Artificial Neural Network Modeling and Mechanism ... - ACS Publications

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Artificial Neural Network Modeling and Mechanism Study for Relaxation of Deformed Rubber Xiu-Juan Wang,†,‡ Xiu-Ying Zhao,†,‡ Qiang-Guo Li,†,‡ Tung W. Chan,§ and Si-Zhu Wu*,†,‡ †

State Key Laboratory of Organic−Inorganic Composites, and ‡Engineering Research Center of Elastomer Materials Energy Conservation and Resources, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, P. R. China § Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States S Supporting Information *

ABSTRACT: An artificial neural network (ANN) was developed to estimate the relaxation property of diene rubber. Regularization was introduced into the ANN and the average prediction accuracy was 98.72%. The sensitivity analysis shows that compressive strain is the crucial influence on the relaxation property. Diene rubber shows a higher relaxation at low compressive strain than at high compressive strain. Molecular simulations show that rubber at low compressive strain possesses high fractional free volume, molecular chain movement, and ozone permeability. The chemical characterization of cross-link density and 2D-FTIR correlation analysis show that the rubber network at low compressive strain is seriously degraded by random scission and the generation rate of the carbonyl group is faster than that of ozonide group, indicating chain scission predominates in ozonation. These fundamental studies are expected to provide a comprehensive understanding of the relaxation property of deformed rubber and guidance for the design of antiaging materials.

1. INTRODUCTION Because of their high permanent set resistance, rubber products, such as seals, hoses, and insulation cables, are widely used in stress service applications.1,2 However, they are not inert materials, and, frequently, time-dependent changes in sealing capability are an important concern, which can be mostly attributed to aging.3 It is nowadays routine to check the stability of rubber against the action of ozone, since the atmosphere of industrialized and polluted towns is rich in ozone at ground level.4,5 Investigations of changes in rubber network by using relaxation measurements, such as permanent set and stress relaxation, regarded as convenient ways of characterizing the relaxation property and assessing the sealing capability of rubbers, have been used by researchers since the 1950s.6−8 Because experimental methods are costly and timeconsuming,8,9 many researchers tried to predict the relaxation property by using theoretical methods, such as the Hertz contact theory, time−temperature−superposition principle, and Arrhenius theory, etc.10−12 Razumovskii et al.2 studied the stress relaxation of polyisoprene vulcanizates during ozone aging and reported that the compressive strain, ozonation time, and ozone concentration did not have a simple linear relationship with the stress relaxation, indicating that conventional theoretical methods are insufficient to meet application requirements. Therefore, establishing a quantitative model based on both the physical and chemical relaxations to predict © XXXX American Chemical Society

the effect of ozonation factors on the relaxation property is useful for industrial applications. Le et al.8 studied stress relaxation and established a quantitative model for the relation between physical relaxation and aging time. Budzien et al.13 studied permanent set and established a constitutive model to describe the chemical relaxation of rubber networks in the compression state. It is generally recognized that the relaxation behavior of rubber is due to both physical and chemical relaxations of the network,10,12 but reports on models taking into account both types of relaxation are few. To fill this gap, we presented an accurate model to describe diene rubber relaxation containing both the physical and chemical relaxations. Artificial neural networks (ANNs) have attracted considerable attention in scientific and engineering applications over the last decades because of their heuristic nature and ability to simulate nonlinear and complex relationships.14,15 Normandin16 and Yousefi17 presented comparisons between an equation of state (EOS) and an ANN and their studies showed that ANNs were powerful models with higher accuracy. Demirhan et al.18 studied the physical properties of styrene− Received: January 3, 2016 Revised: February 28, 2016 Accepted: March 22, 2016

A

DOI: 10.1021/acs.iecr.6b00010 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

find out which ozonation factor possessed the crucial influence on the relaxation property. Second, combined MD simulation and experimental investigations, such as MR-XLD, attenuated total reflection (ATR)-FTIR, and two-dimensional (2D) FTIR experiments were carried out to investigate relaxation mechanisms. The present study aimed at developing an ANN model to quantitatively investigate and predict the influence of ozonation factors on the relaxation property. On the basis of the predicted results of ANN, the combined experimental− theoretical studies provide an in-depth insight into the connections between macroscopic relaxation behavior and microscopic relaxation mechanism of diene rubber in deformed states during ozonation.

