DTA,X-ray and dielectric relaxation studies of 14CB at atmospheric and elevated pressures

The pressure-temperature phase diagram of 4′-tetradecyl-4-cyanobiphenyl (14CB) up to 220 MPa (2.2 kbar) and between 320–400 K was established using DTA. The temperature range of the smectic A (SmA) phase slightly increases with pressure. The layer spacing d at 1 atm was determined as a function of temperature using X-ray diffraction. It was related to the molecular length l by the ratio d/l ? 1.4. The dielectric relaxation measurements in the isotropic and smectic A_d phases of 14CB at 1 atm were performed in the frequency range 10 kHz-3 GHz. Contributions from both principal rotational motions, i.e. around the short and long molecular axes, were separated. The relaxation measurements under high pressure in the SmA phase covered the low frequency process. The longitudinal relaxation time τ₁, characterizing the molecular reorientations around the short axis, was analysed with respect to the pressure and temperature dependences, giving activation volumes, Δ^# V = RT (? ln τ₁ / ?p)_T, and activation enthalpies, Δ^# H = RT(? ln τ₁ / ?T ^-1)_p, respectively. Surprisingly, all the activation quantities characterizing the rotational motions of 14CB molecules under different conditions are nearly the same as those determined recently for the much shorter homologue, 8CB. This indicates that the 14CB molecule is in fact relatively short due to conformational motions of the alkyl tail.     

Positronium annihilation in amine-cured epoxy polymers

Positronium annihilation spectroscopy (PAS) has been used to study the microstructural properties of amine-cured epoxy polymers. We have determined the free-volume “hole” sizes in these polymers by comparing the observed ortho-positronium lifetimes with the known lifetime–free volume correlation for low-molecular-weight systems. The free volumes for four epoxies with different crosslink densities are found to vary significantly over the temperature range between ?78° and 250°C. The free-volume holes for these polymers are found to range from 0.025 to 0.220 nm³. Two important transition temperatures were found: one corresponds to the glass transition temperature T_g determined by differential scanning calorimetry (DSC), and the other occurs about 80–130°C below T_g. The sub-T_g transition temperature is interpreted tentatively as being where hole size reaches dimensions adequate for positronium trapping or else the onset temperature for local mode or side-chain motions. These two transition temperatures plus two additional onset temperatures are found to be correlated with crosslink densities calculated from stoichiometry.     

Positron annihilation lifetime studies of free volume in a polymer electrolyte PEO complexed with NH4I

Positron lifetime spectroscopy has been applied to study the temperature dependence of free-volume properties in a solvent-free polymer–salt complex polyethylene oxide (PEO) doped with ammonium iodide (NH₄I, with NH ≈ 0.076) in the temperature range of 298–353 K. The observed lifetime spectra were resolved into three components and the longest lifetime, τ₃, was associated with the pick-off annihilation of ortho-positronium (o-Ps) trapped by the free volume. The lifetime component, τ₃, and its intensity, I₃, both showed a significant variation with temperature, which followed a different course in the heating and cooling cycle. Changes in the temperature coefficient of τ₃ and I₃ were observed at T ≈ 328 K, the melting point of the sample. This behaviour is correlated to the temperature variation of the electrical conductivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 969–976, 1998     

Free volumes in nematic and smectic liquid-crystalline polymers probed by positron annihilation

Free volumes in thermotropic side-chain liquid-crystalline polymers were probed by positron annihilation technique. Lifetime spectra of positrons were measured in the temperature range between 130 and −60°C in cooling. For a nematic liquid-crystalline polymer (polyacrylate), the lifetime of ortho-positronium (τ₃) was decreased with decreasing temperature above the glass transition temperature (T_g, 21°C) with larger temperature coefficient than that below T_g. The intensity of ortho-positronium (I₃) was constant above T_g. These facts mean that the size of the free-volume holes decreased with the decreasing the temperature but the concentration was almost constant in nematic phase. For a smectic liquid-crystalline polymer (poly(p-methylstyrene) derivative), a discontinuous decrease in the value of τ₃ and that of I₃ were observed at 107°C, which was the transition temperature from smectic to crystalline phase. Such discontinuous changes were not observed for the polyacrylate specimen. This difference was considered to be attributed to the higher-ordered structure of the smectic phase. © 1996 John Wiley & Sons, Inc.     

