Quantum vibration dynamics and deformation of skeleton of polymer molecules

The results of investigation on the temperature dependences of strain of the regularly constructed fragments of the carbon skeleton in linear polymers are reviewed. Stretching of the skeleton is induced under the action of twisting and bending vibrations when both ends of an oscillating chain fragment are fixed. In this case, the anharmonic character of vibrations plays no key role. At temperatures T _t and T _b, the statistics of atomic vibrations changes from quantum to classical, and the slope of the corresponding temperature dependences changes as well. At T < T _t, vibrations are not excited, and the skeleton is extended owing to zero-point vibrations. At T _t, twisting vibrations are induced, and a skeleton of the molecules is extended with temperature linearly. At T _b, bending vibrations are activated, and the slope of the temperature dependences of the strain of the skeleton increases. Additional stretching and an increased amplitude of vibrations of the skeleton carbon atoms are provided owing to the scattering of stretching vibrations at the boundaries of crystals.     

Transport properties of annealed,drawn low-density polyethylene (LDPE)

The specific concentration c_a of methylene chloride, the zero-concentration diffusion coefficient D₀, and the concentration coefficient γ_D of the diffusivity in drawn and annealed LDPE were measured. The influence of the drawing rate, of annealing with the ends of the sample free and fixed and the effects of time of standing at room temperature after annealing were investigated. The observed transport properties are in good agreement with the microfibrillar model of fibrous structure, its relaxation during annealing, and the slow crystallization of relaxed tie-molecules upon standing at room temperature.     

Time dependence of mechanical and transport properties of drawn and annealed linear polyethylene

Linear polyethylene both as drawn, or drawn and subsequently annealed with free ends, changes its length, density, crystallinity, elastic modulus, sorption, and diffusivity as the sample stands completely unrestrained at room temperature. Most of these changes occur during the first few hours. But they are important on a molecular scale since they suggest strongly that drawn, and drawn and annealed samples are far from equilibrium. As a consequence of the tendency of each mobile tie molecule in the amorphous conformation to retract and to crystallize, the specimen approaches but does not reach complete equilibrium. The transient seems to be caused by slow crystallization of tie molecules which creates crystalline bridges across the amorphous layers.     

Stepwise annealing of poly(butylene terephthalate)

Annealing of poly(butylene terephthalate) (PBT) was studied by differential scanning calorimetry (DSC) and small angle X‐ray scattering (SAXS) measurement. A PBT sample was annealed at a recrystallization temperature where recrystallization occurs with a maximum rate in the heating process of the sample. In the subsequent annealing steps, the annealed sample was annealed repeatedly at the recrystallization temperatures, and the stepwise annealing sample was obtained. Peak melting temperature (T_m) and sharpness of DSC peak of the stepwise annealing sample increased with the annealing step. A high melting‐temperature sample was obtained in a short time, and T_m increased up to 238.5°C which is higher than all the T_m values that appear in the literature. The long period calculated from SAXS curves of the stepwise annealing sample increased with the annealing step. The increase of crystallite size and perfection of the crystal in the stepwise annealing process is suggested. Annealing experiment indicated that T^°_m should be higher than about 235°C. T_m increased linearly with the annealing temperature of the final step in the stepwise annealing (T_a). The equilibrium melting temperature (T^°_m) for PBT was estimated to be 247°C by the application of a Hoffman–Weeks plot to the relation between T_m vs. T_a. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2420–2429, 1999     

A revised equation for estimating the vapour pressure of low-volatility substances from isothermal TG data

Previous investigators have used the Langmuir vaporisation relation to estimate the vapour pressures of low-volatility compounds from thermogravimetric data. However, this equation is strictly valid for evaporation into a vacuum only. For measurements conducted at finite pressures, molecular diffusion must be taken into account. A revised equation is proposed: dm _A/dt8M _A P _A D _A B/T. It is also shown that the proportionality between vapour pressure and vaporisation rate is very general. It arises from the assumptions of ideal gas behaviour, Raoult's law and a negligible concentration of the sample compound far from the sample surface. This revised version was published online in August 2006 with corrections to the Cover Date.     

