Effect of temperature and molecular weight on enthalpy relaxation in polystyrene

Isothermal enthalpy relaxation in polystyrene was measured as a function of temperature and molecular weight on a differential scanning calorimeter. Relaxation spectra were derived from the data and expressed as a distribution of relaxation times. For a given molecular weight the relaxation spectra at different temperatures could not be superimposed by a shift in time. The relaxation curves of samples of different molecular weights could be superimposed only when the difference between the temperature at which the relaxation was monitored (T_a) and their respective T_g was the same. The relaxation spectrum at any temperature for a given molecular weight was also expressed as a distribution of energies. The average energy represented by this distribution was associated with an activation energy required for the motion of a chemical repeat unit. The activation energy extracted from the temperature shift in the relaxation spectra corresponded to the motion of a statistical unit (Kuhn's segment) in polystyrene.     

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.     

Entanglement and network formation in polystyrene: Viscoelastic behaviour from pulsed NMR

A series of NMR proton spin-spin relaxation measurements in three monodisperse polystyrene samples over a range of temperatures shows the conditions required for the existence of a dynamic network in polystyrene due to entanglements. The density of entangled units, N_e, i.e. their number per unit mass, can be determined by this NMR technique and is found to decrease with increasing temperature, in a manner which indicates its dependence on free volume, as in viscosity. The T₂₁ relaxation time for low molecular weight-polystyrene and T_2S for high molecular weight polystyrene increase with increasing temperature approximately as does (viscosity)^−0.5. The NMR data provide a quantitative value for the elastic modulus, and its dependence on temperature, both being in agreement with the experimental data previously obtained from viscoelasticity. The model can be extended to analyse creep and subsequent recovery. The transition in viscosity from a M¹ to a M^3,4 can also be deduced from the NMR results.     

Properties of amorphous and crystallizable hydrocarbon polymers. II. Rheology of linear and star-branched polybutadiene

Some results are reported on the linear viscoelastic properties of polybutadienes with narrow-molecular-weight distributions. The zero shear viscosity η₀ varies as M^3.4 in the linear samples, and viscosity enhancement is found in star-branched samples with long arms, in good agreement with results reported earlier by Kraus and Gruver. The temperature coefficient of viscosity appears to be slightly larger in stars when the arms become long. The steady state recoverable compliance J is 2.1 × 10 ^?7 cm²/dyn in linear samples of high molecular weight, but it increases to values as much as 10 times larger in the stars. The plateau modulus G, obtained from a composite curve for the linear samples, is 1.32 × 10⁷ dyn/cm². The terminal relaxation spectrum of the stars is too broad to allow an evaluation of plateau modulus.     

Studies of micro-brownian motion of a polymer chain by the fluorescence polarization method. I. Fluorescent conjugates of polyacrylamide

Polyacrylamide having a fluorescent residue at the chain end was prepared by polymerization of acrylamide in the presence of a fluorescent dye. The segmental motion of the chain end in dilute solution was studied by the fluorescence polarization method on the fluorescent polyacrylamide conjugates thus obtained. The linear relation between 1/p and T/η₀ held for every sample studied in aqueous media, where p is the degree of polarization of the fluorescence, T is the absolute temperature, and η₀ is the viscosity of the medium. The mean relaxation time 〈ρ〉 of the conjugate was evaluated from these data as a function of the molecular weight of the conjugate. The value of 〈ρ〉 increased slightly with molecular weight, varying from 3.3 × 10^?9 to 7 × 10^?9 sec. The absolute values of 〈ρ〉 and its molecular weight dependence suggest that 〈ρ〉 represents the mean rotational relaxation time for the cooperative motion of about ten monomeric units at the chain end. The effect of the mean extension of polymer chain on the segmental motion was found to be negligible.     

Phosphorescence studies of relaxation effects in bulk polymers. II. Emission depolarization study of relaxation mechanisms in poly(methyl methacrylate)

