In situ SAXS studies of a prototypical RAFT aqueous dispersion polymerization formulation: monitoring the evolution in copolymer morphology during polymerization-induced self-assembly

Small-angle X-ray scattering (SAXS) is used to characterize the in situ formation of diblock copolymer spheres, worms and vesicles during reversible addition–fragmentation chain transfer (RAFT) aqueous dispersion polymerization of 2-hydroxypropyl methacrylate at 70 °C using a poly(glycerol monomethacrylate) steric stabilizer. 1H NMR spectroscopy indicates more than 99% HPMA conversion within 80 min, while transmission electron microscopy and dynamic light scattering studies are consistent with the final morphology being pure vesicles. Analysis of time-resolved SAXS patterns for this prototypical polymerization-induced self-assembly (PISA) formulation enables the evolution in copolymer morphology, particle diameter, mean aggregation number, solvent volume fraction, surface density of copolymer chains and their mean inter-chain separation distance at the nanoparticle surface to be monitored. Furthermore, the change in vesicle diameter and membrane thickness during the final stages of polymerization supports an ‘inward growth’ mechanism.


Materials
The following materials were used without further purification unless stated.

Synthesis of PGMA45 macro-CTA
PETTC RAFT agent (0.90 mmol, 0.30 g), GMA monomer (44.2 mmol, 7.08 g), ACVA (0.20 mmol, 49.8 mg, CTA/ACVA molar ratio = 5.0) and anhydrous ethanol (11.14 g, 40% w/w) were weighed into a 50 mL round-bottomed flask, placed in an ice bath and purged with N2 for 30 min. The sealed flask was immersed into an oil bath set at 70 °C and stirred for 120 min (GMA conversion = 76%, as determined by 1 H NMR studies in CD3OD). After 120 min, the reaction mixture was diluted with methanol (25 mL) and precipitated into excess dichloromethane (twice). The precipitate was dissolved in deionized water and any residual dichloromethane was removed under reduced pressure. The purified product was freeze-dried overnight to afford a PGMA macro-CTA as a yellow powder. 1 H NMR (CD3OD) indicated a mean degree of polymerization of 45 for this precursor. GPC analysis (DMF eluent, refractive index detector, series of near-monodisperse poly(methyl methacrylate) calibration standards) indicated an Mn of 12 900 g mol -1 and a Mw/Mn = 1.20.

Kinetic studies of the RAFT Aqueous Dispersion Polymerization of HPMA at 70 o C when targeting PGMA45-PHPMA200 vesicles
PGMA45 macro-CTA (49.9 mg, 6.61 μmol), HPMA monomer (0.191 g, 1.32 mmol; target DP = 200), DSS (5.77 mg, 26.4 μmol, HPMA/DSS molar ratio = 50), and ACVA (0.60 mg, 2.20 μmol, CTA/ACVA molar ratio = 3.0) were weighed into a 10 mL round-bottomed flask and purged with N2 gas for 20 min. Deionized water (2.18 mL, 10% w/w formulation), separately degassed with N2 for 30 min, was then added. A sample was immediately taken for 1 H NMR analysis, and the reaction solution was degassed for a further 5 min prior to immersion in an oil bath set at 70 o C. The 'zero time' (t = 0 min) for this polymerization was arbitrarily taken to be the point when the degassed reaction solution was first immersed in the 70 o C oil bath, rather than the time at which the reaction solution had reached this temperature. Aliquots were subsequently removed under N2 via syringe at various time intervals for 1 H NMR, DLS and TEM analysis. Each aliquot was quenched by dilution in D2O at 20 o C. Monomer conversions were normalized using the DSS as an internal standard and are expressed relative to the HPMA/DSS molar ratio observed at 'zero time'. For both TEM and DLS analysis, aliquots were diluted fifty-fold with deionized water at 20 o C to produce 0.20% w/w dispersions.

In situ SAXS studies of the RAFT Aqueous Dispersion Polymerization of HPMA at 70 o C when targeting PGMA45-PHPMA200 vesicles
PGMA45 macro-CTA (50.0 mg, 6.63 μmol), HPMA monomer (0.191 g, 1.33 mmol; target DP = 200), ACVA (0.60 mg, 2.21 μmol, CTA/ACVA molar ratio = 3.0) and deionized water (2.17 mL, 10% w/w formulation) were weighed into a 14 mL sample vial and purged with N2 for 30 min. This reaction solution was then transferred via degassed syringe to the SAXS cell (containing a magnetic flea and equipped with a magnetic stirrer unit) which had been separately purged with N2 for 20 min. Once the SAXS cell was attached to the sample stage in I22 and aligned relative to the SAXS beam, the HPMA polymerization was initiated using a water-circulating jacket to heat the cell up to 70 °C as the X-ray beam shutter was opened. The polymerization was monitored until no further evolution in the 1D SAXS pattern was observed, at which point it was assumed that the reaction was complete.

