# PTFE Crystal Growth in Composites: A Phase-Field Model Simulation Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

**r**, t), is used to describe the phase evolution over time and space: Ψ(

**r**, t) = 0 and Ψ(

**r**, t) = 1. These denote the liquid phase and the complete crystalline phase, respectively. The total free energy of the system, F, consists of the local free energy density, f

_{local}[38], and the gradient free energy density, f

_{grad}, which is Equation (1):

_{0}is the value of Ψ in a stable solidification state [30,40], κ

_{0}is the interface gradient coefficient (related parameters of the interface thickness). β(θ) = 1 + εcos(jθ) represents the interface anisotropic growth rate [41], where ε is the anisotropic strength, j is the number of modes, and θ is the angle between the interface normal and the reference axis.

_{T}/(ρC

_{P}), Κ = ΔH/C

_{P}(related parameters of the latent heat); parameters ρ, C

_{P}, κ

_{T}, and ΔH represent density, specific heat capacity, thermal conductivity, and melting heat, respectively.

## 3. Results and Discussion

#### 3.1. Effects of Polymer Intrinsic Properties

#### 3.2. Effects of Crystallization Process Factors

#### 3.3. Effects of Biphasic Interface and Crystal Nucleus Shape

## 4. Conclusions

## Supplementary Materials

_{s}(anisotropic mode j = 4). (a–d) T

_{s}= 20 K, τ = 40, 120, 200, 280; (e–h) T

_{s}= 25 K, τ = 40, 120, 200, 280; (i–l) T

_{s}= 30 K, τ = 40, 120, 200, 280; (m–p) T

_{s}= 35 K, τ = 40, 120, 200, 280, Figure S2: Morphology of PTFE crystal evolution under various supercooling degrees, T

_{s}(anisotropic mode j = 6). (a–d) T

_{s}= 20 K, τ = 40, 120, 200, 280; (e–h) T

_{s}= 25 K, τ = 40, 120, 200, 280; (i–l) T

_{s}= 30 K, τ = 40, 120, 200, 280; (m–p) T

_{s}= 35 K, τ = 40, 120, 200, 280, Figure S3: Morphology of PTFE crystal evolution under various supercooling degrees, T

_{s}(anisotropic mode j = 36). (a–d) T

_{s}= 25 K, τ = 40, 80, 120, 160; (e–h) T

_{s}= 30 K, τ = 40, 80, 120, 160; (i–l) T

_{s}= 35 K, τ = 40, 80, 120, 160; (m–p) T

_{s}= 40 K, τ = 40, 80, 120, 160, Figure S4: Morphology of PTFE crystal evolution with different dimensionless latent heat, $\widehat{\mathrm{K}}$. (a–d) $\widehat{\mathrm{K}}=2,\tau =40,80,120,160$; (e–h) $\widehat{\mathrm{K}}=3,\tau =40,80,120,160$; (i–l) $\widehat{\mathrm{K}}=4,\tau =40,80,120,160$; (m–p) $\widehat{\mathrm{K}}=5,\tau =40,80,120,160$; (q) dimensionless temperature distribution of Figure S4d; (r) local detail of Figure S4q, Figure S5: Morphology of PTFE crystal evolution with different aniso-tropic strengths, ε. (a–d) ε = 0.01, τ = 40, 120, 200, 280; (e–h) ε = 0.02, τ = 40, 120, 200, 280; (i–l) ε = 0.031, τ = 40, 120, 200, 280; (m–p) ε = 0.04, τ = 40, 120, 200, 280, Figure S6: Morphology of PTFE crystal evolution with different interface thickness related parameters, ${\widehat{\kappa}}_{0}$. (a–d) ${\widehat{\kappa}}_{0}=0.4,\tau =40,80,120,160$; (e–h) ${\widehat{\kappa}}_{0}=0.8,\tau =40,80,120,160$; (i–l) ${\widehat{\kappa}}_{0}=1.2,\tau =40,80,120,160$; (m–p) ${\widehat{\kappa}}_{0}=1.6,\tau =40,80,120,160$ [30,31,38,39,40,41,48,49,50,51].

