*Article* **Multi-Objective Optimizations for Microinjection Molding Process Parameters of Biodegradable Polymer Stent**

#### **Hongxia Li 1, Kui Liu 1, Danyang Zhao 1, Minjie Wang 1, Qian Li 2,\* and Jianhua Hou <sup>2</sup>**


Received: 18 October 2018; Accepted: 15 November 2018; Published: 19 November 2018

**Abstract:** Microinjection molding technology for degradable polymer stents has good development potential. However, there is a very complicated relationship between molding quality and process parameters of microinjection, and it is hard to determine the best combination of process parameters to optimize the molding quality of polymer stent. In this study, an adaptive optimization method based on the kriging surrogate model is proposed to reduce the residual stress and warpage of stent during its injection molding. Integrating design of experiment (DOE) methods with the kriging surrogate model can approximate the functional relationship between design goals and design variables, replacing the expensive reanalysis of the stent residual stress and warpage during the optimization process. In this proposed optimization algorithm, expected improvement (EI) is used to balance local and global search. The finite element method (FEM) is used to simulate the micro-injection molding process of polymer stent. As an example, a typical polymer vascular stent ART18Z was studied, where four key process parameters are selected to be the design variables. Numerical results demonstrate that the proposed adaptive optimization method can effectively decrease the residual stress and warpage during the stent injection molding process.

**Keywords:** polymeric stent; injection molding; residual stress; warpage; kriging surrogate model; design optimization

#### **1. Introduction**

Polymeric stents are a promising prospect [1]. However, the thin-walled tubular surface of polymeric stents has a discontinuous mesh structure. Furthermore, the stent has a tiny entirety, big length-to-diameter ratio, partial precision and unique structure, which greatly limits the machining and application of polymeric stents. The traditional machining method for stents is laser cutting. However, there are some uncontrolled machining problems, such as cutting seam width, surface roughness, taper of cut, back injury, slag, recast layer, etc. Fortunately, Clarke et al. presented an innovative technique for manufacturing polymer stents through the injection molding process [2]. This method provides a new line of thought for the high efficiency machining of stents. The injection molding stents have many remarkable advantages such as its strong reproducibility, high molding efficiency, good surface quality, good material condensation orientation, good molding consistency, etc.

At present, the injection molding method is not widely used in stent manufacturing. An important cause is that the parameters greatly influence molding quality of the polymeric stent during the injection molding process. Moreover, it is hard to determine a reasonable process parameter combination for the injection molding process, and this can easily result in some problems. For example, the flow of the melt is difficult to manage or the melt flows unevenly, it is hard to fill the mold cavity, the relatively large residual stress in the stent's cavity results in difficulty in demolding, and the stent undergoes a warpage phenomenon after demolding. Therefore, there is a need to investigate the effect of some important process parameters, such as mold temperature, melt temperature, flow rate and packing pressure, on stent quality. A reasonable process parameter combination is able to ensure the molding quality of the polymeric stent. Some scholars have conducted studies on the effect of injection molding process parameters on product quality. Liu et al. studied how the mold temperature affected the shrinkage of rapid heat cycle injection molded parts [3]. Duo performed the Taguchi experiment to investigate the effect of the injection molding process parameters, such as packing time, molding temperature and cooling time, on the warpage of flat tiny devices [4]. Jiang et al. revealed the great influence of mold temperature on the structure and mechanical properties of microinjection molding PP products [5]. In the meantime, Singh et al., Annicchiarico et al. and Mohan et al. conducted a detailed study of the effect of injection molding process parameters on the quality of injection molding products, providing a reference value for the stent injection molding process [6–8]. The above-mentioned studies were based on the effect between process parameters and product quality indicators, and some of these scholars were able to establish a function relationship between process parameters and quality indicators from the perspective of the optimal design. Based on the combination of the artificial neural network and genetic algorithm, Shen et al. optimized the injection molding process parameters, and improved the volume shrinkage of parts [9]. Based on the software tools, Florin et al. optimized the microinjection molding process of polymer medical apparatuses and instruments [10]. Kitayama et al. realized the multi-objective optimization of volume shrinkage and clamping force in the plastic injection molding process through the sequential approximate optimization method [11]. Based on Taguchi, ANOVA and the artificial neural network method, Oliaei et al. investigated the warpage and shrinkage optimization of biodegradable polymer injection molding plastic spoon parts [12]. Dang proposed a general framework for optimizing injection molding process parameters [13]. Kashyap et al. presented a detailed summary of related methods for the optimization of injection molding process parameters [14]. Kitayama et al. performed a multi-objective optimization of process parameters in plastic injection molding for simultaneously minimizing the warpage, cycle time and clamping force using radial basis function [15]. These studies have laid a solid foundation for the process parameter control of the stent injection molding process.

However, the polymeric vascular stent has a thin-walled tubular network structure with micro-scale geometry (strut width and thickness of 0.1 mm), large ratio of length to diameter and local precision, which make molding quality very sensitive to changes in process parameters. Furthermore, the relationship between process parameters and molding quality is very complicated, non-linear, implicit and multimodal. In addition, the number of functional assessments is extremely time consuming. In this case, if using a conventional optimization method (such as a gradient-based algorithm), it will be difficult to get a global optimization design for the process parameters. Here, it is worth recommending that the surrogate modeling, which mainly consisting of the Kriging method, can effectively solve the engineering problems mentioned above [16]. It is well known that the microscopic properties of polymer materials affect macroscopic properties, but the relationship is complex, and the computational process is highly time-consuming [17]. Fortunately, one of the great benefits is that the surrogate model actually calculates material properties at the micro level, which can save the computation time. The surrogate model can establish a suitable approximation functional relationship between process parameters (input) and molding quality (output), thus taking the place of the complicated engineering calculation process at lower computational cost. In this respect, Gao et al. [18], Li et al. [19] have done a lot of related work. Gao et al. used Surrogate-based process optimization for reducing warpage in macro-injection molding. Li et al. have developed a multi-objective optimization based on the Kriging method. The method was applied to optimize

the geometry of the biodegradable polymer stent, which finally showed that the stent expansion performance could be successfully improved.

In the present paper, the multi-objective process optimization about process parameters and molding quality was researched by constructing the adaptive optimization algorithm based on Kriging surrogate modeling. The Kriging model was applied to establish an approximate functional relationship between stent molding quality (residual stress and warpage) and injection molding parameters, thus making it possible to avoid the time-consuming finite element reanalysis in microinjection molding process optimization. The optimization iterative process is based on approximate functional relationships to decrease the computation time. Meanwhile, the 40 trial sample points were obtained by using the Optimal Latin Hypercube Sampling Method (Optimal LHS) [20]. Also, the expected improvement (EI) function plays a huge role when performing the adaptive optimization process. Even in the case of small sample sizes, the local and global searches can also be balanced, making it more likely to find global optimization designs. The finite element method based on MOLDFLOW (Autodesk Moldflow Insight 2012, Autodesk Inc., San Rafael, CA, USA) was ran simultaneously to model the injection molding process of the stent to obtain the response of molding quality under the specific process parameter combination. The combination of the numerical results and the design optimization method of the study facilitates further optimization studies and development of a method for further manufacturing a polymer stent by a microinjection molding process.

