Dimer model

M. H. Kim, H. Park. Critical behavior of an interacting monomer-dimer model. Phys Rev Lett 73 2579-2582, 1994. 

To complete this overview of chain models, we mention the dimer models, which represent the amphiphiles by just two units attached to each other [153-157]. They have been used to study curved bilayers [153], the kinetics of phase separation between oil and water in the presence of surfactants [155], and some aspects of self-assembled micelles [154,157] (see below). 

Figure 2 Models for the carbon-terminated 3C-SiC(001)c(2x2) surface (a) staggered C=C-dimer model, (b) C2 groups in Si bridge sites. Cf. text.

The dimer model proposed by Wilson [83] was found not to exhibit a nematic phase but smectic A and B phases and so, although semi-realistic features are included, the model is not able to reproduce the behaviour of real dimers such as the a,co-bis(4 -cyanobiphenyl-4-yloxy) [87], which exhibit nematic phases, although liquid crystal dimers exhibiting smectic phases are also known [88]. In these simulations, the GB-GB interaction appears to be too strong and so the system forms a smectic phase in which the GB and LJ units... 

Iki and Hori discussed the crystal structures of the compounds CPnOB and nOPCB in relation to the mesophase behaviour considering the dimer model proposed by Cladis et al. [99] for this kind of molecule in the liquid crystalline phase. 

Gierer, J. Opara, A. E. Enzymic degradation of lignin. Action of peroxidase and laccase on monomeric and dimeric model compounds. Acta Chem. Scand. 1973, 27,... 

Note that in the dimer model the absorption intensity depends on A and p. 

Note that both the delocalized and dimer models can be used to explain temperature dependence of the absorption spectra of R26.Phe-a RCs. This is due to the fact that the interactions [Eq. (2.48b)] among Bchls except for that between B and Ih are small compared with the diagonal element Hamiltonian in Eq. (2.48a). 

We calculate three models (1) the dimer model presented in this work (2) the dimer model employed by Scherer et al. and (3) the delocalized model. Table V lists the calculated results as a function of temperature. The anisotropy values for r(ei,e2) at 295 K are found to be quite different between the dimer and delocalized models. The difference is about 53%. Meanwhile, the differences at other temperatures are within about 13-14%. For r(e2,23), the differences are within 24-28%. Table Valso lists the angle between B and B2 in the special pair of R26.Phe-a RCs as a function of temperature. 

The Anisotropy Between the Transition Dipole Moments of the Chromophores in the Dimer Model... 

To investigate this dendritic effect, a dimeric model compound was synthesized which mimics the tethered relationship of two catalytic units within one branch of the PAMAM dendrimer. All dendritic catalysts were more active in the HKR than the parent complex. Furthermore, the dendritic catalysts also displayed significantly higher activity than the dimeric model compound. The authors proposed that this positive dendritic effect arises from restricted conformation imposed by the dendrimer structure, thereby creating a bigger effective molarity of [Co(salen)] units. Alternatively, the multimeric nature of the dendrimer, may lead to higher order in productive cooperative interactions between the catalytic units. 

C. Emmeluth, M. A. Suhm, and D. Luckhaus, A monomers in dimers model for carboxylic acid dimers. J. Chem. Phys. 118, 2242 2255 (2003). 

Fig. 12.7 lllusrration of the idea of the random an infinite number of possibilities of interdomain dimer" model. For each molecule the orientation orientations in a dimer are shown, of a selected NH vector is indicated only three of... 

In order to assess whether intramolecular cooperativity could occur within the dendrimeric [Co(salen)]catalyst the HKR of racemic l-cyclohexyl-l,2-ethenoxide was studied at low catalyst concentrations (2xl0 " M). Under these conditions the monomeric [Co(salen)] complex showed no conversion at all, while the dendritic [G2]-[Co(salen)]catalyst gave an impressive enantiomeric excess of 98% ee of the epoxide at 50% conversion. Further catalytic studies for the HKR with 1,2-hexen-oxide revealed that the dendritic catalysts are significantly more active than a dimeric model compound. However, the [Gl]-complex represents already the maximum (100%) in relative rate per Go-salen unit, which was lower for higher generations [G2] (66%) and [G3] (45%). 

Table I. Degradation Mechanism of Lignin Dimer Models...

The EXAFS of Mn in photosystem II looks very much like that of a mixed-valence di-/j-oxo-bridged Mn dimer model compound (33,35). In particular, the Mn-Mn distance of 2.7 A in photosystem II is characteristic of a di-/j-oxo-bridged structure. Recent EXAFS data have indicated that a second Mn-Mn distance of 3.3 A may also be present (37-38). Although a clear picture of all of the Mn-Mn distances is not yet available, the EXAFS results are consistent with a structure in which two di-/j-oxo bridged Mn dimers are present in close proximity. 