butadiene rubber and showed that an ANN was useful for carbon black grade selection. Wu et al.19 estimated the fatigue life of natural rubber by using ANN technology. Currently, the radial basis function (RBF) has drawn considerable attention because of its potential to approximate nonlinear behavior. Li et al.20 proposed an RBF−ANN model to predict the polymer physical property. The above studies confirm the effectiveness of neural computing methods in describing the physicochemical properties of rubbers. To the best of our knowledge, the present work is the first attempt to propose an RBF−ANN model to quantitatively predict and understand the effects of ozonation factors on the relaxation properties of rubber. Relaxation mechanisms have been studied by a large number of experimental techniques including magnetic resonance-crosslink density (MR-XLD) measurement21 and Fourier transform infrared spectroscopy (FTIR).22 Furthermore, two-dimensional (2D) correlation FTIR, proposed by Noda,23 which not only improves the spectral resolution of overlapping FTIR spectra but also offers the sequence of spectral intensity changes, has been developed to study various types of spectra. Although the experimental determination of macroscopic relaxation behavior and microcosmic mechanism is the preferred method, not all of the properties can be feasibly measured by experiments, and thus other alternatives have to be considered. Molecular simulation techniques that can offer a comprehensive understanding of the structure−property relations of materials at a molecular level have been applied widely in studying the fractional free volume (FFV),24 cohesive energy density (CED),25 and relaxation mechanism of rubber.13 Moreover, molecular simulation techniques have been successfully used to model the diffusive behavior of small gaseous penetrants in polymeric matrices, thus offering a predictive tool to calculate the penetrant diffusion coefficient (D).26,27 Similarly, grand canonical Monte Carlo (GCMC) simulation methods have been used to model sorption isotherms and the solubility coefficient (S) of gaseous penetrants in polymeric matrices.28 The free volume diffusion model has been used to explain the observed physical relaxation in a polymer.29 In an effort to illustrate the physical relaxation mechanism, we comprehensively investigated the fractional free volume (FFV), cohesive energy density (CED), and self-diffusion coefficient by using molecular dynamics (MD) simulation. By combining the simulated diffusion and solubility coefficients, the effects of compressive strain on ozone permeability in rubber were also evaluated. Andrews et al.30 developed a molecular theory to describe chemical permanent set. The two-network hypothesis was proposed to interpret the relaxation mechanism of rubber aging. Chemical relaxation, which is irreversible, involves primarily cross-linking and scission events because of the formation and breakage of covalent bonds. Thus, we investigated nuclear magnetic cross-link density and chemical network to gain the underlying mechanism that governs chemical relaxation. In addition, 2D-FTIR correlation spectroscopy was used to obtain further insight into the competing destruction mechanisms of the rubber network at a molecular level. An outline of this study is as follows. First, an improved RBF−ANN was proposed to predict the relaxation property (in this work, permanent set was used to characterize the relaxation property) of diene rubber, namely natural rubber (NR), butadiene rubber (BR), and chloroprene rubber (CR). Moreover, a sensitive analytical method31 was introduced to

2. MATERIALS AND METHODS 2.1. ANN Modeling. Since no first principle model is available for rubber relaxation behavior during ozonation, we resort to the framework of RBF−ANN as a predict estimator and an analytical expression. A multiple input and single output RBF can be represented as a linear function approximation; that is, M

y(x) = ω T h(x) =

∑ ωihi(x)

(1)

i=1

where y(x) ∈  is the output of RBF, h = {h1(x), h2(x), ..., hM (x)}T ∈ N × 1

is the basis function vector, and ω = {ω1 , ω2 , ..., ωM }T ∈ M × 1

is the linear parameter vector. N and M are the dimensions of the input vector and basis function vector, respectively. The superscript T denotes the operation of matrix transposing. The basis function provides the nonlinear mapping from input space to basis space. As a typical local approximate function, the Gaussian function is chosen as the basis function in our study; that is, ⎧ (x − c )T (x − c ) ⎫ i i ⎬, hi(x) = exp⎨− 2 2σ ⎭ ⎩

i = 1, 2, ..., M (2)

where x = {x1 , x 2 , ..., xM }T ∈ N

is the input vector, ci ∈ N × 1 is the ith center vector that can be determined according to the distribution of experimental data, and σ ∈  is the width parameter that is the only tuning parameter. When all of the parameters in the basis functions are determined and a labeled input−output training sample data set with the length of S is given, we can use the off-line batch method to solve the linear parameter vector ω immediately. In convex optimization, this task can be expressed as finding an optimal vector to minimize the following objective function: ω* = arg min{|| H̃ ω − y ̃ ||22 + ε || ω ||22 } ω

(3)

where H̃ ∈ S × M is the sample observed output matrix of the basis function, and ỹ ∈ S × 1 is the sample observed output vector. They are defined as B


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Figure 1. Models for molecular simulation (gray atom is C, green atom is H, and red atom is O).

