Invariant Property of the Distribution of Aa1, ..., Aas - Bb1, ..., Bbt-Type Ideal Polymerization

Xiao, Xin; Li, Z. S.; Sun, Chuanhao; Tang, An‐Na

doi:10.1021/ma00112a020

Cited by 11 publications

(5 citation statements)

References 6 publications

(9 reference statements)

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“…The latter treatment has recently been generalized to non-linear polycondensation by using more general invariant properties of the molecular weight distribution function holding before and after the gel point. 27 The first two invariants given in this literature are I a ≡ Ψ A (1p)(1q)/q and I b ≡ Ψ B (1p)(1q)/p in our notations. Obviously, they both give the association constant 1/λ AB , and hence remain unchanged before and after gelation.…”

Section: Sol/gel Transition and The Postgel Regimementioning

confidence: 99%

“…Thus the volume fraction of the unassociated molecules is one of the invariants of the molecular distribution function. The latter treatment has recently been generalized to non-linear polycondensation by using more general invariant properties of the molecular weight distribution function holding before and after the gel point . The first two invariants given in this literature are I a ≡ Ψ A (1 − p )(1 − q )/ q and I b ≡ Ψ B (1 − p )(1 − q )/ p in our notations.…”

Section: Sol/gel Transition and The Postgel Regimementioning

confidence: 99%

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Thermoreversible Gelation with Two-Component Networks

Tanaka

Ishida

1999

Macromolecules

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This paper studies thermoreversible gelation in two-component polymer mixtures (A/B) in which both polymers carry associative groups capable of forming reversible pairwise bonds. The type of association is classified into the following three main categories: (i) association of polymers within the same species (AA and BB); (ii) association only between the different species (AB); (iii) all associations allowed (AA, BB and AB). On the basis of a recent theory of associating polymers, we derive possible phase diagrams for interpenetrating networks, alternating networks, and randomly mixed networks corresponding to each category, with special attention to the interference between gelation and macroscopic phase separation. For all types, homogeneously mixed networks are most easily stabilized near the stoichiometric concentration where the total number of A associative groups in the mixture agrees with that of B associative groups.

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Section: Sol/gel Transition and The Postgel Regimementioning

confidence: 99%

Section: Sol/gel Transition and The Postgel Regimementioning

confidence: 99%

Thermoreversible Gelation with Two-Component Networks

Tanaka

Ishida

1999

Macromolecules

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“…Such a distribution is obtained by renormalization of the parameters of the SCD of the macromolecules present in the reaction system at the stage preceding gelation. The validity of this assertion, proved earlier for arbitrary ideal polycondensation [12], was reestablished many years later for particular cases of homopolycondensation of monomer RA f B g [290], as well as for copolycondensation of monomers R i A f i i ði ¼ 1; …; mÞ and S j B g j j ðj ¼ 1; …; nÞ [291].…”

Section: Ideal Model Of Polycondensationmentioning

confidence: 74%

Development of a quantitative theory of polycondensation

Кучанов

2004

Progress in Polymer Science

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“…Equation 19 enables us to find an invariant property of an average physical quantity as that in polycondensations proposed by Xiao and co-workers. 20 For an average physical quantity…”

Section: The Properties Of the System In The Postgel Regimementioning

confidence: 99%

“…Equation 19 enables us to find an invariant property of an average physical quantity as that in polycondensations proposed by Xiao and co-workers . For an average physical quantity ℋ( N 1 , N 2 , {λ μν }) defined by ℋ( N 1 , N 2 , {λ μν }) = Σ m , n ℋ m , n 𝒫 m , n ( N 1 , N 2 , {λ μν }) with ℋ m , n being only related to the index m and n , this invariant property states that if ℋ( N 1 , N 2 , {λ μν }) in pregel is known, then the corresponding quantity ℋ‘ in postgel can be directly obtained via the replacement of the system variables N 1 , N 2 and {λ μν } by the corresponding sol variables , and { } in the postgel regime.…”

Section: The Properties Of the System In The Postgel Regimementioning

confidence: 99%

Sol−Gel Transition in Nonlinear Hydrogen Bonding Solutions

Wang

Hong

2007

Macromolecules

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Hydrogen bonding (HB) in a mixed nonlinear system consisting of A a 1 D d 1 and Ā a 2 D̄ d 2 types of molecules is studied with the different activities of the groups being taken into account. Under the framework of the mean field theory, the partition function concerned the HB process of the system is given by two different statistical viewpoints. By which the equilibrium free energy of the system in the pregel regime, the law of mass action of HB process and the equilibrium size distribution of the HB clusters are carried out. The sol−gel phase transition is shown to take place in such a HB system with the gelation condition being given, and then the sol and gel free energies in the postgel regime are also obtained. Furthermore, the scaling laws satisfied by the kth moments and the gel fraction near the critical point are obtained for describing this kind of phase transition.

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Invariant Property of the Distribution of Aa1, ..., Aas - Bb1, ..., Bbt-Type Ideal Polymerization

Cited by 11 publications

References 6 publications

Thermoreversible Gelation with Two-Component Networks

Thermoreversible Gelation with Two-Component Networks

Development of a quantitative theory of polycondensation

Sol−Gel Transition in Nonlinear Hydrogen Bonding Solutions

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