Decoupling the Electrical and Entropic Contributions to Energy Transfer from Infrared Radiation to a Power Generator

The interaction between infrared radiation and a power generator device in time is studied as a route to harvest infrared, and possibly other electromagnetic radiations. Broadening the spectrum of the usable electromagnetic spectrum would greatly contribute to the renewable and sustainable energy sources available to humankind. In particular, low frequency and low power radiation is important for applications on ships, satellites, cars, personal backpacks, and, more generally, where non-dangerous energy is needed at all hours of the day, independent of weather conditions. In this work, we identify an electric and an entropic contribution to the energy transfer from low power infrared radiation to the power generator device, representing electrical and thermal contributions to the power generation. The electric contribution prevails, and is important because it offers multiple ways to increase the voltage produced. For example, placing black-colored gaffer tape on the illuminated face doubles the voltage produced, while the temperature difference, thus the entropic contribution, is not sensitive to the presence of the tape. We recognize the electric contribution through the fast changes it imparts to the voltage output of the power generator device, which mirror the instabilities in time of the infrared radiation. The device thus acts as sensor of the infrared radiation’s behavior in time. On the other hand, we distinguish the entropic contribution through the slow changes it causes to the voltage output of the power generator device, which reflect the relative delay with which the two faces of the device respond to thermal perturbations.


Introduction
A power generator (PG) device can be used to harvest electromagnetic (EM) and, in particular, infrared (IR) radiation.The interaction between the radiation and the device is a complex phenomenon of energy transfer ( ∆E ).The rate of energy transferred from the EM radiation per area a of the device is the Poynting vector P a = × =

S E H
, where E and H are the electric and magnetic fields, respectively, and P is power.Therefore, because of E and H , the interaction between radiation and device involves the charges on the device surface.Electromagnetic radiation with large frequency ν interacts through, e.g., Compton scattering [1], X-ray photoelectron effect [2], photoelectric effect [3], photovoltaic effect [4], and plasmon generation [5].
Electromagnetic radiation with low frequency ν , e.g. in the IR and microwave regions, resonates with molecu- lar rotation and oscillation frequencies [6] or generates polaritons [7]- [10].When the photon frequency ν or energy hν , where h is Planck's constant, do not match with the frequency or the energy of a specific pheno- menon involving charges, the energy of the EM radiation contributes to temperature T changes.In photosynthesis this phenomenon is known as internal conversion [11].
We name the energy transferred from the EM radiation to a PG device through the action of the electric E and magnetic H fields as the electric contribution: where q is the charge and V voltage.We name the energy transferred through changes in temperature T at entropy Σ as the entropic contribution: The energy transferred from IR and microwave radiation is usually associated with the entropic contribution in Equation (2).For example, sun light gives the sensation of temperature increase, and therefore of warmth, on human skin.The microwave radiation in microwave ovens is used to increase the temperature, i.e., cook food and heat-up beverages.Similarly, through laser radiation it is possible to increase temperature, even with nanoscale control [12].
The effects of the electric contribution q V ∆ =∆ el E are less apparent in the energy transfer from low frequency and low power EM radiation.In the current literature, the existence of the electric contribution is acknowledged [13]- [16], but the interplay between the electric and the entropic contributions is not investigated.Specifically, there is a lack of knowledge of 1) the possibility of decoupling the electric from the entropic contributions, 2) the factors that promote the electric over the entropic contribution, or vice-versa, 3) the existence of a threshold where one contribution prevails over the other, and 4) the benefits of the electric over the entropic contributions, or vice-versa.
In this work we aim at decoupling ∆ el E and ∆ en E in a PG device illuminated by low power IR radiation.The device is expected to respond to the entropic contribution by exploiting the Seebeck effect [17]- [20], i.e. producing a voltage difference V ∆ directly proportional to the temperature difference T ∆ applied to the two faces of the PG device, so that V S T ∆ =− ∆ .Here, S is the Seebeck coefficient.On the other hand, we expect the PG device to also respond to the electric contribution through its capacitor-type of structure consisting of a sequence of conducting and insulating layers, as illustrated in Figure 1.For the device used in this work, the sequence is, starting from the face illuminated by the IR radiation, a copper (Cu) plate, a layer of pillars made of adoped Bi 2 Te 3 -based alloy, another Cu plate, and, finally, an alumina (AlO) plate.On the Cu plates there are electrons whose surface density q a σ = is sensitive to the E and H fields of the IR radiation, thus enabling changes in the electric contribution q V ∆ =∆ el E .In our experiment, the voltage difference ( )