⎡ h (x ̃ ) h (x ̃ ) 2 1 ⎢ 1 1 ⎢ h1(x̃2) h2(x̃2) H̃ ≡ ⎢ ⋮ ⎢ ⋮ ⎢ ⎣ h1(x̃S) h2(x̃S)

⋯ hM (x1̃ ) ⎤ ⎥ ⋯ hM (x̃2)⎥ ⎥ ⋱ ⋮ ⎥ ⎥ ⋯ hM (x̃S)⎦ S×M

⎡ y1̃ ⎤ ⎢ ⎥ ⎢ y2̃ ⎥ and ỹ ≡ ⎢ ⎥ ⎢⋮⎥ ⎢ ỹ ⎥ ⎣ S⎦

∂y ∂y ⎛ ∂y ̅ ∂ωT h ∂h ⎞ ∂xj̅ = ·⎜ · ⎟· · ∂xj ∂y̅ ⎜⎝ ∂ωT h ∂h ∂xj̅ ⎟⎠ ∂xj

ω* = (H̃ TH̃ + ε I)−1H̃ Tỹ

(5)

⎧ (x − c )T (x − c ) ⎫ i i ⎬ 2 2 σ ⎩ ⎭

∑ ωi* exp⎨−

This expression provides a means to derive the sensitivity coefficient from each input variable (i.e., each element xi in input vector x) to the unique output variable y. The sensitivity coefficient is defined as the partial derivative of the output variable to one input variable xi, and quantitatively reflects how importantly this input variable can affect the corresponding output change. Let x̃ ij be the jth element of the ith input sample. Assume that all of the experimental input−output data x̃ ij and yĩ are normalized separately into the range of [0, 1] by using the following representations: x̃ij − min x̃ij i

max x̃ij − min x̃ij i

i

,

and

yi̅ =

i

This representation is used to analyze the importance of the four variables in section 3.2. 2.2. Molecular Simulation. All simulations were performed by using Material Studio version 7.0 (Accelrys, San Diego, CA) and the theoretical calculations were performed by using the Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force field, which has been widely adopted to predict the structural and thermophysical condensed phase properties of polymers.32,33 The electrostatic and van der Waals forces were calculated by using the atom-based summation method with a cut off value of 12.5 Å.34 The Maxwell−Boltzmann35 profiles were used to set the initial velocities. 2.2.1. Polymer Packing Model Construction and Validation. To choose a sufficient large packing model size, NR models with different numbers of repeat units were built and dynamic simulations were performed to calculate the solubility parameter (δ, square root of the cohesive energy density).36 Figure S1 (Supporting Information) shows the dependence of δ on the number of repeating units. The results show that as the number of repeating units reaches 50, δ approaches a stable value and is close to the experimental value (of 17.0 (J cm−3)1/2).37 For sufficiently high mobility of chains and manageable computing time,38 packing models were constructed with 50 repeating units and five chains. The method used for constructing and equilibrating rubber packing models was described previously,34 with a few minor changes as discussed below. Figure 1 shows the process of building periodic boundary cells. First, the repeating units (Figure 1a) and polymer chains (Figure 1b) were built by using the Build Polymers module. The periodic boundary cells (Figure 1c) were constructed by using the Amorphous Cell module to simulate the polymer system38 and refined by using the basic-refine protocol.39 The energy of the cells was minimized to a convergence value of 1.0 × 10−5 kcal−1 mol−1 Å−1 by using the Smart Minimizer method.40 Compressive strains (0%, 25%, 30%, and 35%) were respectively applied to the cells. To ensure that the rubber was under uniaxial stress,

(6)

x̅ ij =

M ⎧ (x − c )T (x − c ) ⎫⎛ ci(j) − xj̅ ⎞ i i ̅ ⎬⎜⎜ ·∑ ωi exp⎨− ̅ ⎟⎟ 2 max x̃ ij − min x̃ ij i = 1 2σ 2 ⎭⎝ σ ⎩ ⎠

max yi ̃ − min yi ̃

(8)

where I is an M-order identity matrix. After the above procedures, the RBF model is determined with the following analytical expression:

i=1

=

i

where x̃i ∈ N × 1 and yĩ ∈  are the ith input and output training samples. The last term ε∥ω∥22 in eq 3 is an λ2regularization penalty term, and ε ∈  is the regularization parameter that can be chosen as a small positive value. λ2 regularization can significantly improve the robustness of training and predicting. The solution of eq 3 can be obtained analytically by solving the normal equation in a least-squares problem:

M

M ⎧ (x − c )T (x − c ) ⎫⎛ ci(j) − xj̅ ⎞⎞ ∂xj̅ ∂y ⎛ i i ̅ ⎟⎟⎟⎟ · ⎬⎜⎜ ·⎜⎜∑ ωi exp⎨− ̅ 2 ∂y ̅ ⎝ i = 1 2σ 2 ⎩ ⎭⎝ σ ⎠⎠ ∂xj

S×1

(4)

y(x) = ω*T h(x) =

=

yĩ − min yĩ max yĩ − min yĩ (7)

On the basis of eqs 6 and 7, the partial derivative of the output variable y with respect to the input variable xj can be obtained as the following differentiation chain: C


