polymers

Article Investigation of Interface Thermal Resistance between Polymer and Mold Insert in Micro-Injection Molding by Non-Equilibrium

Can Weng 1 , Jiangwei Li 1, Jun Lai 1, Jiangwen Liu 2,* and Hao Wang 3 1 College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China; [email protected] (C.W.); [email protected] (J.L.); [email protected] (J.L.) 2 College of Mechanical and Electrical Engineering, Guangdong University of Technology, Guangzhou 510000, China 3 Department of Mechanical Engineering, Faculty of Engineering, National University of Singapore, Singapore 117575, Singapore; [email protected] * Correspondence: [email protected]; Tel.: +86-189-2512-1296

 Received: 29 September 2020; Accepted: 14 October 2020; Published: 19 October 2020 

Abstract: Micro-injection molding has attracted a wide range of research interests to fabricate polymer products with nanostructures for its advantages of cheap and fast production. The transfer between the polymer and the mold insert is important to the performance of products. In this study, the interface thermal resistance (ITR) between the (PP) layer and the nickel (Ni) mold insert layer in micro-injection molding was studied by using the method of non-equilibrium molecular dynamics (NEMD) simulation. The relationships among the ITR, the temperature, the packing pressure, the interface morphology, and the interface interaction were investigated. The simulation results showed that the ITR decreased obviously with the increase of the temperature, the packing pressure and the interface interaction. Both rectangle and triangle interface morphologies could enhance the heat transfer compared with the smooth interface. Moreover, the ITR of triangle interface was higher than that of rectangle interface. Based on the analysis of (DOS) for PP-Ni system, it was found that the mismatch between the phonon DOS of the PP and Ni atoms was the main cause of the interface resistance. The frequency distribution of phonon DOS also affected the interface resistance.

Keywords: micro-injection molding; interface thermal resistance; non-equilibrium molecular dynamics; phonon density of state

1. Introduction With the rapid developments of micro-electro-mechanical systems (MEMS), parts containing nanostructures can be used in self-cleaning surfaces [1], lab-on-chip devices [2], biomedical detection [3], optical technology [4] and other fields. In recent years, micro-injection molding has aroused extensive research interests to fabricate polymer products with nanostructures due to its advantages of low cost and short cycle [5,6]. During micro-injection molding of nanostructured parts, the interfacial heat transfer between the filled polymer and the mold insert will affect the quality of nanostructures [7–9]. It is believed that the interfacial thermal resistance is an important parameter to study the interfacial heat transfer characteristics in micro-injection molding for nanostructures. The “interface” here refers to the interface between the polymer melt and the mold . And the interface thermal resistance (ITR) is not equal to the thermal contact resistance (TCR). The ITR refers to the thermal resistance of two surfaces in full contact at the atomic scale, while the TCR refers to the thermal resistance caused by the gap

Polymers 2020, 12, 2409; doi:10.3390/polym12102409 www.mdpi.com/journal/polymers Polymers 2020, 12, 2409 2 of 12 between two contact surfaces. The TCR between the polymer and the mold insert was studied by numerical simulation and experimental methods [10,11]. For example, Hong et al. conducted numerical simulation to study the relationship between the filling behavior of polymer melt and TCR in injection molding [11]. The computational fluid dynamics simulation based on continuum mechanics would be failed to accurately explain and predict the ITR between the polymer and the mold insert at the nanoscale. Therefore, the molecular dynamics (MD) simulation method provides the possibility to study the interfacial heat transfer in nanostructures. Pina-Estany et al. studied the heat transfer coefficient (HTC), between the and the nickel mold insert in different nanocavity areas. The results showed that increasing the surface-to-volume could improve the thermal transport properties [12]. The study of ITR in injection molding by MD method is rarely reported in the literature. However, the non-equilibrium molecular dynamics method to study the heat transfer characteristics in polymer nanocomposites or microelectronics would provide us inspiration and guidance [13–17]. Ju et al. simulated the ITR of bi-layer nanofilms with different interfacial temperatures, layer thicknesses and mass ratios using MD simulation methods, but in this case, their model built with virtual atoms has limited practical significance [15]. Barisik et al. used MD simulation to analyze temperature dependence of thermal resistance at the water/ interface. It was found that interface resistance increased with the increase of temperature for high surface, and the opposite behavior was true for low wetting surfaces [16]. Vo et al. established the MD model to study Kapitza resistance under different - interaction intensities and found that the interface thermal resistance decreased with the increase of the solid-liquid interaction intensity [17]. Focusing on the improvement of interfacial thermal transport, Luo et al. investigated the effects of graphene size, interfacial bonding strength, and polymer density on interfacial thermal transport [18]. Zhang et al. studied the ITR between polyethylene (PE) and silicon substrate and found that the increase of temperature and contact strength could significantly improve the interfacial thermal conductivity [19]. Similarly, Hu et al. found that the increase of bonding strength could improve the interfacial thermal conductivity of the silicon-polyethylene interface [20]. The purpose of this was to study the heat transfer between the polymer and the mold insert during micro-injection molding. The non-equilibrium molecular dynamics (NEMD) simulation was carried out to investigate the effects of the temperature, the packing pressure, the interface morphology, and the interfacial interaction on the ITR between the polypropylene (PP) layer and nickel (Ni) layer. Furthermore, the phonon density of state (DOS) was introduced to understand the mechanism of interfacial heat transfer.

