Enthalpic incompatibility between two steric stabilizer blocks provides control over the vesicle size distribution during polymerization-induced self-assembly in aqueous media

SAXS studies confirm that a judicious binary mixture of enthalpically incompatible steric stabilizer blocks enables the synthesis of relatively small, well-defined vesicles via polymerization-induced self-assembly in aqueous media.

Two of the earliest RAFT aqueous dispersion polymerization formulations involved the use of poly(glycerol monomethacrylate) (PGMA) or poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC) as the water-soluble precursor block to grow a hydrophobic structure-directing PHPMA block. 23,[33][34][35][36] Numerous studies have indicated that PGMA and PMPC are highly attractive building blocks for the rational design of nanobiomaterials owing to their proven biocompatibility. [37][38][39][40][41][42][43][44][45][46][47] Similarly, poly(ethylene glycol) (PEG) is a well-known biocompatible polymer that can be utilized as a hydrophilic steric stabilizer. 6,26,[48][49][50][51][52][53][54][55] In particular, PISA enables PEG-PHPMA thermoresponsive worms and vesicles to be readily prepared directly in aqueous solution. 8,48,49,54 The worms form so, freestanding physical gels that can be used for 3D cell culture but the vesicles tend to be relatively large and rather polydisperse in terms of their size distribution. 38,48,[55][56][57][58] Controlling the particle size distribution of block copolymer vesicles is an important and long-standing scientic problem, with various ingenious strategies being reported in the literature. [59][60][61][62][63][64][65][66][67][68][69] For example, Luo and Eisenberg reported that judicious use of a binary mixture of two AB diblock copolymers enabled the preparation of low-dispersity vesicles. 61,70,71 More specically, using a relatively long and a relatively short poly(acrylic acid) (PAA) stabilizer block in combination with a common hydrophobic polystyrene (PS) block led to spatial segregation across the vesicle membrane. The longer PAA chains were preferentially expressed at the outer leaet, while the shorter chains were located within the more sterically-congested inner leaet, with this conguration lowering the free energy for the vesicle morphology. Luo and Eisenberg later demonstrated that the same principle was also applicable for spatial segregation of two chemically distinct corona blocks -PAA and poly(4-vinylpyridine)across a PS membrane. 72 However, these studies utilized a traditional post-polymerization processing route that required a water-miscible co-solvent and a relatively low copolymer concentration. Thus, it does not provide a scalable route to well-dened vesicles. Subsequently, Gonzato et al. showed that this 'binary mixture of steric stabilizers' concept was also valid for PISA formulations by demonstrating the synthesis of relatively small, low polydispersity vesicles using RAFT alcoholic dispersion polymerization. 73 Both dynamic light scattering and small-angle X-ray scattering (SAXS) studies indicated a signicant reduction in the width of the vesicle size distribution. However, as far as we are aware, this approach has not yet been reported for any aqueous PISA formulations. This omission is perhaps surprising given the strong interest in using block copolymer vesicles for a wide range of biomedical applications, including intracellular delivery of drugs, 74-76 genes 77-79 or antibodies, 80 antibacterial agents 81,82 for autonomous locomotion 83 or chemotaxis 84 and for encapsulation of therapeutic enzymes. 51,57,58,85 Herein, we report the rational synthesis of relatively small diblock copolymer vesicles with narrow size distributions directly at 10% w/w solids using an aqueous PISA formulation. This is achieved by employing two chemically dissimilar stabilizer blocks of differing degrees of polymerization (see Scheme 1). These two stabilizers are non-ionic PEG and zwitterionic Scheme 1 Schematic representation of the RAFT aqueous dispersion polymerization of HPMA at 50 C to produce (A) vesicles at 25% w/w solids; (B) vesicles at 10% w/w solids and (C) [x + (1 À x) ] À vesicles at 10% w/w solids.
PMPC, whose mutual enthalpic incompatibility has been previously reported by Blanazs and co-workers. 86 We use SAXS analysis to demonstrate that using such a binary mixture of enthalpically incompatible stabilizers is essential to exert the desired control over the vesicle size distribution during aqueous PISA. In contrast, a binary mixture of chemically identical stabilizers appears to reduce the breadth of the vesicle size distribution but only produces relatively large vesicles, which are considered to be less useful for many potential biomedical application.

