Foaming Mechanism of Polypropylene in Gas-Assisted Microcellular

Mar 16, 2018 - In our recent study, it is reported that gas-assisted microcellular injection molding (GAMIM) is a promising method to fabricate plasti...
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Study on the foaming mechanism of polypropylene in the gas-assisted microcellular injection molding Junji Hou, Guoqun Zhao, Lei Zhang, Guiwei Dong, and Guilong Wang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05389 • Publication Date (Web): 16 Mar 2018 Downloaded from http://pubs.acs.org on March 16, 2018

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Study on the foaming mechanism of polypropylene in the gas-assisted microcellular injection molding Junji Hou, Guoqun Zhao*, Lei Zhang, Guiwei Dong, Guilong Wang Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan, Shandong 250061, PR China

* Corresponding author E-mail address: [email protected] (Guoqun Zhao)

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Abstract In our recent study, it's reported that the gas-assisted microcellular injection molding (GAMIM) is a promising method to fabricate plastic foams with good surface quality, high weight-reduction and improved mechanical performance. To clarify the foaming mechanism, the crystallization behaviors of polypropylene in both conventional injection molding (CIM) and gas-assisted injection molding (GAIM) were studied. It's found that the GAIM can significantly promote melt crystallization and refine crystals. To explore the improvement mechanism of crystallization, a numerical model was developed to simulate the filling and cooling processes of CIM and GAIM. The simulation results show that the much stronger shear field and the faster cooling rate lead to the refinement of crystals in GAIM. Finally, a crystallization-driven cell nucleation model was proposed to explain the improved foaming behavior of polypropylene in GAMIM. This paper provides a deep understanding of the foaming behavior and hence benefits the foaming process design.

Keywords: microcellular injection molding; gas-assisted injection molding; gas-assisted microcellular injection molding; crystallization; foaming; numerical simulation

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1 Introduction Microcellular plastics are the foams with cell sizes of 0.1−10 µm, and cell densities of 109−1015 cells/cm3.1-3 Compared with the regular plastic foams with much larger cells, the microcellular plastics have many advantages, such as high specific strength, excellent thermal and sound insulation, and good energy absorbing capacity.4 Thus, they show a promising future in many industrial fields, for example, construction, automotive and packaging.4,5 Microcellular injection molding (MIM) is a superior technology to produce microcellular plastics due to its high efficiency, outstanding design ability, and ability in directly producing parts with complex shape.6,7 In spite of the advantages, the MIM suffers from several obvious defects. First, the foamed part has poor surface quality due to many silver streaks and swirl marks on the surface.8-11 Second, the injection molded part's weight-reduction is limited,9 even for the low-pressure MIM, during which the shot size is usually 65−95% of the cavity volume,12 the molded part with uniform cells for weight-reduction higher than 20% is not easy to fabricate.13 In addition, the foamed part has a seriously deteriorating mechanical performance,9 particularly for the ductile performance.7 For improving the injection molded foam's surface quality, the efficient method is to suppress foaming in the filling stage or re-dissolve the gas in stretched bubbles on the part surface into the polymer melt. It has been reported that adopting gas counter pressure,14,15 reducing the blowing agent content,11 and increasing the mold cavity temperature10,16-18 can improve surface quality of the injection molded foam. However, these methods cannot help to improve the mechanical performance or increase the weight-reduction of the molded part. The limited weight-reduction of the part molded by the conventional MIM is due to the foaming occurs in a restricted space. To increase the weight-reduction, the key issue is to increase the free space for cell expansion. For this purpose, the foam injection molding with mold opening method was developed.19-23 In this process, a full-shot size of polymer/gas solution is first used to fully fill the mold cavity, then the mold is opened for an expected distance to provide free space for foaming. However, it is difficult to control the part's shape and dimension accuracy,

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especially for the part with complex geometry. To improve the part's mechanical performance, the previous studies were mainly focused on the modification of the polymer matrix by adding fillers.13,24-26 The additives themselves can not only enhance polymer matrix but also refine cells,24,26 so the stress concentration caused by undesired cellular morphology can be decreased. In order to simultaneously endow foamed parts with good surface quality, high weight-reduction and improved mechanical performance, the gas-assisted microcellular injection molding (GAMIM) method was introduced for preparing the foamed polypropylene (PP) part in our previous work,27 and the foamed PP part meeting the aforementioned requirements was successfully fabricated. Although the foaming process of PLA and TPU by using the foam injection molding with gas-assisted processing have been studied in the researches of Mark et al.,28,29 the surface quality and mechanical property of the part were not concerned. The GAMIM is actually the combination of the gas-assisted injection molding (GAIM) and MIM. Its technical principle is illustrated in Figure 1. The implementation process of GAMIM is briefly stated as follows. First, in order to reduce the part’s weight, a rather small volume of the polymer/gas solution is used to fill mold cavity. In this process, the injected melt generates phase separation due to a sudden pressure drop, and the numerous non-uniform cells shown in Figure 1(a) are formed inside the melt. Second, the high-pressure assisted gas is injected into mold cavity, and the assisted gas pushes the melt to fully fill the mold cavity. Then the assisted gas is held for building a high cavity pressure. The non-uniform cells formed in the first foaming process can be re-dissolved into the melt by assisted gas's compression, as shown in Figure 1(c), so the surface defects are reduced or eliminated. By the aid of the assisted gas, the foaming and melt filing processes can be decoupled. Finally, a subsequent foaming is triggered by the assisted gas’s rapid release, and the foamed part with uniform cells which is better for mechanical properties will be obtained, as shown in Figure 1(d).

