Crystallization Mechanisms of Poly(vinylidene Fluoride-co-chlorotrifluoroethylene): Nucleation Transitions, Growth Kinetics, and Microstructure Evolution

Abstract

The crystallization kinetics of FK-800, a commercial semicrystalline copolymer of chlorotrifluoroethylene and vinylidene fluoride (poly­(CTFE-co-VDF)), dictate its microstructure and functional performance. Crystallization occurs between the glass transition (T _g ≈ 31 °C) and melting point (T _m ≈ 110 °C), with grain boundaries playing a key role in applications such as memristors, where they regulate filament growth. This study integrates in situ atomic force microscopy (AFM), grazing-incidence wide-angle X-ray scattering (GIWAXS), and differential scanning calorimetry (DSC) to characterize nucleation, growth, and morphology across the full crystallization window. Hot-stage AFM reveals a transition from homogeneous to heterogeneous nucleation near 45 °C and a shift from reaction-limited to diffusion-limited growth above 60 °C. Kinetics are analyzed using Lauritzen–Hoffman, Turnbull–Fisher, and Avrami models to extract surface free energies and activation barriers. A multiscale modeling framework is developed in which nucleation densities and growth rates measured by AFM are used to reconstruct Avrami kinetics, which are then validated against coverage data, and extrapolated to predict bulk crystallization behavior observed by DSC. GIWAXS confirms a primarily flat-on chain orientation at all temperatures, linking orientation to domain morphology. This integrative approach quantitatively connects nanoscale crystallization dynamics with macroscopic phase evolution, establishing a quantitative framework for modeling crystallization across time, temperature, and length scales.

1. Introduction

Fluoropolymers such as FK-800 are well-known for their exceptional chemical resistance, thermal stability, and low surface energy, which make them useful in advanced applications ranging from coatings to electronics. FK-800, a random copolymer nominally 75 mol % chlorotrifluoroethylene (CTFE) and 25 mol % vinylidene fluoride (VDF), forms semicrystalline domains when heated between its glass transition temperature (T _g ∼ 31 °C) and its melt temperature (T _m ∼ 110 °C). The size of the domains and the degree of crystallization both play critical roles in determining the mechanical, thermal, and optical properties of the material. Recently, FK-800 has been used as the separation layer in filament-based memristors with exceptionally high cycling rate. In memristors, the grain boundaries are the location of filament growth, meaning that the polymer microstructure directly impacts filament density and performance. Although the crystallizing phase in the form of the, poly­(CTFE) homopolymer, has been quantitatively studied using optical techniques to measure temperature-dependent spherulitic growth rates, there are no detailed reports on the crystallization kinetics of FK-800, or similar PCTFE-co-VDF copolymer blends, particularly in solution-processed, thin film geometries of interest for coatings, electronics and binders.

Crystallization in polymers involves an interplay between nucleation and growth, influenced by both thermodynamic and kinetic factors. Hot-stage atomic force microscopy (AFM) has emerged as a transformative tool for studying these processes at the nanoscale. − Unlike bulk characterization methods, AFM enables in situ, high-resolution visualization of morphological changes during crystallization, offering insights into nucleation, growth, and microstructure. For instance, studies on poly­(ethylene oxide) (PEO) have demonstrated the formation of depleted regions surrounding growing crystallites, which provided evidence of diffusion-limited growth mechanisms. These findings highlighted the influence of local molecular mobility and concentration gradients on crystallization behavior. Research on poly­(bisphenol A-co-decane) investigated the role of environmental factors such as temperature in controlling lamellae branching and growth rates. Similarly, ultrathin films (<100 nm) of poly­(3-caprolactone) exhibited rapid flat-on lamellar growth, showcasing the effects of substrate interactions and film thickness on lamellar orientation and crystallization kinetics. Together, these studies demonstrate the ability of AFM to track nucleation, growth, and morphological evolution in diverse polymer systems, offering mechanistic insights that inform material design and processing strategies.

Despite the progress achieved in understanding polymer crystallization, significant gaps remain in the literature. Only a few studies span the full crystallization range between T _g and T _m , and few studies model this behavior. Nucleation phenomena are often not well-characterized, particularly in terms of quantitative measures such as nucleation rates and nucleation densities. Few studies systematically distinguish between heterogeneous and homogeneous nucleation mechanisms. Further, while Avrami modeling is commonly applied to describe polymer crystallization in bulk samples, it has not been employed in AFM studies where nanoscale features can be resolved. Moreover, Avrami models inherently assume specific nucleation and growth behaviors, yet these parameters are rarely measured independently to validate model assumptions. In this context, due to the accessible crystallization temperature range and the relatively slow kinetics, FK-800 serves as a model polymer for quantitative crystallization measurements that can test kinetic models.

This study investigates the temperature-dependent crystallization kinetics of ultrathin film FK-800 using hot-stage AFM coupled with complementary grazing-incidence wide-angle X-ray scattering (GIWAXS) to measure crystallite orientation. By examining nucleation mechanisms, growth dynamics, and crystalline coverage across the full crystallization range from the glass transition temperature to the melt temperature, we aim to (1) extract fundamental surface energies and activation barriers, and (2) elucidate transitions between kinetic and thermodynamic regimes that impact microstructure and effective parameters such as the Avrami exponent and Avrami rate constant. To interpret these dynamics, we apply three classical models that together provide a coherent theoretical basis for assigning temperature-dependent regimes. Lauritzen–Hoffman theory is used to describe the temperature dependence of crystal growth under reaction-limited conditions and is applied to early time radial growth data to extract activation barriers and pre-exponential factors. Turnbull–Fisher theory governs homogeneous nucleation and is extended here to include a constant term representing temperature-independent heterogeneous site density. Avrami theory provides a framework for analyzing the full temporal evolution of crystallization, linking growth mode (reaction-limited vs diffusion-limited) and nucleation mechanism (instantaneous vs progressive) to the observed exponent. Following validation of Avrami fits against physical models derived from measured nucleation density and island growth rates, we extend the 2D Avrami model into 3D to compare with bulk samples analyzed using Differential Scanning Calorimetry (DSC). Together, these measurements and models provide a predictive framework for crystallization across the full time–temperature landscape.

2. Results

2.1. Morphological Evolution of Crystallization

Hot-stage AFM imaging was used to quantify important crystallization kinetics including nucleation density, nucleation rate, island size, island growth rate, and fractional coverage. Ultrathin film samples (∼50 nm) were prepared in an amorphous state by spin-casting onto plasma-cleaned silicon, followed by annealing at 120 °C for 20 min to ensure solvent removal and minimize preformed crystallites. Films are considered ultrathin when their thickness is less than 100 nm but exceeds the polymer radius of gyration in the melt, R _g . The melt-state R _g is estimated to lie between 3 and 12 nm, with the lower bound derived from a freely jointed chain model for a 1030-mer with 2.6 Å monomer lengths and the upper bound based on the measured R _g in ethyl acetate. These limits span ideal Gaussian coil to more realistic chain stiffness and expansion in solution.

A thickness of 50 nm was selected because it is several times larger than R _g (approximately 4–17 times), ensuring that polymer chains retain bulk-like conformations and that substrate interactions do not strongly dominate segmental dynamics or diffusion. At the same time, the film is thin enough to enable reliable nucleation analysis by AFM: the probability of multiple nuclei forming at the same XY location is low, facilitating accurate domain counting and growth tracking.