Results and discussion
Targeting the vesicle morphology It is well known in the block copolymer literature that asymmetric diblock copolymer compositions must be targeted to access vesicle phase space. This was originally established by Eisenberg and co-workers using traditional post-polymerization processing via a solvent switch in dilute solution 87,88 but it is equally valid for PISA syntheses. 33,35 This design rule can be explained in terms of the geometric packing parameter P introduced by Israelachvili and co-workers to account for surfactant self-assembly, 89 which has been subsequently validated for the self-assembly of amphiphilic diblock copolymers. 90 If P is greater than 0.50, then vesicles are favored unless there are other constraints, in which case kinetically-trapped spheres may be formed. 91

Vesicle synthesis strategy
Informed by this design rule, Sugihara and co-workers reported that targeting PMPC 25 -PHPMA 400 via aqueous PISA at 25% w/w solids produced a rather polydisperse vesicular morphology at 70 C. 34 In the present study, a closely-related aqueous PISA formulation was used to produce PMPC 28 -PHPMA 450 vesicles (Scheme 1a) by targeting the same relatively high copolymer concentration and a slightly longer structure-directing PHPMA block. A lower reaction temperature of 50 C was also employed but the most important difference is that a carboxylic acidfunctionalized RAFT agent was used to prepare the PMPC precursor block. This was a deliberate choice because this ionizable end-group is known to inuence the electrophoretic behavior of block copolymer nano-objects, 92,93 which was expected to aid discrimination between the three types of vesicles shown in Scheme 1. To ensure the formation of pure PMPC 28 -PHPMA 450 vesicles, PISA syntheses were conducted at low pH to prevent endgroup ionization reducing the packing parameter, which would inevitably lead to kinetically-trapped spheres. 92,93 The HPMA polymerization proceeded to more than 99% conversion within 4 h and GPC studies (refractive index detector, 3 : 1 chloroform/ methanol eluent) indicated a relatively high blocking efficiency (see Fig. S2 †). A relatively broad molecular weight distribution was obtained (see Table S1 †) but this was not unexpected given the known contamination of the HPMA monomer with a dimethacrylate impurity, which inevitably leads to branching when targeting a relatively high degree of polymerization (DP). 33 Indeed, a relatively high dispersity was also reported by Sugihara et al. 34 Similarly, the PEG 113 -PHPMA 400 formulation outlined in Scheme 1b has already been reported by Warren et al., who obtained relatively large polydisperse vesicles when conducting such aqueous PISA syntheses at 10% w/w solids. 48 In the present study, a HPMA conversion of more than 99% was achieved within 4 h at 50 C, while 3 : 1 chloroform/methanol GPC studies indicated an M n of 45 400 g mol À1 and an M w /M n of 1.45 for the PEG 113 -PHPMA 400 chains (see Fig. S2 and Table S1 †). These GPC data are similar to that reported by Warren and coworkers. 48 Bearing in mind the earlier PISA studies by Gonzato et al., 73 we hypothesized that using a judicious binary mixture of a relatively long PEG 113 stabilizer and a relatively short PEG 45 stabilizer while targeting a sufficiently long structure-directing PHPMA block should yield small vesicles with a relatively narrow size distribution. However, this strategy proved fruitless, as summarized in Fig. S3 and S4. † Regardless of the PEG 113mole fraction employed, only relatively large and/or polydisperse vesicles (or even less well-dened structures) could be obtained. 94 To address this unexpected problem, we speculated that a binary mixture of a pair of chemically dissimilar stabilizer blocks should enhance the apparently weak segregation of the long and short chains across the vesicle membrane and ideally also simultaneously reduce the vesicle size. According to Blanazs and co-workers, PEG 114 and PMPC 50 homopolymers are sufficiently enthalpically incompatible to form an aqueous biphasic solution, while PEG 114 -PMPC 23 diblock copolymers forms a range of structures exhibiting long-range order in concentrated aqueous solution. 86 Thus we explored the synthesis of hybrid vesicles using the PISA formulation outlined in Scheme 1c. Based on the prior studies by Eisenberg et al., 72 this strategy should result in the relatively long PEG 113 stabilizer chains being preferentially expressed at the outer leaet of the vesicle membrane, while the relatively short PMPC 28 chains should be located within the vesicle lumen. The PEG 113 mole fraction was systematically varied when preparing a series of [x PEG 113 + (1 À x) PMPC 28 ] À PHPMA 400 nano-objects. Given the well-known tendency for the PEG 113 stabilizer block to produce either oligolamellar vesicles or insoluble precipitates when targeting longer PHPMA blocks at high solids, 48 these PISA syntheses were conducted at 10% w/w solids to ensure formation of unilamellar vesicles. More than 99% HPMA conversion was achieved within 4 h and a high blocking efficiency was obtained for each of these aqueous PISA syntheses (see Fig. S2 and Table S1 †).
