Dynamics of Polymer Solutions

In the Rouse-Zimm bead spring model of polymer solution dynamics, the long-range global motions are associated with a broad spectrum of relaxation times given by equation (10) and where tj is the relaxation time of the h such normal mode of the chain 

In the free draining. Rouse, case the eigenvalues Ay are given by  

Beme and R. Pecora, Dynamic Light Scattering , Wiley-lnterscience, New York, 1976. A. Z. Akcasu and H. Gurol,/. Polym. Sci., Potym. Phys. Ed., 1976,14,1. 

Many papers have appeared in which QES results have been reported, and some of these have been mentioned earlier, when the collapse and cross-over effects were discussed.Others are concerned with polymer characterization per se and are not discussed here (see Chapter 12). Here we examine a few areas of controversy, or illustrate novel methods that may prove useful in the future. 

The concentration dependence of the diffusion coefficient in the dilute regime has been investigated by a number of groups, but Vrentas et al. have suggested that the comparison with theory was not satisfactorily performed. They point out that the coefficient from 

In the first two chapters, we learned about thermodynamics (free energy, osmotic pressure, chemical potential, phase diagram) of polymer solutions at equilibrium and static properties (radius of gyration, static structure factor, density correlation function) of dissolved polymer chains. This chapter is about dynamics of polymer solutions. Polymer solutions are not a dead world. Solvent molecules and polymer chains are constantly and vigorously moving to change their positions and shapes. Thermal energy canses these motions in a microscopic world. 

Solntion dynamics deals with the motion of molecules dissolved in a solvent. A typical mode of motion is center-of-mass diffusion. A nonuniform concentration distribution is leveled to a uniform distribution as the solution approaches the equilibrium state. Viscosity of the solution is another form of dynamics. Slowly moving solute molecules increase the viscosity more than fast moving molecules. 

Solvent viscosity makes the motion overdamped and therefore relaxadonal. Different modes of motion are observed over an extended range at the low frequencies. 

A small change in the thermodynamic properties of the solution, as represented by A2, leads to a shift in the dynamics, typically the time scale of motion and dependence on the concentration and the molecular weight. It ofteu happeus that the shift in the dynamic properties is more pronounced compared with the shift in the static properties. Thus, how the time scale depends on the polymer concentration, the molecular weight, and the temperature gives us an important piece of information on the state of the polymer molecules, especially their interactions with the solvent molecules. 

In Chapter 3, we will learn about the dynamics of an isolated polymer chain in the dilute solution limit and the first-order change in the dynamics with polymer concentration. We will also learn typical experimental methods to investigate the dynamics—dynamic light scattering and viscosity. The dynamics of polymer solutions above the overlap concentration will be discussed in Chapter 4, along with their thermodynamics. 

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W. Paul, K. Binder, D. Heermann, K. Kremer. Dynamics of polymer solutions and melts. Reptation prediction and scaling of relaxation times. J Chem Phys 95 7726-7740, 1991. 

The dynamics of polymer solution is governed by the hydrodynamic interaction between moving segments mediated by the solvent [90,91]. This interaction is long range and couples the motions of the different segments strongly. In this... 

Gels usually consist of small amount of polymer as a network and a lai amount of solvent. Therefore when we discuss the dynamics erf polymer gels, we are tempted to deal with these Is from the stand point of the dynamics of polymer solutions. However, since the polymer chains in a gel are connected to each other via chemical bonds and/or some kinds of sj cific interaction, sudi as, hydrogen bonding or hydrophobic interaction, the gel has to be treated as a continuum. In addition, gels behave as an assembly of springs due to the entropy elasticity of polymer chains between the crosslink points. Therdbre, the dynamics of polymer gels is well described in terms of the theory of elasticity... 

Macromolecules play a central role in chemical technology and indeed in biology. Their role and the richness of their properties mean that a whole series of monographs would be required to constitute a comprehensive treatise. This book concentrates on one aspect, the dynamics of polymers in the liquid state. That is, the dynamics of polymer solutions and melts, where in the last decade it has become possible to offer theories which explain the salient features of these systems. 

For linear polymers, the topological constraints do not affect the static problems at all since all configurations are accessible. However, the topological interaction seriously affects the dynamical properties since it imposes constraints on the motion of polymers. Indeed it is a crucial factor in the dynamics of polymer solutions above the overlap concentration.t... 

The reader who is interested in a detailed discussion on the dynamics of polymer solutions (also) at higher conversions is referred to [42, 46], Some interesting contributions on the termination kinetics in these regimes can be found in [47-60],... 

Equation (41) ensures that the time averages resulting from (40) are equivalent to the canonical ensemble averages. The algorithm is rather robust, and very useful if one is just interested in static averages of the model. However, when one considers the dynamics of polymer solutions, one must be aware that the additional terms in (40) seriously disturb the hydrodynamic interactions, for instance. This latter problem can be avoided by using a more complicated form of friction plus random force, the so-caUed dissipative particle dynamics (DPD) thermostat [225-227]. 

Physicists and physical chemists developed the technique for three purposes curiosity about the statistical nature of light as a tool to study critical phenomena and as a way to probe the dynamics of polymer solutions." Early on it was used to measure the diffusion coefficient of macromolecules, from which a hydrodynamic size was calculated. A few industrial users tried it for submicron particle sizing, mostly to replace TEM measurements in QC applications. The approach proved rather awkward in those early days. 

The Phenomenology examines what we actually know about polymer motion in solution. The objective has been to include every significant physical property and experimental method, and what each method shows about polymer motion. The list of methods includes several that have not heretofore been widely recognized as revealing the dynamics of polymer solutions. Undoubtedly there are omissions and oversights, for which 1 apologize. The reader will note occasional discussions that speak to particular models, but experiment comes first, while comparison with various hypotheses is postponed. 

N. V. Orr and T. Sridhar. Probing the dynamics of polymer solutions in extensional flow using step strain rate experiments. J. Non-Newtonian Fluid Mech., 82 (1999), 203-232. 

A number of scaling arguments relevant to the dynamics of polymer solutions have been given by de Gennes. ... 

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