Average molar weight

Here, the quantities jn ° and ji are, respectively, the chemical potentials of pure solvent and of the solvent at a certain biopolymer concentration V is the molar volume of the solvent and n is the biopolymer number density, defined as n C/M, where C is the biopolymer concentration (% wt/wt) and M is the number-averaged molar weight of the biopolymer. The second virial coefficient has (weight-scale) units of cm mol g. Hence, the more positive the second virial coefficient, the larger is the osmotic pressure in the bulk of the biopolymer solution. This has consequences for the fluctuations in the biopolymer concentration in solution, which affects the solubility of the biopolymer in the solvent, and also the stability of colloidal systems, as will be discussed later on in this chapter. 

Figure 6.2 Effect of sucrose on the self-assembly / disassembly of sodium caseinate in aqueous medium (ionic strength = 0.01 mol/diu3, 22 °C) on the basis of combined static and dynamic light scattering. Upper plots refer to pH > pI, i.e.. ( ) pH = 7.0, ( ) pH = 6.0, (A) pH = 5.5 (a) weight-average molar weight, A/w (b) structure-sensitive parameter p. Lower plots refer to pH < p/, i.e., ( ) pH = 3.9, (A) pH = 3.5 (c) weight-average molar weight, A/w (d) structure-sensitive parameter p.

Figure 6.5 Temperature dependence of the characteristics of sodium k-carrageenan particles dissolved in an aqueous salt solution (0.1 M NaCl). The cooling rate is 1.5 °C min-1, (a) ( ) Weight-average molar weight, Mw, and (A) second virial coefficient, A2. (b) ( ) Specific optical rotation at 436 nm, and ( ) penetration parameter, y, defined as tlie ratio of the radius of the equivalent hard sphere to the radius of gyration of the dissolved particles (see equation (5.33) in chapter 5). See the text for explanations of different regions I, II, III and IV.

Figure 6.11 Effect of ionic strength on (a) weight-average molar weight, Mw ( ), and second virial coefficient, A2 ( ), of p-casein in solution at pH = 5.5 and 22 °C, as determined by static light scattering and (b) average droplet diameter, c/43 (A.), and extent of gravity creaming ( ) of p-casein-stabilized emulsion (11 vol% oil, 0.6 wt% protein, pH = 5.5, 22 °C).

Similar to the above discussed processes, the photoinitiation of the copolymerization between cyclohexene and AN in the presence of pyromellitic dianhydride or phthalic anhydride is based on the sequence of PET and proton transfer [30]. Consequently, the copolymerization rate with the former acceptor (Rp = 1.6x 10-4moll-1 s-1) is higher than this of the latter (Rp = 1.4x 10-4moll-1 s-1 [AN] = 4.5 mol l-1, 30°C). Interestingly, the average-molar weights of the alternating copolymers lie between 1000-2000 g mol- The reason for this very small value is possibly an efficient primary radical termination due to the formation of the two radicals IV and V see Eq. (4). Exact polymer characterization data are not available, so far. 

For the power consumed by the compressor, we assume polytropic behavior and 100% efficiency in this example. MW gas is the average molar weight, T is the operating tanperature, ti<. the isentropic efficiency, P fonn the reforming pressure, the initial pressure, F the total flow in (kg/s), and W the power consumed by the compressor. 

For the nanocomposites prepared with non-modified clay (Cloisite Na and with Cloisite 25A, it is clear that the clay content does not affect the polymer molar masses and the polydispersity index. For all the composites, the number average molar weights (Mn) of extracted PCL chains are around 20,000 g mol with polydispersity indexes of about 2.0. This range of molecular weight fits well the expected values computed from the initial monomer-to-tin molar ratio by assuming selective and quantitative initiation by the tin alkoxide groups. 

Reactor order for sulfur and hydrogen, respectively Average molar weight, g/gmol Reaction order for nickel and vanadium Number of moles of species i, mol,... 

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