V t ∆
, generated by the PG device through the electric and the entropic contributions, and the temperature difference ( )

T t ∆
, related to the entropic contribution, are observed as a function of time t.The measurements capture the first minutes after starting the illumination, and in the 30 hours thereafter.We hypothesize that changes in slowly vary the amplitude of the surface electron density ( ) ,t σ r .To prove this hypothesis, we study the power ( ) P t of the IR radiation using a power-meter sensor and compare its behavior with that of ( )

( )
T t ∆ .Summarizing, we consider the total energy transfer in time from the IR radiation to a PG device as the sum of the electric and the entropic contributions such that: Consequently, we assume the voltage difference ( ) V t ∆ produced by the PG device in time to be the addition of two summands: The first summand relates to the electric and the second to the entropic contribution.The term ( ) S q t = − Σ can be associated with the Seebeck coefficient.
We will show that with the low power irradiation employed in our measurements, the electric contribution can be decoupled from the entropic contribution, and largely dominates.Decoupling the two contributions is important for IR energy harvesting, because the electric contribution offers a variety of ways to increase the voltage produced by the PG device, e.g. by placing black-colored gaffer tape on the illuminated face of the device, as we will show in Appendix-1.The entropic contribution, instead, is limited by the temperature difference ( ) T t ∆ established between the two faces of the PG device.

Experimental Set-Up
For this experiment, continuous broadband IR radiation in the middle IR (MIR) region (i.e.frequency between 1 350 -7500 cm − , or wavelength between 20 -2.2 m µ ) was produced by a globar (Q301) source.The power ( ) P t of the IR radiation was monitored versus time using a power-meter sensor Coherent Power Max RS PS19, sensitive to the 300 -11000 nm wavelength range, and to the 100 µW to 1 W power range.The voltage difference ( ) V t ∆ , generated by the electric and the entropic contributions to ∆ tot E according to Equation (4), was produced using a PG device 07111-9L31-04B by Custom Thermoelectric Inc.The device consists of a sequence of layers: 1) a Cu plate on the face exposed to the IR radiation, 2) a layer of pillars made of a doped Bi 2 Te 3 -based alloy, 3) another Cu plate, and 4) an AlO plate.The Cu plate not illuminated by the IR radiation is non-continuous, as highlighted through the white hole in the left side of Figure 1(a) and Figure 1(b).In the away architecture, illustrated in Figure 1(a), we established the continuity by placing the sample holders, made of anodized aluminum, in contact with the non-continuous Cu plate.Thus, the Cu plate together with the sample holder behaves as the electrode of a capacitor.The illuminated Cu plate, instead, was free of contact with the sample holder.In the toward architecture, pictured in Figure 1

Results and Discussion
a) Behavior in time of ( )

P t
In the 100 seconds immediately after starting the illumination of the power-meter sensor, ( ) P t , displayed in Figure 2(a), rises exponentially as follows: where off P and osc P are the offset value and half of the separation between MAX P and min P , respectively.The critical time cP t is the point in time in which ( )  b) Action of the IR radiation on ( )

