Svetlana Yu Tsareva
email: svetlana.tsareva@univ-lorraine.fr

Edward Mcrae

Fabrice Valsaque

Xavier Devaux

Dose-dependent isotherm of Kr adsorption on heterogeneous bundles of closed single-walled carbon nanotubes

Keywords: Single-walled carbon nanotubes bundles, Kr adsorption isotherms, High-resolution transmission electron microscopy, DRIFT spectroscopy

We present 77K isotherms of krypton adsorption on bundles of closed highly-pure HiPco single-walled carbon nanotubes (SWCNTs). Two volumetric adsorption protocols were used, one with an increasing Kr dose per injection (IAD), one with a constant dose (CAD). Detailed microstructural examination showed that the SWCNTs combine into small bundles (of 25-30 SWCNTs) which are heterogeneous in diameter with a consequential range of interstitial channel (IC) shapes and sizes, some of which are large. The IC-sites are the subnanoscaled pores with alternating enlargements and constrictions along the tube axes. This results in adsorption dosing (AD) dependent characteristics of the low-pressure region of the isotherm. In the IAD protocol an equilibrium pressure drop with increasing AD is noted. Using the CAD protocol, different branches are observed. Well-pronounced substeps were established which we interpret as corresponding to the formation of various phases of confined Kr with different atoms arrangement. The height of a given substep obtained in different measurements depends on the AD value which can strongly influence the population of the site. Some substeps existing only for certain values of AD suggests the existence of a certain selectivity or of a preferential phase formation according to this value.

Introduction

Carbon nanotubes (CNTs), and especially single-walled carbon nanotube bundles, are remarkable adsorption substrates because of their unique structural properties. A single-walled carbon nanotube (SWCNT) bundle may be represented schematically as a quasi-one-dimensional structure with arrays of four different possible adsorption sites [START_REF] Williams | Monte Carlo simulations of H2 physisorption in finite-diameter carbon nanotube ropes[END_REF][START_REF] Muris | Where are the molecules adsorbed on single-walled nanotubes?[END_REF].

These include the 1D sites located in the grooves (G) separating two adjacent outer tubes, the inner channels of CNTs (T) if they are open and the interstitial channels (IC). The external walls (E) of the outermost SWCNTs in a bundle are the sites of 2D adsorption.

T-and IC-sites are what are referred to in other fields as nanopore channels. The adsorption inside pores is defined by the size and the geometry of the channels (Maddox et al 1995;[START_REF] Horikawa | Capillary condensation of adsorbates in porous materials[END_REF][START_REF] Sadeghi | Toward an Equation of State for Water inside Carbon Nanotubes[END_REF][START_REF] Cimino | Experimental and theoretical studies of scanning adsorption-desorption isotherms[END_REF][START_REF] Puibasset | Fluid adsorption in linear pores: a molecular simulation study of the influence of heterogeneities on the hysteresis loop and the distribution of metastable states[END_REF][START_REF] Nguyen | Pore connectivity and hysteresis in gas adsorption: A simple three-pore model[END_REF]. Whether endohedral adsorption inside open SWCNTs can occur is determined by the ratio of adsorbate to CNT diameter [START_REF] Kuznetsova | Enhancement of adsorption inside of single-walled nanotubes: opening the entry ports[END_REF][START_REF] Babaa | Opening of single-walled carbon nanotubes: evidence given by krypton and xenon adsorption[END_REF][START_REF] Jakubek | Two confined phases of argon adsorbed inside open single walled carbon nanotubes[END_REF][START_REF] Jakubek | Endohedral condensation and higher exohedral coverage on open singlewalled carbon nanotubes at 77 K[END_REF]Arab et al. 2006). The size of IC-sites in closely-packed homogeneous-diameter nanotube bundles is smaller than that of the T-sites. In fact, they are subnanoscaled. Therefore, some authors have refuted the possibility of any adsorption in the IC-sites [START_REF] Talapatra | Gases Do Not Adsorb on the Interstitial Channels of Closed-Ended Single-Walled Carbon Nanotube Bundles[END_REF] for Ne, Xe and CH4.

On the other hand, [START_REF] Calbi | Dilation-Induced Phases of Gases Absorbed within a Bundle of Carbon Nanotubes[END_REF] calculated that some gases can enter the IC-sites upon a coherent bundle dilation. They predicted that the lattice dilation for He and Ne would be less than 0.5%. In the case of H2, Ar and CH4 the expansion would be more significant and could reach ~2.5%. Filling of interstitial sites by He [START_REF] Stan | Interstitial He and Ne in nanotube bundles[END_REF], Ne [START_REF] Stan | Interstitial He and Ne in nanotube bundles[END_REF], CH4 [START_REF] Muris | Methane and Krypton Adsorption on Single-Walled Carbon Nanotubes[END_REF]Lohnson et al. 2003;[START_REF] Shi | Gas Adsorption on Heterogeneous Single-Walled Carbon Nanotube Bundles[END_REF], N2 [START_REF] Fujiwara | Gas adsorption in the inside and outside of single-walled carbon nanotubes[END_REF], O2 [START_REF] Fujiwara | Gas adsorption in the inside and outside of single-walled carbon nanotubes[END_REF], Kr [START_REF] Muris | Methane and Krypton Adsorption on Single-Walled Carbon Nanotubes[END_REF], Ar [START_REF] Shi | Gas Adsorption on Heterogeneous Single-Walled Carbon Nanotube Bundles[END_REF][START_REF] Bienfait | Adsorption of Argon on Carbon Nanotube Bundles and its Influence on the Bundle Lattice Parameter[END_REF], Xe [START_REF] Shi | Gas Adsorption on Heterogeneous Single-Walled Carbon Nanotube Bundles[END_REF]) has been reported.

Neutron scattering measurements accompanying the adsorption experiments have shown that there is no dilation when Ar [START_REF] Bienfait | Adsorption of Argon on Carbon Nanotube Bundles and its Influence on the Bundle Lattice Parameter[END_REF] or CH4 [START_REF] Johnson | Neutron diffraction and numerical modelling investigation of methane adsorption on bundles of carbon nanotubes[END_REF]) is adsorbed in the bundle. [START_REF] Johnson | Neutron diffraction and numerical modelling investigation of methane adsorption on bundles of carbon nanotubes[END_REF] thus suggested that the filling of IC-sites is accompanied by tube deformation, or an ovalization. When methane is forced into IC-sites, the tubes deform but the nanotube carbon atoms furthest from the methane remain close to their original positions. Distortion of SWCNTs in a bundle has been proven in some works [START_REF] Vodenitcharova | Mechanical interaction between single-walled carbon nanotubes during the formation of a bundle[END_REF][START_REF] Jiang | Measurement of radial deformation of singlewall carbon nanotubes induced by intertube van der Waals forces[END_REF][START_REF] Zang | On the mechanics of single-walled carbon nanotubes[END_REF][START_REF] López | Novel Polygonized Single-Wall Carbon Nanotube Bundles[END_REF]. For example, for bundles of two identical SWCNTs (1.56 and 2.05 nm) in diameter [START_REF] Jiang | Measurement of radial deformation of singlewall carbon nanotubes induced by intertube van der Waals forces[END_REF] determined that the flattening values could reach respectively 2.2% and 3.4% of the diameter. The deformation is a function of CNT diameter as was confirmed by a highresolution transmission electron microscopy investigation [START_REF] Abrams | Radial deformation measurements of isolated pairs of single-walled carbon nanotubes[END_REF]. So, the deformation of SWCNTs in the bundle might be an important factor in adsorption, both modifying the size of IC-sites and allowing the stabilization of the adsorbed molecules [START_REF] Johnson | Neutron diffraction and numerical modelling investigation of methane adsorption on bundles of carbon nanotubes[END_REF].

For a given adsorbate, the accessibility of the IC-sites depends on the tube diameters. Arab et al. (2007) estimated for a perfect bundle formed by three (10,10) SWCNTs that the passage from repulsive to attractive energies is extremely rapid for tube radii around 0.7 and 1.0 nm for Kr and Xe, respectively. In reality, bundles are inhomogeneous due to the heterogeneity of the SWCNT diameter distribution. Bundles containing a distribution of nanotube diameters always give structures with packing defects that may form relatively large ICs [START_REF] Shi | Gas Adsorption on Heterogeneous Single-Walled Carbon Nanotube Bundles[END_REF]) which consequently may be accessible to an adsorbate according to its size.

Rare gas adsorption isotherms of SWCNTs are more informative than those based on measurements with nitrogen since they allow distinguishing the 1D and 2D adsorption sites. Generally speaking, there are two inclined steps as the relative equilibrium pressure progressively increases [START_REF] Muris | Where are the molecules adsorbed on single-walled nanotubes?[END_REF][START_REF] Babaa | Opening of single-walled carbon nanotubes: evidence given by krypton and xenon adsorption[END_REF]Arab et al. 2006;[START_REF] Johnson | Neutron diffraction and numerical modelling investigation of methane adsorption on bundles of carbon nanotubes[END_REF]. The lower pressure step represents adsorption on higher binding energy sites (G-, T-and IC-sites). The higher pressure step corresponds to the exohedral adsorption on the external surface of the bundles (E-sites).

A presence of impurities such as amorphous carbon, hollow carbon shells or carbon-covered catalyst particles complicates the interpretation of adsorption isotherms since they may also constitute adsorption sites. These can modify the shape of an isotherm by smoothing or even leading to the disappearance of the steps.

