Article pubs.acs.org/Macromolecules
Cite This: Macromolecules XXXX, XXX, XXX−XXX
Growth Kinetics of Stacks of Lamellar Polymer Crystals Sumit Majumder,† Hanna Busch,‡ Purushottam Poudel,† Stefan Mecking,‡ and Günter Reiter*,†,§ †
Institute of Physics and §Freiburg Materials Research Center, University of Freiburg, 79104 Freiburg, Germany ‡ Department of Chemistry, University of Konstanz, 78457 Konstanz, Germany
Downloaded via UNIV OF NEW ENGLAND on October 27, 2018 at 04:01:50 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: Most theoretical concepts of polymer crystallization have evolved around monolamellar single crystals as model systems. However, such approaches do not account for an important and unique aspect of crystallization of long flexible molecules: the correlated stacking of lamellar crystals. In our experimental work, we focus on the growth kinetics of such stacks of lamellae in thin films of poly(nonadecane methylphosphonate). Interestingly, concurrent with a decrease in lateral lamellar growth, we observed an increase in vertical growth, that is, an increase in the number of stacked crystalline lamellae. Intriguingly, in contrast to lateral lamellar growth, the rate of such vertical growth increased with decreasing degree of undercooling. Moreover, we show the possibility of forming three-dimensional polymer quasi-single crystals. Some of the formed stacks of lamellar crystals were about 100 times thicker than the initial film; that is, they had a thickness of about 20 times the contour length of the polymer and contained about 800 stacked lamellae. We propose that growth kinetics of stacking of lamellae is governed by (i) the probability of forming self-induced nuclei, (ii) the detachment probability of crystalline stems, and (iii) the influx of molten polymers toward the growth front.
■
INTRODUCTION Crystallization of linear polymers generally leads to metastable lamellar structures.1−11 The kinetically selected thickness of such lamellae is typically several orders of magnitude smaller than the fully extended polymer.1,4,6−8,11 Thus, lamellar crystals necessarily contain rather short crystalline chain sequences. These crystals coexist with disordered sequences like chain folds on the surface of the crystalline lamellae.9,12,13 The lateral extension of lamellar crystals is often quite large, up to many micrometers, but their thickness is typically only a few nanometers.1,8,11−16 The size of such lamellar crystals can sometimes be so large that they can be seen even by the naked eye. The envelope of a lamellar crystal grown from a single starting point, that is, a single crystal, reflects the symmetry of the unit cell of the crystal lattice.8,10,17−20 However, due to morphological instabilities occurring at the growth front, monolamellar single crystals can adopt a variety of different morphologies.21−24 The lateral growth rate (G) of a lamellar crystal depends mainly on two physical processes: interfacial kinetics and diffusion of molten polymers toward the growth front.2,4,7,11,20,25,26 At a given film thickness and at a given temperature, lamellar crystals generally grow at a constant rate.2,10,18,20,26,27 During crystallization, a depleted region of constant width (Wd) develops between the crystal growth front and the surrounding reservoir of molten polymers.2,16,20 Wd controls the rate at which molten polymers reach the growth front and can be correlated with the polymer diffusion coefficient (D) and with G of a lamellar crystal by Wd ≈ D/ G.21,24,28,29 At low supercooling, interfacial kinetics, which is the low probability for permanently attaching a polymer © XXXX American Chemical Society
sequence at the growth front, dominates over diffusion. By contrast, D dominates at high supercooling. As a result, the dependence of G on crystallization temperature (Tc) exhibits a bell-shaped curve.30 While concepts of lamellar growth have been developed, we have yet to understand in detail how polymers form threedimensional structures consisting of stacks of correlated lamellae.9,14,15,18,20 Scattering experiments done on such structures grown from an undercooled melt or in a supersaturated solution revealed that all lamellae in a stack were in crystallographic registry.9,14,31,32 It has been shown that such stacks can be generated via self-induced nucleation.18 In thin polymer films, the probability of self-induced nucleation depends on the width of the side branches of a growing lamellar crystal, followed by growth of secondary lamellae, which is controlled by, anong several other parameters, the availability of molten polymers on the fold surface of the initiating lamellar crystal. Experiments on micrometer-thick polymer films indicate that growth of stacked crystalline lamellae can be influenced by the amount of surrounding molten polymers.3 However, the physical processes controlling the growth kinetics of stacks of lamellar crystals have yet to be identified. Adding side branches along the crystallizable sequences of the polymer chain (e.g., polyethylene copolymers) can significantly affect the growth kinetics of polymer crystals.33−37 Recent advances in polymer chemistry have opened new paths Received: August 16, 2018 Revised: October 12, 2018
A
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 1. Simultaneous lateral and vertical growth of a polymer crystal. Contrast-enhanced optical micrographs show the temporal evolution of a crystal formed in a ≈35 nm thin film. The crystal grew isothermally at 71 °C, and the crystallization times were (a) t0, (b) t0 + 600 s, and (c) t0 + 1200 s. All images have a size of 55 × 55 μm2. (THF) solutions of the polymer onto UV−ozone-cleaned silicon wafers (cleaned by exposing the wafers to UV light in a humid atmosphere for 30 min).46 The thickness of the films (h) was controlled by changing solution concentration and spinning speed. h was measured by atomic force microscopy (AFM) after applying a scratch in the thin films. The crystallization experiments were done on a hot stage, connected to a steady flow of nitrogen, with precise temperature control (precision = 0.1 °C). Thin films were crystallized according to two different temperature protocols. For the first protocol, films were annealed for 5 min at Ta = 75 °C (i.e., 2 °C above Tm,DSC). Subsequently, these films were quenched to Tc for isothermal crystallization. G of the lamellar crystals varied significantly with temperature, even for changes as little as 0.5 °C. Here, we present crystallization studies for the temperature range 67−71 °C. Below 67 °C, the rate of crystallization was too fast to be observable by optical microscopy. At temperatures above 71 °C, no primary nucleation events were observed, even after waiting for hours. On the basis of the second temperature protocol, we were able to change the nucleation density at a constant crystallization temperature via a self-seeding mechanism.47 First, thin films were crystallized completely by following the first temperature protocol with Tc = 67 °C. Subsequently, the crystalline structures were ripened for few minutes at Ta = 72 °C, followed by annealing at the self-seeding temperature (Tss) and quenching back to the desired Tc. The crystallization process was directly observed under an optical microscope (AxioImager A2m, Zeiss) in the bright-field reflection mode in real time. Superposition of white light reflected from the air− film interface and from the film−substrate interface may lead to destructive interference at characteristic wavelengths, which depend on the thickness of the film. As a result of these wavelengths missing in the spectrum of the reflected light, specific colors are observed, representing the thickness of the polymer film. In this work, the interference colors of thin films and crystals enabled us to identify the height qualitatively with nanometer resolution (also see interference colors corresponding to different film thicknesses presented in Figure S1).48 After crystallization, thin films were quenched to room temperature. Atomic force microscopy (AFM; JPK Instruments AG) was used to characterize the resulting crystal structures in ambient atmosphere. As the polymer has a glass transition temperature lower than room temperature, crystallization or reorganization could occur during cooling or even at room temperature. Thus, in order to visualize formation of stacks of lamellar crystals directly in real time, we performed in situ AFM experiments at Tc.
for synthesizing extremely precise polyethylene copolymers. Acyclic diene metathesis (ADMET) and ring-opening metathesis polymerization (ROMP) have been used to synthesize polyethylene copolymers (termed precision polymers), where the side groups are precisely spaced by x CH2 units, with x ranging from 4 to 74.38−40 The size of the side groups and the length of the methylene sequences in a precision polymer significantly affect their crystallization kinetics.33,36 In longchain aliphatic polymers, van der Waals interactions between methylene sequences mainly direct crystallization, while the side groups are often found to perturb the crystallization process.36,41 Precision polymers with bulky side groups represent interesting model systems for studying the growth kinetics of stacks of lamellar crystals. Recent computer simulations as well as experimental studies on bulk samples have reported the possibility to form multilayered lamellar crystals of precision polymers.35,42,43 However, we still lack a detailed understanding of the controlling parameters for vertical growth, that is, for the increase in number of superposed lamellae in a stack. In this work, we have used thin films of an in-chain phosphonate-substituted polyethylene, poly(nonadecane methylphosphonate), as a suitable model system to identify parameters influencing the growth of a stack of lamellar crystals normal to the fold surface. For a given crystallization temperature, we observed two stages that controlled the growth of stacks of lamellae. Furthermore, for a set of separated lamellar crystals, the distance between these crystals allowed us to tune the transition from lateral to vertical growth, meaning the growth in number of lamellae in a stack.
■
MATERIALS AND METHODS
For our experiments we used poly(nonadecane methylphosphonate) (PE19Me) with molecular weight (Mw) 10 850 and dispersity Đ < 1.6. This polymer was synthesized by polycondensation of long-chain diols with dichlorophosphonic compounds.43 The methylphosphonate groups were positioned precisely after every 19th CH2 unit along the polymer chain. The length of each (CH2)19 repeat sequence was ≈3 nm. The polymer consisted of ≈30 such sequences. The nominal melting temperature (Tm,DSC) of the polymer was ≈73 °C, and the glass transition temperature was ≈20 °C.43 In recent times, precision polymers have been used extensively to understand the influence of side-branch incorporation on crystallization and melting behavior of polyethylene lamellar crystals.33,36,37,44,45 In the thin films studied here, of an in-chain phosphonate-substituted polyethylene, high lateral growth velocity and high probability of primary nucleation were observed at Tc near Tm,DSC. Polymer thin films (ranging from ≈20 to ≈35 nm thickness) were prepared at room temperature by spin-coating dilute tetrahydrofuran
■
RESULTS AND DISCUSSION Optical microscopy allows us to follow the crystallization process in thin films in real time. A number of crystallization parameters like growth rate or morphological features can be measured directly and can be compared with results from computer simulations and theoretical predictions.2,17,47 Figure 1 shows optical micrographs of a typical PE19Me crystal growing at 71 °C in a ≈35 nm thin film. Interestingly, as B
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 2. Influx of molten polymers to the growth front governs lateral growth rate. (a) Lateral advancement (r − r0) of the crystal shown in Figure 1 as a function of (tC − t0), with a crystal radius r = r0 at tC = t0, along the directions indicated by colored arrows in the inset. The black dotted line indicates the initial slope of (r − r0) with (tC − t0). (b) Normalized inverse gray-scale intensity (IN) profiles show the depletion zone ahead of the crystal growth front for different tC, along the direction indicated in the inset. The intensity values were normalized to the intensity value of the unperturbed film. Both insets have a size of 35 × 35 μm2. (c) Plot of Wd (left axis) and G (right axis) of the crystal as a function of (tC − t0).
