Test chain

For example, if many chains are perfectly aligned, e.g. in the z-direction, the probability of the test chain also placing its segments in the z-direction becomes strongly enhanced. The oriented molecules leave an open corridor in the direction of the director. In terms of the vacancy probability, it is an event that it is enhanced with respect to the classical mean-field prediction. As a result, the test... 

The jamming effect, i.e., the slowing down of the longitudinal diffusion of a polymer chain by the head-on collision with other chains, can be treated by a model similar to that proposed by Cohen and Turnbull [112] for self diffusion of small molecules in a fluid. This model assumes that if at least one surrounding polymer chain exists within the critical hole ahead of a test chain, both collide, and this prevents the test chain from diffusing longitudinally. With this assumption, we express the longitudinal diffusion coefficient Dp of the test chain as... 

In the last particular situation, the motion of a test chain is also coupled to the motion of neighbouring macromolecules, and the diffusion coefficient is determined both by the length of the test macromolecule M and by the length of the ambient macromolecules Mq... 

The reliability and sensitivity of the probe method has been emphasised. It circumvents almost completely the perturbations inherent to some other probe techniques (electron spin resonance, fluorescence). In particular, free chains appear to be ideal, non-perturbative NMR probes for testing chain segment orientation in strained rubbers. The solvent probe method is easy to handle and unexpensive, since it does not require the synthesis of... 

For 100 < P < 1000, the measured diffusion coefficients for N = P no longer follow the N 2 reptation prediction. In the same range of N values, D remains proportional to N 2 if P N, i.e. if the motion of the chains surrounding the test chain are frozen down during the diffusion time of the test chain. The comparison of the data obtained with N = P and with N P clearly puts into evidence the acceleration of the dynamics associated with the matrix chains, similarly to what has yet been observed with other polymers [11, 12, 42 to 44] or in solutions [10]. This acceleration, by a factor close to three, can be attributed to the constraint release mechanism [7, 8, 13], the effects of fluctuations of the test chain inside its tube [9] being a priori the same in the two situations P = N and P N. 

From the theoretical point of view, the first refinement of the reptation approach has been to introduce the collective dynamics of the chains in terms of the constraint release process[7, 8, 13]. Due to the motions of the surrounding chains, some constraints which constitute the tube may disappear during one reptation lime, and thus give more freedom to the test chain. Quantitative attempts have been made to take into account these additional... 

Another important relaxation process in entangled melts is constraint release, depicted in Fig. 3-27. When an end of a surrounding chain moves past a test chain, an entanglement constraint restricting the motion of the test chain is released, and a portion of the latter is freed to reorient (Graessley 1982 Montfort et al. 1986 Pearson 1987 Viovy et al. 1991). Constraint release can only be completely neglected for the case of an isolated chain... 

Consider a random-walk chain of no monomer units in a n dium which is densely filled with the contours of other chains. For the moment take the ends of the test chain to be fixed. Let its surrounding be r resented by a permanently connected rigid lattice of uncrossable lines enveloping the chain contour. We assume that the effect of this obstade lattice on the conformations of the chain is specified simply by a distance scale, the mesh so d, as follows. Pieces of the diain which have a mean quare end-to-end distance (r ) much smaller than (F can explore aU conformations with the same probability as free chains of the same length. For loiter pieces, the presence of the obstacles (and the fact that the pieces are connected in a definite sequence between the fixed end points of the... 

Last year Roginsky and coworkers determined the chain-breaking activity of thirteen hydroquinones, P-QH2, during azo-initiated oxidation of styrene, ... known as the most suitable oxidation substrate for testing chain-breaking antioxidants . Their results provide a useful comparison with antioxidant activities of monophenols studied under similar conditions (e.g. Section ni.B.l), therefore their results are reproduced in summary form for compounds XX in Table 8. The following conclusions can be drawn from the results ... 

Let us consider the states of a chain made of Nx monomers, in solution successively in its own monomer, in its dimer, in its trimer, etc. In the first case, the repulsive interaction between monomers of the chain produces a gyration swelling 3 G which obeys the laws already observed. In the other extreme case where the test chain finds itself in a melt of other identical chains, the repulsive interaction is screened and the test chain is in a quasi-Brownian state. In intermediate situations the swelling 3E0 of the test chain of Nx monomers varies with the number N of monomers (per chain) of the solvent chains. Observation of the variation law of XG with N clearly reveals the structure of polymer solutions. Such observation requires the labelling of the chain made of iV, monomers therefore it is appropriate to use neutron scattering. Kirste and Lehneh2 made the experiment with blends of polydimethylsiloxane (PDMS)... 

Now, let s defrost the surrounding chains. Then more opportunities for the test chain will arise. Some of the neighboring chains will start moving away. Therefore, some constraints and entanglements that had formed the tube (Figures 12.4 and 12.5) will gradually disappear (or decay ). However, as P.G. de Gennes showed, this effect is not important. The chain will snake out of the frozen tube much sooner than it takes the... 

In order to find rj and r, we will pick a chain and explore its tube in more detail. The tube is created by other chains. If they come into contact with the test chain, they act as obstacles to the chain s motion. However, we have seen that only a small proportion of such contacts can really limit the chain s choice of conformations. This proportion is of the order of 1/Ng. These are the contacts which can be regarded as effective cross-links. 

