Crystallization Kinetics of Poly(ethylene oxide) under Confinement in

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Crystallization Kinetics of Poly(ethylene oxide) under Confinement in Nanoporous Alumina Studied by in-situ X-ray Scattering and Simulation Cui Su, Yu Chen, Guangyu Shi, Tang Li, Guoming Liu, Alejandro J. Müller, and Dujin Wang Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b01968 • Publication Date (Web): 13 Aug 2019 Downloaded from pubs.acs.org on August 17, 2019

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Crystallization Kinetics of Poly(ethylene oxide) under Confinement in Nanoporous Alumina Studied by in-situ Xray Scattering and Simulation Cui Su†,§, Yu Chen‡, Guangyu Shi†,§, Tang Li‡, Guoming Liu*,†,§, Alejandro J. Müller‖,⊥ and Dujin Wang†,§ † Beijing National Laboratory for Molecular Sciences (BNLMS), CAS Key Laboratory of

Engineering Plastics, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ‡ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, P. R. China

§ University of Chinese Academy of Sciences, Beijing 100049, China

‖ POLYMAT and Polymer Science and Technology Department, Faculty of Chemistry, University

of the Basque Country UPV/EHU, Paseo Manuel de Lardizabal 3, 20018 Donostia-San Sebastián, Spain ⊥ IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

CORRESPONDING AUTHOR * E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT While a relatively complete understanding of the nucleation and orientation of polymers under confinement in 1D nanochannels has been achieved, crystallization kinetics investigation of confined polymers is still rare. In this work, we investigate the crystallization kinetics of poly(ethylene oxide) (PEO) confined in AAO templates with different pore sizes using in-situ wideangle X-ray scattering (WAXS). The crystallization kinetics results were fitted with the Avrami equation. The Avrami index was determined by both “isothermal step crystallization” (ISC) and insitu WAXS. The crystallization process of polymers under one-dimensional nanopore confinement is simulated by a "one-dimensional lattice model". Based on this model, it is shown that homogeneous nucleation with the simultaneous growth of multiple crystal planes with drastically different growth rates could result in Avrami indexes lower than one. INTRODUCTION With the development of nanoscience and nanotechnology, the crystallization behavior and physical properties of polymers under nanoscale confinement are attracting much attention.1,2,3,4,5,6,7 With uniform, parallel nano-channels, the nanoporous anodic alumina oxide (AAO) templates have been widely used as a model system for 2D confinement.7,8,9,10 The crystallization of polymers within AAO templates has been studied including several aspects like nucleation, orientation, and crystallization kinetics. When confined into nanodomains, the nucleation mechanism of polymers changes from heterogeneous to either homogeneous or surface nucleation.11,12,13 The polymer crystals generally adopt a texture with the chain axis perpendicular to the AAO wall.10,12,14 Recent studies supported the mechanism of “the fastest growth directions parallel to the pore axis”15 and a complete orientation model has been proposed considering the nucleation rate and crystal growth rate.16 The contribution of heterogeneous nucleation is reduced to nearly zero, when the number of nanochannels is much larger (several orders of magnitude larger) than the number of heterogeneities present in the bulk polymer before infiltration.7,9 Within the small volume of the confinement space, the polymer inside micro- or nano-domains is expected to finish the crystallization process (where it will achieve a specific saturation crystallinity degree) very soon after a nucleus is formed. The


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nucleation becomes the rate-determining step, i.e., the overall crystallization kinetics is "nucleationdominated" at nanoscale level. As a consequence, the overall crystallization rate of confined micro or nanodomains is reduced by several orders of magnitude in comparison with those for bulk polymers.2,3,17,18,19,20 In fact, it is difficult to compare the crystallization rate at the same crystallization temperature. An exceptional case was reported by Guan et al. on the cold crystallization of PLLA,21 where accelerated cold crystallization from the glassy state was observed which was explained by the surface nucleation effect of AAO walls. The crystallization kinetics of polymers is generally discussed in terms of Avrami equation22,23: 1 ― 𝑉𝑐(𝑡) = exp [ ―𝑘(𝑡 ― 𝑡0)𝑛]

