clouds in the blue sky, Figure 1, we may think that the water molecules are .... Corresponding States Law, do not work for molecular interactions, which reflect.
The Chapter 2 for the Discovering the Cluster World book: 2. Clusters in the Nature
2.1 The Clusters in Space Numerous material objects around us have been formed by an action of chemical forces and intermolecular interactions during the cooling process of gaseous clouds, which in the young Universe consisted originally mainly of free moving atoms, ions and electrons. The Universe at its birth was in a plasma state with ionized atoms and free moving electrons. The distribution of temperature and density of matter in the Universe is highly heterogeneous. Some zones, such as stars and central regions of planets, till now stay extra hot and dense, but the main territory of the Universe is cold and less dense. The cooling of matter made possible the formation of neutral atoms and molecules. When temperature in certain domains of the Universe becomes low enough, the atoms join in molecules, which lifetime may overcome centuries. So, in these parts of the World the molecules appear as permanently existing elementary components of matter. At temperatures over 1 - 2 thousand Kelvin the dissociation of molecules and over 3 - 6 thousand Kelvin the ionization of atoms dominate over the clusterization, but at lower temperatures the formation of molecular and atomic clusters is possible. The weak attraction forces between molecules, discussed by Rowlinson [5], become able to create a plurality of tiny subnanosized and nanosized molecular complexes. The clusters in galactic gaseous clouds are nuclei and seeds [3] for the growth of nanocrystals or nanodroplets, depending on temperature. At a further lowering of temperature the clusters join in larger complexes, such as interstellar dust particles. The lower is the temperature, the more clusters may be merged together to form solid or liquid visible particles of the galactic dust clouds.
The gravitational attraction collects dust clouds in large material agglomerations, such as asteroids, planets and stars, thus producing the condensation of matter. So, starting from clusters, we come to the formation of stars and planets. The further development of infrared and microwave spectroscopy may give information about processes of clusters growth and merging in galactic dust clouds. Molecular interactions play an important role in formation of the environment, surrounding people on the Earth. Therefore, the investigation of molecular clusters and physics of their formation is vital for Humans. 2.1.1 Clusters as Nucleation Centers In scientific literature a great attention is attracted to the nucleation process [29, 32, 33]. It means the large enough clusters creation, which can serve as nuclei and grow in a supersaturated medium leading to the phase transition. This problem is essential for the vapor-fog transformation and growth of clouds in a supersaturated vapor; crystallization in a supercooled liquid and in a supersaturated solution; formation of aerosols in atmosphere and trails after jets; formation of galactic clouds, and so on. Some agents, such as dust, are supposed to play the role of seeds. For example, in the jet trail formation the soot in the engine exhaust is supposed to be the seed. But the 1D Chain clusters analysis [21, 23] shows that the length of linear clusters may be very large. These extra long clusters at a super saturation may serve as nuclei for the vapor condensation [3].
2.2 The water clusters in atmosphere and laboratories The analysis shows that the water and methanol vapors at low temperatures possess tetramers with giant bond energies and strong orientation of hydrogen bonds. This extra high orientation of bonds and their enlarged bond energies appeal for a new mechanism of intermolecular bonding. 2.2.1 From invisible clusters to visible droplets or snowflakes The water clusters are very influential objects in the Earth atmosphere. The evaporation of water from wet or liquid parts of the Earth surface creates the
upstream of hot and humid air in cyclonic regions. The cooling of lifting air creates favorable conditions for water clusters creation and growth. Observing white clouds in the blue sky, Figure 1, we may think that the water molecules are concentrated only in clouds. But, the blue regions between clouds possess not less concentration of Water molecules, accumulated in invisible tiny clusters, with small dimensions as compared to the wavelength of the visible range of light [3]. A similar process takes place in a morning after a rainless night. The dew, formed from small water clusters [3], covers grass and flowers. At low temperature the water vapor saturation density falls down the real density of vapor. And the excess of water molecules, concentrated mainly in large clusters, forms the dew that falls on grass and flowers. So, clusters behave as nuclei for the dew droplets.
Figure 1. White clouds with visible droplets of water on a blue sky filled with invisible clusters of water. In winter, at down zero Celsius degree, instead of dew, we see a frost on grass and leaves made of smallest crystals of ice, Figure 2. The frost has the same origin as the dew. The frost on cold windows possesses a complex structure with curved thicker lines looking like plumes of some fantastic bird. These lines are formed via some different molecular interaction mechanism than the rest of the window frost. In Siberia, Canada or Alaska in a cold winter day the breathing creates a white cover of frost around mouth and nose, on eyelashes, eyebrows, moustaches, beard, and a fur hat. The air is full of tiniest needles of ice flying in air without falling for
hours. Their origin seems to be similar to the creation of whiskers over the bulk ice in sub saturation conditions [34].
