Introduction

As already revealed by observations in the pioneering works by Keller1, Till2, and Fischer3, polymer crystals usually grow at conditions far away from thermodynamic equilibrium, giving rise to metastable lamellar crystals, often consisting of highly folded chains4,5. It is generally believed that (fast) kinetic pathways determine the (small) thickness of a folded-chain lamellar crystal6,7,8,9. Commonly, the thermal stability of polymer crystal is related to their lamellar thickness10,11, which is typically much less than the chain contour length and the lateral size of the crystal1,12. Since Keller et al.13 found that melting within polyethylene (PE) single crystals was inhomogeneous, it has been widely accepted that polymer lamellar crystals possess a multiplicity of metastable states. In order to quantitatively describe metastable states, a clear definition of metastability is required14. The macroscopic crystal consisting of fully extended polymers of infinite size represents the equilibrium state which we take as the reference state. Therefore, metastability is the difference in stability, often characterized by the melting temperature, between a metastable state and the reference (equilibrium) state. The degree of metastability refers to how far a metastable state deviates from its equilibrium state. For polymer crystals, Keller and Cheng15 have proposed a particular hierarchy of metastabilities: One class of metastable states is related to differences in the lattice parameters (sometimes called classical metastable states) and another class of metastable states is related to the finite and often only nanometer small thickness of lamellar polymer crystals bounded by fold surfaces, which can be described as states of metastable morphologies. However, due to the difficulty to probe differences in the metastability experimentally in real time and with high spatial resolution, fundamental understanding of the corresponding metastable states within polymer crystals still remains limited.

Annealing, i.e., keeping the crystal at a temperature close to but below the melting point, was applied not only for studying melting and thickening behaviour of polymer lamellar crystals, but also for the exploration of differences in the thermal stability within polymer crystals16,17. In general, differences in thermal stability can be resolved better by reducing the heating rate and/or extending the annealing time18,19. However, the annealing process is always accompanied by lamellar thickening or perfecting, which deletes the possibility of resolving possible differences in the stability within the initial polymer crystals19. Similar to the melting process, the well-ordered molecules within polymer crystals can also be transformed to an amorphous state of randomly coiled polymers by dissolution in solvent20,21,22. Apart from chemical constitution and architecture of polymers23, molecular weight and polydispersity24, the type of employed solvent25, environmental parameters and processing conditions26, it has been found that the difference in polymer conformations between amorphous and crystalline states can have a profound influence on solubility and the probability of detachment from a crystal surface and thus the rate of polymer dissolution21.

Our previous results27,28,29 have illustrated that after selective dissolution, i.e., thermodynamically less stable structures dissolved faster than the more stable ones, one can easily distinguish between amorphous and crystalline phases. It was also shown that different polymorphs or crystalline structures grown at different temperatures, reflecting differences in metastability, exhibit differences in solubility which allow for selective dissolution30,31. Related to these observations, several intriguing questions arise: Following selective and progressive dissolution of regions of lower stability, can we detect and quantify differences in metastability and thus solubility even within polymer single crystal? Can we identify a relation between dissolution behaviour of such lamellar crystals and the conditions under which they were grown? Here, we employ the approach of selective dissolution for the investigation of spatial variations in solubility within PEO lamellar single crystals. We will discuss the corresponding mechanisms of dissolution allowing distinguishing differences in the solubility within such single crystals. Selective dissolution of polymer crystals may be employed for gaining a deeper understanding about original differences in stability within polymer crystals determined by the growth kinetics and thus may allow identifying means for regulating melting and dissolution of crystalline polymers.

Results

Kovacs et al.32,33 and Cheng et al.34 found that the habit of low molecular weight PEO single crystals, which were grown from the melt, changed from faceted to circular and back to faceted within a narrow range of supercooling. By contrast, dendritic crystals can be observed when PEO crystallizes in thin films under high supercooling35. In Fig. S2b, we present a topographical image of a dendritic PEO lamellar crystal grown at 49 °C in ca. 9 nm thin films. Within this dendritic PEO crystal, one can clearly identify four main branches grown along (120) normal directions. For the sake of clarity, in Fig. 1a and d we show only one of these main branches for each initial crystal. One crystal (Fig. 1a) was annealed by heating it to 51 °C for 20 min, whereas the other one (Fig. 1d) was washed in toluene at 21 °C for 150 s. From Fig. 1b, we can see that the “empty” spaces between the side branches increased. Furthermore, the lamellar thickness significantly increased (see Fig. 1c). By comparison, the crystal, which was not annealed but washed in toluene at 21 °C, revealed that parts of this crystal (e.g., some side branches and the terminal regions at the edges of the crystal) were removed after washing. However, no obvious increase of lamellar thickness was observed (see Fig. 1e, f). The lamellar thickness is widely accepted to be the characteristic feature that determines crystal stability. Since there are no indications of a change in crystal lattice parameters, from the constant lamellar thickness revealed by time-resolved in situ AFM measurements in Fig. S3, we can safely assume that, in contrast to thermal annealing, selective dissolution does not change the metastability of the crystal.