(1)

where Vc is the relative volumetric transformed fraction, t is the crystallization time, t0 is the induction time, k is the overall crystallization rate constant and n is the Avrami index. The Avrami index n is a characteristic parameter of crystallization that is a measure of the order of the crystallization kinetics. Based on the mathematical derivation of the Avrami index and its physical meaning, Müller et al. 2,24 postulated that the Avrami exponent could be expressed by the addition of two terms: n = nn + ngd

(2)

where nn is related to nucleation and ngd to growth dimensionality. The nn term can have limiting values ranging from 0 to 1, where 0 represents instantaneous nucleation and 1 sporadic nucleation. Fractional values (in between 0 and 1) usually indicate that the nucleation kinetics falls between these two extremes. While a relatively complete understanding of the nucleation and orientation has been achieved, the crystallization kinetics investigation of polymers infiltrated within AAO is rare,7,21 partly because of experimental difficulty. When the nucleation dominates the kinetics and it is no longer heterogeneous but starts at the surface of the template or is homogeneous, the degree of supercooling needed for crystallization is quite large and the temperature dependence of crystallization rate is strong. These facts contribute to an extremely narrow measurement window. Because of the weak signals of polymers infiltrated in nanopores, an “isothermal step crystallization” (ISC) technique is frequently applied.7,24


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Shin et al.25 reported that the Avrami index n of polyethylene (PE) in AAO (1.5 ~ 1.9) was smaller than that of the bulk (n ∼ 2.4). They explained the n value by the homogeneous nucleation together with a partial contribution of crystal growth. A much larger (more than 5 orders of magnitude) value of k for PE in AAO than that for the bulk was observed, which was attributed to the larger number of nuclei in the nanopores.26 It should be noted that the crystallization temperatures selected for the infiltrated PE were 16 ~ 47 ºC lower than those of the bulk. Lower crystallization rate and smaller values of n were also reported in syndiotactic polypropylene (sPP).27 A transition from regime III to regime II was proposed for infiltrated sPP while only regime III was noticed for the bulk sample. Michell et al.28 found that nucleation mechanism for the PEO block (which was the majority block forming the matrix of the material) within a poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) diblock copolymer changed from heterogeneous nucleation (where it forms spherulites in the bulk, as PEO conforms the matrix of the material) to homogeneous nucleation when infiltrated within AAO nanopores. They observed a dramatic drop in the Avrami index down to values roughly between 0.5 and 1 for the infiltrated materials. They explained the n values lower than 1 by considering that growth rate is so fast that nucleation dominates the kinetics (therefore in the equation: n = nn+ngd, the term ngd can be neglected). For sporadic nucleation, an Avrami index of 1 is expected and the overall crystallization kinetics becomes first order. However, if the nucleation is between sporadic and instantaneous, then lower values than 1 are expected. 1,2,3,4,7,9,10,11,12 Cylinder-forming block copolymers exhibit a geometrical structure similar to AAO. The confined crystallization within the microphase-separated domains of block copolymers has been well-studied.29,30,31,32,33,34,35,36,37 However, the factors influencing the crystallization kinetics are rather complicated because the cylinder structure is not exactly uniform and isolated as that in AAO, and the geometry of the confinement space may also change during crystallization in weakly segregated systems.31 Nojima et al.33,34,35,36,37 studied the crystallization behavior of poly(εcaprolactone) (PCL) within poly(ε-caprolactone)-block-polystyrene block copolymers (PCL-b-PS). They found that the crystallization of all the PCL chains under cylindrical confinement showed firstorder kinetics, indicating a “ nucleation dominated ”

crystallization with homogeneous

nucleation. The crystallization rate of PCL was shown to be closely related to the molecular weight