depletion region, characterized by its width Wd and depth hd, increased while the thickness of the surrounding reservoir of molten polymers remained constant. In Figure 2c, we show that a gradual increase in Wd as a function of (tC − t0) was accompanied by a simultaneous decrease of G. An increase in Wd (and also in hd) indicates a decrease in the flow rate of polymers toward the crystal growth front, causing a decrease in G. When Tc was lowered, the morphology of the crystals changed from circular to branched (see also optical micrographs of temporal evolution of crystals formed at 67 and 69 °C in ≈35 nm thin films, presented in Figures S3 and S4, respectively). In Figure 3, we present G versus (tC − t0) for
can be seen in Figure 1, while the crystal grew laterally, the color of the crystal changed, indicating that its height (H) increased with time. More specifically, the evolution in color from dark blue to light blue and further to yellowish-blue implies that the crystal grew significantly in the vertical direction, reaching a height significantly larger than the thickness of the initial film.48 However, most current theories describing polymer crystal growth do not account for physical processes resulting in such vertical growth. After nucleation, polymer lamellar crystals grow by attaching molten polymers diffusing to the growth front. During this process, a depletion region is formed in front of the crystal, which separates the crystal from the reservoir of molten polymers.2,20 The rate at which molten polymers arrive and attach at the crystal growth front after crossing the depletion region and the detachment probability (Pd) from the crystal surface govern G of the growing crystal.2,49 To measure the growth kinetics of the crystals studied here, we followed the lateral advancement (r − r0) of crystal fronts in time. Here, r denotes the radius of a circular crystal after crystallization time tC, assuming the crystals had a radius r0 when tC = t0. Interestingly, as can be seen in Figure 2a, during crystal growth, (r − r0) was not increasing at a constant rate, reflecting a decrease in G. Such a growth process is intriguing, as it is in conflict with constant G during isothermal crystallization as predicted by theories of polymer crystal growth.6,11,49,50 As discussed earlier, G depends on D and Wd. Thus, in order to identify the origin of this slowing of crystal growth, we followed the temporal evolution of the size of the depletion zone surrounding the crystal. When the thickness of a transparent film on a highly reflecting substrate increases from a few nanometers to a few tens of nanometers, the corresponding interference color changes from white to light brown and further to dark brown.48 In Figure 1, one can see that the depletion zone surrounding the crystal had light color, whereas the unperturbed film (h ≈ 35 nm) was dark. This difference in color refers to changes in the areal density of molten polymers; that is, changes in local thickness. From the optical micrographs in Figure 1 converted into gray-scale images, we deduced the thickness profile across the crystal and its surroundings through the inverse gray-scale intensity of the reflected light. This approach allowed us to identify the evolution of the crystal growth front and the surrounding depletion zone (also see Figure S2, which illustrates the procedure we adopted to calculate gray-scale intensity from optical micrographs). As shown in Figure 2b, the size of the
Figure 3. Lateral growth rate dependence on crystallization temperature and on crystallization time. (a) G versus (tC − t0) for crystals grown at various Tc. (b) Normalized G(tC − t0)/G(t0) versus (tC − t0). All crystals were grown in thin films with h ≈ 35 nm.
crystals grown at different Tc. At later stages, growth was affected by nearby growing neighboring crystals. As can be seen in Figure 3a, for a given h, G decreased significantly with Tc. Interestingly, as can be seen in Figure 3b, for Tc = 67 °C, G was about constant during the whole growth process, and no significant change in H of the crystals was observed (see also Figure S3). At higher Tc, G decreased strongly with (tC − t0) and was accompanied by an increase in H (see Figure 1 and AFM in situ measurements presented in Figures S5 and S6). Polymer crystals can grow perpendicular to the fold surface (i.e., vertical growth) either by forming stacks of lamellar crystals or by spiral growth initiated by screw dislocations. Vertical growth via stacking is achieved by formation of new lamellae atop the fold surface of lamellar crystals. Spiral growth originates from screw dislocation characterized by the magnitude of the Burgers vector9,51,52 and is associated with elastic stresses and possibly requiring an angular path larger than 360°.52 To identify the mechanism leading to vertical growth of lamellar crystals in our present work, we performed C
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 4. Vertical growth via the formation of stacks of lamellae. (a−c) Contrast-enhanced optical micrographs of a crystal growing at 70 °C in a thin film with h ≈ 20 nm illustrate vertical growth of stacks of lamellar crystals. The images were taken after (a) t0, (b) t0 + 2 h, and (c) t0 + 4 h. (d) Contrast-enhanced optical micrograph of a crystal formed after 18 h at 71 °C in a film with h ≈ 20 nm. (e) AFM topographic image showing a stack of lamellar crystals for the section indicated by the red box in panel d. (f) Height profile along the black arrow shown in panel e, illustrating that all lamellae had the same thickness of ≈3 nm. Image sizes are (a−c) 30 × 30 μm2, (d) 35 × 35 μm2, and (e) 12 × 12 μm2.
