1 Introduction

Engineering of polymers is not an easy exercise with evolving technology, it often involves complex concepts and processes. The preparation and characterization of nanocomposites with different polymer matrices shows its considerable scientific and technological potential [1,2,3,4]. Advanced nanocomposites stem from the use of slight fractions of nanomaterials with high levels of dispersion to generate remarkable property enhancement as well as favourable cost-effectiveness, including better mechanical, thermal, electrical, and barrier properties [2,3,4,5,6]. Nanomaterials have garnered interest due to their structural diversity and excellent properties, nanostructured materials and their composites have been extensively studied also for energy storage/conversion related applications [3]. The choice of the organic modifier is considered a key parameter for the preparation of nanocomposites. Exfoliation/dispersion cannot develop properly, even in the presence of a compatibilizer, if the organic modifier is not adapted to the chemical nature of the matrix, whatever the processing conditions and the specific mechanical energy provided during mixing [7].

Continuous melting is more suitable to the optimization of nanocomposites materials, since it is easier to control the thermo-mechanical history imparted on the samples [4, 7,8,9,10]. For continuous melting, the extrusion process is more easily up scalable to an industrial level and thus offers the best possibility form future development of nanocomposites materials. The main largest extrusion process is Twin Screw Extruder (TSE), mainly used for the preparation and process of polymeric materials, through compounding and reactive extrusion, in which the residence times are significantly shorter [7, 11]. It is recognized that the extruder process conditions are important variables that must be optimized to effect a high degree of delamination and dispersion [8, 10, 12]. However, inconclusive observations have been made, both the relationship between thermomechanical stresses applied during processing and dispersion levels remain to be fully understood. Numerical modeling can be a very efficient tool to overcome these difficulties. However, it remains a real challenge, as it necessitates to couple flow simulation in complex geometry, reaction kinetics and evolutionary rheological behavior [11]. Moreover, the information needed is sometimes difficult to obtain with the required accuracy. Melting experiments of polyolens on modular co-rotating TSE presented melting initiation mechanisms and melting propagation mechanisms [13, 14]. Several mathematical models have been developed to predict how melting will occur under different prescribed conditions [13,14,15]. Also, a multiple regression analysis, where the platelet count is determined by transmission electron microscopy (TEM). A model including up to quadratic terms in mean residence time, \(\overline{t}\), and variance, \(\sigma ^2\), but with no cross terms [9]. A particle analysis by light microscopy was performed using the software Analysis (Olympus, Japan). A regression equation between sample thickness and area ratio, allowed to calculated the normalized dispersion index value and used to study filler dispersion and distribution [6]. However, due to the limited number of observations in the dataset, the number of fitting parameters must be kept small in order to be meaningful.

Simulations of flow conditions along the co-rotating TSE were performed using Ludovic®  software, which enables the calculation of the main local flow variables like shear rate, filling ratio, melt temperature, pressure, residence time and dissipated energy, from melting zone to die exit [11, 12]. These simulations were carried out by rheological data (flow curves) to establish relationships between nanocomposites structure and processing parameters along the screw profile, where local physical values cannot be precisely measured (or measured at all) during processing.

A multi-objective optimisation method for composite design in real manufacturing industry for promoting sustainability is used in [1, 16, 17]. The interrelationships between multiple objectives (requirements) were analyzed and classified by hierarchical clustering analysis [1]. The linear regression model obtained was compared to other linear regression models which were obtained by other mathematical techniques, and it has been proved to be the best model which has the smallest gap between predicted values and experimental results. With regard to the PP nanocomposites, previously in [18] the focus was on the interaction of the experimental parameters and properties measure results of PP compatibilized nanocomposites. The results obtained using multivariate analysis of variance (MANOVA) allowed the generalization of observed relations between the processing conditions and the properties studied.

