Small‐Angle X‐Ray Scattering Studies of Block Copolymer Nano‐Objects: Formation of Ordered Phases in Concentrated Solution During Polymerization‐Induced Self‐Assembly

Abstract We report that polymerization‐induced self‐assembly (PISA) can be used to prepare lyotropic phases comprising diblock copolymer nano‐objects in non‐polar media. RAFT dispersion polymerization of benzyl methacrylate (BzMA) at 90 °C using a trithiocarbonate‐capped hydrogenated polybutadiene (PhBD) steric stabilizer block in n‐dodecane produces either spheres or worms that exhibit long‐range order at 40 % w/w solids. NMR studies enable calculation of instantaneous copolymer compositions for each phase during the BzMA polymerization. As the PBzMA chains grow longer when targeting PhBD80–PBzMA40, time‐resolved small‐angle X‐ray scattering reveals intermediate body‐centered cubic (BCC) and hexagonally close‐packed (HCP) sphere phases prior to formation of a final hexagonal cylinder phase (HEX). The HEX phase is lost on serial dilution and the aligned cylinders eventually form disordered flexible worms. The HEX phase undergoes an order–disorder transition on heating to 150 °C and a pure HCP phase forms on cooling to 20 °C.


Introduction
It is widely recognized that polymerization-induceds elfassembly (PISA) is ap owerful and versatile platform technology for the rational design of various types of block copolymer nano-objects (e.g. spheres,w orms,v esicles or lamellae). [1][2][3][4] Moreover,P ISA enables the efficient production of such nano-objects in the form of concentrated dispersions, [5][6][7][8] whereas traditional post-polymerization processing routes are typically limited to dilute copolymer solutions. [9][10][11] In essence,P ISA involves chain extension of as oluble homopolymer precursor using as uitable second monomer in an appropriate solvent. When the growing second block reaches ac ertain critical degree of polymerization it becomes insoluble,which drives in situ self-assembly to form nascent nanoparticles. [12,13] Thep olymerization continues within the monomer-swollen nanoparticles,w ith the high local monomer concentration usually producing ar ate acceleration that ensures high conversions (typically > 95 %) within relatively short time scales. [14,15] Thus,t he monomer acts as aconvenient processing aid or co-solvent. In principle, the final diblock copolymer morphology is governed solely by the relative volume fractions of the soluble and insoluble blocks,asindicated by the geometric packing parameter. [11,16] In practice,kinetically trapped spheres can be observed under various reaction conditions. [17][18][19][20] To ensure access to welldefined worms or vesicles,t he insoluble structure-directing block should be relatively long compared to the soluble steric stabilizer block. [3,4,11,21] We,a nd others,h ave demonstrated that the construction of pseudo-phase diagrams is extremely useful for identifying appropriate PISA formulations for the reproducible production of pure copolymer morphologies. [5,15,22] This systematic approach is particularly important when targeting diblock copolymer worms because this elusive morphology typically occupies relatively narrow phase space. [23,24] As aresult, robust design rules are well established for various PISA formulations based on dispersion polymerization. [2,3] Block copolymer worms offer potential applications as thickeners for aw ide range of solvents,i ncluding water, [25,26] polar solvents such as alcohol, [27,28] and non-polar solvents such as n-alkanes,m ineral oil or silicone oil. [14,15,29,30] Moreover, semi-concentrated worm dispersions form relatively soft, free-standing gels at ambient temperature owing to multiple inter-worm contacts. [31] Rheological studies confirm that such gels are highly sensitive to shear-induced flow, [32,33] which enables their injection using asyringe.Certain aqueous worm gels exhibit thermoresponsive behavior;o nc ooling to around 5 8 8C, they undergo ar eversible worm-to-sphere transition that causes in situ degelation. [25] In contrast, worm gels prepared in organic solvents undergo degelation on heating as ar esult of the same morphological transition. [14,[28][29][30] In both cases,t his behavior can be explained in terms of surface plasticization of the worm cores,which leads to as ubtle reduction in the effective packing parameter. [16,34,35] Relatively dilute diblock copolymer worm dispersions have been studied for several decades. [9,10,23,[36][37][38][39] Similarly,the self-assembly of block copolymers in the solid state [40,41] has been exploited for numerous applications,i ncluding the production of synthetic rubber, [42] the design of nanoporous membranes to aid water purification, [43] and polymer electrolytes for batteries or fuel cells. [44,45] It is also well-known that concentrated dispersions of diblock copolymer nano-objects can form lyotropic phases that exhibit long-range order. [46,47] Forexample,intheir seminal study of block copolymer worms in aqueous solution, Bates and co-workers reported that an ear-symmetrical poly(ethylene oxide)-poly(butadiene) (PEO-PBD) diblock copolymer formed hexagonally packed cylinders at or above 10 %w /w copolymer concentration. [36] Similarly,L odge and co-workers reported the lyotropic selfassembly of diblock copolymers in the presence of various selective non-polar solvents. [46,48] In particular,m any phases can be accessed for polyisoprene-polystyrene (PI-PS) diblock copolymers depending on the copolymer concentration and the solvent quality. [48] However,t hese nanostructured solvent-swollen phases are traditionally produced by postpolymerization processing, which is normally conducted in relatively dilute solution using aV OC as aco-solvent.
