# Metal-polymer hybrid chemiresistive sensor for low concentration fast
hydrogen detection

Christina E. Antony  School of Physics, Indian Institute of Science Education
and Research Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551
Praveen S. G  School of Physics, Indian Institute of Science Education and
Research Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551  Adithya
Jayakumar  School of Physics, Indian Institute of Science Education and
Research Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551  Gaana K
School of Physics, Indian Institute of Science Education and Research
Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551  Akshay Yadav
School of Physics, Indian Institute of Science Education and Research
Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551  Nikhil S.
Sivakumar  Department of Physics, IISER Mohali, Knowledge city, Mohali-140306,
India  Niranjan Kamath  Department of Physics, IIT Madras, Chennai-600036,
India  Suma M. N  LPSC Bangalore, ISRO, Benguluru-560008, India  Vinayak B.
Kamble  School of Physics, Indian Institute of Science Education and Research
Thiruvanthapuram, Vithura, Thiruvananthapuram, India-695551  D. Jaiswal-Nagar
<EMAIL_ADDRESS>School of Physics, Indian Institute of Science
Education and Research Thiruvanthapuram, Vithura, Thiruvananthapuram,
India-695551

###### Abstract

Low concentration hydrogen gas detection is of paramount importance both in
space applications as well as medical applications. It is also critically
important for safe handling of hydrogen below the explosive limit. Here, we
report a novel hybrid Pd metal-polymer chemiresistive sensor that can sense
0.5$\%$ hydrogen (H2) gas in ambient conditions of temperature and pressure
with the highest reported sensitivity ($\sim$ 30$\%$) obtained earlier by a
physical deposition technique, making it an extremely good sensor for real
life low concentration hydrogen gas detection. The sensor is easy to fabricate
and is also extremely cost-effective for commercial applications. The obtained
hybrid chemiresistive sensor comprises palladium (Pd) nanocrystals bound by
oxygen and nitrogen atoms of a stabilizer Polyvinylepyrollidone (PVP), grown
on top of a self-assembled monolayer. The exceptional rise time-constant is
proposed to arise from hydrogen loading at the (111) surface of the palladium
nanocrystal which is a very fast process and subsequent fast diffusion of the
H atoms from the surface into the bulk. An effort to increase the number of
available sites by UV-ozone cleaning, resulted in a degradation of the sensing
device due to the poisoning of the available sites by oxygen.

###### keywords:

Hydrogen Sensors $|$ Chemiresistive sensors $|$ Palladium metal $|$ X-ray
photoelectron spectroscopy

Hydrogen gas is an efficient, renewable and clean energy source that can
contribute to solving the problems of depleting world fossil fuel reserves 1.
However, hydrogen is a hazardous gas since it is flammable and explosive in
air and the explosive limit ranges between 4.65 and 93.9 vol$\%$ hydrogen
(H2). Since it is colourless, odourless and tasteless, it is difficult to
detect H2 by human senses. Therefore, alternate robust hydrogen leakage
sensors are required to rapidly sense and quantify the concentration of
hydrogen much below the regulatory range to avoid any potential explosion
hazard associated with using hydrogen as an energy source 2. Hydrogen sensors
are also required in the chemical industry to monitor hydration of
hydrocarbons, synthesis of methanol and ammonia, desulphurisation of petroleum
products etc. 3. Breath hydrogen is an important parameter used in clinical
determination of lactose intolerance, bacterial growth, microbial activity,
diabetic gastroparesis etc. 4 making hydrogen sensors that could detect
hydrogen in the low concentration of 1000 ppm, of immense importance in
biomedical applications. Hydrogen sensors are also needed in aerospace
applications, especially those involving hydrogen fuel propulsion systems,
where detection of hydrogen at low concentrations is necessary to monitor
shuttle launches in order to avoid possible launch failures 2, 5. Similarly,
low concentration hydrogen detection helps in space exploration to estimate
details of universe formation and its evolution 6. So, it is of paramount
importance to develop a safe, reliable, compact, cost-effective and efficient
hydrogen sensor that can not only measure hydrogen gas in low concentrations
with high sensitivity and fast response times but is also easy to fabricate.
Nanostructured materials, whose properties vary significantly compared to
their bulk counterparts due to large surface to volume ratios and quantum-
confinement effects, have been at the forefront of hydrogen sensing research
8, 11, 13, 14, 15, 16, 17, 10, 7, 9, 12. A variety of hydrogen sensors in the
form of nanofibres 7, nanowires 8, nanoclusters 10 etc. have been reported,
that utilize a change in some physical property like mass, volume, optical
constant, work function, resistivity 8, 11, 13, 14, 15, 16, 17, 7, 9, 12, 10
etc. Of these, resistivity based electronic sensors offer an appealing
possibility of cost-effectiveness, durability and reliability due to the ease
of operation, integration with conventional circuit electronics,
miniaturization potential, scalability and portability. Palladium (Pd) metal’s
hydrogen selective catalytic activity is very well known 18, 11, 19, 20, 21.
In this process, the surface of palladium acts catalytically on the incoming
hydrogen molecule breaking the diatomic hydrogen to monoatomic hydrogen which
then diffuse inside the Pd lattice 19 and occupy interstitial sites of Pd
resulting in the expansion of Pd lattice and formation of a hydride of
palladium, PdHx 18, 11, 19, 20, 21. For x $<$ 0.01, a solid solution, PdHα,
gets stabilised due to random occupation of hydrogen while for 0.02 $<$ x $<$
0.6, an octahedral lattice hydride PdHβ is formed 21, 20. The expansion is
smaller than 0.13$\%$ in the PdHα state (a0 = 0.3890 nm for pure Pd and
a${}_{\alpha},_{max}$ = 0.3895 nm for PdH${}_{\alpha},_{max}$) but reaches a
change of 3.5$\%$ from PdH${}_{\alpha},_{max}$ to PdH${}_{\beta},_{min}$. So,
bulk Pd based sensors suffer from a lower limit of sensing since the PdHα to
PdHβ transition happens at $\sim$ 1$\%$ of H2 concentration. However, the
situation changes drastically when Pd is in a nanostructured form since the
surface to volume ratio increases manifolds implying large surface activities,
and hence, reducing the sensing limit to lower values 22, 11.
Chemiresistive sensors are a class of sensors that work on the change in
electrical resistance due to surface adsorption of analyte molecules 23. Such
sensors are easy to fabricate, are very cost effective and have high
miniaturization potential 17. In this work, we report on a novel
chemiresistive sensor that was built by capping Pd nanocrystals with a
stabilizer Polyvinylepyrollidone (PVP). It is known that capping ligands
chemisorbed on the surfaces of metal nanocrystals not only act as stabilisers
but also modify the functionality of the nanocrystals since the attached atoms
or functional groups of the stabilisers affect the nanoparticle’s accessible
surface area, electronic structure properties and surface properties like
catalysis 25, 26, 27, 24. In this regard, even though Pd-PVP structures have
been investigated immensely for their catalytic properties 26, 25, 28, 24,
there have been, surprisingly very few reports on its H2 sensing abilities.
Here, we make a novel architecture of Pd-PVP structure that was built on a
siloxane self- assembled monolayer. The PVP-Pd mole ratio was varied from 0.06
to 0.24 and each architecture that was built for a given PVP-Pd ratio, was
tested for hydrogen sensing. It was found that only the assembly with PVP-Pd
ratio of 0.10 could sense hydrogen. The sensing characteristics were found to
be very good, wherein, the assembly could sense low concentrations of H2 (upto
0.1$\%$) with fast response times ($\sim$ 50 s) and very high sensitivity (
30$\%$ at 0.5$\%$ H2). From detailed x-ray photoelectron spectroscopy
measurements, it was found that the chemisorption of the PVP molecule with the
Pd nanocrystals happened via the oxygen and nitrogen atoms of PVP molecule. It
was also found that the number of bare Pd metal active sites are maximum for
PVP-Pd mole ratio of 0.10, resulting in a sensing response for only this
ratio. The obtained chemiresistive sensor has immense potential for commercial
applications due to its simple and cost-effective method of fabrication that
yielded comparative results on sensitivity and response time obtained by a
physical deposition method 11.