Influence of chemical exchange on the temperature dependence of Eu(fod)3-induced shifts

Temperature dependences of the paramagnetic shifts induced by Eu(fod)₃ in ¹H NMR spectra of ethylene oxide in carbon disulphide solution are obtained in the temperature range from +40 to ? 100°C at 100 MHz and from +30 to ?60°C at 60 MHz. The influence of chemical exchange leads to a decrease of the observed paramagnetic shifts with decreasing temperature. It is shown that a modified Swift and Connick equation can be used to describe the observed dependences. Upper limits of the mean lifetimes of the Eu(fod)₃-ethylene oxide adduct are τ_p < 1·7 × 10^?8 s at 14 °C and τ_p < 1 × 10^?8 s at 20 °C, respectively. The corresponding activation energy is equal to V_a = 13·7 kcal/mol.     

Interaction of two phases in PP/EPDM polymer blend probed by positron annihilation: CONTIN analysis

Positron annihilation lifetime measurements were performed on pure polypropylene (PP), ethylene-propylene-diene monomer (EPDM) rubber, and their blends PP/EPDM with a series of EPDM volume fraction ϕ (= 10–40%). A numerical Laplace inversion technique (i.e., CONTIN algorithm), was employed to obtain the probability distribution functions (PDF) of free-volume radius. We observed that, first, the average free-volume radius in PP/EPDM blends is generally same as that in PP and is much smaller than that in EPDM. Second, the standard deviation σ_R or the width of the free-volume radius PDF in the blend decreases with ϕ in the region of ϕ = 10ndash;30%, and it increases when ϕ increases from 30% to 40%. The difference in the σ_R of the blend and the calculated value σ^c _R according to the simple-mixing rule of PP and EPDM is interpreted by the existence of the two-phase interaction (i.e., the residual thermal pressure and shear stress between PP and EPDM phases in the PP/EPDM blends). The correlation between σ_R, which indicates the interaction of two phases, and the impact strength of PP/EPDM blends was found and discussed. © 1996 John Wiley & Sons, Inc.     

Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

Differences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[?(tτ^*)^1?n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ₀) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ^* and τ₀ predicted by the theory is confirmed also by the experimental data.     

The diffusion of CO2, CH4, C2H4, and C3H8 in polyethylene at elevated pressures

Diffusion and solubility coefficients have been determined for the CO₂^?, CH₄^?, C₂H₄^?, and C₃H₈-polyethylene systems at temperatures of 5, 20, and 35°C and at gas pressures up to 40 atm. Diffusion coefficients were obtained from rates of gas absorption in polyethylene rods under isothermal-isobaric conditions by means of a new diffusivity apparatus. The concentration dependence of the diffusion coefficients was represented satisfactorily by Fujita's free-volume model, modified for semicrystalline polymers, while the solubility of all the penetrants in polyethylene was within the limit of Henry's law. Semiempirical correlations were found for the free-volume parameters in terms of physicochemical properties of the penetrant gases and the penetrant-polymer systems. These correlations, if confirmed, should permit the prediction of diffusion and permeability coefficients of other gases and of gas mixtures in polyethylene as functions of pressure and temperature.     

On the expansion of hole in main chain polymers determined by positron annihilation

The temperature dependence of positron annihilation characteristics, ₃ andI ₃, has been studied on sample of poly(butadiene), poly(isobutylene) and poly(chloroprene). The temperature range was between 15 and 470 K. The rate of expansion of holes or free-volume in all samples was deduced belowT _g as well aboveT _g as appr. 3·10^–3 K^–1 and 2·10^–2 K^–1, respectively. These values are very close to the rate of the mean squared displacement of scatterer<r ²>observed in neutron scattering experiments. A possibility to use an inverse value of free-volume,V _f ^–1 for study of viscoelastic state of polymers is demonstrated.     

