Energetics of Stretching of Conformational Defects in Extended Poly(methylene) Chains

Špitálský, Zdenko; Bleha, Tomáš

doi:10.1002/1521-3919(20011101)10:9<833::aid-mats833>3.0.co;2-q

Cited by 12 publications

(36 citation statements)

References 18 publications

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“…A flip-flop interconversion of the torsional angles within a defect brings about the change from the shorter (kink) into the longer (all-trans) state [8][9][10][11] and liberates the stored elastic energy. In our recent paper [12] the force-length functions F(R) and Young's moduli E of tie chain models containing several conformational defects were reported. Abrupt discontinuities due to gauche-totrans conformational transitions were established on the force-length curves F(R) as well.…”

Section: Introductionsupporting

confidence: 64%

“…[12] The total static potential energy of a molecule U is expressed in the method as the sum of several contributions (2) where the terms U r and U h represent the bond length and bond angle deformation, respectively, U b is the inherent ethane-like torsional potential respecting the cosine type periodicity of the torsional angle b. The term U vdW is a summation of all non-bonded pair interactions in the molecule.…”

Section: Calculationsmentioning

confidence: 99%

“…The length of a molecule relative to the T form can be expressed either by the difference DR = R zz -R d , or by the ratio x = R d /R zz , where R d is the length of a defect molecule. Our previous study [12] was focused on the elasticity of the highly extended PM bridges involving several three-bond sequences g + tg -(the kink defects) or five-bond sequences g + tttg -(the jog defects). Such molecules with the correlated gauche pairs in the defects served as models of tight PM bridges of rather high chain extension ratio x A 0.85.…”

Section: Single-conformer Calculationsmentioning

confidence: 99%

“…The investigated defect chains are designated as nG according to the number of gauche bonds involved (Table 1). For comparison the data for the relevant kink structures 1Ka and 2Ka from the previous paper [12] are included in Table 1. The potential energy of a defect chain U d represents the static conformational energy at 298 K without the vibration contributions and is expressed relative to the energy of the T form (51.79 kJ N mol -1 ).…”

Section: Single-conformer Calculationsmentioning

confidence: 99%

“…The molecules investigated by the MM method contain several uncorrelated gauche defects and should model the "slack" bridges. The data for these models supplement the results from a related study [12] focused on the highly extended tie chains involving the correlated defects of the kink or jog type. The tetrahedral (diamond) lattice MC simulations of the elastic properties of short PM chains were performed under conditions closely matching the MM computations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Energy Elasticity of Tie Molecules in Semicrystalline Polymers

Špitálský¹,

Bleha²,

Cifra³

2002

Macromol. Theory Simul.

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Elastic response of the disordered phase between crystal lamellae in semicrystalline polymers is modelled on the assumption that the stress is transferred by bridging (tie) molecules. The deformation characteristics of short poly(methylene) (PM) bridges were computed by using two methods: (a) the single‐molecule loading by molecular mechanics (MM) calculations and (b) the chain‐ensemble averaging by lattice simulations. The energy elastic functions ensuing from both methods differ considerably. In MM the loading of chains containing numerous gauche defects by an external force F yields the sawtooth‐like profile of the force (F)–length (R) functions brought about by the stress‐induced gauche–trans conformational transitions. The Young's moduli E of PM chains containing several gauche defects can be less than 1% of the all‐trans value ET; by elimination of the defects the moduli steeply increase. In contrast, the ensemble‐averaging approach gives a smooth increase of the (positive) elastic force f with chain length R and a decrease of the (negative) energy component of the elastic force fU with R. Both energy deformation mechanisms, single‐chain loading (by F) and statistical (by fU), are complementary and can simultaneously be operative in the interlamellar (IL) phase. Their proportion in the stretching process should depend on the chain mobility and structural homogeneity (history) of the sample, particularly on the presence of the so‐called rigid amorphous fraction in the IL phase.

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Section: Introductionsupporting

confidence: 64%

Section: Calculationsmentioning

confidence: 99%

Section: Single-conformer Calculationsmentioning

confidence: 99%

Section: Single-conformer Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energy Elasticity of Tie Molecules in Semicrystalline Polymers

Špitálský¹,

Bleha²,

Cifra³

2002

Macromol. Theory Simul.

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Elastic Properties of Poly(hydroxybutyrate) Molecules

Špitálský

Bleha

2004

Macromolecular Bioscience

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Elasticity of various poly(hydroxybutyrate) (PHB) molecules of regular and irregular conformational structure was examined by the molecular mechanics (MM) calculations. Force - distance functions and the Young's moduli E were computed by stretching of PHB molecules. Unwinding of the 2(1) helical conformation H is characterized at small deformations by the Young's modulus E = 1.8 GPa. The H form is transformed on stretching into the highly extended twisted form E, similar to the beta-structure observed earlier by X-ray fiber diffraction. The computations revealed that in contrast to paraffins, the planar all-trans structure of undeformed PHB is bent. Hence, a PHB molecule attains the maximum contour length in highly straightened, but slightly twisted conformations. A dependence of the single-chain moduli of regular and disordered conformations on the chain extension ratio x was found. The computed data were used to analyze elastic response of tie (bridging) molecules in the interlamellar (IL) region of a semi-crystalline PHB. A modification of the chain length distribution function of tie molecules tau(N) due to secondary crystallization of PHB was conjectured. The resulting narrow distribution tau(N) comprises the taut tie molecules of higher chain moduli prone to overstressing. The molecular model outlined is in line with the macroscopically observed increase in the modulus and brittleness of PHB with storage time.

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Isometric and Isotensional Force‐Length Profiles in Polymethylene Chains

Zemanová

Bleha

2005

Macro Theory & Simulations

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Summary: The force‐length curves and related thermodynamic quantities of single polymethylene (PM) chains in the high‐force region were calculated by the statistical mechanics. Two statistical mechanics ensembles (isometric and isotensional) were used to represent the chain stretching under the conditions, respectively, of the fixed length L or of the fixed force F in single‐chain experiments by AFM and related techniques. The input deformation potentials of highly extended conformations of PM chains were obtained from the molecular‐mechanics calculations. Variations of the energy, entropy, and Helmholtz energy with the end‐to‐end length L of chains were computed under the condition of fixed length. The ensuing isometric profile of the mean force 〈F〉(L) is non‐monotonic, featuring a sawtooth‐like pattern of ascending peaks. In contrast, the mechanical equation under isotensional conditions, given by the variation of the mean length 〈L〉(F), shows a conventional monotonous shape with a distinct plateau region at low temperatures. The considerable difference in the shapes of 〈F〉(L) and 〈L〉(F) curves arises from the large fluctuations of mean values due to the small number of conformers present in molecules at high strains. The computed data should be relevant to the AFM stretching experiments on short polyethylenes or on other soft matter materials involving linear paraffinic chains. It is argued that the dual character of elastic response described by the conjugated force profiles is a universal feature of mechanochemistry of chain molecules whenever the chain length discontinuously increases at a transition.Force‐length curves of short polymethylene chains at 300 K.magnified imageForce‐length curves of short polymethylene chains at 300 K.

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Energetics of Stretching of Conformational Defects in Extended Poly(methylene) Chains

Cited by 12 publications

References 18 publications

Energy Elasticity of Tie Molecules in Semicrystalline Polymers

Energy Elasticity of Tie Molecules in Semicrystalline Polymers

Elastic Properties of Poly(hydroxybutyrate) Molecules

Isometric and Isotensional Force‐Length Profiles in Polymethylene Chains

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