## Materials and Methods

### Materials:

Palladium Chloride (PdCl2) which is the metal precursor, was purchased from
Merck-Aldrich and used as such. Poly (N-vinyl-2-pyrrolidone) (PVP, standard
molecular weight of 40,000; Merck-Aldrich) was used as a stabilizer for the
Palladium nanocrystals. Ethanol (C2H5OH) used as the reducing alcohol, was of
guaranteed grade and used without any further purification. Siloxane (N-
chloro(dimethyl)octyl silane, Merck-Aldrich) used for making a self-assembled
monolayer (SAM) was used without any further purification. Synthetic air and
hydrogen gas (4$\%$ dilution) cylinders were purchased from Bhuruka Gas,
India.

### Palladium nanocrystals synthesis:

The synthesis procedure comprises reduction 24 of metal precursor using
ethanol in the presence of capping agent, PVP, at an elevated temperature. So,
an aqueous solution (2mM) of H2PdCl4 was prepared by mixing 106.4 mg of PdCl2
(0.6 mmoL)- the metal precursor, 6 mL of 0.2 M HCl and 294 mL of distilled
water. By mixing 15 mL of as prepared 2mM H2PdCl4 solution with varying
concentrations of ethanol (ranging from 10$\%$ to 70$\%$ vol.) and designated
amount of PVP (ranging from 0.2 mg to 0.5 mg), different solutions were made.
We made four different solutions with PVP$/$Pd ratio as 0.06, 0.10, 0.13 and
0.24. After letting the colloidal nanoparticles to age for two to three days,
the solutions were refluxed in a 250 mL flask for about 15 hours at an
elevated temperature of 378 K, as shown in Fig. 1. Refluxing results in
repeated filtration of the as prepared colloidal solution, resulting in PVP
protected palladium (PVP-Pd) nanocrystals of a narrow size distribution see
(Figs. 3 (a)-(d)).

### Sensing assembly fabrication:

To prepare the substrates for hydrogen gas sensing, glass slides were cut into
rectangles of 1.0 cm x 0.3 cm sizes and degreased by sonicating in an
ultrasonic bath using acetone and isopropanol, for sufficient amount of time.
The cleaned slides were, then, washed with milliQ water. The centre of the
cleaned glass slides was shadow masked with a copper wire of 110 $\mu$m
diameter. A thin layer of gold (Au) film of thickness 50 nm was deposited on
the glass slide using a thermal evporator, to act as contact pads. Prior to
gold layer deposition, a thin wetting layer of chromium was also deposited.
Then, the shadow mask was removed to give an insulating channel of 80 $\mu$m
width. The fabricated substrate was, then, immersed in 0.1M chloro (dimethyl)
octyl silane for 1 hr which results in the formation of a silane self-
assembled monolayer (SAM). In the final stage of sensing assembly fabrication,
colloidal PVP-Pd nanocrystal solution, prepared according to the details
above, was drop casted (20$\mu$l) over the channel in the silane SAM coated
substrate. The assembly was, then, allowed to dry in the room temperature
conditions. The detailed schematic of the entire procedure is shown in Fig. 1.

### Sensing measurement:

Resistance (R) based hydrogen (H2) gas sensing measurements were carried out
in an in-house built gas sensor characterization system 29. H2 and synthetic
air flows towards the chamber were regulated using Alicat Scientific’s mass
flow controllers to achieve desired dilution of the H2 gas. Prior to hydrogen
gas flow, the chamber was purged and saturated with synthetic air. The change
of resistance of the devised assembly described above, upon the sorption of
hydrogen was measured using Keithley’s 2700 Digital multimeter cum data
acquisition system 29, 22.

### Experimental techniques:

Ultraviolet-visible (UV-Vis) spectroscopy was done on Shimadzu’s UV-VIS-NIR
spectrophotometer (Model No. UV 3600). The surface morphology and the size
distribution of the as-formed PVP-Pd nanocrystals were characterized using a
300 kV FEI Tecnai’s (Model No. G2 F30 S – Twin) high resolution transmission
electron microscope (HRTEM). Samples for the HRTEM measurements were prepared
by dropcasting 20$\mu$l of the colloidal solution onto a TEM grid, followed by
natural evaporation of the solvent. To understand the final chemical and
electronic state of PVP-Pd assembly, high resolution x-ray photoelectron
spectroscopy experiments were done using a ESCA Plus spectrometer (Omicron
Nanotechnology Ltd. Germany) equipment with Mg Kα radiation (1253.6 eV). The
instrument is equipped with an auto-charge neutraliser.

## Metal-Polymer chemiresistive hydrogen sensor architechture

Figure 1: Schematic of the steps involved in making the chemiresistive sensor.

As described in the methods section, the novel architechture of our hybrid
metal-polymer chemiresistive sensor consists of a random array of hexagon
shaped Pd metal nanocrystals complexed with PVP molecules, on a siloxane self-
assembled monolayer (SAM) coated on top of bare glass as shown in Fig. 1. The
whole process is divided in four steps (i) fabrication of the substrate with a
channel region in which the palladium nanocrystals can grow, (ii) growth of
self-assembled monolayer (SAM) in the channel region where the particular SAM
was chosen for its known ability of reducing stiction on the surface of bare
glass and enhancing the sensitivity of hydrogen response 11, (iii) preparation
of the colloidal PVP-Pd nanocrystal solution by using the refluxing technique
and (iv) drop-casting the colloidal PVP-Pd nanocrystal solution over the
channel in the silane SAM coated substrate. In order to find the optimal PVP-
Pd hybrid complex that could give a resistive sensing response, different
solutions made of varying PVP$/$Pd mole ratios from 0.24 to 0.06, were drop-
casted onto the SAM layer. The final assembly is shown in Fig. 1.

Figure 2: (Colour online): UV-VIS spectra obtained for H2PdCl4 (green),
unrefluxed solution of H2PdCl4 together with ethanol, water and PVP mixed with
Pd in a PVP/Pd mole ratio of 0.1 (red) and the corresponding refluxed solution
(red).

The H2PdCl4 solution with ethanol, PVP and water is pale yellow in colour
without any refluxing, due to the formation of [PdCl4]2- (Pd(II)) ions 30, 31,
32, 24. These Pd(II) ions form stable complex with nitrogen and oxygen
containing organic compounds, so they co-ordinate to PVP molecules before the
reduction reaction 32, 30, resulting in a PVP-Pd(II) complex. This complex
results in peaks at $\sim$ 220 nm, 240 nm and 410 nm in the UV-VIS spectrum
24, 30, 31, as evident in the spectra marked by arrows in Fig. 2. Green solid
line in Fig. 2 represent the spectra taken with only the H2PdCl4 solution
while the red solid line corresponds to the spectra with ethanol, PVP and
water added to H2PdCl4 and allowed to wait without any refluxing. As can be
clearly seen, the difference in the two spectra (H2PdCl4 alone and H2PdCl4
mixed with PVP, alcohol and water) is negligible. This implies that without
refluxing, [PdCl4]2- ions remain in the solution and Pd(0) atoms are not
formed. However, when the solution is refluxed, all the three peaks disappear
and the absorption spectrum exhibited a typical light-scattering phenomenon,
as evidenced in the spectra displayed in black colour in Fig. 2, clearly
suggesting that [PdCl4]2- ions got reduced from Pd(II) state to Pd(0) state.
During refluxing, Pd(0) ions are stabilized by the hydrophobic interactions
between the hydrophobic alkyl groups of PVP and the metallic Pd surface 33.
Additionally, the absorption in the visible region increased compared to the
ultra-violet region, suggesting the formation of band-like structure for Pd
nanocrystals.

