# Laser sintering of PA12 particles studied by in-situ optical, thermal and X-ray characterization

Prakhyat Hejmady, Lambert C.A. van Breemen, Daniel Hermida-Merino,
Patrick D. Anderson, Ruth Cardinaels

► To cite this version:

Prakhyat Hejmady, Lambert C.A. van Breemen, Daniel Hermida-Merino, Patrick D. Anderson, Ruth Cardinaels. Laser sintering of PA12 particles studied by in-situ optical, thermal and X-ray characterization. Additive Manufacturing, 2022, 52, pp.102624. 10.1016/j.addma.2022.102624. hal-05075670

HAL Id: hal-05075670

https://cnrs.hal.science/hal-05075670v1

Submitted on 20 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

Research paper

# Laser sintering of PA12 particles studied by in-situ optical, thermal and X-ray characterization

Prakhyat Hejmady<sup>a</sup>, Lambèrt C.A. van Breemen<sup>a</sup>, Daniel Hermida-Merino<sup>b</sup>, Patrick D. Anderson<sup>a</sup>, Ruth Cardinaels<sup>a,c,*</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

- In-situ WAXD

- Crystallization

- Polyamide 12

- Additive manufacturing

- Selective laser sintering

## ABSTRACT

The microstructure of products manufactured by selective laser sintering (SLS) is known to be highly dependent on various process and material parameters. The latter thus also affect the final part properties. While most work has focused on ex-situ characterization of the printed parts, little is known about the time-dependent microstructure development during sintering. In this work, we present direct observations of the microstructural evolution during laser sintering of polyamide 12 (PA12) particle doublets by in-situ synchrotron wide angle X-ray diffraction (WAXD), using our in-house developed laser sintering setup. Simultaneously, the neck growth between the particles and the temperature are captured via optical and infrared microscopy. We show that isothermal crystallization experiments under quiescent conditions are not sufficient to describe crystallization in a non-isothermal process like SLS. The enhanced crystallization kinetics in small particles suggests that both temperature and flow play a role. This finding was corroborated by the critical Weissenberg numbers estimated from rheological reptation and Rouse time scales. Furthermore, a microstructure survey has been carried out by microtoming thin slices of the sintered doublets. Both optical and atomic force microscopy reveal significant differences in the crystalline structure of the laser-affected zone as compared to the un-sintered region.

## 1. Introduction

Additive manufacturing has traditionally been used for fast prototyping of complex products. Research and development over the past decade has shown potential in this technique to move from prototyping towards mass manufacturing. Its importance has grown in several sectors such as automotive, instrumentation as well as biomedics and nutrition wherein demands are specific to individual consumer's needs [1-3]. In particular, powder-based techniques for polymers, such as selective laser sintering (SLS), are capable of generating parts with acceptable properties, thereby gaining more interest [4]. Materials used in SLS are initially in powder form. The material is spread in thin layers in a temperature controlled chamber. A laser is then used as heat source to locally raise the material temperature above the melting point to selectively melt the powder, thereby joining powders into a product with a predetermined size and shape [4]. Up to now, extensive research has been done to optimize the SLS process, to produce dense parts with good mechanical or other functional properties and shape

fidelity, as summarized in several recent reviews [1-8]. However, the understanding behind the physical processes involving the material response upon laser impact are not well understood. A major cause for this is the fact that industrial SLS setups do not allow visualization of the process, thereby limiting most studies to ex-situ characterizations.

The range of materials suitable for processing by selective laser sintering is very much dominated by polyamide 12 (PA12) [9]. Due to its narrow melting range and broad processing window, it is an ideal material for laser sintering while avoiding premature coalescence or crystallization of the particles [10]. The mechanical properties are strongly dependent on the solidification process during sintering which governs the resulting macrostructure of the produced material and the occurrence of porosity, voids or cracks [11], but also the crystalline microstructure [12]. Depending on the final temperature and cooling rate, PA12 can undergo phase transitions due to its polymorphism. Four different phases namely the γ-phase, the α-phase, the α'-phase and a mesomorphic phase can be formed, depending on the processing

<footnote><sup>a</sup> Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands</footnote>

<footnote><sup>b</sup> DUBBLE CRG BM26 at ESRF, Netherlands Organization for Scientific Research (NWO), 71 Avenue des Martyrs, 38000 Grenoble, France</footnote>

<footnote><sup>c</sup> Soft Matter Rheology and Technology, Department of Chemical Engineering, KU Leuven, Box 2424, 3001 Heverlee, Belgium</footnote>

<footnote>* Corresponding author at: Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.</footnote>

<footnote>E-mail address: R.M.Cardinaels@tue.nl (R. Cardinaels).</footnote>

<footnote>https://doi.org/10.1016/j.addma.2022.102624</footnote>

<footnote>Received 15 August 2021; Received in revised form 14 December 2021; Accepted 10 January 2022</footnote>

<footnote>Available online 5 February 2022</footnote>

<footnote>2214-8604/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</footnote>
conditions. The hexagonal γ-phase is the most stable phase and forms under slow cooling conditions or after annealing at temperatures between 90 °C and 130 °C [13]. Upon quenching from the melt state to temperatures below 90 °C, a mesomorphic structure forms while at high temperatures above 130 °C, the α'-phase dominates [12]. The α phase is seldomly encountered, since it requires special processing conditions. Calorimetric techniques have been applied to investigate the effect of the cooling process on the crystallization kinetics [14,15] and the nucleation density and crystal growth rate have been quantified at different temperatures [15,16]. Additionally, PA12 has been shown to exhibit a pronounced melt memory, which is linked to its high potential for hydrogen bond formation [17]. Melt memory is caused by insufficient heating temperatures or times. Even though no remaining crystal fragments can be detected, polymer orientation or sticky interactions between polymer chains resulting from the prior crystalline state, can act as nucleation points for crystallization, leading to self-nucleation [18]. The material thus exhibits enhanced crystallization temperatures and faster crystallization. As a more extreme case of memory effects, laser sintered parts sometimes show remaining crystals or crystal fragments at the core of the particles [19], which may act as self-seeds. Up to now, these studies on PA12 merely consider quiescent crystallization. However, it has been shown that flow can influence the crystal morphology and crystallization kinetics of thermoplastic polymers such as polyamide [20]. During laser sintering, polymer particles undergo deformation within relatively short timescales. Therefore, flow effects may play a role in laser sintering.

Apart from being limited by intrinsic material properties, the final part performance is strongly dependent on the processing method and conditions. For instance, comparisons between laser sintered and compression moulded or injection moulded PA12 show that, although laser sintered PA12 can have better intrinsic mechanical properties caused by thicker crystals, porosity, voids and surface roughness cause enhanced brittleness at room temperature [11,12]. In laser sintering the process variables such as heating chamber temperature, laser power [21,22], scan speed [22,23] and interlayer time [21] can influence the consolidation behavior of the powder particles and the resulting microstructure [4]. Intrinsic defects within the part, like poor layer-to-layer adhesion and porosity can arise if the process parameters are not optimized, leading to parts with poor mechanical properties. Moreover, the crystalline microstructure depends on the heating and cooling trajectory. It has been demonstrated that processing conditions affect the spherulite size whereby a low laser energy and large particles can even lead to unmolten cores [19]. The latter can contribute significantly to the brittleness of laser sintered material [24]. Furthermore, powder shape as well as molecular and microstructural parameters play a significant role in the final properties [25]. Hence, powder screening methods for laser sintering powder should include various powder characteristics [26]. Analysis of the process is further complicated by the fact that typically a non-homogeneous temperature profile is present throughout the powder bed and powder particles undergo a complex thermal history [27]. The consequences of in-homogeneous cooling are a varying crystal microstructure along the part [25], and part warpage resulting in deviations of the desired geometry and irreproducible properties [8]. Therefore, knowledge on the local processing conditions is required to link processing to structure and properties.

Although many studies focus on the relations between overall processing conditions on the one hand and resulting microstructure or mechanical properties on the other hand, in-situ characterizations of the sintering process are rather limited. Recently, researchers started to use techniques such as in-situ thermal imaging [28], fringe projection [29] and optical coherence tomography [30] to gain access to the temperature profile of the powder bed [28], as well as its deformation upon sintering [29] and the melt pool depth [30]. However, these methods do not give in-situ access to the neck growth between particles or the crystallization kinetics. On the other hand, hot-stage microscopy has been used to study temperature-dependent sintering rates on a

hot stage in absence of laser heating [31]. No experimental study was found in literature that links, in real time, the flow and non-isothermal temperature profiles observed during laser sintering to the crystallization kinetics. Therefore, our aim is to provide fundamental understanding of the microstructural evolution during laser sintering of doublets of semi-crystalline PA12 particles, using our in-house developed setup [32]. This setup uses a visible light laser, which allows us to deposit a well-known amount of laser energy locally onto one pair of polymer particles. Despite the fact that the majority of commercial laser sintering devices use a CO₂ laser, visible light laser sintering setups are commercially available and used in materials research [33], and provide opportunities for development of low-cost sintering devices [34]. An in-situ study of laser sintering of amorphous polystyrene performed with an earlier version of our setup has been reported elsewhere [35]. The design and development of the setup, as well as a demonstration of its capabilities for in-situ X-ray characterization are already reported in our prior work [32]. In the present work, the obtained crystalline microstructure imaged by X-ray measurements will be correlated with the flow behavior studied by optical microscopy and the temperature profiles acquired by infrared imaging. The possibility to simultaneously characterize these three parameters will allow to shed light on the relevant mechanisms governing microstructure development during laser sintering of semi-crystalline polymers.

## 2. Material and methods

### 2.1. Material

Polyamide 12 (Vestamide L-1700) was obtained in pellet form and free from additives. Its average molecular weight $M_w$, as measured by size exclusion chromatography is 53 kg/mol. The surface tension of molten PA12 was taken from literature, wherein a value of 34.3 mN/m was calculated by determining the cohesive energy density from PVT data, a method shown to be accurate for a wide range of polymers [36]. Furthermore, the thermal conductivity of PA12 ranges from 0.19 to 0.25 W/(mK) [37] and its heat capacity $c_p$ was measured to be 1200 J/(kgK). PA12 was colored black by adding 2 wt% of Nubian Black PC-0870 dye (Orient Chemical Industries co., Ltd) through solution mixing in benzylalcohol at 120 °C. Subsequently, spherical PA12 particles of various sizes, with their radius ranging between 50 µm and 200 µm, were prepared by grinding followed by a thermal annealing protocol as described elsewhere [38]. The absorption of visible light with wavelength 532 nm for thin films with a thickness similar to the size of the spherical particles (≈100 µm) was determined to be 91%. All samples used for calorimetric or rheological characterization as well as sintering experiments were dried for 8 h at 80 °C before each experiment.

