The samples investigated in this work are prepared via the condensation of alkane diols with boric acid. The synthetic procedure follows exactly from our prior work (Soman et al., 2022a). The previously investigated and carefully dried C₁₀ and C₁₂ ethylene vitrimers were prepared in sealed glass tubes flushed with Argon for NMR measurements. We refer to our previous publication for details (Soman and Evans, 2021). The structure of the dynamic networks is shown as in inset in Figure 1A, where we have compiled the terminal relaxation times of these samples. The rheological measurements were already done in the context of our first publication, from which the Arrhenius slopes were determined, but the relaxation times of C₁₀ and C₁₂ were not explicitly published there. The data shows that the networks relax on a 0.1—1 s timescale in the temperature range relevant for the present study. This will be relevant for the discussion below.

For comparison with the crystallization behavior of our vitrimers, NMR crystallization studies were also conducted on a sample of poly (octadecyl methacrylate), PODMA, with an approximate number-averaged degree of polymerization DP _n ≈ 27, which was previously studied by X-ray scattering and DSC (Hempel et al., 2006). The original sample from that study was provided by the authors.

Samples (2–5 mg) were melted into hermetically sealed pans in an Argon glovebox. Crystallization proceeded in the glovebox at ambient temperature. A TA Instruments DSC 25 was used to control the heating and cooling rates as described in the text.

Samples were prepared for X-ray analysis by sealing between two Kapton sheets using epoxy and a spacer. A Xenocs GeniX3D Cu Kα source generated 1.54 Å X-rays and scattering was recorded on a Pilatus 1 M detector. Sample-to-detector distance was calibrated using silver behenate, and 2D data was azimuthally averaged using a MATLAB-based GIXSGUI software to determine intensity as a function of wavevector q.

NMR experiments were conducted on a Bruker minispec mq20 instrument at a Larmor frequency of about 20 MHz. Pulse lengths were in a range of 2.5 and 5 μs for flip angles of 90° and 180°, respectively. A recycle delay of 1 s was sufficient for full T ₁ relaxation of both semicrystalline and amorphous/molten samples. The free induction decay (FID) of the proton signal is measured both directly and after a magic-sandwich echo (MSE-FID) to address the dead-time problem (Maus et al., 2006; Schäler et al., 2015). The latter suffers some intensity loss, which means that we fit the two datasets (restricted to an acquisition time interval of 200 m) simultaneously to a three-component model accounting for the crystalline (index c), amorphous (a), and interfacial (i) regions (Schäler et al., 2015): I t = A c e − a t 2 / 2 ⁡ sin b t / b t + A i e − t / T 2 i β i + A m e − t / T 2 m β m

The MSE leads to a small reduction of the amplitude prefactors, which are the only fitting parameters that are allowed to vary between FID and MSE-FID signals. Sample fits are shown in Figure 1B. Most importantly, these fits provide the crystalline fraction f c = A c / A c + A i + A m , using the amplitudes of the undistorted FID. Since NMR intensities are strictly proportional to proton fractions, f _c reflects crystallinity by weight. Information on the crystal packing is obtained in terms of the second moment of the crystalline lineshape ( M 2 = a 2 + b 2 / 3 ), which depends on the overall strength of multi-proton dipole-dipole interactions as governed by their proximity, i.e., the density. In addition, small-angle librations and conformational fluctuations one the sub-μs timescale lead to a reduction of M ₂ below its rigid-lattice limiting value, owing to the orientation dependence of dipole-dipole couplings (“fast-limit averaging”). M ₂ thus reflects the crystalline perfection of the sample.

The β exponents for the intermediate and mobile amorphous components are stretching parameters reflecting on the one hand dynamic heterogeneity, and on the other hand a partial Gaussian character typical for dipolar dephasing originating from the dominance of residual dipolar couplings in the short network chains (a discussion is given below). This explains why the β values were always ranging between 1 and 2. The T _2i was around and below 0.1 ms in the network melt down to 0.03 ms for fully crystallized samples, while T _2m was around 0.2 ms, staying the same or even increasing somewhat during crystallization. For the given short network chains, T ₂ values are in the range of 0.1–0.2 m, which means that the mobile and intermediate components together reflect inhomogeneities of the network structure. As network chains become part of the crystal, dangling defects with longer T ₂ are left over, thus it increases in some cases.

