First critical concentration

FCC first critical concentration FPI Foodservice and Packaging Institute... 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

The critical concentration at which phase separation first appears on passage to the two-phase region is thus predicted to occur at a very small volume fraction of polymer for a polymer having a molecular weight of a million (a 10 ), for example, y2c=0.01. Substituting Eq. (4) in either of the equations (3), we obtain... 

Simha [53] made the first attempts to model the transition from a dilute to a concentrated solution. He assumed that in the range from lscaling laws a theory has been developed which allows for the prediction of the influence of Mw c and the solvent power on the screening length [54,55]. This theory is founded on the presumption that above a critical concentration, c, the coils overlap and interpenetrate. Furthermore it is assumed that in a thermody-... 

It is a first principle of toxicology that no chemical substance is a poison at all concentrations toxicity occurs only when a critical concentration is reached within vital cells. Whether or not an economic poison will exert a particular deleterious effect depends on the relative rates of absorption as compared with detoxication and elimination, its inherent toxicity, and the physiologic status of the organism. 

The critical concentration at which the first micelle forms is called the critical micelle concentration, or CMC. As the concentration of block copolymer chains increases in the solution, more micelles are formed while the concentration of nonassociated chains, called unimers, remains constant and is equal to the value of the CMC. This ideal situation corresponds to a system at thermodynamic equilibrium. However, experimental investigations on the CMC have revealed that its value depends on the method used for its determination. Therefore, it seems more reasonable to define phenomenologically the CMC as the concentration at which a sufficient number of micelles is formed to be detected by a given method [16]. In practical terms, the CMC is often determined from plots of the surface tension as a function of the logarithm of the concentration. The CMC is then defined as the concentration at which the surface tension stops decreasing and reaches a plateau value. 

The polyester reaction rate is nil at this temperature.) In polymerizing the styrene component within the polyester prepolymer mixture, the first amounts of polystyrene produced early in the reaction remains dissolved until some critical concentration is reached, followed by phase separation, see Figs. 2 and 3. 

SINs. Two SIN compositions were studied, one having 10% oil prepolymer and the other 20% oil prepolymer, both dissolved in the styrene-DVB monomer solution. During the synthesis several morphological changes occurred in the mixture. Early in the reaction all components formed a mutual clear solution which was slightly yellow due to the original color of the prepolymer. As the free radical polymerization of styrene began, the polystyrene first produced remained soluble. At a critical concentration, phase separation... 

Lyotropic liquid crystals are those which occur on the addition of a solvent to a substance, or on increasing the substance concentration in the solvent. There are examples of cellulose derivatives that are both thennotropic and lyotropic. However, cellulose and most cellulose derivatives form lyotropic mesophases. They usually have a characteristic "critical concentration" or "A point" where the molecules first begin to orient into the anisotropic phase which coexists with the isotropic phase. The anisotropic or ordered phase increases relative to the isotropic phase as the solution concentration is increased in a concentration range termed the "biphasic region." At the "B point" concentration the solution is wholly anisotropic. These A and B points are usually determined optically. 

If one follows the solution viscosity in concentrated sulfuric acid with increasing polymer concentration, then one observes first a rise, afterwards, however, an abrupt decrease (about 5 to 15%, depending on the type of polymers and the experimental conditions). This transition is identical with the transformation of an optical isotropic to an optical anisotropic liquid crystalline solution with nematic behavior. Such solutions in the state of rest are weakly clouded and become opalescent when they are stirred they show birefringence, i.e., they depolarize linear polarized light. The two phases, formed at the critical concentration, can be separated by centrifugation to an isotropic and an anisotropic phase. A high amount of anisotropic phase is desirable for the fiber properties. This can be obtained by variation of the molecular weight, the solvent, the temperature, and the polymer concentration. 

As far as chemistry and life sciences are concerned, there are for me and many others two main reasons for this fascination, summarized in Figure 9.4 firstly, above a certain critical concentration, structural order is achieved starting from the chaotic mixture of disordered surfactant molecules. As discussed earlier, this increase of order is attended by an increase of entropy and a decrease of free energy. 

Let us divide the overall volume of the reacting system, V, into two parts first Vi filled up with template coils being in contact with each other (possesses the critical concentration c in g/L) and the second part V2 free from the template. Monomer is divided into these two parts in such a way that concentrations are [M]i and [M]2, respectively. The overall rate of the polymerization Rqv is a sum of the rate in the first part, Ri, and in... 

Van der Linden and Sagis (2001) have suggested that, once a critical concentration for gel formation is known, one can predict, for example, the dependence of the gel elasticity on the concentration of protein. The minimum gelation concentration may be expressed in terms of the basic fibre characteristics like the stiffness and also as a function of salt concentration (Veerman, 2004 Sagis et al., 2004). It is pointed out by van der Linden (2006) that there are two important factors which allow the manipulation of this minimum gelation concentration to an extremely low value. The first factor is that the nano-fibre should be robust against dilution. And the second is that the fibre should robust also with respect to other treatments, especially the adjustment of the pH. It would appear that each of these conditions is satisfied. 

In spite of the fact that the concentration of surfactants in the outer solution is assumed to be smaller than the critical micelle concentration, inside the network, micelles are supposed to be formed. The reason for this assumption is, first of all, intensive adsorption of surfactants on the network as a result of the ion exchange reaction. Moreover, in Refs. [38, 39], it was shown that critical concentration of micelles formation c c" within a polyelectrolyte network is much less than that in the solution of surfactant c° . Indeed, when a micelle is formed in solution immobilization of counter ions of surfactant molecules takes place, because these counter ions tend to neutralize the charge of micelles (see Fig. 13), whereas there is no immobilization of counter ions when the micelles are formed in the network the charge of micelles is neutralized by initially immobilized network charges which do not contribute to the translational entropy (Fig. 13). 

When Co grows, the network volume slightly decreases and the concentration of surfactant q within the network increases. When cjj, exceeds a critical concentration of micelle formation (at this point cq = c, see Figs.14,15), the network collapses because the surfactant molecules aggregated in micelles cease to impose osmotic pressure which causes additional expansion of the network. At relatively small values of the ratio Vf/V, the collapse is continuous (Figs. 14, 15), so that the number of surfactant molecules in micelles increases from zero starting at the concentration c. However, when the ratio Vf/V is sufficiently large, a discrete first-order phase transition takes place. 

A quantitative interpretation of the relation between critical concentration and molecular weight showed that eq. (4.6) should be modified along lines which were probably first given by Onogi, Kobayashi, Kojima and Taniguchi (128). [Cf. also Utrachi and Simha (129)]. 

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