### 2.2. Material characterization

#### 2.2.1. Size exclusion chromatography

A Waters 2996 column was applied for size exclusion chromatography measurements, applying both a photo-diode and a refractive index detector. The average molecular weight was determined from the elution time, after calibration of the column with 11 PMMA calibration standards with molecular weights between 1.10³ and 1.10⁷ g/mol. The solvent used was HFIP (Merck, ≥99.8%).

#### 2.2.2. DSC and flash-DSC

For differential scanning calorimetry (DSC) a Mettler Toledo 823e/700 device was used and fast scanning chip calorimetry was performed with a Mettler Toledo Flash DSC1 Star System with a Huber intracooler TC100. Indium was used to perform the heat flux and melting enthalpy calibration. A heating rate of 10 °C/min was used to determine the peak melting temperature and the melting enthalpy from the second heating run. The second heating run was chosen due to less accurate results in the first heating run because of the limited and
irregular sample-pan contact. Isothermal crystallization experiments were carried out for a temperature range of 70 °C to 170 °C. Nitrogen gas was used to prevent oxidation of the sample. Preconditioning of the sample was done by heating to 220 °C. In FDSC, this temperature was kept for 1 s, after which the sample underwent fast cooling at 1000 °C s⁻¹ to the desired temperature, where it was then kept for long enough time to allow full crystallization. In DSC, a similar protocol was used, whereby the sample was kept at 220° for 3 min and cooled with a lower cooling rate. The peak crystallization times as a function of temperature were determined as the time of maximum heat flow in the exothermal crystallization peaks. All thermal characterizations were performed on PA12 with 2 wt% dye. For PA6, it has been shown that grinding can increase the crystallization temperature due to deformation induced memory effects [39]. Moreover, the solution mixing process, used to dissolve the dye in the polymer, typically leads to a partially unentangled melt, which restores its initial entangled state only after relatively long annealing times [40]. Such an unentangled melt shows accelerated crystallization kinetics due to enhanced chain mobility [40]. To ensure that the crystallization parameters obtained from the calorimetric experiments are representative for the spherical particles used for laser sintering, FDSC was performed on spherical particles with various particle sizes (radius between 50 and 200 µm). These tests showed that the crystallization temperature is not affected by the particle preparation protocol or particle size. An example for isothermal crystallization at 120 °C for two different particle sizes is shown in Supplementary Figure S1.

### 2.2.3. Rheology

An MRC 502 stress-controlled rotational rheometer (Anton Paar) was used for the rheological characterization. The sample was loaded in a plate-plate geometry with a diameter of 25 mm placed inside a nitrogen-flushed convection oven. First, a strain sweep test at 1 Hz was done to ensure that all subsequent characterizations were in the linear viscoelastic regime. Isothermal characterization at 10% strain was performed at temperatures of 162 °C, 170 °C, 180 °C, 190 °C, 200 °C and 210 °C on PA12 with 2 wt% dye. Frequencies were applied from high to low values. Within the time-frame of the experiments, i.e. maximum 20 min, the changes in the dynamic properties with time were negligible, thus indicating limited effects of post-condensation.

### 2.3. In-situ characterization of laser sintering

To understand the microstructure evolution at the interphase of the particle doublets, an in-house laser sintering setup [32] has been utilized. This setup provides the possibility to visualize the flow dynamics and simultaneously perform time-resolved in-situ X-ray experiments, as shown schematically in Fig. 1a. Using an in-house developed micro-positioning setup [32], two similarly sized PA12 particles are placed on the substrate in a heated chamber, wherein the interface is aligned to the X-ray beam as well as to the optical and laser source. Initial conditioning was kept the same for all experiments wherein the heating chamber was heated to 155 °C, which is sufficiently below the melting temperature (178 °C) of PA12, and then cooled down to the desired chamber temperature, before performing in-situ experiments. A known amount of laser energy is sent in one pulse locally at the contact point of the particles and simultaneously the sintering kinetics is captured by optical imaging as well as X-ray scattering. Experiments were performed on PA12 particle doublets with various particle sizes and chamber temperatures, keeping the laser energy, pulse duration and radius of the laser spot fixed at 384 µJ, 1 ms and 15 µm respectively.

Optical images taking from the top were utilized to measure the sintering neck formed between the particles as a function of time. The image sequence was analyzed using Matlab® [32], whereby the neck radius (x in Fig. 1b) growth at the interface of the particles was followed in time. The temperature distribution across the particle surface was measured from the side with an infrared Optris PI640 camera

with lens. At the used working distance, a pixel size of 31 × 31 µm² was achieved. The used emissivity was 0.85 and measurements of the temperature profile of a polymer bead on the temperature-controlled heating bed of the heating chamber confirmed that the camera was providing correct temperature values.

Wide-angle X-ray characterization was performed by placing the setup in the BM26 (DUBBLE) beamline at ESRF in Grenoble (France) [41,42]. X-rays with a wavelength of 0.9799 Å (12.653 keV) and beam cross-section of 100 µm × 100 µm were used. A Pilatus 300 K detector with a pixel size of 172 µm × 172 µm was placed at 409 mm from the sample. This geometrical distance, together with the tilt angle, were calibrated with Al₂O₃ (α-alumina). The Fit2D software [43] developed by the European Synchrotron Radiation Facility was used to analyze the 2D WAXD data. First, a background correction was performed. Then, the scattering patterns obtained from the WAXD experiments were radially integrated over an azimuthal angle of 90° and the intensity was plotted versus the scattering vector q. By fitting the integrated intensity with a double Gaussian-Lorentzian function [13], the peak position and peak width can be determined. The scattered intensity profile just before the polymer starts to crystallize was fitted with an additional Gaussian-Lorentzian function to fit the amorphous background [44]. The crystallinity was calculated from:

$$ \chi_c = \frac{A_c}{A_c + A_a}, \qquad (1) $$

where $\chi_c$ is crystallinity, $A_c$ is the area under the crystalline peak and $A_a$ is the area under the amorphous halo. Since neck growth and crystallization turned out to be sequential processes, the path length through the sample and corresponding attenuation do not change during crystallization characterization. Since preliminary experiments showed a too low scattering intensity in the SAXS range, only WAXD characterization was performed. Therefore, an estimate of the average crystallite thickness (e.g. the size of the coherently scattering domain) perpendicular to the reflecting plane will be made using the Scherrer equation [45]:

$$ L = \frac{K\lambda}{\beta \cos(\theta)}, \qquad (2) $$

where $\lambda$ is the X-ray wavelength, $\beta$ is the peak width at full width half maximum of the diffraction peak profile in radian, $\theta$ is the Bragg angle and K is typically 0.9, but in principle dependent on the crystallite shape [46]. Due to the focussing of the beam, instrumental smearing effects are limited, with broadening caused by the finite beam size amounting up to 5% of the peak width. Therefore, no corrections were applied for instrumental broadening [47]. It should be noted that the detector is covered with a thin kapton film. The latter also exhibits a diffraction peak, which occurs at much lower q values than the crystalline peaks of PA12 and remains unaltered during the sintering experiments.

### 2.4. Characterization of morphology in sintered doublets

To study the crystal morphology, microtomed samples of sintered PA12 doublets are prepared using a Leica RM2235 microtome, to obtain 2 µm thin samples. Sintered doublets are embedded in epoxy resin (Araldite 2015 with 2:1 resin:curing agent ratio, Huntsman) and then microtomed using a glass knife at room temperature. Sections along the long axis of the melt doublets are performed and imaged with polarized light microscopy (Olympus). For atomic force microscopy (AFM), the remaining half of a doublet was further cryo-microtomed at -120 °C by removing several slices of around 40 nm, to achieve good flatness of the exposed surface. AFM measurements were performed using a Bruker QNA MM8 with PeakForce QNM tapping (Bruker) with a sharp tip with a diameter of 1 nm. Spherulite size and lamellar thickness were determined, by mapping out the topography as well as the stiffness at low and high resolution.
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Schematic representation of the experimental method, (b) Estimation of particle radius $a_0$, neck width $x$ (black line) at the interface between two particles and angle $\theta$ between the line connecting a particle center with the outer point of the neck and that connecting the particle centers.</figcaption></figure>

## 3. Results and discussion

To study the effects of particle size and processing conditions on the kinetics of the sintering process and the corresponding morphology development within the material, we study the effect of the particle size and chamber temperature on the process while keeping the laser spot size, laser power and pulse duration constant. The pulse duration is fixed at 1 ms. This is an average value for the typical duration of laser impact on a fixed location in the powder bed from a scanning laser in an SLS process, based on scan speeds between 10 and 1000 mm/s and particle sizes of 50–500 µm [9]. Based on the energy required to completely melt one particle of PA12 with a radius of 100 µm, which is 192 µJ, a pulse energy of 384 µJ, within a fixed laser spot with a radius of 15 µm, is applied at the contact point of the PA12 particles. This corresponds to an energy per unit area (energy density) of 0.54 J/mm², which is an order of magnitude higher as compared to the typical values in commercial laser sintering devices based on CO₂ lasers, where the energy density, defined as the laser power divided by the scan spacing and scan speed is on the order of 0.02–0.04 J/mm² [21]. This is a result of the smaller laser spot size (radius of 15 µm in our device versus values up to 700 µm in commercial devices [11]), which is required to allow precise deposition of the energy at the location of the particle doublet in the present setup. However, the energy will get distributed through part of the particles through diffusion, which results in an effective energy density of the same order of magnitude as that in commercial devices. To investigate the effect of the particle size on the sintering dynamics, we selected doublets of equal-sized particles with radii ranging from 100 µm to 200 µm. The maximum chamber temperature used was 155 °C, which was selected to be around 10 °C below the temperature at which sticking of the particles in the chamber was observed. This is a significantly lower temperature as compared to other studies using commercial PA12 sintering powder, wherein bed temperatures around 185 °C are reported [11,21].

### 3.1. Material characterization

A heat flow curve of PA12 with 2 wt% dye is shown in Fig. 2a. PA12 has a peak melting temperature $T_m$ of 178 °C with a melting enthalpy of 56.4 J/g. This melting temperature is slightly lower as that reported for pristine commercial PA12 SLS powder (186 °C in [11]), which can be attributed to the difference in preparation conditions. The double melting peak shown in Fig. 2 was observed before in literature for PA12. The small first melting peak was attributed to either melting of less stable crystals formed during cold crystallization [16] or to the melt recrystallization of α-PA12 into γ-PA12 [48].

