Dynamic parameters for some poly (n-alkyl methacrylates)

The dielectric relaxation data of poly (n-hexyl methacrylate) and poly (n-octyl methacrylate) by Strella and Chinai are represented in terms of the relaxation function proposed by Havriliak and Negami using the multiresponse techniques developed by Havriliak and Watts to evaluate the parameters and their dependence on temperature. The parameter α which represents the width of the distribution of relaxation times was found to be dependent on temperature whereas the parameter β representing the skewness of the distribution function was found to be independent of temperature. The relaxation process parameters are discussed in terms of Mansfield's jump model.     

Chain dynamic parameters for some acrylic polymers

The dielectric relaxation data of Ishida et al. on a number of acrylic polymers are represented in terms of the relaxation function proposed by Havriliak and Negami using the multi-response techniques developed by Havriliak and Watts. Two of the parameters of this function are interpreted in terms of a temperature dependent distribution of relaxation times. In this method of interpretation the breadth of the distribution function is temperature-dependent while the skewness is not. The temperature dependence of the breadth of the distribution function is similar for most of these acrylic polymers.The parameters of the relaxation function are also interpreted in terms of Mansfield's model which represents intra- and inter-molecular interactions in terms of springs and dash pots. Briefly, increasing the side chain length for the methacrylate series increases the inter-molecular relaxation time which may be due to an increase in the entropy of activation for the orientation process. The difference between the one acrylate in this study and the four methacrylates of the series is a reduction in the intra-molecular relaxation time, apparently due to the lack of the alpha methyl group.     

Dielectric relaxation processes in PVDF composite

The present study aims at the detailed elaboration of the dielectric relaxation behavior in PVDF composites using broadband dielectric spectroscopy and the Havriliak – Negami method. The composites with multi-wall nanotube carbon and zirconium dioxide in PVDF is fabricated using a simple melt mixing method. The polarization behavior in PVDF composites are investigated on the different frequency region with various temperature. The complex dielectric constants are calculated with the aid of the Havriliak – Negami equation. The characteristic parameters in Havriliak – Negami equation were in excellent agreement with the experimental complex dielectric constants. The results of utilizing these calculated parameters to analyze the origination of the polarization relaxation are given. The purposes of this work expect to give a deeper insight into the impact of different fillers on the dielectric relaxation behavior, and it could provide the technique for the discrepancy with the dipolar for interfacial polarization and the filler effect on the dielectric relaxation.     

Dielectric properties of oligomers. VI. End-group effects in vinyl acetate and methyl methacrylate oligomers

Dielectric properties of vinyl acetate and methyl methacrylate oligomers having chemically different end groups were compared. Dielectric measurements were carried out over the frequency range between 23 and 3 MHz and the temperature range between +50 and ?50°C. The static dielectric constants of these oligomers are between 10 and 20. The relaxations were analyzed with the Havriliak–Negami equation. The dielectric properties depend on the chain end groups on the oligomers. The distribution of relaxation times of the vinyl acetate oligomers was wider than that of poly(vinyl acetate). It was concluded that two cooperative motions, that of the principal chain and that of the chain and that of the chain end group, take part in the dielectric relaxation of these short chain molecules.     

A rigorous comparison of theoretical autocorrelation functions with dielectric relaxation parameters for the alpha process of polymers

Recently, tables of parameters used to represent experimental dielectric relaxation data as well as autocorrelation functions have become available. The experimental and autocorrelation function data were represented with the Havriliak–Negami function using rigorous statistical techniques. These tables include not only parameters and their temperature dependencies, but also the confidence intervals for all of the parameters. The important parameters for this work are the two shape parameters, α and β, which represent the width and skewness of the relaxation process, respectively. A comparison is made between the experimental data and several autocorrelation functions by calculating the minimum distance (in units of standard deviations) between the experimental values of αβ parameters for a specific polymer and the αβ parameters corresponding to the autocorrelation functions reported in these tables. Quantities derived from these minimum distances (a distribution function and an error function) are reported for each of the autocorrelation functions. These results are discussed in terms of the basic assumptions of the mode coupling theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1887–1897, 1997     

Comparison of ultrasonic shear wave and dynamic-mechanical measurements in acrylic-type copolymers

