Charles Bouveyron

Pierre Latouche

Rawya Zreik

César Ducruet

Cluster identification in maritime flows with stochastic methods

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Since the original work of [START_REF] Moreno | Who Shall Survive? A New Approach to the Problem of Human Interrelations[END_REF], network data has become ubiquitous in computational social sciences [START_REF] Snijders | Estimation and prediction for stochastic blockmodels for graphs with latent block structure[END_REF]. Applications range from the study of social interactions in historical sciences [START_REF] Jernite | The random subgraph model for the analysis of an ecclesiastical network in merovingian Gaul[END_REF]Villa et al., 2008) to the analysis of maritime flows in geography [START_REF] Ducruet | Network diversity and maritime flows[END_REF]. In particular, network analysis was applied recently to a medieval social network in [START_REF] Jernite | The random subgraph model for the analysis of an ecclesiastical network in merovingian Gaul[END_REF], where the authors consider the clustering of an ecclesiastical network in Merovingian Gaul. Cluster analysis in the network context consists in grouping vertices sharing homogeneous connection profiles.

Both deterministic and probabilistic methods have been used to seek structure in these networks, depending on prior knowledge and assumptions on the form of the data. For example, [START_REF] Hofman | Bayesian approach to network modularity[END_REF] look for specific structures called communities where nodes of the same community are preferentially connected. The alternative strategy of [START_REF] Handcock | Model-based clustering for social networks[END_REF], which is a generalisation of [START_REF] Hoff | Latent space approaches to social network analysis[END_REF], assumes the relations to be conditioned on the projection of the vertices in a social latent space. Another popular method among the community discovery approaches is based on the modularity score of [START_REF] Girvan | Community structure in social and biological networks[END_REF], though asymptotically biased [START_REF] Bickel | A nonparametric view of network models and Newman-Girvan and other modularities[END_REF].

Most of the currently used methods derive from the stochastic block model (SBM) (Wang and Wong, 1987;[START_REF] Nowicki | Estimation and prediction for stochastic blockstructures[END_REF]. The SBM model assumes that each vertex belongs to a hidden cluster and that connection probabilities between pairs of vertices depend exclusively on their unobserved clusters, as in [START_REF] Frank | Cluster inference by using transitivity indices in empirical graphs[END_REF]. In order to perform inference, standard approaches cannot be used in practice. In particular, the expectation maximisation (EM) algorithm [START_REF] Dempster | Maximum likelihood for incomplete data via the EM algorithm[END_REF] cannot be derived because the conditional distribution of the latent groups is intractable. To overcome this issue, variational and stochastic approximations are often used. Thus, [START_REF] Latouche | Overlapping stochastic block models with application to the French political blogosphere[END_REF] used an approximation of the marginal loglikelihood, while [START_REF] Daudin | A mixture model for random graphs[END_REF] considered a Laplace approximation of the integrated classification log-likelihood. A non-parametric Bayesian approach was also proposed by [START_REF] Kemp | Learning systems of concepts with an infinite relational model[END_REF] for estimating the number of groups while clustering the vertices.

Extensions of SBM include the mixed membership stochastic block model (MMSBM) [START_REF] Airoldi | Mixed membership stochastic blockmodels[END_REF] and the overlapping stochastic block model (OSBM) [START_REF] Latouche | Overlapping stochastic block models with application to the French political blogosphere[END_REF]. They both allow a vertex to belong to multiple clusters at the same time. More recent work focused on extending random graph models to dynamic networks [START_REF] Sarkar | Dynamic social network analysis using latent space models[END_REF]Xing et al., 2010;Yang et al., 2011;[START_REF] Dubois | Stochastic blockmodelling of relational event dynamics[END_REF][START_REF] Heaukulani | Dynamic probabilistic models for latent feature propagation in social networks[END_REF]Xu and Hero III, 2013), or dealing with nonbinary networks such as those with weighted edges [START_REF] Mariadassou | Uncovering latent structure in valued graphs: A variational approach[END_REF][START_REF] Soufiani | Graphlet decomposition of a weighted network[END_REF]. Some efforts were also made to take into account covariate information (Zanghi et al., 2010). For instance, the random subgraph model (RSM) [START_REF] Jernite | The random subgraph model for the analysis of an ecclesiastical network in merovingian Gaul[END_REF] was proposed to analyse directed networks with typed edges for which a partition of the vertices is available. For more details, we refer to [START_REF] Goldenberg | A Survey of Statistical Network Models[END_REF][START_REF] Salter-Townshend | Review of statistical network analysis: Models, algorithms, and software[END_REF]; and [START_REF] Matias | Modeling heterogeneity in random graphs through latent space models: A selective review[END_REF] who provided extensive reviews of statistical network models.