2. and Methods The polymer simulated in this study was polypropylene (PP), which has been widely used in the field of automotive lightweight due to its good mechanical properties [21]. The initial density of PP was set to be 0.9 g/cm3 at 298 K and 1 atm. There were 150 chains in the box, and the degree of each chain was 10. In order to eliminate the of PP system and keep it in the energy minimization state, it was necessary to conduct energy minimization and cyclic annealing treatment for PP system. The annealing temperature of PP was 528K. Ni was selected as mold insert , which was constructed by nickel unit cell as FCC structure with (1 0 0) plane. The length and width of the Ni layer were consistent with the dimensions of the PP layer. The interfacial model of Ni-PP system was shown in Figure1. Polymers 2020, 12, x FOR PEER REVIEW 4 of 11 where ω denotes frequency, Dω is the phonon DOS at frequency ω, and Γ𝑡, which is given in Equation (6), is the VAF. Polymers 2020, 12, 2409 3 of 12 Γ𝑡 = ⟨𝑣𝑡𝑣0⟩ (6)

Figure 1. 1.Non-equilibrium Non-equilibrium molecular molecular dynamics dynamics (NEMD) simulation(NEMD) model simulation for the polypropylene-nickel model for the (PP-Ni)polypropylene-nickel system and the (PP-Ni) temperature system profile and th ine temperature a steady state. profile in a steady state.

AThe typical NEMD DOS simulation of the PP-Ni of all- system model was demonstrat used the Consistented in Figure Valence 2. It could Force be Field seen (CVFF) that the to frequencydescribe the range potential of the of phonon intermolecular DOS of interactions PP atoms was [5,22 about]. The 0–100 nonbonded THz. The interactions frequency between range PPof phononmolecules DOS and of moldNi atoms insert was atoms about were 0–20 described THz. Ther bye was Lennard-Jones a considerable (L-J) mismatch potential. between The molecular the two groups,interaction indicating parameters that between there was PP anda remarkable Ni could be ph calculatedonon scattering by Lorentz-Berthelot at the PP-Ni mixing interface. rules This (see behaviorEquations could (1) and clearly (2)). explain The L-J a parametershigh ITR of ofthe di PP-Nifferent system. atoms in this study were shown in Table1. The cut-off distance was 1.25 nm. p εij = εiεj (1)   σij = σi + σj /2 (2) where ε and σ are the energy and distance constants respectively. The subscripts i and j refer to different atom types.

Table 1. Lennard–Jones (L-J) potential parameters for different atom types.

Atom Type Energy Constant ε [eV] Distance Constant σ [Å] H 0.038 2.450 C 0.039 3.875 Ni 11.983 2.282