The dynamic moduli of the material in the molten state are shown as a function of frequency in Fig. 2b. Time–temperature superposition of data obtained between 162 °C and 210 °C, leads to a master curve

<caption>**Table 1**</caption>

Viscosity average relaxation times obtained from small amplitude oscillatory shear rheometry experiments in the temperature range of 162 °C to 210 °C.

<table><thead><tr><th>Temperature (°C)</th><th>Viscosity average relaxation time (s)</th></tr></thead><tbody><tr><td>162</td><td>0.026</td></tr><tr><td>170</td><td>0.019</td></tr><tr><td>180</td><td>0.014</td></tr><tr><td>190</td><td>0.010</td></tr><tr><td>200</td><td>0.008</td></tr><tr><td>210</td><td>0.006</td></tr></tbody></table>

at a reference temperature of 200 °C. Since viscosity determines the resistance to sintering [12], the complex viscosity is determined from the frequency sweep experiments, whereby the temperature dependence of the zero-shear viscosity is given by [49]:

$$a_T = \frac{\eta(T)}{\eta(T_{\text{ref}})} = \exp\left(\frac{-E_a}{R}\left(\frac{1}{T_{\text{ref}}} - \frac{1}{T}\right)\right), \quad (3)$$

with $a_T$ the temperature shift factor, $\eta(T)$ and $\eta(T_{\text{ref}})$ the viscosities at the actual and reference temperature respectively, $E_a$ the activation energy and $R$ the universal gas constant. To construct the master curves in Fig. 2b, the curves of the dynamic moduli were shifted horizontally, whereas the viscosity curves were shifted horizontally and vertically by multiplying respectively dividing the angular frequency and measured viscosity with a shift factor $a_T$. From the shift factors resulting in collapse of all data, the activation energy was calculated to be $E_a = 55.2$ kJ/mol.

The shear rate dependency of the viscosity is captured by the Cross model [49]:

$$\eta_s = \eta_{s,\infty} + \frac{\eta_{s0} - \eta_{s,\infty}}{1 + (\lambda\dot{\gamma})^m}, \quad (4)$$

with model parameters $\eta_{s0} = 167.4$ Pa s, $\eta_{s,\infty} = 0$ Pa s, $\lambda = 6.57 \cdot 10^{-4}$ s and $m = 0.644$. Multimode Maxwell model [49] fitting of the small-amplitude dynamic moduli provides the relaxation time distribution of the polymer, as shown in Supplementary Table S1 for the reference temperature of 200 °C. The viscosity average relaxation time defined as:

$$\lambda = \frac{\sum_{i=1}^{k} \lambda_{i} \eta_{i}}{\sum_{i=1}^{k} \eta_{i}}, \quad (5)$$

with $\lambda_i$ the relaxation time of mode $i$ and $\eta_i$ the viscosity contribution of mode $i$, is given in Table 1 for various temperatures. It ranges from 0.026 to 0.006 s in the temperature range of 162 °C to 210 °C whereby its temperature dependence can be described by Eq. (3).

Whereas the material rheology determines the kinetics of the sintering of the neck region, the crystallization kinetics will affect the solidification. Heat flow curves during isothermal crystallization are
<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) DSC thermograph (heating cycle) of PA12 containing 2 wt% dye, (b) Dynamic moduli of PA12 containing 2 wt% dye at temperatures of 162 °C, 170 °C, 180 °C, 190 °C, 200 °C and 210 °C compiled into a master curve at a reference temperature of 200 °C. Fits of the Cross model and multimode Maxwell model (lines) of respectively the viscosity curve and dynamic moduli.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Exothermic heat flow peak under isothermal conditions at different temperatures using (a) FDSC and (b) DSC, (c) Peak time of crystallization ($t_{1/2}$) as a function of crystallization temperature for PA12 with 2 wt% dye.</figcaption></figure>

shown in Figs. 3a and b and the peak crystallization times are plotted as a function of temperature in Fig. 3c. Due to the symmetry of the heat flow curves, the peak crystallization time corresponds to the half-time of crystallization $t_{1/2}$. Fig. 3c shows that the crystallization speed increases four orders of magnitude when reducing the temperature from 170 °C to 70 °C.

In Fig. 3c, an abrupt change in the temperature dependency of the crystallization rate can be observed around 115 °C. A similar bimodal distribution of crystallization half-times was shown by Rhoades et al. [50] for two grades of PA11. They observed that at high temperatures, the crystallization rates were grade dependent whereas at low temperatures they were grade-independent, thereby allowing to conclude that the phenomenon is governed by the nucleation mechanism. At low undercooling (high temperature) heterogeneous nucleation dominates whereas at high undercooling (low temperature) homogeneous nucleation governs the crystallization process [50]. Paolucci et al. found a similar trend for another grade of PA12 (PA2200 from EOS) be it with an overall faster crystallization [51].

## 3.2. Effect of particle size

In the SLS process it is desired that the polymer particles are fully fused in the final product. Therefore the balance between sintering kinetics and time interval available for sintering plays an important role in the final part properties. To systematically study the sintering process, we probe the dynamics of the sintering process together with the temperature profile of the particles as well as the development of the internal microstructure. Fig. 4a shows a representative set of images for particles with a radius of 125 µm. The chamber temperature is set

at 155 °C, which is about 23 °C below the peak melting temperature of PA12.

From the image sequence in Fig. 4a it can be seen that the instant the laser energy hits the interface of the polymer doublet, at $t = 0$ s, a neck is formed which tends to grow until sintering is completed at around $t = 5$ s. The final obtained neck radius remained the same and no further flow occurred after 5 s. This sintering process is driven by the surface tension and facilitated by the local increase of the temperature at the laser-heated interface of the doublet, which increases the mobility of the polymer chains to enable viscous flow [31]. The evolution of neck radius as a function of time was determined using the image sequence in Fig. 4a and plotted in Fig. 4b as the dimensionless neck radius $x/a_o$. Supplementary Figure S2 shows the results of a repeat experiment, demonstrating the reproducibility of the data. Subsequently, the evolution was fitted with the modified Frenkel model [52]:

$$ \frac{d\theta}{dt} = \frac{\Gamma 2^{-5/3} \cos \theta \sin \theta (2 - \cos \theta)^{1/3}}{\eta a_o (1 - \cos \theta)(1 + \cos \theta)^{1/3}}, \quad (6) $$

where $\Gamma$ is the surface tension, $\eta$ the viscosity, $a_o$ the particle radius and $\theta$ the angle between the line connecting the center of one particle to the outer point of the neck and that connecting the particle centers, as indicated in Fig. 1b. From $\theta$ the dimensionless neck radius $x/a_o$ can be obtained, given by [52]:

$$ \frac{x}{a_o} = \sin \theta \left( \frac{4}{(1 + \cos \theta)^2 (2 - \cos \theta)} \right)^{1/3}. \quad (7) $$

The modified Frenkel model considers viscous sintering under isothermal conditions. Fig. 4 shows that the model describes the initial sintering kinetics well, and using the viscosity $\eta$ as a fitting parameter
<figure><img src="image_7.png" /><figcaption>Fig. 4. (a) Image sequence of sintering for PA12 particle pairs and (b) Comparison of modified Frenkel model (line) with the experimental evolution of the dimensionless neck radius (obtained from the neck radius x in (a), for particle radius a₀ = 125 µm and heating chamber temperature T_c = 155 °C. The viscosity value in the modified Frenkel model corresponds to a constant temperature of 184 °C.</figcaption></figure>

results in a fit value of 270 Pa s, which corresponds to a temperature of 184 °C. Obviously, the slowing down of sintering at later times due to cooling cannot be described with the modified Frenkel model. Contrary to the amorphous PS studied in our previous work, it can be seen in Fig. 4 that the solidification of the particle doublet and cessation of the viscous sintering does not occur immediately after the laser pulse. This can probably be attributed to the fact that solidification is not instantaneous but depends on the crystallization kinetics, which is studied simultaneously via X-ray characterization.

Image sequences as in Fig. 4a were collected for a set of particle doublets with different particle radii. Fig. 5a shows the dimensionless neck radius x/a₀, calculated as a function of sintering time for different particle radii. With increasing particle size, the sintering kinetics slows down and the final x/a₀ value also substantially reduces. The final doublet morphology can be observed for varying particle sizes in Fig. 5b, resulting in partially sintered doublets after cessation of flow. At the later stages of sintering, surface tension is insufficient to overcome viscous losses during flow [52], thereby sintering is halted at an intermediate stage. Besides the slower sintering kinetics at the start of the process, cessation of flow also occurs slightly earlier for the larger particles. The characteristic timescale for isothermal viscous sintering, as determined from the Frenkel model [52], which is (ηs₀a₀/Γ) with ηs₀ the steady state zero-shear viscosity at 200 °C, a₀ the initial particle radius and Γ the surface tension of PA12, is on the order of 0.5 s for a particle radius of 100 µm. Rescaling the sintering times with this characteristic Frenkel time still reveals a slower kinetics for the larger particles, as can be seen in Supplementary Figure S3, similar to our previous work on amorphous polystyrene [35]. By increasing the particle size, the relative volume of the region illuminated with laser energy as compared to the total particle volume decreases, whereby the un-sintered sides act like a heat sink, resulting in a lower temperature at the interface of the particle doublet. Hence, the viscosity that governs the resistance to the sintering process depends on the particle size. It can thus be concluded that the final dimensionless neck radius is dependent on the evolution of the polymer viscosity as a function of time, which is mainly governed by its temperature dependence.

The sintering results clearly show that the particle size indirectly affects the sintering process through its effect on the temperature in the neck region. To investigate this further, the temperature profile during sintering was tracked with an IR camera. Fig. 6a shows the thermal images obtained for particles with a radius of 125 µm at various time points during the sintering process. It can clearly be observed that the heat is dissipated from the bulk to the edges of the particle doublet.

The characteristic time for heat diffusion t_c for this system [53]:

$$t_c = \frac{(2a_0)^2 \rho c_p}{k}, \qquad (8)$$

with a₀ the particle radius, ρ the density, c_p the heat capacity and k the thermal conductivity of PA12, is approximately 0.4 s, which is of the same order of magnitude as the time required for the heated zone to spread out over the particle doublet in Fig. 6a.

