Molecular dynamics of amorphous/crystalline polymer blends studied by broadband dielectric spectroscopy

The molecular dynamics of poly(vinyl acetate), PVAc, and poly(hydroxy butyrate), PHB, as an amorphous/crystalline polymer blend has been investigated using broadband dielectric spectroscopy over wide ranges of frequency (10⁻² to 10⁵ Hz), temperature, and blend composition. Two dielectric relaxation processes were detected for pure PHB at high and low frequency ranges at a given constant temperature above the T_g. These two relaxation peaks are related to the α and α′ of the amorphous and rigid amorphous regions in the sample, respectively. The α′-relaxation process was found to be temperature and composition dependent and related to the constrained amorphous region located between adjacent lamellae inside the lamellar stacks. In addition, the α′-relaxation process behaves as a typical glass relaxation process, i.e., originated from the micro-Brownian cooperative reorientation of highly constraints polymeric segments. The α-relaxation process is related to the amorphous regions located between the lamellar crystals stacks. In the PHB/PVAc blends, only one α-relaxation process has been observed for all measured blends located in the temperature ranges between the T_g’s of the pure components. This last finding suggested that the relaxation processes of the two components are coupled together due to the small difference in the T_g’s (ΔT_g = 35 °C) and the favorable thermodynamics interaction between the two polymer components and consequently less dynamic heterogeneity in the blends. The T_g’s of the blends measured by DSC were followed a linear behavior with composition indicating that the two components are miscible over the entire range of composition. The α′-relaxation process was also observed in the blends of rich PHB content up to 30 wt% PHB. The molecular dynamics of α and α′-relaxation processes were found to be greatly influenced by blending, i.e., the dielectric strength, the peak broadness, and the dielectric loss peak maximum were found to be composition dependent. The dielectric measurements also confirmed the slowing down of the crystallization process of PHB in the blends.     

Vitrification/devitrification phenomena during isothermal and nonisothermal crystallization of poly(aryl–ether–ether–ketone) (PEEK) and PEEK/poly(ether–imide) blends

We have established time–temperature transformation and continuous-heating transformation diagrams for poly(ether–ether–ketone) (PEEK) and PEEK/poly(ether–imide) (PEI) blends, in order to analyze the effects of relaxation control on crystallization. Similar diagrams are widely used in the field of thermosetting resins. Upon crystallization, the glass transition temperature (T_g) of PEEK and PEEK/PEI blends is found to increase significantly. In the case of PEEK, the shift of the α-relaxation is due to the progressive constraining of amorphous regions by nearby crystals. This phenomenon results in the isothermal vitrification of PEEK during its latest crystallization stages for crystallization temperatures near the initial T_g of PEEK. However, vitrification/devitrification effects are found to be of minor importance for anisothermal crystallization, above 0.1°C/min heating rate. In the case of PEEK/PEI blends, amorphous regions are progressively enriched in PEI upon PEEK crystallization. This promotes a shift of the α-relaxation of these regions to higher temperatures, with a consequent vitrification of the material when crystallized below the T_g of PEI. The data obtained for the blends in anisothermal regimes allow one to detect a region in the (temperature/heating rate) plane where crystallization proceeds in the continuously close proximity of the glass transition (dynamic vitrification). These experimental findings are in agreement with simple simulations based on a modified Avrami model coupled with the Fox equation. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 919–930, 1998     

Dynamic light scattering from bulk poly(n-hexylmethacrylate) near and above the glass transition

Photon correlation spectra of polarized scattered light from poly(n-hexylmethacrylate) PHMA (M_w = 1.6·10⁵, T_g = ?5°C) have been studied in the temperature range of ?2–25°C. The experimental time correlation functions over the time range 10^?6?10² s were represented by the Kohlrausch-Williams-Watts (KWW) function exp{?(t/τ)^β} with a virtually temperature-independent distribution parameter β = 0.27 ± 0.02. The observed relaxation functions were also analyzed in terms of a continuous distribution of retardation times L(τ) by means of a direct inverse Laplace transformation. The computed L(τ) distributions reveal a broad single peak structure in agreement with the results of the single KWW fit. The temperature dependence of τ is very similar to that of the shift factors obtained from measurements of the shear modulus and the stress relaxation modulus in the glass-rubber region. Conversely, the values of τ compare well with those extracted from the experimental dielectric loss peaks consistently represented in the time domain by the KWW function. These findings suggest that the slow density fluctuations in bulk PHMA are associated with the primary glass-rubber or α-relaxation, which, however, displays an unusual low apparent Arrhenius activation energy and a rather low β value. PHMA exhibits significant dynamic light scattering with correlation times faster than 10^?6 s near T_g. © 1992 John Wiley & Sons, Inc.     