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(Mw), tethering state34,37, chain end groups36, and confinement size35. In this paper, we investigate the crystallization kinetics of PEO confined in AAO templates. We used the “isothermal step crystallization” (ISC) technique and in-situ wide-angle X-ray scattering (WAXS) to investigate the crystallization process at different temperatures. The half crystallization time (τ50%) and Avrami index n were obtained by fitting the crystallization curve with the Avrami equation. An Avrami index lower than 1 was observed. A 1D lattice model was applied to simulate the crystallization process to understand the experimental observations. EXPERIMENTAL SECTION Materials and Sample Preparation. Poly(ethylene oxide) (PEO) was purchased from Polymer Source Inc. The number-average molecular weight of PEO is 10,000 g/mol and the polydispersity is 1.05. The radius of gyration (Rg) of the PEO chain with Mn = 10,000 g/mol is about 3.8 nm, calculated according to the reference [38]. The AAO templates were purchased from Shanghai Shangmu Technology Co. Ltd. The preparation method of the templates was described in our previous paper.13 The diameters of the templates are 60, 100, 200 and 400 nm, and the pore lengths are 100, 50, 20 and 5 μm. The PEO was infiltrated within AAO nanopores using the same solution infiltration method as described previously.15 Before infiltration, the templates were cleaned with acetone and ethanol. The surface of AAO templates was polished to remove possible residues. Characterization. A Hitachi SU-8020 scanning electron microscope (SEM), operated at 5 kV, was utilized to examine the surface morphology and pore size of AAO templates. All the SEM specimens were coated with platinum to avoid charging. Standard heating and cooling measurements were carried out with a differential scanning calorimeter (DSC Q2000, TA). Indium was used for calibrating the instrument. An amount of ∼ 5 mg was weighed for each infiltrated samples containing the aluminum base. All samples were first heated to 100 ºC and held for 3 min to erase the thermal history. Then the samples were cooled down to -50 °C under nitrogen atmosphere. The temperature scanning rate was 10 ºC/min. The crystallization kinetics was measured by DSC using the “isothermal step crystallization”


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technique24,39 on a PYRIS diamond DSC. The thermal protocol was: (1) all the samples were first heated to 100 ºC and held for 3 min to erase thermal history; (2) the samples were cooled at 100 °C/min to the desired isothermal crystallization temperature for a specific period of time; (3) the samples were heated at 50 °C/min until melting. The melting enthalpy was taken as the crystallization enthalpy corresponding to that specific crystallization time. The in-situ 2D wide-angle X-ray scattering (WAXS) experiments were carried out on a Huber 5-axis diffractometer at the beamline 1W1A of Beijing Synchrotron Radiation Facility (BSRF). The wavelength of the radiation was 0.1549 nm. The detector was Pilatus 100 K (DECTRIS, Swiss). The resolution of the detector was 487×195 pixels (pixel size = 172 × 172 μm2). The sample-todetector distance was 153 mm. The direction normal to the AAO surface is defined as the z-axis, while two lines in the AAO surface perpendicular to each other are defined arbitrarily as the x- and y-axis. The X-ray beam irradiates the sample with an incident angle of 3° along the x-axis. The detector was 18° off the x-axis to capture the diffraction peaks at 2θ ~ 19° and 21°. The samples were mounted onto a DCS 350 domed cooling stage (Anton Paar GmbH). A homemade dome of stainless steel with polyimide windows was used to ensure a vacuum environment upon heating and cooling, and minimizing background diffractions. For the in-situ 2D WAXS experiments, the samples were first heated to 100 °C for 3 min to erase thermal history. Then the samples were cooled at 10 °C /min to the set temperature. 2D WAXS diffraction patterns were collected simultaneously during cooling and isothermal process. The diffraction patterns were collected every 6 s, with an exposure time of 5.9 s. Data recording started from 90 °C. The diffraction patterns at 90 °C were used as the background. RESULTS AND DISCUSSION Crystallization of Infiltrated PEO during Cooling. Figure 1a shows the typical 2D WAXS patterns recorded during the in-situ non-isothermal crystallization process. At temperatures above 0 °C, no diffraction peaks could be observed. When the temperature decreased to about -5 °C, two weak diffraction peaks appeared. Then, with the decrease of the temperature, the intensity of the peaks gradually increased. When the temperature reached -15 °C, the intensity of the peaks almost reached a maximum, and did not change with


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further decreases in temperature. The orientation of the infiltrated PEO crystals has been discussed thoroughly in our previous paper15. When the pore sizes are smaller, and/or the cooling rate is higher, the PEO crystals are preferentially oriented with * ║ 𝒏 (pore axis). When the pore sizes are larger, and/or the cooling rate is lower (1 °C/min), a mixed orientation of coexisting * ║ 𝒏 and * ║ 𝒏 would be observed. For this study, as the cooling rate is relatively fast, a major orientation of * ║𝒏 (pore axis) was observed. A typical 1D intensity profile is shown in Figure 1b. The area of the first diffraction peak (q = 12.1 ∼ 14.3 nm-1) can be extracted at each Tc value and plotted as in Figure 1c. The first derivative of the integrated intensity curve shows a peak that can be considered similar to a non-isothermal crystallization exotherm in the DSC. The results indicate that the in-situ WAXS is an applicable method to monitor the crystallization process.