Based on the thermal images in Fig. 6a, the local temperature at the center of the particle doublets is determined and plotted in Fig. 6b for the different particle sizes. As discussed previously, with reducing particle size, the temperature experienced locally at the interface is higher. From Fig. 6b it follows that initially, at t = 0.01 s, the temperature observed for 100 µm, 125 µm, 150 µm and 200 µm radius is 230 °C, 210 °C, 198 °C and 193 °C respectively. It should be taken into account that the laser pulse duration is only 1 ms in this case and the first temperature measurement occurs after 10 ms. Therefore, the maximum measured temperatures are not the absolute maxima. Fits with the modified Frenkel model of the initial sintering kinetics in Fig. 5 provide viscosity values that correspond to a temperature of 260 °C, 184 °C, 182 °C and 170 °C for particle radius values ranging from 100 µm to 200 µm. For the largest three particle sizes, these temperatures are within the temperature range measured with the IR camera. For the smallest particle size, the isothermal Frenkel model overestimates the temperature. This can partially be caused by the high sensitivity of the model to the initial data points of the sintering kinetics. Moreover, for pairs of small particles, an increased wetting of the substrate was noticed, which may speed up the sintering kinetics. Overall, it can be concluded that the isothermal sintering model has limited applicability for these non-isothermal sintering experiments. To better take into account the fact that the laser sintering process is a non-isothermal process the cooling rates of the different particle sizes are studied.

To assess the cooling rate of the particles in more detail, a simple heat balance of a single particle, cooling down in quiescent air, is set up. When assuming a homogeneous temperature throughout the particle, which is reasonable considering the short heat diffusion time inside the particle, and in absence of significant contributions of radiation, this leads to the following evolution of the particle temperature T_p with time [32]:

$$T_p(t) = (T_{\max} - T_c) \cdot \exp\left(-\frac{hA_t}{mc_p}\right) + T_c, \qquad (9)$$

where m is the particle mass, c_p the heat capacity, h the heat transfer coefficient, A the particle surface area, T_max the maximum temperature at the interface of the particles, and T_c the temperature of the heating
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Effect of particle radius on sintering kinetics of PA12 doublets with heating chamber temperature of T~c~ = 155 °C. (a) Dimensionless neck radius versus sintering time, (b) particle doublets after sintering. In (a) symbols indicate experimental data and lines indicate fits with the modified Frenkel model (Eq. (7)) with the viscosity η used as a fitting parameter.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** (a) Image sequence of IR images for particles with radius a~o~ = 125 µm, (b) Temperature as a function of time obtained for various particle sizes for a heating chamber temperature of T~c~ = 155 °C. Lines in (b) are fits with Eq. (9) resulting in values for h of respectively 192, 191, 209 and 264 W/(m² K) for particle radii ranging from 100 to 200 µm.</figcaption></figure>

chamber. This model was fitted on the temperature profiles in Fig. 6b. The model describes the temperature data relatively well, with only a slightly faster cooling than expected in the final stages for the two smallest particle sizes. The heat transfer coefficient was taken as a fit parameter and varied between 191 and 264 W/(m² K), wherein *h* is the highest for 200 µm radius particles. Based on the consideration that buoyancy-driven flows are negligible at low values of the Rayleigh number [53], the dimensionless Nusselt number is equal to 2 [53], which results in the theoretically expected value of *h* being proportional to 1/a~o~ (Nu = 2a~o~/k, with *k* the conductivity of air) and ranging from 300 to 170 W/(m² K) for particle sizes between 100 µm and 200 µm. The order of magnitude of the calculated heat transfer coefficient is thus correct, but smaller particles are expected to exhibit a higher heat transfer coefficient, which is not confirmed by the data. However, it should be taken into account that the temperature inside the particles is not completely homogeneous and that heat loss to the substrate most probably also contributes [54]. The increasing trend of the heat transfer coefficient with particle size indicates that the Nusselt number is not constant, which may indicate that convection flows are present. Overall, the measured temperature curves and extracted heat transfer coefficients provide relevant input for numerical models of the laser sintering process, which require an accurate description of the temperature evolution [55]. In summary, it can be concluded from Fig. 6b that particles reach a homogeneous temperature of 155 °C after about 0.4 s for 200 µm particles and 0.5 s for 100 µm particles.

Based on the temperature profiles provided in Fig. 6, the viscosity of the polymer at the bridge location during sintering can be predicted

with Eq. (3). The results are presented in Supplementary Figure S4 and show that the viscosity increases during sintering, due to the cooling of the particles. Hereby, larger particles exhibit a higher viscosity due to their lower temperature, as mentioned before. Using the predictions for the viscosity from Figure S4, it is possible to predict the sintering kinetics during non-isothermal sintering. However, it should be kept in mind that these predictions do not take into account effects of crystallization on the rheology. Since precursors of crystallinity can already affect the rheology even at low values of crystallinity (e.g. [56]), the solidification during sintering of a semi-crystalline polymer will be more pronounced as predicted by a simple temperature-dependent viscosity. It can indeed be observed in Figure S5 that even though the temperature-dependent effect accounts for some of the slowing down of the sintering kinetics at later stages, the match with the experimental data is not very good. A similar non-isothermal sintering model was applied on our sintering data for amorphous PS [35] by Polychronopoulos and Vlachopoulos [57]. That comparison shows that even in absence of crystallization, the non-isothermal sintering model does not fully describe the experiments.

The results in Figs. 5 and 6 clearly show that particle size has a major effect on the heating as well as cooling of the particles and hence on the kinetics of the sintering process. Apart from the viscous flow in the material, also the crystallization kinetics and thus the resulting solidification behavior, will depend on the temperature profile. Therefore, WAXD patterns of the central region of the particle doublet, around the neck region, are collected, while sintering. A representative set of images is shown as insets in Fig. 7. No anisotropy along the azimuthal angle occurs in the scattering images, and this is the case for
<figure><img src="image_10.png" /><figcaption>Fig. 7. (a) 3D plot of the radially integrated intensity as a function of scattering vector *q* for the complete acquisition time. The plots in (b), (c) and (d) represent integrated intensity as a function of scattering vector *q* at 1 s, 12 s and 24 s with the corresponding WAXD pattern in the inset. PA12 particles with particle radius of *a*₀ = 125 µm and heating chamber temperature of *T*_c = 155 °C.</figcaption></figure>

all experiments presented in this work. Similar images were obtained for other particle sizes (see Supplementary Figure S6). WAXD patterns were integrated over an azimuthal angle of 90° to plot intensity versus scattering vector *q*. This integrated intensity is then fitted using a double Gaussian-Lorentzian function to determine the peak positions, as shown in Fig. 7. The relevant diffraction peak is the outer bright ring shown in the insets in Fig. 7. The first frames in Fig. 7a are representative of the amorphous hallow, wherein *t* = 0 s corresponds to the instant when the laser hits the polymer, until the polymer starts crystallizing at around *t* = 8 s, shown by a distinct growth of the peak at around *q* = 15.02 nm⁻¹. Based on the peak area, the evolution of the total crystallinity with time can be determined.

Fig. 8 shows the resulting in-situ time-resolved crystallization kinetics for various particle sizes. A repeat experiment for a particle size $a_0$ = 125 µm is shown in Supplementary Figure S7 and demonstrates the reproducibility of the crystallization data. The overall crystallinity value for all the particle sizes is around 21.5%, before and after sintering. However, a pronounced difference in crystallization rate is observed, wherein with increasing particle size the crystallization rate reduces. From the time evolution it can be observed that the onset of crystallization occurs at 5 s to 7 s for particle radii between 100 µm and 200 µm. Comparing these time scales with the sintering kinetics in Fig. 5 shows that crystallization starts after cessation of flow. The half time of crystallization for particle radii of 100 µm, 125 µm, 150 µm and 200 µm is about 11 s, 15.5 s, 17 s, 27 s respectively. These timescales do not correspond to the half time of crystallization estimated under isothermal conditions at 155 °C (chamber temperature), which is 19.5 s. Predictions of the non-isothermal crystallization kinetics have been reported in literature for various PA12 SLS grades, using either the Schneider rate equations [55] or the Ozawa, Jeziory and Nakamura equations [14]. However, this would lead to an even slower crystallization than isothermal crystallization at the chamber temperature, since the temperature decreases from a higher value (with slower crystallization kinetics, see Fig. 3) to the chamber temperature. Hence, the conclusion would remain that crystallization in the sintering process proceeds

<figure><img src="image_11.png" /><figcaption>Fig. 8. Time evolution of crystallinity during the sintering process for PA12 particles with various sizes (particle radius $a_0$ indicated), heating chamber temperature of $T_c$ = 155 °C.</figcaption></figure>

faster than expected from quiescent crystallization experiments with a DSC or flash-DSC. Therefore, non-isothermal crystallization modeling is not performed in the present work. This enhanced crystallization in the laser sintering process may be caused by melt memory effects wherein residual orientation and structuration of polymer chains originating from the prior crystalline structure leads to self-nucleation [18]. Melt memory is particularly strong for polymers with enhanced interchain interactions such as polyamide which exhibits hydrogen bonds [18]. Characterizations of the melt memory in PA12 reported in literature show that self-nucleation is absent at temperatures above 195 °C [17]. However, the residence time at the annealing temperature was 5 min
<table><caption>**Table 2**
Estimated reptation and Rouse times for different temperatures estimated using a multimode Maxwell model fit at 200 °C and Eq. (3) for temperature shifting.</caption><thead><tr><th>Temperature (°C)</th><th>λ<sub>rep</sub> (s)</th><th>λ<sub>s</sub> (s)</th></tr></thead><tbody><tr><td>162</td><td>1.39</td><td>0.053</td></tr><tr><td>170</td><td>1.06</td><td>0.040</td></tr><tr><td>180</td><td>0.76</td><td>0.029</td></tr><tr><td>190</td><td>0.55</td><td>0.021</td></tr><tr><td>200</td><td>0.41</td><td>0.015</td></tr><tr><td>210</td><td>0.31</td><td>0.012</td></tr></tbody></table>

in that work, as compared to timescales less than one second in the present work. Therefore, melt memory effects cannot be excluded. However, taking into account the temperature dependence of the half time of crystallization, as shown in Fig. 3, as well as the fading melt memory with increasing temperature, a slower crystallization kinetics was expected for the smaller particles, which have a higher overall temperature. Therefore, there should be an additional factor playing a role. Laser sintering not only results in non-uniform and time-dependent temperature profiles, but also generates a complex flow field [58]. With varying particle size the deformation rates experienced during the initial sintering stages differ as well, as can be inferred from the sintering kinetics shown in Fig. 5. Therefore a complex interplay between temperature and deformation kinetics can further influence the crystallization kinetics, as being observed in Fig. 8.

