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Surface texture characterization of injection-molded pigmented plastics.

INTRODUCTION

Whether or not a complete car interior gives an aesthetic impression is dependent on the satisfactory combination of many different plastic components. The appearance of each component is mainly described in terms of color and appearance-related surface properties such as gloss and texture.

Injection-molded parts often have purposely imposed surface textures to provide a resemblance to more noble or sophisticated materials, such as natural leather, and this gives a more pleasant and comfortable sensation than a flat surface. In addition, the imprinted texture reduces the gloss, and this is often preferred in the automotive industry. As a consequence, surface characterization and control play an important role in the development of these components.

Nowadays, an increasing number of techniques are suitable for the characterization of rough surfaces in the scale range of particular interest for interior car components (one to hundreds of micrometers in height and from fractions of millimeters up to several millimeters in lateral dimensions). According to their sensing principle, the methods can be classified mainly as mechanical contact stylus, optical non-contact scanning and microscopy techniques (1).

In the main part of this work, an optical scanning technique (optical profilometry) was used to characterize the surface topography. Mechanical profilometry (contact stylus) was in some cases used as a complementary method. Both instruments can be classified as being of the laboratory type, i.e., the measurements are rather time-consuming. It is thus not surprising that interest in faster optical methods to evaluate the surface topography has increased during recent years. For instance, the Swedish Pulp and Paper Research Institute (STFI) has developed the OptiTopo-technique (2), which in principle allows the rapid acquisition and evaluation of a topographic image of a surface by combining two images from the same surface illuminated from two different directions. The application of this optical technique, which will here be described in some detail, to injection-molded plastics has been tested.

Apart from the challenge of finding an appropriate technique to assess surface topography, the choice of suitable descriptors of such a texture may not be a straightforward matter. Traditionally, statistical roughness parameters related to profile height or profile length have been used. However, these two-dimensional (2D) parameters depend on the measurement scale and on the sampling interval (3). Moreover, they are insufficient in that they provide only integrated information about the surface. Mummery (4) described, for example, three clearly different profiles having the same values of the average roughness. This phenomenon can to a large extent be explained by the fact that the average roughness does not differentiate between peaks and valleys (4).

The rapid development with regard to computing capability during recent years has facilitated the use of three-dimensional (3D) parameters for the characterization of rough surfaces. These 3D-parameters constitute mainly a reasonable extension of 2D-descriptors, adding computation and filtering difficulties, but allowing the determination of anisotropy as a new feature (5). The 3D-roughness parameters are classified into four groups, according to the type of property measured: amplitude, spatial, hybrid and functional (6). The latter parameter has been introduced in order to describe characteristics that are important for a specific functional application (5).

Owing to the inherent limitations of global topographical parameters, especially in the evaluation of textured surfaces, spectral analysis of the topography provides an interesting alternative, since such an analysis can indicate whether rough entities form clusters on the surface, are randomly distributed, etc. A spatial wavelength-dependent analysis provides a 'fingerprint' of the surface since the functions employed include both a height distribution parameter and a wavelength descriptor. Auto-correlation functions and power spectral densities are examples of such functions. Characterization of the topography of injection-molded surfaces using such concepts appears not to have attracted great attention so far, but this constitutes a major part of the present work. A more detailed account of these concepts is given in a later section.

The relation between surface heights and spatial wavelengths can also be described using a roughness exponent that gives a fractional dimension instead of the integer Euclidean dimension of regular geometrical objects (7). In such an analysis, the dimension of a rough surface has a value somewhere between 2 and 3. The fractional exponent may be associated with fractal dimension analysis, which has been used to describe 'natural structures' (8) such as coastlines or mountain reliefs, and also rough surfaces resulting from different machining processes, such as grinding, bead blasting or the spark erosion of metal surfaces. For example, Thomas (9) reported fractional exponents of 2.17, 2.14 and 2.39 respectively for the above surface finishes.

The use of a fractional concept to characterize a rough surface is of interest in this context since it may provide intrinsic surface parameters, i.e., parameters with no dependence on instrument characteristics such as evaluation length or area covered, resolution and sampling interval (10).

In the present work, an appropriate description that includes both amplitude and profile directions of deliberately created surface textures is presented. The evaluation has been performed using injection-molded plaques with three different surface patterns. The possible influence on the surface topography of the amount of colorant was also investigated. Most of the experimental work was carried out with an optical profilometer supplemented by contact stylus measurements but in a series of experiments the previously mentioned photometric stereo-method (OptiTopo) was evaluated with regard to its ability to simultaneously assess the topography of the surface. For illustrative purposes, a very regular surface texture of interest to the automotive industry was also included in the study. The ultimate goal of the study is to find a suitable set of surface descriptors that can be used to predict or estimate the reflective properties of a given surface, e.g., its gloss (11). This aspect, however, is treated separately and is not reported in this paper.

