Temperature dependence of molecular motions in bulk polystyrene

Time-resolved optical spectroscopy is used to investigate the reorientation of three rigid probes and one labeled chain in bulk polystyrene. Orientational correlation times for these probes and labels are found to be in the range of 10^?8–10^?10 s at temperatures of 180–300°C. Consistent with previous studies, the attachment of a chromophore into the chain backbone slows its dynamics by about an order of magnitude. The temperature dependences of the correlation times are similar to the temperature dependence of the viscosity. When combined with probe reorientation times near and below T_g, these results indicate that probe reorientation tracks the temperature dependence of the viscosity quite well over twelve decades in time. In contrast, literature results for the translational diffusion of similarly sized probes indicates a substantially weaker temperature dependence near T_g. Thus it appears that a fundamental change in the mechanism of probe motion occurs near T_g. © 1994 John Wiley & Sons, Inc.     

Probe rotation near and below the glass transition temperature: Relationship to viscoelasticity and physical aging

Reorientation times ť_c for two probes in several amorphous polymers near the glass transition temperature T_g are reported. T_g for these polymers ranges from 205 to 459 K. Probe reorientation was measured in the time window from 10⁻² to 10⁴ s with a recently developed photobleaching method. ť_c for a given probe at the T_gs of the different polymers varies more than three decades. Viscoelastic relaxation times characteristic of the Rouse modes of the matrix polymers are closely related to probe rotation times and thus also not constant at T_g. The characteristic length scale of motions responsible for the glass transition varies significantly for the three polymers studied. Preliminary physical aging results indicate that probe reorientation in polystyrene ages slightly faster than the volume.     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Small angle neutron scattering (SANS) studies of diffusion in bulk polystyrene near the glass transition temperature (Tg)

Ultraslow diffusion in bulk polymers has been measured by SANS. The experiment begins by measuring scattering from heterogeneous specimens containing domains of protonated-and deuterated-polymers at temperatures far below T_g. The samples are subsequently held [annealed] above T_g for a known time-interval, then cooled below T_g where SANS is measured again. Scattering changes, from before to after annealing, are analysed to obtain diffusion coefficients. The recent Summerfield - Ullman procedure is used to deconvolute portions of the scattering curve that decrease and increase with annealing time. Because of SANS sensitivity to small distances, the method yields D ≈ 10⁻¹⁸ to 10⁻¹⁵ cm²/s after annealing times of 1–24 h. Data analysis is complicated by “smearing effects” which produce apparent Q-dependent diffusion coefficients. Representative experimental results on polystyrene at 108°–130°C are discussed.     

Effect of nanoscale confinement on the glass transition temperature of free-standing polymer films: Novel,self-referencing fluorescence method

The effect of nanoscale confinement on the glass transition temperature, T_g, of freely standing polystyrene (PS) films was determined using the temperature dependence of a fluorescence intensity ratio associated with pyrene dye labeled to the polymer. The ratio of the intensity of the third fluorescence peak to that of the first fluorescence peak in 1-pyrenylmethyl methacrylate-labeled PS (MApyrene-labeled PS) decreased with decreasing temperature, and the intersection of the linear temperature dependences in the rubbery and glassy states yielded the measurement of T_g. The sensitivity of this method to T_g was also shown in bulk, supported PS and poly(isobutyl methacrylate) films. With free-standing PS films, a strong effect of confinement on T_g was evident at thicknesses less than 80–90 nm. For MApyrene-labeled PS with M_n = 701 kg mol⁻¹, a 41-nm-thick film exhibited a 47 K reduction in T_g relative to bulk PS. A strong molecular weight dependence of the T_g-confinement effect was also observed, with a 65-nm-thick free-standing film exhibiting a reduction in T_g relative to bulk PS of 19 K with M_n = 701 kg mol⁻¹ and 31 K with M_n = 1460 kg mol⁻¹. The data are in reasonable agreement with results of Forrest, Dalnoki-Veress, and Dutcher who performed the seminal studies on T_g-confinement effects in free-standing PS films. The utility of self-referencing fluorescence for novel studies of confinement effects in free-standing films is discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2754–2764, 2008     

