Enthalpy recovery of a glass-forming liquid constrained in a nanoporous matrix: Negative pressure effects

The T _g of organic liquids confined to nanoporous matrices and that of thin polymer films can decrease dramatically from the bulk value. One possible explanation for this phenomenon is the development of hydrostatic tension during vitrification under confinement that results in a concomitant increase in the free volume. Here we present experimental evidence and modeling results for ortho-terphenyl (o-TP) confined in pores as small as 11.6 nm that indicate that, although there is an important hydrostatic tension in the liquid in the pores, it does not develop until near the reduced T _g of the constrained material --well below the bulk T _g. Enthalpy recovery for the o-TP in the nanopores exhibits accelerated physical aging relative to the bulk, as well as a leveling off of the fictive temperature at equilibrium values greater than the aging temperature. An adaptation of the structural recovery model that incorporates vitrification under isochoric conditions is able to provide a quantitative explanation for the apparently anomalous aging observed in nanopore confined liquids and in thin polymeric films. The results strongly support the existence of an intrinsic size effect as the cause of the reduced T _g. Received 3 September 2001     

The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films

We present a detailed study of free polymer surfaces and their effects on the measured glass transition temperature (T_g) of thin polystyrene (PS) films. Direct measurements of the near-surface properties of PS films are made by monitoring the embedding of 10 and 20 nm diameter gold spheres into the surface of spin-cast PS films. At a temperature T = 378K( > T_g), the embedding of the spheres is driven by geometrical considerations arising from the wetting of the gold spheres by the PS. At temperatures below T_g ( 363K < T < 370K), both sets of spheres embed 3-4 nm into the PS films and stop. These studies suggest that a liquid-like surface layer exists in glassy PS films and also provide an estimate for the lower bound of the thickness of this layer of 3-4 nm. This qualitative idea is supported by a series of calculations based upon a previously developed theoretical model for the indentation of nanoscale spheres into linear viscoelastic materials. Comparing data with simulations shows that this surface layer has properties similar to those of a bulk sample of PS having a temperature of 374 K. Ellipsometric measurements of the T_g are also performed on thin spin-cast PS films with thicknesses in the range 8nm < h < 290nm. Measurements are performed on thin PS films that have been capped by thermally evaporating 5 nm thick metal (Au and Al) capping layers on top of the polymer. The measured T_g values (as well as polymer metal interface structure) in such samples depend on the metal used as the capping layer, and cast doubt on the general validity of using evaporative deposition to cover the free surface. We also prepared films that were capped by a new non-evaporative procedure. These films were shown to have a T_g that is the same as that of bulk PS (370±1 K) for all film thicknesses measured (> 7 nm). The subsequent removal of the metal layer from these films was shown to restore a thickness-dependent T_g in these samples that was essentially the same as that observed for uncapped PS films. An estimate of the thickness of the liquid-like surface layer was also extracted from the ellipsometry measurements and was found to be 5±1 nm. The combined ellipsometry and embedding studies provide strong evidence for the existence of a liquid-like surface layer in thin glassy PS films. They show that the presence of the free surface is an important parameter in determining the existence of T_g reductions in thin PS films.     

Molecular dynamics in thin films of isotactic poly(methyl methacrylate)

The molecular dynamics in thin films (18 nm-137 nm) of isotactic poly(methyl methacrylate) (i-PMMA) of two molecular weights embedded between aluminium electrodes are measured by means of dielectric spectroscopy in the frequency range from 50 mHz to 10 MHz at temperatures between 273 K and 392 K. The observed dynamics is characterized by two relaxation processes: the dynamic glass transition (α-relaxation) and a (local) secondary β-relaxation. While the latter does not depend on the dimensions of the sample, the dynamic glass transition becomes faster (≤2 decades) with decreasing film thickness. This results in a shift of the glass transition temperature T _g to lower values compared to the bulk. With decreasing film thickness a broadening of the relaxation time distribution and a decrease of the dielectric strength is observed for the α-relaxation. This enables to deduce a model based on immobilized boundary layers and on a region displaying a dynamics faster than in the bulk. Additionally, T _g was determined by temperature-dependent ellipsometric measurements of the thickness of films prepared on silica. These measurements yield a gradual increase of T _g with decreasing film thickness. The findings concerning the different thickness dependences of T _g are explained by changes of the interaction between the polymer and the substrates. A quantitative analysis of the T _g shifts incorporates recently developed models to describe the glass transition in thin polymer films. Received 12 August 2001 and Received in final form 16 November 2001     