The crystallization kinetics in Fig. 8 suggests that the flow history experienced by the material during sintering has an impact on the subsequent crystallization process. It is well-known that the underlying mechanism for flow-induced crystallization processes depends on the deformation rate [59]. Different flow regimes were defined based on a critical Weissenberg number, $Wi = \dot{\gamma}\lambda$, where $\dot{\gamma}$ is the deformation rate and $\lambda$ the relaxation time. The orientation and stretch of molecules can be characterized by the reptation time, $\lambda_{rep}$ and Rouse time $\lambda_s$ respectively, which are correlated by [60]:

$$ \lambda_s = \frac{\lambda_{rep}}{3Z}, \qquad (10) $$

where $Z = M_w/M_e$ is the average number of entanglements per chain. The entanglement molecular weight of PA12 is around 2 kg/mol [61], with which the measured molecular weight of the used PA12 (53 kg/mol), results in $Z = 26.5$. The largest reptation time is estimated from the longest relaxation time of the multimode Maxwell fit of the dynamic moduli and is presented as a function of temperature in Table 2. This reptation time is representing the high molecular weight tail, which has been suggested to dominate the flow-induced crystallization dynamics [62]. Based on these timescales two characteristic Weissenberg numbers are defined, namely $Wi_{rep} = \dot{\gamma}\lambda_{rep}$ and $Wi_s = \dot{\gamma}\lambda_s$. Chains are in equilibrium if $Wi_{rep}$ and $Wi_s < 1$ and no effect on crystallization will be observed. Orientation of the countour path of the polymer chains occurs when $Wi_{rep} > 1$ and $Wi_s < 1$, which can enhance the number density of crystal nuclei and can eventually induce chain stretching when $Wi_{rep}$ and $Wi_s > 1$ [59].

The deformation rates during laser sintering can be estimated from the growth rate of the neck radius, using the modified Frenkel model, where a purely biaxial flow is assumed, implying a homogeneous extension rate [63]. The extension rate $\dot{\epsilon}$ follows from the sintering kinetics and is given by [52]:

$$ \dot{\epsilon} = \frac{2 \sin \theta}{(1 + \cos \theta)(2 - \cos \theta)} \frac{d\theta}{dt}, \qquad (11) $$

with $\frac{d\theta}{dt}$ as defined in Eq. (6). Fig. 9 shows that the sintering kinetics is fast initially and tends to slow down in time due to the reduced driving force. The maximum deformation rates estimated during the initial sintering stage from Fig. 5a for 100 µm and 200 µm particle radii are 5.0 s⁻¹ and 0.2 s⁻¹ respectively, as shown in Fig. 9. Using the reptation and Rouse times from Table 2 and the maximum deformation

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Evolution of extension rate as a function of time, calculated from the sintering data in Fig. 5, for PA12 particles with different sizes (particle radius $a_0$ indicated), heating chamber temperature of $T_c = 155$ °C.</figcaption></figure>

rate estimates, it can be concluded that the maximum $Wi_{rep}$ is of the order of 1 and $Wi_s$ is smaller than 1, suggesting an enhanced number density of nuclei without polymer chain stretching. From the evolution of the strain rate as a function of time, the total strain experienced by the material can be calculated as:

$$ \epsilon = \int_{0}^{t} \dot{\epsilon} dt. \qquad (12) $$

Hence, for particle sizes of 100 and 125 µm, the material in the neck region experiences a strain of around 1 during sintering.

Based on flow-induced crystallization studies, for instance for PA6 [20], and taking into account that elongational flow has much stronger effects on crystallization than shear flow [64], this strain is expected to be sufficient to enhance the nucleation density, thereby fastening the overall crystallization kinetics. Moreover, flow-induced crystallization effects relax much slower than can be expected from the rheological reptation times [65], which allows the nucleation precursors to survive, even though they are generated by flow at high temperatures. Since the Weissenberg number dictates the flow regime, with increasing deformation rate the crystallization kinetics would be enhanced. This is in agreement with the trend observed in Fig. 8, thereby suggesting that flow affects the crystallization during laser sintering. Models describing the dependency of nucleation density on deformation rate have been proposed and validated for different polymers [66]. However, at present the flow-induced crystallization behavior of PA12 has not been studied in full detail. Moreover, van Drongelen et al. [39] suggest that in case of PA6, apart from flow-induced nucleation, the application of flow may also help in breaking clusters formed by hydrogen bonded chain segments or in distributing them more evenly. Thereby, the physical dynamic links formed by these hydrogen bonds are opened, which affects the chain mobility and thus the crystallization. Taking this into account, quantitative predictions of the trends observed in Fig. 8 are unfortunately not possible at present.

### 3.3. Effect of chamber temperature

Apart from the material characteristics, also the processing conditions affect the crystallization process. To systematically investigate the relevance of the chamber temperature, it was varied between 70 °C and 155 °C, while keeping the particle radius constant. The maximum chamber temperature was restricted to 155 °C since a higher temperature leads to premature coalescence of the particles in absence of laser irradiation, which is ideally not desired during the SLS process. It is expected that, for a given laser energy and particle size, reducing
<figure><img src="image_13.png" /><figcaption>Fig. 10. Effect of chamber temperature on the dimensionless final neck radius for sintering of PA12 particle pairs of radius $a_o$ = 125 µm. The inset shows the particle doublets after sintering.</figcaption></figure>

the chamber temperature results in a lower temperature at the sintering region. This corresponds to a higher viscosity, thereby hampering the sintering process. For the lower chamber temperatures of 70 °C and 110 °C, the solidification process is very fast and the neck ceases to grow within 0.02 s. As a result, the imaging system does not have sufficient acquisition speed to study the sintering kinetics in detail (examples are shown in Supplementary Figure S8). Therefore, we focus on the final sintered neck radius, which is depicted in Fig. 10. For chamber temperatures between 70 °C and 155 °C it can be seen that the final dimensionless neck radius increases with increasing chamber temperature, showing an almost linear behavior in this range of temperatures.

The evolution of the crystallinity is plotted in Fig. 11 for three different chamber temperatures. It can be observed that, even though solidification and crystallization both occur much faster with a lower chamber temperature, the onset of crystallization occurs only after the flow is stopped (the latter happens before 0.02 s as shown in Supplementary Figure S8). Hence, the interface is in the amorphous state during sintering and upon cessation of flow, crystallization starts. The half crystallization time, $t_{1/2}$, at chamber temperatures of 70 °C and 110 °C, for isothermal conditions and non-isothermal laser sintering experiments are of the same order of magnitude, about 0.2 s and 0.4 s respectively. This is different from the case at 155 °C, for which the crystallization observed during laser sintering was faster than under isothermal conditions. At the low chamber temperatures, sintering only occurs to a very limited extent, and crystallization is much faster. This may lead to less pronounced effects of flow-induced crystallization.

### 3.4. Combined effects of chamber temperature and particle size

To further study the combined effects of chamber temperature and particle size, sintering of particles with radii of 100 µm, 125 µm, 150 µm and 200 µm is studied at a reduced chamber temperature of 110 °C. Fig. 12 shows the final dimensionless neck radius as a function of particle size for two chamber temperatures. A more or less linear decrease of the dimensionless neck radius with particle size can be observed, which is similar to the results for amorphous PS [35]. The results suggest a slightly lower dependence on particle size for the highest chamber temperature, which may be intuitive since at higher temperatures the effects of cooling will be less important. The trend is however very subtle.

Fig. 13 shows the evolution of the temperature during sintering. As compared to Fig. 6 for the higher chamber temperature, the particle

<figure><img src="image_14.png" /><figcaption>Fig. 11. Time evolution of crystallinity during the sintering process for 125 µm PA12 particles with various heating chamber temperatures of $T_c$ = 70 °C, $T_c$ = 110 °C and $T_c$ = 155 °C.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12. Effect of heating chamber temperature and particle radius on final dimensionless neck radius of PA12 particles.</figcaption></figure>

size has less effect on the temperature at lower chamber temperature. Whereas for the high chamber temperature, the diffusion of heat through the particles is faster than the cooling process, the opposite situation occurs at the low chamber temperature, the cooling occurs within 0.1 s, which does not give sufficient time for the heat to spread throughout the particles. Hence, particle size plays a less prominent role in the temperature evolution at the particle bridge at low chamber temperature. The corresponding crystallization kinetics is shown in Fig. 13b. Based on Figs. 8 and 13, it may be concluded that the effect of the particle size on the crystallization kinetics is less pronounced for the low chamber temperature. The half time of crystallization under isothermal conditions at 110 °C is estimated from Fig. 3 to be 0.57 s and from Fig. 13b the half time of crystallization is between 0.3 s and 0.5 s for 100 µm and 200 µm particle radii whereby particles undergo complete crystallization within 1.3 s. Accurate estimates of the Weissenberg number are not possible due to the lack of high speed information about the sintering kinetics but the slightly higher temperatures observed for the smallest particles combined with a faster crystallization kinetics suggest effects of flow-induced crystallization, be it to a much smaller extent than at the high chamber temperature
<figure><img src="image_16.png" /><figcaption>**Fig. 13.** (a) Temperature evolution as a function of time from IR imaging at the interphase of a PA12 particle doublet, (b) Time evolution of crystallinity during sintering for PA12 particles, heating chamber temperature of T_c = 110 °C.</figcaption></figure>

of 155 °C. This is most probably caused by the limited flow occurring before solidification in combination with the already fast quiescent crystallization.

### 3.5. Effect of processing conditions on internal microstructure

Apart from providing time-resolved information about the sintering and crystallization process, the second advantage of our small-scale approach is the access to local information about the crystalline microstructure within the bridge region. Depending on the preparation conditions, for example phase separation and precipitation in commercial PA12 grades or emulsification, grinding and gas phase rounding, etc. in newer grades [38], the initial crystalline microstructure of the PA12 material may differ. For instance, Van Hooreweder et al. [11] and Zhou et al. [67] find a combination of α' and γ phase crystals in PA12 SLS powder. However, their characterizations were performed at room temperature whereas it is known that PA12 can undergo phase transitions when kept at elevated temperatures [16]. In the present work, in-situ X-ray characterization in the heating chamber ensures that the actual initial state in the sintering device is considered. Fig. 14 shows the integrated intensity of the WAXD patterns, before and after sintering the particle doublets for chamber temperatures of 155 °C, 110 °C and 70 °C. In Fig. 14a for 155 °C, before sintering a distinct peak is observed at q = 15.0 nm⁻¹ with a shoulder at lower q values. After sintering this shoulder transforms into a secondary peak at q = 14.6 nm⁻¹. The distinct double peaks indicate the presence of the α'-phase, which has a monoclinic unit cell. The small and large peak respectively correspond to the interchain and intersheet distance with d spacings of 0.430 nm and 0.418 nm [68]. It has previously been shown that, given sufficient time, the α'-phase is the stable phase at temperatures above 130 °C [12]. With reducing the chamber temperature to 110 °C (Fig. 14b), the shoulder disappears and the X-ray pattern develops into one sharp peak at q = 15.1 nm⁻¹, with a small decrease in d spacing to 0.416 nm. This characteristic X-ray pattern corresponds to the γ-phase, with a hexagonal packing, being the most stable phase observed for PA12 [50]. In a hexagonal packing, the inter-chain and inter-sheet distance are the same, resulting in a single sharp peak [68]. The difference in characteristic X-ray pattern before and after sintering at 110 °C is very subtle with the only difference being that after sintering the peak becomes sharper, while the overall crystallinity value stays around 21.5%. At a chamber temperature of 70 °C, the X-ray pattern already corresponds to that of the γ-form before sintering. This is expected since the particles were initially conditioned at 155 °C and later slowly cooled down to 70 °C thereby forming the stable γ-form [12]. After sintering, whereby the particle double undergoes a rapid heating and cooling process, a shift in the peak from q = 15.1 nm⁻¹ to q = 15.3 nm⁻¹ is observed. The corresponding d spacing for the γ-form of 0.416 nm reduces to 0.411 nm. This shift towards higher q value and reduction in d spacing has previously been observed while

<caption>**Table 3**</caption>

Mean crystallite thickness perpendicular to the reflection plane, estimated using Scherrer Eq. (2), before and after sintering for various chamber temperatures, for a particle radius of 125 µm.