Phosphorescence depolarization measurements, under steady state polarized excitation, have been used to examine the relaxation behavior of bulk poly(methyl methacrylate) (PMMA). Poly(methyl methacrylate) bearing phosphorescent labels has been synthesized by copolymerization of small quantities of acenaphthylene (I), 1-vinylnaphthalene (II), 2-vinylnaphthalene (III), 1-naphthyl methacrylate (IV), and 2-naphthyl methacrylate (V), respectively, with methyl methacrylate. In no case was depolarization of emission due to probe rotation apparent below the onset of the β-relaxation of the polymer. Rotation of label V was characterized by an activation energy of 94 kJ mole^?1 in excellent agreement with that of the β relaxation measured by conventional relaxation techniques. This result clearly implicates ester motion in the β relaxation. No motion of label I, which cannot move independently of the polymer backbone, was evident in the vicinity of the β relaxation. Above 378 K the activation energy for rotational relaxation of label I of 460 kJ mole^?1 is in excellent agreement with published data for the α transition in PMMA. This result is in accord with the general assumption that backbone segmental motion is involved in the α relaxation. However, backbone motion of lesser temperature dependence (E_a = 115 kJ mole^?1) is apparent from depolarization behavior of probe I between 343 and 378 K. Label II shows three regions of relaxation behavior. In the temperature range above the β transition motion of the label independent of the polymer is evident (E_a = 44 kJ mole^?1). At temperatures in excess of 343 K this motion becomes cooperative with that of the backbone yielding activation energies comparable to those obtained in system I. Label III, while exhibiting depolarization characteristics similar to those of label II in the vicinity of the β relaxation, emitted insufficient intensity to permit estimation of an energy of activation for the motion. The phosphorescence of label IV was completely depolarized over the entire temperature range studied. While phosphorescence intensity and lifetime data may be used to detect the existence of polymeric transitions, the photophysical behavior of the naphthalene species studied is independent of the attachment to the polymer and does not primarily yield information regarding the polymer relaxations.     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Dielectric and impedance properties of Sr(Sm0.5Nb0.5)O3 ceramics

Perovskite types Sr(Sm_0.5Nb_0.5)O₃, (SSN) ceramics have been prepared through solid state reaction route. The scanning electron microscopy provides information on the quality of the samples and uniform grain distribution over the surface of the samples. The field dependence of the dielectric response was measured in a frequency range from 50 Hz to 1 MHz and in a temperature range from 60 °C to 420 °C indicates polydispersive nature of the materials. An analysis of the dielectric constant (?′) and tangent loss (tanδ) with frequency is performed assuming a distribution of relaxation times as confirmed by the scaling behavior of electric modulus spectra. The frequency dependence of the electric modulus peak is found to obey Arrhenius law with activation energy of ∼0.026 eV. The complex plane impedance plot shows the grain boundary contribution for higher value of dielectric constant in the law frequency region. The frequency dependence of electrical data is also analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behavior of imaginary part of electric modulus M″ suggests that the relaxation describes the same mechanism at various temperatures in SSN.     

Precipitation polymerization of acrylamide using vazo-33 as an initiator and acetonitrile/water mixtures as the solvent

Precipitation polymerization of acrylamide initiated by a thermal initiator, Vazo-33 (DuPont Vazo Initiator), was achieved at a solvent composition of acetonitrile/water = 4/6 (vol/vol). The polymerization kinetics were investigated in the acrylamide [M] concentration range 0.86–2.27M, Vazo-33 [I] concentration range 1.4–11.0 × 10^?4M, and temperature range 30–40°C. Polymerization was carried out in reaction ampules and the rate was determined gravimetrically. Number-average molecular weight was obtained from intrinsic viscosity. The precipitation polymerization rate varied as [M]^2.16 and [I]^0.44. Number-average molecular weight was proportional to [M]^1.22 and inversely proportional to [I]^0.31. The overall reaction activation energy was calculated as 17.3 kcal/mol in the temperature range studied. The optimal reaction conditions studied were: acetonitrile/water = 4/6, temperature = 40°C, [M] = 1.95M and [I] = 2.8 × 10^?4M. One hundred percent conversion was achieved in 90 min and a polymer with a number-average molecular weight of 1,200,000 was obtained.     

Critical molecular weight for onset of non-newtonian flow and upper newtonian viscosity of polydimethylsiloxane

The flow curves of fractionated polydimethylsiloxanes of different molecular weights were obtained over a wide range of shear rates, from 3 × 10^?1 to 4.3 × 10⁶ sec^?1, by use of a gas-driven capillary viscometer designed to decrease the experimental error in high shear rate region. Non-Newtonian flow can occur at molecular weights below the critical molecular weight M_c for the entanglement of polymer chain. The critical molecular weight M′_c for the onset of the non-Newtonian flow is identical with that of the segment of viscous flow. For the polymer of molecular weights from M′_c to M_c, the upper Newtonian viscosity increases with an increase in molecular weight. Above M_c, the upper Newtonian viscosity is almost independent of the molecular weight.     