Effect of Temperature Variation on the Characteristics of Microwave Power AlGaN/GaN MODFET

The prime motivation for developing the proposed model of AlGaN/GaN microwave power device is to demonstrate its inherent ability to operate at much higher temperature. An investigation of temperature model of a 1 μm gate AlGaN/GaN enhancement mode n-type modulation-doped field effect transistor (MODFET) is presented. An analytical temperature model based on modified charge control equations is developed. The proposed model handles higher voltages and show stable operation at higher temperatures. The investigated temperature range is from 100 °K–600 °K. The critical parameters of the proposed device are the maximum drain current (I_Dmax), the threshold voltage (V_th), the peak dc trans-conductance (g_m), and unity current gain cut-off frequency (f_T). The calculated values of f_T (10–70 GHz) at elevated temperature suggest that the operation of the proposed device has sufficiently high current handling capacity. The temperature effect on saturation current, cutoff frequency, and trans-conductance behavior predict the device behavior at elevated temperatures. The analysis and simulation results on the transport characteristics of the MODFET structure is compared with the previously measured experimental data at room temperature. The calculated critical parameters suggest that the proposed device could survive in extreme environments.     

Glass transition of the two distinct single-chain particles of poly(N-isopropylacrylamide)

Two distinct single-chain particles of poly(N-isopropylacrylamide) (PNIPAM) in the state of loose coil and compact globule, have been prepared successfully below and above the lower critical solution temperature (LCST) in extreme dilute aqueous solution by the freeze-drying method, respectively. During the preparation of the compact globular single-chain sample, the surfactant of sodium n-dodecyl sulfate (SDS) was added into the system to prevent aggregation of globular single chains formed at a temperature above the LCST. After all the coil has been transformed into the compact globular particle, the SDS molecules were removed by dialysis. The glass transition temperature (T_g) of the two single-chain samples has been measured by differential scanning calorimetery (DSC) in comparison with that of bulk polymer. It was found that the T_g of the single-chain sample in compact-globule state was very near to that of the bulk polymer, whereas the T_g of the single-chain sample in loose-coil state was approximately 6 K lower than that of the bulk polymer. After treating the sample with repeated DSC cycles, the T_g of the single-chain sample in loose-coil state rose up successively near to that of the bulk polymer. These results have been explained in terms of the effect of entanglement on the mobility of the polymer segments in the two distinct single-chain samples.     

The determination of the glass transition temperature by thermally stimulated depolarization currents. Comparison with the performance of other techniques

Several experimental techniques are currently used for the determination of the glass transition temperature, T_g. Thermally stimulated depolarization currents (TSDC) is a thermal analysis technique whose experimental results display a very clean glass transition signature and that, nevertheless, is seldom used as a technique for T_g determination. In the present work we explain how to get the glass transition temperature from TSDC data, and we compare the values obtained for a vast number of glass forming systems (with T_gs in a wide range between ?145 and +180 °C and fragilities between m = 15 and m = 100), with the values obtained by differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). We conclude that the T_g determination by TSDC is direct, accurate and reproducible and that the obtained values correlate very well with those obtained by DSC and DRS. This general survey thus suggests TSDC as a valuable alternative technique for determining T_g.     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.     

