Effect of various formulation ingredients on thermal characteristics of PVC/clay nanocomposite foams: experimental and modeling

2.1 Materials and sample preparation

Suspension grade PVC – K-value 65, Vestolite S6558, Mw=90,000, Mn=40,000 and PDI=2.25 – was provided by Bandar-e-Imam Petrochemical (Mahshahr, Khozestan, Iran). An acrylic processing aid, Paraloid K-400, was purchased from Rohm and Haas (PHL, PA, USA). The NC (Cloisite 30B) was supplied from Southern Clay Products (Gonzaless, TX, USA). All other ingredients were commercial grade products.

Table 1 shows the nanocomposites formulation were prepared using a laboratory high speed mixer. Primarily, the ingredients were loaded into the mixer containing PVC for ~20 min to obtain dry blends. The fusion behavior of each dry blend was melted in a Brabender Plasticorder, PL 2000, equipped with a 65 cm³ mixing chamber, at 165°C and 60 rpm, for 3 min.

2.2 Characterization

The X-ray diffraction (XRD) patterns of the samples were obtained in the 2θ range of 5–70° using a Philips MPDx pert X-ray. The thermogravimetric analysis was conducted using a TG-DTA Perkin-Elmer TGA (USA) at heating rates of 20°C/min, under nitrogen atmosphere.

2.3 Artificial intelligence modeling

In the current study, for creating an efficient model, ANNs and CS-ANN were used. CS is the optimizer added for determining the optimal parameters of the ANN. CS was chosen to solve the problems (23).

The main steps of the CS algorithm are initialization, selection of the set of antibodies for cloning, hypermutation of clones in order to create new individuals with improved capabilities and receptor editing. In the initialization step, a set of antibodies is generated using uniform distribution probability. In order to improve this step, the opposition based learning (OBL) principle is applied. OBL was developed by Tizhoosh (32) as a new scheme for machine intelligence. It is based on the idea that the probability of an individual x to be better than its opposite x¯ is 50%. After random generation of antibodies, respective opposite forms and the affinity can be computed.

The antibodies with the best affinity select for cloning. The clones are then hypermutated using a hypermutation operator. This operator is based on three types of hypermuations (Gaussian, non-uniform and pair wise). Using a random number generator, each time after hypermutation, one of the operators is randomly chosen. The main idea behind this approach is to explore the multiple search directions, and to reduce the probability of getting stuck in local minima.

In the receptor-editing step of the algorithm, the selection of the antibodies for the new generation is performed. The remaining antibodies are replaced with new ones, hence, diversity is being introduced into the population.

Finally, the best solution found by randomly applying the back propagation (BK) or random search algorithm. This variant is an improvement of previously proposed CS-ANN combination called the normalized clonal selection multilayer perceptron neural network and back propagation (nCS-MBK). Differential evolution approaches lead to appropriate results as applied to the model of siloxane organic polyazomethine synthesis process.

The algorithm scheme performed for modeling the process is presented in Figure 1.

Figure 1:

Simplified schema of the modeling methodology.

In the literature, various sorts of parameters are reported to be optimized by algorithms such as connection weights, architecture, learning rules and node behavior (23). In the current study, three categories are evolved; weights, architecture and node behavior.

Optimizing the weights is related to the training procedure, optimizing the architecture implies the identification of the best structure of the ANN (number of hidden layers and number of neurons in each hidden layer), and node behavior is related to the functionality of the nodes (transfer functions). Here, the node can be one of the following transfer functions: linear, bipolar sigmoid, logarithmic sigmoid, tangent sigmoid, sinus, radial basis, triangular basis and logistic. Although, it is possible to explore the multitude of the functions based on a series of practical considerations.

There are various types of ANN models. Among them, the multilayer perceptron feed forward artificial neural network (MLP) has generated great interest. It is a fully coupled ANN, and each input activates all the hidden nodes. The MLP usually has one or more hidden layers, which enable the network to model non-linear and complex functions. Nevertheless, the number of hidden layers is difficult to decide. One hidden layer is normally adequate to provide an accurate prediction and can be the first choice for any practical feed-forward network design.

It is crucial to highlight that the determination of the number of neurons in hidden layers is very important as it affects the training time and generalization property of neural networks. A higher value of neurons in the hidden layer may force the network to memorize (as opposed to generalize) the patterns which have been observed during the training, whereas a lower value of neurons in the hidden layer will waste a great deal of training time in finding its optimal representation. However, there is no general rule used in selecting the number of neurons in a hidden layer. Thus, it is dependent on the complexity of the study system being modeled.