Figure 1. (a) The 2D WAXS images of PEO confined in AAO with a pore diameter of about 100 nm and template pore depth of 100 μm at different temperatures, during the non-isothermal crystallization at a cooling rate of 10 °C/min. (b) The corresponding 1D intensity profile of the 2D WAXS image at -50 °C. (c) The corresponding integrated peak area as a function of temperature,


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the derivative curve, and the non-isothermal crystallization curve by DSC at a cooling rate of 10 °C/min. Figure 2a displays a series of first derivative curves obtained by WAXS during cooling from the melt of different samples. The exact volume of the PEO confined in AAO pores were characterized by optical microscopy (using the method from reference [40]) and SEM. Only one crystallization peak can be observed for each sample indicating clean confining environments (for more on the effect of having uncleaned surfaces, where some polymer film remains and percolates several pores, see ref. 13). Figure S1 shows first derivative of integrated scattering intensity curves of the in-situ WAXS together with DSC curves. The peak temperatures are slightly different for the two measurements. The temperature control of the DSC is much better than in the hot stage, therefore the temperature obtained by DSC is more accurate. The peak temperatures of the in-situ WAXS are plotted in Figure 2b, together with the Tc values obtained by DSC. The Tc calculated using the empirical equation2 deduced from previous reports of homogeneous nucleation of PEO is also shown in Figure 2b. The Tc values from other literature reports are also included.9,12,41,42,43 It is shown that the crystallization temperatures measured by insitu WAXS are very similar to the results of DSC, except that the crystallization temperatures are a little higher (about 2 ~ 3 °C). The crystallization temperature decreased almost linearly with the logarithm of pore volume of the AAO templates, which is in accordance with the empirical equation2.


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Figure 2. (a) The derivative curves of the integral peak area of the in-situ WAXS diffraction patterns for infiltrated PEO within AAO templates with different pore size. (b) Crystallization temperature measured by DSC (Tc, black square), crystallization temperature measured by in-situ WAXS (Tc, purple hollow diamond), the experimental Tc (blue triangles) and calculated Tc using the empirical equation from ref [2] (dashed blue line), Tc values reported by other works with PEO (violet down triangle,9 magenta right triangle,12 pink sphere,41 olive left triangle42, and wine star43), and melting temperatures obtained in this work, measured by DSC (Tm, red circle) of PEO infiltrated in AAO, as a function of pore volume of the AAO templates. The data employed in reference [2] to obtain the empirical correlation represented by the dash blue line comes from many different PEO based materials including block copolymers microdomains, mini-emulsion polymerization droplets, dewetted droplets, etc… In spite of having been measured by different conditions (including both non-isothermal and isothermal experiments at different cooling and heating rates and temperature ranges respectively), the observed trend is clear, the crystallization temperature of homogeneously nucleated PEO increases with pore volume, as the probability of nucleation per pore also increases, as expected. Completing the plot in Figure 2b with


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recent literature data and with the data obtained in the present work, there is a remarkable agreement with some few exceptions to the empirical correlation represented by the dashed blue line in Figure 2b. On the other hand, in Figure 2b we have represented the melting points obtained in the present work as a function of pore volume. The lack of dependence of Tm values on pore volume, even though Tc values change significantly can be explained by possible reorganization processes that occur during the heating scans, which cannot be detected in the present case, in view of the small signals obtained by DSC. Isothermal Crystallization Kinetics of Infiltrated PEO - Effect of Pore Depth. Figure 3 shows the change in diffraction peak area and enthalpy during isothermal crystallization of the infiltrated PEO in AAO templates. The results of the in-situ WAXS (Figure 3a) and ISC (Figure 3b) look quite similar. It is shown that the crystallization rate is very sensitive to the crystallization temperature. A small decrease of crystallization temperature causes a remarkable increase in overall crystallization rate. At temperatures higher than -2 °C, there is almost no crystallization peak found within the observation time (0.5 h) of the in-situ WAXS. The overall crystallization rate at the same temperature is slightly higher for DSC than in-situ WAXS, which is in line with the non-isothermal crystallization results.


