Semi-dilute region

The rheological behavior of storage XGs was characterized by steady and dynamic shear rheometry [104,266]. Tamarind seed XG [266] showed a marked dependence of zero-shear viscosity on concentration in the semi-dilute region, which was similar to that of other stiff neutral polysaccharides, and ascribed to hyper-entanglements. In a later paper [292], the flow properties of XGs from different plant species, namely, suspension-cultured tobacco cells, apple pomace, and tamarind seed, were compared. The three XGs differed in composition and structural features (as mentioned in the former section) and... 

In this work, an experimental study was conducted on gelatin in semi-dilute region in water solution and research the effect of temperature, pH, zeta potential, and ionic strength on hydrodynamic properties by viscometiy, in order to determine the conformational characteristic, and phase transition (Tgei). 

Osmotic pressures of chain polymers in the semi-dilute region (2-20% v) are appreciable and no longer molecular-weight dependent. At 50% v, osmotic pressures of chain polymers are of the order of 100 atm, far greater than any transmembrane pressure used in ultrafiltration T). 

The relationship between observed viscosity and intrinsic viscosity depends on the volume occupied by the polymer chains (dependent on the first power of their concentration) and the interactions between polymer chains (in the dilute and semi-dilute regions, dependent on the second power of their concentration). The resulting equation, eqn. (4.17), is known as the Huggins equation, with kii being the (dimensionless) Huggins coefficient, which measures chain-chain interaction ... 

In another study,BorsaU and Benmouna discussed the static and dynamic scattering properties of ring diblock copolymers in solution [289]. They focused their attention on the semi-dilute region and the case of compositionally symmetric ring diblock copolymers. Differences in the scattering profiles were predicted, the main reason being the presence of connection between the two ends of the chain in the case of ring copolymers. Due to this connectivity effect, different con-... 

In the crossover zone lying between the dilute and the semi-dilute region, the interactions begin to come into play. In order to define the borderline between the dilute and the semi-dilute region, we can simply set C eS3/2 = C X3 = A where A is a constant which must be estimated. Now, in a good solvent, we have... 

The transition between the dilute and the semi-dilute region occurs when the second term becomes equal to the first one (or perhaps slightly larger). Thus, for a good solvent, it is reasonable from an experimental point of view, and simple from a theoretical point of view, to define C by the equality... 

The same criterion does not apply in the semi-dilute region because, then, screening effects must be taken into account. Let us thus consider a semi-dilute solution of Brownian chains. The distance 0 between Brownian chains, the so-called overlap Brownian length , is given by (13.2.4) and, for d - 3,... 

By the way, the intermediate, semi-dilute region is only possible because polymer chains are so extremely long N 1). Indeed, if iV 1 (i.e. if there were small molecules in place of a polymer in the solvent), the two inequalities (f) N / < < 1 would not work together. Therefore, the solution has to be either dilute 4> < 1), in which case the individual molecules hardly interact with each other, or concentrated (f> 1), with... 

The experiments on the effect of methanol on poly(acrylic acid) in solution were carried out at low concentrations, in the so-called semi-dilute region [7]. However, the effects observed almost certainly happen at the higher concentrations used in practical poly(acrylic acid) solutions for preparing glass-ionomer cements. When included in... 

We can determine the value of the unknown exponent m by the following argument. At least in the limit of a high relative molecular mass, we would expect I to depend only on c and not on the relative molecular mass. Thus the scaling exponent m must have a value that removes any N dependence from (5.2.20) and therefore w = —3/4. We conclude that, in the semi-dilute region for polymers in thermodynamically good solvents. 

As usual, we can relate the semi-dilute region to the concentrated regime using blobs as our fundamental units. If, as in Chapter III, we call g = (ca ) the number of monomers per blob, the numter of blobs in the test chain is N/g, and the reptation time is, by a natural extension of eq. (VIII. 13),... 

Viscoelastic measurements are still an important probe of polymer dynamics and structure, but for experimental convenience their use is normally restricted to concentrations above c (cf. ref. 144). Graessley has proposed a method for correlating viscoelastic properties in the semi-dilute region with concentration, including the effect of screening on the chain dimensions a similar discussion has been used by Berry et fl/. ... 

Measurements of the steady shear viscosity in the Newtonian or linear regime yields valuable information on molecular interactions. The molecular weight (Mw) and polymer concentration (C) dependence of the zero-shear viscosity, rjo, of cellulose solutions, exhibits two distinct regions. The dilute regime shows a linear increase of zero-shear viscosity with respect to CMw In the semi-dilute region, the CM is no longer linearly proportional to r o-It is well established for linear, flexible polymer chains that rjo is proportional to [13]. This proportionality for cellulose in the NH3/NH4SCN... 

The values of [17] can be converted to average molecular weight using the Mark-Houwink constants, K and a, allowing the values of c to be plotted at different molecular weights. The boundary line between the dilute and semi-dilute regions is indicated by the lower solid line in Fig. 3.4. The... 

However, the rheological behaviors of associative polymers can be divided into a dilute region and a semi-dilute region by a critical concentration c. At concentrations below c, it is in a dilute region where intramolecular hydrophobic associations within the polymer dominate the behavior of the polymer, and the viscosity decreases with the solution concentration increase. At a concentration above c, it is in a semi-dilute region where intermolecular associations between polymers control the polymer rheology and the viscosity increases with the solution concentration increases (Taylor and Nasr-El-Din 2007). 

Another interesting aspect of associating polymers is the effect of polymer concentration on solubility. Increasing polymer concentration causes the system to pass from a dilute to semi-dilute to gel phase. These transitions can be quite sharp. The dilute region is the region below C (the overlap concentration) the semi-dilute region is above C, and the gel phase is one where a network structure predominates. The behavior of the system in the gel state is currently under study. 

As shown in Chapter 4, the second virial coefficient (A2) is proportional to the excluded volume. However, de Gennes has shown that above the overlap concentration (C ), the effect of excluded volume is screened beyond the correlation length (I) or the distance between two contact points. In the semi-dilute region, chains shrink [equation. (79), Chapter. 4] in the proportion r( ) 4> /" and, likewise, the osmotic pressure decreases by a factor with respect to the value predicted by equation (6.7). 

---