Polyesters containing ring units in the main chain. II. Effects of size and mobility of rings on molecular relaxations

Molecular relaxations of polyesters containing C₅–C₁₅ rings in the main chain have been studied by DSC, dielectric dispersion, and NMR. Results are discussed in relation to the size and mobility of the rings. The T_g or α-relaxation peak moves to higher temperature with an increase in the ring size from C₅ to C₁₂, but the effect is accompanied by an even–odd alternation with ring size. The β relaxations in dielectric dispersion reflect local-mode motion of ester groups and are affected by steric interactions with the rings. Motions of the ring methylenes of C₁₂ and C₁₅ ring units are detected below T_g by broad-line NMR.     

α‐ and β‐Relaxations in neat and antiplasticized polybutadiene

Dielectric spectroscopy was carried out to measure the α‐relaxation (local segmental motion) and the higher frequency, secondary relaxation (β‐mode) in 1,4‐polybutadiene, both neat and containing a nonpolar diluent, mineral oil. The α‐relaxation shifted to lower frequencies (antiplasticization) in the presence of the diluent, suggesting the glass temperature of the latter is higher than the T_g of the polymer (i.e., >187K). The T_g of neat mineral oil cannot be determined directly, due to crystallization. While the diluent increased the magnitude of the α‐relaxation times, it had no effect on the β‐relaxation. Moreover, neither the shape of the α‐relaxation function nor its temperature dependence was influenced by the diluent. From this we conclude that the main effect of the mineral oil was to increase the local friction, without changing the degree of intermolecular cooperativity of the molecular motions. We also find that near the glass temperature, there is rough agreement between the time scale of the secondary relaxation process and the value of a noncooperative relaxation time estimated from theory. This approximate correspondence between the two relaxation times also holds for 1,2 polybutadiene. However, the β‐process cannot be identified with the noncooperative α‐relaxation, and the relationship between them is not quantitative. © 2000 John Wiley & Sons, Inc.* J Polym Sci B: Polym Phys 38: 1841–1847, 2000     

Photon correlation spectroscopy of bulk poly(n-hexyl methacrylate) near the glass transition

Slowly relaxing longitudinal density fluctuations in an optically perfect sample of bulk poly(n-hexyl methacrylate) (PHMA) have been studied by photon correlation spectroscopy in the temperature range 10–36°C. The glass transition temperature for this sample was measured to be T_g = −3°C by differential scanning calorimetry. The optical purity of the sample was verified by Rayleigh-Brillouin spectroscopy and the Landau-Placzek ratio was observed to be 2.3 at 25°C. Light-scattering relaxation functions were obtained over the time range 10⁻⁶-1 s. The shape of the relaxation functions broadened as the temperature was lowered towards the glass transition. Quantitative analysis of the results was carried out using the Kohlrausch-Williams-Watts (KWW) function to obtain average relaxation times, 〈τ〉, and width parameters, β. The width parameter decreased from 0.43 to 0.21 over the temperature interval, as suggested by visual inspection. Average relaxation times shifted with temperature in a manner consistent with previous mechanical studies of the primary glass-rubber relaxation in PHMA. The relaxation functions were also analyzed in terms of a distribution of relaxation rates, G(Γ). The calculated distributions were unimodal at all temperatures. The average relaxation times obtained from G(Γ) were in agreement with the KWW analysis, and the shape of the distribution broadened as the sample was cooled. The rate at which G(Γ) displayed a maximum correlated well with the corresponding frequency of maximum dielectric loss for PHMA. The temperature dependence of these two quantities could be reproduced with an Arrhenius activation energy of 21 Kcal/mol. A consistent picture of the molecular dynamics of PHMA near the glass transition requires a strong secondary relaxation process with a different temperature dependence from the primary glass-rubber relaxation. The present results suggest that the behavior of PHMA is similar to the other poly(alkyl methacrylates). © 1996 John Wiley & Sons, Inc.     