As the dimensionality of the model (number of hidden layers and neurons in the hidden layer) influences the computational costs and there must be a correlation between the training/testing exemplars and model complexity, a series of limitations were imposed on the architecture of the model, which is automatically determined by the optimization procedure. Consequently, the model can have a maximum of two layers with a maximum of 15 and 10 neurons, respectively. On the other hand, in this work, the number of inputs and outputs is determined by the process characteristics, the inputs being represented by NC, ADCA, K-400 and Ca.St and the outputs by T_5%, T_50% and char.

3.1 X-ray diffraction analysis

The extent of interactions and formation of nanocomposites were measured using XRD. Among all samples, 14 samples were selected for XRD analysis. As shown in Figure 2, the XRD diffractograms of all the samples are almost the same. A broad peak at around 2θ=25° is due to PVC (Figure 2–inset). A very intense peak at 2θ=10° and 28 in some samples (4), (8), (11) is due to a low interaction between NC and PVC. However, samples 13, 14, 15 and 18 are mostly exfoliated.

Figure 2:

XRD patterns of PVC and PVC/NC nanocomposites.

3.2 The effect of incorporated ingredients on ash content

Figure 3A shows an obvious increase in ash content versus NC. Upon increasing NC content from 2 to 4 phr, an increase in ash content can be observed. This is due to the barrier effect of the silicate layer, which further affect flame retardancy of the system (5). However, because of clay aggregation in the polymer matrix, further increase in clay content up to 6 phr does not influence the amount of ash content. The so-called phenomenon indicates that the sample with 4 phr clay can be considered as an optimum point.

Figure 3:

The effect of nanocomposite ingredients on the ash content yielded from TG analysis; (A) clay content (phr), (B) ADCA (phr), (C) K-400 (phr), (D) Ca.St. (phr).

The NC may impart two opposite functions into the thermal properties of nanocomposites; barrier effect which improve the thermal stability and a catalytic effect that can impair stability (33). In the current study, a proper incorporation of PVC chain into the silicate layers shows diminution in degradation maxima and reaction profile as compared to the neat PVC. The authors assume that this phenomenon is due to the catalytic effect of Lewis acid sites in silicate layers by catalyzing the hydrolysis of polymer linkages. Moreover, Bordes et al. (34) expressed that the surfactants enhance the degradation of polymer according to the Hoffmann elimination reaction or a nucleophilic attack of ammonium counter-ion. Moreover, the silicate layers can act as a heat source by holding accumulated heat to accelerate the decomposition of the polymer.

Interestingly, by comparison between the samples with various NC content but the same amount of other ingredients, i.e. ADCA, K-400, and Ca.St, the ash content gradually increases. This trend is directly related to the content of the other ingredients. Moreover, upon increasing the NC content, a reduction in T_max is observed. This is true when the content of other ingredients in the samples are the same. This is most probably due to the catalytic effect of NC in the nanocomposites (19), (35). The results are listed in Table 2.

Upon increasing ADCA (Figure 3B), the ash content first increases in the sample with 0.2–0.4 phr ADCA. However, this trend decreases in the sample containing 0.6 phr of ADCA. It must be mentioned that an optimal trend can be obtained in 0.4 phr. The ascending order in the low-to-middle region can be attributed to the population of cells due to ADCA foaming agent. This decreasing trend is typically associated with the formation of large cells having thin skins. These cells can be easily cracked ending in enhanced burning of neat PVC.

In a study on the samples with the same NC, K-400 and Ca.St content and different ADCA content, the ash content gradually increased (Table 2). Thus, a decrease in the thermal degradation profile, i.e. T_max can be also observed in most of the as mentioned samples.

The effect of Ca.St on the ash content of the blends is shown in Figure 3C. The results indicate that upon increasing Ca.St, the ash content increases. However, this trend is not linear. The first increase in ash content could be due to enhanced interlayer distance, or the complicated mechanism of polymeric chain decomposition by Ca.St, whereas, a decrease in ash content might be due to the retardation effect at elevated concentrations of Ca.St (36).

A comparison between the samples containing various K-400 contents shows that in these samples, the ash content gradually increases from 6.1 to 16.9 mg, 3.1 to 17.4 mg and 9.92 to 15.8 mg. Moreover, the increase of K-400 leads to a slight decrease of T_max1, T_max2 and T_max3.

Likewise, the trend in ash content passes an optimum in the case of K-400 (Figure 3D). This would be a characteristic of enhanced dispersion of NC in a polymer matrix, which can be due to the complete interaction. Moreover, it was found that upon increasing the Ca.St content in the samples with the same NC, ADCA, and K-400, the char gradually increases. Based on maximum degradation temperatures, upon increasing Ca.St content, T_max1, T_max2 and T_max3 are decreased.

3.3 The effect of incorporated ingredients on T_5%

Figure 4 shows the effect of the concentrations of ingredients on the initial mass loss (T_5%) of PVC/NC nanocomposites. Analyzing the results based on this criterion, contradictory behaviors considering fluctuations over ingredient concentrations are observed. The optimal trend over NC content (Figure 4A) can be caused by surface modifier concentration attached on the clay surface. In general, the decomposition initiates due to surface modifier degradation at around 200°C.

