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Phase separation and self-assembly in vitrimers: hierarchical morphology of molten and semi-crystalline polyethylene/dioxaborolane maleimide systems

Vitrimers - a class of polymer networks which are covalently crosslinked and insoluble like thermosets, but flow when heated like thermoplastics - contain dynamic links and/or crosslinks that undergo an associative exchange reaction. These dynamic crosslinks enable vitrimers to have interesting mechanical/rheological behavior, self-healing, adhesive, and shape memory properties. We demonstrate that vitrimers can self-assemble into complex meso- and nanostructures when crosslinks and backbone monomers strongly interact. Vitrimers featuring polyethylene (PE) as the backbone and dioxaborolane maleimide as the crosslinkable moiety were studied in both the molten and semi-crystalline states. We observed that PE vitrimers macroscopically phase separated into dioxaborolane maleimide rich and poor regions, and characterized the extent of phase separation by optical transmission measurements. This phase separation can explain the relatively low insoluble fractions and overall crystallinities of PE vitrimers. Using synchrotron-sourced small-angle X-ray scattering (SAXS), we discovered that PE vitrimers and their linear precursors micro-phase separated into hierarchical nanostructures. Fitting of the SAXS patterns to a scattering model strongly suggests that the nanostructures - which persist in both the melt and amorphous fraction of the semi-crystalline state - may be described as dioxaborolane maleimide rich aggregates packed in a mass fractal arrangement. These findings of hierarchical meso- and nanostructures point out that incompatibility effects between network components and resulting self-assembly must be considered for understanding behavior and the rational design of vitrimer materials.


Introduction
Thermoplastics and thermoplastic elastomers are soluble in good solvents and flow when heated above the glass or melting temperature. Thermosets and rubbers do not flow and are not soluble.
Vitrimers, a class of polymers introduced by Leibler and collaborators in 2011, flow when heated, but remain insoluble. 1 Vitrimers are made of polymer networks which contain covalent crosslinks that undergo dynamic associative exchange reactions. The covalent crosslinks in a vitrimer maintain network connectivity at all times and temperatures. Unlike materials employing dissociative crosslinking mechanisms, 2 vitrimers cannot be completely dissolved -even in good solvents. 1,3 Associative exchange reactions permit the network topology to fluctuate and the system to flow when stress is applied, and exchange reaction kinetics control the vitrimer relaxation dynamics and viscosity. 2,4,5,6 The initial reports of vitrimer systems focused on epoxy networks that reorganized via metal-catalyzed transesterification. 1,4,6 Today, the library of dynamic exchange reactions has expanded to include chemistries that are catalytically-controlled (olefin metathesis and transcarbonation) 7,8 or catalyst-free (transamination, 9,10,11 trans-N-alkylation, 12,13 reversible addition of thiols, 14 imine exchange, 15,16 addition-fragmentation chain transfer, 17,18 boronic esterification, 19,20,21 boroxine exchange, 22 and dioxaborolane metathesis). 23 Judicious choice of the exchange reaction offers an avenue for tuning vitrimer mechanical/rheological properties, selfhealing and adhesion ability, and shape memory properties. 5,6,23,24,25,26 Theoretical models have been developed to clarify the relationship between the exchange reaction kinetics and resulting vitrimer material characteristics. 27,28,29,30,31,32 While much of the vitrimer literature focuses on optimizing exchange reactions, diversifying polymer backbones, and applications, 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 less attention has been directed towards exploring incompatibility effects. This question should be particularly important in vitrimer systems, for example, in which the crosslink functional groups and network strands have very different polarizabilities. Here, we show that network element interactions can lead to hierarchical organization of vitrimers at nano-and mesoscopic length scales through micro-phase self-assembly and macroscopic phase separation. Accounting for and taking advantage of such structuring is crucial for understanding vitrimer properties and for applications.
Interactions between functional groups and the polymer backbone induce micro-phase separation in many functional polymers. For polyolefins with grafts incompatible with the backbone monomers, micro-phase separation and formation of interesting nanostructures have been reported. 50,51,52,53 In ionomer systems, where the polymer possesses a small fraction of ionic groups, strong dipole-dipole interactions between ion pairs and dielectric contrast between ion pairs and the polymer backbone drive the formation of clusters. 54,55,56,57,58 For supramolecular polymers, which have side-or end-groups engaged in non-covalent bonding, the combination of directional interactions and dispersion forces can spur the formation of aggregates or long-ranged ordered structures. 59,60,6162,63,64,65 For thermo-reversible covalent networks, van Duin and collaborators recently unveiled micro-phase separation in ethylene/propylene rubbers crosslinked with a dissociative Diels-Alder chemistry. 66 In polymer covalent networks, macroscopic phase separation can also occur as a result of entropic effects. Indeed, when the crosslink density is sufficiently high, the presence of even good solvent may cause the network to undergo a syneresis. 67 Smallenburg et al. predicted that similar entropically driven phase separation into a swollen network and a dilute solution of branched clusters also occurs in dynamic vitrimer systems in the presence of solvent. 3 In bulk molten networks, chains that do not carry crosslinkable groups act as a macromolecular solvent, and phase separation could result from entropic effects -even if all components in the system are compatible.
