An integrated approach towards the study of scratch damage of polymer.

To seek a better understanding of the scratch damage of polymers, an integrated analysis approach is proposed in this article. This integrated approach essentially involves (a) the use of a new scratch test device for testing, (b) employing microscopy techniques and image an analysis tool, VIEEW[R], for studying material damage and scratch visibility, and finally (c) performing finite element (FE) modeling to examine the mechanical response of the polymeric substrate involved during the scratch process. Applying this approach to five model material systems and employing linearly increasing load tests, the findings of the fundamental material science study of the scratch damage of these materials are presented. From the three-dimensional FE analysis, the numerical results generated were able to reasonably predict the scratch damage and provide corresponding mechanistic interpretation. The essential link between material science and mechanics outlines the uniqueness of this approach for studying the scratch damage of polymers.

Keywords: Hardness, scratch resistance, surface analysis, finite element method, polyolefin, thermoplastic olefins

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Being lightweight and easily molded into desired shapes and sizes, polymers are substituting for traditional materials, such as metals, in existing structural applications and are finding their place in new applications. With such an extensive use of polymers, there is a need to carefully scrutinize their performance to ensure reliability. Furthermore, any form of damage, such as a scratch to a material, will inevitably degrade its aesthetic appeal and structural integrity. As such, it is crucial to have a better understanding of how to minimize the scratch damage of polymers. This is particularly the case in the automotive and electronic industries where the aesthetic appeal of their products is of prime concern and any visible scratch damage is undesirable. Concern for aesthetics has led to a need for the quantification of scratch damage visibility on polymeric surfaces and, hence, on the evaluation of scratch resistance.

To date, there is no comprehensible way to evaluate the scratch resistance of polymers. Scratch ([H.sub.s]) and ploughing hardnesses ([H.sub.p]) were first proposed by Williams (1) to quantify the scratch resistance of metals. Briscoe and his colleagues (2) redefined the ploughing hardness as "tangential hardness" ([H.sub.T]) to include the adhesive contribution and specified another new hardness parameter called "dynamic hardness." It is, however, worth noting that Vingsbo and Hogmark (3) had previously defined a parameter that is similar to the tangential hardness, while others (4) had referred to the dynamic hardness as "specific grooving energy."

Scratch visibility is a complex issue, as it involves many different unquantifiable parameters that can affect how an observer perceives a scratch. Many attempts have been made to quantify scratch visibility by measuring the surface reflectivity of the scratch. (5-10) Due to the diverse techniques employed and the lack of systematic studies to correlate scratch features with visibility, (11) the results obtained from one set of experiments are often valid within a set of narrowly defined conditions. It remains to be seen which of these methods, if any, will prove to be the most useful in characterizing scratch visibility.

To gauge both the scratch resistance and visibility of polymers, it is important to perform tests using a reliable scratch test device. Such a test device is defined as one that can produce consistent and reproducible data, and has the reasonable capability and adaptability to changing test conditions to capture the essential scratch characteristics of the test specimen. Many commercial and custom-built testing devices have surfaced in the past few years. Simplistic test methods, like the pencil hardness test, (12,13) have been utilized for macroscopic scale scratch resistance evaluation. On the other hand, others employ more instrumented devices like the "scratching machine," (14-17) Taber test and pin-on-disc machine, (7,18) Ford five-finger test, (8,19-21) single-pass pendulum sclerometer, (2-4,22) scratch apparatus, (23) Revetest scratch tester, (24) needle test, (25) scratch test rig, (9) in-house scratch test apparatus (26) and the "scratch tester." (27) For the micro- and nanometer scales evaluation, there are several commercially available machines, some of which are listed in reference 46, or customized test machines built by individual researchers. (28-31) Scanning probe microscopy instruments, such as the atomic force microscope, (32-34) have also been adopted and improvised by researchers to perform scratch tests at a nanometer scale. For evaluating the scratch surface and subsurface, researchers have used equipment like the optical microscope (OM), (18,24,26) atomic force microscope, (24,26,32,35-38) scanning electron microscope, (14,15,26,39,40) X-ray photoelectron spectroscope, (41) laser confocal microscope, (18) Raman spectroscope, (28) white-light interferometer, (20,24) profilometer, (14,15,42) tribometer, (43) ellipsometer, (28) and scanner. (17,44,45)

A review of the scratch test devices available for macroscopic testing (46) readily reveals that the ranges of normal loads and scratch rates for most devices are rather limited, while some of them may only be good for the evaluation of marred surfaces and, thus, insufficient for the scratch studies. The above-reviewed test devices cannot judiciously determine the exact scratching condition (i.e., load and rate) that causes certain scratch and mar damage. This problem, however, might be overcome if the test device is built with the capability to execute increasing load or rate tests over a scratch length. With that capability, one could readily resolve the critical load or rate at which an expected surface damage occurs. Consequently, this would save laboratory time and labor when determining and comparing the scratch resistance for a given set of polymers.

