Collective dynamics of glass-forming polymers at intermediate length scales

Abstract

Abstract. Motivated by the proposition of a new theoretical ansatz [V.N. Novikov, K.S. Schweizer, A.P. Sokolov, J. Chem. Phys. 138, 164508 (2013)], we have revisited the question of the characterization of the collective response of polyisobutylene at intermediate length scales observed by neutron spin echo (NSE) experiments. The model, generalized for sublinear diffusion -as it is the case of glass-forming polymers-has been successfully applied by using the information on the total self-motions available from MD-simulations properly validated by direct comparison with experimental results. From the fits of the coherent NSE data, the collective time at Q → 0 has been extracted that agrees very well with compiled results from different experimental techniques directly accessing such relaxation time. We show that a unique temperature dependence governs both, the Q → 0 and Q → ∞ asymptotic characteristic times. The generalized model also gives account for the modulation of the apparent activation energy of the collective times with the static structure factor. It mainly results from changes of the short-range order at inter-molecular length scales.

Melts of single-chain nanoparticles: A neutron scattering investigation

“…This crossover is captured by a model proposed by Novikov et al 24 that was later reformulated for the case of glass-forming polymers or systems showing stretched relaxation behavior in general. 25 Such an extended approach was applied 25,42,43 to the case of polyisobutylene (PIB) using the NSE data previously reported in Ref. 44.…”

“…A model has been recently proposed to describe the collective dynamics of glass-forming polymers there and successfully applied to the case of existing data on polyisobutylene (PIB). 25,42,43 This model consists of an interpolation formula that embeds the mesoscopic (nondiffusive) and the high-Q (diffusive) limits of the collective times in an analytical expression as proposed by Novikov et al, 24 1…”

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

“…We note that this is, for instance, the procedure usually followed by the mode coupling theory approximation . Now, to find an appropriate expression for the actual collective structure factor, , we will use the ansatz recently proposed for describing the collective dynamics at length scales larger than the intermolecular distances (i.e., k ‐values lower than that of the first maximum of S ( k )) of glasses and polymers . In the case of polymers and in the k ‐range of interest here, the collective dynamic structure factor in the framework of this ansatz can be approximated by , where results to be independent and , where τ α is an average relaxation time of the α‐process in the system.…”

The universal trend of the non-exponential Rouse mode relaxation in polymer systems: a theoretical interpretation based on a generalized Langevin equation

“…Instead we will use the ansatz recently proposed for describing the collective dynamics at 'intermediate length scales' [i.e., k-values lower than that at the first maximum of S(k)] of glasses 16 and polymers. 17,18 We note that in the case of polyisobutylene (PIB), 17,18 this ansatz was able to describe not only neutron scattering data (k \ 0.2 Å À1 ), but also light scattering results (k B 10 À3 Å À1 ). In the case of polymers and in the k-range of interest here (R g À1 o k o s À1 ) the collective dynamic structure factor S(k,t) in the framework of this ansatz can be approximated by S(k,t) C S(0) exp[À(t/t c ) 0.5 ] where the collective time, t c , results to be approximately k-independent and given by t c = (M L /K bulk )t a .…”

“…In the case of polymers and in the k-range of interest here (R g À1 o k o s À1 ) the collective dynamic structure factor S(k,t) in the framework of this ansatz can be approximated by S(k,t) C S(0) exp[À(t/t c ) 0.5 ] where the collective time, t c , results to be approximately k-independent and given by t c = (M L /K bulk )t a . [16][17][18] Here K bulk is the bulk modulus and M L the longitudinal elastic modulus. The time t a is an alpha (structural) relaxation time corresponding to a k E 0 correlation function.…”