Our NMR-based crystallinity determination, applied to monitor isothermal crystallization of both samples in Figures 2A, B confirms the initial WAXS-based observation that the samples reach high crystallinity of ∼90% within a reasonably short time. This is an astonishingly high crystallinity for polymer samples that are quiescently kept at room temperature, in particular considering the disordered network structure and the short chains. The boric acid ester linkers are thus expected to be part of an ordered fold surface or to form intracrystalline layers, along the lines of recent studies of linear precision polymers (Trigg et al., 2017; Marxsen et al., 2021). To reach such high crystallinity, long-chain polymers are usually annealed at higher temperatures or shear aligned, and have to feature fast chain mobility in the crystals (Schulz et al., 2022). For highly crosslinked networks, it is in fact a peculiarity, as mentioned in the Introduction.

The crystallization kinetics f _c(t) were evaluated by fits to the Avrami function (black solid lines in Figures 2A, B), which revealed Avrami exponents in the range between about 1 and 2. Since the variations were non-systematic across all our data (see also Figure 5 below), arising from uncertainties (noise) in the data at short times (where the initial upturn most sensitively encodes the Avrami exponent) and possible secondary crystallization at longer times, we refrain from reporting and discussing the fitted exponents, but just report crystallization half times t _1/2. These are reliably determined in all cases, as the Avrami fit merely provides a robust interpolation in the data range covering intermediate crystallinities. The values are 830 and 63 min for C₁₀ and C₁₂, respectively, with the large difference mainly attributed to the different undercooling at 20°C. In both samples, the second moment M ₂ continues to grow during crystallization, indicating a gradual densification or a suppression of fast small-angle motions or conformational fluctuations. We thus interpret the observation in terms of an increase in crystal perfection, which, notably, takes place without further significant increase in crystallinity. The previously reported long-time increase in enthalpy of melting (Soman et al., 2022a), which is also shown in the figure, must in this new light be attributed to the increasing crystal perfection observed from NMR rather than percent crystallinity.

The crystallization of the networks was also tracked by WAXS over a 150 days crystallization period (Figures 3A, B). After 1 day of crystallization, the WAXS patterns already indicate a high crystallinity as inferred from the absence of an underlying amorphous halo which is observed in the scan of the amorphous network (0 min scan). In addition to the high crystallinity, the FWHM of the peaks does not show significant variation after the first day indicating a stable crystal size. At room temperature, the C₁₀ eventually undergoes a spontaneous transformation from hexagonal to orthorhombic but not within the first 30 days. In the C₁₂ network, the crystal structure appears to be hexagonal over the entire 150 days window and only transitions to orthorhombic at elevated temperatures of 65°C (to be discussed later).

The M ₂ values for hexagonal and orthorhombic crystals are distinct, and the NMR measurements reveal only hexagonal crystals in the first month, consistent with the prior WAXS data. This is evidenced by the comparison of M ₂ values for a C₁₀ sample crystallized isothermally at 20 °C during heating and cooling with a rate of 1°C/min in Figure 3C. The first heating scan to 40°C reveals a slight decrease of M ₂ in a range below 10⁴ kHz² (accompanied by only a slight decrease in crystallinity from about 0.92 to 0.86). The sample was then cooled again to room temperature, upon which the variation of M ₂ is fully reversible, as evidenced by the second-heating data. Crystallinity actually diminishes above 48°C, and annealing at 50°C leads to a recrystallization into the orthorhombic phase (details to be discussed below in the context of Figure 6A). Importantly, this is directly reflected in the considerably larger M ₂ value of around 1.2 × 10⁴ kHz², which is now typical for similar crystal structures such as those of PE or aliphatic polyesters (Schäler et al., 2013). The orthorhombic crystallinity in the shown T range varies between 79% and 85%. The T-dependence of its M ₂ is even weaker, and depends mostly on thermal expansion. The stronger dependence and lower values of the initial hexagonal phase may be related to enhanced dynamics such as increasing amplitude of local librations or conformational fluctuations (Schäler et al., 2013). It is noted that the M ₂ values for the two phases are too close to allow for a separation of the fractions of either phase by fitting in samples where they coexist. However, in-between values can be interpreted qualitatively in terms of coexistence.