Figure 3: TEM micrographs of PVP-Pd system obtained for PVP/Pd mole ratio of
(a) 0.06, (b) 0.10, (c) 0.13 and (d) 0.24. Inset of each shows a histogram of
the sizes of the resultant Pd NC calculated using the Image J and Scanning
Probe Image Processor software both of which gave consistent results. Average
size obtained by fitting a log-normal distribution to the histograms was
obtained as 8.5 nm, 5.5 nm, 5.1 nm, and 5.3 nm for PVP/Pd ratio of 0.06, 0.1,
0.13 and 0.24 respectively. Top left inset of (c) shows a HRTEM image of a six
faceted nanocrystal obtained for PVP/Pd mole ratio of 0.10. Obtained d-spacing
for (111) and (200) facets have been indicated.

Since the functionality of the hybrid PVP-Pd complex is assumed to be highly
dependent on the size of the Pd nanocrystal (NC) 28, wherein, a small size was
found to have a higher catalytic activity, the hope is that a small size of
the complex has a better possibility of it being responsive to hydrogen gas,
and hence, behaving as a resistive hydrogen sensor. In order to check the
average size of the grown Pd nanocrystals, we subjected them to TEM
measurements, as shown in Fig. 3. From the main panels of Figs. 3 (a)-(d), it
was found that the PVP-Pd NC’s have a hexagonal shaped morphology with uniform
and uni-modal distribution (see the bottom inset of each Fig. 3 (a)-(d)). Top
left inset of Fig. 3 (b) shows a representative HRTEM image of a PVP-Pd NC
produced for a PVP$/$Pd mole ratio of 0.10. All the NC’s produced for other
mole ratio’s have a similar morphology (see Supplementary Fig. 1). The NC was
captured with a (111) facet (shown as red dotted lines) and (200) facet (shown
as yellow dotted lines) 27. From the obtained average size of the hybrid PVP-
Pd complex, it is found that varying the PVP$/$Pd ratio from 0.06 to 0.24
results in an average size of $\sim$ 5 nm for all conplexes barring the ones
obtained for PVP$/$Pd ratio of 0.06 for which the size is slightly higher at
8.5 nm such that all the NC’s grow with two facets, (111) and (200). So, a
small size of $\sim$ 5 nm gives us a possibility of the hybrid PVP-Pd complex
to be responsive to hydrogen gas.

## Hydrogen sensing at ambient conditions:

Figure 4: Hydrogen sensing in the architecture with hybrid PVP$/$Pd complex of
mole ratio 0.10. (a) Increase in resistance upon exposure to 0.5$\%$ H2 gas
and subsequent saturation. Onset of H2 loading and unloading are indicated by
arrows. (b) Same architecture of (a) responsive to step-wise decrease of H2
gas concentration from 0.5$\%$ upto 0.1$\%$ shown as red bars of progressively
decreasing height. Red labels on the right indicate the concentration in
percentage. (c) Log-log plot of the time-constant, $t_{90}$, with $\%$ H2 gas
concentration to identify the kind of diffusion process at work. Red solid
line is a straight fit to the equation 2 and the obtained power-law exponent
$r$ is 0.5. (d) Increase of sensitivity, as defined by equation 3, with
percentage concentration. Pink solid line is a straight line fit to the data
with the slope $m$ = 18.65 and intercept $c$ = 17.45.

To check the hydrogen sensing capabilities of the four different architectures
made with varying PVP$/$Pd mole ratios (0.06, 0.1, 0.13 and 0.24) prepared as
described above and having similar sizes, each of them were subjected to
hydrogen gas of different concentrations. However, even after repeated trials
with architectures prepared in different batches and hydrogen gas exposures of
very high concentrations, it was found that only the architecture with
PVP$/$Pd mole ratio of 0.10, responded to hydrogen gas. Fig. 4 (a) shows the
room temperature resistive response to 0.5$\%$ H2 gas concentration in the
architecture with PVP$/$Pd mole ratio of 0.10 and a SAM concentration of 0.1
M. Prior to hydrogen exposure, synthetic air was flown in the sensing chamber
to saturate the resistance of the device. As can be observed from Fig. 4 (a),
a perfect saturation was not reached and a very slight slope is observed
before hydrogen loading on the device at a starting resistance of $\sim$ 330
k$\Omega$. From 4 (a), it is immediately clear that the device shows an
extremely good response to hydrogen gas, where the resistance increases from
330 k$\Omega$ to 420 k$\Omega$ at which value, it saturates. The rise response
time, $t_{90}$, defined as the time taken to reach 90$\%$ of the saturation
value was found to be $\sim$ 47 s. By comparing the t90 response of various Pd
based resistive sensors under different concentrations of H2 gas (see Table 1
of Supplementary), it can be said that our chemiresistive H2 sensor shows an
exctremely good rise time response in ambient H2 conditions, corresponding to
a real H2 leak environment.
To investigate the sensing performance of the architecture with hybrid
PVP$/$Pd complex of mole ratio 0.10 under exposure to lower concentrations of
H2, we subjected the device to concentrations of 0.4$\%$, 0.3$\%$, 0.2$\%$ and
0.1$\%$ H2 as shown in Fig. 4 (b). The response characteristic to hydrogen at
lower concentrations is similar to that at 0.5$\%$, namely, a very fast
increase in resistance upon hydrogen loading followed by a near-perfect
saturation and a slower decrease on hydrogen unloading. Gardner et al. 34
considered a gas diffusion model in a porous thin film of thickness $x_{0}$,
wherein, the gas diffuses inside the thin film with diffusivity $D$ of the
free gas (related to the film porosity and temperature) and immobolises at
free surface sites. They found the steady-state diffusion time-constant to
vary with concentration $C$ as:

$\tau=kx_{0}^{2}\frac{C^{r-1}}{D}$ (1)

where $k$ is related to adsorption/desorption rate constant and $r$ is the
power-law exponent. So, for a given film thickness $x_{0}$ and diffusivity
$D$, the above equation can be rewritten as

$log\tau=A+(r-1)logC;~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}A=log\bigg{(}\frac{kx_{0}^{2}}{D}\bigg{)}$
(2)

The value of the power-law exponent $r$, then, defines the diffusion process:
for $r>$ 1, the diffusion process is said to be quasi-slow while for $r<$ 1,
the diffusion process is assumed to be quasi-fast. Lower the value of $r$,
faster is the process 34, 35. In order to understand the kind of difussion
process that may be at play in our novel architecture, a log-log plot of
$t_{90}$ vs. concentration $C$ was made as shown in Fig. 4 (c). Since a
$t_{90}$ time-constant mimicks the steady state time-constant $\tau$ very
well, equation 2 can be applied to the experimentally obtained data points, as
shown by the red solid line. A small value of $r$ = 0.5 obtained from the fit,
then, points to the fact that the diffusion of H atoms from the surface into
the Pd complexed PVP film is a very fast process. It was found 36, 37 that H
adsorption on the (111) surfaces compared to those of (100) of a Pd
nanocrystal results in a very fast H2 loading. So, the fast diffusion process
of H atoms implies that the H atoms initially adsorb preferentially on the
(111) surfaces of the hybrid Pd-PVP nanocrystal rather than on its (200)
surface 36, 37.
Time-constant and sensitivity are the two parameters that are usually used to
define the performance of a sensing device 34, 9, 36, 37. So, it is prudent to
check if the very good time-constant values obtained in Figs. 4 (a)-(c) are
also accompanied by good sensitivity values. Accordingly, Fig. 4 (d) shows the
sensitivity variation with $\%$ H2 concentration, defined in the usual way 13,
18 as:

$S=\frac{\Delta
R}{R}~{}~{}\times~{}~{}100\%=\frac{R_{H_{2}}-R_{Air}}{R_{Air}}~{}~{}\times~{}~{}100\%$
(3)

where $R_{Air}$ is the resistance of the sensor exposed to air only and
$R_{H_{2}}$ represents the resistance after exposure to hydrogen gas. From the
graph, it is immediately apparent that excellent values of sensitivity are
obtained in our PVP-Pd novel architecture, where a sensitivity value of
26.7$\%$ is obtained at 0.5$\%$ H2 concentration, similar to the one obtained
on SAM covered glass films made with physical vapour deposition method 11 (see
Table 1 of Supplementary). In a zinc oxide$/$indium oxide core–shell nanorod
based hydrogen sensor prepared by sputtering, a sensitivity of 20.5 was
obtained for 0.05 $\%$ of hydrogen 12, which on extrapolation to 0.5$\%$ of
hydrogen, doesn’t make it go beyond $\sim$ 27$\%$.
In bulk Pd, resistivity increase follows the Sievert’s law where it varies as
square root of hydrogen concentration:

$Sensitivity=\frac{1}{K_{s}}(pH_{2})^{1/2}$ (4)

where $K_{s}$ is the Sievert’s constant and p$H_{2}$ is the H2 partial
pressure in the environment 20, 40, 41. However, from Fig. 4 (d), it can be
seen that a straight line fits the $Sensitivity$ vs. H2 concentration data
very well. A similar linear variation in sensitivity with H2 gas concentration
has also been observed in other reports 17, 14, 11. So, a stronger exponent of
1 compared to the 0.5 value expected from equation 4, suggests that the amount
of hydrogen adsorbed on available sites of our novel architecture is much
higher compared to bulk for a given concentration, due to the very small size
($\sim 5.5nm$) of the nanocrystals 37 as well as the existence of (111) and
(200) facets in the nanocrystals 36 increasing the surface to volume ratio of
a nanocrystal compared to a bulk crystal manifolds. Consequently, the number
of available Pd sites are quite large in our novel architecture.
H2 gas sensing on bulk Pd happens by catalytic dissociation of the incoming H2
gas molecules into two H atoms at the Pd surface, which then move inside the
Pd lattice forming PdHx. The H2 dissociation reaction on the Pd surface is
expected to happen as 38:

$H_{2}+2S_{Pd}\rightarrow 2H\mbox{-}S_{Pd}$ (5)

where $S_{Pd}$ denotes the available surface sites on Pd nanocrystals.
In PdHx, when x $<$ 0.01, a solid solution of PdHα gets formed due to random
occupation of hydrogen, while for 0.02 $<$ x $<$ 0.6, an octahedral lattice
hydride PdHβ is formed. So, in the low concentration range of 0.1$\%$ to
0.5$\%$ of our consideration, a solid solution of PdHα is stabilised. Hence,
the rise in resistance of these structures may, possibly, be happening due to
increase in work function of the PVP-Pd complex due to surface adsorption of
the dissociated H atoms at the available Pd sites 22, 42, 43, 44, 38. A linear
increase in sensitivity with H2 concentration, then, implies progressivly
increasing work function due to progressively increasing surface adsorption of
H atoms. This, in turn, implies that the dissolved H atoms inside the Pd
lattice take up the conduction electrons of Pd and become hydrogen anions 39.
The loss of electrons from the conduction band of the Pd lattice lowers the
Fermi level of the system resulting in an increase in the work-function of the
system 39.

Figure 5: X-ray photoelectron spectroscopy measurements on the novel
architecture with varying PVP$/$Pd mole ratios. (a)-(d) Pd-3d5$/$2 and
Pd-3d3$/$2 core-level spectra for PVP$/$Pd mole ratio (a) 0.24, (b) 0.13, (c)
0.10 and (d) 0.06. Filled black circles in each figure (a)-(l) are the data
points while the superimposed red solid curves on the data points corresponds
to a fit using XPS Peak software. Resolved peaks in each figure are shown by
thin coloured lines, where Pd03d5/2 (pink), Pd${}^{\delta_{1}^{+}}$3d5/2
(orange), Pd03d3/2 (green) and Pd${}^{\delta_{1}^{+}}$3d3/2 (olive) in Figs.
(a)-(d) are marked by arrows. Insets of (a) and (b) represent an expanded view
of the data in the B.E. range of 336-340 eV to show the presence of another
wine coloured resolved peak at (a) 339.1 eV and (b) 338.6 eV. (e)-(f) O-1s
core-level spectra for PVP$/$Pd mole ratio (e) 0.24, (f) 0.13, (g) 0.10 and
(h) 0.06. The resolved peaks corresponding to Pd-3p3/2 (pink),
O${}^{-(2+\nu_{1})}_{(111)}$ (orange) and O${}^{-(2-\nu_{2})}_{(200)}$ (olive)
are marked by arrows. (i)-(l) N-1s core-level spectra for PVP$/$Pd mole ratio
(i) 0.24, (j) 0.13, (k) 0.10 and (l) 0.06. The resolved peaks corresponding to
N3- (pink) and Nδ3- (blue) are marked by arrows.

If surface adsorption of H atoms result in a resistive response of the PVP-Pd
complex only for PVP$/$Pd ratio of 0.10, it must be happening that only for
this ratio of PVP$/$Pd, the number of bare Pd sites on the PVP-Pd complex,
$S_{Pd}$, is largest and sufficient for the phenomenon of surface adsorption
of H atoms to take place. In order to confirm this, we did x-ray photoelectron
spectroscopy (XPS) measurements, an extremely sensitive technique to observe
core-level shifts in binding energies of elements according to their local
environment, on all the architectures with varying ratios of PVP$/$Pd. Figs. 5
(a)-(d) plot the XPS spectra of Pd measured on devices with decreasing
PVP$/$Pd ratio from 0.24 to 0.06 respectively. The spectra of Figs. 5 (a)-(d)
is characterized by two peaks, typical of 3-d core levels governed by spin-
orbit coupling. The first peak at a lower binding energy (B.E.) of $\sim$ 336
eV corresponds to the 3d-5$/$2 spin-orbit level of Pd while the second peak at
a higher B.E. of $\sim$ 341.2 eV corresponds to that of 3d-3$/$2\. The
intensity ratios of the deconvoluted peaks (pink with respect to olive and
orange with respect to light green) occur roughly in the expected ratio of 3:2
corresponding to the multiplicity of the spin-orbit split features. For
brevity, we will only discuss the details of the 3d-5$/$2 spin-orbit level-the
discussions on 3d-3$/$2 level follows exactly. For the PVP$/$Pd ratios of 0.24
and 0.13, the superimposed red curve was deconvoluted to reveal 3 peaks each
for a given spin-orbit level. The main peak, shown in pink, occurs at 335.9 eV
while the other two deconvoluted peaks, shown in orange and brown, occur at
higher B.E.’s of 337.3 eV and 339.1 eV respectively. The main peak corresponds
to palladium in the metallic state, Pd(0) 45, 46, 26, 25, in good agreement
with bulk Pd (335.2 eV) value 47. The slightly higher value of B.E. at 335.9
eV is known to be due to size and electronic effects 48. By studying the
effect of chemisorption of oxygen atoms on the (111) surface of Pd
nanocrystal, Ketteler et al. and Lundgren et al. 49, 47 found the B.E. to
shift by + 1.4 eV from the main Pd(0) peak. So, the occurrence of the second
deconvoluted peak (shown as orange) at a B.E. shift of exactly +1.4 eV is
attributed to the chemisorption of oxygen on the (111) lattice plane of Pd
nanocrystal that gets stabilized (refer to Fig. 3(b)). From free energy
minimization calculations, it was found that the (111) surface has the least
energy followed by (100) surface followed by (110) surface 50, 47. So, the
second lower intensity peak at 339.1 eV is attributed to oxygen coordinated Pd
(200) surface. The shift in B.E. at +3.2 eV is slightly higher than $\sim$
+2.2 eV values reported 51, 52. However, it should be noted that the reported
values were measured on Pd surface with only oxygen and not on a Pd-PVP
composite structure, which may result in slight differences in binding
energies. Since a higher B.E. is a measure of higher oxidation state of an
atom, charge transfer between the chemisorbed PVP molecule and Pd crystal must
happen in such a way that it leads to a withdrawal of electron density from Pd
surface resulting in Pd${}^{\delta^{+}}$ (Pd(II)). So, the two peaks at 337.3
eV and 339.1 eV have been nomenclatured as Pd${}^{\delta_{1}^{+}}$ and
Pd${}^{\delta_{2}^{+}}$ respectively.
Presence of Pd${}^{\delta_{1}^{+}}$ and Pd${}^{\delta_{2}^{+}}$ spectral
features in the XPS spectra of Pd indicates the poisoning of bare Pd metal
sites since chemisorption of PVP ligand with Pd surface happens at these
sites. So, the H2 gas sensing ability of the PVP-Pd complex is critically
dependent on the number of active Pd metal sites whose number can be estimated
by the calculated area ratio of integrated intensity Pd${}^{\delta_{1}^{+}}$.
Higher the ratio, higher is the availability of the free active sites, SPd.
Table 1 below describes the details of area ratios for Pd, O and N obtained
from the XPS data.

