Exploring ion mobility mechanisms in poly indolequinone polymers: a case study on black soldier fly melanin

Black soldier fly (BSF) melanin is a new supply of the brown-black pigment eumelanin. Given that eumelanin is a model bioelectronic material for applications such as medical devices and sensors, understanding BSF melanin’s electrical properties is important to confirm its viability as an advanced material. Presented here is a systematic, hydration dependent alternating current study of BSF melanin utilising both H2O and D2O vapours. There is a clear difference between the vapours, enabling a thorough analysis including Nyquist plots with model circuit analysis, broad band dielectric spectroscopic modelling as well as applying the Trukhan model to understand free ion concentration and mobility changes as a function of hydration. We find that BSF melanin behaves similarly to previous reports on synthetic systems, and the analysis here sheds additional light on potential charge transport changes. Significantly, a key finding is that there are two different mobility mechanisms for ion transport depending on hydration.


Introduction
There are several interlocking societal challenges that require urgent attention including medical sensing & treatment, the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.ubiquitous sensing network, electronic waste (e-waste) and the need for a circular economy [1,2].
Medical sensing & treatment is foremost on the mind of governmental bodies, e.g. the United States National Academy of Engineering has elucidated the need for 'advance health informatics' among its 14 grand challenges for engineering in the 21st century [3].This interest is shared by the pharmaceutical industry, which have coined the term 'electroceuticals', a medical field focused on using electrical signals to affect a medical outcome [4].Consequently, a rapid growth in research is being experienced in the field of bioelectronics, a field at the intersection of the physical, chemical and life sciences that is investigating new types of medical sensors [5,6].
This need for sensors is shared more generally in the concept of the ubiquitous sensor network, the goal of which is to seed the environment with low end sensing devices to monitor variables such as pressure, temperature, humidity etc [1] to enhance control and understanding over a local environment.
However, the above need and use for various sensors will lead to an increase in e-waste, which is already a significant problem due to both the sheer volume of waste generated (45 megatons per year) and the environmentally hazardous materials involved [1].One method to manage e-waste, and indeed waste problems in general, is to adopt a circular economy approach in which recycling plays a major role [7].
Clearly, materials will need to be selected that have desirable sensing properties but can also be sustainable sourced.Furthermore, once used, disposal must lessen environmental impact.As such, biomaterials are key to this endeavour [8].They offer the best potential in the matrix of needs of sensing properties, biocompatibility, easy disposal, and being readily sourced.
Eumelanin is a potential 'work horse' material candidate but it cannot be readily sourced.Usually, one can synthesise the material [12], which runs counter to the ideals of a circular economy or source it from animals such as the cuttlefish [31,32].The latter results in a limited supply since it is a seasonal by-catch and has low yields due to the cuttlefish emptying their sacs when caught.
A second problem is that eumelanin is not readily processed, and is notorious for its insolubility in water and common solvents [9].But now, the ability to produce, in bulk, a water-soluble eumelanin has been recently produced from the pupal exuviae of the black soldier fly (BSF) (Hermetia illucens) [33], an insect which is rapidly being utilised to metabolise and upcycle food waste [34,35].As such, this source of eumelanin is poised to address the aforementioned drawback of eumelanin.A key question regarding this BSF eumelanin (BSF-mel) is whether it retains the desirable properties of eumelanin, especially its electrical properties.Furthermore, can this form eumelanin elucidate the still outstanding scientific questions regarding the origins of the electrical properties of eumelanin?The purpose of this current work is to investigate the electrical properties of BSFmel.Since eumelanin is known to exhibit mixed ion/electronic conduction [23] and have a hydration dependent conductivity [12,22,36], we perform AC conductivity/dielectric spectroscopy on BSF-mel drop-cast films on interdigitated electrodes (IDEs).
The key to the study is that we perform in-situ hydrationcontrolled experiments, utilizing both H 2 O and D 2 O vapours to tease out the electrical response, the first for a natural based eumelanin compound.We further analyse the data indepth and compare the results to what is known from synthetic samples and discover intriguing differences that extend the current understanding of charge transport in eumelanin compounds.

Eumelanin extraction
BSF-Mel powders were provided by the manufacturer INSECTTA Pte.Ltd for on-demand, basic research purposes and used as is.The material is produced via a patented [33] targeted extraction process from the BSF (Hermetia illucens).
Briefly, pupal exuviae were homogenised into ∼0.5 mm pieces and demineralised with 10% (w/w) lactic acid for 3 h at 25 • C. The solid fraction was deproteinated with 1 M sodium hydroxide for 3 h at 50 • C. Following this, BSF-melanin was liberated from the solid fraction by heating with 2 M sodium hydroxide for 3 h at 90 • C. The pH of the supernatant was corrected to 1 with 37% (v/v) hydrochloric acid, in order to precipitate BSF-melanin, which was collected by centrifugation and further subjected to a series of proprietary steps in order to derive a lyophilised, salt-free, water-soluble powder.The latter property is achieved at pH 7.3, lower than a standard synthesis pH of 8.
Sample variation from extraction was quantified by UV-Vis spectra of several batches and shows a consistent, reproducible product (see figure S0).

