SAXS studies of the thermally-induced fusion of diblock copolymer spheres: formation of hybrid nanoparticles of intermediate size and shape

Dilute dispersions of poly(lauryl methacrylate)–poly(benzyl methacrylate) (PLMA–PBzMA) diblock copolymer spheres (a.k.a. micelles) of differing mean particle diameter were mixed and thermally annealed at 150 °C to produce spherical nanoparticles of intermediate size. The two initial dispersions were prepared via reversible addition–fragmentation chain transfer (RAFT) dispersion polymerization of benzyl methacrylate in n-dodecane at 90 °C. Systematic variation of the mean degree of polymerization of the core-forming PBzMA block enabled control over the mean particle diameter: small-angle X-ray scattering (SAXS) analysis indicated that PLMA39–PBzMA97 and PLMA39–PBzMA294 formed well-defined, non-interacting spheres at 25 °C with core diameters of 21 ± 2 nm and 48 ± 5 nm, respectively. When heated separately, both types of nanoparticles regained their original dimensions during a 25–150–25 °C thermal cycle. However, the cores of the smaller nanoparticles became appreciably solvated when annealed at 150 °C, whereas the larger nanoparticles remained virtually non-solvated at this temperature. Moreover, heating caused a significant reduction in mean aggregation number for the PLMA39–PBzMA97 nanoparticles, suggesting their partial dissociation at 150 °C. Binary mixtures of PLMA39–PBzMA97 and PLMA39–PBzMA294 nanoparticles were then studied over a wide range of compositions. For example, annealing a 1.0% w/w equivolume binary mixture led to the formation of a single population of spheres of intermediate mean diameter (36 ± 4 nm). Thus we hypothesize that the individual PLMA39–PBzMA97 chains interact with the larger PLMA39–PBzMA294 nanoparticles to form the hybrid nanoparticles. Time-resolved SAXS studies confirm that the evolution in copolymer morphology occurs on relatively short time scales (within 20 min at 150 °C) and involves weakly anisotropic intermediate species. Moreover, weakly anisotropic nanoparticles can be obtained as a final copolymer morphology over a restricted range of compositions (e.g. for PLMA39–PBzMA97 volume fractions of 0.20–0.35) when heating dilute dispersions of such binary nanoparticle mixtures up to 150 °C. A mechanism involving both chain expulsion/insertion and micelle fusion/fission is proposed to account for these unexpected observations.


Introduction
Block copolymer self-assembly has underpinned numerous remarkable advances in the eld of materials science over the past two decades or so. 1 For example, self-assembly in the solid state has led to the development of block copolymer nanolithography for information storage and nanoltration. [2][3][4][5] Similarly, self-assembly in solution has led to potential applications in microuidic devices, 6 automobile lubricants, 7 viscosity modiers, 8 stem cell storage media 9 and drug delivery. 10 The rst example of well-dened diblock copolymers were prepared by anionic polymerization. 11 This living polymerization technique allows the synthesis of copolymer chains with very narrow molecular weight distributions but it is extremely sensitive to protic impurities and is applicable to only a narrow range of vinyl monomers. Fortunately, developments in the eld of controlled radical polymerization, particularly reversible addition-fragmentation chain transfer (RAFT) polymerization, enable the preparation of many functional block copolymers under much less demanding reaction conditions. [12][13][14][15][16][17][18][19] Traditionally, block copolymer self-assembly in solution has been performed via post-polymerization processing using a solvent-switch method. 1 A much more convenient approach for the preparation of block copolymer nanoparticles involves RAFT-mediated polymerization-induced self-assembly (PISA). 17,[20][21][22][23][24][25][26][27][28] In essence, PISA involves chain extension of a soluble precursor block with a second insoluble block. Block copolymer self-assembly occurs in situ once the growing latter block reaches a critical mean degree of polymerization (DP). Polymerization continues thereaer within monomer-swollen nanoparticles. The high local monomer concentration leads to a rate acceleration while the unreacted monomer acts as a processing aid (or co-solvent). Given a sufficiently short steric stabilizer block, either spheres, worms/cylinders or vesicles obtained depending on the relative volume fractions of each block. In contrast, longer steric stabilizer blocks invariably lead to kinetically-trapped spheres, because sphere-sphere fusion is impeded. [20][21][22] It is well-known that thermal annealing can lead to the exchange of diblock copolymer chains between nanoparticles in polar [29][30][31][32][33][34][35] and non-polar media, as shown by both Lodge and coworkers and Growney et al. [36][37][38][39][40][41][42][43] Two mechanisms have been suggested for this phenomenon: (i) a chain expulsion/insertion mechanism and (ii) a micelle fusion/ssion mechanism. 