Computer simulation study of bulk atactic polystyrene in the vicinity of the glass transition

Molecular dynamics (MD) simulations of bulk atactic polystyrene have been performed in a temperature range from 100 K to 650 K at atmospheric pressure. Local translational mobility has been investigated by measuring the mean square translational displacements of monomers. The long-time asymptotic slope of these dependencies is 0.54 at T>T_g, showing Rouse behavior. Cross-over from motion in the cage to Rouse like dynamics has been studied at T>T_g with a characteristic crossover time follows a power law behavior as a function of T, as predicted by mode-coupling theory (MCT). Local orientational mobility has been studied via the orientational autocorrelation functions, ACFs, (Legendre polynomials of the first and second, order) of both the main-chain and side-group bonds. The relaxation times of the orientational α-relaxation follow the same power law (γ∼2.9) as the characteristic translational diffusion time. Below T>T_g both types of dynamics are described by the same activated law. The ACFs time-distribution functions reveal the existence of activated local rearrangements already above T>T_g.     

Viscoelasticity of nanobubble‐inflated ultrathin polymer films: Justification by the coupling model

The nanobubble inflation method is the only experimental technique that can measure the viscoelastic creep compliance of unsupported ultrathin films of polymers over the glass–rubber transition zone as well as the dependence of the glass transition temperature (T_g) on film thickness. Sizeable reduction of T_g was observed in polystyrene (PS) and bisphenol A polycarbonate by the shift of the creep compliance to shorter times. The dependence of T_g on film thickness is consistent with the published data of free‐standing PS ultrathin films. However, accompanying the shift of the compliance to shorter times, a decrease in the rubbery plateau compliance is observed. The decrease becomes more dramatic in thinner films and at lower temperatures. This anomalous viscoelastic behavior was also observed in poly(vinyl acetate) and poly (n‐butyl methacrylate), but with large variation in the change of either the T_g or the plateau compliance. By now, well established in bulk polymers is the presence of three different viscoelastic mechanisms in the glass–rubber transition zone, namely, the Rouse modes, the sub‐Rouse modes, and the segmental α‐relaxation. Based on the thermorheological complexity of the three mechanisms, the viscoelastic anomaly observed in ultrathin polymer films and its dependence on chemical structure are explained in the framework of the Coupling Model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

23Na NMR in urethane cross-linked polyether solid polymer electrolytes

Sodium triflate/polyether urethane polymer electrolytes ranging in concentration from 0.05 molal to 1.75 molal have been investigated via ²³Na static solid-state NMR. Room temperature spectra and spin lattice relaxation times were consistent with a single narrow resonance indicating the presence of only mobile ionic species. The concentration and temperature dependence of relaxation times, chemical shifts, and linewidth have been investigated. The results suggest either a single species or rapid exchange between a number of species (even at temperatures below the glass transition temperature, T_g). The linewidth decreases with increasing concentration of ions and remains temperature independent below T_g. Below T_g a maximum quadrupolar interaction constant of 2 MHz is calculated. The addition of plasticizer to the polymer electrolyte causes significant chemical shift changes that depend on the solvent donicity of the plasticizer. The linewidth and T₁ relaxation times also depend on the T_g of the plasticized systems. Previous ²³Na NMR literature results are reviewed and qualitative models developed to account for the variation in results. © 1994 John Wiley & Sons, Inc.     

Compression stress relaxation in carbon black reinforced HNBR at low temperatures

Findings of a study of stress relaxation behaviour of hydrogenated nitrile butadiene rubber (HNBR) at nominal compressive strains up to 0.4 and temperatures above and below the glass transition temperature T_g are reported. Two formulations of a model HNBR with 36% acrylonitrile content and carbon black (CB) loading of 0 and 50 phr were investigated. The relaxation function of HNBR is found to be independent of strain at temperatures right above the T_g or at times longer than 10⁻³ s for the deformations employed. CB imparts higher long-term stiffness and also larger relaxation strength at times longer than 10⁻⁴ s to the HNBR, but it does not affect the relaxation behaviour of the rubber in the time span from 10⁻³ – 10⁴ s. In addition, the relationship between the strain energy function of HNBR and temperature is demonstrated to have a complex concave-downward shape which is affected by two competing contributions of entropy elasticity and the stress relaxation.     

