Linear analogs

Hyperbranched poly(ethyl methacrylate)s prepared by the photo-initiated radical polymerization of the inimer 13 were characterized by GPC with a lightscattering detector [51]. The hydrodynamic volume and radius of gyration (i g) of the resulting hyperbranched polymers were determined by DLS and SAXS, respectively. The ratios of Rg/R are in the range of 0.75-0.84, which are comparable to the value of hard spheres (0.775) and significantly lower than that of the linear unperturbed polymer coils (1.25-1.37). The compact nature of the hyperbranched poly(ethyl methacrylate)s is demonstrated by solution properties which are different from those of the linear analogs. 

Figure 10.7 Electrophoretogram of dendritic nucleic acid 4 (lane 2) and a linear analog of identical base composition (lane 3). Lanes 1 and 4 marker dyes xylene cyanol (XC) and bromophenol blue (BPB). (Reprinted with permission from reference 23, copyright (1993) American Chemical Society.)...

One of the first properties of hyperbranched polymers that was reported to differ from those of linear analogs was the high solubility induced by the branched backbone. Kim and Webster [31] reported that hyperbranched polyphenylenes had very good solubility in various solvents as compared to linear polyphenylenes, which have very poor solubility. The solubility depended to a large extent on the structure of the end groups, and thus highly polar end-groups such as carboxylates would make the polyphenylenes even water-soluble. 

Differences in metabolic detoxifIcatlon rates between linear and angular furanocoumarlns observed in our studies were not great. However, the fact that the angular furanocoumarln under study accumulated to appreciably higher levels in body tissues of polyxenes caterpillars than did the linear analog is... 

The dendrimers all have a discrete size, shape, and molar mass. The dendrimers exhibit unique properties such as high solubility in various solvents and increased chemical reactivity compared to their corresponding linear analogs. The intrinsic... 

Pressure sensors that give temperature-corrected, linear, analog voltage output are available from Motorola and other manufacturers. In such sensors, the on-chip electronics correct any temperature effects and nonlinearities in the output of the piezoresistors. The on-chip electronics replace a shoebox-size collection of printed circuit boards. The price of this kind of smart sensor is considerably less than 100. The integration of a large amount of circuitry on the chip allows functions like amplification, offset correction, self-testing, autocalibration, interference reduction, and compensation of cross-sensitivities (6). 

As discussed in Chapter 1, any linear analog filter network may be used. Its performance may always be described by convolution with a filter function, here called sE. Many modern digital filters may be thus described. The instrument employed in the present work used a simple single-stage RC filter of the type analyzed in Section II.D of Chapter 2. 

The characterization of branched or cyclic structures by the g- and h-factors has the disadvantage that the properties of the analogous linear chains must be known. Such characterization requires a great deal of work in preparative chemistry as well as accurate physical chemical measurements, and in some cases the linear analogs are not even known. In such cases, a direct combination of the mean-square radius of gyration and the hydrodynamic radius leads to the very useful dimensionless parameter188. ... 

The thermal properties of the dimers 50a-d relative to the linear analogs were probed by DSC analysis. The pure phenylenevinylene cruciforms 50a and b still form crystalline phases with Tm = 223 and —258 °C, respectively. As the volume of the cruciforms is increased, the intermolecular interactions are reduced, which is documented by the occurrence of amorphous phases with glass transitions at 43 and 142 °C for 50c and d, respectively. A corresponding cruciform trimer 54 was also synthesized by Ma and coworkers [76] following a related protocol, as illustrated in Scheme 3.25. The DSC of 54 confirms the previously discussed trend and 54 is fully amorphous and shows only a Tg at 118 °C [76]. 

Hawker, C. J., Malmstrom, E. E., Frank, C. W., and Kampf, J. P. 1997. Exact linear analogs of dendritic polyether macromolecules design, synthesis, and unique properties J. Am. Chem. Soc., 119, 9903-9904. 

There is no general rule relating the nucleophilic reactivity of cyclic monomer and linear polymer repeating unit, it depends on the nature of heteroatom and the size of the ring which affects the electronic structure of heteroatom. It is a common practice to estimate the order of nucleophilicities on the basis of basicities. Although it is only partly justified, this procedure enables semiquantitative comparisons of known pKa values whereas no universal scale of nucleophilicity exists. Some typical values of pKa for cyclic compounds and their linear analogs are given in Table 8 [99,100],... 

Ladder and cross-linked polymers are more heat resistant than their linear analogs. 

B. Linear Analogies between Higher Peptide Structures. 174... 

Sorm, 1959, 1961a) linear analogies in the structure of ribonuclease have also been detected by Lanni (1960, 1961) using a different approach ( sequence vectors ). The same regularities were mentioned by Schwartz (1959) in the case of the corticotropins. 

---