In contrast, Zhang et al. reported the PISA synthesis of concentrated diblock copolymer worms via the RAFT dispersion polymerization of ac holesterol-based (meth)acrylic monomer in an ethanol/water mixture. [49] Electron microscopy studies indicated that the cholesterol units formed as mectic phase within the worm cores,w hich stabilized this anisotropic morphology over ar elatively wide range of copolymer compositions.M oreover,s mall-angle X-ray scattering (SAXS) provided evidence for the "apparent preferential order" of neighboring worms.H owever,t his was assumed to be as ample preparation artifact rather than alyotropic phase formed during PISA. More recently,Anand co-workers reported the formation of bicontinuous mesophases ("cubosomes") within diblock copolymer microparticles during RAFT dispersion alternating copolymerization of styrene with pentafluorostyrene in ethanol. [50,51] Theaddition of toluene as aplasticizer was required to access these phases, which were obtained by targeting relatively long structuredirecting insoluble blocks.
As far as we are aware,t he formation of bulk lyotropic phases of block copolymer worms during their PISA synthesis has not been previously observed. Herein we report the PISA synthesis of highly concentrated dispersions of diblock copolymer worms that form ah exagonally packed cylinder (HEX) phase when prepared directly in n-dodecane.W eu se SAXS to study (i)the in situ evolution in copolymer morphology and intermediate lyotropic phases that occur during PISA, (ii)the serial dilution that eventually leads to ac onventional dispersion of worm-like micelles,a nd (iii)the effect of thermal annealing on these lyotropic phases.

Results and Discussion
Recently,w er eported ap seudo-phase diagram for PhBD 80 -PBzMA x nano-objects that enables the reproducible PISA synthesis of well-defined spheres,worms and vesicles in n-dodecane. [52] Interestingly,t he formation of ap ure worm phase required such PISA syntheses to be conducted at 40 % w/w solids,w ith lower copolymer concentrations merely producing kinetically trapped spheres.P resumably,t his is because the stochastic 1D fusion of multiple spheres that is required to form worms is not favored under more dilute conditions.A sf ar as we are aware,t his constitutes the most concentrated worm dispersion yet reported for any PISA formulation conducted in non-polar media. [49] More specifically,aPhBD 80 -PBzMA 40 dispersion prepared at 40 %w /w solids formed as tiff,t ransparent gel at 20 8 8Ca nd ah ighly anisotropic worm morphology was confirmed by TEM studies of the serially diluted dispersion (see Figure 1).
In situ SAXS analysis. In our earlier report, [52] these block copolymer nano-objects were characterized using GPC, TEM, DLS and rheology.H owever,n oS AXS studies were undertaken. In the present study,the evolution of copolymer morphology during PISA was monitored using time-resolved SAXS when targeting PhBD 80 -PBzMA 40 worms at 40 %w /w solids.W ea nd others have previously studied the in situ evolution in copolymer morphology for various PISA formulations. [53][54][55][56] This approach enables the onset of micellization to be identified, as well as the observation of sphere-toworm and worm-to-vesicle transitions during the polymerization. [50] Inspecting Figure 2A,B), several stages of structural organization could be identified from the significant changes observed in the SAXS patterns as the BzMA polymerization progressed. Relatively featureless patterns were recorded within the first 28 min of the reaction, suggesting the presence of soluble copolymer chains and/or the formation of relatively loose,i ll-defined aggregates.U nlike in situ SAXS studies of more dilute formulations in which well-defined local minima signified the formation of nano-objects, [53][54][55] there was no evidence for any particle form factor.I nstead, only ab road structure peak was detected ( Figure 2A). This feature became increasingly intense,a nd the peak maximum gradually shifted to lower q over the first 58 min of the polymerization ( Figure S3).
