Polymers molar volume

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

FIGURE 16.3 Dependences of the polymer retention volume on the logarithm of its molar mass M or hydrodynamic volume log M [T ] (Section 16.2.2). (a) Idealized dependence with a long linear part in absence of enthalpic interactions. Vq is the interstitial volume in the column packed with porous particles, is the total volume of liquid in the column and is the excluded molar mass, (b) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interaction between macromolecules and column packing exceed entropic (exclusion) effects (1-3). Fully retained polymer molar masses are marked with an empty circle. For comparison, the ideal SEC dependence (Figure 16.3a) is shown (4). (c) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interactions are present but the exclusion effects dominate (1), or in which the full (2) or partial (3,4) compensation of enthalpy and entropy appears. For comparison, the ideal SEC dependence (Figure 16.3a) is shown (5). (d) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interactions affect the exclusion based courses. This leads to the enthalpy assisted SEC behavior especially in the vicinity of For comparison, the ideal SEC dependence (Eigure 16.3a) is shown (4). 

The concentration effects for the oligomers and also for the excluded (high) polymer species, are usually small or even negligible, k values depend also on the thermodynamic quality of eluent [108] and the correlation was found between product A2M and k, where A2 is the second virial coefficient of the particular polymer-solvent system (Section 16.2.2) and M is the polymer molar mass [109]. Concentration effects may slightly contribute to the reduction of the band broadening effects in SEC the retention volumes for species with the higher molar masses are more reduced than those for the lower molar masses. 

Measurements of sedimentation behaviour of polymer molecule in solution can provide a consideratble amount of information, e.g., hydrodynamic volume, average molar masses and even some indication of molar mass distribution. Such measurements have been extensively used to characterise biologically-active polymers which often exist in solution as compact spheroids or rigid rods. However, sedimentation methods are rarely used to study synthetic polymers and so will be given only brief non-theoretical consideration here. 

Size exclusion chromatography is the premier polymer characterization method for determining molar mass distributions. In SEC, the separation mechanism is based on molecular hydrodynamic volume. For homopolymers, condensation polymers and strictly alternating copolymers, there is a correspondence between elution volume and molar mass. Thus, chemically similar polymer standards of known molar mass can be used for calibration. However, for SEC of random and block copolymers and branched polymers, no simple correspondence exists between elution volume and molar mass because of the possible compositional heterogeneity of these materials. As a result, molar mass calibration with polymer standards can introduce a considerable amount of error. To address this problem, selective detection techniques have to be combined with SEC separation. 

As has been pointed out, for SEC of complex polymers no simple correspondence exists between elution volume and molar mass. It is, therefore, useful to determine the molar mass not via a calibration curve but directly from the SEC effluent. This can be done by using molar-mass-sensitive detectors based on Rayleigh light scattering or intrinsic viscosity measurements [45]. 

Swelling pressure due to polymer network and solvent Specific gravity of polymer Molar density of amine groups in dry network Volume fraction of polymer... 

Gel permeation chromatography (GPC) is the established method for the determination of molar mass averages and the molar mass distributions of polymers. GPC retention is based on the separation of macromolecules in solution by molecular sizes and, therefore, requires a molar mass calibration to transform elution time or elution volume into molar mass information. This kind of calibration is typically performed with narrow molecular mass distribution polymer standards, universal, or broad calibration methods or molar-mass-sensitive detectors like light-scattering or viscosity detectors. 

The glassy polymers such as the aromatic polyamides and polycarbonates have significant hindrances to intramolecular mobility. The data for these materials appear to be correlated fairly well in terms of the "specific free volume" discussed by Lee(52). Structural variations that suppress the ability to pack tend to reduce the quality of the barrier while those that improve the ability to pack produce better barriers. The free volume in this case is defined as the difference between the actual polymer molar volume at the temperature of the system and at 0°K. This latter parameter is determined by group contribution methods. 

T[ = depressed melting temperature, T = melting temperature of the pure polymer, = molar volume of the polymer unit, V, = molar... 

Ratio of polymer molar volume to solvent molar volume Number of segments in the primitive path... 

Voltrme fractiorts imply a temperature dependence and, as they are defined in eqttation (14), neglect excess voltrmes of mixing and, very often, the densities of the polymer in the state of the solution are not known correctly. However, volume fractions can be calcrrlated without the exact knowledge of the polymer molar mass (or its averages). Base mole fractions are sometimes apphed for polymer systems in earlier literature. The valtre for Mo is the molar mass of a basic rmit of the polymer. Sometimes it is chosen arbitrarily, however, and has to be specified. 

Vf the free volume per molar structural unit for a polymer... 

Often, size exclusion chromatograms (SEC) (compare section 11.7, Size Exclusion Chromatography) of polymers under study are expressed as differential representations of molar mass dispersity. The chromatographic retention volumes are directly transformed into the molar masses. This approach renders useful immediate information about tendencies of molar mass evolution in the course of building or decomposition polyreactions but the absolute values of molar mass can be only rarely extracted from it. As a rale, polystyrene calibrations are applied for molar mass calculation so that one deals with the polystyrene equivalent molar masses, not with the absolute values. The resulting dispersity (distribution) functions may be heavily skewed because the linear part of the calibration dependence for the polymer under study may exhibit well different slope compared with the polystyrene calibration, which was employed for the transformation of retention volumes into molar masses. 

Due to the attractive interaction of monomer with the column packing, also its retention volume exceeds V. An important case of the coupled exclusion - interaction processes is in Figure 3 represented by curve d. It mirrors the full mutual compensation of exclusion and interaction, which leads to the independence of retention volume of polymer molar mass. This situation is important for characterization of complex polymers. It allows elimination or at least suppression of the molar mass effect of macromolecules so that their unbiased separation according to another molecular characteristic can be performed. The experimental conditions leading to this specific elution behavior are called critical conditions of enthalpic interactions. They will be more in detail discussed in section 11.8.3. 

FIGURE 15 Schematic representation of etfect of sample concentration on the corresponding retention volume in SEC. M is polymer molar mass, is low molar mass, macromolecules are eluted not far from Mjmolar mass, macromolecules are eluted near V. For detailed explanation, see the text... 

To suppress the effect of certain molecular characteristic on sample retention volume so that the resulting chromatogram reflects mainly or even exclnsively other molecular characteristic(s) of sample. In practice, it is usually attempted to partially or fully suppress the influence of polymer molar mass. In this instance, the coupling of LC retention mechanisms may allow assessment of chemical structure or physical architecture of a complex polymer irrespective of its molar mass average and dispersity. Under favorable conditions, also the constituents of a complex polymer system with similar molar masses can be discriminated and molar mass of one constituent determined. For example, in the case of a two-component polymer system, the molar mass effect can be suppressed selectively for one constituent so that it elutes in a completely different retention volume compared with the retention volume pertaining to SEC. In some cases, the... 

Polymer Molar masses Critical range Used samples Mobile phase Solvent / Nonsolvent Adsorb / Desorb Stationary phase Particle diameter Pore size Column dimension Conditions Temperature Flow rate Inj. volume Detector Analytical application and / or notices Investigators Reference... 

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