In a recent study, O'Neill and co-authors have analysed the divergence of surface winds above the northwest Atlantic. In the time-mean, a band of convergence is found, overlying the Southern flanck of the Gulf Stream. To quantify the impact of storms, they have averaged divergence conditionally on the absence of rain, or have averaged divergence excluding extreme values. In the resulting averages, divergence is found to be positive nearly everywhere, hence the band of convergence is no longer present as convergence. O'Neill and coauthors claim that this absence of convergence in these averages allows to draw conclusions about the mechanisms underlying the atmospheric response to the Gulf Stream. We show that this absence of negative values results from the correlation between rain and divergence: averaging divergence conditionally on the absence of rain automatically implies a positive shift. In consequence, we argue that these statistics do not allow conclusions on the underlying mechanisms, but have the merit of highlighting the essential role of storms in shaping the divergence field in instantaneous fields.

Introduction

O 'Neill et al. (2017) have recently presented a detailed analysis on the relation between surface divergence and the underlying Sea Surface Temperature (SST) anomalies, drawing from a ten-year record of satellite measurements and from a one-year simulation with a regional model.

Their focus was on the relation between the time-mean surface divergence and the fluctuations associated to passing storms. Indeed, the time-mean divergence of surface winds (or of surface stress on the ocean) has been abundantly studied in the past decade, showing a conspicuous relation to SST [START_REF] Small | Air-sea interaction over ocean fronts and eddies[END_REF]; [START_REF] Bryan | Frontal scale air-sea interaction in high-resolution coupled climate models[END_REF] and references therein). In particular, [START_REF] Minobe | Influence of the Gulf Stream on the troposphere[END_REF] convincingly showed that there is convergence on the warm flank of the Gulf Stream and divergence on the cold flank. Yet, this time-mean divergence is of order 10 -5 s -1 , i.e. one order of magnitude weaker than the maximum instantaneous values found in the divergence field (of order 10 -4 s -1 ). These extreme values of surface divergence are often negative values (i.e. convergence) tied to surface fronts and the associated resulting convection (e.g. Figure 4 of [START_REF] O'neill | The Gulf Stream Convergence Zone in the time-mean winds[END_REF]).

O 'Neill et al. (2017) (hereafter ON17) have used different approaches and filters to isolate the contribution of storms to the time-mean signature in divergence. Their systematic analysis provides a novel and valuable outlook on an important aspect of the effect of SST on atmospheric dynamics. Indeed, different mechanisms have been proposed to explain the relation between SST and the overlying winds. On the one hand, the vertical-momentum mixing mechanism relies on the vertical stability of atmospheric boundary layer over SST anomalies [START_REF] Businger | The response of the marine boundary layer to mesoscale variations in sea-surface temperature[END_REF][START_REF] Hayes | The influence of sea surface temperature on surface wind in the eastern equatorial Pacific: weekly to monthly variability[END_REF][START_REF] Chelton | Satellite measurements reveal persistent small-scale features in ocean winds[END_REF]). On the other hand, a pressure adjustment mechanism relies on the hypothesis that the boundary layer is in an Ekman-like balance [START_REF] Lindzen | On the role of sea surface temperature gradients in forcing low-level winds and convergence in the tropics[END_REF][START_REF] Feliks | Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front[END_REF][START_REF] Minobe | Influence of the Gulf Stream on the troposphere[END_REF][START_REF] Lambaerts | Atmospheric response to sea surface temperature mesoscale structures[END_REF].

However the related studies have often focused on the time-mean fields and the interplay of different mechanisms in instantaneous complex flow fields remains unclear.

This problem falls in a broader category of problems common in geophysical fluid dynamics, in which a weak time-averaged signal is dwarfed in any instantaneous flow field by temporary fluctuations. As other examples, one may think of the Hadley circulation, mean currents in the ocean which are often dominated by the mesoscale eddy field, or the Brewer-Dobson circulation [START_REF] Butchart | The Brewer-Dobson circulation[END_REF], for which the ascending motion in the Tropics can only be indirectly inferred, because the associated vertical velocities are dwarfed by the signatures of equatorial waves in any snapshot of the flow field.

We wish to build on the analysis of ON17 and to point out an aspect of the method used in their paper that needs to be emphasized. Indeed, part of the conclusions put forward by ON17 relies on the computation of conditional averages of different fields. However, part of the interpretation of these statistics is not justified. Specifically, they claim that, because of the absence of convergence in 'rain-free' conditions (occurring between 80 and 90% of the time, see figure 2 of ON17), an 'Ekman-Balanced mass adjustment' mechanism (EBMA) cannot be at work. The underlying premise is that this mechanism should be 'persistent', and therefore be present even when averaging over a subset of times, especially a large subset.

The present comment aims merely to point out that conditional averages and other similar filters that are considered by ON17 introduce a bias, because the variable used for the condition is strongly correlated to the variable that is averaged. In the present case, it is not the sign of the averaged divergence that is meaningful, but rather its spatial variations. With that in mind, there is no longer a straightforward transition from ON17's results to an interpretation in terms of mechanisms. Nonetheless, we acknowledge that the study of ON17 has the merit of unveiling the possible role of synoptic storms in shaping the different mechanisms at work in instantaneous winds.

In section 2, a toy model is proposed to illustrate the difficulty in diagnosing the behavior of the marine atmospheric boundary layer (MABL) and storms in instantaneous or time-mean winds. An idealized simulation of storm tracks carried out with the WRF model is then investigated in section 3, both to further illustrate and confirm the statements of section 2, but also to explore how the time-mean divergence may result from a combination of mechanisms. Implications and directions for further research are discussed in section 4.

A toy model for illustrating conditional averages

In order to clarify the interpretation of the observations and model simulations carried out by ON17, we propose to consider a very simplified model.

a. On the sign of the average divergence

Many of the conclusions of ON17 come from the fact that the conspicuous band of convergence on the Southern flank of the Gulf Stream vanishes when divergence is averaged for rain-free conditions only (their figure 1b), or when other filters retaining rain events are used (figure 5b and8b). It is the disappearance of the negative values (in green with their colorbar) which they emphasize. ON17 deduce 'that the existence of the Gulf Stream Convergence Zone in the time-mean winds owes its existence to extreme storm convergences, since removing a relatively small number of data points associated with storms removes the time-mean convergence.' (ON17, end of section 3f, p2397). This line of reasoning bears a fundamental flaw as the conclusions of ON17 are mainly based on the sign of the rain-free time-mean convergence. In fact, it can be shown that any conditional average (here, rain-free conditions) will systematically introduce a positive or negative (here positive) bias in the variable that is averaged (here divergence) if this variable is statistically correlated with the chosen condition. The positive bias arises because rain and surface divergence are not dynamically independent. Hence the sign of the conditionally averaged divergence is not necessarily meaningful.

b. Toy model

A toy model is proposed below with the purpose of illustrating how a conditional average can shift the values of divergence towards positive or negative values, suggesting a different interpretation of ON17's figures. In the present case, our toy model is constructed such that a stationary, weak convergence coexists with random fluctuations that dominate the signal at any time but do not impact the long-term average. This toy model mimics two physical properties of the fields that are considered:

1. Rain and surface divergence are not independent variables: convective rain events are associated with mesoscale motions which include strong convergence roughly beneath the precipitating cell.