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Figure 1. Schematic principle of gas-assisted microcellular injection molding: (a) injecting polymer/gas solution; (b) injecting high-pressure assisted gas; (c) holding the assisted gas; (d) releasing the assisted gas and foaming. In our earlier work,27 it is mainly focused on the clarification of the GAMIM method and its implementation procedure. By comparing the macroscopic properties of PP parts molded by MIM and GAMIM, such as the surface quality, weight-reduction and mechanical performance, it is found that the GAMIM has great superiority and the foaming behavior of PP can be noticeably improved. However, the mechanism behind the improved foaming behavior is unclear. Therefore, this work mainly focuses on revealing the foaming mechanism of PP in GAMIM. The differences melt crystallization behaviors of PP in both conventional injection molding (CIM) and GAIM are firstly studied. Then, a numerical model was developed to simulate the filling and cooling processes of CIM and GAIM. The influence of high-pressure assisted gas penetration on melt crystallization is further revealed by the simulation results. Finally, the crystallization-driven cell nucleation model was proposed to explain the improved foaming behavior of PP in GAMIM. 2 Experimental methods 2.1 Sample preparation The isotactic PP resin (HJ730) used in this study is purchased from Hanwha Total Petrochemical Company in Korea. It has a melt flow rate of 20 g/10 min, and a density of 0.91 g/cm3. The industrial grade compressed nitrogen is used as the physical blowing agent and the assisted gas. The injection molding machine used is Borch BS800-III, 5

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equipped with a supercritical fluid dosing unit purchased from Trexel Inc. and a high-pressure gas control device purchased from Beijing Chn-top Machinery Co., Ltd. The CIM, GAIM, MIM and GAMIM samples are respectively molded by using the mold shown in Figure 2. The mold temperature is 60 °C. The melt temperature is 220 °C. The injection rate is 85 cm3/s. The shot size of CIM is 100%, and for GAIM, MIM and GAMIM, the shot sizes are all 55%. The pressure of assisted gas is 20 MPa and the physical blowing agent's content is 0.3 wt%. The holding time of assisted gas is 5 s, 15 s, 25 s, 35 s and 45 s, respectively.

Figure 2. Structure of mold cavity and shape of injected parts. 2.2 Experimental characterizations After injecting by using the above experimental parameters, the CIM and GAIM samples can be obtained. Figure 3(a) gives the schematic drawing of specimen preparation. The cylinder sample with a diameter of 15 mm is chosen as the characterizing object for CIM. The ring sample, of which the outer diameter is 15 mm and inner diameter is 10.8 mm, is chosen as the characterizing object for GAIM. The length of all the samples is 135 mm. For polarized optical microscopy (POM) observation, according to the marked positions shown in Figure 3(a), the samples are first cut into two kinds of specimens, as shown in Figure 3(b). Then the approximately 15 µm thin slices shown in Figure 3(c) are cut from the above two kinds of specimens using a manual rotating microtome 6

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(YD-2508B, YIDI). Finally, the prepared thin slices are placed on a POM (BX51, OLYMPUS) for observing.

Figure 3. Schematic drawing of specimen preparation: (a) CIM and GAIM sample; (b) specimens for cutting slices; (c) thin slices for POM observation; (d) sampling method for differential scanning calorimetry measurement. A scanning electron microscope (SU-70, HITACHI) is used to characterize the crystal morphology of the CIM and GAIM samples and observe the cellular morphology of the MIM and GAMIM samples. Before characterizing the crystal morphology, the fracture sections along the melt flow direction are etched for 18 h with an acid solution containing 1.3 wt% potassium permanganate (KMnO4).30 All the specimens are then sprayed with platinum for electric conduction. A differential scanning calorimetry instrument (DSC 204 F1, NETZSCH) is employed to study the crystallization behavior of the samples. According to the marked positions shown in Figure 3(b) of the CIM and GAIM samples, the two kinds of slices with a thickness of 2 mm are obtained after cutting. Then, for the two kinds of slices, three small specimens with a weight of about 10 mg are respectively cut off at the positions about 0 µm, 1000 µm, and 2000 µm away from the slice's skin layer, as shown in Figure 3(d), and they are marked as P0, P1000 and P2000, respectively. For these small specimens, each of them is heated from 40 °C to 220 °C at a rate of 10 °C/min under a nitrogen atmosphere using the DSC, and the melting process is recorded. 3 Modeling and simulation 3.1 Governing equations Numerical simulation is an effective method to obtain the internal physical fields of the melt that is difficult to 7