A nuclear magnetic resonance study of toluene-polyisobutylene solutions. 3. Spin-lattice relaxation: Rotational and segmental motion

The spin-lattice relaxation times are determined for the methylene carbon of polyisobutylene (PIB), as well as for the ortho carbon of toluene in toluene-polyisobutylene solutions. The Hall-Helfand correlation function combined with restricted anisotropic rotational diffusion was used to treat the T₁ data of the methylene carbon of PIB. A simple exponential correlation function was used to describe the local motion of toluene in the solutions which falls in the extreme narrowing limit for the solutions studied. Both models described satisfactorily the temperature and field dependence of the spin-lattice relation times. From the temperature dependence of the correlation times for the polymer segmental motion, the free volume of the solution at each concentration is extracted and compared with the values obtained from previous studies of the translational motion of the toluene penetrant. The free volume values extracted from the T₁ data for the methylene carbon of PIB and the self-diffusion data for the toluene were found to be in substantial agreement. The interrelationship of the timescale of segmental motion of the polymer and the translational diffusion of the toluene was also examined and it was found that the two types of motion seem to be correlated in high polymer concentrated solutions. The toluene reorientational motion was found to be much faster than both the polymer segmental motion and the toluene translational diffusion leading to the conclusion that the toluene reorientational motion is uncoupled from these two motions. ©1995 John Wiley & Sons, Inc.     

Effect of reversible structural relaxation on diffusion in bulk metallic glasses

Long time relaxation at temperatures below the calorimetric glass transition causes reversible structural changes in metallic glasses. The resulting enthalpy recovery was measured by means of DSC in Zr_46.8Ti_8.2Cu_7.5Ni₁₀Be_27.5- and Pd₄₀Cu₃₀Ni₁₀P₂₀-bulk glass annealed for different times at 553 K and 542 K, respectively. Relaxation times of about 10⁶ s and 10⁴ s, respectively, were determined. The diffusion coefficients of B, Fe and Co were measured above and below the calorimetric glass transition temperature. Whereas the temperature dependence of these diffusion coefficients in the non-relaxed glasses shows “non-linear” Arrhenius behaviour with a break near the glass transition, the diffusion in the long time relaxed glasses follows a uniform temperature dependence over the entire temperature range with considerably reduced diffusion coefficients below the glass transition. This behaviour can be reversed by annealing the relaxed glasses again at higher temperatures indicating the strong effect of the reversible structural relaxation on the diffusion coefficients.     

Evidence of dynamic heterogeneity as obtained from dielectric and brillouin light-scattering studies of poly(n-hexylmethacrylate)

We report dielectric relaxation and Rayleigh-Brillouin spectroscopic measurements on the side chain polymer poly(n-hexylmethacrylate), PHMA (T_g = 268 K), exhibiting a broad glass transition region. The dielectric loss curves can be represented by single Havriliak-Negami functions in the temperature range of 260–450 K. The width of the distribution relaxation function is a decreasing function of temperature up to T = 333 K ≊ 1.24 × T_g and remains virtually constant above that temperature. This is interpreted as marking the merging of the α-process with a slow β-relaxation in agreement with the value of the cooperativity length associated with the α-mode. Hence above that temperature, the relaxation times confirm well to an Arrhenius temperature dependence. The hypersonic dispersion deduced from the Brillouin spectra (210–550 K) surprisingly peaks at temperatures near T_g which bears no relation to the main α-relaxation. This structural relaxation is rather associated with the side hexyl group motion showing striking resemblance with the hypersonic dispersion in molecular liquids. It is conceivable that the observed damping in PHMA is dynamically related to the internal plasticization effect of the hexyl group. © 1996 John Wiley & Sons, Inc.     

Free volume quantities and viscoelasticity of polymer glasses

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, <to, and average free volume sizes, 〈v_f〉, obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, v*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the v* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T_g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume. © 1996 John Wiley & Sons, Inc.     