Although crystallization kinetics in ultrathin films are known to be suppressed relative to bulk behavior for thicknesses below 100 nm, ,, this reduction can be approximated by a mild correction scaling as (1–a/d), where a ∼6 nm. For the present system with d = 50 nm, this corresponds to a ∼ 12% reduction in growth rate. ,,, Importantly, homogeneous nucleation is not strongly suppressed in this thickness regimeseveral reports have shown that bulk-like nucleation persists down to ∼10 nm, , and that the temperature dependence of reaction-limited growth remains unchanged. Thus, 50 nm provides an experimentally tractable film thickness that balances spatial resolution, statistical reliability, and near-bulk kinetic behavior. In this geometry, the film can be conceptually treated as a two-dimensional slice through a spherulite, with the plane of the film corresponding to the fast-growing radial growth direction. Although AFM height images confirm a small out-of-plane growth component due to vertical lamellar stacking, this contribution is minor compared to in-plane expansion. At 70 °C, for instance, the radial velocity exceeds the vertical velocity by a factor of ∼300 (Figure S1). As shown later by GIWAXS, crystals nucleate in a face-on orientation, such that the fastest crystallographic growth axis lies within the substrate plane. Consequently, areal coverage reflects lateral expansion driven by radial flux, and vertical propagation does not significantly influence the kinetic parameters extracted from our Avrami analysis.

An example of the temporal progression from one hot-stage AFM movie, in this case for thermal aging at 45 °C, is shown in Figure a. AFM height images show that crystallites appeared within the first hour (which was typical at all temperatures for this material lot). Over time, these nuclei grew radially, maintaining an approximately disk-like morphology and eventually merging with other domains. X-ray scattering measurements, described later, indicate that these domains are only partially crystalline, as is common for spherulitic growth. X-ray scattering measurements also confirm that PCTFE is the crystallizing phase. After prolonged aging, the surface became dominated by polycrystalline domains, with minimal purely amorphous regions visible. This progression of nucleation and growth is referred to as first-stage (primary) crystallization, to differentiate it from further ordering due to molecular rearrangements, which is termed second-stage (secondary) crystallization. ,

1.

Exemplary data from hot-stage atomic force microscope movie held at 45 °C. (a) Height AFM images show crystalline domains (bright) that nucleate and grow within the initially amorphous (blue) film when thermally aged. There is drift in this movie so a white oval is used to mark the same location in each frame. All images are 5 μm × 5 μm with z-scale of 30 nm. (b) The area of individual, isolated islands was tracked over time to extract the radial growth rate. (c) Nucleation density versus time. (d) Fraction of the surface covered in domains versus time. The green overlay highlights the time-region corresponding to progressive nucleation.

These movies were reduced to three quantitative metrics: the radial growth rate, the peak nucleation density, and the domain coverage. The radial growth rate was determined by tracking the area of isolated crystals as a function of time, t, and assuming a disk-like morphology to calculate the radius, r(t). The nucleation density was quantified by counting nuclei and normalizing by the image area. Fractional domain coverage was calculated by masking crystalline regions and dividing their area by the total image area. These metrics are summarized in Figure b–d.

In general, island growth rates depend on local concentration and fall off quickly when crystals either compete for the same material or physically merge. To measure growth rates that reflect the intrinsic supersaturation (undercooling) rather than interactions with neighboring domains, we analyzed the growth rate of well-separated, horizontally expanding domains. For example, in Figure a, the three islands in the white oval are considered isolated at 4 h but not at 12 h. To compare growth rates across temperatureswhere we apply the Lauritzen–Hoffman modelwe extract an initial linear growth rate v, assuming reaction-limited kinetics with radial expansion described by r = vt. However, to model the evolution of total surface coverage over time using the Avrami framework (e.g., Figure d), we evaluate growth over longer durations and consider both reaction-limited (r = vt) and diffusion-limited (r = αt ^1/2) behavior, selecting the model that yields the lower root-mean-square error.

The nucleation density (Figure c) increases rapidly over the first 8 h (shaded green) before reaching a plateau (gray band). This behavior suggests progressive nucleation, characterized by a nucleation rate of approximately 2 × 10^–5 μm^–2 s^–1 during the first 8 h. However, because less than 7% of the surface has crystalline domains when nucleation ceases (as seen in Figure d), it is clear that the majority of crystallization occurs by growth of these pre-existing nuclei. For this reason, we approximate this behavior as instantaneous nucleation with a nucleation density given by the peak nucleation density (gray band). A classification of instantaneous nucleation is further supported by later analysis, in which Avrami fits to the temporal evolution of surface coverage is best described by an instantaneous nucleation model when evaluated alongside the independently measured growth mode and nucleation behavior.

The third measurement taken from AFM movies is the fraction of the surface covered by crystalline domains (Figure d). We note that the crystalline regions observed by AFM are polycrystalline and also incorporate amorphous chain morphologies. For this reason, this metric differs from the percent crystallinity obtained by diffraction or differential scanning calorimetry, described later. In the next section, we model the coverage as a function of time using the empirical Avrami equation. This introduces two more crystallization descriptors: the Avrami exponent, n and the Avrami rate constant, k _a .

In summary, to compare crystallization as a function of temperature, we found the most useful metrics to be the initial growth rate (before crystals start to merge), the peak nucleation density, and constants associated with modeling the coverage as a function of time.

2.2. Quantifying Time–Temperature Progression of Crystallization

The crystallization of FK-800 thin films was monitored using hot-stage AFM over a range of temperatures, 35–100 °C, bounded by the glass transition temperature (∼31 °C) and the melting temperature (∼110 °C). Figure compares images of the FK-800 films at each temperature after thermal aging for 24 h. The crystallization temperature visibly influences the morphology, number, and size of the crystals. The temperature series in Figure reveals several notable changes in morphology. First, films at lower temperatures (35 and 40 °C), show a mixture of vertically growing fiber-like crystals and horizontally growing, flat crystals, whereas higher temperatures are dominated by disk-shaped, flat crystals. X-ray scattering data (shown later) shows that flat crystals are face-on whereas vertical crystals are edge-on. Second, the crystal shapes become increasingly round and their edges smoother as the temperature rises. At 80 °C, some crystals exhibit hexagonal facets, indicative of the equilibrium crystal shape, which has been previously observed in the literature for PCTFE single crystals. Third, depleted zones, appearing as darker ’moats’ around crystal edges, progressively widen and deepen as temperature increases from ∼40 to ∼80 °C (Figure S2). These zones likely represent more dilute, stretched polymer regions with higher entropy, affecting both enthalpy and mass transport to growing islands. At temperatures ≥90 °C, depletion zones become less distinct, suggesting that increased molecular mobility smooths the amorphous phase of the film. A fourth notable transition is the significant increase in domain thickness with rising temperatures. Crystals grown at 50 °C for 24 h protrude 2–3 nm above the amorphous film, whereas those formed at 100 °C reach approximately 18 nm in height. This trend likely reflects an increase in the critical length for step motion as the temperature approaches the melting point. Enhanced chain mobility at higher temperature may also facilitate layer-by-layer stacking or secondary crystallization, contributing to thicker vertical growth.

2.

Atomic force microscope images of FK-800 after aging at various temperatures for 24 h. AFM images show crystalline domains (bright) that nucleate and grow within the initially amorphous (blue) film when thermally aged. All images are 5 μm × 5 μm however the z-scale varies from 10 nm for 35 and 40 °C, 20 nm for 45–60 °C and 30 nm for 70–100 °C (z-scale explicitly shown). Time series at each temperature are analyzed to quantify the radial growth rate, nucleation density and crystalline coverage.

In summary, the crystal morphology trends from mixed vertical and horizontally islands (35–40 °C) to “compact seaweed” (45–55 °C) to “compact dendritic” (60–70 °C) to hexagonal (80 °C), to circular (>90 °C). Moats are apparent for the middle temperatures (40–80 °C) and crystals thicken above 60 °C.

Beyond morphology, each time–temperature data set was used to evaluate the radial (r) growth rate, v = dr/dt (measured at early times) and the peak areal nucleation density, ρ (μm^–2). These results are summarized in Figure and Table S1, bracketed between T _g and T _m .

3.

Crystallization metrics as a function of temperature. Arrows indicate that higher temperatures lead to faster crystallization kinetics (mobility) but lower thermodynamic driving force (chemical potential). The glass transition temperature (T _g ∼ 31 °C) and the melt temperature (T_m ∼ 110 °C) are indicated by dashed vertical lines. (a) The island growth rate i.e. radial velocity of individual crystals versus temperature. (b) Nucleation density versus temperature. Inset shows the nucleation density normalized by the first point (nucleation density at T = 35 °C) versus T ^–1ΔT ^–2 on a log-lin plot to highlight the Arrhenius behavior near T _g . Measured data are shown in red and a fit to eq is given in black. (c) Fraction of the surface with crystalline domains versus time.

