Coil size

The determined eddy-eurrent parameter is the inductance of the eomplex impedance measured by impedance analyzer at j=100 kHz. Therefore the impulse response function from chapter 4.2.1. is used for calculation. The depth of the cracks is big in comparison to coil size. For presentation the measured and pre-calculated data are related to their maxima (in air). The path X is related to the winding diameter dy of the coil. 

In order to adequately describe the size of a heater, the heat duty, the size of the fire tubes, the coil diameters and wall thicknesses, and the cor lengths must be specified. To determine the heat duty required, the maximum amounts of gas, water, and oil or condensate expected in the heater and the pressures and temperatures of the heater inlet and outlet must be known. Since the purpose of the heater is to prevent hydrates from forming downstream of the heater, the outlet temperature will depend on the hydrate formation temperature of the gas. The coil size of a heater depeiuLs on the volume of fluid flowing through the coil and the required heat duty. 

For long chains, g2(0 i(0 for whereas g2(0 for t (inner monomers cannot travel further from the center of mass than the coil size, of course). 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

As mentioned above, for sizes on the order of the persistence unit the coil size follows the scaling law,... 

Rfo is the Flory radius describing the coil size at concentrations below c. ... 

For the tensile blob, thermal blob, and concentration blob we find that the coil accommodates external stress (thermal, concentration, or force) through a scaling transition that leads to two regimes of chain scaling. This directly impacts the free energy of the chain, the mechanical response, and the coil size. 

The percent conversion for the onset of the gel effect varies considerably depending on the monomer and the reaction conditions (which determine coil size, viscosity, entanglements). In some systems the gel effect has been reported as occurring at only a few percent... 

The deterioration of the solvent qnality, that is, the weakening of the attractive interactions between the polymer segments and solvent molecules, brings about the reduction in the coil size down to the state when the interaction between polymer segments and solvent molecules is the same as the mutual interaction between the polymer segments. This situation is called the theta state. Under theta conditions, the Flory-Huggins parameter % assumes a value of 0.5, the virial coefficient A2 is 0, and exponent a in the viscosity law is 0.5. Further deterioration of solvent quality leads to the collapse of coiled structure of macromolecules, to their aggregation and eventually to their precipitation, the phase separation. 

Meyerhoff and Cantow (118) compared the relationships between [ /] and MW for polystyrenes prepared in various ways they found that for given Mw isotactic polystyrenes produced with Ziegler catalysts had the highest [ij], followed by low-conversion free-radical polymers both high-conversion (80%) and anionic (Szwarc) polymers had lower [ij]. These differences were all attributed to differences in LCB, though in principle differences in tacticity such as those between Ziegler and free-radical or anionic polymers could produce differences in the coil size in solution and hence in [iy]. 

All factors related to the arrangement of the polymer chain in space are classified as tertiary structure. Parameters measurable directly (the radius of gyration RG, the end-to end distance h, the hydrodynamical radius RH, and the asymmetry in light scattering intensity) or indirectly (interaction parameters, the second virial coefficient A2) are related to the dimensions, such as size and shape of the polymer chain in a specific solvent under given conditions of temperature and pressure. For the exact determination of the coil size of macromolecules, it is necessary to ensure that measure-... 

Likewise, the samples can be arranged in the order of decreasing coil size and increasing branching, as determined by g COrr and g", again using the catalyst systems to identify the samples. The most linear polymers are the reference butyllithium samples followed by the nickel-based polymer, butyllithium, alfin, cobalt based, titanium based, and emulsion. The correction to the branching factor for polydispersity makes the nickel-based and alfin polybutadienes less branched with respect to the other polymers examined. 

In another approach towards eliminating the viscosity measurements, the parameter KM1+a, related to the above, has been reported (7). It is claimed that this could be substituted for the coil-size parameter [rj M. A more complex function relating M to elution volume where no viscosity measurements are made has been proposed by Coll and co-workers (8). This function, derived from the Mark-Houwink equation and the equation of Ptitsyn and Eizner (9), lacks the simplicity of that described above. 

We fch.ua take the segment size smaller and. smaller, at the same time increasing the number of segments so as to keep the unperturbed coil size rv constant. Thus... 

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