In this work we will present Kr isotherms on highly pure HiPco SWCNTs. We have found some unexpected results using our carefully developed protocol. We show that such a protocol leads to even richer results than those found to the present and may yield more detailed information than what is usual for SWCNTs in real bundles with different tube diameters. Through electron microscopy results we present features not only of the diameter distribution but also of the wide range of possible interstitial channel morphologies and dimensions. The results provoke many new questions and we will attempt to furnish some potential interpretations.

Experimental

Samples

The SWCNTs used in this study are HiPco SuperPureTubes™ produced by NanoIntegris.

According to the manufacturer, the diameter range is 0.8-1.2 nm with individual CNT lengths up to 1 m; they contain <5% of metal catalyst impurities. The SWCNTs are bundled. (website: http://www.nanointegris.com/en/downloads see "HiPco Technical Data Sheet") A soft sample oxidation was made by treatment with H2SO4 (2.5M) under microwave irradiation for 20 min at 50°C. The SWCNT acid suspension was neutralized by adding a sodium hydroxide solution (2M, 4 mL). The ox-SWCNTs were washed extensively with water using sonication. The final rinsing was performed with ethanol.

Volumetric measurements

The physisorption studies were carried out using an apparatus with two capacitive pressure gauges allowing measurement between 10 -3 and 1100 Pa (i.e., over the full range of the isotherms) with a resolution of 0.003% of full scale and a precision of 0.5% (in the range 10 -3 -1 Pa) and of 0.2% (in the range 1-1100 Pa) of the reading. A liquid N2 bath temperature stabilization method was used to maintain a constant temperature (77.3 K) of the sample cell containing the adsorbent under study.

The other part of the apparatus (including pressure gauges, inlet manifold, gas reservoir, etc, except the pumps) isolated from the cell by a valve, is stabilized at 30±0.5°C. Krypton is first introduced into this latter part and then into the adsorption cell by opening the valve. Upon adsorption, the cell pressure thus decreases and reaches a limiting value at equilibrium. Equilibration times ranged from 0.3 to 1 h per dose and were chosen experimentally. In several cases, we verified that there was no pressure value change 4 hours after reaching a limiting value. Since the pressure gauges are kept at a higher temperature than the sample vessel, the vapour pressure measurement can be influenced by thermal transpiration, especially in the low pressure region. So, the raw isotherms were corrected for the thermal transpiration effect [START_REF] Takaishi | Thermal transpiration effect of hydrogen, rare gases and methane[END_REF]).

Our experimental setup was optimized so that small mass samples -but with large specific surface areas -could indeed be examined. The sample mass was typically 10 mg. This value allowed precise study of the very first stages of Kr adsorption using the very sensitive capacitance manometers mentioned above. So, this value of sample mass allows introducing a correspondingly small quantity of gas and recording with maximal accuracy the pressure change during adsorption.

The sample was initially outgassed outside the adsorption chamber for 7 days at 100°C to a pressure lower than 10 -4 Pa. After installation in the adsorption set-up, it was additionally outgassed for 1 day at 100°C to a pressure lower than 5.10 -5 Pa. Further isotherm measurements always started with outgassing of the sample at room temperature (20°C) for 16 hours to a pressure of < 5.10 -5 Pa. Krypton (>99.998%, Fluka Analytical) was purified by pumping on the condensed phase inside the apparatus. The experiments were carried out with use of two adsorptive dosing (AD) protocols.

These are designated IAD if the dose is increased from one injection to the next or CAD if the dose is constant.

It should be added that the void volume of the cell was determined without the sample in order to avoid any artifact of "helium entrapment" that could give a S-shaped form to the adsorption isotherms in the ultralow-pressure range, especially in the case of an insufficient equilibrium time.

The volume of the cell was 32 cm 3 whereas that of the sample was 0.13 cm 3 so the sample volume is only 0.4% of the total cell volume.

Our experimental setup is manual not automatic. So, for an experiment that required several days, to continue to draw the isotherm on day n+1, after the outgassing indicated above the dosing for the first point of this day was that of the total quantity of Kr introduced into the cell during day n.

Electron microscopy

Samples were dispersed in absolute ethanol then deposited on a holey carbon film supported by a 300 mesh copper grid. Some of the high-resolution transmission electron microscopy (HRTEM) observations were done using a Philips CM200 operating at 200 kV. The others, HRTEM and scanning transmission electron microscopy (STEM) images, were done with a JEOL ARM 200F equipped with a cold field-emission gun and a probe Cs-corrector (correction of the spherical aberration). The microscope was operated at 80 kV to avoid damaging the SWCNTs. High-angle annular dark-field (HAADF) and bright-field (BF) STEM images were simultaneously obtained for collection semi angles of 45-180 mrad and 0-3.8 mrad, respectively, and a pixel time of 40 s (1024x1024 pixels). For STEM imaging, the operating conditions allowed attaining a resolution close to 0.1 nm for both detection modes (measured on dispersed gold nanoparticles). The chirality of isolated SWCNTs was deduced from the fast Fourier transform (FFT) of the STEM BF images.

Diffuse reflectance IR Fourier-transform (DRIFT) spectroscopy

Infrared spectra of the samples were obtained using a Nicolet 8700 spectrometer equipped with a mercury cadmium telluride (MCT) detector and a KBr beam splitter. Infrared Powder Diffuse Reflectance data were collected with a Harrick Praying Mantis TM attachment and a high temperature reaction chamber. Spectroscopic grade KBr was used as background. The diffuse reflectance Rs of the sample and Rr of potassium bromide, used as a non-absorbing reference powder, were measured under the same conditions. The sample was prepared by mixing the SWCNTs with KBr (SWCNT fraction of 0.001), without compaction. The SWCNT reflectance is defined as R=Rs/Rr. The spectra are shown on a pseudo-absorbance (-logR) scale.

Results and discussion

Structural characterization of SWCNT bundles

Detailed TEM/STEM examinations of the sample show that it is quite free of any catalyst residue.

There are a few carbon impurities. The SWCNT diameter range is somewhat larger than was claimed by NanoIntegris, 0.7-1.6 nm. Fig. 1 illustrates typical micrographs of the sample from low to high magnification.

Fig. 1 (a) presents an overall view. The SWCNTs combine into long bundles between which there are a few scattered metallic particles (arrow) as well as some hollow carbon shells of 4-5 nm in diameter (circle) (Fig. 1 (b)). It was estimated that on average there are 25-30 tubes per bundle.

There is also a significant number of isolated nanotubes and very small bundles of 2 or 3 tubes (Fig. 1 (b-e)). The CNTs are quite straight over lengths of many tens of nm and appear to form loosely bound bundles. The box on Fig. 1 (b) illustrates three tubes all with closed ends, as was the case for most of the tubes observed in this study. Detailed STEM examination established a second type of carbon impurities on the surface of the tubes: small hollow spherical or ellipsoid structures of ~0.7-1.2 nm in size (Fig. 1 (d) and (e)). These hollow carbon "particles" are composed of one layer of carbon and might be fullerenes. The analysis of HRSTEM images shows that the distance between adjacent tubes can be variable. As seen on the BF-STEM image (Fig. 1 (d)), the interwall distance between the two tubes of 0.75 and 1.03 nm in diameter is between 0.34 nm and 0.70 nm. This could be explained by the presence of defects in the SWCNT structure along one (or both) of the tubes. It can also be seen that some hollow carbon particles lie between two tubes, locally increasing the distance between them. Whatever the reason underlying such a variable inter-tube distance, this observation is of particular interest because the regions of high dilation might play a role as additional entry ports to the interstitial channels of a bundle. Fig. 1 (f) is an image of one part of a bundle which is perpendicular to the grid surface. The bundle is constituted of very different carbon nanotubes: the ratio of largest to smallest nanotube diameters is about two. Of particular interest here are the morphing and size of the interstitial channels separating the SWCNTs. Triangular-shaped channels defined by three "closely-packed" tubes are observed but there are other bigger channels (A to D) defined by four tubes (Fig. 1 (f)).

Furthermore, the big tubes in the bundles are slightly deformed as noted for tube 2 on Fig. 1 (f). If other tubes are deformed, the flattering value is within the limits of resolution and it could not be estimated.

The microstructural observations allow concluding that the SWCNTs combine into small bundles.

The SWCNT diameters are heterogeneous with a consequential range of interstitial channel shapes and sizes, some of which are large. The distance between adjacent tubes is highly variable. The majority of SWCNTs are closed. The average diameter of our nanotubes of ~1.2 nm allows for twolinear adsorption lines of krypton on the internal surface if the nanotubes are opened. Indeed, for the nanotubes of 1.2 nm means that there is an empty space in the tube center ~0.86 nm wide. The van der Waals diameter of Kr is 0.404 nm, which would allow the formation of a one-or two-linear structures as well as the layering transition. The structures formed on 1D or quasi-1D sites could have linear or zigzag arrangements [START_REF] Jakubek | Two confined phases of argon adsorbed inside open single walled carbon nanotubes[END_REF][START_REF] Jakubek | Endohedral condensation and higher exohedral coverage on open singlewalled carbon nanotubes at 77 K[END_REF]Arab et al. 2007;Hodak et al. 2003).