An ultrasonic shear wave reflection method was applied to study film formation and temperature dependence of the complex shear modulus (G^*G′ + iG″) in different amorphous films made of aqueous dispersions of acrylic-type copolymers. The data are compared with dynamic-mechanical measurements in the low frequency range. It is shown that the temperature dependence of the storage (G′) and the loss modulus (G″) for both methods can be fitted by the same set of parameters using the Havriliak–Negami function incorporating the Vogel–Fulcher–Tamman–Hesse equation for the temperature dependence of relaxation times. The temperature dependence of the relaxation times obtained from the fits to the ultrasonic shear modulus is compared to the shift factors of the dynamic-mechanical measurements. The agreement between both methods is good. This suggests an almost thermorheological simplicity of the samples for the main glass–rubber relaxation and demonstrates the capacity of the ultrasonic rheometer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1703–1711, 1998     

Effects of thermal history on enthalpy relaxation

The effects of the thermal history on enthalpy relaxation in polymethylmethacrylate (PMMA) have been studied by differential scanning calorimetry (DSC). The temperature dependence of specific heat capacity in the liquid and glassy states, that of relaxation time and the exponent of the Kohlrausch–Williams–Watts function have been obtained by the measurement of the response of heat flux to the sinusoidal temperature variation. The phenomenological model equation as an extension of linear rheology has been applied to enthalpy relaxation. The evolution of entropy under a given thermal history same as the experiment has been calculated and compared with the DSC results. The calculated results reproduce two peaks of specific heat capacity at lower and higher temperatures in the glass transition region: the former is characteristic of PMMA and the latter is observed in typical glassy polymers.     

Analysis of viscoelastic behavior and dynamic mechanical relaxation of copolyester based layered silicate nanocomposites using Havriliak–Negami model

The solid‐state viscoelastic properties are examined for intercalated nanocomposites based on a copolyester and (2‐ethyl‐hexyl)dimethyl hydrogenated‐tallow ammonium montmorillonite. The nanocomposites are prepared via the direct melt intercalation technique using a conventional twin‐screw extruder. Dynamic mechanical thermal analysis of the nanocomposites is conducted using two different test setups. The dynamic mechanical relaxation spectra show an increase in the storage modulus of the nanocomposite over the entire temperature range under study as compared to the pristine polymer (except in the transition region from 70 to 80 °C). These results are analyzed using the empirical Havriliak–Negami (HN) equation. The four temperature independent HN parameters (α, β, E₀, and E_∞) and one temperature dependent parameter (τ, the relaxation time) are determined by solving the HN equation for each temperature over the range of temperatures. The calculated moduli results fit well with the experimental values of the relaxation spectra for the nanocomposites. This study shows that the HN model can be applied to polymer layered silicate nanocomposites, and it can be used to predict their dynamic mechanical properties over a wide range of temperatures and frequencies a priori. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2657–2666, 2004     

One-dimensional models of polymer dynamics. I. Dashpot-spring models applied to a single rotor

The proposion of Clark and Zimm that a dashpot and a spring can be used in place of a set of rotational barriers in polymer dynamics is studied. The simplest possible case is examined here, that of a single rotor. Reasons for altering the Clark–Zimm diffusion equation are presented and an alternative diffusion equation is proposed. The results of both diffusion equations for the correlation function 〈exp[?iθ(0)] exp[iθ(t)]〉 (θ is the angular position of the rotor) are compared with the correlation function for a rotor in an n-fold cosine potential. Although the two diffusion equations differ, both agree well with the n-fold cosine model for barriers above a few k_BT. This agreement is obtained in the absence of adjustable parameters, and motivates the application of these two diffusion equations to polymeric systems.     