The fundamental study of the scratch damage of polymers, if based solely on material science and experimental efforts, may be inadequate. As discussed extensively in literature, (46,47) the geometrical (from large strains and the nature of contact problems) and material (due to plastic yielding and the orientation of polymer chains) nonlinearities of the scratch problem at hand easily make the reliance on analytical approaches for solutions unrealistic. Numerical techniques, such as the finite difference method or finite (FE) element method, (48) can provide the needed solution alternatives to study the scratch problem. Furthermore, parametric studies can be undertaken to evaluate the influence of key factors on the scratch performance of polymers. Ultimately, these key factors can be optimized to improve the scratch resistance of the materials.

[FIGURE 1 OMITTED]

The main objective of this work is to propose an integrated approach towards the study of the scratch damage of polymers. This integrated approach primarily includes the construction of a new scratch test device for scratch tests and the use of microscopy equipment like SEM and OM, and a commercial image analysis tool, VIEEW[R], for scratch damage and visibility evaluation. Using the increasing normal load capability of the new scratch device, a graphical method to furnish scratch hardness is proposed. The study assesses the appropriate use of scratch hardness for quantifying the scratch resistance of a material. Discussion of scratch visibility and its relation to the ductile and brittle modes of fracture is made.

The final component of the integrated approach is the use of FE analysis to gain insight into the mechanical behavior of polymers during the scratch process. A three-dimensional (3D) FE analysis to simulate the experimental test conditions on PP material was carried out. A correlation between the results from the FE analysis and the observed scratch damage mechanism is made.

EQUIPMENT DEVELOPMENT: CUSTOM-BUILT SCRATCH TEST MACHINE

A scratch device was developed for this study. With its main focus on automotive applications, the in-house custom-built scratch machine can perform multipass, multi-indenter, constant load, constant speed, increasing load, and increasing speed tests with the potential to operate at various temperatures. The scratch test unit was comprised of a servo gear-driven motor that drives the scratch tips with either a constant speed that ranges from 0-400 mm/sec or a linearly increased speed ranging from zero to any intended speed up to a peak value of 400 mm/sec. The scratch test device can perform single- or multi-pass tests with up to five scratch tips. Furthermore, the test device was designed to conduct tests with dead weights or computer-controlled spring loads. This allowed the test device to have a wider load range for testing: 0-50 N for dead weights and 0-100 N for spring loads. Spring loads not only allow for the operation of increasing load tests but also prevent the occurrence of chattering of indenters, as observed in tests using the dead weights. (49)

Reference 46 contains a comparison between the functionlities of the new test device and other available devices found in open literature. The comparison reveals that the present test device has the sufficient capabilities and the needed flexibility to perform a wide range of different tests to satisfy various application needs of the polymer industry, despite its relatively low construction cost. As the need grows for a standardized scratch test for automotive applications, initiation of a new ASTM standard using the present test device is underway.

MATERIAL SCIENCE STUDY

Polycarbonate (PC) sheets (Lexan[R] 9034, GE Plastics) and four polypropylene (PP) material systems were selected, and their compositions are shown in Table 1. For the PP systems, the resin and a dark gray coloring pigment were provided and blended by Solvay Engineered Polymers. Plain talc particles, without surface treatment, were provided by Luzenac, Inc. Injection molding of the plaques, having dimensions of 340 mm X 180 mm X 3 mm, was performed by Advanced Composites, Inc. For testing, the plaques were cut and machined into 140 mm X 10 mm X 3 mm plates. All the test specimens were prepared according to ASTM D 618-00 Procedure A. (50)

The custom-built scratch test device, as described in the previous section, was used for all the scratch tests. Tests with a constant scratch speed of 100 mm/sec and a linear increasing normal load ranging from 5-50 N were performed. The tests were conducted at room temperature and the scratch length was set at 100 mm. A stainless steel spherical ball with a diameter of 1 mm was used as the scratch stylus tip.

