Formation of Periodically Modulated Polymer Crystals

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Formation of Periodically Modulated Polymer Crystals Purushottam Poudel,† Sumit Majumder,† Sivasurender Chandran,† Hui Zhang,§ and Günter Reiter*,†,‡ †

Physikalisches Institut and ‡Freiburg Materials Research Center (FMF), Albert-Ludwigs-Universität, 79104 Freiburg, Germany College of Materials Science and Engineering, Donghua University, 201620 Shanghai, China

§

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S Supporting Information *

ABSTRACT: We report novel morphologies with periodic height modulations of isotactic polystyrene (iPS) crystals, resulting from alternating stacks of correlated lamellae. Systematic experiments were performed on iPS films of several thicknesses (h) for varying degrees of ∞ undercooling, ΔT = T∞ m − TC, where Tm and TC are the equilibrium melting temperature and the crystallization temperature, respectively. We demonstrate that the spatial period (λ), i.e., the mean distance between neighboring stacks of lamellae, exhibits a power-law dependence on h and an exponential dependence on 1/ΔT. We propose that self-induced nucleation of stacked layers caused periodic deviation in the growth rate of iPS crystals, yielding periodic height modulations.

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INTRODUCTION Investigating the simple but still distinctly differing macroscopic morphologies generated in the course of crystal growth in polymer thin films provides a unique possibility for learning about fundamentals of the polymer crystallization.1−4 Experimental accessibility of the growth process with high temporal and spatial resolution is provided by conventional microscopy techniques.5−9 However, although intensive investigations have been performed to understand the molecular processes controlling the formation of various morphologies during crystal growth,1−13 many aspects of the underlying mechanisms are still not well understood. The morphology of a crystal is mainly determined by diffusion of the polymer chains toward the growth front of the crystal, the probability that a polymer chain arriving at the crystal surface actually gets attached at the crystal front, and subsequent rearrangement processes of these attached polymer chains to minimize their overall surface tension.14 Transport of long-chain polymer molecules is complicated by constraints imposed by the connectivity of the monomers. Additionally, transport may be slowed down in thin films due to geometric confinement and consequences of chain adsorption onto the substrate.15,16 At high undercooling, polymers often show a spherulitic, polycrystalline morphology. However, growing crystals at temperatures close to the melting temperature results in rather simple morphologies, such as dendritic or faceted single crystals, which exhibit a form (enveloping the crystal structure) that reflects the symmetry of the unit cell.1,4,17−22 Because of chain folding, almost all polymer crystals are metastable and much thinner than they are wide. They can be viewed as quasitwo-dimensional (2D) crystals with a thickness of the order of 10 nm. Furthermore, chain folds at the surface of such lamellar crystals generate amorphous interlayers, prohibiting e.g. epitaxial growth at such surfaces. Thus, each of these quasi© XXXX American Chemical Society

2D crystals has to be initiated independently via homogeneous or heterogeneous nucleation, leading to an ensemble of randomly oriented lamellae. However, stacks of correlated lamellae have been observed frequently, exhibiting features of three-dimensional single crystals.10,23−25 In the search for an appropriate nucleation mechanism, which has the potential of generating correlations between crystalline lamellae, the mechanism of self-induced nucleation of secondary lamellae has been proposed.10 This mechanism can lead to crystal growth in the direction normal to the fold surface, resulting in stacked lamellae, which are separated by amorphous interlayers resulting from chain folding.10,26 Representing a highly fascinating morphological feature of polymer crystallization, periodically banded spherulites have received much attention.6,27−37 These structures have been interpreted in various ways.27−30 Most, but not all, of them are birefringent. Birefringence has been attributed to periodic twisting of lamellae along the radial direction of the spherulites.32−35 On the other hand, nonbirefringent periodically banded structures have been linked to deviations from a constant crystal growth kinetics.9,28,30,36,37 Detailed investigations of nonbirefringent periodically banded spherulites indicated periodic variations of the height resulting from a regularly changing number of stacked lamellar layers.26,28,37,38 However, despite the intensive efforts, we are still lacking a comprehensive understanding of the underlying mechanisms responsible for the periodic repetition of a stacking of lamellae. In a previous publication,26 we have shown that a systematic relaxation of the preparation induced nonequilibrium states control nucleation density, crystallization kinetics, and morphology of the lamellar crystals varying from spherulites Received: June 27, 2018 Revised: July 23, 2018