The SWCNT bundles examined in this study consisted of very different CNTs, containing bigger channels like channels A-D on Fig. 1 (f). Based on the HRTEM images the size is ~0.8x0.44 nm for channel A, ~1.0x 0.5 nm for channel B, ~0.6x0.9 nm for channel C and ~0.9x0.8 nm for channel D.

So here, the formation of two-linear structures of adsorbed Kr is possible. However, the bundles structure are not fixed along their length: the bundles curve, the tubes can comprise defects in their structure or they can be slightly deformed. Furthermore, impurities like hollow carbon particles (Fig. 1 (d)) or metallic catalyst particles can be found between some tubes in the bundles. These can lead to a variable inter-tube distance and consequently to a various sizes and geometries of IC-sites.

These IC-sites can thus be presented as subnanoscale pore channels with alternating enlargements (voids) and constrictions (necks) along their axes. The literature provides some interesting works on molecular simulation of adsorption in the interconnected mesopores (>2 nm) of a variety of shapes, sizes and surface characteristics (Maddox et al 1995;[START_REF] Horikawa | Capillary condensation of adsorbates in porous materials[END_REF][START_REF] Sadeghi | Toward an Equation of State for Water inside Carbon Nanotubes[END_REF][START_REF] Cimino | Experimental and theoretical studies of scanning adsorption-desorption isotherms[END_REF][START_REF] Puibasset | Fluid adsorption in linear pores: a molecular simulation study of the influence of heterogeneities on the hysteresis loop and the distribution of metastable states[END_REF][START_REF] Nguyen | Pore connectivity and hysteresis in gas adsorption: A simple three-pore model[END_REF]. During gas adsorption the pores can exist in two states: first, unfilled, when the pore walls are covered by an adsorbed film but the pore center is occupied by vapor-like adsorbate, and secondly, filled, when the whole pore volume is occupied by a liquid-like, condensed adsorbate. The transition between these states is associated with the capillary condensation and capillary evaporation (desorption) transitions [START_REF] Cimino | Experimental and theoretical studies of scanning adsorption-desorption isotherms[END_REF][START_REF] Horikawa | Capillary condensation of adsorbates in porous materials[END_REF]. When the pore is not blocked and the fluid has an interface with the vapor phase, evaporation occurs at an equilibrium relative pressure which is determined by the pore size.

If the fluid is blocked by narrower pores, it cannot evaporate and hence becomes metastable. The formation inside the pores of bridge-like or large meniscus bridging structures [START_REF] Puibasset | Fluid adsorption in linear pores: a molecular simulation study of the influence of heterogeneities on the hysteresis loop and the distribution of metastable states[END_REF][START_REF] Horikawa | Capillary condensation of adsorbates in porous materials[END_REF]) characterize a metastable adsorption. The number of the metastable phases inside pore depends on the number of pore heterogeneities. The pore of ~1 nm and smaller (example: buckytubes) is too small to exhibit phase transitions such as capillary condensation (Maddox et al. 1995). However, one-or two-linear arrangements can have a low-density (vapor-like adsorbate) or a high-density (liquid-like) state of the structure. Accordingly, a layering transition from a low-to a higher-density state of the structure of adsorbed gas can occur. The liquid-like high-density structures can block the pore. Moreover, a very small subnanometer diameter pores with alternating enlargements and constrictions can be easily blocked by metastable "neck" structures.

Volumetric measurements

Two data sets with the two above-mentioned protocols were acquired for the 77 K isotherms. In the first measurement using the IAD protocol, a full isotherm to 167 Pa was drawn (Fig. 2(a)). Up to 0.05 Pa the Kr was added in doses from 0.06 to 0.157 mmol/g (mmol of Kr at standard temperature and pressure per g of sample); from 0.05 Pa to 3 Pa the doses were from 0.094 to 0.188 mmol/g; from 3 Pa to 20 Pa doses from 0.226 to 0.377 mmol/g, and from 20 Pa up to 167 Pa -0.377 to 2.26 mmol/g. In a second series of measurements we studied more precisely the first part of the isotherm, up to 0.05 Pa (Fig. 3). Here, the CAD protocol was used. The second data set was realized with 11 different adsorptive doses, from 0.083 mmol/g to 1.200 mmol/g. As one can see from Fig. 3, the curves in the low-pressure region (LPR) obtained with the different AD steps, are not superposed.

We will refer to these hereafter as the "branches" of the isotherm.

Before looking at the details, we first note that the isotherm obtained over the full range of pressure comprises two inclined steps. The second step extends from near 0.3 Pa to about 3 Pa (Fig. 2). Its position is independent of the protocol used and of the chosen AD value. This second step has the generally-observed structure for a rare gas adsorption isotherm on SWCNTs [START_REF] Babaa | Opening of single-walled carbon nanotubes: evidence given by krypton and xenon adsorption[END_REF]Arab et al. 2006;[START_REF] Muris | Methane and Krypton Adsorption on Single-Walled Carbon Nanotubes[END_REF]. This is not at all true for the first step located in the LPR between about 0.0007 Pa and 0.05 Pa (Fig. 2 and3) for which there are some intriguing features: the step behavior depends on both the chosen protocol and on the AD value. A pressure drop with increasing AD is noted using the IAD protocol (Fig. 2 (b)) and there are two small vertical substeps.

In the measurements using the CAD protocol, the exact positions of the branches and small substeps depend on the value of AD (Fig. 3).

The measurements obtained with the IAD protocol in the LPR, are represented on Fig. 2 (b). There are two segments of the LPR isotherm each the result of a one-day experiment. Upon increasing the adsorptive dosing from 0.06 to 0.157 mmol/g the equilibrium pressure decreases with increasing AD and a small substep at 680 Pa is observed. The second segment was carried out on the day following the first experiment. The dosing for the first point was 0.938 mmol/g, i.e., the total quantity of Kr introduced in the cell during the first segment measurement. But as one can see the first point (FP) of the second measurement and the last point (LP) of the first one do not superpose.

The equilibrium pressure of FP is lower than that of the LP for the same quantity of adsorbed Kr.

The further points of the second segment were obtained with adsorptive dosing increased step-bystep from 0.087 to 0.147 mmol/g. There are no further drops in the equilibrium pressure as were observed in the first segment. There is a small substep at 2050 Pa.

We suppose that the observed adsorption dosing dependent structure of the low-pressure region of the isotherm is linked to adsorption mainly in the IC-sites since the majority of the SWCNTs are closed. So, even if there exists a small fraction of opened SWCNTs, they cannot define the character of the isotherm. Near the G-sites there can also exist one-or two-dimensional phases of adsorbed gas: the work of Migone's group [START_REF] Talapatra | Existence of novel quasi-one-dimensional phases of atoms adsorbed on the exterior surface of close-ended single wall nanotube bundles[END_REF][START_REF] Talapatra | Higher coverage gas adsorption on the surface of carbon nanotubes: evidence for a possible new phase in the second layer[END_REF] has shown for Ne, CH4, Ar and Xe, that after the grooves are filled, some "stripe" phases may appear before the formation of the second layer on the external surface of bundles. But this manifests itself by the presence of substeps on the second step of the adsorption isotherm.

Let us look more closely at the obtained results. As one can see from Fig. 2 (b), as AD increases from 0.006 to 0.045 mmol/g the equilibrium pressure decreases from 4.12 mPa to 0.68 mPa. This could be explained by the formation of metastable adsorbed phases inside the IC-sites or by intrapore blocking. Fluid-like structures adsorbed in microporous (pore size below 2 nm) materials, due to a strong fluid-wall forces in the very narrow pores have properties that are very different from those of the usual fluid (Maddox 1995). While the bulk melting point of Kr is 115.78 K under ambient pressure, the melting point of Kr adsorbed in the subnanometer sized pores of SWCNTs bundles will be higher. Consequently, the intra-pore diffusion will be highly limited. The formation of specific pore neck structures can block the diffusion inside the pores. Moreover, the neck constrictions in the narrower pores separate the Kr which has diffused more deeply into the pores from the vapor phase, i.e. it leads to metastable adsorption. A subsequent higher pressure AD can remove the diffusion restriction and thus change the adsorption amount and the apparent equilibrium pressure. Indeed, the first portion of Kr is small, 0.006 mmol/g. Part is adsorbed on the most attractive sites leading to a certain value of equilibrium pressure (P) in the cell. The next introduced portion of gas is a little greater (0.008 mmol/g) with the pressure (PAD) of 305 times that of the equilibrium pressure in the cell after the first AD. This sudden pressure increase plays the role of a "piston": the newly arrived Kr adsorbs again on the most stable sites and "pushes" more deeply the already present Kr atoms. If the deeper penetration involves going beyond some constrictions, then we can imagine that some of the adsorbed Kr blocks the pore by formation of liquid-like structure in the pore neck. As a result, the apparent equilibrium pressure in the cell after this second AD is even lower than the previous. The pressure of the third portion of AD (0.017 mmol/g) is 612 times higher than the equilibrium pressure in the cell of the previous step. The Kr undergoes further "push". This process continues up to the point at which the pressure of the new AD is insufficient to further push the confined Kr structure. At this point, the sites are truly filled and no more Kr can be adsorbed here. On the adsorption curve this manifests itself by an equilibrium pressure increase. As the equilibrium pressure in the cell rises, the influence of the pressure of any newly introduced AD of Kr decreases since the smaller difference between P and PAD diminishes so the "piston effect" is less efficient. Another reason is in increased population of sites. This is probably why we can observe the inversion of the isotherm points only in a very low-pressure region when the amount of introduced and adsorbed Kr is small.