Linearization of second-order reaction data

Reaction data described by the second-order growth function A(t) = A_∞(αt) (1 + αt)^?1, where A_∞ is the ultimate value of the product concentration A(t), can be linearized by plotting a suitable function F(t) against the time (t). The slope of the straight line obtained is (2α), where α is the product of the rate constant (k₂) and the initial concentration of either reactant, with the result that k₂ can be determined without knowledge of A?. Optimal determination of the parameter α requires that data taking be limited to the interval 0 ≤ t ≤ T, where (αT) is approximately 4.0. Numerical data derived from an experiment on the exchange of lead by zinc ions in the enzyme carbonic anhydrase are analyzed to illustrate the method. The effects of small errors in the initial concentrations and of small deviations from second-order kinetics are briefly discussed.     

Time–temperature superposition of time-dependent birefringence for low-density polyethylene

The time-dependent birefringence has been measured simultaneously with the stress relaxation on quenched and annealed low-density polyethylene at various temperatures from 10 to 70°C. The strain-optical coefficient increases generally with increasing time, and approaches the equilibrium value, which depends upon the temperature. When the strain-optical coefficient at a fixed time is plotted against temperature, it first increases and then decreases after passing through a maximum at T_max with increasing temperature. The higher the degree of crystallinity, the higher are the equilibrium values of the strain-optical coefficient and T_max. The curves for strain-optical coefficient versus time and relaxation modulus versus time below T_max can be superposed well by a horizontal shift along the abscissa. The optical shift factor obeys the original WLF equation, while the mechanical shift factor is much larger than the optical one. The molecular mechanisms corresponding to this dispersion of the strain-optical coefficient and viscoelastic α_c absorption peak near T_max are discussed.     

Morphology and modulus–temperature behavior of semicrystalline poly(ethylene terephthalate) (PET)

The influence of the thermal history on the morphology and mechanical behavior of PET was studied. The degree of crystallinity (density measurements) and the morphological structure (electron microscopy and small-angle x-ray diffraction) depend on the crystallization temperature. The viscoelastic parameters obtained from the modulus–temperature curves are mainly determined by the morphology of the samples. The glass-transition temperature, T_i, is a function of the crystallinity and the crystallization temperature. It is maximum for a crystallinity between 0.34 and 0.39 for a sample crystallized isothermally between 120 and 150°C. This dependence on crystallization conditions is ascribed to the conformation of the amorphous chain segments between the crystalline lamellae as well as the concentration and the molecular weight of the polymer material rejected during isothermal crystallization. Both factors are supposed to be temperature-dependent. The value of the rubbery modulus is a function of both the volume concentration of the crystalline lamellae and the structure of the interlamellar amorphous regions (chain folds, tie molecules, chain ends, and segregated low molecular weight material). Annealing above the crystallization temperature of isothermally crystallized samples has a marked influence on their morphology and mechanical behavior. The morphological structure and the viscoelastic properties of annealed PET samples are completely different from those obtained with samples isothermally crystallized at the same temperature.     

Oriented crystallization of poly(L‐lactic acid) in uniaxially oriented blends with poly(vinylidene fluoride)

This article describes the oriented crystallization of poly(L ‐lactic acid) (PLLA) in uniaxially oriented blends with poly(vinylidene fluoride) (PVDF). Uniaxially drawn films of PLLA/PVDF blend with fixed ends were heat‐treated in two ways to crystallize PLLA in oriented blend films. The crystal orientation of PLLA depended upon the heat‐treatment process. The crystal c‐axis of the α form crystal of PLLA was highly oriented in the drawing direction in a sample cold‐crystallized at T_c = 120 °C, whereas the tilt‐orientation of the [200]/ [110] axes of PLLA was induced in the sample crystallized at T_c = 120 °C after preheating at T_p = 164.5–168.5 °C. Detailed analysis of the wide‐angle X‐ray diffraction (WAXD) indicated that the [020]/ [310] crystal axes were oriented parallel to the drawing direction, which causes the tilt‐orientation of the [200]/ [110] axes and other crystal axes. Scanning electron microscopy (SEM) suggested that oriented crystallization occurs in the stretched domains of PLLA with diameters of 0.5–2.0 μm in the uniaxially drawn films of PVDF/PLLA = 90/10 blend. Although the mechanism for the oriented crystallization of PLLA was not clear, a possibility was heteroepitaxy of the [200]/[110] axes of the α form crystal of PLLA along the [201]/[111] axes of the β form crystal of PVDF that is induced by lattice matching of d₁₀₀(PLLA) ≈ 5d₂₀₁(PVDF). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1376–1389, 2008     

