Open-form solution

Eq. riO.531 can be anal5 ically solved for given boundary and initial conditions using the method of separation of variables. Obviously, T =f(x,t) = T(x, t). The open-form (i.e., power series) solution will be shown here for the sake of enriching chemical engineering students math-based skills. The faculty or student may jump, however, to Eg. 00.701 and go from there for the sake of using MATLAB as a tool for expressing such an open-form solution. 

The spiroindolinobenzopyran 2 is a classical example of spiropyran and is easily prepared by the condensation of l,3,3-trimethyl-2-methyleneindo-line (Fischer s base) and salicylaldehyde in anhydrous ethanol or benzene (Scheme 2).ia The nucleophilic attack of Fischer s base on the carbonyl group (like an enamine) gives an aldol product, which undergoes ring closure followed by dehydration. This condensation is reversible therefore, an exchange of the salicylaldehyde component of spiropyran with a different salicylaldehyde is possible. For example, when a solution of spiropyran 2 (Scheme 2) was refluxed with 3,5-dinitro-substituted salicylaldehyde, the open form of 6,8-dinitro-BIPS was obtained.2... 

Since in aqueous solutions the cyclic form of monosaccharides is in equilibrium with their corresponding open forms, the a and P structures continually interconvert. At equilibrium, one form usually predominates. For instance, glucose dissolved in water consists of about a 2 1... 

Derivatives of 5-alkyl-2-(l,3,4-oxadiazol-2-yl)thiophenes 168 were synthesized and their photochromic and fluorescent properties studied. A solution of the photochrome was subjected to irradiation over a wide range, including the lines of the mercury spectrum at 313, 365, 405, 436, 546, and 578 nm. It was discovered that the open form of compounds 168 showed strong fluorescence <2002CHE165>. 

The trimer by forming an ester bond between the two terminal functions results in a lactone ring (fusarinine C or fusigen) 88,313). Since the fusarinines are rather labile it is not clear whether the open forms are genuine siderophores, precursors of fusigen or just hydrolysis products 204). The monomers (Z)- and ( )-fusarinine form in aqueous solution at neutral pH (Fe )Lig3 complexes, which are mixtures of A and A isomers 172). 

When the lactam ring is open it will react with iodine. 1 mole of the ring open form of penicillin will react with 8 equivalents of iodine, the intact lactam ring will not react. In this type of titration excess iodine solution is added to a sample of the penicillin and the iodine which is not consumed in the reaction is estimated by titration with sodium thiosulphate. The value obtained for the amount of hydrolysed penicillin in the sample should be no more than 5% of that obtained when all the penicillin in the same amount of sample is completely hydrolysed to the ring-opened form and then reacted with iodine. Most of the pharmacopoeial monographs for penicillins indicate that this test should be carried out. 

The enantiomerically-pure intermediate 1 was prepared from the dioxolanone 4, available in three steps from L-malic acid. Lewis acid-mediated homologation converted 4, a 4 1 mixture of diastereomers, into 5 as a single diastereomer. After establishment of the alkenyl iodide, it necessary to maintain the lactone in its open form. A solution was found in the formation of the Weinreb amide. The final stereogenic center was established by Brown allylation of the derived aldehyde. The alkene metathesis to form 1 was carried out with the commercially-available Schrock Mo catalyst. The authors did not comment on the relative efficacy of alternative alkene metathesis catalysts. 

The action of the base on the phosphonium salt generates the betaine (113) which is considered to exist in solution as the open form rather than the cyclic oxaphosphole (114). NMR evidence confirms the intermediacy of the phosphonium salt (115) and in some instances these salts have been isolated. Further treatment with base affords the ylide which undergoes an intramolecular Wittig reaction to yield the chromene (Scheme 12) (80T3409). 