The NEMD simulation method is a powerful technique to generate the temperature gradient and heat flux in structures [23–26]. As shown in Figure1, the length of the whole system was about Figure 2. Phonon density of states (DOS) of PP atoms and Ni atoms at 353 K. 12.5 nm. There were two fixed layers at both ends of the system, with a thickness of 0.3 nm, to stabilize 3.the Results free ends and and Discussion prevent external energy exchange. Then, the heat source and heat sink layers with a thickness of 0.5 nm were set beside the fixed layer by the Nose-Hoover thermostat, respectively. 3.1.Before ITR the at Different simulation Temperatures of heat conduction, the whole system reached the thermal equilibrium state at the specified temperature under the NVT ensemble. Next, the NVT ensemble was removed. The heat Temperature is an important factor affecting the ITR during the injection molding. It can affect source and heat sink were applied and extracted energy separately under the NVE ensemble to establish not only the fluidity of the polymer melt, but also the motion of . In order to find the the temperature gradient across the junction. For the whole simulation procedure, the integral time relationship between ITR and temperature, at the pressure of 0 MPa, NEMD simulations were step ∆t was 1.0 fs. The total number of simulation steps was 2,000,000, about 2.0 ns. The first 1.5 ns was carried out at different temperatures of 335 K, 350 K, 365 K, 380 K, and 395 K, respectively. The ITR used for system balance, and the last 0.5 ns was used for analysis. The periodic boundary conditions at different temperatures were illustrated in Figure 3. It could be seen that the ITR between the Ni were applied in the x and y directions. The heat flux was 0.001 Kcal/mol (equal to 6.95 10 24 J). × − Finally, the system was equally divided into 50 blocks. When the system reached its steady state, an obvious temperature drop ∆T appeared on the interface. The results showed that there existed an ITR Polymers 2020, 12, 2409 4 of 12 between the PP layer and the Ni layer. The above simulations were completed by LAMMPS [27], an open source molecular dynamics package in a computer cluster with AMD Opteron 6128 processor running in parallel with 40 cores. The heat flux density J along the z-axis can be calculated by Equation (3) [28]: Polymers 2020, 12, x FOR PEER REVIEW 4 of 11 E J = (3) where ω denotes frequency, Dω is the phonon DOSAt at frequency ω, and Γ𝑡, which is given in Equationwhere E is (6), the is energy the VAF. imposed on the system, A is the cross-sectional area of the system and t refers to the total simulation time. Γ𝑡 = ⟨𝑣𝑡𝑣0⟩ (6) The ITR is defined by Equation (4) [17,18]:

∆T R = (4) J where the value of ∆T can be obtained from the temperature drop at the interface between the PP layer and the Ni layer. Thermal energy is the energy of atomic vibrations in nature. From the acoustic mismatch model (AMM) or diffusive mismatch model (DMM), the function of phonons is closely related to the heat conduction [29]. In the vibrations of a three-dimensional lattice, it can be characterized by the phonon DOS in the frequency domain. The simulation results were analyzed from the point of phonon DOS, which was calculated by taking the fast Fourier transform (FFT) of the velocity autocorrelation functions (VAF) of the atoms (see Equation (5)) [30,31]. Z τ D(ω) = Γ(t) cos(ωt)dt (5) 0 where ω denotes frequency, D(ω) is the phonon DOS at frequency ω, and Γ(t), which is given in EquationFigure (6), 1. is theNon-equilibrium VAF. molecular dynamics (NEMD) simulation model for the

polypropylene-nickel (PP-Ni) system andΓ th(te) temperature= v(t)v(0) profile in a steady state. (6)

AA typicaltypical DOSDOS of of the the PP-Ni PP-Ni system system was was demonstrated demonstrat ined Figure in Figure2. It could 2. It be could seen thatbe seen the frequency that the frequencyrange of the range phonon of the DOS phonon of PP atomsDOS wasof PP about atoms 0–100 was THz. about The 0–100 frequency THz. The range frequency of phonon range DOS of of phononNi atoms DOS was of about Ni atoms 0–20 THz.was about There 0–20 was aTHz. considerable There was mismatch a considerable between mismatch the two groups, between indicating the two groups,that there indicating was a remarkable that there phonon was a scatteringremarkable at ph theonon PP-Ni scattering interface. at This the behaviorPP-Ni interface. could clearly This behaviorexplain a could high ITRclearly of the explain PP-Ni a system.high ITR of the PP-Ni system.

FigureFigure 2. 2. PhononPhonon density density of of states states (DOS) (DOS) of of PP PP atoms atoms and and Ni Ni atoms atoms at at 353 353 K. K.

