**1. Introduction**

Plastics are relatively new materials for producing colored materials. As a result, there are few scientific data on plastic color mismatching and its long-term consequences. Plastic fabrication allows for the creation of robust, lightweight plastics in various shapes. In many situations, plastic shapes are favored over metal shapes. Polycarbonate is a rigid, transparent polymer used in a variety of applications. Some factors may significantly impact the color of plastics intended for outdoor use. As a result, it is critical to comprehend how numerous elements can influence material compounding. This research aims to see how processing settings affect color matching for a few grade-color. To generate the proper color with minimal waste, the plastic industry has spent the last few decades seeking to understand the significant challenges involved in plastic color matching procedures. Lambert's law claims that the amount of light absorbed is proportional to the concentration of the absorbing substance. Still, Beers law states that the amount of light absorbed is proportional to the thickness of the absorbing material [1]. Manufacturing technology

**Citation:** Alsadi, J.; Ismail, R.; Trrad, I. An Integrative Simulation for Mixing Different Polycarbonate Grades with the Same Color: Experimental Analysis and Evaluations. *Crystals* **2022**, *12*, 423. https://doi.org/10.3390/ cryst12030423

Academic Editor: Wojciech Polkowski

Received: 6 February 2022 Accepted: 14 March 2022 Published: 18 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

makes colored plastic for plastic process prototyping on a small and medium scale. As a result, the plant receives orders that must be completed in a matter of days.

To summarize, an object's color appearance is determined by the total amount and type of scattering and absorption that occurs. As a result, the item will seem white if there is no absorption and nearly equal levels of scattering at all visible wavelengths; and if the visible light is absorbed by the pigment [2].

Several hundred ingredients are divided into three categories: resins, additives, and pigments. Ingredients and additives combine to create a specific grade of plastic. The pigments give the plastic its color. Because of their surfaces and orientations, the pigments absorb certain hues, while reflecting others randomly.

White light is created by mixing all visible spectrum wavelengths in roughly equal quantities [3]. The light source and observer are replaced with color measurement tools such as a colorimeter or spectrophotometer to standardize color evaluation in the plastic compounding industry [4].

As color is represented in codes or values, this allows for more uniform color recognition. There were two data mining approaches used. One was a decision tree classifier, and the other was online analytical processing (OLAP) (DTC). OLAP assisted in identifying a relationship between factors that resulted in failed batches and parameters with a high rate of alteration. The DTC was proposed as a decision assistance tool for detecting combinations of characteristics that could cause a color mismatch. The DTC investigates characteristics that could lead to color mismatch issues in compounded polymers. To find such factors in the past, OLAP and data mining methodologies were applied [5–7].

Overall, DTC was utilized in this study to investigate possible correlations between the components of color, grade, kind, product, and line. To the best of our knowledge, no research has used DTC for color mismatch analysis, according to our literature review. DTC is used in some relevant manufacturing articles (semi-conductors [8]). Other researchers have used neuro-networks to forecast output colors based on past data [9].

In previous studies, the artificial neural network (ANN) was utilized to eliminate mistakes in polycarbonate color values [10]. The neural network in this paper was used to reduce the errors in color tristimulus values (L\*, a\*, b\*), which directly affect the D.E. calculated [11].

The problem cannot be solved by concentrating on a few situations because the colors' nature is constantly changing. Therefore, this research proposal focuses on determining the fundamental causes of color mismatches in compounded plastics. As a result, plastics firms will reduce waste and boost production. More importantly, it will improve knowledge of the technical challenges of color matching in plastic production. Focusing on resolving challenges for a single product is complex and potentially fruitless because that product may not be duplicated in the future. Compared to the paint industry, color mismatch issues have not been investigated deeply through the plastic compounding business. The parameter(s) creating first-pass color opportunities must be discovered to limit material rejects. Researchers mixed three different titanium dioxide pigments into heavily loaded polyethylene masterbatches, each with a different surface treatment.

They discovered that the three grades' best screw design and operating conditions were considerably different. Processing circumstances or certain combinations of modifiers and additives in the resin system were shown to have a negative impact on the final desired hue [12,13]. Paints and coatings have had a lot of research done on pigment dispersion, but plastics have not gotten nearly as much attention [14,15].

