Entropic-enthalpic repulsion

A different situation arises when studying PMMA-latexes swollen by a nonpolar monomer like styrene which exhibits at ambient temperature a much lower solubihty in water (0.2 g/1) than MMA (15.9 g/1) [55]. Styrene has a very low electron density (see Table 1) in comparison to soUd PMMA and both an enrichment or a depletion of this monomer in the surface layer are easily discernible in a SAXS-experiment [55]. In comparison to the above system PMMA/MMA a critical test of the influence of entropic versus enthalpic forces becomes possible if the entropic wall-repulsion effect prevails styrene should be enriched in a surface layer. Because of the lower electron density of styrene this surface layer must exhibit a lower electron density than the core of the particle. If, on the other hand, the unfavorable enthalpic interactions between styrene and water are decisive, the more polar polymeric component PMMA should be enriched in a surface layer. In that case a surface layer with an enhanced electron density is expected. 

Poly(diallyldimethylammonium chloride) (PDADMAC) and ferri-/ferrocyanide show a similar behavior [233]. In most cases, the ferri-/ferrocyanide (trivalent/ tetravalent hexacyanoferrate[lll]/[ll]) couple exhibits an unexpected interaction pattern with strong cationic polyelectrolytes. Hereby, the trivalent ferricyanide favors complexation compared with the tetravalent ferrocyanide [234, 235]. Although the higher charged ferrocyanide is supposed to release a higher number of monovalent counterions, this entropic contribution is less dominant for the ferrocyanide. This conclusion was derived from entropy measurements [232], clearly emphasizing the enthalpic repulsion between the highly hydrated, weakly polarizable ferrocyanide and the somewhat hydrophobic polymeric backbone [236]. This leads to pronounced ion-specific effects. In contrast, some systems... 

In Equation (10), Vc represents a hard-core repulsion that is entropic in nature since it is linearly dependent on temperature in the expression for energy. Repulsion is generally associated with enthalpic interactions and we can consider the effect of an enthalpic interaction. Since Vc is associated with a single Kuhn unit we consider the average enthalpy of interaction per pair-wise interaction and the number of pair-wise interactions per Kuhn unit,... 

The adsorbed layers between the particles may interpenetrate and so give a local increase in the concentration of polymer segments. Depending on the balance between polymer-polymer and polymer-dispersion medium interactions, this may lead to either repulsion or attraction by an osmotic mechanism. Enthalpic and entropic changes will be involved. If interpenetration takes place to a significant extent, elastic repulsion will also operate. 

The stability of inverse micelles has been treated by Eicke (8,9) and by Muller (10) for nonaqueous systems, while Adamson (1) and later Levine (11) calculated the electric field gradient in an inverse micelle for a solution in equilibrium with an aqueous solution. Ruckenstein (5) later gave a more complete treatment of the stability of such systems taking both enthalpic (Van der Waals (VdW) interparticle potential, the first component of the interfacial free energy and the interparticle contribution of the repulsion energy from the compression of the diffuse part of the electric double layer) and entropic contributions into consideration. His calculations also were performed for the equilibrium between two liquid solutions—one aqueous, the other hydrocarbon. 

The straight-rod model predicts a right-handed cholesteric helix for 96 and a left-handed one for PBLG and schizophylan, which is in agreement with experimental results.280 In the threaded EFJC model, the flexibility of the macromolecular helix can be freely chosen. The handedness of the cholesteric phase is based on entropic hard core repulsion phenomena between the helices and an enthalpic chiral dispersion force. Right-handed mesophases were predicted for solutions of 96, 97, and schizophylan. However, only for 96 this was in agreement... 

Helfand and Tagami model is based on self-consistent field that determines the configurational statistics of macromolecules in the interfacial region. At the interface, the interactions between statistic segments of polymers A and B are determined by the thermodynamic binary interaction parameter, Since the polymers are immiscible, there are repulsive enthalpic effects that must be balanced by the entropic ones that cause chains A and B to intermingle. 

As in the case of macrophase separation, the two competing terms of enthalpic and entropic nature govern the thermodynamics of block copolymers. Similar to binary polymer bends the phase behavior of diblock copolymer melts is primarily controlled by the segregation strength and the volume fractions /a and /b = 1 - /a of the two blocks. Being covalently bonded, repulsive blocks are prevented from separating on a macroscopic level. Hence, the segregation into A- and B-rich domains... 

The first attempt to compile all the factors contributing to the stability of a microemulsion is due to Ruckenstein and Chi [15], who summarized calculations of enthalpic components (van der Waals attractive potential, electrical double layer repulsive potential, and the interfacial stretching and bending free energy) and entropic contributions from the location of droplets. These calculations as well as those following [16] were useful because they revealed the importance of extremely low interfacial tension. 

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