In situ small-angle X-ray scattering studies of sterically-stabilized diblock copolymer nanoparticles formed during polymerization-induced self-assembly in non-polar media

In situ SAXS studies reveal the evolution of copolymer morphology during the PISA synthesis of diblock copolymer nano-objects in mineral oil.

Gel permeation chromatography Molecular weight distributions were assessed by gel permeation chromatography (GPC) using THF eluent. The THF GPC set-up comprised two 5 m (30 cm) Mixed C columns and a WellChrom K-2301 refractive index detector operating at 950  30 nm. The mobile phase contained 2.0% v/v triethylamine and 0.05 w/v % butylhydroxytoluene (BHT) and the flow rate was 1.0 mL min -1 . A series of ten near-monodisperse poly(methyl methacrylate) standards (M p values ranging from 645 to 2,480,000 g mol -1 ) were used for calibration.

H NMR spectroscopy
Spectra were recorded in either CD 2 Cl 2 or CDCl 3 using a Bruker AV1-400 or AV1-250 MHz spectrometer. Typically 64 scans were averaged per spectrum.

Dynamic light scattering
Dynamic light scattering (DLS) studies were performed at 25 °C using a Zetasizer NanoZS instrument (Malvern Instruments, UK) at a fixed scattering angle of 173°. Copolymer dispersions were diluted to 0.10% w/w using n-heptane prior to light scattering studies. The intensity-average diameter and polydispersity of the diblock copolymer nanoparticles were calculated by cumulants analysis of the experimental correlation function using Dispersion Technology Software version 6.20. Data were averaged over thirteen runs each of thirty seconds duration.

Transmission electron microscopy
Transmission electron microscopy (TEM) studies were conducted using a Philips CM 100 instrument operating at 100 kV and equipped with a Gatan 1 k CCD camera. Diluted diblock copolymer solutions (0.10 % w/w) were placed as droplets on carbon-coated copper grids and exposed to ruthenium(VIII) oxide vapor for 7 min at 20 °C and dried prior to analysis. 1 This heavy metal compound acted as a positive stain for the core-forming PBzMA block in order to improve contrast. The ruthenium(VIII) oxide was prepared as follows: ruthenium(IV) oxide (0.30 g) was added to water (50 g) to form a black slurry; addition of sodium periodate (2.0 g) with stirring produced a yellow solution of ruthenium(VIII) oxide within 1 min.
Small-angle X-ray scattering SAXS patterns were collected at a synchrotron source (Diamond Light Source, station I22, Didcot, UK) using monochromatic X-ray radiation (wavelength, λ = 0.124 nm, with q ranging from 0.015 to 1.3 nm -1 , where q = 4π sin θ/λ is the length of the scattering vector and θ is one-half of the scattering angle) and a 2D Pilatus 2M pixel detector (Dectris, Switzerland). Glass capillaries of 2.0 mm diameter were used as a sample holder. For in situ SAXS studies, all reagents were first purged with nitrogen gas for 30 min, as described earlier, before a portion of the deoxygenated solution was transferred into a glass capillary. The capillary was then sealed in order to prevent exposure to oxygen before being placed into the brass holding stage, which was pre-heated to 90 °C using a water circulating bath. SAXS patterns were collected every 2 min for 3 h, or until no further evolution in the pattern was observed. SAXS data were reduced (integration, normalization and absolute intensity calibration using SAXS patterns of deionized water assuming that the differential scattering cross-section of water is 0.0162 cm -1 ) using Dawn software supplied by Diamond Light Source. 2 Selected static SAXS patterns were obtained for 1.0% w/w copolymer dispersions using a Bruker AXS Nanostar instrument modified with microfocus X-ray tube (GeniX3D, Xenocs) and motorized scatterless slits for the beam collimation (sample to detector distance 1.46 m, Cu Kα radiation and 2D HiSTAR multiwire gas detector). SAXS patterns were recorded over a q range of 0.08 nm -1 < q < 1.6 nm -1 . Glass capillaries of 2.0 mm diameter were used as a sample holder, and an exposure time of 1.0 h was utilized for each sample. SAXS data were reduced using Nika macros for Igor Pro by J. Ilavsky. All SAXS data collected at different locations were analyzed (background subtraction, data modelling and fitting) using Irena SAS macros for Igor Pro. 3

