Pinning susceptibility: a novel method to study growth of amorphous order in glass-forming liquids

Abstract

Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems like colloidal glasses and simulations of model glass-forming liquids. In this Letter, we propose an experimentally realizable yet simple correlation function to study the growth of amorphous order. We then demonstrate the validity of this approach for a few well-studied model supercooled liquids and obtain results which are consistent with other conventional methods.Glasses are ubiquitous in nature and are of immense practical importance in our day-to-day lives as well as in modern technology. In spite of knowing their presence and usefulness from the early history of mankind, the nature of the glassy state and the glass transition, where the viscosity of a liquid increases by many orders of magnitude within a narrow temperature or density window, still puzzles the scientific community and is believed to be one of the major unsolved problems in condensed matter physics [1][2][3][4][5][6][7][8][9]. The viscosity of a glass forming liquid increases so dramatically that one is often tempted to believe that viscosity probably diverges at a certain critical temperature associated with a thermodynamic phase transition. Thus, not surprisingly, there are two types of theories on glass transition. The first type assumes that the (ideal) glass transition is a thermodynamic phase transition and glassy states are believed to be a thermodynamic state of matter. This approach is taken by the Random First Order Transition (RFOT) theory [10][11][12]. The other approach is to consider the glass transition to be a purely dynamic phenomenon and the slowdown of dynamics is thought to be a result of an ever increasing number of self-generated kinetic constraints with supercooling [13][14][15].In spite of all the differences in opinion about the existence of a true thermodynamic glass transition, there is a consensus about the existence and growth of correlation lengths along with the rapid increase in viscosity or relaxation time [2][3][4][5][7][8][9]. Recently there have been a lot of progress in identifying at least two different length scales -(a) a dynamic length scale akin to the length scale characterizing the heterogeneity present in the dynamics of supercooled liquids [4,5,8] and (b) a static length scale of the so called "amorphous order" [7,[16][17][18][19][20][21]. Simple two-point density correlation functions have been shown to be unsuitable for the identification of the build up of these correlations in the supercooled liquids. A ...

Effect of heavy impurities on the dynamics of supercooled liquids

“…The arguments c and mimp have been suppressed in the following discussion, and their values have been held fixed at 12.5% and 4096, respectively. This can be related to the pinning susceptibility, χp(t), 20 via the following relation:…”

Soft-Pinning: Experimental Validation of Static Correlations in Supercooled Molecular Glass-forming Liquids

“…Using numerical simulation in Ref. [25], the validity of this relation has been checked, and it has also been shown that this scaling theory works if one uses large size particles having significantly lesser diffusion coefficients to act as 'soft pinning' sites. This finding makes this proposal very attractive to use in experiments, unlike hard pinning, as realizing soft pinning in a natural system will be much easier.…”

“…Although there are many existing methods to extract the desired static length scale, most of them are not useful for experiments on molecular glass-forming liquids. In a recent work [25], it has been shown that it is possible to extract static length-scale in a glass-forming liquid by measuring the response of the system in the presence of a small concentration of solute particles, which have a smaller diffusion constant than the constituent molecules or particles of the supercooled liquid medium. The idea mainly originated from the previous works on the effects of random pinning sites on the dynamics of the supercooled liquids [26,27].…”

“…Using Eq.3, a new susceptibility, "pinning susceptibility" is introduced in Ref. [25] to estimate the static length directly, and it is defined as…”

“…Using simple calculations and a few assumptions in Ref. [25] it is shown that χ max p (T ) ∼ ξ 3 s (T ). The relation states that the peak value of χ p (T ) should give the direct measure of ξ p .…”