In this chapter, we aim to uncover clusters in a maritime flow network extracted from Lloyd's List where geographical information is available as well as the type of preferential commodities. The main goal of this research is to determine the possible influence of geography and cargo specialisation on the emergence of clusters in a maritime network. On the one hand, a maritime network is a multilayered system (or multigraph, multiplex graph), as different fleet types have different logics of circulation that more or less overlap and connect via port nodes. On the other, it is also a multilevel system where global, regional, and local dynamics take place simultaneously to ensure maritime freight and passenger distribution. Such an approach complements the works of [START_REF] Kaluza | The complex network of global cargo ship movements[END_REF] and [START_REF] Ducruet | Maritime constellations: A complex network approach to shipping and ports[END_REF], which used other clustering methods and analysed the different fleets separately, without explicitly including the geographic factor in the partition. Previous works found a strong influence of geographic proximity but other possible logics remained hidden, except for hierarchical tendencies caused by hub-and-spokes configurations in container shipping. It can be hypothesised that the connections between ports are not only determined by geographic proximity but also depend on the intensity and type of circulation, but these elements need to be analysed simultaneously.

The remainder of the chapter is organised as follows. Next section presents the probabilistic model of SBM and RSM. Inference and model selection are also briefly discussed. The data and experimental setup are given afterwards, followed by an experimental comparison of both methods on the Lloyd's dataset, highlighting the advantages of using such techniques.

Probabilistic models for network clustering

This section presents the stochastic block model and the random subgraph model. Inference and model selection are also briefly discussed.

Context and notations

We consider a directed graph G with N vertices represented by its N × N adjacency matrix X. Each edge Xij, describing the relation between the vertices i and j, takes its values in a finite set {0, . . . , C}. Note that Xij = 0 corresponds to the absence of an edge. We assume that G does not have any self-loop, and therefore the entries Xii will not be taken into account. In RSM, a partition P of the vertices into S classes is also assumed to be available. In both cases, our goal is to cluster the network into K groups with homogeneous connection profiles, i.e. estimating a binary matrix Z such that Zik = 1 if vertex i belongs to cluster k, 0 otherwise.

[Figure 12.1 here]

The stochastic block model

The SBM model associates to each vertex of a network a latent variable Zi drawn from a multinomial distribution: where α denotes the vector of class proportions. As in other standard mixture models, the vector Zi sees all its components set to zero except one such that Zik = 1 if vertex i belongs to class q. The model then verifies: and where K denotes the number of components (clusters) of the mixture. Finally, the edges of the network are drawn from a Bernoulli distribution:

where Π = (πkl )kl is a K × K matrix of connection probabilities. According to this model, the latent variables Z1, . . . , ZN are iid and given this latent structure, all the edges are supposed to be independent. Note that SBM was originally described in a more general setting, allowing any discrete relational data. However, in the following we concentrate on binary edges only, i.e. C = 1.

[Figure 12.2 here] [Table 12.1 here] Figure 12.1 presents an example of an SBM network made of nine nodes split into three groups (indicated by the colours). As one can see, on this specific example, the within-cluster connexion probabilities (π••, π••, and π••) seem to be rather large since the nodes of each group are well interconnected. Conversely, connections between nodes of different groups are less frequent, which is due to low values of the betweengroup connexion probabilities (π••, π••, π••, ...). Such a matrix Π corresponds to networks made of communities, which are frequent in social networks, for instance. However, situations where between-group connexion probabilities are larger than within-group connexion probabilities are possible with the SBM model. This type of network is, for instance, very frequent in biology when studying networks of genes. Indeed, it is of interest in such a context to characterise, on the one hand, the regulatory genes and, on the other, the regulated genes. The left panel of Figure 12.2 presents the graphical model associated with SBM, and Table 12.1 summarises the model notations.

