acs.macromol.6b00473

Article pubs.acs.org/Macromolecules

Interface and Confinement Induced Order and Orientation in Thin Films of Poly(ϵ-caprolactone) Wilhelm Kossack,*,† Anne Seidlitz,‡ Thomas Thurn-Albrecht,‡ and Friedrich Kremer† †

Fakultät für Physik und Geowissenschaften, Universität Leipzig, Linnéstr. 5, 04103 Leipzig, Germany Institut für Physik, FG Experimentelle Polymerphysik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle/Saale, Germany

‡

S Supporting Information *

ABSTRACT: Infrared transition moment orientational analysis (IR-TMOA), X-ray diffraction (XRD), and model calculations are combined to study interface and confinement induced order and orientation in thin (h ≈ 11 μm) films of poly(ϵ-caprolactone) (PCL), as prepared by drop-casting on silicon wafers. Depending on the crystallization temperature, 303 K ≤ Tx ≤ 333 K, nonbanded spherulites with a diameter of 1 μm ≤ dS ≤ 500 μm form. Macroscopic order of the crystalline lamellae is imposed by interfacial layers and geometrical confinements of the spherulitc structures (dS > h): radial crystal growth is restricted to a disc of aspect ratio dS/h. Order is quantified by IR-TMOA and XRD pole figure measurements, which both rely on the relative orientation of the sample and the incident radiation and measure, in the case of PCL, the orientation distribution of complementary crystal directions. This enables one to (1) correlate the directions of the transition moments with the crystal axes and (2) estimate the volume fractions of flat-on or edge-on lamellae as induced by the substrate or the free interface as well as the fractions of surface induced or bulk nucleated spherulites in dependence on Tx. It turns out that the contribution of substrate induced spherulitic structures rises with Tx = 323 K up to a value of ∼12 vol %, whereas no indications of edge on lamellae at the free surface are found. For Tx ≤ 308 K nonconfined spherulites (dS < h) dominate the morphology, and furthermore no substrate induced layer is found.

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INTRODUCTION Poly(ϵ-caprolactone) (PCL) is a common biodegradable synthetic polymer.1,2 It is slightly hydrophobic and therefore slowly bioresorbed: an ideal material for temporary implants, fillings, and long-term drug delivery.3−8 Furthermore, PCL is a model system to study polymer crystallization in bulk9−13 and thin films14−16 as well as in block copolymers6,7,13,17 and blends.18−22 This is because of the moderate melting (Tm ≈ 333 K) and glass transition temperature (TG ≈ 213 K) as well as a reasonable thermal stability (up to 530 K).5,14 PCL exhibits an orthorhombic crystal structure that is similar to the one of polyethylene (PE) due to similar chemical structures9,23 (Figure 1). The lattice parameters of PCL are a = 7.496 Å, b = 4.974 Å, and c = 17.297 Å, and the ones of PE are a = 7.40 Å, b = 4.93 Å, and c = 2.534 Å.9,23−25 The difference in c perfectly correlates with the 7 times longer monomer. In contrast to PE, PCL is a so-called crystal fixed polymer and exhibits essentially no intracrystalline mobility,9,11,26,27 presumably due to the strongly polar carbonyl groups undergoing intermolecular coupling. In bulk, PCL crystallizes in isotropic spherulitic structures, and similar objects are visible in micrometer thick, supported films (Figure 2). An ideal spherulite spreads from a single homogeneously nucleated seed until the growth fronts hit an external boundary, like the sample’s surface or neighboring lamellae. Therefore, spherulitic crystallization is a kinetically © 2016 American Chemical Society

controlled process that leads to prismatic shaped structures when confined to thin films.32,33 By branching, bending, and twisting the lamellae fill the full three-dimensional space in a centrally symmetric fashion, with the direction of fastest growth ([010]) aligned radially (Figure 2a).14,32,34−38 Random smallangle twists of the lamellae around the radii lead to nonbanded spherulites, as commonly observed in PCL.34,35,38,39 Presumably, another crystallization step follows involving further, secondary branching.32,40−42 In films with a thickness ≤200 nm significant polymer− surface interactions and extended flat on crystallites of a truncated lozenge shape are observed.14,18,21,42−45 These structures exhibit their [001]-direction ( c̲ ) parallel to the surface normal and gradually adopt spherulitic order upon increasing the film thickness. At the free surface (polymer−air interface) edge on lamellae, predominate, i.e., [100]-direction ( a̲ ) along the surface normal.40,46,47 A general introduction to the field of spherulites can be found in the literature.32,40,48 Only few and furthermore only qualitative IR-based studies exist on the structure of spherulites (especially for the case of PCL).49 This may be related to the fact that the wavelength within the fingerprint region (wavelength about 3−15 μm) is Received: March 5, 2016 Revised: April 8, 2016 Published: April 20, 2016 3442

DOI: 10.1021/acs.macromol.6b00473 Macromolecules 2016, 49, 3442−3451

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different molecular moieties within a spherulite is deduced targeting insights into the mechanism of spherulitic crystallization.

