Solutions of polymer molecules

The soluble blend system is a single phase material in which two components (such as two polymeric species or a polymer and a solvent) are dissolved molecularly as a homogeneous solution in the thermodynamic sense. A miscible polymer blend, a block copolymer in a disordered state, and a polymer solution are examples. Whether a homogeneous solution of this kind is regarded as a soluble blend system or as a dilute particulate system discussed above is often simply a matter of viewpoint. When there is a dilute solution of polymer molecules in a solvent and the focus of interest is the size and shape of the polymer molecules, the theoretical tools developed for the dilute particulate systems are more useful. If, on the other hand, the investigator is interested in the thermodynamic properties of the solution, the equations developed for the blend system are more appropriate. 

The first stage of the reaction, when the system consists of a diluted solution of polymer molecules in their monomer, can be described by conventional kinetics, also used for other types of diluted polymer systems. Although many complicated reaction schemes exist, in reactive extrusion it is convenient to make some assumptions to obtain an acceptable simplification ... 

The term sol-gel is used broadly to describe the preparation of ceramic materials by a process that involves the preparation of a sol, the gelation of the sol, and the removal of the liquid. A sol is a suspension of colloidal particles in a liquid or a solution of polymer molecules. The term gel refers to the semirigid mass formed when the colloidal particles are linked to form a network or when the polymer molecules are cross-linked or interlinked. Two different sol-gel processing routes are commonly distinguished the particulate (or colloidal) gel route in which the sol consists of dense colloidal particles (1 to 1000 nm) and the polymeric gel route in which the sol consists of polyma- chains but has no dense particles >1 nm. In many cases, particularly when the particle size approaches the lower limit of the colloidal size range, the distinction between a particulate and a polymeric system may not be very clear. 

Solutions of polymer molecules differ from solutions of small molecules in several ways. First, the colligative properties differ from the simple mixtures that we considered in Chapters 15 and 16 because polymer molecules are typically much larger than solvent molecules. Second, small molecule solutions have a strong entropic tendency to mix, but polymer solutions do not. Polymers rarely mix with other polymers. This is unfortunate because it would be useful to blend polymers in the same w ay that metals are alloyed, to gain the advantageous properties from each of the components. Third, polymeric liquids, solids, and solutions are rubbery ov 1ng to chain conformational freedom. 

The balance of these forces for dilute solutions of polymer molecules in a small-molecule solvent was first described by PE Rouse [5 and BH Zimm [6. Here is a simple version of their models. Assume that the polymer molecule has been deformed by the applied shear to have an end-to-end distance x = X(). The elastic retractive force per molecule in a d-solvent is given by Equation (32.17), /clastic = -3kTx/Rj, in terms of the mean-square end-to-end length Rj = Nb = 3RqI2. The viscous force exerted per polymer chain on the surrounding medium is /viscous = where 5 is the friction coefficient (see Equation (18.41)) and v = -dxjdt is the velocity of retraction in the direction that opposes the original applied force. You can express Equation (33.29) as a differential equation ... 

The structure of a dilute solution of polymer molecules is investigated in an x-ray scattering experiment. If the molecules are dissolved in a theta solvent, what will the expected slope of the S q) graph be on a log-log plot How will this slope change if the polymer is swollen or collapsed ... 

The behavior of a dilute solution of polymer molecules becomes more and more like that of a suspension of spheres as the concentration is made smaller, because the polymer molecules become more distant from each other and interfere less with each other. We define the intrinsic viscosity, [ j], also called the limiting viscosity number, by... 

In this chapter we have focused attention on various aspects of individual polymer molecules. In the next three chapters we shall examine some properties of assemblies of polymer molecules. Our interest in these chapters will be mostly directed toward samples of pure polymer assemblies of high and low molecular weight molecules-polymer solutions—will be discussed in Part III of this book. 

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,... 

B. Zimm. Dynamics of polymer molecules in dilute solutions viscoelasticity, low birefringence and dielectric loss. J Chem Phys 24 269-278, 1956. 

Small particle size resins provide higher resolution, as demonstrated in Fig. 4.41. Low molecular weight polystyrene standards are better separated on a GIOOOHxl column packed with 5 /u,m resin than a GlOOOHg column packed with 10 /Ltm resin when compared in the same analysis time. Therefore, smaller particle size resins generally attain a better required resolution in a shorter time. In this context, SuperH columns are best, and Hhr and Hxl columns are second best. Most analyses have been carried out on these three series of H type columns. However, the performance of columns packed with smaller particle size resins is susceptible to some experimental conditions such as the sample concentration of solution, injection volume, and detector cell volume. They must be kept as low as possible to obtain the maximum resolution. Chain scissions of polymer molecules are also easier to occur in columns packed with smaller particle size resins. The flow rate should be kept low in order to prevent this problem, particularly in the analyses of high molecular weight polymers. 

In order to form a solution of polymer in solvent, F must be greater than or equal to the forces F and F. If either F or F is greater than F the molecules with the biggest intermolecular attraction will cohere and fail to mix with the dissimilar molecules. Under such circumstances the system will remain two-phased. 

Typically in solution, a polymer molecule adopts a conformation in which segments are located away from the centre of the molecule in an approximately Gaussian distribution. It is perfectly possible for any given polymer molecule to adopt a very non-Gaussian conformation, for example an all-trans extended zig-zag. It is, however, not very likely. The Gaussian set of arrangements are known as random coil conformations. 

Zimm, BH, Dynamics of Polymer Molecules in Dilute Solution Viscoelasticity, Flow Birefringence and Dielectric Loss, Journal of Chemical Physics 24, 269, 1956. 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

Fig. 34.—Schematic representation of polymer molecules in dilute solution.

This treatment, resting essentially on the assumed approximate interchangeability of molecules of solvent and solute in the solution, cannot possibly hold for polymer solutions in which the solute molecule may be a thousand or more times the size of the solvent. The long chain polymer may be considered to consist of x chain segTneTits each of which is equal in size to a solvent molecule x is, of course, the ratio of the molar volumes of the solute and solvent. A segment and a solvent molecule may replace one another in the liquid lattice. In other respects the assumptions required are equivalent to those used above. The polymer solution differs from that containing an equal proportion of monomeric solute in the one important respect that sets of x contiguous cells in the lattice are required for accommodation of polymer molecules, whereas no such restriction applies to the solution of the monomeric solute. The situation is illustrated in Fig. 110. 

Hence the theoretical configurational entropy of mixing AaSm cannot be compared in an unambiguous manner with the experimentally accessible quantity ASm- It should be noted that the various difficulties encountered, aside from those precipitated by the character of dilute polymer solutions, are not peculiar to polymer solutions but are about equally significant in the theory of solutions of simple molecules as well. 

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