Solubility and Enhanced Tension of Solute in Solution

Abstract

In solution, solute molecules B are coupled by attractive forces between them and all other molecules present; and these other molecules enhance the tension in the coupling force between solute molecules an amount π_B, the osmotic pressure of the solution solute. Two equilibria determine the n ^o _B moles of pure solute which dissolve in n ¹⁰ _A moles of pure liquid solvent. If at T the solute is solid and in excess, then 1) the n _B ^lsat moles of B in the n^l _A moles of A in a solution saturated with B are in thermodynamic equilibrium with the solid solute at the same T and p and 2) the n _B ^lsat moles of B and n^l _A moles of A may also be in chemical equilibrium with the moles of new molecular or ionic species formed in the solution. Solute molecules dissolve until the chemical potential of the solution solute, p^l _B(T p, x_B ^lsat), equals the chemical potential of pure solid solute at the same T and p, μ _B ^so(T, p). When the solution is saturated with B and the mole fraction of B is x_B ^lsat = n _B ^lsat/σj n ¹ _j, then the vapor pressures of the solid solute at T and p, the solution solute at T and p, and the pure undercooled liquid solute at T and p-π _B ^lsat are identical. If at T the n _B ^lo moles of pure solute and the n^l _A moles of pure solvent are liquids, then if molecules of B are allowed to dissolve in A while molecules of A are dissolved in B, the resulting solutions may 1) contain only molecules of A and B or 2) contain A and B which also react to form other ionic and molecular species. The two solutions may be identical or they may differ. In all cases, however, the mole ratio of n^l _Bn^l _A in both solutions must be identical.     

Annealing during polymerization of crystalline poly(ethylene terephthalate)

Melt-crystallized poly(ethylene terephthalate) and etched oligomer lamellae from the same polymer have been annealed under vacuum at temperatures between 200 and 260°C and times between 3 and 48 hr. The annealed samples were analyzed through determination of viscosity-average molecular weight, x-ray low-angle spacing, density, heat of fusion, and variation of melting point with heating rate. In all cases it could be shown that the crystal lamellar surfaces remained chemically reactive. Chain folds and chain ends in the surface were converted by chemical reaction to tie molecules between different crystals or different locations on the same lamella.     

Investigation of rapid thermally annealed GaP(001) surfaces in vacuum

Morphology of rapid thermally annealed GaP(001) surfaces has been investigated using spectroscopic ellipsometry (SE), optical microscopy, ex situ atomic force microscopy, electron probe microanalysis (EPMA) and X‐ray photoelectron spectroscopy (XPS). The samples were annealed in vacuum for t = 2 s at temperatures T = 20–900 °C. The SE, optical microscopy and XPS spectra suggest that thermal annealing causes little influence on the GaP surface at T ≤ 600 °C; however, micro‐ and macroscopic roughening occur at T > 600 °C and T ≥ 750 °C, respectively, with a generation of Ga droplets at T ≥ 750 °C. The presence of the Ga droplets is confirmed by the EPMA measurements. The droplet density can be expressed as N_Ga ∝ exp (E_a/k_BT) with an activation energy of E_a ～ 2.3 eV. The XPS data indicate the change in the surface oxide composition from the native oxide to the Ga oxide (Ga₂O₃ and Ga₂O) after annealing at T ≥ 750 °C. Possible annealing‐induced degradation steps are proposed to provide as complete a picture as possible. Copyright © 2010 John Wiley & Sons, Ltd.     

