Dilute and Semidilute Solutions

Polymer chains in dilute solutions are isolated and interact with each other only during brief times of encounter. Increasing the polymer concentration in a solvent leads to a change at a certain stage. As is schematically indicated in Fig. 3.1, a limit is reached when the polymer molecules become closely packed because then they begin to interpenetrate. 

The monomer concentration at this limit can be estimated by regarding that for close-packed polymers this concentration must agree with the mean concentration in a single chain. For expanded chains we find for the critical concentration at the overlap limit, c, the expression 

Since we need a unique expression for the further treatments, we replace the above estimate by an exact equation and write, per definition 

It is interesting to check how the location of changes with the degree of polymerization. For a good solvent, the scaling law Eq. (2.83) applies and we have 

Since ap is always much larger than the actual length of a monomer, we have 

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Recently the wall-PRISM theory has been used to investigate the forces between hydrophobic surfaces immersed in polyelectrolyte solutions [98], Polyelectrolyte solutions display strong peaks at low wavevectors in the static structure factor, which is a manifestation of liquid-like order on long lengths-cales. Consequently, the force between surfaces confining polyelectrolyte solutions is an oscillatory function of their separation. The wall-PRISM theory predicts oscillatory forces in salt-free solutions with a period of oscillation that scales with concentration as p 1/3 and p 1/2 in dilute and semidilute solutions, respectively. This behavior is explained in terms of liquid-like ordering in the bulk solution which results in liquid-like layering when the solution is confined between surfaces. In the presence of added salt the theory predicts the possibility of a predominantly attractive force under some conditions. These predictions are in accord with available experiments [99,100]. 

Dependencies of Viscosity and Modulus in Unentangled Dilute and Semidilute Solutions on c, N, and tn for Low and High Salt Conditions"... 

In polymers, the field-gradient spin-echo methods of measuring self-diffusion have been useful in three more or less distinct areas, the diffusion of polymers in their own melt and in concentrated solutions, in dilute and semidilute solutions, and the diffusion of penetrants and diluents in polymer hosts. A fourth category, the diffusion of bulky or flexible molecules in polymer hosts, is useful for subject matter not closely associated with the first and third category. It should be noted that the work reviewed here represents only a small fraction of the diffusion studies in polymers, including those using other NMR methods. 

Fig. 3.31 Schematic picture of average adsorbed chain conformations in extremely dilute solution (isolated chains on the surface), dilute and semidilute solutions, and the polymer melt. The adsorbed layer thickness increases sharply with increasing concentration, mainly due to the contribution of tails. Significant tail formation occurs as soon as the chains begin to compete for surface sites. (From ref. [144])...

Lipatov, Yu., Todosijchuk, T., Chornaya, V. (1993) Adsorption of polymer mixtures from dilute and semidilute solutions, J. Coll, and Inter/. Sci. 155(2), 283-289. 

While both dilute and semidilute solutions are characterized by the large and correlated fluctuations in segment density, the fluctuations become small in concentrated solutions and can be treated by a simple mean-field theory. 

Ito K, Yagi A, Ookubo N, Hayakawa R. Crossover behavior in high-frequency dielectric relaxation of linear polyions in dilute and semidilute solutions. Macromolecules 1990 23 857-862. 

Let us note in conclusion, that the authors [35] performed the study of dielectric spectroscopy methods of pol5miers d5mamics in diluted and semidiluted solutions and found their results correspondence to Muthuku-mar fractal model [36],... 

Pouliquen G, Tribet C. 2006. Light triggered association of bovine serum albumin and azobenzene modified poly(acrylic acid) in dilute and semidilute solutions. Macromole cules 39(1) 373 383. 

Experimental data were obtained for solutions with polymer concentrations varying from w = 0.50% to w = 4.00% or, equivalently, from c = 0.00431 to c = 0.0348 g cm to be compared with the estimated overlap concentration c = 0.0274 g cm-3 [22]. Hence, the experimental results correspond to polystyrene-toluene solutions in the dilute and semidilute solution regime. 

