Random links

Carboxylate soaps are most commonly formed through either direct or indirect reaction of aqueous caustic soda, ie, alkaH earth metal hydroxides such as NaOH, with fats and oils from natural sources, ie, triglycerides. Fats and oils are typically composed of both saturated and unsaturated fatty acid molecules containing between 8 and 20 carbons randomly linked through ester bonds to a glycerol [56-81-5] backbone. Overall, the reaction of caustic with triglyceride yields glycerol (qv) and soap in a reaction known as saponification. The reaction is shown in equation 1. 

Measurements have now been carried out on endlinked and randomly-linked samples of polybutadiene, polydimethylsiloxane, and randomly-linked samples of cis-polyisoprene. The results are presented here. 

Table I. Threshold Tear Strength T0 of Randomly—linked and Endlinked Elastomers of Varying Mc...

PDMS randomly linked with dicumyl peroxide ... 

Experimentally-determined values of T0 for PDMS networks are plotted in Figure 3 against values of Mc calculated from the elastic coefficient C by means of equation 2. TQ was found to be accurately proportional to M, in accordance with equation 1, with the coefficient of proportionality K being about 0.30, 0.25, and 0.23 J/m2/(molecular weight unit) for the A4, A3, and randomly-linked materials, respectively. These differences are small, barely significant, but in the expected direction. Values of T0 are also shown in Figure 3 for the other materials examined. 

Again, a proportionality to Mc2 was found, in accordance with theory. Moreover, the present values for endlinked PB and randomly-linked PI are in good agreement with previously-reported data on randomly-linked PB, with K = 0.85 J/mz. This is much larger than for the PDMS materials, however. Thus, at the same... 

To explain the difference between the experimental results and theory, Doherty et al. (4J have given an empirical and a theoretical hypothesis. The theoretical hypothesis concerns the question of the meaning to be attached to the concept of the "equivalent random link" in the statistical theory of the randomly-jointed chain. According to Doherty et al., the assumption that the optical properties of the chain are describable by a randomly jointed model, using the same value of n, as for the description of stress has no strictly logical foundation. 

In the derivation of eqn. (7) it was assumed that n (number of equivalent random links) is the same for all chains. For our samples (B2 system, Mw/Mn=1.45), this assumption is definitely not correct. Therefore, it is desirable to obtain birefringence results on networks prepared from monodisperse polymer (in that n is constant), before the validity of n itself is questioned. 

In the case of vancomycin [72], an original study was performed to obtain a well-defined stationary phase structure, since it was reasonably assumed that the antibiotic is randomly linked to the silica by one or both of its amino groups, one belonging to the disaccharide portion (primary), and the other one to the heptapeptide core (secondary). Thus, alternate fluorenylmethyloxycarbonyl (FMOC)-amino-protected derivatives were prepared and immobilized in a packed column, and then vancomycin was recovered by cleavage of the protecting groups. The two defined CSPs obtained, when compared with the CSP produced from native randomly linked vancomycin, showed lower retention and enantioselectivity, also if they still separated the same compounds. Thus, no advantages could be found to choose these phases as an alternative to the native vancomycin CSP. 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

At the end of this section two tables are presented. The purpose of these tables is to show that, for matching solvents, the main predictions of the theory are fairly well obeyed, viz. that the stress-optical coefficient is independent of molecular weight and concentration. On the other hand, an influence of the solvent is clearly noticed. This means that, according to eq. (2.24), the anisotropy (ax — o ) of the random link is influenced by the solvent molecules. This has first been stated by Frisman, Dadi-vanyan and Dyuzhev (66) (see also Section 5.1.2). 

It will be obvious that the treatment of the present section can also be applied to the subchain model (77). As is well-known, this model where every junction point of subchains is assumed to interact with the surroundings, seems to provide a more realistic description of the dynamic behaviour of chain molecules than the simple model used in the proceeding paragraphs, viz. the elastic dumb-bell model where only the end-points of the chain are assumed to interact with the surrounding. One of the important assumptions of the subchain model is that every subchain should contain enough random links for a statistical treatment. From this it becomes evident that the derivations given above for a single chain, can immediately be applied to any individual subchain. In particular, those tensor components which were characterized by an asterisk, will hold for the individual subchains as well. 

In the derivation of the stress-optical relation, as sketched in Section 2.6.1, several points of interest have only scarcely been touched The form birefringence in dilute solution, the nature of the anisotropy of the random link and the background of the quasistatic treatment. 

The most interesting situation exists when the intrinsic optical anisotropy (%— sc2) of the random link is negative, i.e. when the polarizability (a2) perpendicular to the chain direction is the larger one. In this case the form effect, which always works in the same sense, counteracts the effect caused by the (negative) intrinsic anisotropy of the random links. An important feature of the form effect is that its contribution to... 

As has been pointed out (63), this is a rather artificial model and, moreover, its application is quite unnecessary. In fact, (a> can be calculated from the refractive index increment (dnjdc), as has extensively been done in the field of light scattering. This procedure is applicable also to the form birefringence effect of coil molecules, as the mean excess polarizability of a coil molecule as a whole is not influenced by the form effect. It is still built up additively of the mean excess polarizabilities of the random links. This reasoning is justified by the low density of links within a coil. In fact, if the coil is replaced by an equivalent ellipsoid consisting of an isotropic material of a refractive index not very much different from that of the solvent, its mean excess polarizability is equal to that of a sphere of equal volume [cf. also Bullough (145)]. 

So far, no difficulties arise from the simultaneous use of the eqs. (5.4). It will become clear below that this is only due to the fact that the number of random links per molecule does not appear in the third equation. In fact, this equation holds for sufficiently large molecular weights only. However, if the length L can be calculated from the above defined conformation, a straightforward calculation can also be given for the difference of principal polarizabilities (jq — y2)z °f this stretched conformation. One may then write ... 

Fortunately, later calculations reviewed by Birshtein, Volkenstein, Gotlib and Ptitsyn (750) showed that the deviation of ZQ from Z is largest just for the free rotating chain, when compared with a great number of more realistic models. The conclusion was drawn by these authors that, for practical calculation purposes, Zg and Z0 can be equated. This means that, in principle, the optical anisotropy (oq — oq) of the random link, as used in previous sections, can be calculated with the aid of the experimentally accessible s (see below), when the bond polarizabilities are taken from the literature (757). In this way (oq — oq) is calculated as the anisotropy of a stretched piece of chain, containing s monomer units. This latter number is obtained by combining the first... 

Other difficulties are owing to the influence of the solvent. With stiff and bulky chains the so-called micro-form-effect becomes of importance, when the refractive index increment differs considerably from zero (7). In this case the random link approximately acts like a cylinder of length A and with a refractive index different from that of the solvent. Another effect occurs in good solvents which consist of anisotropic molecules. These molecules become oriented along the polymer chain, considerably contributing to its anisotropy [Frisman, Dadivanyan and Dyuzhev (752)]. In this way, the determination of the eigen anisotropy of weekly anisotropic polymer chains becomes rather doubtful. 

From the point of view that the statistically coiled model chain is built up of rigid rods (random links), it seems that eq. (5.10) must be truncated, as eq. (5.11a). 

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