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EXPERIMENTAL SECTION

PCL was purchased from Scientific Polymer Products Inc. (Ontario, NY) (Figure 1) and exhibits a molecular weight of 77.4 kg/mol and a polydispersity of 1.42, as measured by gel permeation chromatography. Films are prepared by drop-casting a chloroform (purity ≥99%, Carl Roth GmbH, Karlsruhe, Germany) solution (concentration ≈2%) onto a nonconductive silicon wafer (Active Business Company GmbH, Munich, Germany). These substrates are transparent in the IR spectral region and do not interfere with XRD reflection measurements. Samples are dried at 363 K and a pressure in the range of mbar, before quenching them to the desired crystallization temperature, Tx, and leaving them for isothermal crystallization. Four different films are obtained: I08 (Tx = 308 K), I313 (Tx = 313 K), I318 (Tx = 318 K), and I323 (Tx = 323 K). One film, NI333, is left in the vacuum after annealing, where it cools down to ambient temperatures within about 1 day, resulting in even larger spherulites (dS ≈ 500 μm). This preparation corresponds to a high Tx ≲ 333 K, which decreases with the distance from the center of the spherulite, i.e., nonisothermal crystallization.

Figure 1. (a) Stick and ball model of the repeat unit of PCL obtained by geometry optimization using density functional theory (B3LYP functionals and 6-311G basis sets)28−31 and (b) crystalline unit cell (framed in red) as proposed by Bittiger et al. and Chatani et al.23,24 Dark and light gray spheres respectively refer to carbon and hydrogen atoms, whereas red ones depict oxygen. The direction of the transition moments (TMs) underlying the discussed IR vibrations (Table 1) are indicated by arrows.

Table 1. Assignments of IR Vibrations of PCLa −1 ν/cm ̅

assignments

ν(CH)

2850−2960

ν(CH), a and c

⊥MC

νc(CH2) ν2c(COC)

2895 1295

⊥MC, ||(CO) ||MC, c̲

″ (COC) ν1a

970

ν′1c(COC)

963

′ (COC) ν1a

957

ν1c(COC)

934

νsym(CH2), c d(CH) + ν(CCO), c ν(CCO) + r(CH2), a ν(CCO) + r(CH2), c ν(CCO) + r(CH2), a ν(CCO) + r(CH2), c

orientation

⊥MC ||MC, || c̲

⊥MC, ⊥ c̲

ref 25, 43, 57 57 19, 43, 58 19, 57, 59 19, 57, 59 19, 57, 59 19, 57, 59

d assigns deformation vibrations, r rocking, and ν stretching. a refers to transition moments (TMs) originating from amorphous units, whereas c refers to crystalline regions. The symbol referring to the vibration, the spectral position (ν̅c) at 396 K, and orientation of the TM with respect to the main-chain (MC) or the crystal directions are given in the first three columns. The orientation of the TM of ν(C O) is not exactly perpendicular to the MC but may exhibit an angle of ≳80°.60 a

Figure 2. Micrographs of a single spherulite of PCL. The insets (b) and (c) show magnifications of the framed region (83 × 83 μm2) in the center of (a). Picture (a) is taken with crossed, (b) with parallel, and (c) with only one polarizer. The contrast is enhanced in (b) and (c), where additionally the gray scale has been inverted. The center of the spherulite is slightly below and right of the cross hairs (visible in all panels). The 4-fold symmetry in (a) and (b) is not a characteristic of the sample but of the polarizing optics. Especially, in (c) the branched lamellae can be seen.

The thickness of the samples is h ≈ 11 ± 1 μm. The diameter of the spherulites, dS, depends on the density of nucleation seeds, which is essentially controlled by Tx in our experiment.34 We determine the average dS for the different films from their micrographs. For I313 we find dS = 28 μm with a rather wide standard deviation of σ = 15 μm. For I318, I323, and NI333 one finds dS ± σ ≈ 97 ± 10, 200 ± 40, and 450 ± 50 μm (Table 2 and Supporting Information). I308 exhibits only spherulites with a diameter below 10 μm. The distributions directly reflect the spatial separation of the spontaneously formed nucleation seeds, which is difficult to control. Fourier transform infrared (FTIR) spectra are recorded with a BioRad-FTS-6000 spectrometer and a resolution of 2 cm−1. Vibrational absorption bands are fitted by sums of pseudo-Voigt profiles after subtraction of a linear tangential baseline (Figure 3 and Table 1).52 Infrared-transition moment orientational analysis (IR-TMOA) is performed after attachment of a rectangular aperture to select a region of homogeneous spherulite size and sample thickness.50,51,53,54 The refractive index of PCL is taken to be n ≈ 1.48, being an average of values reported for similar substances in the VIS (1.46 for poly(R)(−)-β-methyl-ϵ-caprolactone55 and 1.463 for the monomer ϵ-

