Subcritical clusters

The supersatiiration e = 8 i(ctj) is tlie mean value of hip, which reflects the presence of other subcritical clusters in the system. 

By using the classical theory of ion induced nucleation to describe the growth of radon daughters from the free activity mode to the nucleation mode, we loose information about the size of the subcritical clusters. These clusters are all lumped together between the size of a pure H2O ion cluster at 75% r.h. and the size of the critical H2O-H2SO4 cluster. The model only does keep track of the growth by condensation of the radon daughters once they arrived in the nucleation mode. 

The behavior of the stable aerosol is linked to the subcritical particle size range in several ways (1) Stable particles originate from the subcritical size range by nucleation. (2) The growth of stable particles takes place primarily by condensation of the monomer, but also by the scavenging of subcritical clusters. (3) Monomer molecules evaporating from the stable aerosol may return to the total monomer pool. 

Figure 1. Principle of the determination of short-lived cluster redox potential by kinetics methods. The reference electron donor, S of a given potential and the metal atoms are generated by a single puke. During cluster coalescence, the redox potential of the couple E°(M -Mn) progressively increases, so that an effective transfer is observed after a critical time when the cluster potential becomes higher than that of the reference, constituting a threshold. Repeatedly, a new adsorption of excess cations, M, onto the reduced cluster, (n xkch (dlows another electron transfer from S with incrementation of nuclearity. The subcritical clusters Mn(n

The cluster free energy, as a function of number of molecules i within the cluster, is shown for the typical case of ion-induced nucleation in Figure 11.14. The free-energy curves are in fact consistent with the kinetic point of view given above. Thus, for an appropriate value of the supersaturation, the free-energy curve shows a local minimum and a maximum for the case of ion-induced nucleation, corresponding, respectively, to the stable subcritical cluster and the unstable critical cluster. The local minimum disappears for the case of homogeneous nucleation. 

Pulse radiolysis studies of the reactivity of 25 nm Agl particles with e3, in the presence of alcohol have shown that first the semiconductor spectrum at 360 nm is bleached, then silver atoms and clusters at 450-600 nm are formed.The electron transfer between the couple MV /MV and Ag clusters formed on an AgCl crystallite was studied by pulse radiolysis. The coalescence of Ag atoms at the AgCl surface is slow so that, as in the presence of CN, an electron transfer from subcritical clusters to precedes the... 

While supercritical clusters ( > 6 1) (Table 5) accept electrons from MV+" with a progressive increase of their nuclearity (Eqs. 32-34), the subcritical clusters undergo a progressive oxidation by by means of the reactions depicted in... 

When silver or gold atoms are generated from Ag CN)2 or Au (CN)2 in the presence of the methylviologen redox couple MV /MV, oxidation of the smallest clusters is also observed, because coalescence in cyanide solutions is slow (Fig. 4) [54,66]. While supercritical silver clusters ( > 6 1) (Table 3) accept electrons from MV with a progressive increase of their nuclearity, the subcritical clusters undergo a progressive oxidation by (Fig. 5). Actually, the reduced ions MV so produced act as an... 

As E is decreased one observes a change from the unimodal distribution for subcritical clusters to a bimodal form indicating growth of supercritical clusters. Because the system is adiabatic, the biomodal distributions also represent stationary states in which there are maximum supercritical cluster sizes, which, if exceeded, result in destruction of that supercritical cluster size new bonds formed in the system increase the cluster kinetic energy and decrease the pressure of the monomer gas. In the future it would be desirable to extract from the molecular-dynamics calculation accurate values for the free energy of formation of clusters. Such calculations would resolve the differences between the B - D theory and the Lothe-Pound theory. In the future, molecular-dynamics calculations should make possible development of correct mesoscopic and microscopic theories of homogeneous and even heterogeneous nucleation. 

Measurements results from the eicperiments in which only water separated the subcritical clusters of fuel rods are presented in Table I. Whenever neutron poison plates were positioned in the water gap between the fuel clusters,... 

Benchmark Calculations for Subcritical Clusters of 2.35 wt% Enriched UO2 Rods in Water with Fixed Neutron Poisons, B. M. Durst, S. R. Bierman, E. D. Clayton (BNWL)... 

Briefly, the experiments coinsisted of measuring the critical separation distance between three subcritical clusters ol 2.3S wt% 11 enriched UC>2 rods in water. The experiments were of two basic types (a).those in which only water separated the fuel clusters, and (b) those in which selected neutron-absorbing materials were positioned m e water between the fuel clusters. 

S. R. bierman, E D. CLAYTON, and B. M. DURST, Critical Separation Between Subcritical Clusters of 2.35 yrt% U-235 Enriched UOa Rods in Water with Fixed Neutron I>oisons, PNL-2438, Pacific Northwest Labs. (Oct. 1977). 

CRITICAL SEPARATION BETWEEN SUBCRITICAL CLUSTERS OF FUEL RODS IMMERSED IN WATER... 

CRITICAL SEPARATION BETWEEN SUBCRITICAL CLUSTERS OF FUEL RODS IMMERSED IN WATER WITH NON-HYDROGENEOUS REaECTOR WALLS ON EITHER SI DE OF FUEL CLUSTER ARRAY... 

S. R. BIERMAN. B. M. DURST, and E. D. CLAYTON. Criticality Experiments with Subcritical Clusters of 235 wt% and 4.2% U Enriched UO Rods in Water with Uranium or Lead Reflecting Walls. NUREG/CR-0796 (Apr. 1979). 

The objective of this paper is to report on calculations of the benchmark critical experiments regarding the critical separation between subcritical clusters of <2.35 wt% U-enriched UOj rods in water with and without flxed neutron absorbers These calculations will be used for validating a 123-nne-enet oUp cross-section library for analysis for fuel storage pools. 

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