3. Results and Discussion

3.1. ITR at Different Temperatures Temperature is an important factor affecting the ITR during the injection molding. It can affect not only the fluidity of the polymer melt, but also the motion of phonons. In order to find the relationship between ITR and temperature, at the pressure of 0 MPa, NEMD simulations were carried out at different temperatures of 335 K, 350 K, 365 K, 380 K, and 395 K, respectively. The ITR at different temperatures were illustrated in Figure 3. It could be seen that the ITR between the Ni

Polymers 2020, 12, 2409 5 of 12

3. Results and Discussion

3.1. ITR at Different Temperatures Polymers 2020, 12, x FOR PEER REVIEW 5 of 11 Temperature is an important factor affecting the ITR during the injection molding. It can affect not layeronly theand fluidity the PP oflayer the decreased polymer melt, gradually but also with the the motion increase of phonons. of the temperature. In order to find The theITR relationship was about 1.52between × 10 ITRm andKW temperature, with the at IT the at pressure335 K, while of 0MPa, it dropped NEMD about simulations 39% with were the carried IT at out393.17 at di K.ff erentThis changetemperatures of ITR ofwith 335 the K, 350temperature K, 365 K, 380was K, basically and 395 the K, respectively.same as that Thein Ref ITR [32], at di butfferent the temperaturesvalues of the ITRPolymerswere were illustrated 2020 ,about 12, x FOR inthree FigurePEER orders REVIEW3. It couldof magnitude be seen thatsmal theler ITRthan between the experimentally the Ni layer andmeasured the PP values layer5 of 11 11 2 1 reporteddecreased by gradually Zhu [32] with(3.496 the × increase 10 m KW of the). temperature.The reason was The that ITR the was work about in1.52 the above10 referencem KW− × − waslayerwith done theand IT thein atthe PP 335 geometrylayer K, while decreased on it the dropped graduallymacro-scale, about with 39%not the on with increase the the nanoscale IT of at the 393.17 temperature.as in K.this This work. changeThe And ITR ofit was also ITR about withmay be1.52the affected temperature × 10 bym partialKW was contact withbasically the or IT thebulk at same335 disorder K, as while that in the it in dropped Refnear-surface [32], about but region the 39% values withduring the of the theIT experimentat ITR 393.17 were K. about [29].This changethreeThe orders of phonon ITR of with magnitude DOS the of temperature the smaller PP layer than was at three thebasically experimentally different the same temperatures as measured that in was Ref values demonstrated[32], reportedbut the values byin Figure Zhu of [the32 4.] 4 2 1 WithITR(3.496 were the10 increase aboutm KW threeof− temperature,). Theorders reason of the wasmagnitude rate that of the atom smal workicler inmotion thethan above increases.the referenceexperimentally The was higher done measured the in temperature, the geometry values × − thereportedon thelarger macro-scale, by the Zhu kinetic [32] not (energy3.496 on the × of nanoscale 10 them PPKW asatom, in). this Theso work.the reason phonon And was it DOS alsothat maythehas work behigher aff ectedin peakthe by above intensity. partial reference contact That couldwasor bulk done explain disorder in the why geometry in the the ITR near-surface ondecreased the macro-scale, region as the during temperature not theon the experiment increased.nanoscale [29 as]. in this work. And it also may be affected by partial contact or bulk disorder in the near-surface region during the experiment [29]. The phonon DOS of the PP layer at three different temperatures was demonstrated in Figure 4. With the increase of temperature, the rate of atomic motion increases. The higher the temperature, the larger the kinetic energy of the PP atom, so the phonon DOS has higher peak intensity. That could explain why the ITR decreased as the temperature increased.

FigureFigure 3. 3. VariationsVariations of of the the interface interface thermal thermal resist resistanceance (ITR) with different different temperatures.

The phonon DOS of the PP layer at three different temperatures was demonstrated in Figure4. With the increase of temperature, the rate of atomic motion increases. The higher the temperature, the larger the kinetic energy of the PP atom, so the phonon DOS has higher peak intensity. That could explain whyFigure the 3. ITR Variations decreased of the as theinterface temperature thermal resist increased.ance (ITR) with different temperatures.

Figure 4. The phonon DOS of PP atoms at different temperatures.

