The influence of hydrogen bonds on the physical and chemical properties of hydrogen bonding fluid system of A a D d type is investigated from two viewpoints by the principle of statistical mechanics. In detail, we proposed two new ways that can be used to obtain the equilibrium size distribution of the hydrogen bonding clusters, and derived the analytical expression of a relationship between the hydrogen bonding free energy and hydrogen bonding degree. For the nonlinear hydrogen bonding systems, it is shown that the sol-gel phase transition can take place under proper conditions, which is further proven to be a kind of geometrical phase transition rather than a thermodynamic one. Moreover, several problems associated with the geometrical phase transition and liquid-solid phase transition in nonlinear hydrogen bonding systems are discussed.Keywords: hydrogen bonding fluid, equilibrium free energy, geometrical phase transition.Fluids often refer to gases and liquids, which can be called hydrogen bonding (HB) fluid if there are hydrogen bonds formed in the fluid system. Hydrogen bond is a kind of specific interaction contributed by many complicated mechanisms, and plays an important role in biology, chemistry, physics, supramolecular science and crystal engineering [1] . Experimentally, the methods of NMR, IR and X-ray and neutron diffractions are usually used to characterize the relevant properties of HB clusters in various HB fluids [2] and study the influences of hydrogen bonds on the systems. Theoretically, there exist two types of methods involved in investigations on the HB systems. The former aims at the small HB clusters by using, for example, the methods of ab initio [1,3] , molecular dynamics simulation [4] . The latter is focused on the HB systems with a great number of hydrogen bonds, and mainly includes Monte Carlo simulation [5] , percolation model [6,7] , reversible gelation theory [8 -11] and lattice-fluid theory [12][13][14] and so on [15,16] . Indubitably, a large number of early works on the hydrogen bonds provide the basis for further developments in this field.As is well known, there always exist a large number of HB clusters with a wide size distribution in a practice HB system, and it has been an active interest to study various HB clusters since they give rise to significant effects on the physical and chemical properties of the HB systems. As a matter of fact, the formation of hydrogen bonds is a reversible association and the lifetime of a single hydrogen bond is about in the order of 10 −12 s [17] , or even shorter than this. Thus

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A BPh2‐chelated heterochrysene derivative has been synthesized and characterized. Single crystal analysis of its analogous BF2 complex shows that all carbon and nitrogen atoms are almost in a plane, while the boron atoms twist out of this plane with a torsion angle of 28.796° measured between plane OBN and plane C1–C4–C4′. The BPh2 and BF2 compounds emit strong yellow and green light in methylene chloride with high fluorescence quantum yields, respectively. Thermogravimetric analysis results indicate that the thermal stability of both compounds is high. In addition, a photoswitching device was fabricated based on a thin film of the BF2 complex spin‐coated onto single‐walled carbon nanotubes, which produces a steady and reproducible photocurrent response.

Hydrogen bonding (HB) in a mixed nonlinear system consisting of A a 1 D d 1 and Ā a 2 D̄ d 2 types of molecules is studied with the different activities of the groups being taken into account. Under the framework of the mean field theory, the partition function concerned the HB process of the system is given by two different statistical viewpoints. By which the equilibrium free energy of the system in the pregel regime, the law of mass action of HB process and the equilibrium size distribution of the HB clusters are carried out. The sol−gel phase transition is shown to take place in such a HB system with the gelation condition being given, and then the sol and gel free energies in the postgel regime are also obtained. Furthermore, the scaling laws satisfied by the kth moments and the gel fraction near the critical point are obtained for describing this kind of phase transition.

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