Cooper condensation

There could also be a more directly physical (as opposed to chemical) origin. Frohlich " showed in 1968 that an assembly of randomly oscillating similar dipoles could be driven to operate in cooperatively condensed mode if the input power exceeded a certain minimum value. This and a series of stimulating subsequent papers opened a new avenue of cellular studies. " ... 

In the higher pressure sub-region, which may be extended to relative pressure up to 01 to 0-2, the enhancement of the interaction energy and of the enthalpy of adsorption is relatively small, and the increased adsorption is now the result of a cooperative effect. The nature of this secondary process may be appreciated from the simplified model of a slit in Fig. 4.33. Once a monolayer has been formed on the walls, then if molecules (1) and (2) happen to condense opposite one another, the probability that (3) will condense is increased. The increased residence time of (1), (2) and (3) will promote the condensation of (4) and of still further molecules. Because of the cooperative nature of the mechanism, the separate stages occur in such rapid succession that in effect they constitute a single process. The model is necessarily very crude and the details for any particular pore will depend on the pore geometry. 

In general, therefore, there are three processes, prior to the kind of capillary condensation associated with the hysteresis loop of a Type IV isotherm, which may occur in a porous body containing micropores along with mesoporesia primary process taking place in very narrow micropores a secondary, cooperative process, taking place in wider micropores, succeeded by a tertiary process governed by a modified Kelvin equation. 

Fig. 5. Protein folding. The unfolded polypeptide chain coUapses and assembles to form simple stmctural motifs such as -sheets and a-hehces by nucleation-condensation mechanisms involving the formation of hydrogen bonds and van der Waal s interactions. Small proteins (eg, chymotrypsin inhibitor 2) attain their final (tertiary) stmcture in this way. Larger proteins and multiple protein assembhes aggregate by recognition and docking of multiple domains (eg, -barrels, a-helix bundles), often displaying positive cooperativity. Many noncovalent interactions, including hydrogen bonding, van der Waal s and electrostatic interactions, and the hydrophobic effect are exploited to create the final, compact protein assembly. Further stmctural...

G. D. Cooper and A. YjCiXPSmi2cn.,A.ddition and Condensation Polymerisation Processes, Pidvances in Chemistry Series No. 91, American Chemical Society, Washiagton, D.C., 1969, p. 660. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Now — L is the Landau-Ginzburg free energy, where m2 = a(T — Tc) near the critical temperature, is a macroscopic many-particle wave function, introduced by Bardeen-Cooper-Schrieffer, according to which an attractive force between electrons is mediated by bosonic electron pairs. At low temperature these fall into the same quantum state (Bose-Einstein condensation), and because of this, a many-particle wave function (f> may be used to describe the macroscopic system. At T > Tc, m2 > 0 and the minimum free energy is at = 0. However, when T [Pg.173]

One of the most amazing phenomena in quantum many-particle systems is the formation of quantum condensates. Of particular interest are strongly coupled fermion systems where bound states arise. In the low-density limit, where even-number fermionic bound states can be considered as bosons, Bose-Einstein condensation is expected to occur at low temperatures. The solution of Eq. (6) with = 2/j, gives the onset of pairing, the solution of Eq. (7) with EinP = 4/i the onset of quartetting in (symmetric) nuclear matter. At present, condensates are investigated in systems where the cross-over from Bardeen-Cooper-Schrieffer (BCS) pairing to Bose-Einstein condensation (BEC) can be observed, see [11,12], In these papers, a two-particle state is treated in an uncorrelated medium. Some attempts have been made to include the interaction between correlated states, see [7,13]. 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

Like there always exists a vapor under the water, there are excitations on the ground of any condensate. They appear due to quantum and thermal fluctuations. In classical systems and also at not too small temperatures in quantum systems, quantum fluctuations are suppressed compared to thermal fluctuations. Excitations are produced and dissolved with the time passage, although the mean number of them is fixed at given temperature. Pairing fluctuations are associated with formation and breaking of excitations of a particular type, Cooper pairs out of the condensate. Fluctuation theory of phase transitions is a well developed field. In particular, ten thousands of papers in condensed matter physics are devoted to the study of pairing fluctuations. At this instant we refer to an excellent review of Larkin and Varlamov [15]. 