comparable to the characteristic sizes of spherulites, if not larger. Therefore, molecular order cannot be resolved spatially by IR spectroscopy. Here, the macroscopically averaged threedimensional, molecular order parameter tensor of amorphous and crystalline moieties is analyzed by infrared transition moment orientational analysis (IR-TMOA) and X-ray diffraction (XRD) based pole figures (XRD-PF) for 11 μm thick films with spherulites of diameter 1 ≤ dS ≤ 500 μm.50,51 This combination of complementary techniques allows to estimate fractions of differently nucleated lamellae, heterogeneously (at the substrate) or homogeneously (in the bulk), and their orientational correlation with neighboring (or overgrowing) lamellae. Furthermore, the order parameter of 3443


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Table 2. Order Parameter Szz = Sext in 10−2 along the Surface Normal (ẑ)̲ of the Indicated Crystal Directions As Obtained by IRTMOA and XRD-PF and As Calculated Are Given for Spherulites of Diameter to Height Ratio (dS/h), i.e., Different Crystallization Temperatures (Tx)a XRD [10−2] Tx [K]

dS/h

≤333 323 318 313 308

40 18 10 2.5 ≤1

[200] 9 7 2

IR-TMOA [10−2]

[110]

ν1c

−22 −17 −4

−18 −17 −21 −3 1

bulk [10−2]

surf ind (12%) [10−2]

νc(CH2)

ν2c

[100]

[010]

[001]

[110]

[100]

[010]

[001]

[110]

−26 −20 −5 −4

46 26 25 14 −1

19 18 18 11 −3

−38 −37 −35 −22 5

19 18 18 11 −3

−20 −20 −19 −12 3

10 10 10 −3 −18

−38 −35 −32 −3 30

27 26 22 6 −11

−23 −22 −19 −3 15

ν2c refers to the order of [001] directions (Figure 1 and Table 1), νc(CH2) to TMs perpendicular to c̲ and parallel to the CH2 stretching in ̲ b̲ plane. The uncertainty of the IR and XRD data is in the range of 0.05 crystallites, whereas TMs of ν1c are not perpenticular to c̲ but within the a− and 0.1, respectively. The column labelled “surf ind” refers to theoretical values for model spherulites nucleated at the substrate. 12 vol % of these are nucleated from flat on lamellae and have a [100] direction parallel to the substrate (Figure 8e). For a ratio of dS/h = 40, an increase of this fraction to 40 vol % leads to order parameters of 0.40 and −0.23 for [001] and [110], respectively. For dS/h = 2.5, a mixture of 44 vol % bulk-like, 44 vol % substrate induced, and an unchanged 12 vol % fraction of flat on lamellae leads to an Szz of 0.02, 0.11, and −0.07 respectively for [100], [001], and [110]. “Bulk” columns correspond to a model with the nucleus in the centre of the film and without any surface interactions (cf. Figure 8c). a

Figure 3. IR spectra of PCL films on Si crystallized at different temperatures, Tx. Spectra are stacked vertically from bottom up: Tx = 303 K (light blue), Tx = 308 K (cyan), Tx = 313 K (light green), Tx = 318 K (red), Tx = 323 K (brown), and Tx ≤ 333 K (black). Dashed and solid lines respectively refer to s- and p-polarization of an inclination of −50°. Cf. inset in Figure 4. (a) and (b) depict different spectral regions. Spectral positions of the discussed IR-active vibrations are marked by vertical lines (Table 1). caprolactone56) and values of chemically similar polymers (e.g., PE) in the infrared (IR).51 Inclination was varied within β = [−60°,−50°, ..., 60°] and polarization within Φ = [0°, 30°, ..., 180°].50 Additionally, laterally resolved (focused), polarized IR measurements at various positions with a spot sizes between 25 × 25 and 300 × 300 μm2 are performed. And neither does the polarization dependence indicate lateral inhomogeneities of orientation on a length scale above dS; nor do the absorbance values hint to thickness variations larger than 5%. The X-ray diffraction pole figures (XRD-PF) are also obtained under a rotation/inclination of the sample film by β ∈ [0°,10°, ..., 80°] using an Empyrean diffractometer (PANanlytical, Almelo, Netherlands) with an angular resolution of 0.3°.61,62 Three reflections are discussed here: the (110), (111), and the (200) diffraction peak (Figure 4). The former two are found at 2θ = 21.4° and 2θ = 22.1°.23,63 The (200) reflex appears at 2θ = 23.7° and is actually an overlap of the dominating (200) and the weaker (201), (112), (013), and (104) reflections. According to the structure factors reported in the pioneering work of Bittiger et al.,23 the (200) planes contribute about 2/3 to the peak.23,64 Such overlap should lead to an underestimation of the order parameter of [200]. The XRD data are corrected for changes in the XRD absorption and path length due to inclination (β).61 The integrated areas of the lattice reflections are obtained by fitting Gaussian profiles to them after subtraction of a linear baseline. IR-TMOA and XRD Pole Figures. X-ray Diffraction and IR spectroscopy are fundamentally different methods. Both are used here to quantify order: the former measures the orientation distribution of