Our previous report of increasing T _m with crystallization time corresponded to samples heated at a rate of 20°C/min in the DSC (Soman et al., 2022a). As shown below, in our NMR experiments employing much slower heating (about 1°C/min owing to slower heat transfer), we consistently found both samples C₁₀ and C₁₂ to melt at considerably lower temperatures. We have therefore examined the time evolution of the DSC-based T _m of sample C₁₀ using different heating rates spanning from 1°C to 20°C/min. The DSC traces are shown in the Appendix (Figure A1). In all cases an increase is observed with essentially the same slope (Figure 4). Surprisingly, the value of T _m decreases significantly with slower heating rates, a phenomenon also observed in conventional linear PE (Hellmuth and Wunderlich, 1965). This puts the previous T _m results (Soman et al., 2022a), taken to be not too far from equilibrium, into perspective. In that study, the increase in T _m was attributed to increasing crystallinity due to the change in the enthalpy of melting. Here, it is shown that increasing perfection rather leads to the increase in T _m . The higher apparent T _m values at 20°C/min are thus attributed to the superheating of crystals, which refers to the ability to be heated above the equilibrium melting temperature (Hellmuth and Wunderlich, 1965). For polyethylene and polyoxymethylene used in that study, the superheating effect amounted to a ∼4°C–5°C shift for a range of heating rates from 0.6°C to 20°C/min. The effect is much larger in ethylene vitrimers.

In the present work, we deduce from Figure 4 that while the vitrimeric rearrangements and enhanced crystal perfection result in systems which are more stable and melt at higher T _m, the superheating effect, apparent from the large differences between the different heating rates, is affected only little. We hypothesize that the melting kinetics are governed by the timescale of vitrimeric rearrangements, which could be slower in the organized environment between the crystalline alkyl sheets. Note that the total time for a heating cycle ranges from 5—100 min depending on the ramp rate, and the rheological crossover time in the melt state is ∼0.1 s (Figure 1A), indicating ample time for relaxation events and bond exchange to modify the samples during this ramp.

As noted in the Introduction, Kuenstler and Bowman (2023) found that dithioether/thioester-based vitrimers with crystallizable C₁₀ alkyl-dithiol linkers also show a long-time increase in T _m, the absolute value which is of the order of 20°C, thus much lower than in our case. T _m was higher for systems with faster bond-exchange kinetics. The annealing time dependence of T _m was not studied explicitly. The effect was attributed to potential lamellar thickening—which was not measured. This explanation must be reconciled with a system in which the direction-disordered linear dithioether-thioester-dithioether network chain moieties, which feature dynamic exchange at the central thioester bond, may or may not be part of the lamellae, the thickness of which may be further bound by the crosslinks at the termini. Alternatively, only the extended C₁₀ cores of the dithioether units could crystallize in PE-type fashion similar to polymers with alkyl sidechains. This could easily be addressed by NMR studies of this system.

A comparable system with pendant (rather than telechelic) short-alkyl chains, namely, atactic poly (n-octadecyl methacrylate) was studied by Beiner and coworkers (Hempel et al., 2006). For this sample, a similar long-term increase of T _m was observed. In that case, the C₁₈ side-chains form interdigitated layered nanodomains separated by the disordered main chains, which feature a hexagonal crystalline packing with a similar WAXS peak at about 15 nm⁻¹ as in our samples, see Figure 3. The perfecting of the structure over time was detected by a slow increase of both T _m as well as the heat of melting, similar to our vitrimer system. It was suggested that the core parts of the C₁₈ chains crystallize first, forming initially thin lamellar crystals that then thicken to eventually comprise a larger part of the C₁₈ chains.

