Anatoly K. Pogodaev 1, Sergey G. Tikhomirov 2, Olga V. Karmanova 2, Elena A. Balashova 2, Semen L. Podvalny 3, Anastasiya Yu.

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1 Journal of Chemical Semen L. Technology Podvalny, and Anastasiya Metallurgy, Yu. Fatneva 53, 5, 2018, MODELING ELASTOMER PROPERTIES IN PRESENCE OF A COMPOSITE VULCANIZATION ACTIVATOR Anatoly K. Pogodaev 1, Sergey G. Tikhomirov 2, Olga V. Karmanova 2, Elena A. Balashova 2, Semen L. Podvalny 3, Anastasiya Yu. Fatneva 2 1 Lipetsk State Technical University 30 Moskovskaya St , Lipetsk, Russian Federation 2 Voronezh State University of Engineering Technologies 19 Revolution Av , Voronezh, Russian Federation 3 Voronezh State Technical University, 14 Moskovsky Av , Voronezh, Russian Federation karolga@mail.ru Received 21 January 2018 Accepted 15 June 2018 ABSTRACT The vulcanization characteristics of rubber compounds and the physical and mechanical properties of vulcanizates in presence of a composite vulcanization activator with decreased zinc oxide content (Vulkativ) are investigated. The composition of the Vulkativ product includes zinc oxide, a mixture of plant-derived carboxylic acids and shungite. The methods of least squares (MLS) and neural networks are used to process the experimental results. It is shown that the use of neural networks provides the approximation of certain parameters of the polymer composition and properties restoration with a high degree of accuracy. As a result, an approach describing the elastomers properties is suggested. It uses a neural network of filtering properties. It can be used to predict the properties of rubbers depending on the composition of the vulcanization activator used in their compounding. Keywords: mathematical model, polymer composition, viscosity, mechanical properties. INTRODUCTION Modern elastomeric materials that meet the increased operational requirements are created on the basis of new approaches to the compounding formulation of rubber compounds and modeling their properties. One of the ways to solve the problem is to develop new generation multifunctional ingredients, e.g. composite vulcanization activators. The application of new vulcanization systems is considered involving the solution of several problems, such as vulcanization processes intensification with improvement of the rubber compounds and vulcanizates quality, rubber products cost reduction, lack and high cost of conventionally used vulcanizationactive compounds. In this regard, the relevant task is the development and application of mathematical models to describe the impact of the vulcanizing system composition on the properties of the obtained rubber. Traditionally, metal oxides and fatty acids, as well as fatty acids salts [1-3], which guarantee the production of rubbers of a higher complex of physical and mechanical properties, are most widely used as activators of rubber sulfur vulcanization. It has been shown [4-8] that the application of composite vulcanization activators in the form of alloys of zinc oxide and stearic acid (or a mixture of stearic, oleic and other carboxylic acids) prepared in advance provides the required level of physical and mechanical properties of rubbers, even at its content 807