Diffusivity enhancement of water vapor in poly(vinyl alcohol)–fumed silica nano-composite membranes: Correlation with polymer crystallinity and free-volume properties

The diffusion coefficients of water vapor in poly(vinyl alcohol)–fumed silica (PVA–FS) nano-composite membranes were determined using the gravimetric method. Water vapor was observed to diffuse more rapidly in membranes with increased FS content. The vapor diffusion coefficient was determined as 1.2 × 10⁻¹³ m²/s in pure PVA and was observed to increase to 3.0 × 10⁻¹³ m²/s in PVA composites containing 30% FS nano-particles. The free-volumes of PVA–FS membranes were characterized using positron annihilation lifetime (PAL) spectroscopy. PAL results showed that both the ortho-positronium (o-Ps) lifetime and intensity increased with the addition of FS. The intensity (I₃) was found to be higher than the estimated value determined from the linear combination of the data from pristine PVA and FS, and correlated excellently with the polymer amorphous content. The PAL results indicate that a higher FS content in PVA increases the free-volume hole size (a volume increase from 40 to 55 Å³) and free-volume hole density (an I₃ increase from 23 to 28%), resulting in a higher fractional free-volume in the nano-composites. The increase in the relative polymer free-volume with higher FS content was associated with a decrease in the PVA crystallinity, as determined from differential scanning calorimetry measurements. It is postulated that the incorporated FS nano-particles interrupt polymeric chain packing and retard crystallization during membrane formation. More crystalline segments were transformed into amorphous regimes in the nano-composites containing more FS. A correlation between water diffusivity and the fractional free-volume was obtained, and the water diffusivity was successfully expressed by the free-volume theory.     

Phase diagram and dielectric relaxation studies of n-octyl-isothiocyanato-biphenyl (8BT) in the crystalline E phase under high pressure

The pressure-temperature phase diagram of n-octyl-isothiocyanato-biphenyl (8BT) in the pressure range up to 250 MPa (2.5 kbar) and the temperature range 250-400 K was established with the aid of DTA. At 1 atm the substance exhibits exclusively CrE polymorphism. At pressures above 190 MPa, the clearing line splits showing an additional phase which is not yet identified. Dielectric relaxation measurements on the CrE phase of 8BT were performed in the pressure range 0.1-120 MPa and the temperature range 304-345 K. A Debye-type relaxation process was observed in the frequency range 100 Hz-1 MHz. The longitudinal relaxation time τ, characterizing the molecular reorientations around the short axis, was analysed with respect to the pressure and temperature, yielding the activation volume, Δ^# V = RT(? ln τ/?p)_T, and activation enthalpy, Δ^# H = R(? ln τ/? T^-1)_p, respectively. The results are compared with analogous data obtained recently for similar compounds having other liquid crystalline phases (N, SmA).     

Dynamic viscosity of dilute aqueous solutions of poly(acrylic acid) at frequencies of 2–500 kHz

The dynamic viscosity of aqueous solutions of poly(acrylic acid) at a polymer concentration of ca. 0.15 g/100 ml has been measured at frequencies from 2 to 500 kHz as a function of degree of polymerization P, degree of neutralization α, and salt (NaCl) concentration C_s. Relaxation spectra have been obtained from the dynamic viscosity. The spectra in the short relaxation time region can be approximated by the Zimm theory for the conformational relaxation of nonionic polymers. The maximum relaxation time τ₁ of the Zimm spectra is proportional to P² and depends rather moderately on α and C_s. Increased deviation is found, however, in the long relaxation time region, in particular for high values of P and α and low values of C_s. The major part of the deviation is interpreted in terms of rotational relaxation of a molecule as a whole. The rotational relaxation time τ_R is proportional to P³ and increases with increasing α and decreasing C_s. The remaining part of the excess spectra located between τ₁ and τ_R is ascribed to the deviation of the conformational relaxation from the Zimm theory arising from ionization of the polymer.     