S. No. | PVP/Pd ratio | Pd${}^{0}/$Pd${}^{\delta_{1}^{+}}$ | Pd-3p${}_{3/2}/$O${}^{-(2+\nu_{1})}_{(111)}$ | N${}^{3-}/$N-(3-ϵ)
---|---|---|---|---
1 | 0.24 | 4.14:1 | 8.44:1 | 2.53:1
2 | 0.13 | 2.85:1 | 6.12:1 | 1.57:1
3 | 0.10 | 7.60:1 | 18.12:1 | 3.08:1
4 | 0.06 | 5.22:1 | 5.31:1 | 1.66:1
Table 1: Pd${}^{0}/$Pdδ1+, Pd-3p${}_{3/2}/$O${}^{-(2+\nu_{1})}_{(111)}$ and
N${}^{3-}/$N-(3-ϵ) integrated area ratios obtained from XPS spectra for the
novel architecture having varying PVP$/$Pd ratios.

From the Table 1, it can be seen that for the PVP$/$Pd ratio of 0.10, the
integrated area ratio of Pd0:Pd${}^{\delta_{1}^{+}}$ is the maximum,
suggesting that the number of available free Pd sites, SPd, is the maximum at
PVP$/$Pd ratio of 0.10. So, the optimal PVP$/$Pd ratio for maximum available
free Pd sites for adsorption of incoming H2 gas molecules is achieved at 0.10.
Additionally, for the PVP$/$Pd ratio of 0.24 and 0.13, the presence of
additional Pd${}^{\delta_{2}^{+}}$ spectral feature implies a further loss of
bare active sites of Pd metal that may be available for incoming H2 gas
resulting in the absence of sensing in architectures of those ratios.
In order to understand the details of the PVP-Pd interaction, we studied the
XPS spectra of oxygen and nitrogen shown in Figs. 5 (e)-(h) and Figs. 5
(i)-(l) respectively. Figs. 5 (e)-(h) show the O-1s spectra for PVP$/$Pd ratio
varying from 0.24 to 0.06 respectively. The deconvoluted spectra reveals a
main peak (shown as pink) at a B.E. of 532.2 eV for all the ratio’s barring
that of 0.10, where it occurs at a B.E. of 533 eV. It is known that at this
value of energy, the peak corresponding to Pd-(3p3/2) overlaps with O-1s.
However, since the amount of chemisorption of O on Pd is expected to be quite
small, the very intense peak at 532.2 eV is ascribed to Pd-(3p3/2). The
deconvolution also shows the presence of additional peaks, two each for
PVP$/$Pd ratios of 0.24 and 0.13 respectively, but only one peak for the
PVP$/$Pd ratios of 0.10 and 0.06. It is known that when Pd forms an oxide on
its (111) surface, it results in an occurrence of O 1s spectral feature at a
B.E. at 529.8 eV 47. So, the first additional peak at 529.8 eV is attributed
to PdO formation on the (111) surface of Pd that gets stabilized (refer to
Fig. 1). Since the peak is at a lower binding energy as compared to O2-,
charge transfer happens from Pd to O to result in an excess charge on O,
resulting in O${}^{-(2+\nu_{1})}_{(111)}$, where $\nu_{1}$ is positive and
(111) denotes O binding on the (111) surface. The second spectral feature at
534.5 eV is attributed to PdO formation on the (200) surface of Pd 51, 52,
resulting in O${}^{-(2-\nu_{2})}_{(200)}$. So the O-1s spectra shows exactly
similar features as the spectra of Pd shown in Figs. 5 (a)-(d) where two
additional peaks were observed for the PVP$/$Pd ratio of 0.24 and 0.13 but
only one additional peak for the spectra corresponding to PVP$/$Pd ratio of
0.10 and 0.06. However, the N-1s spectra shown in Figs. 5 (i)-(l) shows only
one additional deconvoluted peak (shown in blue) between the B.E range of 401
and 402.5 eV, apart from the main N-1s peak (shown as pink) at a B.E. of
$\sim$ 400.1 eV. The presence of an additional peak at a higher B.E. is a
clear indication of chemisorption of N atom of the PVP ligand on the Pd
surface, such that charge is transferred from N to Pd. The fraction of
N${}^{3-}/$N-(3-ϵ), obtained from area ratio of integrated intensity
N${}^{3-}/$N-(3-ϵ), is found to be maximum for PVP$/$Pd ratio of 0.10, in
exact conformity with the results obtained from Pd’s spectra.

Figure 6: Schematic of Pd’s chemisorption with PVP molecule in different
architectures of varying PVP$/$Pd mole ratios. Schematic illustration of (a)
PVP molecule, (b)-(e) Hexagonally shaped Pd nanocrystals with (111) and (200)
surfaces having chemisorbed PVP molecules with their N (blue) atoms and O
(red) atoms on various surfaces in architectures with PVP$/$Pd mole ratios of
(b) 0.24, (c) 0.13, (d) 0.10 and (e) 0.06. Free surface is marked by an arrow
while a free site is marked by a pink star in (d).