Volume dependence of thermal conductivity and bulk modulus for poly(propylene glycol)

The thermal conductivity λ and heat capacity per unit volume of poly(propylene glycol) PPG (0.4 and 4.0 kg·mol⁻¹ in number-average molecular weight) have been measured in the temperature range 150–295 K at pressures up to 2 GPa using the transient hot-wire method. At 295 K and atmospheric pressure, λ = 0.147 W m⁻¹K⁻¹ for PPG (0.4 kg·mol⁻¹) and λ = 0.151 W m⁻¹K⁻¹ for PPG (4.0 kg·mol⁻¹). The temperature dependence of λ is less than 4 × 10⁻⁴ W m⁻¹K⁻² for both molecular weights. The bulk modulus has been measured in the temperature range 215–295 K up to 1.1 GPa. At atmospheric pressure, the room temperature bulk moduli are 1.97 GPa for PPG (0.4 kg·mol⁻¹) and 1.75 GPa for PPG (4.0 kg·mol⁻¹). These data were used to calculate the volume dependence of $ \lambda ,g\, = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T $. At room temperature and atmospheric pressure (liquid phase) we find g = 2.79 for PPG (0.4 kg·mol⁻¹) and g = 2.15 for PPG (4.0 kg·mol⁻¹). The volume dependence of g, (∂g/∂ log V)_T varies between −19 to −10 for both molecular weights. Under isochoric conditions, g is nearly independent of temperature. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The theoretical model for λ by Horrocks and McLaughlin yields an overestimate of g by up to 120%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 345–355, 1998     

Molecular probe techniques for studying diffusion and relaxation in thin and ultrathin polymer films

Two optically based, molecular probe techniques are employed to study relaxation and small-molecule translational diffusion in thin and ultrathin (thicknesses < ∼200 nm) polymer films. Second harmonic generation (SHG) is used to study the reorientational dynamics of a nonlinear optical chromophore, Disperse Red 1 (DR1) (previously shown to be an effective probe of α-relaxation dynamics) either covalently attached or freely doped in polymer films. Our studies on films ranging in thickness from 7 nm to 1 μm show little change in T_g with film thickness; however, a substantial broadening of the relaxation distribution is observed as film thickness decreases below approximately 150 nm. Experimental guidelines are given for using fluorescence nonradiative energy transfer (NRET) to study translational diffusion in ultrathin polymer films. Appropriate choice of a fluorescence donor species is important along with ensuring that diffusion is slow enough to be measured appropriately. Initial results on the diffusion of a small-molecule probe, lophine, in poly(isobutyl methacrylate) indicates that there is little change in probe diffusion coefficients in films as thin as 90 nm as compared to bulk films. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2795–2802, 1997     

The glass transition in linear low density polyethylene determined by thermally stimulated depolarization currents

New thermally stimulated depolarization currents (TSDC) results on LLD polyethylene functionalized with diethylmaleate polar groups are precisely computer fitted with the direct signal analysis technique. It is shown that the TSDC spectrum consists, with increasing temperatures, of a sub-γ peak, a sharp γ peak, and a β and an α relaxation. The first peak is analyzed in terms of Arrhenius relaxation times, whereas the γ and β transitions could only be fitted by using Vogel-Fulcher temperature dependence for the relaxation times. The best value for T_o obtained from both fittings is 69.7 K. This is a quantitative proof for the identification of the γ transition as one of the dielectric manifestations of the glass-rubber transition for polyethylenes, T_g = 136.5 K, which has been discussed extensively in the literature. The β relaxation, T_gβ = 237 K, has also the expected characteristic of a glass transition; the existence of two T_gs in polyethylene could explain our results. © 1996 John Wiley & Sons, Inc.     