,t σ r
We observed that the power ( ) P t of the IR radiation rises exponentially obeying Equation ( 5) at the start of the illumination, and exhibits a sinusoidal instability in the 50 hours thereafter.For the entire time span, we hypothesize that the IR radiation transfers energy, through electric contribution ∆ el E , to the surface density ( ) To sketch ( ) ,t σ r , we hypothesize that, while hitting the surface of the Cu plate, the IR radiation modulates the electric field E through the sinusoidal instability of the IR power ( ) ( ) ( ) ( ) turn, E and its modulation act on the electrons of the Cu plate with force e = f E, where e is the electron's charge.As in the photoelectric effect [3], f displaces the electrons away from the location in which the IR radiation impinges on the Cu plate, locally decreasing their surface density such that ( ) ( ) . However, unlike in the photoelectric effect, f does not kick the electrons out of the Cu plate.In this process, ( ) ,t σ r varies in time t as well as in space r , i.e. the 2-dimensional (2D) surface of the Cu plate.To allow us versatility in choosing reference system, orientation and phase, we represent the 2D space variable r as the complex variable , where i is the imaginary unit.This choice resembles that adopted to describe light polarization through Jones matrices [23]- [25].Thus, All possible rotations of the reference system, phases, and positions in the 2D plane can be obtained by selecting magnitude and sign of a r , b r , c r , and d r .
With this choice of z , upon starting the illumination, we picture ( ) , where 0 σ and f σ are the initial and final surface electron densities, σ τ the time constant, k a vector with units of inverse length, and ϕ an arbitrary phase.We note that the exponential behavior is modulated by the oscillatory function e y ir k .
In the subsequent 30 hours, from Equation ( 6) we expect ( ) , where the sine function has the frequency 1 4 . With the choice of z discussed above, and utilizing the laws of trigonometric functions for complex variables, we obtain: Here, x v and y v are the instability's propagation velocities along the x and y directions; x L and y L are the lengths of the Cu plate along x and y; finally, x t σ and y t σ are the critical times of the surface electron density's instability along x and y.Considering off σ and osc σ , the equilibrium electron density and its devia- tion from equilibrium, respectively, we obtain ( ) . This integration causes the loss of correlation between the phase of ( )

( )
T t ∆ in the 400 seconds after starting the illumination of the PG device with IR radiation are pictured in Figure 3 and Figure 4 for the away and the toward architectures.We find that the voltage difference where the 0i V ∆ and fi V ∆ terms are the initial and final voltage differences, and the i τ terms are the time constants.These parameters and the number of summands N are summarized in Table 3.In both the away and the toward architectures, the electric contribution is related to the summand with 1 N = and 1 3.8 s τ = . The obtained from the fitting parameters in as in Equation (9).Panels (d), (e), and (f) report the voltage difference ( ) graph with slope and amplitude A, and the dimensionless voltage for the toward architecture in the 400 seconds immediately following the start the illumination of the PG device with IR radiation.Panel (d) highlights the two summands related to the electric (el-1 and el-2) contributions, and the summand related to the entropic (en) contribution.
entropic contribution is related to the summand with larger time constant, 2 55 s τ = , and is labeled with 2 N = .This association is justified because 2 55 s τ = is of the same order of magnitude of 1 30 s T τ = for the temperature difference ( )

T t ∆
in both architectures, as can be seen in Table 3, and further in Appendix-1.The summand with 3 N = , detected only in the toward architecture, is related to an electric contribution because the "decay" in ( ) The rates of increase of ( )     8) and ( 10), respectively.The relationship of the summands with either the electric or the entropic contribution is highlighted.
graph with slope and amplitude T A for the toward architecture in the 400 seconds immediately following the start the illumination of the PG de- vice with IR radiation.(c) highlights the two summands related to the entropic (en-1 and en-2) contribution.
As with the power ( ) P t , the voltage difference ( ) produced by the PG device also rises exponentially in the first few minutes after starting the illumination.However, 0.25 V t ∆ production.We capture the relative behavior of the electric and the entropic contributions to the generation of ( )  8) and its parameters in Table 3 as follows: ( ) Here, the term 2 t τ Τ = is the dimensionless time [22], while 0 are dimensionless voltage parameters.We performed the normalization with respect to the slower summand, i.e. the one related to the entropic contribution with 2 N = .Such a choice leads us to observe an evolution of ( ) in Figure 3(c) and Figure 3(f) on a similar T-scale in both the away and the toward architectures, signifying that the dynamics is not affected by the architecture.On the other hand, from the plateau value at ( ) in the away architecture, we infer that the summands related to the electric and entropic contributions add one to the other, with the former prevailing over the latter because of 1 1 2 2.6 1 => .On the contrary, from the plateau value at ( )  1 V ∆ Τ < in the toward architecture, we conclude that the two summands related to the electric contributions with 1 N = and 3 almost annihilate one another, while the summand related to the entropic contribution survives in the long term.
The temperature difference ( ) ( ) .The parameters and the number of summands M, all related to the entropic contribution, are summarized in Table 3.We observe that 1 2 M ≤ ≤ , and that summands similar to that with 2 M = (rarely detected) in the toward architecture in Figure 4(c .We also note that "decay" appears for ( ) in the toward architecture in Figure 4(c), as opposed to the corresponding voltage difference The slopes of the initial linear regimes in the in the away and toward architectures, respectively.The corresponding amplitudes T A are 0.13˚C and 0.20˚C in the away and the toward architec- tures, respectively.The ratio and temperature difference ( ) ( ) in the away architecture is 7.31 mV C R =  .Overall, Figure 3 and Figure 4 suggest that ( ) ( )


