Cellulose polydispersity

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, / , (,r)108. Hermans describes the loss of correlation along the series of rods by a convolution polynomial . One of Hermans lattice statistics is namedparacrystalby Hosemann [5,117]. Hosemann shows that the field of distorted structure is concisely treated by the methods of complex analysis. A controversial subject is Hosemann s extension of ID statistics to 3D [63,131,227,228],... 

History. Starting from the ID point statistics of Zernike and Prins [116] J. J. Hermans [128] designs various ID statistics of black and white rods. He applies these models to the SAXS curves of cellulose. Polydispersity of rod lengths is introduced by distribution functions, Hermans describes the loss of corre-... 

The polydispersity of softwood milled wood lignin, as measured by M /M = 2.5, is high compared with that of cellulose and its derivatives. 

Naturally occurring cellulose is a polydisperse linear homogeneous polysaccharide based on 1,4-D-glucopyranose repeat units, with an... 

Which of the following is polydisperse with respect to chain length (a) casein, (b) commercial PS, (c) paraffin wax, (d) cellulose, or (e) Hevea brasiliensisl... 

Cellulose is a polydisperse polymer with an average DP in the general range of 3,500-36,000. Native cellulose is widely distributed in nature and is the principle constituent of... 

In contrast, other natural polymers, such as natural rubber (NR), cellulose, and most synthetic polymers, consist of mixtures of many members of a homologous series. These homologues contain varying numbers of units and thus have different molecular weights, and hence the polymers are said to be polydisperse or polymolecular. 

If N 1 for all components of a polymer sample, C and cA are not much affected by polydispersity [73], because the molecular weight dependence of q and cA tends to vanish at large N. Thus, small but clear deviations of the data points for cellulose derivative solutions [34,35,72] from the calculated curves in Figs. 7 and 8 may not be simply attributed to polydispersity. Furthermore, since the Mw/M ratios of the PHIC and PYPt samples were less than 1.1 and 1.2,... 

From another point of view, it can be seen that approximate conformity of cellulose nitrates to both of the asymptotic relations (63) and (89) for [ /] and (SF), respectively, implies that the number 0 should remain essentially constant at its asymptotic value 0, given by Eq. (57). Since it is difficult to assess the polydispersity of cellulose nitrate fractions, the constancy of 0, rather than its numerical value, should be of prime importance in testing the consistency of our conclusions. Doty, Schneider and Holtzer (59) and Newman and Flory (198) both originally reported, that 0 decreased systematically with decreasing molecular weight. Later Holtzer, Benoit and Doty (726) preferred to regard 0 as essentially constant at about 1.9 1021, somewhat smedler... 

Although the chemical structure of cellulose is understood in detail, its supermolecular state, including its crystalline and fibrillar structure is still open to debate. Examples of incompletely solved problem areas are the exact molecular weight and polydispersity of native cellulose and the dimensions of the microfibrils. 

The polymer properties of cellulose are usually studied in solution, using solvents, such as CED or Cadoxen (see Section 9.2). On the basis of the solution properties, conclusions can be drawn concerning the average molecular weight, polydispersity, and chain configuration. However, the... 

Molecular weight measurements have shown that cotton cellulose in its native state consists of about 15,000 and wood cellulose of about 10,000 glucose residues. Some polydispersity data on cellulose derivatives and polysaccharides are shown in Table 3-1. There are indications that the native cellulose present in the secondary cell wall of plants is monodisperse, that is, contains only molecules of one size. In such a case, number and weight average molecular weights ought to be identical. The cellulose in the primary cell wall, on the other hand, which has a lower average molecular... 

The polydispersity of the cellulosic material may be readily determined by the sedimentation equilibrium procedure from the relative distribution of the dispersed particles from the axis of rotation. The... 

Fig. 28. Plot of G (Eq. (62)) vs. reduced chain length x = 2 L/A for fractions of ladder polydichloro-phenylsiloxane in tetrabromoethane (1), bromoform (2), and benzene (3) and cellulose carbanilate in dioxane (4) Theoretical curves are plotted according to Ref. at the following values of polydispersity parameter U = U = 1 (I), 1.4 (II), 1.6 (III), 1.8 (IV)...

Chain length and molecular mass distribution have of course also strong implications for the performance of modified cellulose. For ethers, the degree of polymerization, DP, is usually between 50 and 2000 (300 for esters), as compared with 100 to 3000 for cotton cellulose and 600 to 1000 for wood cellulose. The relatively high polydispersity of the molecular mass originates from the starting material. 

The physicochemical properties of alkylated polysaccharides have received some attention, and details of the structures and conformations of 0-methylcelluloses, and their interaction in micelle junctions, have been included in a thorough discussion of polysaccharide gels and networks. Information on the polydispersity of samples of partially methylated cellulose may be obtained from column fractionation and by fractional precipitation from a solvent-nonsolvent system, but, for a more complete characterization of polydispersity, fractionation with a series of solvent-nonsolvent systems is necessary. The solubility, in water, of polysaccharides that are mainly methylated may be considerably improved by introduction of a few suitable ionizing groups, for example, by reaction with monochloroacetic acid to introduce carboxymethyl ether groups. The general sorption and diflFusion features of hydrocarbons and other... 

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