Molar mass, limiting

Figures 8a and 8b display the polymer mass dependence of Ta, Ti, Tg, and Tq for the F-F and F-S classes of polymers, respectively. All four characteristic temperatures exhibit the same physical trend, that is, growing with increasing M and saturating to constants in the high molar mass limit M oo. Comparison of Figs. 8a and 8b reveals that the variation of these characteristic temperatures with M is generally stronger for the F-S polymers. For instance, the slope of Tg versus 1/M is nearly a factor of 3 larger for the F-S class than the F-F class. All four characteristic temperatures T (a = 0, g, I, A) for the F-S polymers exceed their counterparts for the F-F polymers.

Figure 17. Specific volume Vt and isothermal compressibility (at the glass transition temperature Tg) calculated from the LCT as a function of the inverse number l/M of united atom groups in single chains for constant pressure (P = I atm 0.101325 MPa) F-F and F-S polymer fluids. Both quantities are normahzed by the corresponding high molar mass limits (i.e., by...

Equation (9-114) corresponds to a Gaussian distribution function (see also Section 8.3.2.1). The molar mass can be calculated from the position of the inflection point of the function c = /(r — r ). For proteins in CsCl/ H2O, the lower molar mass limit giving a meaningful measurement is 10 000-50 000 g/mol molecule. The limit is essentially governed by the length of the ultracentrifuge cell ( 1.2 cm) and the optimal values of r — for this length. 

The upper Molar Mass Limit versus the Nature of Mobile Phase. . . 117... 

These results indicate that critical conditions have potential to separate homopolymers at least up to 2000kD. The highest molar mass limit was reached in two thermodynamically good solvents of different polarity. One of the solvents... 

Bulk polymerization of POx at 90-150 "Cyields poly(POx) with molar masses limited to about 6000 gmol", which corresponds to the ratio of the apparent rate constant and the rate constant of chain transfer to monomer (fep/fetriu) of 100. In HMPA at 40 °C, this ratio is equal to 75. Indeed, several factors influence the extent of this chain transfer reaction temperature, initiator, and nature of the counterion. Chain transfer to monomer decreases in the order Na > K > Cs , in agreement with interactions between the metal cation and the oxygen of the monomer. 

The authors demonstrated that the fractions of BzPC also exhibited a thermotropic phase, and that the transition temperature increased sharply with increasing the polymers molar mass (limiting value of 176 °C). 

Molar Mass Interval. GPC columns are offered for different molar mass intervals for larger intervals it is possible to combine some columns of different pore size types or to combine a few so-called mixed bed or linear columns. Both possibilities have their own special advantages and disadvantages mixed bed columns with a linear separation range of more than four molar mass decades are suitable to quickly get an overall view of a new sample, whereas a column set, carefully selected from different pore size types, often has a much better separation efficiency in a limited mass interval (for details, see Sections in and IV). 

The molar mass distribution of hyperbranched polymers is, therefore, always larger than diat of titeir linear homologues and tends toward infinity when conversion becomes close to 1. The use of a B3, comonomer, acting as a chain limiter and core molecule, helps in reducing polydispersity and controlling the molar mass of the final polymer.197... 

Similarly, triphenylphosphine dichloride (TPPCI2) can activate aromatic carboxylic acids in pyridine through the formation of acyloxyphosphonium salts (Scheme 2.30).313 A side reaction between tire intermediate acyloxyphosphonium species and a second carboxyl endgroup leading to the formation of anhydrides has been reported.313 This chain-limiting reaction decreases tire molar mass, while the presence of anhydride linkages in tire chains adversely affects the thermal and hydrolytic stability of the final polyester. 

Scheme 2.34).319 322 Since the alkali metal salt formed does not react with ester groups, the molar mass is not limited by the reverse reaction and this polyesterification can be regarded as a nonequilibrium one. 

Intramolecular chain limiters, 458 Intrinsic viscosities, 162 Intrinsic viscosity-molar- mass equation, 57... 

Step 1 Convert the mass of each reactant into moles, if necessary, by using the molar masses of the substances. Step 2 Select one of the products. For each reactant, calculate how many moles of the product it can form. Step 3 The reactant that can produce the least amount of product is the limiting reactant. 

STRATEGY First, the limiting reactant must be identified (Toolbox M.l). This limiting reactant determines the theoretical yield of the reaction, and so we use it to calculate the theoretical amount of product by Method 2 in Toolbox L.l. The percentage yield is the ratio of the mass produced to the theoretical mass times 100. Molar masses are j calculated using the information in the periodic table inside the front cover of this i book. 

In certain cases the organic dibasic acid is not sufficiently reactive for the purpose of polymerisation, and so it is replaced either with its anhydride or its acid chloride. For example polyamides (nylons) are often prepared by reaction of the acid chloride with the appropriate diamine. In the spectacular laboratory prepatation of nylon 6,6 this is done by interfacial polymerisation. Hexamethylenediamine is dissolved in water and adipyl chloride in a chlorinated solvent such as tetrachloromethane. The two liquids are added to the same beaker where they form two essentially immiscible layers. At the interface, however, there is limited miscibility and nylon 6,6 of good molar mass forms. It can then be continuously removed by pulling out the interface. 

The practical effect shown by this equation is that polymers become more difficult to process as their molar mass increases. For example, doubling the degree of polymerisation leads to an approximately ten-fold increase in melt viscosity. Fortunately, melt viscosity decreases with increasing temperature, so that in many cases the effect of high viscosity for higher molar masses can be overcome. However, there is an upper limit at which polymers can be processed without beginning to degrade so it follows that, at some point, a polymer cannot be processed from the melt at all. 

Having obtained the value of the limiting viscosity number, we can calculate relative molar mass using the semi-empirical equation ... 

HPLC is limited to relatively low molar mass compounds, Le. below 3000. In practice this tends to restrict the technique to dendrons rather than fully formed dendrimers, but it is nonetheless a useful technique, given the importance of establishing high analytical purity of products at each step in a dendrimer synthesis. 

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