We were able to obtain one of these samples and thus conduct an isothermal crystallization run with NMR observation, to be compared with the DSC-based kinetics of Hempel et al. (2006). The results are shown in Figure A2 of the Appendix. Notably, we reproduced the DSC-based kinetics almost quantitatively, with the added value of a reliable absolute-scale crystallinity fraction f _c that actually almost reaches its maximum, corresponding to nearly full crystallinity of the C₁₈ chains. Importantly, the slow long-time logarithmic increase of f _c is also observed, yet accompanied by a nearly constant and comparably low value of M ₂ of about 5,300 kHz². This confirms the suggestion of Hempel et al. (2006) to explain the long-term changes of their system in terms of an increase in actual crystallinity along the C₁₈ stems. This is in contrast to our observations on the vitrimer samples. These are thus special in that the initially formed crystalline structure remains (as indicated by largely invariant sharp SAXS/WAXS peaks, see Figure 3) and perfects internally, as a result of slow vitrimeric rearrangement in the interlayers containing the boric ester groups. Finally, the low M ₂ value of PODMA, and the larger values along with an increase upon annealing from around 8,000–10,000 kHz² for our vitrimers (see Figure 2) illustrate that the hexagonal packing of alkane chains allows for considerable variations in small-angle motions and conformational (dis)order, which in turn have a surprisingly strong effect on the heat of melting.

As observed in the SAXS/WAXS data of Figure 3, the C₁₂ sample can transition from hexagonal to orthorhombic when annealed at 65°C. This transition was tracked using NMR on a C₁₂ network first crystallized for 1 day followed by heating to 50°C in 1700 s (rate of ∼1°C/min) as shown in Figure 5A, where we used the lower temperature so as to be able to compare with isothermal crystallization at the same temperature. This procedure leads to a minor partial melting, and then recrystallization into a denser phase (orthorhombic) but with almost the same crystallinity and a higher perfection. Notably, the M ₂ values decrease first on heating from 20°C to 50°C (see also Figure 2C), suggesting fast (but effectively small-angle) segmental fluctuations with increasing amplitude. Then, they steadily increase to the level expected for the orthorhombic crystal. The increase of M ₂ can be interpreted in terms of increasing crystalline perfection, or simply by a converted fraction. Taking the latter perspective, a conversion half time of 500 min is estimated.

This can be compared with the isothermal crystallization of the same network, that is, cooled directly from the melt to 50°C, revealing a half time of about 1,500 min (Figure 5B). This temperature is apparently below the equilibrium melting point of the hexagonal phase, but is above the annealing temperature required to form the orthorhombic phase. The hexagonal phase forms first (M ₂ of around 8,000 kHz²), and then gradually converts to the orthorhombic phase during the crystallization (M ₂ > 11 kHz²). The crystallinity still reaches f _c ∼ 0.9. The orthorhombic phase does not seem to directly nucleate and we note that this denser phase is effectively at a lower degree of undercooling than the hexagonal phase.

Polymer crystals are known to have memory effects which can take long times to anneal out and fully erase thermal and processing history (Cheng et al., 1986; Bastiaansen et al., 1990; Hamad et al., 2015; Sangroniz et al., 2020). The C₁₀ network was first examined by crystallizing for 3 days or 1 month, followed by heating to 50°C (Figure 6). This temperature is above the melting point of the hexagonal phase initially formed on crystallization at lower temperatures (see Figure 4), and no crystallization directly into the orthorhombic phase was observed with several days at 50°C after cooling from the melt. As expected, both 20°C pre-crystallized samples show essentially complete melting upon heating to 50°C, yet this is now followed by recrystallization directly into the orthorhombic phase (as evidenced by the high and constant M ₂). The 3-day sample (Figure 6A) shows a notable induction period, while the 1-month sample has an even stronger memory effect (Figure 6B) with an apparently shorter induction period and shorter overall crystallization half time. The orthorhombic phase apparently does not nucleate well (or not all) and requires some “memory” facilitating its formation.

The C₁₂ networks were also examined for memory effects, but heating to 50°C is not sufficient to induce the same phenomena as in the C₁₀ networks, as isothermal crystallization from the virgin melt and formation of (or transition into) the orthorhombic phase is already observed at this temperature (see Figure 5A, B). We have thus focused on higher temperatures, where a sample crystallized at 20°C for 1.5 months showing the hexagonal modification melts completely at 65°C and recrystallizes directly into the orthorhombic phase after a lag time of about 1.5 h (Figure 7A). Qualitatively the same behavior was observed for a sample crystallized at 20°C for 20 days after heating to 60°C, where crystallization sets in already after about 20 min (data not shown). In contrast, a virgin melt cooled to the same temperatures did not crystallize.