3.2. ITR with Different Packing Pressures During the injection molding process, the packing pressure would affect the molecular density of polymer. Increasing the packing pressure could make the molecular chains inside the polymer more closely aligned,FigureFigure which 4. TheThe may phonon phonon have DOS DOS an of of impactPP PP atoms atoms on at at different dithefferent ITR. temperatures. In this section, the pressure dependency of the ITR between Ni and PP layers was studied. The outermost layer atoms with a 3.2. ITR with Different Packing Pressures thickness of 0.3 nm was applied forces along the −z direction. The force values for each atom were set toDuring 6.9 × the 10 injection N and molding13.8 × 10 process, N, respectively.the packing pressureThe applied would force affect was the molecularconverted densityto the pressureof polymer. values Increasing of 40.8 theMPa packing and 80.16 pressure MPa, couldwhic hmake were the common molecular values chains of packing inside the pressure polymer in micro-injectionmore closely aligned, molding. which The packing may have time wasan impactset to 20 on ps. the The ITR. NEMD In simulationthis section, of PP-Nithe pressure system wasdependency carried outof the under ITR differentbetween Nipacking and PP pressures. layers was This studied. was compared The outermost with thelayer case atoms where with the a moleculesthickness of in 0.3 3.1 nm were was notapplied under forces pressure. along theThe − zITR direction. at different The force packing values pressures for each atomwere werealso calculated.set to 6.9 ×The 10 results N and were 13.8 shown × 10 in Figure N, respectively. 5 and compared The withapplied those force in Section was converted 3.1. It was tofound the thatpressure the ITR values between of 40.8 the MPa PP layer and and80.16 the MPa, Ni layer whic decreasedh were common with the values increase of ofpacking packing pressure pressure. in micro-injection molding. The packing time was set to 20 ps. The NEMD simulation of PP-Ni system was carried out under different packing pressures. This was compared with the case where the in 3.1 were not under pressure. The ITR at different packing pressures were also calculated. The results were shown in Figure 5 and compared with those in Section 3.1. It was found that the ITR between the PP layer and the Ni layer decreased with the increase of packing pressure.

Polymers 2020, 12, 2409 6 of 12

3.2. ITR with Different Packing Pressures During the injection molding process, the packing pressure would affect the molecular density of polymer. Increasing the packing pressure could make the molecular chains inside the polymer more closely aligned, which may have an impact on the ITR. In this section, the pressure dependency of the ITR between Ni and PP layers was studied. The outermost layer atoms with a thickness of 0.3 nm was applied forces along the z direction. The force values for each atom were set to 6.9 10 14 N and − × − 13.8 10 14 N, respectively. The applied force was converted to the pressure values of 40.8 MPa and × − 80.16 MPa, which were common values of packing pressure in micro-injection molding. The packing time was set to 20 ps. The NEMD simulation of PP-Ni system was carried out under different packing pressures. This was compared with the case where the molecules in 3.1 were not under pressure.

ThePolymers ITR 2020 at di, 12ff, erentx FOR packingPEER REVIEW pressures were also calculated. The results were shown in Figure56 and of 11 compared with those in Section 3.1. It was found that the ITR between the PP layer and the Ni layer decreasedWith the temperature with the increase of 395 of K, packing the value pressure. of ITR With was the only temperature 1.8 × 10 ofm 395KW K, the when value the of ITRpacking was 10 2 1 onlypressure 1.8 was10− 80m MPa,KW while− when it decreased the packing by pressure80.4% under was 80no MPa,packing while pressure. it decreased Therefore, by 80.4% increasing under × nothe packing packing pressure. pressureTherefore, could effectively increasing improve the packing the thermal pressure conductivity could effectively between improve the polymer the thermal and conductivitythe Ni mold insert between in the the micro-injection polymer and the molding Ni mold process. insert in the micro-injection molding process.

Figure 5.5. Variations ofof ITRITR atat thethe didifferentfferent packingpacking pressures.pressures. TheThe insetinset depictsdepicts thethe PP-NiPP-Ni systemsystem ofof thethe applyingapplying pressure.pressure.

By changingchanging the packingpacking pressure,pressure, the PPPP systemsystem waswas moremore compact,compact, andand thethe interatomicinteratomic distance was reduced. The above effects effects could be observedobserved by the radial distribution function (RDF) of carboncarbon atomsatoms inin PPPP molecularmolecular andand nickelnickel atoms.atoms. As shown in Figure 66,, thethe RDFRDF ofof PPPP atomsatoms increasedincreased withwith thethe increaseincrease ofof packingpacking pressure,pressure, whichwhich waswas consistentconsistent withwith thethe resultsresults reportedreported inin some literaturesliteratures [[16,33].16,33]. When PP system was compressed,compressed, the interatomic distance was shortened. ThisThis resulted in in more more PP PP atoms atoms interacting interacting with with Ni Ni atoms atoms at atthe the same same distance. distance. Therefore, Therefore, there there was wasa stronger a stronger effective effective interaction interaction at the at interface the interface between between the PP the layer PP layer and andthe Ni the layer. Ni layer. Similarly, Similarly, the thechange change of ITR of ITRwith with the packing the packing pressure pressure could could also alsobe observed be observed in phonon in phonon DOS. DOS. The phonon The phonon DOS DOSof PP of layer PP layerunder under different different packing packing pressures pressures were were shown shown in Figure in Figure 7. The7. The phonon phonon DOS DOS with with the thepacking packing pressure pressure was wasobviously obviously high higherer than thanthat thatwith withno packing no packing pressure. pressure. In the In same the sameway, with way, withthe increase the increase of packing of packing pressure, pressure, the value the value of DO ofS DOS increases increases significantly, significantly, which which might might enhance enhance the theheat heat transfer transfer across across the theinterface. interface.

