Chain area/cross-section

The repulsive contribution, is due to lateral pressure on each chain. In Marcelja s original treatment, this was set equal to the product of the lateral pressure, 7, and the cross-sectional area of the chain. The cross-sectional area was approximated by ... 

Next we recognize that 6 and X always appear as a ratio in our theory. If we argue that the hole and the polymer chain have comparable cross-sectional areas, we can multiply both the numerator and denominator of the X/6 ratio by this cross section and convert it into the ratio V /V, where is the volume of the flow segment of length X. While we know neither of these volumes directly, there are indications that V /V may be on the order of 10-20 for many linear... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Channels in crystals of thiourea [62-56-6] (87) are comparable but, as a consequence of the larger size of the sulfur atom, have larger cross-sectional areas (0.7 nm) and can trap branched-chain, aUcychc, and other molecules of similar dimensions including polychlorinated hydrocarbons. But they do not include the straight-chain hydrocarbons that work so well with urea. 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Tetrakis(cumylphenoxy)phthalocyanine (5) a PC derivative, having liquid—crystalline-like substituents (38—43) was studied because the cross-section area of the substituents is much larger than that of a normal alkyl chain, and therefore, the requirement of minimized free volume in the assembly may be easier to accomplish. 

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

Polyisobutylene and similar copolymers appear to "pack" well (density of 0.917 g/cm ) (86) and have fractional free volumes of 0.026 (vs 0.071 for polydimethylsiloxane). The efficient packing in PIB is attributed to the unoccupied volume in the system being largely at the intermolecular interfaces, and thus a polymer chain surface phenomenon. The thicker cross section of PIB chains results in less surface area per carbon atom. 

The conditions for surfactants to be useful to form Hquid crystals exist when the cross-sectional areas of the polar group and the hydrocarbon chain are similar. This means that double-chain surfactants are eminently suited, and lecithin (qv) is a natural choice. Combiaations of a monochain ionic surfactant with a long-chain carboxyHc acid or alcohol yield lamellar Hquid crystals at low concentrations, but suffer the disadvantage of the alcohol being too soluble ia the oil phase. A combination of long-chain carboxyHc acid plus an amine of equal chain length suffers less from this problem because of extensive ionisa tion of both amphiphiles. 

Vincent analyzed the tensile fracture stress o, of a broad range of polymers as a function of the number of backbone bonds per cross sectional area ( 2) and found a nearly linear relation, o 2, as shown in Fig. 12. 2 is related to via the theory of entanglements for random walk chains as [74]... 

The cross-sectional area per chain in the hexagonal lattice of irradiated PE varies between 20.6 and 22.0 A. It is, thus, always greater than the cross-sectional area in the rotator phase in paraffins (19.5-20.0 A ), but on average somewhat smaller than that in constrained PE fibers above 7, /, (21.4-22.7 A ). An ethylene-propylene diene copolymer with approximately 64%, 32%, and 4% by weight of each component, respectively, was found to contain hexagonal crystals with a cross-sectional area per chain of 20.3 A". 

A gold alloy chain has a density of 15.0 g/cm3. The cross-sectional area of the chain is 3.00 mm3. What length of chain has a mass of 10.00 g ... 

Number-average molecular weight of relatively long chains is Mn = 18,500 g/mol. Key for the networks where short chains had M, (g/mol) A, 1,100 O, 660 0, 220. Curves are labelled with the mol percent of short chains in the network. Area below curves represents the rupture energy per unit initial cross sectional area and per unit initial... 

Table 1. Comparison of hydrophilic polymers with various chain cross-sectional areas in formation of crystalline complexes with cyclodextrins...

According to Eyring (Moore and Eyring, 1938) and Joly (1956), Newtonian flow in a monolayer is the result of a cohesive attraction between surfactant molecules. For every molecule that flows from higher to lower surface pressure in a motion parallel to the canal walls, there is another molecule ready to fill the hole vacated by the first. The mechanism for this cohesive flow is presumably attractive van der Waals interactions between hydrocarbon chains. This model assumes that the average intermolecular separation in a surface-continuous monolayer does not exceed the cross-sectional area of the molecule as defined by the average molecular area A of the film at the surface pressure n in the pressurized compartment of the viscometer. 

For the intepretation of the rheological results, using the elastic floe model, it is necessary to have a model for the flocculated structure. For the present case, flocculation probably takes place by interpenetration of PVA tails under worse than 9- conditions for the chain. A typical floe may be assumed to consist of strings of particles linked together in a more-or-less three-dimensional network. The compactness of the floe (as measured by Cpp) is related to its strength by the number of chains, n, which pass through unit cross sectional area of the floe (29,31). n can be calculated from the total number of bonds per floe (36), i.e. 

The number of chains of length u which cross a certain fibre cross section is determined by the crossing length distribution h(u) defined in Sect. 3.1.1. The tensile stress in a chain passing through a fibre cross section is calculated in Sect. 3.1.2. The force S per unit area in a cross section can be found from... 

Although the cross-sectional areas of the chains in PpPTA and PE are slightly different, 0.204 and 0.183 nm2, respectively, there is a considerable dif-... 

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