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measure in the injection molding process. For simulations of GAIM, the most used models are 2D Hele-Shaw31 or surface models,32 but these models could not accurately describe some important physical phenomena between the gas and liquid phases.33 In this paper, a 3D non-isothermal transient numerical model of two-phase fluid is established to accurately describe the complicated mass and heat transfer phenomenon between gas and polymer melt. The high-pressure gas (nitrogen) is treated as a fluid, and the process of nitrogen's penetration to the melt can be simplified into the solution of the velocity, pressure and temperature fields of the transient flow between two fluids. Before simulation, in the polymer melt and gas filling process, the following assumptions are taken to simplify the model and calculation: (a) since the filling is driven by the pressure, which is not very high in the filing stage,34-36 the polymer melt and nitrogen can be all assumed as incompressible; (b) the nitrogen merely acts to transfer pressure,35 and the Reynolds number is small in the polymer melt region,37 so the flow type can be considered as laminar flow; (c) since the viscosity of polymer melt is high, the insignificant inertia force and surface tension can be ignored37 and (d) no chemical occurs during the filling process. Based on the assumptions, for simulation of the polymer melt and gas filling process, the relevant governing equations in the numerical model are described as follows: Continuity equation is written as ∇ ⋅U = 0

(1)

where ∇ ⋅ denotes the divergence operator and U denotes velocity vector. Momentum equation is written as

∂ (ρU) ∂t

ε=

+ ∇ ⋅ ( ρ UU ) = −∇ P + ∇ ⋅ (2 µ ε )

(2)

1  ∇ U + (∇ U ) T  2

(3)

where ρ means density, t means time, P means pressure field, µ means kinematic viscosity, and ε is the strain rate tensor of the two-phase system.

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Energy equation used is expressed as

∂ ( ρ C PT ) + ∇ ⋅ ( ρ UC PT ) = ∇ ⋅ ( k ∇ T ) + µγ& 2 ∂t

(4)

γ& = ε ( U ) = 2ε ( U ) : ε ( U )

(5)

where C P means the isobaric heat capacity of the two-phase fluid, T means the temperature field of the mold cavity domain, k is the heat conductivity of the two-phase fluid, and γ& is the modulus of the strain rate tensor. When the filling stage is finished, the velocity field in the system is zero. During the simulation of cooling stage, the convection heat transfer can be ignored, and the energy equation can be expressed as

∂ ( ρ C PT ) = ∇ ⋅ ( k ∇T ) ∂t

(6)

3.2 Interface tracking method In order to determine the interfaces of the two-phase flow, the phase fraction of each phase is calculated. The phase fraction of polymer is defined as α, and the phase fraction of nitrogen is 1-α, correspondingly. The VOF method38 is employed for solving the phase fraction in this paper. It satisfies the following equation:

∂α + ∇ ⋅ ( Uα ) = 0 ∂t

(7)

where, at any time, the phase fraction α of polymer in a mesh element satisfies the following formula:

1, point ( x, y, z, t ) is located in polymer  α ( x, y, z, t ) = 0, point ( x, y, z, t ) is located in nitrogen  0 < α < 1, point ( x, y, z, t ) is located in interface area

(8)

Physical properties Ф in interface region are calculated by the following formula:

Φ = α Φ1 + (1 − α ) Φ2 , (Φ = C P , k , ρ , µ )

(9)

where, Φ1 and Φ2 are the physical properties of polymer and nitrogen, respectively. The physical properties of polymer and nitrogen used are shown in Table 1. Table 1. Physical properties of polymer and nitrogen. Materials

C P (J·kg−1·K −1)

k (W·m−1·K−1)

ρ (kg·m-3)

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µ (m2·s−1)

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PP HJ730

2496

0.15

909.49

Eq. (12)

Nitrogen

1040

0.024

1.13

1.6×10-5

3.3 Viscosity model The Cross-WLF model is used as viscosity model, and it is expressed as

η=

η0

1 + (η0γ& / τ ∗ )

(10)

1-n

− A1 (T −T ∗ )

η 0 = D1 e A (T −T 2



)

(11)

T ∗ = D2 + D3 P A2 = A2 + D3 P

where η is dynamic viscosity, η0 is zero shear viscosity, and n, τ*, D1, D2, D3, A1 and A2 are the parameters depending on materials. The dynamic viscosity of the momentum equation is