The high shear rates, processing temperatures, and processing pressures used in plastics manufacturing operations [16,17] significantly contrast the two dispersion mechanisms. Various scholars have conducted several investigations, during compounding, on the effect of processing parameters on color [18,19]. The minimum processing time is advised to achieve excellent gloss, brilliance, and blend uniformity. Furthermore, for each item, an optimal loading should be utilized; too much pigment is not only expensive but also hazardous because it diminishes impact resistance [20,21]. Increase the duration of the

mixing and decrease the viscosity of resin to solve problems with dispersion or achieving a homogeneous mixture [22,23]. Various researchers have conducted a few investigations on the influence of processing factors on dynamic mixing in a screw extrusion during polymer compounding [18,24].

Many scientists have reviewed polymer blending as an essential field of polymer science. As Sanchez et al. [25] demonstrated, the PC/PBT blends are transparent in the melt stage and somewhat miscible blends in the solid state.

Liang and Gupta (2000) investigated the rheological qualities of a recycled P.C. blended with virgin P.C., concluding that separated P.C. could be added to pure P.C. up to 15% without significantly affecting its properties [26]. Lee S. et al. investigated the rheological and phase behavior of P.C./Polyester blends. They discovered, however, that the combinations do not obey the mixing rule, which is standard in all investigations. They discovered, however, that the combinations do not obey the mixing rule, which is standard in all investigations [27]. Other researchers' experiments on extruders showed that single screw extruders could reach dispersive mixing capabilities comparable to twin-screw extruders [28].

A 45-mm diameter single-screw extruder with eight glass panes was used in another investigation to investigate the color mixing process [29]. The researchers determined where color mixing began and finished by using such an extruder. The quality of mixing was shown to be directly proportional to the maximum processing pressure in the extruder. Furthermore, earlier research has examined how the screw shape and operating conditions affect dispersion performance and torque loading during twin-screw compounding [30].

One of the most significant color matching components taken from a remote location is spectrophotometric measures to create a suitable color standard. Spectrophotometers are valuable quality control equipment for measuring color and defining color variations numerically. However, their function as a device is to reduce a color target to a collection of numbers, which are subsequently sent to a color formulator as a matching target [31,32]. CIELAB is the name of the color measurement method. The values utilized by CIE are named L\*, a\*, and b\*. L\* denotes the difference between light (L\* = 100) and dark (L\* = 0), a\* denotes the green (−a\*) and red (+a\*) difference, and b\* indicates the yellow (+b\*) and blue (−b\*) difference [33,34]. dE\* is used to express deviations in L\*, a\*, and b\*, where:

dE<sup>∗</sup> = (ΔL∗) <sup>2</sup> + (Δa∗) <sup>2</sup> + (Δb∗) <sup>2</sup> (1)

The color difference's amplitude, not its direction, is represented by dE\*. As a quality control measure, colored materials are compared to a standard when being manufactured. Color discrepancies are employed instead of absolute color values. The total color change, dE\*, shows the color difference in the CIELAB color space [17,35].

The findings of designed experiments were analyzed and discussed in this study, which highlights individual and combined influences on output color of three process parameters.

The experimental data confirm the statistical model's fitness [36] by systematically examining resins, additives, and pigments, and how processing conditions and diverse interactions impact them. More precisely, the scientific concerns surrounding the twin co-rotating screw process processing parameters on different grades of the same color were explored. The study's main aim was to develop an equation that might be used to determine differences between the two samples and could be used to any color at any time. To explore the impact of parameters on color and detect non-optimal responses, a five-level controlled response method was used on 45 different treatments. The anticipated regression models were built using the ANOVA for three different grades. Speed, temperature, and F.R. were among the processing characteristics studied. To provide a foundation for process improvement recommendations, experimental data were collected, and statistical analysis was undertaken.

#### **2. Materials and Methods**

The three classes with the highest adjustment when dealing with red pigments were discovered based on preliminary data mining results from the first few months of 2009. In this study, these grades were denoted by the numbers 1, 2, and 3. For the dispersion of color in parts per 100 among these grades, a mixture of two polycarbonate resins and four distinct pigments were utilized (PPH). As indicated in Table 1, all three grades utilized the same color, as were shown in Figure 1.


**Table 1.** Compounding formulation used for three grades.

**Figure 1.** Three grades have different formulations but the same color.

Grades 1 and 2 used a mixture of two polycarbonates resins with various weights of the same pigments, while grade 3 used one poly car resin with the same weight of pigments as grade 2. As a result, resin 1 had a melt flow index (MFI) of 25 g/min, while resin 2 had an MFI of 6.5 g/10 min, where the weights were heavier than water, and the temperature for autoignition was 630 ◦C for all grades. At the industrial plant, three grades were subjected to testing. The materials were extruded at L/D ratios of 37 and Do/Di ratios of 1.55, respectively, utilizing a twin-screw extruder (25.5 mm, 27 kW). There were ten heating zones on the extruder, nine designated on the barrel, and one at the die.