EXPERIMENTAL

Materials

The acrylonitrile-butadiene-styrene terpolymer (ABS) used was a commercial multipurpose injection-molding grade from General Electric Plastics, denoted natural color Cycolac G100. It is characterized by a density of 1.05 g/[cm.sup.3] (ISO 1183), a melt flow rate MFR (220[degrees]C, 10 kg) of 22 g/10 min, a melt volume rate MVR (220[degrees]C/10 kg) of 23 [cm.sup.3]/10 min (ISO 1133), and a melt viscosity MV (260[degrees]C/1500 [s.sup.-1]) of 111 Pas (ISO 11443).

The light beige masterbatch (MB) or colorant in pellet form was supplied by General Electric Plastics. It contained 50% by weight of pigment and 50% by weight of a styrene-acrylonitrile (SAN) copolymer as a carrier, well-known for easy flowing in ABS. A mixture of red, yellow, white and black pigments was used to produce the desired beige color of the masterbatch.

Sample Preparation

The ABS-polymer and the MB were first blended using a co-rotating twin-screw extruder in order to ensure an effective and homogeneous mixing (12). A Werner & Pfleiderer ZSK 30 M 9/2 twin-screw extruder (barrel diameter 30 mm and length-to-diameter ratio L/D of the screws equal to 9/2) was used. The screws were designed for optimal mixing (13). The processing conditions followed the specifications provided by the material supplier. The temperature was set to 80[degrees]C at the hopper, 150[degrees]C, 200[degrees]C, 205[degrees]C at the rear, middle and front zone of the barrel, respectively, and 230[degrees]C at the nozzle. The screw speed was kept at 200 rpm. Extrudates containing different amounts of the master-batch (0, 1, 3, 6 and 10 wt%, corresponding to 0, 0.35, 1.07, 2.18 and 3.74 vol%) were produced. The screws were carefully cleaned between runs. Pellets of each of the blends were obtained from the extrudate using a granulator (Dreher model SG10).

Since ABS is somewhat hygroscopic, the colored pellets were dried at 90[degrees]C for 3 hours in a dry air dryer before injection molding in order to avoid moisture-related defects (14) and degradation.

The test specimens were produced by injection molding with a Ferromatik Milacron K110 machine with a clamping force of 110 tones and a screw diameter of 45 mm. The operation parameters followed the specifications provided by the material supplier and were kept constant for all compositions in order to avoid any possible influence on the appearance of the resulting moldings (15-18). The melt and mold temperatures were 244[degrees]C and 62[degrees]C, respectively, the screw speed was 60 rpm, the injection rate was 23 mm/s, the back and holding pressures were 4 MPa and 50 MPa, respectively, and the injection, pressure holding and cooling times were 1.1, 12 and 20 seconds, respectively.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The specimens obtained were plaques with three fields having different surface textures: smooth (or glossy), fine and coarse (or 'leather-like'). Figure 1 shows details of the latter two textures, which can be classified as engineered and structured (19).

As an extension of the work, two other series of experiments were carried out. One of these included a thermoplastic olefin (TPO) embossed foil (supplied by Benecke Kaliko AG) with a periodic pattern. Figure 2 shows a 3D representation of the structure of this foil obtained using a mechanical contact stylus and also a scanning electron microscope (SEM) image of the same surface. The other experiment was directed more towards the production and imaging of imposed texture. In order to produce the texture in injection-molded specimens, the steel mold was subjected to consecutive etching procedures (20). Here, the surface textures of injection-molded plaques produced using a mold before the final etching and after this etching, also called after-etching, were evaluated and compared. The aim was to assess to what extent the final etching was revealed in the surface of the thermoplastic component.

The images to illustrate the different textures were obtained by means of an optical microscope Leica MZ 125 and a low vacuum scanning electron microscope (LV-SEM) JEOL 5900 LV. Prior to the SEM investigations, the surfaces were coated with an approximately 5-nm-thick carbon layer using an evaporation unit E5050 BIO-RAD from Polaron Division.

Surface Topography Measurement

The equipment used to assess the topographical characteristics was an UBM Optac 2000, which allows 2D- and 3D measurements of form and roughness. It comprises two independent profilometer sensors: one optical and one conventional with a contact stylus. The optical mode combines an autofocus sensor UBC14 with a resolution of 0.12 [micro]m, allowing a maximum measurable height of [+ or -]500 [micro]m, and an air-bearing stage, which provides the movement along a profile. For the contact measurement, the stylus ITF 1000A was used. It has a diamond tip with a nominal radius of 5 [micro]m and a cone angle of 90[degrees]. The stylus load was 0.7 mN. The maximum height measurable using this stylus is [+ or -]1000 [micro]m. Here, the stylus head moves along the sample and can be retracted during the reverse movement of the table.