The measurements in the LPR obtained using the CAD protocol are presented on Fig. 3. It can be seen that the isotherm here has a multi-branch structure. Each branch is the result of a one-day experiment. The equilibrium pressures depend on the value of the adsorption dose. The points obtained for the four smallest AD values used are shown on Fig. 3 (a). On that obtained with the smallest AD (0.083 mmol/g), four substeps 1-4 are noted, at 680, 2050, 3080 and 4820 µPa. When the AD increased to 0.155 mmol/g, there are only two substeps at 3080 and 4820 Pa and their height is greater than in the case of the first branch. The third branch (0.172 mmol/g) is shifted to the right of the two preceding ones, i.e., to a higher equilibrium pressure. It has a substep at 4820 µPa. Increasing AD to 0.192 mmol/g leads to an even greater shift to the right and two new substeps (5 and 6) are observed, at 9740 and 15810 µPa. Further increasing AD up to 0.209 µPa leads to an unexpected downshift on the equilibrium pressure as shown in Fig. 3 (b). However, with respect to the substep obtained at a smaller value of AD, the height of the substep at 680 µPa is greater.

Further increasing the AD from 0.209 to 0.560 mmol/g again progressively shifts the equilibrium pressures to the right (Fig. 3 (c)). Increasing AD to 1.2 mmol/g results again in a downshift (Fig. 3 (c)). We conclude that increasing AD influences the isotherm in a somewhat cyclic manner. Indeed, increasing AD first results in a corresponding progressive shift of adsorption branches to the right.

Then at some higher AD, the new equilibrium pressure shifts to a lower value than the previous and a new branch is created to the left of the previous one. Examination of the LPR of the isotherm with an AD value above 1.2 mmol/g is impossible because any introduction of a greater quantity of Kr leads to saturation of all accessible 1D-sites. As a result, subsequent points of the isotherm correspond to the end of the LPR or the beginning of the second part of the isotherm.

The filling of pore can be accompanied by the formation of the metastable phases like it was described elsewhere [START_REF] Puibasset | Fluid adsorption in linear pores: a molecular simulation study of the influence of heterogeneities on the hysteresis loop and the distribution of metastable states[END_REF]. While the first step on the isotherm represents filling of 1D sites, the occurrence of the substeps at different equilibrium pressures is attributed to various phases with different arrangements of the atoms. The position of the substeps is defined by the binding energy of the sites where this arrangement is realized. Let us look at Fig. 3 (b) on which there are five branches obtained with five different values of AD. The horizontal dashed line is arbitrarily drawn through the value of adsorbed Kr ~0.6 mmol/g. The line crosses the branches obtained with AD values of 0.209, 0.083, 0.155, 0.172 and 0.192 mmol/g at the points situated in the first, third, third, fourth and fifth substeps, respectively. These different points represent adsorption of the same quantity of Kr, but for each of these points the equilibrium pressure in the cell is different and depends on the AD value used. This is plausible if different confined phases of Kr with different densities or arrangements are formed. Wherever the way of adsorption (branch), all branches achieve the same amount of adsorbed Kr at the high pressure limit of the first step that corresponds to the filled sites. In other words, the adsorption inside the pores can pass through the formation of different intermediate metastable phases in the pores with different diameter. But finally, all pores are filled by adsorbate.

In the CAD protocol measurements, for a given value of AD there is no drop in equilibrium pressure as was the case for the IAD protocol. However, the smallest portion of Kr used in the CAD is nearly 14 times higher than the first portion of Kr in the IAD measurements. This means that the switch-back type behavior of the isotherm stemmed from metastable adsorption; it can be observed only through use of very small AD's and only at the very beginning of the LPR of the isotherm when the pore channels are almost empty or only slightly filled. Indeed, a similar pressure drop with increasing AD and the formation of a multi-branch structure in the LPR of the isotherm has been described [START_REF] Jakubek | Two confined phases of argon adsorbed inside open single walled carbon nanotubes[END_REF][START_REF] Jakubek | Endohedral condensation and higher exohedral coverage on open singlewalled carbon nanotubes at 77 K[END_REF] for Ar and Kr adsorption on opened SWCNTs. For the case of Ar, these authors used adsorbate dosing increased step-by-step [START_REF] Jakubek | Two confined phases of argon adsorbed inside open single walled carbon nanotubes[END_REF]. For Kr adsorption the constant adsorption dosing protocol was used [START_REF] Jakubek | Endohedral condensation and higher exohedral coverage on open singlewalled carbon nanotubes at 77 K[END_REF] with a very small AD (~0.07 cm 3 of Kr/g of adsorbent at standard temperature and pressure). Probably, when inside the pore channels there was a few adsorbate, the pores can be blocked by formation of liquid-like structure in the pore neck. Moreover, the adsorbate atoms are fractioned inside the pores forming the a liquid-like meniscus located mainly in the strongly attractive domains of the pore. In the IAD protocol when the pores contain a significant quantity of adsorbate atoms or in the CAD protocol with a large enough AD value, Kr atoms are distributed widely both in the pore necks and in the pore enlargements. The pores are not blocked. A certain partitioning of confined Kr inside the pores with formation of separated metastable phases is possible here, but due to the large population of sites it will not lead to pressure drop with increasing AD.

It is remarkable that the value of equilibrium pressure of the first two substeps is the same for the two used protocols. In addition, in the CAD protocol measurements the positions of certain substeps on different branches are the same but not their heights (e.g., substep 1 of the branches obtained with AD values of 0.083 and 0.209 mmol/g (Fig. 3 (a-b)). The position of a substep on the adsorption isotherm is defined by its binding energy (Arab et al. 2007). The substep height is linked to the population of the sites. The results thus suggest a certain selectivity or a preferential metastable phase formation according to the AD value. There appear to be a certain number of accessible adsorptive sites in which one given adsorbate atomic arrangement can be made. The site filling and the adsorbate structure/density depend on the value of the AD as well as on the AD protocol.

So, we hypothesize that the multi-branch structure and branch switching that we have observed may be explained by the existence of some metastable phases of confined Kr and that a transition from a low-density to a high-density state occurs in the IC-sites.

To examine the possibility of modifying the structural characteristics of CNTs during volumetric measurements or of opening the SWCNTs, we verified the reproducibility of our measurements.

Points from two different measurements with the same adsorptive dosing (0.39 mmol/g) are presented on Fig. 4. The second of these two measurements was carried out one month after the first and between the two, several other adsorption experiments on the same sample were done with different AD values. As can be seen, the results are reproducible. We conclude that even if there exist certain environmental or experimental influences not fully taken into account during our experiments they do not perceptibly affect the characteristics of the isotherm. Moreover, we have carried out the adsorption isotherms for three samplings of the HiPco SuperPureTubes™. The isotherms of all three samplings are absolutely identical which confirms good sample homogeneity and reproducibility of the observed phenomenon. In addition, detailed electron microscopy examinations of the samples after the volumetric measurements did not establish any changing of the structural characteristics.

To verify that the observed adsorption behavior in the LPR is linked to the formation of pore blocking metastable phases inside the IC-sites, we have studied the adsorption of the same HiPco SWCNTs after an H2SO4 treatment. Indeed, [START_REF] Kuznetsova | Enhancement of adsorption inside of single-walled nanotubes: opening the entry ports[END_REF] showed that upon such an acid treatment, the grafted functional groups such as quinone or carboxylic acid block the entry ports of the nanotubes. The very soft conditions of our acid treatment were chosen to avoid the possible cutting or significant opening of SWCNTs, i.e. to preserve the bundle morphology and to graft the functional groups at the sites of the entry ports of IC-and T-pores. It is known [START_REF] Feng | A Vibrational Spectroscopic Study of the Fate of Oxygen-Containing Functional Groups and Trapped CO2 in Single-Walled Carbon Nanotubes During Thermal Treatment[END_REF] that the most reactive sites on the SWCNT bundles are the ends, the bundles curves and the connecting regions between different bundles, i.e. all possible IC entry ports. So, the soft oxidation can allow grafting here of the oxygen-containing functional groups that will block the adsorption inside the pore sites of SWCNT bundles.

A typical DRIFT spectrum of H2SO4-treated SWCNTs, is shown on Fig. 5. There are two bands characteristic of carboxylic acid (at 1730 cm -1 ) and quinone (at 1660 cm -1 ) groups. A very broad band with a maximum near 3250 cm -1 can be identified with -OH from the carboxylic acid or the phenol groups attached to SWCNTs. There is also a triplet at 2900 cm -1 (2960, 2925 and 2850 cm -1 ) that is identified with C-Hn functional groups [START_REF] Kim | Infrared-Active Vibrational Modes of Single-Walled Carbon Nanotubes[END_REF]. A very small broad band of hydroxyl groups as well as a low intensity triplet at 2900 cm -1 are observed on the curve of pure SWCNTs. These functions probably come from the purification procedure that often involves acid treatments to remove metal catalyst impurities from HiPco samples.