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2.3.3. Chemical Network Characterization. Samples taken from the permanent set jig were used to analyze chemical network changes. To characterize the effects of ozonation factors on diene rubber network changes, the cross-link density was analyzed by using a MR-XLD spectrometer (XLDS-15, IIC Innovative Imaging Co., Ltd., Germany). The IIC analysis software package with a nonlinear Marquardt−Levenberg algorithm45 was adopted to analyze the signal decay data. Chemical network changes of samples were characterized by using a Nicolet 8700 FTIR spectrometer (Thermo Fisher Scientific Inc., USA). The specimens were scanned for 32 times from 400−4000 cm−1 at a resolution of 4 cm−1. Before the 2DFTIR correlation analysis was carried out, the spectra were preprocessed to avoid artifacts caused by baseline instabilities and other nonselective effects.46,47 Spectra at different times were selected for 2D-FTIR correlation analysis using the software 2Dshige (Shigeaki Morita, Kwansei-Gakuin University, 2004−2005).

relaxation of the structure perpendicular to the applied strain direction was performed by fixing the applied strain, but adjusting the two normal strain components.41 Then, the cells were annealed at 0.1 MPa from 400 to 150 K for 150 ps to prevent trapping at a local high energy minimum. To further relax the polymer structure, 500 ps of NPT (constant number of molecules, pressure, and temperature) simulation and 500 ps of NVT (constant number of molecules, volume, and temperature) simulation were carried out. Consequently, 2000 ps of NPT simulation was carried out from the end point of the NVT simulation at 298 K and 0.1 MPa by using the Andersen thermostat42 and Berendsen barostat43 for temperature control and pressure control, respectively. Finally, the equilibrated cells were used to analyze the FFV, CED, and permeability (Figure 1d and Figure 1e). Table S1 (Supporting Information) summarizes parameters of the model after equilibration. It shows that the simulated density (ρ) agrees with the experimental value (relative error = 3.2%), and the simulated δ agrees reasonably well with the value taken from the reference37 (relative error = 1.8%). In other words, the rubber packing models, to some extent, can be compared with actual materials. 2.3. Experimental Section. 2.3.1. Materials and Sample Preparation. Commercially available NR (NRRSS1) and CR (CR3211) were provided by Synthetic Rubber Group Co, Ltd., (China) and BR (BR 9000) was provided by Yanshan Petrochemical Co., Ltd., (China). For permanent set measurements, the gums of NR, BR, and CR were homogenized on a two-roll mill. Rubber composites were prepared according to the recipes given in Table S2 (Supporting Information). The optimum vulcanization time for rubber was determined by a P355C2 disc rheometer (Huanfeng Chemical Technology and Experimental Machine Co., Ltd., China). Composites were vulcanized on a hot press under 15 MPa to form samples for testing. 2.3.2. Permanent Set and Physical Property Measurements. The permanent set was studied in the compressive strain range 25% to 35% widely used in industrial applications. The permanent set measurements were carried out on a thickness gauge (Shanghai Precision Instrument Co., Ltd., China) to an accuracy of 0.01 mm according to ASTM D395 Method B. The samples with 25%, 30%, and 35% compressive strains were placed in an ozone chamber (GT-7005-C, Cotech Co., Ltd., China) for testing at elevated ozone concentrations of 75 pphm, 100 pphm, and 125 pphm. The measurements of permanent set as a function of ozonation time and ozone concentration were carried out at room temperature. Permanent set is expressed as the percentage of the deformation retained by the sample: ⎡ t − ti ⎤ %permanent set = ⎢ 0 ⎥ × 100 ⎣ t0 − tn ⎦

3. RESULTS AND DISCUSSION 3.1. ANN Modeling Results. On the basis of the permanent set experiments in section 2.3, an RBF−ANN model is constructed. Previous studies48−50 indicated that the combination of ANN and optimization algorithm improved the accuracy of the network. Regularization51 was introduced into the RBF-ANN. With the compressive strain, ozonation time, ozone concentration, and diene rubber type as the input variables, and the permanent set as the output variable, the ANN has a four-dimensional input layer and a one-dimensional output layer. Also, according to the scales and intervals of the input samples, all input variables are assigned three nodes, and 81 centers in hidden layer nodes are arranged in a 3 × 3 × 3 × 3 grid over the four-dimensional input variable space, including {0, 0.5, 1} for each dimension after normalization transformation. Thus, a 4−81−1 structured ANN is determined. The regularization parameter should be selected as a small positive number and was set at 10−6. The last parameter, the width s of the Gaussian function, is the most important tuning parameter on the approximate performance of RBF. The total 270 samples are randomly and equally divided into the training data set and predicted data set. Over 20 independent runs, the statistical average values and standard deviations of training and testing errors over a wide range of s values are both shown in Figure 2. The RBF has the minimum training error and predicted error and standard deviations in the range of (0.6, 1.2), and thus σ = 1 located in this optimal range is determined. Figure 3 compares the experimental and predicted permanent set values (the values in Figure 3 are normalized

(9)

where t0 is the initial nominal thickness, ti is the final measured thickness, and tn is the gasket thickness (nominal compressed thickness). Positron annihilation spectroscopy (PALS) measurements with a conventional fast−slow ORTEC system44 were used to study the FFV. Ozone permeability in specimens with a thickness of 2 ± 0.02 mm was measured according to ISO2782 on a GDP1000 permeability tester (Ruida Instrument Co., Ltd., China).