2. In the boundary layer, over a sufficiently long time and over a wide enough region, there is no net export or import of air. In other terms, strong convergence must be compensated by divergence in other locations.

The toy model describes the divergence spatial field, assuming that it consists of a permanent feature and random fluctuations that resemble convective events (rain associated to strong convergence values). To simplify we consider only one-dimensional signals, noted d(y,t), where y is a spatial dimension (e.g. transverse to a front of Sea Surface Temperature) and t is time. We assume that the divergence field is the sum of a permanent component, d p (y), and fluctuations d s (y, t) composed on several individual "storms" at each time, centered at random locations y c (t), but all with the same spatial shape (see Appendix), d(y,t) = d p (y) + d s (y, t) .

(1)

Note that, no assumption on the physical origin of the permanent signal is required in the following development as we only want to stress out difficulties in interpreting conditional averages.

We also consider that, at any particular time, d p and d s integrate to zero over the domain of interest and that storms d s occur at random locations with uniform probability so that they cancel out in the long run. In this case, the time-averaged divergence yields d p (y):

d(y) = 1 T T 0 d(y,t ′ ) dt ′ → d p (y) . (2)
Using simple sinusoidal functions, an implementation has been carried out, details are given in the Appendix. For simplicity, at each timestep, 5 "storm" centers are defined at random (uniformly distributed) locations in the domain (of length 2×D = 5000 km). Each storm consists in a region of convergence of maximal magnitude a = 1.0 × 10 -4 s -1 and of width 2 ×l = 100 km, compensated by weaker divergence of maximal magnitude 1.0 × 10 -5 s -1 and over a width L = 500 km on both sides. The stationary signal has a smaller magnitude, of 0.5 × 10 -5 s -1 . Figure 1 illustrates the stationary signal (panel a) and a typical instantaneous divergence field (panel b). It confirms that the stationary signal is dwarfed at any time by the intermittent signal from the fluctuations with much larger amplitude.

In ON17, the conditional average is taken over rain, which is related in some proportion to divergence. To represent this we produce an intermediate field r(y,t) = -d s (y,t) + η, where η is a random Gaussian noise (to make the field r(y,t) more similar to rain, one could set all its negative values to zero). The conditional average is then taken using the condition r > 0 ('rain only') or r ≤ 0 ('rain free'). Figure 2a illustrates the resulting averages obtained for different numbers of timesteps used. In the overall average, the stationary signal d p (y) is recovered (note that a signal different from d p is observed near the boundaries of the domain due to a finite domain effect).

In the rain-free average, the same signal is recovered but shifted to positive values. The shift is sufficient that all values (even in the region of convergence for d p (y)) become positive. In other words, this shift, or positive bias, is larger than the amplitude of d p (y). The 'rain-only' signal is shifted to strongly negative values; again the spatial structure is unaltered but it is hidden in the noise unless a long time average is taken.

The conclusion from this figure is that the conditional average (in the setting of this toy model) shifts the 'rain-free' average towards positive values, but without altering its spatial structure.

Moreover, as the rain-free average excludes the intense values (tied to storms), it is less noisy than the the overall average. The rain-only average including mainly extreme events is by construction very noisy.

c. The positive bias

We now take advantage of the simplicity of this toy model to quantify, in this case, the amplitude of the positive bias. This can be calculated simply in the case when there is no noise, i.e. we average conditionally on the sign of d s (y,t) and we consider only one storm by timestep. The storm locations being uniformly distributed and the spatial shape of d s (y,t) being fixed, the 'rain frequency' χ = p(rain > 0) is uniform across the domain and is given by the ratio of the width of the convergent region (d s < 0) over the width of the domain, 2 × D, such that χ = l/D. The form given to the convergence is such that its average value computed over the convergence zone is -2a/π. Hence the rain-only average is

d RO (y) = d p (y) - 2a π . (3)
As all times are partitioned into rain-free and rain-only, one necessarily verifies

d = d RF (1 -χ) + d R0
χ and the rain-free average can be calculated as

d RF (y) = d p (y) + 2a π l D -l . (4)
The above gives an estimate of the systematic biases introduced by the conditional averaging in absence of noise, i.e. when r(y,t) = -d s (y,t). When a random noise is present, rain and divergence have a less simple relation but are correlated. As the noise increases, the biases decrease in absolute value from their values obtained above, and the asymmetry between rain-free and rain-only means decreases, as illustrated from figure 2b. Nonetheless, because the signature in convergence of the rain events is much larger than that of the stationary signal, a ≫ max(d p (y)), and despite the fact that they occupy a small portion of space (l/(Dl) ∼ l/D ≪ 1), it is likely that the positive bias is sufficient to shift the whole signal of d RF to positive values.

The point that the above toy model illustrates is that the absence of convergence in the rainfree conditional average (d RF (y) < 0) does not rule out the presence of a stationary signal in the divergence field. It merely reflects that divergence and rain are strongly correlated, as illustrated by ON17 (see their figure 4c). We return to this issue below and in section 4.

Idealized atmospheric simulation

In order to bridge the gap between the maps displayed by ON17 and the one-dimensional illustrations from our toy model, we here take advantage of a simulation carried out for investigating the atmospheric response to mesoscale Sea Surface Temperature (SST) anomalies. This simulation will be described in a manuscript currently in preparation. It consists of an idealized set-up of a midlatitude storm-track using the Weather Research and Forecast (WRF) Model [START_REF] Skamarock | A description of the Advanced Research WRF Version 3[END_REF], in a zonally periodic channel and using a gray radiation scheme [START_REF] Frierson | A gray-radiation aquaplanet moist GCM. Part I: Static stability and eddy scale[END_REF]). The domain is 9216 km in both horizontal directions, and extends up to about 20 km (50 hPa) in height.

The horizontal resolution (dx = 18 km) allows a good description of atmospheric storms, leading to a reasonable storm track. Boundary layer processes are represented by the YSU scheme, convection by the Kain and Fritsch scheme, and microphysics by the Kessler scheme. The fixed zonally symmetric SST distribution in the simulation presented here consists of a large-scale meridional gradient with maximal amplitude of 4 K / 100 km. The simulation has been carried out for 4 years and the first 90 days were discarded. Data were recorded every 12h.

a. Conditional averages of surface divergence

Figure 3 shows the rain frequency and the mean rain rate over the whole domain, clearly indicating a preferred location for rain which is south and away from the SST front. This may be compared to Figure 2 of ON17, the comparison suggesting that our simulation has a realistic mean rain rate but overestimates the maximum rain frequency and the meridional contrast in rain frequency over the SST front. This does not matter for the present purpose, which is again to illustrate the systematic bias introduced by the conditional averages and by other similar filters.