Renormalization of kinetic data for the RAFT dispersion polymerization of BzMA
Polymerization kinetic data were obtained for normal 10 mL laboratory-scale PISA syntheses (targeting PSMA 31 -PBzMA 2000 spheres and PSMA 13 -PBzMA 150 vesicles, respectively) by withdrawing multiple aliquots of the reaction solution prior to 1 H NMR analysis (see Figure 4a and Figure S3; blue data sets in each case). In each case these data were fitted to a sigmoid function using Igor Pro software using equation S1 shown below: Here y is the BzMA conversion (%), x is the relative polymerization time and a, b, c and d are arbitrary fitting parameters. This function was then utilized to calculate the polymerization kinetics for the two PISA syntheses conducted in a 2.0 mm glass capillary for the in situ SAXS experiments described above (see Figure 4a and Figure S3; red data sets in each case).

Determination of BzMA volume fraction in PSMA 31 -PBzMA x spherical nanoparticle cores
PSMA 31 -PBzMA x spheres prepared at 20 % w/w solids in mineral oil with x values of 396, 582, 784 or 1470 were diluted to 10% w/w in the same solvent. Then the relevant amounts of BzMA monomer (4-170 μL) and additional mineral oil were added to 2.0 mL aliquots of the above dispersion in order to replicate various time points during the RAFT dispersion polymerization of PSMA 31 -PBzMA 2000 spheres that correspond to BzMA conversions of 19.8%, 29.1%, 39.2% or 73.5%, respectively. Each BzMA-doped dispersion was then heated to 90 °C for 1 h before being sedimented using a Heraeus Biofuge Pico centrifuge at 13,000 S4 rpm (16,060 g) until the spheres were fully sedimented. The resulting clear supernatant, which contains any BzMA monomer not located within the nanoparticle cores, was removed and analyzed via 1 H NMR spectroscopy in CD 2 Cl 2 using triethoxymethylsilane (TEMS) as an internal standard (present at the same concentration as the BzMA monomer prior to centrifugation). The integrated oxymethylene signal due to the TEMS (~ 3.8 ppm) was set to six protons and the NMR signals corresponding to the aromatic protons ([Ar]) of the BzMA monomer were then integrated. The mole fraction of BzMA monomer present within the nanoparticle cores is therefore equal to 1-([Ar]/5). The BzMA volume fraction within the core domain (φ BzMA ) was subsequently calculated by considering the relative volumes of the monomer (as calculated using 1 H NMR spectroscopy; see Figure S1 below for the calibration plot) and the PBzMA core-forming chains within the nanoparticle cores. Given that 100% BzMA conversion corresponds to φ BzMA = 0, these data can be used to calculate φ BzMA at any time point during the PISA synthesis of PSMA 31 -PBzMA 2000 spheres. A plot of BzMA conversion (x) vs. φ BzMA (y) gave a satisfactory fit (R 2 > 0.95) to a logarithmic function of the form: y = -0.234*ln(x) + 1.0656 Figure S1. Conversion vs. volume fraction of BzMA monomer within growing spherical cores (φ BzMA ) calculated for the PISA synthesis of PSMA 31 -PBzMA 2000 spheres at 10% w/w.

Determination of the standard deviation in the molecular weight distribution (MWD)
The standard deviation in the MWD is required in order to determine the maximum error that should be attributed to the number of copolymer chains per self-assembled sphere or vesicle (N agg ). This is because the dominant error in this calculation comes from the uncertainty in the mean volume occupied by one PBzMA core-forming block (V PBzMA ), which is in turn determined by the MWD. Therefore the unimodal MWD determined by THF GPC analysis (see Figure S2) was fitted to a Gaussian model to determine its standard deviation using Equation S2 below: Here y is the retention time (min), x is the detector response, a and b are constants and σ is the standard deviation. This σ value corresponded to either 9.5% or 3.4% of the peak retention time for PSMA 13 -PBzMA 2000 and PSMA 13 -PBzMA 150 diblock copolymers respectively. This parameter was subsequently used as the maximum percentage error for the relevant N agg calculations.