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Figure 3. Evolution of diffraction peak area and enthalpy of infiltrated PEO during isothermal crystallization measured by (a) in-situ WAXS, and (b) ISC of PEO. The fitted curves by the Avrami equation are shown by yellow curves and black curves, respectively. The AAO template has a pore diameter of 100 nm and pore depth of 20 μm.

The peak area evolution curves in Figure 3 can be extrapolated and fitted with the Avrami equation: A(𝑡) = 𝐴0{1 ― exp [ ―𝑘(𝑡 ― 𝑡0)𝑛]}

(3)

in which t is the crystallization time, t0 is the induction time and is set as 0 for current results, A0, k, and n are variables representing the final area, the crystallization rate constant, and the Avrami index, respectively. The crystallization halftime is estimated by fitting the results according to: τ50%

-1

=

(ln2k)

-1/n

(4)

The fitted results are shown in Figure 4. Both the results of WAXS and ISC are shown. The


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Avrami indexes calculated from WAXS range between 0.5 to 1, without a clear temperature dependence. On the other hand, the n values of ISC measurement change continuously from a value between 1 ~ 2 to very small values with increasing crystallization temperature. The overall crystallization rate, expressed by the reciprocal crystallization halftime (τ50%-1) decreased significantly with the increase of crystallization temperature. The qualitative trend is the same for both DSC and in-situ WAXS results. Quantitative differences are due to differences in temperature calibration and temperature control. The overall trend corresponds to the right hand side of the typical bell shape curve that describes the rate of crystallization as a function of Tc values. The trend in the right hand side of the bell shape curve, i.e., a reduction in overall crystallization rate as crystallization temperature increases, is explained by nucleation control (in this case both primary and secondary nucleation as the data comes from overall crystallization rate determination). It is possible to compare the τ50%-1 for the samples with different pore depths (Figure 4e). At all crystallization temperatures, the τ50%-1 increased monotonously with the pore depth (with a slope of ~1 in log-log plot), i.e., lower crystallization rate in shallower pores. This trend is the expected, as confinement increases when pores of smaller volumes are employed. The continuous change of n with temperature is reported in previous studies.24,27 In the ISC measurement, the degree of crystallinity is measured indirectly by the subsequent melting endotherm and no reorganization during heating is assumed. Thus, the ISC results could deviate from real values. The Avrami index obtained by in-situ WAXS is measured directly, this can be considered an advantage over ISC measurements. However, the WAXS signal to noise ratio may be lower because of the small scattering volume and weak scattering intensity of the infiltrated polymer, as well as the fact that temperature control is not as good as DSC. Avrami index values smaller than 1 have been reported.24,27,28 Müller et al.24,28 explained the Avrami indexes lower than 1 by the nucleation dominated kinetics with a nucleation kinetics in between sporadic and instantaneous.


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Figure 4. The plot of Avrami index of (a) in-situ WAXS, and (b) ISC (dashed line stands for n = 1.4), and the plot of crystallization rate of (c) in-situ WAXS, and (d) ISC for PEO infiltrated in AAO with pore diameter of about 100 nm and different pore depth, as a function of crystallization temperature. (e) The plot of crystallization rate (τ50%-1) measured by in-situ WAXS for PEO infiltrated in AAO with pore diameter of about 100 nm as a function of pore depth. Isothermal Crystallization Kinetics of Infiltrated PEO - Effect of Pore Diameter. The effect of pore diameter on the crystallization kinetics of infiltrated PEO was also investigated. The variation of the τ50%-1 with the crystallization temperature is shown in Figure 5a. For all the samples investigated, the τ50%-1 increases with the decrease of crystallzation temperature. Figure 5b shows the relationship between τ50%-1 and pore diameter, for the samples with the same template pore depth (100 μm). The change in the crystallization curve with pore diameter is not as


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regular as that one with pore depth. The τ50%-1 generally increases with increases in pore diameter, i.e., higher crystallization rate in larger pores. But the crystallization rate of the infiltrated PEO within 400 nm AAO decreased as compared to that of the sample with a pore diameter of about 200 nm. The reason of this result is still to be explored. Figure 5c shows the dependence of the crystallization rate (i.e., τ50%-1) with pore volume for all samples (Figure 5c). The crystallization rate increases with pore volume with a strong correlation. The slope of the log-log plot is close to 1. This result support the assignment that homogenous nucleation is the dominating nucleation mechanism in this case (and for all pore sizes examined). A higher overall crystallization rate is probably expected as the nucleation probability per pore increases with pore volume thus accelerating the overall crystallization kinetics.


