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Now, what can be learned from this process to engineer a new economy

Â where we utilize sunlight and convert it into a fuel.

Â Now, this fuel can then be consumed at a later time and convert it to electricity

Â to power the world or convert to heat to give us warmth.

Â In this video, you will learn how to think about an ideal leaf and

Â how an ideal leaf would function and how we can use these ideas to develop and

Â replicate in an engineered device.

Â By the end of this module, you should be able to develop a thermodynamic model for

Â the interaction of a radiation field with a photochemical system, for

Â instance, sunlight and a plant.

Â And now, using this thermodynamic model you should be able to evaluate

Â the potential difference and

Â the amount of work that can be derived as a result of photon absorption.

Â The simplest picture for a system that can absorb photons

Â from a source such as the sunlight is a two-level system.

Â Now, let's consider two-level for

Â the chemical system that consists of a collection of ground electronic states,

Â termed as G, and excited electronic states, termed as E.

Â Now, in systems where electrons are holes which can migrate easily,

Â these collection of states are often referred to as the variance band

Â on the conduction band respectively.

Â Now, each of these electronic bands,

Â usually consist of a number of vibrational sub-states.

Â Now, when the rate of absorption of light quanta,

Â causing excitations from the ground state G to the excited state E is rapid with

Â respect to the thermal equilibrational of populations between the two bands.

Â Then a transition back from the excited state E to the ground state G gives

Â up some free energy which may be stored or used for chemical synthesis.

Â The amount of work that can be done as a result of the absorption of each photon

Â is limited by the product of the free energy change, and the quantum yield for

Â the de-excitation pathway, which is coupled to work production.

Â Now, there are two ways of viewing the excitations

Â caused by the absorption of light.

Â Now, the first view is the photoelectric view.

Â In this view, the way we think about it is,

Â the excitation can be considered as a way to increase the population of

Â electrons in excited states in the excited state by a fixed number.

Â Now, this is accompanied by a decrease in the population of electrons in another

Â set of states, for instance, the ground state.

Â Now this picture is adequate

Â if the device operates primarily through electron migration.

Â Now, a second view point is the photochemical view.

Â Now, in this case the excitation maybe considered as producing

Â an increase in the number of excited state molecular species.

Â And a concomitant decrease in the number of ground state molecular species.

Â Now, this picture's adequate if the light absorption

Â can induce molecular rearrangement in a fast enough time scale.

Â Now, in this video, we will take the photochemical view that is,

Â we will analyze the change in the free energy of the light absorbing molecules

Â to their ground state and to their excited state.

Â Now, the action of light usually depletes the population of the ground state

Â molecules only very slightly,

Â altering the chemical activity of these species to a negligible extent.

Â In the case of the potential difference arising between the bands,

Â this is primarily due to the greatly

Â increased population of molecules in the excited state.

Â In order to evaluate the band to band potential difference mu caused by

Â a radiation field in any given situation, we must first consider the conditions for

Â the equilibrium between the band to band transitions and the radiation feed.

Â Now, if we consider a reversible reaction,

Â then this implies that there is no change in entropy accompanying the admission or

Â absorption of radiation by the photochemical system at any frequency.

Â Let's view this from the perspective of the radiation field,

Â the entropy change corresponding to the loss of a photon of frequency mu

Â from a radiation field may be evaluated by considering an equilibrium

Â at that frequency mu between the field and a black body.

Â Now, remember, the black body is in equilibrium with the radiation field at

Â a frequency mu when the intensity of the radiation field obeys this relation.

Â Now, this relation states that intensity

Â scales as the inverse second power of the speed of light in that medium.

Â 7:37

Now keep in mind that this does not take into account the actual properties

Â of the absorber.

Â This intensity needs to be multiplied by the absorption cross-section of that

Â particular material to evaluate the total rate of excitation and emission.

Â And this is given by.

Â Now, for simplicity, we may assume that the absorption

Â cross-section is independent of the band to band potential mu.

Â Although, this may not always be the case.

Â Now, changes in temperature can largely be ignored.

Â Then, by multiplying the absorption cross-section for band to band

Â excitation to the frequency dependent factors of the intensity, we can find

Â that the emission spectrum as a function of the frequency mu, can be given as.

Â The Planck law of relationship between absorption and

Â emission may be used to calculate the potential developed in a full chemical

Â system whenever the absorption spectrum and the incident light flux are known.

Â Now we have the setup, the background machinery required to analyze our system.

Â Now, the rate of band to band excitations resulting from an arbitrary radiation

Â field, Is, is simply given by an integration over the frequency range.

Â Now, the developed expression for the emission spectrum,

Â we can easily evaluate the rate of radiative decay for

Â a photochemical system having a potential difference mu.

Â Now, the abbreviated frequency integral as L,

Â note that this depends on the properties of the absorption cross-section

Â as a function of frequency for the photochemical absorber.

Â Now, in the ideal limit, these two rates will be equal and

Â can be used to evaluate the maximum possible potential derivable for

Â a photochemical system, having an absorption cross-section,

Â sigma of mu and illuminated by a radiation field Is.

Â However, non-radiative band to band transitions are frequently

Â a significant source of relaxation from the excited state E to the ground state G.

Â Now, for simplicity, we assume that the rate of induced G to E

Â transitions is large with respect to all spontaneous excitations.

Â Then, we can specify that the total rate of decay from the excited state

Â to the ground state is simply kappa times the rate of radiative decay alone.

Â 10:26

Now, as kappa is the reciprocal of the luminescence quantum yield,

Â it may be frequently be determined experimentally.

Â For the remainder of our discussion,

Â we'll assume that kappa is independent of the band to band potential, mu.

Â Although, it appears that this is generally true only for

Â noninteracting excitations obeying Boltzmann statistics.

Â Now, having derived all these expressions,

Â we're now in a position to evaluate the power stored by light absorption.

Â Now work is one of the most popular commodities that can result

Â from photochemical absorption of light.

Â So that the frequency one desires,

Â to maximize the amount of power stored by such a system, is a useful quantity.

Â The amount of power stored is simply a product of two quantities.

Â One, the potential difference developed mu and the second one which is simply

Â the difference between the incoming rate of excitations and

Â the rate of transition from the excited to the ground state that is not coupled

Â to the work storage process.

Â Now, from the expression developed earlier,

Â mu0 is the potential difference developed in the absence of work storage process.

Â We can define the quantum yield for the last process using the following relation.

Â 12:12

Now, the power storage process is approximately maximal when

Â phi loss is equal to kBT divided by mu0.

Â Now, a useful way to understand this relationship is to look at

Â a concrete example.

Â Now, let's consider, that for

Â the chemical absorber that can develop a potential difference of about one wort.

Â This is, for instance, the case for

Â a silicon semiconductor which has a bandgap about 1.1 electron volt.

Â Now, in this case, the loss associated with this device is about

Â 0.1 volts about 10% of the overall available free energy.

Â Hence, the analysis that we have developed is actually an extremely useful and

Â important one that should be taken into account when designing practical

Â devices that use photon as an incoming energy source.

Â To summarize, in this lecture, we developed a relationship that

Â permits a ready calculation of the maximum light-induced

Â chemical potential difference, which can be developed by a photochemical system

Â if we know the incident light intensity, and the absorption spectrum.

Â