The random subgraph model

We consider now the directed graph G with a known partition P of the vertices into S classes, where each edge Xij is categorical, i.e. takes its values in a finite set {0, . . . , C}. Contrary to SBM, RSM can deal with networks where C > 1. In order to simplify the notations when describing the model, we also consider the binary matrix A with entries Aij such that Ai,j = 1 ⇒ Xi,j ;= 0. We also emphasize that the observed partition P induces a decomposition of the graph into subgraphs where each class of vertices corresponds to a specific subgraph. We introduce the variable si which takes its values in {1, . . . , S} and is used to indicate to which of the subgraphs vertex i belongs, for i ∈ {1, . . . , N }.

The data is assumed to be generated in three steps. First, the presence of an edge from vertex i to vertex j is supposed to follow a Bernoulli distribution whose parameter depends on the subgraphs si and sj only: Each vertex i is then associated to a latent cluster with a probability depending on si. In practice, the variable Zi is drawn from a multinomial distribution:

Where A notable point of the model is that we allow each subgraph to have different mixing proportions αs for the latent clusters. We denote hereafter α = (α1, . . . , αS). Finally, if an edge between i and j is present, i.e. Aij = 1, its type Xij is sampled from a multinomial distribution with parameters depending on the latent clusters. Thus, if i belongs to cluster k and j to cluster l:

where the sum over the C types of each vector πkl = (πkl1, . . . , πklC) is:

If there is no edge between the two vertices, the entry Xij is simply set to Xij = Aij = 0.

We point out that the choice of separating the role of the known subgraphs and the latent clusters was originally motivated by a parsimony concern. An alternative approach would consist in allowing the presence of an edge and its type to depend on both the subgraphs and latent clusters. However, this would dramatically increase the number of model parameters to be estimated. Indeed, for a network with S = 6, K = 6, and C = 4, it would require K 2S2(C + 1) + SK = 6516 parameters while RSM only involves S2 + K 2C + SK = 216 parameters.

The right panel of Figure 12.2 presents the graphical model associated with RSM, and Table 12.1 summarizes the model notations. Figure 12.2 allows us to see the conceptual differences between the SBM and RSM models. In particular, the specific role of Aij appears here clearly.

[Figure 12.3 here] Figure 12.3 presents an example of an RSM network made of nine nodes belonging to two subgraphs (denoted through the form of nodes) and split into three groups (indicated by the colours). A main difference with an SBM network is, of course, the presence of several (here C = 2) types of edges and a partition, assumed to be known, of the network into (here S = 2) subgraphs. In this specific case of a network generated according to the RSM model, the probability of an edge relies on two different parameters: γ and Π. The parameter γ governs the possibility of an edge (of any type) between two nodes, and this depends on the subgraphs they belong to. For instance, the presence of an edge between nodes 2 and 7 relies on γQD. Then, if the method decides that an edge exists between those two nodes, the type of the edge is drawn from a multinomial distribution with probabilities π••. Let us recall that π•• is here a vector of C probabilities. It turns out that the specific edge between nodes 2 and 7 was chosen to be of the type "continuous line" and not of the type "dashed line".

Inference and model selection

Given a network, the inference task consists in looking for estimates of the model parameters and cluster memberships. SBM and RSM fall in the family of mixture models for which the expectation maximization (EM) algorithm is the standard inference procedure [START_REF] Dempster | Maximum likelihood for incomplete data via the EM algorithm[END_REF]. It is an algorithmic procedure which iteratively maximizes the likelihood relying on the expected complete data likelihood [START_REF] Mclachlan | The EM Algorithm and Extensions[END_REF]. Unfortunately, the EM algorithm depends on the conditional distribution of the cluster membership matrix Z given the network, which is here intractable. As an alternative, variational approaches can be used to derive an approximate inference scheme (see for instance [START_REF] Jordan | An introduction to variational methods for graphical models[END_REF]. The key point is to approximate the conditional distribution of Z by assuming the conditional independence of Z1, . . . , ZN . The corresponding algorithm is called variational EM (VEM) [START_REF] Daudin | A mixture model for random graphs[END_REF]. Note that an alternative strategy consists in focusing on the optimization of the complete data likelihood (Zanghi et al., 2008). This strategy is often called classification EM (CEM). In this case, the choice of the number K of latent groups cannot be based on the observed likelihood, which is not tractable, but can be done using criteria such as the integrated classification likelihood (ICL) criterion [START_REF] Daudin | A mixture model for random graphs[END_REF].

