Shape transition

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

Fig. IV-19. Fluorescence micrographs showing the shape transitions in monolayers of dimyristoylphosphatidylcholine (DMPC) (84%) and dihydrocholesterol (15%) and a lipid containing the dye, Texas Red. (From Ref. 228.)...

The effects of electric fields on monolayer domains graphically illustrates the repulsion between neighboring domains [236,237]. A model by Stone and McConnell for the hydrodynamic coupling between the monolayer and the subphase produces predictions of the rate of shape transitions [115,238]. 

An essential component of cell membranes are the lipids, lecithins, or phosphatidylcholines (PC). The typical ir-a behavior shown in Fig. XV-6 is similar to that for the simple fatty-acid monolayers (see Fig. IV-16) and has been modeled theoretically [36]. Branched hydrocarbons tails tend to expand the mono-layer [38], but generally the phase behavior is described by a fluid-gel transition at the plateau [39] and a semicrystalline phase at low a. As illustrated in Fig. XV-7, the areas of the dense phase may initially be highly branched, but they anneal to a circular shape on recompression [40]. The theoretical evaluation of these shape transitions is discussed in Section IV-4F. 

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Harde H, Katzenellenbogen N and Grischkowsky D 1995 Line-shape transition of collision broadened lines Phys. Rev. Lett. 74 1307-10... 

Medeiros G ef al 1998 Shape transition of germanium nanocrystals on a silicon (001) surface from pyramids to domes Science 279 353... 

A further feature of the spectmm in Figure 9.24 is the sharp spike at the centre of each P-shaped transition. The reason for this is that saturation of the transition has occurred. This was discussed in Section 2.3.5.2 in the context of Lamb dips in microwave and millimetre wave spectroscopy and referred to the situation in which the two energy levels involved, m(lower) and n(upper), are close together. Under these circumstances saturation occurs when... 

The velocity of the air, flowing through the fan, can be as much as 3 to 4 times the velocity across the face of the tube bundle. Also, the air, coming from the circular shape of the fan, must be distributed across the square or rectangular shape of the bundle. The air plenum chamber is intended to make this velocity and shape transition, such that the distribution of air is uniform across the bundle. Common practice is to install the fan in a chamber, such that the distance from the first row of the tube bundle to the fan is about one-half the fan diameter... 

The dramatic dynamics of the flame-shape change shown in Figure 5.3.1, along with its proposed relationship to the flame instability and flame-generated flow, has periodically sparked an interest in its study. Before reviewing this flame-shape transition phenomenon, it will be useful to trace the history of the "tulip" name and distinguish this particular flame shape from the myriad of others with which it is often equated or confused. 

The situation with respect to HCN is rather different, because it is no longer vahd to approximate the internal rotational constant, B, as independent of the angle 0. As discussed by Efstathiou et al. [10], the form of the most recent potential energy surface [48, 49] shows that the separation of the H atom from the CN center of mass decreases by about 30% between the HCN configuration and the T-shaped transition state, giving the optimized bending potential energy... 

H. Noguchi and G. Gompper, Shape transitions of fluid vesicles and red blood cells in capillary flows, Proc. Natl. Acad. Sci. USA 102, 14159 (2005). 

Another idea, which was originally put forward by Ruzicka (1935) and has ever since provided a common basis for many discussions of reactivity in intramolecular reactions, is that the ring-shaped transition state should be affected by a significant fraction of the strain-energy of the ring being formed. The simplest way to express this idea is by use of (62), where the weighting... 

The structure of the molecule is such that it does not allow the attainment of a chair shaped transition state. 

The reaction occurs suprafacially across the allyl unit through a five-membered ring envelope-shaped transition state. The five-membered cychc transition state of [2,3]-sigmatropic rearrangement shows greater conformational flexibility than the six-membered transition state of [3,3]-sigmatropic rearrangements and should therefore be far more susceptible to the effects of stereochemical control by substituents. ... 

The flow and shape transitions for small and intermediate size bubbles and drops are summarized in Fig. 7.13. In pure systems, bubbles and drops circulate freely, with internal velocity decreasing with increasing k. With increasing size they deform to ellipsoids, finally oscillating in shape when Re exceeds a value of order 10. In contaminated systems spherical and nonoscillating ellipsoidal... 

Chang SS, Shih CW, Chen CD, Lai WC, Wang CRC (1999) The shape transition of gold nanorods. Langmuir 15 701-709... 

SHAPES Transition metal Allured, V. S., Kelly, C., and Landis, C. R. ... 

PS-PMMA Mw = 640-150(1.24-69% PMMA-PS PMMA Mv — 110.50% Toluene -f p-tymene (selective for PS) Micellar shape transition as a function of toluene// -cymene mixture composition. SLS Kotaka el al (1978)... 

TMS enol ether has been shown to rearrange with good enantioselectivity, presumably because the boat-shaped transition state is sterically disfavoured. Rearrangement of the enantiomeric starting material has been used as a key step in a total synthesis of (+)-alline.13... 

Petrov, Peter G., Light-Induced Shape Transitions of Giant Vesicles, 6, 335. 

These results demonstrate that a difference of only one neutron causes a considerable change of the nature of the nuclei at A 100 and that the study of the isotopes with odd nucleon numbers can provide insight into the details of the shape transition. The transition in the Y isotopes seems to be even more rapid than in the Sr and Zr chains where the N = 60 isotones still have coexisting shapes and where the shell-model character of the N 58 isotones at high excitation energies has not yet been tested.Further investigations are, however, needed in order to confirm in detail the proposed interpretation of the level schemes of the Y isotopes and to see whether similarly rapid structure changes occur in the Rb and Nb isotopes at N 60. 

Fig. 2 further illustrates the abruptness of the shape transition. The energy ratio approaches the value of 10/3 characteristic of an axially symmetric rotor for Sr or Zr nuclei... 

In terms of the three limiting group symmetries used in the interacting boson model (IBM), the shape transition of Ru or Pd nuclei can be explained as a SU(5) to 0(6) transition [STA82]. The transition of Sr or Zr nuclei is characterized instead as SU(5) to SU(3). 

For Mo nuclei, the shape transition appears to be more complicated than the above and has not yet been adequately described. 

The nuclei show consistently large deformations of B2 = 0.35-0.45. It thus can be inferred that the predicted prolate to oblate shape transition in this mass region BEN84, NAZ85 occurs by a change of y rather than by large variations of 62. 

In summary we have discussed the shape transition associated with the evolution of finite rotational bands to their points of termination. Many such terminating bands are predicted in configurations with 10-12 valence particles (and holes) relative to a 146Gd core. According to the calculations, the very low energy of the terminating states is a prominent... 

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