Figure 4 shows the time-average and conditional averages of the surface divergence, as in Figure 1 of ON17. The mean surface divergence (panel a) shows a pattern with convergence South of the SST front, and divergence over the SST front and to the North of it, analogous to that displayed over the Gulf Stream by ON17. Mean values (extremes of about ± 0.4 × 10 -5 s -1 ) are quite comparable with the values found from observations. For the conditional averages, as expected, the rain-free divergence is shifted to positive values in all locations (panel b), whereas the rain-only divergence is shifted to only negative values (panel c).

Now, one advantage of this idealized setting is the zonal symmetry of the underlying SST, allowing to average easily in the along-front direction. This averaging leads to the same presentation as for the toy model of section 2. Figure 5 shows the zonally averaged time-mean surface divergence, along with the rain-free and rain-only conditional averages. In addition, the underlying Laplacian of SST is also displayed as an indication of area where surface convergence is expected in the EBMA theory. Again, it is clearly seen that the conditional average displaces the rain-free average to positive values, the rain-only average to negative values. Both conditional averages retain some of the spatial structure present in the all-weather average, but there are also notable differences.

For example, in the rain-free average the central couplet occurs on shorter spatial scales than in the all-weather average. The meaning and interpretation of these differences is not the purpose of the present comment, and would anyhow be tied to specificities of these idealized simulations. The important message is that the conditional average of divergence, conditioned on a variable with which divergence is correlated, leads to a bias which makes the convergent values disappear from the rain-free average. The disappearance of these convergent values does not allow the interpretation made by ON17, i.e. that a stationary (or permanent or persistent) feature be absent from the divergence field.

The same simulation can be used to illustrate another analysis made by ON17, bearing on the statistics of divergence. The skewness of the divergence distribution was emphasized as a crucial parameter (e.g. section 6 of ON17). As a complement to the conditional averages, ON17 examined the average of divergence when extreme values (away from the mean by more than twice the standard deviation) are excluded, or when only extreme values are retained (ON17, figure 5). This was not explored in the toy model because the distribution of divergent values in there was not tied to a physical description of the processes. In the numerical simulation with a mesoscale model it becomes meaningful to explore this distribution. Figure 6 shows maps of the mean divergence overall and filtered divergence excluding extreme values or retaining only those. The format for the first four panels is the same as that of figure 5 of ON17. As shown by panel d, the 2 ×σ filter removes a comparable amount of data (4 to 5%) in the area of maximum convergence. Again, the maps are very similar to the rain-free and rain-only means. In particular, the mean divergence excluding extreme values (Fig. 6b) is positive essentially everywhere, as the rain-free mean (Fig. 4b). Yet, as we saw previously it is not the sign of the mean divergence that is meaningful, but the spatial variations: in both cases the rain-free divergence did retain conspicuously part of the spatial variations present in the overall time-mean. In the last two panels of figure 6 (bottom row), the averaged divergences excluding or retaining extreme values are presented, but removing their domain average. It then becomes apparent that the former includes spatial variations very similar to those of the mean divergence, but slightly weaker. In contrast, the mean including only extreme events consists only of a strong band of convergence, wider than that of the overall mean divergence, and without the positive counterpart to the North. These different spatial structures and relative amplitudes can be better appreciated from the zonally averaged description of these means in figure 7, rather than in maps where the choice of colors guides the eye and interpretation.

It would be very informative in ON17 if their figures 1 and 5 were complemented with similar figures: for example, instead of presenting only the rain-free mean divergence, if a panel was included to show the rain-free mean divergence minus the spatial average over the area shown.

Alternatively, the rain-free divergence could be shown with contours overlaid to the overall mean divergence, so one could see if the spatial variations and features coincide (but the comparison of the amplitudes would remain difficult).

b. Statistics of divergence values

Finally, we use the simulation to explore the overall distribution of the values taken by the divergence, similar to ON17 in their figure 6. The distribution of divergent values in our simulation is shown in figure 8a, showing good qualitative agreement with the distribution displayed from observations by ON17. In particular, we also find that large positive values of divergence are more frequent in rain-only conditions than in rain-free conditions, implying that there is not systematically convergence below rain. But we emphasize that the large positive values are one order of magnitude less likely than negative values. Now it was stressed several times above that divergence and rain are not dynamically independent, and that they are statistically correlated. The simulation allows to document the joint Probability Distribution Function of divergence and rain, shown in figure 8b. The mean divergence, for a given value of rain, is negative and increasingly negative as the rain value increases, as shown by the blue line. This gives another a posteriori justification of the set-up of the toy model, where the intermediate rain field has been built by adding random noise to the divergence. This also allows to revisit how the sign of the rain-only mean divergence is determined. If we write p(e) de the probability that the divergence takes a value between e and e + de, the overall mean divergence can be written:

d = ∞ -∞ e p(e) de , (5)
The rain-only mean divergence (calculating using only values of rain above a threshold ε) is then written

d RO = ∞ -∞ e p(e|rain > ε) de ∞ -∞ p(e|rain > ε) de . ( 6
)
In the integrand of the numerator in equation ( 6), one may decompose the conditional probability on rain being larger than the threshold ε, and write it as the sum of the conditional probabilities knowing that rain is within interval [r, r + dr[: e p(e|rain > ε) = +∞ ε e p(e|r ≤ rain < r + dr)q(r) dr .

with q(r) the probability density function for the rain rate. This yields

d RO = ∞ -∞ e +∞ ε e p(e|r ≤ rain < r + dr)q(r) dr de ∞ -∞ p(e|rain > ε) de = +∞ ε q(r) +∞
-∞ e p(e|r ≤ rain < r + dr) de dr P(rain > ε)

= +∞ ε q(r) ⌈(r) dr P(rain > ε) (8)
with ⌈(r) = +∞ -∞ e p(e|r ≤ rain < r + dr) de. Up to a normalizing factor, ⌈(r) is the average divergence knowing the rain rate. This is calculated in our simulations and shown in figure 8b as the thick blue line. Consistent with the physical expectation that surface convergence and precipitation are highly correlated, the average divergence knowing the rain rate is always negative for values of rain larger than about 1 mm/day, and increasingly negative with increasing precipitation.

This clearly demonstrates that the correlation of convergence and precipitation leads to d RO being negative. In consequence d RF will systematically have a positive shift relative to d. Note that, because strong convergence corresponds to rain-only regions (see Fig. 8a), an analysis based on the 2 σ filter would lead to the same conclusion. The reason is that the condition still is strongly correlated to the divergence itself.

