Plateau molecules

As we can see from Eqs. (32), Xg in the reptation-without-stretching regime N0 <1, while XE NB-Hn NB ) for the very large "plateau molecules. This important change in behaviour indicates that the field-induced disengagement time Xg is less molecular-size dependent but more field dependent for larger molecules. 

If the pulse duration is very long, a plateau molecule has enough time to reorient in the new field direction at the beginning of each new pulse before it reaches its plateau velocity. For example, with the field E=EA, the molecule first stretches out in the x-direction, with ih ) )> iLAcosQ)) t and then reaches its steady-state center-of-mass velocity V =V =Ep, which it keeps for the rest of the pulse. The end-to-end distance is then very small. Similarly, when the field changes... 

V2, while even larger "plateau" molecules for which have a... 

Thus, to separate "plateau molecules with sizes Eq. (64) gives... 

During a complete cycle of duration + field (with E >0) is applied in the forward direction ( + ) for a time and then the field E = -E u (with E >0) is applied in the reverse direction (-) for a time We assume here that E E and and we consider only "plateau molecules for which in continuous fields. It is thus assumed that iV 0 >14 for all molecules under study. 

As usual, this critical time x is expected to be molecular-size dependent. Therefore, for a given set of experimental conditions (i.e. a fixed value of t) all plateau molecules for which will have... 

Note however that V qq=V q when R =, 0 this means that the BRM predicts no enhanced separation of the "plateau" molecules if the two fields are of equal intensities (E. E ), This is because the end-to-end distance is then always given by (hJ L icosQ), giving a time-independent velocity moreover, since the probability of Jumping in the tube against the field is, from Eq.(20a), p exp(-25), with 8=0/i /a iV 0 /3>l, the... 

VII. 4 Conclusion In conclusion, the BRM predicts that field-inversion gel electrophoresis should improve the separation of "plateau molecules if two unequal fields are used. In this case, the reverse field, which is of lesser intensity, serves to reduce the orientation of the reptation tube since this is field-induced, this is much faster than the tube relaxation process which is the basis of the intermittent-field technique. Experimentally, this reptation induced effect has been observed, but a potentially even more powerful "resonance- ike effect has been observed to exist as well. This latter effect leads to band-inversion however, and since it occurs for pulse durations t =x (N)involves chain movements inside its tube and/or movements of only parts of the tube, which have not been discussed in this article. 

The maximum number of latent variables is the smaller of the number of x values or the number of molecules. However, there is an optimum number of latent variables in the model beyond which the predictive ability of the model does not increase. A number of methods have been proposed to decide how many latent variables to use. One approach is to use a cross-validation method, which involves adding successive latent variables. Both leave-one-out and the group-based methods can be applied. As the number of latent variables increases, the cross-validated will first increase and then either reach a plateau or even decrease. Another parameter that can be used to choose the appropriate number of latent variables is the standard deviation of the error of the predictions, SpREss ... 

If a Type I isotherm exhibits a nearly constant adsorption at high relative pressure, the micropore volume is given by the amount adsorbed (converted to a liquid volume) in the plateau region, since the mesopore volume and the external surface are both relatively small. In the more usual case where the Type I isotherm has a finite slope at high relative pressures, both the external area and the micropore volume can be evaluated by the a,-method provided that a standard isotherm on a suitable non-porous reference solid is available. Alternatively, the nonane pre-adsorption method may be used in appropriate cases to separate the processes of micropore filling and surface coverage. At present, however, there is no reliable procedure for the computation of micropore size distribution from a single isotherm but if the size extends down to micropores of molecular dimensions, adsorptive molecules of selected size can be employed as molecular probes. 

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