Dynamic light scattering in solid polymers

The viscosity of an amorphous polymeric solid above its glass transition [T _g (T,P)] increases as the temperature of the solid is decreased or the pressure is increased. Under changes in temperature or pressure, molecular subunits in the polymeric solid undergo configurational changes. Such changes or relaxations have a distribution of relaxation strengths and times. As the solid is cooled or as the hydrostatic pressure on the solid is increased, the relaxation strengths increase and the relaxation times increase. These changes in relaxation or dynamic properties are very dramatic as the empirical T _g is approached. Near T _g the polymeric solid is no longer in volume equilibrium; continued cooling or pressuring at a time rate faster than the average relaxation time will produce a polymeric glass. This glass is a nonequilibrium, amorphous solid. If the glass is held at a fixed temperature and pressure very close to, but below, T _g , the volume of the glass will be observed to relax to its equilibrium value. For temperatures and pressures well below T _g , equilibrium is a much more conjectural concept since the relaxation times become extremely long. It has been proposed^1,2 that there is a characteristic temperature T _g at which an amorphous polymer undergoes a second-order transition to an equilibrium glass with zero configurational entropy (i.e., a noncrystallizable solid).     

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     

Librational dynamics of nitroxide molecules in a molecular glass studied by echo-detected EPR

Nitroxides 2,2,6,6-tetramethyl-4-piperidone N-oxide (tempone), 3-carboxy-proxyl and potassium peroxylamine disulfonate (Fremy salt) in glycerol solution were studied in a wide temperature range near the glass transition temperatureT _g. The echo-detected (ED) electron paramagnetic resonance (EPR) lineshape reveals strong dependence on the time interval τ between the echo-forming microwave pulses which is readily explained by anisotropic phase relaxation. Employing a librational model of molecular motion and the Redfield relaxation theory, spectra were simulated for the τ’s varying in a large interval. The anisotropic relaxation rate increases with temperature increase and it is larger for nitroxide with a larger molecular size. The mean-squared amplitude of motion, obtained from reduced hyperfine splitting in continuous-wave EPR, near T_g linearly depends on temperature which is characteristic of harmonic solids. For tempone in a host crystal 2,2,4,4-tetramethyl-cyclobutan-1, 3-dione the anisotropic spin relaxation rate decreases with temperature increase so the found feature solely belongs to a glassy state. A new approach is proposed for modeling slow wobbling motion in a restricted angular space.     

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.     

Specific heat of around the glass transition

Dynamic calorimetric measurements are performed for the quaternary metallic glass Zr₆₅Al_7.5Cu_17.5Ni₁₀ in order to analyse the dependence on different heating rates for the glass transition temperature T_g. We compare two different temperature programs used for sample relaxation, to estimate the influence of the thermal history on T_g. A lower limit for the glass transition temperature T_g was calculated according to two different models based on the fact, that width and temperature of the glass transition depend on the experimental time scale set by the heating rate: One model assumes a Vogel-Fulcher-Tammann type behaviour, as used to describe more or less “fragile” glass formers and the other assumes an Arrhenius-like behaviour, which is related to “strong” glass formers. The values obtained from both models differ by about 80K. From additional absolute specific heat capacity measurements we calculate the Kauzmann temperature T_K, as a lower limit for the temperature of the glass transition from thermodynamic aspects. Comparing T_K with the temperature values obtained from the two evaluation models we can classify the quaternary metallic glass Zr₆₅Al_7.5Cu_17.5Ni₁₀, to behave more like a “strong” glass former. Received: 23 January 1998 / Received in final form and Accepted: 31 August 1998     