SEM was performed to study the microscale surface damage features using a JEOL JSM-6400 system. Thin sections were prepared for OM observation, under cross-polarized light, using a BX60 Olympus[R] microscope. A flatbed scanner with a resolution of 1200 dpi was used to scan the scratched surfaces in quantifying scratch damage. A commercial image analysis tool, VIEEW, was also used to quantify the surface damage of the specimens.

FINITE ELEMENT ANALYSIS 

As part of a combined effort in equipment development, material science study, and computational simulation, the FE analysis performed was configured to simulate as closely to the actual experimental setup as the computational resources (CPU time, disk space, and memory) would allow.

Using a commercial FE package, ABAQUS[R], (51,52) various modeling considerations* for all the FE analyses were taken into account. Exploiting the symmetry of the problem (Figure 1), the dimensions of the FE computational domain for the polymeric substrate were taken to be 50 mm X 5 mm X 3 mm. For simplicity, a uniform meshing of eight-node 3D linear brick elements was adopted for the computational domain. The nodes on the 1-3 planes at both ends of the FE mesh were restrained in all three directions to simulate the clamping of the specimen during experiments. Since test specimens rest on a rigid desktop, this condition was satisfied by restricting the vertical movement of the nodes on the bottom surface of the FE mesh. Finally, to impose the symmetry of the problem, the nodes on the 2-3 plane were prevented from translating in the 1-direction.

[FIGURE 2 OMITTED]

For the substrate, the material considered was PP. The true compressive stress-strain curve of PP, tested at 21[degrees]C and a strain rate of 0.01/sec by Arruda et al., (53) was used as material input for the FE analysis. The elastic modulus of PP was taken at 1.65 GPa, the Poisson's ratio at 0.4, and the density at 905 kg/[m.sup.3]. In the scratch experiments, the indenter was made of stainless steel. Considering the relatively higher stiffness and yield strength of stainless steel as compared to PP, it is reasonable to assume the 1-mm spherical-tipped indenter to be rigid. With that, the indenter was modeled using a rigid analytical surface whose movement was controlled by a reference node.

A 3D elasto-plastic stress analysis was executed for the study. To describe the evolution of plastic flow in the analysis, von Mises shear yielding criterion with isotropic hardening rule was used. With regard to craze initiation, the critical strain criterion (54) was adopted. To preserve the mesh quality for the elements near the scratched region, the adaptive remeshing capability of ABAQUS (51) was employed. Frictional interaction between contact surfaces was included by using the basic Coulomb friction model with the coefficient of adhesive friction set at 0.3. Two load cases, A and B, were considered for this study. In load case A, a normal load of 30 N on the indenter and a scratch speed of 10 m/sec were kept constant throughout the analysis. For load case B, the normal load increased from 10 N to 30 N while the scratch speed remained constant at 10 m/sec during a scratch.

[FIGURE 3 OMITTED]

RESULTS AND DISCUSSION

Material Science Study

SCRATCH HARDNESS: As introduced by Williams, (1) and for the sake of completeness, scratch hardness, [H.sub.s], is herein defined as the normal load, P, of the scratch tip exerted over the projected load bearing area, A, during a scratch. As an assumption, the load bearing area was approximated as a circle with its diameter being the same as the scratch width, d. It should be noted that this assumption was based on the fact that PP undergoes large elastic and viscoelastic recovery, as documented in reference 5. Thus, scratch hardness can be defined as:

[H.sub.s] = P/A [congruent to] [4P]/[[pi][d.sup.2]] (1)

[FIGURE 4 OMITTED]

Particularly for this study, where increasing-load tests were conducted instead of constant load tests, the normal loads and the resulting scratch widths varied over the scratch length. If scratch hardness is a scratch-related material property, it should remain constant for different loads across the scratch path. Hence, by plotting a projected loading area, [pi][d.sup.2]/4, against the normal load, P, should yield a linear fit with its slope equal to the scratch hardness. It is the objective of this study to assess if the scratch hardness can be a useful parameter for the scratch resistance of polymers.