Dynamic birefringence studies of high-density polyethylene

A rheo-optical investigation has been carried out on a sample of high-density polyethylene (HDPE) in an attempt to examine the nature of the α-relaxation mechanism. Dynamic mechanical and bi-refringence behavior was measured over the frequency range of 0.008-4.3 Hz and temperature range ?40 to 100°C. The dynamic mechanical and birefringence data were reduced to a reference temperature of 50°C by a combination of horizontal and vertical superposition. The significance of the vertical shift factor has been discussed extensively in previous papers and is not dealt with here. An Arrhenius plot was made of the log of the horizontal shift factor versus reciprocal temperature for the mechanical and optical data. The mechanical data exhibited three distinct regions, the slopes of which led to activation energies of 70, 90, and 150 kJ mol^?1. The temperature at which these dispersions occurred suggested the observation of the β, α₁, and α₂ relaxation processes. The optical data contained two distinct regions from which activation energies of 55 and 95 kJ mol^?1 were obtained. The high-temperature α₂ process was not observed in the Arrhenius plot; however, a maximum in K′ and a change in sign of K″ probably reflects a contribution from the α₂ relaxation mechanism.     

Thermoplastic elastomers by hydrogen bonding 1. Rheological properties of modified polybutadiene

Polybutadiene of narrow molecular weight distribution was modified using 4-phenyl-1, 2,4-triazoline-3,5-dione. The degree of modification was 1% and 2% with respect to the repeating units. Hydrogen bonding between the highly polar urazole groups thus incorporated into the polymer gives rise to the formation of a thermoreversible elastomeric network. Dynamic mechanical measurements in the temperature range between 220 and 330 K support the picture of the thermoreversible hydrogen bond interaction. The rubber elastic plateau is shifted to higher temperatures and lower frequencies. The increase in the plateau modulus cannot be attributed solely to the contribution of the network structure but is mainly a consequence of the broadening of the relaxation time spectrum in the modified samples. From the temperature dependence of the shift factors log(a _T ) it is concluded that the general WLF approach fails. The strong temperature dependence of the apparent activation energy of flow is a consequence of the temperature dependence of the hydrogen bond interaction.     

Contribution of Polymer‐Solvent Interactions to Dynamics of Linear Polymers in Dilute Solutions

In this work a theoretical approach to dynamics of linear vinyl polymers in dilute solutions of high viscosity solvents is presented. The calculations for the relaxation time spectra, polymer intrinsic viscosity [η (ω)], complex elastic modulus G*(ω), total intrinsic viscosity [η^T (ω)] and specific heat capacity C (ω) were carried out in the non‐free‐draining limits. The relaxation time spectrum calculated for dynamics of low frequency modes exhibits a Rouse‐like character. Its position and shape corresponds to the ultrasonic relaxation time spectrum observed in the system at 10⁶ Hz. On the other hand, the relaxation time spectrum associated with moderate frequency mode dynamics is narrower and typical for ultrasonic relaxation observed at 10⁷ Hz. The polymer intrinsic viscosity [η (ω)] and elastic modulus G*(ω) are shown to be represented by the model within a low‐frequency range. In turn, the specific heat capacity C (ω) is displayed as a representation of the model in the acoustic region mentioned above. In the high‐frequency range the dynamics is described by the total intrinsic viscosity [η^T (ω)] tending to a plateau where the value is equal to the sum of the single‐bead intrinsic viscosity [η_N] and effective solvent viscosity [η_eff].     

Stress relaxation of monodisperse poly-α-methylstyrene

The viscoelastic properties of monodisperse poly-α-methylstyrenes of molecular weights of 4 × 10⁴ to 50 × 10⁴ were studied by the tensile stress-relaxation method. The relaxation-time spectra as well as the steady-flow viscosity, the steady-state compliance, the maximum relaxation time, and the modulus associated with the maximum relaxation time were determined. The molecular weight dependences of these quantities were compared with the theory of Rouse and Bueche as modified by Ferry, Landel, and Williams, as well as with data on other polymers reported in the literature.     

Temperature and shear dependencies of rheology of poly(acrylonitrile‐co‐itaconic acid) dope in DMF

Poly(acrylonitrile‐co‐itaconic acid) (poly(AN‐co‐IA)) precursor required for carbon fiber production is made into a dope and spun into fibers using a suitable spinning technique. The viscosity of the resin dope is decided by the polymer concentration, polymer molecular weight, temperature, and shear force. The shear rheology of concentrated poly(AN‐co‐IA) polymer solutions in N,N‐dimethylformamide (DMF), in the range of 1 × 10⁵–1 × 10⁶ g mol^?1, has been investigated in the shear rate (γ′) range of 1 × 10¹–5 × 10⁴ min^?1. The zero shear viscosity (η₀) has been evaluated at different temperatures. The temperature dependence of zero shear viscosity conformed to the Arrhenius–Frenkel–Eyring model. The free energy of activation of viscous flow (ΔG_V) values were in the range 5–32 kJ mol^?1 and this value increased with increase in polymer concentration and molecular weight. A master equation for the ΔG_V value of the polymer solution of any and concentration (c) is suggested. The power law fitted well for the shear dependency of viscosity of these polymer solutions. The pseudoplasticity index (n) diminished with increase in polymer concentration and molecular weight. An empirical relation between viscosity (η) and was found to exist at constant shear rate, concentration and temperature. For each , the equation relating n, c, and T was established. Copyright © 2008 John Wiley & Sons, Ltd.     