Discussion and perspectives

ON17 conclude from their analysis 'that the existence of the GSCZ in the time-mean winds owes its existence to extreme storm convergences, since removing a relatively small number of data points associated with storms removes the time-mean convergence' (section 3f, p2397). In the conclusion again they state that 'strong convergences associated with storms explains the existence of the GSCZ in the time-mean winds' (section 6, p2409). They explain that the skewness of the surface divergence distribution, due to the strong convergence signatures of mid-latitude cyclones,

'is sufficient to change the sign of the time mean and the interpretation of the SST influence on divergence. Removing fewer than 4% of the strongest divergence events, or removing fewer than 20% of values in raining conditions, effectively eliminates the GSCZ from the time-mean surface winds' (section 6, p2409). The underlying premise is that, if the convergence band vanishes when only a small portion of values are removed, this feature cannot be 'a persistent feature anchored to the Gulf Stream' (section 4d, p2404).

We disagree with this premise, but this does not invalidate the entire analysis of ON17 and their conclusions. Our disagreement stems from the too strong emphasis on the sign of the rain-free divergence. Our study has put in evidence the bias in this sign because of a dynamical link between surface divergence and precipitation that statistically correlates the two fields. As a consequence, the conditional average shifts the rain-free divergence towards positive values and the rain-only divergence towards strongly negative values. The correlation between precipitation and surface divergence is especially true for the most intense values as can be seen in their figures 4b and 4c. The joint PDF of convergence and precipitation, as shown in figure 8b for our simulations, illustrates clearly this correlation. It would be very interesting to estimate this joint PDF from

observations. Yet, as far as the color bars in their Figure 1, 5, and 13 allow to judge, much of the spatial variations between the rain-free and all weather divergence coincide. Rather than showing the absolute values of the rain-free and rain-only divergence, showing anomalies (relative either to the mean over the domain, or to the field smoothed on large scales) would be less misleading. In the case of the toy-model, the same spatial structure came out in the three averages, but the rainonly average is noisier. In the idealized simulations, the spatial structures of the rain-free average has strong resemblance to those of the overall average, whereas those of the rain-only average display some differences.

In the comparisons of their different figures, ON17 emphasize absolute values and discard the similarity that is often found between the spatial variations. For example, the claim of ON17 that the rain-free divergence in their figure 13b 'bears no resemblance' (p2401) with the SST Laplacian (figure 13h) is at the very least misleading. The spatial variations of both fields, as far as eye can tell, seem very correlated. The colors differ because the rain-free divergence is shifted everywhere to positive values because of the conditional average. Similarly, in the interpretation of their figure 11, the strong similarity at spatial scales less than 1000 km (panels 11a and 11b) is perhaps more significant than the difference in the worth emphasizing than the difference (again a positive shift)

in the spatially lowpass-filtered fields (panels 11c and 11d).

it is worth emphasizing that on spatial scales less than 1000 km (panels 11a and 11b), there is a strong similarity between the time-mean divergence (colors) and the SST Laplacian (contours). Now, to make progress we suggest to make the line of reasoning of ON17 more explicit, and to formulate two different hypotheses:

1. H1. The divergence at any time results from two signals: a stationary signal (related to EBMA), and random fluctuations from storms whose positions vary in time. The signal due to these fluctuations should diminish when averaging over longer times.

2. H2. The divergence at any time only results from storms. The spatial variations of these storms are such that in the time-average they produce the signature that is observed.

Set in the above terms, ON17 claims that the absence of convergence (negative values) in the rain-free average divergence rules out hypothesis H1. The toy model of section 2 merely served to illustrate that this conclusion is not justified: it is possible to have a rain-free divergence everywhere positive and yet to have a stationary signal which is responsible for all of the time-averaged signal. In other words, the absence of convergence in the rain-free divergence (or after filtering out extreme values) does not rule out H1, i.e. the existence of a permanent signal in the divergence.

Now, in our toy model, the shift is uniform in space as the storms were uniformly distributed in space. In contrast to this, in our idealized simulation (see section 3) and in the observations (see panel c of figure 1 of ON17) the shift is not uniform. Introducing spatial variations in the probability of occurrence of the storms in our toy model (see Appendix for description of the modifications of the toy model), one observes that storms still leave a residual signal that is related to the stationary divergence term (Fig. 9). Of course, this is on top on another signal due to the localization in space of storms in relation with H2.

Spelling out explicitly the two hypotheses provides two extreme pictures, and reality is likely, as often, in between. The links between the conditional averages analyzed by ON17 and the underlying mechanisms of the atmospheric response to the SST anomalies are not so simple, as illustrated by the present comment. Now, the detailed and extensive analysis carried out by ON17 does emphasize several important points: the instantaneous fluctuations in the divergence field overwhelms the time-mean, and understanding this response requires to consider how the SST influences storms, in particular in setting their preferred location. We believe that detailed investigations of the instantaneous signature of different mechanisms through which the SST influences the marine atmospheric boundary layer, as sketched in section 5 of ON17, are necessary to properly evaluate the relevance of these different mechanisms. These issues are complex as they depend on the variables and approach considered to quantify one or other mechanism, as will be discussed based on the simulations used in section 3 (Foussard et al, manuscript in preparation).

Acknowledgments. This work was granted access to the HPC resources of IDRIS under the allocation for 2015 and 2016 A0020106852 made by GENCI (Grand Equipement National de Calcul Intensif).

APPENDIX

Implementation of the toy model

The toy model we constructed only depends on the divergence fields d p and d s . We here describe the choices used to implement it. The permanent divergence signal was chosen as

d p (y) = A sin π y 2L , for -2L < y < 2L , = 0 , for |y| > 2L , (A1)
The divergence field is constructed as a sum of d p and of 5 'storms', each centered at a random (uniformly distributed) location within the domain [-D, D]. Each event, relative to its central location, has the following spatial structure:

g(y) = a l L sin (y + l) π L , for -(L + l) < y < -l , = -a cos y π 2 l , for -l < y < l , = a l L sin (y -l) π L , for l < y < L + l , = 0 , for |y| > L + l , (A2)
where -a describes the peak intensity of the convergence (a > 0), where l describes the width of the convergent region, and L describes the width of the surrounding regions where compensating divergence occurs. This definition is consistent with our idea that the net divergence would be zero (i.e. g(y)dy = 0). Then d s takes the form of

d s (y,t) = 5 ∑ i=1 g(y -y i c (t)) (A3)
where y i c (t) is the location of one of the storm centers at time t.

In order to obtain the 'rain' field r(y,t) = -d s + η, a random noise η is added. This noise has normal distribution with zero mean and a standard deviation of σ noise . -1 0 1 2 y in km

LIST OF FIGURES

×10 3 -4 -3 -2 -1 0 1 2 ×10 -5 divergence -2 -1 0 1 2 y in km ×10 3 -4 -3 -2 -1 0

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .

 123456789 Fig. 1. (a) The stationary divergence d p (y) (in s -1 ). (b) Snapshot of the fluctuating component d s (y,t) in s -1 (blue line) and of the resulting full divergence signal d(y,t) (red, dashed line). Note the different vertical scale relative to (a). . . . . . . . . . . . . . . 22 Fig. 2. (a) Time-mean divergence of the toy model, averaged over 10000 timesteps (thick lines), over 1000 timesteps (dashed lines) and 100 timesteps (dotted lines). The green lines correspond to total averages, whereas the blue lines correspond to rain-only and red lines correspond to rain-free conditional averages. (b) Same as (a), but with a noise level of σ = 5 × 10 -5 s -1 instead of 1 × 10 -5 s -1 . In both panels, the black dashed curve is d p . Parameters used for the toy model are given in the Appendix. . . . . . . . . . 23 Fig. 3. Mean rain frequency and mean rain rate (in mm/day) over the 4 years. Contours show the SST field in K. All calculations have been made considering rain rates over 12h superior to 3 mm/day. . . . . . . . . . . . . . . . . . . . . . . . 24 Fig. 4. Surface divergence, in colors and in 10 -5 s -1 , considering : (a) unconditional mean, (b) rain-free conditional mean (c) rain-only conditional mean. Contours show the SST field in • C. . . . . . . . . . . . . . . . . . . . . . . . . . 25 Fig. 5. Zonally averaged unconditional and conditional mean of surface divergence in 10 -5 s -1 . Same quantities as for panels (a), (b) and (c) of Fig. 4, considering the zonal mean of the signals. The light blue line is the Laplacian of SST in 10 -10 K m -2 . . . . . . . . . 26 Fig. 6. Mean Surface divergence, in shadings and in 10 -5 s -1 . (a) for the whole time series, (b) with values smaller than 2 × σ , (c) with only values larger than 2 × σ . (d) percentage of points with deviation from the mean bigger than the 2 × σ threshold. (e-f): Same as (b-c) after subtracting the domain-averaged signal. Contours show the SST field in K. . . . . . 27 Fig. 7. Unfiltered and filtered surface divergence in 10 -5 s -1 . Same quantities as for panels (a), (b) and (c) of Fig. 6, considering the zonal mean of the signals. . . . . . . . . . . 28 Fig. 8. (a) Probability density function of the surface divergence (red curve), calculated from all time outputs and for points within a band of latitudes (3600 km ≤ y ≤ 5600 km). Blue and green dashed lines show respective contributions of the rainy and rain-free points to the unconditional PDF. (b) Joint probability density function of the rain rate (vertical axis, in mm/day) and the surface divergence (horizontal axis, in 10 -5 s -1 ). Color scale is logarithmic. The blue line indicates the conditional mean of the surface divergence for a given rain rate. . . . . . . . . . . . . . . . . . . . . . . . . . 29 Fig. 9. (a) Rain frequency for the modified toy model. (b) Time-mean divergence of the modified toy model, averaged over 10000 timesteps. The green line correspond to total averages, whereas the blue line correspond to d RO /2, the red line to d RF and the dashed black line to d p . The blue dotted curve is d RO minus its spatial average value. It overlaps almost exactly with d p . Parameters used for the toy model are given in the Appendix. . . . . . . . 30

FIG. 3 .FIG. 4 .

 34 FIG. 2. (a)Time-mean divergence of the toy model, averaged over 10000 timesteps (thick lines), over 1000 timesteps (dashed lines) and 100 timesteps (dotted lines). The green lines correspond to total averages, whereas the blue lines correspond to rain-only and red lines correspond to rain-free conditional averages. (b) Same as (a), but with a noise level of σ = 5 × 10 -5 s -1 instead of 1 × 10 -5 s -1 . In both panels, the black dashed curve is d p . Parameters used for the toy model are given in the Appendix.

  FIG. 7. Unfiltered and filtered surface divergence in 10 -5 s -1 . Same quantities as for panels (a), (b) and (c) of Fig. 6, considering the zonal mean of the signals.

The values chosen for the parameters in order to generate the figures were: A = 0.5 × 10 -5 s -1 , a = 1×10 -4 s -1 , l = 50 km, L = 500 km, and D = 2500 km. The number of points in the y direction is ny = 200. Different values for the parameters have been explored. As the noise is increased, the positive bias of the rain-free mean divergence decreases. Nonetheless, as long as the noise is not much larger than a, the positive bias is robust and significant (i.e. sufficient for the rain-free mean to be positive nearly everywhere).

The model was also modified to show that the same results can be obtain when storms are located on the convergence zone. To this end we introduce a parameter 0 < C < 1. For each event, we take two random numbers, r uniformly distributed in [0, 1[ and s with a Gaussian distribution (centered at 0, and with variance 1). The storm position y c is then defined as

Figure 9 was produced with this scheme, still using 5 storms by time step, but without noise (σ noise = 0) and with 10000 timesteps. Parameter C was set to C = 0.4. The other parameters were the same as before.


Mathieu Valetaud

Gabriel Loget

Jeŕome Roche

Nina Husken

Zahra Fattah

Vasilica Badets

Olivier Fontaine

Dodzi Zigah

Keywords: High School/Introductory Chemistry, First-Year Undergraduate/General, Electrochemistry, Electrolytic/Galvanic Cells/Potentials, Hands-On Learning/Manipulatives, Laboratory Instruction

The Electrochemical Pen (EChemPen) was developed as an attractive tool for learning electrochemistry. The fabrication, principle, and operation of the EChemPen are simple and can be easily performed by students in practical classes. It is based on a regular fountain pen principle, where the electrolytic solution is dispensed at a tip to locally modify a conductive surface by triggering a localized electrochemical reaction. Three simple model reactions were chosen to demonstrate the versatility of the EChemPen for teaching various electrochemical processes. We describe first the reversible writing/erasing of metal letters, then the electrodeposition of a black conducting polymer "ink", and finally the colorful writings that can be generated by titanium anodization and that can be controlled by the applied potential. These entertaining and didactic experiments are adapted for teaching undergraduate students that start to study electrochemistry by means of surface modification reactions.

