Nanoscale non-equilibrium dynamics and the fluctuation–dissipation relation in an ageing polymer glass

Abstract

Response functions 1 and fluctuations 2 measured locally in complex materials should equally well characterize mesoscopic-scale dynamics. The fluctuation-dissipation relation (FDR) relates the two in equilibrium, a fact used regularly, for example, to infer mechanical properties of soft matter from the fluctuations in light scattering 3 . In slowly evolving non-equilibrium systems, such as ageing spin 4,5 and structural glasses 6,7 , sheared soft matter 8 and active matter 9 , a form of FDR has been proposed in which an effective temperature 10 , T eff , replaces the usual temperature, and universal behaviour is found in mean-field models 10,11 and simulations 6-8,12 . Thus far, only experiments on spin-glasses 13 and liquid crystals 14 have succeeded in accessing the strong-ageing regime, where T eff > T and possible scaling behaviour are expected. Here we test these ideas through measurements of local dielectric response and polarization noise in an ageing structural glass, polyvinyl acetate. The relaxation-time spectrum, as measured by noise, is compressed, and by response, is stretched, relative to equilibrium, requiring an effective temperature with a scaling behaviour similar to that of certain mean-field spin-glass models.The FDR expresses the equilibrium thermal fluctuations of an observable, O, in terms of available thermal energy, k B T (where k B is the Boltzmann constant), and the linear response of that observable to an applied field, F (ref. 10). It also relates the time (t ) dependence of the fluctuations, found in the autocorrelation function, C(t ) = δO(t + t )δO(t ) t , and the time-dependent susceptibility, χ (t ) = O(t )/F , where F is applied at t = 0. In equilibrium, C(t ) should contain the same information about the dynamics that is found in χ (t ), such as the spectrum of relaxation times. This is seen clearly in plotting χ (t ) versus C(t ) and obtaining a straight line, with a negative slope inversely proportional to temperature 10 . Deviations from the FDR have been intensively studied theoretically in ageing or driven glassy systems, both on the macroscale 8,10 and nanoscale 12 . Ageing occurs in glassy materials that have been quenched from high to low temperature. During ageing, the response functions depend both on time, t , and on the age of the system since the quench, t w . However, χ (t , t w ) and C(t , t w ) need not have the same dependence. This can be understood conceptually by viewing ageing dynamics as hopping on a tilted energy landscape 11 : energy-lowering transitions cause more rapid decorrelation than is possible by thermal energy alone. Prominent glass-transition models 15 place fragile structural glasses 6,16 in the same universality class as mean-field p-spin models with single-step replica symmetry breaking 17 . In such models 10 and simulations of structural glasses 7 , the χ (t ,t w ) versus C(t ,t w ) asymptotically collapse (with increasing t w ) to a single scaling Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. *e-mail: n...

Stationary superstatistics distributions of trapped run-and-tumble particles

“…Notice that position dependence of the v's and of the α's is a necessary but not sufficient condition for the existence of stationary solutions. Further, the relations (7) and (8) lead to a mapping between the stationary solutions of run-and-tumble particles and the corresponding stationary distributions of a drift-diffusion equation of Brownian motion in inhomogeneous media, analogously to the one presented in Ref. [28].…”

“…Notwithstanding this, today there has been great effort made to give a thermodynamic description of active matter [5,6]. On this course, the concept of effective temperature T eff is valuable and has been explored theoretically and experimentally in a variety of systems in nonequilibrium situations [7][8][9][10][11][12][13][14][15][16][17][18], particularly in the dilute regime [19]. More recently, it has been shown that the effective temperature in a two-component active Janus particles can be considered a control parameter (in the sense of a thermodynamics variable) for the observed kinetics and * fjsevilla@fisica.unam.mx; phase behavior [20].…”

Controlling crystal self-assembly using a real-time feedback scheme

“…There is also potential for applications in experiments: attractions between colloidal particles can now be manipulated in real-time, 23,[43][44][45][46][47][48] and correlation-response measurements have also been made. [49][50][51] We hope that the potential for automated self-assembly using real-time feedback will stimulate further studies in this area.…”

A statics-dynamics equivalence through the fluctuation–dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

“…First, L was matched only to t w (irrespectively of the probing time t + t w ). Second, our SDD matched spatial correlation functions whose experimental study is only incipient [9,10].One could think [5] of building an SDD through the Generalized Fluctuation Dissipation relations (GFDR) first introduced in [11] (for related developments see [12][13][14][15][16][17][18][19]). The GFDR are correct at very large times.…”

“…One encounters numerical studies for both Ising [13,16,18] and Heisenberg [21,22] spin glasses, as well as for structural glasses [23][24][25][26][27]. On the experimental side, we have studies on atomic spin glasses [17,19], superspin glasses [10], polymers [9,28], colloids [29][30][31][32][33][34][35] or DNA [36].Here, we perform a detailed simulation of GFDR in the three-dimensional Ising spin glass employing the custommade supercomputers Janus [37] and Janus II [38]. In fact, this has been the launching simulation campaign of the Janus II machine, which was designed with this sort of dynamical studies in mind.…”