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     

Measuring surface and bulk relaxation in glassy polymers

We present a comprehensive study of gold nanoparticle embedding into polystyrene (PS) surfaces at temperatures ranging from T _g + 8 K to T _g − 83 K and times as long as 10⁵ minutes. This range in times and temperatures allows the first concurrent observation of and differentiation between surface and bulk behavior in the 20nm region nearest the free surface of the polymer film. Of particular importance is the temperature region near the bulk glass transition temperature where both surface and bulk processes can be measured. The results indicate that for the case of PS, enhanced surface mobility only exists at temperatures near or below the bulk T _g value. The surface relaxation times are only weakly temperature dependent and near T _g , the enhanced mobility extends less than 10nm into the bulk of the film. The results suggest that both the concept of a “surface glass transition” and the use of glass transition temperatures to measure local mobility near interfaces may not universally apply to all polymers. The results can also be used to make a quantitative connection to molecular dynamics simulations of polymer films and surfaces.     

Initial stage of physical ageing in network glasses

An atomistic view on Johari–Goldstein secondary β-relaxation processes responsible for structural relaxation far below the glass transition temperature (T_g ) in network glasses is developed for the archetypal chalcogenide glass, As₂₀Se₈₀, using positron annihilation lifetime, differential scanning calorimetry, Raman scattering and nuclear magnetic resonance techniques. Increased density fluctuations are shown to be responsible for the initial stage of physical ageing in these materials at the temperatures below T_g . They are correlated with changes in thermodynamic parameters of structural relaxation through the glass-to-supercooled liquid transition interval. General shrinkage, occurred during the next stage of physical ageing, is shown to be determined by the ability of system to release these redundant open volumes from the glass bulk through the densification process of glass network.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Influence of surface interactions on the dynamics of the glass former ortho-terphenyl confined in nanoporous silica

We present results on investigations of the dynamics of the glass forming ortho-terphenyl (oTP) confined in nanoporous silica. Calorimetry experiments showed that the glass transition temperature of the confined liquid, T_gconf, has a non-trivial pore size dependence and is strongly affected by surface interactions. Fluid-wall interactions introduce gradients of structural relaxation times in the pores. The molecules at the surface of the pores are slowed down compared to those at the center of the pores. We focus here on a pore diameter range (7 σ< d < 12 σ, where σ is the molecular diameter), where a large variety of dynamical behavior were observed. Depending on surface properties of the confined media, T _gconf may be smaller or larger than the bulk one. In a quite attractive matrix with a pore size of around 7 nm, the structural relaxation times gradient is important enough to allow the observation of two glass transitions for the same liquid. Effects of fluid wall interactions on the short time dynamics at high temperature were also investigated by quasielastic neutron scattering. The self and collective motions exhibit well above the bulk melting point the same dependence on fluid-wall interactions as at T_g.     

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T _g , the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T _g , revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.     

Thermal and optical analysis of Te-substituted Sn–Sb–Se chalcogenide semiconductors

Bulk amorphous samples of Te-substituted Sn₁₀Sb₂₀Se_70−X Te _X (0≤X≤12) were prepared using a melt quenching technique. Calorimetric studies of the samples were performed using differential scanning calorimetry (DSC) and the glass transition temperature and crystallization temperature were evaluated from DSC scans. The glass transition temperature T _g exhibits a sharp decrease for small Te substitution of X=2, thereafter increases with increase in Te content up to X=10, and then decreases for further Te substitution. The apparent activation energy for glass transition and the activation energy for crystallization were calculated using Kissinger, modified Kissinger, and Matusita equations. The change in glass transition temperature T _g has been explained based on the bond formation energy of different heteropolar bonds. The optical band gap of thermally evaporated thin films of Sn₁₀Sb₂₀Se_70−X Te _X (0≤X≤12) was calculated from reflectance and transmittance data. The optical band gap variation with tellurium content exhibits a sharp decrease for an initial tellurium substitution of X=2 similar to that of the glass transition temperature and thereafter a peak is observed in optical band gap around X=4 composition.     

