Molecular expansion factor

Equation (10) directs attention to a number of important characteristics of the molecular expansion factor a. In the first place, it is predicted to increase slowly with molecular weight (assuming t/ i(1 — 0/T) >0) and without limit even when the molecular weight becomes very large. Thus, the root-mean-square end-to-end distance of the molecule should increase more rapidly than in proportion to the square root of the molecular weight. This follows from the theory of random chain configuration according to which the unperturbed root-mean-square end- o-end distance is proportional to (Chap. X), whereas /r = ay/rl. 

In spite of this, Rijke assumes that the Flory-Huggins expression for AGdil is sufficiently adequate and then finds a molecular expansion factor, a from ... 

Problem 3.12 Deduce from Eq. (3.132) that the molecular expansion factor a should increase with increase in temperature in a poor solvent, decrease with... 

Next we shall examine the molecular weight dependence of the coil expansion factor a to see if the latter can explain the observations of a s greater than 0.5. 

Our primary objective in undertaking this examination of the coil expansion factor was to see whether the molecular weight dependence of a could account for the fact that the Mark-Houwink a coefficient is generally greater than 0.5 for T 0. More precisely, it is generally observed that 0.5 < a < 0.8. This objective is met by combining Eqs. (9.55) and (9.68) ... 

Fig. 144.—The treatment of expansion factor-temperature data obtained from intrinsic viscosities of polyisobutylene fractions in three pure solvents and in ethyl-benzene-diphenyl ether mixtures. Data for fractions having molecular weights Xl6 of 1.88, 1.46, and 0.180 are represented by O,, and Q, respectively. (Fox and Flory. 2)...

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

The plateau adsorbances at constant molecular weight increased linearly with the square root of NaCl concentration. For the same NaCl concentration the adsorbance was nearly independent of the molecular weight. The thickness of the adsorbed layer was approximately proportional to the square root of the molecular weight for the Theta solvent (4.17 M NaCl). For good solvents of lower NaCl concentrations the exponent of the molecular weight dependence of the thickness was less than 0.5. At the same adsorbance and molecular weight the cube of the expansion factor at, defined by the ratio of the thicknesses for good solvent and for Theta solvent, was proportional to the inverse square root of NaCl concentration. 

For adsorption of nonionic polymer, Hoeve (15) and Jones-Richmond (16) attempted to incorporate the excluded-volume effect into the expansion factor, respectively. They suggested that the thickness of the adsorbed layer in good and 0 solvents should be taken at the same adsorbance and molecular weight3 respectively. We may calculate the expansion factor at the bulk NaPSS concentration of 0.02 g/lOOml, since the adsorbances are almost the same for the respective NaCl concentrations, as seen from Figure 5. 

This means that the expansion factor depends only upon the end-to-end length R2(Ms) of chains of molecular weight Ms relative to the chain in 6 conditions. We can derive an effective concentration of the chains since this is related to the overlap concentration of the polymer of molecular weight Ms. ... 

Thus if we know [tj] and [rj]e as a function of molecular weight we can plot the chain expansion factor as a function of concentration. A plot for polybutadiene from the work of Graessley is shown in Figure 5.21 and uses Equation (5.81) to describe the relationship between concentration and intrinsic viscosity. 

Note Expansion factors defined by different dimensional characteristics are not exactly equal, nor need they have a constant ratio as a function of relative molecular mass. 

The size of molecules in solution, measured by , is important both in its own right and because of the effects of changes in on interactions between molecules in solution. For linear polymers, the expansion factor a of Eq. (3.2) can be expressed as a power series in a dimensionless parameter z which is related to the excluded volume per segment pair, p, and the molecular size ... 

B4++ He reaction. This collisional system has been investigated theoretically within the framework of the semiclassical close-coupling formalism using different model potential approaches [2,3] which lead to a discrepancy of about a factor 5 for the double capture cross section values. We have thus performed an alternative study of this system by means of a full molecular expansion method, focusing our attention on the double electron capture process. 

Expansion Factor Flow Increase along Riser Height Because of cracking, the flow rate, the volume, and the superficial velocity of the gas increase. For mean molecular sizes, the following values can be used A, 40 O, 20 E, 9 and G, 3 (27). Then, for a given weight of feed (A), the volumetric flow rate (Q) will be inversely proportional to these mean molecular sizes. Thus ... 

For a nontheta temperature and solvent, the expansion factor is dependent on the molecular weight ... 

Intermediate situations between complete draining and total impermeability can be investigated if Eq. (62 ) is adopted for the draining parameter X in good solvents. If the expansion factor is taken to vary empirically with molecular weight according to an exponential law,... 

The hydrodynamic equivalent molecular dimensions can be related to the unperturbed dimensions by the introduction of a hydrodynamic expansion factor ah. Then Eq. (9.15) reads... 

For a polymer in dilute solution we have seen that 0-5 is proportional to M°Ja, where a is the chain expansion factor (see Chapter 11 note that previously we related °-S to the number of segments, but this is obviously equal to the molecular weight of the chain, M, divided by the molecular weight of segment M. ... 

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