Molecular area equivalent

The measured mass can, in principle, be converted into equivalent mono-layers based on the molecular weight (Mw) of the species in question and the projected molecular area, Ma e.g., for THF, Mw = 72 amu and Ma = 20-40 X 10 16 cm2/molecule, which yields a value of ca. 0.06-0.03 pgTHF per monolayer. Since neither the molecular orientation nor the actual surface area of the specimen are known, due to the rough character of gold films deposited on cold substrates, masses will be given in terms of pg/cm2. 

The critical insertion pressure of the functional signal peptides is 38 dyn/cm, while the estimated equivalent pressure of biological membranes is only 30 dyn/cm. The difference between these values, 8 dyn/cm, can be multiplied by the peptide s assumed molecular area to yield an estimate of the work that can be done by the peptide on insertion. 

More than one hydrogen bond can be formed at once. For example, the adduct between 4,6-dimethyl-pyrimidin-2-one and urea derives its stability from two, intermolecular, non-equivalent N-H- -0(=C) bridges [26, 27], and the physical properties of usnic acid are strongly affected by its three intramolecular hydrogen bridges located in three different molecular areas and having different strengths [28, 29]. 

Based on the available data, it can be stated that a fluorosurfactant film at a water-C02 microemulsion interface appears to be less densely packed than the equivalent hydrocarbon surfactant in water-in-oil phases. The value of 110 A represents approximately twice (xl.87) the physical cross section of two fluorocarbon chains (56 A [52]). For n-alkyl sulfosuccinates the equivalent factor is around 1.55X a close-packed chain cross section [44]. The origin of this may be the finite, although small, solubility of water in CO2, which is not the case in water-oil systems. This comparison of molecular areas is valid only for strongly adsorbed surfactants, i.e., a negligible amount of free monomer in the bulk phases. For the CO2 systems, if there were to be a significant loss of surfactant from the interface, then the effective w value would increase because it would become [D20]/([surfactant],oBi - [surfactant]free) [58]. The upshot would be to reduce the gradient of the... 

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

Polyester plasticizers give the best performance in this area, with performance increasing with molecular weight. Additionally, branched esters have somewhat higher volatUities than their linear equivalents. 

Laminar Flow Normally, laminar flow occurs in closed ducts when Nrc < 2100 (based on equivalent diameter = 4 X free area -i-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundaiy conditions and geometrical configurations. However, true laminar-flow heat transfer veiy rarely occurs. Natural-convecdion effects are almost always present, so that the assumption that molecular conduction alone occurs is not vahd. Therefore, empirically derived equations are most rehable. 

Molecular radius, R was estimated as the radius of equivalent circle to the projection area of the right configuration in Fig. 1. 

GPC analyses were performed with a Waters Model 244 chromatograph using Microstyragel columns. Both differential refractive index and UV (254 nm) detectors were used. THF was the eluant with a flow rate of 2 ml min-1. A benzene internal standard was employed to correct for flow variations and for normalization of the integrated peak areas. The column set was calibrated using nearly monodispersed polystyrene standards and all molecular data are reported as polystyrene-equivalent molecular weights. 

An extraordinary opportunity to manipulate molecular orientation is possible in a monolayer through variation of the surface area (the two-dimensional equivalent of volume, which is symbohzed as A and has units of square angstroms per molecule). The properties most commonly related to surface area are surface pressure it, and surface tension y, both having units of dynes per centimeter. We describe methods for studying the relation of these and other surface properties in the next section, where we also more fully define their meaning. 

---