Bulk and surface molecular orientation distribution in injection-molded liquid crystalline polymers: experiment and simulation.
Thermotropic liquid crystalline polymers (TLCPs) offer excellent mechanical properties with low weight, and thus have potential for use in demanding structural applications (1). Widespread applications are, however, often hindered by potentially high molecular anisotropy in products, usually resulting in unbalanced or undesirable mechanical properties. Especially during injection molding, complex transient nonisothermal thermal and flow history can lead to complex molecular orientation states and a skin-core morphology within the finished parts (2-6). It is well known that a hierarchy of microstructures exists through the sample thickness (3), (7). Elucidation of the factors which govern development of molecular orientation distributions during injection molding, and, further, the ability to accurately simulate these processes are thus necessary prerequisites for optimal manufacturing of TLCP net-shaped molded parts.
The analytical technique most frequently used to map out molecular orientation states in injection-molded TLCPs is two-dimensional wide-angle X-ray scattering (2D-WAXS) in transmission mode (6-8). 2D-WAXS measurements average the molecular orientation across the entire sample thickness (3). In the past, the quantification of the skin layer orientation in a TLCP molded part has often involved the laborious use of 2D-WAXS on microtomed layers. (9), (10). This microtoming method, however, risks potential experimental artifacts associated with the local morphology and states of orientation being disturbed.
Two noninvasive analytical techniques have been used to probe molecular orientation near the sample surface. One is Fourier transform infrared attenuated total reflectance (FTIR-ATR), which probes depths to ~5 [micro]m. Surface orientation states in injection-molded tensile bars fabricated from Vectra [R] A950 of 6-hydroxy-2-naphthoic acid/6-hydroxybenzoic acid (HBA/HNA) random type copolyesters were determined by Pirnia and Sung (4) using FTIR-ATR dichroism. In addition to characterizing the surface orientation parameter, measurements were extended to intermediate layers and core by progressively removing material via milling. The results of a study of the surface orientation of injection-molded Vectra [R] B900 samples using similar methods has been reported by Besaad et al. (11).
A second complementary method of determining surface orientation is NEXAFS spectroscopy (5). NEXAFS is a synchrotron-based soft X-ray spectroscopy that is highly sensitive to the orientation of phenyl ring groups via the partial electron yield (PEY) of Auger electrons excited by 1s[right arrow] [phi]* transition of the C=C bonds. Surface layers with a thickness as small as 2-3 nm can be selectively characterized by using the PEY mode of NEXAFS measurements. This technique has been successfully used to characterize the surface orientation of a pre-commercial liquid-crystalline copolyester based on 4,4' -dihydroxy-[alpha]-methylstilbene [DH[alpha]MS] copolymerized with aromatic di-acids (3), (5). In the present work, a novel macro-driven six-axis sample manipulator was exploited to automatically translate and rotate samples through the required incident and azimuthal angles, enabling a more efficient and precise measurements at off-centerline locations where both the degree and direction of surface orientation must be determined. Surface orientation parameters are determined using an analysis scheme adopted from Pattison et al. (12) and may be directly compared with FTIR-ATR results.
Each of these experimental techniques probes different scales of microstructures within the material. In this article, we adopt the nomenclature used by Rendon et al. (3) to describe the general morphological features of TLCP moldings. Thus, the skin layer describes a specific morphological region of molded articles which includes both: (1) a highly aligned surface layer right at the outer most surface, associated with fountain-flow and rapid solidification at the mold/polymer interface and (2) a thicker "shear-dominated" region near the surface (~0.4 mm). The core is defined to be the region of the sample near the midplane, frequently characterized by weak or transverse orientation states. On the other hand, bulk refers to the orientation state or microstructures averaged across the entire sample thickness. By these definitions, 2D-WAXS in transmission reveals bulk orientation states at any point of interest whereas FTIR-ATR and NEXAFS are probes of surface orientation, albeit with different degrees of depth resolution (FTIR-ATR: ~5 [micro]m; NEXAFS: ~2 nm).
A unique component of this study is coordination of these experimental techniques with process simulations of the molecular orientation distribution in injection-molded TLCPs. Simulation of LCP dynamics under complex flow fields is a difficult task. Although considerable progress has been made to capture fine details of defect proliferation and polydomain textures in simple shear flows (13-15), it is still far out of reach to directly apply these intricate molecular-scale models to complex process flows. Consequently, here we consider the "polydomain" model by Larson and Doi (16) which is based on the linear Leslie-Ericksen theory (14). Distortional elastic interactions between "domains" are treated phenomenologically, ignoring all local details of the director field. Still, the model captures the most essential physics believed to be relevant to LCPs: director tumbling, inter-domain interactions mediated by distortional elasticity, and texture refinement (the tendency for tumbling under shear to produce new defects). More importantly, its relative simplicity allows for straightforward attack of process flows, something that is currently not possible with more sophisticated theories. In recent work, this mesoscopic model was successfully applied to predict the molecular orientation distribution of commercial TLCPs undergoing isothermal extrusion-fed channel flows (17). Here, we extend this simulation strategy to attempt predictions of skin and bulk molecular orientation distributions in TLCP injection moldings.