Dielectric relaxation of poly(ethylenglycol)- b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers above the glass transition temperature

The complex dielectric permittivity has been measured for three poly(ethylenglycol)-b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers with different content of poly(ethylenglycol) (15%, 33% and 80%), and increasing degree of crystallinity (0%, 10% and 20%, respectively). Only the non-crystalline sample shows the normal mode relaxation together with the segmental (α-relaxation) and the Johari-Goldstein (β-relaxation) modes. The crystalline samples show also polarization contributions due to the existence of interfaces between the crystallites and the amorphous phase. The relaxation times of the (α and normal modes can be described by a VFT equation with the same value of T₀. There is a slowing-down of the segmental mode due to the presence of crystallites. The temperature dependence of the α and β relaxations in the copolymers is very similar to that found in pure PPG, while there are significant differences in the case of the normal mode of the non-crystalline sample. The size of the cooperatively rearranging regions CRR, and the width of the glass transition region increase slightly with the degree of crystallinity. The temperature dependence of the size of CRRs is compatible with the prediction of fluctuation theory. No systematic effect of the degree of crystallinity on the β-relaxation has been found. Near T _g the β-relaxation time is close to the primitive time of the coupling model. Received: 31 May 2000     

Segmental Dynamics in net -poly(methyl methacrylate)- co -poly(n-butyl acrylate) Copolymer Networks

Dynamic mechanical spectroscopy and differential scanning calorimetry investigations of segmental dynamics are reported for net-poly(methyl methacrylate)-co-poly(n-butyl acrylate) copolymer networks. Three characteristic temperatures, namely, Vogel (T_∞), glass transition (T _g ), and crossover (T _c ), were used to define cooperativity range and a new reduced temperature parameter (Solidness, S). The results showed that broadness of the α -dispersion (glass transition) and cooperativity length scale at the glass transition temperature decreased with increasing butyl acrylate content and T _g -scaled temperature dependence of the relaxation time (fragility). However, the cooperativity range (T _c –T_∞), decreased with increasing fragility index. Furthermore, the solidness at T _g (S(T _g )) was nearly independent of chemical structure of the samples. Finally, a correlation was found between two measures of cooperativity length scale in the glass transition region, namely, average volume of cooperatively rearranging regions, V _CRR , and the number of basic units in an act of rearrangement in the glass transition region, Z(T _g ), determined from two completely independent experimental techniques.     

Qualitative discrepancy between different measures of dynamics in thin polymer films<Superscript>⋆</Superscript>

We have used ellipsometry to measure the initial stages of interface healing in bilayer polystyrene films. We also used ellipsometry to measure the glass transition temperature T_g of the same or identically prepared samples. The results indicate that as the film thickness is decreased, the time constant for the interface healing process increases, while at the same time the measured glass transition temperature in the same samples decreases as the film thickness is decreased. This qualitative difference in the behavior indicates that it is not always possible to make inferences about one probe of polymer dynamics from measurements of another. We propose a reason for this discrepancy based on a previously discussed origin for reduction in the T_g value of thin films.     

Kinetics of glass transition and thermal stability of?Se58Ge42?xPbx?(9≤x≤20) glasses

Se₅₈Ge_42−x Pb _x (9≤x≤20) glasses have been prepared using conventional melt quenching technique. Differential Scanning Calorimetric (DSC) measurements show single glass transition and double crystallization, which indicate the occurrence of phase separation in the samples. The phases present in the samples were identified using XRD. The kinetics of the glass transition has been studied in terms of the variation of glass transition temperature with composition and heating rate. In addition to this, activation energy of the glass transition (E _t ) has also been evaluated and its composition dependence is also investigated. The thermal stability of these glasses has been investigated using various stability criteria: Deiztal first glass criterion, ΔT, Saad and Poulain weighted thermal stability, H′ and the S-parameter. The values of these parameters were obtained using various characteristic temperatures such as the glass transition temperature, T _g , the onset temperature of crystallization, T _c , and the peak crystallization temperature, T _p . The values of stability parameters show that the phase corresponding to second crystallization is more stable than the phase corresponding to first one. The stability in terms of the lead (Pb) content has been determined considering the values of stability parameters of the phase corresponding to second peak. It was found that the stability increases with the lead content.     

