# Efficient Non-Destructive Detection of Interface Adhesion State by Interfacial Thermal Conductance: A Molecular Dynamics Study

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## Abstract

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## 1. Introduction

## 2. Model and Simulation Method

_{2}monomers, and the carbon atoms at both ends were connected with hydrogen groups. PE is one of the most widely used polymers with many excellent properties. The reliability of the molecular dynamic simulation of interfacial heat conduction between polyethylene and silicon has also been confirmed many times. Therefore, our selection of PE as an adhesive component not only ensured the correct calculations during the simulation process, but also represented a wider range of polymers. To investigate the possible role of finite size effects, we also established another structure with a 100% increase in both the x and y directions of silicon and PE, and conducted interfacial thermal conductance calculations in the same simulation environment as the above model.

## 3. Results and Discussion

#### 3.1. Interfacial Thermal Conductance of a Single Vacuole Model at 500 K

^{3}, which is typical for amorphous PE during the polymer simulation [25], the edges of the voids were fixed using the region and fix wall/region commands. The number of linear polymer chains in the model of Figure 1 was reduced from 26 to 23, 21, and 18, resulting in a reduction of the polymer volume to 88.46%, 80.77%, and 69.23%, respectively, while maintaining a constant density. The effective contact area between the orthorhombic silicon block and the polymer was also reduced proportionally; therefore, the only variable for the calculation of the interfacial thermal conductance of the before-and-after model is the effective contact area between the orthorhombic silicon block and the polymer, and the interfacial thermal conductance was calculated as a function of the effective contact area between the two. The results are shown in Figure 2d. To ensure accuracy, several simulations were performed, as the temperature decay curve needs to be fitted and the rise and fall of temperature can affect the accuracy of the time decay constant τ. The figure shows that the interfacial thermal conductance decreases as the effective contact area between the silicon block and the polymer decreases, indicating that the ratio of the effective contact area is directly proportional to the interfacial thermal conductance and inversely proportional to the void rate. Since the void rate in the polymer binder can affect the adhesion strength, the interfacial thermal conductance calculation can be used to reflect the magnitude of the adhesion strength. Furthermore, we performed interfacial thermal conductance calculations in the same simulation environment and steps for another model that was established with increases in both the x and y directions to investigate the possible role of finite size effects, as shown in Figure 3. The results show that the interfacial thermal conductance of the two models are essentially the same, thus demonstrating negligible finite size effects.

