TOSS sequence

C). MAS spectrum (magic angle spinning, at vr = 3 kHz), no decoupling. (D). MAS spectrum, with decoupling. (E). MAS spectrum, cross polarised and decoupled. (F). MAS spectrum, cross polarised and decoupled, with spinning side bands elimination by special pulse technique (TOSS-sequence). 

Fig. 6 CPMAS NMR spectra of (A) bupivacaine-fb (5% wt/wt) in lipospheres (95% wt/wt) (B) lipospheres (C) difference spectrum of (A) minus (B) (D) bupivacaine-fb. Asterisks ( ) denote spinning sidebands incompletely suppressed by the TOSS sequence. (From Ref. l)...

Where there is a combination of different sites, each of which produces a significant number of sidebands, simplification of the spectrum by removal of the spinning sidebands would be extremely helpful. Dixon (1982) introduced the concept of breaking up the rotation period into intervals separated by 180° pulses. The phase of each spin is inverted by the pulses and the total phase accumulated by each spin can be calculated. Then for all the sidebands to be removed, the sum of the phase for spins contributing to the spinning sidebands needs to vanish, independent of the orientation of the particular crystallite. The basic TOSS sequence has been developed to compensate for imperfections by extension of the applied phase cycles and by paying careful... 

The pulse sequence used most often for this purpose is the TOSS sequence (total suppression of spinning sidebands. Fig. 3.3.9) [Dixl, Gril]. Before the start of data acquisition at r = ts the spin system is prepared by four 180° pulses at well-defined times... 

Fig. 13.4. CPMAS spectra, obtained using the TOSS sequence of (a) pure BMI cured at 493 K and (b) 1.5 1 BMI/DDM cured for 1 h at 418 K. (Reproduced from Ref. [86] with permission from the author.)...

The probability calculated so far is too low because it describes one specific sequence of heads and tails. From the point of view of net displacement, the sequence does not matter. Hence the above results must be multiplied by the number of different ways this outcome can arise. Instead of tossing one coin n times, we could toss n coins drawn at random from a piggy bank. For the first, we have a choice of n to draw from for the second, n - 1 for the third, n - 2, and so on. The total possible ways the toss could be carried out is given by the product of these different choices, that is by n ... 

Statistical considerations make it possible to test the assumption of independent additions. Let us approach this topic by considering an easier problem coin tossing. Under conditions where two events are purely random-as in tossing a fair coin-the probability of a specific sequence of outcomes is given by the product of the probabilities of the individual events. The probability of tossing a head followed by a head-indicated HH-is given by... 

Deterministic Randomness. On the one hand, equation 4.8 is a trivial linear difference equation possessing an equally as trivial solution for each initial point Xq Xn = 2"a o (mod 1). Once an initial point is chosen, the future iterates are determined uniquely. As such, this simple system is an intrinsically deterministic one. On the other hand, look again at the binary decimal expansion of a randomly selected a o- This expansion can also be thought of as a particular semi-infinite sequence of coin tosses. 

Almost everybody is familiar with the notion of probability as applied to games of chance. When discussing dice games, we assign the probability 1/6 to the event a one comes up because there are six faces of the die that are equally likely to come up and the desired face is, therefore, only one possibility out of six. Operationally, the number 1/6 is taken to mean that, in a long sequence of N tosses of the die, approximately 1/6 -N ones will show up. In other words, the... 

Fig. 9 Examples of simplifying solid state NMR spectra by the TOSS and delayed decoupling pulse sequences. Shown is a comparison of the 31P CP/MAS NMR spectrum of fosinopril sodium utilizing the standard pulse sequence (A) and the TOSS routine (B). Also shown is the full 13C CP/MAS NMR spectrum of fosinopril sodium (C) and the nonprotonated carbon spectrum (D) obtained from the delayed decoupling pulse sequence utilizing a 80 /us delay time. Signals due to the methyl carbon resonances (0-30 ppm) are not completely eliminated due to the rapid methyl group rotation, which reduces the carbon-proton dipolar couplings.

The processes of life involve both energetic and entropic factors. When we walk, run, climb, fidget, dance, or toss and turn in bed, we are doing work against physical forces. When we ice fish on a frozen lake in Minnesota, we need to generate heat to keep our body temperature constant. That heat is lost to the enviromnent (an ineffective way to heat Minnesota in the winter but it happens nonetheless). In contrast, when we synthesize DNA in the process of cell division with its precisely ordered sequence of bases or synthesize proteins with their precisely ordered sequences of amino acids, it is entropy that we must overcome, not physical forces or heat exchange. The bottom line is that we need a source of energy to five. 

Pulse sequence for MAS NMR. A) CFMAS. B) CPNAS with TOSS. T is magnetization transfer A, acquisition X,Y, -X are pulse phases and represents a delay. 

Toss a coin 80 times, recording the sequence of heads and tails. Break this sequence into 8 successive groups of 10 tosses, each group representing a random walk of 10 steps in which a step forward of unit length is taken with each head, and a unit step backward with each tail. Calculate a for this somewhat limited data set and compare to the theoretical value of a for an infinite number of random walks rather than the eight recorded here. (You may assume that the mean displacement is zero.)... 

The CP step is an essential building block for pulse sequences in solid-state NMR. The easiest ID experiments that are routinely used for characterization of organic, organometallic and hybrid solids are total suppression of spinning sidebands (TOSS), nonquatemary suppression, and so on. 

Pulse Sequence. In the TOSS pulse sequence a series of usually four (tt) pulses are applied in precisely placed points with respect to the rotor cycle prior to acquisition. The TOSS experiments are designed for MAS rates below 8 kHz. The setup of this experiment is identical to the one for the CP apart from the need for an accurate determination of the S (7T)-pulse. This can be difficult as a standard with relatively short T relaxation time is required. The S ( r)-pulse can also be set using the TOSS pulse sequence indicated by the lowest intensity of spinning sidebands. 

---