From the discussions of Fig. 5, it is clear that PVP chemisorbs on the Pd
nanocrystal on all the devices via its O and N atoms in such a way that oxygen
atom chemisorbs on the Pd nanocrystal at both the (111) as well as the (200)
surfaces on architectures that are prepared in the PVP$/$Pd mole ratios of
0.24 and 0.13, but it only chemisorbs on the (111) surface in the devices of
PVP$/$Pd ratios of 0.10 and 0.06, resulting in an increase in the number of
active sites for H2 absorption for these ratios. Figs. 6 (b)-(e) provide such
a schematic illustration where the chemisorption of the PVP molecules on the
hexagonally shaped Pd nanocrystals are shown via PVP molecule’s O and N atoms.
It can be seen that while all the 6 surfaces (four (111) and two (200)) of Pd
nanocrystals are occupied by PVP molecules for the architectures with PVP$/$Pd
mole ratios of 0.24 and 0.13 (see Fig. 6 (b) and (c) respectively), those with
mole ratios of 0.10 and 0.06 have free surfaces and sites. For instance, O
atoms are not shown to be bound to Pd (200) surfaces of architectures
represented in Figs. 6 (d) and (e). However, since Pd, O and N XPS’ area
ratios are higher for architecture of 0.10 compared to 0.06, the number of
free active sites, SPd is higher for PVP$/$Pd ratio of 0.10. Since the H2
loading happens via the (111) surface which is a very fast process 36, we
observe extremely good rise time constants and sensitivity with the
architecture of PVP$/$Pd mole ratio of 0.10. However, since the H2 unloading
happens via the (200) surface which is a slow process 36, the recovery times
(see Figs. 4) (a)-(b) is not as fast.

Figure 7: Change of XPS spectra of Pd, O, N on the architecture with PVP$/$Pd
mole ratio of 0.10 after ozone cleaning. (a), (c) and (e) represent XPS
spectra of Pd, O and N atoms respectively before ozone cleaning while (b), (d)
and (f) represent the corresponding spectra after ozone cleaning in an
architecture having PVP$/$Pd mole ratio of 0.10. Occurence of new peaks as
well as intensity increase of peaks compared to no ozone cleaning is clearly
visible in Pd and O spectra.

In an effort to further increase the number of bare active sites SPd on the Pd
surface in the architecture with maximum sites, namely, with PVP$/$Pd mole
ratio of 0.10, the architecture was subjected to UV-Ozone cleaning 53, a
technique frequently used to remove compounds on the surface of nanoparticles
without changing the morphological characteristics of the nanoparticles.
However, it was found that the UV-cleaned architecture loses its H2 gas
sensing capability completely! To understand this rather strange result, we
measured XPS on the UV-cleaned architecture. Fig. 7 (b) shows the Pd spectra
after it was subjected to UV cleaning. The change in the spectra without any
UV cleaning (shown in 7 (a)) is remarkable! It can be seen that not only has
the intensity of the Pd${}^{\delta_{1}^{+}}$ peak increased substantially
compared to the uncleaned one, the spectra also shows the presence of another
peak at a lower B.E. of 334.7 eV, suggesting the presence of a Pdδ- species in
the UV-cleaned sample. Additionally, the ratio of
Pd(0)/Pd${}^{\delta_{1}^{+}}$ was found to reduce substantially to 1.27 from
the original 7.6 (see Table 1) indicating the loss of bare Pd metal sites,
which is further confirmed by the presence of the new Pdδ- peak. However, the
change in the O-1s spectra was found to be the most spectacular, as evident
from Fig. 7 (d) where the O-1s spectra is now seen to have two additional
peaks compared to the spectra with no UV cleaning (7 (c)). So, the effect of
oxygen cleaning is to poison the bare Pd sites via O bonding on the Pd sites,
resulting in a loss of free active sites for incoming H2 molecules.
Additionally, the earlier N bonded sites get replaced by O atoms as evident
from the vanishing additional peak of the initial N-1s spectra (Fig. 7 (e)) in
the UV cleaned N-1s spectra (Fig. 7 (f)).

## Conclusions and Outlook

To conclude, we have been able to make a novel chemiresistive hybrid hydrogen
sensor based on palladium nanocrystals and poly (N-vinyl-2-pyrrolidone) (PVP)
polymer that was grown on a siloxane self-assembled monolayer to reduce the
stiction of hydrogen on glass substrate. The novel architecture was found to
have very good hydrogen sensing properties, with a high sensitivity of $\sim$
30$\%$ for a 0.5$\%$ H2 gas and a fast rise response time of $\sim$ 50 s. The
value of obtained sensitivity is similar to the ones obtained using physical
deposition method, making our chemiresistive sensor extremely cost-effective.
A log-log plot of time-constant and concentration revealed the diffusion of H
atoms inside the Pd lattice to be a very fast process. Detailed x-ray
photoelectron spectroscopy measurements revealed the existence of largest
number of bare palladium metal available sites and surfaces only for a given
PVP$/$Palladium mole ratio of 0.10. An effort to increase the number of
available sites by UV-ozone cleaning led to a degradation of the sensing
device due to poisoning of the already available sites by O.
It is clear that the exceptional sensitivity and rise time-constants that have
been achieved in our novel hybrid chemiresistive sensor holds great potential
for future sensor technology since the given response occur at room
temperature and atmospheric pressure conditions, the ambient conditions in
real life applications of a low concentration H2 leak detector or medical
applications of breadth H2 sensor. The exceptional sensing characteristics
were found to arise due to a combination of various factors: (i) small size of
the synthesised palladium nanocrystals with well-defined facets, (ii) fast
diffusion of H atoms from the surface of the palladium nanocrystals onto the
bulk and (iii) H2 loading on the (111) surface that is known to be a very fast
process. In a wider perspective, our results hold promise for next generation
thin film based chemiresistive sensors where variation of the type of self-
assembled monolayer as well as palladium to polymer ratios may vary not only
the size but also the morphology of the grown nanocrystals, wherein, more
facets of (111) could be grown. Such tailoring of properties may lead to thin-
film based sensors that are safe, compact, easy to fabricate, are cost-
effective and have enhanced sensitivity and low response times to meet the
ever increasing demands of low concentration hydrogen gas sensors at ambient
conditions of temperatures and pressures.

## Acknowledgements

P.S.G would like to thank IISER TVM for Institute post-doctoral fellowship and
ISRO RESPOND (Grant No. ISRO/RES/3/762/17-18) for financial support. D.J-N
acknowledges financial support from ISRO RESPOND, Govt. of India (Grants Nos.
ISRO/RES/3/704/16-17 and ISRO/RES/3/762/17-18)

## Author Contributions

D.J-N. and P.S.G. designed research; C.E.A., P.S.G., A.J., A.K., N.S., N.K.,
V.B.K., S.M.N and D.J-N performed research; D.J-N analysed the data and wrote
the manuscript with inputs from all co-authors.

## Additional Information

An Indian patent titled “A chemiresistive hydrogen sensor and a method
thereof” with number 202041035199 has been filed based on this work.

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# Baryon production and net-proton distributions in relativistic heavy ion
collisions

C. B. Yang and Xin Wang  Institute of Particle Physics, Central China Normal
University,Wuhan 430079, People’s Republic of China  Key Laboratory of Quark
and Lepton Physics (CCNU), Ministry of Education, People’s Republic of China

###### Abstract

The higher order moments of the net-baryon distributions in relativistic heavy
ion collisions are useful probes for the QCD critical point and fluctuations.
We study the net-proton distributions and their moments in a simple model
which considers the baryon stopping and pair production effects in the
processes. It is shown that a single emission source model can explain the
experimental data well. Centrality and energy dependence of the distributions
and higher moments is discussed.

###### pacs:

25.75.Gz, 21.65.Qr

##  I Introduction

The investigation of QCD phase diagram is fundamental to our understanding of
strong interactions. At vanishing baryon chemical potential, lattice QCD
calculations predict the occurrence of a cross-over from hadronic phase to the
quark-gluon plasma phase above a critical temperature of about 170-190 MeV YA
; JB . A distinct singular feature of the phase diagram is the QCD critical
point MAS  which is located at the end of the transition boundary. A
characteristic feature of the critical point is the divergence of the
correlation length $\xi$ and extremely large critical fluctuations. In ultra-
relativistic heavy ion collisions, however, because of finite size and rapid
expansion of the system, those divergence may be washed out. As estimated in
MAS , the critical correlation length in heavy ion collisions is not divergent
but about 2-3 fm. Remnants of those critical large fluctuations may become
accessible in heavy ion collisions through an event-by-event analysis of
fluctuations in various channels of conservative hadron quantum numbers, for
example, baryon number, electric charge, and strangeness FLUC . In an energy
scan there would be a non-monotonic behavior of non-Gaussian multiplicity
fluctuations, which would be a clear signature for the existence of a critical
point. In fact, at vanishing chemical potential it has been shown that moments
of conservative charge fluctuations are sensitive indicators for the
occurrence of a transition from hadronic to partonic matter SE .