Figure 2. A frost on grass grown from invisible clusters of Water at low temperatures. A surprising fact, noticed by De Micheli and Licenblat [34], was that the whiskers of ice could grow in sub saturated conditions, while the bulk ice evaporated. It means the strength of bonds in whiskers is much larger than the bond strength in the bulk ice. The same may be stated for clusters. It will be shown in the next chapters that the tetramers in water and methanol vapors possess giant bond energies. In February 1962 at skiing with friends in Northern Ural Mountains the author met a strange form of snow that easily lifted up from tips of skis and could hang before face for a long time. This snow instead of ordinary snowflakes contained tiniest needles of ice, like whiskers. The whisker’s thickness is known to be near 3 mkm. With this small thickness the needle of ice has a large surface-to-mass ratio, supporting its flying. The water clusters participate in the snow making process in snow guns, named also as snow canons. Now all ski resorts are equipped by snow guns not to depend on the weather caprices. A powerful ventilator creates a flow of air with water droplets in it that quickly evaporate creating a cooled oversaturated vapor with a large concentration of water clusters. In this flow another mixture of air and water
is injected under a large pressure, which quickly cools at an expansion, thus creating the seeds for growing snowflakes. It takes approximately 15 meters of flight from the snow gun to form snowflakes. During the time flight the snowflake grows from invisible sizes to dimensions in several millimeters. If we look attentively at a fresh snow, we may notice among snowflakes the needles. They are not usually discussed, because the beauty of snowflakes is more attractive. Nevertheless, the snow needles present for clusters’ researchers a very important analogy: that among clusters may exist linear forms. It will be shown later that the linear 1D Chain clusters in real gases take a wide zone of temperatures and densities, where they dominate over 2D and 3D clusters [21, 23]. A very informative picture can be seen behind the jet plane, such as white traces staying in the sky for a long time. They are of the same origin as the frost: the formation of visible snowflakes or whiskers from invisible clusters, contained in the hot and humid jet engine exhaust [3]. Sometimes the trails are short, with quickly disappearing ends. The duration of traces depends on the water molecules concentration in cold atmosphere at the height of the jet flight. At an oversaturated concentration the trail stays for hours. At a concentration smaller than the saturation one the visible trail disappears quickly, leaving for some time an invisible trace of clusters. The progress in spectroscopy may make these temporary rests of trails visible. But much before the jet planes era it was noticed that elementary particles can leave in a supersaturated medium visible traces, formed by growing clusters. 2.2.2 The cloud chamber, named also as the Wilson chamber The cloud chamber is filled with a vapor of water or alcohol in a supersaturated state. When a charged particle passes through the chamber, the molecules along the particle’s trace may be ionized. The ions attract polar molecules of water or alcohol and give birth to clusters, which can grow to visible sizes in a supersaturated medium and form the mist zone along the trace. The mist trace width and length provide information about the type of the particle, its energy and
direction of movement. The form of the trajectory in magnetic field informs about the charge and mass of the particle. The cloud chamber for long time, from 20s years of last century, had been the main tool for detecting ionizing radiation and estimation of the charged particles movement parameters. Cloud chambers led to many outstanding discoveries, such as the positron and muon discovery by Anderson in cosmic rays. So, clusters have been used in science much before a full understanding of their physics and structure. 2.2.3 Our perception of water clusters We may feel the presence of water clusters in air by our skin [3]. The unbound in clusters molecules (monomers) do not heat or cool our skin: they bring some heat and take it away at the evaporation. When a cluster comes to our skin and then is evaporated in a form of monomers, it receives from our body the energy needed for its dissociation. The water molecules in clusters are joined together due to the cluster bond energy. It is the total energy of all intermolecular bonds in a cluster. So, if the air contains clusters, we feel a cooling effect. In summer this effect may be pleasant, but in winter a wet air makes us suffer from an extra cold. The presented here method [8] provides computation of the clusters’ bond energies [11, 19] and thus permits to estimate the cooling effect of clusters penetrating through our clothes. We may feel the effect of clusters in the perfume of air. And we enjoy wonderful dishes prepared by steaming. The author has shown [4] that clusters of water can dissolve volatile components of a condensed matter. Therefore, in wet air, filled with water clusters, there are more chances for fragrances to be extracted from flowers rather than in a dry air. So, high humidity of air is favorable for enjoying aroma of gardens or fields.
This direction of research may be very productive. The extraction of aromatic substances from leaves and flowers based on clusters of real gases may suggest advantages, such as better selectivity and conservation of fragrances.
2.2.4 A useful analogy To understand different structural forms of invisible clusters we can use the analogy with macroscopic visible forms of molecular complexes. The macroscopic complexes of Water molecules may be in different forms: solid in snowflakes or whiskers and liquid in droplets, Figure 3. The same may be stated for nanosized clusters: at low temperatures they are solid-like, but at elevated temperatures the cluster structure becomes more flexible and liquid-like, with a smaller strength and number of bonds between molecules.
Figure 3. A schematic view of a snowflake, a whisker and a droplet formed from Water clusters at different external conditions. The developed by the author computerized analysis of precise thermophysical data throws the light on this interesting transformation [11, 18, 19].