Ar emarkable change in the 1D SAXS pattern was observed after 1h,whereby three sharp Bragg peaks (principal scattering peak, q* = 0.037 À1 )e merged from the initial broad structure peak, with higher-order peaks located at q/q* = ffiffi ffi 2 p and ffiffi ffi 3 p (Figure 2A,s ee pattern recorded at 60-62 min). Thec orresponding 2D SAXS pattern observed at 62 min ( Figure 2B)s hows as eries of diffraction spots, commonly associated with reflections from crystallographic planes of large domains formed by spheres exhibiting longrange order. [57] After 76 min, additional peaks appeared at q/q* = ffiffi ffi 4 p , ffiffi ffi 6 p , ffiffi ffi 7 p and ffiffi ffi 9 p that grew in intensity as the polymerization progressed ( respectively can be assigned to the observed peaks (see Figure 2C for af ull assignment). [58] Such aB CC structure is usually formed by spherical particles. [59] This is because at this relatively early stage of the polymerization, where the volume fraction of the growing PBzMA block is much lower than that of the PhBD 80 block, the diblock copolymer chains should self-assemble to form spherical micelles. [53] After 78 min, various additional peaks (see square symbols in Figure 2C)a re observed that cannot be assigned to the same BCC phase.T he corresponding 2D scattering pattern ( Figure 2B)r evealed an additional series of diffraction spots located at around 0.03 À1 ,w hich suggests the coexistence of BCC with as econd phase(s). As the BzMA polymerization continues,t he 200 peak of the BCC phase is no longer observed after 90 min ( Figure 2C). Moreover,after this time point the three most intense peaks are located at q/q* = 1, ffiffi ffi 3 p and ffiffi ffi 4 p ,while weaker peaks are located at q/q* = ffiffi ffi 7 p , ffiffi ffi 9 p (Figure 2A,s ee 100-102 min);t his is consistent with ahexagonally packed cylinder (HEX) phase. [48] As the BzMA polymerization proceeds to completion, the two diffraction rings with evenly distributed intensities observed at approximately 0.03 À1 and 0.05 À1 in the 2D SAXS patterns ( Figure 2B  obtained for the SAXS pattern recorded at 1.0 %w /w was obtained using aworm-like micelle model reported in the literature. [60] The dashed black line represents aslope of À1t hat is characteristic of worm-like nano-objects. [26] 1D SAXS patterns are offset by an arbitrary multiplication factor to avoid overlap of the data. diffraction spots most likely produced by large crystallite domains,s uggesting another coexisting phase.A tt he end of polymerization, the most intense scattering peaks are assigned to the HEX phase ( Figure 2A,s ee 268-270 min).
After cooling the 40 %w/w copolymer dispersion to 25 8 8C for 5h,m ost of these features could still be observed, suggesting the persistence of this ordered phase as the dominant structure ( Figure 2C,t op). This cylinder phase comprises locally aligned worms that possess significantly fewer degrees of freedom than the more dilute dispersions of randomly oriented, non-interacting worms that have often been reported for PISA syntheses conducted in non-polar media. [15,29,33,53,61] To the best of our knowledge,this is the first time that any long-range order has been observed for block copolymer nano-objects during their PISA synthesis.
Lyotropicp hase behavior. When the as-synthesized PhBD 80 -PBzMA 40 dispersion was diluted to as ufficiently low concentration for TEM analysis,w ell-defined worm-like micelles were observed ( Figure 1C). This loss of long-range order upon dilution was examined in more detail via sequential dilution of the copolymer dispersion from 40 % w/w to 30, 20, 10, 5o r1%w /w using n-dodecane prior to performing SAXS measurements at 21 8 8C( Figure 2D).