Figure 2. Trained and predicted MSE (mean square error) of a permanent set with respect to width parameter (σ). D


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The RBF−ANN also needs less computation time than the BPANN. Therefore, the proposed RBF−ANN shows greater advantages in predicting the relaxation property of rubber during ozonation. 3.2. Permanent Set Prediction. Figure 4 shows the predicted evolutions of permanent set vs ozonation time and compressive strain. The predicted permanent sets agree well with the experimental values, indicating the validity of the ANN model. The permanent set increases with the increase of ozonation time, probably because of the chain movement and/ or chain scission. More interestingly, the permanent sets of diene rubber are lower under a compressive strain of 35% than under a compressive strain of 25% during ozonation. In other words, the ozone attack on diene rubber is weaker under a compressive strain of 35% than under a compressive strain of 25%. This interesting finding was not incidental. Raab et al.53 found that the stress relaxation of unsaturated rubbers decreased gradually with decreasing strain (between 20% and 50%) under tension in an ozone atmosphere. They studied the macroscopic defects of ozonized rubber to illustrate the physical relaxation mechanism. Also, several different theoretical explanations were given. Newton’s explanation focuses on the number and the size of cracks.54 Another explanation55 relates the crack propagation to the necessity of attaining some critical stress by accumulation of elastic energy sufficient for the generation of the new surface. According to the physical relaxation mechanism, high movements of chains lead to the increase of permanent set under low compressive strain. Meanwhile, diene rubber has isolated double bonds that can be easily attacked by the electrophilic addition on the rubber surface. For ozone destruction of polymeric materials to occur, the ozone has to permeate into the polymer and then fracture the polymer chains, leading to the increase of permanent set. Thus, both physical and chemical relaxations affect the

Figure 3. Comparison between measured and predicted permanent sets of diene rubber.

with reference to the input and output of ANN). The multiple correlation coefficient (MCC) between the experimental and predicted permanent set values was calculated. The results indicate that the designed RBF−ANN model in this study can predict the permanent set of diene rubber with a high accuracy of 0.9872 and has high generalization ability (MSE = 0.0283). Because of the convex quadratic programming theory,52 RBF training avoids the local minimum problem that is common in BP training. Previous studies17,19 have illustrated the theory and algorithm of BP-ANN. To compare RBF−ANN and BP−ANN, a BP−ANN with the identical 4−81−1 structure as the proposed RBF−ANN is trained. The sigmoid and linear functions are adopted in hidden and output layers, respectively. Both RBF−ANN and BP−ANN independently run for 20 times. The training MSE, the predicted MSE, and the computation time of both ANN models are averaged of all runs as the reported value. Obviously, the superiority of the RBF−ANN to the BP−ANN can be seen in Table S3 (Supporting Information). This is especially for the case for the training and predicted MSEs, in which the proposed RBF could predict the rubber relaxation property with high accuracy.

Figure 4. Predicted permanent set vs ozonation time and compressive strain of (a) NR, (b) BR, and (c) CR at an ozone concentration of 100 pphm (solid dots denote experimental values). E


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partial derivative, the greater is the influence of the input vector on the permanent set. The results indicate that (1) the compressive strain possesses higher influence on the permanent set than does the ozone concentration and (2) with the increase of ozonation time, the influence of compressive strain and ozone concentration on the permanent set of NR and BR first increases and then flattens out, while the influence of compressive strain and ozone concentration on the permanent set of CR starts small, but then gradually increases, indicating that CR has better ozone resistance than NR and BR. These results could be due to changes of the cross-link network. To make out the influence of compressive strain on permanent set during ozonation, NR, containing isolated double bonds and being a typical diene rubber, was used to further analyze the physical and chemical mechanisms with a combination of MD simulations and experimental investigations, as discussed in the next sections. 3.3. Effect of Compressive Strain on Physical Properties. 3.3.1. MD Simulation of FFV and Self-Diffusion Coefficient. MD simulation is the most effective technique to study the structural property and physical mechanism of materials under harsh conditions, such as high pressures.56 Free volume is widely used to characterize the efficiency of chain packing and permeate behavior of gas molecules in materials. The FFV can be calculated by the following equation:

permanent set of diene rubber in deformed states during ozonation. Relaxations will be discussed in sections 3.3 and 3.4. To determine which ozonation factor has the greatest influence on the permanent set, we calculated the partial derivatives of compressive strain and ozone concentration with respect to permanent set at different ozonation times. We found that the partial derivative of compressive strain was negative, indicating negative correlation of compressive strain with permanent set, and the partial derivative of ozone concentration is positive, indicating positive correlation of ozone concentration with permanent set. To determine the extent of the influence of compressive strain and ozone concentration on permanent set, we take the absolute value of partial derivatives and compare the amplitudes of the absolute values. The results are shown in Figure 5. The larger is the