Thermal stability and crystallization kinetics of Ge–Se–Cd glasses

The effect is reported of varying cadmium concentration on the glass transition, thermal stability and crystallization kinetics of Ge₂₀Se_{80? x} Cd _x (x = 2.5, 5, 7.5 and 10 at. %) glasses. Differential scanning calorimetry results under non-isothermal conditions for the studied glasses are reported and discussed. The values of the glass transition temperature (T_g ) and the peak temperature of crystallization (T_p ) were found to be dependent on heating rate and Cd content. From the heating rate dependence of T_g and T_p , the values of the activation energy for glass transition (E_g ) and the activation energy for crystallization (E_c ) were evaluated and their composition dependence discussed. The thermal stability of the glasses was evaluated using various thermal stability criteria such as ΔT, H_g and S. The stability calculations emphasize that the thermal stability decreases with increasing Cd content.     

Confinement and processing effects on glass transition temperature and physical aging in ultrathin polymer films: Novel fluorescence measurements

Fluorescence intensity measurements of chromophore-doped or -labeled polymers have been used for the first time to determine the effects of decreasing film thickness on glass transition temperature, T _g, the relative strength of the glass transition, and the relative rate of physical aging below T _g in supported, ultrathin polymer films. The temperature dependence of fluorescence intensity measured in the glassy state of thin and ultrathin films of pyrene-doped polystyrene (PS), poly(isobutyl methacrylate) (PiBMA), and poly(2-vinylpyridine) (P2VP) differs from that in the rubbery state with a transition at T _g. Positive deviations from bulk T _g are observed in ultrathin PiBMA and P2VP films on silica substrates while substantial negative deviations from bulk T _g are observed in ultrathin PS films on silica substrates. The relative difference in the temperature dependences of fluorescence intensity in the rubbery and glassy states is usually reduced with decreasing film thickness, indicating that the strength of the glass transition is reduced in thinner films. The temperature dependence of fluorescence intensity also provides useful information on effects of processing history as well as on the degree of polymer-substrate interaction. In addition, when used as a polymer label, a mobility-sensitive rotor chromophore is demonstrated to be useful in measuring relative rates of physical aging in films as thin as 10 nm. Received 21 August 2001     

Molecular-weight dependence of the glass transition temperature of freely-standing poly(methyl methacrylate) films

We have used transmission ellipsometry to measure the glass transition temperature, T_g, of freely-standing films of atactic and syndiotactic poly(methyl methacrylate) (PMMA). We have prepared films with different molecular weights, MW, (159×10³ < M _w < 1.3×10⁶) and film thicknesses, h, ( 30nm < h < 200 nm). For the high-MW ( M _w > 509×10³) atactic PMMA films, we find that T_g decreases linearly with decreasing h, which is qualitatively similar to previous results obtained for high-MW freely-standing polystyrene (PS) films. However, the overall magnitude of the T_g reduction is much less (by roughly a factor of three) for the high-MW freely-standing PMMA films than for freely-standing PS films of comparable MW and h. The observed differences between the freely-standing PMMA and PS film data suggest that differences in chemical structure determine the magnitude of the T_g reduction and we discuss the possible origins of these differences. Our analysis of the MW-dependence of the T_g reductions suggests that the mechanism responsible for the MW-dependent T_g reductions observed in the high-MW freely-standing films is different than that responsible for the MW-independent T_g reductions observed in the low-MW freely-standing and supported films.     

Mechanical spectroscopy of laser deposited polymers

Pulsed laser deposition (PLD) at 248 nm in ultra high vacuum was used to produce thin poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA) films. The ablation and deposition mechanisms were found to be similar in both systems. Having the same backbone, these polymers differ in the size of their polar side groups leading to changes in their dynamics. Studies of the relaxation processes were performed using mechanical torsion and bending spectroscopy by means of a double-paddle oscillator (DPO) and an in-situ plasma plume excited reed (PPXR), respectively. A strong increase of the mechanical damping was observed during annealing of the polymer films well above the glass transition temperature T _g, while in-situ X-ray measurements did not reveal any structural changes. For PEMA, the glass transition temperature T _g=335 K and the main absorption maximum appear at lower temperatures compared to PMMA (T _g=380 K), allowing one to measure the mechanical properties in a much wider range above T _g.     