#### **2. Materials and Methods**

#### *2.1. PLA Stent Material*

Biodegradable polymeric stents are mainly made of polylactic acid (PLA) and modified materials. In the present study, as an example, the biodegradable polymeric stent was made of semi-crystalline PLA (Manufacturer: Kao Corporation, Trademark: ECOLA S-1010, Tokyo, Japan), with a solid particle density of 1.6416 g/cm<sup>3</sup> and a melt density of 1.4836 g/cm3.

The melt rheology curve of PLA is presented in Figure 1. On one hand, the flow process of the PLA melt under constant temperature exhibits a significant shear thinning behavior. In the actual injection molding process, and within the allowable shear rate of the material, this rheology should be fully used in selecting an appropriate melt flow shear rate, adjusting the melt viscosity, and improving flowability, thereby reaching a better flow and filling ability. On the other hand, the shear viscosity of the PLA melt was correlated to temperature. Within a certain range of shear rate, as a whole, viscosity decreases as temperature increases. Furthermore, the effect of temperature on viscosity can basically be ignored when the melt flow exceeds a certain shear rate. As a result, overall consideration should be given to the effect of temperature and shear rate on melt flowability for full utilization.

The PVT curve of PLA plastic is presented in Figure 2 to investigate the relationship between pressure, volume and temperature. Under specific pressure conditions, the volume ratio of PLA increases as temperature increases. When pressure is relatively small, and as the temperature increases, PLA is converted from a solid particle status into a melt status, and the relationship between the volume and temperature of PLA tends to undergo a staged linear change. Furthermore, there will be a small upward slope near 130 ◦C. This is because PLA is a semi-crystalline material, and 130 ◦C is the crystalline transition temperature. The molecular chain of PLA is converted from a partially ordered arrangement status into an overall disordered status, which results in a relatively big volume expansion. The temperature drop led to significant volume shrinkage. In the injection molding process, consideration should be given to the effect of the material's crystalline. When the pressure is very high, and the temperature increases, a few upward slopes under the crystalline transition temperature appear. This is due to the very high pressure at this moment, which greatly inhibits the movement of the molecular chain and the transition of material volume, resulting in the single linear change of the whole process. Therefore, it is necessary to flexibly control the injection pressure and the injection

temperature due to the characteristics of PLA as a semi-crystalline material when performing the actual injection molding process.

**Figure 1.** The rheological properties of polylactic acid (PLA).

**Figure 2.** The PVT properties of polylactic acid (PLA).

#### *2.2. Biodegradable Polymeric Stent Structure*

The biodegradable polymeric stent made of PLA has good biocompatibility and a relatively short biodegradation period. The structure of this stent is presented in Figure 3: overall length, 13.75 mm; thickness, 0.17 mm; outside diameter, 3.36 mm.

It can be observed that it has a typical thin-walled structure and a large number of discontinuous mesh structures. Full consideration should be given to demolding properties and post-demolding warpage.

**Figure 3.** Generic polymeric stent with straight bridges.

#### *2.3. Microinjection Molding Optimization of Biodegradable Polymeric Stents*

In the PLA stent injection molding process, due to its thin-wall and mesh structure feature, its common phenomena, such as demolding difficulty and post-demolding warpage, greatly influence the efficiency and molding quality of the stent injection molding process. Its demolding process is mainly influenced by the residual stress of the stent in the orientation direction, indicating the stress of parts before ejection, instead of after ejection. An excessively large residual stress in the cavity would cause the stent in the cavity to maintain a relatively high-tension status, which is not good for the demolding process. Warpage is a size deformation caused by the unbalanced change of inner stress. Serious warpage can even influence the normal use of stents. The residual stress and warpage of stents are influenced by processes, such as mold temperature, melt temperature, flow rate and packing pressure. Hence, a smaller residual stress and warpage would be better. Therefore, the four process parameters, that is, mold temperature, melt temperature, flow rate and packing pressure, should be viewed as design variables, while the two evaluation indicators, that is, residual stress of the stent in the orientation direction in the cavity (affecting the stent demolding process) and warpage (affecting the use properties of the stent), should be viewed as objective variables. Consequently, the multi-objective optimization design for the molding quality optimization problem during the stent injection molding process can be defined as follows:

$$\begin{array}{ll}\text{min} & \text{residual stress}(\text{RS}), \text{ warpage}(\text{W})\\\text{s.t.} & \mathbf{x}\_1 \le \mathbf{x} \le \mathbf{x}\_2\end{array} \tag{1}$$

Residual stress refers to the residual stress of the stent in the cavity in the first principal direction. Warpage refers to the total warpage of the stent, where *x* represents the optimization variables, and *x*<sup>1</sup> and *x*<sup>2</sup> represent the upper and lower limits of these optimization variables.

Residual stress and warpage are the two main indicators for stent injection molding quality. However, the RS and W of a polymeric stent varies with significantly different scales, making it difficult to define a suitable weight. Naturally, if both of these are scaled to (0, 1), the weight can be assigned an intermediate value of 0.5. In this case, the optimization problem mentioned above can be written as:

$$\begin{array}{ll}\min & f(\mathbf{x}) = 0.5 \frac{\text{RS} - \text{RS}\_{\text{min}}}{\text{RS}\_{\text{max}} - \text{RS}\_{\text{min}}} + 0.5 \frac{\text{W} - \text{W}\_{\text{min}}}{\text{W}\_{\text{max}} - \text{W}\_{\text{min}}}\\ \text{s.t.} & \mathbf{x} = \begin{bmatrix} T\_{mold} & T\_{mclt} & \upsilon\_{flow} & P\_{pack} \end{bmatrix}^{\text{T}}\\ & 80 \, ^\circ \text{C} \le T\_{mold} \le 90 \, ^\circ \text{C} \\ & 190 \, ^\circ \text{C} \le T\_{mclt} \le 205 \, ^\circ \text{C} \\ & 0.13 \, \text{cm}^3/\text{s} \le \upsilon\_{flow} \le 0.25 \, \text{cm}^3/\text{s} \\ & 75\% \le P\_{pack} \le 90\% \end{array} \tag{2}$$

where RS represents the residual stress of the stent in the cavity in the first principal direction and W is the total warpage. *Tmold* is the temperature of the mold which can cool the melt, *Tmelt* is the melt temperature and has a large influence on the melt flow viscosity, *vflow* is the volume flow rate affecting the molding cycle, and *Ppack* is the packing pressure.

