The photostationary state

The (CH20) is the general formula for a carbohydrate. It was then assumed that the energy stored in the carbohydrate was used in other chemical reactions to synthesize all the other plant materials (proteins, lipids, fats, and so on). It is now clear that amino acids, for example, are immediate products of the photosynthetic reduction of carbon dioxide, and that carbohydrate need not be synthesized first. This is not to minimize the importance of the photosynthesis of carbohydrate, but only to note that many other types of compounds are produced photosynthetically. The overall mechanism and many of the details of the carbon reduction cycle, CO2 to carbohydrate, were worked out by Melvin Calvin and his colleagues, for which he received the Nobel Prize. 

These reactions are mediated through many steps by enzymes, and labile intermediate compounds. It is apparent that between 6 and 12 moles of quanta are required to convert one mole of carbon to carbohydrate. It is an intricate mechanism requiring several stages of pumping energy uphill. 

The dimerization of anthracene offers a convenient example. The reaction 

In the photostationary state we have the additional requirement that dEAjj/dt = 0 so 

If the concentration of monomer, [A], is very large, then this becomes 

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Equation (12-17) is called the photostationary state expression for ozone. Upon examination, one sees that the concentration of ozone is dependent on the ratio NO2/NO for any value of k. The maximum value of k is dependent on the latitude, time of year, and time of day. In the United States, the range of k is from 0 to 0.55 min T Table 12-5 illustrates the importance of the NO2/NO ratio with respect to how much ozone is required for the photostationary state to exist. The conclusion to be drawn from this table is that most of the NO must be converted to NO2 before O3 will build up in the atmosphere. This is also seen in the diurnal ambient air patterns shown in Fig. 12-2 and the smog chamber simulations shown in Fig. 12-3. It is apparent that without hydrocarbons, the NO is not converted to NO2 efficiently enough to permit the buildup of O3 to levels observed in urban areas. 

Aromatic compounds such as toluene, xylene, and phenol can photosensitize cis-trans interconversion of simple alkenes. This is a case in which the sensitization process must be somewhat endothermic because of the energy relationships between the excited states of the alkene and the sensitizers. The photostationary state obtained under these conditions favors the less strained of the alkene isomers. The explanation for this effect can be summarized with reference to Fig. 13.12. Isomerization takes place through a twisted triplet state. This state is achieved by a combination of energy transfer Irom the sensitizer and thermal activation. Because the Z isomer is somewhat higher in energy, its requirement for activation to the excited state is somewhat less than for the E isomer. If it is also assumed that the excited state forms the Z- and -isomers with equal ease, the rate of... 

The photoisomerization of aromatic rings has also been studied using 1,3,5-tri-t-butylbenzene. The composition of the photostationary state is shown below ... 

The sudden consumption of the remaining UDMH, and the increased relative importance of N-nitrosamine formation at -30 minutes into the photolysis can be rationalized by assuming that at that time the [NO I/ENO] ratio, and thus the photostationary state [O3], has become sufficiently high that O3 may be reacting with the hydrazine directly, and that reaction (3) begins to dominate over reaction (10). This results in higher rates of UDMH consumption by the OH radicals formed in the UDMH + O3 reaction (1), and by the OH radicals generated by the reaction of NO... 

Any mechanism which involves isoenergetic, radiationless internal conversion from C, P, or T to a high vibrational level of the ground state would be expected to show a large deuterium isotope effect on the rate of internal conversion. In the direct photolysis of perdeuterio and perhydrostilbene, Saltiel<8a) found no isotope effect on the photostationary state or upon the quantum yields of cis-to-trans and trans-to-cis conversion. 

The 2,4-hexadienes (17)—(19) are of interest because, if a common triplet intermediate (like X, a 1,4 diradical) is involved, the sum of all six quantum yields should be equal to 2, and the individual quantum yields should be predictable from the composition at the photostationary state<83 64) ... 

Also, the photostationary state can be predicted from the ratio of the quantum yields ... 

The photostationary state composition for the benzophenone-sensitized isomerization of 2,4-hexadienes is given in Table 9.2. Table 9.3 gives the measured quantum yields for benzophenone-sensitized isomerization of 2,4-hexadienes along with the calculated quantum yields based on Eqs. (9.47)-(9.49) and the pss values given in Table 9.2. 