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DOI: 10.1021/acs.macromol.8b01366 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Tuning the morphology of crystals by varying film thickness (h) and crystallization temperature (TC). Optical micrographs showing the influence of TC and h on the formation of periodically modulated crystals. Top row (a−c, image size: 67 × 67 μm2) and bottom row (d−f, images size: 50 × 50 μm2) represent films with h ≈ 85 nm and h ≈ 35 nm, respectively. Films were crystallized (a, d) at TC = 130 °C for 160 min, (b, e) at TC = 150 °C for 75 min, and (c, f) at TC = 160 °C for 50 min.

to hexagons of rather uniform height to finally hexagons exhibiting periodic modulation in height. Along similar lines, it has been shown that39 the chosen thermal pathway, for reaching the crystallization temperature, has a significant influence on the crystallization kinetics, including morphologies, in particular in polymer films. In this study, we have systematically investigated the formation of periodically modulated crystals of isotactic polystyrene with a focus on characteristic features of crystal morphology in relation to the growth process. Here, to avoid that preparation/processinginduced nonequilibrium conformational states affect crystallization kinetics, we have used short isotactic polystyrene chains with a molecular weight less than the entanglement molecular weight.40 To conveniently follow the formation of periodically modulated crystals in time, we have chosen thin films (thickness h = 30−140 nm) exhibiting slow crystal growth. Our results indicate that the periodic variation of the height of stacks of correlated lamellae was correlated to periodic deviations from a constant crystal growth rate. The spacing (periodicity) between such stacks was found to increase with increasing crystallization temperature and film thickness, i.e., related to the kinetics of crystal growth. We tentatively relate the periodic formation of stacks of correlated lamellae to the process of self-induced nucleation.10

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silicon substrates at room temperature. h was controlled via the concentration of the solution and the rotation speed of spin coater. After spin coating, to eliminate nonequilibrated states inherited from spin coating, films were annealed for about 3 min at a temperature above Tm, followed by a fast quench to the room temperature. Fast quenching assured that no, or at least only very few, crystal nuclei were formed in the films. These quenched samples were then heated to the desired crystallization temperature (TC) for isothermal crystallization. A Linkam TMS 94 device with a precision of 0.1 °C controlled the crystallization temperature at the hot stage. Real-time inspection of the crystallization process was performed directly under an optical microscope (OM) in an inert atmosphere (nitrogen flow). Atomic force microscopy (AFM) with a high-temperature hot stage was used for in situ microscopic inspection of crystallization. In addition, AFM at ambient temperature was used to visualize morphology and nanoscopic crystalline structures in detail.

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RESULTS AND DISCUSSION

In Figure 1, we show representative optical micrographs of crystals grown in films of two different thicknesses ((a−c): h ≈ 85 nm and (d−f): h ≈ 35 nm) at various temperatures. The differences in colors observed with an optical microscope in reflection imaging mode, resulting from interference of light reflected from the crystal surface and the substrate interface, represent variations in local thickness.41 Thus, the periodically varying interference colors represent periodic variations in the crystal height. For all crystalline structures, periodic variations in height can be clearly seen in optical micrographs (see Figure 1). At low TC, we observed an approximately circular shape of the crystal envelope (its habit), while crystals grown at high TC exhibited hexagonal shapes, reflecting the symmetry of the crystal lattice of isotactic polystyrene.24 The change from a circular to a hexagonal habit of the crystals can be related to the suppression of growth front nucleation26,42 at high TC. At low TC, there exists a nonzero probability to form additional nuclei at the growth front, introducing a variation in

