Visualization and thermodynamic encoding of single-molecule partition functions

TL;DR

This paper introduces a novel method to measure and visualize single-molecule thermodynamics by combining nanoscopic confinement, temperature-controlled microscopy, and computational modeling to encode and decode information at the nanoscale.

Contribution

It presents a new experimental and computational approach to determine thermodynamic quantities of single molecules, overcoming limitations of ensemble averaging.

Findings

Successfully visualized single-molecule probability distributions at different temperatures.

Reproduced experimental molecular states with high accuracy using a Boltzmann weighting model.

Demonstrated encoding of information in position-temperature space for nanoscopic thermal probes.

Abstract

Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and enthalpy at finite-temperatures are challenging to determine with ensemble-averaging alone. Here, we provide a method to access single-molecule thermodynamics, by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, where we directly record finite-temperature time-averaged statistical weights using temperature-controlled scanning tunneling microscopy. The obtained patterns represent a real space equilibrium probability distribution. We associate this distribution with a partition function projection to assess spatially resolved thermodynamic quantities, by means of computational modeling. The presented molecular dynamics based Boltzmann weighting model is able to reproduce experimentally observed molecular states with high accuracy. By an in-silico customized energy landscape we demonstrate that distinct probability distributions can be encrypted at different temperatures. Such modulation provides means to encode and decode information into position-temperature space or to realize nanoscopic thermal probes.