Fig. 1: Comparison of the effect of thermal annealing and selective dissolution on the topography of PEO dendritic crystals.
Fig. 1: Comparison of the effect of thermal annealing and selective dissolution on the topography of PEO dendritic crystals.
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a, d Height images of initial dendritic PEO crystals grown at [(crystallization temperature Tc, crystallization time tc) = (49 °C, 120 s)]. Surface topographies of PEO crystals obtained after (b) thermal annealing at 51 °C for 20 min and (e) selective dissolution in toluene at [(dissolution temperature Td, dissolution time td) = (21 °C, 150 s)], respectively. The scale bars in (a, b, d, and e) represent 2 μm. In accordance with previous studies34,65 on the molecular model of chain packing in a lamellar PEO single crystal, the coordinate system in lower left corner of (d) indicates the orientation of the a∙sinβ- and b-axis of the monoclinic crystal unit cell (see also Fig. S1). The two black arrows labelled a∙sinβ and b indicate the (100) and (010) planes, respectively. c, f AFM height cross-sectional profiles of the lamellae denoted by white dotted lines in (a, b) and (d, e), respectively.

The morphology of the annealed crystals revealed the formation of a few holes (see Fig. 1b). In fact, extensive research36,37,38,39,40,41 has revealed the development of a “Swiss-cheese” morphology in PE or long-chain alkane single crystals following annealing. This annealing-induced structure is characterized by irregularly distributed holes within the crystals, predominantly circular in shape but varying in size. According to Magonov et al.39, the initiation of these holes in annealed single crystals occurs when adequate free volume accumulates at potential void sites. This free volume originates either from vacancy-type defects within the crystalline lattice or from interfacial spaces between the polymer crystal and its supporting substrate, subsequently migrating to the developing void locations. Once all the free volume related to such defects was accumulated in holes, the thickening process then resulted in the buildup of rims around the holes. In order to minimize the surface energy, the shape of the holes is expected to be circular. Surprisingly, within the washed crystal, several rectangular-shaped holes of various sizes were generated (see Fig. 1e). We propose that such rectangular-shaped holes, which may be related to the previously observed “Swiss-cheese” morphology, represent patterns that were initiated by the diffusion and accumulation of vacancy-like defects within the crystal, and then grew by selective dissolution. Due to the rapid diffusion of detached polymer chains into the solvent, the resulting holes are characterized by dissolution along specific crystallographic planes, yielding a rectangular shape of the holes. Most notably, since the competitive processes of lamellar thickening and perfecting of the crystal are not expected to occur under the conditions employed during selective dissolution, the sites and number density of dissolution holes observed here may be considered to be a measure of the distribution and number density of defects within the crystal. In order to verify our hypothesis, we performed a series of experiments to unveil the influence of dissolution temperature (Td), dissolution time (td) and the initial variation in the stability within the lamellar crystal on the resulting dissolution patterns.