Dilution to 30 %w /w resulted in as ignificant increase in domain spacing, as evidenced by as hift in the primary scattering peak to lower q. In addition, the ffiffi ffi 3 p and ffiffi ffi 7 p peaks disappeared, leaving only higher-order peaks corresponding to q/q* = ffiffi ffi 4 p and ffiffi ffi 9 p ( Figure 2D). On dilution, the cylinders should become more loosely packed, which results in the HEX phase losing its six-fold rotation axis symmetry to form stacked layers of cylinders producing first, second and third order reflections (10, 20 and 30, respectively). Moreover,the greater separation distance between neighboring cylinders could result in the disappearance of the ffiffi ffi 7 p peak if its position coincides with the first minimum of the cylinder (worm) form factor observed for more dilute dispersions ( Figure 2D). The emergence of abroad feature beneath the primary scattering peak indicates as ignificant proportion of disordered worms that lack any long-range hexagonal packing. Further dilution resulted in the complete loss of all sharp Bragg peaks.F or example,j ust two very broad structure peaks were observed at ac opolymer concentration of 20 %w /w,s uggesting only rather weak correlation between neighboring particles at this copolymer concentration. These structure peaks disappeared on further dilution:o nly al ocal minimum at q % 0.064 À1 (corresponding to the particle form factor) was discernible at ac opolymer concentration of 5.0 %w /w,w hich is consistent with isolated, non-interacting worms. [26,29,61] Furthermore,the SAXS pattern corresponding to the lowest copolymer concentration (1.0 %w/w) exhibited alow q gradient of approximately À1and could be satisfactorily fitted using aworm-like micelle model [60] (see Figure 2D). SAXS analysis of a1 .0 %w /w dispersion of PhBD 80 -PBzMA 40 worms in n-dodecane indicated am ean crosssectional diameter of around 19 nm for the worm cores.This is in reasonably good agreement with the mean worm width of 22 AE 4nme stimated by digital image analysis of electron micrographs recorded after drying ad ilute copolymer worm dispersion (see Figure 1C). Thus,t hese results suggest that serial dilution of the original 40 %w/w PhBD 80 -PBzMA 40 dispersion using aselective solvent for the PhBD 80 block (n-dodecane) leads to transformation of the hexagonally packed cylinder phase into adisordered worm phase.This is consistent with the lyotropic behavior typically exhibited by diblock copolymers in the presence of as elective solvent. [48,62] It is perhaps noteworthy that the chemical structure of the PhBD 80 -PBzMA 40 diblock copolymer examined herein bears some resemblance to that of PI-PS [57,63] and poly(ethylene-butylene)-polystyrene (EBS/SEBS) [64,65] diblock copolymers,w hose lyotropic selfassembly behavior has been extensively investigated. For these latter two systems,b oth micellar cubic phases and hexagonal phases have often been observed under various conditions. [65,66] To complete this series of measurements on the concentration-dependent self-assembly behavior, the solid-state morphology of the final PhBD 80 -PBzMA 40 diblock copolymer was also assessed. After isolating PhBD 80 -PBzMA 40 from n-dodecane by precipitation into excess ethanol, the resulting dry copolymer powder was analyzed by SAXS over aw ide temperature range ( Figure S4). Only broad, low intensity peaks were observed at 40 8 8C, which suggests weak segregation within ar elatively disordered non-equilibrium phase that is formed following precipitation. [67,68] However, thermal annealing drives further microphase separation, which leads to the appearance of several sharp peaks at higher q. On heating above 100 8 8C, at least three equally spaced peaks are observed at q/q* = 1, 2and 3, indicating the formation of alamellar phase. [46,48] This is consistent with the near-symmetrical structure of this PhBD 80 -PBzMA 40 diblock copolymer:i th as aP hBD volume fraction of 0.45 for which alamellar morphology would be expected in the solid state. [41] Thus,s olvation of the PhBD stabilizer chains by n-dodecane increases the effective volume fraction of this block relative to that of the non-solvated PBzMA block. [53] Such selective swelling switches the preferred morphology from lamellae to close-packed cylinders (or spheres) comprising PBzMA cores. [16,35] Thedomain spacing, L 0 ,for the lamellar phase formed by the PhBD 80 -PBzMA 40 diblock copolymer in the solid state can be calculated using the relation L 0 = 2p/q*. This parameter ranged from 16.8 nm at 108 8 8C(the temperature at which aw ell-defined lamellar phase was first observed during thermal annealing) to 14.7 nm at 280 8 8C. Despite the relatively low molecular weight of this diblock copolymer,i ts order-disorder transition (ODT) temperature is unusually high and could not be observed under the experimental conditions used in the present