2.3 The Clusters in Living Cells In a living cell the macromolecular clusters perform the miracle of life. They easily change own structure under slight external influences and temperature changes [3] and enter the signal chain of a cell. A special branch of science, named as the Supramolecular Chemistry [35], quickly develops now, reflecting molecular interactions between macromolecules in living cells. In spite of low values for individual bonds between parts of macromolecules, a huge number of these bonds between long macromolecules convert weak intermolecular bonds in a powerful factor in life processes. And these bonds also act inside one long macromolecule determining its 3D structure and configurational transformations. The problem of
the proteins’ structural transformation may be connected with the physics of clusters. The hard, liquid and gaseous spheres of Earth with their temperature around 300 K are favorable both for life and for clusters formation. We dare say that the life itself benefits from transformations of clusters, which do not require too much of energy as compared to chemical transformations. The smallest changes in temperature or chemical potentials of basic components result in structural transformations of macromolecular clusters in a living cell. It may be one of basic mechanisms of the living cell functioning. So, to discover the mystery of life we should understand better the molecular interactions [9, 35] reflected in the clusters’ structure and properties.
2.4 The strategy of the Cluster World exploration Entering the world of equilibrium clusters the author had to create a classification of clusters reflecting the types of molecular interactions, clusters’ isomer structures, zones of different isomers domination, zones of soft transition between dominating isomers, clusters’ bond energies and attraction zone volumes. It was needed to move step-by-step from the smallest clusters, dimers and trimers in diluted gases, to larger clusters in denser gases and even in supercritical fluids. The investigation of clusters started from the simplest pure real gases just to build the foundation for more comprehensive cluster theory. 2.4.1 An Approach to Thermophysical Data Processing It was important to elaborate the method of investigation and to formulate the unknown before properties of molecular interactions for different types of clusters in different types of real gases. A usual for chemical compounds diversity of their properties in the case of atomic and molecular clusters also exists. The deeper is penetration in the molecular interactions details, the more individual happen to be the properties of different gases. The universal approaches, such as the
Corresponding States Law, do not work for molecular interactions, which reflect the electronic orbits of atoms and molecules complex quantum structure. The developed by author thermal analysis of regularized experimental thermophysical data method provides a physically clear vision of the cluster fractions’ structure in pure real gases. The method is based on the series expansion of equilibrium thermophysical functions by the Monomer fraction density Dm, introduced by the author in the family of thermophysical properties of fluids [16]. The method is related to the so called inverse mathematical problem arising in the processes of hidden parameters extraction from experimental data and for this reason is very sensitive to errors in experimental data [26]. But utilization of regularized data from the NIST database permits to solve the problem successfully. 2.4.2 The discovery of clusters’ unusual properties The most informative thermophysical function for the clusters’ properties analysis has proven to be the potential energy U = E (T, P) – E (T, 0), where E (T, P) and E (T, 0) are internal energies of real and ideal states of a gas at a temperature T [9]. Its positive density (-UD) divided by the second power of the Monomer fraction density Dm, W2+ = (-UD) / Dm2, is the function W2+ (Dm) to be expanded by Dm. The zero pressure limit of it gives the pair bonding coefficient W2 of the potential energy density series expansion. The temperature dependence W2 (T) permits to estimate the dimer bond energy E2 (T) and the dimer fraction equilibrium constant. The E2 (T) computation met a problem connected with an influence of the elastic monomer-monomer collisions on the W2 (T) values at high temperatures [20]. It got possible to overcome this difficulty by applying the principle of flat bond energy at high T [11, 20]. It is physically clear that the dimer bond energy cannot change at high T, where the energy of thermal movement is much larger than the depth of the potential well binding particles in a dimer. This principle permitted to estimate the elastic monomer-monomer collisions contribution in the W2 (T). It happened that at T < 800 K almost for all investigated gases the monomers’ contribution ∆W2 (T) to potential energy of a gas grows with T linearly. And at T >
800 K there is a slight quadratic addition to ∆W2 (T). The coefficients before T and T2 can be easily found, thus opening possibility to clear the dimer fraction’s contribution into potential energy density of a gas from monomers’ collision contribution. It is a generous present of Nature opening ways to study dimers’ bond parameters in a wide range of temperature! The pair bond parameters form a foundation for large clusters investigations. And here we have been surprised by another present of Nature: a wide area of density and temperature, in which the geometric progression law for clusters’ coefficients acts! It resulted in the discovery of 1D linear Chain clusters [21, 23]. The discovered properties of Chain clusters tell that in their area of domination every particle in the chain cannot have more than two bonds. So, the formation of branches is forbidden for some unknown reason! It is difficult to understand from microscopic considerations, but the thermophysical properties analysis does not let another option than the linear structure of a cluster. It is a real paradox and it paves the way to new discovery of the linear Chain clusters mechanism of formation. Returning back to snowflakes we see that the formation of branches takes place approximately at a millimeter distance between neighbor branches. So, some unknown force prevents from earlier formation of branches in snowflakes. A simple geometric progression law for Chain cluster fractions characteristics permitted to derive Equations of State for their zone of domination. A large width of this zone makes the Chain cluster concept useful for science and practice!