Kinetic studies of the synthesis of [x PEG 113 + (1 À x) PMPC 28 ] À PHPMA 400 diblock copolymer nanoparticles For the synthesis of small vesicles with a relatively narrow size distribution, Gonzato et al. employed a binary mixture of a relatively long and a relatively short poly(methacrylic acid) (PMAA) precursor for the RAFT dispersion polymerization of benzyl methacrylate (BzMA) in ethanol. 73 Both stabilizer blocks were prepared using the same trithiocarbonate-based RAFT agent and it was implicitly assumed that the structure-directing poly(benzyl methacrylate) (PBzMA) chains grown from each of these PMAA stabilizers would have the same mean DP. However, this may not necessarily be the case. This is because the critical PBzMA DP required for micellar nucleation actually depends on the DP of the PMAA stabilizer block. Thus, nucleation should commence at a signicantly lower critical PBzMA DP when using the shorter PMAA 62 block compared to when utilising the PMAA 171 block. In principle, this could be important, because the nascent nuclei quickly become swollen with unreacted BzMA and the ensuing high local monomer concentration leads to a substantial increase in the rate of polymerization. 12,35,95 Thus if micellar nucleation is delayed for the PMAA 171 block, the PBzMA chains grown from this precursor are likely to be shorter than those grown from the PMAA 62 block. Moreover, this suggests that the membranes of the resulting vesicles might comprise a bimodal distribution of PBzMA chain lengths. However, it is perhaps also worth bearing in mind that block copolymer self-assembly can be remarkably tolerant of dispersity effects. 70,[96][97][98] In the present study, we undertook kinetic experiments in order to assess to what extent the critical DP required for micellar nucleation differs for the PMPC 28 and PEG 113 precursors. The conversion vs. time curves and corresponding semilogarithmic plots obtained from 1 H NMR studies are shown in Fig. 1A when using each of these stabilizer blocks in turn for the RAFT aqueous dispersion polymerization of HPMA. As previously reported by Cornel and co-workers, 99 three distinct stages are observed for each polymerization, with the second inection point being assigned to micellar nucleation. As expected, this event occurs at a signicantly earlier stage when using the PMPC 28 precursor. In this case, an eight-fold increase in the rate of polymerization of HPMA occurs aer 48 min, which corresponds to an instantaneous conversion of 30% and hence a critical PHPMA DP of 120. In contrast, a rate acceleration is not observed until 66 min when using the PEG 113 precursor, which corresponds to an instantaneous conversion of 42% and a critical PHPMA DP of 168. Interestingly, a 31-fold rate enhancement is observed in this case, which might be expected to mitigate the anticipated bimodal distribution of PHPMA chain lengths when using a binary mixture of PMPC 28 and PEG 113 stabilizers. Indeed, GPC analyses of nominal binary mixtures of PEG 113 -PHPMA 400 plus PMPC 28 -PHPMA 400 do not provide any evidence for a bimodal molecular weight distribution (see Fig. S2 The kinetic data obtained when employing a binary mixture of 0.60 PEG 113 and 0.40 PMPC 28 stabilizer blocks are shown in Fig. 1B. Perhaps surprisingly, only a single micellar nucleation event is observed for this latter formulation: a nine-fold rate enhancement occurs aer 59 min, which corresponds to 38% conversion and hence a critical PHPMA DP of 152. Thus, micellar nucleation occurs at a time point (and a critical PHPMA DP) that is intermediate between those observed in Fig. 1A. This suggests that these nascent micelles actually comprise a binary mixture of PEG 113 -PHPMA 152 and PMPC 28 -PHPMA 152 chains owing to entropic mixing of the growing amphiphilic copolymer chains during PISA. This interpretation is consistent with the corresponding aqueous electrophoresis data (see later) obtained for the three types of vesicles described in Scheme 1. Thus, our initial concern regarding the potential problem of a bimodal distribution of PHPMA chain lengths being generated during such PISA syntheses appears to be unfounded.
Structural characterization of [x PEG 113 + (1 À x) PMPC 28 ] À PHPMA 400 diblock copolymer nano-objects The TEM images shown in Fig. 2 were used to assign the predominant copolymer morphology and this information was combined with DLS data to construct Fig. 3. This phase diagram is strikingly similar to that reported by Gonzato et al., 73 but differs markedly from that shown in Fig. S3 † for the synthesis of [x PEG 113 + (1 À x) PEG 45 ] À PHPMA 400 nano-objects.