Pressure and volume dependence of thermal conductivity and isothermal bulk modulus up to 1 GPa for poly(isobutylene)

The thermal conductivity λ and heat capacity per unit volume ρc_p of poly(isobutylene)s, one 2.8 in weight average molecular weight and one 85 kg mol⁻¹ in viscosity average molecular weight (PIB-2800 and PIB-85000), have been measured in the temperature range 170–450 K at pressures up to 2 GPa using the transient hot-wire method. At 297 K and atmospheric pressure, λ = 0.115 W m⁻¹ K⁻¹ for PIB-2800 and λ = 0.120 W m⁻¹ K⁻¹ for PIB-85000. The bulk modulus B_T has been measured in the temperature range 170–297 K up to 1 GPa. At atmospheric pressure, the room temperature bulk moduli B_T are 2.0 GPa for PIB-2800 and 2.5 GPa for PIB-85000 with dB_T/dp = 10 for both. These data were used to calculate the volume dependence of λ, At room temperature and atmospheric pressure (liquid phase) we find g = 3.4 for PIB-2800 and g = 3.9 for PIB-85000, but g depends strongly on temperature for both molecular weights. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The best predictions for g are given by the theoretical model of Horrocks and McLaughlin. We have found that PIB exhibits two relaxations, where one is associated with the glass transition. The value for dT_g/dp at atmospheric pressure (for the main glass transition) is about 0.21 K MPa⁻¹ for both molecular weights. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1781–1792, 1998     

Rate coefficients for the reactions of OH with butanols from 298 K to temperatures relevant for low-temperature combustion

Rate coefficients for the reactions of OH with n, s, and iso-butanol have been measured over the temperature range 298 to ∼650 K. The rate coefficients display significant curvature over this temperature range and bridge the gap between previous low-temperature measurements with a negative temperature dependence and higher temperature shock tube measurements that have a positive temperature dependence. In combination with literature data, the following parameterizations are recommended: k_{1,OH + n-butanol}(T) = (3.8 ± 10.4) × 10⁻¹⁹T^{2.48 ± 0.37}exp ((840 ± 161)/T) cm³ molecule⁻¹ s⁻¹ k_{2,OH + s-butanol}(T) = (3.5 ± 3.0) × 10⁻²⁰T^{2.76 ± 0.12}exp ((1085 ± 55)/T) cm³ molecule⁻¹ s⁻¹ k_{3,OH + i-butanol}(T) = (5.1 ± 5.3) × 10⁻²⁰T^{2.72 ± 0.14}exp ((1059 ± 66)/T) cm³ molecule⁻¹ s⁻¹ k_{4,OH + t-butanol}(T) = (8.8 ± 10.4) × 10⁻²²T^{3.24 ± 0.15}exp ((711 ± 83)/T) cm³ molecule⁻¹ s⁻¹ Comparison of the current data with the higher shock tube measurements suggests that at temperatures of ∼1000 K, the OH yields, primarily from decomposition of β-hydroxyperoxy radicals, are ∼0.3 (n-butanol), ∼0.3 (s-butanol) and ∼0.2 (iso-butanol) with β-hydroxyperoxy decompositions generating OH, and a butene as the main products. The data suggest that decomposition of β-hydroxyperoxy radicals predominantly occurs via OH elimination.     

Bisphenol-A polycarbonate–diluent interactions

The effect of low-molecular-weight miscible additives on the sub-T_g (β) relaxation process in bisphenol-A polycarbonate (BPAPC) was studied using high-resolution carbon-13 solid-state NMR. The trend of the spin-lattice relaxation times T₁ at 50 MHz suggests that strong intermolecular interactions occur upon mixing when BPAPC is physically stiffened by the antiplasticizing diluent, diphenylphthalate. The values of ¹³C T₁ at 15 MHz in d-chloroform solutions for similar BPAPC-diluent mixtures suggest that diluent effects on the megahertz mobility of the polymer occur exclusively in the solid state. These results are explained using equilibrium thermodynamics, in the Ehrenfest sense, at the second-order glass transition temperature T_g. Theory predicts that the temperature dependence of the Flory–Huggins interaction parameter ?χ/?T changes abruptly as the polymer-diluent blends are cooled below T_g from the molten state. The difference between ?χ/?T in the liquid and glassy states is the major factor which determines the diluent concentration dependence of T_g. A method is developed to estimate the relative magnitudes of χ for polymerdiluent blends in the glassy state.