EXPERIMENTAL SECTION

Isotactic polystyrene (iPS), synthesized in the group of Prof. R. Mülhaupt (Freiburg, Germany), with a weight-averaged molecular weight of 13 kg/mol (dispersity Đ = 1.9), having more than 90% of isotactic pentads was used. Differential scanning calorimetry (DSC) experiments performed at a rate of 10 °C/min yielded a nominal melting temperature Tm = 200 °C. iPS was dissolved in cyclohexanone at 150 °C to form a homogeneous solution, which was filtered with a polytetrafluoroethylene (PTFE) syringe filter of pore size ≈ 0.22 μm. Films of homogeneous thickness (h), ranging from 30 to 140 nm, were prepared by spin coating iPS/cyclohexanone solutions of variable concentrations onto freshly UV-ozone-treated B


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Figure 2. Periodic variation of the radial growth velocity. (a) Radius (R) from the nucleation center to the crystal growth front (circles, measured along the diagonals of a hexagonal crystal) as a function of growth time (tC) and the corresponding radial growth velocity (G(tC) = dR(tC)/dtC) (squares) for a crystal grown in ca. 105 nm thick film at 160 °C. The red dashed line indicates the mean (constant) slope of R(tC), i.e., a constant growth rate (G̅ ) (indicated by the pink dashed line). (b) Temperature dependence of G̅ for films of various thicknesses, as indicated.

Figure 3. Stacking of lamellar crystals. (a) AFM height images showing a typical periodically height modulated crystal grown for 70 min at 160 °C in a ca. 50 nm thick film. (b) Zoomed-in AFM height image for the region marked by the blue box in (a). (c) Cross-sectional height profile along the black dashed line shown in (b), indicating a constant lamellar thickness of ΔhL ≈ 9 nm. The sizes of the images are (a) 53 × 53 μm2 and (b) 2.6 × 2.6 μm2.

orientation of the crystal unit cell.26,42 However, at high TC, only a single nucleation event (at the center) occurs during the whole growth process, resulting in hexagonally shaped crystals. Furthermore, ahead of the crystal−melt interface, a depletion zone (a valley separating the growing crystal from the surrounding reservoir of the molten polymers) was developing during crystal growth. In addition, in between the depletion zone and the unperturbed reservoir of polymers (the unperturbed film) a thicker region of molten polymers (a halo) was observed for all morphologies.26 Notably, the thickness of the crystalline structures was higher along the diagonals of the hexagons (reflecting the growth tips) than in any off-diagonal direction. This difference in thickness is attributed to the fact that the growth tips were always closest to the reservoir of molten polymers and thus had a higher chance to capture molecules from the surrounding.19 In Figure 2a, we show the radius (R) of a representative periodically modulated crystal as a function of crystallization time (tC). Interestingly, we noticed that R did not increase linearly with tC, but rather showed an oscillatory behavior; i.e., the growth rate G(tC) = dR(tC)/dtC was not constant in time. However, the mean growth rate (G̅ ), indicated by a dashed line in Figure 2a, was constant. For all the periodically modulated structures grown at different TC in films differing in thickness h, we have observed a similar (oscillatory) behavior of R(tC) and G(tC) (refer to Figure S1 of the Supporting Information). The oscillatory growth process is characterized by periodically varying regimes of fast and slow growth, accompanied by periodic modulations of the height of the crystalline structures. In Figure 2b, we summarize the TC-dependent mean growth

