Excluded volume Molecular weight distributions

Molecular weight from osmotic pressure measurements Degree of polymerization and molecular weight distribution Excluded volume from osmotic pressure measurements Theta temperature from second virial coefficient data Evaluation of charges on macroions from osmotic pressures... 

The SEC columns were calibrated using narrow molecular weight distribution water soluble polymer standards sodium polystyrene sulfonate, NaPSS (Pressure Chemical Company, Pittsburgh, PA) and dextrans (Pharmacia Fine Chemicals, Piscataway, NJ). The universal calibration curve proposed by Grubisic et al. (13) was found not to be applicable for these polymer standards. The alternative calibration procedure of Coll and Prusinowski (J ) which incorporates excluded volume effects in the numerical value of the Flory parameter was found to be applicable for this system ( ). The calibration curve for the two-column network system described above is shown in Figure 3. The Kyyy parameter used on the abscissa of Figure 3 is a normalized elution volume parameter defined by Equation 1,... 

Here p can be calculated for various model polymers, and it depends on molecular structure as well as molecular weight distribution ( ). Thus p provides a useful information concerning molecular structure and polydispersity, when the structure is known. For example, polydispersity causes an increase and branching a decrease of p. Excluded volume increases this value. Further examples are discussed in detail in ( ). Here we mention in particular the special case of the f-functional random polycondensates where according to theory the decrease of p is exactly balanced by the increase as the result of the very pronounced polydispersity the p-parameter remains constant in the whole pre-gel region up to the gelpoint. 

In making these comparisons, it is assumed that the characteristic length a is independent of molecular weight, and this will not be the case if excluded volume must be taken into account. However, it is clear that molecular weight distribution has a very large effect on [G ]/ at low frequencies, and also on the steady-state compliance through the relation = lim< -.o[G ]fi/[G"]. These features also appear in concentrated solutions and undiluted polymers (for which the effect of molecular weight distribution was first derived ). 

Keywords Paul Flory Herman Mark Carl Marvel Gaussian chain Excluded volume Rubber Polymer solutions Molecular weight distributions Intrinsic viscosity Herman Staudinger... 

The experimental parameters required in the theory to model the chain and its stiffness are M, [n]o, and an excluded volume parameter. For xanthan we take a log-normal distribution in M between 1x10 and 30x10, with peak at 10x10 and width approximating the observed distribution (3). The intrinsic viscosity at each molecular weight is fixed By the relation [n] = 4.76xl0 ... 

Under ideal SEC conditions, all solutes elute at a retention volume Fkthat is larger than the interparticle volume Vi but smaller than the mobile-phase volume Fr (which is the sum of and the pore volume Vp). The distribution coefficient ATd for elution by ideal SEC is given by Equation (13), in which Kd varies from zero for a fully excluded solute to one for a small molecular weight solute capable of penetrating all the pores ... 

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