Comparison of Young's modulus and specific heat anomalies at the magnetic transition in α′-NaV2O5

We have measured Young's modulus (using a vibrating reed technique) and the specific heat (using ac calorimetry) on the same crystals of α′-NaV₂O₅ at its T_c=34 K magnetic phase transition. Both properties exhibit large, unsymmetrical, and sample-dependent anomalies. While the specific heat results suggest tricritical behavior of the transition, large fluctuation effects are observed in the modulus above T_c. Fits of the modulus in terms of the specific heat, entropy, and free energy suggest that fluctuations are strongly stress- and sample-dependent.     

On the optimal mixing of the exchange energy and the electron-electron interaction part of the exchange-correlation energy

The optimal mixing coefficient C of the exchange energy E_x and the electron-electron interaction part of the exchange-correlation energy W¹_xc in the formula for the total exchange-correlation energy E_xc was expressed through the ratio of the kinetic T_c and potential W_c contributions to the correlation energy E_c. This expression can be derived from a Heavyside step function model of the dependence of W^λ_xc on the coupling parameter of the electron interaction λ. Values of T_c and W_c obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of T_c, W_c, and C on the bond distance was demonstrated for the case of the H₂ molecule. T_c and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate E_xc is strongly dependent on the bond length and has to disappear for weak interaction/large bond distances. The potential of the exchange-correlation hole constructed for H₂ from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). © 1996 John Wiley & Sons, Inc.     

Equilibrium anionic polymerization of β-methoxypropionaldehyde

Anionic polymerization of β-methoxypropionaldehyde (MPA) was carried out in tetrahydrofuran (THF) by using benzophenone–monolithium complex as an initiator. An equilibrium between polymerization and depolymerization was observed at a temperature range of ?90 to ?70°C. From the temperature dependence of the equilibrium monomer concentration, thermodynamic parameters for the polymerization of MPA in THF were evaluated as follows: ΔH_ss = ?4.8 ± 0.2 kcal/mole, ΔH_SS = ?22.4 ± 1.3 cal/mole-deg, and (T_c)_ss = ?59°C. The thermodynamic change upon the conversion of liquid monomer to condensed polymer was computed from both the partial mixing energy of MPA with THF and the linear relationship between the equilibrium volume fraction of MPA monomer and that of the resulting polymer: ΔH_1c = ?4.7 ± 0.2 kcal/mole, ΔS_1c = ?19.5 ± 1.3 cal/mole-deg, and (T_c)_1c = ?35°C.     

Effect of temperature and dopant concentration on the conductivity of samaria-doped ceria electrolyte

The conductivity, σ, of a samaria-doped ceria electrolyte is studied as a function of temperature and dopant concentration, x, which was from 5 to 30 mol%. It is shown that a maximum in σ versus x corresponds to a minimum in activation energy. It is found that the conductivity is completely due to oxygen vacancy conduction. The conductivity increases with increasing samaria doping and reaches a maximum for (CeO₂)_0.8(SmO_1.5)_0.2, which has a conductivity of 5.6×10^–1 S/cm at 800 °C. A curvature at T=T _c, the critical temperature, has been observed in the Arrhenius plot. This phenomenon may be explained by a model which proposed that, below T _c, nucleation of mobile oxygen vacancies into ordered clusters occurs, and, above T _c, all oxygen vacancies appear to be mobile without interaction with dopant cation. In addition, the composition dependences of both the critical temperature and the trapping energy are consistent with that of the activation energy. Electronic Publication     

