Intermolecular spacing

X-ray crystal stmctures (32,46) and molecular mechanics calculations (47,48) now provide specific data about intermolecular spacings between associated dye molecules. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

For sensor applications, a more interesting parameter is the degree of change in the average ion concentration in the intermolecular spaces upon the hybridization event. The model for the theoretical calculations of the average concentration of cations and... 

For the above-described model, the average concentration of cations and anions in the intermolecular spaces can be calculated using equations derived in [51] ... 

FIGURE 7.7 Ratio / of average concentration of cations (upper part of diagram) and anions (lower part of diagram) within the intermolecular spaces before hybridization and after hybridization < > in 1 1 salt solutions with bulk ion concentration of n0 = 0.005, 0.15 and 0.5M, respectively. Rs DNA cell radius. 

Figure 7.7 shows the calculated ratio / of the average concentration for cations and anions within the intermolecular spaces before hybridization and after hybridization . The ratio / is plotted as a function of the DNA cell radius Rs and for 1 1 salt solutions of different bulk-ion concentrations of n() = 0.005, 0.15 (physiological solution) and 0.5 M, respectively. The fraction of both the ssDNA and dsDNA charge compensated by the condensed cations was taken as 0 = 0.8. Two effects can be recognized from Fig. 7.7 ... 

The results obtained with PE multilayers as well as DNA on top of the capacitive EIS sensor could verify their feasibility as transducer for a label-free detection of adsorption, binding, and interactions of charged macromolecules. Nevertheless, our experiments do not enable us to clearly distinguish between the contributions in the signal generation from each of the mechanisms discussed in sections 7.3 and 7.4. Probably, both basic mechanisms, namely, the intrinsic charge of molecules and the ion-concentration redistribution in the intermolecular spaces or in the multilayer, affect the sensor signal by superposition. 

Elastic strain results from a change in the intermolecular spacing and, at least for small deformations, is reversible. 

As the temperature is raised, the vibrational energy increases, because it is kBT in each direction. If we have a simple cubic crystal in which the intermolecular spacing is r then the molar volume is Nar3. The Young s modulus for the crystal is Y and we assume a Hooke s law spring. We can define the local stress as the applied force per molecule, Fm, divided by r2, giving a local strain of x/r where x is the extension caused by the oscillation. Hence ... 

Amorphous materials can be oriented by stretching. In some instances, this orientation is also accompanied by crystallization [3]. Isoprene rubber exhibits such behavior. The positions of the maxima in the amorphous scattering pattern provide a measure of the average intermolecular spacing. Bragg s law may be used to calculate the size of the interplanar spacing [3],... 

The same logic that we used to obtain the Girifalco-Good-Fowkes equation in Section 6.10 suggests that the dispersion component of the surface tension yd may be better to use than 7 itself when additional interactions besides London forces operate between the molecules. Also, it has been suggested that intermolecular spacing should be explicitly considered within the bulk phases, especially when the interaction at d = d0 is evaluated. The Hamaker approach, after all, treats matter as continuous, and at small separations the graininess of matter can make a difference in the attraction. The latter has been incorporated into one model, which results in the expression... 

For each of the A terms in Equation (83) we may substitute the corresponding version of Equation (67). Strictly speaking, each material is characterized by its own intermolecular spacing, and this as well as its y value should be used in Equation (67). In a number of systems that have been investigated, however, the observed range of d0 values is quite narrow, suggesting that d0 can be regarded as a constant, at least as a first approximation. For a variety of polymers a value of about 0.2 nm appears to be a reasonable estimate for d0. With this (assumed constant) value factored out, Equation (83) becomes... 

Verify that the d0 values thus calculated show a relatively narrow distribution around a mean value close to 0.2 nm. Criticize or defend the following proposition As a mean center-to-center intermolecular spacing, this value is on the low side as a back-calculated parameter, however, it probably compensates for deviations from the assumed geometry, breakdown of Equation (33) at short distances, or other shortcomings of the molecular additivity principle. 

Influence of Intermolecular Spacing on Enzymic Hydrolysis of Lecithin Monolayers. When snake venom phospholipase A is injected under a lecithin monolayer, it splits lecithin into lysolecithin and free fatty acid. The change in polar groups of the monolayer results in a change of surface potential. However, if prior to injection of enzyme into the subsolution, a lecithin monolayer is compressed to such a surface pressure that the active site of the enzyme is unable to penetrate the monolayer, hydrolysis does not proceed. For monolayers of dipalmitoyl, egg, soybean, and dioleoyl lecithins the threshold surface pressure values at which hydrolysis does not proceed are 20, 30, 37, and 45 dynes per cm., respectively (40). This is also the same order for area per molecule in their surface pressure-area curves, indicating that enzymic hydrolysis of lecithin monolayers is influenced by the unsaturation of the fatty acyl chains and hence the intermolecular spacing in monolayers (40). 

Even though 1,2-dilinoleoyl and l-palmitoyl-2-linolenoyl lecithins form more expanded monolayers than egg lecithin, their mixed mono-layers with cholesterol follow the additivity rule (48). This can be explained as follows. At low surface pressures, these lecithins have greater intermolecular spacing and hence form intermolecular cavities of smaller height which cannot accommodate cholesterol molecules (Figure 4e). At high surface pressure, the linoleoyl and linolenoyl chains, as opposed to oleoyl chains, do not form cavities in the monolayer (Figure lOi). 

Enzymic hydrolysis of lecithin monolayers is strikingly influenced by the degree of unsaturation of fatty acyl chains and hence by the intermolecular spacing in monolayers. 

Following from formula (4.54), the transfer of energy on excitation of molecules has a noticeable probability even in the case where the impact parameter is much greater than their size d. Since the intermolecular spacings in a condensed medium are of order of d, a charged particle interacts with many of its molecules. The polarization of these molecules weakens the field of the particle, which, in its turn, weakens the interaction of the particle with the molecules located far from the track. This results in that the actual ionization losses are smaller than the value we would get by simply summing the losses in collisions with individual molecules given by formula (5.1). This polarization (density) effect was first pointed out by Swann,205 while the principles of calculation of ionization losses in a dense medium were developed by Fermi.206... 

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