crystal lattice planes, i.e., of periodic electron densities, whereas the latter reveals the quadratically averaged orientation distribution of vibrational transition moments (TMs). Therefore, IR is a moietyspecific probe sensing local TMs of different molecular units (Table 1 and Supporting Information), whereas XRD senses periodic distances. In particular for PCL, the area of the studied diffraction peaks is proportional to the number of (110) and (200) lattice planes with a normal parallel to Δ k̲ after the application of corrections the change in XRD absorption and the change in path length (Figure 5b,d).61 For IR-TMOA the corresponding area scales with the cos2 of the angle between the direction of the TM (e.g., [001] = c̲ in Figure 5a,c) and the eletric field. Therefore, a different variation upon tilting is found. In summary, complementary information is obtained by IR-TMOA and XRD-PF respectively being distance and molecular specific. The presented order parameter tensors, S, are three-dimensional analogues of Herman’s orientation function.50,62 In particular, they record the quadratic average of the number of TMs or lattice planes (with a direction v)̲ oriented in all three spatial directions ̂ ( i ̲ , j̲ ∈ [ x ̂ , y ̂ , z]).

⎛3 1⎞ Sij = C −1⎜ ⟨( v̲ · i ̲ )( v̲ · j̲ )⟩ − ⎟ ⎝2 2⎠ C=

∑ i=x ,y ,z

3444

(1a)

⟨( v̲ · i ̲ )2 ⟩ (1b) DOI: 10.1021/acs.macromol.6b00473 Macromolecules 2016, 49, 3442−3451

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Figure 4. XRD spectra of supported PCL films are shown for various tilt angles: β = 0° (dots), 20° (solid lines), 40° (dashed lines), and 60° (dash-dotted lines). The upper or lower sets of spectra respectively refer to Tx = 323 or 313 K. Additionally, fits according to sums (red) of Gaussian profiles (green) are shown after subtraction of a linear baseline for the spectra for β = 40°. The vertical dashed lines mark the positions of the (110) and (200) reflections respectively at 2θ = 21.5° and 23.8°. Apparently, the position of both reflexes shifts with increasing β to lower values of 2θ. Such shifts indicate problems with the measurement geometry, which are reported to appear regularly for β ≥ 70°.61 The geometry of the setup is depicted in the inset: IR and X-ray beam are shown respectively as blue and black arrows. Tilt angle (β) and sample coordinate system ( x ̂, y )̂ are also indicated (cf. also Figure 5).

Figure 5. (a) Exemplary comparison of IR-TMOA and XRD pole figures (XRD-PF). The sample (gray cuboid) and its coordinate system (red arrows, x ̂, y ,̂ z)̂ are both tilted around the x ̂-axis by β (green arrow). IR and XRD beams are respectively depicted as blue and black arrows. For the former the plane of polarization is also given ̂ and ⊥ = x ̂). Panels (b) and (c) show different (|| ∈ y − ̂ z-plane exemplary arrangements of lamellae (red boxes) with indicated lattice planes and transition moments (arrows) on a substrate (gray cuboid). Such simplified model systems would lead to the spectra (vertically stacked) shown in (d) and (e). (d) The area of the IR absorption bands is related to the components of all TMs along the electric field (E̲ ), (e) whereas the area of the diffraction peak scales with the number of lattice planes parallel to Δ k̲ .