This work shows the meso-and nanostructure of a catalyst-free vitrimer system with an enthalpically incompatible polymer backbone/crosslink moiety pair. Polyethylene (PE), a semicrystalline polyolefin, was used as the model polymer because its strong apolarity makes it immiscible with most compounds. Following the method introduced by Röttger et al., 23 the polymer was converted to a vitrimer using a two-step process. Dioxaborolane maleimide was first grafted onto the PE backbone, and subsequently crosslinked by the addition of bis-dioxaborolane (see Scheme 1). The crosslinks connecting the PE chains may rearrange via a dioxaborolane metathesis exchange reaction. 23 Multi-scale characterization by optical tools, calorimetry, and synchrotron-sourced X-ray scattering revealed that these PE vitrimers undergo complex selfassembly in both the molten and semi-crystalline state. At micron length scales, PE vitrimers macro-phase separate to form a graft-rich percolating network and graft-poor domains. At the nanoscale, enthalpic incompatibility between the PE backbone and grafts induces hierarchical micro-phase separation. The meso-and nanostructures of PE vitrimers are compared with selfassembled structures seen for other associating polymer systems, and the implications of these discoveries are discussed.
Synthesis of graft-functionalized polyethylene and polyethylene vitrimer. 1-[(2-phenyl-1,3,2dioxaborolan-4-yl)methyl]-1H-pyrrole-2,5-dione (i.e., dioxaborolane maleimide) and 2,2'-(1,4phenylene)-bis[4-methyl-1,3,2-dioxaborolane] (i.e., bis-dioxaborolane crosslinker) were prepared according to previously reported schemes. 23 Graft-functionalized PE (PE-g) and PE vitrimer (PEv) were synthesized using reactive mixing followed by extrusion. Functionalization and dynamic crosslinking of PE were conducted using a DSM Explore batch twin-screw extruder (capacity of 5 cm 3 ) with a co-rotating conical screw profile and a recirculation channel. The synthesis was based on the procedure reported by Röttger et al. (see Scheme 1). 23 Table 1 lists the sample names, targeted graft densities, measured graft densities, and measured crosslink densities. To prepare PEg-4 and PE-g-6, PE, dioxaborolane maleimide, and dicumyl peroxide were first mixed in polypropylene bottles. The masses of PE and dicumyl peroxide were fixed to be 2.75 and 0.0014 g, respectively, while the amount of dioxaborolane maleimide was varied to target different graft densities. The mixture was fed into the extruder, which was pre-heated to a barrel temperature of 170 °C and operating at a screw speed of 100 rpm. After a residence time of 8 min, the polymer was released from the extruder. To prepare PE-g-8 and PE-g-12, the PE in the feed reagent mixture was replaced with PE-g-4 and PE-g-6, respectively. All other steps were the same as previously described. To prepare PE-v samples, the aforementioned functionalization step was performed, except the polymer was not released after a residence time of 8 min. Instead, at that time bisdioxaborolane crosslinker was charged into the extruder. For PE-v-4-0.5, PE-v-6-0.5, PE-v-8-0.5, and PE-v-12-0.5, excess crosslinker was administered to fully saturate the graft moieties with crosslinker. For PE-v-12-0.3 and PE-v-12-0.2, deficient amounts of crosslinker relative to the graft moieties were fed into the extruder. After an additional residence time of 6 min, the obtained PEv sample was released from the extruder. Contrary to Röttger et  and aromatic C=C stretching peaks at 1600 and 1500 cm -1 . The bis-dioxaborolane crosslinker exhibited an aromatic C=C stretching signal at 1517 cm -1 . 68 The measured FTIR spectra were decomposed by fitting each characteristic peak to a skewed Gaussian function. The average graft and crosslink densities were quantified using the Beer-Lambert law. For the attenuated total reflection cell, the IR wave penetration depth into the sample (! " ) is nearly a linear function of the wavenumber. 69 Using this approximation and assuming molar absorption coefficients determined from solution are valid in the bulk, the PE-g and PE-v compositions were quantified using Equations 1-3: where # 7 is molar concentration of component <, , = is the area of the peak at wavenumber >, 1 = is the absorption coefficient of the peak at wavenumber >, and 2 = is wavenumber >. 1 -.-/ , 1 -:-. , and  Optical transmission measurements. Transmission measurements were made using a custom-built setup based on previously reported experiments (see Figure S3 for the instrument schematic). 70 A piece of PE, PE-g, or PE-v sample was placed in the middle of a 1 or 0.3 mm thick Teflon™ spacer ring, sandwiched between two glass microscope slides, and put inside a Mettler FP82 hot stage. A 4 kg weight was placed on the heating stage door to compress the sample and improve optical contact between the sample and glass microscope slides. After the sample was annealed at 160 °C for 15 min, a 50 mW HeNe laser beam (wavelength 633 nm) was impinged on the sample, and a lens located downfield from the sample focused the transmitted beam onto a photodiode detector.