For PISA syntheses conducted using relatively low levels of PEG 113 stabilizer (i.e. for either pure PMPC 28 or PMPC 28 -rich formulations), only kinetically-trapped spheres could be obtained at 10% w/w solids. Moreover, using a PEG 113 mole fraction of either 0.4 or 0.5 merely produced mixed phases comprising spheres and vesicles. However, a pure vesicle morphology was observed when employing PEG 113 -rich PISA formulations (see Fig. 2). Furthermore, using PEG 113 mole fractions of either 0.6 or 0.7 clearly afforded the smallest vesicles with the narrowest size distributions (lowest DLS polydispersities). However, in our experience, the polydispersity reported by DLS is a rather crude measure of the breadth of a size distribution. For example, the relatively low DLS polydispersities (<0.10) obtained for [x PEG 113 + (1 À x) PEG 45 ] À PHPMA 400 vesicles when x ¼ 0.7 or 0.8 ( Fig. S3 †) are clearly inconsistent with the corresponding TEM images (Fig. S4 †) since the latter suggest a rather broad size range. Hence we followed the strategy adopted by Gonzato and co-workers, 73 who utilized small-angle X-ray scattering (SAXS) to compare vesicle size distributions. Accordingly, SAXS patterns were recorded for each of the aqueous PISA formulations reported in Fig. 1 and 2 (see Fig. 4). One striking observation is that the two vesicle dispersions identied by DLS as possessing relatively low polydispersities (i.e. x ¼ 0.6 and 0.7) exhibit multiple fringes at intermediate q. This is a well-known signature for particles with relatively narrow size distributions since minima arising from the particle form factor are only partially smeared by the particle size distribution. Moreover, the large polydisperse vesicles formed at higher PEG 113 mole fractions according to DLS (see  Intensity-average diameters and polydispersities were determined for 0.1% w/w aqueous dispersions diluted from the as-synthesized 10% w/ w dispersions using deionized water. S indicates spheres, M indicates a mixed phase of spheres and vesicles, and V indicates that vesicles were the predominant morphology.  Fig. 4). Thus, these two sizing techniques are in rather good agreement. While DLS provides information regarding the vesicle size distribution, SAXS provides additional structural information. However, an appropriate scattering model is required to t SAXS patterns to determine the overall vesicle diameter, size polydispersity, membrane thickness, mean aggregation number, radius of gyration of the stabilizer chains and the solvent volume fraction within the vesicle membrane. TEM analysis (Fig. 2) indicates the presence of two copolymer morphologies: spheres and vesicles. There are well-developed SAXS models for analysing scattering patterns for both types of diblock copolymer nano-objects. 100,101 However, as the current system comprises two types of diblock copolymer chains bearing enthalpically incompatible stabilizer blocks, their spatial distribution within the coronal layer must also be considered. For a vesicle morphology, the PEG 113 and PMPC 28 stabilizer chains could be either randomly distributed or spatially segregated between the inner and outer vesicle leaets. Thus, the well-established scattering model for vesicles 101 requires further renement. Similarly, adjustment must be made to the scattering model for spheres if this morphology is obtained. 100 Fig. 4 (A) Experimental SAXS patterns (symbols) and corresponding data fits (grey lines) obtained for 1.0% w/w aqueous dispersions of [x PEG 113 + (1 À x) PMPC 28 ] À PHPMA 400 nano-objects originally prepared at 10% w/w solids, where the mole fraction (x) ranges from 0.0 (PMPC 28 -PHPMA 400 ) to 1.0 (PEG 113 -PHPMA 400 ). Scattering curves obtained for nano-objects prepared using a PEG mole fraction of 0.1-0.3 could be satisfactorily fitted using the blob-modified spherical micelle model, while the scattering patterns obtained for PMPC 28 -PHPMA 400 spheres were fitted using a well-known spherical micelle model. 100 A well-established vesicle model 101 was employed to fit the scattering pattern recorded for PEG 113 -PHPMA 400 vesicles obtained when x ¼ 1.0. (B) Schematic representation of the segregation fitting parameter f 1 , which indicates the mole fraction of PMPC 28 chains occupying the outer leaflet of the vesicles. (C) Experimental SAXS patterns [same symbols as shown in (A)] recorded for the sub-set of [x PEG 113 + (1 À x) PMPC 28 ] À PHPMA 400 vesicles obtained for x ¼ 0.50-0.90. These patterns were fitted using a refined vesicle model that takes account of the binary mixture of diblock copolymer chains [eqn (16)] using a fixed segregation parameter f 1 of 0.50 (which corresponds to a purely statistical mixture of PEG and PMPC stabilizer chains occupying the outer corona). The grey lines indicate the data fits obtained using this more sophisticated scattering model. In contrast, (D) shows the data fits obtained when f 1 is allowed to vary as a free parameter.