⟨...⟩ refers to the average over all molecules, and C is a normalization constant.50,62 If S is a diagonal matrix, the principal axes of the orientation distribution agree with the coordinate system. Rotational symmetry is found when S is (or can be transformed into) a diagonal matrix with two identical elements. In this case the third element of S is the well-known uniaxial and nematic order parameter of Herman. The area of IR absorption bands is proportional to ⟨( v̲ · i ̲ )( v̲ · j̲ )⟩, whereas for XRD-PF one obtains S by integration of the area (I) of the diffraction peak (Figure 4, eq 2).62

about 20 μm, the same order of magnitude as the reported pitches for diluted and pure PCL (25−100 μm).34,38,39 Such banding is not observed in the samples I323−I308 (Tx ≤ 323 K), which is in agreement with previous studies. 34,38 Consequently, the studied structures are treated as nonbanded spherulites, as further verified by atomic force microscopy (AFM, cf. Supporting Information) and reported in the literature.37,65 Spherulitic growth proceeds along the crystals’ b̲ -axes and is limited by the finite thickness, which leads to nonspherical, but centrosymmetric objects.14,34,36,38 This confinement of the growth direction to the sample plane is enhanced with an increasing ratio of spherulite diameter to film thickness and leads to a macroscopic alignment of the crystalline b̲ -axes within the sample plane. Fewer b̲ -axes along the substrate’s normal are tantamount to fewer a̲ - and c̲ -axes parallel to the film plane, as the three crystal directions are mutually perpendicular. And consequently, we expect preferential order of the a̲ - and c̲ -axes along z .̂ IR-TMOA. The FTIR spectra and corresponding integrated absorbances reveal an increasing anisotropic orientation with increasing size of the spherulitic structures and crystallization temperature, Tx (Figures 3 and 6). As expected from the symmetry of the system, all samples are nearly rotationally symmetric with an extraordinary axes of the orientation distribution along the surface-normal, z .̂ Therefore, only the corresponding component of the order parameter tensor is given (Szz = Sext, Table 2), which is identical to the nematic order parameter (Herman’s orientation function).50,54 Slight biaxialities (Sxx − Syy < 0.04) are attributed to the finite size of

π /2

∫ dβI(β) cos2 β sin β 1 (2Szz + 1) = 0 π /2 3 ∫0 dβI(β) sin β ∝ ⟨( a̲ · z̲ )2 ⟩

(2)

In summary, for IR-TMOA and XRD-PF the three-dimensional order is quantified based on the dependence of the peak areas on the relative orientation of sample and electric field (IR-TMOA: Figures 5 and 6) or scattering vector (XRD-PF: Figures 5 and 7). Both techniques reveal a rotationally symmetric orientation distribution with respect to the surface normal (see below), and consequently all elements of S can be deduced from Szz: Sxx = Syy = −Szz/2, Sxy = Syz = Sxz = 0. In this case Szz corresponds to Herman’s orientation function along the extraordinary axis of the orientation distibution: z.̂

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RESULTS AND DISCUSSION: MACROSCOPIC ORDER Polarized optical micrographs of a spherulite of sample NI333 (nonisothermally crystallized) clearly show radial structures, but the bright and dark patterns are irregularly distributed (Figure 2a). In the center, the region of highest Tx, some indications of ring-like patterns can be supposed. The pitch, extracted from the single ring-shaped pattern in Figure 2, is 3445


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Figure 6. Normalized and stacked integrated absorbance of the band at ∼1295 cm−1 (ν2c) depending on polarization (indicated by “s” and “p”) for each inclination value (separated by vertical dashed lines). This plot is a two-dimensional (sliced) representation of a three-dimensional dependence. Blue circles refer to a crystallization temperature Tx = 303 K; cyan: Tx = 308 K; green: Tx = 313 K; red Tx = 318 K; brown: Tx = 323 K; and black: Tx ≤ 333 K (measured only for −50° ≤ β ≤ 50°). IR-TMOA fits are indicated by solid lines. For each Tx the data are scaled such that the integrated absorbance at normal incidence matches unity and shifted vertically afterward to ease comparison. Cf. Figure 3 for spectra and Table 1 for assignments.

directions is omitted. As the samples exhibit uniaxial alignment along the surface normal (cf. above), we can calculate the order parameter, Sext, of the mentioned lattice planes (eq 2).61,62 Notably, both reflections in the accessed 2θ range shift to lower angles for β ≥ 40° (Figure 4). This is assigned to inaccuracies of the beam path: sample position and alignment become more important at higher β.61,67 The extracted order parameters rely on the full range of β ≤ 90° (eq 2) and consequently suffer from systematic uncertainties. To estimate these deviations, Sext has been derived from the corrected integrated areas and from data being extrapolated from β ≤ 50° to higher values (inset in Figure 4). These two methods lead to alterations in Sext of about 0.1, which increase with the variation in the integrated area (Figure 7). The order parameters and pole distributions reveal a different preferential alignment of the [110] and [200] directions respectively being perpendicular and parallel to surface normal. The orientation of the [110] directions qualitatively resembles the case of spherulites exhibiting [010] directions parallel to the radius (i.e., growth direction).14,36,38,42 If the studied spherulites were strictly centrosymmetric objects, the order parameter of [200] should be identical to the one of the crystalline c̲ -axes (cf. Table 2). But the comparison of IR-TMOA and XRD-PF shows that Sext( c̲ ) > Sext( a̲ ), indicating a significant fraction of flat on lamellae for samples I313−I323 and NI333 (Tx ≥ 313 K). Comparison to Structural Model. In the following, a numerical model of confined, i.e., nonspherical, spherulites is described, by which the order parameters as well as the pole distribution functions of all crystal axes are estimated and compared to measured data. Structural Model: Calculations. Spherulites in substrate supported films are regarded as a set of radially distributed crystallites confined by neighboring spherulites and the film thickness (Figure 8a−c). Consequently, an average spherulite is approximated by a cylinder with the mean diameter of the spherulites, dS, and a height equal to the film thickness, h (cf. inset in Figure 7 and Figure 8a−c; a detailed graphical