Automated temperature control and data collection were achieved using a Mettler FP80 central processor. The transmitted intensity through the sample, A ( , was taken as an average of the recorded intensity over a 5 min period. A / , the incident intensity, was taken to be equal to the transmitted intensity through the empty sample holder. The sample turbidity was determined using Equation S1. Differential scanning calorimetry (DSC). DSC was run using a TA Instruments Discovery DSC. SAXS patterns at the different sample-to-detector distances were merged using the SAXSutilities software package, 71 and subsequently analyzed using custom-made MATLAB (version R2017b) scripts. The background removal procedure and experimental details for the DND-CAT and SWING beamline measurements are detailed in the Supporting Information.

Results
Composition of dioxaborolane maleimide-grafted PE and PE vitrimer. The samples featured in this work are labeled as PE-g-α and PE-v-α-β, where α is the targeted molar ratio multiplied by 1000 of the dioxaborolane maleimide graft to the ethylene monomer, and β is the targeted molar ratio of the bis-dioxaborolane crosslinker to the graft. Actual values, somewhat different from the targets, are gathered in Table 1. The graft and crosslink density of the samples were quantified using FTIR spectroscopy. Figure 1 displays FTIR spectra of PE, PE-g-4, and PE-v-4-0.5. The region between wavenumbers 1750-1420 cm -1 is isolated for quantification because it features characteristic signals. The neat PE spectrum exhibits a CH2 scissoring peak (representing the polymer backbone) and a CH3 scissoring peak (reflecting the presence of branching in the chains).
In addition to the polyolefin peaks, the PE-g-4 spectrum has a distinct C=O stretch signal at 1710 cm -1 that originates from the maleimide segment of the graft. The phenyl ring of the graft produces two weak aromatic C=C peaks at 1600 and 1500 cm -1 . The PE-v-4-0.5 spectrum has the same C=O stretch signal as the precursor, but it only displays a single aromatic C=C peak at 1517 cm -1 -this absorption is related to the crosslinker. Disappearance of the graft aromatic ring signals hints that all of the PE-v-4-0.5 grafts are saturated with crosslinker. In contrast, PE-v-12-0.3 and PE-v-12-0.2 exhibit all three aromatic signals ( Figure S4). After decomposing the spectra to isolate the characteristic peaks ( Figure S5), the graft and crosslink densities of each sample were quantified using Equations 1-3. The measured graft and crosslink densities for PE-g and PE-v samples are listed in Table 1.  Macro-phase separation in the melt state. FTIR reveals the global average composition of PE-g and PE-v. However, the distribution of grafts and crosslinks among PE chains can be non-uniform.
First, the molar mass distribution of the neat PE is broad ( Figure 2). This large dispersity causes the distribution of the number of grafts per PE chain to also be broad, even if the grafting is statistical ( Figure S6). In this ensemble, many PE chains do not have any grafts and cannot participate in the building of a network. Second, PE and dioxaborolane maleimide are strongly interacting. It is well documented that in such a situation the grafting may be non-random. 50 More importantly, macroscopic phase separation in the molten state can occur. Figure 3 shows that a molten blend of PE and 12 wt% of dioxaborolane maleimide is turbid. Such phase separation and, more generally, ingredient incompatibility affects grafting during reactive mixing.  To detect and quantify possible macro-phase separation above the melting temperature of PE-g and PE-v (i.e., when crystallization is turned off), we used a suite of optical tools. Visual inspection showed that unlike the neat polymer, molten PE-g and PE-v were turbid ( Figure 4A), indicating bulk phase separation. Quantitatively, optical transmission measurements suggest the turbidity, which is normalized by sample thickness, arises from both bulk and surface scattering.