H NMR Spectroscopy
All NMR spectra were recorded in either D2O or CD3OD using a 400 MHz Bruker Avance-400 spectrometer (64 scans averaged per spectrum).

Gel Permeation Chromatography (GPC)
Copolymer molecular weights and dispersities were determined using a DMF GPC setup operating at 60 °C and comprising two Polymer Laboratories PL gel 5 μm mixed-C columns connected in series to a Varian 390-LC multidetector suite (refractive index detector only) and a Varian 290-LC pump injection module. The GPC eluent was HPLC-grade DMF containing 10 mM LiBr at a flow rate of 1.0 mL min −1 and DMSO was used as a flow-rate marker. Calibration was conducted using a series of ten near-monodisperse poly(methyl methacrylate) standards (Mn = 625 to 618,000 g mol −1 ). Chromatograms were analyzed using Varian Cirrus GPC software (version 3.3).

Dynamic Light Scattering (DLS)
DLS studies were conducted on 0.20% w/w aqueous dispersions at 25 °C in disposable cuvettes using a Malvern Zetasizer NanoZS instrument, which detects back-scattered light at an angle of 173°. Intensity-average hydrodynamic diameters were calculated via the Stokes−Einstein equation using a non-negative least-squares (NNLS) algorithm. All data were averaged over three consecutive runs.

Transmission Electron Microscopy (TEM)
Removed aliquots were diluted fifty-fold at 20 °C to generate 0.20% w/w dispersions. Copper/palladium TEM grids (Agar Scientific, UK) were surface-coated in-house to yield a thin film of amorphous carbon. The grids were then plasma glow-discharged for 30 s to create a hydrophilic surface. Individual samples (0.20% w/w, 5 μL) were adsorbed onto the freshly glow-discharged grids for 1 min and then blotted with filter paper to remove excess solution.
To stain the aggregates, uranyl formate solution (0.75 %w/v, 5.0 μL) was soaked on the sample-loaded grid for 20 seconds and then carefully blotted to remove excess stain. The grids were then dried using a vacuum hose. Imaging was performed on a Technai T12 Spirit instrument operating at 120 kV and equipped with a Gatan 1 k CCD camera.

Small-Angle X-ray Scattering (SAXS)
SAXS patterns were recorded at an international synchrotron facility (station ID02 at ESRF, Grenoble, France). A monochromatic X-ray beam (λ = 0.0995 nm) and a 2D SAXS detector (Rayonix MX-170HS) were used for these experiments. A q range of 0.004−2.0 nm −1 was used for all measurements, where q = (4π sin θ)/λ, corresponds to the modulus of the scattering vector and θ is half of the scattering angle. A bespoke stirrable reaction cell was used for these time-resolved measurements, see Figure 1 in the main text. SAXS patterns were recorded every 10 seconds for the first 10 min, every 30 seconds for the next 30 min and every 60 seconds thereafter until no further change in the SAXS patterns could be observed. X-ray scattering data were reduced (integrated, normalized, and background-subtracted) using standard routines available at the ID02 beamline. The scattering intensity of water was used for absolute scale calibration of the X-ray scattering patterns. Irena SAS macros for Igor Pro were utilized for modelling and further SAXS analysis. S5

Determining Theoretical DPs
Laboratory-based kinetic data were normalized and fitted to a sigmoid function, see Figure  S1. Figure S1. Renormalization of the polymerization kinetics data obtained by 1 H NMR spectroscopy. Laboratory-based kinetic data are shown as black squares. Red line corresponds to the sigmoid function fit to these data. Both time and conversion have been normalized.
The sigmoid function shown in Figure S1 is described by the following equation: where is the HPMA conversion, is the relative polymerization time and a, b, c and d are arbitrary fitting parameters.
For the sigmoid function fit shown in Figure S1, the values for a, b, c and d are -0

Calculating Individual Block Volumes
To analyze the scattering patterns reported in this study, the scattering models employed require knowledge of both the core and stabilizer block volumes. To calculate the instantaneous DP for the core-forming block, see Section 2.1 above. Armes with this DP, individual block volumes can be calculated using Equation S2: where MW corresponds to the monomer molecular weight, DP is the mean degree of polymerization of the block, is the density and Na is Avogadro's constant.