Thin film deposition
Solutions of BSF-Mel were prepared by stirring in deionized water at a concentration of (20 mg ml −1 ).
Thin films were prepared from approx.10 µl of the solution via drop casting deposition and left to dry in a fume hood at room temperature for several hours.For the electrical measurements, Ti/Au IDEs substrate were used, supplied by MICRUX (Ti/Au thickness, 50 nm/150 nm).Two IDE configurations were employed: a linear configuration (120 finger pairs, 10 µm width, 10 µm finger gap, figure 1 top left) and a round configuration (90 finger pairs, 10 µm width, 10 µm finger gap, figure 1 top right).Relative size of IDE can be seen in figure 1, bottom.Before the drop casting procedure, the IDEs were treated by UV-Ozone (Ossila Ltd) for 5 min.

BSF-mel device preparation and impedance measurements
We performed two sets of environmentally controlled measurements on BSF-Mel by utilising a JANIS Research Cryogen Free Micromanipulator probe station with an attached vapour delivery system.The JANIS was initially pumped down to a vacuum of ∼10 −2 mbar utilising a dry scroll pump.The samples were then exposed to selected values of vapour pressure of H 2 O or of D 2 O from a vial of liquid (degassed).The basic approach has been described elsewhere [23,37,38] but in brief, after the initial pump down, the water vial is opened, and water vapour is bled into a delivery line until a target vapour pressure is read off the pressure gauge (Edwards GK series 0-50 mbar).The samples were then allowed to come to equilibrium (1 h, monitored via electrical impedance spectroscopy (EIS) measurement), electrical measurements were then performed, and the above procedure then gets repeated at a higher vapour pressure until a complete isotherm is obtained.The range of temperatures for the experiments were 20.6 • C-22.0 • C. The vapour pressures obtained were converted into relative humidity accounting for the temperature.This allows for estimating the saturation vapour pressure via Antoine parameters [39].
EIS was performed by using an automated Metrohm Autolab potentiostat PGSTAT302N with a FRA32M module.The AC voltage amplitude, V AC , was fixed at 300.0 mV and the frequency (f ) range was 1.0 MHz-0.1 Hz, taking 10 data points per decade-and the DC offset was 0 V.