<table><thead><tr><th>Chamber temperature (°C)</th><th>155 °C</th><th>110 °C</th><th>70 °C</th></tr></thead><tbody><tr><td>Mean crystallite thickness (nm) before sintering</td><td>11.3</td><td>10.9</td><td>10.1</td></tr><tr><td>Mean crystallite thickness (nm) after sintering</td><td>14.7</td><td>11.1</td><td>10.9</td></tr></tbody></table>

cooling from the melt to room temperature [68]. Similar trends can also be observed in our laser sintering experiments, wherein the peak shifts towards higher q. Though before and after sintering the final temperature is the same namely that of the heating chamber, Fig. 14 shows that the crystal structure can slightly reorganize during sintering at high temperature.

Table 3 shows the estimated crystallite thickness perpendicular to the reflecting plane, as estimated from the Scherrer equation (Eq. (2)), using the WAXD intensity profiles in Fig. 14 at varying chamber temperature for a particle radius of 125 µm. It should be noted that apart from the finite crystallite size, also crystalline disorder, either from lattice strain due to stresses or from fluctuations of the lattice positions, can affect peak broadening [69,70]. However, to correct for these effects, at least two orders of reflections should be observed, for which the accessible q range was too narrow [69]. Therefore, and since these effects are not expected to vary significantly between the different experiments, in the analysis all peak broadening was attributed to the finite crystallite size. The values of the crystal thickness reported in Table 3 correspond well to the reported lamellar thickness of PA12, which is indeed of the order of 10 nm [13,44]. Typically, the lamellar thickness is extracted from a more accurate SAXS characterization. However, the Scherrer equation has been validated as a method to provide reasonable estimates of the lamellar thickness in semi-crystalline polymers [71]. Table 3 shows that with reducing chamber temperature, the thus estimated crystallite thickness tends to reduce. In addition, the crystallite size also tends to be larger after sintering as compared to before sintering. The increase of lamellar thickness with temperature has been reported before for isothermal crystallization [13]. Moreover, melting and recrystallization occurring after laser impact in the heated chamber provides a different temperature protocol than that experienced during preparation of the spherical particles. In the latter case, the particles were quenched in water, which results in a higher cooling speed and lower temperatures, conditions which favor crystals with a smaller lamellar thickness.

To study the crystal morphology at larger length scales than the sub-crystal scale, microtomed samples of sintered PA12 doublets are investigated via polarized light microscopy (POM). Fig. 15 shows images taken at the central plane of the doublets, as a function of particle size and chamber temperature. The laser illuminated zone at the interface of the particle doublets shows up as a bright zone. It can
<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Integrated WAXD intensity and deconvolution analysis of frames before and after sintering for PA12 particle pairs of radius $a_0$ = 125 µm, for heating chamber temperature $T_c$ of (a) 155 °C, (b) 110 °C and (c) 70 °C.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Microtomed 2 µm thin sample of PA12 particle doublets after sintering at a heating chamber temperature $T_c$ of 155 °C, 110 °C and 70 °C, imaged with polarized optical microscopy, for a particle radius of 100 µm, 125 µm, 150 µm and 200 µm. Scalebar represents 100 µm.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Microtomed 2 µm thin samples of PA12 particle doublets with radius $a_0$ of (a) 125 µm and (b) 200 µm imaged with polarized optical microscopy, after sintering with a heating chamber temperature of $T_c$ = 155 °C. Scalebar represents 100 µm.</figcaption></figure>

be hypothesized that the high intensity in this zone as compared to the edges of the doublet is related to a more ordered crystal structure generated during flow as compared to the un-molten zone which results from quiescent crystallization during the particle generation process. Moreover, larger objects are known to exhibit more forward scattering than small objects [72]. Hence, also a difference in spherulite size can be at the origin of the observed difference in brightness. It should be noted that various orientations of the set of crossed polarizers with respect to the sample were used for imaging, but no orientation could be detected. In accordance with the WAXD patterns, this confirms that spherulites and not elongated crystals are formed. Hence, precursors

are created that survive in the melt but are not well-oriented. The bright zone is evident for all particle sizes and chamber temperatures. Its area corresponds well to the laser heated area, as shown in Fig. 6a. For smaller particles, the bright zone extends over a larger part of the particle doublet, as the same amount of energy is then provided to a smaller volume of material. Similarly, the area of the bright zone reduces with reducing chamber temperature. This clearly shows that sufficient heating to cause melting and then recrystallization into a different crystal structure is at the origin of the difference in brightness. Within the laser affected zone, no differences can be discerned between
Un-sintered region

Sintered region

(a) Spherulite

<figure><img src="image_20.png" /></figure>

(b) height mapping

<figure><img src="image_21.png" /></figure>

(c) stiffness mapping

<figure><img src="image_22.png" /><figcaption>**Fig. 17.** AFM images in un-sintered region (left) and inside laser sintered zone (right), showing (a) low resolution height mapping with spherulites indicated by white circles, (b) high resolution height mapping and (c) high resolution stiffness mapping. Sintering of 125 µm PA12 particle doublets at a heating chamber temperature of T~c~ = 155 °C.</figcaption></figure>

the material near the interface and that further away from the interface, at least within the range of length scales that affect the optical images.

Fig. 16 shows an image sequence of sections made along the depth for 125 µm and 200 µm melt doublets. These images show that the bright zone is visible along the thickness of the particle doublet, suggesting that laser energy penetrated completely along the particle width.

Atomic force microscopy (AFM) was performed on a microtomed doublet sintered from 125 µm particles. Fig. 17 shows the topology and stiffness images from locations inside and outside the laser sintered zone. The low resolution height map allows to compare the spherulite size after melt recrystallization in the laser sintered zone (Fig. 17a right), to that in the un-sintered zone (Fig. 17a left). It can clearly be observed that the spherulite size is increased due to the sintering process, as it varied between 8 and 13 µm in the un-sintered zone and between 14 and 18 µm in the laser sintered region. In general, lower temperatures lead to a higher nucleation density [16] and as a result more and smaller spherulites. Since crystallization in the sintered doublet occurred at the chamber temperature of 155 °C whereas

faster cooling occurred during particle production, an increase of the spherulite size after sintering could be expected. For the same locations, high resolution imaging is done to determine the lamellar thickness. Fig. 17b-c show the topography and stiffness maps. It should be noted that the linear features that occur in both images, are most likely caused by defects from the microtoming. Hence, the white high stiffness lines in between the cutting defects are the crystal lamellae. On average, the observations suggest that the lamellar thickness is higher after laser sintering (Fig. 17c right) as compared to before sintering (Fig. 17c left). This observation is in line with the estimated crystallite thickness from the Scherrer equation listed in Table 3. Along the same lines, SAXS results of Paolucci et al. [12] showed a slightly higher lamellar thickness of laser sintered as compared to compression moulded PA12. Although being a microscale feature, the lamellar thickness significantly affects the mechanical properties [12]. Hence, controlling this characteristic provides control over the end-use properties. In conclusion, both at the length scales of the crystallites, probed by WAXD and AFM as at the
length scale of the spherulites, probed by AFM and POM, there is a coarsening of the crystalline microstructure due to laser sintering.

## 4. Conclusions

We present a study of laser sintering of PA12 particle doublets using an in-house developed sintering setup, which mimics the functioning of an SLS machine with the additional capability to perform in-situ X-ray experiments. These results feature information on morphological changes during the sintering process, which can only be studied by in-situ measurements. To determine suitable values for laser energy and chamber temperature, the melt behavior, flow properties and laser light absorption for PA12 polymer with 2 wt% dye were characterized. By simultaneously capturing flow by optical imaging and crystallization kinetics from WAXD patterns, in combination with IR imaging for monitoring the temperature, a complex interplay between temperature, flow and crystallization kinetics is shown. Both smaller polymer particles and a higher chamber temperature cause a faster sintering process and thus more complete sintering, similar to our previous work on amorphous polystyrene. Infrared imaging confirmed that the particle size effect is governed by the higher temperature at the bridge location in case of smaller particles. Cooling after laser impact occurs with a constant heat transfer coefficient, with a value between 150 and 300 W/(m²K). For all studied conditions, sintering of the particle bridge and crystallization occur sequentially. The crystallization kinetics increases with decreasing particle size and decreasing chamber temperature. The latter effect is expected based on the quiescent isothermal crystallization kinetics studied via calorimetry. However, taking into account the temperature dependence of the crystallization kinetics as well as melt memory effects, the faster crystallization in smaller particles is counterintuitive. Estimates of the critical Weissenberg numbers based on the Rouse and reptation times suggest that under the given process conditions, the polymer chains in the bridge region can become oriented but not stretched, which could enhance the nucleation density. Since the deformation rates are larger for smaller particles, this could explain the faster crystallization kinetics for these particles. After sintering, the crystal type in the laser-affected zone depends on the chamber temperature whereby an overall larger spherulite size and lamellar thickness are observed as compared to the unsintered region.

In the future, combining experimental work and numerical simulations will help to extend this work to an actual sintering process involving a powder bed. Furthermore, our work shows that the possibility of flow induced crystallization during laser sintering should be considered when developing numerical models. Finally, several other process parameters like pulse duration and laser energy can influence the sintering as well as the crystallization kinetics, but were not yet studied. It can be concluded that in this work a systematic approach was taken to develop a fundamental understanding of structure development of PA12 polymer particles during laser sintering.