To determine the scratch hardness of a material using this novel approach, scratches were first introduced on the material surface using increasing load tests, as discussed in the Material Science Study section. Two-dimensional VIEEW images of scratch grooves were then produced using direct light scanning. Using these images, scratch widths at various points of the scratch path were measured, according to the definition as provided in Figure 2. At those points of the scratch path where the scratch width measurements were made, the normal load can be readily determined. Finally, by calculating the projected scratch areas from scratch widths and plotting them against the corresponding normal loads, the scratch hardness can be established from the linear fit of the plot, as shown in Figure 3. As observed from this figure, the graph does have a reasonably good linear fit whose slope gives the scratch hardness of the material. The local variation of data points could possibly be attributed to the stick-slip motion of the scratch tip during the scratch process.

Table 2 lists the scratch hardness and mechanical properties of the five considered material systems (Table 1) determined via this graphical approach. Comparing the values in Table 2, a key observation to be drawn is the direct correlation among the tensile modulus, yield strength, and scratch hardness for homopolymer PP and copolymer PP. An increase in tensile modulus and yield strength will result in an improved scratch hardness of a material, which should be expected since scratch is essentially a mechanical deformation process. More importantly, this conclusion might readily point material engineers to a clue on improving the scratch resistance of a material. It should be noted that if PP is compared to PC, the correlation can no longer hold true. This discrepancy might be due to the differences in the scratch damage feature found on the two materials, especially when scratch visibility is to be correlated. Therefore, scratch hardness is only useful for evaluating the scratch resistance of materials when the damage features between the materials are essentially the same.

SCRATCH VISIBILITY: Scratch visibility has hitherto been a complex parameter to quantify, as it requires a comprehensive treatment of optical perception by human vision. Distinguishing a scratch involves the visual ability to detect the change of light scattering. While the objectivity of human vision to perceive scratches remains a precarious issue, looking into the types of material damage or fracture will aid in the understanding of scratch visibility. For polymers, material damage can occur in ductile and brittle manners. Ductile damage generally involves shear yielding of the material while brittle damage is usually characterized by localized crazing and cracking. At high plastic strains from shear yielding and crazing, the materials at points of concern will generate different light refraction patterns that will result in a phenomenon commonly known as "stress-whitening." As for brittle surface cracking, surface roughness of the material will change drastically, leading to diffused light scattering. While it is difficult to discern which type of material damage will make scratch visibility worse, the concept of promoting ductile damage by toughening the base polymers with rubber can still be applied. Then, by further improving the mechanical properties (i.e., elastic modulus and yield strength) of polymeric composite systems, the extent of shear yielding in the material can be controlled. As such, it is conceivable that by carefully working on the material formulation of polymeric systems, the types of damage modes might be altered and/or controlled so as to ultimately reduce scratch visibility.

In this study, untreated talc fillers have been added to two of the four PP systems (Table 1) to enhance the mechanical properties (see Table 2). This section will look into whether the addition of talc fillers will promote ductile damage and affect scratch visibility. The SEM micrograph in Figure 4 shows exposed talc particles in the PP homopolymer after scratching at 30 N and 100 mm/sec. It can be observed from Figure 4 that void formation and ductile drawing had occurred during the scratch process, which is an indication of ductile damage.

To establish a systematic approach for evaluating and comparing the scratch visibility of the considered model PP systems, three scratched specimens for each system were first scanned using VIEEW and the average critical loads for the onset of stress-whitening were then computed, as shown in Figure 5. The results show that for the PP systems, the critical normal load for stress-whitening was the highest for homopolymer since no detectable whitening occurred within the load range, followed by the talc-filled homopolymer, copolymer, and talc-filled copolymer. Figure 5 also compares the size of the stress-whitened area for the various PP systems; the talc-filled polymers show a larger affected area. It is apparent that untreated talc worsens scratch visibility since it not only decreases the critical load for stress-whitening, but also dramatically increases the amount of stress-whitening.

Revisiting the earlier study of scratch hardness where talc fillers have a positive effect on reducing scratch widths, one can conclude that talc fillers do indeed reduce scratch damage but can make scratch visibility worse from extensive ductile damage due to void formation and ductile drawing. To preserve the advantageous benefit of talc on mechanical performance, one can work on reducing scratch visibility by (a) improving the interfacial adhesion between the talc particle and polymer matrix, possibly by special surface treatment; and (b) to reduce the size of talc particles so that void sizes can be minimized to reduce visibility. From these studies of scratch hardness and scratch visibility (using critical normal load for the onset of stress-whitening or total stress-whitened area), we found that it is essential that these two parameters be considered together to correctly define the scratch resistance of a material.

