Birefringence and interface in sequential co‐injection molding of amorphous polymers: Simulation and experiment

Modelings of the interface distribution and flow‐induced residual stresses and birefringence in the sequential co‐injection molding (CIM) of a center‐gated disk were carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model the frozen‐in flow stresses in disks. The compressibility of melts is included in modeling of the packing and cooling stages and not in the filling stage. The thermally induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the relaxation modulus and strain‐optical coefficient functions of each polymer. The influence of the processing variables including melt and mold temperatures and volume of skin melt on the birefringence and interface distribution was analyzed for multilayered PS‐PC‐PS, PS‐PMMA‐PS, and PMMA–PC–PMMA molded disks obtained by CIM. The interface distribution and residual birefringence in the molded disks were measured. The measured interface distributions and the gapwise birefringence distributions in CIM disks were found to be in a fair agreement with the predicted interface distributions and the total residual birefringence obtained by the summation of the predicted frozen‐in flow and thermal birefringence. POLYM. ENG. SCI., 55:88–106, 2015. © 2014 Society of Plastics Engineers     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part II: Effects of processing conditions

The accompanying paper, Part I, has presented the physical modeling and basic numerical analysis results of the entire injection molding process, in particular with regard to both flow‐induced and thermally‐induced residual stress and birefringence in an injection molded center‐gated disk. The present paper, Part II, investigates the effects of various processing conditions of injection/compression molding process on the residual stress and birefringence. The birefringence is significantly affected by injection melt temperature, packing pressure and packing time. However, the thermally‐induced birefringence in the core region is insignificantly affected by most of the processing conditions. On the other hand, packing pressure, packing time and mold wall temperature affect the thermally‐induced residual stress rather significantly in the shell layer, but insignificantly in the core region. The residual stress in the shell layer is usually compressive, but could be tensile if the packing time is long, packing pressure is large, and the mold temperature is low. The lateral constraint type turns out to play an important role in determining the residual stress in the shell layer. Injection/compression molding has been found to reduce flow‐induced birefringence in comparison with the conventional injection molding process. In particular, mold closing velocity and initial opening thickness for the compression stage of injection/compression molding have significant effects on the flow‐induced birefringence, but not on the thermal residual stress and the thermally‐induced birefringence.     

Birefringence in injection‐compression molding of amorphous polymers: Simulation and experiment

The influence of the processing variables on the residual birefringence was analyzed for polystyrene and polycarbonate disks obtained by injection‐compression molding under various processing conditions. The processing variables studied were melt and mold temperatures, compression stroke, and switchover time. The modeling of flow‐induced residual stresses and birefringence of amorphous polymers in injection‐compression molded center‐gated disks was carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model frozen‐in flow stresses in moldings. The filling, compression, packing, and cooling stages were considered. Thermally‐induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the Young's relaxation modulus and strain‐optical coefficient functions. The residual birefringence in injection‐compression moldings was measured. The effects of various processing conditions on the measured and simulated birefringence distribution Δn and average transverse birefringence <n_rr?n_θθ> were elucidated. Comparison of the birefringence in disks manufactured by the injection molding and injection‐compression molding was made. The predicted and measured birefringence is found to be in fair agreement. POLYM. ENG. SCI., 2013. © 2013 Society of Plastics Engineers     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part I: Basic modeling and results for injection molding

The present study attempted to numerically predict both the flow‐induced and thermally‐induced residual stresses and birefringence in injection or injection/compression molded center‐gated disks. A numerical analysis system has been developed to simulate the entire process based on a physical modeling including a nonlinear viscoelastic fluid model, stress‐optical law, a linear viscoelastic solid model, free volume theory for density relaxation phenomena and a photoviscoelasticity and so on. Part I presents physical modeling and typical numerical analysis results of residual stresses and birefringence in the injection molded center‐gated disk. Typical distribution of thermal residual stresses indicates a tensile stress in the core and a compressive stress near the surface. However, depending on the processing condition and material properties, the residual stress sometimes becomes tensile on the surface, especially when fast cooling takes place near the mold surface, preventing the shrinkage from occurring. The birefringence distribution shows a double‐hump profile across the thickness with nonzero value at the center: the nonzero birefringence is found to be thermally induced, the outer peak due to the shear flow and subsequent stress relaxation during the filling stage and the inner peak due to the additional shear flow and stress relaxation during the packing stage. The combination of the flow‐induced and thermally‐induced birefringence makes the shape of predicted birefringence distribution quite similar to the experimental one.     

