ВЫСОКОМОЛЕКУЛЯРНЫЕ СОЕДИНЕНИЯ, Серия А, 2012, том 54, № 1, с. 52-64
: МОДЕЛИРОВАНИЕ
УДК 541.64:536.4
PREDICTION OF GLASS TRANSITION TEMPERATURES OF POLYQUINOLINES AND POLYQUINOXALINES1
© 2012 г. Yanli Liua, Zhengde Tana, and Shihua Zhang6' c
a Department of Chemistry and Chemical Engineering, Hunan Institute of Engineering, Xiangtan, Hunan, 411104, China
b Network Information Center, Hunan Institute of Engineering, Xiangtan, Hunan 411104, China c Key Laboratory of Environmentally Friendly Chemistry and Applications of Ministry of Education, College of Chemistry,
Xiangtan University, Xiangtan, Hunan 411105, China e-mail: liuyanli-8899@163.com, shihua_zh@sina.cn Received May 18, 2011 Revised Manuscript Received August 23, 2011
Abstract—Two molecular descriptors calculated directly from repeating units were used to predict the glass transition temperature (Tg) values of polyquinolines and polyquinoxalines. These polymers were randomly divided into a training set (44 polymers) and a test set (19 polymers). By applying stepwise multiple linear regression analysis, the training set was used to construct a quantitative structure-property relationship model, which was evaluated externally with the test set. The descriptors used have definite physical meaning. Root mean square errors for the training set and the test set were 15.90 K and 17.33 K respectively, which were accurate and acceptable in comparison with existing models. The results indicate that chosen model containing only two molecular descriptors can be applied to predict Tg of polyquinolines and polyquinoxalines, although these polymers have complicated structures.
INTRODUCTION
When an amorphous polymer is heated, the temperature at which it changes from a hard and relatively brittle state into a molten or rubber-like state is called the glass transition temperature (Tg). Below Tg amorphous polymers are in a glassy state and most of their joining bonds are intact. Above Tg polymers become soft and capable of plastic deformation without fracture [1, 2]. Tg is the most important and widely studied characteristic of polymeric material and affects many other polymer properties such as heat capacity, coefficient of thermal expansion, and viscosity. In fact, Tg determines temperature windows for processing and utilizing these material, and is a prerequisite for the prediction and understanding of the mechanical and other properties [3].
Generally, the reported Tg is only average value, as the glass transition temperature depends on the cooling rate, molecular weight distribution, its thermal history and the measurement method [4]. Hence the development of theoretical methods for predicting Tg is needed and interesting.
Numerous researchers have attempted to predict Tg for polymers on the basis of quantitative structure-property relationship (QSPR) models [5—12]. Bicera-no [5] correlated Tg with 13 structural parameters plus the solubility parameter for the data set of 320 polymers. But the model, with a standard error (se) of
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24.65 K, has not been validated with the test data set. Yu et al. [6] developed a linear model with only two descriptors (the molecular traceless quadrupole moment 9 and the molecular average hexadecapole moment O). The model was tested to be accurate, with a root mean square (rms) error of 25.0 K for the training set and a rms error of 20.8 K for the test set. Katritzky et al. [7] used the CODESSA software to develop a four-parameter model (R2 = 0.928) for a set of Tg of 22 polymers. In addition, Katritzky et al. [8] predicted Tg for 88 linear homopolymers using five descriptors calculated by CODESSA software and developed a QSPR model (se = 32.9 K). Mattioni and Jurs [9] generated two artificial neural network models to predict Tg values for two diverse sets of polymers. The rms errors of test sets of the two models were above 21 K.
Askadskii [10, 11] introduced the atomistic approach to calculate the Tg for polymers of any classes as well as for all the polymers with complicate structures. The calculated values of Tg for 1050 polymers indicate that this method is accurate and successful. This approach is more universal than the group contributions method [12]. In fact, the calculation of the group contributions becomes impossible if a polymer possesses a group, whose contribution into Tg is unknown [11]. In the atomistic approach developed by Askadskii [10, 11], contribution of any group is simply composed of the contributions of atoms composing it plus the contribution of specific interactions, if these groups are polar.
1
Polyquinolines and polyquinoxalines are polymers, respectively, having quinoline and quinoxaline structures and known to possess exceptional thermal stability, good mechanical properties, low moisture absorption, and excellent dielectric properties. Over the past three decades polyquinolines and polyquinoxalines have attracted increasing interest of scientists engaged in fundamental research as well as that of companies looking into their application and commercialization. This situation will apparently continue in the future.