As to the origin of this memory effect, one may consider an adapted network mesh topology providing a “melt memory” with pre-arranged chains. This option is, however, unlikely, as the memory is stable for hours, while the terminal (flow) time of the vitrimers, as governed by the bond-exchange process, is well below the second scale (see Figure 1A). To test this hypothesis, or check for the possible remainder of a small crystalline fraction, we compare in Figure 7B two (MSE-)FIDs of melt states at 60°C and 70°C for a sample crystallized for 20 days with and without memory (the latter taken after complete melting at 150°C for about 15 min). For this experiment, the pre-crystallized sample was held at 60°C for 40 min, during which time crystallization set in visibly. It was then further heated to 70°C and held. The shown data are averages of the FIDs taken during the induction times, where the signals did not change visibly and where no stable fitting of a finite crystallinity was possible.

Nevertheless, the direct comparison at 60°C with the data of the equilibrated melt shows that the signal from the samples “with memory” is always decaying somewhat more quickly, the data being compatible with a crystallinity degree on the percent level. The effect is very small but still visible at 70°C, while at 80°C (with data taken after another 40 min holding at 70°C) showed signals that are identical to those of the equilibrated melt within the noise. Thus, the memory is most likely related to the existence of a very small fraction of high-melting crystallites, possibly such ones for which the perfectioning has progressed more. We note that it is expected that the observed differences pertain not just to a minute fraction of crystalline signal but a somewhat decreased T ₂ relaxation time of a part of the sample (i.e., the intermediate fraction in our three-component fit), arising from some degree of immobilization of the chains surrounding the small crystallites.

We can now also rationalize the observations that the late-stage kinetics for memory-aided crystallization are not well captured by the Avrami fits, see the solid lines in Figures 6, 7A. In all these cases, and in contrast to crystallizations from the virgin melt (Figure 2; Figure 5), a more sluggish increase is evident at long times. For the case of C₁₂ (Figure 7A), it was even necessary to exclude the late-stage data in order to fit the data satisfactorily (in the other cases, the Avrami exponents were more ill-defined, being dependent on the number of fitted data points). For a memory effect related to a small fraction of remaining crystallites, their sparsity and inhomogeneous spatial distribution may well be held responsible for such observations.

We finally add some comments on the shape of the melt-state FIDs, which could hold information on a “melt memory”. It is approximately Gaussian, as expected for very short network chains featuring rather large residual dipolar coupling constants arising from the strongly anisotropic motions of the short end-fixed chains (Saalwächter and Heuer, 2006). In other words, the transverse relaxation process (normally characterized by a T ₂ relaxation time) is rather pure dipolar dephasing, where an orientational (“powder”) average combined with multiple multi-spin couplings leads to the well-known Gaussian shape. In case of a homogeneous system, is described by I(t) = exp{(9/40)D _res ² t ²}, where D _res is the residual dipolar coupling, which is inversely proportional to the length of the network strands (Saalwächter and Heuer, 2006). Since in our case D _res is large due to the short strands (corresponding to a high crosslink density typical for thermosets), direct analysis of the FID, which is normally precluded by field inhomogeneities and additional contributions of segmental dynamics, becomes possible. Topological structures such as loops would contribute lower D _res and the relaxation function would become modified/stretched, yet again, no differences are apparent between the cases with and without memory.

Another relevant piece of information in this context is a nearly exponential long-T ₂ tail, for which fitting (not shown) provides a relative fraction of less than 10%. This corresponds to network defects, whose rather low amplitude confirms the high conversion of the networks with its mostly three-functional crosslinks. More in-depth analyses into the network structure and a more stable fitting are possible by using multiple-quantum (MQ) NMR, along the lines of our previous work (Saalwächter and Heuer, 2006). Results along these lines are deferred to a future publication, where we focus on stoichiometrically imbalanced, defect-containing samples.