 10% from NMR results, i.e. 22.9% for gold, 50.3% for DDT and 26.6% for PET. The low-resolution model, Figure S7A, built with these parameters still shows very similar features and the stripe-like elongated domain features remain substantially the same. When the volume fraction is further changed to more than 30%, the resulted model still shows elongated stripe-like domains, but the ligand shell structure becomes unphysical, with large bare-gold domains exposed to solvents. When no constraints are added to the volume fraction, i.e. volume fraction penalty is set to 0, but the gold core size is fixed, similar phase separation features are still observed ( Figure S7B). Other input parameters such as looseness of beads are also changed and all the models are run several times starting from random configuration, yielding always similar results ( Figure S7C).

Supplementary Note 4. Extracting averaged thickness of nanodomains
The averaged domain size was measured as shown below in Figure S6A. The domains composed of one type of the ligand, e.g. PET, is separated from the rest of the bead model. Then the thickness of each separate domain is then measured manually at different points. Histogram of the stripe thickness is then plotted and averaged thickness calculated.

Dissipative Particle Dynamics (DPD)
DPD 1 is a particle-based mesoscopic simulation technique extensively used to model block copolymers 2,3 , mesophases 4 , surfactants 5-7 and polymer phase separations 8 , as well as the assembly of patchy and striped patterns on monolayer protected nanoparticle [9][10][11] . The DPD particles (or beads), each representing a group of small molecules or part of a molecule, interact by conservative, dissipative, and random forces, which are pairwise additive. The net force acting on a bead i can be expressed as F i = ∑ j≠i (F ij C +F ij D +F ij R ) and is calculated by summation over all other particles within a certain cutoff radius, r c , which gives the extent of the interaction range. Let r c , m, and k B T be the unit distance, the particle mass, and the thermal energy, respectively. The conservative force represents the excluded volume interactions between particles i and j in the dimensionless form F ij C = a ij (1 − r ij ) ȓ ij , where r ij = r i − r j , r ij = |r ij |, ȓ ij = r ij /r ij , a ij is the maximum repulsion between particles i and j. The dissipative, F ij D = − γ ω(r ij ) 2 (ȓ ij ·v ij ) ȓ ij , and random forces, F ij R = σ ω(r ij ) ȓ ij ζ/(δt) -1/2 , act as heat sink and source, respectively, and the combined effect of the two forces performs as a thermostat, where γ is a friction coefficient related to the thermal noise amplitude σ via the fluctuation−dissipation theorem, σ 2 = 2γk B T, ω(r) is a weight function, ζ is a normally distributed random variable with zero mean and unit variance that is uncorrelated for different particle pairs, δt is the time step of an integration scheme, and v ij = v i − v j is the relative velocity of the i th and the j th particles. The equations of particle motion, dr i /dt = v i and dv i /dt = F i , are solved using as integration scheme the velocity-Verlet algorithm implemented in LAMMPS [12][13][14] . Finally, when modelling chains two additional forces are acting between bonded beads: a harmonic spring connecting two adjacent particles i and j F ij where k b is a spring constant and r 0 the equilibrium distance between the particles, and F ijz A = 1/2 k θ sin(θ 0 -θ 0 ), where k θ is a spring constant and θ 0 the equilibrium angle between adjacent beads triples ijz in a row.

Models and computational details
The initial structure of the nanoparticle core was constructed by arranging gold coarsegrained units (or DPD beads) on an fcc lattice into an icosahedron of the desired diameter using OPENMD software (v. 2.3) 15 . Each ligand was represented by a flexible chain model of beads connected by harmonic springs. The mesoscale topology was assessed by matching the atomistic (calculated by molecular dynamics (MD) simulations) and mesoscale pair correlation functions for each ligand chain 16 . This resulted in the following mesoscale chains for MUA, DDT, PET, BT, OT: S 1 CM 5 CA 1 , S 1 CD 6 , S 1 CP 1 B 3 , S 1 CB 2 , S 1 CO 4 , respectively. Bead of type S typically represents the sulphur head group, beads CX (where X varies according to the ligand) denote the hydrocarbon units, CA unit mimics the carboxylic moiety. Benzene groups were modelled as a three-beads B rings. The subscripts indicate the bead number for each bead type.
Each ligand was placed close to the NP surface and oriented outward with the head-tail vector along the radial direction, ensuring that the corresponding position on the surface did not have clash with any previously positioned ligand using Packmol package 17 . A random configuration was imposed to arrange the chains on the gold surface. Then, the modified NP was solvated again by Packmol. Each system was tested on three independently generated starting configurations. To ascertain that the morphologies obtained correspond to a thermodynamic equilibrium, simulations were performed starting also from a phaseseparated configuration of the ligands.
The intra-and intermolecular interactions between DPD particles are expressed by the conservative parameter a ij , which inherits the chemical information of the system, and were estimated from atomistic MD simulations rescaling the MD interaction energies onto the corresponding mesoscale a ij parameter values 11,16,18-21 based on the modified PCFF force field (INTERFACE FF), optimized by Heinz and co-workers 22 for hybrid organic and metal interfaces, including gold. According to this computational procedure, two bead-bead interaction parameters have to be chosen. The gold-gold interaction parameter was set to a Au-Au = 49.6, based on our previous calculations 11,21 while we assigned toluene-toluene and tetrahydrofuran-tetrahydrofuran interaction equal to a TOL-TOL = 13.7 and a THF-THF = 35.1, respectively, based on the direct relationship with their isothermal compressibility at room temperature 23  where k b and k θ are the bond and angle spring constants while r 0 and θ 0 are the equilibrium distance and angle between connected beads, respectively.
Each configuration was first relaxed for 1x10 4 steps and a time step of Dt = 0.01τ. Then, at least additional 6x10 6 time steps (Dt = 0.02τ) were performed for productive runs. System equilibration was assessed monitoring temperature, pressure, density, and potential energy behaviour as well as composition of nearest neighbours of head groups. The force cut-off radius r c , the particle mass m i , and k B T (where are k B is the Boltzmann factor and T is the temperature) were taken as units of length, mass and energy. All mesoscale production runs, analysis and imaging were performed using LAMMPS running on GPUs and VMD 24 .  (Figure 12).