In order to perform model selection, it is also possible to consider the two models presented above in a Bayesian framework. The principle is to see the model parameters as random variables and to make assumptions on their distributions. In practice, conjugate prior distributions are chosen to simplify the inference, which can be done either by relying on sampling techniques (as used in [START_REF] Nowicki | Estimation and prediction for stochastic blockstructures[END_REF], such as Markov chain Monte Carlo (MCMC), or Bayesian extensions of the VEM algorithm [START_REF] Latouche | Variational Bayesian inference and complexity control for stochastic block models[END_REF][START_REF] Jernite | The random subgraph model for the analysis of an ecclesiastical network in merovingian Gaul[END_REF]. The latter, called variational Bayes EM (VBEM), is preferred in the context of networks for scaling reasons. Contrary to VEM which maximizes an approximation of the likelihood, VBEM focuses on an approximation of the marginal likelihood where all model parameters and cluster memberships are integrated out. Alternative strategies rely on allocation sampler [START_REF] Daid | Improved Bayesian inference for the stochastic block model with application to large networks[END_REF] or greedy search [START_REF] Côme | Model selection and clustering in stochastic block models with the exact integrated complete data likelihood[END_REF].

The model selection, which mainly consists here in choosing the appropriate number K of groups, can be done afterwards by considering the approximate marginal likelihood. Thus, K is chosen such that the corresponding criterion is maximized.

Application to the maritime network

This section now focuses on the application of both the SBM and RSM methods to a maritime flow network, extracted from the well-known Lloyd's List.

The Lloyds' data Data was obtained from the printed Lloyd's Voyage Record published in October and November 2004, which details for each merchant vessel its successive movements from one port to another. Four main types of vessels are retained (containers, solid bulk, liquid bulk, and passengers/vehicles) calling at the world's 500 largest ports based on their degree (number of connected neighbours in the graph), from the original 2,737 ports or 1,815 port cities referenced in the original dataset, and are complemented by additional sources to retrieve their tonnage capacity (see [START_REF] Ducruet | Network diversity and maritime flows[END_REF]. Each port was assigned to a large region or continent, namely Asia, Europe/Mediterranean, North America, Latin America, Oceania/Pacific, Middle East/Red Sea, and Africa.

Experimental setup

From the raw database of vessel flows, we constructed an adjacency matrix between ports as follows: first, for every pair of ports, we considered the total tonnage of each commodity type by summing overall ship movements between those ports; second, we retained the main commodity type associated to each pair and drew an edge of the corresponding type between the two ports. In practice, the adjacency matrix contains entries ranging from 0 (no movements) to 4 (for the 4 commodity types taken into account). Figure 12.4 presents the adjacency matrix where commodity types are denoted using colours.

[Figure 12.4 here]

In order to apply the SBM and RSM model to those data, we used the mixer and Rambo packages for the R software. The mixer package (version 1.8) implements the VEM, VBEM, and CEM algorithms for SBM. We used the latter method for the inference, mainly because of its scaling properties. The package also allows the selection of an appropriate number K of groups for the data at hand with two criteria, and provides insightful visualisations of the results. We considered the ICL criterion, which is the one available for the CEM algorithm. On the other hand, the Rambo package (version 1.1) proposes the VBEM algorithm for the inference of the RSM model. Model selection is considered based on an approximation of the marginal likelihood. Some meaningful plots allow the visualisation of the clustering results as well. Both algorithms were run for a number K of clusters ranging from 2 to 20 and, for each method, the value of K was chosen such that the associated criterion was maximum.

