Association number

Two-sample plot for data In Example 14.7. The analyst responsible for each data point Is Indicated by the associated number. The true values for the two samples are Indicated by the. ... 

The major advantage of array detectors over point ion detectors lies in their ability to measure a range of m/z values and the corresponding ion abundances all at one time, rather than sequentially. For example, suppose it takes 10 msec to measure one m/z value and the associated number of ions (abundance). To measure 100 such ions sequentially with a point ion detector would necessitate 1000 msec (1 sec) for the array detector, the time is still 10 msec because all ions arrive at the same time. Therefore, when it is important to be able to measure a range of ion m/z values in a short space of time, the array detector is advantageous. 

Table 2. Association Numbers and Fractional Kinetic Orders for Alkyllithium Initiators...

Measurements of polymerization rate and parallel measurements on the resultant polymer microstructure in the butadiene/DIPIP system cannot be reconciled with the supposition that only one of the above diamine solvated complexes (eg. Pi S) is active in polymerization 162). This is probably true of other diene polymerizations and other diamines. The observations suggest a more complex system than described above for styrene polymerization in presence of TMEDA, This result is clearly connected with the increased association number of uncomplexed diene living ends which permits a greater variety of complexes to be formed. 

The initiator association number y depends upon temperature, solvent and concentration of the system and is reported to be between two and seven (2) The association of polystyryl anions results in species A. Ak which do not react with styrene monomer. The macromolecular association is analogous to a reversible termination by combination. 

Use this association to replace the symmetry elements in the body of Table 2 by the associated numbers to give ... 

Unless indicated otherwise in this chapter, n is equal to the number of C-C sigma bonds that span the bridge termini. This definition should become perfectly clear upon inspection of the structures and their associated numbers given in Figure 7. Several structures in the... 

Anionic polymerisation of hydrocarbon monomers is initiated by lithium butyl to produce a living polymer the association number of which in solution is required to elucidate the kinetics. When the living polymer (for example polystyryl lithium) is terminated, the polystyrene can be isolated and a solution then made to determine its molecular weight, M. If the living polymer is associated in solution, the ratio of its... 

Equations 5.28 and 5.30 provide a general matrix approach to the calculation of the sum of squares of residuals. This sum of squares, SS divided by its associated number of degrees of freedom, DF, is the sample estimate, s, of the population variance of residuals, CJ. ... 

The association number of Li amides, such as LrN(SiMe3)2, organolithium compounds bound at the a-position to S or Se atoms, such as LiCH2SePh, and various transition metal complexes was determined at 0°C in THF or at —35°C in Et20, by differential vapor-pressure osmometry. The method allows handling compounds sensitive to autooxidation, moisture and temperature . ... 

As mentioned in Sect. 2.2.3, the biodistribution of HPMA copolymers depends on many factors. Molecular weight influences the uptake in the isolated tissue of yolk sac [266] as well as the elimination in vivo [124, 125,267,268]. Nonspecific increase in the rate of polymer uptake can be achieved by incorporation of positively charged or hydrophobic comonomers into the HPMA copolymer structure, such as methacryloyloxyethyltrimethylammonium chloride [22], N-methacryloyltyrosinamide [21], or N-[2-(4-hydroxyphenyl)ethyl]acrylamide [267]. The incorporation of hydrophobic moieties may influence the solution properties of the HPMA copolymer conjugates [132,134,269]. The interaction with the cellular surface may depend on the association number and the stability of the micelles. 

Typical values of N, the "association number", or weight-average number of chains associated at their ends, are shown in Table II. The values of N were obtained from the relation... 

Comparison of the association numbers found from the viscosity measurements with the invariancy of the kinetic orders from the value one-half clearly demonstrates the mistake (13,14) of expecting the existence of a simple and necessary connection between these two parameters. The assumption (14) that diphenyl ether does not affect the degree of association of polystyryllithium even at the ratio of 150 1 can be seen to be incorrect. 

TABLE 3 DETERMINATION OF ASSOCIATION NUMBER OF BPMg BY CRYOSCOPIC MEASUREMENTS IN BENZENE SOLUTION. 

Concentration of BPMg calculated from U.V. spectra xlf)2 mol.kg-1 Concentration of BPMg calculated from cryoscopic measurements 10 mol.kg l Association number a ... 

An alternative method has been used by Morton (73, 74) which involves an independent measurement of the degree of association of polyisoprenyllithium. Measurements were made of the concentrated solution viscosity of active and terminated polymer solutions. An approximately ten-fold decrease in viscosity was observed on discharging the ion-pair. This corresponds to two-fold association for polyisoprenyllithium in hexane, since in concentrated solutions v) = KMffl. A careful study established that the association numbers were slightly less than two and decreased with temperature. From the data, K2 can be calculated and hence k . In this way it was found that in hexane kp — 3.4 X 103 exp. (— 4100/RT) at 30°, kp = 4.7 litre/mole sec. For practical reasons,... 

However, AmicH° and TA, determined from the temperature dependence of the Gibbs energy, are less sensitive to the association number than is AmicG° itself (Yang ef al. 1995). Assuming that Am cH° is approximately constant within a certain temperature range, eqn 3.7 can be integrated to yield... 

Abbreviations A H Huggins coefficient M, molar mass R, radius of gyration RD, core radius p, association number AmcH°, standard enthalpy of micellization, AmlcG°, standard Gibbs energy of micellization A2, second virial coefficient. Ru, hydrodynamic radius. 

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

It is worth emphasizing that all scaling theories (due to de Gennes, Daoud and Cotton, Zhulina and Birshtein, and Halperin) for block copolymer micelles with a small core and large corona predict that the association number and core radius are independent of the coronal chain length. 

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