the measurement spot and heterogeneities of the spherulites’ diameters (cf. also Supporting Information). The crystallites’ c̲ -axes are preferentially aligned perpendiĉ as can be ular to the surface (parallel to the surface normal z ), ′ and ν2c deduced from the positive order parameter of ν1c (Table 2). The transition moments (TMs) of νc(CH2) and ν1c, both perpendicular to the c̲ -axes, are aligned preferentially parallel to the surface. The former exhibit a larger amplitude of Sext (Table 2), presumably caused by different orientations of the TMs with respect to the unit cell (cf. Table 1). In conjunction with order parameters obtained from XRD and studies on stretched films (to be published), one concludes that the TMs of νc(CH2) and ν1c have their major components along the [110] direction, but not along [100]. For all Tx, the TMs residing in amorphous regions exhibit order parameters within the range of the experimental uncertainty (ν″1a(COC) in Figure 3a; cf. Supporting Information). The reason is that ν″1a(COC) and ν′1c(COC) correspond to strongly overlapping bands, and consequently, the decomposition increases the systematic uncertainties (Figure 3). For samples I323−I308 (Tx ≤ 323 K), we conclude that the molecular order of the amorphous strands is smaller or in the range of 0.1. Presumably, it originates from the rigid, amorphous fractions at the fold surfaces of the lamellae, as crystallization is the only anisotropic, and hence ordering, effect in the experiment.10,32,66 The nonisothermally crystallized sample, NI333, shows interference patterns that complicate the band decomposition further and do not allow a discussion ″ (COC) and ν 1c ′ (COC) for this sample. of ν1a XRD Pole Figures. As expected from the order parameters obtained from IR-TMOA (Table 2), the areas of the (110) and (200) XRD diffraction peaks vary strongly with the inclination angle β ∈ [0°, 10°, ..., 80°] (Figures 4 and 7). In particular, the (110) reflection nearly vanishes for β = 0° and Tx = 323 K, indicating a strong depletion of the [110] directions along the ̂ The pole distribution of [111] directions surface normal ( z ). resembles the one of [110] because the plane normals are nearly identical. Consequently, the discussion of the [111] 3446


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χ determines the direction of the axes in the plane perpendicular to n||̂ . The 33.6° in eq 3c correspond to the angle between [010] and [110] and can be changed to model other directions like [111], which corresponds to an angle of 35.9°. The pole distribution function represents the probability to find a crystal axis in a certain spatial direction. Consequently, by integration over the whole cylinder the three-dimensional order parameters of any crystal direction can be calculated. Only the following parameters are needed for this: (1) the ratio dS/h, as taken from the micrographs, (2) the spherulites growth direction being [010],14,34,36,38 and (3) the value or variation of χ. For a banded spherulite, χ varies continuously with the distance from the seed, whereas in the nonbanded case a random variation is found.37,40,48,65 XRD and IR-TMOA reveal macroscopic averages and hence cannot distinguish between these two types of spherulites. In the calculation, we distribute [001], [100] on a cone around [010] for each point in the model-spherulite (cf. Supporting Information). The AFM and POM pictures reveal not exactly radially aligned lamellae because of branching, splaying and bending (cf. Supporting Information).32,42,68 Therefore, the deviation of the lamellar growth direction from the radii of the spherulite is determined at about 100 positions in an AFM-amplitude picture, from which we then calculate the probability distribution to find a lamella exhibiting a certain angle, ξ, with n||̂ .69 For every infinitesimal volume, ξ is chosen randomly according to this distribution (cf. Supporting Information). Up to here only bulk like objects impinged by the surfaces and the neighboring spherulites are considered. The influence of the surface is modeled in two different ways: (1) We assume a simple three-layer structure that consists of two interface layers: substrate induced flat on crystallites (Figure 8d) and free surface induced edge on lamellae (Figure 8e) as well as the actual spherulites in between (Figure 8c). These may nucleate somewhere (e.g., in the center) of the remaining volume (Figure 7e) or directly at one of the interfacial layers (Figure 7d). (2) A single layer model with an interface induced basal lamellae influencing the orientation of the overgrowing crystallites is modeled as follows. We position the nucleus at the interface and increase the fraction of the spherulite with a certain χ: higher probability of χ = 0° for initially flat on- or χ = 90° for edge on lamellae (eq 3). An exemplary scenario with an interfacial flat on layer at the substrate interface is sketched in Figure 8d. Such a structure is in line with the observations of Mareau and Prud’homme for 200 nm films (cf. also Figure 7f and Supporting Information).14 As bulk-like spherulitic growth is radially symmetric, preferentially aligned lamellae can only originate from an asymmetric position, i.e., the interface. Therefore, such a model is not fully compatible with crystallization seeds in the center of the film (Figure 7g). But for consistency the resulting pole distributions are also given (Figure 7a−c). The fractions of surface induced and bulk like structures depend on complex aspects: e.g., in bulk the crystallization kinetics may be slower compared to the vicinity of the substrate and furthermore exhibit a different temperature dependence. Details concerning the transition from surface induced to bulklike lamellae shall be obtained in future studies of the kinetics and the orientation of thin films of varying thickness (h ∈ [0.1, 1] μm).14