Analysis of the network with SBM

We first analyse the network with SBM. Listing 1 gives the command lines in the R language to run mixer on a binary version of the adjacency matrix (named hereafter X).

Listing 1: Analysis of the network with SBM # L o a d i n g t h e l i br a r y l i b r a r y ( m i x e r ) # B i n a r i z a t i o n o f X X = a s . n u m e r i c ( X ! = 0 ) # C l u s t e r i n g w i t h m i x e r r e s . s b m = m i x e r ( X , q m i n =2 , q m a x = 2 0 , m e t h o d = " c l a s s i f i c a t i o n " ) # V i s u a l i z a t i o n o f t h e c l u s t e r i n g r e s u l t s p l o t ( r e s . Figure 12.5 presents the output of the mixer function. As one can observe, the ICL criterion peaks at K = 10, meaning that an appropriate number of groups for this network seems to be 10 groups for the SBM model. The reorganised adjacency matrix allows us to see different kinds of groups. First, the network comprises one large and sparse group (cluster 1) of ports with few connections. Second, the nine other groups have much larger intra-connection probabilities. We can also note the presence of clusters which tend to connect with nodes of other clusters. Those ports can be considered as hubs. As shown in Figure 12.6, except for cluster 1, most clusters correspond to geographical regions. For instance, it appears that clusters 2 and 3 can be associated with the Europe/Mediterranean and/or North American regions while clusters 4 and 6 mainly include ports from the Oceania/Pacific and Asia regions. Some other clusters, such as cluster 9, are made of hubs which allow ports of different geographic regions to connect.

[Figure 12.5 here] Interestingly, the original SBM model cannot take a priori geographical information into account. Moreover, it only focuses on binary edges and cannot deal with categorical relationships. Nevertheless, by only looking at the presence and absence of flows between ports, one can see that the geographic information is retrieved. This tends to show that the organisation of the maritime network is mainly explained by the geography where the domination and competition between ports occurs within regions.

Analysis of the network with RSM

We then used the Rambo package to cluster the data according to the RSM model. In this case, the adjacency matrix with categorical entries was used in addition to the partition of the ports by continents. Since we provide geographic information about the network nodes to the algorithm, it should be able to focus on other patterns hidden in the data. Listing 2 gives the command lines in the R language to run the RSM function on the adjacency matrix.

Figure 12.7 presents the output of the RSM function. The variational approach finds K = 5 clusters. The reorganised adjacency matrix according to the clusters found is given in Figure 12.8. We observe that clusters can be associated with the use of specific types of vessels. Thus, cluster 2 is made of ports which tend to connect mainly through passenger/vehicle vessels. Moreover, cluster 3 contains ports interacting through solid bulk vessels. Similarly, cluster 4 can be associated with containers and cluster 5 with liquid bulk vessels. Interestingly, there are no strong connection profiles from ports in different clusters. We could have expected ports interacting through a type of vessels to have notable connections with ports associated to other types of vessels. Overall, this is not the case. The clusters found are essentially defined by their ports interacting through specific types of vessels.

[Figure 12.6 here] [Figure 12.7 here] As shown in Figure 12.9, the clusters found are not related to geographic regions, although cluster 3 mainly contains ports from the Europe/Mediterranean region. This is the key advantage of relying on RSM rather than SBM. Since the geographic information is given a priori, the clustering technique for RSM can uncover other patterns present in the data. Here, the results highlight that all the regions are organised through clusters of interacting types of vessels. Moreover, we point out that this methodology allows, by removing the geographical factors present in the data (as shown in the previous section), to assign roles to ports depending on maritime flows.