A study of time dependence of ortho-positronium annihilation in a poly(butadiene) at different temperatures: a meaning of I3 parameter

Positron annihilation measurements as a function of temperature and time have been carried out on a poly(butadiene). The measurements were performed at several temperature points from 14 to 225 K. The measurement time was several hours to four days. The analysis of data shows the following features:

(i) the value of τ₃ does not depend on the rate of cooling or time,

(ii) the value of I₃ depends on the rate of cooling and the history of thermal treatment,

(iii) the dependence of I₃ on time can be described by Debye function. But the rise in I₃ is observed at very low temperatures,

(iv) the I₃ decays to value of I₃ observed during very slow cooling.

Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity

The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 10⁵ to 7.62 × 10⁶ and 0.112–0.329 g/cm³, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10^?4 < k < 1 sec^?1. The Cox–Merz relation η(k) = |η^*(ω)|_ω=k was tested with the experimental result (|^*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η^*(ω)|_ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ₁ > τ₂ > …, and the values of τ₁, τ₂ η₁ and η₂ were determined for some solutions. The relaxation times τ₁ and τ₂ were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η₁ and η₂ were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η₁ and η₂ with increasing k. It was shown that η₁(k) may be evaluated from the relaxation strength G₁(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high c–M systems as well as for low c–M systems.     

Contributions of side groups to the water diffusion in cured epoxy resins (2) study on physical aging

Novolac epoxy resins cured with novolac resin, novolac acetate resin, novolac butyrate resin, and novolac phenylacetate resin named as EP, EPA, EPB, and EPP, respectively, were prepared. Their physical aging behavior at a T_g‐30 °C (30 °C below glass‐transition temperature) was examined by positron annihilation lifetime spectroscopy and differential scanning calorimetry. The ortho‐positronium annihilation lifetime τ₃ variation extent of EP is less apparent than that of the other three esterified samples during physical aging. The time dependence of ops intensity I₃ agreed with the Kohlrausch‐Williams‐Watts (KWW) equation. The relaxation time (τ₀) and nonexponential parameter were calculated. The free volume and enthalpy relaxation rate characterized by the reciprocal of τ₀ and ?ΔH/?logt, respectively, exhibit the same order—EPP > EPB > EPA > EP. These results suggest that the extend and rate of relaxation are not only related to the frozen free volume produced by quenching but also significantly influenced by segmental mobility of the network that attributed to the side‐group flexibility and their interaction with networks. This work also supports the fact that side‐group flexibility and the free‐volume fraction and distribution act in concert to control the water‐diffusion behavior in epoxy networks. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1135–1142, 2003     

The Spin Probe Dynamics and the Free Volume in a Series of Amorphous Polymer Glass-Formers

We report the results of a combined study of the local structure and the reorientation dynamics in a series of five amorphous polymers of different fragility: cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD), cis-1,4-poly(isoprene) (cis-1,4-PIP), poly(isobutylene) (PIB), poly(vinyl methylether)(PVME) and poly (propylene glycol) (PPG) by using two different probe methods. The reorientation dynamics of the molecular spin probe 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) from electron spin resonance (ESR) is related to the annihilation behaviour of the atomic ortho-positronium (o-Ps) one as obtained by positron annihilation lifetime spectroscopy (PALS). It was found that a slow to fast transition in the spin probe rotation mobility at the operationally defined spectral temperature parameter, T_50G, is connected with the mean o-Ps lifetime, τ₃ (T_50G) = (2.04 ± 0.26) ns. Consequently, using the free-volume concept of the o-Ps annihilation in terms of a quantum-mechanical model of o-Ps lifetime this transition can be connected with the occurrence of the mean free volume hole, V_h (T_50G) = (102 ± 17) ų, nearly independent of the chemical composition and the basic structural relaxation parameters of the amorphous polymers investigated. Finally, the free volume hole distribution aspect of the slow to fast transition indicates the presence of a sufficient free volume fluctuation at T_50G for both typical fragile PVME and strong PIB polymer and emphasizes the essential role of free volume in the spin probe dynamics.     

