Solute volume fraction

Figure 14.8 Generational dependence of relative viscosity, tv, on solution volume fraction for the first six generations, G, of PAMAM dendrimers in ethylenediamine (EDA) in comparison with theoretical predictions of Krieger (A), Eiler (B) and Mooney (C) hard sphere models (according to ref. [5])...

Figure 5.2. Free-energy change of mixing for rods and solvent molecules. Free energy change (AGIRT) of (A) solid phase associated with transfer of a solute molecule (macromolecule) from the liquid to the solid state as a function of solute volume fraction (V2) for low (Z = 10) and high (Z = 200) axial ratios and (B) liquid phase as a function of solute volume fraction in the presence (Xi = 0.1) and absence (Xi = 0) of interactions between solute molecules. The diagrams show that separation of solute and solvent molecules occurs spontaneously for high axial ratios above a critical volume fraction and that the free energy of the solvent is raised by inter-molecular interactions.

The virial expansion of Equation (4B-4) is inappropriate as the concentration increases since the series no longer converges at sufficiently high solute volume fractions. In this case,... 

In the conservation of species equation for a binary system (Eq. 3.3.17), it is sometimes assumed that the velocity u is given by the solution to the momentum equation for the solvent. Determine a criterion for this assumption to be valid that is dependent on the solute volume fraction , the ratio of the density of the solvent particle to the density of the solute particle, and the ratio of the velocity of the solute species to the velocity of the solvent species. Is the condition [Pg.80]

In the Wilson equation, the effects of difference both in molecular size and intermolecular forces are incorporated by an extension of the Flory-Huggins relation (5-8). Overall solution volume fractions ( i = XiViJvi) are replaced by local volume fractions, d> which are related to local molecule segregations caused by differing energies of interaction between pairs of molecules. The concept of local compositions that differ from overall compositions is shown schematically for an overall equimolar binary solution in Fig. 5.6, which is taken... 

The hard sphere interaction causes a hquid to sohd transition at a solution volume fraction of 0.545, as described above with leferenee to Figure 3.4. The resulting sohd has an fee lattice. This is shghtly, about 0.001 kT, more stable than its elose packed counterpart at 0.74, the hep lattice. Binary hard sphere systems can form five different lattices of different stoichiometry depending on the size ratio. 

NMR spectra are usually referenced on the 8 scale according to Equation (1). However, when comparing nuclear magnetic properties of different isotopes, frequencies are sometimes expressed in MHz on the H scale. On this scale, the frequency of the reference compound for the nucleus of interest is referenced to the H frequency of TMS, in a dilute solution (volume fraction <1%) in chloroform, in a magnetic field such that its frequency would be exactly 100 MHz. Harris et al list H values for many isotopes in various reference compounds that are extremely valuable to experimentalists. 

FIGURE 3.20 The free energy of interaction per surface site between two plates in the presence of nonadsorbing polymer at various bulk solution volume fractions q),. The left-hand figure shows the results for the 0 solvent (x = 0.5) on the right-hand side are the data for an athermal solvent (x = 0). r = 100, Xs = 0, hexagonal lattice. Reprinted from Scheutjens and Fleer (1982) with permission from Elsevier. 

In order that the deviation from ideality expressed as the activity coefficient may be significant, the selection of a reference for systems should be consistent. The activity coefficient depends, besides the variables of state associated with it, on the concentration units employed (mole fraction, molality etc.). In the case of polymer solutions volume fractions segment fractions and weight fractions Wt are the most convenient [15]. 

In a similar manner to finding a lower consolute solution temperature, can a lower consolute solution volume fraction be found ... 

A critical value of the axial ratio (X ), varying from 4 to 8 for different theories of rigid chains [78], determines the limit at which an nndilnted mesophase becomes absolutely stable [76], implying that when X > X the mesophase is primarily stabilized by hard interaction and compositional changes (lyotropic systems). In this case a critical solute volume fraction (v ) can be defined, decreasing with X according to... 

We briefly review here thermodynamics of a nonideal binary solution. The osmotic pressure Ft is the extra pressure needed to equilibrate the solution with the pure solvent at pressure p across a semipermeable membrane that passes solvent only. The equilibration is attained when the chemical potential of t e pure solvent becomes equal to the chemical potential of the solvent molecule in solute volume fraction at temperature T ... 

Fig. 16 optical absorption spectra for polyTCDD solutions volume fraction of dinethylformamide (OMF) in methanol is indicated. Polymer concentrations ( 10 mol/L) are the all spectra. The spectra are arbitrarily offset. 

Figure 3 Experimental and theoretical osmotic pressure, II, of PBLG in DMF versus solute volume fraction, b is the molecular volume. The datapoints are taken from Refs. 27 and 28 (data set B), and encompass measurements between 15°C and 45°C. Solid line theory based on the Khokhlov-Semenov approach to flexibility in combination with the decoupling approximation and the dimensional separation approach based on Eq. (8) [29]. Upper dotted line extension of isotropic branch. Lower dotted line extension of nematie branch. Dashed-dotted line result for completely rigid molecules. Dashed line Onsager s second virial coefficient-approximation for rigid rods.

Figure 7 Theoretical phase diagram of a system of monodisperse self-assemhhng linear aggregates. (From Ref. 61.) I isotropic phase N nematic phase D -. hexagonal columnar phase. Here P is the persistence length, D is the aggregate diameter, and v is the solute volume fraction. Shaded areas indicate phase coexistence. The dotted lines mark the crossover of the free energies calculated according to Eq. (8). The triangles are experimental coexistence volume fractions, which here were fitted by adjusting certain model parameters.

Mass fraction (dimensionless) is commonly used and is suitable for either solvent or solute. Volume fraction (dimensionless) is commonly used for gaseous solutions. Percent, % (dimensionless), should actually be called parts per hundred (pph) and is widely used in everyday life. Parts per million, ppm (dimensionless), is usually used for solute, which is in a very small amount. Parts per thousand, ppt (dimensionless), is usually used to define salinity of sea water. 

The first term on the right of eqn. (5.21) (to order

Asakura-Oosawa result [eqn. (5.19) with h = 0]. Although the potential energy barrier at h /imax is indicative of a kinetic stabilization effect ( depletion stabilization ), the height of the barrier is predicted to be of no practical significance unless the solute volume fraction is very high. 

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