The plot of the radial growth rate as a function of temperature (Figure a) displays classic glass-like behavior. Growth rates are low near the glass transition temperature (T _g ≈ 31 °C) and increase with temperature, reaching a maximum near 70°, before decreasing again as the temperature approaches the melting point. This peaked behavior arises from the competition between thermodynamic driving forcenamely, the chemical potential differenceand polymer mobility, which governs the crystallization kinetics. In polymer systems, the change in chemical potential is given by $\mathrm{\Delta }\mu ={\mu }_m-{\mu }_c\cong \frac{\mathrm{\Delta }{H}_m\mathrm{\Delta }T}{T_m}$ where subscripts m and c denote the melt and crystalline phases, respectively, and ΔH_m is the enthalpy of fusion at the melting point. For FK-800, the enthalpy of fusion is approximately 36.7 J/g, estimated as 85% of the value for pure PCTFE, and the melting point is approximately 110 °C (374 K).

Thermodynamic considerations alone predict higher crystallization rates at lower temperatures, as shown by the temperature dependence of the chemical potential relative to thermal energy (dashed green line in Figure a). However, polymer mobility also plays a critical role, as the diffusion coefficient increases and viscosity decreases with rising temperature between T _g and T _m . This interplay results in the characteristic peak in the crystallization growth rate between the two limiting cases: low mobility near T _g and low supersaturation near T _m .

The temperature dependence of the radial growth rate can be modeled by ,,

$$G(T)=G_0{\mathrm{e}}^{-\mathrm{\Delta }E/kT}{\mathrm{e}}^{-K_2{T}_m/kT\mathrm{\Delta }T}$$ 1

where ΔE is the activation energy associated with transport to the crystal growth front, and $K_2=\frac{4{\sigma \sigma }_e{b}_0}{\Delta H_m}$ is the activation barrier for incorporation into the crystal. Here, σ is the surface energy of the prism faces, σ _e is the surface energy of the basal face containing chain folds, b₀ is the molecular size of the advancing step, which is 5.52 Å along the prism direction (Figure S3), ΔH_m is the enthalpy of fusion, T _m is the melting temperature, ΔT = T _m –T, and k is the Boltzmann constant. Both ΔE and K ₂ have units of energy. See the Supporting Information for a derivation of the step-advancement barrier in a hexagonal symmetry, including estimates of the critical lengths for step advancement as a function of temperature (Figure S4 and S5). Best fits to the experimental data (Figure S6, Table S2) give ΔE = 0.8–1.0 eV and K ₂ = 0.12–0.14 eV. The surface energy factor is found to be, σσ _e = 6.3–7.6 × 10^–5 J² m^–4, which is approximately 34–40% of the reported values for pure PCTFE (184 erg² cm^–4).

The second parameter measured from AFM images is the areal nucleation density (Figure b). As expected, nucleation density is highest at large undercooling, resulting in films with numerous small crystals. In contrast, films grown at lower undercooling contain fewer but larger crystals when grown to full coverage (Figure ). The full temperature dependence of nucleation density reveals two distinct regimes. Between 35–45 °C, the density decreases exponentially with increasing temperature, characteristic of homogeneous nucleation. This behavior is clearly illustrated in the log–linear inset of Figure b. At higher temperatures, the nucleation density plateaus, indicating that heterogeneous nucleation from a fixed population of pre-existing sites dominates. The crossover between these regimes defines the transition from homogeneous to heterogeneous nucleation.

To describe this behavior, we model the total nucleation density as the superposition of homogeneous and heterogeneous contributions: ,,

$$N=N_0{\mathrm{e}}^{-B/T\mathrm{\Delta }{T}^2}+N_{\mathrm{Hetero}}$$ 2

where the nucleation barrier prefactor B = $\frac{16\sqrt{3}{\sigma }^2{\sigma }_e{T}_m^2}{k\Delta H_m^2}$ derived for a folded-chain nucleus with hexagonal symmetry, and N _hetero is a constant representing the density of heterogeneous nucleation sites. See Supporting Information for a derivation of the nucleation barrier in hexagonal symmetry, the critical nucleation lengths (Figure S7), and a discussion of correction factors for Δμ. To extract B, we first determine N _hetero as the average nucleation density in the plateau region (T > 55 °C), yielding N _hetero = 0.3 ± 0.17 μm^–2. We then fit eq to the nucleation density data between 35 and 50 °C, giving a fit B = 1.7 ± 0.2 × 10⁷ K³ (Figure S8). This corresponds to a surface energy factor σ²σ _e = 3.3 ± 0.3 × 10^–7 J³ m^–6, or approximately 35% of the reported for pure PCTFE (950 erg³ cm^–6).

The third parameter measured from AFM images is the fraction of the surface covered with crystalline domains as a function of time. Figure c summarizes the coverage versus time for ten temperatures between 35° and 100 °C. In general, the crystalline coverage increases rapidly as nucleation and growth occur and then slows as crystals begin to merge. These data indicate that full coverage is achieved most quickly at temperatures near 45–50 °C (gray and green) which is a compromise between high nucleation density and fast island growth.

This graph also shows that as the temperature increases above 50 °C (green to red curves), the asymptotic fractional coverage appears to shift to lower values. This likely reflects an equilibrium between the amorphous and crystalline states. At higher temperatures, the film is less supersaturated, reducing the thermodynamic drive for precipitation, resulting in a lower equilibrium coverage.

2.3. Avrami Fits to 2D Data

The traditional S-shaped curves observed in Figure c are often modeled using the Avrami equation ,

$$\theta (t)={\theta }_{\max }(T)(1-{\mathrm{e}}^{-k_a{t}^n})$$ 3

where, for two-dimensional films, θ­(t) is the areal fraction of the surface that has formed crystalline domains as a function of time, t, θ_max(T) is the temperature-dependent maximum domain coverage which is based on the equilibrium crystalline solubility. The parameter k _a is the Avrami rate constant, while n is the Avrami exponent, typically ranging between 1 and 4 depending on crystallization processes. The values of k _a and n are determined by the nucleation mode, growth rate, and dimensionality of the growth. The thin films described here are quasi-2D, exhibiting primarily lateral growth, with domain aspect ratios defined by lateral domain sizes ranging from hundreds to thousands of nanometers and z-dimensions of approximately 50 nm (corresponding to the film thickness). While the Lauritzen–Hoffman model (eq ) is used to extract activation parameters from early time, reaction-limited growth behavior, the Avrami framework enables analysis of the full temporal evolution, including transitions to diffusion-limited growth.

At small t, the coverage, θ, is proportional to tⁿ and thus the early time curve shape provides information into the growth mechanisms that dictate n. The coverage versus time data sets in Figure c indicate shifts in growth mechanisms, with unconstrained fits yielding Avrami exponents between 1 and 2.

Since the AFM data sets independently measure nucleation, growth, and coverage (Figure ), they offer a rare opportunity to test crystallization models by comparing both calculated and fitted Avrami exponents and rate constants (Scheme ). Multiple scenarios described in Table , can lead to exponents of 1 or 2, as briefly reviewed in Supporting InformationSection 6 (Figure S9). Specifically, n = 1 corresponds to instantaneous nucleation with diffusion-limited growth (eq 4a), while n = 2 can result from either progressive nucleation with diffusion-limited growth (eq 4b) or from instantaneous nucleation with linear growth (eq 4c). Radial growth rates are fit with r = αt ^1/2 for diffusion-limited growth and r = vt for linear growth, and nucleation density is determined by ρ (μm^–2) for instantaneous nucleation or ν′/A (μm^–2 s^–1) for progressive nucleation.

1. Workflow for Modeling Polymer Crystallization Kinetics from Hot-Stage AFM Imaging with Measured Quantities in Yellow and Avrami Models in Blue .