µ=

η ρ

(12)

For PP HJ730 material used in this study, according to the material database of Moldflow software, the values of n, τ*, D1, D2, D3, A1 and A2 are 0.3301, 19385.1 Pa, 2.93023×1017 Pa·s, 263.15 K, 0 K·Pa-1, 40.995 and 51.6 K, respectively. 3.4 Boundary condition The meshed geometric model of cylinder is shown in Figure 4. The polymer inlet, high-pressure gas (nitrogen) inlet, wall and outlet boundaries are also given in the figure. Table 2 lists the setting methods of phase fraction, velocity, temperature and pressure on boundaries, where Uin is the velocity vector of polymer melt on polymer inlet,

Tmelt is the temperature of polymer melt, and tgas is the starting time of filling gas or the end time of injecting polymer melt and it is determined by the shot size and the velocity of polymer melt, and P(t) is the pressure variety of high-pressure nitrogen with time at gas inlet, and Tgas is the high-pressure nitrogen's initial temperature , and

ΓU_filter and ΓP_filter are a mixed boundary condition of filtering gas37 at outlet.

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Figure 4. Meshed geometric model of GAIM. In order to improve convergence speed and calculation efficiency, the hexahedral grid and parallel operation method are used in this paper. In solving the coupled problem of the velocity and pressure field in the momentum equation, the PIMPLE algorithm,39 which is a combinational algorithm of PISO algorithm and SIMPLE algorithm and more suitable for solving the transient problem whose flow field changed strongly, is used. The idea of PIMPLE algorithm is that the sub-relaxation in every time step to obtain a bigger time step (same with the SIMPLE algorithm), and the multiple pressure corrections of PISO is used to fully solve the coupled problem of pressure and velocity in every iteration step. The specific calculation process is detailed described in the reference.40 According to experimental design of injection process, the parameter values of numerical example on boundaries are shown in Table 3. Based on above descriptions, this paper wrote the numerical simulation program by adopting C++ programming language on the development platform of Foam-extend 3.0. Table 2. Setting methods of boundary conditions. Variables

Polymer inlet

Gas inlet

α

α =1

α =  0, t > t gas

U (m /s)

 U in , t ≤ t gas U =  (0, 0, 0), t > tgas

U = U in , t ≤ t gas

P(MPa)

∇P = 0

T (° C )

T = Tmelt

 1, t ≤ tgas

∇U = 0, t > t gas

∇P = 0, t ≤ tgas P = P ( t ) , t > tgas Tmelt , t ≤ t gas T =  Tgas , t > t gas

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Wall

Outlet

∂α =0 ∂n

∂α =0 ∂n

U = ( 0, 0, 0 )

Γ U _ filter

∇P = 0

Γ P _ filter

T = Tmold

T = Tmold

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Table 3. Parameter values of numerical example on boundaries.

Uin (m/s) (0, 0, 0.3)

Tmelt (°C)

tgas (s)

220

0.5

P ( t ) (MPa)

Tgas (°C)

min [ 0.1 + 20(t − 0.5), 20]

25

ΓU _ filter

Γ P _ filter

∇U = 0, α ≤ 0.3

P = 0.1, α ≤ 0.3

U = (0, 0, 0), α > 0.3

∇P = 0, α > 0.3

4 Results and discussion 4.1 Crystallization behavior Figure 5 gives the crystal morphology of the CIM and GAIM samples under the polarized optical microscopy. Figure 5(a)-(c) show the crystal morphology near the skin layer, in the middle layer, and away from the skin layer of the CIM samples with the magnification of 200 times, respectively. Figure 5(d)-(f) show the crystal morphology near the skin layer, in the middle layer and away from the skin layer (near gas channel) of the GAIM samples with the magnification of 200 times, respectively. Figure 5(g) and (h) are the crystal morphology of the CIM and GAIM samples with the magnification of 40 times, respectively. For the CIM sample, it can be seen from Figure 5(a) that, near the skin layer, because the crystal size is small or there are numerous crystals in this region, it is difficulty to observe a typical extinction phenomenon which the spherulitics have under this observation condition. But from the Figure 5(b) and (c), the spherulites exhibit a typical extinction phenomenon, and the crystal boundaries are distinct in the middle layer and away from the skin layer of the CIM sample. This indicates that the crystal size is large in these areas. As shown in Figure 5(g), there is no obvious skin-core structure of the CIM sample, and this may be related to the high mold temperature and large diameter of the sample. For the GAIM sample, similar with the location near the skin layer of the CIM sample, there is also no obvious spherulitic crystal structure under the observation condition, as shown in Figure 5(e)-(f). Besides, the crystal morphology of the GAIM sample shown in Figure 5(h) is similar to that of the CIM sample shown in Figure 5 (g), and there is no obvious skin-core structure.

