Packing linear macromolecule

The solubility parameter introduced by Hildebrand90, rather than the dielectric constant or dipole moment is a characteristic quantity of the solvent which appears appropriate (if no specific solvation effects have to be taken into account) to forecast the micellar solubility of the alkali dinonylnaphthalene sulfonates in the particular solvent. As the solubility parameter of the solvent is increased, the micelles tend to assume a smaller size (Fig. 14). This size reduction gives a looser packing of the DNNS tails and, thus, exposes the more interactive aromatic and polar parts in such a way as to reduce the difference between the solubility parameter of the solvent and the effective solubility parameter of the solvent-accessible portions of the lipophilic micelle. The automatic matching of the solubility parameter for micelle and solvent by reduction of micelle size and packing in solvents of high solubility parameters recalls the behavior of linear macromolecules in solvents of different solvent power. 

The packing fraction of rods is another easily calculated case. It could serve as a model for extended-chain, linear macromolecules. Motifs of other, more irregular shapes are more difficult to assess. The closest packing of rods with circular cross section reaches a k of 0.91 with a coordination number of six. Packing with coordination number four reduces k to 0.79. A random heap of rods which do not remain parallel can result in quite low values for k which should also depend on the lengths of the rods. 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

CrystallinG MultiCOmponGnt Systems. A multicomponent system that crystallizes with a common crystal structure is said to form mixed crystals. Formation of mixed crystals is often possible for components that crystalbze in their pure state with the same crystal shapes (isomorphism). For linear macromolecules, a further condition must be fulfilled, the chain conformations of the components must match. For energy reasons, crystals usually can only be obtained with macromolecules close to their equilibrium conformations. In these conformations, close packing must be achieved with the second component, a rather rare event, although examples are known of limited solubility and cocrystallization with small molecule solvents (9). 

The Eq. (12.7) shows, that the condition H = 0 can be realized for linear object with dimension d = d = 1 only (in fact for separate stretched linear macromolecule [15]), that is, for real solids, having dimension within the range of 2.0 2.95, zero value is unattainable. At minimum value d = 2.0 the magnitude // = 150 MPa, for loosely packed matrix structure with the greatest density, that is, in the case, when nanoclusters and loosely packed matrix structures are undistinguishable, the value = 293 MPa. 

For calculation of packing fractions see, for example, A. Bondi, "Physical Properties of Molecular Crystals, Liquids and Glasses." J. Wiley and Sons, New York, NY, 1968. For linear macromolecules, see B. Wunderlich, "Macromolecular Physics, Vol. 1" Academic Press, New York, NY, 1973. 

Similar considerations apply to best volume flow rates for samples of different molar mass. For high molar mass samples, flow rates should be reduced to avoid shearing the macromolecule in the column. Moreover, a reduced flow rate is necessary because the diffusion coefficients of large molecules will get pretty small. This means that the macromolecule will pass by a pore in the packing material without having the time to enter it, if the linear flow rate is too high. 

Any extended part of a linear polymer molecule exhibits a strong anisotropy of many properties since its atoms and atomic groups are oriented and the macromolecule is actually a one-dimensional crystal . The parallel packing of these parts during the formation of a uniaxially oriented polymer substance imparts the anisotropie properties of a single molecule to the whole polymeric material. 

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). 

Where do soluble lignins fit with respect to conformation They seem to be rather compact molecules in solution—the opposite of the highly expanded cellulose molecule. They are not as compact as a simple solid sphere. Yet, the chains of the lignin macromolecules in solution are more densely packed than those of a linear flexible polymer such as polystyrene... 

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