Impedance data analysis
The EIS spectra of impedance (Z) vs f have been represented in multiple formats.The first employs a Nyquist plot (NP) i.e. the negative imaginary component of the impedance (-Im Z) vs. the real component of the impedance (Re Z).We recall that in a NP the left component of the data set refers to the high frequency region while the right part to the low frequency region [40].The data is then modelled by building up an equivalent circuit that replicates the shape of the data via a combination of resistive (R), pure capacitive (C), peculiar impedances components such as the constant phase (Z CPE ) and diffusion (Z W ) elements (see ESI) to represent the AC electrical response [40].Each circuit element can be assigned to a specific mechanism depending on the AC frequency signal range under consideration.
To analyse data in a NP, we adopted the free downloadable EIS Spectrum Analyzer v.1.0software [41].The equivalent circuits employed herein are depicted in figure 2. The two different circuits shown represents two different regimes, which we will discuss separately.
Figure 2(a) is for drier BSF-Mel, i.e. either to D 2 O at 18% RH or H 2 O at 20%RH.The circuit consists of the Ti/Au contact and other IDE component resistances represented by R ctc , the shunt IDE capacitance C sh is present to simulate the parasitic current shunts at high frequency [42], and the electric double layers at the interface with the electrodes is simulated by a non-ideal capacitance, i.e. a constant phase element (Z CPE,dl ).No additional diffusive Warburg element was used as it did not significantly improve the fit.
Figure 2(b) was applied to both wet D 2 O (30%-97% RH) and H 2 O (28%-92% RH), where an embedded Randle circuit was employed, which is particularly suitable for simulating carrier transport mechanisms in electrolytes placed in between two electrodes [43].The Randle circuit commonly consists of a resistor (R ctc , the contact resistance) placed in series with two branches in parallel: the first branch is constituted by a constant phase element (Z CPE,dl ) or a capacitor (C dl ) representing the charge double layer (dl) forming at the electrolyte/electrodes interface; the second branch refers to the faradaic current and is constructed by two elements in series, which are the charge transfer resistance or ionic charge resistance R ion , and an impedance associated to the charge diffusion (Z W ). To improve fitting, the Randle circuit is sometimes rebuilt by introducing a Z CPE or a specific Warburg Element depending on the behaviour at low frequency (Z CPE /Z wo , figure 2(b)).In particular, the Randle circuit was modified by substituting the Warburg impedance Z W with the more appropriate diffusion element, Warburg finite length, (Z Wo ), given by: where A W is the limited diffusion resistance, D the diffusion coefficient of the electroactive species and δ the Nerst diffusion layer representing a carrier finite-length diffusion with electrode reflective boundary [44][45][46].Z Wo is an element that can be expressed via a complex number (equation S6) and both real and imaginary components can be expressed to be proportional to 1/√ω and also ∼ D 1/2 /δ, following the approaches of other authors for the absorbing element [41,46,47] In the low frequency limit the real part W Or is proportional to the diffusion resistance and the imaginary component W Oc is proportional to 1/√ω and ∼ D/δ 2 (equation S9 & S10).This Randle circuit was then placed within our larger IDE, to which we have also added the Z CPE,IDE and C sh terms.The former characterizes the surface roughness at the electrode/electrolyte interface and the latter the parasitic current shunts at high frequency [41] Notably, the appearance of a Z CPE,IDE at high hydration levels is also contributing to the appearance of electrode polarization (EP) at high hydration levels together with the increase of the Z CPE,dl .
The second way of analysing the EIS data was done via the broadband dielectric spectroscopy (BDS) approach.BDS was performed by the comparative study of the complex dielectric permittivity ε * and the complex AC conductivity, σ * [40].This approach allows understanding by inspecting data in the frequency domain.The complex permittivity ε * is expressed by the real ε ′ and imaginary part ε ′ ′ of the permittivity as in the following equation (equation ( 2)): where ε ′ and ε ′ ′ represent the storage and loss part respectively and is calculated by using the Re (Z) and Im (Z) frequency dispersions following the classical expressions [40]: with C 0 the equivalent geometrical vacuum cell capacitance (i.e.no sample between the electrodes) and with |Z| 2 the modulus squared of the impedance Z.
In the present case the value for C 0 is taken to be the value measured at high frequency for our empty IDE, namely 20 pF for the linear and 10 pF for the round geometry.We also determined the loss factor via [48,49]: which is useful for determining the ratio between the dissipative and dipolar component of the system under test.The Trukhan model is adopted here as a preliminary estimate of the free ion charge diffusion coefficient D via the expression: with L being the distance between the electrodes and ω max being the angular frequency at which tan δ is a maximum.In the present the value for L we take as the distance between each pair of fingers i.e. 10 µm.
The values for tan δ max are related to the Debye length [50], i.e. the distance of the occurrence of the charge screening effect with respect to the applied electric field The free ionic charge concentration n and mobility µ are given by: and where σ ′ (ω max ) AC is the real part of the AC conductivity at ω max .This corresponds to the centre value of the σ ′ AC plateau.Continuing, k B is the Boltzmann constant, T the temperature and e the electronic charge of 1.6 × 10 −19 • C.Here we consider the room temperature values, thus k B T = 0.025 eV.
The complex AC conductivity σ * is determined via the ε * (ω) using the expression [40]: ) . ( The radial frequency dependence of σ * (ω) was discussed considering the radial frequency functional dependence: i.e. in the framework of the Jonscher's classical power (0 < n < 1) and Funke approach (n > 1) [51] and by the addition of a third term representing the nearly constant loss term (NCL) [52].Here σ DC is the DC ionic current, Aω n refers to AC conductivity whose mechanisms will depend on the resulting n values and B is the slope of the linear growth of the conductivity.Typically, for 0 < n < 1 we will refer to a conduction mechanism governed by ionic charge jumps due to translational motion with hopping from delocalized states, whereas for n > 1 the hopping occurs between localized states.The AC permittivity experimental data were fitted using Novocontrol WinFIT 2.0 software allowing to insert up to three relaxation peaks described by the Havriliak-Negami (HN) model.The HN model is generally used to model BDS data showing more than one relaxation time distribution.It is, alongside an additional conductivity term, expressed as follows: ) N (7) where the jth dielectric relaxation function is summed into a superposition.Each function is characterized by a relaxation time distribution peaked at a specific time (τ j ) with characteristic parameters a j , b j , ε ∞j and ∆ε j , the latter of which is termed the dielectric strength and proportional to the area below the j-relaxation time distribution.The parameters a j and b j refers to the symmetry and broadening of the time relaxation distributions.If b j = 1 and 0 < α j < 1, the HN distribution is symmetric and it reduces to the 'Cole-Cole' distribution (C-C) whereas with a j = 1 and 0 < b j < 1, the HN function is an asymmetric distribution termed the 'Cole-Davidson' distribution (C-D).The last term is construed of the ionic DC conductivity σ DC , the permittivity of free space ε 0 and N.This last term adds to the dielectric loss at low frequency due to DC ionic conductivity with N regulating the slope of the straight line underlining the extension of the EP [53][54][55][56].
The set of best fit parameters (a j , b j , σ DC, N) were afterwards used for the calculation of each HNj j = 1,2,.K here K = 3) functions and their superposition leading to the permittivity curve that best fits the experimental data [57].Finally, we determine the frequencies of the maximum of each loss component of a HN function via [57]:

EIS analysis via Nyquist plot
The exposure to H 2 O and D 2 O vapours modify the features of the electrical response as depicted in figure 3. Starting from the dry regime, both sets of results display a pronounced circle corresponding to a high impedance value; under increasing the vapour exposure, the NPs progressively start to manifest a Randle circuit-like response.Corresponding changes in the modelled components, R ion , Z W0 and C dl also occur, but values depend on whether it is H 2 O or D 2 O vapour exposure.It is noteworthy that in the low frequency region the impedance of a BSF-mel film is higher for D 2 O exposure rather than H 2 O, as can be derived by the corresponding wider semicircle observed [58], thus suggesting a lower ionic conductivity when exposed to D 2 O.These results agree also with those observed on cephalopod proteins [58].
Additionally, we discount a significant electronic component to the electrical response for two reasons.Firstly, The NP analysis for the simplest circuit discounts the use of an additional parallel resistance, usually employed for electrons.Indeed, for the diffusion tails that are seen, if electrons are present, one would expect curvature back towards the real axis at low frequency.Secondly, as can be seen in the conductivity and dielectric spectra below (figure 5), the qualitative shapes of the curves are representative of ionic systems [59].Specifically, there is an electrode polarisation regime at low frequency, a flat real conductivity/plateau in an intermediate frequency range indicating diffusion control and then a power law dependence of the real conductivity at high frequency.These trends hold across the hydration range.
The full set of the best fit parameters have been summarized in the table S1 in the ESI.Focusing on the R ion parameter, we found the values under D 2 O exposure were larger than for H 2 O exposure at similar humidity values (see figure 4) [23].The trend line also shows a decrease of four orders of magnitude from low RH to high RH.We recall that in a Randle-type circuit, the R ion resistance is usually associated to the faradaic current R ct when applying a redox potential [60].However, a faradaic current's origin is usually due to redox processes, that is referenced relative to a reference electrode.In our case, our approach is much simpler, and we only apply a softer 0.0 V DC offset.As such, we assume that R ion represents actual ionic current, then under H 2 O we have a higher ionic current relative to D 2 O vapour exposure [60].Whether this is driven by ionic concentration changes or mobility changes, is further explored in the discussions below.
The term assigned to the charge double layer (Z CPE,dl ) forming at the electrodes has for D 2 O exposure, has a value independent of RH (n ∼ 0.6) ), being closer to a capacitor, whereas for H 2 O exposure n increases from ∼0.6 to ∼0.8 with RH (see table S1).The W o element has a peculiar behaviour depending on D 2 O or H 2 O exposure.Given the order of magnitude of the values extracted for the real and imaginary components (table S1), it is consistent with equation S9, i.e. low frequency limit.In this limit, the real part related to the Warburg diffusion impedance decreases in both cases.This is in essence additional evidence for enhanced ionic conductivity as expressed in figure 4. Conversely, the term related to the imaginary part is increasing with RH for H 2 O exposure and decreases for D 2 O exposure.A few situations may account for these behaviours.It could be that the width of the Nerst diffusion layer expands under D 2 O and shrinks under H 2 O, thus implying a greater increase in charge concentration near the electrode under D 2 O than under H 2 O.This is represented at the highest RH by a ZPE element Z CPE,n3 replacing the W o one in both cases, with the n ∼ 0.9 in D 2 O i.e. a more capacitive element, respect to the more diffusive one in H 2 O where n = 0.5 (table S1).On the other hand, the different behaviours for the imaginary component may be due to a decrease in the diffusion parameter for D 2 O (i.e.lower mobility) than under H 2 O (i.e. higher mobility).Of course, it may be that it is a combination of the above.This requires further interrogation, which is the purpose of the next set of analyses.

