Isotropic dilute solution

An ordered solid phase is formed, at equilibrium with a very dilute isotropic solution, when the isotropic solution of PBT is slowly coagulated by gradual absorption of atmospheric moisture. The... 

Since organogelators are in crystalline or lyotropic aggregate states in a gel. the nature of their intermolecular interactions becomes a factor of paramount importance in determining the nature and the intensity of emitted radiation from a gelled sample. Molecular proximity opens possible reactive channels for the excited states that are not available in dispersed solutions. For example, it has been shown that CAB dimerizes in its neat solid, liquid-crystalline, and gelled (fiber) states when exposed to UV radiation [47,48]. (See Structure I.) In dilute isotropic solutions, no photoreaction is observed because the time required for an... 

While only one paper describes the appearance of an anisotropic aqueous solution for a polymer of type D (19), polymers of type A to C have been investigated in more detail recently with respect to formation of liquid crystalline phases (20-23). In the following two sections, the association behavior in dilute isotropic solution and the liquid crystalline phase region is discussed on the basis of some experimental results. The dilute isotropic solutions are of interest with respect to the question whether polymers of type A and B form micelles similar to the corresponding monomeric amphiphiles. The liquid crystalline phase regime gives information whether the linkage of the amphiphiles via a polymer backbone influences the stability of the anisotropic phases and whether the same polymorphism occurs as is known for monomeric amphiphiles. 

Below temperature TB (cloud point for low polymer concentrations) and at a polymer weight fraction lower than wB, isotropic solutions are stable. Above the weight fraction wA and at a temperature below the line AD (clouds points for concentrated polymer concentrations) pure cholesteric phase separates. All other compositions are biphasic, the liquid crystals being in equilibrium with a dilute isotropic solution. At low temperature this domain exists in the small concentration range delimited by wA and wB. Note that TA may be below body or even room temperature. 

The tendency to reduce excluded volume leads to a driving force for the orientation of rods having length/diameter ratio X = L/D >and for the stacking of thin disks (0hard interaction effect is detectable even in diluted isotropic solution and leads, above a critical concentration, to an orientational transition to... 

Figure 9 Chemical structures of Cs-symmetrical bipyridine-based discotics and schematic representation of their propeller-like conformation assembling into linear supramolecular polymers in dilute isotropic solution. Reproduced from Palmans, A. R. A. Vekemans, J. A. J. M. Havinga, E. E. etal. Angew. Chem. Int. Ed 1997, 36, 2648-2651. ...

Consideration of solutions of rodlike polymers at higher concentrations was presented by Flory.i The lattice model used so successfully for the theory of concentrated polymer solutions was extended to include semiflex-ible chains and rods. The theory predicted a miscibility gap between a dilute isotropic solution and an ordered concentrated solution. This theory is presented in Section 9.4. The same solvent quality issues needed to address the thermodynamics of flexible polymer solutions also influence the phase behavior of lyotropic solutions. A description of actual solutions of stiff polymers is also presented. 

Most solutions of rodlike polymers are not athermal. Heat-of-mixing terms can be added to the chemical potentials, just as in the ordinary Flory-Huggins theory of solutions. When the interaction parameter % is large enough, the solution will separate into a dilute phase and a concentrated phase, just as for any polymer solution. There will still be a miscibility gap between dilute isotropic solutions and ordered concentrated solutions. A typical phase diagram for a solution of rods with x = 100 is shown in Figure 9.3. The concentrated phase is now very concentrated and ordered. 

Critical Concentration and Saturation Regions for Poly(terephtalic hydrazide). A typical critical concentration curve for 0-T polymer is shown in Fig. 4 for 10.4% (CH3)4NOH and polymer with ninh of 4.4. Dilute isotropic solutions and anisotropic solutions have very low bulk viscosities. 

This chapter limits itself to P-NMR studies on phospholipids and lysophospholipids in monomeric and micellar states and focuses on the identification of species and aggregation states, as well as on the dynamic processes of migration and reaction kinetics. For this purpose, micelles and mixed micelles are defined as dilute isotropic solutions of phospholipids, either with or without detergents that form spontaneously and are at thermodynamic equilibrium diis definition specifically excludes sonicated or small unilamellar vesicles as well as membranes. These are covered by Smith and Ekiel (Chapter 15). This limitation in scope necessarily requires heavy reliance on work from the laboratory of the authors of this chapter. 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Usually, dilute polymer solutions are isotropic systems, i.e. macromolecular chains can exist in these solutions independently of each other with a random distribution of orientations of the long axes of coils. The solutions of flexible-chain polymers remain isotropic when the solution concentration increases whereas in concentrated solutions of macromolecules of limited flexibility the chains can no longer be oriented arbitrarily and some direction of preferential orientations of macromolecular axes appears, i.e. the mutual orientations of the axes of neighboring molecules are correlated. This means that... 

As the temperature of dilute aqueous solutions containing ethoxylated nonionic surfactants is increased, the solutions may turn cloudy at a certain temperature, called the cloud point. At or above the cloud point, the cloudy solution may separate into two isotropic phases, one concentrated in surfactant (coacervate phase) and the other containing a low concentration of surfactant (dilute phase). As an example of the importance of this phenomena, detergency is sometimes optimum just below the cloud point, but a reduction in the washing effect can occur above the cloud point (95). However, the phase separation can improve acidizing operations in oil reservoirs (96) For surfactant mixtures, of particular interest is the effect of mixture composition on the cloud point and the distribution of components between the two phases above the cloud point. 

The phase behaviour established for concentrated aqueous solutions of PEO-PPO-PEO copolymers has its counterpart in PEO/PBO copolymer solutions. A phase diagram for PE058PB0i7PE0M based on tube inversion experiments is shown in Fig. 4.14 (Luo et al. 1992). The hard gel is isotropic under the polarizing microscope and can be characterized as a cubic phase formed from spherical micelles of a similar size to those in the dilute micellar solution. 

The unique spectral absorption of the Rhodonines contains two visual band components, an isotropic absorption associated with the conjugated dipole molecular structure of the molecule, and a anisotropic absorption associated with an additional resonant slow-wave stmcture intimately associated with the triplet electrons of the oxygen atoms of the molecule. The unusual relaxation properties of these molecules are also associated with these triplet state electrons. The Rhodonines do not fluoresce or phosphoresce significantly while in a dilute liquid solution. 

The study of liquid crystals rapidly becomes complex because both the thermotropic and lyotropic types are polymorphic. The lyotropic type exists in at least six phases according to Brown Johnson. Materials of this type generally exhibit a molecular weight in the range of 250-500. Many of these materials are described as lipids, and frequently as phospholipids. On addition of water to a crystal composed of these materials, the molecular structure initially collapses to form a lamellar structure. Further dilution may result in additional structural changes before an isotropic solution is reached. 

In the opposite case of low temperatures, the accounting for the attractive interaction of rods is necessary, and due to these interactions the solution of rods usually separates into a highly ordered liquid-crystalline phase and a very dilute isotropic phase (Fig. 4). We will refer to this region of the phase diagram as the low-temperature region. 

Ben-Naim s definition has many merits it is not limited to dilute solutions, it avoids some assumptions about the structure of the liquid, it allows to use microscopical molecular partition functions moreover, keeping M fixed in both phases is quite useful in order to implement this approach in a computationally transparent QM procedure. The liberation free energy may be discarded when examining infinite isotropic solutions, but it must be reconsidered when M is placed near a solution boundary. 

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