Dielectric studies of the effects of thermal history on secondary relaxation in bisphenol-a-polycarbonate

The dielectric permittivity and loss of Bisphenol-A-polycarbonate (PC) was measured over the frequency range 100 Hz to 200 kHz and temperature range 77–383 K. One sub-T_g relaxation peak is observed which rapidly broadens with a decrease in temperature. This is attributed to a progressive separation of the γ and β peaks, which at high temperatures are merged to form one peak of high strength. The strength of the sub-T_g relaxations decreases on physical aging of PC but is increased if the sample is quenched from a temperature above its T_g. Slowly cooled PC has a lower strength of its sub-T_g relaxation than a quenched specimen. The thermal history of PC affects the magnitude of its sub-T_g relaxation.     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Sub-TG relaxations in LiClO4-poly (propylene glycol)-2000 solutions

The dielectric permittivity and loss of LiClO₄ solutions in poly (propylene glycol (PPG)), molecular weight 2000, have been measured over a concentration range up to a ratio of Li⁺ to oxygen atoms in PPG of 33.3:100, between 77 and 350 K. The data have been analyzed in both the permittivity and electrical modulus formalisms. Addition of LiClO₄ to poly (propylene glycol) first increases the height of the β-relaxation peak, and ultimately a second sub-T_g relaxation peak at a higher temperature emerges. This is in addition to the β-relaxation peak due to the reorientation of PPG dipoles, whose strength decreases from that in pure PPG-2000. For a fixed temperature, the dc conductivity initially decreases with increasing Li⁺ concentration up to 20 Li⁺ per 100 O atoms and thereafter increases. This concentration corresponds to that at which the T_g of the solution reaches its limiting value of ca. 310 K. It is concluded that the formation of ion pairs causes a second and slower sub-T_g relaxation process and that the increase in the efficiency of chain packing reduces the strength of the β-relaxation of the polymer.     

Thermostimulated depolarization currents and thermoelectret effects in poly(methyl methacrylate)

The electrical dipole relaxation in PMMA has been studied by measuring thermostimulated depolarizing currents. A master curve for the segmental component of the dielectric constant has been constructed. The increment of the dielectric permittivity due to the α-relaxation has been determined. The distribution function of the relaxation times and the average relaxation times in the region from 70°C up to T_g = 105°C have been obtained. A way of describing the electret properties of the polymer is discussed.     

Dielectric relaxation spectroscopy of amorphous and liquid-crystalline side-chain polycarbonates

The molecular dynamics of amorphous and liquid-crystalline (LC) side-chain polycarbonates was studied by dielectric spectroscopy at frequencies from 10⁻² to 10⁶ Hz and at temperatures from −160 to 180°C. ‘Model’ compounds containing no mesogenic side-groups showed two relaxations, which originate from the carbonate group (α, β_m-relaxation). By contrast, in LC-polycarbonates bearing a mesogenic nitrostilbene side group around and above the glass transition temperature T_g up to three relaxation modes were distinguished (α-, λ₁-, λ₂-process); below T_g four secondary relaxations (γ-, β_m-, β_s-, β_sc-relaxation) were observed. The γ-relaxation was found only in compounds possessing an aliphatic spacer linked to the backbone by an ether bond. Apart from β_m-, two additional β-processes were identified as relaxations associated with the mesogenic unit in the glassy (β_s) or in the crystalline state (β_sc).     

Relaxations in thermosets. VI. Effects of crosslinking on sub-Tg relaxations during the curing and aging of epoxide-based thermosets

The dielectric permittivity and loss of diglycidyl ether of bisphenol-A-based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been measured over a temperature range 77–400 K after curing or aging for a predetermined duration. Of the two sub-T_g relaxations, the height of the γ relaxation peak monotonically decreases during both the cure and postcure periods, and the height of the β relaxation peak first increases to a maximum value and then decreases. This decrease is attributed to physical aging effects. The height of the α-relaxation peak decreases. The γ- and β-relaxation peaks become increasingly separated in temperature. A concept of accumulated equivalent curing time which is based upon known chemical kinetics has been introduced for use in both theoretical and practical aspects of the study of thermosets. It is shown that substantial curing of the sample occurs during its slow heating to the curing temperature. The use of this concept in the curing of thermosets is illustrated. A procedure for the analysis of the distribution of relaxation times from a set of results limited in both frequency and temperature range is described. The distribution parameter is 0.20 and 0.16 for the γ and β process, respectively, and remains constant with postcuring and physical aging. The distribution parameter for the α process decreases from 0.60 to 0.36 on curing.     