#### *2.4. Finite Element Method of the PLA Stent Injection Molding Process*

The stent microinjection molding process can be researched by using the finite element method (FEM). The numerical simulation platform based on the MOLDFLOW injection molding process was designed with a stent injection molding runner system, which includes six injecting gates (Figure 4). The runner system uses the cylinder units to divide the grids, which includes 501 cylinder units and 502 nodes, with an injecting system volume of 0.109295 cm3. The stent structure has a uniform wall thickness. Hence, it uses the double-layer grid division, which includes 80,670 triangular units and 40,227 nodes, with a volume of 0.00333709 cm<sup>3</sup> and a grid matching ratio of 92.8%.

**Figure 4.** The injection molding process of stent based on the MOLDFLOW.

The injection molding runner system was adopted to conduct the numerical simulation of the stent injection molding process. The melt filling process is presented in Figure 5. The polymer melt is injected slowly into the cavity from the left end shown in Figure 5 and eventually fills the entire cavity. Compared to the eight filling stages, the filling process along the longitudinal direction is uniform.

**Figure 5.** The injection molding process of a stent.

#### *2.5. Optimization Algorithm*

#### 2.5.1. Approximate Method

The kriging model is an approximation technique that consists of a regression and a non-parametric part, including a polynomial and a random distribution:

$$\hat{y}(\mathbf{x}^i) = \mathbf{F}(\boldsymbol{\beta}, \mathbf{x}^i) + \mathbf{z}(\mathbf{x}^i) = \mathbf{f}^T(\mathbf{x}^i)\boldsymbol{\beta} + \mathbf{z}(\mathbf{x}^i),\tag{3}$$

in which, *β* is the regression coefficient; f(**x***<sup>i</sup>* ) is a polynomial that provides a global approximation of the simulation; and z(**x***<sup>i</sup>* ) is a randomly distributed error that provides an approximation of the simulated local deviation and has the following statistical properties:

$$\begin{aligned} E[\mathbf{z}(\mathbf{x})] &= 0\\ \text{var}[\mathbf{z}(\mathbf{x})] &= \sigma\_z^2\\ \text{corr}\left[\mathbf{z}(\mathbf{x}^i), \mathbf{z}(\mathbf{x}^j)\right] &= \mathbb{R}(\theta, \mathbf{x}^i, \mathbf{x}^j) = \prod\_{l=1}^m \exp\left[-\theta \left(\mathbf{x}\_l^i - \mathbf{x}\_l^j\right)^2\right] \end{aligned} \tag{4}$$

where **x***<sup>i</sup>* and **x***<sup>j</sup>* are any two points in the training samples; R(*θ*, **x***<sup>i</sup>* , **x***j* ) is the correlation function with parameter *θ*, characterizing the spatial correlation between the points of training samples, and in this paper, Gaussian correlation function was used, which can be described as:

$$\mathcal{R}(\theta, \mathbf{x}^i, \mathbf{x}^j) = \exp(-\sum\_{l=1}^n \theta\_k \left| \mathbf{x}\_l^i - \mathbf{x}\_l^j \right|^2) \tag{5}$$

where *n* is the number of design variables; **x***<sup>i</sup> <sup>l</sup>* and **x** *j <sup>l</sup>* are the *l*-th component of the training sample.

#### 2.5.2. Predictor

Given the training samples **S** = [**x**1, **x**2, ... , **x***n*] and corresponding response **Y** = [**y**1, **y**2, ... **y***n*], the response at a new point **x**∗ can be expressed by a linear combination of **Y**

$$\boldsymbol{\hat{y}}(\mathbf{x}^\*) = \mathbf{c}^T \mathbf{Y},\tag{6}$$

The error is

$$
\hat{y}(\mathbf{x}^\*) - y(\mathbf{x}^\*) = \mathbf{c}^T \mathbf{Y} - y(\mathbf{x}^\*),
\tag{7}
$$

Substituting Equation (3) into Equation (7) gives

$$\begin{aligned} \left(\boldsymbol{\mathfrak{y}}(\mathbf{x}^\*) - \boldsymbol{y}(\mathbf{x}^\*)\right) &= \mathbf{c}^T (\boldsymbol{F}\boldsymbol{\beta} + \mathbf{Z}) - \left(\mathbf{f}(\mathbf{x}^\*)^\mathsf{T}\boldsymbol{\beta} + \boldsymbol{z}\right) \\ &= \mathbf{c}^\mathsf{T}\mathbf{Z} - \boldsymbol{z} + \left(\mathbf{F}^\mathsf{T}\mathbf{c} - \mathbf{f}(\mathbf{x}^\*)\right)^\mathsf{T}\boldsymbol{\beta} \end{aligned} \tag{8}$$

where **Z** = [*z*1,*z*2,..., *zn*], **F** = [**f**1,**f**2,...,**f***n*]. To get the unbiased predictor for **x**∗, the mean error at this point should be zero, i.e.,

$$\operatorname{E}(\mathcal{Y}(\mathbf{x}^\*) - \mathcal{Y}(\mathbf{x}^\*)) = 0,\tag{9}$$

And then, FT**c**(**x**∗) <sup>−</sup> <sup>f</sup>(**x**∗) <sup>=</sup> 0. Therefore, we have the mean squared error of the predictor (8),

$$\begin{array}{rcl}\varphi(\mathbf{x}^\*) &=& \operatorname{E}\left[\left(\mathcal{Y}(\mathbf{x}^\*) - y(\mathbf{x}^\*)\right)^2\right] \\ &=& \sigma^2 \Big(1 + \mathbf{c}^T \mathbf{R} \mathbf{c} - 2\mathbf{c}^T \mathbf{r}\Big)^{\prime} \end{array} \tag{10}$$

where

$$\mathbf{r}(\mathbf{x}^\*) = [\mathbb{R}(\boldsymbol{\Theta}, \mathbf{x}\_1, \mathbf{x}^\*), \dots \mathbb{R}(\boldsymbol{\Theta}, \mathbf{x}\_{n'} \mathbf{x}^\*)]\_\prime \tag{11}$$

It represents the spatial correlation between new sample **x**∗ and training samples. **c**(**x**∗) can be obtained by minimizing *ϕ*(**x**∗), i.e.,

$$\begin{aligned} \mathbf{c} &= \mathbf{R}^{-1} \left( \mathbf{r} - \mathbf{F}\widetilde{\boldsymbol{\lambda}} \right) \\ \widetilde{\boldsymbol{\lambda}} &= \left( \mathbf{F}^{\mathsf{T}} \mathbf{R}^{-1} \mathbf{F} \right)^{-1} \left( \mathbf{F}^{\mathsf{T}} \mathbf{R}^{-1} \mathbf{r} - \mathbf{f} \right)^{\prime} \end{aligned} \tag{12}$$

then

$$\mathfrak{G}(\mathbf{x}^\*) = \mathbf{f}(\mathbf{x}^\*)\mathfrak{B} + \mathbf{r}(\mathbf{x}^\*)^\mathsf{T}\mathfrak{Y},\tag{13}$$

where

$$\mathbf{y} = \mathbf{R}^{-1} \left( \mathbf{Y} - \mathbf{F} \hat{\mathbf{B}} \right), \tag{14}$$

Thus, we can predict the function value *y*ˆ(**x**∗) at every new point **x**∗ by using Equation (13).

