Moderate Point: Balanced Entropy and Enthalpy Contributions in Soft Matter

TL;DR

This paper introduces the concept of a 'moderate point' in soft matter, where entropy and enthalpy are balanced, explaining their large fluctuations and sensitivity to conditions, with implications for biological and chemical systems.

Contribution

It defines a quantitative thermodynamic state called the moderate point in soft matter, linking it to maximal fluctuations and spatial correlations, advancing understanding of their unique features.

Findings

Moderate point maximizes order parameter fluctuations.

Response functions and correlation lengths peak at the moderate point.

Soft matter's sensitivity and mesoscopic scales are explained by the moderate point.

Abstract

Various soft materials share some common features, such as significant entropic effect, large fluctuations, sensitivity to thermodynamic conditions, and mesoscopic characteristic spatial and temporal scales. However, no quantitative definitions have yet been provided for soft matter, and the intrinsic mechanisms leading to their common features are unclear. In this work, from the viewpoint of statistical mechanics, we show that soft matter works in the vicinity of a specific thermodynamic state named moderate point, at which entropy and enthalpy contributions among substates along a certain order parameter are well balanced or have a minimal difference. Around the moderate point, the order parameter fluctuation, the associated response function, and the spatial correlation length maximize, which explains the large fluctuation, the sensitivity to thermodynamic conditions, and mesoscopic spatial and temporal scales of soft matter, respectively. Possible applications to switching chemical bonds or allosteric biomachines determining their best working temperatures are also discussed.