Materials and Fabrication
The TLCP used in this study (Fig. 1) is a random copolyester of 73 mol% of poly(hydroxy-benzoic acid) (HBA) and 27 mol% of poly (hydroxy1-naphthoic acid) (HNA), trade name Vectra [R] A950, supplied by Ticona (Florence, KY). It was an unfilled grade with [M.sub.w] and [T.sub.m] of 30,000 g/mol and 280[degrees]C, respectively.
[FIGURE 1 OMITTED]
Before injection molding, sample pellets were dried in a vacuum oven at 120[degrees]C for 20 h. Sample plaques were fabricated using a Boy 30T2 injection molding machine with controlled molding parameters. An insert mold, made by Master Precision Mold Technology (Greenville, MI), was also used. The molded plaque measures 50.8 mm (2") in length, 76.2 mm (3") in width, and 3.2 mm (1/8") in thickness. It was fabricated with a narrow port gate at the midpoint on the longer side, illustrated in Fig. 2a. Typically, the total cycle time was 47 s, the screw speed was 264 rpm, packing pressure was 280 bar (2.8 X [10.sup.7] Pa), the injection fill time was 1 s and cooling time was 16 s. Other process parameters were: injection pressure = 1390 bar, melt temperature = 290[degrees]C, and mold temperature = 45[degrees]C.
[FIGURE 2 OMITTED]
Because NEXAFS is highly sensitive to the surface region of sample plaques, molded plaques underwent extensive surface cleaning to remove any contaminants. The cleaning protocol in this study was performed using a 1% solution of Alconox Liqui-Nox [R] cleaning agent (White Plains, NY) in deionized water, sonicated with a Bransonic 220 ultrasonic cleaner (Danbury, CT) for a duration of 5 min. Both the initial presence of surface contamination and its removal were confirmed by atomic force microscopy (AFM) using a Topometrix 2000 AFM in oscillating mode. The same protocol was adopted in previous NEXAFS studies of TLCP moldings (3).
2D-WAXS and Data Analysis
A detailed map of bulk orientation was determined using transmission 2D-WAXS. Experiments were performed at beam line 5BM-D (DND-CAT) of the Advanced Photon Source at Argonne National Lab. The incident beam had an energy of 25 keV (wavelength 0.496 [Angstrom]), and size of 1 X 1 m[m.sup.2]. A MarCCD [R] detector was used to collect 2D-WAXS patterns at a resolution of 512 X 512 pixels, using a 10 s exposure time. Four characteristic regions were chosen to map out the bulk orientation distribution across the sample plaque (Fig. 2a), which include a vertical scan along the centerline of the plaque, and three horizontal scans evenly spaced by 13 mm (0.5") parallel to the long side. Because of the symmetric flow field with respect to the centerline, measurements on the half of the plaque suffice for this purpose.
Representative WAXS patterns exhibit anisotropy arising from molecular orientation induced by injection molding processing (Fig. 2b and c). As known from the fundamentals of X-ray scattering from rod-like LCP molecules (1), WAXS peaks are observed perpendicular to the average molecular orientation direction. A quantitative representation of the degree and direction of orientation at any particular location is facilitated by extracting a one dimensional azimuthal intensity scan, I([beta]), from a 2DWAXS pattern (Fig. 2c), and computing a second moment tensor of the azimuthal intensity distribution. This analysis scheme is adopted from previous work to elucidate the in situ molecular orientation distribution of a thermotropic liquid crystalline polymer undergoing isothermal extrusion-fed flows via wide-angle X-ray scattering (18). Each point in an azimuthal scan is represented by a unit vector, u, such that [u.sub.1] = cos [beta] and [u.sub.2] = sin [beta] ([beta] is the azimuthal angle measured from the primary filling direction, see Fig. 2c). The corresponding second moment tensor is then calculated by averaging the dyadic product uu weighted by the azimuthal intensity distribution, I([beta]):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where the angled brackets (...) indicate the averaged component. As an example, the 1-2 element is calculated according to:
<cos [beta] sin [beta]> = [[integral].sub.0.sup.2[pi]] cos [beta] sin [beta]I ([beta])d[beta]/[[integral].sub.0.sup.2[pi]] I ([beta])d[beta]. (2)
A background intensity value attributed to external parasitic scattering sources (e.g., air) was subtracted from all the other azimuthal intensity distributions prior to application of Eqs. 1 and 2. The baseline correction value was computed as the lowest intensity observed in the azimuthal intensity scan obtained from the scattering pattern with the highest anisotropy in the plaque.
The degree and direction of the orientation in the scattering pattern may be quantified from the second moment tensor analysis. The degree of orientation, or anisotropy factor (AF), is defined as the difference between the principal values of (uu):
AF = [[square root of](<[u.sub.1][u.sub.1]> - <[u.sub.2][u.sub.2]>).sup.2 + 4<[u.sub.1][u.sub.1]>, (3)
yielding AF = 1 in the limit of perfect orientation, while random molecular orientation yields AF = 0. At center-line locations, calculation of AF is simplified because the symmetry of flow field dictates that off-diagonal elements of (uu) are zero:
AF = <[u.sub.2][u.sub.2]> - <[u.sub.1][u.sub.1]>. (4)
In the limit of perfect orientation along the primary filling direction, AF = 1, whereas perfect orientation transverse to the filling direction yields AF = --1. Random molecular orientation again yields AF = 0.