The extruded melt was then pelletized after being quenched in cold water. These pellets were subsequently formed into rectangular chips (3 × 2 × 0.1 inches), which were measured against a target value via injection molding. Three coupons were created for each experiment at each of the five-parameter values to assure accuracy. Then each voucher was given three readings. The total simulating design data for the tristimulus color value with the three processing parameters were 45 runs, as recorded in Table 2.


**Table 2.** Response surface design 45 runs for 3 grades.

In CIE L\*, a\*, and b\* values, L\* = 67.57, a\* = 1.43, and b\* = 4.8 were chosen as the required color output, while the permitted dE\* was 0.85. Using the Software of Design-Expert, Version 8, Stat-Ease Inc. (Minneapolis, MN, USA), the statistical data were established. Then the data were used to compare and analyze the factors' effect on grades. The ANOVA determined which parameters were significant and whether there was any interaction between them. As previously stated, the study's goal: develop an equation that could help in expecting the L\*, a\*, and b\* tristimulus values.

#### **3. Results**

The design of the experiment was used to do statistical analysis and ANOVA. Using Stat-Ease Design Expert® Version 8 software, the influence of parameters on L\*, a\*, b\*, and dE\* was investigated, as seen in Table 3.



Note: A Temp, B Speed, C Feed Rate, D grade, Y1 L\*, Y2 a\*, Y3 b\* and Y4 dE\*.

#### *3.1. Analysis of Variance (ANOVA)*

Sequential F-tests were run using a linear model as a starting point and adding terms (quadratic and linear if appropriate). The F-statistic was assessed for each model type, and the highest degree and critical elements model was picked. The same procedure was used for all tristimulus values, and only the significant terms were included. The ANOVA table for the sum of squares of a sequential model for dE\* characterization is shown in Table 4. The quadratic model with the Prob > F was < 0.05, the most considerable condition. Furthermore, it was statistically significant (Prob > F was less than 0.0001) because it had a high F value (184.4). As a result, this model was suitable for the dE\* response. The model's adjusted R-square value (97%) also corroborated this, as seen in Table 4.

The adjusted R-square measure was the same as the R-square measure, except that it was scaled down to account for the number of variables in the model. Both measures represent the model's capacity to explain variation in the answer. For example, the observed adjusted R-square value of 97% showed that the model explained roughly 97% of the variability in dE\*. In contrast, about 3% of the variability in dE\* was unknown.

The adjusted R-square value of 0.96 was reasonably close to the predicted R-square value of 0.95. A signal-to-noise ratio was used in the Adeq Precision measurement. It is ideal to have a ratio of more than four. The observed percentage of 35.5 specified that the observed variance is significant compared to the fitted model's underlying uncertainty. In other words, the observed variance was significant in proportion to the fitted model's underlying uncertainty. The design space systems can also be generated by using the exact modeling.


**Table 4.** ANOVA for the color of three grades.

Feed rate (C) and grade (D) had significant effects on dE\*, as shown in Table 4. Their *p*-values (Prob > F) were equal or less than 0.05 (typically ≤0.05), indicating that they were statistically significant models. On the other hand, temperature (A) and speed (B) had large *p*-values, indicating that they were not statistically significant for the dE\* response. The interaction between feed rate (C) and the investigated grades (D) would be statistically significant if a confidence level of 90% was assumed; the *p*-value for this interaction (CD) in the model fitted to dE\* was 0.0583 (see Table 4).

#### *3.2. Simulate Regression Models*

The expected response for each response was determined using multiple linear regression analysis. Equations (2)–(13) depict the response functions for grade 1, 2, and 3 for L\*, a\*, b\*, and dE\*, respectively, as shown in Table 5.



#### *3.3. Point Prediction*

The response surface method was optimized using a "numerical optimizer" for the lowest color value (dE\*) in the feasible region. The Design-Expert response®'s (Minneapolis, MN, USA) optimizer calculated numerous local (feasible area) variables. For each grade, Table 6 provides the predicted tristimulus color values of CIE (L\*, a\*, b\*, and dE\*). Minor deviations were detected in the color values acquired by the optimization process. These discrepancies could be due to a lack of precise temperature control during the extrusion

process, which affects the viscosity of the polymer, as well as the pigment dispersion and ability to obtain the required color.


**Table 6.** Simulate tristimulus color solutions.