During the soft acid treatment used the electrophilic reagent first attacks some C=C bonds producing hydroxyl groups which in turn can be converted into quinone groups, and finally to carboxylic acid groups [START_REF] Zhang | Effect of Chemical Oxidation on the Structure of Single-Walled Carbon Nanotubes[END_REF]. The quinone groups may be considered as intermediates in the oxidation process [START_REF] Zhang | Effect of Chemical Oxidation on the Structure of Single-Walled Carbon Nanotubes[END_REF]. The ratio between the peaks at 1730 cm -1 and 1660 cm - 1 corresponds to the ratio between carboxylic and quinone groups. As the oxidation proceeds, this ratio increases. For our oxidized sample the ratio between carboxylic acid and quinone groups is approximately the same. TEM examination of the ox-SWCNT shows that indeed there is no change in morphology of the sample, i.e., the SWCNTs have not been cut nor is there any significant SWCNT opening. So, the TEM results corroborate the conclusion of the DRIFT analysis: even if some carboxylic acid and quinone groups were grafted on the SWCNT surface, the number is insufficient to change the bundle morphology.

Let us now examine the Kr adsorption isotherm of ox-SWCNTs (Fig. 6): it is significantly different from that of the pure-SWCNTs as shown above. There are no branches or equilibrium pressure drops with either the CAD or the IAD protocols: in fact, the shape of the adsorption curve is independent of the protocol used and of the chosen AD value. The curve starts directly by the first step which extends from about 0.005 to about 0.02 Pa, i.e. it is much narrower than in the case of untreated SWCNTs. The position of the second step coincides with that of pure-SWCNT sample.

As discussed above, the oxidation was chemically "soft" with no tube cutting, creation of few defects and no change in bundle morphology. We suggest that the functional groups are located mainly on the SWCNT ends thereby blocking the entry ports of the ICs similar to the blocking of the tube inner channels as proposed by [START_REF] Kuznetsova | Enhancement of adsorption inside of single-walled nanotubes: opening the entry ports[END_REF]. Such IC-blocking upon oxidation on bundles which are otherwise very similar to our raw bundles, thus strongly supports the our interpretation of the role of the open channels during adsorption.

More extensive experimental investigations in a broad range of temperatures and with other gases such as Ne with a van der Waals diameter of 0.308 nm or Xe with a diameter of 0.432 nm as well as advanced theoretical simulations are necessary to fully understand adsorption in the IC-sites and the formation of various blocking metastable phases with different arrangements of Kr. Additional experiments will be carried out.

Summary and conclusions

In this work we have carefully studied krypton adsorption at 77K on a sample of HiPco SuperPureTubes™. Most of the SWCNTs in the bundles are closed, on average there are 25-30 per bundle and they are heterogeneous in diameter with a consequential range of IC sizes, some of which are large. Moreover, the inter-tube distances are variable, also affecting the size and the geometry of the IC-sites. Such sites in SWCNT bundles can be presented as subnanoscale pore channels with alternating enlargements (voids) and constrictions (necks) along the tube axes.

Two different volumetric adsorption protocols were used, one with an increasing Kr dose per injection, one with a constant dose. We have established adsorption dosing dependent structures of the low-pressure region of the isotherm. To eliminate any possibility of artifacts or that the volumetric protocol itself might modify the CNT structure, studies on different samplings and reproducibility studies using identical protocols confirmed that the results are indeed reproducible.

Detailed electron microscopy examination of the samples after the volumetric measurements strengthened the argument that the volumetric experiments did not change the structural characteristics of the samples.

The new adsorption features include the existence of AD-dependent behavior comprising branches, substeps and branch switching. An equilibrium pressure drop with increasing AD is noted using the IAD protocol which we explain by the formation of metastable adsorbed phases inside the IC-sites or by intrapore blocking.

In the CAD protocol measurements six and in the IAD protocol measurements two wellpronounced substeps corresponding to the formation of various phases of confined Kr were established. The height of the same substep obtained in different measurements depends on the AD value which can strongly influence the population of the site. In the measurements using the CAD protocol, the exact position of the first step is AD-dependent. The increasing AD influences the isotherm in a cyclic manner. Whatever the scenario of the pore filling, all branches achieve the same value of adsorbed Kr at the high pressure limit of the first step of the isotherm that corresponds to the filled pore sites.

Finally, Infrared studies on an acid-treated sample show the existence of carboxylic acid and quinone groups on the nanotube surface. These groups block the entry ports for adsorption on the ICs surface. These lead to a Kr adsorption isotherm the shape of which is independent of the protocol used and of the chosen AD value and thus lend support to the important role of IC sites in the raw samples.

Further experiments are in progress to shed more light on the complex interactions between adsorbate and substrate in these heterogeneous systems.

-Figures -

Fig. 1 :

 1 Fig. 1: TEM (a), HRTEM (b, f), BF-STEM (c, d) and HAADF (e) images of HiPco SuperPureTubes™ sample. The inset at the bottom of image (f) is a zoom of the presented bundle. The blue triangles indicate interstitial channels defined by three tubes; the letters A to D designate ICs defined by 4 tubes.

Fig. 2 :

 2 Fig. 2: (a) 77K isotherm of Kr adsorbed on HiPco SuperPureTubes™ sample. (b) Low-pressure region of the isotherm. The vertical arrows 1 and 2 designate the substeps at equilibrium pressures 680 and 2050 Pa. The first point (FP) of the second measurement and the last point (LP) of the first one are circled. From bottom to top the four horizontal arrows indicate the successive directions of equilibrium pressure evolution.

Fig. 3 :

 3 Fig. 3: (a-c) Low-pressure region of the 77K isotherm of Kr adsorbed on HiPco SuperPureTubes™ sample obtained with the 11 different constant adsorptive doses indicated. The arrows 1 to 6 designate the substeps at equilibrium pressures of 680, 2050, 3080, 4820, 9740 and 15810 Pa.

Fig. 4 :

 4 Fig. 4: Illustration of the good measurement reproducibility. Points from two different measurements with the same adsorptive dosing are indicated by squares and crosses.

Fig. 5 :

 5 Fig. 5: DRIFT spectra of HiPco SuperPureTubes (1) and H2SO4-treated SWCNTs (2).

Fig. 6 :

 6 Fig. 6: 77K isotherm of Kr adsorbed on H2SO4 treated HiPco SuperPureTubes™ sample.

ACKNOWLEDGMENTS

Acknowledgment is made to the French Agence Nationale de la Recherche (ANR) (grant ANR-10-BLANC-0819-01-SPRINT) and the Région Lorraine (grant 30031172) for their support.

The authors thank Prof. C. Carteret, Dr. M. Dossot and Dr. S. Fontana for fruitful discussions and Dr. J.-F. Marêché for important technical assistance.


César Ducruet

Co-evolutionary dynamics of ports and cities in the global maritime network, 1950-1990

Port cities

Much has been said about the evolution of port cities, from the perspectives of planners, architects, sociologists, economists, historians, and geographers alike, especially in terms of changing urban landscape, port morphology, and other interactions between port and city. Although the definition of the port city concept itself has remained blurred [START_REF] Ducruet | The port city in multidisciplinary analysis[END_REF], most studies converged around the idea that large cities will ultimately get rid of their port activity so as to diversify their economy, prevent their citizens from environmental degradation, be more creative and knowledge-based. Various forms of waterfront redevelopment strategies emerged since the 1950s already to value the city's maritime culture and atmosphere for other uses than cargo handling operations and related industries. At the same time, transport chain actors of which the port increasingly saw the city as a constraint to infrastructure expansion for traffic growth and fluidity, as modern terminals were often develop outside of the city's jurisdiction to find available land and gain in both sea and land accessibility.

Port geography contributed to depict these trends by providing spatial models of portcity evolution organised around successive phases, as well as numerous port impact studies and in-depth investigation of particular ports and port cities (Ng et al., 2014). The Anyport model of James [START_REF] Bird | The Major Seaports of the United Kingdom[END_REF] provided a generalisation of the spatial shift of modern port terminals from the upstream city towards downstream deep-sea locations as a response to urban growth and port growth. Brian Hoyle (1989) later modelled the evolution of the port-city interface to explain how cities and ports grew increasingly apart due to technological change in port and shipping operations, favouring the rise of "placeless ports" and new urban challenges in a postmodern society (Norcliffe et al., 1996). Historians as well proposed a stage approach to port city diversification (Murphey, 1989).

Nevertheless and because cities remain more than ever essential consumption and production centres, there remains a debate on whether such a physical and functional separation process is truly universal (Lee et al., 2008) due to its regional diversity and varying intensity. Geographers also contributed to the debate by discussing the fundamentally urban dimension of commodity chains and the integration versus disintegration dynamics taking place in and around port cities (Hesse, 2010(Hesse, , 2013)). Other scholars motivated policy-makers to maintain the benefits of port-city proximity due to the positive externalities provided by cities to ports (Hall and Jacobs, 2012), which was recently illustrated by the creation of new container terminals in the vicinity of certain global cities in order to reduce trucking to and from distant terminals (El Hosni, 2015), such as London, Taipei, Tokyo, and Yokohama. Such examples seem to question the validity of classic port-city evolutionary models.

