Monomers in equilibrium

Surfactant Activity in Micellar Systems. The activities or concentrations of individual surfactant monomers in equilibrium with mixed micelles are the most important quantities predicted by micellar thermodynamic models. These variables often dictate practical performance of surfactant solutions. The monomer concentrations in mixed micellar systems have been measured by ultraf i Itration (I.), dialysis (2), a combination of conductivity and specific ion electrode measurements (3), a method using surface tension of mixtures at and above the CMC <4), gel filtration (5), conductivity (6), specific ion electrode measurements (7), NMR <8), chromatograph c separation of surfactants with a hydrophilic substrate (9> and by application of the Bibbs-Duhem equation to CMC data (iO). Surfactant specific electrodes have been used to measure anionic surfactant activities in single surfactant systems (11.12) and might be useful in mixed systems. ... 

The cac (critical aggregate concentration) values for oleate are in the millimolar range, which means that at the operational concentration of 10-50 mM there will be a signihcant concentration of monomer in equilibrium with the aggregate. This consideration allows us to go back to the question of whether vesicles are chemical equilibrium systems. Oleate vesicles cannot be considered proper chemical equilibrium systems, however they behave in a mixed way, with some features that are typical of micelles in equilibrium (Luisi, 2001). 

A Derivatives of 1 1 complexes As a result of the chirality of ai-[P2-W17O61]10- (Figure 5) solutions of [ Ce(o i-P2Wi706i)(H20)4 2]14 contain enantiomeric pairs of monomers in equilibrium with the meso dimer. Addition of chiral amino acids to such solutions causes a doubling of the 31P-NMR resonances as a result of diastereomer formation presumably caused by coordination of the amino acid to the rare-earth cation (Sadakane et al., 2001). No splitting was observed when similar experiments were carried out with complexes of the achiral a2 isomer. Formation constants for the two diastereomers of the complexes with L-proline were estimated as 7.3 1.3 and 9.8 1.4 M-1. The corresponding proline complex of achiral [Ce W C i)]7- has a formation constant of 4.5 0.1 M-1 (Sadakane et al., 2002). 

Polymerization of 5-, 6-, and 7-membered rings usually proceeds as the reversible process thus after reaching the ultimate (allowed by thermodynamics) conversion of the monomer A, there is still certain amount of this monomer in equilibrium with growing chains. If monomer A can undergo copolymerization with second monomer added, then the second block will be the copolymer of A and B. This indeed has been observed... 

There is again an obvious correlation between reaction order and degree of association. The one quarter order for methyllithium could be explained satisfactorily by the usual assumption that the reactive species is methyllithium monomer in equilibrium with its tetramer. For phenyllithium a partial dissociation would lead to an order between one half and unity, as observed, if the dissociated product only were active. Other schemes involving some reactivity of both species would be equally plausible [101]. The first order behaviour with benzyllithium would require that the major reactive species is the ion-pair and not the free benzyl anion which must be present in small concentration. 

Content of extractable cyclic oligomers and monomer in equilibrium polymers [16]... 

The concentration of actin monomers In equilibrium with actin filaments is the critical concentration (Q). At a G-actln concentration above Q, there is net growth of filaments at concentrations below Q, there is net depolymerization of filaments. 

By equilibrium concentration Szwarc meant a concentration of a given monomer in equilibrium with its own growing species. If there is a multiplicity of growing structures, this monomer is involved in a number of equilibria and the measured value is the copolymerization equilibrium concentration ( stationary concentration ), differing from the equilibrium concentration in homopolymerization. 

Table 7.11. Calculated concentration of monomers in equilibrium with polyoxymethylene solvent nitrobenzene, temp. = 25 °C...

In this type of extraction, micellar structures are retained by correctly selecting the ultrafiltration (UF) membrane (Scamehorn et al., 1988). Hydrophobic species are solubilized within the micelles, but surfactant monomers in equilibrium with the micelles can penetrate the membrane along with the free solutes in equilibrium with those solubilized in the micelles. Whereas several uses for this technique have been suggested, such as the collection of radioactive uranium and plutonium present in acid wastes during nuclear plant decommissioning, from our point of view its principal use is in enantiomeric separation (Overdevest et al., 1998). 