The same measurement conditions were used with both sensors. An area of 16 X 16 [mm.sup.2] was scanned at a speed of 0.50 mm/s. A total of 81 profiles at a distance of 0.2 mm from each other were recorded. The sampling interval within each profile was 0.01 mm.

The measurements were rather time-consuming, taking about 45 min with the optical equipment and about 60 min with the contact stylus for each specimen. All measurements were performed at room temperature (21 [+ or -] 2[degrees]C). The UBM Optac 2000 was controlled by the UBM Messtechnik GmbH Microfocus Measurement and Analysis Software. This software was also used for the evaluation of the 3D-roughness parameters according to DIN 4776, which was superseded in 1998 by ISO 13565-1.2.

The ability of a photometric stereo-method (named OptiTopo) to capture the surface profiles of the injection-molded plaques was also examined. The advantage of this technique is that only short acquisition and evaluation times are involved. The method, described in full detail elsewhere (2), is based on two images, obtained using a CCD-camera, of a surface illuminated from two mutually opposing directions, at an angle of 72[degrees] relative to the normal to the surface. The CCD-camera records images based on the detection normal to the surface of the reflected diffuse light, the specular component of the surface reflection being eliminated using cross polarizers. The evaluation is based on a technique whereby the two images corresponding to the reflected intensities at the two different illuminating angles are combined and processed to obtain the partial derivative of the surface height (a gradient image). This new image is then integrated to give the surface topography. Good agreement between results from stylus scanning and the photometric stereo-technique has been reported for coated paper surfaces (2).

RESULTS AND DISCUSSION

Surface Texture Characterization of Fine Texture Using Profilometers

The different concepts and tools are here considered using the fine texture region of the injection-molded plaques. The coarse and smooth regions of the plaques as well as the more regular pattern are discussed in a subsequent section.

In general, the results obtained with the optical and contact stylus instruments were in very good agreement and it was decided to use the optical sensor results to introduce and illustrate the surface texture descriptors, with an emphasis on the fine texture. The values obtained for the specimens containing 3 wt% MB are shown in all the figures. Consistent data were obtained with the other compositions, and the amount of colorant had virtually no influence on the surface topography, see Table 1, which corresponds to the fact that the apparent shear viscosity of the polymer melts was more or less unaffected by the amount of colorant used (21).

A frequency curve representing the surface heights (or rather the deviations from an average height level) is the simplest or most straightforward way to describe the surface roughness characteristics (22). Figure 3 shows such a frequency curve for the fine texture specimen. The results can be fitted to a probability density function H(z) given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where N is the total number of data points included in the measurement, z the height at a given position x, <z> the mean (average) of heights (set to be zero) and [s.sup.2] the variance. The fine texture may be approximated by a Gaussian distribution of heights with <z> at 0 [micro]m and a variance [s.sup.2] of 32.5 [[micro]m.sup.2] and thus a standard deviation s of 5.7 [micro]m. The maximum deviation from the mean surface profile is evidently of 15-17 [micro]m.

The surface topography is traditionally described in an integral manner using two-dimensional (2D) roughness parameters obtained from profile measurements (23). In the vertical direction z, the most widely used 2D roughness parameters are the average roughness of the profile [R.sub.a] and the root-mean square deviation of the profile [R.sub.q].

[R.sub.a] = [1/l] [l.[integral].0]|[z.sub.n](x)|* dx[congruent to] [1/N] [N.summation over (n=1)]|[z.sub.n](x)| (2)

[R.sub.q] = [square root of ([1/l] [l.[integral].0] [z.sub.n.sup.2] (x) * dx)] (3)

where l is the sampling length in the direction along the profile x (defined as the length of the reference line used for identification of the irregularities) and [z.sub.n] (n = 1, 2,..., N) are the surface heights of discrete points where n is the number of discrete profile points.

A somewhat more complete 2D characterization of the topography is realized by determining the average wavelength of the profile [[lambda].sub.a] or the root-mean square wavelength of the profile [[lambda].sub.q] in the direction of the profile.

[FIGURE 3 OMITTED]

[[lambda].sub.a] = 2 * [pi] * [R.sub.a]/[[DELTA].sub.a] (4)

where [[DELTA].sub.a] = [1/l] [l.[integral].0]|[dz]/[dx]| * dx (5)

[[lambda].sub.q] = 2 * [pi] * [R.sub.q]/[[DELTA].sub.q] (6)

where [[DELTA].sub.q] = [square root of ([1/l] [l.[integral].0] ([dz]/[dx]) * dx)] (7)

Among the 3D roughness parameters (5), [S.sub.a] and [S.sub.q] are the 3D equivalents of [R.sub.a] and [R.sub.q], and are calculated over the whole area A.