Superconductivity of Li under pressure

The superconductivity of Li under pressure is studied by a density functional method. Structural and elastic properties, transition temperature (T_c), density of states (DOS), are considered for the material at ambient and at higher pressures. The calculations, particularly of T_c and DOS as a function of pressure, are compared with other available results. This is in view of the wide difference between the previously predicted maximum T_c-value and those observed by both magnetic susceptibility and electrical resistivity experiments. The present calculations yield better estimates of T_c and other parameters with respect to measured values.     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ⁻ could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ⊗ (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)⊗(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ⊗ (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ⁻ radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ⁿ⁻ fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Thermo-optic coefficients of monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The three thermo-optic coefficients of the biaxial laser host KLu(WO₄)₂ are measured at 633 nm by a deflection method. Their values at 300 K amount to ∂ n _g /∂ T=−7.4×10⁻⁶ K⁻¹; ∂ n _m /∂ T=−1.6×10⁻⁶ K⁻¹ and ∂ n _p /∂ T=−10.8×10⁻⁶ K⁻¹. Nearly athermal propagation directions are found for polarizations along the N _m and N _p dielectric axes.     

Effects of thermal and mechanical history on the viscoelastic properties of rigid poly(vinyl Chloride)

The effects of processing variables on the solid state properties of rigid PVC were studied by evaluating dynamic mechanical and tensile properties for thin film specimens of two different resins. The dynamic measurements were performed over the temperature range ?1]60 to 85°C, encompassing both the low temperature β transition and above ambient a transition (T_g). Engineering tensile strengths and energies to fracture were obtained at ambient conditions for several rates of elongation. Test specimens were prepared by solvent casting and compression molding techniques and subsequently were subjected to various thermal-mechanical histories. The results obtained were similar for both types of specimens and are described below. The various thermal histories considered include: (1) quick quenching from 225°C (samples referred to as “untreated”); (2) very slow (equilibrium) cooling after annealing at T_g; (3) quick quenching from T_g. In addition, the effects of frozen stresses were examined by systematically varying the stresses imposed on samples during the cooling processes 2 and 3. Increasing the load level imposed on specimens during equilibrium cooling resulted in enhancements of the β transition loss dispersion and tensile yield strength. Changes in loading during process 3, however, had little effect on the cooled specimens. But process 3 does alter the relaxation spectrum below T_g so that additional molecular relaxation is induced between T_β and T_α as much as 45°C below the a transition. The anomalous tan δ dispersions thus produced are accompanied by diminished tensile yield strengths and greatly increased energies to fracture. The most extreme case was encountered for the “untreated” specimens which were rapidly quenched from 225°C. The loss tangent data indicate remarkable differences in the region between T_β and T_α. When comparing the dynamic mechanical data with the fracture energy results for the same samples we note that increases in the intensity of the T < T_g anomalous dispersion correlate with increasing energies to fracture. On the other hand, the β transition intensity does not directly correlate. One molecular model which is consistent with these observations assumes that elongation induces a dilation of the polymer. Since most polymers possess Poisson ratios less than 0.5, the dilation will create extra internal volume (including free volume) in the polymer network. The increase in internal volume as elongation proceeds has the net effect of shifting the conditions of testing toward higher temperatures on a molecular relaxation scale permitting a higher level of molecular mobility at ambient conditions. As a sample continues to elongate one of two consequences is encountered: the imposed deformation cannot be accommodated by the available molecular mobility and the specimen fractures; or the deformation results in dilation to the extent that the response properties are shifted into a region of the relaxation spectrum where molecular mobility is sufficient for the specimen to accommodate the imposed deformation and yielding occurs. Yielding is expected if the effective temperature shifts as far as T_g before the sample fractures. In a case where there are additional molecular relaxation possibilities prior to the a transition, such as those in the anomalous dispersion region between T_β and T_α, sufficient dilation for yielding will be encountered before the normal T_g is reached. The anomalous T < T_g relaxation process thus tends to promote increased elongation and higher energies to fracture in PVC.     

