Some words of caution

The blob concept is very successful in describing qualitative features of the concentration crossover from dilute to semidilute solutions. This has led to a discussion of the teiupemture crossover among the - or excluded 

Now consider an isolated chain of length n n. Pazts ut intrinsi-calljr should show only weak interaction effects, the effective 2 -parameter Zb being small. (We ignore thrcc-body interactions.) Thus nj-blobs 

To illustrate this point we consider a specific example. The scaling results for the radius of gyration in the excluded volume limit properly read 

Furthermore we should stress that tire length scales identified by the blob model concern characteristic features of the segment-segment correlations. Thus the appealing picture of a chmn build up from well defined individual blobs should not be taken literally. Rather each segment can be taken aa the center of its correlated blob, and translational im,iariance along the (diain is not destroyed. 

The concentration blob model of scaling theory has been introduced in [DCF+75, FarTC], where it has been shown to qualitatively explain a lot of experiments, A comprehensive review is given in [dG79]- 

For c C c , t n-1/2 the chains are isolated, for c c they strongly overlap and feel the three-body forces. Writing in the 0-region the scaling law for the osmotic pressure as 

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Some word of caution is needed at this point. The notion of electronic bands is of course related to the electronic structure of ordered bulk solids, and applying it to thin films is in principle questionable. Indeed, it is sufficient to associate high transmission probabilities with states of the excess electron in the film which are extended on the scale of the film thickness. In fact, numerical results34 suggest that the correspondence with the band structure of the bulk material is substantial even for very thin films. 

Random copolymers are a special type of statistical copolymer in which the distribution of repeat units is truly random (some words of caution are necessary here because older textbooks and scientific papers often use the term random copolymer to describe both random and non-random statistical copolymers). A section of a truly random copolymer is represented below ... 

Tables 4 through 26 do not contain all data available in the literature, but represent the resnlts of a critical survey. Some words of caution are in order abont the results presented. Deficiencies in methodology become particularly pronounced in the calculation of which are derived respectively from tte...

Some Words of Caution Vendors shorrld not generally be given very important sections for procurement of plant arrd rrrachinery, i.e., other regtrlar activities or operations in the premises shorrld rrot be disturbed as far as possible. 

Some words of caution Be wary of arguments sometimes very self-serving— against licensure. Someone may say that you are working in an employment sector that is under the industrial exemption and, therefore, that you do not need a license. Will you always want to work in that sector Others will oppose licensure because it... 

Intepretation of these (and any other long run) price series requires a little care and some words of caution are perhaps warranted here. While presenting price data in real terms isolates fundamental changes in the... 

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