FFV = 1 −

V0 Vs

(10)

where the occupied volume V0 = 1.3Vw, Vw is the van der Waals’s volume, and Vs is the specific volume. Figure 6 shows the Connolly volume morphology under different compressive strains. The blue and white regions represent the free volumes that were created by inefficient chain packing or the transient gaps caused by chain rearrangement. The free volumes decrease with the increase of compressive strain. Table 1 shows the influence of compressive strain on FFV, we can infer that the increase of compressive strain suppresses the free volume, leading to efficient molecular packing and the decrease of FFV.

Figure 5. Sensitivity of permanent set at different ozonation times for (a) NR, (b) BR, and (c) CR.

Figure 6. Three-dimensional representation of free volume morphology of NR at compressive strains of (a) 0%, (b) 25%, (c) 30%, and (d) 35%. F


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simulated MSD was used to analyze D (average value of all penetrant molecules) by using eq 11. The ozone MSD for NR shows a higher slope at a lower compressive strain (see Figure 8). Table 2 shows the variation of diffusion coefficient with the

Table 1. Self-Diffusion Coefficients of NR at Different Compressive Strains compressive strain

FFVsim (%)

FFVexp (%)

0% 25% 30% 35%

3.73 1.96 1.40 0.97

2.17

self-diffusion coefficientsim (10−7 cm2 s−1)

self-diffusion coefficientexp (10−7 cm2 s−1)

1.55 1.27 1.02 0.06

3.458

Physical relaxation contains the motion and self-diffusion of chains toward new configurations in equilibrium. The mean square displacement (MSD) obtained from the MD simulations can be used to analyze the self-diffusion coefficients by using the Einstein equation:57 D=

1 d lim 6N t →∞ dt

N 2 ⃗ |⟩ ∑ ⟨| ri(⃗ t ) − ri(0) i=1

(11)

where N is the number of molecules, D is the diffusion coefficient of the molecules (penetrant), r(0) is the initial i⃗ position vector, ri(⃗ t ) is its position vector at time t, and 2 ⟨| ri(⃗ t ) − ri(0) ⃗ | ⟩ is the MSD (Figure 7). The initial sharp

Figure 8. Mean square displacement (MSD) curves at different compressive strains of ozone in NR. Each curve consists of average MSD values calculated from three independent packing models.

Table 2. MD Simulation and GC−MC Simulation Values of Diffusivity Coefficient D and Solubility Coefficient S and Predicted Values of Permeability P of Ozone in NR at Different Compressive Strains

D (10−6 cm2 s−1) compressive strain 0% 25% 30% 35%

Figure 7. Mean square displacements (MSDs) of NR at different compressive strains.

sim 4.61 2.74 1.74 1.49

± ± ± ±

exp 0.52 0.31 0.29 0.55

1.062

P (10−13 cm3(STP) cm cm−2 Pa−1 s−1)

Ssim 10−7 cm3(STP) cm−3 Pa−1

sim

exp

± ± ± ±

32.31 18.27 9.27 6.01

31.3

7.01 6.67 5.33 4.03

0.11 0.08 0.10 0.04

compressive strain applied to NR. D decreases with increasing compressive strain because the diffusion of ozone is strongly dependent on the free volume and chain mobility. The solubility of ozone in NR at different compressive strains was studied by a series of GCMC simulation within a certain pressure range to calculate the sorption isotherms with the equilibrated packing models (section 2.2). Then, the curve of the concentration of the penetrant molecule with the pressure is obtained. The Metropolis algorithm60 was used for the simulation with 1 000 000 equilibration steps and 10 000 000 production steps. The penetrant fugacity was converted to pressure by using the Peng−Robinson equation of state. The average concentration of ozone adsorbed in rubber was fitted to the dual sorption model:61

increase of MSD is due to the transient motion of the polymer atoms, which is not in the random walks. The self-diffusion coefficients of NR at different compressive strains were calculated from 1200 to 2000 ps, and the results are listed in Table 1. The increase of compressive strain leads to the decrease of self-diffusion coefficient because the increase of compressive strain decreases the FFV and enhances the polymer chain packing. MD simulation theoretically interprets the effect of compressive strain on the permanent set. The agreement of FFV and self-diffusion coefficient between the experimental and simulated results also highlights the validity of MD simulations in calculating physical properties. 3.3.2. MD Simulation of Microcosmic Ozone Penetration Mechanism in Rubber. Mechanistic investigations lead to the conclusion that the ozonation-induced degradation of materials results from heterogeneous ozonation due to ozone diffusion effects.59 To further study the diffusion behavior of ozone molecules in rubber at different compressive strains, eight ozone molecules were inserted into each rubber model, and each model was equilibrated according to section 2.2. The