^a Areal coverage vs. time is fit using the Avrami equation to extract kinetic parameters and estimate crystallinity. Independently, nucleation density and lateral growth rate measurements are used to calculate rate constants. These are used to reconstruct crystallinity curves, first validating against 2D fits and then extrapolating to 3D crystallization behavior. This extrapolation incorporates growth modessuch as instantaneous vs. progressive nucleation and diffusion-limited vs. reaction-limited growthdetermined from 2D kinetics. Predicted crystallinity is then compared to independent DSC measurements.

1. Avrami Models for 2D Growth.

model	k a (s–n )	n	equation
instantaneous nucleation diffusion-limited growth	k 2D, I, DL = πρα2	1	4a
progressive nucleation; diffusion-limited growth	$$k_{2\mathrm{D},\mathrm{P},\mathrm{DL}}=\pi \frac{{\nu }^{\prime }}{A}{\alpha }^2$$	2	4b
instantaneous nucleation linear growth	k 2D, I, L = πρv2	2	4c

To compare models, the predicted Avrami coverage (using eqs and 4) is overlaid on the experimental data for each temperature (Figure ). Corresponding rate constants under different model assumptions are summarized in Table S4 to facilitate comparison with unconstrained fits. The Avrami exponent, growth mode, and nucleation mode are assessed jointly to ensure self-consistent interpretation of the crystallization process.

4.

Fractional areal coverage versus time for samples held at ten temperatures between 35 and 100 °C. Measured data points (black) are overlaid with calculated Avrami coverage generated using measured nucleation and growth parameters. Three growth modes are evaluated: (i) n = 1, corresponding to instantaneous nucleation with diffusion-limited (DL) growth (orange); (ii) n = 2, representing instantaneous nucleation with linear (Lin) growth (dark blue); and (iii) n = 2, representing progressive nucleation with diffusion-limited growth (light blue). The coverage data transitions from n = 2 at 35–55 °C to n = 1 at 60 °C and above. To aid visualization, the y-scale is reduced for T = 90 and 100 °C and the time scales are reduced for T = 45–60 °C.

At low temperatures (T = 35–55 °C), where the crystallization driving force is high, the coverage evolution is consistent with an Avrami exponent of n = 2. Both progressive nucleation with diffusion-limited growth (light blue) and instantaneous nucleation with linear growth (dark blue) yield n = 2 in two dimensions, and the Avrami fits alone cannot distinguish between these cases. However, independent measurements provide additional constraints: linear fits (r ∝ t) to radial growth data yield lower root-mean-square error (RMSE) than diffusion-limited models (r ∝ t ^0.5) when applied to island expansion, indicating reaction-limited kinetics (Figure S10, Table S3). In parallel, nucleation rates extracted from AFM images show that the nucleation density saturates early, (when surface coverage is below 35%) indicating that nucleation is effectively complete well before the majority of growth occurs (see Figure S10d). Because the growth kinetics, nucleation mode, and Avrami exponent are physically interrelated, the self-consistent interpretation across all data sets supports the instantaneous nucleation with linear growth model. This integrated analysis is compiled and visualized in Figure S10.

At higher temperatures (60–100 °C), a transition in growth mode is evident. Crystals nucleate within the first hour, and only instantaneous nucleation is considered. Avrami fits assuming instantaneous nucleation with diffusion-limited growth (orange) consistently outperform those assuming linear growth (dark blue), indicating a shift in the Avrami exponent from n = 2 to n = 1. This is corroborated by a transition in radial growth behavior: above 60 °C, growth becomes sublinear (r ∝ t ^0.5), consistent with diffusion-limited kinetics (Table S3). Together, these observations indicate that crystallization in this temperature range is best described by instantaneous nucleation combined with diffusion-limited growth, yielding n ≈ 1 in two-dimensions.

Empirically, we observe that the maximum domain coverage, θ_max(T), extracted from unconstrained Avrami fits decreases approximately linearly with increasing temperature near the melting point (Figure S11). To interpret this trend, we consider thermodynamic solubility limits. The maximum crystalline fraction, f_e , achievable at a given temperature is governed by the chemical potential difference between the melt and crystalline phases, and can be expressed as

$$f_e(T)=1-{\mathrm{e}}^{-\mathrm{\Delta \mu }/kT}\mathrm{or}{f}_e(T)=1-{\mathrm{e}}^{-\mathrm{\Delta }{\mathrm{H}}_m\mathrm{\Delta }T/kT{T}_m}$$ 5

Because Δμ ∝ (T_m –T), the equilibrium crystalline fraction f_e (T) decreases approximately linearly as T → T_m , consistent with the AFM observations and unconstrained Avrami fits.

However, crystalline domains, particularly during primary crystallization, exhibit substantial internal disorder, including chain folds, trapped amorphous regions, and structural defects. As a result, the domain crystallinity, f _domain, achieved within individual domains is typically lower than the thermodynamic limit f_e (T) due to kinetic and geometric constraints. The experimentally measured crystallinity, f(T)_measured = θ­(T)f _domain depends on both the domain coverage, θ­(T), and the internal crystallinity within domains, f _domain. Rearranging this relationship gives the maximum domain coverage as θ_max(T) = f _e(T)/f _domain with the constraint that θ_max(T) ≤ 1. Thus, the domain coverage required to account for a given total crystallinity when the domains themselves have a crystallinity of f _domain:

$${\theta }_{\max }(T)=\min \left(1,\frac{f_e(T)}{f_{\mathrm{domain}}}\right)$$ 6

To relate this framework back to the Avrami fits of measured domain coverage, we use DSC data to estimate domain crystallinity. We estimate f _domain using the relation f(T)_measured = θ­(T)f _domain applied at 50 °Cwhere AFM data indicate full coverage (θ = 1). At 50 °C, DSC measurements after 4 days of crystallization, yield a crystalline fraction of approximately 18%. Assuming domain growth is complete at this pointas supported by AFMwe estimate f _domain ≈ 18% for primary crystallization. This sets the final crystallinity for the primary process, similar to the approach used in the Hillier extension of the Avrami equation. To ensure consistency with the long-time crystallization behavior, we scale the f_e (T) curve such that f_e (50 °C) = 22%, matching the observed maximum crystallinity after extended aging. This empirical scaling is reasonable given the uncertainty in our estimate of ΔH_m , which is based on PCTFE (however, both scaled and unscaled curves are shown in the Supporting Information for completeness). The temperature dependence of f_e (T) and θ_max(T) based on eqs and is shown in Figure S12. The results indicate that θ_max(T) declines approximately linearly from one at 60 °C to zero at the melting temperature.

This modeling approach, which has no free fitting parameters, successfully predicts the areal coverage versus time plots based on simple kinetic models. All temperatures can be reasonably described by assuming instantaneous nucleation coupled with reaction-limited growth below 60 °C (dark blue) and diffusion-limited growth above 60 °C (orange). Additionally, a thermodynamic term (eq ) that reduces the crystalline fraction plays a role in decreasing the domain coverage (eq ) above 60 °C.

2.4. Structural Evolution

Grazing incidence wide-angle X-ray scattering (GIWAXS) was used to investigate the structural evolution of FK-800 thin films, specifically identifying the crystallizing phase, the lattice constants, and molecular orientation. Figure presents GIWAXS results for samples aged for 5 days at four temperatures: 25 °C (below T _g , amorphous), 35 °C (high nucleation density, small irregular crystals), 50 °C (compact seaweed morphology), and 70 °C (compact crystals with smooth edges), with corresponding AFM images in Figure S13.

5.