Conclusion

In this chapter, we considered the SBM and RSM models for the clustering of ports in a maritime network created from the printed Lloyd's Voyage Record published in October and November 2004. We pointed out the advantages and the flexibility of the two models, and gave a short review of some of the existing approaches for their inference. In particular, we mentioned the use of variational approximations to derive tractable quantities. The two models gave rise to different and complementary results. By only looking at the presence or absence of connections between ports (SBM), we retrieved mainly geographical clusters highlighting the influence of physical geography and regional markets on port competition and maritime network configuration. However, using the known regions as subgraphs (RSM) and taking into account fleet types uncovered other types of clusters hidden in the data. These clusters are made of ports interacting through specific types of vessels. This allows us to assign a role to each port, by removing the geographical factors.

  s b m ) # S e l e c t i o n o f t h e b e s t S B M m o d e l r e s B e s t = g e t M o d e l ( r e s . s b m )

Listing 2 :

 2 Analysis of the network with RSM # L o a d i n g t h e l i b r a r y l i b r a r y ( R a m b o ) # C l u s t e r i n g w i t h m i x e r r e s . r s m = r s m ( Z , sub , K l i s t = 2 : 6 , n b r e d o =1 , m a x i t = 5 0 , d i s p = T R U E ) # V i s u a l i z a t i o n o f t h e c l u s t e r i n g r e s u l t s p l o t ( r e s . r s m ) # S e l e c t i o n o f t h e b e s t S B M m o d e l r e s B e s t = r e s . r s m $ o u t p u t [ [ 5 ] ] [Figure 12.8 here] [Figure 12.9 here]

  Figure 12.1: An example of a SBM network N.B. The network is made of 9 nodes split into 3 groups (indicated by the colors).According to the SBM model, the directed edges between the nodes are assumed to be drawn from a Bernoulli distribution with probability πkl , where k, l are here colors

Figure 12 . 4 :

 124 Figure 12.4: Adjacency matrix of the Lloyds data organised by continent with categorical edges: containers (black), solid bulk (red), liquid bulk (green), and passengers (blue).

Figure 12 . 5 :

 125 Figure 12.5: Outputs of the mixer function: values of the ICL criterion for the different values of K (top left), reorganised adjacency matrix according to the partition into 10 groups found by mixer (top right), empirical (yellow) and estimated (blue) distributions of the node degrees (bottom left), and network summarizing the relationships between the found latent clusters (bottom right)

Acknowledgements

The authors would like to thank Olivier Joly, Marine Le Cam, and Brahim Ould Ismail at UMR IDEES (Le Havre) for their help on data provision and preparation.

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Throughout port and maritime studies, the link between flows and the socio-economic characteristics of localities has been investigated mostly qualitatively. While systematic international quantitative investigations remain scarce and dispersed, their reliance upon port tonnage statistics tends to ignore maritime linkages. Conversely, maritime network studies remain abstract, where ports are considered only as nodes in a graph. What is the influence of the local economy on the situation in -and specialisation of -maritime networks? Are there significant interrelations between types of maritime flows and types of local economies? Such an approach shall first discuss the wider scientific literature about transport and regional development, with a particular focus on previous quantitative studies. Secondly, this chapter provides an analysis of the Pacific Rim area based on the comparison of vessel movement data and regional socio-economic data collected at the level of subnational entities or port regions. The fact that populations and markets are concentrated on the coastlines of North America, Asia, and Oceania [START_REF] Lee | A tale of Asia's world ports: The spatial evolution in global hub port cities[END_REF] motivated the search for spatial and functional interdependencies between traffic and local economic structure. In addition, the Asian-Pacific Rim "had become the indisputed main generator of containers" in the world (Rimmer, 2014, p. 91) and a major concentration of multinational industrial and logistics corporations.

