Liquid molecular theory

MSE.12. 1. Prigogine et J. Philippot, Theorie moleculaire du point lambda de I helium liquide, (Molecular theory of the lambda point of liquid helium), Physica 18, 729—748 (1952). 

MSE.13. I. Prigogine et J. Philippot, Sur la theorie moleculaire de I helium hquide, II. Le coefficient de dilatation thermique de I hehum liquide (Molecular theory of liquid hehum, II. The coefficient of thermal dilatation of hquid hehum), Physica 19, 227—234 (1953). 

Hirschfelder J O, Curtiss C F and Bird R B 1954 Molecular Theory of Gases and Liquids (New York Wley)... 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

Hirschfelder, J. O., C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley and Sons, New York, 1954. 

Hirschfelder, J.O. Curtiss, C.E. Bird, R.B. Molecular Theory of Gases and Liquids Wiley New York. 1954 Chapter 1. 

D. E. Martire and R. E. Boehm, Unified molecular theory of clrromatography and its application to supercritical fluid mobile phases. 1. Eluid-liquid (absorption) clrromatography , J. Phys. Chem. 91 2433-2446 (1987). 

Continuous transition of state is possible only between isotropic states it may thus occur between amorphous glass (i.e., supercooled liquid of great viscosity) and liquid ( sealing-wax type of fusion ), or between liquid and vapour, but probably never between anisotropic forms, or between these and isotropic states. This conclusion, derived from purely thermodynamic considerations, is also supported by molecular theory. 

Thus, from an investigation of the compressibility of a gas we can deduce the values of its critical constants. We observe that, according to van der Waals theory, liquid and gas are really two distant states on the same isotherm, and having therefore the same characteristic equation. Another theory supposes that each state has its own characteristic equation, with definite constants, which however vary with the temperature, so that both equations continuously coalesce at the critical point. The correlation of the liquid and gaseous states effected by van der Waals theory is, however, rightly regarded as one of the greatest achievements of molecular theory. 

Kinetic-molecular theory provides an explanation on a molecular level for this equilibrium. Evaporation from the liquid occurs as fast moving molecules on the surface escape from the liquid. In turn, molecules in the gas phase strike the liquid and condense, As the concentration (pressure) of gas molecules builds up in the gas phase, the rate of condensation increases. Eventually, a pressure is reached where the rate of condensation and rate of evaporation just balance, and equilibrium is achieved. The equilibrium pressure is denoted by p and is known as the vapor pressure. The magnitude ofp depends upon the substance, composition of the liquid, and any two of our thermodynamic variables such as temperature and total pressure. The criteria for equilibrium that we will now derive provide the thermodynamic relationships that will help... 

Freed J. H. Stochastic-molecular theory of spin-relaxation for liquid crystals, J. Chem. Phys. 66, 4183-99 (1977). 

Different molecular theories have been established [27-32] to describe the viscoelasticity of polymeric liquids. Due to their importance, a brief survey of the different theories will be given below. 

Hirschfelder JO, Curtiss CB, Bird RB (1954) Molecular theory of gases and liquids. John Wiley, New York... 

Lado F (1997) Molecular theory of a charged particle in a polarizable nonpolar liquid. J Chem Phys 106(11) 4707—4713... 

A recent breakthrough in molecular theory of hydrophobic effects was achieved by modeling the distribution of occupancy probabilities, the pn depicted in Figure 4, rather than applying a more difficult, direct theory of po for cavity statistics for liquid water (Pohorille and Pratt, 1990). This information theory (IT) approach (Hummer et al., 1996) focuses on the set of probabilities pn of finding n water centers inside the observation volume, with po being just one of the probabilities. Accurate estimates of the pn, and po in particular, are obtained using experimentally available information as constraints on the pn. The moments of the fluctuations in the number of water centers within the observation volume provide such constraints. 

The gas A must transfer from the gas phase to the liquid phase. Equation (1) describes the specific (per m2) molar flow (JA) of A through the gas-liquid interface. Considering only limitations in the liquid phase, this molar flow notably depends on the liquid molecular diffusion coefficient DAL (m2 s ). Based on the liquid state theories, DA L can be calculated using the Stokes-Einstein expression, and many correlations have been developed in order to estimate the liquid diffusion coefficients. The best-known example is the Wilke and Chang (W-C) relationship, but many others have been established and compared (Table 45.4) [28-33]. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

---