#### 2.5.3. Expected Improvement (EI)

Maximizing expectation improvement is an aspect of the method that adds new points that consider the prediction value and the prediction variance. Expected improvement (EI) calculates the probability of a target's response improvement at a given point. *Y*(**x**) at some point **x** is unknown before sampling at this point. However, kriging can predict its mean *y*ˆ(**x**) and variance *σ*2. Assuming that the response value of the current optimal design is *Y*min, the improvement of the response of this point is *I* = *Y*min − *Y*(*x*) with a normal distribution. Thus, its probability density function is

$$\frac{1}{\sqrt{2\pi}\sigma(\mathbf{x})}\exp\left[-\frac{\left(\mathcal{Y}\_{\text{min}} - I - \mathcal{Y}(\mathbf{x})\right)^{2}}{2\sigma^{2}(\mathbf{x})}\right],\tag{15}$$

Therefore, the expected improvement of the response value is

$$\mathrm{E}[I(\mathbf{x})] = \int\_{I=0}^{I=\infty} I \left\{ \frac{1}{\sqrt{2\pi}\sigma(\mathbf{x})} \exp\left[ -\frac{(\mathbf{Y}\_{\mathrm{min}} - I - \hat{\mathfrak{y}}(\mathbf{x}))^2}{2\sigma^2(\mathbf{x})} \right] \right\} dI,\tag{16}$$

Integrating Equation (16) by parts, it gives

$$\mathbb{E}[I(\mathbf{x})] = \sigma(\mathbf{x})[\mu\Phi(\mathbf{u}) + \phi(\mathbf{u})],\tag{17}$$

where

$$
\mu = \frac{\mathbf{Y}\_{\text{min}} - \hat{\mathbf{y}}(\mathbf{x})}{\sigma(\mathbf{x})} \tag{18}
$$

and where Φ and *φ* are the normal cumulative distribution and density functions, respectively.

#### 2.5.4. The Convergence Criterion

The convergence condition of EI is

$$\frac{EI(\mathbf{x})}{Y\_{\text{max}} - Y\_{\text{min}}} < \varepsilon\_1. \tag{19}$$

where *ε*<sup>1</sup> is the convergence tolerance. *Y*max and *Y*min are the maximal and minimal function values in samples, respectively.

In addition, the predicted value converges to the numerical result to characterize the accuracy of kriging model,

$$|f(\mathbf{x}\_l) - \hat{y}\_l| < \varepsilon\_2 \tag{20}$$

where *f*(**x***l*) is the numerical result; *y*ˆ*<sup>l</sup>* is the predicted value based on kriging; *ε*<sup>2</sup> is the convergence tolerance.

Moreover, the optimization results of the last two iterations should be similar,

$$|f(\mathbf{x}\_l) - f(\mathbf{x}\_{l-1})| < \varepsilon\_3 \tag{21}$$

where *<sup>f</sup>*(**x***l*) and *<sup>f</sup>*(**x***l*−1) are the response values of the last two iterations, respectively. Figure <sup>6</sup> shows the complete process of the optimization algorithm based on the Kriging surrogate model, making this process easier to understand.

**Figure 6.** Complete process of the optimization algorithm based on the Kriging surrogate model.

#### **3. Results**

#### *3.1. Results of Stent Injection Molding Process*

The boundary values of the four design variables were respectively given. Then, 40 initial training sample points were generated using the orthogonal LHS method to build the Kriging surrogate model, with the aim of establishing the approximate relationship between the two objective variables of the stent (residual stress and warpage) and the four design variables.

The design variables included mold temperature *Tmold*, melt temperature *Tmelt*, flow rate *vflow*, and packing pressure *Ppack* and the range of the four process parameters were shown in Table 1.

**Table 1.** The range of the process parameter.


The Kriging surrogate model optimization process needs 20 iterations to obtain the optimal solution corresponding to the minimum values of objective functions. The optimization iterative process is shown in Figure 7.

**Figure 7.** Optimization iterative process. (**a**) Relationship between integrated objective function value and iterations; (**b**) Relationship between residual stress and iterations; (**c**) Relationship between warpage and iterations.

The comparison between the optimal design result and comparable design result is presented in Table 2. The comparable design results, which adopt the intermediate values of the boundary values of the four design variables recommended by MOLDFLOW, correspond to the residual stress and warpage results.


**Table 2.** Comparison of the two design results.

It can be observed that merely the design recommended by MOLDFLOW could not effectively reduce the residual stress and warpage of the stent, while the optimal design based on the iteration process can significantly reduce residual stress and warpage. Compared to the results of the comparable design, residual stress decreased by 20.3% and warpage decreased by 44.6%. Apparently, this was attributable to the enhancement of the molding quality of the stent.

Figures 8 and 9 show the corresponding residual stress and warpage of these two kinds of designs, and the results of the optimal design obviously had smaller residual stress and warpage.

**Figure 8.** The distribution of residual stress of the comparable design and optimal design. (**a**) The distribution of residual stress of the comparable design; (**b**) The distribution of residual stress of the optimal design.

**Figure 9.** The distribution of warpage of the comparable design and optimal design. (**a**) The distribution of warpage of the comparable design; (**b**) The distribution of warpage of the optimal design.

#### *3.2. Results of Single Factor Analysis*

In order to investigate the influences of these four important parameters on the residual stress and warpage of the stent during the injection molding process, it is necessary to carry out a single factor analysis. In the optimal process combination, the influence of the remaining factor on the result was analyzed by fixing three factors, and the results are shown as follows. It revealed that the effects and mechanisms of these four parameters on the residual stress and warpage of the stent are significantly different.