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Figure 5. The plot of crystallization rate (τ50%-1) measured by in-situ WAXS for PEO (a) infiltrated in AAO with different pore diameters as a function of crystallization temperature, (b) infiltrated in AAO at different crystallization temperatures as a function of pore diameter, (c) infiltrated within AAO templates at different crystallization temperatures as a function of the pore volume. "One-Dimensional Lattice Model" Simulation. A simple "one-dimensional lattice model" proposed in our previous paper16 is used to simulate the crystallization kinetics of polymer crystallizing within AAO one-dimensional nanopores . By this model, the crystallization kinetics of crystals with uniform orientation growing inside the AAO nanopores with random homogeneous nucleation and 1D growth can be followed. In this model, the polymer inside AAO is simplified by a 1D lattice with: L: the pore length, unit: lattice sites, in analogy to the length of AAO pore; p: the nucleation probability, unit: nucleation probability per step per site, in analogy to the nucleation rate in real experiments; G: the growth rate of the crystal along the lattice, unit: number of sites per unit step, in analogy to the crystal growth rate in real experiments; If there are two kinds of crystal growth orientations in the AAO nanopores, the two orientations are assumed to be orientation 1 with the (h1k10) crystal plane growing along the pore axis, and orientation 2 with the (h2k20) crystal plane growing along the pore axis. Then: G1: the growth rate of the crystal along the lattice with orientation 1, unit: number of sites per unit step; G2: the growth rate of the crystal along the lattice with orientation 2, unit: number of sites per unit step. The units are omitted in the following text for simplicity. The nucleation process corresponds to the abrupt change of the property of a certain lattice. Once a lattice is nucleated, the crystallization will extend to the adjacent lattices at an expansion rate of G. At each step, the uncrystallized lattices are scanned to decide which are nucleated and then consider the growth of the existing nuclei. This step is repeated until all the lattices are “crystallized” (Figure 6a). Every simulation result is the average of 1000 times to ensure good statistics.


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The simulation parameters are shown in Table 1, with conditions I to IV. Under each condition, L and G are fixed while p is varied. Typical crystallization curves are shown in Figure 6b. The time evolution of crystallinity can be fitted with the Avrami equation. For examples, the Xc1 obtained by the parameters of L = 1000, G = 1, p = 0.01 (high nucleation density and low growth rate) exhibited n = 1.75. And the Xc2 obtained by the parameters of L = 1000, G = 1000, p = 0.0001 (low nucleation density and high growth rate) exhibited perfect first order kinetics (n = 0.99). With this tool, we are able to investigate the crystallization kinetics of polymers in 1D nanopores by systematically changing the nucleation rate and growth rate. We first consider solely the influence of nucleation rate by fixing L and G (Figure 6c). It can be observed that when G and L are fixed, the τ50%-1 decreases almost “linearly” with p-1 in log-log scale. Figure 6d shows the n values of the simulation using different G and p but fixed L. Three regions can be recognized. On the right side where p is very small, n is roughly 1. This is the typical “first-order kinetics” regime where the nucleation is the rate determining step. In the left side region with higher p, the n increases to 2, which corresponding to the homogeneous, sporadic nucleation and 1D growth of crystals.

Table 1. The parameters of the simulation under condition I to VIII. I II III IV V VI VII VIII

L

G

G1

G2

1000 1000 1000 1000 1000 1000 1000 10000

1 5 100 1000 -

5 100 1000 1000

1 1 1 1


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Figure 6. (a) Schematic illustration of the "one-dimensional lattice model" to simulate crystal growth within AAO templates. (b) Evolution of crystallinity as a function of time. The data was simulated with the parameters: L = 1000, G = 1, p = 0.01 (Xc1, black square, n = 1.75) and L = 1000, G = 1000, p = 0.0001 (Xc2, red circle, n = 0.99), respectively. The solid curves are the fitted line. (c) The plot of τ50%-1 as a function of the normalized growth rate G/L/p for different series of simulation parameters. L = 1000, G = 1. (d). The change of Avrami index n as a funciton of the normalized growth rate G/L/p for different series of simulation parameters (L = 1000).