The present study aims at a comprehensive assessment of the different PP nanocomposites properties. The rheological properties of polymer–based nanocomposites have deserved an intensive scientific interest, particulary the oscillatory or dynamic flow [9, 12, 19, 20]. Dynamic behavior of the nancomposites, under different processing conditions, are highly dependent on elastic properties of polymeric materials. Oscillatory flow results of PP/organoclay nanocomposites are analyzed considering the processing conditions effect of nanostructure on organoclay C15A particles, since the presence of a nanostructure in the amorphous polymer matrix alters considerably the viscoelastic behavior in the terminal zone. For that, in this work, several clustering techniques are used to aggregate similar experimental results obtained under different processing conditions.

2 Experimental Setup

Maleated polypropylene (PP-g-MA) was used as a compatibilizer to allow clay dispersion. For continuous melting, the PP nanocomposites were prepared at fixed composition (80/15/5; w/w/w, wt.%) of PP/PP-g-MA/C15A in a modified co-rotating TSE, a Leistritz LSM 30.34. Mixing element is the combination of diversified Kneading Disks (KD) with left-handed/right-handed configuration and/or the adjustable thickness [15]. The 29D long screws, are built through mixing zones separated by feeding elements [18]. Two different screw configurations, with the same numbers and position of conveying and mixing elements, with KD staggered positively (\(90^\circ \)) and negatively (\(-30^\circ \)) were applied to vary the flow and shear conditions. The KD positively and negatively staggered are considered as the low screw intensity (P1) and high (P2), respectively. Relatively to the last one, it is believed that a high shear screw profile (P2) is adequate to ensure the necessary dispersion levels. Different screw speed (N), temperatures (T) and outputs (Q) were chosen.

The processing temperatures selected (T1, T2 and T3, respectively, 170, 180 and 190 \(^\circ \)C) for compounding were set along the barrel and die. The screw speed (N1 = 150 rpm or N2 = 300 rpm) and feed rate (Q1, Q2 or Q3, respectively, 2, 4 or 6 kg.h\(^{-1}\)) were also set. Melting of PP nanocomposites in a modular TSE was carried out as a function of: (i) screw profile, (ii) screw speed, (iii) barrel temperature and (iv) feed rate. Samples were collected along the extruder and at die exit (Fig. 1) and immediately frozen in liquid nitrogen, prior to characterization.

Rheological measurements were performed using a parallel plate rheometer, referenced as a Paar Physica MCR 300. The experiments were carried out in small amplitude oscillatory shear. The samples were characterized in the linear domain through frequency sweep measurements, at a temperature of 180 \(^\circ \)C and a constant strain of 5%, from 0.01 to 100 rad.s\(^{-1}\). This type of characterization allows to highlight the presence of a percolated network formed by the nanofillers [19, 20]. Indeed, for the range of shear rates encountered in extrusion (10–100 s\(^{-1}\)), there is quite no difference in viscosity between matrix and nanocomposite [10]. Thus, rheological data (flow curves) of the PP/PP-g-MA nanocomposites were considered at low frequency (up to 7.2 rad.s\(^{-1}\)) to test the samples.

Fig. 1.
figure 1

Sampling devices and location along the TSE

Full size image
Fig. 2.
figure 2

Effect of P and N, T and Q on the evolution of G’ along the extruder

Full size image

For PP based nanocomposites whatever the processing condition and position along the extruder, an increase of the complex viscosity is observed, which is characteristic of a percolated network formed by the clay platelets [19, 20]. This clearly indicates that the clay tactoids were exfoliated during mixing, at least partially [18]. In the tested conditions, C15A layers are easily dispersed in the PP matrix, compatibilized with PP-g-MA, even though P2N1 and P2T1 provides better results. Morphological evolution along the extrusion profile, independently of processing conditions, revelead that microscale dispersion primarily happens in the melting zone, whereas discontinuous exfoliation is, generally, observed along the mixing zones, up to the die exit (Fig. 2). The results indicate that exfoliation is mainly issued from clay tactoids and small aggregates, emphasizing the crucial role of primary microscale dispersion on the final structure and properties of the nanocomposites [3, 7,8,9]. This result showed that not only screw profile and processing conditions are important processing parameters but the also evolution of dispersion along the screw axis. Actually, flow along the restrictive screw elements generates the stresses and residence time levels required for a good development of both intercalation and exfoliation. Still, local influences of stress and residence time may cause significant viscous dissipation [10,11,12] which, in turn, could decrease matrix viscosity and facilitate its draining out from the C15A clay galleries, total or partially, and the evolution will either develop much slower, remaining basically constant, or reversion may be observed, depending on the selected processing conditions. To identify the local differences a new methodology is used and presented next.