[S.sub.a] = [1/A] [[integral].A]|z(x,y)| * dx * dy (8)

[S.sub.q] = [square root of ([1/A] [[integral].A] [z.sup.2](x,y) * dx * dy)] (9)

Table 1 includes the values of [S.sub.a] and [S.sub.q] for the fine structure obtained with the profilometer.

Correlation Functions

The spectral approach (5) makes use of the height-correlation function or auto-correlation function [[GAMMA].sub.z]([lambda]), which characterizes the correlation of heights at two different positions

[[GAMMA].sub.z]([lambda]) = <z(x + [lambda]) * z(x)> - <z(x)>[.sup.2] (10)

where [lambda] is the spatial wavelength and <...> denotes an average value. Obviously [lambda] denotes the difference in position between the two height values. In this work the two-dimensional counterpart of Eq 10 was used, taking into account variations in both x- and y-directions.

The auto-correlation function for the fine texture is shown as a function of the spatial wavelength in Fig. 4. It decreases monotonously with increasing [lambda] and approaches zero at [lambda] [congruent to] 0.2 mm.

[FIGURE 4 OMITTED]

By analogy with the surface height distribution, the auto-correlation function can also be fitted to a Gaussian type of relation.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where [s.sup.2] is the variance around the average height and [xi] the lateral correlation length, i.e., the value of the spatial wavelength [lambda] at which the auto-correlation function drops to some fraction of its initial value, often taken as 1/e, i.e.:

[[GAMMA].sub.z]([xi])/[[GAMMA].sub.z](0) = 1/e. (12)

Figure 4 also includes the fit of the experimental values to [[GAMMA].sub.z] ([lambda]) given by Eq 11 with a constant [xi]-value of 0.06 mm for a specimen containing 3% MB. Similar values of the correlation length were also obtained at other concentrations of the MB colorant, see Table 1.

There was no directional dependence of [[GAMMA].sub.z] ([lambda]) or of H(z), indicating that the topography can in a sense be regarded as isotropic. Since [[GAMMA].sub.z] ([lambda]) decreases monotonically from its maximum at [lambda] = 0 without any local maximum, this indicates that the fine structure can be regarded as being a random surface.

According to Eq 11, the auto-correlation function is equal to [s.sup.2] at [lambda] = 0. In the case of the plaque containing 3% MB by weight, the variance was 32.4 [[micro]m.sup.2], which agrees well with the variance of the height distribution, which was 32.5 [[micro]m.sup.2]. A similar behavior was noted at all colorant concentrations used, see Table 1.

The information contained in the auto-correlation function can also be presented in terms of a power spectral density function P([lambda]), which can be obtained as the Fourier transform of [[GAMMA].sub.z] (f) (24):

P([lambda]) = [[infinity].[integral].-[infinity]] [[GAMMA].sub.z](f) * [e.sup.-j2[pi]f[lambda]] * df (13)

where f is the spatial frequency.

This type of presentation is in some cases preferred, since local peaks at certain wavelengths in the spectrum can conveniently be attributed to defects induced, e.g., by a physical event associated with a certain size. An example of the power spectral density function is shown in Fig. 5 for the specimen containing 3% MB by weight.

When presenting or discussing spatial distributions of material properties or parameters, e.g., mass distributions, it is customary to present the data in terms of the variance per unit spatial wavelength as a function of the wavelength in a double-logarithmic graph, as shown in Fig. 5. Presenting the power (variance) distribution in this way, however, may lead to difficulties in some cases in estimating the contributions at long and short wavelengths. In the case of describing mass distributions, for example, local maxima corresponding to certain non-random disturbances or patterns may be difficult to observe because of the strong negative slope (-2) that characterizes the power spectral density of random "white noise" in the double-logarithmic diagram. "White noise" denotes equal power (variance) per frequency unit.

[FIGURE 5 OMITTED]

In order to circumvent this difficulty, a procedure adopted from the papermaking field (25) can be useful. In this approach, the density in variance/wavelength units is replaced by a modified spectrum expressed in variance/(logarithmic wavelength band) units to match the logarithmic wavelength axis. (This approach is also quite common in the audio field, where, for instance, sound power in an octave band 100-200 Hz may be compared with another octave band, e.g., 1000-2000 Hz, and is plotted at the same height if powers are equal.) The modified spectrum is obtained by a point-wise multiplication with the corresponding wavelength (thereby compensating for the increase in band-width with increasing wavelength) and a scaling factor representing the relative logarithmic bandwidth (e.g., variance/octave or variance/decade). For completeness, this procedure was also applied to the data obtained here for the fine texture. It did not, however, reveal any clear maximum in the spectrum, which is not surprising since the fine texture has already been seen to be random in character.

