Micelle formation molecular thermodynamic

Since they act as surfactants, copolymers are added in only small amounts, typically from a thousandth parts to a few hundredth parts. Theoretically, Leibler [30] showed that only 2% of a diblock copolymer may thermodynamically stabilize an 80%/20% incompatible blend with an optimum morphology (submicronic droplets). However, in practice kinetic control and micelle formation interfere in this best-case scenario. To a some extent, compatibilization increases with copolymer concentration [8,31,32], Beyond a critical concentration (critical micellar concentration cmc) little or no improvement is observed (moreover, for high amounts, the copolymer can act as a plasticizer). Copolymer molecular weight influence is similar to that of the concentration effect. For example, in a PS/PDMS system [8,31,32], when the copolymer molecular weight increases, domain size decreases to a certain extent. Hu et al. [31] correlated their experimental results with theoretical prediction of the Leibler s brush theory [30]. Leibler distinguishes two regimes to characterize the behaviour of the copolymer at the interface... 

These systems also provide an understanding of the molecular basis of interfaces, since the amphiphile molecules consist of alkyl chains and hydrophilic groups. Thermodynamic analyses on surface adsorption and micelle formation of a anionic surfactants in water were described by surface tension (drop volume) measurements. These data are analyzed in Table 3.19. These data show that at 20°C (Table 3.20) the magnitude of surface tension changes nonlinearly (varying from 1.7 to 0.7 mN/m per CH2) with alkyl chain length. 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

Single molecules or micelles associate spontaneously in a thermodynamic equihbrium at a definite critical micelle concentration within a biocoUoidal system [47]. Analogously to micelle formation in liquid systems, aggregation of surfactants at a surface depends on a critical hemi-micellar concentration [48, 49]. The removal of the hydrophobic molecular region from the hydrophihc interface... 

It is well established that when an amphiphilic block copolymer is dissolved in a selective solvent at a fixed temperature, above a specific concentration called the critical micelle concentration (cmc), micellisation occurs. Below the cmc, only molecularly dissolved copolymer chains (unimers) are present in the solution, while above the cmc multimolecular micelles are in thermodynamic equilibrium with the unimers. This process is in analogy to classical low molecular weight surfactants, differing in that the cmc is much lower in the case of block copolymers macrosurfactants. The self-assembly arises from the need of the copolymer chains to minimise energetically unfavourable solvophobic interactions. Therefore, micelle formation is dictated by two opposite forces, the attractive force between the insoluble blocks, which leads to aggregation, and the repulsive one between the soluble blocks preventing unlimited growth of the micelle. At the same time, the interaction of the soluble blocks and the solvent is responsible for the stabilisation of the micelles [1, 10]. 

The molecular thermodynamic theory for micelle formation has heen worked out with increasing sophistication following the pioneering work of Israelachvili, Mitchell, and Ninham.26 The most comprehensive reports on micelle formation are those of Nagarajan and Ruckenstein and of Shiloah and Blankschtein. Many other theoretical approaches have been used in recent years to account for the formation of micelles and their properties thermod3mamics of small systems, the self-consistent field lattice model, the scaled particle theory, and Monte-Carlo and molecular dynamics MD simulations. MC and DC simulations are presently much in favor due to the increased availability of fast computers. A prediction common to all these theories is that micelles represent a thermodynamically stable state and that micellar solutions are single-phase systems. Several recent results of MD and (MC) simulations are in agreement with experimental results. ... 

As indicated above, an important characteristic of a surfactant in solution is its solubility relative to the critical concentration at which thermodynamic considerations result in the onset of molecular aggregation or micelle formation. Since micelle formation is of critical importance to many surfactant applications, the understanding of the phenomenon relative to surfactant structures constitutes an important element in the overall understanding of surfactant structure-property relationships. 

The primary mechanism for energy conservation is adsorption of surfactant molecules at various available interfaces. However, when, for instance, the water-air interface is saturated conservator may continue through other means (Figure 12.3). One such example is the crystallization or precipitation of the surfactant from solution, in other words, bulk phase separation. Another example is the formation of molecular aggregates or micelles that remain in solution as thermodynamically stable, dispersed species with properties distinct from those of an isotropic solution containing monomeric surfactant molecules (Myers, 1992). 

The aggregation of amphiphilic molecules into micelles is, from a physico-chemical point of view, an example of the formation of a molecular complex. The total thermodynamic description of the aggregation would involve a series of stability constants, including their variation with salt concentration. In most applications, it is neither feasible to obtain such detailed information nor necessary from a practical point of view. The characteristic cooperative nature of the micellization makes it often possible to describe the aggregation process using only a few parameters. It has,... 

We begin here a brief survey of thermodynamic principles that pertain to formation and self assembly of large scale aggregates of molecular units, such as polymers, micelles, vesicles, or similar macromolecules. We follow the exposition of Israelachvily. ... 

In the acidic route (with pH < 2), both kinetic and thermodynamic controlling factors need to be considered. First, the acid catalysis speeds up the hydrolysis of silicon alkoxides. Second, the silica species in solution are positively charged as =SiOH2 (denoted as I+). Finally, the siloxane bond condensation rate is kinetically promoted near the micelle surface. The surfactant (S+)-silica interaction in S+X 11 is mediated by the counterion X-. The micelle-counterion interaction is in thermodynamic equilibrium. Thus the factors involved in determining the total rate of nanostructure formation are the counterion adsorption equilibrium of X on the micellar surface, surface-enhanced concentration of I+, and proton-catalysed silica condensation near the micellar surface. From consideration of the surfactant, the surfactants first form micelles as a combination of the S+X assemblies, which then form a liquid crystal with molecular silicate species, and finally the mesoporous material is formed through inorganic polymerization and condensation of the silicate species. In the S+X I+ model, the surfactant-to-counteranion... 

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