Small angle X-ray scattering (SAXS) models In general, the X-ray scattering intensity, I(q), from a dispersion of uniform nano-objects can be expressed as: .; r k ÞJðr 1 ; .; r k Þdr 1 .dr k (1) where F(q, r 1 , ., r k ) is the form factor, r 1 , ., r k is a set of k parameters describing the structural morphology, J(r 1 , ., r k ) is the distribution function, S(q) is the structure factor and N is the number density of nano-objects per unit volume expressed as: .; r k ÞJðr 1 ; .; r k Þdr 1 .dr k where V(r 1 , ., r k ) is the volume of the nano-objects and 4 is their volume fraction in the dispersion. The spherical micelle form factor to be used in eqn (1) can be expressed as: 100,102 F mic (q, where r 1 is the core radius of the spherical micelle and R g is the averaged radius of gyration of the corona blocks. To model spherical micelles comprising a binary mixture of PEG 113 and PMPC 28 blocks, the R g was calculated based on their relative volume fractions using an approximate radius of gyration for each pure block [R gPEG ¼ 2.6 nm and R gPMPC ¼ 1.4 nm]. These R g values were estimated assuming that the repeat unit length of PMPC is 0.255 nm (the length of two C-C bonds in a trans conformation). Thus, the total contour length of a PMPC 28 block is L PMPC28 ¼ 28 Â 0.255 nm ¼ 7.15 nm. Similarly, the contour length of an ethylene glycol repeat unit is 0.37 nm (estimated from the known crystal structure of PEG homopolymer), 103 hence the total contour length of a PEG 113 block is L PEG113 ¼ 113 Â 0.37 nm ¼ 41.81 nm. Assuming a mean PMPC Kuhn length of 1.53 nm (based on the known literature value for PMMA) 104 and a mean PEG Kuhn length of 1.0 nm, 105 the estimated unperturbed radius of gyration for each block was determined using R g(PEG or PMPC) ¼ (contour length Â Kuhn length/6) 0.5 . The selfcorrelation term for the corona blocks is given by the Debye function: The core and corona block X-ray scattering contrast is given respectively. x s , x c , and x sol are the scattering length density (SLD) of the core block (x HPMA ¼ 11.11 Â 10 10 cm À2 ), the mean SLD of the corona blocks (x PMPC ¼ 11.6 Â 10 10 cm À2 and/or x PEG ¼ 10.85 Â 10 10 cm À2 ) and the SLD of the solvent (x water ¼ 9.42 Â 10 10 cm À2 ), respectively. The mean SLD of the corona formed when using binary mixtures of PEG 113 and PMPC 28 stabilizer blocks was calculated based on the relative volume fractions of these two components. V s is the volume of the core block and V c is the mean volume of the corona block calculated from the PEG 113 and PMPC 28 block volumes (V PEG and V PMPC , respectively) using their relative volume fractions. Block copolymer volumes were obtained from the relation V ¼ M w; pol rN A using the following densities: r PMPC ¼ 1.28 g cm À3 , r PEG ¼ 1.17 g cm À3 and r HPMA ¼ 1.21 g cm À3 (see ESI for further details †). Here M w,pol is the mean molecular weight of the stabilizer block (PEG 113 or PMPC 28 ) as determined by 1 H NMR spectroscopy and N A is Avogadro's constant. The amplitude of the sphere form factor is used for that of the core self-term: where A sigmoidal interface between the two blocks was assumed for the spherical micelle form factor [eqn (3)]. This is described by the exponent term in eqn (5) with a width, s, to account for the decaying scattering length density at the core-shell interface. The s value was xed at 2.5Å during tting. The form factor amplitude for the spherical micelle corona is given by: Here m c (r) denotes the radial prole, which can be expressed by the linear combination of two cubic splines using two tting parameters s and a that correspond to the width of the prole and the weight coefficient, respectively. This information, along with the approximate integrated form of eqn (7) can be found elsewhere. 106,107 In principle, randomly distributed PEG 113 and PMPC 28 stabilizers within the vesicle corona should produce domains with differing SLDs. Such SLD uctuations within the self-assembled nano-objects would lead to additional scattering at high q. Similar structural formation has been incorporated into a well-known scattering model for spherical micelles using a 'blob' model. 102 In this case, it is assumed that the form factor for the uctuations ('blobs') can be described by the known analytical expression for polymer chains. Thus, SLD uctuations within the micelle corona are incorporated within the spherical micelle form factor [eqn (3)] with the scattering amplitude of the 'blobs' expressed as: where R gblob is the 'blob' radius of gyration and the corona form factor is expressed as: F co (q, r 1 ) ¼ [n blob (n blob À 1)j 2 (q, R gblob )A co 2 (q, r 1 ) + n blob F c (q, R gblob )]/n blob 2 where n blob ¼ A 1 V obj V blob , A 1 is a tting parameter related to the number of 'blobs' formed in the studied nano-object, the 'blob' volume is given by V blob ¼ 4 3 pR gblob 3 and V obj is equal to the spherical micelle corona volume V sco ¼ 4 3 p½ðr 1 þ 2R g Þ 3 À r 1 3 .