'Fractal' Concepts as Topography Descriptors

The use of fractal concepts (including a fractional exponent) can be considered as an alternative to the statistical parameters approach and spectral analysis (26). Fractal surfaces are scale-invariant structures, having a similar appearance independent of the scale of observation. In practice, the fractal stability should cover at least two to three decades in order to be useful. However, in this case it was noted that this self-similar behavior extended for only about one decade in spatial wavelength. Consequently, a discussion of theories based on fractal geometry is avoided. Nevertheless, its methodology seemed to be useful for our purposes.

In order to perform a 'fractal' analysis, a height-to-height correlation function or heights difference function [C.sub.z]([lambda]) must first be evaluated (27). [C.sub.z]([lambda]) is defined as the mean square height fluctuation of the surface as a function of the horizontal length scale (or spatial wavelength) [lambda].

[C.sub.z]([lambda]) = <(z(x + [lambda]) - z(x))[.sup.2]> (14)

Here, the two-dimensional counterpart of Eq 14 was used, i.e., considering z(x,y).

Figure 6 shows the correlation function [C.sub.z]([lambda]) as a function of the spatial wavelength for the fine-textured surface of the injection-molded plaques containing 3% MB by weight. From this graph, a set of topographical descriptors can be extracted or defined as indicated. A fractional exponent 2H, where H is the Hurst-exponent, is first identified as the slope of the linear part of the curve corresponding to wavelengths clearly below 0.1 mm. The fractional dimension D is then obtained (27) as:

D = 3 - H (15)

Furthermore, two characteristic correlation lengths that define the maximum length scales below which fractional behavior is fulfilled can be determined from the coordinates of the transition point, or corner wavelength, of the correlation function [C.sub.z]([lambda]). The first is a lateral correlation length [[xi].sub.//], which is the wavelength where [C.sub.z]([lambda]) deviates from the power law behavior with the exponent 2H. The second correlation length [[xi].sub.[perpendicular to]] is an amplitude-related length (or in the z direction), and it is calculated from the value at which [C.sub.z]([lambda]) attains a constant value corresponding to [[xi].sub.[perpendicular to].sup.2] for [lambda] > [[xi].sub.//]. (D, [[xi].sub.[perpendicular to]], [[xi].sub.//]) thus constitute a set of surface descriptors that completely define surfaces.

The correlation length in the amplitude direction of the profile [[xi].sub.[perpendicular to]] and the variance [s.sup.2] of the Gaussian distribution of surface heights H(z) are related (27) according to:

[s.sup.2] = [[xi].sub.[perpendicular to].sup.2]/2 (16)

Table 1 includes the values of D, [[xi].sub.//] and [[xi].sub.[perpendicular to]] for the fine texture obtained for all different amounts of added MB used here. The corresponding [s.sup.2]-values were obtained from Eq 16. The [s.sup.2]-values obtained from the 'fractal' analysis were clearly similar to those of the distribution function H(z) from the histogram in Fig. 3. The correlation length in the direction of the profile [[xi].sub.//] was also similar in magnitude to the correlation length [xi] associated with the auto-correlation function [[GAMMA].sub.z]([lambda]), being of the order 0.07-0.08 mm in both cases and at all MB colorant levels.

[FIGURE 6 OMITTED]

If D = 2 is taken to represent a flat surface (11), it is clear that the fine-textured surface has a rather rough character, where D is in the range 2.3-2.4 irrespective of the concentration of colorant.

Surface Texture Characterization of the Fine Pattern Using the Photometric Stereo Method

Figure 7 shows a SEM micrograph of the fine-textured region. The distribution of heights H(z) can readily be determined using the OptiTopo technique. However, the H(z)-distribution obtained in this way differs significantly from that evaluated with the classical profilometer techniques as shown in Fig. 8. It was also found that the H(z)-distribution obtained with OptiTopo changed shape when the colorant concentration was varied (Fig. 9). More specifically, the higher the colorant concentration, the greater were the measured heights.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

The photometric stereo-method thus appears to have some limitations in measuring specimens of the kind considered here. A point-wise comparison was therefore made between the two techniques. The optical UBM was taken as a reference from which a 2D profile with an approximate length of 5 mm was selected and the corresponding line scanned with OptiTopo was then matched using an iterative procedure, where the 2D UBM profile was matched against the OptiTopo image applying spatial, angular and scaling compensation parameters. It was then possible to compare the same physical line scanned using the two different techniques.

Figures 10 and 11 show the results for 3% and 10% MB samples, where the correlation coefficients are 0.78 and 0.92 respectively. The major difference can be largely explained as being due to a combination of a lack of optical homogeneity and an insufficient scattering power of the samples (the scattering power improving with increasing pigment content). A high scattering power of the material is needed to minimize the transmission of light into the bulk of the material, and to ensure that the reflected light is representative of the local surface slopes. Even though the correspondence between the two instruments is very good for a heavy pigmented sample, the local precision is not perfect. One limitation can be described as an out-of-range problem. Since the OptiTopo instrument is designed for paper, a range of 30 [micro]m is definitely too large. Another limitation is linked to the principle of the instrument, which requires that light has to strike all areas of the sample in a homogeneous way, and this is not true for very deep valleys.

