Differentiation of non-black fillers in rubber composites using linear discriminant analysis of principal components

1 Introduction

Fillers are mainly used in rubber compounding to enhance the physical properties of rubber composites. They can also be utilized to lower the cost of rubber compounds and impart special properties such as color, impermeability, oil resistance, etc. [1, 2]. The rubber industry employs a wide range of fillers. Carbon black has been the most important filler for rubber composites in terms of reinforcement [1, 2]. However, the dependence of carbon black from petroleum feedstock, its polluting nature, and imposed restriction in color have prompted rubber manufacturers to use non-black fillers [3, 4, 5, 6, 7, 8, 9]. Among non-black fillers, precipitated silica provides the highest degree of reinforcement [10]. Other non-black fillers include clays, calcium carbonate, silicates, talc, and metal oxides [1, 2, 10, 11, 12]. Silane coupling agents improve the chemical compatibility of non-black fillers with rubber matrices for more efficient reinforcement [1, 2, 6, 7, 9, 10, 12]. Recently, rubber nanocomposites demonstrate excellent mechanical properties due to the addition of organoclay at low loadings [13, 14, 15]. The organic modification of clay using quaternary ammonium salts allows intercalation and exfoliation of clay nanoplatelets in the rubber matrix. This translates to improved dispersion of the non-black filler in the rubber matrix and enhanced reinforcement.

Design of rubber composites for a specific application requires the particular selection of the type of filler. With a large number of fillers available in the market, rubber manufacturers must be able to differentiate fillers from one type to another based on its effect on the processibility and the final material properties of the rubber composite. However, fillers are currently classified according to their reinforcing effect or function. Waddell and Evans [10, 11] categorized non-black fillers as non-reinforcing, semi-reinforcing, reinforcing, or highly reinforcing based on the surface area of the filler and the corresponding hardness of the rubber compound. Mouri [2] differentiated non-black fillers according to function: reinforcing, diluent, or those adding special traits like color, electrical conductivity, flame resistance, etc. Aside from physical reinforcement, non-black fillers also affect other important properties of rubber composites such as vulcanization characteristics and heat aging resistance [3, 4, 16, 17, 18, 19]. Analysis of material properties is usually performed in a univariate approach, where each property is investigated separately from the others. Such a method of analysis is slow and difficult especially when a large number of properties is involved. On the other hand, a multivariate approach in analyzing the material properties results in the retrieval of global information from all the properties at the same time [20].

In order to examine various material properties simultaneously for the differentiation of non-black fillers in rubber composites, linear discriminant analysis (LDA) was used. LDA classifies an observation into a group if the Mahalanobis squared distance of the observation to the group center is the minimum. Each group has a linear discriminant function. For each observation, the group with the smallest squared distance has the largest discriminant function [21, 22, 23]. In this study, an observation corresponds to a set of material properties measured from a sample of the rubber composite. Meanwhile, a group indicates a known type of filler used to prepare the rubber composite.

In this study, 19 different material properties were measured from a set of 30 experimental rubber composites. The analyzed properties were vulcanization characteristics (minimum and maximum elastic torques, scorch and curing times, cure rate index) and mechanical properties (tensile stress at specified elongations, tensile strength, strain at break, hardness) before and after heat aging. Rubber compounders use these properties to compare and assess different product formulations. A high correlation exists among the analyzed properties (multicollinearity), e.g. maximum elastic torque correlates with tensile properties and hardness of rubber [24]. Multicollinearity decreases the classification ability of LDA [23] with the discriminant function poorly predicting the membership of observation into a group. Following the suggestion of Næs and Mevik [23], the principal components (PCs) were first derived from the data set of properties and used it as input to LDA. PCs are uncorrelated variables that are linear combinations of the observed variables [25], e.g. the measured properties of the rubber composite. A few PCs can represent an appreciable amount of variation present in the original variables [25, 26]. In other fields of research, LDA of PCs has been successfully used to differentiate bricks [27], olive cultivars [28], fishes [29], ballpoint pen inks [30], gasoline [22], olive oils [31], and wines [32].

This paper evaluates how vulcanization characteristics and mechanical properties before and after heat aging of rubber composites differentiate and predict the type of non-black filler using LDA of PCs. This paper also determines which specific set of material properties, e.g. vulcanization characteristics, mechanical properties, or combined, best discriminate between different types of non-black filler in rubber composites.

2 Experimental

3 Results and discussion

The minimum number of PCs needed to represent the variation in the material properties of rubber composite depends on the type of data input (see Figure 1). Following Kaiser’s rule [25], the first PC (PC1) already captures the variation in the mechanical properties of rubber composite before heat aging (data input M). The variations in vulcanization characteristics (data input V) and mechanical properties after heat aging (data input MA) require at least the first 2 PCs. Combining data inputs does not significantly increase the required number of PCs, e.g. first 2 PCs forV+MandM+ MA; first 3 PCs for V+MAandV+M+ MA. The eigenvalue at PC1 increases with the number of material properties included in the data input. Each material property in the data input has a variation that contributes to the magnitude of PC1’s eigenvalue [25, 26].

Figure 1

Eigenvalue as function of the number of PCs for different data inputs.

The PC1 calculated from data inputs M, MA, and M + MA explains more than 75% of the variation in the material properties (see Figure 2). Meanwhile, the PC1s from the other data inputs only retain 50 - 65% of the initial information. The addition of the second PC (PC2) further increases the amount of retained information by more than 80% in all data inputs. Four PCs allow more than 95% of the relevant information from the different data inputs to be explained.