Estimating the Stabilizer Chain Length (Rg)
A PGMA45 precursor was employed as the steric stabilizer in this study. The experimental Rg for this precursor in aqueous solution was calculated to be 1.81 nm by fitting its SAXS pattern to a Gaussian chain model. The contour length of such PGMA45 chains can be estimated by assuming each monomer repeat unit comprises two carbon bonds in an all trans configuration, which equates to a segment length of 0. This estimated Rg agrees well with that obtained experimentally from SAXS fitting suggesting that it is a physically reasonable value.

Maximum error in the mean aggregation number
The standard deviation in the molecular weight distribution (MWD) is required in order to determine the maximum error associated with the mean aggregation number for the spheres and vesicles (i.e., Ns and Nv, respectively). This is because the dominant error in this calculation comes from the uncertainty in the mean volume occupied by one core-forming PHPMA block, which in turn is determined by the MWD of the PGMA45-PHPMA200 diblock copolymer. Therefore, the MWD determined by DMF GPC analysis of the laboratory-scale synthesis (see the black trace shown in Figure S2) was fitted to a Gaussian model (see blue trace in Figure  S2) to estimate this standard deviation using Equation S3, as shown below: Here a and b are constants, is the retention time, is the detector response and σ is the standard deviation. This σ value corresponded to 6% of the peak retention time for the PGMA45-PHPMA200 diblock copolymer. This parameter was subsequently used as the maximum percentage error for the relevant Ns (or Nv) calculations. Figure S2. DMF gel permeation chromatogram (black trace) obtained for the final PGMA45-PHPMA200 diblock copolymer chains produced by the laboratory-scale RAFT aqueous dispersion polymerization of HPMA at 70 °C targeting 10% w/w solids. The blue trace depicts a Gaussian fit to the black trace.

N agg , S agg , and d int equations
It is possible to calculate the mean number of copolymer chains per nano-object (Ns, Nw or Nv for spheres, worms or vesicles; generically denoted herein as Nagg), the mean number of copolymer chains per unit area (Sagg), and the average distance between two copolymer chains at the core-shell interface (dint). The corresponding equations are given below with explanatory cartoons provided where required. where φ sol is the solvent volume fraction within the spherical cores, Rc is the core radius, Vc is the volume of the core [see Equation S2] and Rs is the sphere radius (i.e. Rs = Rc + 2.Rg).    Figure S7. Postmortem TEM image recorded after the in situ SAXS experiment conducted using the stirrable SAXS cell at 70 °C while targeting PGMA45-PHPMA200 vesicles at 10% w/w solids. The final copolymer morphology corresponds to polydisperse vesicles. S14 Figure S8. DMF GPC traces for the final reaction mixture recorded after (i) the laboratorybased synthesis (black line) and (ii) the in situ SAXS experiment (blue line) when targeting PGMA45-PHPMA200 vesicles at 70 °C and 10% w/w solids. Clearly, there are minimal differences between these two GPC traces, indicating that essentially the same copolymer chains are obtained in each case.

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, Σ Ω ( )] can be expressed as: where ( , 1 , … , k ) is the form factor, 1 , … , k is a set of parameters describing the structural morphology, Ψ( 1 , … , k ) is the distribution function, ( ) is the structure factor and is the nano-object number density per unit volume expressed as: where ( 1 , … , k ) is the volume of the nano-object and is the volume fraction of nanoobjects.