We also simulated the situations when there are two kinds of crystal growth orientations in the AAO nanopores, as has been shown to be a common phenomenon recently.13,15,16 The two orientations are assumed to be orientation 1 with the (h1k10) crystal plane growing along the pore axis, and orientation 2 with the (h2k20) crystal plane growing along the pore axis. They have different growth rates, G1 and G2, respectively. It is assumed that for homogeneous nucleation, the nucleation rate p is the same for the two orientations. In the same group of data of the simulation, L, G1, and G2 are kept constant, and only the nucleation probability per site p is changed. The simulation parameters are shown in Table 1. Typical crystallization curves are shown in Figure 7a.


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Figure 7. (a) Evolution of crystallinity as a function of time. Xc1 (black squares) and Xc2 (red circles) are the crystallinity of the crystals with orientation 1 and orientation 2, respectively. The sum of Xc1 and Xc2 gives the overall crystallinity Xc (blue triangles). The data was simulated with the parameters: L = 1000, G1 = 100, G2 = 1, p = 0.00001. The solid curves are the fitted line. (b) The plot of overall crystallization rate (τ50%-1) as a function of the normalized growth rate (G1+G2)/L/p. L = 1000, G1 = 100, G2 = 1. (c) The plot of Avrami index n of the overall crystallinity as a function of the normalized growth rate (G1+G2)/L/p, for different series of simulation parameters. G2 = 1. (d) Schematic illustration of the "one-dimensional lattice model" to simulate the crystal growth of polymer crystal with two orientations in AAO templates. Red: fast growing orientation; blue: slow growing orientation.

Figure 7a shows the change of crystallinity as a function of time. The evolution of Xc1, Xc2, and Xc with time under particular crystallization conditions (V ~ VIII) can be fitted with the Avrami equation. The results of the Avrami fit are shown in Figure 7b, 7c, S3 and S4. It is shown that when G1, G2, and L are fixed, the τ50%-1 decreased with the increase of the normalized growth rate (G1+G2)/L/p, i.e., the decrease of nucleation probability per site. And the values of the crystallization


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rates of crystals with orientation 1 (τ50%-1) and τ50%-1 are basically the same (Figure S3). It is shown in Figure 7c that when the ratio of G1/G2 = 5, as the normalized growth rate increases, the overall Avrami index n first increases and then decreases. The value of n is between 1 and 1.9. When G1/G2 is high, the value of n varies between 0.4 and 1.2. Figure S4 showed that the trends of n1 (the Avrami index of crystals with orientation 1) and n are basically the same. When G1 is low (G1 = 5), the crystallization mechanism is basically the same as that of conditions I to IV. As the normalized growth rate increases, the overall crystallization kinetics changed from one dimensional crystal growth controlled, to nucleation and one-dimensional crystal growth simultaneously controlled, and finally to nucleation controlled. When G1/G2 is high (100 or higher), it is interesting to find that the fitted result of n can be lower than 1. We speculate that the reason for this is related to the high nucleation probability. When the nucleation probability is high, it is very likely to have two or more nucleation sites within one nanopore. In this case, the nucleus with a lower growth rate (G2) can act as a “block” for the fast growing crystals (G1). This will retard the overall crystallization of the sample. A schematic is shown in Figure 7d. At t = 4, the red cells cannot grow to the right side because of the blue crystal. Only when a new red nucleus is formed, the right side will be filled with red crystal. Crystals with the (hkl) plane (l ≠ 0) aligned along the pore axis, whose growth would be blocked by the pore wall,14 may also be treated as a crystal plane growing along the pore axis with extremely low growth rate, and act as a “block” for the fast growing crystals. It must be noted that the above analysis assumes the crystal cannot grow “through” other crystals. When the nucleation probability is extremely low, even if G1/G2 is high, statistically there is only one nucleus within one nanopore. Once nucleated, the crystal will fill the nanopore without being stopped by another nucleus. Under these conditions, the crystallization is nucleation controlled with n = 1. Remarks on the Crystallization Kinetics under Confinement. Both the primary nucleation and secondary nucleation (crystal growth) show a "bell-shaped" curve with respect to temperature.44 The crystallization rate increases with temperature on the low-