■ INTRODUCTION

Electrodeposition is an electrolytic process that uses electric current to form a coating on a conductive object. It is mainly applied to impart new surface properties to conductive objects, [START_REF] Harper | Mechanisms for Microstructure Evolution in Electroplated Copper Thin Films near Room Temperature[END_REF][START_REF] Imisides | The Use of Electropolymerization to Produce New Sensing Surfaces: A Review Emphasizing Electrode Position of Heteroaromatic Compounds[END_REF][START_REF] Rosenberg | Copper Metallization for High Performance Silicon Technology[END_REF] but can also be used to visually study electrochemical reactions. [START_REF] Parker | An Inexpensive Electrodeposition Device and Its Use in a Quantitative Analysis Laboratory Exercise[END_REF][START_REF] Loget | Propulsion of Microobjects by Dynamic Bipolar Self-Regeneration[END_REF] The most common technique employing the concept of electrodeposition is electroplating, where a metal cation (M n+ ) is reduced to the corresponding metal (M) at a cathodic electrode following the reaction:

+ → + - n M e M n ( 1
)
Electroplatings are usually performed using two planar electrodes, which are connected to a power supply and are placed in a beaker containing the electrolyte. When the electrical current flows through the cell, the cations are reduced and a newly formed metal layer can be observed on the cathodic electrode surface. [START_REF] Harper | Mechanisms for Microstructure Evolution in Electroplated Copper Thin Films near Room Temperature[END_REF][START_REF] Imisides | The Use of Electropolymerization to Produce New Sensing Surfaces: A Review Emphasizing Electrode Position of Heteroaromatic Compounds[END_REF] This is a typical experiment where the students can clearly see the color difference between the immersed and, thus, modified part of the cathode and the rest of the cathode, which remains unchanged.

With the endeavor to employ visually detectable electrochemical reactions for the purpose of writing and erasing, we developed an electrochemical pen (EChemPen). This is a pentype device which bases on a regular fountain pen principle.

The pen comprises a cylindrically shaped insulating shield, which contains the electrolyte and a metal wire wound around a wooden toothpick, as the core of the pen. A conductive surface acts as the second electrode, which can be locally modified by a localized, visual electrochemical reaction ("writing process"). This reaction is triggered as soon as the electrolyte solution is dispensed at the tip, which brings the two electrodes into electrical contact.

In the modern world where students use digital devices such as smartphones, tablets, and stylus to write on a daily basis, the inkless writing mode and the high-end functionality of our EChemPen aroused the students' interest for electrochemistry during a laboratory experiment. From a teacher's point of view, the various electrochemical concepts employed in the EChemPen present a lot of teaching material. Furthermore, these experiments only require cheap chemicals and materials and produce reproducible modifications that can be easily observed with the bare eye due to their strong colors.

To stimulate the students' interest, we propose to realize surface modifications using the EChemPen, as described in the following. The key point is that not only the electrochemical reactions has been studied but also the manufacturing of the DOI: 10.1021/acs.jchemed.5b00149

EChemPen (Figure 1), which has given insights into the mechanisms of electrochemistry. The manufacturing is easy, quick, and only requires cheap materials, which promises a wide applicability also in short lessons or in schools with a limited budget. These type of experiments that use household resources are attractive to the students and great fun to teach. [START_REF] Campbell | Simple Methods for Production of Nanoscale Metal Oxide Films from Household Sources[END_REF]7 Commercial electrochemical pen can be found; it is used in industry to study corrosion 8 but mostly to decorate jewelry. 9,10

■ MATERIALS

The following equipment and chemicals were used for the different versions of the EChemPen: a power supply (with a potential up to 100 V), button cells, copper wires (1 mm in diameter) coated with an insulating polymer, alligator clips, a metallic spoon, titanium foils, gold surfaces, toothpicks, a heat gun, heat shrinkable tubes, wooden pencils, 1 mL pipet tips, cotton, copper beads, distilled water and aqueous solutions of copper sulfate, sulfuric acid, and pyrrole.

Fabrication and Operation of the EChemPen

We fabricated and tested three versions of the EChemPen (see Figure 2) in order to demonstrate the versatility of the concept and to evaluate the optimal design. The simplest version involves a toothpick and is powered by an external power supply, while the more elaborated one is powered by an integrated battery. The fabrication of these three models is described in the following subsections.

Toothpick-Based EChemPen. The toothpick-based EChemPen (Figure 2 A) uses a regular toothpick as the tip of the pen and a copper wire as the electrode, which is wrapped around the toothpick close to one of its sharp extremities. A direct electrical contact between the copper wire and the electrode surface on which the writing will occur must be avoided in order to prevent an electrical short circuit. The other end of the wire was connected to the power supply. An insulating heat shrink tube was placed around the assembly of toothpick and copper wire in order to avoid any direct contact between the copper wire and the hand of the user. Even if this precaution allows avoiding any hazardous electrical risk, the use of insulating gloves is mandatory during the use of the EChemPen. As shown in Figure 1, the EChemPen was used like a dip pen with the ink as the electrolytic solution that mediates the electrodeposition. As it is often the case in conventional electrochemical experiments, the EChemPen writing is potentiostatic, i.e., the operator fixes the potential and the current flow is controlled automatically by the power supply. As soon as the EChemPen touches the conductive surface, the electrolyte solution forms a conductive bridge between the copper wire and the conductive surface, which closes the electrical circuit. Therein, the copper wire acts as the anode (or cathode) and the conductive surface acts as the cathode (or anode) and will be modified. During writing, the electrolyte bridge moves with the tip of the EChemPen, and thus, the modified area can be directly controlled by the hand of the operator. The electrolyte must be regularly reloaded to continue writing.

Pencil-Based EChemPen. The wood at both end of a pencil was removed in order to expose the graphite rod. The current will flow through the graphite to reach the end of the pipet tip where the graphite is in contact with the electrolyte. The power supply can either be directly connected to the graphite rod with a crocodile clip or an electrical connector can be interconnected to avoid breaking the fragile graphite rod. As can be seen in Figure 2B, a 1 mL pipet tip was used to form the end of the electroplating pencil. First, the end of the pipet tip was cut to enlarge the opening to 3 mm. A cotton patch was inserted at the end of the tip and a 3 mm copper bead was used as the active electrode material; it was incorporated into the pencil by pushing it on the cotton with the tip of the pencil. This 3 mm metal bead can be replaced by any conductive material that prevents the electrolyte solution getting into direct contact with the pencil lead. Then, the pencil was inserted into the pipet tip and the length of the graphite rod was adjusted to be in electrical contact with the metal bead. Finally, 3 holes were created around the pipet tip, between the metal bead and the end of the pipet to allow draining the air when filling the pencil with electrolyte. Battery-Powered EChemPen. A battery-powered EChemPen can also be easily fabricated. Even if using a power supply allows controlling the applied potential difference and thus to electrochemically modify the spoon surface, using a battery-powered EChemPen has the convenient benefit of being portable and more attractive to students as a wireless device. The wireless EChemPen is fabricated from a marker pen: the marker was first disassembled and the felt fabric was profusely rinsed to avoid the presence of any chemical. Then, a small toothpick with a wound copper wire was inserted as the writing tip and a cartridge was put over the toothpick as the electrolyte tank (see Figure 2B). Three button cells of 1.5 V were used in a serial configuration, one above the other, to give the desired potential difference (4.5 V). The positive side of the upper battery was connected to the gold surface by using a copper wire taped on its surface and the same procedure was used to connect the negative side of the lowest battery to the tip. This pen works like a real fountain pen where the electrolyte is provided automatically by the cartridge, and thus, it does not require reloading the tip by dipping during the writing process. A metal tip should not be used in order to avoid a short circuit between the tip and the surface.