GIWAXS data illustrating the changes in molecular orientation and ordering as a function of temperature. (a) Scatter plots for samples aged for 5 days at 25, 35, 50, and 70 °C. (b) Scatter intensity as a function of the radial scattering vector integrated over an azimuthal angle of χ = 78° ± 18 which encompasses the (10•1) to (10•4) peaks. (c) Integrated intensity at q_r = 1.2 ± 0.4 Å^–1 for each sample as a function of azimuthal angle (defined relative to z-axis) from ∼7 (out-of-plane) to 85° (in-plane). The intensity and angles are corrected for the Ewald sphere geometry. Dashed lines show the sin­(χ) envelope expected for isotropic scattering. Regions above the sin­(χ) baseline reflect oriented scattering. The degree of orientation increases with temperature, as indicated by the growing excess near in-plane angles (χ > 60°). (d) Representative AFM height profiles of crystal thickness after 1 day of aging, showing distinct amorphous and crystalline regions. In all plots, the amorphous film is represented by a solid black line and samples thermally aged at 35, 50, and 70 °C by blue, green, and orange lines, respectively. At 50 and 70 °C, the scatter plots exhibit diffraction spots consistent with the polymer backbone aligned perpendicular to the substrate, indicative of flat-on orientation. Additional time points shown in shown in Figure S14.

X-ray scatter plots (Figure a) reveal clear temperature-dependent ordering. Below T _g (black line), films exhibit a broad amorphous peak at q_r ≈ 1.17 Å^–1, denser than the melt-phase value (q_r ≈ 1.013 Å^–1 at 200 °C), indicating a more compact quenched amorphous state. The corresponding azimuthal intensity distributions, corrected for the Ewald sphere curvature and scattering volume (Figure c) is uniform, confirming isotropic molecular orientation and a randomly oriented polymer backbone.

At 35 °C the onset of crystallization is evident: radial plots (Figure b, blue) show emerging crystalline peaks superimposed on an isotropic background, and the azimuthal distribution begins to deviate from an isotropic distribution. This structural transition coincides with AFM observations of small, irregular crystallites at 35 °C that evolve into well-defined crystalline domains at higher temperatures.

To quantify orientation, azimuthal intensity profiles spanning χ = 7°–85° were extracted at q _r = 1.2 ± 0.4 Å^–1, background-subtracted to correct for local scattering volume, and multiplied by sin­(χ) to account for Ewald sphere geometry (Figure c; see Supporting Information Section 7 for details). The resulting sin­(χ)-corrected profiles capture the full angular distribution of scattered intensity and enable direct quantification of molecular orientation. Dashed sin­(χ) curves are overlaid as references for an ideal isotropic distribution. The increasing excess above this baseline with temperature reflects a growing fraction of oriented scatter, particularly near the in-plane direction. By integrating the area above the isotropic envelope, we estimate that the oriented fraction increases from ∼5% at 35 °C to 31% at 70 °C, with the remainder attributed to isotropic scattering. In contrast, the amorphous film exhibits a flat azimuthal intensity profile that closely follows the expected sin­(χ) baseline, indicating a randomly oriented backbone.

While GIWAXS geometry does not capture scattering near χ ≈ 0°, and cannot produce full pole figures without sample tilting, the azimuthal plots serve as a quantitative proxy for orientation distributions in thin-film systems. To facilitate comparison with prior studies, we report Hermans factors , of 0.05, 0.01, −0.10, and −0.10 for the amorphous, 35, 50, and 70 °C samples, respectively. While this metric is less sensitive to multimodal or nonaxial orientation distributions, it remains a common benchmark for assessing overall alignment in semicrystalline polymers.

At 50 and 70 °C, distinct Bragg reflections appear in the 2D GIWAXS patterns indicating the formation of highly oriented crystalline domains. To quantify molecular orientation and extract lattice parameters, we analyzed four distinct reflections located at q_r = 1.16, 1.18, 1.23, and 1.29 Å^–1 with corresponding azimuthal positions at 82°, 75°, 68°, and 62°. These reflections were indexed by best-fit analysis as the $(10\mathrm{1̅}1)$ , $(10\mathrm{1̅}2)$ , $(10\mathrm{1̅}3)$ and $(10\mathrm{1̅}4)$ planes of a hexagonal unit cell (Table S5), arising from the periodicity along the polymer chain axis.

From this indexing, we extract lattice parameters a = 6.37 Å^–1 and c = 41.2 Å^–1, in close agreement with literature values for PCTFE, reported by Miyamoto et al. (a = 6.4 Å^–1, c = 42.5 Å^–1) and Mencik et al. (a = 6.438 Å^–1 and c = 41.5 Å^–1). The strong in-plane scattering of the backbone peaks confirms that the polymer backbone is oriented perpendicular to the substrate, consistent with a flat-on crystal orientation. By analogy with PTFE, the polymer is expected to adopt a helical conformation with noninteger monomer repeat units, assembled into a 6-fold symmetric arrangement. The absence of $(10\mathrm{1̅}0)$ diffraction suggests that basal plane reflections are suppressed due to a lack of strict periodicity along the c-axis.

The azimuthal positions of the chain backbone Bragg reflectionsclustered near the in-plane directionindicate that the corresponding lattice planes are oriented nearly perpendicular to the substrate. Given that these planes are orthogonal to the polymer chain axis, the observed scattering geometry directly implies that the polymer backbone is aligned perpendicular to the substrate, consistent with a flat-on orientation. This assignment is further supported by self-consistent fitting of both q-values and azimuthal angles across the four indexed reflections (Table S5).

Radial GIWAXS profiles and corresponding Voigt fits for each aging condition are provided in the Supporting Information (Figure S15). These fits isolate crystalline peaks from the amorphous background and enable extraction of a relative volumetric crystallinity index. We observe a systematic increase in crystalline peak area with temperature and aging time, reaching a maximum of ∼50% by volume (Figure S16). It is important to note that the GIWAXS-derived values represent a relative crystallinity index based on fitted peak areas over a limited q-range (0.8–1.8 Å^–1), rather than an absolute mass fraction.

To provide additional structural insight, we extracted coherent scattering lengths, which are commonly used as approximations of crystallite sizes. These were calculated using the Scherrer equation applied to Voigt-fitted full width at half-maximum (fwhm) values from GIWAXS measurements, with corrections for instrumental broadening. Although approximate, these estimates reveal modest crystallite coarsening with both aging and increasing temperature. At 35 °C, crystallite size increases from 4.3 to 8 nm over 5 days. At 50 °C, sizes grow to approximately 10 nm, and at 70 °C, a plateau is observed near 11–12 nm across all aging times. These crystallites are significantly smaller than the micron-scale crystalline islands observed by AFM, indicating that each AFM-resolved domain comprises multiple smaller crystallites and is thus polycrystalline as expected. While the temperature-dependent trend supports thermally driven ordering, these values should be interpreted as lower bounds due to the simplifying assumptions inherent in the Scherrer analysis.

While crystallinity increases with temperature, it does not directly correlate with domain coverage. Domain coverage rises from ∼80% at 35 °C to full coverage at 50 °C but declines to ∼60% at 70 °C. Despite this reduction, the thicker, islands observed at 70 °C exhibit stronger diffraction intensity, implying enhanced lamellar stacking and internal ordering. This emphasizes that domain coverage alone does not equate to crystallinity and that domain disorder can influence diffraction intensity independently of coverage.

2.5. Avrami Fits to 3D Data

Linking AFM-based measurements with widely used thermal analysis techniques can expand our understanding of crystallization processes. AFM enables independent measurement of nucleation density and growth rate, allowing direct validation of model predictions through coverage measurements. While thermal analysis quantifies enthalpy changes and glass transition temperature, providing insights into phase transitions and crystallization kinetics. Integrating these methods provides an opportunity to improve predictive power and to validate model choices.

To evaluate how well simplified, analytic models capture crystallization behavior, we extended a two-dimensional Avrami modelparametrized from AFM-derived nucleation densities and growth ratesto three dimensions and compared the resulting predictions with differential scanning calorimetry (DSC) data (Scheme ). This approach provides a quantitative test of model validity and helps to distinguish regimes of primary crystallizationwhere Avrami analysis is applicablefrom secondary crystallization, where it is not. Differential scanning calorimetry measurements include the glass transition temperature, melting onset and peak temperatures, and the integrated enthalpy during melting. Representative thermograms and melting peak shapes are shown in Figures S17 and S18, with summary data in Table S6.