The effect of mold temperature on the residual stress and warpage of the stent is presented in Figure 10. As illustrated by the curve change trend, mold temperature has a relatively significant influence on the residual stress and warpage of a stent. Raising the mold temperature could decrease the warpage. As for the PLA semi-crystalline material, high mold temperatures can reduce the flow viscosity of the melt, causing the melt to easily flow and enhance mold-filling efficiency. A relatively high mold temperature can decrease the temperature difference of the melt, cool the melt uniformly, reduce shrinkage deformation, and prevent defects, such as depression, deformation, etc. Excessively high mold temperatures and being close to the boundary value expands the volume of the melt, causes warpage, and prolongs the cooling time, thereby reducing production efficiency. Raising the mold temperature is attributable to improving surface roughness, reducing inner stress and the degree of

orientation, enhancing the strength of the weld line and product density, which thereby reduces the impact strength of the streamline direction, and reduces residual stress in the cavity.

**Figure 10.** The effect of mold temperature on the residual stress and warpage.

The effect of melt temperature on the residual stress and warpage of a stent is presented in Figure 11. As for the PLA semi-crystalline material, with its small crystalline tendency, the melt temperature would mainly affect the viscosity, flowability and molecular orientation of the melt. On one hand, enhancing the melt temperature would expand the volume of the melt, reducing the amount of material into the cavity. Furthermore, this would cause the loose status of the polymer in the orientation direction, and enhance the molecular chain orientation ability, resulting in an increase in warpage. On the other hand, enhancing the melt temperature can reduce the viscosity of the melt, and enhance the shear rate of the melt shear rate, when the injection pressure and packing pressure remain unchanged. This is attributable to the transfer of the pressure to the cavity, reducing the warpage. In general, as for the latter, viscosity has a relatively significant influence on temperature-sensitive materials. As for the former, viscosity has a relatively significant influence on non-temperature-sensitive material. PLA melt viscosity is relatively sensitive to temperature. Therefore, enhancing the melt temperature, as a whole, can reduce warpage. Furthermore, enhancing the melt temperature can effectively reduce melt viscosity. This would cause filling to be more uniform and reduce residual stress in the cavity. The stent has a number of uniformly-distributed injecting gates, which are contributive to the transfer of pressure, increasing the material supplement, reducing the shrinkage of the flat plate, and decreasing the warpage. Therefore, the effect of melt temperature on residual stress and warpage is the comprehensive result of these above-mentioned factors.

The influence of flow rate on the residual stress and warpage of the PLA stent is presented in Figure 12, showing a non-linear relationship obviously. The flow rate of the melt in the cavity is basically controlled by the flow rate of the injection. If the cavity structure is the same as other conditions, a relatively small flow rate would cause the melt to flow slowly in the cavity, and the melt compressed at the injecting gate can be fully loosened during the slow flow process. Furthermore, the melt has a relatively small uniformly-distributed residual stress in the follow-up packing and cooling process, which makes the warpage very small. With the increase in flow rate, the quicker the melt flows in the cavity, the bigger the flow and shear rate of the melt is, and the higher its shear stress becomes. Typically, the above-mentioned facts result in the higher residual stress of a stent, and even serious warpage. With the further increase in flow rate, the flow and shear rate of the melt increases. At the same time, melt viscosity also decreases to make the melt easily flow, and allow the cavity to be filled well, which can reduce residual stress and warpage. Apparently, the flow rate can affect the looseness and viscosity of the melt; weighing the proportion of these two by adjusting the flow rate can effectively reduce residual stress and warpage. Indeed, a relatively small flow rate correlates to longer injection molding time, while a relatively large flow rate correlates to greater injection pressure. In the

actual molding process, equipment and production efficiency should be considered. Furthermore, as for various types of materials, the effect of the flow rate on residual stress and warpage is relatively complex, because the mold-filling rate of the melt depends on the flow rate, while the effect of the mold-filling rate on plastic product properties is also relatively complex, which is correlated to the type of material.

**Figure 11.** The effect of melt temperature on the residual stress and warpage.

**Figure 12.** The effect of packing pressure on the residual stress and warpage.

The effect of packing pressure on the residual stress and warpage of a stent is presented in Figure 13. As for the thin-wall stent structure of the PLA material, merely relatively low packing pressure can ensure the relatively small warpage and residual stress. As for thin-walled parts, a relatively high packing pressure increases residual stress, causing non-uniform shrinkage, thereby resulting in a relatively larger warpage. Indeed, plastics and products with a relatively large viscosity, and have relatively high requirements in small wall thickness, a long process and high accuracy, needs a relatively high packing pressure. The present study considers these from the perspective of the optimal design.

**Figure 13.** The effect of packing pressure on the residual stress and warpage.

#### **4. Discussion**

As for the biodegradable PLA polymeric stent, the shortage of an accurate and effective manufacturing method is a potential limit to the development of polymeric stents. A PLA stent, which has low mechanical strength and an extremely tiny volume, is a typical precision thin-walled product. Due to its complex stent structure and tiny local size, the microinjection molding stent is greatly different from products manufactured by conventional microinjection molds. The stent product has a large length-to-diameter ratio, and a relatively low surface continuity, which influences the flowability of the polymeric melt in the cavity. Therefore, it would be difficult to completely fill the cavity during the experiment process. This is one of main difficulties of microinjection molding. In addition, the stent can easily form weld marks on the surface, and the number of the weld marks is expected to be more than that of conventional injection molding products.

In the design process, injection molding process parameters should be repeatedly adjusted to meet the quality requirements of plastic parts. The unreasonable parameters in the injection molding process, such as mold temperature, melt temperature, flow rate, and packing pressure, can result in serious residual stress and warpage of the stent. A relatively large residual stress in the cavity can result in difficulties during the demolding process, and even damage the stent during the demolding process. Furthermore, a relatively large warpage can greatly influence the product's use properties, and even its normal use.

In the present study, in order to reduce residual stress and warpage in the polymeric stent injection molding process, the study on the effect of process parameters, such as mold temperature, melt temperature, flow rate and packing pressure, can provide guidance in selecting the process parameter combination during the injection molding process. The scope of the studied process parameters are as follows: mold temperature (80, 90), melt temperature (190, 205), flow rate (0.13, 0.25), and packing pressure (75%, 90%). Therefore, the purpose of the optimal design in the stent injection molding process was to maximize the residual stress and warpage of the stent, thereby reducing the difficulties of demolding and the use properties of the product. Compared to the results of the comparable design, residual stress decreased by 20.3%, while warpage decreased by 44.6%. These apparently contributed to enhancing the molding quality of the stent. It should be acknowledged that the present study came to this conclusion based on the PLC material, without a setting of a cooling waterway, and without considering the effect of the actual cooling process. When the stent materials were different, or the mold structure was different from that in the present study, this would result in the optimal results of the stent's different process parameters. Of course, when investigating polymer stent of different materials or different structures, the optimization results of the injection molding process will be different. This research highlights how the surrogate model can be established and used to optimize

the stent injection molding process in order to demonstrate that the process can be designed and improved through this important approach.

