Freeness

Refining and Fractionation. These processes are used to alter and select cellulose properties so the final sheet has the desired properties (51). Properties of recycled fibers differ from those of fibers prepared directly from wood. For example, recovered chemical fibers have lower freeness, an apparent viscosity leading to different water drainage characteristics on paper machines. Recovered fibers also have iacreased apparent density, lower sheet strength, iacreased sheet opacity, inferior fiber—fiber bonding properties, lower fiber sweUiag, lower fiber flexibiUty, lower water reteatioa, reduced fiber fibrillatioa, and much lower internal fiber delamination. 

Sch.-R., abbrev. Paper) Schopper-Riegler degree of freeness (of pulp). 

Now we want to show that given a pair (A,B) of lists over a two symbol alphabet, say a,b, we can effectively construct a scheme P(A,B) such that P(A,B) is free if and only if the Correspondence Problem for (A,B) has NO solution. It will then follow that freeness is undecidable. For it if were decidable whether a scheme is free, then we could decide the Correspondence Problem as follows Given (A,B), construct P(A,B), turn on the machine which decides whether P(A,B) is free if P(A,B) is free print the answer NO - (A,B) has no... 

We can extend this result a little. If we examine Example III-4, we see that we have altered P(A,B) to form P(A,B) by changing subschema (n+1). Since f and g are assumed to be distinct from the function letters a and b and from each other, if we enter (n+1) with different values for u and v the subscheme will not violate the definition of freeness. But if ws enter (n+1) with val(u) = val(v), then the subscheme behaves like the scheme in Example III-2, which we have seen is not strongly equivalent to any free scheme. Hence, similar arguments will show that now P(A,B) is strongly equivalent to some free scheme if and only if the Correspondence Problem for (A,B) has no solution. 

We shall briefly examine a condition on schemes which implies freeness and which can be tested. We do this primarily because it gives us our first example of an equivalence preserving global transformation on schemes. This is a topic we study more closely in the next chapter. 

The transformation t does not necessarily preserve freeness if the original scheme is not liberal. The basic idea is that a test should occur only after one of its variables has been assigned to. This is accomplished by performing all possible... 

Improve the proof in Section C that freeness is undecidable by using the correspondence problem to show that freeness is undecidable for schemes with one monadic predicate letter and two monadic function letters (i.e. show how to construct for A and B a scheme P(A,B) with one monadic predicate and two monadic functions such that P(A,B) is not free if and only if the correspondence problem has a solution). 

Moss and Pilkiewicz (1974) used crown ethers to determine the freeness of carbenic species by comparing the relative reactivities of various alkenes towards phenylbromocarbene [192], generated either by treatment of benzal bromide [194] with t-BuOK or by photolysis of phenylbromodiazirine [193]. The results (Table 48) show that the reactive species produced by these... 

Hackh s Diet (1944), p 357-L defines "freeness as die extent to which a pulp for the manuf of paper has not been hydrated by beating. Accdg to J.N. Stephenson, Edit, "Preparation and Treatment of Wood Pulp", McGraw-Hill, NY, Vol 1(1950), pp 943-56,... 

The following freeness testers are described in the above book ... 

Pulps 50% maple, 35% birch, 15% poplar beaten to 400 Canadian Standard Freeness. 

Exposure of Bleached Pulp. Bleached pulp, based on 50% hardwood and 50% softwood kraft, jordaned to a Canadian standard freeness of 300-350 mL, was kindly supplied by Andrew Chase of the University of Maine. Unaged handsheets made from this pulp contained 85% a-cellulose (3) and 5% hot-1%-alkali-soluble matter (4). In the experiment illustrated in Figure 1, sheets were exposed in the Atlas 6500-W xenon-arc Fade-ometer equipped with Pyrex-glass filters the air temperature was 31 °C, and the relative humidity was 27% the black-panel temperature was 65 °C. Halfway through the reported period of... 

The pulp to be treated with cellulolytic enzymes should first be screened in a laboratory flat screen to remove any shives. The screened pulp is beaten either in a laboratory Hollander beater (TAPPI Standard Method T 200 os-70) or in a PFI mill (TAPPI Standard Method T 248cm-85), depending on the amount of pulp to be treated, to a final Canadian Standard Freeness of 200-300 ml. The beating operation helps convert shives into fibers and improves the digestibility of the pulp towards cellulolytic enzymes. The pulp is dewatered to a consistency of approximately 25% and stored in a polyethylene bag after fluffing. 

Occurrence, formation, structure and reactions. Wiley-Interscience, New York,. 597-637 Gummerus M (1985) Sulphite treatment of TMP rejects. Part 1. Properties of fibre fractions at various freeness levels and their influence on the reject pulp. Pap Puu 11 635-647 Heitner C, Hattula T (1988) Ultra-high-yield pulping. Part VI The effect of sulphonation on the development of fibre properties. J Pulp Pap Sci 14 J6-J11 James AN, Tice PA (1965) The presence of carboxyl groups in lignosulfonate preparations. Tappi 48 239-244... 

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