We study, using the classical density functional theory (DFT), the fragility and short-time elastic constants of a soft-sphere liquid. For the amorphous state, the order parameter is the inhomogeneous density function |$\rho({\bf r})$| which is described in terms of Gaussian density profiles centered on a set random lattice points |$\{{\bf R}_i\}$|⁠. The latter is characterized in terms of the Bernel pair function |$g_\mathrm{B}(r)$|⁠. Based on the Adam–Gibbs-type relation between the |$\alpha$| relaxation time |$\tau_\alpha$| and the configurational entropy |$\mathcal{S}_{\rm c}$|⁠, a thermodynamic fragility |$m_\mathrm{T}$| for the liquid is defined. The concentration or average density of the liquid is treated as the control parameter here instead of temperature. The configurational entropy of the liquid is calculated using the DFT model. Variations in the short-range structure of the amorphous state are made with different choices for the value of |$g_\mathrm{B}(r)$| at short distances, and its implications on the correlation between fragility |$m_\mathrm{T}$| and the softness index |$n$| are studied. The dependence of Poisson’s ratio |$\nu$| on the softness index |$n$| of the interaction potential is also obtained from the density dependence of the metastable state free energy. The correlation between |$m_\mathrm{T}$| and |$\nu$| follows.

中文翻译：

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硬球极限内脆性的经典密度泛函理论模型

我们使用经典密度泛函理论（DFT）研究软球液体的脆性和短时弹性常数。对于非晶态，阶次参数是非均匀密度函数| $ \ rho（{\ bf r}）$ | 用以一组随机晶格点| $ \ {{\ bf R} _i \} $ |⁠为中心的高斯密度分布图来描述。后者的特征在于Bernel对函数| $ g_ \ mathrm {B}（r）$ |⁠。基于| $ \ alpha $ |之间的Adam–Gibbs类型关系 弛豫时间| $ \ tau_ \ alpha $ | 以及配置熵| $ \ mathcal {S} _ {\ rm c} $ |⁠，热力学脆弱性| $ m_ \ mathrm {T} $ |定义了液体。此处，将液体的浓度或平均密度而不是温度作为控制参数。使用DFT模型计算液体的结构熵。| $ g_ \ mathrm {B}（r）$ |的值具有不同的选择，可以使非晶态的短程结构发生变化。在短距离内，及其对脆性| $ m_ \ mathrm {T} $ |之间的相关性的影响 和柔软度指数| $ n $ | 被研究。泊松比的依存度| $ \ nu $ | 柔软度指数| $ n $ | 还从亚稳态自由能的密度依赖性获得相互作用势的绝对值。之间的相关性| $ m_ \ mathrm {T} $ | 和| $ \ nu $ | 如下。