Molecular volume difference method linear

The basic principles are described in many textbooks [24, 26]. They are thus only sketchily presented here. In a conventional classical molecular dynamics calculation, a system of particles is placed within a cell of fixed volume, most frequently cubic in size. A set of velocities is also assigned, usually drawn from a Maxwell-Boltzmann distribution appropriate to the temperature of interest and selected in a way so as to make the net linear momentum zero. The subsequent trajectories of the particles are then calculated using the Newton equations of motion. Employing the finite difference method, this set of differential equations is transformed into a set of algebraic equations, which are solved by computer. The particles are assumed to interact through some prescribed force law. The dispersion, dipole-dipole, and polarization forces are typically included whenever possible, they are taken from the literature. 

In this chapter we presented two structural measures of molecular shape that can be used as predictor variables in MLR (multiple linear regression) analysis of structure-activity studies - cylindrical (8,G) and ovality ( in, i = 1,2,3) molecular descriptors - and two inexpensive overlapping methods useful for quick receptor mapping - MTD (minimal topological difference) and MVD (minimal volume difference). A subsequent statistical analysis of QSAR models developed with these shape molecular descriptors explained well the variance in the observed reactivity data (8 descriptor of cylindrical shape) and biological activity of retinoids (MTD) and sulfonamides (MVD). 

The hydrodynamic volume separation mechanism of SEC, along with the different molecular size/weight relationships of branched and linear polymers of identical chemical composition, can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper both conventional SEC and SEC/LALLS are used to obtain data about branching in samples of poly(vinyl acetate) (PVA) and polychloro-prene (PCP). 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

To calculate the contributions of all molecular groups to retention (adsorption equilibrium constant) ai, ARmi under some standard conditions, it is necessary to determine the retention volumes Vm (Va) or capacity factor k or Rm values from Rp data for a number of compounds possessing different amounts of such groups and to solve the systems of linear equations (2 or 3 or 5) by the least -squares method. 

The specific surface area (Sbet) was evaluated by 2-parameters linear BET plot in the range p/p° 0.01-0.2. The total pore volume (Vj) was evaluated by Gurvitsch rule. Mean pore size (doFi) and pore size distributions were calculated using DFT method, based on molecular statistical approach. It was applied over the complete range of the isotherm and was not restricted to a confined range of relative pressure or pore sizes. Pore size distribution was calculated by fitting the theoretical set of adsorption isotherms, evaluated for different pore sizes, to the experimental results. DFT model was particularly effective for evaluation in the borderline range between micro and mesopores [14]. 

---