41,[44][45][46][47][48] Theoretical studies by Halperin 45,46 and experimental observations made by Lund and co-workers 31,35 and Lodge and coworkers [36][37][38][39]41,49,50 suggest that the former mechanism is much more likely for diblock copolymer micelles (a.k.a. stericallystabilized nanoparticles). On the other hand, Armes and coworkers have suggested that particle-particle fusion is likely to play an important role during certain PISA syntheses, for which unreacted monomer plays an important processing role as a co-solvent. Indeed, such a fusion mechanism seems to be the most likely explanation for the in situ self-assembly of highly anisotropic diblock copolymer worms, whose formation is favored at higher copolymer concentrations. 21,22,[51][52][53] In principle, chain expulsion/insertion and micelle fusion/ssion could each play important roles during RAFT PISA.
Herein we examine copolymer exchange for various binary mixtures of dilute copolymer dispersions comprising poly(lauryl methacrylate)-poly(benzyl methacrylate) (PLMA 39 -PBzMA x ) spherical nanoparticles with mean core diameters of 21 AE 2 nm and 48 AE 5 nm, respectively. These kineticallytrapped spheres were prepared in n-dodecane via RAFTmediated PISA using a previously reported protocol; 22,53 the core-forming PBzMA x block DP (x) was either 97 or 294. Variable temperature small-angle X-ray scattering (SAXS) studies provide valuable insights regarding the behavior of these nanoparticles when annealed separately at 150 C with regard to their degree of core solvation and change in aggregation number. Annealing binary mixtures of this pair of nanoparticles over a wide range of relative volume fractions leads to the formation of a series of new hybrid nanoparticles. Time-resolved SAXS studies are used to examine the time scale for this hybridization process and also to examine its mechanism. This powerful characterization technique provides compelling evidence for the presence of weakly anisotropic intermediate species during the in situ evolution in copolymer morphology. Under certain conditions, weakly anisotropic nanoparticles can also be obtained as the nal copolymer morphology from such hybridization experiments.

Results and discussion
Preparation and characterization of PLMA-PBzMA spheres in n-dodecane Well-dened PLMA 39 -PBzMA x spherical nanoparticles (where x is either 97 or 294) were prepared at 20% w/w solids in n-dodecane using a well-established RAFT-mediated PISA protocol. 22,53 A PLMA 39 precursor was chain-extended with BzMA monomer, with micellar nucleation occurring once a critical PBzMA core DP was attained (Scheme 1). High BzMA monomer conversions (>97%) were achieved in both cases according to 1 H NMR spectroscopy analysis of the crude reaction mixtures, aer dilution with sufficient CDCl 3 to ensure nanoparticle dissolution ( Fig. S1 and eqn (S1) in the ESI †). Both types of diblock copolymer nanoparticles were dissolved in THF prior to GPC analysis (Fig. S2 †). Relatively narrow unimodal molecular weight distributions were obtained (M w /M n # 1.20), suggesting pseudo-living character for this RAFT dispersion polymerization. A clear shi to lower retention time for each diblock copolymer compared to that for the PLMA 39 precursor indicated a high blocking efficiency in each case. For closelyrelated PISA formulations, Fielding et al. reported that targeting higher PBzMA DPs simply led to progressively larger kinetically-trapped spherical nanoparticles when utilizing a sufficiently long PLMA stabilizer block. 22 In the present study, SAXS patterns recorded at 25 C for a 1.0% w/w dispersion of PLMA 39 -PBzMA x nanoparticles could be tted using a spherical micelle model 54,55 (eqn (S2)-(S13) and Table S1 †). This approach indicated spherical nanoparticle core diameters of 21 AE 2 nm and 48 AE 5 nm for the PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres, respectively (Fig. S3, Tables S2 and S3 †). The mean radius of gyration for the PLMA 39 stabilizer chains was approximately 2.0 nm in both cases. This is consistent with the radius of gyration of 1.9 nm obtained by tting the SAXS pattern recorded for a 1.0% w/w solution of PLMA39 homopolymer in n-dodecane (Fig. S4 †) using the Debye function. 56 SAXS pattern for the larger nanoparticles revealed an additional diffuse peak at q $ 0.8 nm À1 (Fig. S3B †). We account for this feature by including a Gaussian function in the data t. This high q feature indicates a length scale of approximately 8 nm, which corresponds to twice the radius of gyration of the PBzMA chains ($4 nm) within the nanoparticle cores.