rates (G̅ ) observed during the formation of periodically modulated crystals of iPS. Similar to previous observations, we found that the growth rate followed a bell-shaped curve with increase in TC.43−45 From Figure 1, it became clear that the crystalline structures have periodic modulations in their height, implying a complementary growth process in the direction normal to the direction of lateral lamellar growth. Such three-dimensional growth is only possible by the superposition of lamellae either induced by screw dislocations or caused by stacking of lamellae.46 The limited resolution of optical microscopy cannot provide sufficiently detailed structural information on the crystal structures. Thus, we have used AFM for a detailed analysis of morphology and microstructure of the periodically modulated crystalline structures. In Figure 3a, we display such details for structures grown in ca. 50 nm thick film at 160 °C. Consistent with result of Figure 1, periodic height modulations within structures of hexagonal symmetry were detected by AFM (Figure 3a). As seen in Figure 3b, the elevations in the crystalline structure consisted of stacked flat-on lamellae. Such stacks were periodically repeated, leading to the observed height-modulated crystal. The corresponding cross-sectional height profile (Figure 3c) showed that these stacked lamellae were parallel to each other and had an identical thickness (ΔhL ≈ 9 nm). Stacking of lamellae in the direction normal to the lamellar surface represents a mechanism for growing polymer crystals in three dimensions. As all lamellae were oriented parallel to the substrate, these crystalline structures were not birefringent, confirming the absence of lamellar twisting.26,38 As the C


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Figure 4. Characterizing the crystal−melt interface. (a) AFM height cross-sectional profiles of the periodically modulated crystal shown in Figure 3a, taken along the diagonal (blue line) and the off-diagonal (red line) as indicated through the arrows in the AFM image Figure 3a shown in the inset. The profiles along diagonal and off-diagonal directions were merged by multiplying the distance of the off-diagonal part by 1/cos 30° (≈ 1.15) (refer to Figure S2). (b) Details of the region of the height profile marked by a dotted rectangle in (a), indicating a depletion zone ahead of the crystal front and the halo surrounding the depletion zone. Dd, Dw, and hB represent the depth, width, and thickness of the molten polymer layer at the deepest point of the depletion zone, respectively. ΔH(ti) represents the height of the stack of crystalline lamellae closest to the growth front at time ti in the course of its formation. (c) Cartoons show the development of periodically stacked lamellae during the growth of a periodically modulated crystal in thin films. (d) Molecular details corresponding to the region in (c) marked by the red dashed rectangle summarizing the growth process, distinguishing between molten (green) and crystalline (blue) regions. The self-induced nucleation process is sketched by the red crystalline stems.

heights of the stacks along the direction of the diagonals were higher than that of the height of the stacks in the off-diagonal directions. To follow the formation of stacks of correlated lamellae in time, we have mounted a hot stage under an AFM and measured topographic and phase images in situ at TC. The growth process started with the formation of a rounded center, followed by the periodic appearance of stacks of lamellae. The minimum thickness of the regions in between these stacks was found to be significantly lower than the thickness of the surrounding molten film and often had the thickness of a single lamella. Once the width of this thin region ahead of the growth front reached a certain value, a new stack started to emerge by piling up many lamellae. The process was repeated in the course of time, ultimately leading to the observed periodically modulated crystalline structure (refer to Figure S3). Figures 5a−d show a series of AFM height images of a periodically modulated structure formed at 150 °C in a ca. 75 nm thick film. The height profiles of the crystal were determined during growth as indicated by black, red, blue, and pink dashed lines in Figures 5a−d, respectively. As an arbitrary reference, we started with the height profile measured at time t0 (black line in Figure 5e). The beginning of the formation of another stack became visible about 4 min later (red line in Figure 5e). As time progressed, the newly formed stack advanced both laterally but also vertically (blue and pink lines in Figure 5e). We have measured the increase in height of the stack [ΔH(ti) = H(ti) − hB] from the series of AFM height profiles as described in Figure 4b. hB and H(ti) represent the thickness of the molten polymer layer at the deepest point of the depletion zone and the height of the stack of lamellae in the course of crystal growth, respectively (refer to Figure S4).