■ HAZARDS

The students must wear protective glasses, gloves, and a lab coat at all times. They must avoid skin contact with solids and solutions and dispose of the solutions as instructed by their teacher. They must wash their hands before leaving the laboratory. To avoid electric risk they must wear gloves.

■ ELECTROPLATING OF COPPER

As a first example, we describe the local electroplating of copper onto a surface of stainless steel, in this case a spoon. This experiment is shown in Figure 3 and in video 1 (provided in Supporting Information). Here, the pencil-based EChemPen, filled with a solution of copper sulfate (0.5 M), was used. The copper spoon was connected to the power supply with a crocodile clip. The electrodeposition of copper will occur at the surface according to the following reaction:

+ → + - Cu 2e Cu 2 0
(2)

To perform this reduction reaction, the surface has to act as a cathode and, thus, needs to be connected to the negative pole of the power supply. The EChemPen was connected to the positive pole and acted as an anode where the counter reaction, the oxidation of the copper bead (that was located inside the tip), occurred:

→ + + - Cu Cu 2e 0 2 (3)
A potential of 20 V was applied, which led to the local deposition of metal copper at the surface of the spoon where the tip of the EChemPen is located. This phenomenon was used for writing the word "NSYSA", as shown in Figure 3. This is a classical electrochemistry experiment where the negative electrode is the cathode and the positive electrode is the anode. The current flows through the electrolyte solution, which brings the tip into electrical contact with the surface.

After writing with metal copper, we showed that the copper writing can be easily erased just by inverting the polarity of the EChemPen. When the surface of the spoon is connected to the positive pole of the power supply, it becomes an anode, which triggers the dissolution of the copper according to reaction 3. On the contrary, the copper bead becomes a cathode and the previously dissolved copper ions have been deposited on the bead following reaction 2. This simple phenomenon can be used to erase the copper writing, as it can be seen in Figure 3 and video 1. Now that we have shown that the EChemPen can be used for writing on the negative pole by the cathodic reduction of a metal salt, we will show in the following that it can also be used for the anodic electrodeposition of a conducting polymer.

■ ELECTRODEPOSITION OF A CONDUCTING POLYMER Electrodeposited conducting polymers (the main examples being polypyrrole, polyaniline, polythiophene, and poly(3,4ethylenedioxythiophene)) are materials of strong interest in the domains of sensors, 11 actuators 12 and electrochromic devices. [START_REF] Beaujuge | Color Control in Pi-Conjugated Organic Polymers for Use in Electrochromic Devices[END_REF] As shown in Figure 4A, the electrodeposition of polypyrrole (PPy) proceeds through the oxidation of pyrrole. This generates a radical cation, which reacts with another radical cation to form oligomers. The solubility of the polymer decreases with its length and PPy ultimately precipitates at the surface. [START_REF] Sadki | The Mechanisms of Pyrrole Electropolymerization[END_REF][START_REF] Diaz | Electrochemistry of Conducting Polypyrrole Films[END_REF] The EChemPen is used here to generate this conducting polymer locally on gold. The gold surfaces can be used several times after cleaning with a tissue soaked with ethanol in order to remove the electrodeposited polymer. Nevertheless, the polymer can be formed at any other conductive surface that can undergo at least 1.5 V/NHE [START_REF] Tabba | Anodic Oxidation Potentials of Substituted Pyrroles: Derivation and Analysis of Substituent Partial Potentials[END_REF] without being damaged (i.e., platinum or carbon), which corresponds to the potential required for the oxidation of pyrrole to polypyrrole.

The experiments shown in Figure 4B were performed by using the simple toothpick configuration connected to a power supply, while the electropolymerization shown in Figure 4C was performed with the battery-powered portable configuration. The electropolymerization occurs at the gold anode, and the reduction of water (reaction 4) occurs as counter reaction at the copper-wire cathode.

+ → + - - 2H O 2e 2OH H 2 2 (4)
Figure 4B shows the result of the electropolymerization using the toothpick configuration. A potential of 4 V was applied to write the word "NSYSA". The symbols shown in Figure 3C were written with the portable configuration using three button cells of 1.5 V each, which corresponds to a potential difference of 4.5 V in this case. These experiments show the simplicity of the two EChemPen configurations and that this concept can be used for the straightforward writing employing the electropolymerization of PPy. In the following, we introduce a last experiment that can be performed by students with the EChemPen.

■ ANODIZATION OF TITANIUM

Anodization is an electrochemical process where an oxide layer is formed on a metal surface. The anodization of titanium is an electrochemical technique of first interest, and since it is applied in various industrial processes, it is also of strong interest in current scientific research. [START_REF] Lee | One-Dimensional Titanium Dioxide Nanomaterials: Nanotubes[END_REF][START_REF] Kuang | Application of Highly Ordered TiO2 Nanotube Arrays in Flexible Dye-Sensitized Solar Cells[END_REF] Furthermore, applying anodization to the EChemPen enables us to visualize the effect of the potential difference applied during the electrochemical experiment. Indeed, the applied potential controls the thickness of the created titanium oxide layer, which is linked to the color of the anodized area. Thus, the color of the formed titanium oxide layer can be directly controlled by the applied potential. [START_REF] Diamanti | Interference Colors of Thin Oxide Layers on Titanium[END_REF][START_REF] Gaul | Coloring Titanium and Related Metals by Electrochemical Oxidation[END_REF] In these experiments, titanium was locally anodized for the creation of a colored writing. An acid solution (H 2 SO 4 at 0.5 M) was used as electrolyte without any soluble precursor, which suppresses the competing deposition reaction. The acid solution only serves as electrolyte and ensures sufficient ionic conduction between the pen and the surface. The titanium itself was oxidized to titanium oxide according to the following reaction:

+ → + + + - Ti 2H O TiO 4H 4e 2 2 (5)
The anodization of titanium is a process that is used in the production of jewelry to obtain surfaces with different colors. 8 With the use of the toothpick-based EChemPen, the five different potentials 20, 30, 40, 50, and 60 V were applied using the power supply. As shown in Figure 5, these potentials gave titanium layers of the colors brown, purple, blue, light blue, and yellow, respectively.

The anodization of titanium generates a thin film of TiO 2 . The thickness of this film is typically in the order of tens to hundreds of nanometers and depends on the applied potential. In these nanoscale films, light that reflects from both the top and the bottom surface of the TiO 2 film can constructively or destructively interfere to produce different colors.