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Shape design of the filler and the location of the crystal nuclei. (

**a**) Circular crystal nuclei, (

**b**) rodlike crystal nuclei, (

**c**) curved crystal nuclei.

**Figure 2.**The relationship between the supercooling degree and the number of branches of a PTFE crystal with different anisotropic modes (evolution of time τ = 160).

**Figure 3.**The relationship between the number of branches of a PTFE crystal and latent heat (anisotropic mode j = 6, evolution of time τ = 160).

**Figure 4.**The relationship between the number of branches of a PTFE crystal and anisotropic strength (anisotropic mode j = 6, evolution of time τ = 160).

**Figure 5.**The relationship between the number of branches of a PTFE crystal and interface thickness (anisotropic mode j = 6, evolution of time τ = 160).

**Figure 6.**Morphology evolution diagram of a PTFE crystal with different nucleus shapes with a second-phase filler. (

**a**–

**c**) Circular crystal nucleus, (

**d**–

**f**) rodlike crystal nucleus, (

**g**–

**i**) curved crystal nucleus, (

**j**,

**k**) two examples of the defining aspect ratio (AR) for the effective branches.

**Figure 7.**Details of PTFE crystal morphology at the biphasic interface of different fillers. (

**a**–

**c**) Details of Figure 6c; (

**e**) morphology evolution diagram of a PTFE crystal with a rodlike nucleus shape with second-phase filler (evolution time τ = 180); (

**d**,

**f**–

**i**) details of (

**e**).

Material Parameter | Model Parameter |
---|---|

${T}_{m}=327\mathbb{C}$ | $D=1\times {10}^{-9}{\mathrm{m}}^{2}/\mathrm{s}$ |

${T}_{m}^{0}=340\mathbb{C}$ | $d=1\times {10}^{-7}\mathrm{m}$ |

${T}_{c}=315\mathbb{C}$ | ${\xi}_{0}=0.95$ |

$\rho =2.3\times {10}^{3}{\mathrm{kg}/\mathrm{m}}^{3}$ | $\Delta \widehat{t}=2.5\times {10}^{-5}$ |

$\Delta H=8.2\times {10}^{4}\mathrm{kJ}/\mathrm{mol}$ | $\Delta \widehat{x}=\Delta \widehat{y}=1.5\times {10}^{-2}$ |

${C}_{p}=6.788\times {10}^{4}\mathrm{kJ}/\left(\mathrm{mol}\cdot \mathrm{K}\right)$ | |

${\kappa}_{T}=0.256\mathrm{W}/\left(\mathrm{m}\cdot \mathrm{K}\right)$ | |

$\sigma =1.86\times {10}^{-2}{\mathrm{J}/\mathrm{m}}^{2}$ |

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**MDPI and ACS Style**

Fan, M.; He, W.; Li, Q.; Zhou, J.; Shen, J.; Chen, W.; Yu, Y.
PTFE Crystal Growth in Composites: A Phase-Field Model Simulation Study. *Materials* **2022**, *15*, 6286.
https://doi.org/10.3390/ma15186286

**AMA Style**

Fan M, He W, Li Q, Zhou J, Shen J, Chen W, Yu Y.
PTFE Crystal Growth in Composites: A Phase-Field Model Simulation Study. *Materials*. 2022; 15(18):6286.
https://doi.org/10.3390/ma15186286

**Chicago/Turabian Style**

Fan, Ming, Wenhao He, Qiangzhi Li, Jing Zhou, Jie Shen, Wen Chen, and Yuanying Yu.
2022. "PTFE Crystal Growth in Composites: A Phase-Field Model Simulation Study" *Materials* 15, no. 18: 6286.
https://doi.org/10.3390/ma15186286