#### **5. Conclusions**

The present study presents a multi-objective optimization method combined with the Kriging surrogate model to improve PLA stent injection molding process parameters, with the aim of enhancing the injection molding quality of micro absorbable polymeric stents. The Kriging surrogate model coupled with DOE methods was adopted to establish the approximate relationship between objective function and design variables. These results show that the proposed optimization method could be effectively used for the microinjection molding process. These results indicate that it is very useful based on the proposed optimization method to improve the molding quality during the microinjection molding process. This exhibits a novel methodology for the injection molding process design of polymer stents, representing a new research direction. The combination of this optimization method and experimental verification can play an important role in the process design of injection molding stents.

**Author Contributions:** H.L., D.Z., M.W., Q.L. and J.H. were responsible for the design, data collection and overall investigation, and established the optimization model. H.L. and Q.L. were responsible for the optimization method. H.L. and K.L. were responsible for the finite element analysis and the writing of the paper.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant no.11502044 and 51675079), the Fundamental Research Funds for the Central Universities (grant no.DUT17RC(3)104) and National Center for International Research of Micro-nano Molding Technology & Key Laboratory for Micro Molding Technology of Henan Province Joint Open Fund (grant no. MMT2017-03).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Laser-Assisted Thermal Imprinting of Microlens Arrays—Effects of Pressing Pressure and Pattern Size**

#### **Keisuke Nagato \*, Yuki Yajima and Masayuki Nakao**

Department of Mechanical Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan; yajima@hnl.t.u-tokyo.ac.jp (Y.Y.); nakao@hnl.t.u-tokyo.ac.jp (M.N.)

**\*** Correspondence: nagato@hnl.t.u-tokyo.ac.jp; Tel.: +81-3-5841-6361

Received: 30 January 2019; Accepted: 22 February 2019; Published: 25 February 2019

**Abstract:** Polymer films with nano- or microstructured surfaces have been widely applied to optical devices, bioplates, and printed electronics. Laser-assisted thermal imprinting (LATI), in which a laser directly heats the surfaces of a mold and a thermoplastic polymer, is one of the high-throughput methods of replicating nano- or microstructures on polymer films. Only the surfaces of the mold and polymer film are heated and cooled rapidly, therefore it is possible to replicate nano- or microstructures on polymer films more rapidly than by using conventional thermal nanoimprinting. In this study, microlens arrays (MLAs) were replicated on polymethylmethacrylate (PMMA) films using LATI, and the effects of the pressing pressure (10−50 MPa) and the pattern size (33- and 5-μm pitch) of the MLA on the filling ratio were investigated by analyzing a microlens replicated using different laser-irradiation times (0.1−2 ms). The filling ratio increased with increasing pressing pressure and laser-irradiation time in the replication of MLAs with varying sizes, while the flow of the PMMA varied with the pressing pressure and laser-irradiation time. It was found that during filling, the shape of the polymer cross-sectional surface demonstrated a double and single peak in the 33- and 5-μm-pitch patterns, respectively. This was because the depth of the heated area in the 33-μm-pitch pattern was smaller than the pattern size, whereas that of the 5-μm-pitch pattern was comparable to (or larger) than the pattern size.

**Keywords:** laser-assisted thermal imprinting; pressure; pattern size; thermoplastic polymer; microlens array

#### **1. Introduction**

Nano- or microstructured polymer surfaces perform various functions, such as hydrophilic or hydrophobic interactions with liquids, reduction of friction or sticking to solid surfaces, demonstrating an anchoring effect for adhesives, and optical or photonic behaviors. In terms of their use in optical or photonic capacities, antireflection structures have been fabricated to reduce light reflection and to increase the incident light transmittance in solar cells, flat panel displays and so forth [1]. Microlens arrays (MLAs) are fabricated on OLED devices, or OLEDs are fabricated on polymer films with photonic crystal surfaces [2–6] to improve the light extraction efficiency of organic light-emitting diodes (OLEDs). Furthermore, various nanostructures have been fabricated on polymer films for organic photovoltaic cells [7] and nanopillars have been fabricated for plasmonic biosensing [8]. As described above, nano- or microstructures are expected to become more commonly applied to various optical and photonic devices.

For these applications, it is necessary to fabricate nano- or microstructures on polymer films with a high throughput and low cost. Nanoimprint lithography (NIL), which was developed by Chou et al., is one of the highest-throughput and most inexpensive methods of fabricating nano- or microstructures [9]. To obtain nano- or microstructured surfaces on polymer films, three main kinds

of nanoimprint method have been proposed and developed: thermal nanoimprinting [9], ultraviolet (UV) nanoimprinting [10], and soft lithography [11]. UV lithography involves the use of a UV-curable polymer which is coated and molded and then cured using UV light. Soft lithography involves the use of thermocurable polymer coatings, which are cured post heating. These lithography techniques possess advantages associated with the use of soft molds and the use of low applied pressures because of the low viscosity of polymers. Flexible substrates can thus be coated and highly-functional materials, such as those possessing ferroelectric functionality, can be used [12,13]. On the other hand, thermal nanoimprinting is a direct imprinting method used to fabricate nano- and microstructures on polymer films. Therefore, it has the advantage of simplicity in terms of the manufacturing process because of the absence of a coating process [14]. In thermal nanoimprinting, a mold with a nano- or microstructured surface is heated and pressed directly onto a thermoplastic polymer film. The polymer is heated to a temperature above its glass transition temperature (*Tg*), causing it to flow and fill the nanoor microstructures of the mold. The mold and polymer are then cooled and demolded. Nano- or microstructures can be replicated on polymer films using these simple procedures. This simplicity has increased the popularity of thermal nanoimprinting among researchers as both a promising and convenient method [15].

The mold and polymer require heating and cooling in the thermal nanoimprinting process. The reduction in cycle time is thus limited by the thermal conductivities and specific heat capacities of the mold and polymer. On the other hand, in laser-assisted nanoimprinting, which was developed by Chou et al., nano- or microstructures are replicated by heating only the surfaces of a mold and a substrate using a laser [16]. Xia et al. and Grigalinunas et al. replicated the nanostructures of a glass ¯ mold on a thermoplastic polymer film [17,18]. Grigalinunas et al. also demonstrated nanoimprint ¯ lithography by using an Si mold and a CO2 laser [19]. Nagato et al. fabricated nanostructures of diamond-like carbon on a glass mold and replicated them on thermoplastic polymer films in a predefined area by scanning with a laser. They also demonstrated that laser heating reduced the cycle time for thermal imprinting below that associated with conventional thermal nanoimprinting [20].

