ВЫСОКОМОЛЕКУЛЯРНЫЕ СОЕДИНЕНИЯ, Серия А, 2013, том 55, № 8, с. 1055-1060
СТРУКТУРА И СВОЙСТВА
УДК 541.64:536.4:539.2
PREDICTION OF GLASS TRANSITION TEMPERATURE OF POLYACRYLATE USING A QUANTITATIVE STRUCTURE PROPERTY RELATIONSHIP MODEL1
© 2013 г. J. B. Tongab, X. M. Xuab S. L. Liuab, T. Cheab, Y. F. Lia'b, Z. Huab, and Y. L. Mengab
a College of Chemistry and Chemical Engineering, Shaanxi University of Science & Technology, Xi'an 710021, China b Key laboratory of Auxiliary Chemistry & Technology for Chemical Industry, Ministry of Education, Shaanxi University of Science & Technology, Xi'an 710021, China e-mail: jianbotong@yahoo.com.cn (J.B. Tong) Received May 29, 2012 Revised Manuscript Received January 24, 2013
Abstract — Quantitative structure property relationships are systematically studied for glass transition temperature simulation of polyacrylate. A newly developed descriptor-generalized correlative index is used for the expression of chemical structure of polyacrylate. A multiple linear regression model is built after screening some insignificant parameters with the stepwise multiple regression technique. The correlation coefficient ^cum and cross-validated correlation coefficient Qcum are 0.991 and 0.985, respectively. Furthermore, the superior performance of the MLR model is tested by the external set, the correlation coefficient is Qext = 0.920. In conclusion, generalized correlative index descriptor can be used for estimating and predicting glass transition temperature of polyacrylate.
DOI: 10.7868/S0507547513080126
INTRODUCTION
Nowadays, polyacrylate has been applicated universally [1]. Due to the different functional group, polyacrylate can show different characteristics. According to the flexible of the polyacrylate molecular, they always have a low glass temperature. It is widely that the polyacrylate have been used in the field of decoration material, thermal glue adhesive, finishing agent, cosmetics and so on. Emulsion of the polyacrylate is one of the most commonly synthetic emulsions in recent years. They are always used as the coating adhesive and special rubber due to their outstanding ability on heat resistance, oxidant, and oil as well as strong adhesive function on both polar and non-polar surface. However, the application of these kinds of materials always constrained by the deficiency such as lower heat resistance temperature, using temperature, lower surface hardness and lower impact properties [2]. As a result, glass temperature Tg actually plays an importance role in their application and processing, testing their heat resistance function and indicting their nature and performance. Since that, Tg is a significant nature in high polymer synthesis and application [3, 4]. Since most kinds of physical parameters in molecule system can be well represented by the quantum chemical calculation, it is widely used in the quantitative structure-property relationship (QSPR) researches [5—9]. In this article, the generalized correlative in-
dex (GCI) has been used to simulate and to predict the glass temperature Tg of polyacrylate.
MODEL AND METHOD IN THEORETICAL AND MODELING STUDIES
Description of Structure
According to the huge number and uncertainty of polymer, we can use the monomer instead and end the chain with hydrogen [10, 11]. Then we can get the relationship between Tg and structure [12]. The structures are shown in Scheme 1 [13, 14].
H R,
I 11
*—C—C-*
H J^
œ O
I
R
-2
H R1
I I 1
H-C—C-H
H J^
O O
I
R
2
Scheme 1.
1 The article is published in the original.
Introduction of the Correlative Concepts with Generalize Correlation Index
Incorporating ideas of "facing to users" and "self-adaptability" into modern molecular structural characteristic (MSC) methods, GCI is proposed via some definitions as atomic branched degree (ABD), property correlative parameters (PCP), generalized correlative function (GCF) and distance-relational function (DRF).
Atomic branched degree (ABD) abstracts the non-hydrogen atom in organic compound as a topological
Table 1. 4 atomic types with different atomic branched degrees and 10 kinds of correlative terms among them
Atomic branched degree 1 2 3 4
1 1-1 1-2 1-3 1-4
2 2-2 2-3 2-4
3 - 3-4
4 4-4
picture. All the structure informations are given by the way that how top atoms connect with each other. From a topological perspective, local topological characteristic can be embodied into the embranchment degree of certain vertex in connection with other ones in different amounts. Thus ABD is defined as numbers of atoms binding to nonhydrogen atoms (Table 1). As a result, we define the ABD as the number of non-hydrogen bond in the compound. Absolutely, for most of the organic molecular, its ABD varies only from 1—4 (except methane).
Property correlative parameter (PCP): as is well known, atom sustains molecular external properties as the basic unit. In GCI, PCP is primarily defined by the users themselves, which is not specially restricted and targets to possibly relate with practical applications. PCP is often categorized in three different ways. (a) Fundamental atomic attributions, that is related only with atomic types, e.g. atomic weight, VDW bulk, and electronegativity; (b) Atomic status attribution, that is not only related to the atomic type, but also to the hybridized state and chemical environments, e.g. hydrophobic property and hybridized state; (Table 2 has listed several common atomic hybridization state indexes (AHSI) and their relative values) (c) Atomic experimental attribution, that is directly derived from experimental measurements, e.g. nuclear magnitude resonance, eigenvalue spectrum etc. What should be elucidated is that large difference in the order of magnitude would be induced due to disunified units among different kinds of properties. Thus sp3 C is served as the standard atom and relative property correlative parameter (RPCP) is defined as the ratio of other atoms to that, thus fulfilling a direct calculation of generalized indexes.