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

The photometric stereo-method was also used to characterize the coarse texture, but owing to the limitations of the technique, the results are not discussed here.

Characterization of the Smooth and Coarse Textures

The smooth and coarse textures were also scanned using the profilometer techniques (mainly the optical one) and characterized by the set of descriptors already mentioned.

The surface height function H(z) of the smooth (glossy) surface had a standard deviation s of 0.29 [micro]m, and it had a Gaussian shape (corresponding to waviness). The auto-correlation function indicated that the texture was of the random type with a standard deviation s of 0.30 [micro]m. The 'fractal' analysis gave an exponent D of 2.02 which certainly illustrates that the surface is almost perfect, i.e., very smooth.

Figure 12 is a scanning electron micrograph of the coarse texture. The structure, which is not of a random-type, can be said to be 'leather-like' and consists of peaks or hills with a diameter of approximately 2 mm separated by valleys with an average width of 0.6 mm.

The surface heights function H(z) for the coarse region obtained with the optical profilometer (Fig. 13) is a bimodal distribution. The left-hand peak is associated with the topography of the valleys, whereas the right-hand peak characterizes the texture on the hills. The distance between the maxima of the two distributions constitutes a measure of the depth of the valleys in the 'leather-like' structure. In this case, it is of the order of 0.1 mm. The standard deviation of the left-hand distribution amounts to s = 6 [micro]m, whereas that of the right-hand distribution is 10.7 [micro]m. It is quite clear that the topographies within the valleys and on the hills are not identical. The results are summarized in Table 2.

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

The 3D roughness parameters [S.sub.a] and [S.sub.q] do not provide any additional information and are thus not further discussed here. Using the spectral approach, it is, however, possible to obtain characteristic parameters (after separating the two height distributions) corresponding to the topography of the hills and of the valleys, see Table 3.

The auto-correlation function for each of the two separated distributions could not in a satisfactory manner be fitted to a function of the type given by Eq 11 (Gaussian), and a corresponding correlation length [xi] for each of the distributions could not then be properly obtained. The corresponding standard deviations for the plaque containing 3% MB (from the auto-correlation functions) were 5-6 [micro]m and ca. 9 [micro]m, respectively, in fair agreement with the results from the surface height function H(z).

The 'fractal' analysis gave a lateral correlation length for the topography in the valleys of about 0.1 mm, whereas [[xi].sub.//] for the hill-distribution amounted to approximately 0.15 mm. The standard deviations evaluated from the amplitude-related [[xi].sub.[perpendicular to]] were in accordance with the corresponding results from the height function H(z), see Table 3. As is evident in Table 3, the fractal exponents associated with the valleys were lower than those of the hills, indicating a smoother structure in the former case.

In this context, it may be of interest also to consider the entire height distribution, i.e., not separate it into two distributions. The corresponding auto-correlation function is shown in Fig. 14. At wavelengths longer than 1 mm, local maxima appear, indicating a non-random periodic component. This component is presumably related to the hill-valley pattern imposed on the surface of the plaque.

Example of a Regular (Periodic) Texture

A polymer foil, based on TPO, embossed with a very regular pattern was included in this study. An illustration of the texture obtained with the contact stylus is given in Fig. 2. A planar cross section along the profile (parallel to the height direction) reveals an almost (but not perfect) sinusoidal height variation with a maximum amplitude of about 130 [micro]m and a wavelength of about 1.5 mm. The corresponding surface height distribution H(z), Fig. 15, exhibits two rather sharp peaks separated about 260 [micro]m from each other. The function H(z) is not perfectly symmetrical, since the variation is not perfectly sinusoidal. It is, however, clear that distributions of this kind are difficult to consider as being of the Gaussian type.

[FIGURE 14 OMITTED]

The auto-correlation function evaluated from Eq 10, shown in Fig. 16, also exhibited a pronounced periodic behavior with the peaks separated by a distance of 1.5 mm, i.e., the spatial wavelength of the imposed pattern. The same type of periodicity was also observed in the 'fractal' analysis.

The results presented clearly illustrate the ability of the spectral analysis (and the 'fractal' analysis) to detect periodic disturbances or patterns. This was also evident in the characterization of the coarse structure described earlier.

After-Etching of a Mold

Plaques of an ABS-polymer were injection-molded first using a mold where the intended pattern had not been subjected to a final etching (commonly called after-etching) and then with the same mold after the final etching. The imposed pattern resembled the coarse 'leather-like' structure analyzed earlier, but it was not identical. The injection molding conditions were identical in these two cases.