F c (q, R gblob ) is expressed using a function analogous to that given in eqn (4). The mean aggregation number for the spherical micelles is given by: where x sol is the volume fraction of solvent (water) in the PHPMA micelle cores. The micelle core radius, r 1 , is the only parameter that is assumed to be polydisperse and is described by a Gaussian distribution. Therefore, the polydispersity function in eqn (1) can be written as: where R s is the mean micelle core radius and s R s is its standard deviation. In accordance with eqn (2), the number density per unit volume for the micelle model is expressed as: Here 4 represents the total volume fraction of copolymer forming the spherical micelles and V(r 1 ) is the total volume of copolymer in a spherical micelle: A structure factor, S(q), was included in this model to account for the repulsive interactions arising from the anionic carboxylate end-group on each PMPC 28 stabilizer chain. Since the micelles are not perfectly centrosymmetric, eqn (1) should be rewritten as: 108 where the scattering amplitude of the spherical micelles is expressed as: A hard-sphere structure factor, S(q) ¼ S PY (q, R PY , f PY ), (solved using the Percus-Yevick closure relation) was introduced to account for interactions between spherical micelles, 108 where R PY is the effective interparticle correlation radius and f PY is the effective volume fraction. Although this structure factor is not strictly correct in this case, it nevertheless provides a useful analytical expression. 109 For vesicles, the form factor in eqn (1) is given as where some terms are the same as those in the spherical micelle model and F c (q, R gPEG ) and F c (q, R gPMPC ) are each expressed using functions that are analogous to eqn (4). Following the original vesicle model, 101 it is assumed that an equal number of stabilizer chains occupy the outer and the inner vesicle corona. However, the vesicle form factor equation was modied to account for the two different stabilizer blocks (PEG 113 and PMPC 28 ). The amplitude of the membrane self-term is given by: Here R in ¼ r 1 À 1 2 r 2 is the inner radius of the membrane, r 2 is the outer radius of the membrane (in this case, r 1 is the radius from the centre of the vesicle to the middle of its membrane and r 2 is the thickness of the hydrophobic part of the membrane), V in ¼ 4 3 pR in 3 , and V out ¼ 4 3 pR out 3 . F(qR out ) and F(qR in ) are dened by expressions that are analogous to those used in eqn (6). The mean vesicle aggregation number, N v (r 1 , r 2 ), is given by: where x sol is the volume fraction of solvent (water) 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: Here j(q, R gPEG ) and j(q, R gPMPC ) are the form factor amplitudes for the PEG and PMPC corona blocks, respectively, expressed using a function that is analogous to that employed in eqn (8). The X-ray scattering contrast for the PEG 113 or PMPC 28 stabilizer chains is given by respectively. In this model, the mole fractions of PEG 113 , x, and PMPC 28 , (1 À x), are expressed as f PEG and f PMPC ¼ 1 À f PEG , respectively. If f PEG $ 0.5 the coefficients in eqn (19) indicating the proportion of PEG 113 and PMPC 28 blocks located within the outer leaet of the vesicle membrane are expressed as a random distribution of the PEG 113 and PMPC 28 stabilizer chains between the outer and the inner vesicle leaets. Importantly, an f 1 value of zero indicates that all PMPC 28 stabilizer chains are preferentially located in the inner vesicle leaet, i.e. within the vesicle lumen. In contrast, an f 1 value of unity indicates that these stabilizer chains are exclusively located in the outer vesicle leaet (Fig. 4B). The form factor for the inner and outer vesicle corona is described as: For such n blob calculations, V obj is equal to the vesicle corona volume Herein, the mean thickness of the outer and inner vesicle corona were calculated as the average diameter of the outer and inner corona block, For the vesicle model, it was assumed that R v (the mean radius from the centre of the vesicle to the middle of the membrane) and T m (the mean vesicle membrane thickness) have nite polydispersity. Assuming that each parameter has a Gaussian distribution, the polydispersity function in eqn (1) can be expressed as: where s R v and s T m are standard deviations. Following eqn (2), the number density per unit volume for the vesicle model is expressed as: Here 4 is the total copolymer volume fraction forming the vesicles and V(r 1 , r 2 ) is the total volume of copolymer chains within a vesicle: Since the vesicles are signicantly larger than spherical micelles, the structure factor for vesicle interactions only makes a signicant contribution at low q. Unfortunately, this region was not well-resolved in our synchrotron SAXS experiments. Thus, it was assumed for SAXS analysis of the vesicles that the structure factor is close to unity [S(q) ¼ 1 in eqn (1)]. The programming tools available within Irena SAS macros for Igor Pro were used to implement the scattering models. 110 Model ttings were performed using the least-squares method.

SAXS analysis
The above structural models for spheres and vesicles produced reasonably good ts to the corresponding experimental SAXS patterns (Fig. 4). Unfortunately, the rst minimum in the form factor at q < 0.004Å À1 corresponding to the overall vesicle diameter is not sufficiently resolved to observe the associated secondary minimum at q $ 0.008Å À1 (Fig. 4). This is likely to be the result of smearing at low q (close to the beamstop) caused by the nite X-ray beam cross-section and the pixel size of the X-ray detector. This technical problem has some repercussions for the data ts. To overcome this problem, the most affected data points close to the beamstop (including the rst minimum and below) were excluded from the tting range. The resulting structural parameters were then used to recalculate scattering patterns over the entire experimental q range (Fig. 4). A summary of the structural parameters derived from data ts to the SAXS patterns shown in Fig. 4 is provided in Table 1.
The initial morphology assignment by TEM informed our choice of scattering model, with satisfactory data ts being achieved in all but one case (x ¼ 0.40). Data ts to the experimental SAXS patterns of the kinetically-trapped spheres obtained using a relatively high proportion of PMPC 28 stabilizer chains could be achieved using the blob-modied spherical micelle model (Fig. 4A). Exceptionally, the scattering pattern recorded for the PMPC 28 -PHPMA 400 spheres (which would not be expected to exhibit SLD variations across the sphere corona) was tted using the classic spherical micelle model. 100 For spheres obtained when using a PEG 113 mole fraction (x) of 0.10-0.30, the structural information derived from such data ts was consistent with DLS studies, suggesting that all three formulations produced spheres with comparable micelle core radii and overall diameters [calculated using D s ¼ 2(R s + 2 R g )] with relatively low polydispersities of 10-12%. Furthermore, R gblob values were comparable to the radii of gyration of the stabilizer chains, indicating that similar inhomogeneous blobs were generated across the sphere coronas.
