Volume parameters

Appendix C-1 gives corresponding-state parameters and UNI-QUAC surface and volume parameters. 

VSTR = O Connell characteristic volume parameter, cm /g-mol ZRA = Rackett equation parameter RD = mean radius of gyration, A DM = dipole moment, D R = UNIQUAC r Q = UNIQUAC q QP = UNIQUAC q ... 

Corresponding-State Parameters and UNIQUAC Surface and Volume Parameters... 

STRUCTURAL VOLUME PARAMETER OF UKIQUAC EQUATION STRUCTURAL AR A aARAMETEP FOR UNIOUAC EQUATION STRUCTURAL AREA PARAMETER FOR MODIFIED UNIOUAC EQUAT ION... 

All parameters of interest with respect to fragmentation will be discussed. The extent of damage or injury caused by these fragments is, however, not covered in this volume. (Parameters of the terminal phase include first, fragment density and velocity at impact, and second, resistance of people and structures to fragments.)... 

Very little has been published covering such nonideal, but very realistic, situations. Two publications by Wiederman (1986a,b) treat nonideal gases. He uses a co-volume parameter, which is apparent in the Nobel-Abel equation of state of a nonideal gas, in order to quantify the influence on flragment velocity. The co-volume parameter is deflned as the difference between a gas s initial-stage speciflc volume and its associated perfect gas value. 

For a maximum value for the scaled pressure p = 0.1, a reduction in Vj of 10% was calculated when the co-volume parameter was applied to a sphere breaking in half. In general, fragment velocity is lower than that calculated in the ideal-gas case. Baum (1987) recommends that energy E be determined from thermodynamic data (see Section 6.3.2.3) for the gas in question. 

Cm = CmO (exp (—Kmet 7)) — exp(—Ke 7)) With bi-exponential kinetics it can be difficult to select the appropriate volume term, since several volume parameters can be derived. 

Equation (23) was found to be obeyed by a number of systems such as poly(ethyl acrylate)-benzene, rubber-benzene, and poly(methyl acrylate)-ethyl acetate [12], According to the equation, a plot of [In(DT/D0)] l versus ([)[ will yield a straight line, and from its slope the free volume parameter p can be determined. To construct this plot,/( / , 0) is first calculated as [27]... 

In the classical theories of polyelectrolytes, the chain expansion is characterized by the electrostatic excluded volume parameter, zel with ... 

Equilibrium state, 24 642. See also Equilibrium progress toward, 24 649 Equilibrium value, 14 611 Equilibrium volume parameters, from density measurements, 13 435-436 Equimolar counterdiffiision, 1 39-40 drift flux correction, 1 55-58 Equipment. See also Failure mode and effects analysis (FMEA)... 

The model is evaluated by means of provided case test data. Industry case data are modified by values and selected volume parameters for confidentiality reasons, Therefore, optimization results will not match directly with the actual business. However, the provided data are realistic in order to test sensitivity of the model and to compare model reactions applying different scenarios. Two test types are conducted ... 

The parameters modified in each tests are either value or volume parameters with both having impact in the overall volume and value situation in the value chain. The parameters modified are perceived as key parameters in value chain planning, planners are confronted with. 

In a series of papers, Diphant has been used to probe the microviscous properties of various polymer oils, and free volume parameters have been extracted. 4,88 90) In a comparative study of Excimer and TICT probes, it could be shown that the response of these probes is frozen out at lower temperatures, as can be expected from the large reaction volume necessary, whereas the TICT reaction still shows sizable rates at these high-viscosity conditions. (26) Moreover, this study also showed that the free volume fraction measured by the TICT probes is larger than that measured by Excimer probes. 

The dual fluorescing type 2 compounds DMABN and its ester derivatives have been used to extract detailed free volume parameters, especially for the case where the probes are covalently linked to the polymeric backbone, e.g., by an oxymethylene chain of variable length/97-101 As the TICT reaction requires a comparatively large reaction volume, the measurable effects are especially strong in solutions of these labeled polymers but they tend to disappear for the pure polymer due to its too-large... 

Fig. 3. Theoretical density profile of dendritic structures of generations 2-7 [12]. The radial volume fraction properly normalized to unity at the center of the molecule is plotted against the radial distance to the origin. All data has been calculated assuming a realistic excluded volume parameter of the segments of the dendrimer. Reproduced with permission from [12]...

Volume and Sterio Parameters. We have noted above that sterio effects are directed quantities. This is the underlying basis of the MSI principle. In contrast to the vectorial behavior of sterio effects volume and bulk parameters are scalars. In order to clarify the difference between sterio and volume parameters we shall make use of substituent sets which are Isoohorlo (constant volume) or isosterlo (constant /). We define the quantities... 

Once ftE calibration and test sets are defined, SIMC. models are estimated using ini rank estimates Offom PCA) and default class volumes (from the software fKrkage). The samples in the test set arc predicted and the results evaimtedaa detennine if modification of the tanks and/or class volumes is needed (see Habit 4 for details of this evaluation). If the number of misclassifi-cations is anacccptable, the rank and class volume parameters are adjusted and the pswress repeated. 

Here a0 is a constant called the effective bond length of the chain, and as(z) is a dimensionless quantity called the linear expansion factor of the chain. The latter depends on long-range interactions between pairs of monomer units and chain length through the so-called excluded-volume parameter z. For details of these quantities characterizing the dimensions of random-coil polymers, the reader is referred to a recently published book by Yamakawa (40). At this place we simply note that as tends to unity in the absence of excluded-volume effect. 

Some degree of relationship between steric effect parameters and volume parameters must be expected. Consider for example monatomic substituents. A single atom, X, may be considered sperical. Its volume is therefore given by the expression for the volume of a sphere. 

This is indeed borne out by correlating Vw for monatomic X with rv for the set including H and halogen, lOOr2 = 90.0, further inclusion of OH, SH, NH2, and PH2 results in lOOr2 = 95.3. Note however, that when the cylindrical groups, CN and C=CH are also included the lOOr2 value falls to 85.8. To demonstrate even more clearly the sharp difference between steric effects and volume parameters we... 

---