study (i.e., it must exceed 280 8 8C, Figure S4). Such observations suggest that this is ah igh c diblock copolymer system that should enable the construction of nanostructured materials comprising sub-10 nm domain spacings. [69] In this context, we note that structurally similar PI-PS diblock copolymers also possess arelatively high c value. [63] Variable-temperature SAXS studies. Va rious diblock copolymer nano-objects prepared via RAFT dispersion polymerization have been reported to exhibit thermoresponsive behavior. [14,25,[28][29][30]61,[70][71][72] In some cases,s uch thermally induced transitions between copolymer morphologies can result in physical (de)gelation. To investigate the thermoresponsive behavior of the PhBD 80 -PBzMA 40 nano-objects in ndodecane,t he as-synthesized 40 %w /w dispersion was subjected to temperature-dependent SAXS studies.A t 25 8 8C, the initial dispersion mainly comprised peaks attributed to ah exagonal cylinder phase,a lthough an unassigned peak on the high q side of the 10 reflection suggests coexistence of as econd phase(s), see Figures 2C and 3A.O nh eating this concentrated dispersion up to 90 8 8C, the 20 reflection assigned to the hexagonal phase decreases in intensity,while anumber of additional peaks are observed. Notably,t he primary peak position shifts to higher q on heating ( Figure 3A). This temperature-dependent reversible peak shift is likely to be related to the greater degree of solvation of the PBzMA coreforming block at elevated temperature. [61] In recent studies, such core solvation reduced the mean aggregation number of spherical nanoparticles comprising either PMMA or PBzMA cores,r esulting in the formation of smaller nano-objects at high temperature. [73,74] In the present study,g reater core solvation at the reaction temperature would account for the shorter inter-micelle distances.I ndeed, the diffraction peaks are observed at higher q values at 90 8 8Ct han at 25 8 8C. At 130 8 8C, SAXS studies reveal ad iffuse isotropic peak that overlaps with ad iffraction peak accompanied by two higher order Bragg peaks at q/q* = ffiffi ffi 3 p and ffiffi ffi 7 p ( Figure 3A). All the Bragg peaks disappear to leave just as ingle diffuse peak on further heating up to 145 8 8C, which indicates an ODT. [59,68,75] On cooling the resulting disordered phase from 150 8 8Ct o 100 8 8C, as eries of Bragg spots reappear in the 2D SAXS patterns ( Figure 3B). Ther elative peak positions at q/q* = 1 and ffiffi ffi 2 p suggest that PhBD 80 -PBzMA 40 forms aBCC phase at 100 8 8C, although there are too few peaks to enable an unambiguous assignment. However,further cooling produced qualitatively different SAXS patterns.A tl east seven peaks are observed at or below 90 8 8C, with peak positions corresponding to neither aBCC nor aHEX phase.
Thefirst three peaks are closely spaced (around 0.03 À1 ) and resemble the peak pattern expected for hexagonally close-packed (HCP) spheres.T his phase has been previously observed on numerous occasions for both block copolymers [57,77] and surfactant lyotropic liquid crystals. [78,79] Data analysis using peak-indexing protocols available within Data-Squeeze 3.0 software [76] confirmed that all SAXS peaks observed on cooling from 90 8 8C( Figure 4A)t o2 5 8 8Cw ere consistent with an HCP phase (see Figure 4C for experimental vs.t heoretical peak indexing). Thea ppearance of diffraction spots within the 2D SAXS pattern suggests that this concentrated diblock copolymer dispersion comprises large domains of HCP phase with differing orientations (Figure 3B). [57] TheH CP phase has two characteristic unit cell parameters,describing the nearest neighbor spacing within one layer (a HCP ), and the interlayer spacing between two layers with the same packing (c HCP ), as shown in Figure 4C a HCP ,a nd hence c HCP /a HCP = 1.63, which is in good agreement with the experimental data. Close inspection of the HCP phase diffraction patterns indicates anomalous peak broadening behavior,w ith the 110 peak being sharper than the 102 peak located at lower q (Figure 4A). Since the 110 peak belongs to afamily of peaks such that hÀk = 3 n (where n is an integer), this observation suggests the presence of stacking faults within the HCP structure.T his is because broadening of the 110 reflection is independent of stacking faults while the 102 peak broadening is sensitive to such structural imperfections. [80] Similar observations are often reported in the literature for close-packed diblock copolymer spheres. [81] Thet hermal annealing experiment suggests that HCP spheres is the thermodynamically preferred phase for a40% In each case, the temperature was increased or reduced at 5 8 8Cintervals and the dispersion was equilibrated for 10 min at each temperature prior to data acquisition.1DSAXS patterns are offset by an arbitrary multiplication factor to avoid overlap of the data.