For nonvanishing A in Eq. (1) the color symmetry is broken. Two of the three quark color degrees of freedom are coupled to bosonic Cooper pairs in the color antitriplet state which can form a Bose condensate.One can combine the chemical potentials Hu, Hd of u and d quarks by introducing Hq = (hu + Hd)/2 and hi = (hu — Hd)/% as the Lagrange multipliers related to, respectively, the quark number density nq and the isospin asymmetry n/. In thermal equilib-... 

Boring, A.M. and Smith, J.L. (2000) Plutonium condensed-matter Physics. In Challenges in Plutonium Science, ed. Cooper, N.C. (Los Alamos Science, Los Alamos, NM, USA), Vols. I—II Issue 26, p. 90. 

As a corollary to the cases above, the aldehyde may also contain a proximal center of asymmetry. In these cases the resident chirality in both the enolate and the aldehyde can influence the generation of new asymmetry in either a mutually cooperative (consonant) or an antagonistic (dissonant) fashion. The consonant or dissonant diastere oface selection imparted to both condensation partners has been referred to as double stereodifferentiation (83,109). This issue becomes important in the lasalocid A aldol bond construction illustrated in eq. [93]. This pivotal aldol condensation has been examined in detail... 

Fuel cell operation entails (1) coupled proton migration and water fluxes in the PEM, (2) circulation and electrochemical conversion of electrons, protons, reactant gases, and water in CLs, and (3) gaseous diffusion and water exchange via vaporization/condensation in pores and channels of CLs, GDLs, and EEs. All components of an operating cell have to cooperate well in order to optimize the highly nonlinear interplay of these processes. It can be estimated that this optimization involves several 10s of parameters. 

While there are several books that deal with the subject matter of this volume, the only one that develops the statistical mechanical approach is T. L. Hill s monograph (1985), which includes equilibrium as well as nonequilibrium aspects of cooperativity. Its style is quite condensed, formal, and not always easy to read. The emphasis is on the effect of cooperativity on the form of the PF and on the derived binding isotherm (BI). Less attention is paid to the sources of cooperativity and to the mechanism of communication between ligands, which is the main subject of the present volume. 

Mg (but not Na" ") results in a structure that is equivalent to the 30-nm compact fiber in the extent of condensation [49]. Finally, the independent and critical function of core histone N-termini in chromatin condensation was demonstrated by showing that nucleosomal filaments reconstituted from core histones lacking their N-terminal domains are unable to condense into folded structures upon an increase of Mg " ", despite the presence of properly bound histone H5 ([50,51], see also Ref. [52] for the discussion of the special role of H3 and H4 tails). Thus, the presence of HI is not a sine-qua-non condition for salt-induced chromatin folding, which can proceed in Hi s absence and is an intrinsic property of filaments consisting of spaced core particles. A key question is how many of the features of the native 30-nm compact fiber are due to the presence of histone HI From the available data it seems that HI may influence the intrinsic folding pathway of the chromatin filament by stabilizing a single ordered conformation. This property can have much to do with the cooperativity of HI interactions within chromatin but also with the way HI is bound to the nucleosome and with the efifect it exerts on the path of linker DNA. 

Bis(dichloroboryl)benzene (6) is an important starting material which lends itself to facile derivatization. As shown by Piers, it cleanly reacts with bis(penta-fluorophenyl)zinc to afford the corresponding bidentate Lewis acid 13 (Scheme 7) The molecular structure of diborane 13 has been determined and is shown in Fig. 1. In this structure, the vicinal boron atoms are held at 3.26 A and from one another and seem to be ideally positioned to cooperatively interact with monoatomic anions. The fully fluorinated version of this bidentate Lewis acid has also been prepared. Original efforts focused on the use of 1,2-bis(dichloroboryl)tetrafluorobenzene 14 as a starting material (Scheme 8). This compound could be observed in the early stage of the reaction of trimeric perfluoro-o-phenylenemercury (4) with boron trichloride, but was found to be unstable toward condensation into 9,10-dichloro-9,10-dihydro-9,10-diboraoctafluoroanthracene 15. The successful synthesis of the fully fluorinated... 

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