Spherical micelle model
The spherical micelle form factor for Equation S4 is given by: 4 ( ) = 2 2 2 ( , ) + 2 ( , ) + ( − 1) 2 2 ( ) + 2 2 where is the core radius of the spherical micelle, is the radius of gyration of the PGMA corona block. The X-ray scattering length contrast for the core block and the corona block is given by s = s ( s − sol ) and c = c ( c − sol ), respectively. Here s , c and sol are the X-ray scattering length densities of the core block ( PHPMA = 11.11  10 10 cm -2 ), the corona block ( PGMA = 11.94  10 10 cm -2 ) and the solvent ( sol = 9.42  10 10 cm -2 ), respectively. s and c are the volumes of the core block ( PHPMA ) and the corona block ( PGM 45 ), respectively. These volumes were calculated using Equation S2, see Section 2.2. The sphere form factor amplitude is used for the amplitude of the core self-term: where ( s ) = 3[sin( s ) − s cos ( s ) ( s ) 3 . A sigmoidal interface between the two blocks was assumed for the spherical micelle form factor. This is described by the exponent term with a width accounting for a decaying scattering length density at the core-shell interface of the deblock copolymer micelle (or nanoparticle). This value was fixed at 2.5 during fitting.
The form factor amplitude of the spherical micelle corona is: The radial profile, c ( ), can be expressed by a linear combination of two cubic b splines, with two fitting parameters s and a that correspond to the width of the profile and the weight coefficient, respectively. The self-correlation term for the coronal block is given by the Debye function: where g is the radius of gyration of the PGMA coronal block. The aggregation number, s , for the spherical micelle is given by: where sol is the volume fraction of solvent within the micelle cores (formed by the PHPMA block in the present case). An effective structure factor expression proposed for interacting micelles 5 has been used in Equation S4 to give: Herein the form factor of the average radial scattering length density distribution of micelles is used as s mic av ( ) = s [ s s ( , s ) + c c ( )] and PY ( , PY , PY ) is a structure factor for hard-sphere interactions based on the Percus-Yevick approximation, 6 where PY is the interaction radius and PY is the hard-sphere volume fraction. The micelle model assumes a polydispersity for one parameter ( s ), which can be described by a Gaussian distribution. Thus, the polydispersity function in Equation S4 can be represented as: where s is the standard deviation for s . In accordance with Equation S5, the number density per unit volume for the micelle is expressed as: Here is the copolymer volume fraction and ( 1 ) is the total copolymer volume in a spherical micelle [ ( 1 ) = ( s + c ) s ( 1 )].

Worm-like micelle model
According to Equation S4, the form factor for a worm-like micelle can be expressed as: Unless stated otherwise, all parameters are the same as those described in the spherical micelle model (see Equation S6).
The self-correlation term for the cross-sectional volume-average radius w within the worm core is: ( ) = worm ( , w , w ) cs worm 2 ( , w ) (S15) where cs worm 2 Here 1 is the first-order Bessel function of the first kind, and a form factor worm ( , w , w ) for self-avoiding semi-flexible chains represents the worm-like micelles, where w is the Kuhn length and w is the mean contour length. A full expression for the chain form factor can be found elsewhere. 7 The mean aggregation number for the worm-like micelle, w , is given by: where sol is the volume fraction of solvent within the worm-like micelle core. The possible presence of semi-spherical caps at the two ends of each worm is neglected for this form factor.
A polydispersity for one parameter ( w ) is assumed for this worm-like micelle model, which can be described by a Gaussian distribution. Thus, the polydispersity function in Equation S4 can be represented as: Here is the standard deviation for w . In accordance with Equation S5, the number density per unit volume for this worm-like micelle model is expressed as: Here is the copolymer volume fraction and ( 1 ) is the total copolymer volume in a wormlike micelle [ ( 1 ) = ( s + c ) w ( 1 )].

Vesicle model
The represents a sigmoidal interface between the two blocks, with a width in accounting for a decaying scattering length density at the membrane surface. The value of in was fixed at 2.5 during fitting. The mean vesicle aggregation number, v , is given by: where sol is the solvent volume fraction within the vesicle membrane. Assuming that there is no penetration of the hydrophilic coronal blocks into the hydrophobic membrane, the amplitude of the vesicle corona self-term is expressed as: where the term outside the square brackets is the form factor amplitude of the corona block such that: For the vesicle model, it is assumed that two parameters are polydisperse: the radius from the centre of the vesicle to the centre of the membrane ( m ) and the membrane thickness ( m ). Each parameter is considered to have a Gaussian distribution, hence the polydispersity function in Equation S4 can be expressed in each case as: Where m and m are the standard deviations for m and m , respectively. According to Equation S5, the number density per unit volume for the vesicle model can be expressed as: Here is the copolymer volume fraction and ( 1 , 2 ) is the total copolymer volume [ ( 1 , 2 ) = ( s + c ) ( 1 , 2 )].
Programming tools within the Irena SAS Igor Pro macros 9 were used to implement the scattering models.