Non-gaussian effects in the cage dynamics of polymers

The correlation between the fast cage dynamics and structural relaxation is investigated in a model polymer system. It is shown that the cage vibration amplitude, as expressed by the Debye-Waller factor, and the relaxation time $\tau_\alpha$ collapse on a single universal curve with a simple analytic form when the temperature, the density, the chain length and the monomer-monomer interaction potential are changed. For the physical states with the same $\tau_\alpha$ coincidence of the mean-square displacement, the intermediate scattering function and the non-Gaussian parameter is observed in a wide time window spanning from the ballistic regime to the onset of the Rouse dynamics driven by the chain connectivity. The role of the non-Gaussian effects is discussed.Comment: 8 pages, 5 figure

Connectivity effects in the segmental self- and cross-reorientation of unentangled polymer melts

The segmental (bond) rotational dynamics in a polymer melt of unentangled, linear bead-spring chains is studied by molecular dynamics simulations. To single out the connectivity effects, states with limited deviations from the Gaussian behavior of the linear displacement are considered. Both the self and the cross bond-bond correlations with rank ℓ=1,2 are studied in detail. For ℓ=1 the correlation functions are precisely described by expressions involving the correlation functions of the chain modes. Several approximations concerning both the self- and the cross-correlations with ℓ=1,2 are developed and assessed. It is found that the simplified description of the excluded volume static effects derived elsewhere [D. Molin et al., J. Phys.: Condens. Matter 18, 7543 (2006)] well accounts for the short time cross-correlations. It also allows a proper modification of the Rouse theory which provides quantitative account of the intermediate and the long time decay of the rotational correlations with ℓ=1

Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbours whereas its average escape time, the structural relaxation time $\tau_\alpha$, increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between $\tau_\alpha$ and the rattling amplitude, expressed by the Debye-Waller factor (DW), was carried out. Molecular-dynamics (MD) simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density $\rho$, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The simulations evidence the scaling between the $\tau_\alpha$ and the Debye-Waller factor. An analytic model of the master curve is developed in terms of two characteristic length scales pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply $\tau_\alpha$ divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.Comment: 8 pages, 11 figure

The kinetic fragility of liquids as manifestation of the elastic softening

We show that the fragility $m$, the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities ($33 \le m \le 115$), leading to a fragility-independent elastic master curve extending over eighteen decades in viscosity and relaxation time. The master curve is accounted for by a cavity model pointing out the roles of both the available free volume and the cage softness. A major implication of our findings is that ultraslow relaxations, hardly characterised experimentally, become predictable by linear elasticity. As an example, the viscosity of supercooled silica is derived over about fifteen decades with no adjustable parameters.Comment: 7 pages, 6 figures; Added new results, improved the theoretical sectio

Excluded-volume corrections to the single-chain static properties of a polymer melt: Temperature, density and potential effects

Excluded-volume effects on single-chain statics are introduced by analytic corrections to the Rouse results. The final expressions do not depend on free parameters. They are compared with numerical simulations of a polymer melt for different values of the temperature, the density and the interaction potential. Density and interactions control the energy landscape of the system, whereas the temperature selects the accessible regions. The agreement between the theory and the Rouse modes does not depend markedly on the temperature with some improvement for the first modes (large length scales). Differently, increasing the packing and the stiffness of the monomer-monomer interaction reduces the deviations for the first modes, but it leaves the magnitude of the deviations for the high-indexes modes (short length scales) nearly unaffected or with some tendency to increase. The scaling properties of the corrections are briefly discussed. (C) 2007 Elsevier B.V. All rights reserved

Scaling between structural relaxation and caged dynamics in Ca(0.4)K(0.6)(NO(3))(1.4) and glycerol: free volume, time-scales and implications for pressure-energy correlations

The scaling of slow structural relaxation with fast caged dynamics is seen in the molten salt Ca(0.4)K(0.6)(NO(3))(1.4) (CKN) over about 13 decades of the structural relaxation time. Glycerol scaling has been analysed in detail. In glycerol, the short-time mean-square displacement , a measure of the caged dynamics, is contributed by the free volume. It is seen that, in order to see the scaling, the observation time of the fast dynamics must be shorter than the time-scales of the relaxation processes. Systems with both negligible (like CKN, glycerol and network glassformers) and high (like van der Waals liquids and polymers) pressure-energy correlations exhibit scaling between the slow relaxation and the fast caged dynamics. According to the available experiments, an isomorph-invariant expression of the master curve of the scaled data is indistinguishable from a simpler non-invariant expression. Instead, the latter agrees better with the simulations on a wide class of model polymers

Scaling between structural relaxation and caged dynamics in Ca 0.4

The scaling of the slow structural relaxation with the fast caged dynamics is evidenced in the molten salt Ca_{0.4}K_{0.6}(NO_{3}$)_{1.4} (CKN) over about thirteen decades of the structural relaxation time. Glycerol caling was analyzed in detail. In glycerol, the short-time mean-square displacement , a measure of the caged dynamics, is contributed by free-volume. It is seen that, in order to evidence the scaling, the observation time of the fast dynamics must be shorter than the time scales of the relaxation processes. Systems with both negligible (like CKN, glycerol and network glassformers) and high (like van der Waals liquids and polymers) pressure-energy correlations exhibit the scaling between the slow relaxation and the fast caged dynamics. According to the available experiments, an isomorph-invariant expression of the master curve of the scaled data is not distinguishable from a simpler not-invariant expression. Instead, the latter grees better with the simulations on a wide class of model polymers.Comment: 10 pages, 4 figures, XII International Workshop on Complex System

Universal scaling between structural relaxation and caged dynamics in glass-forming systems: Free volume and time scales

It is shown that the Debye-Waller factor (DW), a measure of the cage dynamics, is contributed by free-volume in o-terphenyl (OTP) and glycerol. An elementary ansatz provides an alternative way to get the reduced OW from Positron Annihilation Lifetime Spectroscopy (PALS). The ansatz supports the scaling of the slow relaxation with the fast caged dynamics over about ten decades in relaxation times in OTP and glycerol. Both PALS and neutron scattering experiments show that, in order to evidence the scaling, the observation times must be shorter than the time scales of the relaxation processes. (C) 2010 Elsevier B.V. All rights reserved

Universal scaling between structural relaxation and vibrational dynamics in glass-forming liquids and polymers

If liquids, polymers, bio-materials, metals and molten salts can avoid crystallization during cooling or compression, they freeze into a microscopically disordered solid-like state, a glass(1,2). On approaching the glass transition, particles become trapped in transient cages-in which they rattle on picosecond timescales-formed by their nearest neighbours; the particles spend increasing amounts of time in their cages as the average escape time, or structural relaxation time tau(alpha), increases from a few picoseconds to thousands of seconds through the transition. Owing to the huge difference between relaxation and vibrational timescales, theoretical(3-9) studies addressing the underlying rattling process have challenged our understanding of the structural relaxation. Numerical(10-13) and experimental studies on liquids(14) and glasses(8,15-19) support the theories, but not without controversies(20) (for a review see ref. 21). Here we show computer simulations that, when compared with experiments, reveal the universal correlation of the structural relaxation time (as well as the viscosity eta) and the rattling amplitude from glassy to low-viscosity states. According to the emerging picture the glass softens when the rattling amplitude exceeds a critical value, in agreement with the Lindemann criterion for the melting of crystalline solids(22) and the free-volume model(23)