[FIGURE 15 OMITTED]

[FIGURE 16 OMITTED]

Figure 17 shows the surface height distribution H(z) of the imposed pattern on the plaques before and after the final etching. The distribution was determined using the laser profilometer. Evidently, both distributions were rather skew and not really of a Gaussian shape. From this graph, the main result of the final etching appears to be a more clearly developed bimodal distribution. This is quite clear from the shape of H(z).

The topography was also characterized in terms of spectral concepts, here exemplified by the power spectral density function P([lambda]), Fig. 18. The curves are almost parallel over the wavelength region covered, but the after-etching produced an upward shift of the curve. One interpretation is that the final etching leads to a more distinct pattern (at all wavelengths) in the molded surface. This is also a desired result. The spectral density also revealed some weak periodicity in the pattern at wavelengths in the millimeter range. This was also evident in the shape of the auto-correlation function (not shown here).

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

CONCLUSIONS

Imposed surface textures on injection-molded plastic parts used in interior car components can be characterized in detail by spatial wavelength-dependent analyses, including height density distributions, auto-correlation functions, power spectral densities and height-to-height correlation functions. These functions constitute an interesting alternative to the traditional roughness parameters since they provide detailed information in both amplitude and profile directions and thus permit periodicity recognition. The information provided by these kinds of approach is likely to constitute an important tool for linking the surface topography and its optical response or appearance. This will be dealt with in a separate paper.

The descriptors used here can also be of value when evaluating the influence of the injection molding parameters on the surface topography, especially when tailoring the surface appearance in a desired direction and also, as indicated here, when manufacturing molds for polymer processing.

OptiTopo proved to be a valuable but limited tool for pigmented plastics at least in its present stage. It was found to be useful for pattern recognition (surface plane), but not for height measurements. In its present form, the technique could mainly be used in surface control when the colorant concentration is constant; its lower precision being compensated for by its measuring speed. The OptiTopo device was designed for measuring paper surfaces, so that the underlying approach and main settings were optimized for the optical response of coated paper surfaces that can, and in some extent do, differ from plastics. A possible instrumental development could be an adaptation of the software to the optical response of pigmented plastics in order to improve the precision. Other changes to include scaling factors or to modify the present settings of the digital filters could be feasible. To improve the illumination homogeneity of the full surface of the sample (including the deeper valleys), a decrease in the illumination angle could be considered, although this could be at the expense of a reduction in the signal-to-noise ratio.

NOMENCLATURE
ABS Acrylonitrile-butadiene-styrene
 terpolymer
L/D Length-to-diameter ratio of the screw
MFR Melt flow rate [g/10 min]
MVR Melt volume rate [[cm.sup.3]/10 min]
MV Melt viscosity [Pas]
MB Masterbatch
TPO Thermoplastic olefin
SAN Styrene-acrylonitrile copolymer
2D Two-dimensional
3D Three-dimensional
c Colorant volume concentration [/] or [%]
f Spatial frequency [1/mm]
j Imaginary number
l Sampling length [mm]
n Number of profiles
s Standard deviation [[micro]m]
[s.sup.2] Variance [[[micro]m.sup.2]]
x, y Lateral lengths [mm]
z, z(x,y) Height [[micro]m]
<z> Mean (average) of heights [[micro]m]
A Area [[[micro]m.sup.2]]
[C.sub.z]([lambda]) Height-to-height correlation function
 [[[micro]m.sup.2]]
D Fractional exponent [/]
H Hurst exponent [/]
H(z) Probability density function
 [counts/[micro]m]
N Total number of profiles
P([lambda]) Power spectral density function
 [[[micro]m.sup.2]/mm]
[R.sub.a] Average roughness (2D) [[micro]m]
[R.sub.q] Root-mean-square roughness (2D)
 [[micro]m]
[S.sub.a] Average roughness (3D) [[micro]m]
[S.sub.q] Root-mean-square roughness (3D)
 [[micro]m]
[lambda] Spatial wavelength [mm]
[[lambda].sub.a] Average wavelength (2D) [mm]
[[lambda].sub.q] Root-mean-square wavelength (2D) [mm]
[xi] Lateral correlation length [mm]
[[xi].sub.//] Lateral correlation length [mm]
[[xi].sub.[perpendicular to]] Amplitude correlation length [mm]
[DELTA]a Average wavelength of a profile [mm]
[DELTA]q Root-mean-square wavelength [mm]
[[GAMMA].sub.z]([lambda]) Height-correlation or auto-correlation
 function [[[micro]m.sup.2]]

Table 1. Parameters Characterizing the Fine Sample Region, Units in mm.