Figure 5. Switching from lateral to vertical growth. (a−c) Contrast-enhanced optical micrographs show two neighboring branched crystals growing at 69 °C in ≈35 nm thin film. Images were taken after (a) t0 + 900 s, (b) t0 + 4000 s, and (c) t0 + 14 000 s. Images a−c each have a size of 190 × 60 μm2. (d) Normalized inverse gray-scale intensity (IN) for the cross-section along the black arrow indicated in panel a, showing that the reservoir of molten polymers between the crystals was depleted with (tC − t0). The scans represented by cyan, red, and green lines correspond to optical micrographs a, b, and c, respectively. All intensity values were normalized to the gray-scale intensity of the initial film thickness. (e) (r − r0) and G as a function of (tC − t0) for the branch indicated by the white arrow in panel a.
experiments with thinner films at Tc near Tm,DSC. Figure 4a−c shows optical micrographs of a typical PE19Me crystal, growing in ≈20 nm thin film at 70 °C. In Figure 4a, the crystal morphology revealed only the existence of stacks, containing a large number of superposed secondary lamellae. Furthermore, while the lateral extension of the crystal increased, the number of lamellae in the stack also gradually increased with time, leading to a change in interference color from light brown at initial stages (Figure 4a) to dark brown (Figure 4b) and further to bluish-brown (Figure 4c). However, when the difference in lateral extension of two consecutive lamellae was smaller than ≈1 μm, optical micrographs could not resolve individual lamellae separately. Thus, in Figure 4a− c, compared to the lamellae near the center of the crystal, the ones in the stack near the edge cannot be distinguished individually. Similar problems of lateral resolution occurred for crystals higher than ≈100 nm (Figure 4d). However, closer inspection by AFM confirmed that such high crystals also
contained stacks of lamellar crystals (Figure 4e). Analyzing the crystal morphologies of Figure 4a−e, we conclude that all lamellae were orientated parallel to the substrate.9,14,18,53−55 Moreover, it has been shown in previous experiments that the number of stacks per unit area increased with h.18 Compared to films with h ≈ 20 nm, we may expect a higher number density of stacks of lamellae for crystallization of films with h ≈ 35 nm. Therefore, it is difficult to distinguish individual stacks of lamellae and individual lamellae within a stack in the optical micrographs of Figure 1 (h ≈ 35 nm). Interestingly, the thickness of each lamella in such a stack was ≈3 nm, equivalent to the distance between two phosphonate groups along the polymer backbone (Figure 4f), consistent with experiments performed on similar systems.35,36,42 This implies that, in the course of crystallization, the polymer chains folded preferentially at positions of the phosphonate groups that were not included in the crystalline structure. D
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 6. Formation of three-dimensional (3D) crystals in thin films. (a−c and e−g) Contrast-enhanced optical micrographs of crystals formed at 71 °C in ≈25 nm thin films, taken after (a, e) t0, (b, f) t0 + 8 h, and (c, g) t0 + 16 h. The self-seeding temperatures (Tss) were 75 °C for panels a−c and 74 °C for panels e−g. The lower the value of Tss was, the higher was the number of remaining seeds leading to a larger number of simultaneously growing crystals, that is, higher number density of crystals. All six optical micrographs have a size of 200 × 200 μm2. (d, h) AFM height images of the crystals indicated by (d) the red box in panel c and (h) the black box in panel g (also see high-resolution AFM images of these crystals presented in Figures S7 and S9, respectively). AFM images have sizes of (d) 35 × 35 μm2 and (h) 15 × 15 μm2.
Thus, during the initial stages of growth shown in Figure 5, the high influx of molten polymers caused a low number of detaching polymers. Accordingly, lamellar crystals grew predominantly in the lateral direction (Figure 5a). However, at later stages, when the influx of the molten polymers to the growth front decreased drastically, the polymer segments at the growth front had more time to detach. These detached polymer segments could also diffuse onto the fold surface and eventually became attached at self-induced nucleation sites, leading to the formation of secondary lamellae. Accordingly, we observed a reduction of G and a concomitant increase in H. Motivated by the results presented in Figure 5, we performed experiments on thin films with different nucleation densities, that is, different separation distances between crystals. The nucleation density was controlled by applying the second temperature protocol (i.e., a self-seeding approach) as described in the Materials and Methods section. Vertical growth of stacks of lamellae, that is, an increase in number of lamellae in a stack, requires a high probability of self-induced nucleation on basal lamellae and on the consecutive lamellae on top. As an attempt to find out if there is a limit to the number of superposed secondary lamellae in a stack, we performed isothermal experiments with very high nucleation density to stop lateral lamellar growth and to initiate vertical growth at comparatively short crystallization times. Intriguingly, the resulting stacks of lamellar crystals exhibited significant differences in height, ranging from a few hundreds of nanometers up to even a few micrometers (Figure 6) and high-resolution AFM height images confirmed the stacking of lamellae, each having a thickness of ≈3 nm (see Figures S7, S8 and 4e). For example, the crystalline stack shown in Figure 6h contained about 800 lamellae. In the course of crystal growth, gaps between adjacent branches of a lamellar crystal act as sinks for molten polymers diffusing on the fold surface.18 Thus, during crystallization, noncrystalline nonadecane methylphosphonate sequences may
