Molecular mass average

For a polypeptide chain of 100 residues in length, a rather modest size, the number of possible sequences is 20 , or because 20 = lO, lO unique possibilities. These numbers are more than astronomical Because an average protein molecule of 100 residues would have a mass of 13,800 daltons (average molecular mass of an amino acid residue = 138), lO such molecules would have amass of 1.38 X lO " daltons. The mass of the observable universe is estimated to be 10 proton masses (about 10 daltons). Thus, the universe lacks enough material to make just one molecule of each possible polypeptide sequence for a protein only 100 residues in length. 

It should be stressed that the observed critical strain-rate for bond fracture (sf) in the case of a polydisperse fraction refers to the longest chain present in the sample. This quantity is significantly different from the critical strain-rate (r ) defined with respect to an average molecular mass whose value could be determined only after careful consideration of the degradation kinetics. 

Mr averaged molecular mass between crosslinks as calculated from... 

In order to calculate the average molecular mass MR of the network strands, the mass m, of the giant macromolecule is devided by the number N of strands in the network. 

Mc averaged molecular mass of strands between crosslinks, f functionality of junction (f = 3),... 

Table 3.1. Young s modulus E at T = 500 K and average molecular mass between crosslinks...

In the Eqs. (3.1) and (3.3), a second term can be introduced to account for the average molecular mass 1V1E between entanglements of chains [5, 29] ... 

The dashed line in Fig. 3.2 corresponds to a linear regression calculation yielding Me = 8 kg/mol for the average molecular mass between entanglements if no chemical crosslinks are present (MR - oo). This result agrees reasonably with values for various thermoplastics as determined from elasticity measurements on melts [30, 31, 32], Examples are given in Table 3.2. 

Tgoa glass transition temperature of the uncrosslinked polymer Mc average molecular mass between crosslinks tj> empirical factor... 

Activation volumes of the polymers according to Eq. (6.5) were calculated with t, = 0.5ay and plotted in Fig. 6.6 versus the average molecular mass Mc of network strands. The volume of a molecular strand is plotted also... 

Kuokkanen (1985) determined complexation constants for 4-tert-butyl- and 4-chlorobenzenediazonium tetrafluoroborate with polyethylene glycols of average molecular mass 300, 600, 1000, and 2000 under the same experimental conditions as mentioned above. The constants are significantly lower than those with... 

A protein, designated cyctochrome c", isolated from the methylotrophic bacterium Methylophilus methylotrophus, has been studied extensively because of its unusual properties and was found to have an average molecular mass of 14293.0 Da and to contain 124 amino acid residues. The A-terminal sequence to residue 62 had been determined and the heme binding site had been located at Cys-49 and Cys-52 [12]. Further studies were concerned with determining the remainder of the sequence. 

In POLYM the output data of KINREL are used with compositional information to calculate the number and mass average molecular masses (Rn and Rm, respectively) and number and end-group average functionalities (fp and fg> respectively) in the pre-gel region in all stages. In addition, the network characteristics such as sol fraction, mj, and the number of elastically active network chains per monomer (5), Ng, are calculated in the post-gel regime of stage 3. 

Figure 3 Size fractionation of EDTA-soluble polyuronides from Rutgers and transgenic fruit juice processed by cold- and hot-break methods. Pectin from processed juice was extracted as ethanol-insoluble solids and size fractionated on a Sepharose CL4B column. Under the same chromatographic conditions, elution of the branched dextrans with average molecular mass 2000, 500, 252, 151, 40 and 17.7 kD-peaked in fraction number 46, 50, 54, 62, 67 and 72, respectively. Modified from Thakur et al. [23].

The average molecular mass Mj was determined by solving the equation, following the methods in (12). 

SEC-GC-FID, according to Figure 7.40, has been used to carry out the simultaneous determination of the polymer average molecular masses and molar mass distribution and the concentration of additives [984]. The effluent was split and adsorbed on PTV packing material before GC analysis. The choice of PTV... 

Figure 8.1 Heme (iron protoporphyrin IX) structure. The most frequently observed cleavages in LDMS of the intact species are denoted. Heme elemental composition is C34H32N404Fe monoisotopic molecular mass is 616.176 Da average molecular mass is 616.487 Da.

The polyester sizes used have a much lower average molecular mass than polyester fibres. These structures (10.69) contain sulphonic acid groups and may be water-soluble or water-dispersible types. The degree of sulphonation is low [171]. If these resins are subjected to a high pH, the sulphonate groups can be hydrolysed, giving an insoluble resin that is very difficult to remove from the fibres. 

For correlation with most physical properties (mechanical strength, optical scattering), mass average molecular mass of a polymer Mw" appears more satisfactory. Higher-power averages like z-average molecular mass "Mz" seem to better correlate with rheological properties. Expressions of M , Mw and Mz are... 

End group quantification is thus a useful method for number average molecular mass determination. Also, if the end group concentration is higher than the value calculated from an independent Mn determination, chain branching can be deduced and quantified. 

The obvious definition of the number average, Mn, of the distribution is the position on the M-axis that divides the area under the n (A/)- curve in equal parts (cf. Fig. 1.3). Because of the fact that n M) is normalized to 1, each of the subareas is equal to 0.5. As 50% of all the molecules are shorter than Mn, the other 50% are longer than Mn. Bearing in mind the normalization, the number average molecular mass is... 

Figure 1.3. The number average molecular mass, M , is the position that divides the area under the corresponding distribution in equal parts... 

Two heat-sensitive organic liquids of an average molecular mass of 155 kg/kmol are to be separated by vacuum distillation in a 100 mm diameter column packed with 6 mm stoneware Raschig rings. The number of theoretical plates required is 16 and it has been found that the HETP is 150 mm. If the product rate is 5 g/s at a reflux ratio of 8, calculate the pressure in the condenser so that the temperature in the still does not exceed 395 K (equivalent to a pressure of 8 kN/m2). It may be assumed that a = 800 m2/m3, /x = 0.02 mN s/m2, e = 0.72 and that the temperature changes and the correction for liquid flow may be neglected. 

The reactive nature of compound 22 is illustrated by the series of transformations shown in Scheme 7.12, in which its Zr—C bond reacts selectively with electrophilic reagents to produce a-haloboronates 36—38. Compound 22 also catalyzes the polymerization of styrene. The polymers thus obtained had weight-average molecular masses in the range 75000—100000 with polydispersities of 1.8—2.1. An X-ray analysis of 22 confirmed it to be a four-coordinate Zr complex with two cyclopentadienyl rings, chlorine, and the aliphatic C-l carbon atom as the ligands (Fig. 7.4). 

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