Bulk samples were thermally aged at 35, 50, 60, and 70 °C and measured at 16 time points over 38 days. Two samples were measured per condition and values were averaged. For a subset of conditions, 4–5 replicates were measured to estimate error bars (Table S7). Crystallinity was extracted from the integrated enthalpy as described in the Methods section. The values were normalized to the highest measured crystallinity (22.1%) to obtain the fraction crystalline, which was plotted as a function of time in Figures and S19. Error bars represent a measurement uncertainty of ± 0.9 wt % crystallinity, which corresponds to ± 0.04 on the normalized crystallinity scale. Normalized values below 0.04 fall below the threshold for reliable detection by the instrument.

6.

DSC data of samples aged at (a) 35 °C, (b) 50 °C, and (c) 70 °C over 38 days. Crystallinities are normalized to the highest measured value (22.1%) to obtain the fraction crystalline. Error bars indicate a ±0.9 wt % uncertainty in crystallinity, equivalent to ±0.04 when expressed as a normalized fraction. DSC data points are overlaid with a 3D Avrami model (solid line) using kinetic parameters extracted from hot-stage AFM movies. The maximum domain coverage (θ_max) was adjusted to match the fast-rising phase (<10 days) of the DSC data, attributed to domain nucleation and growth. The subsequent slow increase in crystallinity corresponds to rearrangements within the domains and along domain boundaries, leading to enthalpy release. (d) The glass transition temperature as a function of % crystallinity for samples aged at 35, 50, 60, and 70 °C. The T_g of the amorphous state (black dot) measures 31.3 ± 0.2 °C, increasing to 33.2 ± 0.7 °C (shaded region) during domain growth. During secondary crystallization (points rimmed in black) T _g decreases.

DSC data across all temperatures exhibit a characteristic progression: an initial rapid crystallinity increase, associated with domain nucleation and growth (primary crystallization), followed by a slower increase due to rearrangements (secondary crystallization). , Primary crystallization was modeled using eq , with rate constants and Avrami exponents derived from physical models parametrized by AFM measurements of thin films. To extrapolate from 2D to 3D, the analysis assumes that the quasi-two-2D films represent a radial slice through a spherulite, with growth dominated by lamellae oriented such that their fast-growing direction points radially outward, sustained by a radial flux from the surrounding amorphous phase. Mathematically, circular domains in 2D correspond to spherical spherulites in 3D. To extend nucleation behavior from 2D to 3D, we assume that areal nucleation density (ρ) scales to volumetric density via a ρ^2/3 transformation. Based on film growth findings, crystallization was assumed to follow instantaneous nucleation with reaction-limited growth below 60 °C and diffusion-limited growth above 60 °C. The governing equations are summarized in Table .

2. Avrami Models for 3D Growth.

3D model	k a (s–n )	n	equation
instantaneous nucleation diffusion-limited growth	$$k_{3\mathrm{D},\mathrm{I},\mathrm{DL}}=\frac{4\pi }{3}{\rho }^{3/2}{\alpha }^3$$	1.5	7a
instantaneous nucleation linear growth	$$k_{3\mathrm{D},\mathrm{I},\mathrm{L}}=\frac{4\pi }{3}{\rho }^{3/2}{v}^3$$	3	7b

Calculated rate constants and Avrami exponents based on eq 7 are provided in Table S8. Plots of the Avrami equation (eq ) using these k_a and n values are shown as solid curves overlaid on DSC data points. The Avrami equation models domain growth rather than secondary growth, so the domain coverage, θ_max(T), was adjusted to correspond to the primary crystallization region.

Although this 3D Avrami model is parametrized by measurements and based on fundamental growth modes, we acknowledge that several physical differences between thin films and bulk samples may influence the accuracy of this mapping. In spherulitic growth, lamellae are generally understood to propagate radially with their basal surfaces aligned parallel to the radial direction. In ultrathin films exhibiting flat-on orientation, this corresponds well to the lateral growth direction observed by AFM. However, in bulk systems, lamellar bundles are typically tens to hundreds of nanometers thickand can be significantly larger than the ∼50 nm thickness of our films. As a result, radial growth rates in bulk are expected to be modestly higher, estimated at ∼10%. In addition, while our film thickness exceeds the polymer radius of gyration, subtle confinement effects or substrate interactions may still influence nucleation kinetics or chain mobility.

Additionally, bulk crystallization may be modulated by mesoscale structural processes such as lamellar twisting, branching, and splitting, which are largely suppressed in 2D systems. These features contribute to morphological complexity and can alter local growth kinetics through curvature or self-avoidance effects within growing lamellar bundles. Such processes are not captured in the simplified nucleation-and-growth framework used here but may contribute to deviations between predicted and observed crystallinity, particularly at longer times. Despite the simplicity of the model and the use of 2D-derived nucleation densities and growth rates, the predictions perform well in the primary growth region of the crystallization curve suggesting that the model captures the dominant features of the crystallization process.

This approach visually distinguishes domain growth contributions from other molecular ordering processes. Once domain growth concludes, the slow, approximately linear, rise in crystallinity (shaded in gray) is attributed to adjustments within domains and at boundaries. Crystallinity increases during secondary crystallization have slopes of 0.08, 0.12, 0.11, and 0.16% per day for 35, 50, 60, and 70 °C, respectively. For temperatures above 50 °C, the slope decreases over time, arguing for a plateau with a maximum crystallinity near 22 mass % for 50 and 60 °C (Figure S20a).

The glass transition temperature (Figure d) also exhibits distinct trends linked to primary and secondary crystallization. The amorphous state (solid black dot) has a T _g of 31.3 ± 0.2 °C, increasing to 33.2 ± 0.7 °C during domain growth, independent of crystallization temperature. During secondary crystallization, T _g decreases with slopes of −0.02, −0.04, −0.04, and −0.08 °C per day (Figure S20b) for 35, 50, 60, and 70 °C, respectively (points rimmed in black). Notably, the greatest T_g reduction is not linked to the most crystalline sample (50 °C, green) but rather to higher crystallization temperatures (60 °C, yellow; 70 °C, orange), where increased mobility and thicker crystals lead to T_g dropping as much as 2° below the amorphous state.

3. Discussion

This study explored a broad time–temperature crystallization window, with measurements conducted between T _g + 4 °C and T _m – 10 °C, providing a comprehensive view of the crystallization kinetics of FK-800. Figure summarizes key transitions in nucleation mode, growth mode, and morphology with temperature.

7.

Overview of FK-800 crystallization showing kinetic and morphological transitions. Graph insets show zoomed images of individual crystal morphologies at a time before domains impinge. X-ray scattering confirms a flat-on orientation (chain axis perpendicular to substrate) across all temperatures. AFM images of the microstructure are shown after 96, 96, 500, and 400 h of aging for 35, 55, 80, and 100 °C respectively. Images are 10 μm × 10 μm, with z-scale of 50 nm.

A transition from homogeneous to heterogeneous nucleation is identified near 45 °C that is quantitatively based on measured nucleation densities and a two-component theoretical model. While prior studies used AFM to detect nucleation events at the nanometer scale, , to our knowledge, this is the first to quantify nucleation densities and rates using AFM in polymer systems. We identify homogeneous nucleation by the exponential increase in nucleation density with undercooling, and heterogeneous nucleation by the temperature-independent nucleation density. This approach has been widely applied in conjunction with optical microscopy, ,, and AFM extends this approach to submicron features, enabling kinetic quantification at earlier times and closer to T _g and T _m , where feature sizes are smaller.

While many AFM studies have examined radial growth and filament velocities in different polymer systems, ,− ,,− systematic investigations across a broad range of undercoolings have been conducted for only a few systems. , In this work, kinetic data were modeled to extract surface energies and activation barriers. From nucleation data, we estimated σ²σ _e = 3.3 ± 0.3 × 10^–7 J³ m^–6 and from velocity data, σσ _e = 6.3 × 10^–5–7.6 × 10^–5 J² m^–4, yielding surface free energies of σ = 0.004–0.005 J m^{– 2} and σ _e = 0.012–0.018 J m^{– 2} with a ratio σ _e /σ between 2.4 and 4.5. Knowledge of the surface energies allows us to calculate the critical lengths for both nucleation (Figure S7) and step motion (Figure S5) as a function of temperature. The critical lengths are proportional to ΔT ^–1 and therefore diverge near the melting point but remain below the film thickness for all temperatures evaluated.