Simulation of injection‐compression molding for optical media

A numerical simulation of a coining type of injection‐compression molding is developed. A hybrid finite element/finite difference method is employed to model the temperature and pressure fields of the process using a non‐isothermal compressible flow model. Simulation results for CD‐R molding with respect to injection pressure and mold displacement are compared with experimental observations using an optical grade of polycarbonate. The simulation shows similar trends as experimental observations on the dependence of various processing parameters such as melt temperature, mold temperature, and packing pressure. However, the mold displacement measurement does not show the effect of punch delay time as does the simulation, and needs further investigation.     

Residual birefringence in modified polycarbonates

The residual birefringence in quenched and injection‐molded specimens of bisphenol‐A polycarbonate (BAPC) homopolymer and its copolymers with substituted bisphenol‐A is investigated. The chemical modifications lead to a different stressoptical behavior in the melt and glass state, which generates differences in the residual birefringence of molded specimens. In this way the origins of the residual birefringence can be interpreted in a better way. In quenched samples it is found that the level of birefringence depends on the stress‐optical coefficient in the glassy state, but the unbalance of the birefringence distributions scales with the stress‐optical coefficient in the melt state. This supports the idea that transient thermal stresses present during vitrification induce molecular orientation, which is responsible for the unbalance of the distributions. The residual birefringence distributions in injection‐molded specimens all display a broad plateau in the core, as is usually observed in BAPC. The level of the plateau is found to scale with the stress‐optical coefficient of the melt state. This is a proof for the interpretation of this plateau being induced by transient thermal stresses during vitrification and not by residual stresses. It cannot be eliminated by optimizing molding conditions but only by drastically reducing the stress‐optical coefficient in the melt state.     

Thermal birefringence in freely quenched multilayered slabs of amorphous polymers: Experiment and simulation

The simulation of the gapwise distribution of the thermally‐induced residual birefringence and stresses in freely‐quenched PS‐PC‐PS and PC‐PS‐PC multi‐layered slabs in water was carried out to calculate the gapwise distribution of the transient and residual birefringence. The modeling was based on the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation. The master curves for the Young's relaxation modulus and strain‐optical coefficient functions obtained earlier for PS and PC were used in the simulations. The obtained numerical results provided the evolution of the thermally‐induced stress and birefringence with time during and after quenching. The predicted gapwise residual birefringence distribution in these slabs was found to be in a fair agreement with the measured results. In addition, the gapwise distribution of the thermally‐induced residual birefringence in the multi‐layered PS‐PMMA‐PS, PMMA‐PS‐PMMA, PMMA‐PC‐PMMA, and PC‐PMMA‐PC slabs quenched from different initial temperatures was measured. Explanations were provided for the observed gapwise distribution of the thermal residual birefringence in each layer of these slabs including the effect of the initial temperature. POLYM. ENG. SCI., 54:2097–2111, 2014. © 2013 Society of Plastics Engineers     

Experimental investigation and numerical simulation of injection molding with micro‐features

Injection molding of thin plates of micro sized features was studied in order to manufacture micro‐fluidic devices for bioMEMS applications. Various types of mold inserts—CNC‐machined steel, epoxy photoresist, and photolithography and electroplating produced nickel molds—were fabricated and tested in injection molding. The feature size covers a range of 5 microns to several hundred microns. Issues such as surface roughness and sidewall draft angle of the mold insert were considered. Two optically clear thermoplastics, PMMA and optical quality polycarbonate, were processed at different mold and melt temperatures, injection speeds, shot sizes, and holding pressures. It was found that the injection speed and mold temperature in injection molding greatly affect the replication accuracy of microstructures on the metal mold inserts. The UV‐LIGA produced nickel mold with positive draft angles enabled successful demolding. Numerical simulation based on the 2D software C‐MOLD was performed on two types of cavity fillings: the radial flow and the undirectional flow. The simulation and experimental data were compared, showing correct qualitative predictions but discrepancies in the flow front profile and filled depth.     