Initiated by the morphology-based self-induced nucleation mechanism, in the course of crystallization, stacks of lamellae form on the fold surface of the basal lamella.18,53 Figures 1 and 4a−c indicate that the number of lamellae in such stacks increased over time, causing vertical growth. Such vertical growth was influenced by the influx of molten polymers. In the following isothermal crystal growth experiments, we aimed to identify consequences caused by variations in influx of molten polymers to the growth front. In Figure 5a−c, we followed by optical microscopy the growth of crystalline branches of two neighboring crystals growing at 69 °C. The corresponding inverse gray-scale intensity scans of the reservoir of molten polymers between these crystals are shown in Figure 5d. At the beginning, the crystals grew mainly in the lateral direction (see also Figure 5e). However, at the later stages, when the depletion zones ahead of the two opposing crystals overlapped, the influx of molten polymers to the growth fronts of both crystals decreased drastically, causing a reduction in G (Figure 5d,e). As long as these crystals advanced laterally, without mutually influencing their growth, we did not observe any significant increase in H (Figure 5d,e). Surprisingly, as the thickness of the reservoir of molten polymers in the surrounding of these crystals decreased with (tC − t0), lateral growth slowed significantly (Figure 5e). Concomitantly, the height of the stacks of lamellar crystals increased, as deduced from the change in interference color of the crystals (see Figure 5a−c). When a polymer, diffusing from the reservoir of molten polymers toward a crystal, arrives at the crystal growth front, it needs several attempts to attach a segment definitely at the growth front, according to a Boltzmann term related to Pd, which depends on the heat of fusion per unit volume (Δhm) and on Tc.2,17 At Tc, already attached polymer segments have a nonzero probability to detach from crystal surface.17 However, the time available for detachment depends on the rate at which additional molten polymers arrive at the crystal growth front. E
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 7. Nucleation mechanism for the formation of new lamellae on a stack of lamellae. Schematic diagrams (viewing lamellar crystals from the side) indicate the nucleation mechanism leading to the formation of new lamellae on top of the fold surface of a basal lamellar crystal. The methylphosphonate groups are indicated by red dots when attached to a crystalline stem and by pink dots when linked to amorphous sequences. (a) Two adjacent crystalline branches of a (dendritic) basal lamella are separated by a gap at time t0. The fold surface of this crystal contains dangling chain ends (sky blue) and amorphous polymer sequences (blue, green, and orange). (b) At a later time t1, noncrystalline sequences are inserted into the gap (indicated by the green and orange chains). (c) The inserted sequences nucleate the formation of a new lamella on the fold surface of the basal lamella at time t2. (d) At time t3, this process of inducing nucleation through dangling noncrystalline sequences on the fold surface is repeated, initiating the formation of subsequent lamellae atop a stack of lamellae. Here t0 < t1 < t2 < t3.
be inserted in such gaps, which induced the formation of a new lamella on the fold surface of the basal lamella (Figure 7a− c).18,53 Such a nucleation mechanism resulted in parallel arrangement of lamellae in a stack, where any two consecutive lamellae share one or more polymer sequences.18,53,56 From our experimental results, we anticipate that the presence of bulky phosphonate groups in PE19Me reduced the probability of adjacent chain reentry during crystal growth and thus apparently increased the probability of forming self-induced nuclei on the fold surface of lamellae. Furthermore, on the fold surface, dangling and not yet crystalline sequences attached to crystalline stems in the underlying lamella may be favorable for nucleation of a subsequent lamella atop a stack of lamellae (Figure 7d). As a result, even at Tc close to Tm,DSC, polymer crystals contained a high number of self-induced nuclei on the fold surface (see Figure 1). Under such conditions, we were able to form micrometer-high stacks containing many hundreds of lamellae (see Figure 6h). We emphasize that the crystalline structures in Figure 6 reached heights (H) ranging from a few tens to hundred of times the initial film thickness and were formed in rather thin films, with h equivalent to only a few times the length of the repeat sequence. Furthermore, some of the formed crystals exhibited an H/r ratio up to about 0.3 (Figure 6h), which opens up the possibility to form threedimensional quasi-single polymer crystals with equal sizes in all three dimensions. Previous experiments indicate that the probability of selfinduced nucleation on the fold surface can be controlled by h and Tc.18 As shown in Figure 5, the growth of secondary and subsequent higher-order lamellae is governed by transport of molten polymers to the fold surface, which depends on h. To quantify the vertical growth of crystals with time, we followed the height of isolated crystals at their growth front (HI) with (tC − t0) in ≈35 nm thin films at different Tc values directly by AFM (Figure 8; in situ AFM images are shown in Figures S5 and S6). Interestingly, HI increased with (tC − t0) at a rate that increased with Tc. This is surprising, as a faster increase in HI with increasing Tc is opposite to the observed decrease in G with increasing Tc. As the polymer lamellar crystals studied in this work exhibited a high probability of self-induced nucleation for all Tc values (see Figures 1, 4, and 5), we believe that the growth of
Figure 8. The rate at which stacks of crystals grow in height increases with crystallization temperature. Increasing height of the crystal growth front (HI) as a function of (tC − t0), for various Tc values is shown (obtained from in situ AFM experiments; see also Figure S5 and S6). The crystals were formed in a film with h ≈ 35 nm. The green star indicates HI after t0 + 1000 s at 69 °C (see Figure 5a).