When tting vesicles comprising a binary mixture of PEG 113 and PMPC 28 stabilizer chains, two scenarios were considered when assessing the spatial distribution of these stabilizer chains across the inner and outer vesicle leaets. Initially, SAXS patterns were tted assuming a statistical distribution (f 1 ¼ 0.5) of PEG 113 and PMPC 28 stabilizer chains across the inner and outer leaets (see Fig. 4C and the upper row of each PEG 113 mol fraction between 0.5 and 0.9 in Table 1 for tting results). Owing to the large number of parameters, R gPEG and R gPMPC were xed at their estimated values of 2.6 nm and 1.4 nm, respectively. The second scenario involved tting the segregation parameter, f 1 , using the data t obtained in the rst scenario as a starting point (see Fig. 4D and the lower row of each PEG 113 mole fraction between 0.5 and 0.9 in Table 1 for tting results). This conservative approach was adopted owing to the large number of parameters involved in the rened vesicle model. In addition, R gblob and its related tting parameter were xed when tting f 1 .
Clearly, the data ts achieved for both the rst and second scenarios appear to be very similar (compare Fig. 4C and D). However, it is emphasized that the minimized chi-squared value was always reduced by about 5% in the latter case, with the vesicle radius (R v ), membrane thickness (T m ) and their associated polydispersities (s R v and s T m ) varying very little when tting f 1 ( Table 1). Given that the main contribution to the overall X-ray scattering comes from the hydrophobic PHPMA chains within the vesicle membranes rather than the hydrophilic PEG 113 and PMPC 28 stabilizer chains, this apparently modest reduction in the chi-squared value is considered to be signicant. Thus, tting f 1 simply provides a statistically better t, rather than revealing any new structural features arising from the microphase separation of the PEG 113 and PMPC 28 stabilizer chains across the vesicle membrane. Typically, f 1 tended towards zero whenever this parameter was not constrained. According to Fig. 4B and Table 1, these very low f 1 values determined for x ¼ 0.6-0.9 indicate that the majority of the PMPC 28 chains are located within the vesicle inner leaet, suggesting substantial enthalpic incompatibility between the PEG 113 and PMPC 28 blocks. In the case of the (0.5 PEG 113 + 0.5 PMPC 28 ) À PHPMA 400 formulation (i.e. x ¼ 0.5 in Table 1, for which f 1 ¼ 0.14), a plausible explanation is that there are more PMPC 28 chains than can be accommodated within the inner leaet, causing some of these chains to occupy the outer leaet despite the presence of the PEG 113 chains. Alternatively, TEM analysis indicated that a minor population of spheres are also present in this case (Fig. 2), which might be expected to affect the f 1 value [N.B. A satisfactory data t could nevertheless be obtained using the modied vesicle model simply because the much smaller spheres make a negligible contribution to the Xray scattering].
According to TEM analysis, the rst pure vesicle phase is formed by the (0.6 PEG 113 + 0.4 PMPC 28 ) À PHPMA 400 formulation. Interestingly, these vesicles also exhibit the lowest standard deviation (s R v ) for the mean vesicle radius (R v ). In this case, the size polydispersity (which is calculated as a variance, i.e. s R v /R v Â 100%) is 13%. SAXS analysis indicates higher polydispersities as the PEG 113 mole fraction is increased up to 0.9. Moreover, the f 1 data ts suggest that optimum microphase separation is achieved for the (0.6 PEG 113 + 0.4 PMPC 28 ) À PHPMA 400 formulation, which corresponds to the formation of vesicles with the lowest polydispersity. Thus, the above suggestion that the x ¼ 0.5 formulation simply contains too many PMPC 28 stabilizer chains to be accommodated within the inner leaet of the vesicles seems to be physically reasonable. Conversely, the x ¼ 0.7 formulation contains too few PMPC 28 chains to fully occupy the inner leaet, thus requiring some PEG 113 chains to be co-located within the vesicle lumen. As the PEG 113 mole fraction is increased, the PEG 113 and PMPC 28 chains are increasingly unable to maintain complete microphase separation across the membrane, despite the majority of the PMPC 28 chains being located within the vesicle lumen. This suggests that the enthalpic incompatibility between the PEG 113 and PMPC 28 chains drives the formation of relatively small, low polydispersity vesicles.