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Figure 5. Crystal morphology under the polarized optical microscopy: (a)-(c) the crystal morphology near the skin layer, in the middle layer, and away from the skin layer of the CIM samples; (d)-(f) the crystal morphology near the skin layer, in the middle layer, and away from the skin layer of the GAIM samples; (g) the crystal morphology of the CIM samples with the magnification of 40 times; (h) the crystal morphology of GAIM samples with the magnification of 40 times. In order to accurately characterize the crystal size of the CIM and GAIM samples, Figure 6 gives SEM micrographs of the samples etched by the etchant. Figure 6(a)-(c) correspond to the observed positions a, b, and c of the CIM samples shown in Figure 5(g), and it can be seen that with the distance from the skin layer increasing, the crystal size increases for the CIM sample. The main reason is that the crystals near the skin layer cannot fully grow because of the low temperature in this area. On the contrary, the melt away from the skin layer has a high 13

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temperature, and the crystals have a sufficient time for growth before the melt cooling down, so the crystal size is relatively coarse.41 Figure 6(d)-(f) correspond to the observed positions d, e, and f of the GAIM samples shown in Figure 5(h). For the GAIM sample, the crystal size away from the skin layer (near gas channel) is slightly larger, as shown in Figure 6(f), the crystal size near the skin layer is secondly larger, as shown in Figure 6(d), and the crystal size in the middle layer is the smallest, as shown in Figure 6(e). However, the crystal sizes in these areas have little difference overall. Moreover, in the same observation positon, the crystal size of the CIM sample is much larger than that of the GAIM sample. The CIM sample's average crystal size is 30 µm, and the GAIM sample's average crystal size is 15 µm. The result indicates that the average number of nuclei generated in GAIM is four times as many as that in CIM. It can be confirmed that the GAIM can refine the crystal size and stimulate nucleation of melt crystallization.

Figure 6. SEM micrographs of the samples etched by the etchant: (a)-(c) the crystal morphology near the skin layer, in the middle layer, and away from the skin layer of the CIM samples; (d)-(f) the crystal morphology near the skin layer, in the middle layer, and away from the skin layer of the GAIM samples. Figure 7 shows the DSC endothermic thermograms of the CIM and GAIM samples, respectively. Among these curves, P0, P1000, and P2000 represent the specimens that are sampled at the positions about 0 µm, 1000 µm, and 14

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2000 µm away from the skin layer (as shown in Figure 3(d)), respectively. It can be found that the melting curves in Figure 7 are all single peak curves. For the CIM sample, the three melting curves almost have the same peak temperature, that is, the melting temperature is essentially the same. But for the GAIM sample, there are some differences among the peak temperature, and the temperature corresponding to the peak of curves P0, P1000, and P2000 are 168.26 °C, 166.95 °C, and 164.97 °C, respectively. This demonstrates that the melting point is gradually reduced from the GAIM sample's skin layer to the gas channel.

Figure 7. DSC endothermic thermograms of the different samples: (a) CIM samples; (b) GAIM samples. In order to quantitatively compare the melting enthalpy of the two samples, based on the DSC curves shown in Figure 7, the two samples' melting enthalpy is calculated and shown in Table 4. From the table, it can be seen that with the distance from the skin layer increasing, the melting enthalpy increases for the CIM sample. That is, the farther away from the skin layer, the greater the melt's crystallinity is. Because the melt away from the skin layer has a relatively high temperature, and the crystals have a sufficient time for growth, the crystallinity in this area is high. For the GAIM sample, the specimen (P1000) at the middle position has the lowest melting enthalpy, and the other two specimens (P0 and P2000) almost have the same melting enthalpy. The main reason is that, compared with the other two specimens, the specimen P1000 has the most nuclei, which can make the crystals grow imperfectly, and the crystallinity is reduced. Besides, at the same sampling location, the melting enthalpy of the CIM specimens is 15

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greater than that of the GAIM specimens, that is, the crystallinity of the CIM sample is larger than that of the GAIM sample. This means that, although the GAIM can stimulate nucleation of melt crystallization, it cannot increase the melt's crystallinity. In the next section, by combining the results of numerical simulation, this paper will further explore the reason why the GAIM can stimulate nucleation of melt crystallization but not increase the melt's crystallinity. Table 4. Melting enthalpy (∆Hm (J·g-1)) of the specimens. P0