Variable temperature SAXS analysis of spherical nanoparticles
It is well-known that copolymer chain exchange can occur between spherical diblock copolymer nanoparticles in nonpolar media at elevated temperature. Moreover, such exchange is sensitive to both temperature and the DP of the core-forming block. 38,41 It is also known that the cores of PLMA-PBzMA nano-objects become progressively more solvated with hot solvent at elevated temperature. 8,53 It seems likely that the greater chain mobility associated with this solvent plasticization facilitates the chain expulsion/insertion mechanism, making the thermally-activated redistribution of copolymer chains more likely. Herein, variable temperature SAXS was used to study the degree of core solvation and integrity of PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres at elevated temperature. In an initial series of experiments, dispersions of both types of nanoparticles were diluted in turn to 1.0% w/w using n-dodecane and scattering patterns were recorded in each case during a 25-150-25 C thermal cycle (Fig. S3 †). Heating PLMA 39 -PBzMA 97 spheres alone led to a progressive change in the scattering pattern, which returned to its original form aer cooling from 150 C to 25 C (Fig. S3A †). In contrast, heating the larger PLMA 39 -PBzMA 294 spheres up to 150 C produced almost no discernible change in the scattering pattern ( Fig. S3B †). SAXS patterns recorded for the PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres at various temperatures were tted to a well-known spherical micelle model with an additional Debye function to account for a minor fraction of molecularly-dissolved PLMA 39 -PBzMA x chains (see eqn (S2)-(S13) in the ESI †). [54][55][56] Satisfactory data ts could be obtained for both types of nanoparticles by assuming that the change in mass density (which affects both the scattering length density and the individual block volumes) for the PLMA corona block and the PBzMA core-forming block was equal to that reported by Fetters and co-workers for poly(n-butyl methacrylate) and polystyrene, respectively (Table S1 †). 57 SAXS analysis indicated minimal change in mean diameter for both types of spherical nanoparticles on heating up to 150 C (Fig. 1, Tables S2 and S3 in the ESI †). However, a progressive increase in the solvent volume fraction (X sol ) within the nanoparticle cores was Scheme 1 A PLMA 39 precursor block is chain-extended with BzMA monomer in n-dodecane via RAFT-mediated PISA to form stericallystabilized spherical nanoparticles. SAXS analysis (see Fig. S3, Tables S2 and S3 in the ESI †) indicated that final PBzMA DPs of 97 and 294 produced mean core diameters of 21 AE 2 nm and 48 AE 5 nm, respectively. observed when heating the smaller PLMA 39 -PBzMA 97 spheres. Moreover, a drastic reduction in nanoparticle concentration from 0.67 to 0.45% v/v was observed on heating to 150 C. To account for this observation, the Debye function 56 was used to include a population of molecularly-dissolved PLMA 39 -PBzMA 97 chains in the data t, such that this population becomes progressively larger at higher temperatures. Returning to 25 C led to complete desolvation of the nanoparticle cores and the nal data t at this temperature indicated that only a minor population of PLMA 39 -PBzMA 97 chains remained molecularly dissolved (Table S2 †).
