Figure 1 is an overview of the hierarchical simulation used to obtain the S–S curves of the block copolymers.
The following is a brief description of the method; the details are available in the literature [3, 4]. In the first step, SCFT calculations are conducted to obtain the phase-separated structures of the block copolymers. Next, the chain configurations for the CGMD simulations are generated by the density biased Monte Carlo algorithm (DBMC) proposed by Aoyagi et al. . The generated structures were relaxed with the NVT ensemble followed by the NPT ensemble. The temperature T was set to 0.3 [ε/kB], which is below the glass transition temperature of the glassy A domain (ε is the energy unit of the Lennard–Jones potential). The pressure for NPT was set to maintain the density at approximately 0.85 [m/σ3], where m is the mass of the bead and σ is the length unit of the Lennard–Jones potential.
The system was subjected to tensile deformation to elucidate its elastic behavior. The unit cell was elongated in one direction with constant deformation speed. We used the Parrinello–Rahman constant stress algorithm with fixing the cell angles to control the stress in the directions perpendicular to the deformation. The deformation speed was set so that the initial deformation rate was 1.0 × 10−4 [τ−1], where τ is a time unit of the system, and deformation continued up to a strain of 3.0.
All calculations were conducted using the OCTA system , which is a platform for the simulation of soft material. The SUSHI  and COGNAC  programs within the OCTA system were used for SCFT calculations and CGMD simulations respectively.
Figure 2 shows the 3DCNN architecture used in the present study. The training data were sets of the local volume fractions of the A segment fA(r) in each 64 × 64 × 64 grid point (obtained from the SCFT calculations) and the array of stress at strains from 0 to 3.0 at intervals of 0.03 (a total of 101 points). Four convolutional layers and two max-pooling layers were followed by flatten and dense layers. A rectified linear unit (ReLU) function was used to activate each layer except the last one. Dropout with a 0.5 drop rate was applied after each of the two max pooling layers and the first dense layer to avoid overfitting.
The 3DCNN was implemented using TensorFlow 2.3.0 . We assigned 80% and 20% of all the data for training and validation, respectively. The training step was executed for 1000 epochs with a batch size of 32.
This study focuses on the elastic property of TPEs, in which the glassy (A) segments are minor components, and phase-separated structures are observed. The total volume fractions of the A segments fA of the ABA copolymers were set at values between 0.15 and 0.50 with intervals of 0.05. The χNs for the SCFT calculations were set to 80 for fA values less than or equal to 0.2, and to 40 for the remaining fA values. The chain length N for CGMD simulations was set to 80, and the numbers of A and B segments in a chain are determined from the fA. The total number of chains was set to 2970.
The physical properties and miscibility were controlled by the cutoff distances of the Lennard–Jones potential. The cutoff distances between the A-A and B-B segments were set to 2.5 and 21/6 σ to demonstrate glassy and rubbery properties, respectively. The cutoff distance between A and B was set to maintain phase-separated structures. Twenty phase-separated structures were obtained for each fA with different initial random seeds for the SCFT calculations. Tensile deformation was applied to the x-, y-, and z-directions, and three S–S curves were obtained from one structure. A total of 480 sets of structures and S–S curves were prepared.