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The thermal imprint process of polymer micro-patterning is widely applied in areas such as manufacturing of optical parts, solar energy, bio-mechanical devices and chemical chips. Polycarbonate (PC), as an amorphous polymer, is often used in thermoforming processes because of its good replication characteristics. In order to obtain replicas of the best quality, the imprint parameters (e.g., pressure, temperature, time,
Nowadays microstructures have a very wide range of applications. They are used for beam shaping, splitting and steering [
Hot embossing is the most popular manufacturing process, and is well suited for producing dedicated microstructures with high aspect ratios and small distortions [
filling ratio of microstructure [
non-uniform mold imprint [
adhesion between mold and polymer [
surface roughness [
long cycle time [
However, it is not enough to optimize the parameters of hot imprint process. It is also necessary to take into account the different technological equipment, materials,
The literature analysis shows that there is not enough information about polycarbonate material behavior in mechanical hot imprint processes. The imprint process involves finite temperature-dependent deformation of a thermoplastic material. As a result, it is costly to establish experimentally the process behavior for these materials, leading to a critical need for improved simulation capabilities. The material behavior is highly sensitive to variations of temperature and strain rate. Furthermore, numerical simulation is essential to push the limits of hot imprinting to smaller length scales where high precision is critical. The polymethyl methacrylate (PMMA) is most numerically analyzed at different temperatures and state of the material. Therefore, an elastoplastic polycarbonate material model is designed and analyzed by the finite element method in this paper. It is necessary to investigate the stress and strain state in each step of the process. The filling ratio of the polymer in the mechanical hot imprint process is studied based on numerical simulation and experimental research. Heating, imprinting, and demolding steps in the hot imprint process are investigated in detail by a numerical simulation study. Therefore the aim of this paper is to create finite element model (FEM) of a nickel mold hot imprint into polycarbonate, which corresponds to the experiment conditions.
The finite element model of the nickel mold hot imprint process into polycarbonate near the glass transition temperature, which is created with COMSOL Multiphysics 3.5a, is presented in this section. Many scientists divide the mechanical hot imprint process into four steps: heating, imprint, cooling and demolding. However we are making assumption that after the imprint step the temperature of polymer decreases very quickly. Therefore the cooling step was not analyzed separately. The scheme of the modified hot imprint process, which consists of three steps: heating, imprinting and demolding, is presented in
The modeling and simulation methodology by FEM, which includes geometrical modeling, boundary conditions, meshing, material properties, process conditions and governing equations is schematically presented in
The Green-Lagrange strain-displacement
Here
Heat transfer conductivity is described according to the formula:
COMSOL Multiphysics solves contact problems using an augmented Lagrangian method. This method is a combination of the penalty and Lagrange multiplier methods. This means a penalty method with penetration control. The system is solved by iteration from the determined displacement. These displacements caused by incremental loading, are stored and used to deform the structure to its current geometry. If the gap distance between the slave and master boundaries at a given equilibrium iteration is becoming negative (
Generally it is impractical to use FEM to analyze periodical micrometer-scale patterning of the mold, but if the cross-sectional shape of the mold is constant in one direction, as in
A two-dimensional (2-D) FEM model of a nickel mold (lamellar profile with period of 4 μm) and polycarbonate substrate with boundary conditions is presented in
The accuracy and convergence of the solution depends on the choice of mesh as well. The mesh of the model, using triangular elements, is presented in
Materials used for the mold and substrate, and their properties are listed in
Polycarbonate's density, thermal conductivity, heat capacity, elastic modulus and Poisson's ratio as functions of temperature were taken from COMSOL Multiphysics 3.5a material library (
In the polycarbonate during hot imprint process large deformations are induced. The micro hot imprint process is being performed near the glass transition temperature of polycarbonate, where it behaves like elasto-plastic material. The mold and substrate are restrained from moving in the
The polycarbonate material model with a nonlinear behavior is an elasto-plastic material, where the stress-strain relationship or the constitutive equation is:
Thermal strain depends on the present temperature
For elasto-plastic material:
The polycarbonate as an elasto-plastic material that has yield criterion and hardening model settings. The yield criterion is interpreted as an equivalent stress
The yield stress level is given by:
The polycarbonate
The hardening model is a phenomenon where yield stress increases with further plastic strain. Isotropic hardening has been proposed to define the modification of the yield surface during plastic deformation. Using this hardening model, it was assumed that the initial yield surface expands uniformly without distortion and translation as plastic flow occurs. The isotropic tangent modulus
The model was solved using heat transfer and the solid stress-strain application modes with thermal contact problem between nickel mold and polycarbonate. This multiphysical hot imprint model of polycarbonate includes the heat transport, structural mechanical stresses and strains resulting from the temperature distribution. It allows us to evaluate temperature distributions and stresses in the polycarbonate during the hot imprint process.