To investigate the dissolution process of polymer crystals, a PEO lamellar crystal was washed in toluene at Td = 20.5 °C. Figure 2a shows an overlay of AFM height images, i.e., the various morphologies of the same PEO crystal during dissolution at 20.5 °C for times up to 1110 s. The AFM images were collected after successive dissolution steps in toluene, each lasting for 30 s. Figures 2b–f and S5a–c show that the morphological changes of the crystal at different dissolution stages. In the early stage of dissolution (i.e., within td = 300 s), two distinct pathways were clearly observed in the dissolution of dendritic crystal. It is visible that the branches grown along the (120) normal directions started to dissolve along the contour lines. Later on, they shrank along particular crystallographic planes (see Fig. 2b). By contrast, the branches oriented along directions other than the (120) normal direction always dissolved along the contour lines (see Fig. 2c, d). More importantly, the latter dissolved completely within 300 s, which was much faster than the former, even when their height and width were rather similar (see Fig. S4e). As can be seen in Fig. 2e, the side branches grown along the (120) normal directions partially remained up to 750 s of washing in toluene within the middle stage, and dissolved away after 780 s. Subsequently, the remaining part of the main branches grown along the (120) normal directions continued to dissolve along particular crystallographic planes, and gradually shrank with increasing td at the late stage of dissolution (see Fig. 2f). It should be noted that the morphological changes which take place in this work are different from those reported for “picture-frame” crystals. “Picture-frame” crystals have generally been the result of recrystallization or solid-state thickening caused by annealing crystals supported on a substrate, which were previously grown in a dilute solution6,36,42,43,44,45. In contrast, since we used a pure solvent for each dissolution step, the corresponding global and local polymer concentrations around the crystal were extremely low, causing a negligible re-attachment rate during dissolution.

Fig. 2: Temporal evolution of morphology in PEO lamellar crystals induced by selective dissolution and the dissolution kinetics of PEO lamellar crystals.
Fig. 2: Temporal evolution of morphology in PEO lamellar crystals induced by selective dissolution and the dissolution kinetics of PEO lamellar crystals.
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a A false-colour overlay of AFM images showing the contour of a PEO crystal taken at different times (td) in the course of selective dissolution in toluene at Td = 20.5 °C. The bare substrate is represented in a grey colour. The initial PEO crystal was grown at (Tc, tc) = (49 °C, 120 s). Overlays of AFM images for the td-range of: (a) 0 ~ 1110 s, (b–d) 0 ~ 300 s; (e) 330 ~ 780 s and (f) 810 ~ 1110 s, respectively. The time intervals (Δt) between two successive layers for (a–e) and (f) are 30 s and 60 s, respectively. The scale bars represent 2 μm. g Time dependence of the dissolution velocity (Vd) along individual rough (120) and smooth (120) faces, respectively. The error bars indicate standard deviation of the replicate measurements. The brown and blue dashed lines correspond to the constant values, reached after a certain time, of the dissolution velocity along the R(120) and S(120) faces, respectively, which are designated as Vd,R and Vd,S. The dissolution velocity of the branches grown along directions normal to (120) planes is denoted as Vd,R-S(120), representing the transition from the dissolution of R(120) planes to the dissolution of S(120) planes. h Plot of the overall dissolution velocity (Vd,total) versus time during dissolution at Td = 20.5 °C.

Figure 2 revealed that the dissolution of dendritic PEO crystals occurs along specific crystallographic planes. Computing the growth habit of PEO crystals with the help of the Frank-Seto model, Ungar et al.46,47 concluded that the fold planes in PEO crystals are (100) and (120). They also proposed that the apparent (140) facets of PEO crystals grown from the melt are in fact rough (120) faces of variable tilt, which resulted from a high secondary nucleation rate and unequal spreading rates of layers in opposite directions due to the asymmetry of the (120) crystallographic planes. Therefore, we suggest that during early stages the dissolution of PEO dendritic crystals is mainly along the rough and smooth (120) planes, designated as R(120) and S(120), respectively. The branches grown along the (120) normal directions firstly and rather fast dissolved along R(120) faces (see Fig. 2b). As these rough faces of variable tilt were consumed (almost) completely with time (see Fig. 2e), dissolution of the crystal was eventually along S(120) faces. Accordingly, we denoted the initial dissolution velocity of the branches grown along (120) normal directions as Vd,R-S(120), representing the transition from the dissolution of R(120) planes to the dissolution of S(120) planes. Besides, Fig. 2c shows that branches grown along (010) normal directions dissolved mainly along the contour line with a dissolution velocity equal to Vd,R(120), as they most likely consisted of a number of serrated, microscopic R(120) planes. Figure 2 also shows that the gaps between the final trunks of dendritic branches widened with Vd,S(120) along S(120) planes.

