Correlation between non-Debye behavior andQbehavior of the α relaxation in glass-forming polymeric systems

Abstract

By means of quasielastic neutron scattering we have shown that the dynamics of the a relaxation on three different polymeric glasses shows a clear non-Debye behavior on a mesoscopic time scale. The spectral shape is found to be independent of temperature and momentum transfer (Q). The characteristic relaxation time follows a power-law Q dependence, r(Q)ccQ~n (n > 2), n being dependent on the system. We found that the Q behavior and the non-Debye behavior are directly correlated. These results have important implications concerning the physical mechanisms behind the dynamics of the a relaxation.PACS numbers: 64.70.Pf, 61.12.ExThe dynamics of the a relaxation in glass-forming systems above and near their glass-transition temperature range has been a subject of increasing interest over the past several years. It is now experimentally well established that the shape of the relaxation function characterizing the dynamics of the a relaxation shows a clear non-Debye behavior. In the time domain this behavior can be well described by means of the Kohlrausch-Williams-Watts "stretched exponential" function (pit) =exp[ -(t/ Tww)^] HI, which can be derived from different theoretical models. Here TWW is a characteristic relaxation time and p is a shape parameter ranging between 0 and 1. In the frequency domain, several empirical forms have been proposed to describe the non-Debye behavior, the most general being the Havriliak-Negami relaxation function 0*(ft>) = [l + (/COTHN) 0 ] ~~y [2]. Here a and y are two shape parameters 0<a,/<l and THN is a relaxation time. However, almost nothing is known about the Q dependence of the shape parameters and the relaxation times which characterize the dynamics of the a relaxation (Q being the modulus of the change of the wave vector in a scattering experiment). Results from photon correlation spectroscopy (a light scattering time-domain technique) suggest that the characteristic magnitudes of the a relaxation do not depend noticeably on Q at the small-(? values covered in such experiments (£>~10~3 A" 1 ) [3]. Information about the Q behavior of the a relaxation in a mesoscopic time scale (10~, 0 -10 -7 s) can be obtained by means of quasielastic neutron scattering in a high-g range roughly between 0.1 and 5 A -1 . Several papers have been published recently in the field of the dynamics of glass-forming systems studied by neutron scattering techniques [4][5][6][7]. However, most of these studies aim to check the mode-coupling theories of the glass transition. In a previous paper [8] we reported preliminary results corresponding to a glass-forming polymeric system poly (vinyl methyl ether), PVME. In this Letter we report on incoherent quasielastic neutron scattering mea-surements performed on three structurally different glass-forming polymeric systems including PVME. We have focused our attention on the Q dependence of the magnitudes characterizing the dynamics of the a relaxation.The samples investigated were poly(vinyl methyl ether), polyvinyl chloride) (PVC) and poly(bisphenol A, 2hydrox...

Self- and Collective Dynamics of Syndiotactic Poly(methyl methacrylate). A Combined Study by Quasielastic Neutron Scattering and Atomistic Molecular Dynamics Simulations

“…38,47 As shown in previous publications, 48,49 such a Gaussian process leads to a relation between the stretching exponent and the Q dispersion of the characteristic times τ w ∝ Q -2/ . While at low Q this relationship is rather well fulfilled in PMMA, around Q ≈ 0.8 Å -1 severe deviations appear.…”

“…In the case of simple diffusion, the dispersion law relating the characteristic time scale τ with Q is given by τ ∝ Q -2 . However, for protonated glass-forming polymers, much stronger Q dependences are generally reported 34,48,49 for the time scale associated with the R-relaxation. Usually, in such cases, exponents close to 4 are found, which have been correlated with the non-Debye behavior of the intermediate scattering function.…”

“…Usually, in such cases, exponents close to 4 are found, which have been correlated with the non-Debye behavior of the intermediate scattering function. 48 It is well established that in the BS window the signal produced by hydrogen motions in the structural relaxation regime is well described in terms of the Fourier transform of a KWW function in the time domain; i.e., S s (Q,t) takes an analogous form of eq 6:…”

Study of the structure and dynamics of poly(vinyl pyrrolidone) by molecular dynamics simulations validated by quasielastic neutron scattering and x-ray diffraction experiments

“…In those cases, the exponent x of the Q −x dependence of τ KWW (Q) changes from x 2 at Q Q * c , to x = 2/β indicative for Gaussian behavior at lower Q. 41 …”

Collective dynamics of glass-forming polymers at intermediate length scales

“…In order to obtain an analytical expression for τ D c (Q) based in the Sköld's approximation, we first need an analytical description of the selfcorrelation function (this is naturally a KWW function) and the associated incoherent characteristic time. In the Gaussian approximation -which is usually well fulfilled for polymers at Q-values below and around the first structure factor peak-the Q-dependence of the characteristic time in a KWW self-correlation function is given by [27] τ…”