In contrast to the smaller nanoparticles, data ts obtained for the larger PLMA 39 -PBzMA 294 spheres indicated minimal change in their mean diameter and degree of core solvation when thermally annealed at 150 C. Moreover, the SAXS data ts indicate a rather more subtle increase in the relative concentration of the molecularly-dissolved PLMA 39 -PBzMA 294 chains compared to that of the spherical nanoparticles (Table S3 †). In summary, the above variable temperature SAXS experiments indicate that the cores of the larger spheres are much less plasticized by hot solvent compared to the smaller spheres, which means that the former nanoparticles are much less likely to undergo dissociation (i.e. expulsion of individual copolymer chains).
The mean core diameter for the highly solvated PLMA 39 -PBzMA 97 nanoparticles at 150 C is comparable to that of the same non-solvated nanoparticles at 25 C. This implies a signicant reduction in the volume-average aggregation number, N agg , (i.e. the mean number of copolymer chains per nanoparticle) at elevated temperature. This parameter was calculated using eqn (1): where R is the nanoparticle core radius and V s is the volume occupied by a single PBzMA core-forming block. The calculated N agg values are plotted against temperature for both PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres (Fig. 2). The mean N agg for the former spheres was signicantly reduced from 205 at 25 C to 142 at 150 C, which is consistent with the formation of a secondary population of molecularly-dissolved diblock copolymer chains. Returning to 25 C led to the formation of spheres with a slightly lower N agg (171) than the original nanoparticles. It seems likely that annealing PLMA 39 -PBzMA 97 spheres at 150 C enables the diblock copolymer chains to rearrange to form spheres that lie closer to the thermodynamically-preferred size compared to the original spheres formed via RAFT-mediated PISA at 90 C. Furthermore, these results suggest that a small fraction of molecularlydissolved PLMA 39 -PBzMA 97 chains remain dissolved aer returning to 25 C. In contrast, the minimal change in nanoparticle core diameter (along with the lack of solvation) observed for the larger PLMA 39  An equivolume binary mixture of PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres at 1.0% w/w solids was heated up to 150 C for 1 h to examine the possibility of thermally-activated exchange of copolymer chains between such nanoparticles. In initial experiments, thermal annealing of an equivolume binary mixture of these two types of nanoparticles leads to the formation of well-dened spherical nanoparticles of intermediate mean diameter (see Scheme 2). TEM analysis conrmed a well-dened spherical morphology for both types of nanoparticles prior to heating. As expected, the binary dispersion exhibited two distinct populations prior to thermal annealing. Interestingly, TEM analysis of this binary mixture aer heating to 150 C for 1 h indicated a single population of spherical nanoparticles exhibiting an intermediate mean particle diameter (Fig. 3). These TEM observations were supported by SAXS experiments performed at   Fig. 3). According to general scattering theorems, the scattering intensity in the low q region of the X-ray scattering pattern (q $ 0 A À1 ) is proportional to the nanoparticle volume. 59 Thus larger nanoparticles cause stronger X-ray scattering in this regime. Furthermore, the gradient of the pattern in this low q region is sensitive to the nanoparticle shape. For example, a zero gradient indicates the presence of isotropic spheres. In contrast, anisotropic nanoparticles exhibit a negative gradient in this low q region. Thus, platelets/disks or vesicles possess a gradient of À2, while long thin rods are characterized by a gradient of À1 (with less anisotropic rods typically possessing gradients ranging between zero and À1). 60 The scattering patterns recorded for the two initial dispersions, their equivolume binary mixture and the nal hybrid nanoparticles exhibited approximate zero gradients at low q, which indicates the presence of spherical non-interacting nanoparticles in each case. Moreover, the scattering pattern recorded for the initial binary mixture of nanoparticles could be satisfactorily tted using the known size distribution for each component by simply varying the relative concentrations of the two types of nanoparticles (Table S4 †). The SAXS pattern recorded for the annealed binary dispersion is consistent with the TEM images shown in Fig. 3: the local minimum in the scattering curve clearly falls between the two minima observed for the original large and small spherical nanoparticles, which conrms that hybrid spherical nanoparticles with an intermediate mean diameter are obtained aer heat treatment. The scattering pattern recorded for these hybrid nanoparticles was tted to the same spherical micelle model using a mean PBzMA core volume calculated from the known proportions of the two nanoparticle populations (Table S4 †). Assuming complete entropic mixing, this t to the scattering curve gave a mean volume-average core diameter of 36 AE 3 nm, which is consistent with the number-average core diameter of 34 AE 3 nm estimated from TEM analysis (Fig. 3D). This conrms that the dimensions of the hybrid nanoparticles lie between those of the two initial nanoparticle dispersions.