Effect of process conditions on birefringence development in injection-molded parts. I. Numerical analysis

Analysis of the injection-molding process based on Leonov viscoelastic fluid model has been employed to study the effects of process conditions on the residual stress and birefringence development in injection-molded parts during the entire molding process. An integrated formulation was derived and numerically implemented to solve the nonisothermal, compressible, and viscoelastic nature of polymer melt flow. Simulations under process conditions of different melt temperatures, mold temperatures, filling speeds, and packing pressures are performed to predict the birefringence variation in both gapwise and planar direction. It has been found that melt temperature and the associated frozen layer thickness are the dominant factors that determine the birefringence development within the molded part. For a higher mold temperature, melt temperature, and injection speed, the averaged birefringence along gapwise direction is lower. The birefringence also increases significantly with the increased packing pressure especially along gate area. The simulated results show good consistency with those measured experimentally. © 1995 John Wiley & Sons, Inc.     

A study on the characteristics of antiplasticized polycarbonates and their optical disk substrates

The characteristics of antiplasticized polycarbonates (PC) and their optical disk substrates were investigated. Meta‐terphenyl (m‐tPh) was chosen as an antiplasticizer. Blends of PC with small amounts of added m‐tPh were injection molded to form optical disk substrates. The flow properties of the blends were significantly improved by the common plasticizing effect of antiplasticizer at the melt state. The effect also induced reduction in internal stress, causing birefringence of the substrate. The increased stiffness and decreased glass transition temperature of the antiplasticized PC caused better flatness of the substrate and better microreplication of the groove geometry, respectively. It also resulted in embrittlement of the substrates, known to be a typical characteristic of antiplasticization. The antiplasticizer decreased the water absorption of the blends and also caused increased stiffness of the blends. The increased stiffness was associated with the elimination of secondary mechanical loss transition at low temperatures. From these results, the ideal viscoelastic property behavior of a polymer for an optical disk substrate to achieve better microreplication, better flatness, and low birefringence was proposed; that is, exhibiting lower modulus above glass transition temperature and higher modulus at the regions below glass transition temperature for the polymer of interest. Polym. Eng. Sci. 44:1877–1884, 2004. © 2004 Society of Plastics Engineers.     

Study of birefringence character of injection- and compression-molded polycarbonate and its interpretation

Birefringence development in molded polycarbonate is of great importance in the manufacture of optical discs. It is important in characterizing birefringence to realize that we are dealing not with a scalar but with the anisotropy of the refractive index tensor–and with the orientation and shape of the refractive index ellipsoid. This usually varies heterogeneously; i.e., point-to-point through the thickness of molded parts. We present here an experimental study of the shapes and orientations of refractive index ellipsoids in injection- and compression-molded polycarbonate parts. We consider the variations in ellipsoid character as a function of molding conditions such as injection rate and quench. In injection-molded parts, the refractive index ellipsoid is coaxial with the flow direction in the center of the parts, but varies with position in the direction of the mold walls. In some cases, the extinction angle reaches a maximum at the mold wall and in other cases, there is an intermediate maximum. In the central “flow-thickness” direction plane, the transverse axis of the refractive index ellipsoid is perpendicular to this plane. The birefringence (in principal axis coordinates) in the flow-thickness direction plane exhibits an intermediate maximum whose position and magnitude vary with molding conditions. In some cases, multiple maxima exist. In compression-molded parts, a principal axis is normal to the mold wall. The results are interpreted in terms of the Rheo-Optical Law using flow-induced orientation and residual stress mechanisms. If the contribution of the residual stress to the birefringence can be subtracted, we may compute biaxial orientation factors. We do this for a case that has low residual quench stresses.     