 Frequency
 Distribution, 3D-
 H(z) Roughness
% wt [s.sup.2] s [S.sub.a] [S.sub.q]
MB * [10.sup.-6] * [10.sup.-3] * [10.sup.-3] * [10.sup.-3]

 0 34.8 5.9 4.5 5.7
 1 33.6 5.8 4.5 5.7
 3 32.5 5.7 4.5 5.6
 6 34.8 5.9 4.6 5.7
10 32.5 5.7 4.4 5.5

 Auto-Correlation, Fractional Exponent,
 [[GAMMA].sub.z] ([lambda]) [C.sub.z] ([lambda])
% wt [s.sup.2] s D
MB [xi] * [10.sup.-6] * [10.sup.-3] [/]

 0 0.07 36.4 6.0 2.34
 1 0.07 30.8 5.5 2.33
 3 0.06 32.4 5.7 2.36
 6 0.07 31.4 5.6 2.33
10 0.06 29.1 5.4 2.30

 Fractional Exponent,
 [C.sub.z] ([lambda])
% wt [xi].sub.[perpendicular to].sup.2] [s.sup.2]
MB [[xi].sub.//] * [10.sup.-6] * [10.sup.-6]

 0 0.08 73.8 36.9
 1 0.08 64.9 32.5
 3 0.09 67.1 33.5
 6 0.08 68.4 34.2
10 0.08 62.4 31.2

 Fractional Exponent,
 [C.sub.z]([lambda])
% wt s
MB * [10.sup.-3]

 0 6.0
 1 5.7
 3 5.8
 6 5.8
10 5.5

Table 2. Parameters for Characterization of the Coarse Region, Units in
mm. Subindex 1 Refers to the Topography Associated With the Valleys and
Subindex 2 to the Corresponding for the Hills.

 Frequency Distribution,
 [H.sub.1](z), [H.sub.2](z)
% wt [s.sub.1] [s.sub.2]
MB <[z.sub.1]> * [10.sup.-3] <[z.sub.2]> * [10.sup.-3]

 0 -57 5.5 37.2 10.5
 1 -57 4.7 37 10.3
 3 -57 6.0 34.3 10.7
 6 -57 5.8 33.8 10.6
10 -57 5.3 32.6 10.8

 3D-Roughness
% wt [S.sub.a] [S.sub.q]
MB * [10.sup.-3] * [10.sup.-3]

 0 32.0 35.73
 1 32.92 36.49
 3 31.16 35.02
 6 31.37 35.20
10 30.88 34.70

Table 3. Parameters for Characterization of the Coarse Region After
Separation Into Two Distributions, Units in mm. The Plaque Contained 3%
MB.

 Frequency 3D-
 Distribution, H(z) Roughness
% wt [s.sup.2] * s * [S.sub.a] * [S.sub.q] *
MB <z> [10.sup.-6] [10.sup.-3] [10.sup.-3] [10.sup.-3]

distr. 1 -57 34.8 6.0 25.5 5.0
distr. 2 34.3 114.5 10.7 88.8 9.4

 Fractional Exponent,
 [C.sub.z]([lambda])
% wt D [[xi].sub.[perpendicular to].sup.2]
MB [/] [[xi].sub.//] * [10.sup.-6]

distr. 1 2.47 0.11 57
distr. 2 2.37 0.15 192

 Fractional Exponent,
 [C.sub.z]([lambda])
% wt [s.sup.2] s
MB * [10.sup.-6] * [10.sup.-3]

distr. 1 28.5 5.3
distr. 2 96 9.8


ACKNOWLEDGMENTS

We thank General Electric Plastics for supplying the material, F. Henareh (Volvo Car Corporation) for his assistance with the microscopes, C. Frennfelt (Volvo Technology Corporation, VTEC. Goteborg Sweden) for all the help provided with the laser and stylus measurements and M. Kolseth Lind (Swedish Pulp and Paper Research Institute, STFI) for helping with the OptiTopo measurements. The contributions of Dr. K.-M. Jager (Borealis AB, Stenungsund Sweden) in the form of critical and very constructive debates and Dr. J. A. Bristow for the linguistic revision of the manuscript are acknowledged.

Finally, we thank the Swedish Agency for Innovation Systems (Vinnova) and Volvo Car Corporation for their financial support of the project.

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INGRID ARINO (1,2), ULF KLEIST (1), GUSTAVO GIL BARROS (3), PER-AKE JOHANSSON (3), and MIKAEL RIGDAHL (2,3*)

(1) Department of Interior and Climate Engineering, Volvo Car Corporation SE-405 31 Goteborg, Sweden

(2) Department of Materials Science and Engineering Chalmers University of Technology SE-412 96 Goteborg, Sweden

(3) Swedish Pulp and Paper Research Institute Box 5604, SE-114 86 Stockholm, Sweden

*To whom correspondence should be addressed.

E-mail: mikael.rigdahl@me.chalmers.se
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Author:Arino, Ingrid; Kleist, Ulf; Barros, Gustavo Gil; Johansson, Per-Ake; Rigdahl, Mikael
Publication:Polymer Engineering and Science
Article Type:Editorial
Date:Sep 1, 2004
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