In situ SAXS studies of the kinetics of nanoparticle hybridization
To explore the nanoparticle hybridization mechanism, in situ SAXS measurements were performed while heating a 1.0% w/w dispersion comprising an equivolume binary mixture of PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres up to 150 C (Fig. 4). A scattering pattern for the initial binary mixture was recorded at 20 C, with two distinct minima representing the bimodal nature of the initial nanoparticle dispersion (Fig. 3). Aer heating up to 150 C at 30 C min À1 , the rst scattering  In situ SAXS patterns recorded when heating a 1.0% w/w nanoparticle dispersion comprising a 1 : 1 v/v binary mixture of 21 AE 2 nm PLMA 39 -PBzMA 97 and 48 AE 5 nm PLMA 39 -PBzMA 294 spheres up to 150 C at a heating rate of 30 C min À1 . As expected, two minima are discernible in the initial pattern recorded for this binary mixture at 20 C. However, the final scattering pattern obtained after annealing for 20 min at 150 C shows two minima (denoted q 1 and q 2 ) that correspond to a single population of spherical nanoparticles of intermediate diameter (36 AE 4 nm).
pattern recorded at this temperature also exhibited these two minima. However, maintaining this dilute binary dispersion at 150 C produced a low q gradient of À0.55 within 7.0 min. Thereaer, a low q gradient of approximately zero was again observed (within a further 12.5 min). The nal scattering pattern acquired aer thermal annealing for 20 min at 150 C exhibited two minima that correspond to a single population of spherical nanoparticles (Scheme 2). [N.B. For these two features, we nd that q 1 R ¼ 4.49 and q 2 R ¼ 7.73, where R corresponds to the core radius of the nal hybrid spherical nanoparticles, Fig. 4.] Thus R is calculated to be approximately 18 nm in each case, which indicates a mean particle diameter of $36 nm. In summary, these in situ SAXS studies strongly suggest that the transformation of the initial binary mixture of spheres (Fig. 3C) into a single population of spheres of intermediate diameter (Fig. 3D) involves weakly anisotropic transient species.
The scattered X-ray intensity at an arbitrary q value of 0.019 nm À1 (Fig. 5A), and the low q gradient in the 0.019 nm À1 < q < 0.035 nm À1 interval (Fig. 5B) were plotted against time to further investigate the mechanism of formation of the nal hybrid nanoparticles. Using a heating rate of 30 C min À1 , the nal temperature of 150 C was achieved within 4.3 min during these in situ SAXS experiments. Inspecting Fig. 5, both the scattered intensity and the low q gradient begin to change just below 150 C, suggesting that nanoparticle hybridization has already commenced prior to the target temperature being attained. A pronounced maximum in scattered X-ray intensity is observed at around 7.0 min (Fig. 5A), which roughly corresponds to the formation of the most anisotropic transient species as judged by the change in the low q observed gradient (Fig. 5B). It should also be noted that the initial scattered X-ray intensity of 199 cm À1 is higher than the nal intensity (159 cm À1 ) (Fig. 5A). This is understandable because the X-ray scattering at low q is proportional to the volume of the scattering objects. As a result, X-ray scattering from the original equivolume binary mixture of large and small nanoparticles should be dominated by the former population, which also scatter more strongly than the nal spheres of intermediate size [this latter point is readily illustrated by simple calculation, i.e. The progressive change in the low q gradient during thermal annealing indicates the formation of weakly anisotropic species (mean aspect ratio ¼ 2-3). This unexpected observation suggests that the change in copolymer morphology is unlikely to simply involve expulsion of PLMA 39 -PBzMA 97 copolymer chains from the smaller nanoparticles and their subsequent insertion into the larger PLMA 39 -PBzMA 294 nanoparticles. This is because such a copolymer chain exchange mechanism should simply reduce the diameter of the smaller nanoparticles while increasing that of the larger nanoparticles. 61 Given that a spherical morphology has the lowest possible surface area per unit mass, it is difficult to envisage how such mass transport could result in the formation of non-isotropic nanoparticles. It seems much more likely that the transient anisotropic species are instead obtained via a fusion/ssion process, despite the relatively low copolymer concentration (1.0% w/w) used for these thermal annealing experiments. However, given that the extent of core solvation and mean aggregation number strongly depend on the DP of the core-forming block ( Fig. 1 and 2), relatively few of the longer PLMA 39 -PBzMA 294 chains are expected to be expelled from the larger nanoparticles at 150 C. Actually, the gradual increase in X-ray scattering intensity at q ¼ 0.019 nm À1 and the low q gradient of approximately zero indicates that the initial nanoparticles become progressively larger at 150 C while maintaining their spherical morphology (Fig. 5, red lines and  arrows). Thus, this observation suggests that the expelled PLMA 39 -PBzMA 97 chains are simply incorporated within the larger PLMA 39 -PBzMA 294 spheres for the rst 3.2 min.