However, although it has already been demonstrated that various nanostructures could be replicated on polymer films using laser-assisted thermal imprinting (LATI), this has only been achieved in a few instances. When microstructures are replicated on a polymer film using LATI, the polymer cannot effectively fill the microstructures of the mold, and the microstructures can therefore not be completely replicated. This is because it takes a finite amount of time for the polymer to flow and fill the microstructures of the mold. The flow of the polymer is caused by the applied pressure generated by pressing the mold onto the polymer film and the decrease in viscosity of the polymer is caused by laser heating. Therefore, the pressing pressure and laser-irradiation time both have an important effect on the filling ratio of the polymer (Figure 1).

**Figure 1.** Schematic showing complete and incomplete replication.

In this study, microstructures were replicated on polymer films using LATI and the phenomenon of polymer filling was investigated. MLAs with different pattern sizes were used as microstructures and the effects of the pressing pressure, and the pattern size of the MLA, were investigated and the filling ratio was measured by analyzing a microlens replicated using different laser-irradiation times.

#### **2. Experimental**

#### *2.1. MLA Molds*

Figure 2 shows scanning electron microscope (SEM) (semi-inlens field-emission type, SU-8010, Hitachi High-Technologies Corporation, Tokyo, Japan) secondary-electron images of the Ni concave molds with MLAs used in this study. It is possible to fabricate MLAs with various pattern sizes, which are used to improve the light extraction efficiency of OLEDs [21]. One of the MLAs used in this study had a lens diameter of 30 μm, a lens depth of 14 μm, and a pitch of 33 μm, and the other had a spherical lens diameter of 4.2 μm, a lens depth of 2.1 μm, and a pitch of 5 μm. The microlenses were arranged in a regular triangular lattice on both MLAs. The Ni concave molds for the MLAs were constructed using electroforming on convex master molds. Each Ni concave mold had a size of 10 × 10 mm<sup>2</sup> and a thickness of 200 <sup>μ</sup>m. The convex master molds for the electroforming process were prepared using photolithography and etching on a glass substrate. The mold surfaces were treated with a lubricant for the nanoimprinting mold, which was a hydrophobic coating material (DURASURF, Harves Co. Ltd., Saitama, Japan). A polymethylmethacrylate (PMMA) film was used as a thermoplastic film. The PMMA film had a thickness of 75 μm and *Tg* of approximately 89 ◦C (HBA002P, ACRYPLEN, Mitsubishi Chemical Corporation, Tokyo, Japan).

**Figure 2.** Scanning electron microscope (SEM) images of the microlens arrays (MLAs) in the Ni concave molds all shown as 30◦-tilted views. (**a**) 33-μm-pitch MLA, (**b**) 5-μm-pitch MLA, and (**c**) magnified view of 5-μm-pitch MLA.

#### *2.2. Experimental Setup and Conditions*

Figure 3 shows the experimental setup for the LATI process. A pressure-sensitive paper (Prescale MS R270 10M, of range: 10–50 MPa and accuracy: <±10%, Fujifilm Corporation, Tokyo, Japan) was used to measure the pressing pressure. The pressure was applied using an air cylinder (Misumi, Tokyo, Japan). The pressure-sensitive paper was placed on the Ni concave mold, and the paper and mold were pressed onto a glass plate with a thickness of 15 mm. The pressure applied to the pressure sensitive paper was then measured. In this study, the pressure measured using the pressure-sensitive paper was defined as the pressing pressure. The pressing pressure was set to 10, 20, 30, 40, or 50 MPa by adjusting the air pressure in the cylinder. The above procedure was conducted for each Ni concave mold [11].

After the measurement of the pressing pressure, the pressure-sensitive paper was removed and a PMMA film was placed on the Ni concave mold. The PMMA film and mold were then pressed onto the glass plate with pressing pressures of 10, 20, 30, 40, or 50 MPa. A continuous-wave single-mode fiber laser (SPI Lasers, Southampton, UK) with a wavelength of 1070 nm, 100 W power, and 500 μm diameter was used in this study to irradiate the surface of the Ni concave mold. After the laser was scanned once along a line of length 10 mm, the PMMA film was switched to an unimprinted one and the laser-irradiation time was varied by varying the scanning speed. The scanning speeds were 240, 320, and 500 mm/s for the 33-μm-pitch MLA and 1000, 2000, and 5000 mm/s for the 5-μm-pitch MLA. The laser irradiation-time was defined as the laser-irradiation diameter divided by the scanning speed. The laser-irradiation times were calculated to be 1.0, 1.6, and 2.1 ms for the 33-μm-pitch MLA and 0.10, 0.25, and 0.50 ms for the 5-μm-pitch MLA. Then, for each condition, the MLA replication on the PMMA film was analyzed using a laser microscope (OLS4100, Olympus Corporation, Tokyo, Japan) and the filling ratio of the PMMA was calculated. The height within each cell of area 0.125 × 0.125 <sup>μ</sup>m2 was obtained using the laser microscope. The product of the height and area of each cell was then summed for each replicated microlens, and the sum was defined as the volume of the replicated microlens. The volume of the microlens was calculated for each concave master mold. The filling ratio was then defined as the volume of the replicated microlens as a percentage of the volume of the microlens on the concave master mold.

**Figure 3.** Schematics of (**a**) measurement of the pressing pressure and (**b**) replication by scanning the laser along a line.

#### **3. Results and Discussion**

#### *3.1. Replication of 33-μm-Pitch MLA*

Figure 4 shows the relationship between the filling ratio and the pressing pressure for each laser-irradiation time in the replication of the 33-μm-pitch MLA. In addition, Figure 4 shows laser microscopic images taken at pressing pressures of 10, 30, and 50 MPa for the laser-irradiation time of 1.6 ms, an image taken at a pressing pressure of 40 MPa and laser-irradiation time of 1.0 ms, and an image taken at a pressing pressure of 20 MPa and laser-irradiation time of 2.1 ms. The filling ratio increased with increasing pressing pressure and laser-irradiation time. This tendency showed that the higher the pressing pressure, the faster the PMMA flowed and filled the mold. When the pressing pressure was increased, the thermal contact resistance between the PMMA film and the Ni mold decreased. The temperature of the PMMA then increased because of the increase in heat input, and the viscosity of the PMMA decreased. This decrease in the viscosity allowed the PMMA to flow more easily. At a pressing pressure of 50 MPa, although the filling ratio was approximately 100% for the laser-irradiation times of 1.6 and 2.1 ms, it was only approximately 60% for the laser-irradiation time of 1.0 ms. This was due to the laser irradiation being insufficient for the laser-irradiation time of 1.0 ms. When the laser irradiation was insufficient, the depth of the PMMA experiencing a temperature exceeding *Tg* was smaller than the lens depth of the 33-μm-pitch MLA. The filling ratio was almost identical when the pressing pressure and laser-irradiation time were 40 MPa and 1.0 ms, 30 MPa and 1.6 ms, and 20 MPa and 2.1 ms, respectively. In the laser microscopy images obtained under these conditions, the height difference between the highest area and the center of the replicated microlens decreased with increasing laser-irradiation time. This tendency showed that the temperature of the PMMA exceeded *Tg* not only in the mold contact area but also in the noncontact area when sufficient laser irradiation was provided, causing the PMMA to flow in both the contact area and the noncontact area. On the other hand, when the laser irradiation was insufficient, the temperature of the PMMA only exceeded Tg in the contact area and the PMMA flowed only in the contact area. As can be seen in the result associated with an irradiation time of 2.1 ms and pressing pressure of 50 MPa, the filling

