Parameters Measuring Intermolecular Interactions

The number of molecules per unit volume v is 6.02 x 1023 c/M. If the molecular centers are distributed randomly, the product vV is the average number of other molecules with centers lying within the pervaded volume of any one molecule. Accordingly, v V is a measure of the potential degree of coil overlap, and with = 2.68 xlO23  

Simha and Zakin (126), Onogi et al (127), and Comet (128) develop overlap criteria of the same form but with different numerical coefficients. Accordingly, flow properties which depend on concentration and molecular weight principally through their effects on coil overlap should correlate through the Simha parameter c[ /], or cM , in which a is the Mark-Houwink viscosity exponent (0.5 a 0.8). If coil shrinkage, caused by the loss of excluded volume in good 

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Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The applications of quantitative structure-reactivity analysis to cyclodextrin com-plexation and cyclodextrin catalysis, mostly from our laboratories, as well as the experimental and theoretical backgrounds of these approaches, are reviewed. These approaches enable us to separate several intermolecular interactions, acting simultaneously, from one another in terms of physicochemical parameters, to evaluate the extent to which each interaction contributes, and to predict thermodynamic stabilities and/or kinetic rate constants experimentally undetermined. Conclusions obtained are mostly consistent with those deduced from experimental measurements. 

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

Rotational-echo double-resonance (REDOR)(75,79) is a new solid-state NMR technique which is sensitive to through-space carbon-nitrogen interactions between selectively 13C and 15N-enriched sites separated by up to 5A (20-22). The parameter directly measured in a REDOR experiment is the heteronuclear dipolar coupling constant DCN, which is in itself proportional to the inverse third power of the intemuclear distance, rCN. It is this dependence on (icn)3 which accounts both for REDOR s ability to accurately measure short distances and its insensitivity to longer-range interactions. As a technique which can probe, in detail, intermolecular interactions over a distance range of 5A, REDOR is well suited to studying the distribution of small selectively-labeled molecules in polymer delivery systems. 

Due to their better biomimetic properties, phospholipids have been proposed as an alternative to 1-octanol for lipophiiicity studies. The use of immobilized artificial membranes (lAM) in lipophiiicity determination was recently reviewed and we thus only briefly summarize the main conclusions [108]. lAM phases are silica-based columns with phospholipids bounded covalently. lAM are based on phosphatidylcholine (PC) linked to a silica propylamine surface. Most lipophiiicity studies with lAM were carried out using an aqueous mobile phase with pH values from 7.0 to 7.4 (log D measurements). Therefore, tested compounds were neutral, totally or partially ionized in these conditions. It was shown that the lipophiiicity parameters obtained on I AM stationary phases and the partition coefficients in 1-octanol/water system were governed by different balance of intermolecular interactions [109]. Therefore the relationships between log kiAM and log Poet varied with the class of compounds studied [110]. However, it was shown that, for neutral compounds with log Poet > 1, a correspondence existed between the two parameters when double-chain lAM phases (i.e., lAM.PC.MG and IAM.PC.DD2) were used [111]. In contrast, in the case of ionized compounds, retention on lAM columns and partitioning in 1 -octanol / water system were significantly different due to ionic interactions expressed in lAM retention but not in 1-octanol/water system and due to acidic and basic compounds behaving differently in these two systems. 

With bonded, NP-HPLC sorbents, such as the porous aminopropylsilica sorbents, the distribution constant, abSii, can be equated with the solubility parameter, 6, which in turn is a measure of the intermolecular interaction energy per unit volume of the polypeptide in a pure liquid such that... 

In contrast to NaCl or tetramethylammonium bromide, also shown in Fig. 4, the concentration dependence of the density is less marked. However, the slopes of the density curves measured at 20 °C and 35 °C for DADMAC increase with the concentration. This indicates a change of the interaction with water is likely caused by the formation of ordered structures such as associates [32, 37]. The greatest change of the slope is located at approximately 1.5 mol L 1. The influence of this monomer structure formation on the polymerization behavior will be discussed in Sect. 4. The non-linear concentration dependence of the viscosity is illustrated in Fig. 5. Here, a strong increase of this solution parameter is observed at approximately 1.5 mol L 1 indicating a change of intermolecular interactions [32,37]. 

Since solvatochromic parameters are derived from direct measurements of the energy resulting from intermolecular interaction, they can be used to predict solubility, which is determined by solute-solute, solvent-solvent, and solute-solvent interaction energies. For nonself-associated liquid aliphatic compounds with a weak or nonhydrogen-bond donor (Taft etal., 1985 Kamlet etal., 1986), the solubility in water at 29S was related to molar volunWjf, hydrogen-bond basicity j and polarity/polarizability (jf) by a linear solvation energy relationship (LSER) as in Equation 3.55 ... 

We suggest to employ the parameter / as some measure of localization of intermolecular interactions—that is, of a spread of short-range forces in a liquid The lower the value of f the stronger these forces at larger distances. We estimate roughly this spread as a linear length of the curved part (1 —/)p of the well ... 

In conclusion, it is apparent that the use of the Br nsted coefficient as a measure of selectivity and hence of transition state structure appears to be based on extensive experimental data. However, the many cases where this use of the Br nsted coefficient is invalid suggest that considerable caution be used in drawing mechanistic conclusions from such data. The limitations on the mechanistic significance of a require further clarification, but the first steps in defining them appear to have been taken. The influence of change in the intrinsic barrier and variable intermolecular interactions in the transition state, both of which will result in a breakdown of the rate-equilibrium relationship, as well as internal return appear to be some of the key parameters which determine the magnitude of the Br nsted coefficient in addition to the degree of proton transfer. 

The van der Waals parameters a and b are measures of the attractive energy in intermolecular interactions and size, respectively. It is, therefore, reasonable to express for a mixture these parameters in terms of LCs. 

All NMR parameters including the Joc coupling have been measured by Jackowski et al for 1,2- C-enriched acetylene in various solvents. They have found that the Jcc coupling is the most sensitive to intermolecular interactions it varies from 174.78 Hz for an isolated molecule to 165.8 Hz for the molecule dissolved in acetone. 

Descriptors are atomic or molecular parameters or even molecular properties that contain information about the energy of each type of intermolecular interaction. They can be classified into two broad categories empirical and theoretical. Empirical descriptors depend on experimental measurements thus, they are available for a limited number of solutes (16). Theoretical descriptors are derived from the solute structure they are usually based on ab initio or semiempirical quantum chemistry calculations or on the connectivity of atoms in the molecule. With the proper use of dedicated software, the number of structural descriptors that can be assigned to a given solute is practically unlimited. Comprehensive compilations of the literature (17,18) register over 2000 known theoretical descriptors. 

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