However, a signicant increase in X-ray scattering intensity is observed aer 3.2 min, which is accompanied by an abrupt change in the low q gradient. These observations are consistent with the formation of larger, weakly anisotropic nanoparticles, e.g. dimers/trimers. The subsequent reduction in X-ray scattering intensity and return to a low q gradient of  Fig. 4 caption for further experimental details). The red lines and arrows indicate that a significant change in both the low q gradient and the scattered X-ray intensity occurs after 3.2 min, which corresponds to approximately 116 C.

Edge Article
Chemical Science approximately zero indicate the gradual evolution of these transient species into the nal isotropic spheres of intermediate core diameter. Presumably, this latter process is driven by the minimization of surface free energy (see below for a proposed mechanism).

Effect of varying the relative volume fraction of small nanoparticles on copolymer morphology
Varying proportions of small PLMA 39 -PBzMA 97 spheres were annealed with large PLMA 39 -PBzMA 294 spheres in an attempt to produce the anisotropic intermediate species as a nal hybrid copolymer morphology. These binary mixtures were prepared at various volumetric ratios at 20% w/w solids, then diluted to 1.0% w/w using n-dodecane and heated to 150 C for 1 h. PLMA 39 -PBzMA 97 volume fractions ranging from 0.05 to 0.50 were examined in these nanoparticle fusion experiments. Indeed, TEM analysis of the annealed dispersions revealed formation of the anticipated weakly anisotropic nanoparticles (mean aspect ratio ¼ 2-3) when using PLMA 39 -PBzMA 97 volume fractions of between 0.20 and 0.35 (Fig. 6). However, it is perhaps worth emphasizing that such species always co-exist with a variable population of spheres. Further insight regarding the formation of these kinetically stable hybrid nanoparticles was obtained by SAXS analysis (Fig. S5 †). Scattering patterns for these dispersions were recorded at 1.0% w/w solids aer thermal annealing at this concentration. The structure factor can be assumed to be unity for such dispersions and the approximate zero gradient observed at low q indicated a spherical morphology in most cases. However, a non-zero gradient was observed at low q when using PLMA 39 -PBzMA 97 volume fractions of 0.20, 0.25, 0.30 or 0.35, indicating the presence of anisotropic nanoparticles. Moreover, these scattering patterns could not be tted using a spherical micelle model (eqn (S2)-(S13) in the ESI) (Fig. S5 †). These observations are consistent with TEM studies of these four thermally-annealed dispersions, for which a variable population of weakly anisotropic nanoparticles was observed at 20 C (Fig. 6). These SAXS patterns were further analyzed by calculating nanoparticle dimensions (i.e. either the mean sphere diameter or a cross-sectional diameter for the dimer/trimer species) from the q value of the rst minimum (particle dimension ¼ 4.49/q min , where 4.49 corresponds to the rst minimum for the spherical form factor), and plotting such sizes against the corresponding PLMA 39 -PBzMA 97 volume fraction (Fig. 7). A modest monotonic increase in sphere diameter was observed for PLMA 39 -PBzMA 97 volume fractions up to 0.15. At higher volume fractions (0.20-0.35), a population of weakly anisotropic transient particles is indicated by the gradual reduction in mean particle dimension, i.e. the effective cross-section of the dimers/ trimers (Fig. 7). Finally, using a higher proportion of small PLMA 39 -PBzMA 97 spheres (volume fraction ¼ 0.40-0.50) leads to a gradual reduction in the mean sphere diameter. In this case, it appears that there is a sufficiently high concentration of PLMA 39 -PBzMA 97 chains to generate a single population of spheres of intermediate size, as observed in Fig. 3 and 6.

