Freed function

Ja is called Ayant function, and is the limit of the Freed function when xn oo ... 

Hwang L-P and Freed J H 1975 Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids J. Chem. Rhys. 63 4017-25... 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

Rostov, K.S. Freed, K.F., Mode coupling theory for calculating the memory functions of flexible chain molecules influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997,106, 771-783... 

The successful of recovery of RNase A functional activity by a heat-induced AR method suggested the possibility of recovering RNase A immunoreactivity as well. The immunoreactivity of native RNase A and RNase A that was incubated at a concentration of 4 mg/mL in 10% neutral buffered formalin for 1 day and then freed of formaldehyde by dialysis against PBS was compared using capture enzyme-linked immunosorbent assay (ELISA). Selected fractions that... 

After excision, the skin should quickly be freed from subcutaneous fat and stored deep frozen at — 20°C to — 30°C in tightly sealed plastic bags. It may then be stored for up to several months without impairing barrier function, provided that repeated thawing and freezing is avoided [77-79],... 

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

An important theoretical development for the outer-sphere relaxation was proposed in the 1970s by Hwang and Freed (138). The authors corrected some earlier mistakes in the treatment of the boundary conditions in the diffusion equation and allowed for the role of intermolecular forces, as reflected in the IS radial distribution function, g(r). Ayant et al. (139) proposed, independently, a very similar model incorporating the effects of molecular interactions. The same group has also dealt with the effects of spin eccentricity or translation-rotation coupling (140). 

We defer the discussion of the effects of (r) until Section VII.C and begin with the special case, referred as a force-free diffusion, with a uniform distribution of electron spins outside the distance of closest approach with respect to the nuclear spin. Under the assumption of the reflecting-wall boundary condition at rjs = d, Hwang and Freed found the closed analytical form of the correlation function for translation diffusion (138) ... 

The second category of methods uses a more general approach, based on fundamental concepts in statistical mechanics of the liquid state. As mentioned above, the Hwang and Freed theory (138) and the work of Ayant et al. (139) allow for the presence of intermolecular forces by including in the formulation the radial distribution function, g(r), of the nuclear spins with respect to the electron spins. The radial distribution function is related to the effective interaction potential, V(r), or the potential of mean force, W(r), between the spin-carrying particles through the relation (138,139) ... 

Figure 10. LCT configurational entropy ScT as a function of the reduced temperature 5T = (T — To)/To for low and high molar mass F-F and F-S polymer fluids at constant pressure of P = 1 atm (0.101325 MPa). The product ScT is normalized by the thermal energy k To at the ideal glass transition temperature To- (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005 American Chemical Society.)...

Figure 22. The configurational entropy Sc per lattice site as calculated from the LCT for a constant pressure, high molar mass (M = 40001) F-S polymer melt as a function of the reduced temperature ST = (T — To)/Tq, defined relative to the ideal glass transition temperature To at which Sc extrapolates to zero. The specific entropy is normalized by its maximum value i = Sc T = Ta), as in Fig. 6. Solid and dashed curves refer to pressures of F = 1 atm (0.101325 MPa) and P = 240 atm (24.3 MPa), respectively. The characteristic temperatures of glass formation, the ideal glass transition temperature To, the glass transition temperature Tg, the crossover temperature Tj, and the Arrhenius temperature Ta are indicated in the figure. The inset presents the LCT estimates for the size z = 1/of the CRR in the same system as a function of the reduced temperature 5Ta = T — TaI/Ta. Solid and dashed curves in the inset correspond to pressures of P = 1 atm (0.101325 MPa) and F = 240 atm (24.3 MPa), respectively. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005, American Chemical Society.)...

Many biological cells contain degradative enzymes (proteases) that catalyze the hydrolysis of peptide linkages. In the intact cell, functional proteins are protected from these destructive enzymes because the enzymes are stored in cell organelles (lysosomes, etc.) and released only when needed. The proteases are freed upon cell disruption and immediately begin to catalyze the degradation of protein material. This detrimental action can be slowed by the addition of specific protease inhibitors such as phenylmethyl-sulfonyl fluoride or certain bioactive peptides. These inhibitors are to be used with extreme caution because they are potentially toxic. 

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