#### 3.2. Interfacial Thermal Conductance of a Single Vacuole Model at 400 K

#### 3.3. Interfacial Thermal Conductance of a Multiple Vacuole Model at 500 K

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zheng, R.; Lin, J.; Wang, P.-C.; Zhu, C.; Wu, Y. Effect of adhesive characteristics on static strength of adhesive-bonded aluminum alloys. Int. J. Adhes. Adhes.
**2015**, 57, 85–94. [Google Scholar] [CrossRef] - Heinzmann, C.; Weder, C.; de Espinosa, L.M. Supramolecular polymer adhesives: Advanced materials inspired by nature. Chem. Soc. Rev.
**2016**, 45, 342–358. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sun, S.; Li, M.; Liu, A. A review on mechanical properties of pressure sensitive adhesives. Int. J. Adhes. Adhes.
**2013**, 41, 98–106. [Google Scholar] [CrossRef] - Pethrick, R.A. Design and ageing of adhesives for structural adhesive bonding—A review. J. Mater. Des. Appl.
**2014**, 229, 349–379. [Google Scholar] [CrossRef] - Kadioglu, F.; Adams, R.D. Flexible adhesives for automotive application under impact loading. Int. J. Adhes. Adhes.
**2015**, 56, 73–78. [Google Scholar] [CrossRef] - Ghobril, C.; Grinstaff, M.W. The chemistry and engineering of polymeric hydrogel adhesives for wound closure: A tutorial. Chem. Soc. Rev.
**2015**, 44, 1820–1835. [Google Scholar] [CrossRef] - Saboori, A.; Aversa, A.; Marchese, G.; Biamino, S.; Lombardi, M.; Fino, P. Application of Directed Energy Deposition-Based Additive Manufacturing in Repair. Appl. Sci.
**2019**, 9, 3316. [Google Scholar] [CrossRef][Green Version] - Yang, M.; Rosentrater, K.A. Life Cycle Assessment of Urea-Formaldehyde Adhesive and Phenol-Formaldehyde Adhesives. Environ. Processes
**2020**, 7, 553–561. [Google Scholar] [CrossRef] - Shi, C.Y.; Zhang, Q.; Tian, H.; Qu, D.H. Supramolecular adhesive materials from small-molecule self-assembly. SmartMat
**2020**, 1, e1012. [Google Scholar] [CrossRef] - Bao, Z.; Gao, M.; Sun, Y.; Nian, R.; Xian, M. The recent progress of tissue adhesives in design strategies, adhesive mechanism and applications. Mater. Sci. Eng. C Mater. Biol. Appl.
**2020**, 111, 110796. [Google Scholar] [CrossRef] - Martinsen, K.; Hu, S.J.; Carlson, B.E. Joining of dissimilar materials. CIRP Ann. Manuf. Technol.
**2015**, 64, 679–699. [Google Scholar] [CrossRef][Green Version] - Szabelski, J.; Karpinski, R.; Machrowska, A. Application of an Artificial Neural Network in the Modelling of Heat Curing Effects on the Strength of Adhesive Joints at Elevated Temperature with Imprecise Adhesive Mix Ratios. Materials
**2022**, 15, 721. [Google Scholar] [CrossRef] [PubMed] - Vassilopoulos, A.P. The history of fiber-reinforced polymer composite laminate fatigue. Int. J. Fatigue
**2020**, 134, 105512. [Google Scholar] [CrossRef] - Bahraminasab, M.; Sahari, B.B.; Edwards, K.L.; Farahmand, F.; Hong, T.S.; Arumugam, M.; Jahan, A. Multi-objective design optimization of functionally graded material for the femoral component of a total knee replacement. Mater. Des.
**2014**, 53, 159–173. [Google Scholar] [CrossRef] - Kulisz, M.; Rudawska, A.; Maziarz, M.; Miturska, I.; Szala, M.; Badurowicz, M.; Cel, W.; Chmielewska, M.; Czyż, Z.; Falkowicz, K.; et al. Impact of Selected Structural, Material and Exploitation Factors on Adhesive Joints Strength. MATEC Web Conf.
**2019**, 252, 01006. [Google Scholar] [CrossRef][Green Version] - Zuo, P.; Vassilopoulos, A.P. Review of fatigue of bulk structural adhesives and thick adhesive joints. Int. Mater. Rev.
**2020**, 66, 313–338. [Google Scholar] [CrossRef] - Back, J.-H.; Hwang, J.-U.; Lee, Y.-H.; Baek, D.; Park, J.-W.; Kim, H.-J.; Kim, J.-H.; Song, H.-K.; Yoo, M.-J. Morphological study and mechanical property of epoxy-foam adhesives based on epoxy composites for automotive applications. Int. J. Adhes. Adhes.
**2018**, 87, 124–129. [Google Scholar] [CrossRef] - Sun, P.; Qin, B.; Xu, J.F.; Zhang, X. High-Performance Supramolecular Adhesives. Macromol. Chem. Phys.
**2022**, 224, 2200332. [Google Scholar] [CrossRef] - Back, J.H.; Baek, D.; Shin, J.H.; Jang, S.W.; Kim, H.J.; Kim, J.H.; Song, H.K.; Hwang, J.W.; Yoo, M.J. Resistance to Cleavage of Core(-)Shell Rubber/Epoxy Composite Foam Adhesive under Impact Wedge(-)Peel Condition for Automobile Structural Adhesive. Polymers
**2019**, 11, 152. [Google Scholar] [CrossRef][Green Version] - Miturska-Baranska, I.; Rudawska, A.; Doluk, E. Influence of Physical Modification of the Adhesive Composition on the Strength Properties of Aerospace Aluminum Alloy Sheet Adhesive Joints. Materials
**2022**, 15, 7799. [Google Scholar] [CrossRef] - Teng, X.; Jin, M.; Ding, C.; Lu, C. A rapid screening method for thermal conductivity properties of thermal insulation materials by a thermochemiluminescence probe. Chem. Commun.
**2020**, 56, 12781–12784. [Google Scholar] [CrossRef] - Wang, J.; Zhang, Z.; Shi, R.; Chandrashekar, B.N.; Shen, N.; Song, H.; Wang, N.; Chen, J.; Cheng, C. Impact of Nanoscale Roughness on Heat Transport across the Solid–Solid Interface. Adv. Mater. Interfaces
**2019**, 7, 1901582. [Google Scholar] [CrossRef] - Li, S.; Chen, Y.; Zhao, J.; Wang, C.; Wei, N. Atomic structure causing an obvious difference in thermal conductance at the Pd-H2O interface: A molecular dynamics simulation. Nanoscale
**2020**, 12, 17870–17879. [Google Scholar] [CrossRef] - Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys.
**1995**, 117, 1–19. [Google Scholar] [CrossRef][Green Version] - Hu, M.; Keblinski, P.; Li, B. Thermal rectification at silicon-amorphous polyethylene interface. Appl. Phys. Lett.
**2008**, 92, 211908. [Google Scholar] [CrossRef] - Faken, D.; Jónsson, H. Systematic analysis of local atomic structure combined with 3D computer graphics. Comp. Mater. Sci.
**1994**, 2, 279–286. [Google Scholar] [CrossRef] - Hu, M.; Keblinski, P.; Schelling, P.K. Kapitza conductance of silicon–amorphous polyethylene interfaces by molecular dynamics simulations. Phys. Rev. B
**2009**, 79, 104305. [Google Scholar] [CrossRef] - Wei, N.; Xu, L.; Wang, H.Q.; Zheng, J.C. Strain engineering of thermal conductivity in graphene sheets and nanoribbons: A demonstration of magic flexibility. Nanotechnology
**2011**, 22, 105705. [Google Scholar] [CrossRef] [PubMed] - Chen, Y.; Zhang, Y.; Cai, K.; Jiang, J.; Zheng, J.-C.; Zhao, J.; Wei, N. Interfacial thermal conductance in graphene/black phosphorus heterogeneous structures. Carbon
**2017**, 117, 399–410. [Google Scholar] [CrossRef][Green Version] - Jund, P.; Jullien, R. Molecular-dynamics calculation of the thermal conductivity of vitreous silica. Phys. Rev. B
**1999**, 59, 13707–13711. [Google Scholar] [CrossRef][Green Version] - Lampin, E.; Palla, P.L.; Francioso, P.A.; Cleri, F. Thermal conductivity from approach-to-equilibrium molecular dynamics. J. Appl. Phys.
**2013**, 114, 033525. [Google Scholar] [CrossRef] - Li, L.; Yu, Y.; Ye, G.J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X.H.; Zhang, Y. Black phosphorus field-effect transistors. Nat. Nanotechnol.
**2014**, 9, 372–377. [Google Scholar] [CrossRef] [PubMed][Green Version] - Melis, C.; Colombo, L. Lattice thermal conductivity of Si
_{1−x}Ge_{x}nanocomposites. Phys. Rev. Lett.**2014**, 112, 065901. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) The simulation model setup for the thermal relaxation method. (