11-methoxy-11-oxoundecanoic acid-d 18
Following a modified method of Darwish et al. 1 , dimethyl undecanedioate-d 18 (10.6 g, 40.4 mmol) was dissolved in anhydrous methanol (20 mL). Barium hydroxide hexahydrate (6.5 g, 20.6 mmol, 0.51 equiv.) was partially dissolved in anhydrous methanol (20 mL) and added to the solution of the diester. The suspension was stirred at room temperature for 24 h. The solid was collected via vacuum filtration and washed with cold methanol (2 x 50 mL). The solid was suspended in water (150 mL) with stirring, to which HCl (1 M) was added until the solid dissolved. The solution was extracted with diethyl ether (2 x 150 mL). The combined organics were washed with brine, dried over Na 2 SO 4 and evaporated under reduced pressure to give a clear, colourless oil (7.2 g, 72% crude yield). 1 H NMR analysis ( Figure 16) showed the product contained ~16% of the undesired diacid due to the disproportion in the integration values of the residual proton signals of the methylene units next to the acid and the ester groups. It was decided to continue on to the next step without purification. 1 (Figures 16-18) Methyl 11-hydroxyundecanoate-d 18 Following a modified method of Darwish et al. 1 , crude 11-methoxy-11-oxoundecanoic acidd 18 (6.8 g, 27.4 mmol), was dissolved in anhydrous THF (50 mL) and cooled to 0 °C, to which borane-methyl sulfide complex (10 M, 3.8 mL, 38 mmol), was added drop-wise under an inert atmosphere. The solution was maintained at 0 °C for 2 h and allowed to come to room temperature overnight. Methanol (5 mL) was added dropwise and stirred for a further 2 h. The solution was sparged with N 2(g) and the solvent removed under reduced pressure.
Water and diethyl ether were added, with the aqueous layer extracted 2x with diethyl ether. The combined organics were sequentially washed with NaHCO 3 solution, brine and dried over Na 2 SO 4 and evaporated to give a clear oil. The oil was purified on silica by automated chromatography using petroleum ether/ethyl acetate mobile phase, to give a clear, colourless oil (3.7 g, 58%). 1

Methyl 11-bromoundecanoate-d 18
Methyl 11-hydroxyundecanoate-d 18 (3.7 g, 15.8 mmol) was dissolved in anhydrous dichloromethane (80 mL), to which triphenylphosphine (6.2 g, 23.7 mmol, 1.5 equiv.) was added. The mixture was cooled in an ice bath and stirred for 45 min. N-Bromosuccinimide (4.2 g, 23.7 mmol, 1.5 equiv.) was added portion-wise, and the solution stirred at 0 °C for 2 h and then allowed to warm to room temperature. The dark orange solution was evaporated to remove the CH 2 Cl 2 , and petroleum ether added. The white precipitate (triphenylphosphine oxide) was removed via filtration, and the filtrate concentrated and purified on silica by automated chromatography using petroleum ether/ethyl acetate mobile phase, to give a clear, pale yellow oil (3.0 g, 64%).

11-mercaptoundecanoic acid-d 18
Followed a modified procedure, 2 methyl 11-bromoundecanoate-d 18 (3.0 g, 10.1 mmol), and thiourea (0.81 g, 10.6 mmol, 1.05 equiv.) were refluxed in absolute ethanol (15 mL) for 2 h. Upon cooling to room temperature, a solution of NaOH (3.2 g, 40.4 mmol, 4 equiv., 10 mL) was added dropwise, and the solution stirred overnight at room temperature. The cloudy solution was refluxed for a further 3 h, and upon cooling the precipitate was removed via filtration and dried under vacuum. The solid was recrystallised from hexane to give a cream coloured solid (1.84 g, 77%).  2.1 g Phenyl acetic acid was dissolved in 40ml dry THF under ice bath and then dropwise added to the solution of 1.5 g lithium aluminium hydride in 30 ml dry THF. The reaction mixture was stirred at room temperature overnight. The reaction was quenched by adding HCl and most of the THF was evaporated. The mixture was dissolved in EtOAc and washed with H2O and brine, dried (1.8g, 90%).
1.8 g phenylethanol was dissolved in 20ml dry DCM and was added dropwise 10ml DCM solution of 1.61ml PBr3. The reaction mixture was allowed to stir for 3 hours and quenched with 5ml M-Q water and then washed three times with brine, NaHCO3 solution and H2O. The product was dried with rotavap at 60 degrees, yielding 1.47 g 2-Phenylethyl bromide (81%).