Molecular weight equations

Note that fw, = w,/E,w, is the weight fraction of particles in class i. Since the weight of material in a particular size class is given by the product of the number of particles in the class and their molecular weight, Equation (15) may be written as... 

First, calculate apparent molecular weight, Equation 3-35. 

Branched PEI has a very compact structure in solution, as evidenced by its reduced viscosity at low ionic strength which only slightly increases by increasing the charge density of the polymeri4>. Moreover, the value of a in the intrinsic visco-sity/molecular weight equation fr ] = KM is very low (0.39)57) as compared with that of most linear polymers (0.6-0.8). 

S 18 Sharples, A., and H. M. Major Determination of constants in the intrinsic viscosity molecular weight equation (cellulose acetat). J. Polymer Sci. 27, 433 (1958). 

Very accurate quadratic fits may be obtained from Equation 11, although Equation 12 is not so accurate and is not so well justified theoretically however, it is the simplest available description. Note that the volume fraction, cf>, must be used and that this implies the use of partial molar volume and knowledge of molecular weight. Equation 11 works remarkably well and applies equally well to bovine serum albumin and casein. 

The phenylcyclopropylcarbene generated upon irradiation of phenylcyclopropyl-diazomethane (166) in benzene, hexafluorobenzene or saturated and unsaturated hydrocarbons leads to 1-phenylcyclobutene (167) in nearly quantitative yield on the other hand, the cyclopropylcarbene formed on irradiation of 2,3-biscyclopropylstilbene oxide (168) leads to secondary photo-products of higher molecular weights (equation 115). ... 

On the other hand, for polyesterification (an example of a stepwise reaction), the rate and degree of polymerization depend on the number of functional groups in the system, regardless of whether they are on the monomer, the high polymer, or any species intermediate in molecular weight (Equations 11, 12, and 13) ... 

An illustrative computation from Des Coudres results is as follows. He found 0.510 x 10 volt for the ratio E/h for 2.71 molal potassium chloride. Multiplying the product EF/h by 101 to reduce it to absolute units, and dividing by the value 980.7, also in absolute units, for g, the acceleration due to gravity, yields 5.02 grams. The values of the other terms in equation (8a) are Voi, = 18.36 cc., t aci - 31.3 cc. and p = 1.111. From these figures and the molecular weights equation (8a) gives the value 0.50 for the cation transference number of potassium chloride. If the same values of the transference number are obtained as are found by other methods it is evident that a correct analysis of the mechanism of the process has been made. Such a comparison is made in Table I. The values of the... 

M is determined exactly from the repeat unit composition. The repeat unit length can be measured by using an interactive molecular modeling program. The rotational degrees of freedom of the backbone can be counted by using the rules provided in Section 4.C. The new quantitative structure-property relationships developed in this book for V and p (Chapter 3), Ecoh (Chapter 5), Tg (Chapter 6), critical molecular weight (Equation 11.25 combined with Equation 11.24), molar Rao function (Section ll.B), molar Hartmann function (Section ll.B), characteristic ratio (Chapter 12), and surface tension (Chapter 7), allow the application of various derived correlations for mechanical properties to all polymers built from the nine elements (C, N, O, H, F, Si, S, Cl and Br) included in the scope of our work. 

For polymers containing no monofunctional monomers, these end-group concentrations determine the number-average molecular weight (Equation 34), as indicated in Equation 37. 

In the case of the pathological globulin the angular dependence data could be accounted for equally well by thin rods 563 A. long or by spheres 414 A. in diameter. A sphere of this size would have a molecular weight of about 30-io6 whereas the actual molecular weight (equation (54) is 1.16 106. These considerations, of course, exclude the spherical model. 

This relation has been confirmed experimentally. It follows, therefore, that since <1> is regarded as a universal constant, the average dimensions of polymer molecules in solution can be estimated from knowledge of their intrinsic viscosities and molecular weight (Equation 12.71). Specifically, the unperturbed dimensions can be calculated from the value of K. 

Figure 3.13. Schematic illustrating change in melting temperature with molecular weight (equation 3.137).

If the reactant gas is methane, the most abundant ions formed are CH5+ and C2H5+, which then become the reactant ions. On collision with the sample molecules, these ions donate a proton to form what is termed a quasi-molecular ion [M + H]+ at a mass 1 Da higher than the molecular weight (Equation 4.4). 

The excluded volume of a coil is characterized by the expansion factor K. The term a depends on z [equation (4-44)] and z depends on the molecular weight [equation (4-43)]. Thus with equation (4-44), a becomes a complicated function of the molecular weight. 

To clarify the dependence of D2 on molecular weight. Equation 88 is rewritten as... 

Chain termination (step c in Equation 22.5) can occur by one of several processes. In some cases, a "chain transfer" agent, such as hydrogen, is added to the polymerization process to control the molecular weight (Equation 22.6). - These reagents terminate the... 

Tanaka and co-workers [158] have used the high-temperature turbidimetric titration procedure originally described by Morey and Tamblyn [153] for determining the MWD of cellulose esters. This method has been applied to the measurement of the MWD of PP. They found that the type of MWD of this polymer is a log-normal distribution function in a range of I M) (cumulative wt%) between 5 and 90%. The effect of heterogeneity in the MWD of PP on the viscosity-molecular weight equation was examined experimentally - the results agreed with those calculated from theory. Strict temperature control ( 0.15 °C) is necessary in these determinations [159]. 

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