We traced the dissolution velocities as a function of td along R(120) and S(120) faces, respectively. In Fig. 2g, we plotted the value of Vd,R(120), Vd,S(120), and Vd,R-S(120) against td. Both, Vd,R(120) and Vd,S(120) showed initially a slight decrease and then stayed constant during further dissolution. Such a slight reduction in Vd,R(120) and Vd,S(120) at the very initial stages of dissolution can probably be attributed to accelerated crystal growth occurring in the course of the quenching process after isothermal crystallization, generating a transition zone with a width of ca. 1 µm, which is less stable and thus dissolves somewhat faster. However, crystalline structures grown at constant temperature dissolved at a constant velocity. As shown in Fig. 2g, the brown and blue dashed lines correspond to the eventually reached constant values of the dissolution velocity along the R(120) and S(120) faces, respectively, which we designated as Vd,R and Vd,S. Remarkably, Vd,R was about five times faster than Vd,S. Interestingly, the initial value of Vd,R-S(120) was quite similar to Vd,R, then dropped by a factor of 5 during the first 400 s and eventually became constant at the value of Vd,S. Therefore, our observations indicate that the transition from the dissolution of rough to the dissolution of smooth planes is responsible for the decay of the total dissolution velocity (Vd,total) with time (see Fig. 2h), which averages the dissolution velocity of all crystalline faces.

Further, to better identify the origin for the significant differences in dissolution behavior between branches, which were growing in different directions during crystallization, we have followed the growth of distinct branches in time and determined their growth rate. In Fig. 3, we explored the growth of six individual branches of a PEO dendritic crystal at 49 °C in situ by optical microscopy, starting from the crystallization time of 40 s (see the insert in Fig. 3a). Among the six, four main branches were along the (120) normal direction and two along the (010) normal direction (i.e., along the b axis), designated as MB120 and MB010, respectively. Due to Mullins-Sekerka growth instabilities, dendritic side branches were generated, emerging from the MB120 branches and growing along various crystallographic planes (see Fig. 3a–c). Most significantly, we found that the faster growing side branches, which emerged from the MB120 branches, gradually surrounded the slower growing MB010 branches and thus finally prevented their further growth (see Fig. 3c).

Fig. 3: In situ observations of crystal growth.
Fig. 3: In situ observations of crystal growth.
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a–d Optical micrographs showing the evolution of a PEO crystal growing at 49 °C in a ca. 9 nm thin film. The insert in lower left corner of (a) is the micrograph of the PEO dendritic crystal at tc = 40 s. e Height image of the dendritic PEO crystal grown at (Tc, tc) = (49 °C, 170 s), i.e., the crystal before dissolution experiments. f Surface topography of PEO crystal obtained after selective dissolution in toluene at (Td, td) = (23 °C, 30 s). g The growth kinetics in terms of branch length (Lc–L0) as a function of (tc–t0). Lc and L0 are the branch length at tc and t0, respectively. Please note that the value of t0 for MB120, B1 and B2 is the same as for MB010, B3, and B4, respectively.

To quantitatively corroborate this physical picture, we measured the length, L, of main and side branches along various crystallographic planes. Figure 3g shows the growth kinetics in terms of branch length (Lc–L0) as a function of (tc–t0) for different branches. Here, Lc and L0 are the branch length at tc and t0, respectively. One can clearly see that the length of branches growing along (120) normal directions (e.g., the ones labelled as MB120, B1, and B2) increased linearly with time (L ~ t), whereas that of branches growing along (010) normal directions (e.g., the ones labelled as MB010, B3, and B4) eventually increased in a sublinear fashion with time, i.e., growth slowed down. If we would assume a power law dependence for the observed time window, this would yield L ~ t 0.88±0.04. The branches along (120) normal directions grew faster (~0.28 μm/min) than the ones along (010) normal directions (~0.16 μm/min). Most interestingly, the former survived but the latter disappeared after selective dissolution at 23 °C for 30 s (see Fig. 3f).

Previous studies48,49,50 showed that for crystals with a size (R) increasing linearly in time (t), i.e., R ~ t, their growth is nucleation-limited. By contrast, if R increases in time as R ~ t0.5, the crystal growth is diffusion-limited. However, in accordance with the marginal stability criterion of Langer and Müller-Krumbhaar51, Taguchi et al.52,53 have found that the growth rate of the leading growth tips was constant during growth (linear growth), and proposed, corroborating conclusions previously obtained by Sekerka54, that surface kinetics, transport (diffusion), capillarity and surface nucleation control the growth process. The leading growth tip still advances at a constant velocity even in the diffusion controlled growth. Therefore, we suggest that the growth of tips of branches along (120) normal directions (which follows L ~ t) is mainly controlled by (secondary) nucleation, while other branches of the dendritic crystal, including the branches along (010) normal directions, are profoundly affected by temporal changes in the number of polymers diffusing towards the growing branches.

