## The Janus Fluid: A Theoretical PerspectiveThe state-of-the-art in the theoretical statistical physics treatment of the Janus fluid is reported with a bridge between new research results published in journal articles and a contextual literature review. Recent Monte Carlo simulations on the Kern and Frenkel model of the Janus fluid have revealed that in the vapor phase, below the critical point, there is the formation of preferred inert clusters made up of a well-defined number of particles: the micelles and the vesicles. This is responsible for a re-entrant gas branch of the gas-liquid binodal. Detailed account of this findings are given in the first chapter where the Janus fluid is introduced as a product of new sophisticated synthesis laboratory techniques. In the second chapter a cluster theory is developed to approximate the exact clustering properties stemming from the simulations. It is shown that the theory is able to reproduce semi-quantitatively the micellization phenomenon. |

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### Contents

1 | |

2 Clustering and Micellization in a Janus Fluid | 21 |

A Connection with Wertheim Association Theory | 42 |

B The Excess Internal Energy per Particle of the Clusters | 43 |

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### Common terms and phrases

attractive BMCSL canonical ensemble Carnahan-Starling approximation Chem cluster diameter cluster theory clustering properties colloidal particles compressibility factor configurational partition function correlation function critical point detailed balance energy per particle equilibrium cluster concentrations excess internal energy Fantoni free energy function of density gas branch Giacometti Granick hard-sphere hemisphere high temperature hydrophobic ideal gas approximation integral equation integral equation theories interactions intra-cluster configurational partition Janus fluid Janus particles Kern and Frenkel Kern-Frenkel model low temperature micellization phenomenon microscopic Molecular dynamics Monte Carlo data Monte Carlo method Monte Carlo simulations n-cluster number of particles pair-potential patch perturbation theory phase diagram Phys potential energy radial distribution function reduced excess internal reduced temperature reproduce the micellization sample Sciortino self-assembly soft matter sphere SpringerBriefs in Physics square-well statistical physics structure factor surfactant thermal thermodynamic perturbation theory thermodynamic quantities vapor phase vesicles Zinter ρσ