The angle of orientation is computed from the eigenvector associated with the smaller principal value of the second moment tensor as follows:
[chi] = [tan.sup.-1]((-<[u.sub.1][u.sub.1]> + <[u.sub.2][u.sub.2]> + [[square root of](<[u.sub.1][u.sub.1]> - <[u.sub.2][u.sub.2]>).sup.2 + 4<[u.sub.1][u.sub.2]>.sup.2)/2<[u.sub.1][u.sub.2]>). (5)
NEXAFS and Data Analysis
NEXAFS experiments were performed at the NIST beam line U7A at the National Synchrotron Light Source at Brookhaven National Lab. The capabilities of this beam line have been described in detail elsewhere (12), (19). The soft X-ray beam is elliptically polarized with polarization factor of 85%. The beam line optics deliver an incident photon flux and energy resolution approximately of 5 X [10.sup.10] photons/s and 0.1 eV, respectively. NEXAFS PEY spectra were collected with a channeltron electron multiplier fitted with an electrostatic three-grid high-pass electron kinetic energy filter. A grid bias of--100 V was used.
In our experiments, a novel six-axis sample manipulator installed in the experimental chamber of U7A was utilized to facilitate the selection and scanning of incident and azimuthal rotations of the sample. Plaque samples were cut in half at their centerlines to provide the necessary clearance at the maximum translational and rotational displacements when using the six-axis manipulator. Symmetry of flow was assumed. Nine surface positions of a sample plaque (Fig. 2a) were interrogated; macros were programed to execute the necessary sample manipulations for the incident and azimuthal angle scans required to determine the surface orientation direction and corresponding surface order parameter, S, at each position. This approach totally eliminates the laborious manual rotation of small sample squares cut from plaques at positions of interest previously used to elucidate the molecular orientation at off-centerline locations (3). A correction scheme was implemented to offset the displacement of the illuminated spot on the sample surface caused by the azimuthal and vertical rotation of the sample plaque, allowing the X-ray beam to hit the exact same spot each time the sample was rotated azimuthally and the incident angle was adjusted.
The preferential orientation of the copolyester polymer molecules in the surface region (~2 nm) was examined with the PEY signals obtained as described above. Details of the technique as applied to semifluorinated polymers and a pre-commercial liquid crystalline polymer appear elsewhere (3), (5), (19), (20). At each location, and for each azimuthal sample angle, [phi], PEY spectra for the carbon K edge were collected for incident angles (relative to the sample surface) [theta] = 30[degrees], 40[degrees], 50[degrees], 60[degrees], 70[degrees], 80[degrees], and 90[degrees]. Spectra in the energy range of 280 eV-315 eV were then normalized by the incident energy flux, and the relative intensities, I([theta]), for the 1s[right arrow][pih] * peak associated with the phenol ring C=C bonds were recorded. Representative PEY spectra collected on a centerline location show that the [phi.sup.*] (C=C) peaks from the in-plane phenol rings are minimized when the polarized beam is perpendicular to the surface, i.e., [theta] = 90[degrees] and the complementary [sigma] orbital peaks are maximized (Fig. 3a). According to Stohr and Samant (21), the peak intensities I([theta]) should follow:
[FIGURE 3 OMITTED]
I([theta]) = A + B [sin.sup.2] [theta] (6)
regardless of the degree of orientation. The coefficients A and B are extracted from plots of peak intensity according to Eq. 6 (Fig. 3b), and may, in turn, be converted to a surface molecular order parameter, [S.sub.surface], using an expression developed by Kramer and coworkers (3), (12):
[S.sub.surface] = (1 - 2(A + B)/A + B/6P (3P - 1) (7)
where P is the polarization factor of the elliptically polarized X-ray (0.85 for the experiments reported here). In this definition, [S.sub.surface] = 0 describes the case where the molecules are randomly oriented along the sample surface. When [S.sub.surface] is positive, it is due to the alignment of the molecular axes along the examined direction while [S.sub.surface], = 1 indicates perfect alignment of the polymer molecules in that direction. The incident angle range of 30-90[degrees] was selected to reduce secondary effects that may be induced by minor surface roughness or instrumental anomalies (3), (5) This angular range yielded the most consistently linear behavior in plots according to Eq. 6, with the best confidence limits for the slope, B. Equation 7 will yield a maximum in molecular orientation when the plane of incidence aligns with the preferential surface orientation direction. Along the centerline, symmetry dictates that molecular orientation lie along the filling direction. At positions away from the centerline, however, the surface orientation direction was determined by rotating sample plaque azimuthally (i.e., rotation about the sample normal, indicated by angle [empty set] in Fig. 3a) via six-axis sample manipulator with an increment of 5[degrees] and recording each set of corresponding PEY scans. The particular azimuthal rotation angle associated with maximal [S.sub.surface] reveals the surface orientation angle.