Figure 4:

The effect of nanocomposite ingredients on the T_5% yielded from TG analysis; (A) clay content (phr), (B) ADCA (phr), (C) K-400 (phr), (D) Ca.St. (phr).

In the early step, by increasing ADCA from 0.2 to 0.4 phr, T_5% is not influenced as thermal decomposition affects mainly cell walls. A further increase of ADCA concentration causes a decrease in thermal decomposition degree, most probably due to the effect of ADCA in the intercalation of clay platelets (Figure 4B). As illustrated in Figure 4C and D, a similar trend was observed, i.e. an increase in K-400 and Ca.St leads to the alteration of ash content.

The results indicate that the presence of ADCA, K-400 and Ca.St affect the dispersion of clay in the polymer matrix. Moreover, the barrier effect is much greater and dominates the catalytic effect of clay. However, a decrease in T_5% is observed almost in all the PVC/NC samples, most probably due to the un-interacted modifiers presence on the surface of silicate layers.

3.4 The effect of incorporated ingredients on T_50%

Figure 5A and B show the relation between NC and ADCA incorporated in polymer matrix versus T_50%. The trend is almost linear due to the irrespective effect of NC and ADCA on T_50%. It can be concluded that at T_50% the polymer degradation is higher than in other ingredients. A linear trend with a positive slope indicates that T_50% increases upon the increase of K-400 content (Figure 5C). This phenomenon was observed in the range of 4–8 phr of K-400. In fact, K-400 increases the uniformity and stability of the cells. In the case of Ca.St, the trend is not linear. The results indicate that upon increasing Ca.St, approximately a similar trend of degradation can be observed in both 50% (Figure 5D) and 5% mass loss. Here, the initial increase indicates homogenous dispersion of nano particles in the polymer matrix. The better dispersion affects the strength properties of the systems by controlling the easy motion of the polymer. However, this decreasing trend associated with higher Ca.St content maybe due to the incomplete interaction over formation of agglomeration.

Figure 5:

The effect of nanocomposite ingredients on T_50% yielded from TGA analysis; (A) clay content (phr), (B) ADCA (phr), (C) K-400 (phr), (D) Ca.St (phr).

3.5 Modeling

In order to model the process, the experimental data was divided into training (75%) and testing (25%). These percentages were chosen based on practical considerations, and based on ANN. A set of 10 simulations were performed based on the CS approach, the preliminary results indicating that, due to the different influences of the inputs on the outputs, generating a single model with all the three outputs is not feasible. Therefore, the initial model with four inputs and three outputs split into three models, each having four inputs and one output. The average results for 50 simulations and the best model (based on fitness function) for the model structure is presented in Table 3. The architecture is denoted with x, y and z indicating the number of inputs, neurons in the hidden layer and outputs, respectively.

The fitness function used to determine the best ANN model for each parameter is based on the MSE in the training phase (Eq. 1),

The methodology determines one and two hidden layer models; however, the best one is neural networks with two hidden layers. This indicates that the inner relations between process conditions and the output parameters are complicated to model the process with simple relations.

The main parameters of three ANN models considered for T_50% and char are listed in Table 4. Each model is referred to its architecture. The neuron is denoted as H(a.b) in the hidden layer (a is the number of hidden layers and b is the number of neurons in the layer). The activation functions corresponding to neurons are denoted as li for linear, tanh for bipolar sigmoid, logsig for logarithmic sigmoid, tansig for tangent sigmoid, sin for sinus, radbas for radial basis, tribas for triangular basis and logi for logistic.

Although, the neurons can bear one of the eight activation functions (Table 4). In all the models, the neurons have only logsig and tansig functions. Logsig converts the input and transforms it into the range (0,1), while, tansig transforms the input into (–1,1). One explanation for the automatic process favoring these non-linear functions is that prior to training and testing, the data is normalized in the interval (–1,–1). Consequently, the application of these functions keep the interval unchanged and the internal penalty function is eliminated.

The performance of three-parameter models is also assessed by comparing the predictions and the experimental data (Figure 6). In all three cases, for the testing data (which was randomly selected from the experimental set), the average absolute relative error (AARE) and correlation were computed, 2.65% and 0.49 (for T_5%), 1.11% and 0.74 (for T_50%), 11.14% and 0.70 (for char). In the case of T_5%, the correlation is very low and the MSE in the testing phase is highest. The training phase and consequently its fitness achieve a good value. It can be deduced that the generalization capability of the model is low. On the other hand, for T_50%, the AARE attains the lowest value but highest correlation.

Figure 6:

Comparison between the neural network predictions and the experimental data for the testing dataset; (A) T_5%, (B) T_50% and (C) Char vs. exemplars.