DAMAGE OF SILICONE RUBBER INDUCED BY PROTON IRRADIATION

In this paper, the damage to methyl silicone rubber induced by irradiation with protons of 150 keV energy wasstudied. The surface morphology, tensile strength, Shore hardness, cross-linking density and glass transition temperaturewere examined. Positron annihilation lifetime spectrum analysis (PALS) was perfomed to reveal the damage mechanisms ofthe rubber. The results showed that tensile strength and Shore hardness of the rubber increased first and then decreased withincreasing irradiation fluence. The PALS characteristics τ_3 and I_3, as well as the free volume V_f, decreased with increasingirradiation fluence up to 10~(15) cm~(-2), and then increased slowly. It indicates that proton irradiation causes a decrease of freevolume in the methyl silicone rubber when the fluence is less than 10~(15)cm~(-2), while the free volume increases when thefluence is greater than 10~(15)cm~(-2). The results on cross-linking density indicate that the cross-linking induced by protonirradiation is dominant at smaller proton fluences, increasing the tensile strength and Shore hardness of the rubber, while thedegradation of rubber dominates at greater fluence, leading to a decrease of tensile strength and Shore hardness.     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

Computer simulation of brownian motion of a polyelectrolyte molecule (charged bead-spring model)

A Langevin equation of motion for a charged bead-spring statistical chain is written in difference form and the relaxation and equilibrium behavior of the chain is studied by computer simulation. Results are presented for the behavior of end-to-end length h, principal axes of the polymer ellipsoid L₁, L₂, L₃, and chain contour length c in terms of their averages, root mean square values, root mean square fluctuations, orientations, and relaxation strengths and times. The simulation was made with various sets of parameters, bead number N, charge on the bead q, and radius of ion atmosphere around the bead k^?1. It is found that 〈h²〉^1/2 and 〈L₁²〉^1/2 increase more strongly with increasing q and decreasing κ than 〈L₂²〉^1/2, 〈L₃²〉^1/2, and 〈c₁²〉^1/2, indicating that the chain is expanded in three dimensions and at the same time is extended along the end-to-end direction. The relaxation time τ_rot of rotation of the end-to-end vector, which is proportional to N² at q = 0, increases with increasing q and tends to be proportional to N³ for an extended chain, while the relaxation time τ_conf of the magnitude of h is almost independent of q and is always proportional to N². It is concluded that the extended chain possesses a well-defined end-to-end axis and the chain rotates as a whole with a relaxation time τ_rot which is much longer than τ_conf. The complex viscosity of the chain is calculated from the Fourier transform of the time–correlation function of momentum flux and is found to have a frequency spectrum similar to that observed for aqueous solutions of poly(acrylic acid). The dominant mode appearing in the low-frequency range is evidenced to arise from the rotation of the extended chain.     

Effects of polymer chain disentanglement on NMR properties. II. 13C magnetic relaxation in polystyrene

The transverse magnetic relaxation of ¹³C_α nuclei has been studied in concentrated solutions of polystyrene. The magnetic relaxation rate was measured as a function of molecular weight at several temperatures (313,318, and 323 K) and at several concentrations (0.53, 0.43, and 0.34 g/cm³). The spin-system response of these nuclei in natural abundance exhibits a characteristic evolution from pseudosolid properties to liquidlike one, induced by decreasing the molecular weight of polymer molecules. This evolution is analogous to that already observed in protons attached to polyisobutylene or polydimethylsiloxane chains; it is assumed to be induced by an increase of the disentanglement rate of polymer chains. The spin-system response may be considered as reflecting single-chain magnetic properties, because of the low concentration of ¹³CC_α nuclei, although all chains are in dynamic interaction with one another. The NMR disentanglement transition is interpreted in terms of a two-step motional averaging effect involving submolecules. A numerical analysis of NMR properties is given using a model of polymer chain relaxation based on a multiple-mode relaxation process, characterized by (i)a terminal relaxation time τ^v₁ depending upon M³, the molecular weight, and approximately proportional to the polymer concentration C (like the reptation time); (ii)a relaxation-time spectrum analogous to a Rouse spectrum; (iii)a terminal relaxation time τ^v₁ = 2.5 × 10^?2s for M = 2.5 × 10⁵, C = 0.53 g/cm³ in carbon tetrachloride at 313 K.