Statistical mechanics approach to a general hyperbranched polymer system consisting of ABg monomers and Cf cores

Zhao, Zuo-Fei; Li, Yuanfeng; Yao, Ning; Wang, Haijun; Ba, Xinwu

doi:10.1016/j.polymer.2013.12.036

Cited by 5 publications

(8 citation statements)

References 47 publications

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“…(28). The above equation shows that the specific heat C V is closely related to the temperature T, bonding energy ε, and conversion x.…”

Section: Several Thermodynamical Properties Of the Systemmentioning

confidence: 97%

“…Recently, the method of statistical mechanics has been applied to study a series of SCVP systems [25][26][27][28], and the equilibrium free energy and law of mass action were given in their explicit expressions. Furthermore, some average physical quantities such as polymeric moments and mean square radius of gyration can be correlated with thermodynamic quantities of the system.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that, throughout the paper, the classical assumptions of ideal polymerization have been adopted, namely, (1) all the double bonds of vinyl group A are of equal reactivities; (2) all the double bonds of vinyl group A react independently; and (3) the intramolecular reaction is excluded throughout the paper. In fact, these approximations had been used in previous studies [15][16][17][18][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…To study the related physical and chemical properties of a system with a great number of species, the method of statistical mechanics is often used as a powerful theoretical tool [25][26][27][28]. In this section, two kinds of partition functions would be constructed from different viewpoints, then the equilibrium free energy, law of mass action, and the size distribution function are given in their explicit forms.…”

mentioning

confidence: 99%

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Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

Zhao

Yao

et al. 2015

Sci. China Chem.

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A new self-condensing vinyl polymerization system consisting of * AB f -type inimers is studied by the principle of statistical mechanics. To obtain the relevant average properties of the system, a differential equation satisfied by the polymeric moment of interest is given, and as a result the zeroth, first, second, and third polymeric moments together with the size distribution function of hyperbranched polymers (HBPs) are explicitly presented. As an application of the method of statistical mechanics, several thermodynamic quantities such as the equilibrium free energy, law of mass action, isothermal compressibility, internal energy, and the specific heat associated with the polymerization are all derived. Furthermore, the scaling behavior of asymptotic size distribution function is discussed, by which a reasonable interpretation of the polydispersity index near the end of polymerization can be made. Also, the expressions of some structural parameters such as the numbers of inimers, terminal units, chain units, branched units, and the degree of branching (DB) are calculated. It is found that a high functionality is helpful to improve the DB of the resultant HBPs. These results show that the functionality f has a significant effect on the thermodynamic quantities and structural properties of HBPs. partition function, law of mass action, internal energy and specific heat, polydispersity index, structural parameter

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“…(28). The above equation shows that the specific heat C V is closely related to the temperature T, bonding energy ε, and conversion x.…”

Section: Several Thermodynamical Properties Of the Systemmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

Zhao

Yao

et al. 2015

Sci. China Chem.

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“…Hyperbranched polymers usually have good solubility and low viscosity compared to the linear analoges. [1][2][3][4][5][6][7][8][9][10][11][12] Combining of chemically stable amide bonds with hyperbranched structures not only retained excellent thermal and flame-resistant properties of aromatic polyamides, but also decreased melt viscosity and excellent solubility which improved the processability. [13][14][15][16][17][18][19][20] Moreover, introduction of flexible aliphatic units into the main chain is another method to improve the processability of aromatic polyamides.…”

Section: Introductionmentioning

confidence: 99%

Phosphorus-containing polymers from THPS. II: synthesis and property of phosphorus-containing hyperbranched aromatic-aliphatic polyamides