w/w PhBD 80 -PBzMA 40 dispersion in n-dodecane.M oreover, the phase transformations observed during thermal annealing suggest that the unassigned SAXS peaks observed during the PISA synthesis (see Figure 2A,B) most likely belong to ac oexisting HCP phase.I np rinciple,t he low q shoulder accompanying the first peak of the BCC and HEX phases observed at 0.029-0.031 À1 should correspond to the 100 reflection of the HCP phase that is observed at 0.030 À1 after thermal annealing ( Figure 3B,2 5 8 8C), while the second unidentified peak at 0.039-0.041 À1 coincides with the 102 reflection. Applying the same HCP peak-indexing protocol to the patterns recorded at ca. 72 min during in situ SAXS studies confirmed that every unidentified peak could be assigned to Miller indices of an HCP phase ( Figure 4B). This suggests that the HCP phase coexists with the BCC phase for reaction times between 72 and 76 min and remains thereafter with the HEX phase until the end of the polymerization.
Since the PhBD 80 -PBzMA 40 diblock copolymer forms closed-packed spheres under thermodynamic conditions that can coexist with other morphologies during copolymer synthesis,t his suggests an alternative interpretation for the product that is formed after cooling the final copolymer dispersion to 25 8 8C ( Figure 2A). Thed iffraction pattern was initially attributed to aHEX cylinder phase ( Figure 2C,top). However,o ne unassigned peak at 0.033 À1 becomes more prominent for longer annealing times at elevated temperatures ( Figure 3A,see SAXS patterns between 35 and 60 8 8C) does not belong to the HEX phase.I nf act, all but the principal diffraction peak can be assigned to af ace-centered cubic (FCC) structure formed by close-packed spheres by using the 002 peak position (q = 0.033 À1 )asareference for the FCC lattice period (a FCC = 37.0 nm;F igure S5A). However,t he most intense 111 peak of the FCC phase is slightly offset from the principal peak maximum, suggesting that if the observed pattern arose from an FCC phase then another phase must also be present. Thec opolymer chains selfassemble to form worm-like micelles ( Figure 1C,D), and all but one of the peaks (q = 0.033 À1 ,a ssigned to the 002 reflection of FCC) can be assigned to the HEX cylinder phase ( Figures 2C and S5B). Hence it seems likely that both the FCC and HEX phases coexist in the final product after cooling to ambient temperature.T his interpretation is supported by the SAXS patterns recorded at elevated temperatures ( Figure S5C), where peak positions shift to reveal two sets of peaks that can be assigned to FCC and HEX phases.
Thus the sequence of phases formed during the PISA synthesis is BCC!BCC + HCP (with stacking faults)! HEX + HCP (with stacking faults), where the hexagonal cylinder phase (HEX) directly replaces the BCC phase.Such BCC!HEX morphological transitions are well-documented for various block copolymer systems in the literature. [47,57,66,[82][83][84][85] X-ray diffraction patterns indicate that, on cooling the 40 %w /w copolymer dispersion to ambient temperature,t he HCP phase (with its stacking faults) is transformed into an FCC structure of close-packed spheres. Thus,t he final copolymer dispersion at 25 8 8Ci sc omposed of HEX and FCC (possibly with associated stacking faults) formed by worm-like and spherical micelles,respectively.