As described in the previous section, the hot imprint process was divided into three steps: heating, imprinting and demolding. The initial temperature of the mold and polycarbonate is 293 K, the same as the ambient temperature and the imprint force is equal to zero at the beginning of the heating step. In this step the temperature of the mold increases up to the chosen 421 K and through the initial contact between mold ridges and polycarbonate substrate it was preheated (
Polycarbonate is elastic, due to this the polymer from the contact area moves to the empty cavity of the mold. The cavity of the mold is partially filled with heated polycarbonate. After the heating a steady variation of temperature in the range from 295 K (in the bottom of polycarbonate) to 413 K (in the place of contact with the mold) was observed; this is presented by contour lines (
During the imprint step (
In the demolding step, the hot mold (
One of the most important qualitative parameters in a hot imprint process is the filling ratio of the mold's microrelief. It is defined as a ratio of filled area and total area of microstructure.
The elastic strain appears when the mold displacement reaches 0.21 μm, and plastic strain appears when the mold displacement reaches 0.9 μm and then when the mold is demolded residual strains appear in the polycarbonate.
The numerical model was verified experimentally. The same experimental scheme as in the numerical simulation was used. A lamellar microstructure of 4 μm period and 100 nm depth was replicated into polycarbonate (3 mm thickness) for 15 seconds at 148 °C and under 5 atm pressure. Flat embossing experiment was performed using a flat thermal pressure device (designed at the Institute of Materials Science of Kaunas University of Technology, Kaunas, Lithuania). The original construction ensures controlled pressure, force, temperature and exposure time (
In order to compare the area of the microstructure imprinted onto the polycarbonate with the area of the nickel mold, data from AFM measurements were used. Experimental results were integrated using Simpson's rule. Calculations show that the area not filled with polycarbonate is about 10%, whereas the theoretically empty area is 4%. Graphical comparison of the theoretical microrelief with the experimental one (red line) is presented in
A mathematical non-linear model of the hot imprint process of a nickel mold into polycarbonate was created using an elasto-plastic material model. The finite element model, implemented by COMSOL Multiphysics software, allows us to determine temperature fields, displacements and stresses in each step of the hot imprint process. The filling ratio of the mold is the main parameter of the replica's quality. Therefore dependence of the empty cavity
The finite element model was verified using experimental investigations. In the experimental and numerical results, lamellar form replicas were observed, and differences between experimentally and numerically obtained filling ratios are within allowable limits. In addition the average measured depth of the replica is about 100 nm, the same as the calculated value.
The research was supported by Lithuanian State Science and Studies Foundation and the Research Council of Lithuania.
The authors declare no conflict of interest.
Diagram of the mechanical hot imprint process.
The hot imprint process modeling.
Cross-sectional shape of (
Computational scheme of the nickel mold hot imprint into polycarbonate.
Finite element mesh of the system of nickel mold and polycarbonate.
Thermal dependencies of polycarbonate material properties (COMSOL Multiphysics 3.5a material library).
Von Mises stress distribution (color map, Pa) and temperature fields (in Kelvins) represented by lines in the polycarbonate after the heating process.
Distribution of total displacements (in meters) after heating process.
Von Mises stress distribution in the deformed polycarbonate (in Pa) and total displacements (in meter) represented by arrows after imprint step.
Areas of the permissible yield and profile of the experimental microrelief represented by the red line.
The dependence of non-filling cavity
(
Material properties of the mold and substrate.
Nickel | Polycarbonate | |
8.908 × 10^{3} | ||
90.9 | ||
13.4 × 10^{−6} | 6.5 × 10^{−5} | |
445 | ||
200 | ||
0.31 |