Figure 7. Pole distributions (I(β)/∫ dβI sin β) of (110) and (200) planes in supported PCL films are depicted respectively as squares and circles for crystallization temperatures (a) Tx = 323 K, (b) 318 K, and (c) 313 K. Data for inclinations of β ≥ 70° are obtained by extrapolation. Uncertainties result on the one hand side from the determination of the integrated area (Figure 4) being in the range of 5%. On the other hand, normalization involves all data including the extrapolation to β = 90°, leading to a higher uncertainty of the overall level of the data (cf. Figure 4). The dashed and solid lines result from the structural model and refer to [110] and [200] directions, respectively. Different colors refer to the different structural models depicted in (d)−(g): Green (d) and blue (g) refer to a layer model with 1.3 μm of flat on lamellae and bulk like spherulites nucleated respectively at the bottom and in the center of the remaining volume. Black (f) and red (g) correspond to spherulites with an increased likelihood of flat on oriented lamellae (12%). The nucleus and the growth directions are respectively depicted by stars and dashed lines (cf. Table 2).

representation can be found in the Supporting Information). In bulk, the distance of the seed from the right or left neighbor and upper or lower surface is purely random. Therefore, the nucleus of an average spherulite is positioned laterally in the center. The volume is split into infinitesimal cubes, each holding three perpendicular vectors: n||̂ being the radial direction, n⊥̂ and n′̂ ⊥. For convenience n′̂ ⊥ is defined to be in the x -̂ y ̂ plane and n″̂ ⊥ = n||̂ × n′̂ ⊥. All three inherent directions of a crystalline lamella can be identified or derived from n||̂ , n′̂ ⊥ and n″̂ ⊥. In particular, for a lamella with its [010]direction along the radii (n||̂ ), the directions [100], [010], [001], and [110] are given as follows (Figure 8c and Supporting Information). [001] = cos χ n⊥̂ ′ + sin χ n⊥̂ ″

(3a)

[100] = sin χ n⊥̂ ′ + cos χ n⊥̂ ″

(3b)

[110] = sin(33.6°)[100] + cos(33.6°) n||̂

(3c)

(3d)

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Figure 8. Micrograph and scheme of a substrate supported, impinged spherulite (not to scale). (a) Micrograph of PCL crystallized at Tx = 323 K (contrast enhanced). The width of the framed region is 275 μm. Nonspherical, flat spherulitic objects form that impinge each other.32 (b) Lamellar crystallites grow radially out of a nucleation seed (star) and form a nonbanded spherulite that is confined by the film boundaries and neighboring spherulites. The crystal faces are denoted a ({100}) and c ({001}). The inset depicts a lamella with polymer backbones indicated by black lines and unit cells in red. Panel (c) depicts geometrically confined crystallization within the thin film, whereas (d) shows a flat on layer (shaded in green) as induced by the substrate and (e) and edge on layer (shaded in green) as induced by the free surface. The lamellar crystallites grow (gray shaded arrows) preferentially along the b̲ direction. In all panels, the sample reference frame is indicated by x ̂, y ,̂ and z,̂ whereas the crystal directions are indicated by a̲ ([100]), b̲ ([010]), and c̲ ([001]).

