The concept of structural temperature

In this section, we shall discuss the theoretical aspects of this problem. Starting with the concept of structural temperature which bypasses the need to define the structure, we formulate the problem within the exact framework of the MM approach. This approach naturally leads to the application of the Kirkwood-Buff theory, which provides only the sign of the structural changes. Finally, we present a simple measure of the amount of structural change in the solvent induced by a simple solute. 

Bernal and Fowler (1933) introduced the idea of structural temperature, which is defined as follows. Suppose one measures some physical property 0 for pure water and for an aqueous solution, both at the same temperature T and pressure P. In this section, P will be fixed and therefore omitted from the notation. We denote the change in the property 0 due to the addition of Ns solute molecules by 

consider the change in the same property 0 for pure water caused by a change in temperature  

The structural temperature of the solution, with Ns moles of s at temperature T, is defined as the temperature T for which we have the equality 

Note that the concept of the structural temperature, though using the concept of structure, does not define the concept of the structure of water. The idea underlying this definition is qualitatively clear. It is intuitively clear that, however we choose to define the structure of water, this quantity must be a monotonically decreasing function of the temperature. Therefore, the changes in the structure can be detected on a corresponding temperature scale.  

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From a kinetic viewpoint, salinity action on the water solution structure is similar to the action of temperature and pressure. This was a reason to compare the effect of temperature and pressure, on the one hand, and salinity, on the other, on the mobility of solution components, and therefore, on its structure. In this connection John Desmond Bernal (1901-1971) and Ralph Howard Fowler (1889-1944) introduced the concept of structural temperature of the solution. Under their definition, structural temperature of a given solution is equal to the temperatme of pine water with the solution s structural properties (viscosity, density, refraction, etc.). Ions with positive hydration work as lowering of temperature and have structural temperature below the solution temperature ions with negative hydration - as increase of temperature, and their structural temperature is higher than the solution s temperature. Non-polar compounds occupy plentiful space, thereby lowering the intensity of translation motion of the water molecules, lowering the structural temperature of the solution, as in a case of positive hydration. 

Long ago Bernal and Fowler (1933) introduced the concept of the structural temperature of aqueous solutions. This is that temperature, Tsu, at which pure water would have effectively the same inner structure as the water in a solution at the temperature T. They suggested that Tstr could be estimated from viscosity, x-ray diffraction, Raman spectroscopy, etc., but did not provide explicit methods and values. TheD20 vs. H2O isotope effects on x-ray Raman spectra indicate (Bergmann et al. 2007) that D2O has a structural temperature lower by 20 K than H2O at ambient conditions. This is ascribed to the inherently stronger hydrogen bonding in the heavy water. The concept of structural temperature has by now been practically abandoned, however. 

The concept of structural temperature of aqueous electrolytes has more or less been abandoned in recent years. 

The concept of structural temperature, though a useful operational definition of the structure of water, is not entirely satisfactory since it is generally dependent on the property (f). Using different properties for the same solution, we can get different structural temperatures. Nevertheless, in the old literature, it was common to classify different solutes in terms of their structural temperature, which in turn classifies solutes according to whether they are structure makers or structure breakers. ... 

For instance, if a solute increases the viscosity of water, it seems reasonable to attribute this effect to the increase in the structure of the solvent. This reasoning led to the introduction of the concept of structural temperature, which is defined as follows ... 

The influx of genomic sequence information has led to the concept of structural proteomics, the determination of protein structures on a genome-wide scale. A structural proteomic project used the sequenced genome of the thermophilic Methanobacterium thermoautotrophicum as a source of targets for structure determination.As expected, proteins from M. thermoautotrophicum possess high thermostability with a transition midpoint temperature between 68 and 98 °C. Small proteins were C- and N-labelled and their solution structures were solved using multinuclear and multidimensional NMR spectro-scopy. The project was also extended to some proteins from Thermotoga maritima ... 

Kivelson and Tarjus (1998) have considered the attractive possibility of invoking the concept of "structural frustration" in supercooled liquids, to account for the observed liquid viscosity behaviour. Around the melting temperature, T (7>1.37 g), most melts behave normally in the sense of exhibiting an Arrhenius temperature... 

In all of these models, the hydrogen bonds, or the structure of liquid water, were traditionally emphasized as the main molecular reasons for the anomalous behavior exhibited by liquid water. However, underlying this relatively ill-defined concept of structure (which was much later defined in statistical mechanical terms see Sec. 2.7) lies a more fundamental principle which can be defined in molecular terms, and which does not explicitly mention the concept of structure yet is responsible for the unusual properties of liquid water. This principle was first formulated in terms of generalized molecular distribution functions in 1973. It states that there exists a range of temperatures and pressures at which the water-water interactions produce a unique correlation between high local density and a weak binding energy. Clearly, this principle does not mention structure. As will be demonstrated in this section, it is this principle, not the structure per se, which is responsible for the unique properties of water as well as of aqueous solutions. ... 

The atomic reflecting power Fn as a function of sin B/l or of dhjcl depends on the structure of the atom and also on the forces exerted on the atom by surrounding atoms, inasmuch as the temperature factor (also a function of dh]c ) is included in the J -curve. Values of F for various atoms have been tabulated by Bragg and West. Nov it is convenient to introduce the concept of the atomic amplitude function An, defined by the equation... 

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

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