stacks of lamellae was mainly controlled by the transport of molten polymers to the fold surface and was not limited by nucleation of new lamellae on top of the fold surface. At a given h, G decreased with increasing Tc, reflecting an increase in Pd. Therefore, at high Tc, a large number of detached polymers have a chance to diffuse onto the fold surface. Accordingly, stacks of lamellar crystals grew faster in height at Tc close to the melting temperature of the crystals (Figure 8), while G was higher at low Tc. For example, at Tc = 67 °C, Pd was low, and thus the number of polymers diffusing onto the fold surface was also low. Thus, stacks of lamellar crystals did not show significant vertical growth (see also Figure S3). Comparing results shown from Figures 1 and 2 with those from Figures 5 and 8, we can conclude that lateral and vertical growth of stacks of lamellar crystals are interdependent. Lateral growth of the stacks of lamellar crystals is favored when Pd is low and/or the influx of molten polymers to the growth front is high. By contrast, vertical growth through stacks of increasing number of superposed lamellae is favored when either Pd is high or the influx of molten polymers to the growth front is low.
■
CONCLUSIONS Studying the growth process leading to formation of stacks of correlated lamellae, we showed that the growth of such stacks F
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
(8) Keller, A. A Note on Single Crystals in Polymers: Evidence for a Folded Chain Configuration. Philos. Mag. 1957, 2 (21), 1171−1175. (9) Wunderlich, B. Macromolecular Physics, Volume 1: Crystal Structure, Morphology, Defects; Academic Press: New York and London, 1973; DOI: 10.1016/B978-0-12-765601-4.X5001-X. (10) Kovacs, A. J.; Gonthier, A.; Straupe, C. Isothermal Growth, Thickening, and Melting of Poly(ethylene Oxide) Single Crystals in the Bulk. J. Polym. Sci., Polym. Symp. 1975, 50 (1), 283−325. (11) Welch, P.; Muthukumar, M. Molecular Mechanisms of Polymer Crystallization from Solution. Phys. Rev. Lett. 2001, 87 (21), No. 218302. (12) Keller, A.; Cheng, S. Z. D. The Role of Metastability in Polymer Phase Transitions. Polymer 1998, 39 (19), 4461−4487. (13) Doye, J. P. K.; Frenkel, D. Mechanism of Thickness Determination in Polymer Crystals. Phys. Rev. Lett. 1998, 81 (10), 2160−2163. (14) Reneker, D. H.; Geil, P. H. Morphology of Polymer Single Crystals. J. Appl. Phys. 1960, 31 (11), 1916−1924. (15) Geil, P. H. Polymer Single Crystals; Wiley: New York, 1963. (16) Reiter, G.; Sommer, J. Polymer Crystallization in Quasi-Two Dimensions. I. Experimental Results. J. Chem. Phys. 2000, 112 (9), 4376−4383. (17) Grozev, N.; Botiz, I.; Reiter, G. Morphological Instabilities of Polymer Crystals. Eur. Phys. J. E: Soft Matter Biol. Phys. 2008, 27, 63− 71. (18) Zhang, H.; Yu, M.; Zhang, B.; Reiter, R.; Vielhauer, M.; Mülhaupt, R.; Xu, J.; Reiter, G. Correlating Polymer Crystals via SelfInduced Nucleation. Phys. Rev. Lett. 2014, 112 (23), No. 237801. (19) Price, F. P. Growth Habit of Single Polymer Crystals. J. Chem. Phys. 1959, 31, 1679−1680. (20) Poudel, P.; Chandran, S.; Majumder, S.; Reiter, G. Controlling Polymer Crystallization Kinetics by Sample History. Macromol. Chem. Phys. 2018, 219 (3), 1700315. (21) Langer, J. S.; Müller-Krumbhaar, H. Stability Effects in Dendritic Crystal Growh. J. Cryst. Growth 1977, 42, 11−14. (22) Sekerka, F. Role of Instabilities in Determination of the Shapes of Growing Crystals. J. Cryst. Growth 1993, 128, 1−12. (23) Mullins, W. W.; Sekerka, R. F. Morphological Stability of a Particle Growing by Diffusion or Heat Flow. J. Appl. Phys. 1963, 34 (2), 323−329. (24) Langer, J. S. Instabilities and Pattern Formation in Crystal Growth. Rev. Mod. Phys. 1980, 52 (1), 1−28. (25) Reiter, G.; Sommer, J.-U., Eds. Polymer Crystallization: Obervations, Concepts and Interpretations; Lecture Notes in Physics, Vol. 606; Springer: Berlin and Heidelberg, Germany, 2003; DOI: 10.1007/3-540-45851-4. (26) Dalnoki-Veress, K.; Forrest, J. A.; Massa, M. V.; Pratt, A.; Williams, A. Crystal Growth Rate in Ultrathin Films of Poly(ethylene Oxide). J. Polym. Sci., Part B: Polym. Phys. 2001, 39 (21), 2615−2621. (27) Keller, A.; Pedemonte, E. A Study of Growth Rates of Polyethylene Single Crystals. J. Cryst. Growth 1973, 18 (2), 111−123. (28) Goldenfeld, N. Theory of Spherulitic Crystallization. J. Cryst. Growth 1987, 84 (4), 601−608. (29) Brener, E.; Müller-Krumbhaar, H.; Temkin, D. Structure Formation and the Morphology Diagram of Possible Structures in Two-Dimensional Diffusional Growth. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1996, 54 (3), 2714−2722. (30) Umemoto, S.; Kobayashi, N.; Okui, N. Molecular Weight Dependence of Crystal Growth Rate and Its Degree of Supercooling Effect. J. Macromol. Sci., Part B: Phys. 2002, 41 (4), 923−938. (31) Casas, M. T.; Puiggalí, J.; Raquez, J.-M.; Dubois, P.; Córdova, M. E.; Müller, A. J. Single Crystals Morphology of Biodegradable Double Crystalline PLLA-b-PCL Diblock Copolymers. Polymer 2011, 52 (22), 5166−5177. (32) Hong, S.; MacKnight, W. J.; Russell, T. P.; Gido, S. P. Orientationally Registered Crystals in Thin Film Crystalline/ Amorphous Block Copolymers. Macromolecules 2001, 34 (8), 2398−2399.