P1000

P2000

CIM

103.35

103.41

109.52

GAMIM

98.18

80.83

98.35

4.2 Shear and temperature fields Figure 8 shows the shapes of the GAIM samples obtained by the numerical simulation and experiment, where Figure 8(a) is the simulation result and Figure 8(b) is the experiment result. The red color represents the polymer melt, and the blue color represents the nitrogen. As shown in Figure 8(a), when the injection time is 0.5 s, the polymer melt fills 55% of the whole sample's volume. Then the high-pressure nitrogen is injected to the polymer melt through the gas inlet. After the time interval of 0.24 s, that is, when the time is 0.74 s, the high-pressure nitrogen penetration to the melt makes a hollow cavity in the melt. Once the time reaches 0.75 s, the length of the hollow cavity in the melt increases significantly. So the high-pressure nitrogen penetration to the melt is an accelerating process. When the time is 0.751 s, the polymer melt arrives at the end of the sample, and this time is the termination time of the simulation for GAIM. Figure 8(b) shows the axis section of the sample obtained in the experiment of GAIM. Because the sample is translucent, it is difficult to distinguish the wall thickness and the hollow cavity when taking picture. For this reason, the solid part of the sample's axis section was painted with the red color, and a green paper was placed at the bottom of the sample as the background. Comparing the simulation

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result of 0.751 s in Figure 8(a) with the experiment result in Figure 8(b), it can be found the hollow cavity's shape obtained by simulation is in good agreement with that obtained by experiment. The only difference is that the end shape of the hollow cavity obtained by simulation is a semi-ellipsoid, but the end shape of the hollow cavity obtained by experiment is a sharp cone. The reason is that the part shrinks due to the melt's cooling during the high-pressure nitrogen's holding time in actual injection molding process, and for reducing shrinkage, the high-pressure nitrogen continues to push the melt to fit the mold cavity. This phenomenon is termed as secondary gas penetration,42,43 while the melt shrinkage and the secondary gas penetration are ignored in the simulation. In the numerical simulation, the assumption of the incompressible melt was introduced. As a result, there is a little of difference between the simulation and experiment results. In order to approach the experimental results more closely, the PVT property of the material should be taken into account, that is, the compressibility of the melt can't be ignored. In future work, we will try to establish the relevant PVT model of the material, and couple it to other equations for further simulations. In fact, the residual wall thickness of the actual GAIM sample is 2.1 mm, and the residual wall thickness obtained by simulation is 2.05 mm, so the simulation result is also in good agreement with the experiment result for the residual wall thickness.

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Figure 8. Shapes of the GAIM samples obtained by the numerical simulation and experiment: (a) simulation result (b) experiment result. Figure 9 gives the simulation results of the shear rate along the radial direction of the samples. The abscissa axis indicates the radial distance on the cross section of the samples, and ±7.5 mm represent the upper and lower end on the cross section of the samples, respectively. Curve 1 and curve 2 shown in Figure 9(a) are the shear rate distribution on section 1 (20 mm away from the gate) and section 2 (40 mm away from the gate) of the CIM samples, respectively. From curve 1 and curve 2, it can be seen that near the upper and lower end of the sample, the melt's shear rate reaches the maximum value, and at the center of the sample, the melt's shear rate reaches the minimum value. By comparing curve 1 and curve 2, it is found that the maximum shear rate of curve 1 is slightly larger than that of curve 2. This indicates that the maximum shear rate of the melt near the gate is greater than that of the melt away from the gate in the melt filling process for CIM. Due to the filling pressure dropping along the melt flow direction in melt filing process, the filling speed also drops, and this makes the shear rate decrease. Curve 3 and curve 4 shown in Figure 9(b) are the shear rate distribution on section 3 (40 mm away from the gate) and section 4 (80 mm away from the gate) of the GAIM samples, respectively. As shown in the curves, the melt's maximum shear rate also appears near the upper and lower end of the GAIM sample, but the maximum shear rate of the melt away from the gate is greater than that of the melt near the gate. As the nitrogen continuously fills, the pressure in the hollow cavity will continue to increase, and the nitrogen will accelerate the filling of the melt. As a result, the melt's shear rate increases accordingly with the distance from the gate increasing. By comparing curve 2 in Figure 9(a) with curve 3 in Figure 9(b), it can be seen the melt's shear rate of the GAIM sample is much greater than that of the CIM sample on the same cross section. This is mainly caused by the nitrogen rapidly pushing the melt to fill the mold cavity. In a word, the melt's maximum shear rate of GAIM is about 45 times larger than that of CIM.

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Figure 9. Simulation results of the shear rate along the radial direction of the samples: (a) CIM samples; (b) GAIM samples. Figure 10 shows the variation of the melt temperature with the cooling time at the position 1.5 mm away from the skin layer of the CIM and GAIM samples. As shown in the figure, the melt temperature of GAIM drops faster than that of CIM. This indicates that the cooling rate of GAIM is faster than that of CIM. Because the high-pressure nitrogen penetration to the melt makes the part have a thin residual wall thickness, the heat transfer between melt and mold wall is fast for GAIM. However, for CIM, the heat is transferred from the sample's center to the mold wall, and the thickness from the CIM sample's center to the mold wall is far larger than the residual wall thickness of the GAIM sample, so the heat transfer between melt and mold wall is slow.