Reaction phase diagram. In addition to the observed phase transitions,t he gradual shift in the Bragg peaks to lower q during the BzMA polymerization indicates progressively larger domain spacings.M ore detailed analysis of the SAXS patterns enables the varying dimensions of these ordered phases to be assessed. In the early stages of the polymerization, the system comprised ad isordered array of micelles which most likely possess ap seudo-spherical morphology.T he mean distance between nearest neighbor micelles (D DIS )c an be estimated from the structure factor peak maximum (q*) using the simple relationship D DIS ¼ 2p/ q*. SAXS patterns recorded in situ during the polymerization indicate the presence of aBCC phase between 60 and 74 min, with the unit cell size increasing from 24.1 to 26.6 nm during this interval. From these dimensions,t he nearest neighbor center-to-center distance (D BCC )c an be calculated from the  Figure 3B). B) Additional peaks (black squares) that are observed in coexistencewith the BCC (upper pattern, gray diamonds) and hexagonal( lower pattern, gray triangles) phases can be assigned to Miller indices originating from the HCP sphere phase (see black squares). SAXS patterns are offset by an arbitrary multiplication factor to avoid overlap of the data. C) Correlation between the theoretical q values for Bragg peaks corresponding to an HCP phase and the experimental data determined from (A). The HCP phase comprises the unit cell shown in the inset, in which spheres are arranged within an HCP lattice with characteristic unit cell dimensions( a HCP and c HCP ). unit cell size using the equation D BCC ¼ ffiffi 3 p a BCC 2 . [57] Similar structural parameters can be calculated for the HEX phase, which becomes the dominant phase within 80 min. Themean center-to-center distance for nearest neighbor cylinders (D HEX )can be calculated using a HEX ¼ D HEX ¼ 2d 10 ffiffi 3 p . [57] Finally, within the coexisting HCP phase,t he center-to-center distance (D HCP )f or neighboring spherical micelles is simply the unit cell parameter a HCP ,i.e., D HCP ¼ a HCP . [57] Mean inter-micelle distances increase from 20.9 to 23.1 nm between 60 and 74 min. This greater inter-separation distance between neighboring micelles is the result of the mean micelle core radius increasing by approximately 1.1 nm as the core-forming PBzMA block grows longer. There is also am odest increase in the mean inter-cylinder separation distance,f rom 22.2 nm after 80 min to 23.2 nm at the end of the BzMA polymerization.
From the SAXS patterns recorded over the course of the BzMA polymerization, the mean distance between spherical micelle cores or cylinder cores can be plotted as afunction of time ( Figure 5, right axis). To enable assignment of precise diblock compositions at specific time intervals,kinetic studies were performed targeting a4 0% w/w dispersion of PhBD 80 -PBzMA 40 worms in n-dodecane at 90 8 8Cusing in situ 1 HNMR spectroscopy.T he resulting BzMA conversion vs.t ime curve ( Figure S5) was used to calculate the instantaneous mean degree of polymerization (DP) for the growing PBzMA block ( Figure 5, left axis) and plotted alongside the domain spacing data. It is noteworthy that ac onstant domain spacing was observed after around 150 min for both the cylinder and the HCP phases.T his is consistent with the conversion vs.t ime curve obtained from 1 HNMR studies,w hich confirmed that 95 %B zMA conversion was achieved within this timescale ( Figure S5). Hence the instantaneous mean DP of the PBzMA block can be calculated at any given time point during the in situ SAXS experiments,w hich enables the morphological development to be understood in terms of the diblock composition.
Ther eaction phase map indicates that, although the dspacing increases over the course of the reaction, large jumps occur during the phase transitions.For example,when passing from the disordered to the ordered micellar phase,the mean inter-micelle distance increases significantly from approximately 17 to 21 nm. This onset of long-range order is considered to be at ransition between weakly and strongly segregated states,and it occurs when the mean PBzMA DP is approximately 27. [86] This phase change is accompanied by significant changes in the conformation of each block. More specifically,a st he enthalpic interaction between the two blocks increases,t hey become more perturbed from their Gaussian coil conformations. [87] Simultaneous stretching of both the core-forming and corona-forming chains,w hich is required to minimize their interfacial contact area, results in adramatic increase in the mean separation distance between micelle cores.After approximately 72 min, which corresponds to an instantaneous diblock composition of PhBD 80 -PBzMA 31 ,a nH CP phase coexists with the BCC phase with virtually the same inter-sphere spacing being determined for these two phases.