was almost perfect. The LATI process possibly did not reach 100% filling because of shrinkage due to rapid cooling after the laser irradiation. However, the filling was successful using the various pressing pressures applied in this study.

**Figure 4.** Filling ratio as a function of pressing pressure for each irradiation time in the replication of the 33-μm-pitch MLA.

#### *3.2. Replication of 5-μm-Pitch MLA*

Figure 5 shows the relationship between the filling ratio and the pressing pressure for each laser-irradiation time in the replication of the 5-μm-pitch MLA. In addition, Figure 5 shows laser microscopic images taken at pressing pressures of 10, 30, and 50 MPa for the laser-irradiation time of 0.25 ms, and an image taken at a pressing pressure of 50 MPa and laser-irradiation time of 0.10 ms. For the laser-irradiation times of 0.10 and 0.25 ms, the filling ratio increased with increasing pressing pressure and laser-irradiation time. For the laser-irradiation times of 0.25 and 0.50 ms, the filling ratio decreased for some pressing pressures. These decreases in the filling ratio may have been due to calculation errors because the PMMA filled the mold almost completely according to the laser microscopy image obtained at a pressing pressure of 50 MPa and laser-irradiation time of 0.25 ms. The filling ratio was approximately 60% at a pressing pressure of 50 MPa and laser-irradiation time of 0.10 ms. This is because the laser irradiation was insufficient for the laser-irradiation time of 0.10 ms. The filling ratio was almost identical when the pressing pressures and laser-irradiation times were 50 MPa and 0.10 ms, and 10 MPa and 0.25 ms, respectively. The laser microscopy images obtained under these conditions showed that the height difference between the highest area and the center of a replicated microlens was almost identical. This indicated that the temperature of the PMMA exceeded *Tg* not only in the mold contact area, but also in the noncontact area, causing the PMMA to flow from both the contact area and the noncontact area. For an irradiation time of 0.50 ms, the filling ratio was unstable up to approximately 5% throughout the range of pressing pressures. One of the reasons for this is the limitation in accuracy of the laser microscope. A 5% reduction corresponds to a 2% or 3% error in measured length, which equates to 100 or 150 nm error over 5 μm. To investigate this stability, more precise measurements, such as might be attained using an atomic force microscope (AFM), are necessary. The other reason for this 5% disparity is that the heated and low-viscosity area was deeper than shorter irradiation time and the effect of supplying the polymer from underneath and that of escaping the pressure to unirradiated area in planar direction.

**Figure 5.** Filling ratio as a function of pressing pressure for each irradiation time in the replication of the 5-μm-pitch MLA.

#### *3.3. Comparison of Surface Shapes during Imprinting*

This section discusses the differences in the shape of the polymer surfaces after undergoing the LATI process. As shown in Sections 3.1 and 3.2, the leading surface of the polymer in the cavity of the 33- and 5-μm-pitch MLAs showed double and single peaks in the cross-section view after imprinting, respectively. Figure 6 shows the schematic of the heat conduction and polymer flow for the 33- and 5-μm-pitch MLAs. In the larger cavity, the depth of the heated area was smaller than the scale of the cavity and the polymer near the contact surface preferentially decreased in viscosity and a resultant double peak was formed, as shown in Figure 6a. In the smaller cavity, the depth of the heated area was comparable to, or larger than, the scale of the cavity and all the polymer around the contact surface was heated and the resultant polymer flow caused a single peak as shown in Figure 6b. To more comprehensively analyze the polymer flow phenomena seen in Figure 6a,b, experiments should be conducted using MLA with other sizes ranging from between 33 and 5 μm pitch. Applying simulations that incorporate the modelling of viscoelastic body behavior [22–24] to the MLA imprinting process would also be useful. Furthermore, other parameters such as laser power, spot diameter, and offset temperature are important and further investigation of these parameters would expand the discussion.

**Figure 6.** Schematics showing heat conduction and polymer flow during the laser-assisted thermal imprinting (LATI) process applied to (**a**) 33-μm-pitch and (**b**) 5-μm-pitch MLAs.

#### **4. Conclusions**

33- and 5-μm-pitch MLAs were replicated on PMMA films using LATI. The effects of the laser-irradiation time, the pressing pressure, and the pattern size of the MLA were investigated by analyzing the replicated microlens and measuring the filling ratio. In the replication of the 33-μm-pitch MLA, the filling ratio increased with increasing pressing pressure and laser-irradiation time. However, for a laser-irradiation time of 1.0 ms, the PMMA did not fill the mold completely because of insufficient laser-irradiation even though the pressing pressure was increased to 50 MPa, which was the highest pressing pressure applied in this study. Furthermore, the area of the PMMA in which the temperature exceeded *Tg* and the flow of the PMMA varied with laser-irradiation time. In the replication of the 5-μm-pitch MLA, the filling ratio also increased with increasing pressing pressure and laser-irradiation time. By comparing the surface shapes during filling, it was found that the cross-sectional surface shape possessed a double and single peak in the 33- and 5-μm-pitch pattern, respectively. The depth of heated area of the 33-μm-pitch pattern was smaller than the pattern size, whereas that of the 5-μm-pitch pattern was comparable to or larger than the pattern size. Future experiments will need to be conducted with patterns of other sizes along with simulation modelling of heat conduction and polymer flow to expand on the current discussion. MLA performance characteristics, such as light-extraction efficiency, will also be verified as part of future work.

**Author Contributions:** Conceptualization, K.N.; methodology, K.N. and Y.Y.; validation, Y.Y.; data curation, Y.Y.; writing—original draft preparation, Y.Y.; writing—review and editing, K.N.; project administration and funding acquisition, M.N. and K.N.

**Funding:** This study was founded by JSPS KAKENHI Grant Numbers 24246027 and 26709004 from the Ministry of education, Culture, Sports, Science and Technology (MEXT), Japan.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*