Figure 10. Variation of the melt temperature with the cooling time at the position 1.5 mm away from the skin layer of the CIM and GAIM samples. 19

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In related literatures,44-46 it has been pointed out that the shear action helps to induce nucleation. From the simulation result in Figure 9, the high-pressure nitrogen penetration to the melt in GAIM produces a stronger shear effect on the melt compared with CIM. Under this strong shear, a large number of nuclei are induced in melt crystallization process, and the number of crystals in a GAIM is increased. In addition, the residual wall thickness of the GAIM sample is 2.1 mm, and the shear rate in the middle layer (about 1 mm away from the skin layer of the GAIM sample) almost corresponds to the curve peak shown in Figure 9 (b), that is, the melt in the middle layer of the GAIM sample is subjected to a strong shear action. As a result, the melt in the middle layer has the largest number of nuclei and the smallest crystal size, as shown in Figure 6 (e). However, the GAIM has a rapid cooling rate which is unfavorable to the melt crystallization, so the crystallinity of the final sample is reduced. It should be noticed that the obviously oriented crystals are not found in this paper. Although the strong shear can make the polymer chain stretched or oriented along the flow direction, the molecule chain relaxation in the cooling process will disrupt the orientation. The comprehensive effect of these two factors will determine the microstructure with oriented crystals or spherulites,44,47 so the strong shear is just one of the necessary conditions to induce the oriented crystals. 4.3 Foaming mechanism Figure 11 shows the samples' fracture sections and the cell morphology of the foamed area under SEM. Figure 11(a) represents the samples obtained by microcellular injection molding (MIM), and Figure 11(b)-(f) represent the samples obtained by gas-assisted microcellular injection molding (GAMIM) under the gas holding time of 5 s, 15 s, 25 s, 35 s and 45 s, respectively. As shown in Figure 11(a) and (b), the number of cells is relatively small, and the cell size distribution is very uneven for the MIM sample and the GAMIM sample under the gas holding time of 5 s. With the gas holding time increasing, when it reaches 25 s, the number of cells increases, and the cell size distribution is very uniform, as shown in Figure 11(d). However, with the further increase of gas holding time, the

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number of cells reduces again, and the cell size increases, as shown in Figure 11(e) and (f). From the fracture sections, which can macroscopically assess the overall foaming quality, it also can be seen the foaming quality under the gas holding time of 25s is the best. Because the melt is still in a high temperature, and cells are formed mainly via homogeneous nucleation in MIM and in GAMIM under the short gas holding time, the final number of cells (cell density) is small. When cells grow in the PP melt with a high temperature and a low melt strength, cells are susceptible to coalesce and rupture. As a result, the final cell size distribution is non-uniform. With the increase of gas holding time in GAMIM, the melt temperature can be reduced, and the melt begins to crystallize. When the foaming occurs, there are a lot of imperfect crystals for the heterogeneous nucleation of cells,6,48 so the final number of cells is increased. Moreover, the melt strength can be also increased due to the decrease of the melt temperature and the melt crystallization. This increased melt strength can effectively suppress the cell coarsening and rupture. Therefore, the cell density is the largest and the cell size distribution is the most uniform at the most appropriate gas holding time. However, with the gas holding time further increasing, the melt temperature decreases greatly, and the formed crystals tend to be perfect. As a result, the cell nucleation is inhibited, and the number of cells begins to decrease in the final sample. At the same time, the cell size will also slightly increase with a definite amount of foaming agent.

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Figure 11. Samples' fracture sections and cell morphology of the foamed area under SEM: (a) MIM samples; (b)-(f) GAMIM samples under the gas holding time of 5 s, 15 s, 25 s, 35 s and 45 s. Figure 12 gives the schematic illustration of foaming mechanisms of the two kinds of foam injection molding. In MIM, the high temperature polymer/gas solution shown in Figure 12(a)-I is formed after mixing the polymer and physical foaming agent by the screw. When the high temperature melt is injected into the mold cavity, the melt pressure drops, and cells begin to nucleate. Since the melt crystallization hardly occurs at this time,20 the cell nucleation mainly belongs to homogeneous nucleation, and the number of cells is small, as shown in Figure 12(a)-II. After cell nucleation, the melt temperature is still high and the melt strength is low, so cells are easy to coalesce and rupture in the growing process. As the melt cools down, the melt strength increases, but this limited increase of melt strength still does not inhibit the coarsening of cells. And at this moment, the crystals shown in Figure 12(a)-III begin to appear in the melt. Subsequently, the cells and crystals continue to grow, as shown in Figure 12(a)-IV. In short, for MIM, cell nucleation occurs and cells grow in the environment where the melt temperature is high, no crystallization occurs, and the melt strength is low. This foaming environment is harmful for the tailoring of cell morphology. In GAMIM, after a proper gas holding time, the nuclei begin to form in the melt, as shown in Figure 12(b)-II. Since the nitrogen content (0.3 wt%) in the melt is very small, the nitrogen dissolved 22