Measuring port-city interdependence on a larger scale

Most of the time, empirical investigations of port-city evolution remained focused on specific places and projects, at the level of the urban waterfront. As already discussed by Ducruet and Itoh (2015), there are very scarce large-scale analyses of port-region and port-city interdependences (see also Chapter 16 by Ducruet and Itoh on port regions and material flows). Numerous analyses looked at the changing economic impact of ports on their local economy based on a variety of disaggregated data but in turn, these studies remained impossible to compare to one another and over time given the diversity of sources and methods to measure spillovers, related employment, and value added. Looking at the geographical determinants of the port and maritime industries, several works concluded to a stronger influence of urban size (often measured by the number of inhabitants) than port size (as measured by total tonnage or containerised cargo volume) on the distribution of port and maritime services in Australia (O'Connor, 1987, 1989), Canada (Slack, 1989), and at the world scale (Jacobs et al., 2010). Such results suggested that while physical cargo handling operations are more and more performed outside large cities, the latter keep concentrating more "white-collar" office-based activities such as brokers, insurers, and traders. More dynamic analyses came to the similar conclusion that the correlation between port and city was no longer relevant, given the lack of a significant statistical correlation between port traffic growth and urban population growth in France (Steck, 1995) and the decline of the linear correlation between port traffic volume and urban population in India (Kidwai, 1989). A more systematic, global measurement of the relationship between port and urban development was proposed by [START_REF] Ducruet | Frontline soldiers of globalisation: Port-city evolution and regional competition[END_REF]) over the period 1970-2005. It also confirmed the decreasing correlation between traffic and population, but was solely based on container throughput volumes.

Another drawback of the port-city literature is the rarity of a network approach. Jacobs et al. ( 2010) did provide a classification of port cities based on their situation in the global network of maritime advanced provider services and their port throughput, but it remained rather static and did not address the distribution of physical flows among port cities. More likely in geography and elsewhere are studies of cities in abstract models of urban interaction where actual flows are absent, or in other types of networks such as airlines, roads and railways, but no study has ever been done about the urban dimension of maritime networks [START_REF] Ducruet | Cities and transport networks in shipping and logistics research[END_REF][START_REF] Ducruet | Network science and spatial science: Review and outcomes of a complex relationship[END_REF]. Graph-theoretical and statistical methods were used to explain, for instance, the accessibility and centrality of cities and regions in airline networks by their population and Gross Domestic Product [START_REF] Choi | Comparing world city networks: a network analysis of Internet backbone and air transport intercity linkages[END_REF]Neal, 2011;Wang et al., 2011;[START_REF] Dobruszkes | An analysis of the determinants of air traffic volume for European metropolitan areas[END_REF]. For other transport modes, [START_REF] Cattan | Barrier effects: the case of air and rail flows[END_REF] analysed barrier effects in air and rail flows among European cities, and Guerrero and Proulhac (2014) revealed distinct relationships between the urban hierarchy and the spatial distribution of the respective export volumes of wholesalers and manufacturing companies in France. One aspect of maritime centrality for cities was explored, however, when investigating the respective role of maritime and airline networks in the combined air-sea centrality of cities, but without taking into account other urban data [START_REF] Ducruet | The port city in multidisciplinary analysis[END_REF]. The same applies to other types of inter-city linkages, which were analysed regardless of other urban attributes, such as those of multinational firms in various sectors (Rozenblat, 2010;Taylor, 2012). with the exception of Jacobs et al. (2011) showing the limited influence of container port traffic on the amount of maritime advanced producer services in world cities.

Reconciling port cities and maritime networks

This chapter proposes to palliate the aforementioned lack of a global and dynamic view by an analysis of combined maritime traffic and urban population data. This is the first-ever analysis of maritime flows in relation to cities based on rigourous harmonisation and manipulation of multiple historical data sources. It aims to measure the influence of urban demographic size on the distribution of global maritime flows, as a means to re-explore the existing literature on ports and cities. It also engages in a wider debate on whether urban development had become increasingly virtual, to such extent that material flows (and their related infrastructures) are increasingly disconnected from human settlements and planning/development priorities (Hall and Hesse, 2012). It gives paramount importance to the definition of the port city itself as a spatial unit, considering not only the locality of the port, but also the extended urban environment at a city-region (or urban area) level, which is more of a morphological nature and has the advantage of being comparable over time and across space. Another innovation compared with previous work is the application of a graphtheoretical framework thanks to the extraction of vessel movement data from the Lloyd's List corpus, in particular the Lloyd's Shipping Index providing information on the last known movement of each vessel recorded. For the first time, not only traffic and population weights are considered when statistically measuring port-city relationships, but also effective maritime linkages between port cities, here by the cumulated number of vessel calls.

Such a global and dynamic approach will test the extent to which the global maritime network is centralised by larger cities, and how has the correlation between maritime traffic and urban population evolved over time. This research has, therefore, wider implications than for the sole port-city issue. The topological features of spatial networks have rarely been confronted to the socio-characteristics of its nodes [START_REF] Ducruet | Network science and spatial science: Review and outcomes of a complex relationship[END_REF]. Providing a demographic weight to ports thus allows testing numerous ideas about the dependence of maritime networks upon a hierarchy of urban places rather than considering nodes only as ports or terminals. Because it is often the case that several ports belong to the same morphological urban area, the analysis is more compact and aggregated and thus may shed new light about port-city evolution in the last decades. For practical reason of data availability, and because the research is still in progress, the proposed analysis is limited to the period 1950-1990. One main hypothesis is based on the literature on port cities and maritime networks: the initially strong link between maritime flows and urban development has gradually declined. Yet, such a hypothesis might be questioned thanks to a renewed methodological framework where port cities and maritime flows are observed in a radically different way than in the past.

Data and methodology

First of all, this research was motivated by the availability of demographic data in the Geopolis database, which provides the number of inhabitants in urban areas based on morphological criteria over the period 1950-1990(Moriconi-Ebrard, 1994). It was preferred to other possible sources, such as the United Nations, as Geopolis rests on a more robust definition of the city. It includes cities having at least 100,000 inhabitants in 1990. This database was completed by Populstat for the rest of the period (Lahmeyer, 2006) to zoom on specific port cities at the end of the chapter. Both databases have the advantage to be historical and to consider urban areas rather than sole administrative boundaries.

With reference to Figure 20.1, each port or terminal was associated to the nearest urban centre taking into account urbanization patterns, physical proximity, road accessibility, and urban system layout. This manual method was preferred to any automatic matching in a Geographical Information System (GIS) to avoid putting together cross-border locations belonging to radically different socio-economic contexts. More precisely, two levels of urban activity have been distinguished, city and urban area. The city level is the municipality where the port is located, i.e. the smallest administrative area that is often eponym of the port itself, but not in all cases. The urban area level is the agglomeration or urban morphological area, with two possibilities: the urban area to which the city belongs, or a more distant, inland urban area that connects by road the city, the latter being the maritime outlet of the former. Two or more cities may be included in the same urban area, such as Tokyo and Yokohama that are administratively distinct cities but belong to the same morphological entity. The same methodology applied to coastal and river port cities.

A third type occurred, that is the combination of coastal and inland, especially in the case Santos urban area (Brazil) being the gateway of Sao Paulo urban area, i.e. two urban areas next to each other.

[Figure 20.1 here] As a result, it was possible to aggregate many ports and terminals altogether that in fact serve the same city, and gain in spatial coherence. For instance, we calculated that London port itself accounted for about 85-90% of the urban area's total vessels calls between 1890 and 1965, but it rapidly dropped since then until reaching 26% in 2008, with the gradual shift of terminals and traffic to deep-sea terminals along the Thames River and up to Felixstowe (Figure 20.2). Although the two curves went through similar evolutions over the whole period, the gap has widened following the shift of modern terminals towards suburban, deep-sea locations outside of the urban core. This is a typical example that confirms the accuracy of the Anyport model [START_REF] Bird | The Major Seaports of the United Kingdom[END_REF] in which such a trend was observed around the same period. Notably, Felixstowe set up Britain's first container terminal in 1967 and at the same time, between 1960 and 1980, the so-called London Docklands were gradually closed and the port activity relocated to Tilbury, Thamesport, and Felixstowe. This long-term view is currently in progress when it comes to the whole sample of ports worldwide. Port activity corresponds to the number of vessel calls calculated from the Lloyd's Shipping Index.

[Figure 20.2 here] Because the population data was available only every decade, it was decided to calculate the year-on-year average for the intermediate years of 1965, 1975, and 1985, to better see a trend in the association between population and traffic. As a result and considering only the urban area level, the global port-urban database concentrates a noticeable proportion of world ports and population, with about 500 urban areas considered for this time period (Table 20.1). The share of ports included in urban areas has increased, but the share of population and vessel calls has decreased, which is mainly due to the exclusion of smaller cities by Geopolis. Nevertheless, this sample is very representative of global maritime activity, as it remains around 80% of total vessel calls over time. This is already in itself an indication that maritime traffic is more likely to concentrate in larger cities. In addition, the urban areas exerting maritime trade have always been three times larger on average than other cities in terms of demographic size. Although such evidences are insufficient to conclude to mutual port-city growth effects, it confirms the observation that port cities enjoyed stronger dynamics due to their direct access to international trade networks [START_REF] Dogan | Giant cities as maritime gateways[END_REF].

[Table 20.1 here]

The changing correlation between traffic and population

One possible way to further check the respective influence of urban size and maritime traffic distribution is to look at the linear correlation among them and at the changing share of city size classes (quantiles) (Table 20.2). Despite certain fluctuations, maritime traffic is distributed hierarchically as its share increases along with population. The distribution among the six classes is relatively stable over time. Noticeable changes can be highlighted, however. For instance, the largest cities regularly dominate world traffic but their share has dropped from 59.4% to 49.7% between 1951 and 1990, while the share of the smallest cities has almost doubled, from 2.8% to 5.3%. In fact, traffic gradually shifted from the largest cities towards smaller ones, as each class gained around 2% over the period. This shift largely explains the decreasing concentration of maritime traffic among cities, as seen with the Gini coefficient (0.724 to 0.684) and the Herfindahl index, but the latter has been more stable than the first.