BDS data analysis
3.2.1.Frequency dependent complex spectra.The real and imaginary part of the dielectric permittivities, ε ′ and ε ′ ′ respectively, and conductivities, σ ′ and σ ′ ′ respectively, of the  BSF-Mel layers exposed to H 2 O and D 2 O are displayed separately for two RH regimes (low and high) in figure 5. Note, low and high regimes are only loosely connected to that of the NP analysis.The reason behind this choice is due to the dielectric spectral features displaying a substantial modification for RH values higher than ∼40% for both vapours, hinting at modification in the ion transport mechanisms due to hydration.
The dielectric features in figure 5 are progressively evolving with RH and is replicating to a certain extent that has been already observed for synthetic melanin [23], with the additional advantage of our frequency range being lowered down to 0.1 Hz, enabling an enhanced range to investigate ionic charge dynamics.The increase in RH causes a development of a plateau at low frequency in ε ′ and a sharp increase of σ ′ up to a plateau underlining the extention of the EP with hydration.This behaviour is similar in fashion to what is observed in ionic polymer electrolytes or ionic liquid when increasing the temperature [49,[61][62][63][64], which implies a similar action between temperature and hydration as environmental variables [22].
Turning to the RH range of ∼20%-∼40% (figures 5(b) and (f)), the real part of the conductivity follows the Johnsher's power law (n < 1), evidencing a non localized hopping regime.The frequency extention of this power law depends on the hydration level, which is then followed by a NCL region, i.e. n = 1.The hopping regime is characterized by n values of 0.6-0.5 under H 2 O and 0.7-0.6 under D 2 O exposure.As described in the methods section, values closer to n = 1 suggest a higher charge localization; therefore we infer that the larger values for n under D 2 O is a hint of more charge localization vis-à-vis H 2 O, maybe due to a higher energy barrier of formation [51].In the same RH regime, the ε ′ curves show a tail and a kink with increasing RH at the low frequency region, the former ending with a plateau corresponding to the value of the static dielectric constant ε R .at high frequency.
In the RH regime of ∼50%-∼95%, the real part of the AC conductivity (figures 5(d) and (h)) displays a sharp increase ending with a plateau and the tail of the NCL region whose onset progressively shifts toward frequencies higher than 0.1 MHz.The best fit of σ ′ to equation ( 6) returned values of n larger than 1.0, which following the Funke theory [51], suggests that the jump relaxation occus between localized states.This observation should be noteworthy, as it suggests that there may be some qualitative change in the charge structure of melanin with increasing hydration.The sharp increase in σ ′ corresponds to the plateau in ε ′ and together with σ ′ ′ behaviour and progressively appearing of ε ′ ′ bumps, marks the frequency extention of the EP.It is noteworthy the wider frequency extension of the EP region in the case of D 2 O relative to the H 2 O exposure data set, which is consistent with the idea of an increase in the Nerst diffusion length as discussed under the NP analysis.As such, we suggest that this analysis of the complex permitivity and conductivity data would imply that the underlying reason for the qualitative difference in the complex component of the Warburg element was due to a greater rate of expansion of the Nerst diffusion layer relative to the diffusion constant.As to the latter quantity, it will be explored below.