Decreasing the sample thickness from 1 mm to 0.3 mm causes turbidity to rise, hinting that some turbidity comes from surface roughness ( Figure 4B). Optical phase contrast microscopy confirms that PE-g and PE-v have rough surfaces ( Figure S7). For optical turbidity measurements, the contribution from the bulk is better measured on 1 mm thick samples. At a constant thickness of 1 mm, the turbidity for both PE-g and PE-v increases as the grafting density increases ( Figure 4C), thus demonstrating that grafting causes the system to macro-phase separate. Macro-phase separation also causes PE-v materials to achieve relatively high soluble fractions. Figure 5 compares experimentally measured and expected soluble fraction values for PE-v materials with varying crosslink density. The solid curve, which is the estimated weight fraction of chains with 0 grafts (as calculated using Equation S2), represents the minimum possible soluble fraction for a system with statistically distributed non-dynamic crosslinks and the molecular weight distribution of the neat PE. The measured soluble fractions, however, are significantly higher than the lower-bound. This discrepancy arises because the soluble portion of the vitrimer not only contains chains with 0 grafts, but also chains with a small amount of grafts.
As shown in Figure 6 and Table 2, the soluble portion of PE-v-4-0.5 shows a C=O stretch signal whose integration corresponds to a graft density of 1.2 ± 0.1 grafts per 1000 ethylene units.
Conversely, the insoluble portion of vitrimer exhibits a C=O stretch peak that correlates to 8.5 ± 0.2 grafts per 1000 ethylene units. The insoluble materials of the other PE-v samples are also richer in graft than their initial vitrimers ( Table 2). The measured graft densities for the insoluble portion of PE-v-4-0.5 and the corresponding soluble portion satisfy the material balance with the initial vitrimer. Turbidity measurements and optical phase contrast microscopy of the insoluble portion of PE-v samples may be seen in Figure S8. Unlike the PE-g and PE-v samples, the turbidity of the insoluble portion of PE-v is not linearly proportional to the graft density. Furthermore, while the surface of the insoluble portion still retains a rugged topography, the feature sizes are smaller.
As mentioned previously, the expulsion of graft-poor chains from the percolating vitrimer network is propelled by not only PE/dioxaborolane maleimide incompatibility, but also entropy.
In the case of the PE-v melt, the soluble portion acts as a macromolecular solvent that swells the vitrimer.
Macro-phase separation in the semi-crystalline state. Modification of PE by grafting, copolymerization, or crosslinking generally leads to a lower overall crystallinity fraction, though the extent of that decrease depends on the chemistry. For example, grafting of maleic anhydride onto high-density PE causes minimal changes in crystallinity, while the addition of glycidyl methacrylate creates a moderate change. 72,73 For PE ionomers, neutralization of the pendant acid groups leads to large decreases in crystallinity and may cause a low temperature melting transition to appear. 74,75,76,77 For peroxide and radiation crosslinked PE, the crystallinity decreases as the crosslink density and, vicariously, the insoluble fraction increase. 78,79,80 For PE-v, macro-phase separation significantly influences the relationship among the crystallinity, crosslink density, and the insoluble fraction. Figure 7 displays the normalized crystallinity of PE, PE-g, PE-v, and insoluble portion of PE-v samples. ( Figure S9 is the corresponding DSC traces, Figure S10 displays the non-normalized crystallinities, and Table S1 tabulates the crystallization temperature, melting point, and melting enthalpy). The normalized crystallinity of the PE-g samples is within error of the neat PE crystallinity, suggesting that grafting of the dioxaborolane maleimide has minimal effect on the PE crystallinity fraction. The PE-v data shows that the addition of crosslinker causes the crystallinity to decrease to ~ 65 wt% of PE, and    Table S2). Polarized optical microscopy, however, reveals that PE-g and PE-v do not form spherulites ( Figure S23).  To test the hypothesized hierarchical nanostructure, the PE-g, PE-v, and insoluble portion of PE-v SAXS patterns were fit to an aggregate-fractal scattering model. The model features H 5"E , the form factor of polydisperse spheres (Equations S8-S11), and I '%&3 , a mass fractal structure factor with functional form where B is the scattering vector, F is the fractal dimension, G is the fractal length scale, and L '%&3 M is an amplitude factor that describes the scattering contrast between the fractal components and the matrix. 87,88 Because the low-and high-B shoulder onsets differ by at least an order of magnitude, the total scattering intensity was approximated to be the sum of scattering from the mass fractals and the individual aggregates: where D 5"E is the average aggregate radius, d is the aggregate radius standard deviation, and L 5"E and L '%&3 are the amplitude factors for scattering from an individual aggregate and mass fractal, respectively.