SAXS models
In general, the intensity of X-rays scattered by a dispersion of nano-objects [usually represented by the scattering cross section per unit sample volume, ] can be expressed as: where is the form factor, is a set of k parameters describing the structural ( , 1 ,…, ) 1 ,…, morphology, is the distribution function, S(q) is the structure factor and N is the nano-Ψ( 1, …, ) object number density per unit volume expressed as: where is volume of the nano-object and φ is their volume fraction in the dispersion. ( 1, …, )

Spherical micelle model
The spherical micelle form factor for Equation (S3) is given by: 4 _ ( ) where R s is the core radius of the spherical micelle, R g is the radius of gyration of the PSMA corona block. The core block and the corona block X-ray scattering length contrast is given by and , respectively. Here ξ s , ξ c and ξ sol are the X-ray scattering where M n,pol corresponds to the number-average molecular weight of the block determined by 1 H NMR spectroscopy. The sphere form factor amplitude is used for the amplitude of the core self-term: where . A sigmoidal interface between the two blocks was assumed for the spherical micelle form factor [Equation (S6)]. This is described by the exponent term with a width σ accounting for a decaying scattering length density at the micellar interface. This σ value was fixed at 2.5 during fitting.
The form factor amplitude of the spherical micelle corona is: The radial profile, μ c (r), can be expressed by a linear combination of two cubic b splines, with two fitting parameters s and a corresponding to the width of the profile and the weight coefficient, respectively. This information can be found elsewhere, 6, 7 as can the approximate integrated form of Equation (S7). The self-correlation term for the corona block is given by the Debye function: where R g is the radius of gyration of the PSMA coronal block. The aggregation number of the spherical micelle is: where x sol is the volume fraction of solvent in the PBzMA micelle core. An effective structure factor expression proposed for interacting spherical micelles 8 has been used in Equation (S3): Herein the form factor of the average radial scattering length density distribution of micelles is used as and is a hard-sphere interaction structure factor based on the Percus-Yevick approximation, 9 where R PY is the interaction radius and f PY is the hard-sphere volume fraction. A polydispersity for one parameter (R s ) is assumed for the micelle model which is described by a Gaussian distribution. Thus, the polydispersity function in Equation (S3) can be represented as: where σ Rs is the standard deviation for R s . In accordance with Equation (S4), the number density per unit volume for the micelle model is expressed as: where φ is the total volume fraction of copolymer in the spherical micelles and is the 1 ( ) V r total volume of copolymer in a spherical micelle . [ where is the inner radius of the membrane, is the outer radius of the original work in which they were first described. 11 The exponent term in Equation (S14) represents a sigmoidal interface between the blocks, with a width σ in accounting for a decaying scattering length density at the membrane surface. The value of σ in was fixed at 2.5. The mean vesicle aggregation number, N v , is given by: where x sol is the solvent (i.e. mineral oil) volume fraction within the vesicle membrane.
A simpler expression for the corona self-term of the vesicle model than for the spherical micelle corona self-term was used due to the fact that the contribution to the scattering intensity from the corona block in this case was much less than the contribution from the membrane block.
Assuming that there is no penetration of the solvophilic coronal blocks into the solvophobic membrane, the amplitude of the vesicle corona self-term is expressed as: where the term outside the square brackets is the factor amplitude of the corona block polymer chain such that: which would be affected by the structure factor of concentrated vesicle dispersions were not well resolved in the performed SAXS measurements and, therefore, were excluded from the fitted pattern [i.e. only SAXS data for q > 0.06 nm -1 were used for the fitting and the structure factor in Equation (S3) was set to unity, S(q) = 1]. Programming tools within the Irena SAS Igor Pro macros 3 were used to implement the scattering models.