Hartley model

The early Hartley model [2, 3] of a spherical micellar stmcture resulted, in later years, in some considerable debate. The self-consistency (inconsistency) of spherical symmetry witli molecular packing constraints was subsequently noted [4, 5 and 6]. There is now no serious question of tlie tenet tliat unswollen micelles may readily deviate from spherical geometry, and ellipsoidal geometries are now commonly reported. Many micelles are essentially spherical, however, as deduced from many light and neutron scattering studies. Even ellipsoidal objects will appear... 

Haas-Laursen, D. E., Hartley, D. E. and Conway, T. J. (1997). Consistent sampling methods for comparing models to CO2 flask data, /. Geophys. Res. 102, 19059-19071. 

F. Minari and B. Pichaud, Dislocations and Free Surfaces in the Micro-plastic Deformation of F.C.C. Metals , in Dislocation Modelling of Physical Systems", Edrs. M. F. Ashby, R. Bullough, C. S. Hartley, and J. P. Hirth, p. 551, Pergamon Press, New York, USA (1980). 

Figure 1. Flux passing through model septum as a function of partition coefficient at different times (t) after application. Redrawn from Hartley and Graham-Bryce (13).

Arborol Dendrimers. The spherical topology of dendrimers resembles the size and shape of the Hartley model (1936) of a micellar aggregate formed by surfactant molecules (Fig. 11.2 Tomalia et al. 1990). Micellar stmctuies have a dynamic, spherical structure possessing a close-packed, solvent-incompatible core surrounded by an open, solvent-compatible layer. 

Figure 11.2 A comparison of the Hartley micellar model with the structure of an amphiphilic dendrimer.

Although McBain suggested over 80 years ago that soap molecules form micellar structures of lamellar and spherical shape (McBain 1913), most of the subsequent work focused on spherical micelles. The earliest concrete model for spherical micelles is attributed to Hartley (1936), whose picture of a liquidlike hydrocarbon core surrounded by a hydrophilic surface layer formed by the head groups, has been essentially verified by modern techniques, and the Hartley model still dominates our thinking. We present an overview of the structure of the micelle first and then go on to examine the details a little bit more closely. 

Hartley P, Neill D, Hagler M, Kors D, Vogel G. Procedure- and age-dependent hyperactivity in a new animal model of endogenous depression. Neurosci Biobehav Res 1990 14 69-72. 

Hartley s, Kono s, Kifer s, D-Optimal Quantitative Regression models... 

A further reduction of experimental effort may be achieved by the selection of special designs developed, for example, by HARTLEY [1959], BOX and BEHNKEN [1960], WESTLAKE [1965], and others. In these designs the ratio of experiments to the number of coefficients necessary is reduced almost to unity. (This situation is somewhat different from regression analysis or random selection of experiments where, in principle, k experiments or measurements are sufficient to estimate k parameters of a model. In experimental design the optimized number of experiments is derived from statistical consideration to encompass as much variation of the factors as possible.)... 

Soil moderately persistent in soil with t,/2 = 20-100 d (Willis McDowell 1982) t,/2 5-7 months (Hartley Kidd 1987) t,/2 = 50 d from screening model calculations (Jury et al. 1987b) ... 

Matis, J. and Hartley, H., Stochastic compartmental analysis Model and least squares estimation from time series data, Biometrics, Vol. 27, 1971, pp. 77-102. 

Spontaneous models Spontaneous osteoarthritis Dunkin Hartley [36]... 

At this point it is important to note that this equation assumes that the controlling mechanism for heat transfer is conduction. Later, Hartley and Richards(H) developed a diffusion model for the hot surface drying of sheet materials. 

Returning to the Nissan and Hansen model, they use a finite difference numerical analysis model to determine both the temperature profile of a sheet material and the subsequent water removal as it passes over the cylinder. Their experimental results match well with the predicted values. However, their experiments were limited to a cylinder surface temperature of 93.3°C. Accordingly, the maximum vapor pressure of the evaporated water is less than one atmosphere. The diffusion model advanced by Hartley and Richards is in close agreement with experimental work of Dreshfield(12l. However, the boundary conditions are still relatively uncertain since the convective flow region outside the sheet is relatively unknown. Later work by this author studies this convective flow. 

Aromatic acids and aldehydes (e g, vanillic acid/vamlhn) 6 Lignin model compounds (e g, guaiacyl and veratryl glycerol fi-guaiacyl ethers, substituted phenylcoumarans and acetophenone dimers Hartley and Buchan 1979, Villeneuve et al 1982, Pecina et al 1986, Bourbonnais and Paice 1987, Pometto and Crawford 1988 Bourbonnais and Paice 1987... 

FIGURE 51.1. PBPK-PD model schematic of sarin in Hartley guinea pig. This model structure allows for the simulation of experimental studies with dosing hy intravenous or subcutaneous dosing, and inhalation exposure. This model design was after Gearhart et al. (1990) and was adapted to simulate the pharmacokinetics and pharmacodynamics of sarin in the guinea pig. 

A relatively simple spectroscopic model of O3 absorption in the middle ultraviolet has been proposed (Adler-Golden et al., 1982). This model assumes that the internal energy of an O3 molecule adds fully to that of the absorbed ultraviolet photon and that the quantum yield of O ( Eh) varies smoothly from zero at some threshold energy (calculated as being 32900 cm ) to unity 600 cm above this threshold. The model, which is quite successful in rationalizing the observed Hartley band spectrum for vibrationally excited O3, accurately reflects the experimental temperature dependence of the ( Dz) yield at 313 nm and also predicts a dependence of oCdj) ) upon wavelength in the region above 304 nm that is quite similar to that observed in a previous experimental study... 

Models nonlinear in 6 need careful treatment. Direct iteration with Eq. (6.3-10) often fails because of the limited range of the expansions 6). Gauss-Newton iteration schemes with steps adjusted by line search work well [Booth, Box, Muller and Peterson (1958) Hartley (1961, 1964) Box and Kanemasu (1972, 1984) Bard (1974) Bock (1981)] when A e is well-conditioned and 6 unrestricted, but give difficulty otherwise. 

Figure 1. Schematic representation of the Hartley oil drop model [5] for an anionic micelle.

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