In the diffusion-limited regime, growth is controlled by the rate of diffusion of polymer to the growth face. The growth front may become unstable and thus roughen55. Especially when the degree of undercooling is high, the crystal growth fronts are highly unstable, leading to the generation of a multitude of crystalline branches49. On the other hand, for example at low supercooling, nucleation controlled growth may generate flat growth faces of rather large lateral extension, i.e., facets56. As a consequence, in our cases, the growth of branches in a direction different to the (120) normal direction is significantly affected by diffusion of a decreasingly smaller number of polymers to the growing branch, resulting in the formation of rough (120) faces. By contrast, tips of branches along (120) normal directions exhibit growth of molecularly smooth interfaces (see Fig. 3g), while the curved portion on the sides of these growth tip are influenced by the strong gradients in the surrounding diffusion field, resulting in a kinetically unstable growth front57.

Therefore, the difference in dissolution behavior between branches may be related to the changes in the values of the thermodynamic driving force and the kinetic barrier for dissolution of polymer stems or chains from rough faces. Similar to the growth rate9, the dissolution rate of lamellar polymer crystals is also the result of an interplay between kinetic barrier and driving force. It should be noted that these two main factors both depend on the degree of undercooling. Dissolution is opposite to crystallization but has some analogy to melting. Above the critical dissolution temperature Td,cr, the free energy drops caused by the increase in entropy of the system induced by dissolving the ordered crystal. There, at any given dissolution temperature in an almost infinitely dilute solution, the free energy difference upon dissolving a polymer from a rough face is higher than from a smooth one. Therefore, the driving force for dissolution is larger for rough faces. Furthermore, dissolving a chain or stem from a rough crystalline face requires to generate less “new” surfaces (on the average, molecules have fewer nearest crystalline neighbors on a rough surface). Thus, the corresponding kinetic barrier for detachment of a stem or a chain from rough faces is expected to be lower. Consequently, at any given temperature above Td,cr, dissolution of rough faces is faster than that of smooth faces.

Although phase transitions are controlled by thermodynamic parameters, in the majority of experimentally observed cases, the kinetics of the transitions practically determines the properties of the finally obtained metastable states5,58. As a consequence of the complexity of the resulting metastable states of chain-folded polymer crystals, they possess an intrinsically broad temperature range for the so-called melting region and exhibit processes of recrystallization and reorganization, affecting also the melting kinetics of superheated crystals59,60. In our study, the presented results confirm that the growth kinetics during crystallization affects metastability and dissolution kinetics of different branches in dendritic crystals, resulting in a significant difference in dissolution velocity of the various crystalline branches. We note that such a difference in metastability between side branches generated during the growth process cannot be detected easily during thermal annealing because of the simultaneously occurring crystal thickening and perfecting during such treatment (see Fig. 1b).

To determine the temperature dependence of the observed decay of the total dissolution velocity with td, we investigated dissolution of lamellar crystals at different temperatures (Td). In Fig. 4, we present changes in morphology of PEO crystals obtained after washing them in a toluene bath at different Td for varying dissolution times (td). All initial crystals were prepared by crystallization at 49 °C for 2 min. Subsequently, these crystals were washed in toluene at temperatures ranging from 19 °C to 23 °C. We observed that the overall dissolution velocities (Vd,total) for all samples showed a decay with td (see Fig. S5). Besides, rectangular-shaped holes were formed in all these samples (see Fig. 4a–e). Intriguingly, two of the edges of these dissolution holes, which developed within the main crystalline branches, corresponded to the directions along the S(120) planes. As fast growing crystallographic planes are disappearing rapidly during crystal growth, the habit of a polymer single crystal is mostly determined by the slowest growing planes14,34. In analogy to crystal growth, we anticipate that the shape of the dissolution holes is dominated by the slowest dissolution direction, which was along the S(120) planes.