Changes in superstructure and mechanical properties of poly(ethylene‐2,6‐naphthalate) fibers with critical necking tension

Poly(ethylene‐2,6‐naphthalate) fibers were zone‐drawn under a critical necking tension (σ_c) defined as the minimum tension needed to generate a necking at a given drawing temperature (T_d). In the zone drawing under σ_c, the neck was observed from 110 to 160 °C. The superstructure in a neck zone induced at each T_d was studied. The σ_c value decreased exponentially with increasing T_d and dropped to a low level at a higher T_d. The draw ratio increased rapidly with T_d increasing above 90 °C, but the birefringence and degree of crystallinity decreased gradually. To study the molecular orientation in the neck zone, we measured a dichroic ratio (A_‖/A_?) of a C? O band at 1256 cm^?1 along a drawing direction in the neck zone with a Fourier transform infrared microscope. A_‖/A_? at T_d = 110 °C increased rapidly in the narrow neck zone, and that at T_d = 140 °C increased in the edge of the wide neck zone. Wide‐angle X‐ray diffraction patterns of the fibers obtained at T_d = 130 °C and lower showed three reflections due to an α form, but those at T_d = 140 and 150 °C had reflections due to the α form and a β form. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1629–1637, 2001     

Mechanical and transport properties of drawn low-density polyethylene

Quenched, quenched and annealed, and slowly cooled branched low-density polyethylene films were drawn at 25, 40, and 60°. The true draw ratio λ^L of the volume element was obtained and used to characterize the dependence on plastic deformation of the density, drawing stress, and work of plastic deformation, and the sorption and diffusion of methylene chloride. The effects observed are similar but less drastic than on linear high-density polyethylene. In particular, the transformation from the original lamellar to the final fibrous structure seems to be fastest for λ^L between 3 and 4. But the changes of vapor transport clearly indicate that the transformation is not yet complete even at the highest draw ratio λ^L = 6, just before the sample breaks. Annealing at 90°C of the drawn samples with free ends restores or even increases the transport properties beyond those of the undrawn sample without causing the fibrous structure to revert to the original lamellar structure.     

Calorimetric relaxation and glass transition in poly(propylene glycols) and its monomer

The glass transition temperature T_g of propylene glycol (PG) and poly(propylene glycols) (PPGs) of molecular weight up to 4000 has been measured by differential scanning calorimetry, and the activation energy and change in heat capacity ΔC_p have been determined in the glass transition range. The activation energy increases with an increase in the molecular weight of the polymer, and ΔC_p measured at a fixed heating rate decreases. The increase in T_g with molecular weight is remarkably more rapid for poly(propylene glycols) than for other polymers, and a limiting value of T_g is reached for a chain containing 20 monomer units. These results are discussed in terms of the Fox-Flory and the entropy theories. The calorimetric relaxation times are comparable with the extrapolated dielectric relaxation times. The initial increase of ΔC_p from PG to PPG 200 is attributed to the decrease of H-bonding sites from 12 in 3 monomers to 4 on polymerization to PPG 200 and further decrease with increase in molecular weight to an increasingly large amplitude of the β-process at T < T_g.     

Physical aging in poly(ethylene naphthalene-2,6-dicarboxylate) in relation to sorbed water,enthalpic relaxation,and mechanical properties

Amorphous poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) films (～ 220 μm thick), stored in ambient atmosphere for different periods of time and after annealing at different temperatures below T_g = 123°C, for different times, have been investigated by infrared spectroscopy (FTIR), microhardness, and differential scanning calorimetry (DSC). FTIR spectroscopy and weight measurements reveal the presence of water which is easily removed by annealing of the films. Films again recover their initial weight and absorption bands after 1-2 days storage in ambient atmosphere. Samples annealed at different temperatures T_a for different times t_a show an increasing microhardness for relatively short times of t_a. The microhardness passes through a maximum at an annealing time depending on T_a, and it decreases toward values somewhat larger than the initial ones. The changes observed in the microhardness and in the values of the excess enthalpy with storage time of the samples at room temperature depend on the physical aging as well as on the content of water of PEN films. © 1995 John Wiley & Sons, Inc.     