One very important result is the decreasing linear correlation between traffic and population. The linear function was in all cases the best fit between the two variables. Interestingly, the correlation coefficients obtained for port urban areas (i.e. the port city itself) are always lower than when including non-port urban areas (i.e. distant cities served by the port). Indeed, numerous inland cities are the true engines of port activity, despite road distance between port and city, and taking into account such an important aspect has been beneficial to the results1 . Another results is that the correlation has somewhat stabilised, creating a widening gap with the one obtained based on coastal urban areas only. This directly relates to the «hinterland effect» by which ports situated in minor coastal cities may have handle traffic volumes far beyond the needs of their host city, so that considering the nearby inland urban area as the city of reference improved the coherence of the results. While the correlation coefficient for coastal cities dropped only by half, the one based on coastal and inland cities lost only one point.

[Table 20.2 here]

Urban centrality in the global maritime network

The relationship between centrality and demography

Another important dimension of the research is the influence of demographic size on the centrality of cities in worldwide maritime flows. Commonly accepted measures of node centrality were calculated and compared (Table 20.3) so as to reveal their possible link with demographic size. Overall, all indicators exhibited a declining correlation with urban population, especially since 1960. Betweenness centrality, which corresponds to the number of occurrences of nodes on shortest paths in the entire graph, had the highest correlation in 1951, superseded by degree centrality, a more local measure (i.e. number of adjacent neighbours), since 1960. Eccentricity always had a lower correlation, while the clustering coefficient is negatively correlated and remains around -0.2. This negative score means that despite its low significance, the ability of nodes to be a star in the network (i.e. lower scores correspond to hubs with poorly connected neighbours) is more likely to apply to larger cities.

The latter evidence is confirmed when looking at the average clustering coefficient by classes of urban size (quantiles). While for all cities the clustering coefficient has regularly decreased, suggesting a general evolution of the network towards a hub-andspokes or «scale-free» structure, the largest cities always score the lowest, as they tend to be the hubs for multiple, poorly connected and smaller cities. With a few exceptions, the average clustering coefficient increases from one class to another as population increases, which suggests that as cities get smaller, their ability to centralise maritime flows decreases. Yet, the gap between the average clustering coefficient of the smallest and the largest cities has narrowed over time, from 0.32 to 0.15, which means that the probability for hub functions to concentrate at larger cities has somewhat become more blurred than in the earlier decades. Lastly, the rich-club coefficient that divides the link density (or completeness) among larger cities by the link density among all cities shows that larger cities tended to be around five times better connected with each other. Thus, the urban hierarchy certainly influences, at least partly, the spatial distribution of the global maritime network, notwithstanding important changes. Yet, it is also important to address how hierarchically connected are cities of various size in the network.

[Table 20.3 here] The analysis of priority linkages is a useful method to further understand the influence of urban hierarchies on the distribution of maritime flows. At the level of city size classes (Table 20.4), the share of vessel calls distributed between urban areas of similar size (intra-class) always remained lower than for the flows between other cities, and it has even decreased over time, from 48% in 1951 to about 38% in 1990. In comparison, the share of flows between adjacent classes oscillated around 20% of inter-class flows, while flows between demographically opposed cities (i.e. largest to/from smallest) increased from 0.9% to 13.8%. Overall, largest cities connect primarily with each other, as the two top classes (5 and 6) have a combined share of 82.7% of total intra-class flows in 1951, but this share dropped to 62.8% in 1990.

Such elements motivate the reference to the declining clustering coefficient on the level of the entire network, as one may conclude to the growing centralisation of network flows, especially around larger cities, which become more connected to smaller ones due their increasing role as intermediary hubs in the network.

[Table 20.4 here] Additional evidence was obtained from the analysis of network assortativity (Table 20.5). As defined by Newman (2002), assortativity (or assortative mixing) is measured by the Pearson correlation coefficient of degree between pairs of linked nodes. It indicates whether nodes of similar (or dissimilar) size preferentially connect to each other in a network. Urban area population was preferred to degree in this chapter to elucidate whether city size plays a role in the distribution of maritime flows. Assortativity was calculated with Python NetworkX package based on real population numbers and their logarithm, and on binary or weighted city-to-city matrix. Results were insignificant when considering binary linkages (presence or absence of a link). Taking into account weighted edges provided a positive and growing assortativity of the network, especially between 1970 and 1990, and this was even truer with logs for urban population. Despite the growing centralisation of maritime flows by larger cities (towards smaller cities) and just like scale-free networks in general, large hubs strongly connect each other while multiplying links towards smaller nodes.

[Table 20.5 here]

Cities in nodal maritime regions

Priority linkages may also be mapped based on the nodal region algorithm (or single linkage analysis) by which only the largest flow link of each node is kept in the graph (see also Appendix 20.1). Such a method helps revealing which nodes centralise flows in a tree graph and eventually the hidden subsystems composing the network. In this analysis, urban area population is taken as the referent metric to map nodes (Figure 20.3), while nodal regions are positioned using a Gem-Frick visualisation algorithm in the TULIP software to put major nodes and components at the centre of the figure and less important ones at its periphery. One first observation is that the number of large connected components has decreased from seven in 1951 to two-three in 1990, which underlines both the growing integration of global trade (Feenstra, 1999) and centralisation of the global maritime network around fewer pivotal hubs -the latter being an illustration of the declining clustering coefficient observed in Table 20.3. A second observation is that the geographic dimension of the components has fundamentally changed through a reinforced regionalisation of maritime flows. The hubs of these components tend to gradually restrict their dominance towards geographically close port cities, whereas in the beginning of the period, it was often the case that port cities from different, distant continents were included in the same subgraph. This brings concrete evidence about the shift from a colonial, centre-periphery system to a more polycentric one based on intra-regional freight distribution where the logistical factor had become prominent.

The extent to which larger cities always dominate smaller cities can be discussed based on this analysis. In 1951, the central hubs of the three largest components are also the world's largest port cities, namely London, Tokyo, and New York. It is not a coincidence that exactly these three nodes are titled "global cities" by Sassen (1991) in the title of her masterpiece on the matter, although her essay did not pay much attention to the port and maritime function of these cities per se. These major maritime nodes dominate a large number of other ones through the principle of transitivity, not only in their close vicinity but also through long-distance trade exchanges, such as London directly or indirectly centralising flows connecting Europe with Africa, Australia, and the Americas.

However, the demographic size of certain port cities is not always reflected by an equivalent position in the maritime network. Some port cities have simply faced trade decline despite their demographic growth, such as Bombay and Calcutta following the demise of the British Empire and the 1947 independence, and Buenos Aires facing internal political tensions that gradually eroded its previous prosperity. The large, global city of Paris (France) being a river port 250 kilometres from the coast always appeared as a terminal node. This is also the case of Great Lakes cities such as Chicago, Toronto, and Detroit which maritime accessibility is hampered by the necessary passage through the St. Lawrence Seaway before reaching international sea routes. Conversely, port cities such as Al-Kuwait or Basrah in 1960 enjoyed a strong nodal position regardless of their smaller urban size mostly due to the boom of oil business in the Middle East. But the most impressive example of this gap is the outstanding centrality of Antwerp and Rotterdam in the European component, especially since 1970, despite a relatively minor urban dimension compared with other world port cities, as they became Europe's largest gateways and still occupy this role nowadays, together with Hamburg, the latter being three times larger by its population. The same phenomenon occurred in Asia, where Singapore and Hong Kong, which are still large cities, gradually became the major hub ports for a number of even larger cities such as Bangkok, Jakarta, Shanghai, and Karachi. The latter ports became constrained by urban growth as shipping lines centralised their networks upon a few, strategically located transhipment nodes. London and New York have become minor ports in the network in 1990, despite their urban size and the volume of their traffic, due to the reorientation of major trunk lines towards external hub ports in North Europe and the Caribbean, respectively. With the exception of Tokyo, Osaka, Sao Paulo and Los Angeles, most of the largest cities have become somewhat peripheral in the maritime network in 1990.

Another reason is the influence of political events and transitions, as seen with the isolation of the Barcelona, Bilbao, and Shanghai components in 1951, their respective governments having imposed trade barriers with the outside world at the time (i.e.

Franco and Mao rules). However, Shanghai integrated the larger Tokyo component through Singapore in 1960 and Hong Kong in 1970. Perhaps, the isolation of the Alexandria (Egypt) component can be explained by the imminent revolution officially dated in 1952. Other examples include the Kiel/Murmansk dyad in 1960 in a context of Cold War, and the Tel-Aviv/Haifa (Israel) component in 1970 and 1980 that did not include neighbouring ports until becoming part of the larger Venice component in 1980. This is also the case for Beirut/Lattakia in 1970 and 1980 before and during the civil war, and of Havana (Cuba) connecting principally Cuban ports, Rostock (East Germany), and Varna (Bulgaria) in 1970 also reflecting upon the Cold War era. In 1980, Havana still stands apart but has one connexion with Vigo in Spain, and although it integrated the larger Singapore component in 1990 it was through Odessa (Ukraine) as part of the USSR trading system.