2 Journal of Chemical Technology and Metallurgy, 53, 5, 2018 decrease by up to 20 %, and improves the dispersion of the rubber mixture components. Thus the technological and vulcanization properties of rubber compounds are affected. Vulkativ [6, 9], a composition of zinc oxide, fatty acids and fillers (activated bentonite, shungite), is a vulcanization activator of a reduced zinc oxide content. The alloy of zinc oxide with fatty acids has to be obtained in the course of the first stage. This is followed by the introduction of fillers aiming to improve the functional properties of the obtained product and to provide the required release form. It is assumed that the mixing mode of the components and their mass content determine the vulcanization characteristics of the compounds as well as rubbers physical and mechanical properties. The purpose of the work was to determine the influence of the mass composition of the Vulkativ vulcanization activator and the mode of its production on the vulcanization and the physical and mechanical properties of the elastomers based on it, as well as to develop algorithms for predicting quality parameters of rubber and to evaluate their accuracy. EXPERIMENTAL The composition of the researched vulcanization activators is given in Table 1. Vulcativ [6] was an alloy of zinc oxide and fatty acids on a mineral carrier (bentonite). Vulcativ consisted mainly of unsaturated fatty acids - ca 50 % of oleic acid and ca 15 % of linoleic acid. Vulcativ contained also saturated acids: 30% of stearic acid and 5 % of palmitic acid. The zinc content of Vulcativ was ca 26 %. At the final stage of obtaining the Vulcativ product, shungite was injected to the reaction mass. It proceeded for 4 min at 25 o C or for 7 min at 40 o C. Using the researched vulcanization activators, rubber mixtures of the following composition were obtained, phr: SBR - 1, ; MBTS vulcanization accelerator 3.0; sulfur 2.0; vulcanization activator 4.0, carbon black N The compounding of the rubber mixtures was performed on a two roll open mill (320 mm 150 mm) at 60±5 С according to ASTM-D The vulcanization properties of the investigated rubber compounds were determined by Monsanto vulcameter at 160 C according to ISO 3417:2002. The following vulcanization characteristics were determined: M L - minimum torque, which was the measure of the effective viscosity of the rubber compounds studied; M H - maximum torque as a measure of the vulcanizate stiffness; t s - vulcanization induction period and t 90 - optimum vulcanization time. Vulcanization was performed on a hydraulic press with electric heating at 150 o C for 20 min. The mechanical properties of the compounds were determined on an Instron tensile testing machine at a crosshead speed of 500 mm/min according to ASTM-D The following parameters of vulcanizates were determined: modulus at 300% elongation (M 300 ) according to ISO 37:2002; tensile strength (σ) according to ISO 37:2002; relative elongation (ε) according to ISO 37:2002. Table 1. Composition of vulcanization activators (mass content). Components Standard Experimental ZnO Fatty acids Bentonite Schungite

3 Semen L. Podvalny, Anastasiya Yu. Fatneva RESULTS AND DISCUSSION The data obtained during the experiments for each initial component mixing mode (Tables 2, 3) shows that there are such initial components proportions that provide the rubbers requirements [9]: conditional tension with elongation 300% M MPa, conditional tensile strength σ 23MPa, elongation at break ε 420 %. In addition, the mixing mode at a higher temperature (40 C) and longer time (7 min) allow obtaining higher quality parameters of rubber in case of different proportions of the initial components. It is noted that the properties of rubber obtained for 7 min at 40 C change with the initial components mass content more monotonously when compared to those of rubber obtained for 3 min at 25 C. The original components of Vulcativ were processed in three ways for each mode of mixing (see Tables 2,3). In the first process, each of the eight outputs (rubber properties) is restored by an MLS second-order polynomial with four independent variables based on Eq. (1) corresponding to Vulkativ composition (mass parts of shungite, bentonite, fatty acids, zinc oxide ). However, the presence of 4 inputs (mass fractions of shungite x 1, bentonite, carboxylic acids, zinc oxide ) hampers the construction of an approximating polynomial of high orders. Thus, for a second-order polynomial having 4 inputs are unknown:, 15 coefficients (1) The polynomial order increase provides to obtain a more accurate description of the output value, but leads to an increase of the number of unknown coefficients and, hence, to an increase of the number of equations for their determination according to MLS. Thus, 35 coefficients have to have to be determined for a third-order polynomial with 4 input values. An alternative method of describing the behavior of output values is to approximate those using neural networks [11-14]. A neural network, in contrast to MLS, restores points for several output values simultaneously while performing the filtering procedure of the values available of the training sample. In the second process, data are processed using a multilayer neural network with a linear activation function in the output layer and a sigmoidal function in hidden layers. The number of output layer neurons corresponds to the number of approximated properties Table 2. Properties of rubbers with activators obtained in a mixing mode 25 о С 3 min. Parameters Standard Experimental M L,dNm M max,dnm t s, min t 90, min M 300,MPa σ,mpa ε, %