Tan

Sun

Zhang

et al. 2015

Designed Monomers and Polymers

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Phosphorus-containing hyperbranched aromatic-aliphatic polyamides are prepared via direct polymerization of triacid (B 3 ) with different diamines (A 2 ), which for improving the processability of aromatic polyamides while keeping exellent thermal and mechanical property. The triacid (B 3 ), tris(2-carboxyethyl)phosphine oxide (TCEPO), is synthesized from tetrakis(hydroxymethyl)phosphonium sulfate and its structure is verified by Fourier transform infrared, 1 H, 13 C and 31 P NMR spectroscopy. Then, the polycondensation reaction of TCEPO with p-phenylene diamine, 4,4′-oxyphenylene diamine and 4,4′-methylenedianiline result in three phosphorus-containing hyperbranched aromatic-aliphatic polyamides, and the degree of branching is found between 0.66 and 0.71. Gel permeation chromatography measurement reveal that all hyperbranched aromatic-aliphatic polyamides have moderate number-averaged molecular weights and narrow molecular weight distribution. The Dynamic mechanical thermal analysis results show all polymers have two glass transition temperatures (T g ) in the temperature range 85.3-128.0°C and have high storage modulus about 1.52-3.19 GPa at 50°C. The TGA results reveal the initial degradation temperatures (T 5 ) and the temperatures for 10% gravimetric loss (T 10 ) for the hyperbranched aromatic-aliphatic polyamides are in the range of 214-250 and 256-333°C, and the maximum decomposition temperatures (T m ) are about 500°C, and also the char yields of polymers at 850°C are about 39.4-48.4%, which indicate good thermal stability.

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Theoretical Methods of the Size Distribution Function for the Products of Hyperbranched Polymerization

Hao

Zhou

Nie

2020

Macro Theory & Simulations

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wide application of the hyperbranched polymers. To solve this problem, people first need to understand the relationship between monomer type, reaction conditions, and product structure parameters.In fact, the theoretical development of hyperbranched polymers has been in step with the experimental work, and guides the experimental development. At first, the resin with highly free branched structure was prepared mainly based on A a , and A a +B b type approaches. [13,14] This kind of polymerization is easy to gel. Flory carried out the theoretical research on hyperbranched polymers in 1940s. [15][16][17] He first demonstrated the possibility of preparing highly branched polymers from polyfunctional monomers, and calculated the critical gel conditions and relative molecular weight distribution of three functional and four functional branched monomers by means of probability statistics. In 1952, he further predicted the possibility that AB g type monomers could form highly branched polymers via condensation polymerization and derived the molecular weight distribution function for the products obtained by the probability method. [18] From another point of view, Stockmayer thinks that polymerization is similar to that of gas liquefaction. By using statistical mechanics methods of non-ideal gases, he derived the gelation conditions and size distribution functions of products for the A a , A 2 +A a , and A 2 +A a +B 2 (a > 2) type branching reactions. [19][20][21] Like the experiment of hyperbranched polymer synthesis, a new round of theoretical research climax also originated from the work of Kim et al. in the 1980s, [7][8][9] when they first synthesized highly branched polyphenylene with AB 2 monomer, and named this kind of product hyperbranched polymer. Because of its unique structure and characteristics, it is expected that it will be widely used in many fields, which has attracted the general attention of academia and industry. Hawker et al. [22] and Kim et al. [7][8][9] proposed the definition of the degree of branching (DB) of hyperbranched polymers by comparing them with perfectly branched dendrimers, Frey et al. [23,24] derived the formula of degree of branching for AB g hyperbranched polymers by kinetic and statistical methods respectively. Müller and Yan et al. developed the kinetic theory for AB 2 polycondensation and SCVP, and derived the analytical expressions of branching degree, polymerization degree distribution function, and other molecular parameters for the products. [25,26] Then Yan and Zhou [27][28][29][30][31] extended the kinetic method to the polycondensation of more general AB g type monomers and the reaction system in the presence of the In the theory of hyperbranched polymerization, due to the difficulty of deriving isomers of conformations, the early Flory's probability method and Stockmayer's statistical mechanics method have been rarely used. In this work, a new and easy way to derive the total number of configurations is developed, which can extend the application of the two theoretical me...

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Statistical mechanics approach to a general hyperbranched polymer system consisting of ABg monomers and Cf cores

Cited by 5 publications

References 47 publications

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

Phosphorus-containing polymers from THPS. II: synthesis and property of phosphorus-containing hyperbranched aromatic-aliphatic polyamides

Theoretical Methods of the Size Distribution Function for the Products of Hyperbranched Polymerization

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