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in the PP melt has a diminutive plasticization effect. Thereby, this plasticization can only counterbalance the nitrogen's negative hydraulic pressure effect on crystallization,49,50 and the nitrogen's effect on melt crystallization can be ignored.51 Therefore, in the presence of the nitrogen, a large number of nuclei can also be generated and the crystals are refined in GAMIM. When the high-pressure nitrogen is released, the foaming gas in the melt begins to nucleate. Here, besides the homogeneous nucleation of cells, the heterogeneous nucleation of cells also occurs around these numerous crystals. This nucleation mode can be described as the crystallization-driven cell nucleation. So the nucleation density is increased, as shown in Figure 12(b)-III. After a proper gas holding time, the melt temperature can be reduced, and the melt strength can be increased. So the cell coarsening can be effectively prevented, as shown in Figure 12(b)-IV. In a word, the foaming process occurs after the melt crystallization in GAMIM, and the crystals can drive nucleation of cells. The strong shear in GAMIM generates a large number of crystals, of which the boundaries can provide a lot of nucleation sites. In addition, these crystals can also cause a local stress on the melt around them.20,48 These two factors are very helpful for the crystallization-driven nucleation of cells, which plays an important role on the improvement of the PP's foaming behavior in GAMIM. Moreover, the decrease of the melt temperature and the melt crystallization make the melt strength increase. As a result, the cell morphology of GAMIM can be greatly improved.

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Figure 12. Schematic illustration of foaming mechanisms of the two kinds of foam injection molding processes: (a) MIM; (b) GAMIM. 5 Conclusions In this paper, the crystallization behaviors of PP in conventional injection molding (CIM) and gas-assisted injection molding (GAIM) were studied. The three-dimensional numerical model was established to simulate the filling and cooling processes of CIM and GAIM. The effect of the high-pressure gas penetration on melt crystallization was also revealed. The cell morphology of microcellular injection molding (MIM) and gas-assisted microcellular injection molding (GAMIM) was investigated. The foaming mechanism of PP in GAMIM was finally proposed. The following conclusions were drawn: (1) The GAIM can stimulate nucleation of melt crystallization and refine crystals, so the average crystal size of the GAIM sample is smaller than that of the CIM sample. The crystal sizes in the positions with different distances away from the GAIM sample's skin layer have little difference, while the crystal size increases with the increase of the distance from the skin layer of the CIM sample. (2) In GAIM, the gas penetration to the melt brings a strong shear action, and the thin residual wall thickness helps to accelerate the heat transfer between the melt and mold cavity. This strong shear can induce nucleation of the melt, and help to reduce the crystal size. However, the fast heat transfer and the large existing nuclei make the crystal grow inadequately, so the crystallinity of the GAIM sample is smaller than that of the CIM sample. (3) For MIM, cell nucleation occurs and cell grows in the environment where the melt temperature is high, no crystallization occurs, and the melt strength is low. This foaming environment is very harmful for the tailoring of cell morphology. But for GAMIM, when the foaming process begins, a large number of crystals has formed in the melt. The mode of crystallization-driven cell nucleation can help to greatly enhance the nucleation of cells. In addition, after a proper gas holding time, the melt temperature can be reduced, and the melt strength can be

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increased. Therefore, the foaming behavior of PP in the GAMIM is significantly improved. Author Information Corresponding author * E-mail address: [email protected] (Guoqun Zhao). ORCID Guoqun Zhao: 0000-0002-9387-801X Notes The authors declare no competing financial interest. Acknowledgements The authors are grateful to the financial support from the Climbing Program for Taishan Scholars of Shandong Province of China (NO. 20110804) and National Natural Science Foundation of China (NO. 51405267). The work was also financially supported by State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology (No. P2018-002). References (1) Park, C. B.; Baldwin, D. F.; Suh, N. P. Effect of the pressure drop rate on cell nucleation in continuous processing of microcellular polymers. Polym. Eng. Sci. 1995, 35, 432−440. (2) Doroudiani, S.; Park, C. B.; Kortschot, M. T. Effect of the crystallinity and morphology on the microcellular foam structure of semicrystalline polymers. Polym. Eng. Sci. 1996, 36, 2645−2662. (3) Matuana, L. M.; Park, C. B.; Balatinecz, J. J. Cell morphology and property relationships of microcellular foamed PVC/wood-fiber composites Polymer. Polym. Eng. Sci. 1998, 38, 1862−1872. (4) Wang, L.; Hikima, Y.; Ishihara, S.; Ohshima, M. Fabrication of lightweight microcellular foams in injection-molded polypropylene using the synergy of long-chain branches and crystal nucleating agents.

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