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temperature side and the crystallization rate decreases with temperature at high-temperature side. For bulk PEO, the crystallization temperature between -4 ~ -12 ºC is rather low and should be at the left-hand side of the curve. However, the experimental result shows that the crystallization rate decreases with crystallization temperature. This means that the temperature dependence of the crystallization rate is still on the right side of the "bell-shaped" curve for infiltrated PEO. Within the small volume of the confinement space, it is generally assumed that the crystal growth step is much faster than the nucleation step under high supercoolings in the confined system. The polymers inside micro- or nano-domains are expected to finish their crystallization process (where they will achieve a specific saturation crystallinity degree) very soon after a nucleus is formed. As a result, the overall crystallization kinetics will be first order, with the overall crystallization rate depending only on the nucleation rate per pore.29,30,31 The nucleation-dominated kinetics with n = 1 is the most popular result for confining systems, although other values have been reported (1.5 ~ 1.9 for PE25 and 0.5 ~ 2.5 for sPP27). Other explanations were proposed to explain the n = 1 behavior. For example, the n = 1 in PEO-b-PS diblock copolymers was explained by the one-dimensional crystal growth and athermal nucleation.45 Values of n < 1 have been reported for several highly confined block copolymer phases and for infiltrated block copolymer systems.24,28 Müller et al.24,28 have proposed that the Avrami indexes lower than one can be explained by nucleation processes that are in between sporadic and instantaneous. In this work, we have shown that n varies between 1 and 2 if the crystal can fill the whole pore without any hindrance, corresponding to nucleation dominated kinetics with sporadic nucleation, and 1D growth of sporadically nucleated crystals, respectively, depending on the ratio of nucleation rate and growth rate. However, if there is blockage of crystal growth within the pores, the crystallization kinetics may no longer be nucleation controlled and growth rates could become comparable to nucleation rates, then fractional n values could be observed. A new finding here is that crystal growth can play a role (in addition to nucleation)when there are multiple crystal planes growing simultaneously with drastically different growth rates. CONCLUSIONS


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We measured and analyzed the crystallization kinetics of PEO confined in AAO nanopores with different pore diameters and depths using the in-situ WAXS and DSC isothermal step crystallization (ISC) method. Both of the two methods showed that the reciprocal crystallization halftime increased rapidly with crystallization temperature, indicating that the temperature is still on the right-hand side of the “bell-shaped” curve. The crystallization rate increased with pore volume, which agrees with the previous assignment of homogeneous nucleation. The Avrami index n is close to or smaller than 1. We used a "one-dimensional lattice model" to simulate the crystallization kinetics of the polymer under one-dimensional nanopore confinement. It is shown that the Avrami index n is close to 1 for low nucleation rates and is close to 2 for higher nucleation rates. When there are multiple growing crystal planes with drastically different growth rates, a reduction in crystal growth rates may be produced. As growth becomes comparable with nucleation, fractional n values can be observed. In previous literature, Avrami indexes of 1 or lower have always been explained by considering that the overall crystallization kinetics depends on nucleation only, as growth in confined spaces would be too large to be a limiting factor in the kinetics. However, in this work, our simulation suggests that in the case of AAO nanopores, the blockage of spacing filling crystals within the confined domains could result in Avrami indexes lower than 1 with contributions of both nucleation and growth terms. SUPPORTING INFORMATION The nonisothermal crystallization curves by DSC and in-situ WAXS; the plot of reciprocal crystallization halftime as a funciton of the normalized growth rate (G1+G2)/L/p; the plot of reciprocal crystallization halftime as a funciton of the normalized growth rate (G1+G2)/L/p; the plot of Avrami index as a function of the normalized growth rate (G1+G2)/L/p. ACKNOWLEDGEMENTS This work is supported by the National Key R&D Program of China (2017YFE0117800) and the National Natural Science Foundation of China (NSFC, 21873109). G. L. is grateful to the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2015026). G. L., D. W., and A. J. M. acknowledge European funding by the RISE BIODEST project (H2020-MSCA-RISE2017-778092).


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Crystallization Kinetics of Poly(ethylene oxide) under Confinement in

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