Debye

Summary

The debye (symbol: D) (dɛˈbaɪ; dəˈbɛiə) is a CGS unit (a non-SI metric unit) of electric dipole moment named in honour of the physicist Peter J. W. Debye. It is defined as e-18 statcoulomb-centimeters. Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb (generally called e.s.u. (electrostatic unit) in older scientific literature), which were separated by 1 ångström. This gave a convenient unit for molecular dipole moments. :{| |- |height=30|1 D ||= 10−18 statC·cm |- |height=30| |= 10−18 cm5/2⋅g1/2⋅s−1 |- |height=30| |= 10−10 statC·Å |- |height=30| |≘ 1/{{val|299,792,458}} C·m |- |height=30| |≈ 3.33564e-30C·m |- |height=30| |≈ 0.3934303e·a0 |- |height=30| |≈ 0.2081943e⋅Å |- |height=30| |≈ 0.02081943e·nm |- |} Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric hom

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The partial molar volume, .hivin.V, and the partial sp. vol., .hivin.n, were estd. for more than 25 polyelectrolyte structures. The materials investigated by d. measurements in highly dild. aq. solns. (c < 10-2 monomol/L) included both synthetic polyelectrolytes and chem. modified natural polymers. Through a detailed anal., related to the chem. structure and macromol. parameters, a linear dependence between the copolymer compn. and the partial vols. could be identified for diallyldimethylammonium chloride/acrylamide copolymers. Additivity could also be shown for sodium cellulose sulfate having various degrees of substitution. For a homologous series of poly(vinylbenzyltrialkylammonium chloride)s, a linear correlation between the molar mass of the monomer unit and the partial molar volume was obtained. No influence of the d.p. was obsd. as long as the contour length exceeds the Debye length. The exptl. results were used to evaluate the general applicability of the additivity schemes of Durchschlag and Zipper, as well as Gianni and Lepori, to polyelectrolytes. Agreement between exptl. and calcd. partial vols. strongly depends on the chem. structures. In the case of the synthetic polycations, the deviations are in a similar range for both models though somewhat smaller for the Gianni/Lepori model. The use of the Durchschlag/Zipper model yields much better agreement for the anionic biopolymers with deviations generally less than 3%. The tendency of the empirical models is correct; however, the precision may be improved by regressing of parameters from the exptl. results. The new exptl. data may also be useful in polyelectrolyte characterization. [on SciFinder (R)]

1999

Following the original idea of Debye, we define and extract a gauge-invariant screening mass from the complex static in-medium heavy-quark potential V-Q (Q) over bar, recently obtained from lattice QCD. To this end we derive a formula using concepts from both effective-and classical field theories that faithfully reproduces both the screened real-and the imaginary part of the lattice potential with a single temperature dependent fit parameter m(D)(T). Using values of the real part of V-Q (Q) over bar in a gluonic medium, we obtain Debye masses compatible with HTL perturbation theory. (C) 2015 The Authors. Published by Elsevier B.V.

Elsevier2016

A general description of the electrolytic cond. behavior of highly charged strong polyelectrolytes in dil. and semidilute aq. solns. is presented. For the first time this model considers the effects of the molar mass, charge d. (for charge distances less than the Bjerrum length), polyelectrolyte concn., and the ionic strength adjusted by both the polyelectrolyte concn. (cp in monomol L-1) and added simple salt concn. (cs in mol L-1). Above the overlap concn. (c*) the molar mass influence is weak; below c* the equiv. cond. (L) increases strongly when cp decreases (cp > cs). The following relations were found: Lmax .apprx. cs-1/5 and Lmax .apprx. M-2/5 (M is molar mass). The cond. behavior can be qual. explained in terms of Manning's theory with an addnl. change of the interaction parameter fc. An empirical dependence of fc on the ratio of the Debye length to the contour length (lD/L) was found. Three concn. regimes differing in the polyion-counterion interaction were identified; these are characterized by the conditions: (lD/L < 4p)-1/2, (4p)-1/2 < lD/L < 1, and lD/L > 1, resp. The model describes polyelectrolyte solns. characterized by arbitrary (including zero) salt concn. [on SciFinder (R)]

1999