### CRediT authorship contribution statement

**Prakhyat Hejmady:** Methodology, Investigation, Formal analysis, Writing – original draft. **Lambèrt C.A. van Breemen:** Conceptualization, Methodology, Writing – review & editing, Supervision, Funding acquisition. **Daniel Hermida-Merino:** Methodology, Writing – review & editing. **Patrick D. Anderson:** Conceptualization, Writing – review & editing, Supervision, Project administration, Funding acquisition. **Ruth Cardinalis:** Conceptualization, Methodology, Formal analysis, Writing – review & editing, Supervision, Funding acquisition.

### Acknowledgments

This work forms part of the research programme of the Brightlands Materials Center (BMC), Netherlands. We acknowledge NWO, Netherlands for financing beam time at ESRF and the European Synchrotron Radiation Facility, France for provision of synchrotron radiation facilities. We thank Prof.Dr.Ir. L.E. Govaert for providing the PA12 polymer. We thank Dr.ir. T.A.P. Engels for the discussions and Dr. M. Tian from DSM for performing the AFM imaging. Dr.ir. F. Paolucci is acknowledged for performing the SEC measurements. We thank P. Schmit from the Physical Chemistry group at TU/e for the microtomy training and the use of the microtome.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.addma.2022.102624.

### References

[1] S. Ligon, R. Liska, J. Stampfl, M. Gurr, R. Mulhaupt, Polymers for 3d printing and customized additive manufacturing, Chem. Rev. 117 (15) (2017) 10212–10290, http://dx.doi.org/10.1021/acs.chemrev.7b00074.

[2] C. Gonzalez-Henriquez, M. Sarabia-Vallejos, J. Rodriguez-Hernandez, Polymers for additive manufacturing and 4d-printing: Materials, methodologies, and biomedical applications, Prog. Polym. Sci. 94 (2019) 57–116, http://dx.doi.org/10.1016/j.progpolymsci.2019.03.001.

[3] S. Yuan, F. Shen, C. Chua, K. Zhou, Polymeric composites for powder-based additive manufacturing: Materials and applications, Prog. Polym. Sci. 91 (2019) 141–168, http://dx.doi.org/10.1016/j.progpolymsci.2018.11.001.

[4] R. Brighenti, M. Cosma, L. Marsavina, A. Spagnoli, M. Terzano, Laser-based additively manufactured polymers: a review on processes and mechanical models, J. Mater. Sci. 56 (2) (2021) 961–998, http://dx.doi.org/10.1007/s10853-020-05254-6.

[5] H. Wu, W. Fahy, S. Kim, H. Kim, N. Zhao, L. Pilato, A. Kafi, S. Bateman, J. Koo, Recent developments in polymers/polymer nanocomposites for additive manufacturing, Prog. Mater. Sci. 111 (2020) 100638, http://dx.doi.org/10.1016/j.pmatsci.2020.100638.

[6] L. Tan, W. Zhu, K. Zhou, Recent progress on polymer materials for additive manufacturing, Adv. Funct. Mater. 30 (43) (2020) 2003062, http://dx.doi.org/10.1002/adfm.202003062.

[7] Y. Wang, Z. Xu, D. Wu, J. Bai, Current status and prospects of polymer powder 3d printing technologies, Materials 13 (10) (2020) 2406, http://dx.doi.org/10.3390/ma13102406.

[8] M. Schmid, A. Amado, K. Wegener, Materials perspective of polymers for additive manufacturing with selective laser sintering, J. Mater. Res. 29 (17) (2014) 1824–1832, http://dx.doi.org/10.1557/jmr.2014.138.

[9] R.D. Goodridge, C.J. Tuck, R.J.M. Hague, Laser sintering of polyamides and other polymers, Prog. Mater. Sci. 57 (2) (2012) 229–267, http://dx.doi.org/10.1016/j.pmatsci.2011.04.001.

[10] D. Drummer, F. Rietzel, D. Kühnlein, Development of a characterization approach for the sintering behavior of new thermoplastics for selective laser sintering, Physics Procedia 5 (2010) 533–542, http://dx.doi.org/10.1016/j.phpro.2010.08.081.

[11] B. Van Hooreweder, D. Moens, R. Boonen, J.-P. Kruth, P. Sas, On the difference in material structure and fatigue properties of nylon specimens produced by injection molding and selective laser sintering, Polym. Test. 32 (5) (2013) 972–981, http://dx.doi.org/10.1016/j.polymtesting.2013.04.014.

[12] F. Paolucci, L. Govaert, G. Peters, In situ waxd and saxes during tensile deformation of moulded and sintered polyamide 12, Polymers 11 (6) (2019) 1001, http://dx.doi.org/10.3390/polym11061001.

[13] L. Li, M.H.J. Koch, W.H. de Jeu, Crystalline structure and morphology in nylon-12: A small-and wide-angle x-ray scattering study, Macromolecules 36 (5) (2003) 1626–1632, http://dx.doi.org/10.1021/ma025732l.

[14] M. Zhao, K. Wudy, D. Drummer, Crystallization kinetics of polyamide 12 during selective laser sintering, Polymers 10 (2) (2018) 168, http://dx.doi.org/10.3390/polym10020168.
[15] C.J.G. Plummer, J.E. Zanetto, P.E. Bourban, J.A.E. Mânson, The crystallization kinetics of polyamide-12, Colloid Polym. Sci. 279 (4) (2001) 312-322, http://dx.doi.org/10.1007/s003960000425.

[16] F. Paolucci, D. Baeten, P.C. Roozemond, B. Goderis, G.W.M. Peters, Quantification of isothermal crystallization of polyamide 12: Modelling of crystallization kinetics and phase composition, Polymer 155 (2018) 187-198, http://dx.doi.org/10.1016/j.polymer.2018.09.037.

[17] X. Liu, Y. Wang, Z. Wang, D. Cavallo, A. Muller, P. Zhu, Y. Zhao, X. Dong, D. Wang, The origin of memory effects in the crystallization of polyamides: Role of hydrogen bonding, Polymer 188 (2020) 122117, http://dx.doi.org/10.1016/j.polymer.2019.122117.

[18] L. Sangroniz, D. Cavallo, A. Muller, Self-nucleation effects on polymer crystallization, Macromolecules 53 (12) (2020) 4581-4604, http://dx.doi.org/10.1021/acs.macromol.0c00223.

[19] H. Zarringhalam, N. Hopkinson, N. Kamperman, J. de Vlieger, Effects of processing on microstructure and properties of sls nylon 12, Mater. Sci. Eng. A 435-436 (2006) 172-180, http://dx.doi.org/10.1016/j.msea.2006.07.084.

[20] R. Massaro, P. Roozemond, M. D'Haese, P. van Puyvelde, Flow-induced crystallization of polyamide-6, Int. Polym. Process. 33 (3) (2018) 327-335, http://dx.doi.org/10.3139/217.3524.

[21] M. Pavan, M. Faes, D. Strobbe, B. Van Hooreweder, T. Craeghs, D. Moens, On the influence of inter-layer time and energy density on selected critical-to-quality properties of pa12 parts produced via laser sintering, Polym. Test. 61 (2017) 386-395, http://dx.doi.org/10.1016/j.polymertesting.2017.05.027.

[22] A. Franco, L. Romoli, Characterization of laser energy consumption in sintering of polymer based powders, J. Mater Process. Technol. 212 (4) (2012) 917-926, http://dx.doi.org/10.1016/j.jmatprotec.2011.12.003.

[23] D. Stoia, L. Marsavina, E. Linun, Correlations between process parameters and outcome properties of laser-sintered polyamide, Polymers 11 (11) (2019) 1850, http://dx.doi.org/10.3390/polym11111850.

[24] S. Dupin, O. Lame, C. Barrès, J.-Y. Charmeau, Microstructural origin of physical and mechanical properties of polyamide 12 processed by laser sintering, Eur. Polym. J. 48 (9) (2012) 1611-1621, http://dx.doi.org/10.1016/j.eurpolymj.2012.06.007.

[25] M. Schmid, R. Kleijnen, M. Vetterli, K. Wegener, Influence of the origin of polyamide 12 powder on the laser sintering process and laser sintered parts, Appl. Sci. 7 (5) (2017) 462, http://dx.doi.org/10.3390/app7050462.

[26] L. Verbelen, S. Dadbakhsh, M. Van den Eynde, J.-P. Kruth, B. Goderis, P. Van Puyvelde, Characterization of polyamide powders for determination of laser sintering processability, Eur. Polym. J. 75 (2016) 163-174, http://dx.doi.org/10.1016/j.eurpolymj.2015.12.014.

[27] S.-L. Sindinger, C. Kralovec, D. Tasch, M. Schagerl, Thickness dependent anisotropy of mechanical properties and inhomogeneous porosity characteristics in laser-sintered polyamide 12 specimens, Addit. Manuf. 33 (2020) 101141, http://dx.doi.org/10.1016/j.addma.2020.101141.

[28] W. Wroe, J. Gladstone, T. Phillips, S. Fish, J. Beaman, A. McElroy, In-situ thermal image correlation with mechanical properties of nylon-12 in sls, Rapid Prototyping. J. 22 (5) (2016) 794-800, http://dx.doi.org/10.1108/RPJ-10-2015-0158.

[29] N. Southon, P. Stavroulakis, R. Goodridge, R. Leach, In-process measurement and monitoring of a polymer laser sintering powder bed with fringe projection, Mater. Des. 157 (2018) 227-234, http://dx.doi.org/10.1016/j.matdes.2018.07.053.

[30] M. Gardner, P.J. Lewis, A.A. McElroy, S. Estrada, J. Fish, T. Beaman, A. Milner, In situ process monitoring in selective laser sintering using optical coherence tomography, Opt. Eng. 57 (4) (2018) 041407, http://dx.doi.org/10.1117/1.OE.57.4.041407.

[31] C.T. Bellehumeur, M.K. Bisaria, J. Vlachopoulos, An experimental study and model assessment of polymer sintering, Polym. Eng. Sci. 36 (17) (1996) 2198-2207, http://dx.doi.org/10.1002/pen.10617.

[32] P. Hejmady, L.C. Cleven, L.C.A. van Breemen, P.D. Anderson, R.M. Cardinaels, A novel experimental setup for in situ optical and x-ray imaging of laser sintering of polymer particles, Rev. Sci. Instrum. 90 (8) (2019) 083905, http://dx.doi.org/10.1063/1.5106406.

[33] Y. Gueche, N. Sanchez-Ballester, S. Cailleaux, B. Bataille, I. Soulairol, Selective laser sintering (sls), a new chapter in the production of solid oral forms (sols) by 3d printing, Pharmaceutics 13 (2021) 1212, http://dx.doi.org/10.3390/pharmaceutics13081212.

[34] M. Mapley, Y. Lu, S. Gregory, J. Pauls, G. Tansley, A. Busch, Development and validation of a low-cost polymer selective laser sintering machine, HardwareX 8 (2020) e00119, http://dx.doi.org/10.1016/j.ohx.2020.e00119.

