The empirical diclectric decay function y ( t ) -= exp -( f / ~~) p may be transformed analytically to give the frequency dependent complex dielectric constant if p is chosen to be 0.50. The resulting dielectric constant and dielectric loss curves are non-symmetrical about the logarithm of the frequency of maximum loss, and are intermediate between the Cole-Cole and Davidson-Cole empirical relations.Using a short extrapolation procedure, good agreement is obtained between the empirical representation and the experimental curves for the a relaxation in polyethyl acrylate. It is suggested that the present representation would have a general application to the a relaxations in other polymers.

Aim The aim of this study is to answer the questions: (1) do small organisms disperse farther than large, or vice versa; and (2) does the observed pattern differ for passive and active dispersers? These questions are central to several themes in biogeography (including microbial biogeography), macroecology, metacommunity ecology and conservation biology.Location The meta-analysis was conducted using published data collected worldwide. MethodsWe collected and analysed 795 data values in the peer-reviewed literature for direct observations of both maximal dispersal distance and mass of the dispersing organisms (e.g. seeds, not trees). Analysed taxa ranged in size from bacteria to whales. We applied macroecology analyses based on null models (using Monte Carlo randomizations) to test patterns relative to specific hypotheses. ResultsCollected dispersal distance and mass data spanned 9 and 21 orders of magnitude, respectively. Active dispersers dispersed significantly farther ( P < 0.001) and were significantly greater in mass ( P < 0.001) than passive dispersers. Overall, size matters: larger active dispersers attained greater maximum observed dispersal distances than smaller active dispersers. In contrast, passive-disperser distances were random with respect to propagule mass, but not uniformly random, in part due to sparse data available for tiny propagules. ConclusionsSize is important to maximal dispersal distance for active dispersers, but not for passive dispersers. Claims that microbes disperse widely cannot be tested by current data based on direct observations of dispersal: indirect approaches will need to be applied. Distance-mass relationships should contribute to a resolution of neutral and niche-based metacommunity theories by helping scale expectations for dispersal limitation. Also, distance-mass relationships should inform analyses of latitudinal species richness and conservation biology topics such as fragmentation, umbrella species and taxonomic homogenization.

The empirical dielectric decay function +(t) = exp -( t / ~~) f i , O< p 9 1 has been transformed analytically and numerically into the frequency dependent complex dielectric permittivity. It is shown that empirical curves give a very satisfactory representation of the dielectric a relaxations observed in polyethyl acrylate, polyvinyl acetate, polyvinyl octanoate, polymethyl acrylate, polypropylene oxide and amorphous polyethylene terephthalate. It is suggested that the present empirical representation is far more satisfactory than existing functions for non-symmetrical loss curves. It is also suggested that the success of the empirical representation may imply that the dipole moment correlation function is a non exponential decay function of time rather than arising from a weighted sum of exponential decay functions. In addition the accuracy of the transformation of transient data into frequency domain data-via the Hamon approximation, is examined for the empirical representation, and it is shown that the transform is accurate for log m0 >0, but significant corrections may have to be applied for / 3 >0.5 and log wz0< 0.

Dielectric relaxation spectroscopy (DRS) and differential scanning calorimetry (DSC) have been used simultaneously as a means of following the isothermal cure of the diglycidyl ether of Bisphenol A with 4,4‘-diaminodicyclohexylmethane in the temperature range 290−353 K. The dielectric permittivity and dielectric loss of the thermosetting mixture have been measured as a function of reaction time over the frequency range 101.2−105 Hz. The evolution of the dielectric properties was studied as the curing temperature was lowered to values close to the solidification of a sample. The kinetics of the cure have also been determined, using calorimetry, for four reaction temperatures over the whole range of conversion up to the point where the system vitrifies and the reaction becomes diffusion-controlled. Correlations between the changes in molecular dynamics and the chemical kinetics occurring during the thermosetting process have been made in some detail, and a theoretical working model has been developed that allows DRS to predict the course of the reaction in the vitrification range. Previous interpretations of dielectric events in this vitrification region, based on experimental kinetic and dielectric results, are reexamined.