Polymer solutions overlap concentration

Low temperature The polymer is in a good solution state and possesses the shape of an expanded coil. At low concentration, the polymer molecule has no contact with other molecules (single polymer chain). If the diluted solution is irradiated, radicals were produced and some polymer chains react. Molecules with high molecular weight, mostly branched, are formed (Quemer et al. 2004). Irradiation of a higher-concentrated polymer solution (semi-diluted polymer solution with concentration above the overlap concentration ), results in a homogeneous macroscopic (bulky) gel. 

In HOPC, a concentrated solution of polymer is injected. The concentration needs to be sufficiently higher than the overlap concentration c at which congestion of polymer chains occurs. The c is approximately equal to the reciprocal of the intrinsic viscosity of the polymer. In terms of mass concentration, c is quite low. For monodisperse polystyrene, c is given as (4)... 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

The s.a.n.s. experiments were carried out using the D17 camera at the I.L.L., Grenoble. Data were collected at two wavelengths, 0.8 and 1.4 nm at a sample to detector distance of 1.8 m. The overlapping spectra were combined to give a sufficiently wide Q range to enable the data to be numerically inverted to obtain the density distributions. The latex dispersions were prepared at a solids concentration of 4% and polymer solution concentrations between 200 and 300 ppm. 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

Non-dilute solutions also allow for theoretical descriptions based on scaling theory [16, 21]. When the number of polymer chains in the solution is high enough, the different chains overlap. At the overlapping concentration c , the long-scale density of polymer beads becomes uniform over the solution. Consequently c can be evaluated as... 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

In order to resolve these challenges, it is essential to account for chain connectivity, hydrodynamic interactions, electrostatic interactions, and distribution of counterions and their dynamics. It is possible to identify three distinct scenarios (a) polyelectrolyte solutions with high concentrations of added salt, (b) dilute polyelectrolyte solutions without added salt, and (c) polyelectrolyte solutions above overlap concentration and without added salt. If the salt concentration is high and if there is no macrophase separation, the polyelectrolyte solution behaves as a solution of neutral polymers in a good solvent, due to the screening of electrostatic interaction. Therefore for scenario... 

In essence, the model divides a reactive polymer solution into a dispersed polymer-rich phase (phase 1), within which the concentration of functional groups is defined by the polymer morphology and structure, and a solvent-rich phase which contains no functional groups (phase 0). The individual polymer molecules are modeled as spheres of polymer-rich phase stuck at points of an imaginary lattice in solution. If the polymer concentration is sufficiently high, another phase enters the calculations which consists of overlapping polymer-rich spheres (phase 2). 

Surface pressure was measured as a function of surface concentration for monolayers of linear and cyclic polydimethylsiloxanes. In addition, the comparisons of linear and cyclic polymer above the overlap concentration c lead to the surprising conclusion that even for three-dimensional semi-dilution solutions, the ratio c/c was not a universal reduced concentration [174]. 

Sufficiently dilute polymer solutions may be viewed as systems in which islands of polymer coils scattered in the sea of a liquid solvent occasionally impinge and interpenetrate. By this way, the spatial distribution of chain segments in them is quite heterogeneous and undergoes appreciable fluctuations from time to time. As the polymer concentration increases, the collision of the islands becomes more frequent and causes the chains to overlap and entangle in a complex fashion. 

The way to remove entanglements, viz. the manner in which topological constraints limit the drawability, is seemingly well understood and crystallization from semi-dilute solution is an effective and simple route to make disentangled precursors for subsequent drawing into fibers and tapes [ 17,18]. A simple 2D model visualizing the entanglement density is shown in Fig. 3. Here 0 is the polymer concentration in solution and 0 is the critical overlap concentration for polymer chains. 

In the basic model, put forward by Asakura and Oosawa (5), the hard spherical particles immersed in a solution of macromolecules are considered to be surrounded by depletion layers from which the polymer molecules are excluded. When two particles are far apart with no overlap of the depletion zones, the thermal force acting over the entire particle surface is uniform. However, when the particles come closer, such that their depletion zones begin to overlap, there is a region in which the polymer concentration is zero and the force exerted over the surfaces facing this region is smaller compared to that exerted over the rest of the surface. This gives rise to an attractive force between the two particles which is proportional to the osmotic pressure of the polymer solution. 

The bis-urea thin filaments can be very long in non-polar solvents such as 1,3,5-trimethylbenzene. Consequently, these solutions show a high viscosity r]/r]Q = 8 at a concentration C = 0.04 molL and at T = 20 °C) and a high concentration dependence of the viscosity (ri/rio C ) [43]. As in the case of UPy based supramolecular polymers, the value of this exponent is in agreement with Cates s model for reversibly breakable polymers [26,27]. However, the solutions are not viscoelastic, even at concentrations well above the overlap concentration [43]. Consequently, the relaxation of entanglements, probably by chain scission, must be fast (r < 0.01 s). 

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