Chain tangential

A minimalist extraction buffer is often recommended for protein purification [25], since most additives provide only a marginal improvement in yields, but will increase costs significantly. The removal of phenolics, for example by tangential-flow ultrafil-tration/diafiltration [25], is an important step that should be carried out as early as possible in the purification procedure, since these molecules can become covalently linked to amino acid side chains and can oxidize certain residual groups [123]. 

The first phenomenological model for description of polymer dynamics in concentrated solutions and melts was proposed in 1971 by P.de Gennes [50]. In this classical work, it was assumed that due to entanglements, the chain motions in the direction normal to the chain contour are blocked up and only tangential ones are possible. This kind of chain motion in the effective tube was called reptation. In the absence of external fields, the chain can escape from the tube by either of the free tube ends. 

In the persistent chain there are no points of easy bending the persistent macromole-cule prefers the conformations exhibiting a constant small curvature. Thus, as soon as the chain elements in the liquid-crystalline globule are oriented mainly in the tangential direction (see Sect. 4), the small globule formed by the persistent chain must display the tendency to form the cavity in the middle of the globule. In this case, the globule assumes the shape of either a torus or a spherical layer. 

Fig. 11. Coordinate system of a worm-like chain. X, Y and Z are ortogonal axes with the origin at the mid-poUit of the chaia Axis Z is tangential to the chain contour at the coordinate origin. Xj, y and Z are coordinates of the i-th chain element...

Another method of characterizing the asymmetry of the molecular shape is related to the choice of the main direction in the molecule. In the principle axis Z in Fig. 11 tangential to the worraJike chain at its middle point can be chosen as this direction. However, in this system of coordinates the asymmetry of the shape of the molecule is adequately expressed only in the range of conformations close to a rod whereas for the Gaussian coil conformation (x — < ), according to Eq. (29), p is equal to unity and the coil is herical (see also Pig. 13). Hence, the asymmetry of the shape of the Gaussian coil cannot be adequately expressed by a system of coordinates determined by the middle element of a worm-like chain. 

Let <5 denote the length of the connector chain pulled out from the polymer by a force / as shown in Fig. 8. When 6=1, where l is the total connector chain length, the chain is completely pulled out and the force/vanishes. Assuming that the chains are pulled out normal to the interface so that the tangential component of the pullout force is zero, then a, the traction stress component normal to the planar interface, is related to the force/and 2, the number of chains crossing a unit area of the interface, by ct=/2. a is related to the rate of chain pullout <5(f, x) and the remaining chain length l - by ... 

A valuable overview of the global dissemination of persistent organic compounds has been given (Wania and Mackay 1996), and application of fugacity models to the distribution of PAHs (Mackay and Callcott 1998). Attention should also be directed to the different physiology and biochemistry of the organisms as well as to their trophic level important details of food chains are, however, noted only tangentially in this account. 

In the perturbed hard-chain theory (PHCT) of Beret and Prausnitz [14] and Donohue and Prausnitz [15], the reference fluid is modeled as chains of tangential hard spheres. Since the fluid is stiU composed of hard spheres, albeit bonded, the CS eos is applied with modification to account for the bonding. The hard-sphere-chain equation is... 

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