Adlerol, i.e. l-(3,4-dimethoxyphenyl)-3-hydroxy-2-(2-methoxyphenoxy)propan-l-ol, is a well-established dimeric model compound of lignin and, as such, its oxidation to the ketone-derivative Adlerone, i.e. l-(3,4-dimethoxyphenyl)-3-hydroxy-2-(2-methoxyphen-oxy)propan-l-one, has been taken as a benchmark reaction (Scheme 20) to evaluate the efficiency of several chemo-enzymatic procedures. 

For the present discussion, a number of these conversions are of relevance. Phenolic dimeric model compounds of the 0-1, 0-0-4 and phenyl coumaran type are degraded via Ca-arene cleavage yielding methoxy-... 

Fig. 1.15. The STM images of Si(lOO) surface at different bias, (a) At a bias of -1.6 V, the occupied bond between the two atoms in a dimer, is imaged, (b) At a bias + 1.6 V, the unoccupied dangling bond on each Si atom is imaged. Notice that the resolution in (b) is much sharper than that in (a). Lower, the dimer model with the dangling bonds is schematically shown. (Reproduced from Hamers, 1989a, with permission.)...

From a technological point of view, Si(OOl) is one of the most important surfaces. Most integrated circuits are made on it. In the LEED experiments, a (2X1) diffraction pattern is observed, which indicates a reconstruction to double the periodicity in one direction. Several models have been proposed. A high-resolution STM study by Tromp et al. (1985) shows unambiguously that the dimer model is correct In the bulklike terminated surface, each of the top-layer atoms is bonded to two atoms in the second layer, leaving two dangling bonds on each top-layer atom. 

The carbonate radical has been measured up to 300°C, and the temperature-independent spectrum is known [19]. This independence is kept up to 400°C into supercritical water. Formation and decay behavior were measured precisely [69], and a dimer model for the carbonate radical has been proposed [79]. 

Each WCP dimer model consists of two purine bases (G and A) and two pyrimidine bases (C and T). According to the calculations, the two highest-lying orbitals HOMO and HOMO-1 of each duplex are mainly locahzed on the purine nucleobases, whereas the two occupied MOs following at lower energies, HOMO-2 and HOMO-3, are locahzed on pyrimidine nucleobases. Therefore, the purine-purine electronic coupling provides the dominant contribution to the hole transfer matrix elements, irrespective whether the bases belong to the same or to opposite strands. 

Since the properties of any material are related to its structure, the conformational aspect of these studies cannot be neglected. The emphasis of the latter paper (56) was, however, primarily concerned with the electronic structure of the dimeric model compound, and how this information might be compared to experimental facts. Upon completion of the calculations, it began to appear that the results were seriously flawed. It was... 

The adsorption of diatomic or dimeric molecules on a suitable cold crystalline surface can be quite realistically considered in terms of the dimer model in which dimers are represented by rigid rods which occupy the bonds (and associated terminal sites) of a plane lattice to the exclusion of other dimers. The partition function of a planar lattice of AT sites filled with jV dimers can be calculated exactly.7 Now if a single dimer is removed from the lattice, one is left with two monomers or holes which may separate. The equilibrium correlation between the two monomers, however, is appreciable. As in the case of Ising models, the correlation functions for particular directions of monomer-monomer separation can be expressed exactly in terms of a Toeplitz determinant.8 Although the structure of the basic generating functions is more complex than Eq. (12), the corresponding determinant for one direction has been reduced to an equally simple form.9 One discovers that the correlations decay asymptotically only as 1 /r1/2. 

The dimer species, M2, was described by Huster (21) as a simple dissolved diatomic molecule. Such a species would be very unstable with respect to the ammoniated species, M + and e and may be ruled out by thermochemical data. The expanded metal dimer model of Becker, Lindquist, and Alder, in which two ammoniated metal ions are held together by a pair of electrons in a molecular orbital located principally between the two ions, is just as difficult to reconcile with optical, volumetric, and NMR data as the expanded metal monomer. In order to account for the similar absorption spectra of e, M, M2 (and any other species such as M or M4 that might exist at moderate concentrations of metal), Gold, Jolly, and Pitzer (16) assumed that species such as M and M2 consist of ionic aggregates in which the ammoniated electrons remain essentially unchanged from their state at infinite dilution. 

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