**b**) Top view of a single vacuole model.

**Figure 2.**(

**a**) Temperature evolution diagram of polymer and silicon with time during simulation. (

**b**) Evolution of temperature difference between polymer and silicon with time during simulation. (

**c**) The heat capacity of silicon at 400 K is calculated and linearly fitted by calculating the relationship between temperature and energy. (

**d**) The relationship between the interfacial thermal conductance of a single vacuole model at 500 K and effective contact area ratio.

**Figure 3.**(

**a**) Another model that increases the width in both the x and y directions. (

**b**) The relationship between the interfacial thermal conductance and the effective contact area ratio of the two models at 500 K shows that there is basically no size effect.

**Figure 4.**(

**a**) The initial 0 ns temperature of the layer of silicon at around 300 K; (

**b**,

**c**) show the temperature distribution of the process in 0.28–0.32 ns and 0.88–0.92 ns; and (

**d**) shows the final 0.25 ns temperature of around 350 K.

**Figure 5.**(

**a**) The heat capacity of silicon at 350 K is calculated and linearly fitted by calculating the relationship between temperature and energy. (

**b**) Relationship between the interfacial thermal conductance of single vacuole model at 400 K and the effective contact area ratio.

**Figure 6.**(

**a**) Top view of single vacuole model. (

**b**) Top view of multiple vacuole model. (

**c**) The heat capacity of silicon at 400 K is calculated and linearly fitted by calculating the relationship between temperature and energy. (

**d**) The relationship between the interfacial thermal conductance of a multiple vacuole model at 500 K and the effective contact area ratio.

**Figure 7.**(

**a**) The initial 0 ns temperature of the layer of silicon at around 300 K; (

**b**,

**c**) show the temperature distribution of the process in 0.38–0.42 ns and 0.68–0.72 ns; and (

**d**) shows the final 0.25 ns temperature of around 350 K.

Atom 1 | Atom 2 | σ(Å) | ϵ(eV) |
---|---|---|---|

C | C | 3.5000 | 0.00286 |

C | H | 2.9580 | 0.00193 |

Si | Si | 2.4799 | 0.00173 |

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**MDPI and ACS Style**

Guo, J.; Ma, N.; Chen, J.; Wei, N. Efficient Non-Destructive Detection of Interface Adhesion State by Interfacial Thermal Conductance: A Molecular Dynamics Study. *Processes* **2023**, *11*, 1032.
https://doi.org/10.3390/pr11041032

**AMA Style**

Guo J, Ma N, Chen J, Wei N. Efficient Non-Destructive Detection of Interface Adhesion State by Interfacial Thermal Conductance: A Molecular Dynamics Study. *Processes*. 2023; 11(4):1032.
https://doi.org/10.3390/pr11041032

**Chicago/Turabian Style**

Guo, Jianhua, Niping Ma, Jiale Chen, and Ning Wei. 2023. "Efficient Non-Destructive Detection of Interface Adhesion State by Interfacial Thermal Conductance: A Molecular Dynamics Study" *Processes* 11, no. 4: 1032.
https://doi.org/10.3390/pr11041032