Dense self-interacting lattice trees with specified topologies: From light to dense branching

Nemirovsky, A. M.; Dudowicz, Jacek; Freed, Karl F.

doi:10.1103/physreva.45.7111

Cited by 51 publications

(59 citation statements)

References 42 publications

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“…Also the number of bonds is independent of the polymers' branching architecture and can be calculated as follows [113]: (65) All other topological coefficients of Table 1 depend on the architecture of the polymer. This architecture is described by the number of branching points , where describes the branching degree, that means the number of bonds which meet at one repeating unit.…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…This can be generalized to higher branching degrees as can be seen in Table 2; whereas it has to be mentioned that in polymer chains only branching points with degree up to four exists. With help of Table 2 an equation can be derived, which can be used to calculate the number of possibilities [113]: (68) Figure 3. Number of two consecutive bonds up to a branching degree of four.…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…3 1 4 3 5 6 6 10 7 15 The factor is reduced by each chosen bond and the factor 1/2 appears because of the indistinguishability. In an analogous manner the number of ways of choosing three or four bonds can be described [113]: (69) (70) where describes the contribution of a linear chain [113]:…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…The chosen bonds are marked by broken lines. This can be generalized for a linear polymer with monomers as follows [113]:…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…The total number of branching points is [113]: (66) where is the number of branching points of degree in which bonds meet.…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

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Phase Diagrams for Systems Containing Hyperbranched Polymers

et al. 2012

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Abstract:Hyperbranched polymers show an outstanding potential for applications ranging from chemistry over nanotechnology to pharmacy. In order to take advantage of this potential, the underlying phase behaviour must be known. From the thermodynamic point of view, the modelling of these phase diagrams is quite challenging, because the thermodynamic properties depend on the architecture of the hyperbranched polymer as well as on the number and kind of present functional end groups. The influence of architecture can be taken into account via the lattice cluster theory (LCT) as an extension of the well-known Flory-Huggins theory. Whereas the Flory-Huggins theory is limited to linear polymer chains, the LCT can be applied to an arbitrary chain architecture. The number and the kind of functional groups can be handled via the Wertheim perturbation theory, applicable for directed forces between the functional groups and the surrounding solvent molecules. The combination of the LCT and the Wertheim theory can be established for the modelling or even prediction of the liquid-liquid equilibria (LLE) of polymer solutions in a single solvent or in a solvent mixture or polymer blends, where the polymer can have an arbitrary structure. The applied theory predicts large demixing regions for mixtures of linear polymers and hyperbranched polymers, as well as for mixtures made from two hyperbranched polymers. The introduction of empty lattice sites permits the theoretical investigation of pressure effects on phase behaviour. The calculated phase diagrams were compared with own experimental data or to experimental data taken from literature. OPEN ACCESSPolymers 2012, 4 73

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Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…The chosen bonds are marked by broken lines. This can be generalized for a linear polymer with monomers as follows [113]:…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

“…The total number of branching points is [113]: (66) where is the number of branching points of degree in which bonds meet.…”

Section: Application To Hyperbranched Polymersmentioning

confidence: 99%

See 3 more Smart Citations

Phase Diagrams for Systems Containing Hyperbranched Polymers

et al. 2012

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Lattice Cluster Theory of Multicomponent Polymer Systems: Chain Semiflexibility and Specific Interactions

Foreman

Freed

1998

Advances in Chemical Physics

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Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

et al. 2018

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The associating lattice cluster theory (ALCT) is developed in this work. It is especially useful for describing mixtures of oligomers of varying architecture. As the influence of the structure is predicted, it can also be applied in cases in which pure component data are lacking. ALCT is used here for the calculation of liquid–liquid equilibria (LLE) in the system oleic acid (OA) + formic acid (FA) + formoxystearic acid that is interesting for biopolymer production. Experimental studies of LLE in that system were carried out at 296, 313, and 333 K. Ternary mixtures were prepared from the educts OA and FA using heterogeneous acidic catalysis. Quantitative NMR spectroscopy was applied for the analysis. For the educt system also the excess enthalpy was studied by isothermal titration calorimetry. The prediction of the ternary LLE by ALCT succeeds. © 2018 American Institute of Chemical Engineers AIChE J, 65: 783–791, 2019

show abstract

Dense self-interacting lattice trees with specified topologies: From light to dense branching

Cited by 51 publications

References 42 publications

Phase Diagrams for Systems Containing Hyperbranched Polymers

Phase Diagrams for Systems Containing Hyperbranched Polymers

Lattice Cluster Theory of Multicomponent Polymer Systems: Chain Semiflexibility and Specific Interactions

Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

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