Figure 6. The radial distribution function of atoms in the PP layer with respect to nickel atoms.

Polymers 2020, 12, x FOR PEER REVIEW 6 of 11

With the temperature of 395 K, the value of ITR was only 1.8 × 10mKW when the packing pressure was 80 MPa, while it decreased by 80.4% under no packing pressure. Therefore, increasing the packing pressure could effectively improve the thermal conductivity between the polymer and the Ni mold insert in the micro-injection molding process.

Figure 5. Variations of ITR at the different packing pressures. The inset depicts the PP-Ni system of the applying pressure.

By changing the packing pressure, the PP system was more compact, and the interatomic distance was reduced. The above effects could be observed by the radial distribution function (RDF) of carbon atoms in PP molecular and nickel atoms. As shown in Figure 6, the RDF of PP atoms increased with the increase of packing pressure, which was consistent with the results reported in some literatures [16,33]. When PP system was compressed, the interatomic distance was shortened. This resulted in more PP atoms interacting with Ni atoms at the same distance. Therefore, there was a stronger effective interaction at the interface between the PP layer and the Ni layer. Similarly, the change of ITR with the packing pressure could also be observed in phonon DOS. The phonon DOS of PP layer under different packing pressures were shown in Figure 7. The phonon DOS with the packing pressure was obviously higher than that with no packing pressure. In the same way, with Polymersthe increase2020, 12 of, 2409 packing pressure, the value of DOS increases significantly, which might enhance7 ofthe 12 heat transfer across the interface.

PolymersFigure 2020, 6.6.12 The, Thex FOR radialradial PEER distribution distribution REVIEW function function of carbonof carbon atoms atoms in the in PPthe layer PP layer with respectwith respect to nickel to atoms.nickel7 of 11 atoms.

Figure 7. TheThe phonon phonon DOS DOS of of PP PP atoms atoms at different different packing pressures.

3.3. ITR ITR Under Under Different Different Interface Morphologies The micro-injectionmicro-injection molding, molding, the the interface interface between between the polymerthe polymer and theand mold the insertmold wasinsert usually was usuallynot smooth. not smooth. However, However, the interface the interface morphology morphology of the mold of the insert mold mayinsert aff mayect theaffect ITR. the In ITR. this In study, this study,two types two of types interface of interface morphologies morphologies were proposed, were proposed, i.e., the rectangulari.e., the rectangular and the triangularand the triangular interface interfacemorphologies, morphologies, as shown as in Figureshown8 b.in TheFigure temperature 8b. The profilestemperature of di ffprofileserent interface of different morphologies interface weremorphologies illustrated were in Figure illustrated8a. There in Figure were the 8a. small Ther temperaturee were the small gradients temperature inside the gradients composite inside layer the of compositePP and Ni atomslayer of for PP both and rectangle Ni atoms and trianglefor both interface rectangle morphologies. and triangle Comparedinterface morphologies. to the smooth Comparedinterface, the to compositethe smooth layer interface, could reducethe composite the temperature layer could drop reduce of the interface,the temperature and the temperaturedrop of the interface,drop was usedand the to calculatetemperature theITR. drop Also, was theused temperature to calculate drop the ofITR. rectangle Also, the interface temperature was lower drop than of rectanglethat of triangle interface interface. was lower A larger than temperature that of triangle drop interface. at the interface A larger represented temperature a larger drop thermal at the interfaceresistance. represented The results a larger showed thermal that the resistance. thermal resistanceThe results of showed triangular that interfacethe thermal was resistance larger than of triangularthat of rectangular interface interface.was larger The than ITR that of diofff erentrectangular interfacial interface. temperatures The ITR forof thedifferent rectangular interfacial and temperaturesthe triangle interfaces for the rectangular was shown and in Figurethe triangle9. It was interfaces interesting was toshown find outin Figure that both 9. It thewas rectangular interesting toand find the out triangle that both interfaces the rectangular could reduce and the the triangle ITR, compared interfaces with could the reduce smooth the interface. ITR, compared Meanwhile, with the ITRsmooth of the interface. triangle interfaceMeanwhile, was the higher ITR thanof the that tr ofiangle the rectangularinterface was interface. higher Thethan phonon that of DOS the rectangularof PP layer withinterface. different The interface phonon morphologiesDOS of PP la wereyer with shown different in Figure interface 10. Obviously, morphologies the phonon were shownfrequencies in Figure of the 10. rectangle Obviously, and the trianglephonon interfacesfrequencies were of the higher rectangle than that and of the the triangle smooth interfaces interface. Thiswere willhigher contribute than that to theof microinjectionthe smooth interface. molding This process will ofcontribute surface microstructural to the microinjection products molding such as processgrating structureof surface or supermicrostructu hydrophobicral products structure. such as grating structure or super hydrophobic structure.

