Ice structures inside single wall carbon nanotubes

Abstract

Water is the most important liquid present on our planet. It plays a fun damental role in both geological and chemical processes [1] and it is also essential for life [2]. Even if we are familiar with this liquid in our every day life we have not completely understood its properties from a scienti c point of view. This is a liquid as important as it is mysterious. There are more then 60 known anomalies in the water behavior [3, 4]. These anomalies concern its phase, its density, its structure, its thermody namics and its dynamics and they are encountered over all its puzzling phase diagram. All this anomalies probably come from the capability of water molecule to form hydrogen bonds. Nowadays the study of the water is one of the most interesting eld in physics. A huge amount of theoretical, compu tational and experimental works [1,3,4] have been carried out to understand the phase diagram and the peculiar properties of water. Since most of the liquid water anomalies arise upon cooling when the temperature is near or below to the freezing temperature, an explanation to the anomalies of water can be found in the so called supercooled regime. Water is in the super cooled regime when it is in the liquid state but below the freezing temperature. The supercooled condition is obviously a meta stable state. This regime can be achieved with an accurate setup of the experiment, but there are experimental limits that prevent us from going down in temperature at will. This region of the phase space in which is not possible to observe liquid water, in a metastable state, it known as no man's land . However this limit is not due to thermodynamic constraints [4], the homogeneous nucleation is in fact a kinetic constraint and it is function of the cooling rate and of the observation time. This means that in the future it will be possible investigate the no man's land. Due to the di culties of experiments, molecular dynamics simulation are often use in the study of the liquid phase of water upon supercooling and it is possible to investigate the no man's land. Rahman and Stillinger in the 1971 performed the rst molecular dynamics simulation of liquid water [5]. Starting from that rst work the contribution of the simulation was crucial 1 2 to the development of our knowledge in this eld. In many relevant phenomena in di erent elds like geology and biology water is con ned in di erent environments. The behavior of water in con tact with hydrophilic or hydrophobic surfaces is central in many studies of biological and geological systems. Therefore the study of con ned water is an issue of wide interest as it allows us not only to investigate the general properties of water [6, 7] but it also has applicative purposes [8]. Moreover the con nement can prevent the crystallization and make possible to study the no man's land. The studies of water solution are also very relevant in the understanding of biological an chemical systems. The investigation of aqueous solutions can help to shed light on the numerous mysteries of bulk water. In fact the presence of solutes in water is known to a ect thermodynamic quantities such as the boiling point, the freezing point and the vapor-liquid critical point [9 11]. Solutions of electrolytes are more easily supercooled than bulk water, as the temperature of homogeneous nucleation shifts downward upon increasing the solutes content [12]. Among con ning structures carbon nanotubes (CNTs) have attracted in recent times a great interest due to their fascinating properties that made them potentially useful in a wide variety of applications. These cylindrical nanostructures are formed by one or more layers of graphene. Among the numerous applications [13] are the use of CNTs in electronic devices [14] and their usage in Biology and Medicine [15, 16]. There are also a considerable number of applications connected to water. For example, the study of the water ow through atomic smooth surface of a carbon nanotubes [17] and its enhancement found by both theoretical calculations [18] and experiments [19], or the study of membranes made by carbon nanotubes that can be also used as lter in desalination mechanisms for di erent solutions like the NaCl aqueous solution [20, 21]. Water can ll the space inside a single walled carbon nanotube (SWCNT) [22, 23] and it was found both experimentally [24 26] and by simulation [27, 28] that it easily crystallizes. The water ordered structures that form inside the SWCNTs are called ice nanotubes [29]. Importantly and unexpectedly it was recently experimentally discovered by an MIT group [30] that water freezes already at boiling conditions inside the nanotube. Thus, the hydrated SWCNTs can be considered as possible candidates for the latent thermal storage in diverse systems [31]. The main theme in this PhD thesis is the study of