Velocity data were used to extract an activation barrier for diffusion, yielding ΔE ≈ 0.9 eV. This relatively high value is likely attributable to the high specific density of FK-800 (2.04) and its quenched amorphous initial state. We also note that the shape of the theoretical growth rate curve given by eq (Figure ), over predicts radial growth rates near T _g and under predicts growth rates near T _m , suggesting that G ₀, ΔE and K ₂ may not be strictly independent of temperature as this model assumes.

Importantly, this is the first study to quantitatively extract kinetic parameters from AFM data, that include fundamental parameters described above as well as Avrami rate constants and exponents in both 2D and 3D. Avrami predictions based on measured nucleation and island growth parameters show good agreement with experimentally measured coverage vs time data over the full temperature range. The Avrami model includes a temperature-dependent maximum domain coverage, θ_max(T) which decreases from 1 to 0 between 60 °C and the melting temperature that reflects the increasing solubility near the melting temperature (Figure S12). DSC data of thermally aged samples further support this term, showing melting onset between 75 and 98 °C, well below the melting temperature (Table S6). This suggests that, within this range, the crystallized samples must partially convert their crystalline phase to the amorphous phase to reach equilibrium, indicating they have exceeded their solubility limit.

A growth-mode transition from linear to diffusion-limited (DL) occurs near 60 °C. Initially, we hypothesized that DL growth was linked to depleted zones (moats) acting as diffusion barriers around crystal edges, as reported by Taguchi et al. Moats first appear at ∼40 °C, deepen and widen with temperature, but diminish above ∼90 °C (Figure S2). However, since linear growth persists up to ∼60 °C and DL growth is still observed above 90 °C, where moats are less pronounced, their presence does not correlate with the growth-mode transition in our system. The disappearance of moats at high temperatures likely results from increased molecular mobility, which facilitates amorphous phase rearrangement and surface smoothing. When mobility is sufficiently high, depleted zones redistribute, leading to a uniformly thinner amorphous film rather than localized moats. Their transient nature is illustrated by time-dependent evolution; moats observed at 80 °C after 24 h (Figure ) are largely absent after 500 h of aging (Figure ).

Instead, DL growth appears correlated with increasing crystal thickness. Below 60 °C, domains protrude less than 5 nm above the film surface, increasing to nearly 30 nm by 100 °C (cross sections shown in Figure S2). This trend likely reflects multilamellar stacking or lamellar thickening as the critical step length, L*, increases with temperature (Figure S5). At elevated temperatures, the vertical buildup of crystalline domains out of the plane of the amorphous reservoir may require material transport through the crystal or along grain boundariespathways that are less efficient than lateral in-plane transport. As a result, the kinetics become increasingly limited by diffusion, even as molecular mobility in the amorphous phase increases.

Morphological evolution aligns with literature on ultrathin films. , The growth morphology evolves from irregular domains at high driving forces to compact seaweed-like patterns, then to dendritic structures with re-entrant corners, and finally to the equilibrium hexagonal shape. At the highest temperatures, the hexagonal corners become fully rounded, forming nearly circular shapes.

Crystallization kinetics directly impact final morphology and, thus, material performance. In systems dominated by instantaneous nucleation, domain size is inversely proportional to nucleation density, resulting in a Voronoi-like tessellation with convex cells and a deterministic average size. Based on this, average domain diameters are ∼0.2, 0.4, and 0.7 μm for 35, 40, and 45 °C, respectively, increasing to ∼1.1 μm at 50 °C and above. However, above ∼70 °C, domains cease radial growth before achieving full coverage, due to solubility limits and average size begins to decrease with temperature. Images from the end of hot-stage AFM experiments (Figure ) illustrate how nucleation mode, growth mode, and solubility constraints collectively determine microstructure.

4. Conclusions

This study establishes a robust, multiscale framework quantifying and interpreting crystallization kinetics in semicrystalline polymers by integrating in situ AFM, GIWAXS, and DSC. By combining nanoscale imaging and bulk thermal analysis, we directly link thin-film crystallization behavior to bulk crystallinity. Nucleation and radial growth rate data measured by AFM enabled extraction of fundamental parameters, including surface free energies and diffusion activation barriers that define the energetic landscape of crystallization. AFM, imaging also revealed key temperature-dependent transitions: a shift from homogeneous nucleation to heterogeneous nucleation near 45 °C, and from linear to diffusion-limited growth above 60 °C.

These experimentally measured kinetic inputs were incorporated into physically grounded Avrami models, which accurately predicted the time evolution of crystalline coverage and matched direct experimental fits. This validation demonstrates that the Avrami kinetics can be mechanistically interpreted when informed by nanoscale data. Furthermore, we extended this 2D-based model to predict 3D crystallization behavior by identifying and incorporating the relevant growth modessuch as the nucleation mode and the transition from linear to diffusion-limited growthachieving quantitative agreement with DSC-derived crystallinity.

GIWAXS complemented these analyses by confirming the identity of the crystallizing phase as PCTFE, verifying that molecular orientation favored in-plane growth along the fastest crystallographic axis, and providing the lattice parameters a and c required to calculate step heights in activation barrier models. It also yielded estimates of coherently scattering domain sizes from peak broadening, which correspond to crystallites within the larger AFM-resolved domains, although these values are not independently verified in this study. Finally, peak integration produced a crystallinity index that captures relative trends, supporting findings from AFM and DSC measurements.

Together, these findings establish a multiscale framework in which thin-film measurementswhen interpreted through physically grounded modelscan yield predictive insight into bulk crystallization. This approach offers a transferable toolkit for understanding and controlling crystallization kinetics in functional polymer systems, with direct implications for tuning microstructure and optimizing processing across scales.

5. Experimental Methods

5.1. Materials

FK-800 (3M) is a linear, random copolymer composed nominally of 75 ± 4 mol % chlorotrifluorethylene (CTFE) and 25 ± 4 mol % vinylidene fluoride (VDF) monomer residues with number average molar masses in the range of ∼20 KDa to 160 kDa. We expect composition differences to affect the kinetics, for this reason this study used one lot to focus on temperature effects. The lot used in this study had a specific density of 2.04, a melting temperature of 110 °C, and was composed of 76 mol % CTFE per manufacturer, which corresponds to a molecular weight of 103.89 g/mol and 0.85 CTFE mass fraction. We estimate a heat of fusion for FK-800 (36.7 J/g) that is 85% of the heat of fusion of PCTFE (43.1 J/g). Gel permeation chromatography coupled with multiangle light scattering (GPC-MALS) was used to measure the weight-average molecular weight (M _w ) of 120.8 kDa, a dispersity (M _w /M _n ) of 1.13 and radius of gyration ∼11.9 nm (in ethyl acetate). Ethyl Acetate (Sigma-Aldrich) was used as received.

5.2. Sample Preparation

Thin film samples were prepared by spin-casting solutions of 1 wt % FK-800 in ethyl acetate onto plasma-cleaned 10 mm × 10 mm 100-silicon wafers. The films were subsequently annealed at 120 °C for 20 min under a nitrogen atmosphere to remove residual solvent and then rapidly quenched below T _g in water to ensure an amorphous starting state. Final film thicknesses were measured using atomic force microscopy scratch tests and ranged between 45 ± 5 nm. Bulk samples for DSC were prepared by melting FK-800 powders at 150 °C in a nitrogen environment overnight. Melted samples were immediately quenched in liquid nitrogen to preserve the amorphous state. Samples were then aged in ovens in a nitrogen environment at 35, 50, 60, and 70 °C for up to 38 days. Bulk and thin film samples were stored in a refrigerator (4 °C) to preserve their crystalline state when not being thermally aged or measured.

