Quantum-behaved Particle Swarm Optimization Based Study On Glass Transition Temperatures Of Polymers With Support Vector Regression

The glass transition temperature (Tg) is one of the most important properties of amorphous polymer, which is involved in many frontier issues in dynamics and thermodynamics and is also an important problem among the theories of condensed matter physics. Glass state is a thermodynamic non-equilibrium state. The transition does not take place in a fixed point, but in a range of temperature. Furthermore, the Tg value determing by experiment is affected by experimental condition, such as the duration of experiment, surrounding pressure, etc. Therefore, using various measuring approaches to measure the Tg of polymers would result in different degree of deviation (sometimes it is even more than10K). The physical/chemical properties of polymers are usually depended on polymeric structural and constitutional features, the relationship between them is quite complex, to investigate and recognite the regularity has very important significance to accurately predict Tg for polymers.In this thesis, several traditional and modern regression approaches are employed to model the relashionship between Tg and structures of polymers. It is focused on the application of support vector regression (SVR) method combined with quantum-behaved particle swarm optimization (QPSO) for predicting the Tg of different types of polymers including polymethacrylates, vinyl polymers, styrenic copolymer and polyacrylamides. The main contents of this thesis are as follows:(1) Based on six quantum chemical descriptors (L, Etotal, qC6, a, α and Etherm), which were calculated directly from the structure of the monomer with the Gaussian03program, at the DFT/B3LYP/6-31G(d) level, the hybrid PSO-SVR is proposed to establish a model for predicting the Tg of37polymethacrylates. The prediction performance of SVR was compared with those of reported MLR and ANN models. The results show that the root mean squre error (RMSE), mean absolute percentage error (MAPE) and correlashion coefficient (R2) calculated by SVR model are superior to those achieved by MLR or ANN models for the identical25training samples and7test samples. Moreover, in order to validate the generalization performance of the established SVR model, the Tg indices of other5independent polymethacrylates were predicted by the established SVR model. The results reaveal that the MAE=6.8K which demonstrates that the established SVR model is more reliable to be used for prediction of the Tg values for unknown polymethacrylates possessing similar structure. Additionally, to further validate the confidance of the constructed SVR model, the whole37samples used in this study are also partitioned into the training, test and independent sets in the ratio of50%,25%and25%by using k-Nearest Neighbor (kNN). The statistic MAEs of Tg calculated by the re-constructed SVR model for the test set and independent set are7.44K and8.OK respectively, which is also acceptable in practice. A phenomenon can be found empirically by comparison the prediction results of the test and independent samples that, in general, the more the number of training samples is, the greater the prediction and generalization ability of SVR would be.(2) Based on four descriptors (the rigidness descriptor (ROM) resulted by hydrogen-bonding moieties group and/or rings, the chain mobility (n), the molecular average polarizability (a) and the net charge of the most negative atom(q)) derived from the polymers’monomers structure, the SVR approach combined with QPSO and spectral structure activity relationship (S-SAR), are proposed to establish models for prediction of the Tg of202vinyl polymers. The prediction performance ofQPSO-SVR and S-SAR were compared with that of reported ANN model. The results demonstrated that the comprehensive modeling and prediction ability (RSE=18.55K,R2=0.9253) of SVR model surpasses those of S-SAR (PMSE=22.02K, R2=0.8952) and ANN (RMSE=20.195K, R2=0.9120) models by applying identical training and validation samples. Furthermore, apart from the124training samples and64test samples, other10independent vinyl polymers’s Tg were also predicted by the established SVR model for the sake of validation the predicting performance of the established SVR model. The MAE, MAPE and R2for the independent set predicted by SVR also reached14.132K,4.25%and0.9475, respectively. These illustrate that the SVR model is more suitable to be used for prediction of the Tg values for unknown vinyl polymers’s possessing similar structure.(3) Based on3chemical descriptors (the heat capacity at constant Cy, the average polarizability of a molecular a and the most positive net atomic charge on hydrogen atoms q+) calculated directly from the structure of the monomer with the Gaussian03program, at the DFT/B3LYP/6-31G(d) level, the SVR approach combined with QPSO, is used to predict the Tg of48styrenic copolymers. The sensitivity analysis of each descriptor on the Tg was conducted according to the established QPSO-SVR models. The statistic MAEs for the training samples and test samples are1.60K and3.03K respectively, which are superior to those (5.47K and5.38K) of QSPR reported in a literature. For styrenic copolymers, on the basis of the sensitivity analysis results, the most significant descriptor is the Cv (its average sensitivity is0.014514), the second significant descriptor is the a (its average sensitivity is0.01305) and the third significant descriptor is the q+(its average sensitivity is0.008235). This is also quite consistent with that of the reported t-test. It reflects that the sensitivity index can be employed to determine the relative influence magnitude of different chemical descriptors on Tg accurately.The studies in this thesis demonstrated that the prediction accuracy of QPSO-SVR model is superior to those of other regression methods including multivarivate linear regression, artificial neural network, etc., and its generalization ability also surpasses those of them. The results suggest that the QPSO-SVR is an effective and powerful technique, and it may be further developed to be a potential application tool in research and development of polymer materials and provides a new clue in computer-aided design/sythesis of novel polymer with desired Tg.