On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

Effect of nonionic surfactants on the state of water in cement systems (by NMR relaxation data). 2. A model of the pore space

The state of water in cement compositions containing polypropylene glycol (PPG) and hexanol in the course of their hardening for a time up to 28 days was studied by the NMR relaxation technique. A model of the porous structure formed in the process of cement hardening, which takes into account the distribution of water in pores of cement stone in the presence of additives, is proposed. It is shown that, in the absence of additives, the number of large pores in cement stone (being the largest defects, these pores determine the strength of cement stone) noticeably decreases with increasing the hardening time from 7 to 28 days. PPG and hexanol have different effects on the structure of cement stone in the process of its hardening. According to NMR data, the presence of PPG results in the formation of large-size pores (19 - 35 μm), whose number increases with increasing hardening time and the additive concentration. In the presence of hexanol (1%), the content of macropores in cement stone is close to their content in the reference sample; however, in the presence of hexanol, this level of macropore content is attained in shorter hardening times (about 7 days)

Effect of nonionic surfactants on the state of water in cement systems (by NMR Relaxation Data). 1. The state of water in the course of structure formation

The state of water in bound-disperse structures formed in the course of cement hardening and the effect of surfactants [polyethylene glycol (PEG), polypropylene glycol (PPG), and hexanol] on this state and also the state of water in freely-disperse structures in hydrated cements in the presence of the same surfactants at different extents of their adsorption were studied by the NMR relaxation technique. It is established that, in the semilog scale, the envelope of spin-echo signals from protons in the samples with a water-to-cement ratio of 0.3 can be decomposed into three components (for samples containing PPG or hexanol additives, into four components) corresponding to protons of different water fractions varying in the course of formation of the structure of cement stone. The maximum change with time was found for the occupancy of the shortest T2 component. During several hours of cement hardening, the occupancy of this water fraction ranged up to 96 - 97% (from the total signal of water protons). Consideration of adsorption isotherms and NMR relaxation data for samples containing PPG and hexanol additives suggests that the mobility of water molecules, which determine the intermediate T2 components, is associated with the behavior of water near the interface in the presence of adsorbed substances. It is shown that, in the presence of additives, boundary layers of water are changed. At the end of the second week of the hardening process, the fraction of the short T2 component ranged up to 78 - 84% from the total proton signal. A scheme of the water distribution in pores of cement stone in the presence of additives and its interrelation with relaxation processes are discussed

Effect of nonionic surfactants on the state of water in cement systems (by NMR Relaxation Data). 1. The state of water in the course of structure formation

The state of water in bound-disperse structures formed in the course of cement hardening and the effect of surfactants [polyethylene glycol (PEG), polypropylene glycol (PPG), and hexanol] on this state and also the state of water in freely-disperse structures in hydrated cements in the presence of the same surfactants at different extents of their adsorption were studied by the NMR relaxation technique. It is established that, in the semilog scale, the envelope of spin-echo signals from protons in the samples with a water-to-cement ratio of 0.3 can be decomposed into three components (for samples containing PPG or hexanol additives, into four components) corresponding to protons of different water fractions varying in the course of formation of the structure of cement stone. The maximum change with time was found for the occupancy of the shortest T2 component. During several hours of cement hardening, the occupancy of this water fraction ranged up to 96 - 97% (from the total signal of water protons). Consideration of adsorption isotherms and NMR relaxation data for samples containing PPG and hexanol additives suggests that the mobility of water molecules, which determine the intermediate T2 components, is associated with the behavior of water near the interface in the presence of adsorbed substances. It is shown that, in the presence of additives, boundary layers of water are changed. At the end of the second week of the hardening process, the fraction of the short T2 component ranged up to 78 - 84% from the total proton signal. A scheme of the water distribution in pores of cement stone in the presence of additives and its interrelation with relaxation processes are discussed