. The electric contribution affects only ( ) . Thus, we conclude that the electric and entropic contributions in the interaction of IR radiation with a PG device are decoupled.To further support this conclusion, in Appendix-1 we will compare the trends of the values of ( ) upon activating the PG device with IR radiation, as done so far, and conductive heat transfer from a 100 Ω resistor and a 0.02 A current.Only the entropic contribution is activated in this case because the produced power of 0.04 W, corresponding to a temperature of ≈24˚C on the PG device, is too low to produce significant blackbody radiation to trigger the electric contribution.d) Behavior of ( ) We observed another possible behavior in Figure 6, displaying data collected with the away architecture.In this case, ( )

T t ∆
, which is flat as hypothesized in Section 3(b).The instability of ( ) 6(a) is non-periodic, as predicted in Section 3(b).Thus, to find a suitable fitting function, we recall the hypothesis in Section 3(b) where we pictured the time-dependence of ( ) as captured by a hyperbolic secant function with no phase relationship with ( ) P t and no sinusoidal periodicity.Thus, we propose: In this expression,     t , it does not correlate with the behavior in time of ( ) graph in Figure 6(c), where stable and unstable fixed points [20] alternate in a complex fashion without periodicity.Since the time-dependence is enclosed in a hyperbolic secant function, we name the instability in ( ) V t ∆ in Equation (11) and Figure 6(a) as hyperbolic instability.We establish the lack of correlation between ( ) 3) The c t term in Table 4 is found at 11.65 h, which is reasonably close to the average cP t at 16 2 ± in Table 2.
These observations further support our hypothesis in Section 3(b) relating the sinusoidal instability of ( ) on the Cu plate.In Appendix-2 we will show that the hyperbolic instability in ( )

V t ∆
, selected according to the criterion established in Section 3(d), occurs frequently in our observations.We will provide further evidence of the link between c t and cP t .Finally, we will prove the lack of phase rela- tionship between ( ) Equation ( 12) is nonlinear because of the 3 rd order partial differential of ( ) V t ∆ with respect to time t.The equation resembles the Korteweg-de Vries (KdV) equation [26] [27] after eliminating the space-dependence, and flipping the space variable with time t.In order for ( )

V t ∆
in Equation ( 11) to be a solution of Equation ( 12), we select the σ and ς coefficients by rewriting Equation ( 12) as: ( ) ( ) ( ) By substituting Equation (11) into Equation ( 13), we obtain: The time-dependent coefficient ( ) ( ) ( ) of Equation ( 13) stands for nonlinear effects [26], and infers that a complex dynamics is hidden in the hyperbolic instability of ( ) [29].In Figure 7 we graph ( ) using the parameters reported in Table 4 for the away architecture.Despite the complexity of Equation ( 14 , or simply, the "acceleration" of the inverse voltage.Such identification points out the existence of nonlinear "forces" that continuously push and slow down the changes in ( )

V t ∆
. We plan on further investigating this topic.