Structural relaxation of stacked ultrathin polystyrene films

The T_g depression and kinetic behavior of stacked polystyrene ultrathin films is investigated by differential scanning calorimetry (DSC) and compared with the behavior of bulk polystyrene. The fictive temperature (T_f) was measured as a function of cooling rate and as a function of aging time for aging temperatures below the nominal glass transition temperature (T_g). The stacked ultrathin films show enthalpy overshoots in DSC heating scans which are reduced in height but occur over a broader temperature range relative to the bulk response for a given change in fictive temperature. The cooling rate dependence of the limiting fictive temperature, T_f′, is also found to be higher for the stacked ultrathin film samples; the result is that the magnitude of the T_g depression between the ultrathin film sample and the bulk is inversely related to the cooling rate. We also find that the rate of physical aging of the stacked ultrathin films is comparable with the bulk when aging is performed at the same distance from T_g; however, when conducted at the same aging temperature, the ultrathin film samples show accelerated physical aging, that is, a shorter time is required to reach equilibrium for the thin films due to their depressed T_g values. The smaller distance from T_g also results in a reduced logarithmic aging rate for the thin films compared with the bulk, although this is not indicative of longer relaxation times. The DSC heating curves obtained as a function of cooling rate and aging history are modeled using the Tool-Narayanaswamy-Moynihan model of structural recovery; the stacked ultrathin film samples show lower β values than the bulk, consistent with a broader distribution of relaxation times. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2741–2753, 2008     

Effect of stereosequences on crystallinity and properties of zone‐drawn poly(vinyl alcohol) microfibrils

To effectively orient the molecular chains of novel syndiotactic poly(vinyl alcohol) (PVA) microfibrillar fiber (PVA fibril), a high‐temperature zone‐drawing method was adopted. The PVA fibrils were directly prepared from the saponification and in situ fibrillation without a spinning procedure. The maximum draw ratio of the PVA fibril increased with a decrease in the syndiotactic diad (r‐diad) content, indicating that the deformability of PVA molecules was lowered in higher syndiotactic PVA. Degree of crystal orientations up to 0.990 were achieved by stretching the PVA fibril with the r‐diad content of 65.1% and the original degree of crystal orientation of 0.902 at 250 °C close to its crystal melting temperature (T_m). When the same draw ratio was applied to the fibrils, a higher crystal orientation was achieved for the fibrils having higher syndiotacticity. Wide‐angle X‐ray data show that the longitudinal crystal sizes of drawn PVA fibrils were larger in higher syndiotacticities. The degree of crystal orientation, crystallinity, T_m, longitudinal crystal size, and tensile strength of the maximum drawn PVA fibril with a r‐diad content of 65.1% were 0.99, 0.97, 279 °C, 187 Å, and 4.66 N/tex, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1263–1271, 2001     

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture

Stress–strain and rupture data were determined on an unfilled styrene–butadiene vulcanizate at temperatures from ?45 to 35°C and at extension rates from 0.0096 to 9.6 min^?1. The data were represented by four functions: (1) the well-known temperature function (shift factor) a_T; (2) the constant strain rate modulus, F(t,T), reduced to temperature T₀ and time t/a_T, i.e., T₀F(t/a_T)/T; (3) the time-dependent maximum extensibility, λ_m(t/a_T); and (4) a function Ω(χ) where χ = (λ ? 1)λ_m⁰/λ_m, in which λ is the extension ratio and λ_m⁰ is the maximum extensibility under equilibrium conditions. The constant strain rate modulus characterizes the stress–time response to a constant extension rate at small strains, within the range of linear response; λ_m is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress–strain curve of the material in a reference state of unit modulus and λ_m = λ_m. The shift factor a_T was found to be sensibly independent of extension. At all values of t/a_T for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λ_m⁰ = 8.6 and that the largest extension ratio at break, (λ_b)_max, is 7.3. Thus, rupture always occurs before the network is fully extended.     

Glass transition kinetics of some Se-Te-Ag chalcogenide glasses

Summary The present paper reports the Differential Scanning Calorimetric (DSC) study of some Ag doped Se-Te chalcogenide glasses. DSC runs were taken at different heating rates. Well-defined endothermic and exothermic peaks were obtained at glass transition and crystallization temperatures. The variation of glass transition temperature T_gwith Ag concentration has been studied. It has been found that T_gdecreases with increase in Ag concentration. The heating rate dependence of T_gis used to evaluate the activation energy of glass transition (DE_t). The value of<span style='font-size:10.0pt; font-family:"SymbolProp BT";mso-bidi-font-family:"SymbolProp BT"'>DE_thas been found to increase with increase in Ag concentration followed by nearly constant value at higher concentrations of Ag.