Partial specificity

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

The subscripts 1,2,3 refer to the main solvent, the polymer, and the solvent added, respectively. The meanings of the other symbols are n refractive index m molarity of respective component in solvent 1 C the concentration in g cm"3 of the solution V the partial specific volume p the chemical potential M molecular weight (for the polymer per residue). The surscript ° indicates infinite dilution of the polymer. 

Based on the assumption that the total specific volume can be calculated as the sum of the partial specific volumes of the initial and forming components, and expressed pj by TaF5 molar fraction - N,- using equation (64), an equation representing the total variable density of the melt (p ) can be written as follows ... 

Table 3 Refractive index increment and partial specific volume of hyaluronan (M 10 g/mol) determined at different salt concentrations (from [28])...

Po and rio are the densities and viscosities of the solvent, P2o,w and rj2o,w the corresponding values at 20.0 °C in water, v is the partial specific volume, which for neutral polysaccharides can often be reasonably estimated from the carbohydrate content [31] and takes on values between 0.5-0.7 ml/g for... 

The amount of hydrated biopolymer and of free water in the biopolymer-water system, the thermodynamic notion of partial specific volume has been introduced and is frequently determined. The relation to Vsp, the specific volume, is shown by the equation ... 

Combination of the Perrin function, p often referred as the frictional ratio due to shape with the frictional ratio (f/fo) enables the degree of expansion of the molecule (vh/ w ) to be estimated, where Vh, (cw / g) is the volume of the swollen molecule (Polysaccharide or protein + associated solvent) per unit mass of polysaccharide and v is the partial specific volume (essentially the anhydrous molecule) ... 

The viscosity increment was determined as v = B v = 172.7 ( 2 5 for spheres) where B is the viscosity coefficient characteristic of a given solue-solvent pair, and amounts to (9.91 0.24)xl0" ff/ A g" for PGA in aqueous solution. is the partial specific volume of the macromolecular component equal to [Pg.612]

The partial specific volume of the monomeric unit in PGA was found to be approximately 3 per cent higher than the value of D-galacturonic acid... 

V being the (partial) specific volume of the polymer and m=xV/v the mass of a polymer molecule. The sign and magnitude of the total free energy change AF for a given distance a depends, through J, on or on — exactly as we have pointed out previously... 

D = mass fraction of i xt = mole fraction of i V = partial specific volume of i c = molar concentration of mixture r = mass concentration of i M = molecular weight of i. 

The hydrodynamic properties of Ustilago cytochrome c were investigated by Thelander (86). He found the partial specific volume to be 0.721 ml/g and the molecular weight, by sedimentation equilibrium, to be 15,500. The latter value, although higher than that given by summation of the constituent amino acid residues (i.e., 11,877, see Table 3), indicates that the protein is monomeric. 

Ni is Avogadro s number, / the particle friction coefficient, u the velocity and v the partial specific volume of the solute [79,80]. Inertial forces are negligible and the balancing of the above forces yields the sedimentation coefficient ... 

Derechin and coworkers noted the anomalous behavior of gramicidin A in absolute ethanol79. The apparent partial specific volume increased with decreasing concentration of gramicidin. The same was not true for aqueous-ethanol solutions. 

An operation can be constrained by multiple specifications. Alternatively, the multiple specs can be combined into a single, more complex specification. Here, first, is an operation constrained by multiple partial specifications ... 

Typically, a design type will be specified with a model drawn inside it using specification types. Only a design type can participate in an action, and every type that is specified as participating in an action is a design type. Specification types do not really have actions of their own, but partial specifications (effects) can be attached to them for convenience, as shown in Section 3.8.7. 

In fact, many partial specifications that you find in models don t constitute a complete type specification at all—they have attributes but no actions. Strictly speaking, any object... 

The view that the clay surface perturbs water molecules at distances well in excess of 10 A has been largely based on measurements of thermodynamic properties of the adsorbed water as a function of the water content of the clay-water mixture. There is an extensive literature on this subject which has been summarized by Low (6.). The properties examined are, among others, the apparent specific heat capacity, the partial specific volume, and the apparent specific expansibility (6.). These measurements were made on samples prepared by mixing predetermined amounts of water and smectite to achieve the desired number of adsorbed water layers. The number of water layers adsorbed on the clay is derived from the amount of water added to the clay and the surface area of the clay. 

Sedimentation equilibrium Absolute requires only centrifuge measurements and partial specific volume of solute Time-consuming measurement and interpretation somewhat limited mol. wt. range 5... 

Sedimentation- diffusion Absolute fairly fast Requires 3 separate determinations (diffusion coefficient, sedimentation constant and partial specific volume) <5... 

The partial specific volume is the increase in the volume of a solution caused by the presence of the solute and is defined as the volume occupied by 1 kg of the solute in 100 kg of the solution. The value may be calculated using the densities of both the solvent (p) and the solution (ps) ... 

The value of the partial specific volume for proteins is approximately 0.7 while for nucleic acids the value varies around 0.5. 

The radius of the peptide molecule can be calculated from the molecular mass, Avogadro number, and the partial specific volume. 

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