Diffusion Monte Carlo study of correlation in the hydrogen molecule

The diffusion Monte Carlo (DMC) method shows that correlation in H₂ produces a set of three spatial changes: (i) an enhancement in the electron density distribution n( r ) in the left and right anti‐binding regions that include separately the immediate vicinity of each of the two nuclei, (ii) a reduction in n( r ) in the binding region intervening between the two nuclei as a counterbalance, and (iii) a concomitant increase in the equilibrium internuclear separation. It is stressed that the correlation energy E^c (= T^c + V^c) for diatomic molecules be defined by the difference in the total energy between the exact and the Hartree–Fock (HF) variational calculations that are performed at individually optimized internuclear separations. It is this definition that makes it possible to involve a significant contribution from a correlation‐induced change in the equilibrium internuclear separation as part of the correlation energy and to relate (i) and (ii) to (iii) in consistency with the electrostatic theorem. The present calculations fulfill the virial theorem to an accuracy of ?V/T = 2.00 for DMC and ?V^HF/T^HF = 2.000 for HF. The present correlation energy E^c = ?0.0408 hartree is not only in good agreement with the most accurate value previously reported, but also can be analyzed into all its components in accordance with the correlational virial theorem 2T^c + V^c = 0. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Equibiaxial deformation of poly(4-methyl-1-pentene) by a forging process

Poly(4-methyl-1-pentene) (PMP) has been uniaxially compressed by a forging (equibiaxial) process. The rheology of the process has been examined for this semicrystalline polyolefin, melting point about 235°C. The yield energy, area under the compressive stress-strain curve up to the yield point, as a function of temperature was found to consist of two linear components of different slope. These two linear relations arise from the glassy and crystalline phases of PMP. The intercept temperature (T_i) at zero yield energy for the glassy phase has been evaluated. The attainable maximum compression ratio without sample rupture (CR_max) increased steadily on increasing forging temperature above T_i, and below T_m. In this range, the crystalline relaxation temperature (T_c), evaluated from an Arrhenius plot of yield stress was 160°C. Above T_c, a CR_max of 240 was reached. This value is five times higher than that attained for isotactic polypropylene (i-PP). However, the draw efficiency evaluated by elastic recovery in the plane direction of PMP (0.76) is lower than for i-PP (0.97). Differential scanning calorimetry analyses showed that the melting peak became a complex doublet on increasing compression ratio ( > 100). The drawing and stress-strain behavior of PMP are compared with i-PP. © 1994 John Wiley & Sons, Inc.     

Crystallization and dissolution temperatures of poly(vinyl alcohol) crystal lamellae

Poly(vinyl alcohol) single crystal platelets having a stepheight of approximately 100 A. were obtained by isothermal crystallization from dilute triethylene glycol solution. Material crystallized at temperature T_c redissolved in the same solvent at a higher temperature T_s. A plot of T_c versus T_s gave a straight line of slope 0.47. Extrapolation of this line to T_c = T_s gave (T_m)∞, which may be regarded as the dissolution temperature of the crystal of infinite stepheight. (T_m)∞ for this sample in triethylene glycol was 220°C. The crystalline nature of the platelets was established by electron and x-ray diffraction techniques. A total of three Bragg d spacings having the values of 3.9, 4.4, and 4.6 A. (±0.05 A.) were measured. These spacings were indexed as the (200), (101), and (101 ) reflections, respectively, of the monoclinic unit cell of Bunn. The x-ray diffractogram exhibits sharp intensities of the (101 ) and (101) reflections. The crystallinity calculated from the density of the poly(vinyl alcohol) precipitated from dilute solutions in triethylene glycol was 42%. Although the overall degree of crystalline perfection of this poly(vinyl alcohol) is low, the linear relationship between T_s and T_c and the formation of definite shaped single crystals when crystallized from dilute solution suggest that poly(vinyl alcohol) crystallizes in the same manner as other semicrystalline polymers.     

Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory

A previously developed model of simple penetrant diffusion is extended to encompass complex penetrants of idealized molecular shape, characterized by dimensions of length, width, and thickness. Expressions are obtained for D(0,T), the diffusion coefficient at zero penetrant concentration (c), and the fractional increase in D(0,T) as a function of c and temperature (T). The model predicts that D(0,T) will exhibit Arrhenius behavior at temperatures well above T_g and gives the limiting activation energy as a function of penetrant thickness and the polymer energy/distance constants used previously. For T_g < T ? T_g + 150 K the model requires two new disposable parameters, in addition to the jump-length parameter of the simple penetrant theory. These parameters, however, have precise physical meanings (all are lengths) and together with the penetrant dimensions and polymer constants determine the absolute magnitude of the diffusion coefficient as well as its relative dependence on c and T. For T ? T_g + 40 the relative concentration dependence may be calculated in terms of the penetrant dimensions and polymer constants only.     

Comments on a paper by Axelson and Mandelkern concerning 13C NMR spectra of polymers

It is shown that the ¹³C NMR spectral collapse temperatures T_c reported by Axelson and Mandelkern tend to give a constant ratio of T_c/T_g averaging 1.21 ± 0.05 and independent of T_g or of polymer structure. It is further shown that T_c is not a high-frequency value for T_g because this would require T_c/T_g to decline with increasing T_g. T_c/T_g agrees in numerical value with T_u/T_g, where T_ll is the liquid-liquid transition lying above T_g. Direct comparison of T_c and T_u for four polymers PIB, PnBA, atactic PP, and isotactic PMMA shows very close agreement. The various results suggest, but do not prove, that T_c from ¹³C NMR spectroscopy may be a new, direct measure for T_ll. A measured T_c of 233K for linear PE is compatible with a T_g near 195 K (233/195 = 1.19), whereas a T_g of 148 K gives the ratio 233/148 = 1.57, which is outside any value shown in tabulated form.     

Investigation on LCST behavior of a new amorphous/crystalline polymer blend: Poly(n‐methyl methacrylimide)/poly(vinylidene fluoride)

The liquid–liquid phase‐separation (LLPS) behavior of poly(n‐methyl methacrylimide)/poly(vinylidene fluoride) (PMMI/PVDF) blend was studied by using small‐angle laser light scattering (SALLS) and phase contrast microscopy (PCM). The cloud point (T_c) of PMMI/PVDF blend was obtained using SALLS at the heating rate of 1 °C min^?1 and it was found that PMMI/PVDF exhibited a low critical solution temperature (LCST) behavior similar to that of PMMA/PVDF. Moreover, T_c of PMMI/PVDF is higher than its melting temperature (T_m) and a large temperature gap between T_c and T_m exists. At the early phase‐separation stage, the apparent diffusion coefficient (D_app) and the product (2Mk) of the molecules mobility coefficient (M) and the energy gradient coefficient (k) arising from contributions of composition gradient to the energy for PMMI/PVDF (50/50 wt) blend were calculated on the basis of linearized Cahn‐Hilliard‐Cook theory. The kinetic results showed that LLPS of PMMI/PVDF blends followed the spinodal decomposition (SD) mechanism. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1923–1931, 2008     

Solvent crazing of “dry” polystyrene and “dry” crazing of plasticized polystyrene

The critical strain ε_c for crazing of polystyrene in each of a variety of organic liquids has been measured along with the degree of swelling of the polymer by the liquid and the attendant reduction in the glass transition temperature T_g of the polymer. The critical strain for the crazing in air and the T_g of each of a set of specimens molded from mixtures of o-dichlorobenzene and polystyrene have also been determined. Correlations of ε_c with T_g in the two cases are identical within experimental error for the first 40°C of T_g reduction; these results imply (1) that organic liquids do not exercise a significant surface energy role in solvent crazing and (2) that their only roles are associated with flow processes. Correlation of solvent crazing ε_c with solubility parameter of the crazing fluid is very poor for several reasons that are discussed.     