Recently, the higher order moments of net-baryon distributions in heavy ion
collisions at RHIC energies have aroused great interest both experimentally
STAR  and theoretically THEO1 ; THEO2 ; THEO3 ; THEO4 . Experimentally,
neutrons can not be detected easily and the reconstruction efficiency is very
low for strange hadrons. Fortunately, theoretical calculations confirmed that
the net-proton distribution can be a meaningful observable for the purpose of
detecting the critical fluctuations of net baryons in heavy ion collisions NP
. The theoretical interest on these higher order moments comes from the
discovery of the relation between the moments and the thermal fluctuations
near the critical points. It is shown that the higher order moments have
stronger dependence on the correlation length $\xi$ and are therefore more
sensitive to the critical fluctuations. If some memory of large correlation
length persists in the thermal medium in hadronization process, this must be
reflected in higher order moments of the distributions. It has been predicted
MAS2  that the third moment, called skewness, is proportional to $\xi^{4.5}$
and fourth moment, or kurtosis, proportional to $\xi^{7}$ while the second
moment proportional to $\xi^{2}$. More importantly, the moments are closely
related to the susceptibilities of the thermal medium. It has been argued that
information of QCD phase diagram and the critical point can be obtained from
the energy dependence of those moments THEO1 . The moments of net-proton
distributions are studied with different theoretical models such as AMPT and
UrQMD THEO3 , HIJING LUO , and hadron resonance gas model FK  etc. All those
theoretical models are quite complicated and many microscopic processes are
involved, and as a result many parameters can be tuned in the investigations.
Therefore, the underlying physics behind the experimental results on the
higher order moments of the net-proton distribution is not very transparent
from the model studies. In addition, those studies focused on the moments only
and made no direct comparison with the experimentally obtained distributions.

In this paper, we will investigate the net-proton distributions in Au+Au
collisions at $\sqrt{s_{NN}}=200{\rm GeV}$ from very simple physics
considerations: baryon stopping and baryon pair production. These physics
effects are well known from studying heavy ion collisions in the past decades.
We will show that such simple physics can be used to reproduce the
experimentally observed net-proton distributions at different colliding
centralities with parameters chosen properly. Then higher moments can be
calculated numerically from the distributions. In this way the centrality
dependence of those moments can be predicted.

This paper is organized as follows. In next section, we will address the
physics points in our considerations for an emission source. Analytical
expressions for the net-proton distribution will be given. The model will be
used to fit the experimental data on the distribution. The model can fit the
data nearly perfectly. The centrality dependence of the moments will then be
predicted. Also the moments at LHC energies are discussed. The last section
will be for a brief summary.

##  II Model consideration for an emission source

It was well established that the net-baryon number would be zero in heavy ion
collisions in central rapidity region if there were no nuclear stopping in the
processes. Because the nuclear stopping effect depends on the collision energy
and the size of the system, the baryon number stopped in a rapidity region is
closely related to the number of participant nucleons $N_{\rm part}$. In more
central collisions the net baryon number will be larger. We consider a case in
which all final state baryons are assumed being produced from one emission
source. The initial mean nucleon number in the source is denoted as $B$ which
may be different for different colliding centralities. Considering the
randomness and independence of the nucleon-nucleon collisions in a heavy ion
collision, the probability of finding $N_{0}$ baryons stopped in the kinematic
region under investigation can be assumed, with the given mean number $B$, as

$P_{0}(N_{0},B)=\frac{B^{N_{0}}}{N_{0}!}\exp(-B)\ .$ (1)

Out of those $N_{0}$ stopped nucleons, some of them are proton, others
neutrons. The probability of finding $N_{p}$ protons from $N_{0}$ nucleons is

$Q_{0}(N_{0},N_{p})=C^{N_{p}}_{N_{0}}\rho^{N_{p}}(1-\rho)^{N_{0}-N_{p}}\ $ (2)

with $\rho=Z/A$ the fraction of proton in the nucleus. The above formulas
determine the distribution of net proton number in the source in the initial
state of the collisions.

Then one can consider the baryon production in the collisions. Baryons can be
produced from various channels. The baryon number is a conserved observable,
thus baryons must be produced in baryon-antibaryon pairs. The pair production
may be independent, and as a result of the independence, the probability for
producing $M$ baryon pairs must be a Poissonian with the given mean number of
produced pairs $\mu$ as a parameter

$P_{0}(M,\mu)=\frac{\mu^{M}}{M!}\exp(-\mu)\ .$ (3)

The parameter $\mu$ depends on the colliding centrality. For more central
collisions, the colliding system is larger, therefore $\mu$ should be larger,
and more nucleon-antinucleon pairs can be produced in the process.

It is the right place to compare the number distributions used in this paper
and in others. We use a Poisson distribution for the baryon pair distribution,
supposing the independent production of the pairs. In chen  the distributions
for both proton and anti-proton are assumed Poissonian, implying that protons
and anti-protons are produced completely independently. Therefore the baryon
number conservation may be violated in any event. In begun , a canonical
ensemble is employed to derive the number distribution for $\pi$ systems. This
is reasonable because there are a lot of $\pi$ particles in the final state of
heavy ion collisions. But a simple transportation of the method to the case
for baryon production may be problematic, because the relevant baryon particle
number may be not large enough for an equilibrium statistical description.

In the strong production of nucleon-antinucleon pairs, isospin is conserved.
Suppose that $N_{1}$ protons, $N_{2}$ anti-protons, $N_{3}$ neutrons and
$N_{4}$ anti-neutrons are produced in the process, the conservation of isospin
reads $N_{1}-N_{2}=N_{3}-N_{4}$ if the effect from the presence of mesons is
neglected. Thus we have $N_{1}+N_{4}=N_{2}+N_{3}=M$. The probability of
finding $N_{1}$ protons can be assumed as

$Q_{1}(N_{1},M)=2^{-M}C_{M}^{N_{1}}\ .$ (4)

In writing this equality, we assume that all the produced pairs are within the
kinematic range detected experimentally. Of course, this is a rather rough
approximation. In fact, some of the produced nucleons can go out of that range
and cannot be included in measuring the net-protons in the event. The effect
from limited kinematical acceptance can be taken into account by introducing
one more parameter for the probability of the produced baryon in the detected
region. To avoid this complexity, in this paper, such an effect is effectively
treated as having the number of pairs $M$ a little smaller in the event.
Therefore, the value of the parameter $\mu$ obtained from the fitting in this
paper should be a little bit smaller than the real one. In the same way, the
probability of finding $N_{2}$ anti-proton is $Q_{1}(N_{2},M)$. Then the
distribution of net-proton $\Delta p$ from an emission source can be expressed
as

$\displaystyle P(\Delta
p)=\sum_{N_{0},N_{p},M,N_{1},N_{2}}P_{0}(N_{0},B)Q_{0}(N_{0},N_{p})$
$\displaystyle Q_{1}(N_{1},M)Q_{1}(N_{2},M)P_{0}(M,\mu)\delta_{\Delta
p,N_{p}+N_{1}-N_{2}}\ .$ (5)

By inserting an identity expression
$\delta_{m,n}=\int_{0}^{2\pi}dxe^{i(m-n)x}/2\pi$, the above equation can be
rewritten as

$\displaystyle P(\Delta p)$ $\displaystyle=$
$\displaystyle\int_{0}^{\pi}\frac{dx}{\pi}e^{-(2B\rho+\mu)\sin^{2}\frac{x}{2}}\cos(x\Delta
p-B\rho\sin x)\ .$ (6)

As can be seen from the above expression, the net-baryon distribution depends
on two combined parameters, $B\rho$ and $\mu$ instead of $B,\rho$ and $\mu$
separately. One can check easily that $B\rho$ is the mean value of the
distribution $P(\Delta p)$.