Formation of rippled surface morphology during Si/Si （100） epitaxy by ultrahigh vacuum chemical vapour deposition

The Si epitaxial films are grown on Si (100) substrates using pure Si2H6 as a gas source using ultrahigh vacuum chemical vapour deposition technology. The values of growth temperature T_g are 650 ℃, 700 ℃, 730 ℃, 750 ℃, and 800 ℃. Growth mode changes from island mode to step-flow mode with T_g increasing from 650 ℃ to 700 ℃. Rippled surface morphologies are observed at T_g = 700 ℃, 730 ℃, and 800 ℃, but disappear when T_g = 750 ℃. A model is presented to explain the formation and the disappearance of the ripples by considering the stability of the step-flow growth.     

The effect of compositional variations on the glass-transition and crystallisation temperatures in Ge-Se-In glasses

The glass-transition (T_g) and crystallisation (T_x) temperatures of glassy Ge_xSe_yIn₁₂ (7≤x≤28) have been determined from differential scanning calorimetry measurements. The variations of T_g and T_x with composition have been specified. It has been found that T_g reaches a maximum at 614 K for the composition Ge_23.33 Se_64.67 In₁₂ while T_x passes through a minimum at 740 K for the same composition. The values of the cohesive energies of the studied compositions have also been estimated using the chemical bond approach method. It is found that the composition Ge_23.33Se_64.67In₁₂ possesses the maximum cohesive energy. These results are explained in terms of the structure of Ge-Se-In glasses. Received: 12 March 2001 / Accepted: 29 March 2001 / Published online: 23 May 2001     

Enthalpy Relaxation Study of Poly(Vinyl Chloride) Films Based on the Time-Temperature Superposition Principle

Abstract

In the enthalpy relaxation of poly(vinyl chloride), a decrease in enthalpy upon the isothermal ageing was measured using the differential scanning calorimetry method as a function of ageing time (t_A) and ageing temperature. The range of the ageing temperature was from 56?°C (T_g ? 25?°C) to 72?°C (T_g ? 9?°C) where T_g denotes the glass transition temperature. The limiting value of the decrease in enthalpy was determined by applying a stretched exponential function to the measured enthalpy data. The relaxation function (?) was derived from the measured enthalpy and the construction of a master curve was tried by shifting the ? ? t_A curves of the respective ageing temperatures horizontally. Although there was no agreement between the shift factors (a_T) and the relaxation times of the ? ? t_A curves, the superposition was successfully constructed and the a_T values obtained for the poly(vinyl chloride) sample were found to be comparable to those reported for viscoelastic experiments over a broad temperature range above and below T_g carried out for different polymers. The origin of the decrease in enthalpy was briefly discussed in terms of the chain dynamics in the isothermal condition.     

Thermal properties and structures of chlorocadmate, bromocadmate, and bromochlorocadmate glasses

Glass transition temperatures (T_g), crystallization temperatures (T_x), and ¹¹³Cd magic-angle spinning (MAS) NMR spectra of the chlorocadmate, bromocadmate, and bromochlorocadmate glasses and the CdCl₂, CdBrCl, and CdBr₂ crystals have been measured. The T_g and T_x, and thermal stabilities (T_x−T_g) decreased with increasing Br-content. No enhancement of (T_x−T_g) of bromochlorocadmate glasses by anion-mixing was observed. The CdCl₂ and CdBr₂ crystals gave the isotropic chemical shifts of 183 and −24 ppm, which are assigned to the CdCl₆ and CdBr₆ octahedra, respectively. The isotropic chemical shifts of CdBrCl crystal (186, 166, 135, 101, 63, 25 and −21 ppm) were assigned to CdBr_nCl_(6−n) (n=0-6) octahedra, respectively. It was found that the Br and Cl atoms in CdBrCl randomly occupy chlorine sites in the CdCl₂ structure. The ¹¹³Cd MAS NMR spectra revealed that the chlorocadmate, bromocadmate, and bromochlorocadmate glasses are composed of the CdCl₆, CdBr₆ and CdBr_nCl_(6−n) octahedra (n=0-6), respectively, and that the Cd²⁺ in all the bromochlorocadmate glasses was more preferentially bonded to Br⁻ than Cl⁻. The relationship between the thermal properties and the anion coordination environments around Cd²⁺ in these glasses is discussed.