4 Journal of Chemical Technology and Metallurgy, 53, 5, 2018 Table 3. Properties of rubbers with activators obtained in a mixing mode 40 о С 7 min. Experimental Parameters Standard M L,dNm M max,dnm t s, min t 90, min M 300,MPa σ,mpa ε, % of the polymer composition and varies from one to four. The number of hidden layers and neurons in each hidden layer varies depending on the level of approximation complexity. In the third process, a several-step delay in the input feed is organized to train the neural network and to obtain the filtering properties of the network. The initial components mass fractions are the inputs of the neural networks, while the properties of the end product obtained during two parallel experiments, M L, M max, t s, t 90, M 300, σ, ε, are the outputs of the network. The approximation of the rubbers properties is performed on the ground of four basic parameters (t 90, M 300, σ, ε). The coefficients of the polynomials (1) obtained by the method of the least squares describing these output parameters are presented in Table 4. The constructed neural network with four inputs and one output consists of two layers. The linear activation function is used in the output layer, while the sigmoidal function is used in the hidden one consisting of 50 neurons. In order to provide filtering properties of the network, its trial retraining is performed with 2 and 3 step delay in data input. The 2-step delay yields a smaller root-mean-square error, so this delay is used in the final training of the network. The comparative results referring to the approximation accuracy via a second-order polynomial, the neural network without delay and with a 2-step delay of inputs at the optimal vulcanization time, the conditional stress at 300% elongation, the conditional Table 4. Coefficients of polynomials describing the properties of a polymer composition. Notation Coefficients of the polynomial t 90 M 300 σ ε a a a a a a a a a a a a a a a

5 Semen L. Podvalny, Anastasiya Yu. Fatneva а) b) c) d) Fig. 1. Results of approximation of rubber properties experimental values (+) by a neural network in absence (solid line) and presence of a delay (dashed line) as well as by a second-order polynomial (dot-dash line): а - t 90 (min), b - М 300 (MPa), c - σ (MPa), d - ε (%). tensile strength, and the elongation at break are given in Fig. 1. For clarity, the dependence of these parameters on only one (the most important) input, such as zinc oxide content, is plotted graphically. A neural network without a delay restores most accurately the experimental data (Table 4). However, their spread for each parameter requires smoothing the dependence. In this connection, the description via polynomials or a neural network with delay possessing filtering properties is more acceptable. The approximation errors obtained in using a neural network with filtering properties are less than those the second-order polynomial descrtiption (Table 4). Thus, the results of processing experimental data provide to abandon the approximation of a function by using the method of least squares in favor of neural networks. The developed approach to approximating the finished product properties is extended to an ensemble of outputs and it is possible to simultaneously restore from two to four outputs of the neural network corresponding to the considered properties of rubber. The architecture of the neural network to approximate an ensemble of 4 properties is most complex. The network consists of 3 layers. 100 neurons are used on the first hidden layer, while 50 - on the second one. The output layer consists of 4 neurons, 4 signs are sent to the network input reflect- 811

6 Journal of Chemical Technology and Metallurgy, 53, 5, 2018 Table 5. A mean square error and an absolute value of the mean relative error of approximation of individual rubber parameters. Description method Mean square error Mean relative error t 90 (min) М 300 (MPa) σ (MPa) ε,% t 90 (min) М 300 (MPa) σ (MPa) ε,% Polynomial Neural network Filtered network ing the mass composition of Vulcativ components. The data of the mixing mode experiment proceeding for 7 min at a temperature of 40 C are used for training the network. It is conducted in absence and presence of a 2-step delay of inputs. The results of approximation of the ensemble of 4 parameters are represented graphically (Fig. 2) in a simplified way as a dependence on the zinc oxide content of Vulkativ. а) b) ZnO ZnO c) d) ZnO ZnO Fig. 2. Results of approximation of experimental values (+) in the ensemble of parameters: а - t 90 (min), b - М 300 (MPa), c - σ (MPa), d - ε (%) by a neural network in absence (solid line) and presence of a delay (dashed line). 812