Proposed mechanism for nanoparticle hybridization
Taking into consideration the TEM images and SAXS data discussed above, a tentative two-stage mechanism is proposed in   Fig. 1 and 2). This causes the latter nanoparticles to grow in size, which simply leads to the formation of larger hybrid spheres provided that the volume fraction of the smaller PLMA 39 -PBzMA 97 nanoparticles is less than 0.20. However, above this critical volume fraction a second series of events occurs (see Stage 2). Now the growing hybrid nanoparticles interact with one (or more) of the smaller, solventswollen spheres and undergo fusion and internal rearrangement to form weakly anisotropic intermediate species. The surfactant-like individual copolymer chains then adsorb onto and interact with these relatively unstable intermediates, which undergo ssion to form at least two hybrid spheres of intermediate size. This hypothesis is consistent with the observations made during the in situ SAXS experiment ( Fig. 4 and 5). In particular, the initial increase in scattered X-ray intensity at q ¼ 0.019 nm À1 for the rst 3.2 min corresponds to Stage 1, since the low q gradient remains close to zero (indicating that only spheres are present). However, the scattered X-ray intensity then increases signicantly with a concomitant reduction in the low q gradient to À0.55 being observed at 7.0 min. This indicates the formation of relatively large, weakly anisotropic intermediates. Such species can be obtained as a nal morphology if the volume fraction of smaller PLMA 39 -PBzMA 97 nanoparticles lies between 0.20 and 0.35. However, at higher volume fractions, these smaller nanoparticles provide a sufficient quantity of surface-active individual copolymer chains to interact with these anisotropic intermediates. This causes the latter species to undergo ssion, which produces the nal hybrid spheres of intermediate diameter. This hypothesis is consistent with a prior study by Chambon and co-workers, 62 who found that diblock copolymer vesicles prepared via aqueous PISA could be disrupted to form much smaller spheres when exposed to an ionic surfactant. This ssion event is responsible for the gradual reduction in the scattered X-ray intensity and the low q gradient shown in Fig. 5.
Revisiting the representative TEM images shown in Fig. 3, we calculate (see ESI † for further details) that approximately eleven small (21 AE 2 nm) PLMA 39 -PBzMA 97 spherical nanoparticles interact with each large (48 AE 5 nm) PLMA 39 -PBzMA 294 sphere to form approximately four hybrid nanoparticles of 36 nm diameter. This calculation should be borne in mind when considering Scheme 3 (i.e. n ¼ 11, m ¼ 1 and p $ 4 for the thermal annealing experiment described in Fig. 3). However, this rather rudimentary analysis suffers from poor statistics. Thus, we also reexamined the corresponding SAXS data obtained for the thermally-annealed nanoparticles. This enabled us to calculate a fusion ratio that was remarkably close to that obtained from the above TEM image analysis (n $ 9, m ¼ 1 and p $ 4), see Table S6 in the ESI. †  Fig. 6 and corresponding SAXS patterns in Fig. S5 †). Hybrid nanoparticle dimensions (i.e. either sphere diameter or mean cross-sectional diameter of the dimers/trimers) were calculated from the q value for the first minima in the corresponding SAXS patterns (particle dimension ¼ 4.49/q min , where the numerical factor corresponds to the first minimum for a spherical form factor).