In the above equation Tc is the ceiling temperature for the equilibrium monomer concentration. It is a function of the temperature. Because the heat content is a negative quantity, the concentration of the monomer (in equilibrium with polymer) increases with increasing temperatures. There are a... 

The monomer concentration can remain constant for two reasons. First, a steady state can exist in which consumption of monomer by polymerization is directly compensated by subsequent diffusion of free monomer into the latex particle. The monomer concentration is then always lower than the saturation concentration at equilibrium. Second, the monomer concentration in the latex particles will be constant when the Gibbs interfacial energy A Gy and swelling A Gq cancel, so that the Gibbs energy of the monomer in equilibrium will be zero ... 

In the above equation, T. is the ceiling temperature for the equilibrium monomer concentration. It is a function of the temperature of the reaction. Because the heat content is a negative quantity, the concentration of the monomer (in equilibrium with polymer) increases with increasing temperatures. There are a series of ceiling temperatures that correspond to different equilibrium monomer concentrations. For any given concentration of a monomer in solution, there is also some upper temperature at which polymerization will not proceed. This, however, is a thermodynamic approach. When there are no active centers present in the polymer structure, the material will appear stable even above the ceiling temperature in a state of metastable equilibrium. 

In the stock solutions containing 2280 ppm of silica at pH 9-10 there must have been an appreciable concentration of monomer in equilibrium with the polymer. Based on the calculated particle sizes this would amount to at least 2.6, 2.2. and 1.7... 

Baumann (68b) found that when different amounts of aluminum ion were added to a solution of monomer (420 ppm SiOj), more silica remained in the molybdate reactive state than when no aluminum was present. With no aluminum present, after 4 days there remained 130 ppm of molybdate-reactive silica as monomer in equilibrium with 290 ppm of relatively inactive high polymer. But when aluminum was present in the Al Si atomic ratio of 1 7, there remained about 200 ppm of molybdate-reactive silica. It can be interpreted that the alumina had combined with silica to form an aluminosilicate that later was decomposed by the strongly acidic molybdate reagent liberating additional active silica that appeared as monomer. 

A general theory of polycondensation equilibrium in silicic acid solutions was proposed by Stbber (94). From it he deduced the concentration of monomer in equilibrium with polymers of different degrees of condensation. Further data are needed to check the validity of the complex equations that were developed. 

Almost all the initial stages in the polymerization of monomer to oligomers and three-dimensional particles 1-2 nm in diameter occur in only a few minutes at above pH 7. Thereafter the polymerization involves only the increase in size and decrease in numbers of silica particles. At the same time, the concentration of monomer in equilibrium with these particles decreases as the average particle diameter increases. 

Oligomers decline when inert polymer begins to appear. The reaction rate with molybdate decreases rapidly to 0.1 between 3.75 and 4.75 days. It is probably at this stage that nucleation of colloidal particles begins. The oligomers dissolve and the silica is deposited upon the nuclei. The nuclei grow and the concentration of monomer in equilibrium decreases. The particle size can then be calculated from the concentration of monomer. The proportion of monomer drops to 5% after 90 days, which is 5% of 4000, or 200 ppm. This corresponds to the solubility of 2 nm particles. 

Thermodynamically a linear dependence of log CMC on log NaCl concentrations can be predicted for ionic detergents (155). Bile salt solutions above their CMC s can be considered to consist of monodisperse micelles and monomers in equilibrium. With this assumption the law of mass action can be applied (161). Let represent a bile salt, n the number of bile salt anions present in the micelle, Na+ its univalent counterion and m the number of counterions bound to a micelle (M). Then at equilibrium between A , Na, and M... 

Here AH is the enthalpy absorbed that brings about a total conversion and is obtained by integration of the DSC output, and Q T) is obtained by partial integration from the start of the endothermic transition to a temperature T. The fraction of nonmicellized monomer in equilibrium with micelles can be obtained from the definition of a and the mass balance of surfactant ... 

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