C = kDp +

C H′ bp 1 + bp

(12)

where C is the equilibrium concentration (cm (STP) cm−3 (polymer)), p is the absolute pressure (Pa), kD is the Henry sorption parameter (cm3 (STP) cm−3 pa−1), CH′ is the Langmuir capacity parameter, and b is the Langmuir affinity parameter (Pa). These parameters can be obtained from the nonlinear least-squares fit to the average adsorption isotherm 3

G


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Industrial & Engineering Chemistry Research data. Accordingly, the solubility S was determined from the average adsorption isotherms as the slope of the adsorption isotherm in the limit of zero pressure: S = lim

p→0

C = kD + C H′ b p

relaxation rate. The XLD decreases with the decrease of compressive strain owing to chemical degradation, an indication that a lower compressive strain is more aggressive toward degradation than a higher compressive strain. Rubber without the application of compressive strain (0%) has the highest XLD, indicating that compressive strain leads to the rubber network damage, and low compressive strain facilitates the ozone penetration in rubber and the rubber network damage. XLD studies provide evidence that the original network of the samples is degraded by random scission along the main chains and theoretically explain that samples at low compressive strains with low network densities, exhibiting the greatest relaxation. The XLD results illustrate the ANN prediction of permanent set in Figure 4. 3.4.2. Changes in FTIR Spectrum During Ozonation. In the present context, we will analyze the FTIR spectral assignments most relevant to the molecular level description of the chemical relaxation process. FTIR spectral changes of the ozonized NR samples are shown in Figure 10. The peak at 1375 cm−1 remains unchanged in intensity because the vibrational mode involved (C−H asymmetric bending −CH3) is not significantly affected during ozonation. Four major structural changes can be recognized in the FTIR spectrum. The first change involves the appearance of a broad peak between 3650 and 3100 cm−1 (Figure 10a), with a maximum of 3400 cm−1, which is assigned to the formation of hydroperoxide, hydroxyl, and/or carboxylic acid. The second change involves the C−H stretching vibration (Figure 10b, Figure 10d). The four peaks at 2935, 2860, 1440, and 830 cm−1, which are due to the C−H antisymmetry stretching in methylene units, C−H symmetry stretching in methylene units, C−H bending vibration in methylene units, and C−H out of plane vibration in cis-CH2CH2, respectively, decrease slightly in intensity. The third change involves the appearance of aliphatic carbonyl groups, as indicated by the maximum peak at 1727 cm−1 (Figure 10c). This broad peak is due to the formation of aldehyde, ketone, carboxylic acid, and/ or carbonyl groups. The relative intensity of this peak increases gradually and reaches a maximum after 7 days of ozonation. This band is also an evidence of chain scission of the rubber network. The last change involves the appearance of the characteristic peak for ozonide at 1025 cm−1, suggesting that ozone causes a cross-link of the rubber. This peak assignment is consistent with conclusions drawn from previous studies.63,64 The appearance of ozonide groups also explains a relatively slow increase of the permanent sets following their initial rapid increase (see Figure 4). The peak at 1110 cm−1 is due to C− O−C stretching. The relative intensity of the peaks at 1025 and 1100 cm−1 increases rapidly on the first day and reaches a maximum after 1 day of ozonation. From the FTIR data, attack by ozone clearly occurs at the unsaturated vinyl groups, as shown in Scheme 1. An attack by ozone on double bonds gives complexes of ethers, carbonyl, and ozonide in abundance. To distinguish the relative rate of ozonation products at different wavenumbers and to get further

(13)

The sorption isotherms of ozone penetrant are linear (only Henry sorption), as shown in Figure 9. The concentration (C)

Figure 9. Sorption isotherms of ozone in NR. Each curve consists of average concentration (C) values calculated from three independent packing models.

of ozone decreases with the increase of compressive strain. The S values of ozone at different compressive strains were calculated from the model parameters (see eq 13). As shown in Table 2, both the S and D of ozone in rubber decrease with increasing compressive strain. The permeability P values can be calculated by the relation P = D × S. The variations of the permeability of the rubber with compressive strain are compared and the results highlight the validity of molecular simulation in investigating the ozone transport mechanism in diene rubber. A low compressive strain leads to a high P of ozone, which favors the ozone attack of the rubber network. The influence of compressive strain on the degradation of the network is characterized in the next sections. 3.4. Effect of Compressive Strain on Chemical Property. 3.4.1. Chemical Network Analysis. Cross-link density measurements were carried out to obtain chemical information on the rubber networks. The MR-XLD results of NR after 10 days of ozonation at an ozone concentration of 100 pphm are shown in Table 3. With the decrease of compressive strain (between 25% and 35%), the motion of intercross-link chains [A(Mc)] decreases, but the motion of free chains [A(T2)] increases, indicating that the percentage of intercrosslink chains decreases and the percentage of free chains increases in the network. Furthermore, the transverse relaxation time of the cross-link network (T2) also increases because a low total cross-link density (XLD) is beneficial to the motion of intercross-link chains resulting in a decrease in transverse

