Understanding flow behaviors of supercooled liquids by embodying solid-liquid duality at particle level

Understanding the flow behaviors of supercooled liquids presents a major challenge in liquid-state physics due to the strong nonlinearity and rich phenomena. To unravel this complexity, we introduce the concept of local configurational relaxation time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>τ</a:mi> <a:mi>LC</a:mi> </a:msub> </a:math> , which allows us to embody the solid-liquid duality, proposed by Maxwell for phenomenologically describing materials’ response to external load, at the particle level. The spatial distribution of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>τ</b:mi> <b:mi>LC</b:mi> </b:msub> </b:math> in flow is heterogeneous. Depending on the comparison between the local mobility measured by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>τ</c:mi> <c:mi>LC</c:mi> </c:msub> </c:math> and the external shear rate, the shear response of local regions is either solidlike or liquidlike. In this way, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>τ</d:mi> <d:mi>LC</d:mi> </d:msub> </d:math> plays a role similar to the Maxwell time. By applying this microscopic solid-liquid duality to different conditions of shear flow with a wide range of shear rates, we describe the emergence of shear thinning in steady shear and predict the major characteristics of the transient response to start-up shear. Furthermore, we reveal a clear structural foundation for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>τ</e:mi> <e:mi>LC</e:mi> </e:msub> </e:math> and the solid-liquid duality associated with it by introducing an order parameter extracted from local configuration. Thus, we establish a framework that connects microscopic structure, dynamics, local mechanical response, and flow behaviors for supercooled liquids. Finally, we rationalize our framework in terms of activations from energy basins that are facilitated by shear. This model illustrates how local structure, convection, and thermal activation collectively determine <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>τ</f:mi> <f:mi>LC</f:mi> </f:msub> </f:math> . Notably, it predicts two distinct response groups, which well correspond to the microscopic solid-liquid duality.