Revisiting the Dielectric Relaxation of Ethylene-Vinylacetate Copolymers: Influence of Microstructure

The dielectric relaxation behavior of a series of ethylene-vinylacetate (EVA) copolymers was investigated by measuring the complex dielectric permittivity in a broad frequency and temperature range. Crystallinity of EVA copolymers was estimated by differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS). The shape of the higher temperature relaxation, appearing above the glass transition temperature T _g depends on the VA content. It was found that this relaxation was asymmetric for VA concentrations higher than 40 wt% and changed to a symmetric shape at lower VA values. Concurrently, as the VA content decreased, a major broadening of the relaxation over a wide frequency range was observed. It is found that the dielectric relaxation was preserved on going through the melting range of the semicrystalline samples, although it exhibited changes of its characteristic parameters that are typical for segmental relaxation appearing at T _g. This finding allows one to associate this relaxation to the segmental motions at T _g in the amorphous phase and not to the existence of interfacial regions.     

Dynamics of α-Tocopherol Acetate: Proton Relaxation Studies Supported by Molecular Dynamics Simulations

Dynamical properties of α-tocopherol acetate (commonly known as vitamin E) have been investigated in a broad temperature range (below and above the glass transition) by means of proton spin–lattice relaxation. Two distinct relaxation processes have been detected in the studied temperature range. One of them, present in the solid phase, has been attributed to reorientation of methyl groups. In order to identify the motional process leading to the proton relaxation above the glass transition temperature (T _g), molecular dynamics (MD) simulations have been performed, which provided time correlation functions for several internuclear vectors in the molecule. The high-temperature relaxation process is primarily due to dynamics of the aromatic rings of the tocopherol molecule; however, a considerable contribution of diffusion of the aliphatic chain cannot be excluded. Comparing the nuclear magnetic resonance (NMR) results with MD and relaxation data of dielectric spectroscopy (DS) available in the literature (K. Kamiński, S. Maślanka, J. Zioło, M. Paluch, K.J. McGrath, C.M. Roland, Phys Rev E 75:011903-7, 2007; E. Szwajczak, J. Świergiel, R. Stagraczyński, J. Jadżyn, Phys Chem Liq 47:460–466, 2009), the motional process observed in NMR relaxation studies above T _g has been identified with the δ process observed in DS.     

dielectric relaxation in VDF<Subscript>60</Subscript>/Tr<Subscript>40</Subscript> and VDF<Subscript>88</Subscript>/Te<Subscript>12</Subscript> polar copolymers embedded in porous glass matrices

The dielectric properties of composite materials prepared by embedding P(VDF₆₀/Tr₄₀) and P(VDF₈₈/Te₁₂) polar copolymers in porous glass matrices with a mean flow-through pore diameter of around 320 nm were investigated in the temperature range 200–450 K. Strong dielectric relaxation, the characteristic time of which conformed to the Williams-Landel-Ferry law, was observed in the vicinity of glass transition point T _g of an amorphous fraction of polymer inclusions. An increase (≈10 K) in the T _g temperature of the amorphous fraction of incorporated polymeric materials was detected.     

Glass transition and dynamics of single and stacked thin films of poly(2-chlorostyrene)

The glass transition temperature and the dynamics of the α-process have been investigated using dielectric relaxation spectroscopy for single and stacked thin films of poly(2-chlorostyrene) (P2CS). The stacked film consists of 10 layers of single thin films with thickness of 12 nm or 18 nm. The glass transition temperature T _g of the single thin films of P2CS is found to decrease with decreasing film thickness in a similar way as observed for polystyrene thin films. The magnitude of the depression of T _g for the stacked thin films is larger than that of the single thin films with corresponding thickness. The depression of the temperature at which the dielectric loss shows a peak due to the α-process at a given frequency, T _α, is larger than that of the single thin films, although the magnitude is smaller than that of T _g . Annealing at a high temperature could cause the T _g and T _α of the stacked thin films to approach the values of the bulk system.