underlying mechanism for inducing the formation of stacks of correlated lamellae, a morphology-based self-induced nucleation mechanism on the fold surface of lamellar crystals has been identified.10 Self-induced nucleation and subsequent growth of the stacked lamellae are significantly influenced by the amount of available molecules, which depends on the initial film thickness. To quantify the periodic height modulations of the crystalline structures, we present in Figure 4a AFM height cross-sectional profiles for the crystal shown in Figure 3a. These height profiles illuminate the alternating formation of periodic peaks and valleys within the crystalline structure, highlighting periodic variation in number of stacked lamellae associated with the kinetics of crystal growth, mainly controlled by the diffusion process of polymers toward the crystal.9 The formation of additional lamellae in a stack, allowing for growth in the vertical direction, requires a sufficient amount of available molecules in the surrounding reservoir. As a result, we may anticipate that the variations in height of the crystalline stack originate from the regular change in the amount of available polymers. In the AFM height cross-sectional profiles (Figure 4), we can clearly identify a depletion zone and a halo ahead of the crystal front. We have characterized the depletion zone by defining its depth (Dd) and width (Dw) (see Figure 4b), which are parameters controlled by the influx of polymers to the crystal growth front, where these polymers get integrated into the crystal.4 At a quite early stage of crystallization, i.e., just after nucleation, a large amount of molten polymer chains was available in regions close to the growing crystal. Thus, the central part of the crystalline structure shown in Figure 3a was higher than the height of the subsequent stacks (see Figure 4a). In agreement with Figure 1, Figure 4a shows that the D


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gradient in the depletion zone, ahead of the crystal growth front, is related to the gradient in number of molecules available for attachment. Thus, the influx of polymers toward the growth front can be related to the depth of the depletion zone (Dd). The variation of Dw and Dd with crystallization time is displayed in Figure 7.

Figure 5. Temporal evolution of the crystal height during growth. (a− d) Series of AFM height images (image size: 21 × 10 μm2) observed in situ for a crystal growing at TC = 150 °C in a ca. 75 nm thick film for different crystallization times ti (as indicated in (e)), emphasizing the details of the structures formed at the growth front. (e) AFM height cross-sectional profiles in the direction of the dashed arrows shown in (a−d). The inset emphasizes the region between the green dotted lines where a new stack of lamellae is forming at the growth front.

Figure 7. Periodic variations of the depletion zone. Variations of the depth (Dd) and the width (Dw) of the depletion zone with crystallization time (ΔtC). Dd and Dw were determined according to the definitions described in Figure 4b. The crystal was grown at 150 °C in a ca. 75 nm thick film.

Figure 6 shows variations of the height (ΔH) and radial growth velocity (G) of the growth front of the crystal as a

For a given diffusion rate, the total number of molecules (per unit time) getting attached to the crystal growth front is significantly affected by Dw and Dd and hence influences the morphology of the crystal structures. For instance, as Dd becomes larger, the supply of polymer to the fold surface is slowed down. Independent of Dd, the basal crystalline lamella is always in contact with molten polymers and advances with time, even if the minimum thickness (hB) of the depletion zone is less than the thickness (ΔhL) of the basal lamella. As more polymers diffuse from the surrounding molten film into the depletion zone, the amount of available polymers increases and nucleation on the fold surface of the basal lamella starts again, initiating the formation of another stack of crystalline lamellae. The periodic morphology of the resulting crystalline structure implies that the repeated nucleation of such stacks and their growth in the vertical direction are directly related to the variation of Dw and Dd, defining the size of the depletion zone. A stack grew until Dd reached its maximal value. Once hB became as small as approximately the thickness (ΔhL) of a single lamella, only the basal lamella continued to grow. However, as the growth of only one lamella allowed to integrate less polymers into the crystalline structure, the depletion zone was replenished with polymers diffusing from the surrounding molten film into the depletion zone. Thus, hB increased again. Through the mechanism of self-induced nucleation on the basal lamella, the formation of a new stack of crystalline lamellae was initiated. This process repeated periodically, resulting ultimately in the formation of a periodically modulated crystalline structure. To quantify and summarize our results better, we performed crystallization experiments at various temperatures on films of various thicknesses, ranging from 30 to 140 nm. As a parameter for characterizing the morphology, we used the spatial period (λ) of the modulations, i.e., the mean distance between neighboring stacks of lamellae. For better statistics, we defined λ as the distance (L) from the center of the crystalline structure to the growth front (along the diagonals for hexagonal shapes) normalized with the number (N) of