Scheme 3 Schematic representation of the two-stage mechanism proposed for the changes in copolymer morphology that are observed during thermal annealing of a binary mixture of 21 AE 2 nm and 48 AE 5 nm diblock copolymer spheres at 150 C. Here, the n, m and p values refer to the number density of each type of nanoparticle. In Stage 1, the smaller PLMA 39 -PBzMA 97 spheres undergo partial dissociation to form copolymer chains, which then become incorporated into the larger spheres to produce hybrid spheres with a mean diameter greater than 48 nm. If the volume fraction of these smaller spheres is less than 0.20, this is the final copolymer morphology. However, using higher volume fractions of this component leads to Stage 2, whereby the 21 nm spheres undergo fusion with the larger hybrid spheres to form weakly anisotropic transient species. The latter then undergo fissionmost likely mediated by incorporation of further PLMA 39 -PBzMA 97 chainsto form spheres of intermediate size (e.g. 36 nm diameter). This mechanism is consistent with the SAXS data shown in Fig. 3-5 and 7 and the TEM images shown in Fig. 3 and 6.
The driving force for the fusion process is likely to be the (partial) solvation of the nanoparticle cores by the ingress of hot solvent at elevated temperature. This inevitably leads to enhanced copolymer chain mobility, which in turn enhances the probability of micelle fusion. Indeed, we have recently published NMR evidence for such core solvation for a related PISA formulation in non-polar media. 17 We suggest that using a higher annealing temperature (>150 C) is likely to affect the nanoparticle hybridization mechanism. Under such conditions, the PLMA 39 -PBzMA 294 nanoparticles may also undergo dissociation to form molecularly-dissolved copolymer chains. Clearly, this hypothesis warrants further studies. Finally, one reviewer of this manuscript has suggested that the micelle fusion/ssion mechanism demonstrated herein is unlikely to apply to nanoparticles (micelles) of equal size. This is because there is no difference in free energy in this case. This may explain why a copolymer chain exchange mechanism appears to operate in such instances. 41

Conclusions
RAFT-mediated PISA was used to prepare sterically-stabilized PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 diblock copolymer spheres in n-dodecane, with mean core diameters of 21 AE 2 nm and 48 AE 5 nm, respectively. Variable-temperature SAXS analysis of these dilute dispersions at 150 C indicates substantial core solvation and a signicant reduction in aggregation number for the smaller PLMA 39 -PBzMA 97 spheres. In contrast, changes were much less pronounced for the larger PLMA 39 -PBzMA 294 spheres: aer returning to 25 C, approximately the same core diameters were observed before and aer thermal annealing.
Annealing an equivolume binary mixture of these two dispersions at 1.0 % w/w led to the formation of hybrid nanoparticles with an intermediate mean core diameter of 36 AE 3 nm. This suggests that the copolymer chains expelled from the PLMA 39 -PBzMA 97 spheres exhibit surfactant-like behavior and cause ssion of the larger PLMA 39 -PBzMA 294 spheres. Moreover, in situ SAXS studies during such experiments revealed an upturn in the low q gradient. This indicates the presence of weakly anisotropic transient species, which then induce fusion to form the nal hybrid spherical nanoparticles of intermediate size.
Further insights regarding the nanoparticle hybridization mechanism were obtained by annealing a series of binary mixtures with varying proportions of PLMA 39 -PBzMA 97 and PLMA 39 -PBzMA 294 spheres at 1.0% w/w solids. Spherical nanoparticles of intermediate size were produced for PLMA 39 -PBzMA 97 volume fractions of between 0.40 and 0.50. Interestingly, using volume fractions between 0.05 and 0.20 yielded spherical nanoparticles with slightly larger mean particle diameters than the original PLMA 39 -PBzMA 294 spheres. This suggests that the hybridization mechanism involves initial expulsion of copolymer chains from the small PLMA 39 -PBzMA 97 spheres and their subsequent incorporation within the larger PLMA 39 -PBzMA 294 spheres. Moreover, TEM and SAXS analyses indicate that weakly anisotropic nanoparticles can be obtained as a nal (mixed) copolymer morphology over a restricted range of compositions (e.g. volume fractions of 0.20-0.35 for the smaller PLMA 39 -PBzMA 97 spheres) when heating such binary mixtures of spheres up to 150 C. As far as we are aware, such non-isotropic species have not been observed for any nanoparticle hybridization experiments reported in the literature. Finally, we provide the rst compelling experimental evidence for a micelle fusion-ssion mechanism in such systems. A two-stage mechanism that involves both expulsion/insertion and micelle fusion/ssion events is proposed to account for our observations.

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