Summary and Significance
We identify and decouple an electric and an entropic contribution to energy transfer from low power infrared radiation to a power generator device.The electric contribution is related to the effects of the electric E and magnetic H fields in the infrared radiation and is detected through the voltage produced by the power generator device.The entropic contribution is mainly related to the temperature difference between the faces of the device.Two observations enable us to decouple the electric and entropic contributions.First, the electric contribution imparts faster rates of increase of the voltage difference ( ) produced by the power generator device immediately after starting the illumination with infrared radiation.Second, the electric contribution generates a hyperbolic instability in the 30 hours after starting the illumination.The entropic contribution changes slowly and simply reflects the relative delay with which the two faces of the power generator device respond to thermal perturbations.
Our preliminary studies suggest that it is important to learn to exploit the electric contribution, because it offers a variety of ways to increase the voltage produced by the power generator device.For example, blackcolored gaffer tape on the illuminated face doubles the amount of voltage produced, as discussed in Appendix-1, while the temperature difference, thus the entropic contribution, is not sensitive to the presence of the tape.Our findings are relevant for understanding the mechanisms for harvesting IR radiation, and possibly other electromagnetic radiations, through a power generation device as an alternative energy source.The future efforts will be devoted to overcome the limitations of the present work: 1) understand the relationship among infrared source power, surface charge density on the power generator, and produced voltage, 2) clarify the behavior of the power generator as a capacitor, and 3) investigate the role of infrared radiation power on the results.

Figure 1 .
Figure 1.Schematics of the away (a) and toward (b) architectures of the PG device.In the away architecture (a) the face of the PG device exposed to the IR radiation is free from contact with the sample holder.In the toward architecture (b), the illuminated face is in contact with the sample holder.The PG device is a stack of conducting (Cu plates), non-conducting (AlO plate), and semiconducting (set of pillars made of a doped Bi 2 Te 3 -based alloy) layers.

Figure 2 .
Figure 2. (a) Exponential rise, as in Equation (5), of the power ( ) P t versus time of the IR radiation emitted by the globar source in the 100 seconds immediately after starting the illumination of the power-meter sensor; (b) Graph of ( ) ( ) d , d P t P t t   ∆     in the same time interval of (a) reporting the slope and amplitude P A ; (c) The power ( ) P t in the 50 hours after starting the illumination of the power-meter sensor; (d) Same as (c), with the vertical scale expanded to highlight the sinusoidal instability region fitted with Equation (6).The zero of the time-scale coincides with the start of the illumination with the IR radiation.The parameters cP t and P H are labeled; (e) Graph of

!
We observe the sinusoidal instability of ( ) P t , which modulates the amplitudes of the electric E and magnetic H fields of the IR radiation, to persist beyond the 50 h time interval in Figure2(d).
Because of the capacitor-type structure of the PG device, with overall capacitance C, we expect

Figure 3 (
a) and Figure 3(d) fits a sum of exponential functions:

Figure 3 .
Figure 3. Panels (a), (b), and (c) correspond to the away architecture and refer to the 400 seconds immediately following the start the illumination of the PG device with IR radiation.(a) Voltage difference ( ) V t ∆ with fitting curves obeying Equation (8) highlighting the summands related to the electric (el) and the entropic (en) contributions; (b) Graph of

Figure 3
Figure 3(d) because of the non-continuity of the Cu plate opposite to the IR radiation illustrated in Figure 1(b).The large value of 03 1.1 mV V ∆ = signals that the toward architecture tries to avoid the "decay" by pumping up the voltage production.

Figure 3 (b) and Figure 3
the toward architecture.The amplitudes A, also derived from Figure 3(b) and Figure 3(e), are 0.95 mV and 0.66 mV in the away and the toward architectures, respectively.
(bottom rows) in the away and toward architectures in the 400 seconds immediately following the start of the illumination of the PG device with IR radiation.The corresponding experimental data are shown in Figure 3(a) and Figure 3(d), and Figure 4(a) and Figure 4(c).The indexes N and M indicate the number of summands in Equations (

Figure 4 .
Figure 4. Panels (a) and (b) correspond to the away architecture and refer to the 400 seconds immediately following the start of the illumination of the PG device with IR radiation.(a) Temperature difference ( ) T t ∆ with exponential behavior as in ( ) P t shown in Figure 2(b).We ascribe this discrepancy to the activation process occurring in the PG device to start the ( ) ], pictured in Figure 3(c) and Figure 3(f), and derived from Equation (

