Recognition of adsorption phase transition of polymer on surface by neural network

Abstract

Traditional Monte Carlo simulation requires a large number of samples to be employed for calculating various physical parameters, which needs much time and computer resources due to inefficient statistical cases rather than mining data features for each example. Here, we introduce a technique for digging information characteristics to study the phase transition of polymer generated by Monte Carlo method. Convolutional neural network (CNN) and fully connected neural network (FCN) are performed to study the critical adsorption phase transition of polymer adsorbed on the homogeneous cover and stripe surface. The data set (conformations of the polymer) is generated by the Monte Carlo method, the annealing algorithm (including 48 temperatures ranging from <i>T</i> = 8.0 to <i>T</i> = 0.05) and the Metropolis sampling method, which is marked by the state labeling method and the temperature labeling method and used for training and testing of the CNN and the FCN. The CNN and the FCN network can not only recognize the desorption state and adsorption state of the polymer on the homogeneous surface (the critical phase transition temperature <i>T</i><sub>C</sub> = 1.5, which is close to the critical phase transition temperature <i>T</i><sub>C</sub> = 1.625 of the infinite chain length of polymer adsorbed on the homogeneous surface regardless of the size effect), but also recognize the desorption state, the single-stripe adsorption state and the multi-stripe adsorption state of polymer on the stripe surface(the critical phase transition temperature <i>T</i><sub>1</sub> = 0.55 and <i>T</i><sub>2</sub> = 1.1, which are consistent respectively with <i>T</i><sub>1</sub> = 0.58 and <i>T</i><sub>2</sub> = 1.05 of polymer adsorbed on the stripe-patterned surface derived from existing research results). We obtain almost the same critical adsorption temperature by two different labeling methods. Through the study of the relationship between the size of the training set and the recognition rate of the neural network, it is found that the deep neural network can well recognize the conformational state of polymer on homogeneous surface and stripe surface of a small set of training samples (when the number of samples at each temperature is greater than 24, the recognition rate of the polymer is larger than 95.5%). Therefore, the deep neural network provides a new calculation method for polymer simulation research with the Monte Carlo method.