To minimize the number of free-floating parameters during the model fitting, two assumptions were made. First, the aggregate size was assumed to be less than or equal to the amorphous layer thickness of the semi-crystalline materials. This assumption relies on the observations that the nanostructure length scales were the same in both the melt and semicrystalline states, and that the grafts and crosslinks persist in the amorphous fraction. Presumably, formation of crystal lamellae pushes the aggregates into the amorphous layers (see Figure S24).
To be consistent with this physical picture, the upper bound for D 5"E should be half the measured amorphous layer thickness (i.e., 1.5-2.5 nm). The aggregate-fractal model also does not fit the data if D 5"E < 1.5 nm. Therefore, D 5"E was fixed to be 2 nm for all samples. Second, L 5"E was assumed to be linearly proportional to the graft density. The justification for this assumption stems from preliminary model fits to a 2-term Debye-Bueche scattering model ( Figure S25 and Table S3), which revealed that the high-B shoulder scattering contribution was linearly proportional to grafting density. Increasing graft density likely increases the number of aggregate scatterers.
Invoking this assumption, preliminary free fits to the aggregate-scattering model were used to develop a calibration curve that enabled L 5"E to be calculated a priori ( Figure S26). By limiting both D 5"E and L 5"E , the model fits were performed using only four free-floating parameters: d, L '%&3 , F, and G.
The aggregate-fractal scattering model describes the PE-g, PE-v, and insoluble portion of PE-v SAXS data very well (Figures 10A and S27). Figure S28A shows that the fitted values for d are essentially the same for all samples (~1.4 nm), but the estimated values for the fractal parameters hint at interesting structure relationships. L '%&3 and F seem to be sensitive to the reactive mixing and extrusion feed composition (Figures S28B and S28C). PE-g-8 and PE-v-8-0.5 have similar L '%&3 and F values as the feed PE-g-4 that was used for their synthesis. The same relationship exists among PE-g-12, PE-v-12-0.5, and the feed PE-g-6. This phenomenon may possibly be related to the distribution of the dioxaborolane maleimide grafts along the feed PE-g backbone. Lowering the ratio between crosslinker and graft also alters L '%&3 ( Figure S29). As seen in Figure 10B, G is similar between a particular PE-g sample and its corresponding PE-v specimens (both initial and insoluble material). This length scale, which decreases as the precursor PE-g grafting density increases, ranges from 70-30 nm. Because the measured values are much larger than the radius of gyration for a single PE chain (~10 nm), G does not describe the distance between two aggregates. Instead, G is commensurate with the PE crystal lamellae dimensions. As revealed by the electron density correlation functions, the average lamella thickness is about 16 nm, while the lateral dimensions are likely larger. The resemblance between these length scales suggests that G is related to the crystallization of the PE backbone. Based on X-ray scattering analyses, unfavorable enthalpic interactions between PE and the dioxaborolane maleimide graft seem to drive PE-g and PE-v to self-assemble into hierarchical nanostructures. The discovery of these structures, which persist in both the molten and semicrystalline states, illustrates the rich polymer physics of vitrimer materials made of interacting strands and dynamic crosslinks.  Macro-and micro-phase separation also occur in the semi-crystalline state. The DSC results suggest that the overall PE crystallinity differs between the crosslinked graft-rich and graftpoor phases. Remarkably, however, the crystallite dimensions (i.e., unit cell parameters, periodicity, and lamellae and amorphous layer thicknesses) in neat PE, PE-g, and PE-v are basically the same. This hints that crystallization of PE located between aggregates is more difficult, but crystallites that do form are just like the ones in regular PE. The lack of an effect likely stems from the relatively sparse graft densities of the samples. In molar terms, the grafting densities explored in this study are relatively low (< 2.5 mol%). Moreover, both aggregation and formation of fractal assemblies of aggregates leave large regions with no dioxaborolane maleimide. In these regions, PE can readily crystallize. The relatively little molar amounts of grafting in these samples, however, are enough to inhibit spherulite growth. The complete elimination of spherulites is also seen in PE ionomer systems, where clustering of the ions is thought to reduce the lateral lamellae dimensions and disturb the lathlike growth of spherulites. 89,90 A similar mechanism potentially occurs in the PE-g and PE-v materials. The similarity between the fractal length scale G and the PE crystallite dimensions suggests that crystallization also influences the aggregate packing. Overlap of the low-B region in the molten and semi-crystalline SAXS patterns shows that the G values of the two states are identical, hinting that the aggregate packing arrangement must be able to accommodate the growth of crystallites.