The main idea of GCI is focused on an indirect reflection of the overall molecular structures via ex-
pressing correlativeness among different atomic properties. This correlativeness does not reflect the two changing trends in a specific interaction manner: one varies in a negative manner with the increase or decrease of interatomic distances and the other varies in a negative manner with the change in atomic properties. GCI is then given out by above-mentioned assumption, i.e. the function collections satisfying conditions of positively and negatively related with atomic properties and interatomic distance. The formula is as follows:
G([n, n], dif; a) = [ni, nj] ■/(df a), (1)
where a is the function-determined parameter set, n and n represent the property-correlative parameters between the atoms i and j, dy is the certain of distance measurement between atom i and j. Obviously, the above formula indicates that atomic correlativeness has a positive relation with its property where negatively relates with the distance d. So once satisfying a negative relation with distance d, the function f(a; dij) could be served as distance relationship function (DRF). The common DRFs include Gaussian, reciprocal, and exponential.
The Calculation of GCI
According to the ABD, the atoms of organic molecules can be divided to 4 types, thus, 10 interatomic interactions exist in all different kinds of atoms. We named it as GCI. The equation is given as follows,
gcik_ L = ^ ^ G(a; n, n,, dj
i e Kj e L
( 1 < K < L < 4 ; i * j),
(2)
where n and G(-) are the relevance of specific atom chosen by user and GCF, respectively, dy is the shortest relative bond-distance the ration between shortest bond distance between atoms i and j and C—C bond distance. At the same time, the ration of some chemical bond length and C—C single bond length is called relative bond-length.
Calculation Example
Take polyacrylate for example, the computational process of generalized correlative index were intro-
Table 2. Atomic hybridization state indexes (AHSI) and their relative values
Atom Csp3 Csp2 C ^sp Nsp3 Nsp2 Nsp Osp3 Osp2 Ssp3 Ssp2
Atomic hybridization state indexes 1.25 1.67 2.50 1.49 2.24 4.47 1.84 3.67 1.16 2.31
rahsi 1.00 1.34 2.00 1.19 1.79 3.58 1.47 2.94 0.93 1.85
Table 3. Structures of 22 polyacrylates and their calculation data of Tg
Number R1 R2 V31 V21 V46 V16 T¡, K Tb, K
1 H CH3 3.2827 1.6481 — 0.8702 1.5709 282 278.015
2 H CH3CH2 2.4639 1.1953 —1.4596 2.304 251 251.488
3 H CH3(CH2)2 1.9233 0.9072 — 1.8453 2.7837 229 230.108
4 H CH3(CH2)3 1.6383 0.7596 -2.056 3.0458 217 218.298
5 H CH3CH2CH(CH3) 3.3745 1.8785 0.3061 4.1011 256 259.857
6 H (CH3CH2)2CH 2.626 1.3825 0.8345 5.4947 257 235.231
7 H CH3(CH2)5 1.4736 0.6766 —2.1889 3.211 216 208.226
8 H CH3(CH2)6 2.0213 0.9754 1.6701 7.0189 213 218.382
9 H CH3(CH2)7 1.9515 0.9272 1.8703 7.3015 208 216.370
10 H CH3(CH2)8 1.9301 0.9121 1.964 7.4214 216 212.795
11 H CH^CH^ 1.9247 0.9082 2.0001 7.4644 213 213.260
12 H (CH3)2CH 4.1679 2.4195 —0.2222 2.7075 272 282.061
13 H (CH3)3C 6.5696 4.3413 —0.8702 1.5709 304 310.977
14 CH3 CH3CH2 4.7387 2.6814 —0.115 2.3778 324 321.755
15 CH3 CH3(CH2)2 4.1241 2.3192 —0.2385 3.1195 306 299.829
16 CH3 CH3(CH2)3 3.8081 2.1406 —0.3296 3.5012 293 288.058
17 CH3 (CH3)3C 9.0837 6.0667 —0.0052 1.165 380 368.591
18 CH3 CH3(CH2)5 3.6296 2.0439 —0.4023 3.7266 268 287.130
19 CH3 (CH3)2CH 6.5624 4.0252 0.1632 1.822 354 355.456
20c CH3 (CH3)2CHCH2 5.6647 3.494 0.9516 3.871 326 316.849
21c CH3 CH3(CH2)7 3.7705 2.1169 —0.4056 3.9477 253 296.284
22c CH3 CH3 5.9727 3.4374 —0.0029 1.1799 378 366.630
Note. a Observed value, b predicted value, c test set.
duced. Scheme 2 shows (a) the molecular structure of polyacrylate, (b) the dehydrogen structure of poly-
acrylate and (c) the topological structure of polyacrylate.
3 I 2
¿•CS H2
O O—C—CH3
C^C2 C3
o5—c6—C7
3
5 6 c
Scheme 2.
GCI1—3 - RAHSI1R
■A
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