5.3. Atomic Force Microscopy

Crystallization kinetics were studied using an Asylum Research Cypher and Jupiter AFM equipped with a temperature-controlled hot stage. The AFM stage was equilibrated at the desired crystallization temperature (35–100 °C) for several hours prior to the start of the experiment to minimize temperature gradients. Samples were then mounted onto the hot stage and imaged for up to 16 days. AFM imaging was performed in tapping mode using AC160 tips with typical spring constant of 25 N/m, resonant frequency of 300 kHz, and sensitivity of 60 nm/V. Height, Phase and Amplitude images were captured at regular intervals, ranging from 5 min to 1 h, at 512 × 512 pixels. For a 5 μm image this corresponds to a pixel-resolution of 9.8 nm which is comparable to typical tip radius (7 nm). The drive frequency was chosen at the resonant frequency and the phase adjust to 90°; imaging used free amplitudes of 500 mV and set points of ∼400 mV such that imaging typically occurred in the repulsive mode (phase ∼ 70°) and had dither amplitudes of ∼24 nm, comparable to the maximum feature sizes expected.

To assess whether the AFM tip influenced crystallization kinetics during imaging, we periodically scanned a larger area to check for scan box artifacts or statistical variations. Examples showing the absence of scan boxes are shown in Figure S21 and S22. No evidence of tip-induced perturbations was observed under the specified imaging conditions. At the end of the movie, we examined one to two additional regions to determine whether the imaged area was representative of the overall film. Examples with coverage and nucleation density measurements in three locations shown in Figure S22.

Images were analyzed using Gwyddion software. Nucleation density was calculated by counting the number of crystalline nuclei in AFM images (N) and normalizing by the image area (A). Error bars represent counting statistics (√N A ^–1). Growth rates were determined by tracking the effective radius of isolated crystals over time, assuming a disk-like morphology. Between 3 and 12 individual crystal radii were measured over 4–8 time points within each movie sequence. Radius-versus-time data for each crystal were fit independently to extract growth rates. The average growth rate and its uncertainty were obtained as the mean and root-mean-square (RMS) of all fits, with each reported value reflecting approximately 35 individual radius measurements (range: 12–96). The assignment of linear versus diffusion limited growth was based on the root-mean-square error. Error and goodness of fit are given in Table S3. The crystalline surface coverage was measured by masking the crystalline regions and dividing their area by the total image area. Time-dependent coverage data were fitted to the Avrami equation to extract rate constants and exponents, with each fit based on 6–12 measurements.

5.4. X-ray Scattering

Grazing Incidence Wide-Angle X-ray Scattering (GIWAXS) measurements were conducted at beamline 7.3.3 of the Advanced Light Source using an X-ray energy of 10 keV (wavelength = 0.124 nm) with an energy bandwidth of ΔE/E ≈ 1%. Instrument broadening is estimated at 1%. Silver behenate was used to calibrate the energy axis. The sample-to-detector distance was 286.005 mm. Data were collected using a Pilatus 2 M detector with a resolution of 1475 × 1679 pixels and a pixel size of 172 μm.

Incident angles were initially surveyed from 0.1° to 0.2° in 0.02° increments before selecting 0.16° for the majority of measurements. The incident beam had a rectangular profile of 300 μm in height and 700 μm in width. Measurements were performed in a helium environment with an exposure time of 30 s. Data reduction and analysis were carried out using Nika (v1.826) supplemented by custom Python codes developed in-house.

Samples were analyzed after ex situ thermal aging at 35, 50, and 70 °C for 1, 5, and 6 days. Scattering patterns were processed to determine crystallinity and preferred orientation. An in-plane powder distribution was assumed, consistent with AFM imaging. For detailed analysis methods, refer to the fitting procedures in the Supporting Information. The strongest peak, corresponding to the $(10\mathrm{1̅}2)$ reflection, was observed at q = 1.18 Å^–1, with a corresponding Bragg angle of approximately 6.7°.

5.5. Differential Scanning Calorimetry

Measurements were conducted using a TA Instruments DSC 2500. Approximately 10 mg of each sample (weighed to ± 0.0001 g) was sealed in a DSC pan (TA Instruments). A prerun baseline with an empty pan was subtracted to reduce instrumental drift and temperature-dependent background contributions. Samples were positioned at the bottom of the pan for optimal thermal contact. The temperature program consisted of equilibration at −60 °C, a ramp to 200 °C at 20 °C/min, a 5 min isothermal hold at 200 °C, cooling to −60 °C at 20 °C/min, and a final ramp to 200 °C at 20 °C/min. Data analysis was performed using TRIOS software. Two samples were measured for each condition (and their values averaged). This corresponds to 78 measurements with 16 to 22 measurements per temperature series. For three sample conditions 4–5 replicates were measured resulting in standard deviations of 0.26%, which reflects sample-to-sample variability and measurement reproducibility (Table S7). Representative heat flow curves are plotted in Figures S17 and S18. The glass transition temperature was defined as the midpoint of the inflection curve and is shown in Figure d. The onset of melting and the temperature at the peak of the melting curve are tabulated in Table S6. The crystallinity was calculated using the formula:

$$\mathrm{Crystallinity}(\%)=100\frac{\mathrm{\Delta }{H}_{\mathrm{measured}}}{w\mathrm{\Delta }{H}^{0,\mathrm{PCTFE}}}$$

where the weight fraction for FK-800, w, is 0.85 and the enthalpy of melting for PCTFE, ΔH ^0,PCTFE, is 43.1 J/g.

We conservatively estimate the integration uncertainty to be ±0.3 J/g, based on signal-to-noise considerations and baseline sensitivity for low-enthalpy transitions. This corresponds to an uncertainty of ±0.8 wt % crystallinity for FK-800. Propagating this with the pooled standard deviation yields a total estimated uncertainty of ±0.9 wt % crystallinity. Samples aged 8 h or less showed no detectable melting peak above the noise floor, indicating crystallinity below the instrument detection threshold. The first measurable crystallinity was observed after 24 h of aging.

No exothermic peak is observed during cooling from the melt, enabling quenching into the glassy state. Additionally, no cold-crystallization peak appears during the second heating ramp, ensuring the erasure of thermal history and allowing the study of the full crystallization range from T _g to T _m (Figure S17).

5.6. Thermodynamic Estimates

The chemical potential was estimated using

$$\mathrm{\Delta }{\mu }_{\mathrm{molecule}}=\frac{\mathrm{\Delta }{H}_m^{0,\mathrm{FK}-800}(T_m-T)}{T_m}$$

where ΔH _m = 43.1 J/g represents the enthalpy of fusion for pure PCTFE, and is adjusted for FK-800 composition as ΔH _m = 0.85ΔH _m ≈ 7.5 × 10⁷ J/m³ = 6.33 × 10^–21 J/molecule. The melting temperature was taken as T _m = 383.15°K (110 °C). The entropy is estimated to be ΔS ≈ 1.65 × 10^–23 J/(molecule °K).

Glossary

Abbreviations

AFM

atomic force microscope

GIWAXS

grazing incidence wide-angle X-ray scattering

DSC

differential scanning calorimetry

CTFE

chlorotrifluoroethylene

VDF

vinylidene fluoride

PCTFE

polychlorotrifluoroethylene

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.5c00905.

• Morphology, kinetic data, nucleation barrier derivation, Avrami growth models, structural evolution, DSC analysis, and extrapolation to 3D models (PDF)

†.

University of Illinois at Urbana–Champaign, Materials Science and Engineering, 104 S. Goodwin Ave., Urbana, Illinois 61801, United States

C.A.O. and J.P.L. designed the study. E.C. and X.X. synthesized the samples. E.C. and C.A.O. conducted AFM studies and analysis. X.X. performed DSC measurements and analysis. C.A.O., X.X., E.C. carried out X-ray scattering experiments and data analysis. C.A.O. wrote the initial draft of the manuscript. All authors contributed to data interpretation, reviewed, and approved the final version of the manuscript.

The authors declare no competing financial interest.