Dependence of molecular size

There has been little experimental data on the generation dependence of molecular size to discriminate between the two models until recently. Some... 

FIGURE 3. Dependence of molecular size on pH due to carboxylate repulsion (upper) and intramolecular hydrophobic bonding (lower). 

As demonstrated by numerous experiments, temperature does not much influence the exclusion processes (compare Equation (17)) in eluents, which are thermodynamically good solvents for polymers. In the latter case, dependence of molecular size, more exactly of hydrodynamic volume of macromolecules (see sections 11.2.4 and 11.7.3.1) on temperature is not pronounced. The situation is different in poor solvents (see section 11.2.4), in which the hydrodynamic volume of macromolecules extensively responds to temperature changes. 

In order to convert a GPC chromatogram into a molar mass distribution (MMD) curve it is neeessary to know the relationship between molar mass (Af) and Vg. This relationship results from Equation (3.186) due to the dependence of molecular size upon M. The molecular size of a polymer molecule in solution can be taken as its hydrodynamic volume (Section 3.4.2) which from Equation (3.79) is proportional to [ij]M where [i/] is the intrinsic viscosity. Hence it can be predicted that log([i/]A/) will decrease approximately linearly with Vg. From the Mark-Houwink Equation (3.160)... 

One of the most sensitive tests of the dependence of chemical reactivity on the size of the reacting molecules is the comparison of the rates of reaction for compounds which are members of a homologous series with different chain lengths. Studies by Flory and others on the rates of esterification and saponification of esters were the first investigations conducted to clarify the dependence of reactivity on molecular size. The rate constants for these reactions are observed to converge quite rapidly to a constant value which is independent of molecular size, after an initial dependence on molecular size for small molecules. The effect is reminiscent of the discussion on the uniqueness of end groups in connection with Example 1.1. In the esterification of carboxylic acids, for example, the rate constants are different for acetic, propionic, and butyric acids, but constant for carboxyUc acids with 4-18 carbon atoms. This observation on nonpolymeric compounds has been generalized to apply to polymerization reactions as well. The latter are subject to several complications which are not involved in the study of simple model compounds, but when these complications are properly considered, the independence of reactivity on molecular size has been repeatedly verified. 

The two constants kj and k describe exactly the same kind of diffusional processes and differ only in direction. Hence they have the same dependence on molecular size, whatever that might be, and that dependence therefore cancels out. 

This situation seems highly probable for step-growth polymerization because of the high activation energy of many condensation reactions. The constants for the diffusion-dependent steps, which might be functions of molecular size or the extent of the reaction, cancel out. 

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, M. This is defined by the expression... 

Molecular Rotational Diffusion. Rotational diffusion is the dominant intrinsic cause of depolarization under conditions of low solution viscosity and low fluorophore concentration. Polarization measurements are accurate indicators of molecular size. Two types of measurements are used steady-state depolarization and time-dependent (dynamic) depolarization. 

Rysee, H. J. P. a membrane effect of basic polymers dependent on molecular size. Nature 1967. 215, 934—936. 

A simple estimate of the diffusion coefficients can be approximated from examining the effects of molecular size on transport through a continuum for which there is an energy cost of displacing solvent. Since the molecular weight dependence of the diffusion coefficients for polymers obeys a power law equation [206], a similar form was chosen for the corneal barriers. That is, the molecular weight (M) dependence of the diffusion coefficients was written as ... 

Our system provides for several forms of calibration function, but we generally use "universal" calibration (5) and represent the dependence of the logarithm of hydrodynamic volume on retention volume by a polynomial, as in Figure 6. Note that the slope of the function changes dramatically near the ends of the range of applicability. The calibrants at the ends of the range exert a dramatic influence on the form of the fitted polynomial. This behavior demonstrates that the column set must be carefully chosen to fractionate the desired range of molecular sizes. 

The first factor k. 1 = 35, is expected to be temperature dependent via an Arrhenius fjfpe relationship the second factor defines functionality dependence on molecular size the third factor indicates that smaller molecules are more likely to react than larger species, perhaps due to steric hindrance potentials and molecular mobility. The last term expresses a bulk diffusional effect on the inherent reactivity of all polymeric species. The specific constants were obtained by reducing a least squares objective function for the cure at 60°C. Representative data are presented by Figure 5. The fit was good. 