FTIR-ATR Dichroism and Data Analysis
The sample surface orientation was also analyzed by infrared spectroscopy using the Seagull[R] Variable Angle Reflectance Accessory in a Thermo-Nicolet Nexus 670 FTIR spectrometer. The Seagull was equipped with a Ming-Sung ATR Rotator, a ZnSe ATR crystal, and a wire grid polarizer. The polarizer was set for s-polarization and the Seagull accessory was set for an incident angle of 55[degrees]. This incident angle was selected to be slightly above the experimental critical angle for the samples examined. Each sample was oriented on the sampling stage of the ATR Rotator so its cut edges corresponded to the 0[degrees] and 90[degrees] settings. A background spectrum was recorded using the ATR crystal without a mounted sample, and then sample spectra were collected with the ATR Rotator set at positions ranging from -10[degrees] to 90[degrees] in 10[degrees] increments. Spectra were collected over a wavenumber range from 4000 [cm.sup.-1] to 650 [cm.sup.-1], with 4 [cm.sup.-1] resolution, and were signal averaged over 32 scans. Data were analyzed using the OMNIC Software, V.6.1A provided by Nicolet.
Considerable effort was expended to resolve any instrumental issues and assure the reproducibility of the data. Specifically, it was found that: (1) the use of a calibrated torque wrench to reproducibly tighten the sample back plate of the Seagull ZnSe ATR crystal stage and (2) using samples molded or milled (on the back side) to a thickness of less than 1.6 mm, are critical in obtaining the good crystal to surface contact required for reproducible results.
Nine square samples (roughly 1 cm by 1 cm) were cut from positions in the plaques corresponding to those studied using NEXAFS. The ATR spectra were converted to absorbance units and baseline corrected. Two examples of spectra (collected on an off-center location, denoted by the symbol * in Fig. 2a) taken perpendicular [A] and parallel [B] to the preferential orientation are shown in Fig. 4; absorption bands were assigned based on literature reports (4), (22), (23). From these data, dichroic ratios were determined using the 1504 [cm.sup.-1] absorption band associated with in-plane aromatic ring bending. Orientation functions ([[Florin].sub.xy]) were calculated from the acquired dichroic ratios ([D.sub.xy] = [A.sub.x]/[A.sub.y]) as described by Pirnia and Sung (4), where [A.sub.x] and [A.sub.y] are the absorbances parallel and perpendicular to the principle molecular orientation, respectively. The orientation function ([Florin]) is defined as
[FIGURE 4 OMITTED]
The orientation function should be comparable to the order parameter ([S.sub.surface]) measured using NEXAFS. Similarly, [Florin] is equal to 1.0 for perfect flow direction orientation and zero for random orientation. As with NEXAFS, the surface orientation direction was inferred through azi-muthal rotation of the sample, finding the sample rotation angle which maximized [Florin], yielding measurements of both the degree and direction of surface orientation at each of the nine interrogated positions (Fig. 2a).
Our simulations employ the Larson-Doi model (16), which describes the orientation of textured "polydomain" LCPs under flow. As in recent work evaluating Larson-Doi model predictions of TLCP orientation distributions in isothermal extrusion-fed channel flows (17), we draw upon an analogy with fiber orientation models to facilitate simulations of orientation during injection molding using commercial software tools. Complete details on this approach may be found in that study (17).
The simplest theory to predict TLCP dynamics under flow is the Ericksen model (24), written as an evolution equation for the nematic director, n, which indicates the direction about which molecules are spontaneously ordered in the liquid crystalline state:
[partial derivative]n/[partial derivative]t = n [omega] + [lambda](n D - nnn: D). (9)
Here, D and [omega] are, respectively, the rate of deformation and vorticity tensors, and [lambda] is a material constant known as the tumbling parameter. Direct measurements of [lambda] have not been possible in commercial TLCPs. However, the molecular orientation behavior observed in simple shear and complex channel flows suggests that they are of the tumbling type (6), (18), (25-27), corresponding to |[lambda]| < 1. In this case, Eq. 9 is identical to the equation governing the orientation of an isolated, axisymmetric particle suspended in a viscous liquid under flow (28) (in which case [lambda] is determined by the particle's aspect ratio). This analogy is central to our modeling strategy.
Because the fundamental hydrodynamics of the nematic director and elongated particles are identical (Eq, 9), there is a nearly exact analogy between the Larson-Doi polydomain model for liquid crystal polymers and the Folgar-Tucker fiber orientation model (29) widely used in composites processing. Both models are written as evolution equations for the second moment tensor of the orientation distribution function:
D/Dt <nn> = [[omega].sup.T] * <nn> + <nn> * [omega] + [lambda](D * <nn> + <nn> * D - 2 <nnn>: D) + Interaction term, (10)
<nn> = [integral] nn[psi] (n)dn = T. (11)
For later convenience, T is introduced as shorthand for the second moment tensor. The hydrodynamic terms are identical between the two models. The appearance of the fourth moment tensor in Eq. 10 necessitates the use of a closure approximation. Larson and Doi adopted the simplest quadratic closure, but a large variety of candidate closures have been developed and evaluated for the case of fiber orientation modeling (30).