For NI333 (Tx ≲ 333 K, dS/h ≈ 40) an even higher fraction of a flat on crystallites (∼40%) is expected based on the IRTMOA results (Table 2, no pole figures measured). Secondary nucleation and other effects that lead to orientationally correlated lamellae are supposed to act within the extended a̲ − b̲ plane of the lamella and not via the fold surface. Therefore, orientational correlations in c̲ direction over 1.3 μm, i.e., ∼50 lamellar thicknesses, are peculiar but have been reported in the literature before.13,14,54,70 Cheng and coworkers studied similar orientational correlations and assigned these to a tethering of chains, soft epitaxy, confinement, and a stretching of the polymer coils.13,71 For I313 (Tx = 313 K, dS = 2.5), i.e. weak confinement, the agreement of model and measurement declines because of two reasons: (1) The impact of heterogeneous spherulite diameters on the macroscopically averaged order is much stronger for low dS/h (Table 2 and Supporting Information). (2) And as the transition from cylindrical to spherical objects must be continuous, the model begins to fail here. In sample I308 and also for Tx < 308 K, we find a high density of nucleation seeds and negligible order parameters of the [001] axes, proving the dominance of the nucleation and growth within the bulk phase at low Tx (Table 2).

Structural Model: Discussion and Comparison. The order parameters along the surface normal (Sext) based on such model calculations are compared to the values determined by XRD and IR-TMOA in Table 2. For bulk-like model-spherulites (dS/ h ≤ 1) all order parameters vanish.a Whereas in the confined case, dS/h > 1, Sext of [010] (growth direction) decreases on expense of Sext([100]) and Sext([001]). Both directions are perpendicular to [010] and therefore exhibit equal order parameters (Figure 8c and Supporting Information). This ordering is a purely geometric effect resulting from the confinement of the radial strands to a disc of aspect ratio dS/ h. In a cylinder of aspect ratio of dS/h = 1, one would find a standard deviation of σrad ≈ 41°, for the orientation distribution of strictly radially growing lamellae. For higher values of dS/h, like 10 or 18, σrad = 8° or 5°, respectively. For dS/h ≥ 8, the growth direction is confined very effectively (σrad ≤ 10°). Consequently, differences of the order between systems with high aspect ratios are small (“bulk” column in Table 2). And similarly, in these cases variations in dS/h do not play an important role for the order induced by geometrical confinement. Modeling substrate interactions, which lead to a preferential flat on orientation, increase the alignment of the [001] axes with the surface normal on expense of the [100] directions (Figure 8e).14 Edge-on lamellae would increase the order parameter of the [100] axes reducing the one of [001]. No strong differences are found between the three-layer and the single-layer model, as long as the nucleus of the spherulitic structures is in the same position (Figure 7). The order parameters and pole distributions as measured by IR-TMOA and XRD agree best with model calculations using about 12 vol % of flat on lamellae and nucleation seeds at the bottom of the PCL film (Table 2 and Figure 7). In the threelayer model this corresponds to a basal layer of about 1.3 μm.

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CONCLUSIONS AND SUMMARY The results from IR-TMOA and XRD measurements in comparison with model calculations reveal that the substrate supported spherulites retain a bulk like morphology (∼90 vol %) to a large extent for crystallization temperatures Tx ≤ 323 K (samples I323−I313). But macroscopic order appears because of the confined crystal growth: The spherulites’ diameters, dS, are larger than the film height, h. Furthermore, interactions with the substrate lead to heterogeneous nucleation at the interface and flat on lamellae (Figure 8), contributing to the measured 3448


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Macromolecules order as well. The flat on alignment extends into the film for about 1.3 μm, as deduced from comparing the measurement with model calculations. The impact of the free surface on the macroscopic order appears to be minor, as only weak macroscopic edge on aligned lamellae is found (≤1 vol %). The temperature dependence of these volume fractions is assigned to the dynamic interplay of the different nucleationand-growth kinetics in the ∼11 μm thick films. For large Tx (and large dS/h) substrate induced nucleation and the related growth play a vital role. For Tx < 313 K (meaning dS/h ≲ 1), bulk-like spherulites dominate. Improving the model and determining the mentioned fractions, growth-and-nucleation rates in detail, demands further quantitative, thickness, and temperature dependent, kinetic and orientation studies (possibly utilizing chemically modified substrates72).

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00473. Major orientation directions and statistical uncertainties as resulting from IR-TMOA; an atomic force micrograph to evaluate the deviation of the growth direction from the radii; the size distributions of the spherulitic structures; and some further details concerning the model of confined spherulites (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (W.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Deutsche Forschungsgemeinschaft within the SFB TRR 102 for financial support and Prof. Kay Saalwächter of the Martin-Luther-Universität Halle-Wittenberg for fruitful discussions.

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ADDITIONAL NOTE The model volume is cylindrical not spherical; therefore, for dS/h = 1 small order parameters are obtained with an inverted sign, i.e., a swapped major orientation direction, when compared to the case of dS/h > 1. a

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