3 Methodology

Classification and clustering analysis are commonly used in industrial applications. While classification attempts to assign new subjects into existing groups based on observed characteristics, clustering divides subjects into different clusters so that the within-cluster variations are small compared with the variation between clusters. The goal of this unsupervised learning tecnique is to assign each subject into one of the clusters based on some similarity measure [22,23,24]. There are many methods available in literature for clustering analysis.

In this work four clustering algorithms are considered, namely: (i) Hierarchical Agglomerative Clustering (HAC) algorithm, that initially places each observation in its own cluster and then the clusters are successively joined together by their “closeness”, determined by a dissimilarity matrix. The number of clusters can be estimated by applying cuts at a chosen height in the dendrogram; (ii) iterative method K-means which minimizes the within-class sum of squares for a given number of clusters. It starts with an initial guess of the clusters center and placing each observation in the cluster to which it is closest to. Next the cluster centers are updated until the cluster centers no longer move; (iii) Partitioning Around Medoids (PAM), that although similar to K-means, is consider more robust since it admits the use of other dissimilarities besides the Euclidean distance; (iv) Fanny performs fuzzy clustering, where each observation may present partial membership to each cluster, indicated by a vector of probabilities.

In order to assess the cluster quality, different measures may be used [22]. Internal validation measures (IVM) consider only intrinsic information in the data. In fact, only the dataset and the clustering partition as input are used. Three very often used IVM are: (i) connectedness, (ii) compactness, and (iii) separation of the cluster partitions. Connectedness indicates the extension to which observations are placed in the same cluster as their nearest neighbors. Compactness evaluates cluster homogeneity, by looking at the intra-cluster variance. Separation quantifies the degree of separation between clusters, typically by measuring the distance between clusters centroids. Since compactness increases with the number of clusters, but separation decreases, popular methods combine the two measures into a single score. Dunn’s index and silhouette width are examples of non-linear combinations of the compactness and separation [25]. The silhouette width lies in \([-1, 1]\), while Dunn’s index and silhouette width vary from zero to \(\infty \), and both should be maximized. In contrast, the connectivity takes a value between zero and \(\infty \) and should be minimized.

4 Results and Discussion

In this section we present the results concerning G’ for low frequencies, more precisely frequencies up to 7.2 rad.s\(^{-1}\). The samples were collected at three locations along the TSE: L/D = 9.5, 11 and 32 (see Fig. 1). Figure 3 shows the evolution of G’ as the frequency increases. For L/D = 9.5 Fig. 3 suggest that G’ curves may be separated into two groups. The curves relative to P2N1 present a very similar behavior and appear to distinguishing from all the others. While for L/D = 11 the curves all seem very similar. Finally, for L/D = 32 the G’ curves seem divided into two groups, the first includes P2N1 and P2T1 experiment curves.

Fig. 3.
figure 3

G’ at L/D = 9.5 (left), 11 (center) and 32 (right)

Full size image

For assessing if the groups of curves depicted in Fig. 3 are in fact significant, four clustering algorithms were consider, namely: HACFootnote 1, K-means, PAM and fanny, briefly distinguished in Sect. 3. Previously to the analysis, a z-score standardization was applied to the variables. The most adequate clustering algorithm and number of clusters was selected from the four algorithms and three validation measures, described in Sect. 3. The results were obtained using the clValid [21] package from R and are depicted in Figs. 4, 5 and 6.

