Open association

The equilibrium constant for molecule-related open association is defined as CKm-i)o = [Mp,]/[ Mn- 1 ] [ Ml ] (6-78) 

If the association occurs, for example, via the end groups, then it can be assumed that the equilibrium constant defined above is independent of the degree of association N oi the multimers produced  

according to Equation (6-78), A o[Mi] = [A/n]/[Afi] still holds, and since the content of dimers must be smaller than that of monomers, A o [ Afi ] is always smaller than 1. Consequently, Equation (6-80) can, according to the rules valid for such series, be given as 

Analogous calculations give for the apparent mass-average molar mass in the theta state 

Equilibrium constants for molecule-related closed association are defined by 

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Vent and drain openings associated with hydrocarbon fluids or gases... 

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3,..., n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules ... 

B. Rearrangement of Hydrogen Bonds Mechanism of Open Associates Formation... 

The arrangement of hydrogen bonds in hydrogen-containing compounds, which takes place in condensed phases (liquid, liquid crystal, and solid) due to the phase transition, is often accompanied by the appearance of open associates with their following polymerization, or clustering as it happens in... 

This is testimony to a partial dissociation of cyclic dimers with the formation of open associates and monomers. In Refs. 57,58, 60 the quantitative estimations of the relative number of different building blocks as functions of temperature and phase of the sample have been made. For reference, the infrared spectra of n-carbonic and perftoralkylbenzoic acids, which do not possess mesomorphic properties, have been studied as well. 

Heating over the melting temperature is accompanied by amplification of the intensity of bands resulted from monomers (612, 1730, and 3550 cm-1) and decay of the intensity of bands stemming from cyclic dimers (940, 1690, and 2900 cm-1). That is, with heating, cyclic dimers dissociate into monomers the quantity of open associates holds constant in the framework of the mesophase (Fig. 21). These clusters (i.e., open associates), which feature a certain order... 

Figure 21. Relative content of cyclic dimers (x), open associates (A), and monomers (O) in different phase states of the 7AOBA ( , ) are the data for dilution of the 7AOBA in CCI4. The vertical dashed lines correspond to the phase transition temperatures. (From Ref. 57.)...

Cyclic dimers, open associates, and monomers exist also in the liquid state however, with temperature the dynamic equilibrium is shifted to monomers. Note that a more simple pattern of the molecular structure is set with dissolving of the acids studied in CCLp Only cyclic dimers and monomers are found at equilibrium, and the quantity of monomers increases with dilution of the solution or with its heating open associates do not arise. The enthalpy of hydrogen bond of dimer molecules in the solution is approximately the same as in the crystal at the same temperature. 

Note that as follows from expression (430) in the range close to the phase transition, the temperature dependence of proton transfer rate (435) is expressed as T1/2exp( —const/ 1). Here, the first factor is responsible for the creation of open associates, and it prevails over the second one for T > Tc. Below Tc in the first factor the exponent 1 /2 remains however, the absolute value of the second factor increases, which accounts for the lack of open associates in the solid state 2 phase in this temperature range. 

On the other hand, in the experiments [57,58,60] the samples, when heated to Tc (see Fig. 21), exhibited open associates whose formation was completed in... 

As we mentioned in Section V, near the temperature of phase transition to the metaphase the solid state of alkyl- and alkoxybenzoic acids is unstable in relation to the formation of hydrogen-bonded open associates. The associates merge in polymer chains, which can include over 10 acid molecules. Let us treat how the statistical model described above can account for such a behavior of the associates. 

We shall consider potentials that describe the interaction between dimers ( aa), between dimers and open associates ( ab)> and between open associates O bb) [see expressions (548)-(550)]. It is reasonable to assume that the potentials 7/a a and 37 a n are typical van der Waals that is, 37 a a = — Caa-(g/rf and 7/ n —Cab (g/r)6, where Cy are constants. Notice that the two peculiarities are important (i) open associates can be regarded as impurities to the main matrix (dimers), and (ii) open associates feature a larger dipole moment in comparison with dimers. These two circumstances (see Ref. 282)... 

Here d is the dipole moment of the open associate formed by alkyl- or alkoxybenzoic acid molecules, and r is the distance between two interacting associates. 

The number of ABA/OABA molecules, which enter in the cluster, can be easily estimated. Indeed, let the dipole moment of the open associate be equal to 7D, that is, (7/3) x 10 271 C m (note that long molecules linked through hydrogen bonds are characterized by a large proton polarizability [6]) the distance between two associates, g, is approximately 0.26 nm the temperature of the phase transition, T(, is 320 K. Substituting these values into expression (574) we obtain... 

Figure 2. Theoretical relationship between the association constant Ka and DP, using a simple isodesmic association function, or multistage open association model.

Fig. 2 Growth mechanisms. Schematic theoretical variation of DP (or length) with unimer concentration for linear supramolecular polymerization according to (a) multistage open association (b) helical growth (c) growth-coupled-to-orientation. C and C are eritieal eoneentrations coiresponding to (b) and (c). Occurrenee of liquid-eiystalline phases (N. H, L) is indicated. From Ref. [1]. Copyright 2002 Wiley-VCH.

Two simple cases can be distinguished for the stoichiometry. Open association is the term given to a consecutive process ... 

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