Fig. 4: Changes in morphology of PEO lamellar crystals induced by selective dissolution in toluene at different temperatures (Td).
Fig. 4: Changes in morphology of PEO lamellar crystals induced by selective dissolution in toluene at different temperatures (Td).
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Initial PEO crystals were grown at (Tc, tc) = (49 °C, 120 s). The false-colour overlay of the contour of AFM height images of PEO crystals during selective dissolution in toluene at Td = (a) 19.5 °C; (b) 21 °C, (a) 21.5 °C; (b) 22 °C, and (c) 23 °C for different times. The bare substrate is represented in a grey colour. The time intervals (Δt) between two contour lines for (a) and (b–e) are 60 s and 30 s, respectively. The scale bars represent 2 μm. f Dependence of Vd,R and Vd,S versus the reciprocal dissolution temperature (1000/Td) for PEO lamellar crystals generated at 49 °C.

For each dissolution temperature Td, it is possible to distinguish between the dissolution velocities of rough and smooth faces, allowing to derive Vd,R and Vd,S. Figure 4f shows as a function of Td the obtained values of Vd,R and Vd,S, respectively. For the investigated temperature range from 19 °C to 23 °C, both Vd,R and Vd,S clearly decreased with Td. This decrease followed an Arrhenius law: Vd(Td) = Vd,0 exp(Ed/RTd), where Ed is the detachment energy for the transport of one mole of polymer chains from the crystal lattice to the solvent, and with Vd,0 being a constant assumed to be independent of temperature. In Fig. 4d, the activation energy Ed for the dissolution of PEO lamellar crystals is obtained by plotting the logarithm of the values of Vd,R and Vd,S versus the reciprocal dissolution temperature (1000/Td). From these plots, we concluded that the value of Ed for the dissolution of rough and smooth faces are 420 ± 40 kJ/mol and 650 ± 50 kJ/mol, respectively. Such high values of Ed reflect the significant energy required for the detachment of a crystalline stem or a whole chain from the lateral surface of the crystal.

In the following, we compare the value of Ed = 650 ± 50 kJ/mol with the melting enthalpy per monomer of 8.66 kJ/mol, derived for melting one ethylene oxide (C2H4O) group inside a PEO crystal61,62. We consider that, compared to the interior of the crystal, polymers at the crystal surface have fewer interactions with neighbouring molecules [for a flat surface, we assume a reduction by ca. 1/3 (or 1/4)] and consequently a lower interaction energy63. Based on this argument, we arrive at an energy of 5.8 kJ/mol (or 6.6 kJ/mol) for detaching one C2H4O group from a crystal surface. In our experiments, the PEO chains had a molecular weight of 4600 g/mol and contained ca. 104 C2H4O groups. If we want to detach all these monomers simultaneously, using the assumed value of 5.8 kJ/mol (or 6.6 kJ/mol) for detaching one C2H4O group, we would obtain ≈ 600 kJ/mol (or ≈ 700 kJ/mol) [= 104 monomers × 5.8 kJ/mol (or 6.6 kJ/mol)]. Thus, the activation energy of 650 kJ/mol derived from our experiments relates well with the dissolution of a whole chain, i.e., the simultaneous detachment of all its crystalline monomers. From the measured value of the lamellar thickness of ca. 10 nm, we conclude that crystals formed at 49 °C consisted mainly of twice-folded chains35. Therefore, based on the measured detachment energy, three crystalline stems had to detach simultaneously from the smooth faces of lamellar crystal. Furthermore, the lower value of the detachment energy of 420 kJ/mol may also reflect the detachment of whole polymer chains from rough faces of lamellar crystal, assuming that the polymers have fewer neighbors (reduced by about 1/3 compared with that of the smooth faces). The obtained values of Ed quantitatively confirm that rough faces possess a lower energy barrier for dissolution and are consistent with the measured difference in dissolution velocities. Similar to an increase in melting temperature, the dissolution temperature or the dissolution velocity also change with lamellar thickness (see Fig. S6). We observed that crystals formed at Tc between 47 and 49 °C were similar in terms of thickness and their dissolution patterns. Nonetheless, especially for the cases of 47 °C and 48 °C, crystals exhibited significant differences in dissolution velocity of the branches grown along (120) normal directions. However, crystals formed at higher Tc showed increase in lamellar thickness and a more compact morphology, indicating higher thermal stability (higher melting temperature) accompanied with a decrease in the value of Vd,total, measured for dissolution at Td = 22 °C. In the future, it will be interesting to systematically study if the detachment energy Ed depends on the temperature Tc at which the crystals have been grown. With increasing Tc, we anticipate a small increase in Ed which should be proportional to the reduction of the number of monomers in the non-crystalline regions consisting of chain folds and loops. The here presented experimental approach opens the door for systematic studies in this direction.