con ned water in SWCNT's , with particular focus on the structures of ice nanotubes. I per formed molecular dynamics simulations using for water molecule, for the rst time inside SWCNT, a very realistic potential: the TIP4P/ICE [32]. This 3 model was designed to study the solid phases of water and gives also the best overall ices phase diagram and the best predictions for the densities of several ice forms. Other molecular dynamics simulations on water in car bon nanotubes focusing on solid/liquid transition [27,29] have used a model, TIP4P, that has a freezing temperature in the bulk phase 42.65 K lower than experimental bulk water at ambient pressure [33]. This inevitably leads also to a downward displacement of the freezing temperatures inside the carbon nanotubes. I also studied aqueous solutions in this thesis. I participated to an anal ysis on anion hydration aqueous ionic solutions. Then I also performed two preliminary study on two other systems composed by a ionic aqueous solu tion of NaCl and an aqueous solution of methane in SWCNT. In the case of the sodium chloride we were interested to the possible inclusion of ions in the structure of ice nanotubes and more in general on the e ect of the ions in the freezing. In the case of CH4 our goal was to study the e ect of a strong con nement in the process of hydrates formation. An hydrate is a water cage of water molecules that surrounds the methane and it usually forms under extreme condition of pressure. This thesis is structured as follows. In Chapter 1 a general picture of the scienti c background of our knowl edge of the water physics is provided. In this chapter is illustrated how the structure of water is connected to its capability to form an hydrogen bond network. The central part of this chapter is dedicated to the water anoma lies. In this section are presented the most known of the several anomalies of water as: the density anomaly, the behavior of the thermodynamic response functions and the anomaly of the di usion coe cient. The last section is ded icated to the supercooled regime and is presented one of possible explanations of the anomalous behavior of water. This theory considers the presence of a liquid-liquid critical point in the no man's land. In Chapter 2 is presented an overview of the solid phase of water and the so called ice rules. The only two phases that will be illustrated in detail are the ice Ih and the ice XI, in order to present the issue of proton ordering that was crucial for our work. In the last section are presented the main characteristic of the sixteen ice forms that are actually known. In Chapter 3 I illustrate the methodology used in this work. Starting from the main elements of the molecular dynamic technique I enter in the details of the potentials used. The last section is dedicated to the TIP4P/ICE that is the water model that I used for our study. The main argument of Chapter 4 is the liquid solid transition of wa ter inside SWCNT's. After a detailed discussion of the model used for the nanotube, describing the geometry and the potential used, the details of the 4 simulation are reported. We simulated the cooling process along the ambient pressure isobar of water con ned in nanotubes of ve di erent diameters In the last part of this chapter we compare our results to the recent experimental result of the MIT group and the previous MD study. Chapter 5 is about the analysis of the ice nanotubes structures. In the rst part is illustrated how the ordering of water grows upon decreasing temperature. The structures of the ice nanotubes are discussed i the n central part of this chapter where the theoretical structures of ice nanotubes are compared with the radial distribution function obtained in our simulations. Finally in the last section I discus the issue of proton ordering that we found in the ice nanotube structure. In Chapter 6 it is reported an analysis done on the e ect that ions solu tion have on bulk water. It is shown how the ions alter the radial distribution function of the water atoms. In this chapter it is also discussed the issue of the ions hydration. In Chapter 7 I discus the simulation details and the preliminary results of our study of systems made by an NaCl ionic aqueous solution con ned in a SWCNT. The simulation of solutions with two di erent concentration was designed according to the result presented in the previous chapters. The last part of this chapter deals with the simulation details and the results of our study on CH4 and water solution con ned in a SWCNT. Two systems made by nanotubes of di erent diameter an lled with an aqueous solution of methane are studied, the concentration of the methane in the solution was the same. The Last Chapter contains the nal remarks and general conclusions of the present Thesis. Possible outlooks are also outlined, especially on the Chapter 7 whose results are preliminary.