[FIGURE 5 OMITTED]

Finite Element Analysis

SCRATCH DAMAGE PROCESS: Like many computational techniques, FE analysis can yield a rich database of numerical results to describe the time evolution of a mechanical deformation process. These results can, in turn, be reproduced graphically to gain insight into the deformation process. For our concerned scratch problem, understanding the scratch damage requires the knowledge of the mechanical response of the material around the indenter, which might further allow one to make a prediction about the local material deformation and fracture.

[FIGURE 6 OMITTED]

Figure 6 includes plots of the maximum principal stress variations along the length AB of the FE mesh (Figure 1) at various time intervals during a scratch. Here, discussion focuses on the results for Load Case A. The maximum principal stress plots in Figure 6 exemplify the stress state of the material around the indenter tip. At the beginning of the scratch step (t = 0 sec) where the deformation remains predominantly that of an indentation, the material beneath the 1-mm tip was under compression while the surrounding material was in tension; such a stress variation has been reported analytically. (5, 56) Once scratching occurs, the maximum principal stress profiles change to reveal that the material beneath the front section of the indenter tip was under compression while the material under the back section of the tip was in tension. Tensile stresses can also be observed for material in the regions ahead of the indenter.

Though the maximum principal state of stress for the material around the indenter is now known, there is still a need to make a link to the possible fracture patterns. To achieve that, one can review the direction at which the maximum principal stresses act for the elements around the indenter, as presented in Figure 7. In Figure 7, arrows pointing outwards indicate that the maximum principal stresses are tensile while inward-pointing arrows signify compressive stresses. For clarity, elements with compressive maximum principal stress are differentiated from those with compressive stresses by their green shading.

[FIGURE 7 OMITTED]

Figure 7a shows that tensile stresses were present for the elements behind and away from the indenter tip, which is consistent with the results shown in Figure 6. The state of maximum principal stress is generally compressive for the elements right under the front section of the indenter. The tensile stress vectors for the elements directly behind the tip are generally in the 2-direction while the stress vectors in the far left rows of elements are in the vertical 3-direction and with slight biases in the 2-direction [Figure 7a]. This suggests that as the indenter moves, the material directly behind the indenter will be stretched in the direction of the scratch. If a fracture does occur, it is likely that cracks will form perpendicular to the scratch direction. As the indenter continues to plow forward, the same materials are now pulled outwards in the vertical direction, in addition to being stretched in the scratch direction, possibly leading the materials to be spalled off. Such a spallation or delamination is commonly observed during scratch testing of coated systems. (57) It was noted that tensile stresses were found in the outer-most row of elements ahead of the indenter. As shown in Figure 7b, the stress vectors of these elements were stretched outwardly in the 1-direction, suggesting that the material in that region might tear apart as the indenter plows through, forming cracks parallel to the scratch direction.

Through the study of the maximum principal stress and its directionality in the materials beneath and around the indenter tip during a scratch, a phenomenological deduction of the damage mechanism was proposed and can be related to fracture mechanisms like crazing, as discussed below.

ASSESSMENT OF CRAZE INITIATION: Fracture mechanisms such as crazing, voiding, debonding, and cracking can cause stress-whitening in polymers. Hence, there is a need to look into the possible initiation of these fracture processes before one can proceed to address the issue of scratch-whitening. The scope of the present study focuses mainly on craze initiation. The governing criteria for craze initiation can also be linked to voiding, debonding, and cracking because these fracture processes are fundamentally related to the same type of stress/strain components, i.e., the critical strain, the maximum dilatation, and the maximum hydrostatic tensile stresses. Of the various criteria for craze initiation, the critical strain criterion by Bowden and Oxborough (54) was adopted. This criterion states that crazing occurs when the strain in any direction reaches a critical value and that this critical strain depends on the hydrostatic tensile stress. (54) Using this criterion, the compressive stress (pressure) contour plots at four different time intervals are given in Figure 8 for Load Case B. Only negative values of the pressure contours are presented, as they correspond to hydrostatic tensile stresses. Inset plots in each of the figures contain the maximum principal strain data that are limited to positive values.

