Vibrational motions, transport properties

Phospholipids, which are one of the main structural components of the membrane, are present primarily as bilayers, as shown by molecular spectroscopy, electron microscopy and membrane transport studies (see Section 6.4.4). Phospholipid mobility in the membrane is limited. Rotational and vibrational motion is very rapid (the amplitude of the vibration of the alkyl chains increases with increasing distance from the polar head). Lateral diffusion is also fast (in the direction parallel to the membrane surface). In contrast, transport of the phospholipid from one side of the membrane to the other (flip-flop) is very slow. These properties are typical for the liquid-crystal type of membranes, characterized chiefly by ordering along a single coordinate. When decreasing the temperature (passing the transition or Kraft point, characteristic for various phospholipids), the liquid-crystalline bilayer is converted into the crystalline (gel) structure, where movement in the plane is impossible. 

The ability to generate an equilibrium ensemble from a dynamical trajectory has a number of useful features. One can obtain not only ordinary static equilibrium properties from Eq. [25], but also dynamical information. In fact, dynamical information is available on two levels. On the one hand, equilibrium time correlation functions can be calculated, leading to the prediction of vibrational spectra, transport coefficients and so on. On the other, the trajectory allows access to the microscopic detailed motion of individual atoms. Therefore, one can, in a sense, visualize at an atomistic level the dynamical behavior of the system as a function of time, which can lead to valuable insights about chemical reaction mechanics, structural rearrangements, and other details of the system that can be captured only by visualization at this level of detail. 

When applying the results of the kinetic theory of polyatomic gases, one has to take into account the influence of vibrational and sometimes hindered rotational modes on the transport properties. The kinetic theory of molecules possessing vibrational modes of motion is still in its formative stages and is nowhere near as well-developed as that of rigid rotor molecules (see Section 14.2). Thus, the type of analysis that has been carried out for nitrogen is not possible in its entirety for polyatomic fluids. Nevertheless, a modified analysis, based on an empirical extension of the kinetic theory of diatomic gases, turned out to be possible (Hendl et al. 1991,1994 Vesovic et al. 1994). 

The existence of Arnold diffusion is irrelevant to the properties of separatrix manifolds, which still mediate the transport of chaotic trajectories within the regions of phase space they control. However, if Arnold diffusion is present in a given multidimensional system, the possibility exists for chaotic motion initially trapped between two nonreactive (trapped) KAM layers to eventually become reactive. This would presumably manifest itself as an apparent bottleneck to the rate of population decay, as chaotic trajectories slowly leak out from the region occupied by regular KAM surfaces into the portion of phase space more directly accessible to the hypercylinders. However, transport via the Arnold diffusion mechanism typically manifests itself on time scales much larger than those that we observe in numerical simulations (Arnold diffusion usually occurs on the order of thousands of mappings, or vibrational periods), and so it seems improbable that this effect would be observed in a typical reaction dynamics simulation. It would be interesting to characterize the effect of Arnold diffusion in realistic molecular models. 

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