Birefringence in gas‐assisted tubular injection moldings: Simulation and experiment

The influence of the processing variables on the birefringence and polymer/gas interface distribution is analyzed for polystyrene moldings obtained by gas‐assisted injection molding (GAIM) under various processing conditions. The processing variables studied were: melt and mold temperatures, shot size, gas pressure, injection speed, and gas‐delay time. Measurements and viscoelastic simulations of the radial distribution of birefringence components, Δn and n_rr ? n_θθ, the variation of the average birefringence, 〈n_zz ? n_θθ〉, along the molding and polymer/gas interface along the length of spiral‐shaped tubular moldings are presented. The polymer/gas interface distribution and flow stresses were simulated using a numerical scheme based on a hybrid finite element/finite difference/control volume method. The birefringence was calculated from the flow‐induced stresses using the stress‐optical rule. Simulations qualitatively agreed with measurements and correctly described theeffect of the processing variables on the birefringence andthe polymer/gas interface distribution in GAIM moldings. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

The birefringence and anisotropic planar shrinkage of polycarbonate/organoclay injection moldings

The main objective of the present work was the study of the effect of organoclay on planar shrinkage anisotropy of polymeric injection‐molded products by means of a rheological technique, in conjunction with birefringence measurements, performed on polycarbonate/organoclay samples. Polarized optical microscopy at elevated temperatures revealed that the birefringence due to the ordered‐silicate layers had a negative contribution to the overall birefringence of the samples. The maximum value of the calculated‐order parameter based on these results was found to be near unity, indicating an appreciable degree of flow alignment for the silicate layers. Different states of silicate layer orientation, with some layers aligned parallel to the in‐plane direction at the skin layer or partially tilted from the planar direction at the core region, were observed through the optical analysis along the thickness direction. The anisotropic shrinkage measurements showed that organoclay reduced both in‐flow and cross‐flow shrinkages, resulting in a low extent of planar shrinkage anisotropy. This can be attributed to the flow alignment of clay particles closely parallel to the in‐plane direction. Prolonged relaxation of the flow‐induced molecular orientation combined with faster solidification were also found to play an appreciable role in the decreased shrinkage anisotropy. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Modeling and experimental study of birefringence in injection molding of semicrystalline polymers

The prediction of birefringence developed in injection moldings is very important in order to satisfy required specification of molded products. A novel approach for the numerical simulation of the flow-induced crystallization and frozen-in birefringence in moldings of semicrystalline polymers was proposed. The approach was based on the calculation of elastic recovery that becomes frozen when the flow-induced crystallization occurred. The flow effect on the equilibrium melting temperature elevation due to the entropy reduction between the oriented and unoriented melts was incorporated to model crystallization. To find the entropy reduction and the frozen-in elastic recovery during crystallization, a non-linear viscoelastic constitutive equation was used. From the ultimate elastic recovery the crystalline orientation function was calculated. The crystalline and amorphous contributions to the overall birefringence were obtained from the crystalline orientation function and the flow birefringence, respectively. The birefringence profiles were measured and predicted in moldings of polypropylenes of different molecular weights obtained at various melt temperatures, injection speeds, holding times and mold temperatures. The resulting predictions were in fair agreement with corresponding experimental data.     

Numerical modeling of injection/compression molding for center-gated disk: Part II. Effect of compression stage

In the accompanying paper, Part I, we have presented a physical modeling and the associated numerical analysis of the injection molding process with a compressible viscoelastic fluid model. In Part II, effects of the compression stage in the injection/compression molding process are presented. Numerical results showed that the injection/compression molding process reduced birefringence as compared with the injection molding process. In this respect, the injection/compression molding process seems to be more suitable for manufacturing precise optical products of good optical quality than the injection molding process. Effects of the packing stage on the birefringence distribution in the injection/compression molding process were found to be similar to those in the injection molding process. Our numerical results show that the birefringence becomes smaller as the melt temperature gets higher and the closing velocity of the mold gets smaller with the flow rate and the mold temperature affecting the birefringence insignificantly. As far as the density distribution is concerned, the flow rate, melt temperature, and mold closing velocity have insignificant effects on the density distribution in comparison with the mold temperature.     

