Bimodal dependence

In detailed studies examining the influence of the volume fraction of the organic modifier, i] , on A Hearn and Grego have shown (/7n-/7c, 30,44, 54a) for a large variety of peptides, polypeptides, and proteins that bimodal dependencies exist between and log A over the full 0 < 1 range for... 

The results just described are not. universal. In particular, the occurrence of transient bimodality depends on the size of the system, on its intrinsic parameters (Uo> ry 6, 6 ), and on the initial conditions. Generally speaking, for very large systems and for fixed parameters and initial conditions bimodality is bound to disappear, but the dependence of this trend on size is a weak one. Denoting by At the time interval of bimodality, one finds that... 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Using both condensation-cured and addition-cured model systems, it has been shown that the modulus depends on the molecular weight of the polymer and that the modulus at mpture increases with increased junction functionahty (259). However, if a bimodal distribution of chain lengths is employed, an anomalously high modulus at high extensions is observed. Finite extensibihty of the short chains has been proposed as the origin of this upturn in the stress—strain curve. 

The mode of distribution is simply the value of the most frequent size present. A distribution exhibiting a single maximum is referred to as a unimodal distribution. When two or more maxima are present, the distribution is caUed bimodal, trimodal, and so on. The mode representing a particle population may have different values depending on whether the measurement is carried out on the basis of particle length, surface area, mass, or volume, or whether the data are represented ia terms of the diameter or log (diameter). 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

What is clear from all these experiments is that DA can have a bimodal effect depending on how much is applied or released, and which receptors are involved. Excitation is more common at low concentrations and inhibition at higher ones. What happens in vivo is not clear but in vivo voltammetry certainly suggests that the extracellular concentration of DA can be very high and this would favour the more commonly observed inhibition. 

A solution to this problem (Hansen and Ottino, 1996a) reveals that the cluster size distribution is bimodal, as expected, with c(x,t) for large x dependent upon the initial conditions (Fig. 35a). The distribution thus does not approach a self-similar form and the scaling results just given are not valid for this problem. This is a result of the non-homogeneous relative rate of breakup. 

Molecular weights of polysilane polymers depend upon the exact method of synthesis, as well as the purity of the dichlorosilane starting materials. Bimodal molecular weight distributions are commonly reported, as shown in Figure 1, but under some conditions... 

Slomianka L, Rungby J. West Ml, et al. 1989. Dose-dependent bimodal effect of low-level lead exposure on the developing hippocampal region of the rat A volumetric study. Neurotoxicology 10 177-190. 

Figure 7 Typical dependence of nominal stress against elongation for two unimodal networks having either all short chains or all long chains, and a bimodal network having some of both.

Equi-biaxial extension results have been obtained by inflating sheets of unimodal and bimodal networks of PDMS [114,115]. Upturns in the modulus were found to occur at high biaxial extensions, as expected. Also of interest, however, are pronounced maxima preceding the upturns. Such dependences represent a challenging feature to be explained by molecular theories addressed to bimodal elastomeric networks in general. 

In contrast, the hydrodynamic radius distribution recorded for aqueous solutions of copolymers with a low grafting density is bimodal, with a contribution from small entities of = 5-30 nm, assigned to single polymer chains, and a contribution from larger particles of = 80 = 150 nm (Fig. 24b, c). The relative importance of the two populations depends on copolymer concentration the relative amount of the larger particles increases with increasing copolymer concentration. 

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