Dielectric relaxations and electrical conductivities of poly(alkyl methacrylates) under high pressure

Dielectric properties of four methacrylate polymers (methyl, ethyl, n-butyl and n-octyl) were studied in the frequency range 0.0001 cps–300 kcps at temperatures above and below the glass transition temperature and at various pressures up to 2500 atm. At temperatures well above T_g a single relaxation peak (α′ peak) was observed in the case of the higher n-alkyl methacrylates. However, this peak was split into two peaks, α and β, with decrease in temperature or increase in pressure. The molecular motions corresponding to the α and the β relaxation processes are the micro-Brownian motions of amorphous main chains and of flexible side chains, respectively. From the temperature and the pressure dependence of the average dielectric relaxation time of these polymers the single relaxation process (the α′ process) was attributed to the micro-Brownian motion of the main chain coupled with that of the side chain. The effects of temperature and pressure on the d.c. conductivity of these polymers were also studied.     

Conductance and relaxations in the glassy and rubber states of aqueous poly( vinyl pyrrolidone): A cryofixation medium

The dielectric permittivity and loss of poly(vinyl pyrrolidone), molecular weight 40,000, containing 40% (by weight) water have been measured over the temperature range 77–325 K and frequency range 12 Hz to 0.1 MHz. A prominent relaxation due to rotational diffusion of water molecules in a hydrogen-bonded structure occurs at T < T_g (237 K). The half-width of the dipolar relaxation spectra is 2.27 decades and is temperature independent, which is strikingly different from the corresponding features of pure polymers. It is concluded that H-bonded amorphous solid water persists in the glassy polymer matrix and that the H-bonded structure contains the pyrrolidone side groups of the randomly oriented chain. The relaxation peak at T near T_g is masked by a large dc conductivity which, when expressed in terms of electric modulus, has a spectrum of half-width 1.37 instead of 1.14 decades expected for dc conductivity alone. The contribution from dipolar reorientation in the glass-rubber range of the PVP-H₂O solution is smaller than that in its sub-T_g relaxation.     

Characteristic length of the glass transition

The definition of molecular cooperativity is discussed. The characteristic length of the glass transition describes the size of this cooperativity. Differential scanning calorimetry (DSC) and heat capacity spectroscopy (HCS) results of a series of poly(n-alkyl methacrylates) (alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, and octyl) and a series of statistical copolymers poly(n-butylmethacrylate-stat-styrene) are discussed in terms of molecular cooperativity in the αβ splitting region, where a high-frequency dispersion zone a splits off into the main transition zone α and a Goldstein Johari process β at lower frequencies. The characteristic length tends to small values of order one monomer diameter in the splitting region for scenarios with an α relaxation onset. The statements about the size scale of cooperativity are conditional upon certain assumptions leading to the equation used for calculation of this size from HCS and DSC data. The step height of heat capacity (Δc_p) and, with less certainty, the square root of the cooperativity volume or number (V^1/2_α or ^1/2_α) are proportional to the temperature distance from the cooperativity onset, T = T_ons. © 1996 John Wiley & Sons, Inc.     

Molecular dynamics in fluorinated side-chain maleimide copolymers as studied by broadband dielectric spectroscopy

A series of alternating maleimide (MI) copolymers with fluorinated side chains have been investigated using broadband dielectric spectroscopy. The side chains consist of fluoroalkane (–C _x F_2x+1, x=1, 7, 9) end groups connected to the main chain via methylene spacers. The experiments were carried out in a frequency range of 0.1 Hz to 10 MHz and at temperatures between 120 K and 500 K. The fluorinated MI copolymers show a fast sub-T _g (β) relaxation characterized by an Arrhenius-type temperature dependence with activation energy in the range of 30–37 kJ/mol. Two more processes (α and δ-like) are observed, corresponding to independent relaxations of the main chain and the fluoroalkane domains respectively. For shorter side chains, the δ-like process is not observed but instead another relaxation process, α _S , occurs at temperatures higher than either the α and δ-like processes. When compared with unfluorinated MI copolymers, the fluorinated MI copolymers show the δ-like process and a slower β-relaxation unlike their unfluorinated counterparts. A model to explain the molecular origin of the four processes is proposed, supplemented by differential scanning calorimetry and published WAXS/SAXS data.     