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

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

Investigation of Viscoelastic Properties of Amorphous Selenium near Glass Transition Using Depth‐Sensing Indentation

Abstract

New procedures involving depth‐sensing indentation are used to measure the submicron scale elastic modulus, hardness, viscosity, and activation energy and volume for creep of amorphous selenium below glass transition. The accurate measurement of Young's modulus in a highly viscoelastic situation using depth‐sensing indentation remains a challenge, and a creep correction procedure is employed here to measure the modulus. The measured Young's modulus exhibits a strong decreasing trend from ～10 GPa to 4.4 GPa as temperature increases from ～302 K to 309 K, in reasonably good agreement with bulk behavior. Two new procedures are also proposed here to measure the viscosity. The measured shear viscosity decreases from ～1×10¹² Pa‐s to ～2×10¹⁰ Pa‐s when the temperature increases over the same range, and the variation with temperature is found to obey an Arrehnius rate equation. The activation energy for the viscous creep process is found to be ～463 kJ/mol. Both the viscosity and the activation energy are lower than the bulk values, and this is thought to be due to the much higher stress levels of over 200 MPa involved in the nanoindentation experiments here. The apparent activation volume exhibits a rising trend from 1.04×10^?31 to 2.35×10^?30 m³ over the same temperature range.     

Tensile flow and stress–strain behavior over a wide temperature range for poly(butyl methacrylate) with a broad molecular weight distribution

The poly(butyl methacrylate) studied is a polymer with a normal molecular weight distribution and a relatively low molecular weight close to M_c, the critical molecular weight from the viscosity–molecular weight relation. The polymer was subjected to uniaxial extension and shear over a temperature range which included T_g. It was found that in the region of T_g an increase in applied stress is accompanied by a decrease both in the temperature shift factor a_T and in the activation energy for relaxation and rupture of polymer melts. Close attention is given to the long-term durability of the polymer. As is expected in the temperature range below T_g, its dependence on the stress is exponential, whereas at temperatures above T_g a power law fits the data. In the latter case a log-log plot of the long-term durability versus stress can be represented by two intersecting straight lines which can be replotted as a generalized straight line if the long-term durability values are normalized by the viscosity.     

Structural and steric isomerism of polypropylenes

The structural and steric isomerism of propylene polymers has been estimated on the basis of solution properties as well as infrared and high-resolution nuclear magnetic resonance spectra. Three general types of polypropylenes were prepared: polymers prepared with the cationic catalytic system AlCl₃–C₂H₅Cl, stereoblock polymers obtained by successive extraction from a commercial product and isotactic polymers of low molecular weight obtained by thermal degradation of a highly isotactic polymer followed by hydrogenation with Adam's catalyst in dioxane at 40°C. The characterization of all samples was accomplished by equilibrium ultracentrifugation, vapor-pressure osmometry, viscometry, and gel-permeation chromatography. It is found that the molecular chain of cationically prepared polymer is somewhat branched owing to structural isomerism during polymerization. Isoamyl acetate is found to be a theta solvent for stereo-block as well as for atactic and syndiotactic polymers; the theta temperature is determined as the temperature at which the light-scattering second virial coefficient A₂ vanishes. A close correlation is found between the theta temperature and stereoisomerism. The absorbances of the 1154 and 974 cm^?1 bands in the infrared spectra decrease with decreasing molecular weight; in addition to the mere existence of alternating CH₂ and CH(CH₃) groups in the polymer chain, rather long sequences of this type are required for the appearance of these bands. Changes in the absorption band at 997 cm^?1 show that chains consisting of over ten isotactically connected monomer units can assume a helical conformation. From the high-resolution NMR spectra of different polypropylenes, including isotactic polymers of low molecular weight, it is found that in estimating the microstructure, account must be taken of the effects of stereoisomerism within tetrads of monomer units on the apparent widths of the methylene proton resonances. If substantial concentrations of several of the possible types of tetrads are present (i.e., if the tactic sequence lengths are quite short), then it is difficult to determine the relative amounts of tactic dyads accurately from the 100 Mcps methylene proton resonances.