The first theories that implemented a proper balance of intramolecular interactions and conformational elasticity of the branches were developed by Daoud and Cotton [21] and by Zhulina and Birshtein [22-24]. These theories use scaling concepts (the blob model), originally developed by de Gennes and Alexander to describe the structure of semidilute polymer solutions [64] and planar polymer brushes [65, 66]. Here, the monomer-monomer interactions were incorporated on the level of binary or ternary contacts (corresponding to good and theta-solvent conditions, respectively), and both dilute and semidilute solutions of star polymers were considered. Depending on the solvent quality and the intrinsic stiffness of the arms, the branches of a star could be locally swollen, or exhibit Gaussian statistics [22-24]. 

Kita R, Kircher G, Wiegand S (2004) Thermally induced sign change of Soret coefficient for dilute and semidilute solutions of poly(A-isopropylacrylamide) in ethanol. J Chem Phys 121(18) 9140-9146... 

This equation is valid both in dilute and semidilute solutions. Unlike with dilute solutions, the scaling argument does not predict molecular weight dependence explicitly. (This must be so since one can derive the same formula for the self-diffusion constant Dq. Further information is needed to distinguish the functional form of D pp from that of Dc-) If one assumes that is independent of the molecular weight, then one has... 

Prior to renormalization, it is necessary to distinguish between two limiting cases of dilute and semidilute solutions of short chains. 

The rheological behavior in dilute and semidilute solution is quite usual and... 

Computer simulation has also been used to study the solution properties of rigid-rod polymers (161,279,362). It has been foimd that the local structure and d5mamics of different rigid-rod polymers may be quite different but global motions in dilute and semidilute solutions are expected to be very similar (375). Based on the Broersma and Tirado-de la Torre relations, the translational and rotational coefficients, A and Dr, of rigid-rod polymers in dilute (or semidilute) solutions can be written in the forms... 

Chapter 1.05, written by Andrey V. Dobrynin, is concentrates on the properties of charged maaomolecules, including the main concepts in this field, properties of polyelectrolytes in dilute and semidilute solutions, and poor solvent behavior of charged polymers. 

The effect of added salt on the conformation of polyelectrolyte chains in dilute and semidilute solutions was investigated by Stevens and Plimpton [151], At high salt concentrations the electrostatic interactions between charged monomers are screened and the chain conformations are similar to those observed for good solvent, R As the salt concentration... 

Cotton IP, Famoux B, Jannink G, Straziel C (1973) Dilute and semidilute solutions—light and neutron-scattering and osmotic-pressure. J Polym Sci Part C Polym Symp 42 981-985... 

Liu RG, Gao X, Adams J, Oppermann W (2005) A fluorescence correlation spectroscopy study on the self-diffusion of polystyrene chains in dilute and semidilute solution. Macromolecules 38(21) 8845-8849... 

Study the solution behavior of amphiphilic hyperbranched block and graft copolymers, and answer how the branching effect affects their phase behavior in dilute and semidilute solutions. 

In the previous two chapters, we discussed the design strategy synthetic detail of various Seesaw-type macromonomers and perfect hyperbranched (co)polymers. In this chapter, we will focus on the solution properties of these novel hyperbranched (co)polymers in dilute and semidilute solutions. 

Solution Properties of Amphiphilic Hyperbranched Copolymer Chains in Dilute and Semidilute Solutions... 

All the experiments were performed at room temperature, using a FICA 50 light scattering apparatus with a vertically polarized incident beam at Xo = 546nm. The clarification of dilute and semidilute solutions was obtained by centrifugation (15000 rpm during 2h). The solvents were redistilled twice before use. 

Steady (SFG) and pulsed (PEG) field gradient NMR techniques have been widely used to study the self-diffusion of polymers in melts, dilute and semidilute solutions. The NMR self-diffusion measurements are based on local differences in Larmor precession frequencies when applying a... 

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