Since disentanglement occurs only as a result of solvent penetration, we can use the result of equation (25) in equation (23) to yield k = 0.5. hi other words, we treat the mobility of die chains surrounding the test chain similar to solvent mobility and this makes the result of equation (25) analogous to the one in equation (23). Since equation (19) is always true, we can write... 

We consider volume elements A and B separated by a distance r, and denote a test chain by L and any other coexisting chain by L . The function h r) is proportional to the average density fluctuation produced in B when there is a bead of L in A. Equation 2.21 shows that it consists of the intrachain contribution hi r) and the interchain contribution ( z/iV)/z2(r). The function hi r) depends on the interactions between paired beads of L in the presence of all L. We note that these interactions include the constraint that the beads of L... 

We consider what happens to a test chain in a polymer solution when chain overlap takes place. With increasing concentration, each bead of the test chain sees in its neighbor more beads of other chains, so that chances of intrachain... 

To scrutinize the screening effect we look at a subchain (ij) between beads i and j of the test chain. As it becomes longer, the subchain is surrounded with more beads of other chains and hence undergoes a stronger screening effect. Therefore, if we denote the end-distance expansion factor for the subchain (ij) by we can expect that aR ij) decreases monotonically to unity with... 

In solutions of a simple electrolyte, anions cluster around a cation owing to the attrac-tion between them, and screen the repulsion between cations. In solutions of a neutral polymer, in which bead-bead interactions are repulsive, the clustering of beads of other chains around each bead of the test chain is caused by the thermodynamic force which tends to maximize the mixing of beads. 

Employer s copy of the drug test chain of custody and control form ... 

Figure 4.19. The tube model. The effect of the surrounding chains on any test chain (shown bold) is to confine its motion to a tube (shown shaded). The test chain can move only by wriggling along the tube - this motion is called reptation .

Reptation assumes that the mobility of the matrix polymer plays no role in the relaxation of the tube constraint felt by a test molecule. However, if the matrix chains were very much more mobile than the test chain, additional lateral motion of the chain might be permitted by virtue of the constraining chains themselves moving away. This type of motion is called constraint release or tube renewal , and may be operative if some of the matrix chains are significantly shorter or intrinsically more mobile than the test chain (Green 1991, Composto etal. 1992). 

If circumstances change requiring DOT post-accident tests, the driver must be sent for another round of tests, even in he/she just completed your non-DOT tests under company policy. You cannot substitute the non-DOT (which should have been on a non-DOT daig testing chain of custody and non-DOT breath alcohol testing form) for DOT compliance. 

Test results includes Copy of alcohol test form, with results Copy of drug test chain of custody form Documents sent to the employer by the MRO Documentation of any refusal to submit Documents provided by a driver to dispute results and Previous employer test results (see 382.301 (c), 40.25, and 391.23). See 40.333 and 382.401. ... 

Figure 8 Reptation of a chain within a tube. (A test chain [black] reptates through a tube with walls formed by segments of the chains [gray]).

Diffusion. The translational diffusion coefficient D is the most commonly measured transport property of polymer solutions, but as there are several distinct types of diffusion, care must be taken to interpret D properly. For c < c, Brownian motion of isolated chains in a homogeneous solvent defines the dilute solution diffusion coefficient Dq. As c increases toward c and above, chain-chain interactions modify the friction felt during chain motion. Under these conditions, the tracer- or self-diffusion coefficient Dtr is measured by tracking the path of a single chain in a macroscopically imiform mixture of chains and solvent. To distinguish the test chain from neighbors so that its path can be identified, the chain... 

Our discussion of reptation has been limited to completely dense systems—e.g., a dry network with closely spaced entanglement points or a polymer melt of very long chains, incorporating one extra test chain. To... 

We discuss first the case where the network is replaced by a semi-dilute solution of concentration c, composed of chains with a large degree of polymerization N. In this solution we add one test chain (N) and ask for the reptation time of the test chain T( (c). For simplicity we choose an ather-mal solvent (a = u, or x = 0). 

As usual, we can relate the semi-dilute region to the concentrated regime using blobs as our fundamental units. If, as in Chapter III, we call g = (ca ) the number of monomers per blob, the numter of blobs in the test chain is N/g, and the reptation time is, by a natural extension of eq. (VIII. 13),... 

To understand the dynamics of one chain in a melt, it is convenient to start from a slightly different problem. We consider one test chain of Ni monomers, embedded in a monodisperse melt of the same chemical species, with a number N of monomers per chain. We consider three types of motion for the test chain reptation, tube renewal, and Stokes-Einstein friction. We first describe tube renewal and show that this is probably negligible for most practical purposes. Then we discuss competition between reptation and Stokes-Einstein friction. 

The basic process associated with this word was introduced in Ref. 14 and is shown in Fig. VIII. 10, where we see one entanglement constraint being altered when one of the ambient chains (F) has an extremity in the immediate vicinity of the test chain (F,), the relative positions of (F) and (Fj) may change qualitatively in a very short time. This may be viewed as a modification of the tube. 

Using the ideal value R(Ni) = 1/oNf. we can compare DstokeANt) with rep( i)" We find that reptation dominates only when N, < A. Thus, we are led to expect two regimes for the test chain (i) Ni < N, The test chain is statistically ideal and moves by reptation. 

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