Polymers average molar mass determination

For Flory Huggins like models it can be shown that the mass average molar mass determines the shape and position of the spinodal. For the hole theory other moments of the molar mass distribution become important also. The exact influence of the molar mass distribution on the complete phase diagram of polymer solutions is a topic of current research. The description of the spinodal conditions are almost quantitative without the introduction of empirical parameters. The cell free volume is very important for this quantitative success. 

If it is possible to analyse end groups of a particular specimen of polymer, it may be possible to use the data to determine number average relative molar mass. If the molecules are branched the degree of branching can be measured from a combination of end group analysis and relative molar mass determination (determined by an alternative method). 

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... 

In order to facilitate the reader, the chapter is split into various sections. Section 15.2 deals with instrumentation, sample preparation, and matrices, remaining sections deal with the analysis of ultrapure polymers, polymer mixtures in which backbones are identical, and polymer mixtures in which backbones are different, respectively. The final section deals with the determination of average molar masses. 

Here, /u ° and ju are, respectively, the chemical potentials of pure solvent and solvent at a certain concentration of biopolymer V is the molar volume of the solvent Mn=2 y/M/ is the number-averaged molar mass of the biopolymer (sum of products of mole fractions, x, and molar masses, M, over all the polymer constituent chains (/) as determined by the polymer polydispersity) (Tanford, 1961) A2, A3 and A4 are the second, third and fourth virial coefficients, respectively (in weight-scale units of cm mol g ), characterizing the two-body, three-body and four-body interactions amongst the biopolymer molecules/particles, respectively and C is the weight concentration (g ml-1) of the biopolymer. 

Recently, Siu et al. [139] studied the effect of comonomer composition on the formation of the mesoglobular phase of amphiphilic copolymer chains in dilute solutions. The copolymer used was made of monomers, N,N-diethylacrylamide (DEA) and N,N-dimethylacrylamide (DMA). like PNI-PAM, PDEA is also a thermally sensitive polymer with a similar LCST, but PDMA remains water-soluble in the temperature range (< 60 °C) studied. At room temperature, copolymers made of DMA and DEA are hydrophilic, but become amphiphilic at temperatures higher than 32 °C. Before the association study, each P(DEA-co-DMA) copolymer was characterized by laser light scattering to determine its weight average molar mass (Mw) and its chain size ( Rg) and (R )). The copolymer solutions (6.0 x 10 A g/mL) were clarified with a 0.45 xm Millipore Millex-LCR filter to remove dust before the LLS measurement. 

Our calculation of (ro2) is therefore, for polymer solutions, only valid for theta conditions. We shall consider this case in somewhat more detail. We have seen that for the determination of the viscosity average molar mass, the Mark-Houwink... 

An isolated linear macromolecule generally tends to assume a random coil configuration. Only for very stiff polymers a rod like configuration is assumed. Several types of measurements can be used to determine the dimensions of the random coil configuration. Conversely, if the appropriate relationships have been established, the same measurements can be used to determine the average molar mass of a given polymer. 

Knowing the values of a and K, for a polymer-solvent system, the viscosity-average molar mass Mvis can be easily determined from intrinsic viscosity measurements. 

A graph of Kc/R9 versus c gives a straightline with slope 2 B2 and intercept = 1/Mm. This permits determination of Mm, the mass-average molar mass of the polymer. 

Number-Average and Viscosity-Average Molar Mass. For a polydisperse polymer, any determination of molar mass must yield an average of some sort. When a col-ligative property such as osmotic pressure is used, the average is a number average ... 

The number-average is the common average used, for example, to determine the average denomination of the coins in your pocket. The number traction of each type of coin (n ) is multiplied by its denomination Mm)-Substituting Eq. (1.27) into Eq. (1.23) shows that the ratio of the molar mass of a polymer with AT monomers and the number-average molar mass Mn relates the number fraction and weight fraction of molecules ... 

For branched polymers and for linear polymers that do not have an established Mark-Houwink equation, SEC is typically used in conjunction with light scattering and viscosity detectors. These detectors measure the weight-average molar mass and viscosity of each elution volume. In principle, this experiment directly determines both M and [rj] for any polymer that is soluble in the SEC solvent, but in practice the determination also requires that the polymer have an appreciable difference in refractive index from the solvent so that in Eq. (1.88), dn/dc >0.05 mL g . Often a new polymerization is not understood sufficiently to know for certain whether the polymer produced will have branched chains present or... 

Determine the number-average molar mass of the polymer and the second virial coefficient of the solution Aj. 

The mass of the linear polymer chain is thus related directly to the number of monomer units incorporated into the chain (DP) and will be Mq x DP, where Mq (g/mol) is the molar mass of the monomeric repeat unit. Thus, if all chains grew to exactly the same DP, then Mq X DP, would be the molar mass of the polymer. If the end groups on the chain can be readily and uniquely analysed, then an average molar mass, M , or number-average molecular weight (as discussed in the next section) can be immediately determined since, if there are amol/g of end group A and hmol/g of end group B then... 

Linear polymers are usually characterized in solution. However, if enough crosslinking has occurred, such as in the vulcanization of elastomers, the polymer will swell but cannot dissolve in typical solvents. Then, it is impossible to derive molar mass (molecular weight) information from solution behavior. However, the average molar mass of the chains in the polymer network can be determined from swelling (1,2). 

Determination of the number-average molar mass M involves counting the total number of molecules, regardless of their shape or size, present in a unit mass of the polymer. The methods are converuently grouped into three categories end-group assay, thermodynamic, and transport methods. 

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