Liquid-state experiments

To address the problem of entanglement at room temperature NMR liquid-state experiments, let us start from our generic density matrix ... 

The general conclusion of the authors is that there is more to quantum information processing than entanglement and that, keeping in mind the limitations of room temperature liquid-state experiments, the NMR of these systems is an excellent test bed for the principles of quantum information and quantum computation. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

The principal dilTerence from liquid-state NMR is that the interactions which are averaged by molecular motion on the NMR timescale in liquids lead, because of their anisotropic nature, to much wider lines in solids. Extra infonnation is, in principle, available but is often masked by the lower resolution. Thus, many of the teclmiques developed for liquid-state NMR are not currently feasible in the solid state. Furthemiore, the increased linewidth and the methods used to achieve high resolution put more demands on the spectrometer. Nevertheless, the field of solid-state NMR is advancing rapidly, with a steady stream of new experiments forthcoming. 

This chapter simnnarizes the interactions that affect the spectrum, describes the type of equipment needed and the perfomiance that is required for specific experiments. As well as describing the basic experiments used in solid-state NMR, and the more advanced teclmiques used for distance measurement and correlation, some emphasis is given to nuclei with spin / > dsince the study of these is most different from liquid-state NMR. 

In such an experiment the material actually adsorbed by the solid (the adsorbent) is termed the adsorbate, in contradistinction to the adsorptive which is the the general term for the material in the gas phase which is capable of being adsorbed. The adsorption is brought about by the forces acting between the solid and the molecules of the gas. These forces are of two main kinds—physical and chemical—and they give rise to physical (or van der Waals ) adsorption, and chemisorption respectively. The nature of the physical forces will be dealt with in the next section meanwhile it is convenient to note that they are the same in nature as the van der Waals forces which bring about the condensation of a vapour to the liquid state. 

As has been known since the experiments of Andrews [1,2], one can pass continuously from the gas state to the liquid state and back by increasing the... 

Judging by these results the angular momentum relaxation in a dense medium has the form of damped oscillations of frequency jRo = (Rctc/to)i and decay decrement 1/(2tc). This conclusion is quantitatively verified by computer experiments [45, 54, 55]. Most of them were concerned with calculations of the autocorrelation function of the translational velocity v(t). However the relation between v(t) and the force F t) acting during collisions is the same as that between e> = J/I and M. Therefore, the results are qualitatively similar. In Fig. 1.8 we show the correlation functions of the velocity and force for the liquid state density. Oscillations are clearly seen, which point to a regular character of collisions and non-Markovian nature of velocity changes. 

It is curious that the chair- boat problem, which is most associated with small, liquid-state molecules, arises in the context of solid-state research (B3, II). Although the paucity of useful experiments militates against a definitive solution here E3), the frequency independence of the NMR second moment (E2), the absence of an observable free-induc-tion decay (Tj <25 fis) in the pulsed NMR spectrum (El), and the smoothness of the absorption mode itself (SI), all argue against the... 

No solid state NMR experiment is able to obtain spectra comparable to those routinely recorded in the liquid state. Thus multiplets become broad singlets and, if close together, overlap to give a broad signal envelope . While the differentiation of aromatic and aliphatic protons is simple, the information available is, from the point of view of structure determination, very limited. Thus we shall not provide an example. 

This paper reviews the experiences of the oil industry in regard to asphaltene flocculation and presents justifications and a descriptive account for the development of two different models for this phenomenon. In one of the models we consider the asphaltenes to be dissolved in the oil in a true liquid state and dwell upon statistical thermodynamic techniques of multicomponent mixtures to predict their phase behavior. In the other model we consider asphaltenes to exist in oil in a colloidal state, as minute suspended particles, and utilize colloidal science techniques to predict their phase behavior. Experimental work over the last 40 years suggests that asphaltenes possess a wide molecular weight distribution and they may exist in both colloidal and dissolved states in the crude oil. 

The price to pay for getting the higher intermediate frequency in such a convenient way would be the less clock-jitter tolerance, so that the apparent resolution of the resonance line can be degraded compared with that obtained in the conventional detection scheme. For this reason, we demonstrated the high-resolution liquid-state NMR experiment, in which the resonance line width was on the order of Hz. In fact, we observed a drift of the peak position when we used a less stable clock... 

We note that optimal control is a universal tool for experiment design and has also, in solid-state NMR spectroscopy, found additional applications in the design of homonu-clear dipolar recoupling [41], broadband rf pulses and quantum gates [71], building blocks of symmetry-based recoupling experiments [129], quadrupolar multiple-quantum MAS experiments [165], and improved pulses for quadrupolar nuclei [166]. Numerous references to further applications with regard to liquid-state NMR can be found in [72]. 

---