[35] P. Hejmady, L.C.A. van Breemen, P.D. Anderson, R.M. Cardinaels, Laser sintering of polymer particle pairs studied by in situ visualization, Soft Matter 15 (6) (2019) 1373-1387, http://dx.doi.org/10.1039/C8SM02081G.

[36] B.B. Sauer, G.T. Dee, Surface tension and melt cohesive energy density of polymer melts including high melting and high glass transition polymers, Macromolecules 35 (18) (2002) 7024-7030, http://dx.doi.org/10.1021/ma0202437.

[37] J. Mark, Physical Properties of Polymers Handbook.

[38] P. Hejmady, L. van Breemen, P. Anderson, R. Cardinaels, A processing route to spherical polymer particles via controlled droplet retraction, Powder Technol. 388 (2021) 401-411, http://dx.doi.org/10.1016/j.powtec.2021.04.058.

[39] M. van Drongelen, A. Stroeks, G. Peters, Kinetics of the deformation induced memory effect in polyamide-6, Eur. Polym. J. 72 (2015) 296-308, http://dx.doi.org/10.1016/j.eurpolymj.2015.09.028.

[40] A. Pawlak, J. Krajenta, A. Galeski, The crystallization of polypropylene with reduced density of entanglements, J. Polym. Sci. B 55 (9) (2017) 748-756, http://dx.doi.org/10.1002/polb.24328, epdf/.

[41] W. Bras, I. Dolbnya, D. Detollenaere, R. van Tol, M. Malfois, G. Greaves, A. Ryan, E. Heeley, Recent experiments on a combined small-angle/wide-angle x-ray scattering beam line at the esrf, J. Appl. Crystallogr. 36 (3) (2003) 791-794, http://dx.doi.org/10.1107/S002188980300400X.

[42] G. Portale, D. Cavallo, G.C. Alfonso, D. Hermida-Merino, M. van Drongelen, L. Balzano, G.W.M. Peters, J.G.P. Goossens, W. Bras, Polymer crystallization studies under processing-relevant conditions at the saxes/waxs dubble beamline at the esrf, J. Appl. Crystallogr. 46 (6) (2013) 1681-1689, http://dx.doi.org/10.1107/S0021889813027076.

[43] A.P. Hammersley, et al., Fit2d: an introduction and overview, in: European Synchrotron Radiation Facility Internal Report ESRF97HA02T 68, 1997, p. 58, URL http://www.esrf.eu/computing/scientific/FIT2D/FIT2D_INTRO/fit2d.html.

[44] N. Dencheva, T.G. Nunes, M.J. Oliveira, Z. Denchev, Crystalline structure of polyamide 12 as revealed by solid-state 13c nmr and synchrotron waxes and saxes, J. Polym. Sci. B 43 (24) (2005) 3720-3733, http://dx.doi.org/10.1002/polb.20672.

[45] P. Scherrer, Bestimmung der inneren struktur und der größe von kolloidteilchen mittels röntgenstrahlen, in: Kolloidchemie Ein Lehrbuch, Springer, 1912, pp. 387-409, http://dx.doi.org/10.1007/978-3-662-33915-2_7.

[46] A. Monshi, M.R. Foroughi, M.R. Monshi, Modified scherrer equation to estimate more accurately nano-crystallite size using xrd, World J. Nano Sci. Eng. 2 (3) (2012) 154-160, http://dx.doi.org/10.4236/wijnse.2012.23020.

[47] B. Pauw, Everything saxes: small angle scattering pattern collection and correction, J. Phys.: Condens. Matter 25 (2013) 239501, http://dx.doi.org/10.1088/0953-8984/26/23/239501.

[48] N. Ma, W. Liu, L. Ma, S. He, H. Liu, Z. Zhang, A. Sun, M. Huang, C. Zhu, Crystal transition and thermal behavior of nylon 12, E-Polymers 20 (1) (2020) 346-352, http://dx.doi.org/10.1515/epoly-2020-0039.

[49] C.W. Macosko, Rheology Principles, Measurements and Applications, URL https://www.wiley.com/en-us/Rheology%3A+Principles%2C+Measurements%2C+and+Applications-p-9780471185758.

[50] A.M. Rhoades, N. Wonderling, C. Schick, R. Androsch, Supercooling-controlled heterogeneous and homogenous crystal nucleation of polyamide 11 and its effect onto the crystal/mesophase polymorphism, Polymer 106 (2016) 29-34, http://dx.doi.org/10.1016/j.polymer.2016.10.050.

[51] F. Paolucci, M.J.H. van Mook, L.E. Govaert, G.W.M. Peters, Influence of post-condensation on the crystallization kinetics of pa12: from virgin to reused powder, Polymer 175 (2019) 161-170, http://dx.doi.org/10.1016/j.polymer.2019.05.009.

[52] O. Pokluda, C.T. Bellehumeur, J. Vlachopoulos, Modification of frenkel's model for sintering, AIChE J. 43 (12) (1997) 3253-3256, http://dx.doi.org/10.1002/aic.690431213.

[53] W.M. Rohsenow, J.P. Hartnett, Y.I. Cho, et al., Handbook of Heat Transfer, Vol. 3, McGraw-Hill, New York, 1998, URL https://books.google.nl/books/about/Handbook_of_Heat_Transfer.html?id=M3pUAAAAMAAJA&redir esc=y.

[54] C. Balemans, P. Hejmady, R. Cardinaels, P.D. Anderson, Towards unraveling the sintering process of two polystyrene particles by numerical simulations, Korea-Aust. Rheol. J. 31 (4) (2019) 285-295, http://dx.doi.org/10.1007/s13367-019-0028-z.

[55] C. Balemans, S. Looijmans, G. Grosso, M. Hulsen, P. Anderson, Numerical analysis of the crystallization kinetics in sls, Addit. Manuf. 33 (2020) 101126, http://dx.doi.org/10.1016/j.addma.2020.101126.

[56] P. Roozemond, M. van Drongelen, Z. Ma, A. Spoelstra, D. Hermida-Merino, G. Peters, Self-regulation in flow-induced structure formation, Macromol. Rapid Commun. 36 (4) (2015) 385, http://dx.doi.org/10.1002/marc.201400505.

[57] N. Polychronopoulos, J. Vlachopoulos, The role of heating and cooling in viscous sintering of pairs of spheres and pairs of cylinders, Rapid Prototyp. J. 26 (4) (2020) 719, http://dx.doi.org/10.1108/RPJ-06-2019-0162.

[58] C. Balemans, M.A. Hulsen, P.D. Anderson, On the validity of 2d analysis of non-isothermal sintering in sls, Chem. Eng. Sci. 213 (2020) 115365, http://dx.doi.org/10.1016/j.ces.2019.115365.

[59] J. van Meerveld, G.W.M. Peters, M. Hütter, Towards a rheological classification of flow induced crystallization experiments of polymer melts, Rheol. Acta 44 (2) (2004) 119-134, http://dx.doi.org/10.1007/s00397-004-0382-7.

[60] M. Doi, S.F. Edwards, S.F. Edwards, The Theory of Polymer Dynamics, Vol. 73, Oxford University Press, 1988, URL https://books.google.nl/books/about/The_Theory_of_Polymer_Dynamics.html?id=dMzGyWs3GKcC&redir esc=y.

[61] S. Wu, Chain structure and entanglement, J. Polym. Sci. B 27 (4) (1989) 723-741, http://dx.doi.org/10.1002/polb.1989.090270401.

[62] M. Seki, D. Thurman, J. Oberhauser, J. Kornfield, Shear-mediated crystallization of isotactic polypropylene: The role of long chain - long chain overlap, Macromolecules 35 (7) (2002) 2583-2594, http://dx.doi.org/10.1021/ma011359q.
[63] E. Scribben, D. Baird, P. Wapperom, The role of transient rheology in polymeric sintering, Rheol. Acta 45 (6) (2006) 825-839, http://dx.doi.org/10.1007/s00397-005-0039-1.

[64] C. Hadinata, D. Boos, C. Gabriel, E. Wassner, M. Rillmann, N. Kao, M. Laun, Elongation-induced crystallization of a high molecular weight isotactic polybutene-1 melt compared to shear-induced crystallization, J. Rheol. 51 (2) (2007) 195-215, http://dx.doi.org/10.1122/1.2426977.

[65] D. Cavallo, F. Azzurri, L. Balzano, S.S. Funari, G.C. Alfonso, Flow memory and stability of shear-induced nucleation precursors in isotactic polypropylene, Macromolecules 43 (22) (2010) 9394-9400, http://dx.doi.org/10.1021/ma1020193.

[66] P.C. Roozemond, R.J.A. Steenbakkers, G.W.M. Peters, A model for flow-enhanced nucleation based on fibrillar dormant precursors, Macromol. Theory Simul. 20 (2) (2011) 93-109, http://dx.doi.org/10.1002/mats.201000059.

[67] Y. Zhou, S. Xi, Y. Huang, M. Kong, Q. Yang, G. Li, Preparation of near-spherical pa12 particles for selective laser sintering via plateau-rayleigh instability of molten fibers, Mater. Des. 190 (2020) 108578, http://dx.doi.org/10.1016/j.matdes.2020.108578.

[68] C. Ramesh, Crystalline transitions in nylon 12, Macromolecules 32 (17) (1999) 5704-5706, http://dx.doi.org/10.1021/ma990494o.

[69] R. Bonart, R. Hosemann, R. McCullough, The influence of particle size and distortions upon the x-ray diffraction patterns of polymers, Polymer 4 (1963) 199-211, http://dx.doi.org/10.1016/0032-3861(63)90026-0.

[70] N. Murthy, Analysis of meridional x-ray diffraction pattern of the $\gamma$ form of nylon 6 and comparison of paracrystalline and microstrain models of lattice disorder, J. Polym. Sci. B 24 (3) (1986) 549-561, http://dx.doi.org/10.1002/polb.1986.090240306.

[71] Z.-G. Wang, B. Hsiao, B. Fu, L. Liu, F. Yeh, B. Sauer, H. Chang, J. Schult, Correct determination of crystal lamellar thickness in semicrystalline poly(ethyleneterephthalate) by small-angle x-ray scattering, Polymer 41 (5) (2000) 1791-1799, http://dx.doi.org/10.1016/S0032-3861(99)00327-4.

[72] Q. Zhang, D. Myers, J. Lan, S.A. Jenekhe, G. Cao, Applications of light scattering in dye-sensitized solar cells, Phys. Chem. Chem. Phys. 14 (43) (2012) 14982-14998, http://dx.doi.org/10.1039/C2CP43089D.