Fig. 4.
figure 4

Internal validation for G’ at L/D = 9.5

Full size image

For L/D = 9.5, we can observed that for all algorithms the connectivity is minimized for two clusters, also Dunn’s index and silhoutte width are maximized for two clusters (Fig. 4). Considering L/D = 11, two is the number of clusters that minimizes the connectivity, for any of the algorithms (Fig. 5). The number of clusters that maximizes the Dunn’s index is five for HAC, K-means and PAM algorithms, and four for the fanny algorithms. The silhoutte width is maximized for two clusters. Finally, for L/D = 32, we can observed that for all algorithms the connectivity is minimized for two clusters, also the Dunn’s index and the silhoutte width are maximized for two clusters.

Fig. 5.
figure 5

Internal validation for G’ at L/D = 11

Full size image
Fig. 6.
figure 6

Internal validation for G’ at L/D = 32

Full size image

Table 1 summarizes the internal validation results. For most cases Dunn’s index and silhouette width the best solution was obtained using the HAC methods for all locations along the TSE. Concerning with connectivity PAM is the best algorithm for L/D = 11 and L/D = 32, while HAC is the best for L/D = 9.5. The number of clusters (#C) is two for all cases except for L/D = 11 with Dunn’s index (Table 1). Taking this into consideration, two clusters and HAC method are considered. The two clusters are also suggested by the screeplots in Figs. 7, 8 and 9.

Table 1. Optimal scores
Full size table

Concerning the TSE location L/D = 9.5 (Fig. 7), the first cluster consists of the replications of the experiment P2N1, that corresponds to the processing conditions with the highest shear screw profile (P2) and the lower screw speed (N1). Therefore the different replications under these processing conditions present similar behavior, with high dispersion. The second cluster includes the flow curves for all the other processing conditions, indicating the different conditions do not yield significant differences in the nanolayers dispersion.

Fig. 7.
figure 7

Scree plot and dendrogram for G’ curves at L/D = 9.5

Full size image
Fig. 8.
figure 8

Scree plot and dendrogram for G’ curves at L/D = 11

Full size image

The cut height of the clusters for the TSE location L/D = 11 (Fig. 8) is smaller than the one for L/D = 9.5 (Fig. 8), which is in line with the flow curves behavior observe in Fig. 3. In fact, at L/D = 11 the flow curves present quite similar behavior for different processing conditions. From the two clusters in Fig. 8 it is not possible to asses that the processing conditions favor, for this particular TSE location, the material dispersion. At die (L/D = 32), the two clusters indicate that high screw profiles (P2) with low temperatures (T1) or high screw profiles (P2) with low velocities (N1) favor nanolayers dispersion. In fact, all the replications under conditions P2N1 and P2T1 present very similar flow patterns (Fig. 9). For the other processing conditions the dispersion pattern is quite different from the one presented for P2N1 and P2T1.

Fig. 9.
figure 9

Scree plot and dendrogram for G’ curves at L/D = 32

Full size image

5 Conclusion and Future Work

In this paper the structural features of organoclay C15A dispersions in PP/PP-g-MA, under different processing conditions were considered. The rheological results (\(G'\) curves) at frequencies up to 7.2 rad.s\(^{-1}\), of the resulting PP nanocomposite samples are investigated in detail along the screws (L/D = 9.5, 11 and 32). For this purpose four clustering techniques and three internal validation measures are used to aggregate similar experimental results obtained under different processing conditions.

The results show that hierarchical clustering yields the best results and two is the best number of clusters. Two clusters are evident for L/D = 9.5. The first cluster contains P2N1 experiments, corresponding to highest shear screw profile and lower screw speed, where higher dispersion is obtained. The other cluster contains all the other experiments. Therefore the different processing conditions have no significant effect for the second cluster. These evidence is not so clear for L/D = 11, with G’ values very similar between experiments. For this particular TSE location, it is not possible to asses that processing conditions favor material dispersion. At die exit the two clusters are well divided and high screw profiles with low temperatures or high screw profiles with low speeds favor dispersion.

In future we intend to study if other material properties are grouped according for the same processing conditions. The same clustering techniques can be used and one may compare if the membership is similar with the one obtained for G’. We intend also to investigate other material measures such as TEM.