Ngai K L, Capaccioli Simone, Paluch Marian, Prevosto Daniele
Dipartimento di Fisica, Università di Pisa , Largo B. Pontecorvo 3, I-56127, Pisa, Italy.
J Phys Chem B. 2014 May 22;118(20):5608-14. doi: 10.1021/jp502846t. Epub 2014 May 14.
When the thickness is reduced to nanometer scale, freestanding high molecular weight polymer thin films undergo large reduction of degree of cooperativity and coupling parameter n in the Coupling Model (CM). The finite-size effect together with the surfaces with high mobility make the α-relaxation time of the polymer in nanoconfinement, τ(α)(nano)(T), much shorter than τ(α)(bulk)(T) in the bulk. The consequence is avoidance of vitrification at and below the bulk glass transition temperature, T(g)(bulk), on cooling, and the freestanding polymer thin film remains at thermodynamic equilibrium at temperatures below T(g)(bulk). Molecular dynamics simulations have shown that the specific volume of the freestanding film is the same as the bulk glass-former at equilibrium at the same temperatures. Extreme nanoconfinement renders total or almost total removal of cooperativity of the α-relaxation, and τ(α)(nano)(T) becomes the same or almost the same as the JG β-relaxation time τ(β)(bulk)(T) of the bulk glass-former at equilibrium and at temperatures below T(g)(bulk). Taking advantage of being able to obtain τ(β)(bulk)(T) at equilibrium density below T(g)(bulk) by extreme nanoconfinement of the freestanding films, and using the CM relation between τ(α)(bulk)(T) and τ(β)(bulk)(T), we conclude that the Vogel-Fulcher-Tammann-Hesse (VFTH) dependence of τ(α)(bulk)(T) cannot hold for glass-formers in equilibrium at temperatures significantly below T(g)(bulk). In addition, τ(α)(bulk)(T) does not diverge at the Vogel temperature, T₀, as suggested by the VFTH-dependence and predicted by some theories of glass transition. Instead, τ(α)(bulk)(T) of the glass-former at equilibrium has a much weaker temperature dependence than the VFTH-dependence at temperature below T(g)(bulk) and even below T₀. This conclusion from our analysis is consistent with the temperature dependence of τ(α)(bulk)(T) found experimentally in polymers aged long enough time to attain the equilibrium state at various temperatures below T(g)(bulk).
当厚度减小到纳米尺度时，独立的高分子量聚合物薄膜在耦合模型（CM）中的协同度和耦合参数n会大幅降低。有限尺寸效应以及具有高迁移率的表面使得聚合物在纳米限域中的α弛豫时间τ(α)(nano)(T)远短于其在本体中的τ(α)(bulk)(T)。其结果是在冷却时，在本体玻璃化转变温度T(g)(bulk)及以下避免了玻璃化，并且独立的聚合物薄膜在低于T(g)(bulk)的温度下保持在热力学平衡状态。分子动力学模拟表明，在相同温度下达到平衡时，独立薄膜的比容与本体玻璃形成体相同。极端的纳米限域使得α弛豫的协同性完全或几乎完全消失，并且在平衡状态下以及低于T(g)(bulk)的温度下，τ(α)(nano)(T)变得与本体玻璃形成体的JG β弛豫时间τ(β)(bulk)(T)相同或几乎相同。利用通过对独立薄膜进行极端纳米限域能够在低于T(g)(bulk)的平衡密度下获得τ(β)(bulk)(T)这一特性，并使用τ(α)(bulk)(T)与τ(β)(bulk)(T)之间的CM关系，我们得出结论：对于在显著低于T(g)(bulk)的温度下处于平衡状态的玻璃形成体，τ(α)(bulk)(T)的Vogel-Fulcher-Tammann-Hesse（VFTH）依赖性不成立。此外，正如VFTH依赖性所暗示并由一些玻璃化转变理论所预测的那样，τ(α)(bulk)(T)在Vogel温度T₀处并不会发散。相反，在低于T(g)(bulk)甚至低于T₀的温度下，处于平衡状态的玻璃形成体的τ(α)(bulk)(T)的温度依赖性比VFTH依赖性弱得多。我们分析得出的这一结论与在足够长的时间老化以在低于T(g)(bulk)的各种温度下达到平衡状态的聚合物中实验发现的τ(α)(bulk)(T)的温度依赖性一致。