Figure 6. Periodic variations in crystal growth. The variation of the height of the crystal (ΔH) and the growth rate (G) with crystallization time (ΔtC). The symbols triangles, stars, diamonds, and circles represent the successive stacks of lamellar crystals S1, S2, S3, and S4, respectively, indicated on the AFM height image (34 × 10 μm2) on the top of the graph. The crystal was grown at 150 °C in a ca. 75 nm thick film.

function of ΔtC (= tC − t0, where t0 defines the time at which we began to follow the growing crystals in real time). It can be seen that simultaneously to the increase in the height of the stack of lamellar crystals, G(tC) decreased. Consequently, when the height of the crystalline stack reached its maximum value, we observed a minimum in the growth rate, followed by a renewed increase in G(tC) and the formation of another stack of correlated lamellae. This process repeated periodically in the course of the growth process, resulting in periodic height modulations on the crystalline structure. During the growth process, polymers had to pass the depletion zone before they reached the crystal growth front. The diffusion length (l0) is proportional to Dτa , with D being the diffusion coefficient of the polymers in the film and τa being the time interval between two polymers getting sequentially attached to the crystal. l0 is related to the width of depletion zone (Dw), which is also determined by the interfacial kinetics.4 It can be conceived that the film thickness E


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Figure 8. Thickness (h) and temperature (ΔT) dependence the periodicity (λ) of the height modulations: Periodicity (λ) of periodically heightmodulated crystalline structures as a function of (a) normalized film thickness (h/cuc) and (b) normalized reciprocal value of the degree of undercooling

∞ Tm ΔT

( ). The dashed lines represent the fits of eqs 1 and 2 for (a) and (b), respectively, to the experimental data (symbols). The error

bars of λ were derived from the analysis of more than ten independent measurements.

periodic stacks along this path, i.e., λ = L/N. In Figure 8, we display the thickness and temperature dependence of the period λ. In Figure 8a, we plotted λ as a function of normalized film thickness (h/cuc) for all values of TC. As an appropriate normalization constant for film thickness, we used the unit cell parameter along the chain axis (cuc) for isotactic polystyrene, where cuc = 0.66 nm.24,47 The observed variations of λ(h/cuc) seen in Figure 8a suggested the existence of a power-law relation between λ and h: λ(h) = ATC

ij h yz jj zz jj c zz k uc {

β

(1)

Figure 9. Master plot allowing to predict variations of the period of height modulations as a function of h and ΔT. The periodicity

where ATC (in units of micrometers) is a constant for a given value of TC. The mean value for the exponent β = 0.7 ± 0.05 was obtained by averaging the exponents obtained from fitting eq 1 to all curves in Figure 8a individually. Clearly, λ values, and thus values of ATC, were larger for higher crystallization temperatures, indicating a relation between λ and TC (refer to Figure S5). In Figure 8b, we show the variation of λ with temperature, for films of different thicknesses, as a function of normalized reciprocal degree of undercooling,

Tm∞ ΔT

( ). Here,

T∞ m

(λ(h,ΔT)) is plotted as a function of

i αT ∞ y λ(ΔT ) = Ah expjjjj m zzzz k ΔT {

ij h yz i αT ∞ y λ(h , ΔT ) = λ 0 jjj zzz expjjjj m zzzz j c uc z k ΔT { k {

β

(3)

where λ0 is a fitting constant. An intriguing collapse of all data points onto a single master curve (having a common slope of λ0 = 12 ± 0.5 nm) was observed. Apart from the observed quantification, we believe that eq 3 provides important insight into the processes underlying the observed periodic modulations. For instance, for the same iPS, an exponential decay of the self-induced nucleation probability with reciprocal degree of undercooling was reported. The number density (nS) of self-induced nuclei was found to be inversely proportional to the square of the width of the side branches of the underlying basal lamella and decreased with decreasing degree of undercooling.10 A similar temperature dependence of λ and nS supports our central assumption of a correlation between the observed periodic modulation and the nucleation of secondary lamellae. While a periodic modulation of polymer crystals has been observed before,30,50 we performed to our knowledge the first quantification of λ as a function of h and ΔT. Furthermore, we presented clear indications for the underlying self-induced nucleation mechanism, which provides possibilities to tune crystalline morphologies in a systematic way.