Each model includes an interaction term. In the Fulgar-Tucker model, hydrodynamic interactions between fibers are modeled as an effective rotational diffusivity that is proportional to shear rate * [gamma]:
Interaction term = -6[C.sub.I[gamma]] (<nn> - 1/3 I) (12)
The strength of the interactions is governed by an interaction coefficient, [C.sub.1]. A similar term appears in the Larson-Doi model, in this case intended to model interdomain interactions mediated by distortional elasticity:
Interaction term = [epsilon]l (<nn> -1/3I) (13)
The parameter [epsilon] controls the strength of these inter-domain interactions. Since distortional elastic effects depend on the length scale of the texture, an additional variable, l, is introduced in this expression, representing a defect density. This variable obeys its own evolution equation:
dl/dt = [l.sub.[gamma]] - [l.sup.2] (14)
In steady flows, Eq. 14 predicts that l = * [gamma]; that is, defect density increases with increasing shear rate, a phenomenon known as "texture refinement" (31). For steady, homogenous flows, the analogy between the Larson-Doi and Fulgar-Tucker models is exact. Here, we make an additional assumption that l = * [gamma] even in unsteady flow, such that the defect density remains instantaneously equilibrated to the local deformation rate. Since the Folgar-Tucker model is widely implemented in commercial polymer process simulators, this analogy facilitates direct application of existing software tools to perform the Larson-Doi simulations of interest.
Our simulations were performed using Moldflow MPI[R], a commercial software package that predicts flow fields during injection molding processing. This software incorporates the Folgar-Tucker fiber orientation model, allowing for corresponding microstructural predictions. Simulations were performed using a "2.5D" mid-plane simulation method based on a Hele-Shaw approximation (32). For the plaque geometry considered here, this approach reduces computational effort while retaining a realistic description of the spatially varying mixed shear-extensional kinematics that are believed to be responsible for the orientation patterns generated during molding (6).
The desired plaque geometry and associated mid-plane mesh were generated by tools within the MPI software suite. Process variables were chosen to match the real injection molding process, including filling time (1 s), cooling time (16 s), melt temperature (290[degrees]C), and mold temperature (45[degrees]C). The key parameters in the Larson-Doi model are the tumbling parameter, [lambda], and the elasticity parameter, [epsilon]. Although the former is, in principle, a unique material property, quantitative measurements are extremely rare (33) and nonexistent for commercial TLCPs. The latter parameter is purely phenomenological. On the basis of our previous parametric studies (17), the simulations reported here used [lambda] = 0.95 and [epsilon] = 0.03, values that captured the orientation behavior of TLCPs in steady channel flows. These values were implemented through appropriate selection of the relevant parameters in the fiber orientation model (fiber aspect ratio and interaction coefficient, [C.sub.1],). Simulations were performed using the "orthotropic 4" closure approximation (17), (34).
In presenting and discussing computed orientation states, we adopt a Cartesian coordinate system in which "x" denotes the filling direction and "z" denotes the thin dimension of the plaque. In both surface and bulk orientation measurements, the molecular orientation state is probed in the x-y plane. As a result, the following two-dimensional projection of the orientation tensor contains the relevant information for comparison to experimental data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
Since X-ray scattering data reflect bulk orientation states averaged through the sample thickness, we report simulation results in terms of the thickness-averaged orientation tensor, (T). At any desired location on the plaque, the difference in the principal values of (T) provides a quantitative measure of the average degree of anisotropy:
Anisotropy factor = [[square root of](<T.sub.xx> - <T.sub.yy>).sup.2 + 4<T.sub.xy>.sup.2], (16)
while the average direction of molecular orientation is obtained from the principal directions of (T) within the x-y plane. Defined by Eq. 16, the anisotropy factor ranges from 0 for a random isotropic distribution of orientation, to 1 for the perfect domain alignment in the x-y plane. Along the centerline axis of a symmetric flow field, the principal directions will coincide with the x and y coordinate axes. This allows a simpler measure of anisotropy factor, ([T.sub.xx]) - ([T.sub.yy]), which can range from +1 for perfect alignment along the x-direction, to -1 for perfect alignment along the transverse, v-direction. The similar definition of anisotropy factor derived from 2D-WAXS experiments facilitates direct quantitative comparison between experimental data and simulations. However, it is important to recognize that these polydomain simulations (and the associated second moment description of the orientation) only treat the distribution of director orientation. Conversely, experimental data also reflect the local spread of molecular orientation with respect to the director (as characterized by the molecular order parameter (35)). As a result, it is anticipated that that anisotropy predicted by simulations will be systematically higher than corresponding experimental measures of molecular orientation. Predicted orientation distributions were extracted from the simulations at the same locations studied experimentally. (Fig. 2).
To obtain depth-resolved information on the molecular orientation state, the plaque thickness was discretized into 20 discrete laminae in the z-direction. Orientation distributions calculated in channel flow demonstrate that Larson-Doi simulations are capable of realistically predicting differences in orientation between a shear-dominated "skin" and the "core" where superimposed extension can dominate (17). Given the high surface specificity of the spectroscopies used here (~2 nm and ~5 [micro]m for NEXAFS and FTIR-ATR, respectively), however, even the finest depth discretization possible within the software cannot provide direct predictions of the experimentally measured surface orientation states. Further, although the standard "midplane" simulation approach used here provides a realistic description of kinematics away from the filling front, it fails to predict three-dimensional phenomena like fountain flow, which are expected to strongly impact surface orientation. Previous NEXAFS and 2DWAXS studies on a pre-commercial TLCP revealed that the orientation in the aligned surface layer closely follows that of the thicker shear-dominated skin region (3). As a first test of ability of Larson-Doi simulations to capture aspects of the surface orientation distribution, we extract predictions of skin orientation from the outermost simulation laminae, using procedures described in detail in reference (17).
