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Monte Carlo simulation is performed to study the adsorption properties of polymers on an attractive surface. Annealing method is adopted to simulate the adsorption characteristics and conformational changes of polymer chains driven by an external driving force F. In simulations using cooperative motion algorithm, the ensembles of monomers located at lattice sites are connected by non-breakable bonds. When the external force is F=0, the finite-size scale method can be used to determine the critical adsorption temperature (Tc) of the polymer chain on the attractive surface, but when the external force is F>0, the dependence of the average number of surface contacts M> on the chain length N is unrelated to temperature T. Therefore, Tc cannot be obtained by the finite-size scale method. However, the pseudo-critical adsorption temperature Tc can be estimated by a function of the average number of surface contacts M> and the temperature T for the chain length N=200. And then Tc decreases with external force F increasing. The phase diagram is obtained for the polymer chain between the desorbed state and the adsorbed state under temperature T and external driving force F. Furthermore, the influence of the external driving force on the conformation of the polymer chain is analyzed by the mean square radius of gyration of polymer chains. The critical adsorption point Tc can be checked roughly by the minimum location of the mean square radius of gyration or by the variation of its components in the Y and Z direction perpendicular to the external force. With the increase of the external force F for adsorbed polymer, the temperature T can determine whether polymer is changed from the adsorption state to the desorption state and where the force is located at the transformation. There are two different cases, that is, the polymer can be desorbed at the temperature Tc* TTc and the polymer cannot be desorbed at T Tc*. In this paper, we discuss these two cases for the adsorption of polymer on the attractive surface:weak and strong adsorption. In the first case, the adsorption is strongly influenced by the external driving force. By contrast, in the strong adsorption, the adsorption is weakly influenced by the external force. Our results unravel the dependence of adsorption of polymer on external driving force, which is also consistent with the phase diagram of adsorption and desorption of polymer chains.

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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>_C = 1.5, which is close to the critical phase transition temperature <i>T</i>_C = 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>₁ = 0.55 and <i>T</i>₂ = 1.1, which are consistent respectively with <i>T</i>₁ = 0.58 and <i>T</i>₂ = 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.