= 242

(2)

αTm∞ ΔT

( ) exp( ), resulting in the h c uc

∞ αT m ΔT

β

where Ah (in units of micrometers) is a constant for a given value of h. By fitting eq 2 to the data of Figure 8b, we have obtained, α = 0.75 ± 0.06 (averaging the value of α obtained from fitting eq 2 to all curves in Figure 8b individually). From Figure 8, it became clear that λ was affected by the rate of transport of molten polymers toward the growth front of crystal, defined by both h and ΔT. Motivated by this observation, we combined eqs 1 and 2 and plotted in Figure 9 λ(h,ΔT) as a function of

h c uc

line represents a fit of eq 3 to the experimental data (symbols), yielding a slope of 12 ± 0.5 nm.

°C is the equilibrium melting temperature of iPS, and ΔT = T∞ m − TC is the degree of undercooling. For a proper modeling of the data, we have used an exponential function of the following form: 48,49

β

( ) exp( ). The dashed

relation F


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(6) Xu, J.; Guo, B. H.; Zhang, Z. M.; Zhou, J. J.; Jiang, Y.; Yan, S.; Li, L.; Wu, Q.; Chen, G. Q.; Schultz, J. M. Direct AFM Observation of Crystal Twisting and Organization in Banded Spherulites of Chiral poly(3-Hydroxybutyrate-Co-3-Hydroxyhexanoate). Macromolecules 2004, 37 (11), 4118−4123. (7) Liu, Y. X.; Chen, E. Q. Polymer Crystallization of Ultrathin Films on Solid Substrates. Coord. Chem. Rev. 2010, 254 (9), 1011−1037. (8) Kailas, L.; Vasilev, C.; Audinot, J.-N.; Migeon, H.-N.; Hobbs, J. K. A Real-Time Study of Homogeneous Nucleation, Growth, and Phase Transformations in Nanodroplets of Low Molecular Weight Isotactic Polypropylene Using AFM. Macromolecules 2007, 40 (20), 7223−7230. (9) Duan, Y.; Zhang, Y.; Yan, S.; Schultz, J. M. Situ AFM Study of the Growth of Banded Hedritic Structures in Thin Films of Isotactic Polystyrene. Polymer 2005, 46 (21), 9015−9021. (10) 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), 237801. (11) Jukes, P. C.; Das, A.; Durell, M.; Trolley, D.; Higgins, A. M.; Geoghegan, M.; Macdonald, J. E.; Jones, R. A. L.; Brown, S.; Thompson, P. Kinetics of Surface Crystallization in Thin Films of Poly (Ethylene Terephthalate). Macromolecules 2005, 38 (6), 2315− 2320. (12) Reiter, G. Some Unique Features of Polymer Crystallisation. Chem. Soc. Rev. 2014, 43 (7), 2055−2065. (13) Hatwalne, Y.; Muthukumar, M. Chiral Symmetry Breaking in Crystals of Achiral Polymers. Phys. Rev. Lett. 2010, 105 (10), 107801. (14) Reiter, G.; Strobl, G. R. Progress in Understanding of Polymer Crystallization; Springer: Berlin, 2007; Vol. 714. (15) Reiter, G.; Sommer, J.-U. Polymer Crystallization in Quasi-Two Dimensions. J. Chem. Phys. 2000, 112 (9), 4376−4383. (16) Sommer, J. U.; Reiter, G. Polymer Crystallization in Quasi-Two Dimensions. II. Kinetic Models and Computer Simulations. J. Chem. Phys. 2000, 112 (9), 4384−4393. (17) Glicksman, M. E.; Lupulescu, A. O. Dendritic Crystal Growth in Pure Materials. J. Cryst. Growth 2004, 264 (4), 541−549. (18) Keller, A. Polymer Single Crystals. Polymer 1962, 3, 393−421. (19) Grozev, N.; Botiz, I.; Reiter, G. Morphological Instabilities of Polymer Crystals. Eur. Phys. J. E: Soft Matter Biol. Phys. 2008, 27 (1), 63−71. (20) Blundell, D. J.; Keller, A.; Kovacs, A. J. A New Self-Nucleation Phenomenon and Its Application to the Growing of Polymer Crystals from Solution. J. Polym. Sci., Part B: Polym. Lett. 1966, 4 (7), 481− 486. (21) Kovacs, A. J.; Straupe, C. Isothermal Growth, Thickening and Melting of Poly(ethylene-Oxide) Single Crystals in the Bulk: III. Bilayer Crystals and the Effect of Chain Ends. J. Cryst. Growth 1980, 48 (2), 210−226. (22) Point, J. J.; Kovacs, A. J. A Critical Look a T Some Conceptual Aspects of Kinetic Theories of Polymer Crystal Growth. Macromolecules 1980, 13 (2), 399−409. (23) Hong, S.; Macknight, W. J.; Russell, T. P.; Gido, S. P.; Keck, W. M. Orientationally Registered Crystals in Thin Film Crystalline/ Amorphous Block Copolymers. Macromolecules 2001, 34 (8), 2398− 2399. (24) De Rosa, C.; Auriemma, F. Crystals and Crystallinity in Polymers: Diffraction Analysis of Ordered and Disordered Crystals; John Wiley & Sons, Inc.: Hoboken, NJ, 2013. (25) Kovacs, A. J.; Straupe, C.; Gonthier, A. Isothermal Growth, Thickening, and Melting of Polyethylene Oxide) Single Crystals in the Bulk. II. J. Polym. Sci., Polym. Symp. 1977, 59 (1), 31−54. (26) Poudel, P.; Chandran, S.; Majumder, S.; Reiter, G. Controlling Polymer Crystallization Kinetics by Sample History. Macromol. Chem. Phys. 2018, 219 (3), 1700315. (27) Wang, Z.; Alfonso, G. C.; Hu, Z.; Zhang, J.; He, T. Rhythmic Growth-Induced Ring-Banded Spherulites with Radial Periodic Variation of Thicknesses Grown from Poly(ε-Caprolactone) Solution with Constant Concentration. Macromolecules 2008, 41 (20), 7584− 7595.