RESULTS AND DISCUSSION
Bulk Orientation Distribution
Because of the comparative ease of 2D-WAXS experiments, detailed measurements of bulk molecular orientation in the injection-molded plaque were obtained along the centerline and in transverse scans. Two-dimensional vector plots provide an informative survey of the measured orientation distribution (Fig. 5a). In this representation, the length of the lines/vectors is proportional to the average degree of molecular orientation, whereas their direction denotes the average direction at that particular location. Model predictions (Fig. 5b) capture the major features of the bulk orientation distribution measured experimentally. The molecular orientation generally tracks the local streamlines expected during mold filling. Computed anisotropy values are somewhat larger than experimental data, as expected due to the fact that the model predictions do not account for the local distribution of molecular orientation around the director. The degree of orientation is suppressed in much of the plaque, but enhanced in the edge regions far away from the center-line. This behavior has been attributed to the variations in both shear and extension as a function of depth in the plaque (6), (18). During mold filling, shear rate vanishes in the midplane of the mold cavity. Extension transverse to the filling direction in the core region leads to a reduction in overall orientation. Toward the edges of the mold cavity, this transverse stretching should vanish, leading to enhanced orientation along the local flow direction. Similar orientation states were found in injection-molded DH[alpha]MS copolyester plaques by Rendon et al. (6), echoing qualitative characteristics of orientation fields measured in diverging isothermal channel flows (6), (18). The influence of transverse extension is most apparent along the centerline. Near the injection gate, the strong transverse stretching renders the orientation distribution nearly isotropic. Toward the end of the plaque, the orientation state clearly flips; in this region, shear rates vanish, while transverse stretching becomes very strong owing to the presence of a stagnation point. These effects are manifested in both experiments and simulations, albeit to varying degrees.
[FIGURE 5 OMITTED]
Although the vector plots of Fig. 5 are informative, detailed quantitative comparison between experimental measurements and model predictions provides deeper understanding on the spatial molecular orientation states along the plaque, and is a more stringent test of the performance of Larson-Doi model in TLCP injection molding. The model captures the qualitative features of centerline orientation distributions quite well (Fig. 6; here, Eq. 4 is used in computing anisotropy factor). Immediately following the injection gate, the average molecular orientation is low due to the strong transverse extensional flow induced by the drastic expansion in flow cross section as polymer exits the narrow gate. MOLDFLOW [R] assumes a random orientation state at the inlet, whereas in reality, one anticipates some orientation generated by upstream shearing. This difference may account for the strong negative values predicted in the Larson-Doi simulations in this region. In the near downstream, ~20-30 mm away from the injection gate, a maximal degree of molecular orientation is found. The reason is that the strong transverse extensional flow at the gate disappears in the downstream region, while shearing persists. This promotes growth in the degree of orientation. After this maximum is reached around the midpoint on the centerline, an indistinct plateau emerges, and after that the bulk orientation state starts to degrade. Approximately 40 mm downstream from the injection gate, the anisotropy factor changes sign, indicating a flipping in bulk alignment from the filling direction to the transverse direction. The anisotropy factor ultimately becomes strongly negative at the end of the mold cavity as the stagnation point at the end of the plaque is reached. This behavior is very similar to that found in previous work on similar DH[alpha]MS moldings (6). In this stagnation region, the TLCP can experience arbitrarily large extensional strains, while shear rates vanish. As a result, transverse extension over whelms shear, and the orientation flips. Although the Larson-Doi simulations capture each of these features qualitatively, it under predicts the magnitude of the orientational "flipping" that takes place near the end of the mold cavity.
[FIGURE 6 OMITTED]
Away from the centerline, both the degree and direction of the bulk molecular orientation vary in a complex way due to the spatially varying competition between shear and extension (Figs. 7 and 8). Larson-Doi simulations (Fig. 7b) again capture the qualitative features of the experimentally measured bulk anisotropy factor distribution (Fig. 7a). As noted earlier, simulated anisotropy values are generally somewhat larger than their experimental counterparts, particularly apparent in regions further away (~30 mm) from the centerline where high degrees of molecular orientation are both predicted and observed. These cross sectional data again demonstrate the generally low degree of bulk orientation in much of the plaque, resulting from competition between shear and transverse stretching (6), (18). An enhancement in anisotropy factor clearly demonstrates the dominance of shearing kinematics over extension in regions near to the plaque edge.
[FIGURE 7 OMITTED]
At the farthest downstream region studied (38 mm away from the injection gate, square symbols) the bulk orientation state exhibits a local minimum ~20 mm away from the centerline, then a local maximum (~10 mm away from the centerline) before reaching a minimum value at the centerline. Although not reproducing the full amplitude of these inflections, the Larson-Doi simulations capture this trend quite faithfully. The discrepancy is particularly evident near the centerline, where, as previously noted, the simulations under predict the influence of transverse extension as the stagnation point is approached.