Discussion and conclusions
The time scale for relaxation of the aggregates into a more homogeneous packing is likely exceptionally long (>> 48 hrs). Many kinetic obstacles operate even in the molten state -e.g., enthalpic barrier of transporting a dioxaborolane maleimide moiety through a PE-rich region, exchange reactions occurring mostly within a single aggregate, and PE chain entanglements. Thus, memory effects of sample synthesis and preparation are expected to be difficult to erase by simple thermal annealing.
Additional studies are needed to elucidate the details of the nanostructure dimensions and dynamics, but the implication of the current findings is clear: self-assembly must be considered when designing vitrimer systems. Similar to block polymers and ionomers, micro-phase separation in vitrimers can be potentially exploited to enhance mechanical and rheological properties.
Specifically, the melt dynamics could be optimized for a particular application or process by balancing the exchange reaction kinetics and crosslink association strength. Macro-phase separation may also be employed to aid in vitrimer processing. For instance, the astonishingly short stress relaxation times of PE vitrimers potentially result from the graft-poor macrophase acting as a lubricant for the graft-rich percolating network. 23

Notes
The authors have no competing financial interest.

Acknowledgements
We are very grateful to Pierre-Antoine Albouy and Doru Constantin for helping us perform   Phase contrast optical microscopy S10 Turbidity and phase contrast optical microscopy of insoluble portion of PE-v samples S12 Differential scanning calorimetry data of PE, peroxide crosslinked PE, PE-g, PE-v, and insoluble portion of PE-v samples S13 Small-angle X-ray scattering pattern background removal S17 Comparison of initial PE-v and insoluble portion of PE-v SAXS patterns S18

Preparation of peroxide crosslinked polyethylene
Peroxide crosslinked polyethylene was prepared by reactive mixing followed by extrusion.
The procedure was performed using a DSM Explore batch twin-screw extruder (capacity of 5 cm 3 ) with a recirculation channel and a co-rotating conical screw profile. First, neat polyethylene (PE) and 3 wt% of dicumyl peroxide were mixed in polypropylene bottles. The mixture was charged into the extruder, which was set to a temperature of 170 °C and a screw speed of 100 rpm. After a residence time of less than 10 s, the mixture was extruded, directly placed into a disc-shaped mold     where + % is the incident intensity, + -is the transmitted intensity, and / is the sample thickness. S1  Table 1 in the main text. Figure S4. Comparison of aromatic C=C signals in FTIR spectra for PE-v-12-0.5, PE-v-12-0.3, and PE-v-12-0.2. Spectra were shifted for clarity. Figure S5 displays the decomposed FTIR spectra for the PE-g and PE-v samples. Each characteristic peak was fit to a skewed Gaussian equation. Figure S5. Decomposed FTIR spectra for samples of (A) PE-g, (B) PE-v with varying graft density, and (C) PE-v with varying crosslink density. The PE-v-12-0.5 spectra in (B) and (C) are the same. The black, green, and brown fit lines correspond to signals from the PE backbone, dioxaborolane maleimide graft, and bis-dioxaborolane crosslinker, respectively. Spectra were shifted for clarity.