Table 3. MR-XLD Results of NR after 10 Days of Ozonation at Ozone Concentration of 100 pphm compressive strain 0% 25% 30% 35%

XLD (10−4 mol g−1) 1.64 1.08 1.13 1.49

± ± ± ±

0.02 0.03 0.03 0.03

Mc (g mol−1)

A(Mc) (%)

A(T2) (%)

± ± ± ±

89.96 86.80 87.71 88.35

9.59 13.08 11.77 10.42

8.27 8.68 8.59 8.40

0.02 0.02 0.02 0.02 H

T2 (ms) 4.40 4.62 4.55 4.51

± ± ± ±

0.02 0.29 0.24 0.27


Article


Figure 10. ATR-FTIR spectra of NR at compressive strain of 30% and ozone concentration of 100 pphm in wavenumber ranges (a) 3650−3100 cm−1, (b) 3050−2800 cm−1, (c) 1800−1000 cm−1, (d) 1000−650 cm−1 at various ozonation times. Arrows indicate the direction of change.

Scheme 1. Mechanism of Reaction Following Ozonation of Diene Rubber. X Represents H, CH3, or Cl

details about the change of network, 2D correlation analysis was used. The construction and physical meaning of the peaks in the 2D spectrum have been clearly illustrated in the literature.65 The most significant 2D-FTIR spectra (see Figure 11) are obtained in the region 1000−1800 cm−1. The calculated synchronous and asynchronous spectra at [1727, 1100 cm−1] and [1100, 1025 cm−1] have positive peaks. According to Noda rules,23 in the dynamic spectrum, the component at 1727 cm−1 forms faster than that at 1100 cm−1 and the component at 1100 cm−1 forms faster than that at 1025 cm−1. The combined FTIR and 2D-FTIR study shows that ozone molecules mainly attack CC instead of −CH3 in diene rubber specimens at compressive strains. In the ozonation process, new functional groups are identified, the generation rates of which follow the order ketones, aliphatic, and carboxylic acid carbonyl groups (I, VI, and VII) > ozonide (III) > ozonide (IV and V). We can

conclude that during the ozonation of diene rubber at compressive strains, chain scission tends to predominate.

4. CONCLUSIONS A radial basis function ANN consisting of permanent set, ozonation factors, and diene rubber type was established to predict the relaxation property. A sensitivity analysis based on the analytical expression generated by the ANN indicated that the compressive strain is the crucial factor affecting the relaxation property. Moreover, an interesting finding offered by the model is that the relaxation property increases with the decrease of compressive strain of the diene rubber during ozonation. Both molecular simulations and experimental studies were employed to systematically elucidate the effects of compressive strain on the relaxation property. The molecular simulation I


Article


Figure 11. 2D-FTIR correlation spectra in the wavenumber range 1000−1800 cm−1 for NR network subjected to ozonation at ozone concentration of 100 pphm and compressive strain of 30%. Keys: Panels a and c show synchronous spectra; panels b and d show asynchronous spectra.

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results show that with the increase of compressive strain, the fractional free volume, self-diffusion coefficient, and ozone permeability of the rubber decrease. The rubber under high compressive strain is unfavorable to ozone attack. Meanwhile, the chemical characterization of cross-link density and 2DFTIR correlation analysis show that with the increase of compressive strain, cross-link network degradation becomes slow. The chemical characterization verified the molecular simulation result that the permeability of ozone in the rubber decreases with the increase of compressive strain. Besides, 2DFTIR results indicate that ozone mainly attacks the unsaturated vinyl groups and the generation rate of the carbonyl group is faster than that of ozonide. The relaxation property depends on chain rearrangement, scission, and cross-link, and chain scission plays the main role. Our results demonstrate that the proposed ANN can be used to accurately predict the relaxation property and the service life of materials. Molecular simulations and 2D-FTIR correlation analysis could provide physical and chemical insights into uncovering relaxation mechanisms at the molecular level. Simulation technologies are believed to play a key role in the future design of ozonation resistant materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 86-010-6444923. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial supports of the National Natural Science Foundation of China (Grant No. 51473012 and No. 51320105012) and the Ministry of Science and Technology of China (Grant No. 2014BAE14B01).

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b00010. Simulated solubility parameter of NR (Figure S1); structure of RBF (Figure S2); parameters of the MD model (Table S1); recipes of rubber composites (Table S2); and statistical parameters of the comparison models (Table S3) (PDF) J


Article

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