Number-average molecular weight of polymers

Vapor Pressure Osmometry - The number average molecular weights of polymers with Mn < 20,000 were determined using "Model 232A Molecular Weight Apparatus, Wescan Instruments, Inc., 3018 Scott Blvd., Santa Clara, CA 95050". Toluene was used as solvent and the instrument was calibrated using polystyrene of Mn 9,000 and 20,400. 

Mn = number average molecular weight of prepolymers XN = Nt/Mt = number average degree of polymerization Mr = (Xn)(Mn) = number average molecular weight of polymer in an equivalent random network A = mole fraction of difunctional prepolymer 1 — A = mole fraction of monofunctional prepolymer f = average functionality... 

This model, of the Rideal type, is of general applicability and includes and explains the most relevant phenomena involved in Ziegler-Natta polymerization. Mathematical formulation of the proposed reaction scheme led to the following equations for polymerization rate Rp and number average molecular weight of polymer Mn, in the absence of hydrogen ... 

Table 15.9. Calculated and measured number average molecular weight of polymers isolated after first and second stage of sequential polymerization of 1,3-dioxolane and 1,3-dioxepane initiated by triflic anhydride. [M]o (A and B) from 2 to 3 mol I 1, [I]q from 10"3 to 10 2 mol 1 1109>...

The colligative properties of dilute polymer solutions can be used to accurately measure Mn, the number average molecular weight of polymers [524,525]. This class of techniques is... 

It has been indicated already (see section 3.1.1) that, under some circumstances, NMR studies of end-groups can lead to values of number-average molecular weights of polymers. It has been found for polyMMA prepared using [jS, jS- C]AIBN[l] and for polySTY made with [a-AIBN[9] that satisfactory results can be obtained. The conditions for recording the spectra must be carefully selected and it is necessary to have information on the average number of initiator fragments per polymer molecule, i.e. on the relative importance of combination and disproportionation in the termination steps of the polymerizations and also on the frequencies of transfer reactions. 

The number-average molecular weight of polymer increases proportionally with monomer conversion. 

One polymer is formed for each initiator molecule, so that the number average molecular weight of polymers or block segments can be predicted from the reaction stoichiometry. Multifunctional initiators with functionality n can form stars with n arms. 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

In the next section we shall describe the use of Eq. (8.83) to determine the number average molecular weight of a polymer, and in subsequent sections we shall examine models which offer interpretations of the second virial coefficient. 

Polymetallocarbosilanes. PolymetaHocarbosilanes having a number-average molecular weight of 700—100,000 can be prepared by reaction of polycarbosilane, /2 2 fx where R is H, or lower alkyl, with a tetraalkyl titanate, to give a mono-, di-, tri-, or tetrafunctional polymer... 

Cast material is stated to have a number average molecular weight of about 10. Whilst the Tg is about 104°C the molecular entanglements are so extensive that the material is incapable of flow below its decomposition temperature (approx. 170°C). There is thus a reasonably wide rubbery range and it is in this phase that such material is normally shaped. For injection moulding and extrusion much lower molecular weight materials are employed. Such polymers have a reasonable melt viscosity but marginally lower heat distortion temperatures and mechanical properties. 

The commercial polymer was said to have a number average molecular weight of 250000-350000. Because of its regular structure (Figure 19.4 it is capable of crystallisation. 

The resulting ladder polymer LPPP 12 possesses a number average molecular weight of 25000, which corresponds to the incorporation of 65 phenylene units. No structure defects could be detected using NMR spectroscopy. LPPP 12 is... 

The number-average molecular weight of a polymer may be controlled by offsetting the stoichiometry of two dissimilar mutually reactive difunctional monomers. The polymer will have the same endgroup functionality as that of the monomer used in excess. For a generic polymer made from a difunctional monomer AA with A functional groups and an excess of difunctional monomer BB widt B functional groups, r is defined as... 

Attempted polymerization of ds-7,9 dioxabicyclo[4.3.0]nonane 43 with phosphorus pentafluoride as initiator at temperatures ranging from -25 to 0 °C provided only a cyclic dimer 44 in high yield35. Under similar conditions trans-7,9-dioxabicyclo-[4.3.0]nonane 45 polymerized almost instantly to polymer 46 with number average molecular weight of several thousands, along with a small amount of a cyclic dimer 47. 

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