Solid state a.c. conductivity and FT-IR spectral analyses for the conflicting effects of proton mobility and association in some azophenol derivatives of cyclic phosphazene

Variable strength H-bonding affects the mobility and so electric conduction of protons differently. Also, variable extent mesomerism modifies electric conduction with varying dielectric features. Both these molecular modifiers are properly cited using azophenol derivatives as model compounds for discussion of their consequences in the varying features of electric conduction. The electric permittivity shows low-frequency dispersion characteristic of ionic conduction over mobile charge carries; the mobility shifts at a critical temperature T _c, being structure dependent. The frequency-dependent Z′′-Z′ layout changes with temperature from linear at low temperatures to semicircular above T _c within a frame of temperature-sensitive dipole-ionic mediated conduction. The a.c. conductivity, σ_ac, increases with frequency and temperature and becomes frequency insensitive, like d.c. conductivity, σ_dc, above the T _c because of the escalating contribution from the d.c. conduction. The mesomeric structure seems to prompt a dipole-based electric conduction of high relaxation energy over the strongly associated phenolic protons that may be thermally activated above the T _c into a much lower relaxation energy protonic conduction of up to two orders higher conductivity. The protonic conduction emerges at a T _c that falls with a drop in the relaxation energy following a similar order of increasing proton mobility and mesomerism in the azophenol derivatives: azocatechol>azoquinol>azoresorcinol. On the molecular level, variable temperature infrared spectroscopy reveals higher proton mobility and mesomerism for the azocatechol derivative that demonstrates its higher protonic conductivity at lower T _c and relaxation energy, compared to the azoquinol and azoresorcinol derivatives. This is well verified in the light of conflicting intramolecular H-bonding that assists the proton mobility in azocatechol whereas it associates the protons in azoresorcinol more than in azoquinol. Electronic Publication     

Pressure dependence of the dielectric properties and phase transitions of polyvinylidene fluoride (PVDF) and a copolymer with trifluoroethylene

The frequency, temperature, and hydrostatic pressure dependences of the dielectric properties, molecular relaxations, and phase transitions in PVDF and a copolymer with a 30 mol% trifluoroethylene were investigated. The β-relaxation peak temperature T_β and the melting temperature T_m of both polymers, and the ferroelectric transition temperature T_c of the copolymer, are strong increasing functions of pressure. The magnitudes of the pressure derivatives of T_β, T_c, and T_m increase in the order of the “transition” temperatures, i.e., T_β(P) < T_c(P) < T_m(P). These results can be qualitatively understood in terms of the nature of the molecular motion and/or reorientation processes involved. The results on the copolymer suggest that pressure should induce a ferroelectric-paraelectric transition in PVDF below T_m, but such a transition was not observed over the limited pressure range of the present experiments. The relaxational dynamic (not static) nature of the melting process in these materials is indicated by the observed dependence of T_m on probe frequency. The frequency (or rate) and strong pressure dependences of T_m of PVDF provide a rational explanation for why it is possible to use this polymer as a piezoelectric shock-wave gauge to relatively high shock pressures and the accompanying high temperatures.     

Multiple melting behavior of poly(butylene succinate). II. Thermal analysis of isothermal crystallization and melting process

The multiple melting behavior of poly(butylene succinate) (PBSu) was studied with differential scanning calorimetry (DSC). Three different PBSu resins, with molecular weights (MWs) of 1.1 × 10⁵, 1.8 × 10⁵, and 2.5 × 10⁵, were isothermally crystallized at various crystallization temperatures (T_c) ranging from 70 to 97.5 °C. The T_c dependence of crystallization half‐time (τ) was obtained. DSC melting curves for the isothermally crystallized samples were obtained at a heating rate of 10 K min⁻¹. Three endothermic peaks, an annealing peak, a low‐temperature peak L, and a high‐temperature peak H, and an exothermic peak located between peaks L and H clearly appeared in the DSC curve. In addition, an endothermic small peak S appeared at a lower temperature of peak H. Peak L increased with increasing T_c, whereas peak H decreased. The T_c dependence of the peak melting temperatures [T_m(L) and T_m(H)], recrystallization temperature (T_re), and heat of fusion (ΔH) was obtained. Their fitting curves were obtained as functions of T_c. T_m(L), T_re, and ΔH increased almost linearly with T_c, whereas T_m(H) was almost constant. The maximum rate of recrystallization occurred immediately after the melting. The mechanism of the multiple melting behavior is explained by the melt‐recrystallization model. The high MW samples showed similar T_c dependence of τ, and τ for the lowest MW sample was longer than that for the others. Peak L increased with MW, whereas peak H decreased. In spite of the difference of MW, T_m(L), T_m(H), and T_re almost coincided with each other at the same T_c. The ΔH values, that is crystallinity, for the highest MW sample were smaller than those for the other samples at the same T_c. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2039–2047, 2005     

