Tubes like constraints

Firstly, the essential correctness of the tube picture has only recently been established in a remarkable series of experiments. The complex monomer diffusive self-correlation predicted has now been seen in field-gradient NMR. Reptative motion across an interface was the only successful explanation of time-resolved neutron reflectivity. Neutron Spin Echo (NSE) can now be extended in time sufficiently to identify the tube diameter directly. A series of massive many-chain numerical simulations have shown tube-like constraints with sizes identical to those obtained by rheology via the plateau modulus Go and NSE). 

The word reptation was created by De Gennes in 1971 (see De Gennes23). The term tube model is used to describe complete theories that incorporate Rouse and reptation motions within a tube-like constraint of the surrounding polymer chains. 

The next type of motion in the above theory corresponds to the overall reptational (sliding) motion of the polymer chain within its tube-like constraint. This motion affects the orientation of bonds, not only because the constraining tube is itself curved, but also because in places it may be sufficiently large to accommodate tight loops of chain. As a particular bond is pulled past the extremity of a loop, it may reverse its direction completely. The loss of angular correlation B t) which results is not exponential, and is therefore not strictly describable by a correlation time. Instead,... 

The other relaxation process is associated with fluctuations in conformation and should operate in both liquids and networks. The tube of constraints around the contour of any chain is composed of molecular strands, acting (crudely) like the bars of a cage. 

The Edwards tube model of polymer entanglements was already discussed in Section 7.3.1. The topological constraints imposed by neighbouring chains on a given chain restrict its motion to a tube-like region (see Fig. 7.10) called the confining tube. The motion of the chain along the contour of-... 

Reptation and tube length fluctuations of surrounding chains release some of the entanglement constraints they impose on a given chain and lead to Rouse-like motion of its tube, called constraint release. Constraint release modes are important for stress relaxation, especially in polydisperse entangled solutions and melts. 

Theoretical treatment of the statistical properties of linear polymers (LPs), shown schematically in Figure 7.1a, have been in existence since the 1950s (Rouse, 1953), and have undergone continuous refinement. In particular, tube theories (viz. reptation) (de Gennes, 1971 Doi and Edwards, 1986), and subsequent refinements, like constraint release (Viovy et al., 1991) and contour length fluctuation (Frischknecht and Milner, 2000) are some of the greatest... 

It suggests that it is not the size of the ring but the number of electrons present in it determines whether a molecule would be aromatic or antiaromatic. In fact the molecules with An+ 2) n electrons are aromatic whereas with (An, 0) n electrons are antiaromatic. Thus, benzene, cyclopropenyl cation, cyclobutadiene dication (or dianion), cyclopentadie-nyl anion, tropylium ion, cyclooctatetraene dication (or dianion), etc. possess (4 + 2) ti electrons and hence aromatic whereas cyclobutadiene, cyclopentadienyl cation, cycloheptatrienyl anion, cyclooctatetraene (non-planar) etc. have An n electrons which make them antiaromatic . Systems like [10] annulene are forced to adopt a nonplanar conformation due to transannular interaction between two hydrogen atoms and hence their aromaticity gets reduced even if they have (An + 2)n electrons. On the other hand the steric constraints in systems like cyclooctatetraene force it to adopt a tube-like non-planar conformation which in turn reduces its antiaromaticity. Various derivatives of benzene like phenol, toluene, aniline, nitrobenzene etc. are also aromatic where the benzene ring and the n sextet are preserved. In homoaromatic " systems, like cyclooctatrienyl cation, delocalization does not extend over the whole molecule. 

Figure 5.26. Running along the centre of the tube is a primitive chain. This is the shortest path down the tube. The deviations of the polymer chain from this path can be considered as defects. The motion of these kinks or defects in the chain away from the primitive path allows the chain to move within the tube. The polymer creeps through the tube, losing its original constraints and gradually creating a new portion of tube. This reptilian-like motion of the chain was named by de Gennes from the Latin reptare, to creep, hence reptation.

The action is like a piston (in a shock tube), which would act on the products as constraint forcing them forward at a velocity higher than the C—J particle velocity.. If the constraint were suddenly removed, the "overdriven detonation would be expected to return to the normal rate. In some cases, it may remain above normal for a long time (Ref 51, p 284). In experiments conducted by Deffet et al (Ref 28a), two expl compns were used in 22-mm diam columns. In this diam, one compn detonated at 3250 m/sec, while the other at 1970. 

The constraints changed from one trial configuration of the reaction system to the next, but typically included things like the minimum coolant temperature to permit efficient utilization of the heat of reaction as process steam, the maximum allowable aldehyde concentration in the condensed crude product to avoid refining and product specification problems, and a prescribed reactor pressure drop to insure adequate flow distribution among the reactor tubes at a minimum energy cost. All of these are implicit constraints — they establish the maximum or minimum levels for certain response variables. Explicit constraints comprise the ranges for search variables. 

Figure 1 Schematic representation of one chain among obstacles, a) The chain is constrained by the obstacles, b) By local fluctuations, the chain changes its conformation. The probability of forming a loop (dashed line) is very small (strong entropy loss), and the role of the extemities is dominant, c) The chain reptates like a snake in the virtual tube (thin line) envelope of all the topological constraints exerted on it by the obstacles. The tube is progressively redefined from the extremities, as schematically presented by the two situations at time t and t , with t >t.

Once the arrangement of atoms in the macromolecule has been determined, one can proceed to analyze the results. At this stage it is essential to take into consideration the resolution of the structure determination, the extent to which refinement of the structure has been possible, the constraints and restraints used in the refinement, and the overall R value. At 6 A resolution a protein molecule looks like a folded solid tube, and no atomic detail can be found. At 3.5 A resolution more information is obtained and bulky side chains might even be discerned. Many protein structure determinations can only be carried out to 2.2-2.5 Aresolution and the overall atomic arrangement can be deduced by use... 

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