In-phase states

Infinite-order sudden approximation (IOSA), electron nuclear dynamics (END), molecular systems, 345-349 Initial relaxation direction (IRD), direct molecular dynamics, theoretical background, 359-361 Inorganic compounds, loop construction, photochemical reactions, 481-482 In-phase states ... 

Roos, Y.H. 1998. Role of water in phase-transition phenomena in foods. In Phase/State Transitions in Foods (M.A. Rao and R.W. Hartel, eds), pp. 57-93. Dekker, New York. 

Figure 7.11. Glass transition temperature of the 7S and IIS soy globulins as a funetion of moisture content by DSC and RMS (Copyright 1998 Horn Understanding phase transitions and chemical complexing reactions in 7S and IIS soy protein fractions by Morales-Diaz and Kokini (In Phase/State Transitions in Foods, Rao and Hartel (Eds.)). Reproduced by permission of Roudedge/Taylor Francis Group, LLC.)...

Hoseney, R. C. 1998. Gelatinization phenomena of starch, in Phase/State Transitions in Foods Chemica, Structural, and Rheological Changes, eds. M. A. Rao and R. W. Hartel, pp. 95-110, Marcel Dekker, Inc., New York. 

This calculation shows that the in-phase state is (linearly) neutrally stable. That s discouraging technologically—one would like the array to lock into coherent oscillation, thereby greatly increasing the output power over that available from a single junction. 

Since the calculation above is based on linearization, you might wonder whether the neglected nonlinear terms could stabilize the in-phase state. In fact they don t a reversibility argument shows that the in-phase state is not attracting, even if the nonlinear terms are kept (Exercise 8.7.11). 

Now that the analysis has been completed it can be seen what the function of various elements in the pulse sequence is. The first pulse and delay generate magnetization on proton which is anti-phase with respect to the coupling to carbon-13. The carbon-13 90° pulse turns this into multiple quantum coherence. This forms a filter through which magnetization not bound to carbon-13 cannot pass and it is the basis of discrimination between signals from protons bound and not bound to carbon-13. The second carbon-13 pulse returns the multiple quantum coherence to observable anti-phase magnetization on proton. Finally, the second delay A turns the anti-phase state into an in-phase state. The centrally placed proton 180° pulse refocuses the proton shift evolution for both the delays A and tv... 

A substance can exist as a gas, liquid, or solid. The gas state exists at low pressure. Within a range of temperature, depending on the substance, as the pressure is increased at a constant temperature, the gas condenses into a liquid. At temperatures above the range, the gas stays unchanged in phase state to very high pressures. At temperatures below the range, the gas condenses upon compression directly into a solid. 

Figure 13.11 Mixtures of lactose and sucrose cause changes in phase/state behavior. Solid lines represent behavior of sucrose, dashed lines represent behavior of lactose, and dashed line represents a mixture of sucrose and lactose. (From Hartel 1993 with permission.)...

One-, two-, and three-component systems will be considered. A one-component system is one substance that defines composition uniquely throughout a diagram. Temperature and/or pressure are usually the variables under consideration to define the state of a system. In phase transition work, variables such as density, heat capacity, optical properties, etc. may be measured to determine changes in phase state as the variables of state are changed. If there are no transitions in a one-component system in a region under consideration, there is very limited phase chemistry as such. 

Figure 7.16 Pulse sequence diagram for Tj CPMG experiment. The dashed line on the echoes shows the rate at which spins lose coherence among themselves. Spin states are reported at specific times (a) net magnetisation flipped onto the transverse plane for signal detection (b) spins dephasing from the y direction (c) P gQ pulse which reverse spins instantaneous phase angles (d) spins rephasing towards the y direction. Panels (e) and (f) show spins in-phase states (signal echoes).

---