Regions, material flows, and maritime networks

A great variety of research throughout the academic literature has addressed the link between regional development and material flows. Reference to such flows is often implicit, however, as for instance in urban economics and location theory [START_REF] Fujita | The Spatial Economy: Cities, Regions and International Trade[END_REF]McCann and Shefer, 2004;[START_REF] Beyers | Economic structure, technological change and location theory: the evolution of models explaining the link between cities and flows[END_REF], in regional development theory [START_REF] Dawkins | Regional development theory: conceptual foundations, classic works, and recent developments[END_REF], and in studies of economic growth and globalisation (Scott and Storper, 2003), and of commodity chains, global production networks, and world cities [START_REF] Leslie | Spatializing commodity chains[END_REF][START_REF] Dicken | Chains and networks, territories and scales: Towards a relational framework for analysing the global economy[END_REF][START_REF] Derudder | Commodity Chains and World Cities[END_REF]. Empirical investigations are often qualitative case studies of particular places and contexts. Quantitative analyses are done mostly at the national level [START_REF] Harrigan | Specialization and the volume of trade: do the data obey the laws?[END_REF], while those done at the regional (sub-national) level mainly focus on mobility and communication flows, without always measuring their interdependence with local socio-economic development. One example is evolutionary economic geography, which analyses regional branching and industry relatedness by looking at flows of labour, firms, and knowledge (Boschma and Frenken, 2011a). More specialised studies of (freight) traffic flows do exist, but they often ignore the local context, such as studies of transport networks addressing issues of accessibility and connectivity [START_REF] Ducruet | Structure and dynamics of transportation networks: Models, concepts, and applications[END_REF].

The few existing empirical studies of material flows in relation to their local environment come from very diverse schools of thought and methods, of which urban ecology and regional science. As reviewed by Ducruet and Itoh (2015), regional scientists focused on the impact of transport infrastructure on the intensity of trading flows and on the location of economic activities, with applications to ports focusing on infrastructure quantity, quality, its influence on trade, economic development, manufacturing costs, private investment, capital stock, employment, etc. Other approaches included measuring the local determinants of regional exports in terms of transport costs and sea access, the influence of gross regional product on airline accessibility and urban centrality of cities, and the distribution of supply chain networks in relation to urban hierarchy (see [START_REF] Guerrero | Freight flows and urban hierarchy[END_REF].

The case of ports and port regions offers mixed evidence, and local socio-economic development in relation to ports has not been fully studied from a maritime network perspective. On the one hand, certain studies confirmed the weakening spatial fix of port traffic as a combined effect of shipping line concentration and service rationalisation, new port development outside urban cores to avoid congestion, with a growing gap between white-collar urban regions and blue-collar port regions in terms of economic structure, wage level, economic productivity, and presence of advanced producer services. But despite their sometimes global focus, such empirical studies mostly focused on Western cases, such as the United States, Canada, and Europe [START_REF] Ducruet | Commodity variety and seaport performance[END_REF] or richer countries (Ducruet, 2009;Ducruet et al., 2015). Yet, large European port gateways may expand their hinterlands further inland but at the same time maintain strong local linkages through heavy industrial complexes [START_REF] Bottasso | The impact of port throughput on local employment: Evidence from a panel of European regions[END_REF]Botasso et al., 2013;[START_REF] Guerrero | Deep-sea hinterlands: Some empirical evidence of the spatial impact of containerization[END_REF]. Nevertheless, the majority of studies contradicting the erosion of port-region linkages are of Asian essence (see [START_REF] Fujita | The role of ports in the making of major cities: Self-agglomeration and hub-effect[END_REF] for a general discussion). In Japan, port investment had significantly positive effects on GDP and private capital (Kawakami and Doi, 2004) as did port efficiency on shipping cost and GDP growth [START_REF] Doi | A computable general equilibrium analysis of efficiency improvements at Japanese ports[END_REF]. In China, industrial productivity had a positive influence on port traffic growth [START_REF] Cheung | Port city factors and port production: analysis of Chinese ports[END_REF], while port-related added value had a positive impact on regional economic growth [START_REF] Deng | Evaluation of the relevance measure between ports and regional economy using structural equation modeling[END_REF], sometimes depending on the location, stage of economic development, and land transport density of the different provinces (Song and van Geenhuizen, 2014). Despite a diversity of methods and outcomes, these studies remain bound to single-country datasets and neglected the importance of maritime linkages between (subnational) port regions (see a complementary discussion in Chapter 20 by Ducruet et al. on port cities).

The network analysis of maritime flows has progressed rapidly in the last decade or so (see Chapter 1 for an overview), but little has been done about their local socioeconomic embedding. In terms of commodity specialisation, [START_REF] Ducruet | Network diversity and maritime flows[END_REF] demonstrated the strong influence of commodity diversity on port centrality and maritime network structure, but without discussing the role of industrial linkages.