The tted R gblob values for vesicles comprising both PEG 113 and PMPC 28 stabilizer blocks were comparable when assuming f 1 ¼ 0.5. These values are also similar to those determined for the spheres, indicating that similar inhomogeneous 'blobs' are produced within both types of coronal layers. In addition to conrming the formation of larger, more polydisperse vesicles when using higher PEG 113 mole fractions (x > 0.7), SAXS analysis -a R s is the spherical micelle core radius, R v is the distance from the centre of the vesicle to the middle of the vesicle membrane and s R denotes the corresponding standard deviations for these two parameters. T m is the vesicle membrane thickness and s T m denotes the standard deviation of this parameter. D s or D v are the sphere or vesicle diameter respectively. R gblob is the radius of gyration of the inhomogeneous 'blobs' within the coronal layer of stabilizer chains. f 1 is the segregation parameter which indicates the fraction of PMPC stabilizer chains located within the outer corona, and an asterisk (*) indicates when f 1 was xed at 0.50 during tting (N.B. 'n.d.' denotes 'not determined').
also indicated a monotonic (albeit modest) reduction in vesicle membrane thickness with increasing PEG 113 mole fraction. The overall vesicle diameter was calculated using D v ¼ 2(R v + 0.5T m + 2R gPEG ). R gPEG was used as the f 1 data ts suggest that, in most cases, the vesicle outer leaet contains solely PEG 113 chains.
Allowing for the effect of polydispersity, these SAXS-derived volume-average diameters are in reasonably good agreement with the z-average diameters reported by DLS ( Table 1). As expected, the biggest deviations are observed for relatively large polydisperse vesicles, because DLS is more biased towards larger nano-objects.
Effect of pH and salt on colloidal stability of vesicles The corresponding zeta potential vs. pH curves determined for each type of vesicle are shown in Fig. 5B. These three curves are consistent with the mobility data. Thus, the PEG 113 -PHPMA 400 vesicles exhibit zeta potentials close to zero, as expected for the non-ionic PEG chains. In contrast, the PMPC 28 -PHPMA 450 vesicles exhibit quite strongly negative zeta potentials (e.g. À33 mV at pH 9) owing to ionization of the carboxylic acid end-group (pK a $ 4.7) 92 on the PMPC chains. Finally, the hybrid [0.6 PEG 113 + 0.4 PMPC 28 ] À PHPMA 400 vesicles exhibit only weakly negative zeta potentials (À16 mV at pH 9). This is consistent with most of the PMPC chains being preferentially located within the lumen, rather than being expressed at the outer leaet of such vesicles. Fig. 6 shows the relative change in intensity-average diameter with added salt (up to 3.0 M ammonium sulfate) for PEG 113 -PHPMA 400 vesicles (blue curve), [0.6 PEG 113 + 0.4 PMPC 28 ] À PHPMA 400 vesicles (red curve), and PMPC 28 -PHPMA 450 vesicles (green curve). All data are normalized to the intensity-average diameter of each type of vesicle as determined in deionized water. It is well known that PEG can be readily salted out in the presence of sulfate anions, 113 whereas PMPC is  highly tolerant to added salt up to 5 M. 114,115 Thus the addition of just 0.50 M ammonium sulfate leads to a substantial increase in the apparent size of the PEG 113 -PHPMA 400 vesicles, indicating signicant occulation. In contrast, the PMPC 28 -PHPMA 450 vesicles remain colloidally stable even in the presence of 3.0 M ammonium sulfate. Importantly, the [0.6 PEG 113 + 0.4 PMPC 28 ] À PHPMA 400 vesicles undergo incipient occulation in the presence of 2.0 M ammonium sulfate. This suggests that most of the PEG chains are expressed at the outer leaet of the vesicle membrane, which is consistent with the aqueous electrophoresis data shown in Fig. 5.

Conclusions
In summary, judicious use of a binary mixture of a relatively long non-ionic PEG steric stabilizer and a relatively short zwitterionic PMPC steric stabilizer enables the rational synthesis of rather small (<200 nm diameter) hybrid diblock copolymer vesicles with a relatively narrow size distribution (size polydispersity ¼ 13-16%) at 10% w/w solids in aqueous solution via polymerization-induced self-assembly. Aqueous electrophoresis and salt-induced occulation studies provide evidence for the relatively long PEG chains being preferentially expressed at the outer leaet of the vesicle membrane. SAXS studies conrm that systematic variation of the relative proportions of the zwitterionic and non-ionic steric stabilizers is required to achieve optimal control over the vesicle size distribution. SAXS analysis also provides further evidence for connement of most of the PMPC chains to the inner leaet of the vesicles. Importantly, control experiments conducted using a binary mixture of chemically identical long and short PEG stabilizer blocks only produced relatively large vesicles which are less useful for potential biomedical applications. Thus, enthalpic incompatibility between the two types of steric stabilizers appears to offer a decisive advantage in this context. We anticipate that the reproducible and scalable synthesis of highly biocompatible small vesicles with relatively narrow size distributions reported herein will drive new developments in the eld of nanobiotechnology.

Conflicts of interest
There are no conicts to declare.