Cold crystallization and thermal shrinkage of uniaxially drawn poly(ethylene 2,6-naphthalate) by solid-state coextrusion

Solid-state coextrusion has been used to prepare uniaxially drawn films from isotropic poly(ethylene 2,6-naphthalate) (PEN) of a minimum degree of crystallinity (ca. 5%) both below and above its glass transition temperature T_g. The onset of cold crystallization (T_c) of the drawn films has been studied as a function of the extrusion temperature (ET) and the draw ratio (EDR). It has been shown that T_c decreases markedly on draw, as much as 95°C, and, at constant draw ratio T_c goes through a minimum in the T_g region. For undrawn PEN, annealing below 153°C has no significant effect on T_c. To evaluate the crystallization rate constant (k) and the activation energy (E_a) of the drawn specimens, a nonisothermal DSC procedure has been used. With increasing EDR, k increases markedly and E_a goes down over threefold compared with the undrawn polymer. At high ET, strain-induced crystallization has also been shown to play an important role in lowering E_a for cold crystallization. Thermal shrinkage above T_m indicates a high elastic recovery, underlining the efficiency of deformation, ca. 93%, achieved by solid-state coextrusion.     

A model for dynamic relaxations in amorphous polymers. II. Extensions and generalizations of formalism and application to poly(methacrylates)

Extensions and generalizations of a new model for the dynamic relaxations in amorphous polymers, and its application to the poly(methacrylates), will be presented. The sizes of moving subunits will be extrapolated for the β and γ relaxations in several poly(methacrylates), by working backward from the relaxation temperatures (T_r) observed at frequencies of 1 to 100 Hz to subunits giving T_cs comparable to those T_rs. A general form will be proposed for activation energy distributions; and used to derive relaxation time distributions satisfying the experimental trends. The good agreement between the calculated T_c and the T_r observed dynamically at frequencies of 1 to 100 Hz will be shown to result from the nature of these distributions. The loss peak observed at very low temperatures by isochronal sweeps at very low frequencies is therefore caused by the dissipation of applied energy in localized domains. At sweep frequencies of 1 to 100 Hz, T_r ≈ T_c, and energy dissipation begins to take place over regions spanning the entire polymer. This delocalization of the energy dissipation is relevant to the effects of molecular level factors on many mechanical and thermodynamic properties of amorphous polymers. The effects of activation entropy and of dynamic excess entropy will be shown to be small in magnitude but important in terms of fully understanding relaxation behavior. Physical aging will be shown to result in a slight increase in the calculated characteristic temperatures. Finally, it will be shown that the relaxation behavior of the moduli and the compliances share some important common features with many other physical phenomena of seemingly very different nature.     

Rayleigh light scattering in concentrated polymer solutions above the cloud point

Optical heterodyne scattering measurements are presented for concentrated solutions of unreticulated cis-polybutadiene as a function of temperature. For a heptane volume fraction ν, the second derivative of the free energy with respect to concentration varies approximately as ν^?2·9 (T-T_c), where T_c is the spinodal temperature.     

