Scaling in kinetics of supercooled liquids.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
B Zhang, D M Zhang, D Y Sun, X G Gong
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引用次数: 0

Abstract

The present study introduces a renormalization-based approach to investigate the relaxation dynamics within supercooled liquids. By applying a numerical scale transformation to potential energies along the temporal axis, we have established a novel framework that elucidates the underlying kinetics of supercooled liquids. Our findings indicate that the skewness of the potential energy distribution attains its maximum at a characteristic time scale (Δ_{CTS}), which exhibits a scaling law with temperature [Δ_{CTS}∝(T-T^{*})^{-γ}]. This scaling relationship is characterized by an exponent γ that experiences a discontinuous transition at a critical cooling rate, signifying a kinetic-like phase transition. We further find that the product of γ and the logarithm of the cooling rate is approximately constant. This constant, however, varies depending on whether the cooling rate is above or below the critical value, effectively classifying supercooled liquids into two regimes: a glass-forming regime (GFR) and a crystal-forming regime (CFR). Furthermore, we identify that T^{*} corresponds to the glass transition temperature for GFR (T_{g}) and the crystallization temperature for CFR (T_{c}), respectively. We have successfully developed a theoretical model, which not only derives the scaling law but also provides profound insights into the physical implications of Δ_{CTS}, γ, and T^{*}. This research delineates the differences between GFR and CFR and offers a fresh perspective for exploring the nature of glasses. The findings contribute to the broader understanding of the dynamics of supercooled liquids and the mechanisms of glass formation.

过冷液体动力学中的标度。
本研究引入了一种基于重整化的方法来研究过冷液体中的弛豫动力学。通过将数值尺度变换应用于沿时间轴的势能,我们建立了一个新的框架,阐明了过冷液体的潜在动力学。结果表明,势能分布的偏度在特征时间尺度(Δ_{CTS})达到最大,随温度变化呈标度规律[Δ_{CTS}∝(T-T^{*})^{-γ}]。这种标度关系的特征是指数γ在临界冷却速率下经历不连续转变,表明类似动力学的相变。我们进一步发现,γ与冷却速率的对数的乘积近似为常数。然而,这个常数取决于冷却速率是高于还是低于临界值,有效地将过冷液体分为两种状态:玻璃形成状态(GFR)和晶体形成状态(CFR)。此外,我们确定T^{*}分别对应GFR的玻璃化转变温度(T_{g})和CFR的结晶温度(T_{c})。我们成功地建立了一个理论模型,该模型不仅推导了标度定律,而且对Δ_{CTS}, γ和T^{*}的物理含义提供了深刻的见解。本研究描述了GFR和CFR之间的差异,为探索玻璃的本质提供了一个新的视角。这些发现有助于更广泛地理解过冷液体的动力学和玻璃形成的机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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