Estimated graft distributions for PE-g and PE-v
The large molecular weight dispersity of the initial PE (Đ = 7.5, see Figure 2) causes the number of grafts per chain distribution to be broad. To estimate this distribution for each sample, a simple statistical model -which assumes dioxaborolane maleimide adds to the PE backbone in a random manner -was employed. S2 In this model, 0 is the degree of polymerization of the chain S8 and 0 1 is the number of grafts on the chain backbone. The number fraction of chains with 0 segments and 0 1 grafts, 2, may be described as the product of two separate distributions 2(0, 0 1 ) = 4(0) × 6(0, 0 1 ) = 4(0) 0! (0 − 0 1 )! 0 1 ! 9 : ; (1 − 9) :=: ; where 4 is the molecular weight distribution of all PE chains, and 6 is the 0 1 distribution for chains with length 0. 6 was estimated using the binomial distribution, where 9 is the average mole fraction of grafts. Because all chains encompassed by 4(0) have identical degrees of polymerization, the number and weight fractions of chains with different 0 1 are equivalent. 4 was determined using the high-temperature size-exclusion chromatography trace of the neat highdensity PE (see Figure 2). The calculated distributions from this model indicate that the PE-g samples not only have a wide graft number distribution, but also that they contain a considerable fraction of chains that have no grafts or well below the global average ( Figures S6A-S6D). Figure   S6E details the weight fraction of chains with 0 grafts for each sample. For PE-v, the nonfunctionalized chains are not incorporated into the network; they act as a diluent and can be a source of macroscopic phase separation. S10

Phase contrast optical microscopy
Phase contrast optical microscopy was performed using a LEICA DMR DAS microscope equipped with a 10×/0.30 HC PL Fluotar objective lens. A 150 µm thick film of the sample was put between a glass microscope slide and glass coverslip, and then placed into a Linkam Scientific LTS350 heating stage. The sample was annealed at 160 °C for at least 5 minutes before phase contrast micrographs were recorded. Figure S7A shows that neat molten PE, a homogeneous material, has a uniform surface contrast. In contrast, peroxide crosslinked PE has a more heterogeneous surface contrast that is attributed to surface roughness ( Figure S7B). PE-g-4 also displays heterogeneous surface contrast ( Figures S7C). When dynamic crosslinker is added to the system, the surface morphology becomes strikingly different. As seen in Figure S7D,    Figure S10 exhibits the overall crystallinity values, while Table S1 tabulates the > ? , > @ , and ∆B @ for all samples.   Peroxide crosslinked PE 109 ± 1 120 ± 1 187 ± 5

Small-angle X-ray scattering pattern background removal
All small-angle X-ray scattering (SAXS) patterns presented in this manuscript were first processed by subtracting a background pattern of an empty sample cell sealed with two layers of 25 µm Kapton film. The SAXS patterns of molten neat and peroxide crosslinked PE after this first background removal are presented in Figure S11A. where + is the SAXS pattern intensity, G is the regression slope, and I is the regression intercept.
Figures S11B and S11C feature the background regression for the PE-g-4 SAXS pattern. The final SAXS pattern was produced by subtracting the calculated background contribution ( Figure S11D).
To avoid the influence of background subtraction artifacts, only the region between 0.01 nm -1 ≤ C ≤ 1 nm -1 was used in subsequent SAXS pattern analyses.  Figure S12 contains the SAXS patterns of PE-v with varying crosslink density and insoluble portion of PE-v samples. Figure S13 compares the SAXS patterns of the initial PE-v samples against their corresponding insoluble portion of PE-v samples. Figure S14 shows that the vertically-shifted SAXS pattern of each initial PE-v sample overlaps the SAXS pattern of its analogous insoluble portion.

Influence of annealing time and temperature on SAXS patterns
The nanostructure of molten PE-v-12-0.5 under varying conditions was examined using synchrotron-sourced SAXS at both beamline SWING at the SOLEIL Synchrotron Source (Saint-Aubin, FR) and the DND-CAT beamline 5-ID-D at the Advanced Photon Source in Argonne National Laboratory (Argonne, IL). For measurements performed at SWING, the sample-todetector distance was 6.1 m, the X-ray wavelength was 1.03 Å, and the 2D scattering patterns were collected by a Eiger 4M CCD detector. For experiments performed at DND-CAT, the sample-todetector distance was 8.5 m, the X-ray wavelength was 1.03 Å, and the 2D scattering patterns were collected by a Rayonix CCD area detector. To probe the influence of annealing time, PE-v-12-0.5 was initially heated at 160 °C for 5 min inside a Linkam hot stage placed in the X-ray beam path.
After collecting a SAXS pattern, the sample was removed from the hot stage and immediately placed onto a heating plate pre-heated to 160 °C. The sample was annealed on the heating plate for 48 hrs, and then immediately transferred into the hot stage pre-heated to 160 °C. The transfer time was less than 5 seconds. Figure S15A shows that despite the large difference between

Wide-angle X-ray scattering patterns
Synchrotron-sourced wide-angle X-ray scattering (WAXS) patterns for PE, peroxide crosslinked PE, PE-g, PE-v, and insoluble portion of PE-v samples are featured in Figure S19. All WAXS patterns display the characteristic Bragg reflections of the PE orthorhombic unit cell with space group Pnam (see Table S2 for peak indexing). From the WAXS patterns, the unit cell parameters J, I, and K were measured using the GSAS-II Crystallography software package. S6 The measured unit cell parameters are approximately the same for all samples ( Figure S20), suggesting that the presence of the grafts and crosslinks -at the densities examined in this work -have minimal influence on the PE unit cell dimensions.