Dielectric relaxations of chitosan: The effect of water on the α‐relaxation and the glass transition temperature

In this work thermal relaxations of chitosan are reported by using a novel methodology that includes subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content. When all these aspects are taken into account, two relaxations are clearly revealed in the low frequency side of the impedance data. We focus on the molecular motions in neutralized and non‐neutralized chitosan analyzed by dielectric spectroscopy in the temperature range from 25 to 250 °C. Low and high frequency relaxations were fitted with the Havriliak and Negami model in the 10^?1 to 108 Hz frequency range. For the first time, the low frequency α‐relaxation associated with the glass‐rubber transition has been detected by this technique in both chitosan forms for moisture contents in the range 0.05 to 3 wt % (ca. 18–62 °C). A strong plasticizing effect of water on this primary α‐relaxation is observed by dielectric spectroscopy and is supported by dynamic mechanical analysis measurements. In the absence of water (<0.05 wt %) the α‐relaxation is obscured in the 20–70 °C temperature range by a superposition of two low frequency relaxation processes. The activation energy for the σ‐relaxation is about 80.0–89.0 kJ/mol and for β‐relaxation is about 46.0–48.5 kJ/mol and those values are in agreement with that previously reported by other authors. The non‐neutralized chitosan possess higher ion mobility than the neutralized one as determined by the frequency location of the σ‐relaxation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2259–2271, 2009     

Generalized Rouse–Zimm theory for polymer solutions

Generalized Rouse–Zimm equations are derived using a local equilibrium ansatz for the segment distribution function. The relaxation frequencies depend on excluded-volume effects and other interactions such as entanglement in semidilute solutions through exact static correlation functions. For the case of ring polymers general expressions are given for diffusion coefficients and mean-square displacements. By use of the “blob” model, explicit results are presented for a dilute good-solvent system.     

Water sorption by poly(tetrahydrofurfuril methacrylate)'s

Polymers consisting of poly(heterocyclic methacrylate)s are considered as potential materials for clinical applications such as drug delivery and cartilage repair. Much of the success of these systems has been attributed to the complex nature of their water sorption properties. Dielectric permittivity is very sensitive to water sorption. Dielectric relaxation spectroscopy studies have been carried out on two heterocyclic poly(methacrylate)s: poly(tetrahydrofurfuryl methacrylate) (PTHFMA) and poly(3‐methyl tetrahydrofurfuryl methacrylate) (P3MTHFMA). The isochrones representing the dielectric losses show in both cases high conductivity at low frequencies and high temperatures. In PTHFMA two conductive processes are observed, which can be associated to the existence of two types of water sorption. These effects have been analyzed and were removed from the dielectric spectra by using classical empirical equations. Both polymers show ostensible α‐relaxation centered in the vicinity of 350 K at 10⁰ Hz. This relaxation was analyzed by means of the empirical Havriliak‐Negami equation. Reminiscent β‐relaxation could also exist. Both polymers present well defined γ and δ subglass absorptions at approximately 120 K, 160 K for PTHFMA and 125 K, 163 K for P3MTHFMA, at 10⁰ Hz, associated to local intramolecular relaxations in side groups. These relaxations were analyzed using semiempirical symmetric model. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 109–120, 2008     

Effect of change in the physical properties of water at its peculiar temperature points on the dielectric behavior of sodium polyacrylate

The behavior of sodium polyacrylate is studied via broadband dielectric spectroscopy. The non-Debye response in the frequency range 0.1 Hz–1.0 MHz, the non-Markovian dispersion in the infralow-frequency range, and the anomalies of dielectric permittivity and ac conductivity near “peculiar” temperatures of water (20, 35, 50, and 75°C) are ascertained experimentally. These facts make it possible to assign sodium polyacrylate to disordered media, in which the temperature behavior of dielectric parameters is described by the Kohlrausch–Williams–Watts relaxation function.     

Dielectric relaxation study of N -methyl formamide with glycols using time domain reflectometry technique

The dielectric relaxation study that is static dielectric permittivity (∈₀) and relaxation time (τ) of amide of N-methyl formamide (NMF) with increasing volume percent propylene glycol (PLG) and BLG has been carried out at different temperatures. The time domain reflectometry (TDR) technique has been used to measure reflection coefficient in frequency range of 10 MHz to 20 GHz. The dielectric parameters have been obtained by fitting experimental data with the Havriliak–Negami equation. The experimental observation shows that the static dielectric permittivity and relaxation time decreases with increasing temperature. The experimental observation also shows that the static dielectric permittivity decreases and relaxation time increases with increasing percentage volume of Propylene glycol (PLG) and Butylene glycol (BLG) in NMF. The nature of (?₀) and (τ) is same for the temperature ranges (20, 30, and 40°C). The thermodynamic parameters enthalpy (ΔH) and entropy (ΔS) of the binary mixture are also reported in this work.     

