A Volume-Conserving Mechanism

A volume-conserving mechanism such as hula-twist (H-T) that requires a concomitant twisting of the double bond and the adjacent single bond to accomphsh the double-bond ds-trans isomerization, different from the usual one-bond rotation mechanism. 

Figure 4.10 cis-Xo-trans isomerization of c/s-C2 in diethyl ether-isopentane (1 1) at 77 K by a volume-conserving mechanism [38]. (Reproduced with permission.)... 

Warshel first postulated the bicycle-pedal (BP) mechanism as a volume-conserving mechanism for photoisomerization.In it, two alternating double bonds rotate concertedly with only the two CH units turning in and out of the plane of the molecule. 

Fletcher s example is of great importance. It is the clearest, simplest treatment of a situation where only one material moves, but moves by two separate mechanisms—a volume-conserving viscous change of shape plus a diffusive mass transfer from higher-compression sites to lower-compression sites. The two mechanisms resemble those operating in situation (1), the elastic permeable host plus mobile fluid Fletcher clearly brings to light the fact that the two movement mechanisms remain distinct even when the same material travels by them both. 

Three different photoisomerization mechanisms of singlet excited polyenes have been proposed (1) one-bond twist, a typical process observed in fluid solutions but also in glassy media,525 553 565 (2) the bicycle-pedal mechanism involving simultaneous rotation about two original double bonds, assumed to occur in a constraining environment,566-568 and (3) a volume-conserving two-bond hula twist 531 569 510 (Scheme 6.7). In some cases, the existence of the last mechanism has been ruled... 

The hula twist mechanism (HT, Fig. 2.3B), first validated with carotenoids, is not consistent with the time-scale of photoisomerization of chromoproteins since CTI of the retinal chromophore, which is inserted deep inside the protein, necessitates a major reorganization of the peptide molecular framework. Therefore, a new volume-conserving mechanism, called bicyclic pedal (BP, Fig. 2.3C), was proposed. In fact, all these mechanisms are still a topic of discussion since chromoprotein photo-intermediates highlighted by recent studies do not confirm this hypothesis. In particular, several photo-products of the retinal Schiff base in the... 

A control volume is a volume specified in transacting the solution to a problem typically involving the transfer of matter across the volume s surface. In the study of thermodynamics it is often referred to as an open system, and is essential to the solution of problems in fluid mechanics. Since the conservation laws of physics are defined for (fixed mass) systems, we need a way to transform these expressions to the domain of the control volume. A system has a fixed mass whereas the mass within a control volume can change with time. 

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

All conservation equations in continuum mechanics can be derived from the general transport theorem. Define a variable F(t) as a volume integral over an arbitrary volume v(t) in an r-space... 

The photoisomerization of all-s-trans-all-trans 1,3,5,7-octatetraene at 4.3 K illustrates the need for a new mechanism to explain the observed behavior [150]. Upon irradiation, all-s-trans-all-trans 1,3,5,7-octatetraene at 4.3 K undergoes conformational change from all-s-trans to 2-s-cis. Based on NEER principle (NonEquilibrium of Excited state Rotamers), that holds good in solution, the above transformation is not expected. NEER postulate and one bond flip mechanism allow only trans to cis conversion rotations of single bonds are prevented as the bond order between the original C C bonds increases in the excited state. However, the above simple photochemical reaction is explainable based on a hula-twist process. The free volume available for the all-s-trans-all-trans 1,3,5,7-octatetraene in the //-octane matrix at 4.3 K is very small and under such conditions, the only volume conserving process that this molecule can undergo is hula-twist at carbon-2. 

Several years ago, we found that the isomerization of n-butylammonium ( Z,Z)-muconate produces the corresponding EE-isomer in a high yield in the crystalline state under photoirradiation [41]. This solid-state photoisomerization was re e e< t0 he a one-way reaction and no EZ-isomer was formed during the reaction, unsaturated compounds such as olefins, polyenes, and azo compounds generally undergo reversible one-bonded photoisomerization to form a mixture of omers. Previously, we pointed out the possibility that the isomerization of the but thni(i er Va ves the s°hd state f°ll°ws the bicycle-pedal reaction mechanism, et al [4 eta s °ffhe molecular dynamics ofthe reaction had not been clarified. Saltiel react an< fl have independently discussed volume-conserving... 

Z-E isomerization via simple geometric inversion (one-bond flip, OBF, Fig. 2.3A) involves the torsional relaxation of the perpendicular excited state via an adiabatic mechanism which implies a non-volume-conserving process. This is not compatible with the ultrafast CTI in polyenes, in particular retinyl chromophores, and two other possible ways of photo-CTI have been proposed over the past 15 years [11]. 

According to molecular mechanics calculations the protein matrix of wild-type GFP forms a cavity around the chromophore that is complementary to an excited state conformation in which the phenol and imidazolidinone rings are perpendicular to each other - a conformation that was obtained by a concerted t and cp 45° HT [48]. Therefore even though an HT motion in wild-type GFP may not be more volume conserving than the cp-OBF, it still occurs as it is intrinsically favoured [49] and is complementary with the protein matrix surrounding the chromophore. Similar behavior has been proposed for PYP [13]. 

Fig. 4 Electro-opto-mechanical effect of a monodomain nematic gel observed (a) without polarizer and (b) with crossed polarizers. A 26-pm thick gel with = 4 mol% is placed in a 40-pm thick EO cell filled with a nematic solvent (5CB). The 5CB content in the gel is 82 vol%. An AC field (E) with an amplitude of 750 V and a fi equency of 1 kHz is imposed in the z-direcUon. The field induces a two-dimensional deformation, i.e., a shortening of ca. 20% in the r-direction, no dimensional change in the y-direction, and a lengthening of ca. 20% in the z-direction (due to volume conservation). The appearance of the gel (and surrounding 5CB) under cross-polarized conditions changes from bright to dark as a result of the almost full rotatirai of the director toward the field direction. A and P stand for the optical axes of analyzCT and polarizer, respectively. An mpeg movie is available in the supporting information of [31]...

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