Figure 2

Cumulative explained variance as function of the number of PCs for different data inputs.

Aluminosilicate and silica composites can be differentiated from bentonite composites using vulcanization characteristics as sole input to PCA (see Figure 3A). The difference in elastic torque (ML and MH) and cure rate (CRI)

Figure 3

PCA of data input V. Distribution plots of the rubber composites (A) and material properties (B) on PC1 and PC2.

enables the separation of the 2 non-black fillers from bentonite (see Figure 3B). Both aluminosilicate and silica have surface areas higher than bentonite due to their smaller particle size which contribute to high viscosity and elastic torque of rubber composites [34]. All aluminosilicate composites have negative PC1 values where CRI is positively associated. Silane treatment of the aluminosilicate contributes to the increase in the cure rate [35].

Aluminosilicate and silica composites can also be distinguished from bentonite composites using mechanical properties of unaged samples (see Figure 4A). The clustering of aluminosilicate and silica composites in the positive PC1 axis indicates higher tensile stress at varied strains (100%Mod, 200%Mod, and 300%Mod) and hardness than bentonite composites (see Figure 4B). Similar to elastic torque, the high surface areas of aluminosilicate and silica also increase the tensile stress responses and hardness of rubber composites [34].

Figure 4

PCA of data input M. Distribution plots of the rubber composites (A) and material properties (B) on PC1 and PC2.

The use of mechanical properties of heat-aged samples in PCA results in better discrimination among the 3 non-black fillers (see Figure 5A). Aluminosilicate and silica composites are differentiated from bentonite composites in the PC1 axis due to high tensile stress responses and hardness (see Figure 5B). PC2 separates the aluminosilicate from silica composites through the values of A-TS and A-SB. After heat aging, silica composites have higher TS and SB than aluminosilicate composites.

Figure 5

PCA of data input MA. Distribution plots of the rubber composites (A) and material properties (B) on PC1 and PC2.

Clustering of rubber composites according to the type of filler also occurs when different material properties are combined as input to PCA (see Figure 6). Aluminosilicate and silica composites are easily distinguished from bentonite composites with data input V + M (see Figure 6A)

Figure 6

Distribution plots of the rubber composites on PC1 and PC2 for the generated data inputs: V + M (A), V + MA (B), M + MA (C), and V + M + MA (D).

where the PC1 axis is heavily influenced by ML, MH, tensile stress at varied strains, TS, SB, and hardness (see Figure 7A). With the addition of mechanical properties of heat-aged rubber composites in the data input, i.e. V + MA (Figure 6B), M + MA (Figure 6C), and V + M + MA (Figure 6D), aluminosilicate is differentiated from silica. In data inputs V + MA and M + MA, aluminosilicate composites have higher PC2 values than silica composites. On this direction, the discrimination is mainly due to the variation in scorch and curing times, TS and SB before and after heat aging of rubber composites (see Figure 7B and 7C). In data input V + M + MA (see Figure 6D), aluminosilicate is separated from silica in the PC2 axis mainly due to differences in scorch and curing times and A-SB (see Figure 7D).

Figure 7

Distribution plots of the material properties on PC1 and PC2 for the generated data inputs: V + M (A), V + MA (B), M + MA (C), and V + M + MA (D).

The loading plot from data input V + M + MA (see Figure 7D) shows the type of correlation among the 19 material properties of rubber composites. MH strongly correlates with the mechanical properties of unaged and aged samples (positive correlation with tensile stress at varied strains and hardness; negative with SB). This confirms the use of MH as a good indicator of tensile properties and hardness of rubber vulcanizates [24] even after heat aging. At the same time, ML correlates well with the TS of heat-

aged samples. Meanwhile, the negative correlation of CRI with ts2 and tc90 is due to the given inverse relationship between these parameters [33].

LDA reveals that when 2 PCs are used (which explains > 80% of the total variation in the data input), the classification of non-black filler in the rubber composites ranges

from 76.7 - 93.3% correct (see Figure 8). At 2 PCs, data inputs MA and M + MA show the highest percentage of correct classification. Further increasing the number of PCs used in the LDA results to improvement in classification. Data input MA achieves 100% correct classification of non-black fillers with 6 PCs (100% of the total variation in the data input). Among the generated data inputs, V + MA obtains 100% correct classification using 7 PCs. For data inputs containing many material properties as predictors, PCA proves to be beneficial in reducing the dimension of the input data, e.g. from 13 material properties to 7 uncorrelated PCs for V + MA, before usage in LDA.

Figure 8

LDA of data inputs. Percentage of correct classification as function of the number of PCs.

4 Conclusion

Aluminosilicate, bentonite, and silica filler in natural rubber composites can be differentiated using LDA of PCs. Pretreatment of material properties with PCA allows visualization of data patterns that are related to the type of non-black filler. PCA also removes the correlation among material properties and reduces the number of predictors for LDA. Among the material properties tested as input data, the mechanical properties of the rubber composite after heat aging effectively differentiate and classify the non-black filler in the samples.

LDA of PCs has already been applied to differentiate and classify important materials. The results of this study demonstrate that the same method can be utilized to identify fillers using the material properties of the rubber composite as input. This multivariate approach has the potential to assist manufacturers in differentiating and selecting other compounding ingredients such as accelerators and process oils in the design of rubber products.