However,w hen the BCC phase evolves to form aH EX phase (at an intermediate PhBD 80 -PBzMA 33 composition), the mean inter-cylinder distance within the 2D hexagonal phase is significantly smaller-by up to 2nm-than the intersphere distance within the co-existing HCP phase (and indeed the precursor BCC phase). Park et al. reported similar observations for PS-PI diblock copolymers dissolved in diethyl phthalate (a selective solvent for the polystyrene block) during at hermally induced transition from aB CC/ HCP phase to ahexagonal lyotropic phase. [57] These findings suggest that the spherical micelles fuse to form cylinders along the BCC h111i direction during the BCC-to-hexagonal cylinder phase transition. [65] If this is correct, then the mean distance between columns of spheres that fuse along the h111i directions should be equivalent to the inter-cylinder distance. Thevalue calculated for the BCC phase just prior to the phase transition (22.0 nm) agrees rather well with the inter-cylinder distance of 22.2 nm determined after the transition. The observed transformation of spheres into worms during the PISA synthesis is favored because of the crystallographic relationship between BCC and HEX phases.H owever, spheres packed in another (e.g.H CP) phase maintain their particle morphology until the BzMA polymerization is complete.A sf ar as we are aware,t his is the first demonstration that such aphase transition can be induced during the synthesis of diblock copolymer chains.I nt his context, it is noteworthy that Hillmyer and co-workers reported using RAFT polymerization in the absence of solvent to drive microphase separation in the solid state,b ut the resulting Figure 5. A) Reaction phase map recorded during the PISA synthesis of PhBD 80 -PBzMA 40 diblock copolymer nano-objects at 40 %w/w solids in n-dodecane. Colored symbols denote domain spacingsw ithin different phases calculated from time-resolved SAXS data, while black crosses indicate the mean degree of polymerization (x)ofthe insoluble PBzMA block calculated from in situ 1 HNMR studies. The two dashed lines shown on the left indicate the approximate time points at which the disorder-order and order-order phase transitions occur.B )Schematic cartoonsi llustrate the inter-sphere distances for the hexagonally close-packed( HCP) and body-centeredcubic (BCC) phases and the inter-cylinder distance for hexagonally packed cylinders (HEX). The green spheres and cylinders represent the PBzMA cores of nanoobjects that form structured arrangements within acontinuousphase comprising PhBD 80 chains and n-dodecane. diblock copolymers did not form such highly ordered structures. [88][89][90] Conclusion Time-resolved SAXS has been used to monitor the evolution in copolymer morphology that occurs during the PISA synthesis of PhBD 80 -PBzMA 40 diblock copolymer worms at 90 8 8Ci nn-dodecane when targeting 40 %w /w solids.Asthe structure-directing PBzMA block grows during this PISA synthesis,t here is ag radual evolution from molecularly dissolved copolymer chains to spheres to closepacked spheres (BCC/HCP phases) to afinal mixture of HEX and HCP phases (where HEX denotes hexagonally packed cylinders-or partially aligned worms-and is the major phase). SAXS analysis suggests that this HEX phase is generated via sphere-sphere fusion within the BCC phase.T o the best of our knowledge,this is the first time that any longrange order has been observed for block copolymer nanoobjects during their PISA synthesis.Itisemphasized that this is achieved using an amorphous core-forming block, rather than a(liquid) crystalline block. [49] Serial dilution of the HEX/ HCP phase leads to the formation of ad isordered phase comprising mainly non-interacting worms at 1.0 %w /w. Thermal annealing of the as-synthesized 40 %w /w PhBD 80 -PBzMA 40 dispersion induces acylinder-to-sphere transition at 150 8 8Ct op roduce ad isordered sphere phase.O nc ooling to 25 8 8C, the spheres form an HCP lattice,j ust like the minor phase that co-existed with the HEX phase during PISA. The observation of al amellar phase for the near-symmetric PhBD 80 -PBzMA 40 diblock copolymer in the solid state indicates that selective swelling of the PhBD 80 block by ndodecane results in myriad ordered morphologies that are generated during the BzMA polymerization and/or upon thermal annealing.F inally,t he basic principles of block copolymer self-assembly suggest that our observations should also apply to other PISA formulations. [11,46,48] However, further work is required to confirm such generic behavior.