Polymers coil molecule

The Zimm model predicts correctly the experimental scaling exponent xx ss M3/2 determined in dilute solutions under 0-conditions. In concentrated solution and melts, the hydrodynamic interaction between the polymer segments of the same chain is screened by the host molecules (Eq. 28) and a flexible polymer coil behaves much like a free-draining chain with a Rouse spectrum in the relaxation times. 

The lowermost curve in Fig. 45 represents P(0) plotted against according to Eq. (31) for random coil molecules. The results of similar calculations for spherical and for rod-shaped particles of uniform density are shown also. The curve for the former of these is not very different from that for randomly coiled polymers at corresponding values of the abscissas the factor P(0) for rods differs appreciably, however. 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

For polymer melts or solutions, Graessley [40-42] has shown that for a random coil molecule with a Gaussian segment distribution and a uniform number of segments per unit volume, a shear rate dependent viscosity arises. This effect is attributed to shear-induced entanglement scission. 

The expansion of a polymer coil is determined by its interaction with the solvent. The more favorable the interaction between the polymer segments and the solvent molecules (good solvent), the better the polymer dissolves and the more the coil expands. 

Since microgels are intramolecularly crosslinked macromolecules of colloidal dimensions, it is necessary for their synthesis to control the size of the growing crosslinked molecules. This can be achieved by carrying out polymerization and crosslinking in a restricted volume, i.e. that of a micelle or of a polymer coil. Thus, two general methods of microgel synthesis are available (1) emulsion polymerization, and (2) solution polymerization. 

One of them assumes the possibility of a compression of polymer coils at average concentrations down to the dimensions less than in the -solvent. The alternative is based on the existence of the wide distribution of macromolecule dimensions in any time.It is rather natural to assume an increase of the probability of intramolecular reaction with an increase of the dimensions of the macromolecule.. e. more extended conformations go to the gel-fraction and more coiled remain in the sol. With the increase of solution concentration the distances between coils are diminished and the critical dimensions, necessary for a transition into the gel are decreased too. This process will be accompanied by a decrease of the average dimensions of molecules in sol. 

The reaction of a polymer in solution involves a considerably higher local concentration of functional groups than that indicated by the overall polymer concentration. Polymer molecules are generally present in solution as random-coil conformations. The concentration of functional groups is high within the polymer coils and zero outside [Alexandratos and Miller,... 

The concentrations of the small-molecule reactant inside and outside are the same for soluble polymers unless there is some special effect responsible for attracting or repulsing the reactant from the polymer coils. Such situations are described in the remainder of Sec. 

The concentration of a small molecule reactant inside the polymer coils can be lower than outside when one uses a poor solvent for the polymer. This results in lower local and overall reaction rates. In the extreme, a poor solvent results in reaction occurring only on the surfaces of a polymer. Surface reactions are advantageous for applications requiring modification of surface properties without affecting the bulk physical properties of a polymer, such as modification of surface dyeability, biocompatibility, adhesive and frictional behavior, and coatability [Ward and McCarthy, 1989]. 

Enhanced reaction rates have also been observed in some instances of decreased polymer solubility with conversion when the precipitating polymer absorbs the small-molecule reactant. Adsorption results in an increased concentration of the reactant at the actual polymerization site (the polymer coils). Similar effects are observed if a catalyst is adsorbed onto the precipitating polymer [Beresniewicz, 1959]. 

We have used the uncharged polysaccharide dextran as a model describing the behaviour of water-soluble polymers. The dextrans used in this study have about 95 % oc-(l - 6) linkages within the main chain and side chains the 5 % non-a-(l -> 6) linkages are starting points of branched chains of which most are only stubs of about two glucose units 9). Therefore, while there is some branching in dextran, albeit low, its solution behaviour is that of a linear, random-coil molecule l0,ll). 

Since the polar groups repel each other, the expanded random coil molecules tend to become stiff rods. The nonpolar portions of the water-solubilized polymer face toward the organic phase at the organic-aqueous interfaces, and the polar portions preferentially point away from the organic phase. 

In order to understand the source of this force, consider two particles separated by a distance d as shown in Figure 13.17. The dispersed polymer molecules exert an osmotic pressure force on all sides of the particles when the particles are far apart, that is, when d > Rg. Then, there is no net force between the two particles. However, when d < Rg, there is a depletion of polymer molecules in the region between the particles since otherwise the polymer coils in that region lose configurational entropy. As a consequence, the osmotic pressure forces exerted by the molecules on the external sides of the particles exceed those on the interior (see Fig. 13.17), and there is a net force of attraction between the two particles. The range of this attraction is equal to Rg in our highly simplified model. 

Boss, et al., fitted Gq. (17) to their data vs. vdi enabling them to determine fp and D . At solvent concentration approaching vdiI = 0.95, the data revealed an enhancement above the value predicted by Eq. (17) as fitted to the lower-concentration data. The authors argued that under these circumstances macroscopic inhomogeneities in concentration (and hence in the free-volume distribution) should exist and enhance the diffusivity. Above v > 0.99 the polymer coils no longer overlapped substantially, depriving the solvent molecules of a set of obstacles fixed with respect to the laboratory, and solvent diffusion became related principally to intrinsic viscosity. 

Aharoni has stated that the observed rates of crystallization in polymers are inconsistent with the times required for random-coil molecules to separate themselves from the melt, and claims this as support for the collapsed coil model (43). No numerical comparisons are given, and it is difficult therefore to judge the basis for his assertion. 

Garvey et al.85) made a similar sedimentation study on poly(vinyl alcohol) adsorbed on polystyrene latex particles. Adsorbance of the polymer was also measured. Both the thickness of the adsorbed layer and the adsorbance increased linearly with the square root of the molecular weight. The volume occupied by a polymer molecule in the adsorbed layer was approximately equal to that of the effective hydrodynamic sphere in bulk solution. However, the measured values of LH were greater than the hydrodynamic diameters of the polymer coils in solution. Thus, it may be concluded that adsorbed poly(vinyl alcohol) assumes a conformation elongated in the direction normal to the surface. 

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