Urocanic acid (2-propanoic acid 3-[lH-imidazol-4-yl] is located superficially in the stratum comeum. Metabolism of epidermal UCA does not occur in situ due to the absence of urocanase, resulting in the accumulation of UCA in the epidermis. Upon UV exposure, naturally occurring trans-UCA converts to the d.s-isomer, in a dose dependent manner, until the photostationary state is reached, when equal quantities of trans- and m-UCA are found in the skin.15 Based on an analysis of the action spectrum for UV-induced immune suppression, and the fact that no immune suppression was observed in mice whose stratum comeum was previously removed by tape stripping, De Fabo and Noonan suggested that urocanic acid was the photoreceptor for UV-induced immune suppression.16 Since the initial experiments many others have documented, the ability of ris-UCA to initiate immune suppression, documented its presence in the serum of UV-irradiated mice, and demonstrated that m-UCA plays a role in UV-induced skin cancer induction. (For a more complete review of the role of m-UCA in immune suppression see two excellent reviews by Norval and colleagues.1718)... 

Similar isomerizations of clopenthixol (354) and chlorprothixene (355) were observed but, unlike flupenthixol (353), the photostationary states of these mixtures differed significantly in their isomer ratios from those of the drugs as normally supplied. It was pointed out that the photoisomerizations could affect their potencies [195]. 

Explain the dependence of the composition of the photostationary state on the wavelength of radiation used for irradiation. 

This ratio is called the photostationary state composition. In the photostationary state, the rate of formation of each isomer from the nonvertical excited state is equal to its rate of removal by absorption of light. There is a roughly equal probability of the relaxation of the nonvertical excited state forming either the cis or the trans isomer and so the main factor influencing the photostationary state composition is the competition for absorbing light. This will, of course, depend on the relative values of the molar absorption coefficients of the two isomers at the particular wavelength chosen. 

Consider the absorption spectra of the two geometrical isomers, shown in Figure 8.3. The photostationary state obtained on direct irradiation depends principally on the wavelength of light used, because of competitive absorption by the two ground-state isomers. If a wavelength is chosen that is absorbed more strongly by the trans isomer than by... 

Consider the photosensitised cis-trans isomerisation of stilbene The two isomers have different triplet energy levels (247kJmoT1 for the cis and 205kjmol-1 for the trans). The proportion of the cis isomer in the photostationary state varies with the energy of the photosensitiser (ET), as shown in Figure 8.5. 

Figure 8.5 Effect of the sensitiser triplet energy on the percentage of cis-stilbene in the photostationary state...

This reaction can occur either thermally or photochemically, with the equilibrium position (thermal reaction) depending on the thermodynamic stability of the reactant and product, and the photostationary-state composition depending on the relative values of the absorption coefficients at the wavelengths used. 

The concentrations of electrons and holes in the conduction and valence bands, n and p, in the photostationary state under photon irradiation are expressed, respectively, in Eqn. 10-1 ... 

In the case in which the photoexcited pairs of electrons and holes are relatively stable so that thermal equilibrium is established between phonons and electrons in the conduction band as well as between phonons and holes in the valence band, we can define individually the electrodiemical potentials of photoexcited electrons and of holes in the photostationary state. Here, thermal equilibrium is not established between the photoexcited electrons in the conduction band and the holes in the valence band. The electrochemical potential, thus defined, for the photoexcited electrons and holes is caUed the quasi-Fermi level of electrons nCp, and the quasi-Fermi level of holes,[Schockley, 1950 Gerischer, 1990]. 

In the photostationary state, the current of hole transfer, i, across the electrode interface is the sum of the current of hole transport, i, and the current of photoexdted hole generation, ifb., as shown in Eqn. 10-21 ... 

In the photostationary state, Eqn. 10—44 equals the transfer current of anodic holes across the electrode interface shown in Eqn. 10-39. 

Stedman, D. H., and J. O. Jackson. The photostationary state in photochemical smog. Int. J. Chem. Kinet. Symp. 1 (Chemical Kinetics Data for the Lower and Upper Atmosphere) 493-501, 1975. 

