Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
Phys Rev Lett. 2013 Nov 27;111(22):228301. doi: 10.1103/PhysRevLett.111.228301. Epub 2013 Nov 26.
We measure the activation energy Ea for the diffusion of molecular probes (dyes and proteins of radii from 0.52 to 6.9 nm) and for macroscopic flow in a model complex liquid-aqueous solutions of polyethylene glycol. We cover a broad range of polymer molecular weights, concentrations, and temperatures. Fluorescence correlation spectroscopy and rheometry experiments reveal a relationship between the excess of the activation energy in polymer solutions over the one in pure solvent ΔEa and simple parameters describing the structure of the system: probe radius, polymer hydrodynamic radius, and correlation length. ΔEa varies by more than an order of magnitude in the investigated systems (in the range of ca. 1-15 kJ/mol) and for probes significantly larger than the polymer hydrodynamic radius approaches the value measured for macroscopic flow. We develop an explicit formula describing the smooth transition of ΔEa from the diffusion of molecular probes to macroscopic flow. This formula is a reference for the quantitative analysis of specific interactions of moving nano-objects with their environment as well as active transport. For instance, the power developed by a molecular motor moving at constant velocity u is proportional to u2exp(Ea/RT).
我们测量了分子探针（半径为 0.52 至 6.9nm 的染料和蛋白质）在模型复杂液体-聚乙二醇水溶液中的扩散和宏观流动的激活能 Ea。我们涵盖了广泛的聚合物分子量、浓度和温度范围。荧光相关光谱和流变学实验揭示了聚合物溶液中激活能超过纯溶剂的过剩值ΔEa与描述系统结构的简单参数之间的关系：探针半径、聚合物水动力半径和相关长度。在研究的系统中，ΔEa 的变化超过一个数量级（约 1-15kJ/mol），并且对于明显大于聚合物水动力半径的探针，它接近测量到的宏观流动的值。我们开发了一个描述从分子探针扩散到宏观流动的平滑过渡的显式公式。该公式是对移动纳米物体与其环境之间的特定相互作用以及主动运输进行定量分析的参考。例如，以恒定速度 u 运动的分子马达所产生的功率与 u2exp(Ea/RT)成正比。