PE crystallite dimensions quantification via electron density correlation function analysis
The dimensions of the PE crystallite lamellae may be quantified by converting the SAXS patterns of semi-crystalline PE, PE-g, and PE-v into electron density correlation functions. S7,S8,S9 For a two-phase system composed of isotropically distributed stacks of parallel lamellae, the intensity distribution, L(C), is described by where C is the scattering vector, P Q is the electron radius, P is the distance along the trajectory that is normal to the surface of a lamellae stack, and W(P) is the one-dimensional electron density correlation function. The inverse Fourier transform of Equation S4 gives If the two-phase layer system is not perfectly ordered (i.e., fluctuations of intercrystalline spacings, varying lamellae thicknesses, and diffuse interfaces), W(P) exhibits a characteristic shape that is similar to a damped sine wave. 7 Various features of the characteristic shape correspond to the average amorphous layer thickness (/^) and the long period spacing (/ _ ). The average lamella thickness (/ ? ) is the difference between / _ and /^. where +(C) is the SAXS scattering pattern intensity in arbitrary units. Despite the use of arbitrary units, `(P) has the same characteristic shape and horizontal positioning as W(P), so determination /^, / _ , and / ? is the same. Figure S21A displays the estimated `(P) curves for neat PE. The curve peak corresponded to an / _ value of 21 ± 1 nm. /^ was found by finding the intersection between the `(P) minimum and X`/XP, which is an extrapolation of the linear portion of the curve near P = 0. /^ was estimated to be 4 ± 1 nm. Accordingly, / ? was 16 ± 2 nm. To satisfy the two-state model assumption for the PE-g, PE-v, and insoluble portion of PEv SAXS patterns, the scattering contribution of the amorphous nanostructure was first removed. This was achieved by subtracting the shifted melt pattern from the semi-crystalline SAXS pattern.
The resulting `(P) curves and estimated crystallite dimensions are displayed in Figures S21B-21D and S22A, respectively. The local degree of crystallinity, a b , is given by the quotient of / ? / _ ⁄ . For all samples, a b remains around a value of 0.80 ( Figure S22B), which contrasts the values and trend for the total crystallinity measured by DSC. This discrepancy -also seen in other systems -is due to the fact that a b only describes the crystallinity within the lamellar stacks, while S33 the crystallinity measured by DSC characterizes the entire sample. 8 To convert a b to a mass fraction basis, crystalline and amorphous PE densities of 1.000 and 0.853 g/mL, respectively, were used. S10 For the graft and crosslinker, a density of 1.4 g/mL -a typical value for small molecules -was assumed. S11 Hypothesized semi-crystalline nanostructure for PE-g and PE-v Figure S24 illustrates the hypothesized semi-crystalline nanostructure for PE-g and PE-v materials. It is posited that nucleation and growth of PE crystal lamellae confine the graft-rich aggregates into the amorphous layers. Figure S24. Hypothesized nanostructure of semi-crystalline PE-g and PE-v materials.

SAXS pattern fits to the 2 term Debye-Bueche scattering model
In addition to the aggregate-fractal scattering model, SAXS patterns were also fit to the following empirical 2 term Debye-Bueche scattering model: where + is the SAXS pattern intensity, C is the scattering vector, d efg and d ijki are the amplitude factors of the low-and high-C shoulders, respectively, and h efg and h ijki are the corresponding length scales associated with those features. Model fitting was performed using custom-made S36 MATLAB (version R2017b) scripts. Although both terms in this model are generic scattering equations, S13 the model describes the measured SAXS patterns very well ( Figure S25A). Table S3 lists the estimated values for d efg , h efg , d ijki , and h ijki . The linear relationship between d ijki and graft density suggests that the high-C shoulder scattering intensity is directly proportional to the volume fraction of some minority component in the sample (Figure S25B). l(P) = r st" Γ(r + 1) where l is the normalized Schulz-Zimm distribution, S14 P is the aggregate radius, C is the scattering vector, Φ represents the square root of the hard sphere form factor, v 1_i is the average aggregate radius, r is the Schulz-Zimm distribution width parameter, and y is the standard deviation of the aggregate radius. To fit the data to the model, d 1_i , the amplitude factor for scattering from an individual aggregate, was assumed to be linearly proportional to the graft density. Based on this assumption, a calibration curve was developed to enable calculation of d 1_i a priori. Specifically, preliminary model fits -in which v 1_i was set to 2 nm and the parameters d 1_i , y, d z{^? , |, and