Role of conformation entropy in determining the phase transitions of polymeric systems

Abe, Akihiro; Takeda, Takanori; Hiejima, Toshihiro

doi:10.1002/1521-3900(200003)152:1<255::aid-masy255>3.0.co;2-z

Cited by 8 publications

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“… b The melting point observed from trans -PCHC of P meso = 0.99 c From the intercept at x –1 = 0 ( x → ∞) of a ⟨ r 2 ⟩ 0 / nl 2 versus x –1 plot, where x is the degree of polymerization. d S conf = ( R / x )[ln Z + T d(ln Z )/d T ], where R is the gas constant, T is the absolute temperature, and Z is the partition function of the whole chain. − The isotactic and syndiotactic trans -PCHC chains have the same Z and S conf values. e The geometrical parameters averaged at 25 °C with the chloroform energy set. Symbols: l̅ , averaged bond length (in Å); θ̅, averaged bond angle (in deg); and , average dihedral angle (in deg) of the ξ conformation.…”

Section: Resultsmentioning

confidence: 99%

“… d S conf = ( R / x )[ln Z + T d(ln Z )/d T ], where R is the gas constant, T is the absolute temperature, and Z is the partition function of the whole chain. − The isotactic and syndiotactic trans -PCHC chains have the same Z and S conf values. …”

Section: Resultsmentioning

confidence: 99%

“…The configurational entropy ( S conf ) is due to the conformational difference between the unperturbed (Θ solution, melt, or amorphous state) and perfectly regular states. − The S conf value of isotactic trans -PCHC tends to decrease with polarity of the environment and increase with temperature. The statistical weight matrices of ( S , S )-units are derived from those of ( R , R )-units by the symmetry operation, and hence the partition function ( Z ) and the S conf value obtained therefrom are independent of P RR and P meso .…”

Section: Resultsmentioning

confidence: 99%

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Configurational Statistics of Poly(cyclohexene carbonate)

2020

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Conformational characteristics of poly(cyclohexene carbonate) (PCHC) have been investigated via molecular orbital (MO) calculations and NMR experiments on model compounds. The MO energies established through comparison with the NMR experiments were applied to the rotational isomeric state scheme with Bernoulli and Markov stochastic processes to yield configurational properties such as unperturbed characteristic ratio, its temperature coefficient, configurational entropy, tacticity entropy, and coherence number of PCHC chains including various stereosequences. trans-PCHC composed of (R,R)- and/or (S,S)-repeating units prefers a tg+t conformation in the O–CH–CH–O bond sequence of the (R,R)-unit, and its unperturbed characteristic ratio depends considerably on stereoregularity: isotactic, 29, and syndiotactic, 0.83 (in chloroform at 25 °C). cis-PCHC comprising (R,S)- and/or (S,R)-units exclusively adopts either g–g+g+ or g–g–g+ conformation in the O–CH–CH–O bond sequence of the (R,S)-unit partly owing to intramolecular hydrogen bonds, and the dependence of the characteristic ratio of cis-PCHC on stereoregularity would be completely opposite to that of trans-PCHC: isotactic, 0.59, and syndiotactic, 25. In terms of the abovementioned characteristic parameters, properties of PCHCs synthesized so far with stereospecific catalysts are discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Configurational Statistics of Poly(cyclohexene carbonate)

2020

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“…The configurational entropy (often termed conformational entropy) can be calculated fromwhere R is the gas constant, x is the degree of polymerization, T is the absolute temperature, and Z is the partition function of the whole chain. At a phase transition such as melting, the S conf value corresponds to the entropy change at constant volume and is related to that ((Δ S ) p ) at constant pressure and that (Δ S v ) due to the volume change (Δ V ) by 40,41 where Δ S v = (α/β)Δ V with α and β being the thermal expansion coefficient and isothermal compressibility, respectively. The S conf /(Δ S ) p ratio has been estimated as, for example, 0.8–0.9 for polyethers and polythioethers 42 and 0.5–0.7 for polyesters, 27 while amorphous elastomers exhibit comparatively small S conf /(Δ S ) p values such as 0.5 (natural rubber) and 0.6 (gutta percha).…”