##  III Comparison with the experimental data

The expression Eq. (6) enables us to compare the calculated net-proton
distributions from an emission source to the experimental data from STAR STAR
, as shown in Fig. 1. The parameters used are tabulated in TABLE 1. The
parameters show the expected behaviors from central to peripheral collisions.
As one can see from the figure, the agreement with the data is very good over
five orders of magnitude. Almost all calculated points for $F(\Delta p)$ lie
within the experimental error bars.

Figure 1: The net-proton distributions from single emission source. The points are from Ref. STAR , and the curves are calculated from Eq. 6. centrality | $N_{\rm part}$ | $\mu$ | $B\rho$
---|---|---|---
0-5% | 351.4 | 14.5 | 1.65
30-40% | 114.2 | 5.5 | 0.632
70-80% | 13.4 | 0.83 | 0.075
Table 1: Fitted parameters for Fig. 1

To make predictions for the net-proton distributions at other centralities,
one can parameterize the values of parameters $\mu$ and $B\rho$ tabulated in
TABLE 1 by polynomials of the number of participants $N_{p}$ as

$\displaystyle\mu$ $\displaystyle=$ $\displaystyle 0.171+0.0495N_{p}-2.5\times
10^{-5}N_{p}^{2},$ (7) $\displaystyle B\rho$ $\displaystyle=$
$\displaystyle(-4.63+5.99N_{p}-3.7\times 10^{-3})/1000.$ (8)

From this parameterization, one can calculate the moments for the
distributions easily. The obtained moments are shown, as functions of the
number of participants $N_{\rm part}$, in Figs. 2-5. The corresponding
experimental data from STAR  are shown in the figures for comparison. The
calculated mean, variance, skewness and kurtosis are well in agreement with
the data. The good agreement shows that the basic merits for the baryon
production mechanism have been exhibited in our model consideration.

Figure 2: The mean net-proton from multiple emission sources. The points are
from Ref. STAR , and the curve is from our model calculation. Figure 3: The
variance for the net-proton distributions from multiple emission sources. The
points are from Ref. STAR , and the curve is from our model calculation.
Figure 4: The skewness for the net-proton distributions from multiple emission
sources. The points are from Ref. STAR , and the curve is from our model
calculation. Figure 5: The kurtosis for the net-proton distributions from
multiple emission sources. The points are from Ref. STAR , and the curve is
from our model calculation.

In Ref. THEO4 , the observed moments are related to the ones from one emission
source by using the central limit theorem. This expectation is deduced from
the independent emission of particles from each source. In fact, if the
baryons are produced from $N_{S}$ identical sources, one can get relations of
the moments for the measured distributions and those for the emission sources
as

$\displaystyle M$ $\displaystyle=$ $\displaystyle M_{i}N_{S},$
$\displaystyle\sigma$ $\displaystyle=$ $\displaystyle\sigma_{i}\sqrt{N_{S}},$
$\displaystyle S$ $\displaystyle=$ $\displaystyle S_{i}/\sqrt{N_{S}},$
$\displaystyle\kappa$ $\displaystyle=$ $\displaystyle\kappa_{i}/N_{S},$

where quantities with subscript $i$ are for moments from one emission source.
From the above expressions on centrality dependence, one can expect constant
$S\sigma$ and $\kappa\sigma^{2}$ for all $N_{\rm part}$. In our fitting with a
single emission source, both $\mu$ changes strongly with centrality. As a
result of the centrality dependence of $B\rho$ and $\mu$, the centrality
dependence of the moments are well reproduced, as can be seen from Figs. 2-5.
One can also calculate moment products $S\sigma$ and $\kappa\sigma^{2}$. The
centrality dependence of the products are shown in Fig. 6. In the $N_{\rm
part}$ range shown, $S\sigma$ increases a few percent, while
$\kappa\sigma^{2}$ is almost exactly 1, as expected from the hadron resonance
gas model HRG .

Figure 6: The moment products, $S\sigma$ and $\kappa\sigma^{2}$, for the net-
proton distributions from multiple emission sources as functions of $N_{\rm
part}$. The dotted line is for $\kappa\sigma^{2}=1$ expected from the hadron
resonance gas model.

With the good agreement with STAR data at RHIC energy at hand, one can go one
step further to predict the higher order moments of the net-proton
distributions at LHC energies. For specific, let the center-of-mass energy of
the colliding nucleon-nucleon pair be 2.76TeV. From fitting data in STAR  one
can find the center-of-mass energy dependence of the parameter $B\rho$ and
extrapolate to LHC/ALICE energy. In this way, one gets $B\rho\simeq 0$ at
$\sqrt{s_{NN}}=2.76$ TeV. To get the parameter $\mu$ at LHC/ALICE, one can
write $\mu\propto\exp(m_{p}/T)$, with $T$ being the effective emission
temperature of the sources and $m_{p}$ the mass of proton. In Tem  the
effective temperature of the medium is given as a function of the center-of-
mass energy $\sqrt{s}$ as

$T=T_{\rm Lim}/[1+\exp(2.6-\ln(\sqrt{s})/0.45)]$

with $T_{\rm Lim}=164$ MeV. At LHC, the center of mass energy is much higher
than at RHIC, so the value of parameter $\mu$ is much smaller than obtained in
the above. The smaller value of $\mu$ will allow more baryon pairs to be
produced from a source. The predicted moments are shown in Fig. 7. Now the
mean value of the distribution is zero. Because of zero mean value, the net-
proton distribution at LHC/ALICE is symmetric about 0 and one gets zero value
for the skewness. Since the kurtosis is zero for Gaussian distributions,
extremely small $\kappa$ value at large $N_{\rm part}$ at LHC energies means
that the net-proton distributions at LHC energies can be well parameterized by
Gaussian, but not for small $N_{\rm part}$.

Figure 7: The moments for the net-proton distribution from multi-emission
sources at $\sqrt{s_{NN}}=2.76$ TeV.

##  IV Conclusion

The higher order moments of the net-proton distributions in relativistic Au+Au
collisions at $\sqrt{s_{NN}}=200{\rm GeV}$ are studied from a simple model
with effects from initial baryon stopping and final baryon pair emission taken
into account. We have demonstrated that by employing a single emission source
model, the distributions at different collision centralities can be well
reproduced. Then the higher order moments for the distributions can be
calculated without new free parameters. The calculated moments agree well with
the experimental results. The predicted moments for LHC Pb+Pb collisions need
to be verified experimentally.

It should be mentioned that nothing else is assumed in this model except an
initial net-proton and a finite probability for producing baryon pairs from
sources. Therefore, our model has nothing to do with thermal equilibrium
and/or critical fluctuations. Because our model consideration is based on
normal physics effects, our results can be used as a baseline for detecting
novel physics in the processes.

###### Acknowledgements.

This work was supported in part by the National Natural Science Foundation of
China under Grant No. 11075061 and by the Programme of Introducing Talents of
Discipline to Universities under No. B08033. The authors thank Dr. X.F. Luo
for sending us the experimental data. We are grateful to N. Xu and X.F. Luo
for valuable discussions.

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