Chain correction factor

Chain branching Correction factor Chain branching Correction factor... 

On the other hand, the correction factor by which W r) is altered through this refined treatment, namely, exp[ —(9n/20)(r/r, ) ] from Eq. (16), depends both on n and on r/Vm If the distance of separation of the ends of the chain lies in the vicinity of its root-mean-square value, i.e., if r / then... 

A terminal chain may rearrange similarly, but each of a pair of entangled internal chains is prevented from doing so by the permanent chemical structure, as is clear from Fig. 93. Inasmuch as the terminal chains are not thus involved, we should expect the correction factors for terminal chains occurring in Eqs. (30) and (30 ) to be valid. The correction for entanglements should be expected to enter as a factor modifying the entire expression for Ve. Unfortunately, there is at present no theoretical basis from which to estimate this factor, except to note that it presumably will be a function of p. 

We assume that the chains were oriented parallel to the film plane but the chain direction were distributed randomly in the film plane. In this case, the correction factor for the chain orientation, , is 3/8. Consequently, the xSx value of the PTV cast film was calculated to be 1.2 x 10 9 esu, which is comparable to that of the highly oriented vacuum-deposited polydiacetylene film at the resonance with the exciton absorption. 

Inserting the Rouse rate W(, 3Q9 K)=(7 0.7)xl0 AVns (Table 3.2) obtained from single chain structure factor measurement into Eq. 3.18 the solid line is obtained. It quantitatively corroborates the correctness of the Rouse description at short times. The data also reveal clearly a transition to a law, though Eq. 3.36 would predict the dotted line. The discrepancy explains itself in considering the non-Gaussian character of the curve-linear Rouse motion (Eq. 3.38). Fixing and d to the values obtained from the single chain struc-... 

The empirical correction factors 4> (calculated on assumption that for all networks swollen in pure water % from Eq. (6) should be 0.48) change between 0.05 and 0.3 (see Ref. [48] for salt I the data are in Fig. 8). Generally, we can say that the effect of the positive charge on the formation and extent of transition is 5 to 10 times smaller than the effect of MNa. There are probably several reasons for the low value of (a) positive charges are localized at a larger distance from the main chain (smaller influence on the chain conformation) (b) due to the... 

Good analyses of triglycerides require careful attention to reproducible conditions and the use of standards and correction factors. Liquid phases that have been used with some degree of success all have high temperature limits in excess of 300°C and include some long-chain hydrocarbons as well as silicone polymery usually polysiloxanes such as OV-1, SE-30, OV-17, SE-52, and JXR (8). ... 

The values of fa were calculated by Equation 4 for all ranges of the cumulative fraction. The results of the calculation enabled us to compare the characteristics of GPC performances at two different times. In this treatment any difference in the GPC performance—e.g., resolution—was expressed in terms of the correction factor, ft, to the chain length, Ai. 

As shown in the central chain, upper part in Fig. 1, ( HELP from matrix RM ),the analyst can now use the correction factor from Eq 2 and substitute it for the unknown correction factor X(aE,X) in Eq 1. This enables a correction to be made of the value observed in the unknown sample. In summary the analyst simply substitutes X(aE,X) for K(aE,Z). 

Thus the matrix reference material has fulfilled another function than the AS function for the analyst, a function which is not located in the traceability chain, but outside the chain it enables the analyst to make an independent assessment of the possible magnitude of the conversion factor K, thus assessing - possibly reducing - the uncertainty of the measurement by carrying out a correction . But even this correction carries an uncertainty which must be evaluated. The problem of this correction factor has been treated elsewhere in more technical detail under the name recovery factor ... 

The phrase related to implies that the relationship is known and valid. This will only be realized if the relationship at every step of the process is clearly defined and valid. Hence the requirement for an unbroken chain of comparisons. The parallel between these issues and those addressed by method validation is worth noting. Validation is the process of establishing that a method is capable of measuring the desired measurand (analyte), with appropriate performance characteristics, such as level of uncertainty, robustness, etc. It should also address systematic effects, such as incomplete recovery of the analyte, interferences, etc. These latter issues can be dealt with by designing a method to eliminate any bias, at a given level of uncertainty, or if that is not possible, to provide a means of correcting for the bias. This may be done at the method level, by applying a correction factor to all results, or at the individual measurement level. 

To use Stokes law with chains or fibers, several approaches are available. Traditionally a correction factor k, known as the dynamic shape factor, is defined such that... 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

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