■ STUDENT RESULTS

The toothpick EChemPen was used by the students to perform copper deposition on metallic spoon. The students completed the experiment in 1 h. They found difficult the step where the copper wire is put around the toothpick because the wire should not be too long to avoid direct contact with the surface, but it still needs to be close to the end of the toothpick. Some of them were surprised by the bubbles that appear during the writing process. The bubbles came from water reduction. If the writing is too long, the EChemPen will stop working if it is not refilled. Others students were afraid by the increase in the temperature at the end of the toothpick, and possibly on the spoon (because of the Joule effect) that could appear if the writing is too long. When writing with the copper solution, the letters may not appear like usual nice orange-red color of metallic copper but darker. It is because copper oxide can also be formed. As a general impression, the students found the experiment funny and interesting. Thanks to this experiment, concepts such as oxidation and reduction reaction that seemed difficult to assimilate previously became easy to learn. They understood the role played by the anode, cathode, and the polarity of the electrodes in different electrochemical reactions.

■ CONCLUSION

In summary, we presented the EChemPen, a simple device that can be built by students to write electrochemically. The three proposed laboratory experiments based on the electroplating of copper, the electropolymerization of pyrrole, and the anodization of titanium introduce electrochemistry to students in a new attractive way. Students can manufacture their EChemPen themselves and compare their results. The experiments produce results that are directly visualized and that can be tuned by changing simple parameters such as the polarity and the potential value. We believe that the EChemPen presents an educationally very stimulating mean for teaching students different concepts of electrochemical reactions. Furthermore, these experiments are very well suitable for a surface modification course, including analytical chemistry or instrumental analysis, and could also be adapted for classroom demonstrations.

■ ASSOCIATED CONTENT

* S Supporting Information

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.5b00149.

Instructor notes (PDF, DOCX) Student handouts (PDF, DOCX) Screenshots of video (PDF)

Video showing the use of the EChemPen to write on a spoon (AVI)

Introduction to electrochemical reaction with the electrochemical Pen

Safety Considerations:

Wear protective glasses, gloves and a lab coat at all times. Avoid skin contact with solids and solutions. Dispose of the solutions as instructed by your teacher. Wash your hands before leaving the laboratory.

To avoid electric risk never work without gloves.

Introduction:

Chemical reactions where electrons are transferred from one reactant to another are called redox reactions or oxido-reduction reactions. A redox reaction can be decomposed in two half-reaction, the oxidation and the reduction. During the oxidation a species will lose one or more electrons whereas during the reduction a species will gain one or more electrons. Electrochemistry allows driving non spontaneous redox reactions using electricity.

An example of reduction reaction is the formation of a metal from the corresponding ions.

M z+ + ze -→ M An example of oxidation reaction is the dissolution of a metal M → M z+ + ze - Purpose:

You will write your initials, on the metallic object provides by your teacher (spoon, key…) by using the method of electroplating. Each initial should be made of a different metal. At the end of the experiment you must find a method to remove your initial using electrochemistry. 1. Manufacturing of the electrochemical pen.

Cut 30 cm of the insulated copper wire. At both ends remove 1 cm of the insulated layer, roll up the copper wire around the tooth pick by letting 0.5 cm between the end of the copper wire and the end of the tooth pick. During the experiment the copper wire must not touch the surface of the spoon.

Put a heat shrinkable tubes around the tooth pick and the copper wire and use the heat gun to stick together the tooth pick and the copper wire, see figure 1 for the final electrochemical pen. Prepare two electrochemical pens, one for each solution.

Figure 1 .

 1 Figure 1. Scheme showing the principle of the EChemPen.

Figure 2 .

 2 Figure 2. Pictures showing the fabrication of the three versions of the EChemPen. (A) Toothpick-based EChemPen. (B) Pencil-based EChemPen with (1) 1 mL pipet tip; (2) cotton patch; (3) 3 mm copper bead; (4) holes for air draining. (C) Battery-powered EChemPen with (1) pen body; (2) contact clip; (3) batteries; (4) toothpick; (5) felt fabric; (6) ink cartridge; (7) wires.

Figure 3 .

 3 Figure 3. Writing/erasing of copper letters on a spoon, for more information, check video 1 in Supporting Information. (A) writing with copper; (B) full text; (C) copper erasing.

Figure 4 .

 4 Figure 4. (A) Mechanism of electropolymerization. Electrodeposition of polypyrrole (B) using the EChemPen (toothpick configuration). (C) using the portable EChemPen.

Figure 5 .

 5 Figure 5. Titanium oxidation using the EChemPen.

  leads with crocodile clips at both ends -insulated copper wire -wire stripper -Heat shrinkable tubes (not essential) can be replace by a simple scotch tap -Heat Gun (not essential) Procedure:

Figure 1 :

 1 Figure 1 : Toothpick-based electrochemical pen

Figure 2 :

 2 Figure 2 : spoon and electrochemical pen connected to a battery.

■ AUTHOR INFORMATION

Corresponding Author *E-mail: dodzi.zigah@u-bordeaux.fr.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We thank Alexander Kuhn and Laurent Bouffier for the fruitful discussions, Xolali Zigah for his participation to the video clip.

Instructor notes

We recommend to use the electrochemical pen as a supplementary exercise to complete a classic experiment when electroplating is studied. This experiment can be made by two students in one hour.

On Figure 1 we detailed the fabrication of the electrochemical pen using the tooth pick. The copper wire is wind around the tooth pick then a heat shrinkable tube (or a scotch tape) is used to fix the copper wire to the tooth pick and to avoid direct contact between the experimenter and the tooth pick to prevent counters shock. Because two electrolytic solutions are used to write, the students need to build two pens in order to avoid contamination of the second solution by the first one.

Bubbles and increasing of temperature can happen during writing. The bubbles are H 2 and O 2 produced by water reduction and oxidation respectively. When writing with the copper solution the letter may not appear like usual nice orange-red color of metallic copper but darker. It is because copper oxide can also be formed. Indeed, water electrosplitting reactions also induce local pH changes in the solution. But to simplify the problem, and the equations for the Cu 2+ reduction teachers should speak only about metallic copper. The oxidation reaction is water oxidation and also oxidation of the copper wire.

2

To remove the writing using the electrochemical pen you just need to inverse the polarity. Indeed if now the spoon is connected to the positive borne oxidation reaction will happen on the spoon by consequence Cu and Zn can be oxidized in Cu 2+ and Zn 2+ respectively. On Figure 2 we described the fabrication of the battery-powered electrochemical pen. The batteries (LR44) are put one above the other inside the corps on the pen. A scotch tape is used to fix the copper wires on the first and on the last battery. The Titanium foil used was purchased from Alfa-Aesar, the thickness was 250 µm. Before used titanium was rinsed successively in ethanol, acetone and distilled water.