Discussion

In this work, we presented an experimental approach based on selective dissolution of polymer lamellar crystals. This approach allowed to reveal differences in metastability within dendritic poly(ethylene oxide) single crystals, isothermally grown in thin films. Because dissolution at relatively low temperatures was rather rapid, polymers within the crystals did not have sufficient time for perfecting and thickening. The observed dissolution velocities of branches grown along distinct crystallographic planes was nearly constant for rough and smooth faces, respectively, but differed by up to a factor of about five. Here, we demonstrated that the growth kinetics affected the dissolution kinetics, a consequence of differences in features at the molecular level of branches, i.e., rough or smooth faces. For the transition from rough to smooth faces, the overall dissolution velocity first decayed with time before arriving at a constant value. From the temperature dependence of the dissolution velocities, we derived values of the detachment energies of 420 ± 40 and 650 ± 50 kJ/mol for dissolution along rough and smooth faces, respectively. These values of the detachment energy indicate that polymers chains on a rough crystalline face have ca. 1/3 fewer neighboring (interacting) molecules. Both values can be related to the energy required to detach whole crystalline chains from the rough and smooth lateral surface of the crystal, respectively. Based on the here employed experimental approach, our study provided insight into the relation between growth kinetics and the resulting metastability of polymer crystals.

Methods

Materials and sample preparation

In this study, we used poly(ethylene oxide) (PEO) with an average molecular weight (Mn) of 4.6 kg/mol and a polydispersity of 1.14, as received from Sigma-Aldrich. PEO was dissolved in acetonitrile at a concentration of 0.3 wt-% and heated for 1 h at 70 °C, which is well above the nominal dissolution temperature of 40 °C64. After cooling to room temperature, the solution was spin cast onto silicon substrates (P111-type, UV ozone treated for 1 h) at a spin speed of 4000 rpm for 30 s. A commercial spin-coater (KW-4A, Institute of Microelectronics, Chinese Academy of Sciences, China) was used here. For the present study we used exclusively films of a thickness of about 9 nm, as measured by a spectroscopic ellipsometer (Alpha-SE ellipsometer, J.A.Woollam, USA).

Crystallization temperature protocol and procedure of selective dissolution

The temperature protocol adopted for melt crystallization of the PEO films is shown in Fig. S2a. Firstly, PEO thin films were heated at a rate of 30 °C/min from room temperature to 70 °C and held there for 3 min. Then, the specimens were cooled at a rate of 10 °C/min to the pre-set isothermal crystallization temperature (Tc) and kept there for varying crystallization times (tc). After that, the samples were immediately quenched to room temperature. The experimental temperature was controlled by a Linkam THMS 600 hot stage (Linkam Scientific Instruments, Tadworth, UK). The sample chamber was kept under a constant flux of dry nitrogen.

The selective dissolution of PEO crystals was performed by dipping the specimen into a solvent, that is, into toluene at different dissolution temperatures (Td = 19–23 °C). The solvent was poured into the vial, and its temperature was controlled by a silicone oil bath (JULABO circulator, FS 18, Germany). The experiments were performed at an ambient temperature close to the given Td, which was controlled by an air conditioner system. After holding the specimens at Td for 30 s or 60 s, they were retracted from the solvent and dried in a flow of nitrogen. For a given Td, this dissolution step was repeated several times, adding up to a total dissolution time td. Please note that pure solvent was used for each dissolution step. Figure S7 shows the remaining patterns of PEO crystals obtained after dissolution at Td = 21 °C for different times td. By colouring and overlaying these AFM height images (Fig. S7a–n), we create a false-colour overlay of the crystal periphery, depicting the changes in morphology of the same PEO crystal in the course of selective dissolution, colour-coded by dissolution time (td), as shown in Figure S7o.

Characterization techniques

To observe changes in the morphology of PEO lamellar crystals, atomic force microscopy (AFM) measurements were performed under nitrogen conditions using a scanning probe microscope (Dimension Icon, Bruker, USA) in the ScanAsyst mode. As AFM tips for this work, we used silicon nitride probes (model, SCANASYST-AIR; spring constant, 0.4 N/m; tip radius, 12 nm; frequency, 70 kHz). In situ AFM characterizations were carried out by a NanoWizard IV AFM (JPK Instruments AG, Germany) using the QI mode and RTESPA-300 (Bruker) cantilevers having a nominal spring constant of 40 N/m.