Phase transitions and relaxation processes in ethylene-vinyl acetate copolymers probed by fluorescence spectroscopy

The steady-state fluorescence of pyrene and anthracene are used to investigate the relaxation processes of several random ethylene-co-vinyl acetate copolymers, EVA, with defined comonomer compositions (EVA-9, EVA-18, EVA-25, EVA-33 and EVA-40). The temperature of the relaxation processes are compared with those of low-density polyethylene (LDPE) and poly(vinyl acetate) (PVAc). The polymer relaxation processes are assigned to T_g=300-310 K (glass transition temperature of the PVAc); T_α=270-300 K (relaxation processes of the ethylene units present in LDPE and EVA); T_g=220-250 K (glass transition of the LDPE and of the EVA); T_γ or T_β=160-190 K (relaxation processes of interfacial defects of methylenic chains of LDPE and rotation of the acetate group of the PVAc and the EVA); and T_γ=90-130 K (relaxation processes of small sequences of methylene units of LDPE and end groups of PVAc). An Arrhenius-type function was employed as an attempt to represent the experimental data of fluorescence intensity versus temperature above the γ-relaxation temperature. As obtained with other techniques, there is not a simple relationship between the polymer relaxation processes and the vinyl acetate content that can be explained by the morphology in these copolymers.     

Molecular dynamics and conduction mechanism of poly(vinyl chloride-co-vinyl acetate-co-2-hydroxypropyl acrylate) terpolymer containing ionic liquid

Dielectric spectroscopy (DS) measurements were performed to probe the segmental dynamics and ion mobility of poly(vinyl chloride-co-vinyl acetate-co-2-hydroxypropyl acrylate) terpolymer dopped with different amounts of tetrabutylammonium tetrafluoroborate ([TBA] [BF₄]) ionic liquid (IL). Differential scanning calorimetry (DSC) was also employed to trace the change in the glass transition temperature (T_g) at different loads of IL. The DSC measurements revealed a remarkable reduction in the PVVH T_g from 344 to 310 K just by adding 20 wt% of IL. The DS measurements revealed three relaxation processes named α, β₁, and β₂. The α-process is related to the segmental motion of PVVH while the β₁ and β₂ are due to the restricted local dynamics of side chains. The segmental relaxation times (α-relaxation) speed up with increasing the concentration of IL due to the plasticization effect of IL on polymer chains. The temperature dependence of α-relaxation follows the Vogel-Fulcher-Tammann (VFT) relation with dynamic glass transition between 323 and 294 K in agreement with the DSC measurements. The β₁ and β₂-relaxations have an Arrhenius temperature dependence. The temperature dependence of ionic conductivity obeys the VFT behavior indicating the coupling between the segmental motion of PVVH chains and ion transport. Polaronic tunneling is the predominant conduction mechanism in PVVH and its composites. The specific capacitance increases with increasing both the temperature and IL concentration.     

Effects of diluent on molecular motion and glass transitions in polymers. III. The system poly(vinyl acetate)–toluene

Dielectric measurements, differential thermal analyses (DTA), and broad-line proton magnetic resonance (NMR) measurements are reported on the system poly(vinyl acetate)–toluene. Four dielectric relaxations were observed between 80 and 400°K. From proton NMR measurements on solutions in toluene and in deuterated toluene, the relaxation processes can be assigned, respectively, to segmental motion of poly(vinyl acetate), α; motion of side group, β′ rotation of toluene, β; local motions of poly(vinyl acetate) and toluene, γ, in order of appearance with decreasing temperature. Two stepwise changes in DTA traces have been observed and can be assigned as glass transition points T_gI and T_gII. Comparison of these glass transition points with temperatures at which dielectric relaxation times for the α and β processes are 100 sec, indicate that segmental motion of poly(vinyl acetate) and rotation of toluene are frozen-in at T_gI and T_gII, respectively. Activation plots for the α process conform to the Vogel–Tamman equation. In terms of the parameters A, B, and T₀ of the equation, T_gI can be represented by an expression of the form T_gI ≈ T₀ + B/(A + 3). In the range of concentration above 50% by weight, A and B are almost independent of concentration but T₀ varies strongly. The nature of the secondary dispersions is also discussed.