Data and predictions of the average bulk orientation angle also demonstrate the strong performance of the Larson-Doi model in predicting fine details of the molecular orientation distribution (Fig. 8). The positive angles reflect the clockwise rotation of the average orientation direction observed away from the centerline in the right hand portion of the plaque where data were collected. There is excellent qualitative and quantitative agreement between simulations and experiments for the orientation angle distributions measured at the first two cross sectional locations (13 and 25 mm downstream of the injection gate, circles, and triangles, respectively). At both centerline and edge, the orientation is essentially parallel to the x-axis, while rotating substantially away from this direction at intermediate due to the spreading of the polymer melt as it fills the mold. Moving from 13 to 25 mm, the molecular orientation progressively aligns towards the dominant filling direction (maximum orientation angle drops from ~46[degrees] to 25[degrees] in both experiment and simulation) due to the increasing dominance of shear in determining the orientation state. At the farthest downstream location studied (38 mm away from the injection gate, squares), greater discrepancies between experiment and simulation are found. As in the case of the anisotropy factor data (Fig. 7), the experimental data show more dramatic inflections in the orientation angle distribution in this region. The fact that discrepancies are largest in the region close to the end of the mold cavity suggests that details of the end stages of the mold filling process are not being completely captured in the simulations. To further explore this issue, we plan further experiments and simulations on "short shot" plaques to test model performance prior to the point where the melt impinges on the end of the cavity.
[FIGURE 8 OMITTED]
Surface Orientation Distribution
FTIR-ATR and NEXAFS were utilized to map out the surface orientation distribution at nine representative centerline and off-center locations (Fig. 9). It is the first time that these two techniques, both sensitive to the orientation near to the top surface, are compared and further validated by each other. The surface orientation distributions are shown by vector plots, constructed in a similar way as the bulk orientation vector plots presented in Fig. 5, with the length of the vectors proportional to the average degree of molecular orientation, while its direction denotes the average direction at that particular location. Numerical values of surface angle and orientation parameters are also listed for each location to facilitate quantitative comparisons. Clearly, the surface orientation distributions from NEXAFS (Fig. 9a) and FTIR-ATR (Fig. 9b) demonstrate good agreement with each other despite the different depths that are naturally probed using these two techniques. This is consistent with earlier observations that surface orientation closely tracks that found in the thicker skin layer encompassing both the immediate surface layer (examined here by NEXAFS and FTIR-ATR) as well as the thicker shear-dominated region (3), (6) The measured surface order parameters are quite large (typically ~0.7 or greater), comparable to the highest degree of orientation found in bulk orientation experiments (Figs. 6 and 7).
[FIGURE 9 OMITTED]
It is believed that highly aligned surface layers are produced by "fountain flow" and fast solidification during the mold filling (2), (6). In accord with this concept, the surface orientation states at the farthest downstream location do not degrade, in contrast to the bulk orientation distribution where transverse extension generated as melt impinges on the end of the mold cavity leads to actual flipping of molecular orientation. Similarly, at locations close to the plaque edge (the three points farthest away from the centerline), the surface orientation state does not align towards the prevailing filling (x) direction observed in bulk orientation states (Fig. 5). At these locations, polymer molecules at the surface have large azimuthal orientation angles relative to the centerline, ranging from 30 to 60[degrees]. This evidence strongly supports the argument that the surface orientation states were set by rapid solidification experienced at the mold front during filling. Thus, the azimuthal orientation angles measured via FTIR-ATR and NEXAFS are set at the moment when polymer molecules were first injected into the mold cavity. Most notably, the orientation angle measured by FTIR-ATR and NEXAFS equals 30[degrees] at the point farthest away from both the injection gate and the centerline, which decidedly differs from that (near 0[degrees]) found in bulk 2D-WAXS measurements (Fig. 8). For the example shown (Fig. 9), the directions of maximum orientation obtained by FTIR-ATR in the region of the lower right side of the plaque are often rotated away from the centerline clockwise by roughly 10[degrees] compared to those obtained using NEXAFS. This is possibly due to an increased contribution from extensional flow at the greater depth below the surface to which FTIR-ATR probes (~5 [micro]m).
Bulk Versus Surface Orientation Distribution
There are significant differences between experimentally measured bulk and surface orientation distributions (Fig. 10a; here, we select the NEXAFS data to represent the surface orientation state for comparison to bulk 2D-WAXS results). To further explore relationship between bulk and surface orientation states, we turn to the depth-resolved orientation state predictions from the simulations. As discussed earlier, the limited depth resolution possible within MOLDFLOW [R], and the simplifications imposed by the Hele-Shaw approximation used in these simulations, do not allow direct simulation of orientation in the extremely thin surface layers interrogated by NEXAFS and FTIR-ATR. As a starting point, we instead extract the computed orientation state associated with the thicker, shear-dominated skin region (~0.4 mm or ~15% of the plaque thickness), using procedures described in detail elsewhere (17). According to the previous work on DH[alpha]MS plaques with the same geometry, the magnitude of molecular orientation in the skin region is somewhat lower than that present in the surface layers, but their orientation angles agree well with each other (3). In other words, successful prediction of how orientation evolves in the skin region may be hoped to yield relevant information in the surface region.
