Confining tube

Fig. 3.13 Schematic sketch of the different time regimes of reptation a unrestricted Rouse motion for b local reptation, i.e. Rouse relaxation along the confining tube, and...

With this, all relevant lengths scale with Therefore, for early times the fraction of still-confined tube segments must behave as ... 

The experimental apparatus consisted of a TEKNA-type induction plasma torch (PL-035LS) with a quartz confinement tube of 25 mm and a water cooled steel chamber connected to a cyclone. The plasma plate power of 21 kW was provided by a four turn, water cooled induction coil from an RF generator operating at an oscillator frequency of 3 MHz. High purity argon was used both as plasma and sheath gas with flow rates of 20 and 601 min-1, respectively. In order to raise the low enthalpy and heat conductivity of the argon plasma gas, hydrogen was also mixed into the sheath gas with a proportion of 10% (v/v). 

Various stressors, e.g., soiled rat bedding, confinement tube, or predator sounds (see Note 18). 

In 1851, Stokes derived Eq. (4.1) from the model of solid spherical particles falling independently through a homogeneous liquid without Brownian motion, slippage, and wall effects. Slippage is an inconstant rate of fall wall effects refer to axial orientation in the outermost planes of fluid in contact with a surface, and the differential velocity of flow in the outermost and innermost planes of a fluid in a confining tube ... 

Where / is the temperature dependent coefficient (fi = f(T)) and a is the index of the burning rate, which describes the pressure dependence. For deflagrations a < 1, however, this value increases to a > 1 for detonations. The DDT transition can occur when an explosive is ignited in a confined tube, where the gases formed cannot fully escape. This results in a sharp increase of the pressure and reaction velocity. Therefore, in a detonating explosive, the reaction velocity can increase above the speed of sound, turning the deflagration into a detonation. 

The desirable situation for the occurrence and linear propagation of a detonation for homogeneous explosives exists in confined tubes or cylindrical shaped explosives, in which the system should not fall below the critical diameter (characteristic for every individual explosive) as it otherwise causes the wave front to be disturbed ( loss of energy to outside) and therefore the detonation velocity will be reduced. While for many secondary explosives one inch is a good tube diame-... 

The diameter of the confinement tube has to be above the critical diameter (see Ch. 3, Fig. 3.2). While for many secondary explosives 1 inch is a good diameter to start with, for primary explosives usually much smaller diameters (ca. 5 mm) are sufficient. In any case measurements with different tube diameters are recommended in order to ensure convergence of the detonation velocity on increasing tube diameter (to make sure to be above the critical diameter). 

In regenerators the porosity Hg of the matrix is not constrained by pressure considerations, but the overall porosity that includes the confining tube must not exceed the value given by equation (29). However, high values of the matrix porosity may lead to insufficient matrix heat capacity. The heat capacity ratio is given by... 

In the subsequent 20 years (1960-80), the main principles of modern polymer physics were developed. These include the Edwards model of the polymer chain and its confining tube (Chapters 7 and 9), the modern view of semidilute solutions established by des Cloizeaux and de Gennes (Chapter 5), and the reptation theory of chain diffusion developed by de Gennes (Chapter 9) that led to the Doi-Edwards theory for the flow properties of polymer melts. 

Each monomer is constrained to stay fairly close to the primitive path, but fluctuations driven by the thermal energy kT are allowed. Strand excursions in the quadratic potential are not likely to have free energies much more than kT above the minimum. Strand excursions that have free energy kT above the minimum at the primitive path define the width of the confining tube, called the tube diameter a (Fig. 7.10). In the classical affine -and phantom network models, the amplitude of the fluctuations of a... 

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-... 

The average contour length (L) of the primitive path (the centre of the confining tube, see Fig. 7.10) is the product of the entanglement strand length a and the average number of entanglement strands per chain N/N. ... 

Reptation steps (a) formation of a loop at the tail of the snake and elimination of the tail segment of the confining tube ... 

In the simple reptation model, there is a delay in relaxation (the rubbery plateau) between te and the reptation time of the chain trep [Eq. (9.11)]. By restricting the chain s Rouse motions to the tube, the time the chain takes to diffuse a distance of order of its size is longer than its Rouse time by a factor of 6 N/N. This slowing arises because the chain must move along the confining tube. The reptation time of the chain trep — 0.2 s is measured experimentally as the reciprocal of the frequency at which G = G" in Fig. 9.3 at low frequency (see Problem 9.8). In practice, this time is determined experimentally and tq, Te and Tr are determined from Trep-... 

The confining tube in a semidilute solution. Thick circles are the correlation blobs of the chain. Thin empty circles are the correlation blobs of surrounding chains. 

At the Rouse time of an entanglement strand tg, the chain in semidilute solution finds out that it is trapped in the confining tube. The stress relaxation modulus between and the reptation time r ep is almost con-... 

Thus, a typical tube length fluctuation is of the order of the root-mean-square end-to-end distance R of the chain and the confining tube has a wide range of typical lengths ... 

The number of Kuhn monomers in each arm of the star is and the effective spring constant of this harmonic potential is 7. Most of the time, the length of the confining tube of an arm is close to its equilibrium value... 

The length of the confining tube of the backbone is Lbb to the reptation time of the backbone ... 

Single-chain motion of the P-mer within its confining tube by reptation and tube length fluctuations. 

The reptation time of the P-mer is Tep(P) and the constraint release time Tube given in Eq. (9.85). The faster of the two types of motion controls the diffusion of the P-mer. For constraint release to significantly affect terminal dynamics, the Rouse relaxation time of the confining tube Ttube must be shorter than the reptation time of the P-mer Tep( ) ... 

Very long P-mers have the constraint release time [Eq. (9.85)] shorter than their reptation time. Such very long P-mers relax and diffuse by constraint release (Rouse motion of their tubes) before they get a chance to reptate out of their confining tubes. For shorter P-mers, the reptation time Tep( ) is shorter than the constraint release time Ttube and reptation dominates... 

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