Permittivity best fit via HN modelling and underlying polymer dynamics.
The dielectric permittivities at selected RH values have been fitted using the HN formalism (equation ( 7)).The full set of the best fit parameters are summarized in the ESI, table S2.Example fits can be seen in figure 6.The assignement of each HN peak to a corresponding relaxation processes was done either by depending on the permittivity behaviour, or by making a comparative analysis with the AC conductivity (figure 5).In the range of ∼20% to ∼40% RH (both vapours) we see at RH 20% and 30% a contribution from the permittivity relaxation at high frequency corresponding to the regime where the Jonscher's hopping region transitions to the NCL, which we will label as HN NCL in the ESI.At ∼40% the EP is captured (HN EP ) at an oscillator frequency of 0.2 Hz and 0.5 Hz (D 2 O and H 2 O respectively) In the conductivity, this correspond to the starting of the Funke regime (visible as a short straight line in the region 0.1 Hz-1.0 Hz, figures 5(b) and (f)) still followed at higher frequency by the Jonscher's hopping one.At these intermediate RH values, the dielectric strengths (∆ε) for HN EP and HN NCL , differ about three orders of magnitude.A peak at 0.2 Hz was already observed for similar hydration levels in HN EP but no equivalent to the HN NCL was modelled, although the latter is a feature often observed in ionic conductors [52,63,65].
Representative complex permittivity spectra results for the RH range from ∼50% to ∼100% and HN best fits are shown in figure 6 for a sample on a linear IDE (example used at 70% RH), with tables S2(a) and (b) (ESI) summarizing the full set of best fit parameters.The complex permittivity spectra evolves in a fashion like that observed in a variety of structures seen in many polyelectrolytes or ionic conducting membranes, when increasing the temperature [61,62,[66][67][68][69].Therefore, we opt to interpret the dielectric behaviour in BSF-mel in a similar fashion, but using RH instead as the independent environmental variable.The data was modelled by the superposition of three HN functions.First of all, no peak was assigned to the NCL/hopping transition region as it was found to progressively move to higher frequencies and out of our measurement range (see figure 5).Given that the dielectric behaviour of BSF-mel have similarities with those seen in ionic conducting polymers, we assigned the other three peaks as the α and β relaxations, which relate to the inner polymer structures, and the highest frequency to electrode charging, i.e.HN EP .
Generally in pemittivity spectra, both α and β relaxations are due to the formation of polymeric chains whose aggregate dimensions and distances are modified during hydration and deuteration, which then change the 'polymer' chain aspect ratio [69].In this particular case, we venture to attribute the lower frequency α-relaxation to chain diffusion in the hydrated/deuterated BSF-Mel polymer whereas the βrelaxation is associated with polymer structures that can be associated with the diffusion from hydronium/dihydronium ion hopping mechanisms.One can relate the α and β relaxations peak frequencies (f α/β,MAX ) to a diffusion coefficient (D) via [69,70]: with D α = D chain being for the chain diffusion for the αrelaxation and l the radius of gyration R g of the chains.For βrelaxation, it implies that smaller aggregates have a diffusion of D β = D aggrepate and l the distance between the aggregates.The observed blue shifts in f α and f β when increasing the RH (see figure 7) hint respectively at the reduction of the aggregate radius (α-relaxation) and the distance for aggregate movement (β-relaxation), implying a coalescence of progressively smaller aggregates in continuous layer [69,[71][72][73] and/or an increase in the diffusion coefficients The dielectric strengths ∆ε (see table S2 ESI) of the αrelaxations display a slight increase both under H 2 O and D 2 O exposure whereas in the β ones it increases in D 2 O and is almost constant in H 2 O, which may be a consequence of deuteration of the polymer backbone.
The maxima f EP for the HN EP also display a blue shift vs. RH (figure 7).We recall that the f EP represent the frequency of the fully developed EP, whereas the frequency of the maxima in the loss factor (equation ( 3)) refers to the start of the EP.Both this frequency and loss factor are reciprocally related to the Debye length L D .Therefore, one can infer that L D decreases with increasing RH.
The dielectric stength ∆ε EP were also found directly related to the f EP and to the double layer capacitances (see figure S4), represented by the Z CPE,dl .The peak frequency f EP and ∆ε EP were lower in the case of D 2 O exposure vis a vis H 2 O.The former hints that in the case of D 2 O the slower response (low f EP ) is likely to be due to the higher mass of deuterated hydronium ions whereas the latter can be explained as due to the lower ion concentration, n ion , of D 2 O free ionic charges.