Indeed, Larson-Doi model predictions of the relative degree and direction of bulk versus skin orientation states (Fig. 10b) successfully predict the main features of the bulk versus surface orientation distributions measured across the molded plaque (Fig. 10a). As previously noted, bulk simulation data (solid vectors) demonstrate somewhat stronger alignment than the 2D-WAXS measurements. Conversely, skin simulation data (gray vectors), show somewhat weaker alignment than the NEXAFS measurements. This discrepancy is most likely related to the neglect of important physics associated with polymer stretching and solidification at the mold front in the modeling approach used here.
[FIGURE 10 OMITTED]
Figure 10 illustrates the strong--and dissimilar--spatial dependences of bulk and surface/skin orientation across the sample plaque. Along the centerline, molecules tend to flip due to strong transverse stretching as they approach the stagnation point at the end of mold cavity, leading to low bulk anisotropy factors. There is, however, no trace of these extensional flow effects on the surface/ skin orientation. In the middle vertical region studied (~17 mm away from the centerline, but not too close to the edge), bulk and surface/skin orientation angles are in good agreement with each other, although the corresponding degrees of orientation are very different owing to the depth dependence of the degree of molecular orientation. Closest to the plaque edge (~28 mm away from the centerline), bulk and surface/skin orientation states differ strongly in both degree and direction of orientation. Although the surface/skin orientation state is set at the point of rapid solidification of the materials adjacent to the cold mold cavity wall as the melt front first arrives, the bulk orientation state continues to evolve with further mold filling, receive a strong influence of the dominant shearing kinematics near to the edge bringing the orientation direction closer to the vertical filling direction.
Larson-Doi simulations successfully predict many fine details in the bulk and surface/skin orientation distributions induced during injection molding of commercial liquid crystalline polymers. This success is in some sense remarkable given the range of assumptions and approximations implicit in these calculations, such as decoupling of fluid mechanics and microstructural evolution, setting defect density equal to the local instantaneous shear rate (l = [gamma]) and so on. These simulation results also demonstrate the effectiveness of the fiber model analogy, which allowed simulations to be readily performed using existing and commercially available software.
Three analytical experimental techniques interrogated the molecular orientation state over different scales, yielding insights into the spatial and depth dependence of the molecular orientation state. NEXAFS and FTIR-ATR produced similar pictures of the surface orientation distributions, despite differences in their intrinsic depth sensitivity (~2 nm and ~5 [micro]m, respectively). The fairly good agreement between these methods provides the first extensive consistently check between these two noninvasive, highly surface-sensitive techniques.
Skin orientation predictions (to a depth of ~0.4 mm) from Larson-Doi simulations capture many features present in the NEXAFS and FTIR-ATR data, reinforcing a previous suggestion that orientation in skin and surface regions are closely related (3), (6). Thus, simulations of skin orientation provide a computationally economical estimate of surface orientation distributions.
The NEXAFS experiments were carried out at the NIST/Dow Soft X-ray Materials Characterization Facility at beam line U7A at the National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the United States Department of Energy, Division of Materials Sciences and Chemical Sciences. Wide-angle X-ray scattering experiments were conducted at the DuPont-Northwestern-Dow Collaborative Access Team (DND-CAT) Synchrotron Research Center located at Sector 5 of the Advanced Photon Source of Argonne National Laboratory. DND-CAT is supported by the E.I. DuPont de Nemours & Co. the Dow Chemical Company, and the National Science Foundation through Grant DMR-9304725 and the State of Illinois through the Department of Commerce and the Board of Higher Education Grant IBHE HECA NWU 96. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Basic Energy Sciences, Office of Energy Research, under Contract No. W-31-102-Eng-38. The authors thank Lowell Thomas (M.M.I.) for his assistance in sample fabrication, Kathey Robertson (M.M.I.) and Dick Nyquist for their assistance in the IR measurements and the assignment of absorption bands, and Judy Eastland (M.M.I.) for library support. The authors thank Ticona for their kind donation of Vectra A950. Certain commercial equipment is identified in the article in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the items identified are necessarily the best available for the purpose.
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Jun Fang, (1) Wesley R. Burghardt, (1) Robert A. Bubeck, (2) Susan M. Burgard, (2), (3) Daniel A. Fischer (4)
(1) Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208
(2) Michigan Molecular Institute, Midland, Michigan 48640
(3) Saginaw Valley State University, University Center, Michigan 48710
(4) National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Correspondence to: Wesley R. Burghardt: e-mail: email@example.com
Contract grant sponsor: National Science Foundation; contract grant numbers: DMI-0521771, 0521823.
View this article online at wileyonlinelibrary.com.
[c] 2010 Society of Plastics Engineers
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|Author:||Fang, Jun; Burghardt, Wesley R.; Bubeck, Robert A.; Burgard, Susan M.; Fischer, Daniel A.|
|Publication:||Polymer Engineering and Science|
|Date:||Sep 1, 2010|
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