Doolittle relationship

The WLF relationship can be derived from the Doolittle relationship that links the mobility M to the free volume fraction ... 

Loutfy and coworkers [29, 30] assumed a different mechanism of interaction between the molecular rotor molecule and the surrounding solvent. The basic assumption was a proportionality of the diffusion constant D of the rotor in a solvent and the rotational reorientation rate kOI. Deviations from the Debye-Stokes-Einstein hydrodynamic model were observed, and Loutfy and Arnold [29] found that the reorientation rate followed a behavior analogous to the Gierer-Wirtz model [31]. The Gierer-Wirtz model considers molecular free volume and leads to a power-law relationship between the reorientation rate and viscosity. The molecular free volume can be envisioned as the void space between the packed solvent molecules, and Doolittle found an empirical relationship between free volume and viscosity [32] (6),... 

The importance of free volume effects in diffusional processes at a molecular level should be further emphasized. An empirical relationship between viscosity and free volume was proposed by Doolittle ... 

The three most important factors in the equation are the viscosity and the thermodynamic parameters G and Gm- The viscosity can be approximated between the liquidus temperature, Tuq, and the liquid-+glass transition temperature, Tg, by a Doolittle expression involving the relative free volume (Ramachandrarao et al. 1977) while G can be calculated using the relationship... 

Doolittle DJ, Muller G, Scribner HE. 1987. Relationship between hepatotoxicity and induction of replicative DMA synthesis following single or multiple doses of carbon tetrachloride. J Toxicol Environ Health 22 63-78. 

Keeling PJ, Doolittle WF (1997) Evidence that eukaryotic triose-phosphate isomerase is of a-proteobacterial origin. Proc Natl Acad Sci USA 94 1270-1275 Kollman JM, Doolittle RF (2000) Determining the relative rates of change for prokaryotic and eukaryotic proteins with anciently duplicated paralogs. J Mol Evol 51 173-181 Kumar S, Rzhetsky A (1996) Evolutionary relationships of eukaryotic kingdoms. J Mol Evol 42 183-193... 

An alternative explanation of the VFT model (28) is based on the free volume concept introduced by Fox and Floury [66-68] to describe the relaxation kinetics of polystyrene. The main idea behind this approach is that the probability of movement of a polymer molecule segment is related to the free volume availability in a system. Later, Doolittle [69] and Turnbull and Cohen [70] applied the concept of free volume to a wider class of disordered solids. They suggested a similar relationship... 

Investigating the viscosity of a homological series of liquid normal paraffins, Doolittle [84] pointed out that the direct relationship between viscosity ( resistance to flow ) and free volume ( relative volume of molecules per unit free space ) is an intuitive hypothesis and the experimental dependence is described better by a logarithmic equation... 

As pointed out by Doolittle, the relationship between the viscosity of liquids and their free volume remained for a long time only an intuitive hypothesis though it described quite well numerous experimental results. A theoretical approach to the solution of the problem of the relationship between the viscosity of liquid and its free volume was generalized for the first time by Eyring [85] in terms of the absolute reaction rates theory. The formulas obtained by Eyring pointed to a qualitative relationship between viscosity and the ratio of the volume occupied by liquid molecules C to the volume occupied by holes through which molecules jump to the neighboring position ... 

It increases from zero for T > Tg to 0.8 for T < 7g - 10 K. Equation (42) provides a simple relationship between AH and p in the interpretation of the transition of the relaxation time from a Doolittle-WLF dependence to an Arrhenius form near Te as mentioned in Fig. 7. 

Doolittle WF Phylogenetic classification and the universal tree. Science 1999 284 2124-2128. Bruns TD, Vilgalys R, Barns SM, Gonzalez D, Hibbett DS, Lane DJ, Simon L, Stickel S, Szaro TM, Weisbuig WG, Sogin ML Evolutionary relationships within the fungi Analyses of nuclear small subunit rRNA sequences. Mol Phylogenet Evol 1992 1 231-241. 

Batchinski (1913), and more recently Doolittle and Doolittle (1957), developed an empirical relationship between the viscosity and the free volume, from which the relaxation time Ty can be extracted ... 

It is not only DNA that seems to have been shared by organisms there is good reason to believe that mitochondria (the energy generators of cells) and chloro-plasts (the sites of photosynthesis in plant cells) may once have been prokaryotes that were ingested by, or entered into a symbiotic relationship with, other prokaryotes (Doolittle 1998). 

These observations suggest a lateral transfer of cellulose synthase from cyanobacteria to D. discoideum. However, while the primary and secondary endo-symbiotic events that led to the evolution of plastids in plants and algae provide a clear mechanism for the transfer of a cyanobacterial cellulose synthase to photosynthetic organisms, such a mechanism is lacking for D. discoideum. Cyanobacterial genes are known to exist in eukaryotes which have secondarily lost plastids. However, there is no evidence for the existence of an endosymbiotic relationship between ancestors of D. discoideum and a cyanobacterium. Therefore, if a lateral transfer occurred, it was likely xenologous, possibly via a food ratchet mechanism (Doolittle 1998). 

The following relationship between viscosity of a polymer melt and its free volume can be written on the lines of Doolittle s equation [80] as... 

The free volume theories state that the glass transition is characterized by an iso-free volume state, i.e. they consider that the glass temperature is the temperature at which the polymers have a certain universal free volume. The starting point of the theory is that the internal mobility of the system expressed as viscosity is related to the fractional free volume. This empirical relationship is referred to as the Doolittle equation. It is a consequence of the universal William-Landel-Ferry (WLF) equation and the Doolittle equation that the glass transition is indeed an iso-free volume state. The WLF equation, expressed in general terms, is ... 

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