Miscellaneous. Aside from the oxidation chemistry described, only a few catalytic applications are reported, including hydrogenation of olefins (114,115), a, [3-unsaturated carbonyl compounds (116), and carbon monoxide (117) and the water gas shift reaction (118). This is so owing to the kinetic inertness of osmium complexes. A 1% by weight osmium tetroxide solution is used as a biological stain, particulady for preparation of samples for electron microscopy. In the presence of pyridine or other heterocyclic amines it is used as a selective reagent for single-stranded or open-form B-DNA (119) (see Nucleic acids). Osmium tetroxide has also been used as an indicator for unsaturated fats in animal tissue. Osmium tetroxide has seen limited if controversial use in the treatment of arthritis (120,121). 

The aldehyde or ketone group of monosaccharides can undergo an intramolecular reaction with one of its own hydroxyl groups to form a cyclic, hemiacetal or hemiketal structure, respectively (Fig. 20). In aqueous solutions, this cyclic structure actually predominates. The open-chain aldehyde or ketone form of monosaccharides is in equilibrium with the cyclic form, but the open structure exists less than 0.5% of the time in aqueous environments. It is the open form that reduces Fehling s or Tollen s... 

Since in aqueous solutions the cyclic form of monosaccharides is in equilibrium with their corresponding open forms, the a. and p structures continually interconvert. At equilibrium, one form usually predominates. For instance, glucose dissolved in water consists of about a 2 1 ratio of p-D-glucose to a-D-glucose. Although their chemical constituents are identical, the biochemical properties between the a and the P forms can be quite different. Monosaccharides linked together to form disaccharides and polysaccharides cannot continue to interconvert and are therefore frozen in the a or p forms. Changing one monosaccharide in a complex carbohydrate to its opposite... 

Inherently, the orf/zo-phenylene spacer induces only a weak energy difference between the closed and open forms, but the ground-state structure of all MPB 7b-d was found to be well-defined, with or without P-B interaction. A different situation was observed for the related DPB 8a and TPB 9.24 The corresponding nB NMR signals (<5 = 43.1 ppm for 8a and 50.1 ppm for 9) are in between those of triarylboranes ( 70 ppm) and tetracoordinate derivatives thereof ( 0 ppm), suggesting a rapid equilibrium in solution between the open and closed forms (Figure 12). This hypothesis was further corroborated by low-temperature NMR experiments and DFT calculations. The minima associated with the open and closed forms were found to be almost isoenergetic (AG < 3 kcal/mol at 25 °C). 

Diarylethene switches are present in two, rapidly exchanging conformations (P and M helicity), which upon photochemical ring-closure lead to the RR or SS enantiomers in equal amounts. The authors showed that aggregation of a chiral diarylethene switch in the open form 283 leads to selection of only one of the helical forms of 283 in the gel state. Subsequent photochemical ring-closure of 283 to 284 in the gel state proceeds with 96% diastereoisomeric excess and a photosta-tionary state (PSS) of 40%, whereas in solution, no stereoselection is observed. 

Unlike the still-unknown 277-pyran which exists exclusively in the ring-opened form, 277-thiopyran is a well-characterized molecule. Nevertheless, the S-C(2) bond can be cleaved and this is the basis of the photochromic properties observed with spirobenzothiopyrans. Irradiation at 365 nm of the spiro[2/7-l-benzothiopyran-2,2 -indoline] 273 in both the solid state and in solution results in opening of the thiopyran ring and the formation of a colored metastable zwitterionic merocyanine (Equation 21). The open form exhibits solvatochromism, with Amax 588 nm in methanol and 673 nm in acetone. In solution, the thiopyran unit reforms rapidly when irradiation ceases, but continuous irradiation leads to the growth of crystals of the open form <2002JOC533>. 

These molecules display keto-enol tautomerization as illustrated in Fig. 11. The open-form keto-acid salts and the closed-form butenolides exist in a pH-dependent equilibrium in solution, and at physiological pH both forms exists. In principle, the biological activity could reside in either or both forms. 

When the ring opens in solution, C-l becomes the carbon atom of the aldehyde group, which has reducing properties. Only the open-chain form has reducing properties the ring forms are nonreducing because they lack an aldehyde group. 

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