Trukhan modelling and ionic charge concentration and mobility extraction.
Overall, the values of σ ′ at the plateau in AC measurements are considered the DC conductivity values.In our case we obtain the value at the frequency of the maximum of the loss factor (see figure S2 in ESI).For the full RH range it can be seen (figure S6) that the conductivity ranges between 10 −11 S cm −1 -10 −5 S cm −1 under D 2 O exposure and from 10 −10 S cm −1 -10 −6 S cm −1 under H 2 O exposure, in line with previous observation on thin films of synthetic melanins [23,74].These observations are also consistent with the 4-6 orders change in the ion resistance as discussed under the NP analysis.
To investigate the charge transport properties further, we employ the methods of Trukhan, which thus far has not been employed on these materials.The advantage of this approach is that it will allow potential insights into the mobile charge concentration and mobility, which has been noted as sorely needed to advance understanding of these polyindole quinone materials [12,36,38,75].
The first step in the analysis is to obtain the Debye lengths L D , which were obtained via equation ( 4) and is depicted in figure 8.These lengths scales were found to be systematically larger under D 2 O exposure versus H 2 O, with both vapours leading to a decrease with increasing RH.Notably, such a change in the Debye length is again commonly observed in ionic conducting polyelectrolytes when increasing temperature [50].As above, such a similarity suggests that in melanin the RH has a role equivalent to temperature [22].
Using equation ( 4) the ion concentration n ion was calculated (figure 8 and table S2).The data show that the ionic charge concentration and conductivity increases with increasing RH, in-line with previous interpretations where it is expected that dissociation of carboxylic acids [75] and protonated semiquinones from a comproportionation reaction would supply protons for conduction [74,76].What is striking is that the charge concentration for BSF-mel is systematically higher under H 2 O exposure than for D 2 O exposure, but the rate of increase is greater under D 2 O.This is an interesting result in light of previous work on synthetic melanins [64].In the work by Rienecker et al the rate of the DC conductivity increase with hydration under D 2 O was greater than under H 2 O, which is also observed in this work (figure S6, ESI).In the aforementioned work the reason given for this different rate of increase was due to a greater generation rate of charges induced by D 2 O.This was argued to be due to a systematic shift in the underlying equilibrium chemistry induced by the kinetic isotope effect, i.e. the greater mass of deuterium relative to hydrogen.This initial inference from Rienecker et al [64] appears to have been confirmed, as there does appear to be a greater generation rate of mobile charges under D 2 O.
Although the IDE geometrical configuration affects the overall order of magnitude of the ion charge concentration and conductivity, the behaviour vs. the RH is maintained (see ESI); as a matter of fact the ratio n (D 2 O)/n (H 2 O) was found almost to be the same in both device configurations, returning an ion concentration one order of magnitude lower in the case of n (D 2 O) in all the RH range.As such, the effect of geometry can be discounted on the qualitative trends observed.
As would be noticed, there is no one-to-one correspondence between the ionic charge concentration and the conductivity.Given this, the mobility of the charges must now be considered, since mobility changes are certainly to be anticipated.The mobility was calculated using equation ( 4), with the results depicted in figure 9.The first thing of great note is that the mobility changes, both under D 2 O and H 2 O are ∼4-5 orders of magnitude.This would suggest that the primary conductivity change as a function of hydration is driven by the mobility changes, and not by the concentration changes, contrary to the literature of the past decade [12,76].These observations also contradict previous work in which muon spin resonance work implied that the proton mobility was constant of the same hydration range [76].As such, the analysis presented here must be treated with caution.However, this does not mean that the Trukhan approach is not viable, as these previous observations and discussions can all remain true, e.g. the muon particle used in [76] within the time scale observed may not be applicable to the frequencies probed in this work.What this situation does highlight is that going forward a major effort on investigating mobility effects must be made.In this framework, it is mandatory to perform a more careful estimate of the ionic charge density, generally requiring a correction factor or its evaluation via other techniques [77].
With caution, we continue and note that there appear to be two ranges for µ vs. RH.The first, lower RH regime (0%-50%) show comparable mobility values, maybe slightly lower ones for D 2 O vs H 2 O, whereas the higher RH regime starts to show a saturation of the mobility and divergence between D 2 O and H 2 O, with D 2 O paradoxically showing a higher mobility.
The low RH regime corresponds to the localised hopping regime in the frequency dependent hopping seen in figure 5, due to the observed n < 1.Furthermore, this low regime behaviour is also consistent with the slightly higher power law exponent observed for the D 2 O dataset.As for the low RH regime, the high RH regime can be identified alongside the different hopping mechanism that manifests itself as seen in figure 5. Other inelastic neutron scattering [36] and IR spectral studies [75] have noted that there is a qualitative change in water vibrational modes between drier and wetter conditions, which would imply different water structures in the material.Indeed, these authors suggested that a change in mobility may occur and may indeed yield different conductive entities, e.g.hydronium vs Zundel ion.The analysis pursued here do appear to indicate that at the very least we should expect a change in mobility mechanism as melanin is hydrated.The remaining issue is the apparent higher mobility exhibited when exposed to D 2 O.One would expect a lower mobility due to the kinetic isotope effect.If the Trukhan model is applicable to these high hydration levels, then the D 2 O data is suggesting that whatever the mechanism is for conduction, a standard appeal to mass difference is not going to be sufficient explanation, as the result is opposite to what one may expect.Indeed, a different approach should be considered, maybe along the lines of considering the difference in the Gibbs free energies of H 2 O and D 2 O and how it affects the energy landscape the ionic entities find themselves in.
Overall, more experimental as well as theoretical work is needed to tease out the mobility mechanism in melanin.

Conclusions
A number of key results have emerged from this study.The first is that the hydration dependent conductivity behaviour of BSF-mel is comparable to a number of other works on synthetic melanins, implying similar charge transport properties.The natural advantage the BSF-mel has is its processability and potential upscaling of production, making it a promising sensing material to fit within a circular economy model.
This indepth work has yielded deeper knowledge of the melanins in general [23].The higher quality data and extensive quantitative modelling, including the Trukhan analysis, has returned new insights into the charge transport mechanism of hydrated melanins.For example, there is a change in mobility mechanism going from low to high hydration states.Furthermore, the data also is consistent and confirms previous inferences as to the behaviour of ionic concentration changes.The double layer capacitances measured at high hydration levels, paves the route for the exploitation of this readily and sustainable sourced biopolymer in a variagate set of bioelectronic applications.
As such, we envisage its implementation as an electrochemical double layer capacitor in batteries and charge storage devices.It may also constitute a suitable and/or gate for organic transistors.Additional data supports this notion given the magnitude and shape of the hysteresis loops (data not shown) and the behaviour seen in the NPs at high hydration.Also, given the humidity dependence, the reactive free radicals sites of the material and physicochemical properties, we envisage sustainably produced humidity and/or other classes of vapor impedance-based sensors.Lastly, by tuning the properties with other components, BSF melanin may be used in biological assays of electroceutical devices.This is particularly relevant given the good biocompatibility of the material [78].Work on such devices exploiting the high processability of BSF melanin are in progress.