Long periods in slow-cooled linear and branched polyethylene: Part II

It is shown that the long periods L in slow-cooled polyethylene materials obey the general law L = L⁰ + αr_w, where r_w is the weight average dimension of the coil before crystallization, and L⁰ is a parameter of the order of l_c, the crystalline core thickness, which increases as the cooling rate V decreases. α is a parameter independent of M and V but decreasing with the number of long-chain branches per molecule. The two terms in the above relation are, respectively, the contributions of crystalline and amorphous layers. For cooling rates from 800°C/min to 0.2°C/min, it is shown that the temperature T_c of crystallization is constant; hence the change of morphology (long period, crystalline core thickness, crystallinity) cannot be explained by supercooling. The increase in long period and crystallite thickness in slow-cooled materials with decreasing cooling rate is interpreted in terms of annealing of the crystallized materials between the crystallization temperature T_c and the secondary transition temperature T_αc. Crystallization proceeds by a two-step process of solidification and annealing. During the annealing stage, the mobility of the chains in the crystalline phase is due to defects; the kinetics of thickening is then governed by the mobility (or nucleation) of the defects appearing above T_αc. In the proposed model of crystallization, the assumption that the energy of activation is proportional to T_αc explains the observed laws L ≡ l_c ≡ log t_a, where the annealing time t_a is equal to (T_c ? T_αc)/V. The model applies also to polymers crystallized from the melt and subsequently annealed.     

X-ray Photon Correlation Spectroscopy of Dynamics in Thermosensitive Gels

Summary : Temperature-sensitive hydrogels undergo a volume phase transition (VPT) when heated above a critical temperature T_c. For the poly(N-isopropyl acrylamide) (PNIPA)-water system, T_c. = 34 °C. Below T_c the gels are transparent and highly swollen. On warming above T_c they promptly turn white and start to deswell. The rate of deswelling, however, can be orders of magnitude slower than that of swelling below T_c. The unstable intermediate structure above T_c, can retain the solvent and conserve the sample volume for may days, even with millimetre-sized samples. Light scattering observations of the internal structure of these gels above T_c are precluded by their strong turbidity. Small angle X-ray scattering measurements (SAXS), on the other hand, are less subject to multiple scattering as X-rays penetrate more easily into the bulk material. Conventional (incoherent) SAXS observations reveal intense scattering from smooth internal water-polymer interfaces with an estimated surface area of about 7 m²/g in the swollen gel. The dynamics in the off-equilibrium high temperature state, investigated by X-ray photon correlation spectroscopy (XPCS), displays a relaxation rate that is linearly proportional to the wavevector q, rather than to q² as in diffusion processes. The physical origin of this relaxation is consistent with jamming, a phenomenon that is common in other disordered systems.     

Evaluate the minimum bubble nucleation energy of freon-12 using superheated-liquid-droplet technique

An experimental method was conducted to evaluate the minimum bubble nucleation energy of freon-12 for application in the superheated-liquid-droplet (SLD) technique. The minimum energy needed for an incident particle to cause the bubble nucleation is based on the theoretical calculation ofW _min /ηkr _c value. The calculated value may mislead the result of measured intensity due to its under/overestimation ofW _min /ηkr _c values at various temperatures. Nevertheless, the experimental evaluation ofW _min /ηkr _c of freon-12 for causing the bubble nucleation is barely touched because the proper methodology has not developed fully. The minimum energy needed to produce the bubble nucleation, can be evaluated by mixing the alpha-emitting nuclides with the SLD. By direct hitting the SLD with alpha-particle, the energy deposited inside the SLD may cause the bubble nucleation if the deposited energy is larger than theW _min /ηkr _c of freon-12 droplet at that specific temperature. The experimental evaluated values in this study agree with the theoretical estimation in 78% for SLD emulsion temperature within 22–34°C. Tests suggest that to apply the SLD in measuring the alpha-emitting nuclides, the emulsion temperature should be maintained below 30°C to get a maximum efficiency and to avoid interference from beta or gamma event.