CONCLUSIONS We observed the formation of crystalline structures with periodic height modulations in thin films of iPS, resulting from the periodic formation of stacks of correlated lamellar crystals. We proposed that growth of these stacks in the direction vertical to the fold surface of the basal lamella was initiated through a self-induced nucleation mechanism controlled by the morphology and growth of the basal crystalline lamella. Following crystal growth in situ revealed that periodic stopping of growth of stacked lamellae and subsequent reinitiation of a new lamellar stack were accompanied by periodic changes of the size of the depletion zone ahead of the crystal growth front. The spatial period (λ), i.e., the mean distance between neighboring stacks of lamellae, was found to depend on film 0.7 ± 0.05

, and the degree of underÅÅ (0.75 ± 0.06)Tm∞ ÉÑÑ ÑÑ. Our experiments cooling (ΔT), λ ∼ expÅÅÅ ÑÑÖ (ΔT ) ÅÇ suggest that self-induced nucleation is capable of generating long-range correlations between stacks of crystalline lamellar layers as expressed by periodic height modulations.

thickness (h), λ ∼

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( )Ä h c uc

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01366. Supporting text and Figures S1−S6 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (G.R). ORCID

Sivasurender Chandran: 0000-0003-0547-0282 Günter Reiter: 0000-0003-4578-8316 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the fruitful discussions with Professor Murugappan Muthukumar, Professor Jun Xu, and the members of the International Research Training Group (IRTG-1642)−Soft Matter Science, funded by Deutsche Forschungsgemeinschaft (DFG). Funding by the BadenWürttemberg Stiftung is acknowledged. S.C. acknowledges funding via DFG through the project CH 1741/2-1.

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Formation of Periodically Modulated Polymer Crystals

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