The fourth type of mechanism is exclusion although perhaps inclusion would be a better description. Strictly, it is not a true sorption process as the separating solutes remain in the mobile phase throughout. Separations occur because of variations in the extent to which the solute molecules can diffuse through an inert but porous stationary phase. This is normally a gel structure which has a small pore size and into which small molecules up to a certain critical size can diffuse. Molecules larger than the critical size are excluded from the gel and move unhindered through the column or layer whilst smaller ones are retarded to an extent dependent on molecular size. 

These techniques are of particular interest in that they provide a means of separating molecular species which are difficult to separate by other techniques and which may be present in very low concentrations. Such species include large molecules, sub-micrometre size particles, stereo-isomers and the products from bioreactors (Volume 3). The separations can be highly specific and may depend on molecular size and shape, and the configuration of the constituent chemical groups of the molecules. 

Figure 4.2. Variation of heat capacity with temperature as calculated from the equations of Frenkel et al. [4]. The differences observed between isotopic species and the way heat capacity depends on molecular size and structure can be described thermodynamically, but they must be explained by the methods of quantum-statistical thermodynamics. The right-hand scale is for H2 and D2 the left-hand scale is for the other compounds.

The distribution of a-, P- and y-CDs is highly dependent on the origin of biocatalyst used (See section on Cyclodextrin Glucanotransferases). Product distributions maybe altered by the addition of specific precipitants, such as aromatics and long chain alcohols 9, 20), Depending on molecular size, these precipitants preferentially complex with specific CD species and are removed from solution. 

Many companies have tried to develop peptidic renin inhibitors. Unfortunately these are rather large molecules and not unexpectedly poor absorption was often observed. The role of physicochemical properties has been discussed for this class of compounds. One of the conclusions was that compounds with higher lipophilicity were better absorbed from the intestine [29]. Absorption and bile elimination rate are both MW-dependent. Lower MW results in better absorption and less bile excretion. The combined influence of molecular size and lipophilicity on absorption of a series of renin inhibitors can be seen from Figure 1.7. The observed iso-size curves are believed to be part of a general sigmoidal relationship between permeability and lipophilicity [30-31] (for further details see Chapter 3). 

Compounds can cross biological membranes by two passive processes, transcellu-lar and paracellular mechanisms. For transcellular diffusion two potential mechanisms exist. The compound can distribute into the lipid core of the membrane and diffuse within the membrane to the basolateral side. Alternatively, the solute may diffuse across the apical cell membrane and enter the cytoplasm before exiting across the basolateral membrane. Because both processes involve diffusion through the lipid core of the membrane the physicochemistry of the compound is important. Paracellular absorption involves the passage of the compound through the aqueous-filled pores. Clearly in principle many compounds can be absorbed by this route but the process is invariably slower than the transcellular route (surface area of pores versus surface area of the membrane) and is very dependent on molecular size due to the finite dimensions of the aqueous pores. 

Colligative properties are dependent on the number of particles present and are thus related to M . M values are independent of molecular size and are highly sensitive to small molecules present in the mixture. Values of are determined by Raoult s techniques, which are dependent on colligative properties such as ebulliometry (boiling point elevation), cryometry (freezing point depression), osmometry, and end-group analysis. 

Protein transfer from the brain into CSF, and from blood into CSF, follows the law of diffusion as a function of molecular size. The diffusion-related transfer of proteins into CSF is the cause for molecular size-dependent discrimination (i.e., selectivity) of the barrier function. As a consequence, we have larger CSF/ serum quotients for the smaller molecules QAlb > QIgG > QIgA > QIgM. Again, the smaller albumin molecule equilibrates faster between blood and CSF than do the larger molecules of IgG, IgA, or IgM. 

Use of the differential refractometer detector is applicable to all polymers having refractive indices different from that of the solvent. However, a correction must be made if the polymer refractive index depends on molecular size, such as at very low molecular weights. 

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