Elongation flow studies of DNA as a function of temperature

The response of T4‐phage DNA molecules to an elongational flow field was monitored by flow‐induced birefringence as a function of temperature. The flow‐induced birefringence observed in this study was localized in the pure elongational flow area with a critical strain rate, indicating that the birefringence was attributed to a coil–stretch transition of DNA molecules. The slight decrease in the birefringence intensity with increases in temperature to 40°C was explained by a thermal‐activation process. At temperatures above 50°C, flow‐induced birefringence decreased remarkably, and no birefringence was observed at temperatures above 60°C. After the flow experiments, ambient temperature was reduced back to room temperature, and flow experiments at room temperature were performed again. Flow‐induced birefringence was recovered almost completely in samples for which the first flow measurements were made at temperatures below 53°C. Irreversible changes were observed for samples for which the first flow experiments were performed at temperatures above 55°C. The temperature dependence of UV‐absorption spectra revealed that the double‐strand DNA helix began to partially untwine at a temperature over 50°C, and duplexes became almost completely untwined at a temperature over 55°C. A comparison of electrophoresis patterns for untwined molecules showed that flow‐induced scission of DNA molecules occurred in a sample solution in flow experiments performed at 65°C, while no molecular weight reduction was observed in the sample solution at 55°C. In this article, this difference between the untwined DNA molecules is discussed on the basis of the thermally activated bond scission (TABS) model. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 1357–1365, 2002     

The effect of injection molding process parameters on mechanical and fracture behavior of polycarbonate polymer

In this work, the mechanical and failure behavior of injection molded aviation standard optical grade polycarbonate (PC) was investigated through uniaxial tensile testing. The effect of different injection molding process parameters including injection velocity, packing pressure, cooling time, mold temperature, and melt temperature were determined to observe their effect on yield and postyield behavior of PC. Out of these examined parameters, the mold and melt temperature show significant effect on mechanical behavior of studied polymer. The yield and flow stresses in polymer increase with the increase in mold and melt temperature during injection molding. However, other process parameters i.e., packing pressure, injection velocity, and cooling time showed little effect on mechanical performance of the polymer. The molded specimens were annealed at different temperatures and residence time to evaluate its effect on mechanical behavior and fracture morphology. The yield stress increases gradually with the increase in annealing temperature and time. The annealing treatment also changed the failure mode of PC specimens from ductile to brittle. In addition to process parameters, the effect of increased loading rate was also undertaken which shows substantial effect on mechanical and failure behavior of PC. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44474.     

Production and analysis of injection molded micro‐optic components

Plastic micro‐optic components (smaller than 1 mm in overall dimension, with lenses on the order of 50 microns in radius) will be very useful in future digital imaging and MEMS technologies. Computational fluid dynamics (CFD) and finite element analysis (FEA) predicted the influence of different processing parameters upon the final shape of micro‐optic parts made from polystyrene, polycarbonate, and polymethylmethacrylate. Small‐scale phenomena such as surface tension and mold‐melt slip velocity were included in the models. The simulations were compared to physical parts, through birefringence and interferometry techniques, which permitted assessment of the computer modeling. The predicted radius of curvature trends match the measured trends, and the maximum difference between the predicted and corresponding measured radius of curvature was roughly 3.4%. The average difference between simulation and experiment for astigmatism and comatic aberration was less than 25%. Symmetry assumptions were tested and validated in more than 85% of the measured cases. Polym. Eng. Sci. 44:564–579, 2004. © 2004 Society of Plastics Engineers.     

注塑工艺对聚碳酸酯曲面透光件光学角偏差的影响

分析了注塑工艺参数、测试方位角和俯仰角对聚碳酸酯（PC）曲面薄壳透明制品光学角偏差的影响。考虑多方面影响机理,必须针对具体制品结构尺寸、材料、模具浇注系统和成型条件,才能获得最优成型工艺。塑化时,为保证熔体均匀并防止降解,螺杆转速宜在中速范围内,背压不宜过高（如4 MPa）,储料余量不宜过多;注射熔体温度选择285 ℃左右,模具温度90 ℃以上,略微升高温度有利于流动和松弛,使制品结构均匀而减小角偏差;保压促进流动致密,但过高则容易产生流痕,适度延长保压时间可均化密度和应力,获得高光学性能;所制备样品角偏差值在8′以下,可满足一般透明件要求。