[FIGURE 8 OMITTED]

From these figures, it is apparent that crazes are likely to form in the regions ahead of and around the front sides of the moving indenter. As the indenter thrusts forward, the crazes ahead of the indenter, if they exist at all, will be ruptured based on the previously mentioned scratch damage mechanism. As such, the only crazes that can probably be observed are located along the side ridges of the scratch groove. With regard to Load Case B, it can be inferred that there will be a point along the scratch path where the maximum principal strain would increase to a critical value, beyond which crazing would occur.

As presented, the experimental findings contribute to the current knowledge of the scratch damage of polymers by proposing a reliable graphical approach to determine the scratch hardness of a material. Scratch hardness has been shown to be a crucial parameter for ranking and quantifying the scratch resistance of different materials. Through our study of stress-whitening, talc additives were found to improve on the tensile modulus, yield strength, and scratch hardness, but aggravate the scratch visibility. However, the ductile or brittle mode of failure showed no link to scratch visibility. The use of FE analysis brought forth a more complete understanding of the scratch process. The results generated shed light on the damage mechanism that takes place during a scratch and illustrates the types of deformation a material will undergo, which might include cracking and crazing.

CONCLUSION

An integrated approach that combines equipment development, material science, and numerical simulation was proposed to examine the scratch damage of polymers. For equipment development, a new scratch test device was constructed with the capability to perform a wide range of scratch tests. Our material science study revealed that scratch hardness, as computed by the graphical method, can be treated as an important parameter for scratch resistance. Using VIEEW, scratch visibility was evaluated for different polymeric systems. The addition of talc fillers into the base polymeric system improved the scratch hardness but resulted in worse scratch visibility as compared to unfilled polymer systems. Finally, for numerical simulation, three-dimensional finite element analyses were performed to elucidate the mechanical response of polymer during scratching. Based on the numerical results, a phenomenological deduction of the scratch damage process was presented and was in agreement with published experimental findings. With the use of the critical strain criterion, a prediction on the regions of the craze and/or crack formation was also made.

Table 1 -- Composition of Material Systems

                                                           Coloring
                                                           Compound
Material System  Material Type               Filler (wt%)  (wt%)

1                Polycarbonate (Lexan [R])   --            --
2                Homopolymer PP              --            2NCA (2%)
3                Homopolymer PP              Talc (20%)    2NCA (2%)
4                Copolymer and PP blend      --            2NCA (2%)
5                Copolymer and PP blend      Talc (20%)    2NCA (2%)

Table 2 -- Scratch Hardness and Mechanical Properties (a) of Test
Materials Systems (55)

                                                              Yield
                           Scratch Hardness  Tensile Modulus  Strength
Material                   (MPa)             (GPa)            (MPa)

Polycarbonate (Lexan [R])  55.8              2.38             62.00
Homopolymer PP             55.8              1.73             33.47
Homopolymer PP + Talc      59.4              2.73             35.30
Copolymer PP               27.4              1.07             22.55
Copolymer PP + Talc        29.6              1.55             23.28

(a) Mechanical properties reported from manufacturer data sheet.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial support provided by the Texas A & M Scratch Behavior Consortium (Advanced Composites--Brian Coleman; BP Chemical--Costas Metaxas; Luzenac-Richard Clark; Solvay Engineered Polymers--Edmund Lau; and Visteon--Beth Wichterman and Rose Ryntz) in this research endeavor. The authors would like to acknowledge the generous loan of equipment from Atlas Materials Testing Technology, arranged by Fred Lee. The authors would also like to acknowledge the financial support from the State of Texas (ARP #32191-73130) and Defense Logistic Agency (SP0103-02-D-0003). The third author acknowledges the Oscar S. Wyatt Endowed Chair for supporting the research. Special thanks are also extended to the Society of Plastics Engineers--South Texas Section, for their generous donation of equipment for this research.

*One may refer to Lim et al. (47) for a more detailed description of the FE modeling approach.

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G.T. Lim, M.-H. Wong, J.N. Reddy, and H.-J. Sue([dagger]) -- Texas A & M University*

* Department of Mechanical Engineering, College Station, TX 77843-3123.

[dagger] Author to whom correspondence should be addressed. Email: [e-mail].