Another observed factor is the persistence of specialised long-distance linkages such as those based on maintained colonial ties, as seen with the Dunkirk component in 1951 comprising Le Havre, Brest, Bordeaux together with colonial ports (Madagascar, Vietnam, Benin, Congo, and Senegal) and the Lisbon component in 1951, 1960and 1970 including Porto, Angolese, and Guinea-Bissau ports. To some extent, the Marseilles component that remains isolated until 1990 may be placed in this category, since it has a relatively smaller size than the largest components and mostly includes French and African ports, reflecting upon the somewhat independent French trading system. Lastly, the isolation of certain smaller components from the larger ones may also be caused by coastal morphology and geographic proximity.

Port-urban trajectories

This research can potentially shed more light on the long-term evolution of port cities. The selection of a few examples is a first step in such a direction. The analysis benefited from the inclusion of additional urban data drawn from the Populstat database (Lahmeyer, 2006), still at the level of urban areas rather than the sole administrative unit. Comparing urban population and maritime traffic (Figure 20.4) shows that the number of vessel calls and of inhabitants for London have underwent two opposed trajectories over the period: a parallel growth and decline . While vessel traffic is significantly and statistically explained by urban population in both cases, with about 88% and 67% for the determination coefficient on the power-law line, it remains only around 15% for the whole period. As mentioned in the methodological section, there has been a rapid traffic shift towards modern terminals situated outside the urban core alongside drastic waterfront redevelopments in the Dockland area. Nevertheless, welcoming ever-bigger ships had led to a decreasing number of port calls, due to increasing ship size, while a large proportion of UK traffic became rerouted via Benelux ports and notably Rotterdam, as seen in Figure 20.3. Such factors can explain at least partly London's traffic evolution. But at the same time, London's population has also shrunk over time, in similar ways than traffic, although the two evolutions may not be directly interdependent. Population stagnation or decline in large Western cities is a general phenomenon that is caused by wider demographic trends such as ageing and urban sprawl.

In the case of Shanghai, the determination coefficient over the whole period remains moderately significant (45%), but it is much higher when splitting the period in two, namely 1890-1946 (76%) and 1951-2008 (73%). In 1949, a major political change occurred, namely the proclamation of the People's Republic of China, causing a drastic traffic declining which had recovered in accordance with the urban system. Contrary to the general belief that China as a whole was closed to international trade under Mao rule, port activity resumed rather rapidly already in the 1960s, while the spatial distribution of maritime traffic overlapped again the urban hierarchy of coastal port cities. This was also demonstrated by Wang and Ducruet (2013) in their analysis of Chinese port tonnage over the period 1868-2010 based on customs and ministry data, concluding to a strong resilience of the port system to political disturbances. The direct impact of China's official opening to foreign investment and international trade in 1978, known as the Open Door Policy led by Deng Xiaoping, is clearly illustrated by rapid traffic growth between 1975 and 1980. Urban population, fed by massive inmigration from rural areas, grew steadily since then, backed by ongoing industrialisation (Wand and Ducruet, 2012).

[Figure 20.4 here]

Conclusion

The link between port and city had often been analysed at the intra-urban level in previous research, where the separation process, both physical and functional, had been most visible. Expanding the analysis at the urban area level for the period 1950-1990 through a systematic quantitative approach of hundreds of port cities allowed confirming a growing disarticulation between the global urban hierarchy and the global maritime network. Yet, the magnitude of urban development remains an essential factor to explain maritime traffic distribution across the globe, notwithstanding the rise of less-urbanised hub ports and the influence of other factors such as site constraints, political contexts, and the changing pattern of trade routes. This first-ever dynamic and global analysis of combined maritime and urban data from a network perspective could, at least, fill this lack in the related urban and transport literature, which was still very much monographic or focused on other types of networks.

Further research shall concentrate on refining the statistical approach to port-city evolution, by applying more sophisticated tests on maritime and urban time series data, especially to check the direction of their mutual influence, and the possible regional logic behind such an influence. This will necessitate to fully exploiting the potential of the Populstat database for all cities, which goes back to the nineteenth century and prolongs the time coverage up to the 2000s. Including more many smaller cities and urban areas will inevitably improve the results in terms of global port-city correlation, traffic distribution, and evolution. The analysis of port-urban trajectories should be expanded so as to check whether comparable trends can be extracted and compared. In particular, certain properties such as assortativity or clustering may translate subsequent industrial and regional changes, such as the emergence of huband-spokes systems in liner shipping and the prolonged Asian growth.

  It is the case of the North Adriatic component of Rijeka/Trieste/Venice in 1960, of the Southern African component Cape Town/Durban in 1951 and 1960. The Sydney/Melbourne component has always been apart from 1951 to 1990. Numerous other intra-European components fall in this category based on specialised intra-regional trades. [Figure 20.3 here]

Figure 20 . 1 :

 201 Figure 20.1: Methodology for port-city matching Source: own realisation

Figure 20

 20 Figure 20.4: Port-urban trajectory of London and Shanghai, 1890-2008 Source: own elaboration

Table 20 .1: Characteristics of the port-urban database, 1950-1990

 20

		Quantiles	1951	1960	1965	1970	1975	1980	1985	1990
		6	59.4	59.4	56.9	56.8	56.9	49.2	49.7	49.7
	Share of world vessel calls (%)	5 4 3 2	18.9 8.3 6.4 4.1	15.5 10.6 7.3 3.8	18.7 10.8 6.2 4.6	18.6 10.1 6.9 4.6	15.4 11.3 8.2 5.6	22.4 11.7 7.8 5.2	20.8 10.1 8.5 6.3	20.2 11.1 8.1 5.6
		1	2.8	3.4	2.7	2.9	2.6	3.7	4.7	5.3
		Total	100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
	Correlation (Pearson)	Coastal urban areas Coastal & inland urban areas	0.521 0.485 0.404 0.408 0.326 0.315 0.338 0.288 0.559 0.581 0.535 0.572 0.511 0.467 0.498 0.437
	Traffic	Gini coefficient	0.724 0.710 0.704 0.696 0.712 0.697 0.684 0.684
	concentration	Herfindahl index	0.012 0.011 0.010 0.009 0.011 0.010 0.009 0.011

Table 20 .2: City sizes and traffic distribution, 1950-1990

 20

		Quantiles	1951	1960	1970	1980	1990
		6	0.434 0.417 0.413 0.371 0.361
	Average clustering coefficient*	5 4 3 2	0.532 0.539 0.457 0.398 0.377 0.584 0.567 0.493 0.476 0.422 0.580 0.562 0.547 0.488 0.512 0.627 0.587 0.543 0.500 0.476
		1	0.756 0.663 0.676 0.560 0.515
		All	0.542 0.542 0.534 0.487 0.465
		Clustering coefficient*	-0.231 -0.251 -0.255 -0.202 -0.210
	Correlation	Degree centrality Betweenness centrality* 0.507 0.494 0.449 0.452 0.344 0.462 0.521 0.469 0.465 0.423
		Eccentricity*	0.312 0.356 0.325 0.312 0.232
	Rich-club coefficient	5.597 5.959 5.166 4.974 4.843

Table 20 .3: City sizes and network measures, 1950-1990

 20

	N.B. zero values are excluded for variables marked with *
		Quantiles	1951 1960 1970 1980 1990
		6	67.5	63.8	50.3	44.4	45.3
		5	15.2	13.5	16.9	20.4	17.5
	Intra-class (%)	4 3 2	11.9 5.0 3.8	12.5 9.1 3.5	12.6 6.0 3.1	11.0 7.7 4.5	12.3 8.7 5.8
		1	2.2	4.5	2.9	3.3	5.5
		All	48.0	43.9	39.0	34.7	37.8
	Inter-class (%)	Opposed (1/6) Adjacent All	0.9 22.5 52.0	7.6 19.7 56.1	10.1 21.4 61.0	12.5 22.1 65.3	13.8 20.6 62.2

Table 20 .4: Maritime flows and urban homophily, 1950-1990

 20

	Urban weight	Population (raw)	Population (log)
	Links weight unweighted	weighted	unweighted	weighted
	1951	-0.0297	0.0406	-0.0183	0.0974
	p	0.0053	9.98E-10	0.0865	5.88E-49
	1960	-0.0425	0.0029	-0.0420	0.0773
	p	5.18E-06	0.6119	6.50E-06	7.39E-40
	1970	-0.0278	0.0414	-0.0274	0.0814
	p	0.0011	4.35E-14	0.0013	8.36E-50
	1980	-0.0126	0.1024	-0.0108	0.1394
	p	0.1601	4.57E-65	0.2310	1.81E-119
	1990	-0.0117	0.1177	0.0041	0.2032
	p	0.1587	9.08E-111	0.6215	0.0

Table 20 .5: Evolution of network assortativity, 1950-1990

 20

The synthesis provided by the OECD (2014) on port-city development included a figure showing the relationship between inland cities and coastal ports, distinguishing amongst independent metropolis (large port city far away from an inland core), short-range corridor (coastal and inland cities belong to the same morphological area), long-range corridor (port city under the shadow of the inland city within a

200km radius), and dependent satellite (large inland city near a minor port city). The four possible types of spatial configuration were discussed in terms of self-agglomeration or lock-in effects based on the model ofFujita and Mori (1996) about the development of port cities.

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. [313847] 'World Seastems'.

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