Figure 4 (
a) and Figure4(c), surprisingly exhibits negative values, indicating that behavior is typical when the PG device faces the IR radiation with the Cu plate.Nevertheless, we find that the temperature difference ( )T t ∆rises exponentially as follows: and final temperature differences, respectively, and the Ti τ terms are the time constants.These time constants reflect the fact that generally ) exhibit an extremely large time constant of

Figure 4 (b) and Figure 4 (P t in Figure 2
Figure 4(d), are negative, as those of ( ) P t in Figure 2(b), and

6 .Figure 5
30 hours after starting the illumination of the PG device as pictured in Figure 5 and Figure We observed one possible behavior in Figure 5, which displays the data collected with the toward architecture.The voltage difference exhibits an instability around the 20 th hour.No instability is detected in (c) and Figure 5(d), respectively.This finding suggests that a strong correlation exists among ( ) ascribe to the capacitor-type of structure of the PG device, as predicted in Section 3(b).

Figure 6 (.
a), exhibits an instability around the 12 th hour which is uncorrelated with the trends occurring in The lack of correlation highlights the lack of coupling between the electric and the entropic contributions.Since the trends of the two temperatures are identical, we show only ( ) IR T t in Figure6(b).We omit to display ( ) set, respectively.The positive or negative sign of osc V ∆ corresponds to a downward or upward concavity, respectively, of the instability.The critical time c t is the instant in which the maximum osc V ∆ value is achieved.Finally, the term H indicates the half width at half maximum (HWHM), or minimum (depending upon the sign of osc V ∆ ) of the instability.The magnitude of off V ∆ corresponds to the long term equilibrium voltage

Figure 5 .
Figure 5. Panels (a), (b), (c), and (d) correspond to data collected from the toward architecture in the whole time span of about 30 hours following the start of the illumination of the PG device with IR radiation.(a) Voltage difference ( ) V t ∆ .(b) H are reported in

Figure 6 (
a), and were obtained by placing the zero of the time-scale at the start of the illumination.We highlight that, since ( ) IR T t in Figure 6(b) does not peak at c

Figure 6 .ble
Figure 6.Panels (a), (b), and (c) correspond to data collected from the away architecture in the whole time span of about 30 hours following the start of the illumination of the PG device with IR radiation.(a) Voltage difference ( ) V t ∆ exhibiting

Figure 6 (
Figure 6(a) collected from the away architecture in the time interval of about 30 hours following the start the illumination of the PG device with IR radiation.The parameters off V ∆ ,

Figure 7 .
Figure 7. "Acceleration" of the inverse voltage ( ) t Ωfor the away architecture obtained from Equation (14) using the pa-

(b), we
left non-continuous the Cu plate opposite to the IR radiation, while the illuminated Cu plate was kept in contact with the sample holder.

Table 1 .
Summary of the experimental parameters in the main text and in the appendices.
t undergoes small sinusoidal instabilities shown in Figure2(d) in which the vertical scale has been expanded.The instability, due to small periodic fluctuations in the closed sample compartment, can be fitted with: P t , shownFigure 2(c), reaches a plateau.Howev- er, in multiple data sets, we always observe that ( ) P

Table 2 .
(Top rows) Fitting parameters 0 P , The unit for time in the bottom rows of this table is the hour ([h]). of the electrons on the illuminated Cu plate of the PG device, and contributes to producing f P , and P τ of the IR power ( ) 0 e P t f P t P P τ − = + in Equation (5) in the 100 seconds immediately following the start of the illumination of the power-meter sensor with IR radiation from the globar source.The rate of increase of the power ( P ρ ), and the amplitude P A in this time interval, derived from the P H of the sinusoidal instability ( ) P t in the 50 hours following the start of the illumination of the power-meter sensor with IR radiation from the globar source.The parameters cP t and P H are labelled in Figure 2(d).

Table 3 .
Fitting parameters i

Table 4 ,
labelled in

Table 4 .
The unit for time is the hour ([h]).