Deuteration has been previously shown to cause an increase in the lifetime of triplet free-base porphyrins ( 7). This has been attributed to the strong coupling of N-H tautomerism with nonradiative decay. In the case of mesoporphyrin IX the increase upon deuteration is approximately two-fold ( ) As indicated in Table III deuteration of the picket fence porphyrin results in little change in the photostationary state composition but an almost twofold increase in the quantum yield of 4,0 -> 3>1. As stated above there is no measurable deuterium isotope effect on the thermal reaction the proportionate increase in quantum yield and triplet lifetime upon deuteration of the picket fence porphyrin is thus completely consistent with the adiabatic mechanism described above. Although the evidence amassed does not completely rule out other possibilities, it seems that the photoatropisomerization is to date best described by the adiabatic pathway in which the porphyrin ground and excited state potential surfaces are modified much as illustrated in Figure 3. 

When thioamides 24f-h were irradiated in benzene with a high-pressure mercury lamp, iV-isopropyl-P-thiolactam 26 and 1,3,5-dithiazine 28 were obtained (Scheme 15 and Table 10, entries 1,3, and 5). Considerably different photochemical behavior was observed between that in solution and in the solid state. Powdered thioamide 24f was irradiated in the solid state at 0 °C until 19% conversion, because the solid changed to amorphous at around 20% conversion. In this case, only dithiazine 28f was obtained as the sole photoproduct (entry 2). On the contrary, photolysis of 24g gave a new type of p-lactam 27g as a main product in 88% yield in addition to dithiazine 28g (12%) the P-lactam 26g was not detected at all (entry 4). Photochemical ( ,Z) isomerization of (Z)-24g was also observed in the early stage of the reaction, where the ratio of the photostationary state was ZIE=1.9. In the case of 24h, P-thiolactam 27h was ob-... 

According to this relationship, also referred to frequently as the photostationary state, the ratio of concentrations of 03, NO, and N02 should be a constant given by the ratio of rate constants for photolysis of N02 and for the reaction of NO with 03. Since k4 [usually referred to as p(N02)] changes with the solar zenith angle, this ratio of concentrations is also expected to change during the day. 

Richards and Pisker-Trifunac50 have irradiated cw-styrylferrocene (14) under several different sets of conditions and in all cases high conversion to the frans-isomer was the only reaction observed. It is noteworthy that no cyclobutane or oxetane derivatives are formed. The same seems to apply to ferrocenyl analogs of stilbene. That is, no ring formation is observed and the photostationary state consists almost exclusively of the Jrans-isomer. 

In the initial work135,136 on the sensitized isomerization of stilbene, it was found that quinone sensitizers gave photostationary states which were trans-rich relative to those predicted by energy transfer (Fig. 3). The original plot of sensitizer triplet energy versus isomer ratio of the photostationary state therefore showed several maxima and minima. Later work on the rates of energy transfer from various sensitizers to stilbene proved that the plot was in fact a smooth curve and that the photostationary states observed with quinones were not the true ones.137 Irradiation of benzene solutions of... 

A kinetic analysis of the effect of DCA concentration on the photostationary state showed that in benzene, 28% of the intimately associated pairs [DCA + zra s-stilbene ] underwent energy transfer before separating. 

In an attempt to probe further into the complex photochemical system involved, the isomerization of stilbenes adsorbed on silica gel was examined.9 It was observed that the time required for establishment of the photostationary state was significantly increased (by a factor of 3) and that the composition of the photostationary state changed from 93y cis isomer in cyclohexane solution to 60% cis isomer in the silica gel matrix. Though not definitive, this evidence supports Fischer s triplet mechanism, 53 as we have previously reported.9... 

The electron transfer from Ru(bpy)2+ to MV2+ is very rapid, the order being 10s—10 M-1 s . But the irradiation of an aqueous solution of both the compounds does not give a photoresponse at the electrode dipped in that solution, because the back electron transfer from MV+ to Ru(bpy)j+ is also very rapid thereby no photochemical products are accumulated in the photostationary state (Scheme 6), However, when Ru(bpy)2 + is modified on the electrode surface by utilizing polymer coating, the electrode shows photoresponse 95), Such a modification of the electrode makes it photoresponsive, to afford a new type of photodiode. 

In this project students review the Chapman cycle mechanism in detail and some photochemistry concepts including the photostationary state. A key element of this project is its focus on an important chemical mechanism and the use of exploratory options for predicting ozone concentrations as a function of time while reviewing other fundamental chemical kinetics concepts. Mathcad is used as the symbolic mathematics engine for solving the requisite differential equations and ample instruction is provided to students to guide them on the use of the software in this project. 

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