is governed by mainly three physical parameters: the detachment probability of crystalline stems, the probability of forming self-induced nuclei, and the rate of transport of molten polymers toward the growth front. Our findings indicate that it is possible to form three-dimensional quasi-single crystals, consisting of stacks of correlated lamellae. Such vertical growth is in competition with a lateral growth of lamellae, which is favored for low Pd and/or high influx of molten polymers to the growth front. We believe that, for a more profound understanding of polymer crystallization, we need to implement additional features into existing theoretical concepts to account for such a competition of lateral and vertical growth.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01765.
■
Nine figures showing correlation between film thickness and interference colors, gray-scale intensity measurement for calculating width of depletion zone, in situ measurement of radial advancement of crystals, AFM in situ measurement of radial advancement and height of crystals, height profiles of stacks of lamellar crystals, and micrometer-high quasi-single crystal (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected]. ORCID
Hanna Busch: 0000-0002-4684-727X Purushottam Poudel: 0000-0002-2452-2634 Stefan Mecking: 0000-0002-6618-6659 Günter Reiter: 0000-0003-4578-8316 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We acknowledge fruitful discussions with the members of the International Research Training Group (IRTG-1642)-Soft Matter Science, funded by the Deutsche Forschungsgemeinschaft (DFG). This work was funded by the BadenWürttemberg Stiftung.
■
REFERENCES
(1) Reiter, G. Some Unique Features of Polymer Crystallisation. Chem. Soc. Rev. 2014, 43, 2055−2065. (2) Reiter, G.; Sommer, J.-U. Crystallization of Adsorbed Polymer Monolayers. Phys. Rev. Lett. 1998, 80 (17), 3771−3774. (3) Toda, A.; Keller, A. Growth of Polyethylene Single Crystals from the Melt: Morphology. Colloid Polym. Sci. 1993, 271, 328−342. (4) Lauritzen, J. I.; Hoffman, J. D. Extension of Theory of Growth of Chain-Folded Polymer Crystals to Large Undercoolings. J. Appl. Phys. 1973, 44 (10), 4340−4352. (5) Keller, A. Solution Grown Polymer Crystals. Kolloid Z. Z. Polym. 1969, 231 (1−2), 386−421. (6) Lauritzen, J. I.; Hoffman, J. D. Formation of Polymer Crystals with Folded Chains from Dilute Solution. J. Res. Natl. Bur. Stand., Sect. A 1960, 64A, 73−102. (7) Lauritzen, J. I.; Hoffman, J. D. Formation of Polymer Crystals with Folded Chains from Dilute Solution. J. Chem. Phys. 1959, 31 (6), 1680−1681. G
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
(50) Strobl, G. The Physics of Polymers: Concepts for Understanding Their Structures and Behavior; Springer: Berlin and Heidelberg, Germany, 2007; DOI: 10.1007/978-3-662-03488-0. (51) Wunderlich, B. Macromolecular Physics, Volume 2: Crystal Nucleation, Growth, Annealing; Academic Press: New York and London, 1976. (52) Keller, A. Regular Rotation of Growth Terraces in Polymer Single Crystals. Colloid Polym. Sci. 1967, 219 (2), 118−131. (53) Poudel, P.; Majumder, S.; Chandran, S.; Zhang, H.; Reiter, G. Formation of Periodically Modulated Polymer Crystals. Macromolecules 2018, 51 (15), 6119−6126. (54) Núñez, E.; Gedde, U. Single Crystal Morphology of Starbranched Polyesters with Crystallizable Poly(ε-caprolactone) Arms. Polymer 2005, 46 (16), 5992. (55) Díaz, A.; Casas, M. T.; Puiggalí, J. Preferential Incorporation of Azelaic Acid Units into the Crystalline Phase of the Copoly(Alkylene Dicarboxylate) Derived from 1,9-Nonanediol and an Equimolar Mixture of Pimelic and Azelaic Acids. Polymers 2015, 7 (9), 1871− 1894. (56) Kovacs, A. J.; Gonthier, A. Crystallization and Fusion of Selfseeded Polymers. Kolloid Z. Z. Polym. 1972, 250 (5), 530−552.