Figure 8. (a) The temperature profiles of different interface morphologies; (b) rectangular and triangular interface topographies.

Polymers 2020, 12, x FOR PEER REVIEW 7 of 11

Figure 7. The phonon DOS of PP atoms at different packing pressures.

3.3. ITR Under Different Interface Morphologies The micro-injection molding, the interface between the polymer and the mold insert was usually not smooth. However, the interface morphology of the mold insert may affect the ITR. In this study, two types of interface morphologies were proposed, i.e., the rectangular and the triangular interface morphologies, as shown in Figure 8b. The temperature profiles of different interface morphologies were illustrated in Figure 8a. There were the small temperature gradients inside the composite layer of PP and Ni atoms for both rectangle and triangle interface morphologies. Compared to the smooth interface, the composite layer could reduce the temperature drop of the interface, and the temperature drop was used to calculate the ITR. Also, the temperature drop of rectangle interface was lower than that of triangle interface. A larger temperature drop at the interface represented a larger thermal resistance. The results showed that the thermal resistance of triangular interface was larger than that of rectangular interface. The ITR of different interfacial temperatures for the rectangular and the triangle interfaces was shown in Figure 9. It was interesting to find out that both the rectangular and the triangle interfaces could reduce the ITR, compared with the smooth interface. Meanwhile, the ITR of the triangle interface was higher than that of the rectangular interface. The phonon DOS of PP layer with different interface morphologies were shown in Figure 10. Obviously, the phonon frequencies of the rectangle and the triangle interfaces were higher than that of the smooth interface. This will contribute to the microinjection molding process of surface microstructural products such as grating structure or super hydrophobic Polymers 2020, 12, 2409 8 of 12 structure.

FigureFigure 8.8. (a(a)) The The temperature temperature profiles profiles of di offferent different interface interface morphologies; morphologies; (b) rectangular (b) rectangular and triangular and Polymers 2020, 12, x FOR PEER REVIEW 8 of 11 triangularinterface topographies. interface topographies.

FigureFigure 9. 9. VariationsVariations of of ITR ITR with with diffe differentrent interface morphologies.

FigureFigure 10. 10. TheThe phonon phonon DOS DOS of of PP PP atoms atoms under under different different interface morphologies. 3.4. ITR with Different Interfacial Interactions 3.4. ITR with Different Interfacial Interactions From the microscopic point of view, the interaction strength of the interface would directly affect From the microscopic point of view, the interaction strength of the interface would directly the movement behavior of molecules at the interface, and then affect the heat transfer characteristics of affect the movement behavior of molecules at the interface, and then affect the heat transfer characteristics of the two groups of atoms at the interface [18]. In order to change the contact strength of Ni-PP system in which the interactions were van der Waals forces, the energy constants describing the interfacial van der Waals forces were changed by 2, 3, 4, 5 times of the original value (𝜀 ), respectively. (𝜀), respectively. As shown in Figure 11, the ITR between the PP layer and the Ni layer was weak when the interfacial interaction was strong. The results showed that the heat transfer across PP-Ni interface could be enhanced by increasing the surface energy of mold insert materials in micro-injection molding. Figure 12 depicted the phonon DOS of PP atoms under three interfacial interactions. At the low frequency of 0–20 THz, the matching degree of DOS of nickel atoms and DOS of PP atoms was higher, which resulted in the decrease of ITR for PP-Ni system.