Figure 1 .
Figure 1.BSF-mel layer dropcast on a linear (top left) and round (top right) IDE at a concentration of 20 mg ml −1 .

Figure 2 .
Figure 2. Equivalent circuits adopted for the best fitting of the experimental NPs data (see figure 3 below) on BSF-mel layers.The best fit parameters have been summarized in table S1 in the ESI.The circuit in (a) refers to the NPs obtained at the lower relative humidity values of D 2 O and H 2 O; (b) scheme of the circuit adopted for all the other values of vapor pressures for both solvents; a Z CPE was used at the highest values of D 2 O or H 2 O vapor pressure instead of a Warburg element to capture electrode polarization effects.

Figure 3 .
Figure 3. NP representations of a BSF-layer on a linear IDE under exposure of D 2 O (red curves, upper column) and H 2 O (blue curves, lower column).Relative humidity are expressed as RH (%).The insets are the magnified views of the NPs in the high frequency region.Similar behaviors were observed on IDE round geometries (figures S1 and S2 in ESI).

Figure 4 .
Figure 4. R ion vs. RH (%) based upon the best fits to the NPs circuit (c) in figure 2. Depicted are the D 2 O (red triangles) and H 2 O (blue stars) data sets.The colored lines are the best fits using an exponential decay function, R ion = R ion,0 + A exp (−RH/RH 0 ) where RH 0 is a 'decay constant' with values of 5.8% for D 2 O and 4.1% for H 2 O.

Figure 5 .
Figure 5. Real (solid lines) and imaginary (dotted lines) parts of the complex dielectric permittivities (a), (c), (e), (g) and the corresponding complex conductivities (b), (d), (f), (h) of the BSF-mel layers.The data is organised by exposure to H 2 O (upper row) and D 2 O (lower row) in the low (a), (b), (e), (f) and high (c), (d), (g), (h) RH regimes.The cyan vertical straight lines are representative of the frequency of the electrode polarization (EP) and nearly constant loss (NCL) at RH = 40% and 42% whereas the orange lines refer to those of the EP and NCL at RH = 92% and 97.5% for H 2 O and D 2 O respectively.

Figure 6 .
Figure 6.Experimental dielectric losses ε ′ ′ vs. f (triangles and diamonds in the low and high RH regimes, respectively) for a representative BSF-mel layer on a linear IDE under similar increasing values of the H 2 O and D 2 O relative humidities.Best fit cuves, HNα ,β,EP functions and the linear conductivity term labeled with σ @

Figure 7 .
Figure 7. Values of the peak frequencies of the various HN peaks as a function of RH of D 2 O (a) and H 2 O (b) exposure of the BSF-mel.Each symbol refers to a specific HN function: triangles for NCL relaxation (H NCL ); squares for α-relaxation (HNα); circles for β-relaxation (HN β ); inverted triangle for EP (HN EP ).The increase of the peak frequency vs RH (same colors of the symbols for similar RH ranges) indicates a blue shift for all the relaxation processes.

Figure 8 .
Figure 8. Debye lengths L D (left) obtained from equation (4) and free ion charge concentration (right) obtained from equation (4) as a function of RH for BSF-mel on a linear IDE.Solid symbols represent the Debye length and open symbols the charge concentration.Red data is for D 2 O exposure and blue data for H 2 O exposure.

Figure 9 .
Figure 9. Free ionic charge mobilities µ vs RH for H 2 O (blue symbols and lines) and D 2 O (red symbols and lines) vapours, calculated by adopting the Trukhan model (see methods section) for a round (round symbols) and linear (squared symbols) IDE geometries.
PONa3_00369 SISTEMA; This work has been funded by Italian Ministry of University and Research (MUR), PRIN MUSSEL-2017YJMPZN MUSSEL.R G acknowledges the European Union-NextGenerationEU under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem grant ECS00000041-VITALITY-Spoke 9.For A B M: 'This work was also supported by the UKRI Research Partnerships Investment Fund through the Centre for Integrative Semiconductor Materials.'