(33) Tasaki, M.; Yamamoto, H.; Hanesaka, M.; Tashiro, K.; Boz, E.; Wagener, K. B.; Ruiz-Orta, C.; Alamo, R. G. Polymorphism and Phase Transitions of Precisely Halogen-Substituted Polyethylene. Macromolecules 2014, 47 (14), 4738−4749. (34) Zhang, X.; Zhang, W.; Wagener, K. B.; Boz, E.; Alamo, R. G. Effect of Self-Poisoning on Crystallization Kinetics of Dimorphic Precision Polyethylenes with Bromine. Macromolecules 2018, 51 (4), 1386−1397. (35) Trigg, E. B.; Gaines, T. W.; Maréchal, M.; Moed, D. E.; Rannou, P.; Wagener, K. B.; Stevens, M. J.; Winey, K. I. SelfAssembled Highly Ordered Acid Layers in Precisely Sulfonated Polyethylene Produce Efficient Proton Transport. Nat. Mater. 2018, 17, 725−731. (36) Santonja-Blasco, L.; Zhang, X.; Alamo, R. G. Crystallization of Precision Ethylene Copolymers. In Polymer Crystallization I: From Chain Microstructure to Processing; Advances in Polymer Science, Vol. 276; Auriemma, F., Alfonso, G., de Rosa, C., Eds.; Springer: 2015; pp 133−182; DOI: 10.1007/12_2015_346. (37) Matsui, K.; Seno, S.; Nozue, Y.; Shinohara, Y.; Amemiya, Y.; Berda, E. B.; Rojas, G.; Wagener, K. B. Influence of Branch Incorporation into the Lamella Crystal on the Crystallization Behavior of Polyethylene with Precisely Spaced Branches. Macromolecules 2013, 46 (11), 4438−4446. (38) Song, S. F.; Guo, Y. T.; Wang, R. Y.; Fu, Z. S.; Xu, J. T.; Fan, Z. Q. Synthesis and Crystallization Behavior of Equisequential ADMET Polyethylene Containing Arylene Ether Defects: Remarkable Effects of Substitution Position and Arylene Size. Macromolecules 2016, 49 (16), 6001−6011. (39) Smith, J. A.; Brzezinska, K. R.; Valenti, D. J.; Wagener, K. B. Precisely Controlled Methyl Branching in Polyethylene via Acyclic Diene Metathesis (ADMET) Polymerization. Macromolecules 2000, 33 (10), 3781−3794. (40) Baughman, T. W.; Wagener, K. B. Recent Advances in ADMET Polymerization. In Metathesis Polymerization; Advances in Polymer Science, Vol. 176; Springer: Berlin and Heidelberg, Germany, 2005; pp 1−42; DOI: 10.1007/b101318. (41) Alamo, R. G.; Mandelkern, L. Thermodynamic and Structural Properties of Ethylene Copolymers. Macromolecules 1989, 22 (9), 1273−1277. (42) Trigg, E. B.; Stevens, M. J.; Winey, K. I. Chain Folding Produces a Multilayered Morphology in a Precise Polymer: Simulations and Experiments. J. Am. Chem. Soc. 2017, 139 (10), 3747−3755. (43) Busch, H.; Majumder, S.; Reiter, G.; Mecking, S. Semicrystalline Long-Chain Polyphosphoesters from Polyesterification. Macromolecules 2017, 50 (7), 2706−2713. (44) Gao, R.; He, X.; Shao, Y.; Hu, Y.; Zhang, H.; Liu, Z.; Liu, B. Effects of Branch Content and Branch Length on Polyethylene Crystallization: Molecular Dynamics Simulation. Macromol. Theory Simul. 2016, 25 (3), 303−311. (45) Miao, W.; Wang, Z.; Li, Z.; Wang, B.; Zheng, W.; Chen, Z. R. Epitaxial Crystallization of Precisely Chlorine-Substituted Polyethylene Induced by Carbon Nanotube and Graphene. Polymer 2016, 94, 53−61. (46) Chandran, S.; Handa, R.; Kchaou, M.; Al Akhrass, S.; Semenov, A. N.; Reiter, G. Time Allowed for Equilibration Quantifies the Preparation Induced Nonequilibrium Behavior of Polymer Films. ACS Macro Lett. 2017, 6 (11), 1296−1300. (47) Xu, J.; Ma, Y.; Hu, W.; Rehahn, M.; Reiter, G. Cloning Polymer Single Crystals through Self-Seeding. Nat. Mater. 2009, 8 (4), 348− 353. (48) Schäffer, E. Instabilities in Thin Polymer Films: Structure Formation and Pattern Transfer. Dissertation, Universität Konstanz, 2001; http://kops.uni-konstanz.de/handle/123456789/4766. (49) Reiter, G.; Strobl, G. Progress in Understanding of Polymer Crystallization; Lecture Notes in Physics; Vol. 714; Springer: Berlin and Heidelberg, Germany, 2007; DOI: 10.1007/3-540-47307-6. H
DOI: 10.1021/acs.macromol.8b01765 Macromolecules XXXX, XXX, XXX−XXX