The goal of this article is to produce a robust QSPR model that could predict Tg values for polyquinolines and polyquinoxalines by using only two molecular descriptors, which are calculated from the repeating units of these polymers.
MATERIALS AND METHODS
Totally, 63 polyquinolines and polyquinoxalines and their respective experimental Tg values [13] are listed in Table 1. As can be seen, the entire set contains a wide range of Tg values (489—690 K) and is characterized by a high degree of structural variety. The experimental Tg values were randomly divided into a training and a prediction sets. The training set included 44 polymers; while the prediction set included 19 polymers.
Generally, the stiffness (or mobility) of the polymer chain has effects on Tg values. The flexibility of these polymer chains can be expressed with the descriptor Nf, which is defined as the number of —O— groups in a repeating unit. For example, the descriptor NF for the polymer of no. 1 is 2, since there are two —O— groups.
WHIM descriptors (Weighted Holistic Invariant Molecular descriptors) are used widely in QSPR/QSAR studies [14]. WHIM descriptors are built in such a way as to capture relevant molecular 3D information regarding molecular size, shape, symmetry, and atom distribution with respect to invariant reference frames [14, 15]. Within the WHIM approach, a molecule is seen as a configuration of points (the atoms) in the three-dimensional space defined by the Cartesian axes (x, y, and z). In order to obtain a unique reference frame, principal axes of the molecule are calculated. Then, projections of the atoms along each of the principal axes are performed and their dispersion and distribution around the geometric centre are evaluated. Six different weighting schemes are adopted: the unweighted case (u), atomic mass (m), the van der Waals volume (v), the Sanderson atomic electronegativity (e), the atomic polarizability (p) and the electrotopo-logical state indices of Kier and Hall (s) [15].
For example, the WHIM descriptor Du is obtained from the following expression:
Du = n + n + (!)
where nk (k = 1, 2, 3) is related to the density of the atoms distribution, i.e. to the quantity of unfilled space
per projected atom — and has also been called emptiness: the greater the nk values, the greater the projected unfilled space. nk can be represented by:
nk =
Xk x nAT
_ X k
I
k = 1, 2, 3,
(2)
where t refers to atomic coordinates with respect to the principal axes; i is the i-th atom in a molecule; nAT is the number of atoms in molecules; X refers to eigenvalues of the weighted covariance matrix S and is related to molecular size. The elements of the covariance matrix are:
I wa - qj)(qtk- qk)
Sjk -
- i=1
nAT
I
i=l
(3)
w,
where q^ represents the j-th coordinate (j = 1, 2, 3) of the /-th atom, qj is the average of the j-th coordinates and Wj the weight of the /-th atom. For the unweighted case u, Wj is equal to one. A fundamental role in the WHIM descriptor calculation based on a principal components analysis (PCA) is played by the eigenvalues X2 and X3 of the weighted covariance matrix of the molecule atomic coordinates [15].
To calculate WHIM descriptors, the polymers were represented by their repeating units end-capped by two carbon atoms. For example, the compound
H3C.
N.
CH3
was used to represent the polymer
(No. 1 in Table 1). The molecular structures of the repeating units (end-capped by two carbon atoms) were sketched using Chem Draw ultra module of CS Chem Office Version 8.0. The sketched structures were then transferred to Chem3D module for generation of three dimensional structure (3D). The sketched structures were subjected to energy minimization using molecular mechanics (MM2) until the RMS gradient value became smaller than 0.1 kcal/mol A. The energy minimized molecules were subjected to re-optimization via AM1 method in Gaussian 03 [16] without applying symmetry or structural constraints. After optimizing
n
Table 1. Molecular descriptors and Tg values for 63 polymers
No.
Polymers
Nf
Du
Tg, K (exp)
Tg, K (calc)
The training set
N
0.431
0.425
0.440
0.429
0.416
0.487
0.485
524
581
539
618
550
546
585
536
593
532
591
542
566
567
1
2
2
1
3
2
4
1
5
2
6
1
7
1
No.
Polymers
Nf
Du
Tg, K (exp)
Tg, K (calc)
10
11
12
13
14
O
O
0.453
0.414
0.454
0.377
0.397
0.398
0.376
598
643
663
658
678
583
690
653
635
669
661
8
1
9
0
0
0
0
1
0
№э. Polymers N Du Т, K(exp)
1 I
15 0 0.430 653
у
16 1 0.398 588
о
^ч, н /V
1 2г~\Рк/—\1 }
УС^уТУ
17 1 0.421 593
18 гт 0 0.403 665
19 99 0 0.380 652
^^ к к! ГТ
О
20 0 0.466 623
6 к IX
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