Polymers 2020, 12, 2409 9 of 12

the two groups of atoms at the interface [18]. In order to change the contact strength of Ni-PP system in which the interactions were van der Waals forces, the energy constants describing the interfacial van der Waals forces were changed by 2, 3, 4, 5 times of the original value (ε0), respectively. As shown in Figure 11, the ITR between the PP layer and the Ni layer was weak when the interfacial interaction was strong. The results showed that the heat transfer across PP-Ni interface could be enhanced by increasing the surface energy of mold insert materials in micro-injection molding. Figure 12 depicted the phonon DOS of PP atoms under three interfacial interactions. At the low frequency of 0–20 THz, the matching degree of DOS of nickel atoms and DOS of PP atoms was higher, which Polymers 2020, 12, x FOR PEER REVIEW 9 of 11 Polymersresulted 2020 in, the12, x decrease FOR PEER of REVIEW ITR for PP-Ni system. 9 of 11

FigureFigure 11. 11. TheThe ITR ITR with with different different interface interface interaction interaction strengths. strengths.

FigureFigure 12. 12. TheThe phonon phonon DOS DOS of of PP PP atoms atoms with with different different interface interface interactions. interactions. 4. Conclusions 4. Conclusions In this paper, the NEMD simulations for micro-injection molding were carried out to investigate In this paper, the NEMD simulations for micro-injection molding were carried out to the ITR between the PP layer and the Ni layer. The result showed that the ITR reduced about 24.38% investigate the ITR between the PP layer and the Ni layer. The result showed that the ITR reduced when the temperature increased from 335 K to 393 K. The results of ITR at different packing pressures about 24.38% when the temperature increased from 335 K to 393 K. The results of ITR at different indicated that the increase of packing pressure could enhance the heat transfer between the PP layer packing pressures indicated that the increase of packing pressure could enhance the heat transfer and the Ni layer. In addition, the interfaces of rectangle and the triangle could reduce the ITR compared between the PP layer and the Ni layer. In addition, the interfaces of rectangle and the triangle could with the smooth interface. At last, interfacial interaction strength also affected the ITR. The stronger reduce the ITR compared with the smooth interface. At last, interfacial interaction strength also the interactions, the smaller the interface thermal resistance. affected the ITR. The stronger the interactions, the smaller the interface thermal resistance. The mechanisms of ITR were discussed from the point of phonon DOS of the PP-Ni system. There was a considerable mismatch between the phonon DOS of the two groups, which resulted in the phonon scattering across the interface. This behavior could clearly explain the considerable ITR of the system. For different temperatures, packing pressures, interface morphologies and interface . interactions. The peak value of the phonon DOS can better reflect the size of the interface thermal resistance: the larger the peak value, the smaller the interface thermal resistance value will be.

Author Contributions: Data curation, C.W. and J.L. (Jiangwei Li); formal analysis, C.W. and J.L. (Jiangwei Li); software, J.L. (Jiangwei Li) and J.L. (Jun Lai); methodology, J.L. (Jun Lai); project administration, J.L. (Jiangwen Liu) and C.W.; resources, C.W.; supervision, C.W. and H.W.; writing—original draft, J.L. (Jiangwei Li); writing—review and editing, H.W. All authors have read and agreed to the published version of the manuscript.

Polymers 2020, 12, 2409 10 of 12

The mechanisms of ITR were discussed from the point of phonon DOS of the PP-Ni system. There was a considerable mismatch between the phonon DOS of the two groups, which resulted in the phonon scattering across the interface. This behavior could clearly explain the considerable ITR of the system. For different temperatures, packing pressures, interface morphologies and interface interactions. The peak value of the phonon DOS can better reflect the size of the interface thermal resistance: the larger the peak value, the smaller the interface thermal resistance value will be.

Author Contributions: Data curation, C.W. and J.L. (Jiangwei Li); formal analysis, C.W. and J.L. (Jiangwei Li); software, J.L. (Jiangwei Li) and J.L. (Jun Lai); methodology, J.L. (Jun Lai); project administration, J.L. (Jiangwen Liu) and C.W.; resources, C.W.; supervision, C.W. and H.W.; writing—original draft, J.L. (Jiangwei Li); writing—review and editing, H.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science of China, grant number 51775562 and 51675105. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

ε The energy constant σ The distance constant σi,j Distance between the atom i and j J Flux density E The energy imposed on the system A The cross-sectional area ∆T Temperature difference R The interface thermal resistance

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