7 Semen L. Podvalny, Anastasiya Yu. Fatneva Table 6. Mean square error and an absolute value of the mean relative error of approximation of the ensemble of four rubber parameters. Description method Neural network Filtered network Mean square error Mean relative error t 90 (min) М 300 (MPa) σ (MPa) ε,% t 90 (min) М 300 (MPa) σ (MPa) ε,% The quality of approximation of the parameters ensemble is comparable with the quality of approximation of rubber individual properties (Table 6). The relative elongation approximation at rupture ε (%) during the restoration of the rubber properties complex is more accurate than that for the description of a separate property, which is confirmed by the data of Tables 5 and 6. As a part of the properties ensemble, a neural network in absence and presence of a delay restores the conditioned voltage at an elongation of 300% with nearly the same accuracy as for one output. There is a slight decrease in accuracy in using neural networks for the description of optimal vulcanization time and conditional tensile strength as a part of the properties complex. A neural network with an input delay provides to obtain the properties of a four-parameter composition with an average relative error not exceeding 3% (Table 6). Besides, it has filtering properties. Thus, it can be used to predict the properties of compositions of polymeric materials. In the simplest case, properties referring to the points from the intervals defined by the available experimental data can be predicted (Table 7). The obtained results provide the prediction of the properties of large groups of compositions of polymeric materials. Fixing the values of some outputs and varying the rest of the outputs in the considered range of values, it is possible to construct surfaces for predicting polymer materials properties. Of greatest interest in this paper is the identification of zinc oxide and shungite content effect on the properties of the end product. In this connection, surfaces for predicting output values from shungite and zinc oxide content for a number of fixed values of bentonite and fatty acids concentrations are constructed. Fig. 3 shows the surface for predicting the properties of polymeric materials for a filler concentration of the activator and the fatty acids equal to 1. The analysis of the dependencies in Fig. 4 shows that for samples with Vulkativ composite activator the vulcanization optimum is reached most rapidly at a zinc oxide content of 0.3 % % by weight and a shungite content of 1.2 % % by weight; a high level of elastic-strength properties of rubbers is ensured by the presence of a zinc oxide content of 0.6 % % by weight and a shungite content of 0.4 % % by weight of the test samples. The data of mathematical modeling provide the optimization of the composition of the composite vulcanization activator depending on the specific rubber requirements. Table 7. Simulation of an operation of a neural network with filtering properties. Inputs Outputs Shungite 3 2,1 0,7 Bentonite ZnO Fatty acid t 90, min М 300, МPа σ, МPа ε, %

8 Journal of Chemical Technology and Metallurgy, 53, 5, 2018 а) b) c) d) Fig. 3. Prediction properties of the ensemble of parameters: а - t 90 (min), b - М 300 (MPa), c - σ (MPa), d - ε (%) for a neural network with filtering properties for 7 min mixing at 40 C. 814 CONCLUSIONS The mixing mode of the initial components of Vulcativ composite vulcanization activator proceeding for 7 min at 40 C provides to obtain higher quality parameters of rubber for different proportions of the initial components than the mode taking place for 3 min at 25 C. The properties of the rubber obtained using the first mode change more monotonously. The comparative analysis of the methods of experimental data processing makes it possible to abandon the approximation of a function by using the method of least squares (MLS) in favor of neural networks, since the parameter approximation accuracy determined by a neural network is higher than that of MLS. The use of neural networks allows the approximation of both certain parameters of the polymer composition and the restoration of the ensemble of properties with a high degree of accuracy, while the complexity of neural network architecture grows with the increase of the number of properties of the restored ensemble. The proposed approach for describing the properties of polymeric materials using a neural network with filtering properties can be used to predict the properties of new products and to select the composition of a composite vulcanization activator in accordance with specific rubbers requirements. Acknowledgements The work was performed with the financial support of the Ministry of Education and Science of the Russian Federation within the framework of the Federal Target Program Research and development on priority directions of scientific-technological complex of Russia for through grant agreement # of October 27, Unique identifier PNIER RFMEF157715X0205.

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