Section: Resultsmentioning

confidence: 99%

Structure–Property Relationships of Poly(ethylene carbonate) and Poly(propylene carbonate)

Sasanuma

Takahashi

2017

ACS Omega

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Conformational characteristics of poly(ethylene carbonate) (PEC) and poly(propylene carbonate) (PPC) have been revealed via molecular orbital (MO) calculations and nuclear magnetic resonance (NMR) experiments on model compounds with the same bond sequences as those of the polycarbonates. Bond conformations derived from the MO calculations on the models were in exact agreement with those from the NMR experiments. Both PEC and PPC were indicated to adopt distorted conformations including a number of gauche bonds and cover themselves with negative charges, thus failing to form a regular packing and remaining amorphous. The MO data were applied to the refined rotational isomeric state (RIS) calculations to yield configurational properties such as the characteristic ratio, its temperature coefficient, the configurational entropy, and average geometrical parameters of unperturbed PEC and PPC chains. In the RIS calculations on PPC, the regio- and stereosequences were generated according to the Bernoulli trial or Markov stochastic process. In consequence, it was shown that the configurational properties of PPC do not depend significantly on its regio- and stereoregularities. The internal energy contribution to rubberlike chain elasticity, calculated from the temperature coefficient of the characteristic ratio, has indicated the possibility that PEC and PPC will behave as elastomers. The practical applications and potential utilizations of the polycarbonates are discussed on the basis of the conformational characteristics and configurational properties.

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“…The underlining principle for the spatial arrangement of the mesogenic units is essentially the same as that argued before. 6 For the dimers, efforts have also been made to elucidate the molecular arrangement in the LC state by employing other techniques such as the 13 C-13 C dipolar COUpling and I 3 C Chemical shift anisotropy determination by 13 C NMR, 1 7 and the magnetic susceptibility measurements by SQUID. 18 All these studies favorably support the mesophase structure depicted above ( Figure 5).…”

Section: Cc)mentioning

confidence: 99%

Phase Behaviors of Mainchain Liquid Crystals. 2H NMR and Pressure–Volume–Temperature Analysis of Dimer and Trimer Model Compounds

Abe

Takeda

Hiejima

et al. 1999

Polym J

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ABSTRACT:Our previous studies on the structure-property relation of dimer liquid crystals (LC), :x.w-bis(4-cyanobiphenyl-4' -yloxy)alkanes (CBA-11. n = 9. l 0). have been extended to include trimer compounds, 4.4' -bis[w-(4-cyanobiphcnyl-4' -yloxy)alkoxy]biphenyls (CBA-Tn. 11=9.10), comprising three mesogenic units jointed by two intervening spacers. These nematic-LC-forming compounds were chosen as a model for the mainchain-type polymer LCs on the assumption that the spatial configuration and thermodynamic roles of the flexible spacer arc nearly identical as long as the chemical structure of the repeating unit is similar. The 2 H NMR method was extensively used to elucidate the oricntational characteristics of these molecules in the mesophase. The analysis of binary mixtures with a low molar mass (monomer) LC gave an important information regarding the mesophase structure ofCBA-Tn as well as CBA-11. The pressure-volume-temperature (PVT) relation was determined to estimate the constant-volume transition entropies at the interphase such as crystal/nematic LC/isotropic melt. The results were found to be favorably compared with the conformational entropy changes derived on the basis of the rotational isomeric state analysis of the 2 H NMR data. Finally. an important role of the flexible spacer was emphasized in determining the molecular ordering as well as thermodynamic properties of mainchain-type LCs.

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Role of conformation entropy in determining the phase transitions of polymeric systems

Cited by 8 publications

References 0 publications

Configurational Statistics of Poly(cyclohexene carbonate)

Configurational Statistics of Poly(cyclohexene carbonate)

Structure–Property Relationships of Poly(ethylene carbonate) and Poly(propylene carbonate)

Phase Behaviors of Mainchain Liquid Crystals. 2H NMR and Pressure–Volume–Temperature Analysis of Dimer and Trimer Model Compounds

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