Viscoelastic characterization of phenolic resin–carbon fiber composite degradation process

Viscoelastic characteristics of cured phenolic resin–carbon fiber composite materials were investigated through glass transition and degradation reaction processes in the high‐temperature region up to 400°C. A typical glass transition of the crosslinked thermoset polymer was followed by irreversible degradation reactions, which were exhibited by the increasing storage modulus and loss modulus peak. A degradation master curve was constructed by using the vertical and horizontal shift factors, both of which complied well with the Arrhenius equation in light of the kinetic expression of degradation rate constants. Using an analogy to the Havriliak–Negami equation in dielectric relaxation phenomena, a viscoelastic modeling methodology was developed to characterize the frequency‐ and temperature‐dependent complex moduli of the degrading thermoset polymer composite systems. The temperature‐dependent relaxation time of the degrading composites was determined in a continuous fashion and showed a minimum relaxation time between the glass transition and degradation reaction regions. The capability of the developed modeling methodology was demonstrated by describing the complex behavior of the viscoelastic complex moduli of reacting phenolic resin composite systems. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 907–918, 1999     

Structure–dynamics relationships of the α‐relaxation in flexible copolyesters during crystallization as revealed by real‐time methods

The evolution of the α‐relaxation during an isothermal crystallization process of a series of flexible copolyesters of hydroxybutyrate (HB) and hydroxyvalerate (HV) has been followed in real‐time by wide‐angle X‐ray scattering and dielectric complex permittivity measurements. The change of the dielectric parameters with crystallization time can be phenomenologically described in terms of the Havriliak‐Negami equation. The dielectric strength follows a sigmoidal‐shaped pattern similar to that shown by the crystallinity. A reduction of the overall mobility with crystallization time of the polymeric chains in the amorphous phase has been observed. This slowing down effect depends on the HV molar content. The influence of the chain flexibility on the crystalline‐induced restriction has been discussed in the light of similar studies carried out with more rigid polymers. Dielectric experiments suggest that the progressive immobilization of polymer segments as crystallization proceeds cannot be exclusively associated with the amount of crystalline material. Differences in microstructure, depending on the HV molar content, seem to be responsible for the observed behavior. The progressive broadening and symmetrization of the α‐relaxation with increasing crystallization time has been explained as due to a restriction of the large‐scale motions of the polymeric chains, as the material is being filled in with crystals. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 37–49, 1999     

Defect-diffusion models of dielectric relaxation

Dielectric relaxation due to defect-diffusion in liquids, as introduced by Glarum, is considered for the case that reorientation of a molecule at time t ? 0 may be due not only to the nearest defect at t = 0, but to any defect in the liquid. For one-dimensional diffusion one then obtains the empirical relaxation function introduced by Williams and Watts with β = 0.5, and for three-dimensional diffusion a result only slightly differing from that for a single relaxation time. It is concluded that a model of dielectric relaxation by diffusion of defects only leads to considerable deviations from a single relaxation time when the diffusion is restricted in some way.     

Evidence for the γ‐relaxation in the light scattering spectra of poly (n‐hexyl methacrylate) near the glass transition

The full range of relaxation processes present in optically pure poly‐(n‐hexyl methacrylate) (PHMA) was studied using Rayleigh–Brillouin and photon correlation spectroscopy (PCS). Brillouin shifts, linewidths, and Landau–Placzek ratios (LPR) were measured over the temperature range from ?11 to 21 °C. The Brillouin splitting and linewidth were consistent with previous studies of PHMA, but the LPR was much lower, indicating that the scattered light primarily comes from intrinsic density fluctuations. Relaxation functions of the same PHMA sample were measured using PCS over the temperature range 0.5–52.5 °C. The average relaxation times calculated from a Williams–Watts fit follow a VFT temperature dependence, with the stretching parameter β decreasing with decreasing temperature. The distribution of relaxation times reveals a merging of the α and β‐relaxations over this temperature range, and the temperature dependent width confirms that there are at least two processes with separate temperature dependences. Furthermore, there appears a process at short times in the correlation function window at low temperatures. This upturn at the fastest relaxation times is attributed to the γ‐relaxation present in higher order methacrylate polymers. The effect of the γ‐relaxation is discussed in terms of the dynamic behavior over 12 decades in time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1504–1519, 2005