Rosenfeld scaling

Evidence from computer simulations shows the correlation between D and excess entropy, obtained by Goel et al. [7]. The excellent agreement demonstrates the vahdity of the Rosenfeld scaling relation. 

We discussed the above derivation to bring out the essence of the Rosenfeld scaling relation, which is valid when a system is ergodic with fast transitions between the configurational states of the system, so that the diffusion coefficient increases with entropy. 

In 1977, Rosenfeld proposed a connection between thermodynamical and dynamical properties of liquids [52,53]. The main Rosenfeld s statement claims that the transport coefficients are exponential functions of the excess entropy. In order to write the exponential relations, Rosenfeld introduced reduction of the transport coefficients by some macroscopic parameters of the system. For the case of diffu sion coefficient, D = D p )/ kBT/m) ),wheTem is the mass of the particles. The Rosenfeld scaling rule can be written as... 

The breakdown of the Rosenfeld relation along isotherms can be seen from the following speculation. The regions of different anomalies do not coincide with each other. In particular, in the case of core-softened, fluids, the diffusion anomaly region is located inside the structural anomaly one. It means that there are some regions where the diffusion is still normal, while the excess entropy is already anomalous. But this kind of behavior cannot be consistent with the Rosenfeld scaling law. 

However, from this speculation, it follows that the Rosenfeld scaling should hold true along the trajectories that do not contain anomalies, that is, isochors and isobars. In our recent publication [48], we considered the Rosenfeld relation along isotherms and isochors. Here we bring these trajectories for the sake of... 

Lode EG, Rosenfeld A, Yuan QS, Root TW, Lightfoot EN. Refining the scale-up of chromatographic separations. J Chromatogr 1998 796 3-14. 

Q. Zheng, R. Rosenfeld, S. Vajda, C. DeLisi. Determining protein loop conformation using scaling-relaxation techniques. Prot. Science. 1993, 2, 1242-1248. 

K.K. Stewart, A.G. Rosenfeld, Exponential dilution chambers for scale expansion in flow injection analysis, Anal. Chem. 54 (1982) 2368. 

Stewart and Rosenfeld [32] looked at the subject from a different angle. They concluded that the use of volumes as large as those employed In this FIA mode permit the linear ranges of the calibration graphs to be significantly widened. As a result, they proposed the denomination scale-expansion techniques as an alternative to FIA titrations . 

Diffusion-entropy scaling relation the Rosenfeld relation... 

The Rosenfeld relation between scaled diffusion and excess entropy is defined below [5] ... 

Y. Rosenfeld, Relation between the transport coefficients and the internal entropy of simple systems. Phys. Rev. A 15 (1977), 2545-2549 A quasi-universal scaling law for atomic transport in simple fluids. J. Phys. Condens. Matter, 11 (1999), 5415-5427. 

In his original works, Rosenfeld considered hard spheres, soft spheres, Lennard-Jones system, and one-component plasma [52,53]. Thereafter, the excess entropy scaling was applied to many different systems, including core-softened liquids [17,18,51,54,55], liquid metals [56,57], binary mixtures [58,59], ionic liquids [60,61], network-forming liquids [54,60], water [62], chain fluids [63], and bounded potentials [51,64,65]. 

Based on the scaled particle theory results [79-81], Rosenfeld came up with the following functional form [78, 82-84],... 

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