Crossing port throughput and regional data across both developed and developing countries could show that core economic regions, which are richer and more densely populated, concentrate international and valued traffic (general cargo, containers), while peripheral regions, which specialise in the primary sector, concentrate more bulky flows (Ducruet and Itoh, 2015). Such an analysis was inspired by recent works on place-and path-dependency in economic geography (Boschma andFrenken, 2011a, 2011b;Neffke et al., 2011) as well as previous discussions on commodity specialisation and regional specialisation (Tabuchi and Thisse, 2002).

A network methodology can push further our understanding of port-region linkages in several ways. In line with previous research based on port throughput data, it can elucidate whether maritime traffic specialisation is related with economic sector specialisation, if certain socio-economic characteristics influence nodes' position in the network, and if similar types of port regions strongly connect each other, and through which type of commodity flow. To some extent, this chapter searches for technological coherence (Boschma and Frenken, 2011b) between flows and spaces.

Mutual specialisation effects across Pacific Rim port regions

Data and methodology

One first step has been to obtain vessel movement data from one issue of the Lloyd's Shipping Index published in 2008, which covered 88.8% of the world fleet capacity measured in deadweight tonnage according to UNCTAD (2008). The 23,675 recorded vessels were categorized into five main types for the sake of simplicity (general cargo, container, liquid bulk, solid bulk, and passenger/vehicle), measured in deadweight tons (DWT). A total of 518 ports were recorded in 13 countries of the Asia-Pacific region, for which socio-economic data at the regional (subnational) level was available (Table 16.1), resulting in 124 port regions. Regional data was collected for the year 2009 except for China and Taiwan ( 2010) and selected according to potential effects and links with vessel traffics (Table 16.2). The local economy is described via seven variables: employment in three main economic sectors (primary, secondary, and tertiary), demographic weight (or population share), population density, gross regional product (GRP), and unemployment rate. Regional variables were transformed into location quotients based on national average to avoid possible biases caused by structural differences among countries in terms of economic structure and statistical definitions.

Five traffic categories cover the whole spectrum of port and maritime activities, alongside the shares of inbound and domestic traffic and the share of regional traffic in the national total. Traffic categories were weighted (Charlier, 1994) in order to better reflect their potential cargo value and employment generation power at the docks and terminals. The variables (indicators) of (port) traffic categories for each region indicate the share in total regional traffic except for the share of regional traffic in (total) national traffic. Lastly, this empirical analysis includes network centrality variables (indicators) calculated at the global level of the worldwide graph: degree centrality (or number of links) and hub function (or position of networks), for discussing interdependencies between the socio-economic profile of the port region and its connectivity in the maritime network. The hub function of the port region is the inverse value of its clustering coefficient1 : higher values underline a strong bridge or hub position towards immediate neighbours in the graph.

The study sample represents 49.9 percent of total world traffic, with a slightly higher share for containers (60.5 percent) and solid bulk (67.4 percent) than passengers and vehicles (47.1 percent), general cargo (36.9 percent), and liquid bulk (32.9 percent). This traffic structure reflects the intensity of container flows across the Asia-Pacific, such as between China and the United States, and the growing trade of raw materials such as cement, coal, metals, and minerals from Australia. The selected port regions constitute subnational administrative entities in each country, such as Chinese provinces and American states, where one or more ports operate. Such a level of analysis allows mixing regional and port traffic variables in a common database and takes into account the local or captive hinterland of ports, where most clients are located and where port-related activities concentrate, such as in the port city or port cluster. It is unfortunately impossible to distinguish local trade from transit trade in maritime statistics as the same region may be the origin/destination of flows but also a gate to access inland core regions beyond local needs [START_REF] Itoh | Market area analysis of port in Japan: An application of fuzzy clustering[END_REF]. For instance, inland rural regions may ship their exports through a port situated in an urban region acting as the main gateway [START_REF] Löfgren | Spatial Networks in Multi-region Computable General Equilibrium[END_REF], and vice-versa.

A simple, linear regression between total vessel traffic and total port tonnage2 showed a significant relationship with a determination coefficient of 0.49 and 0.57 for nonweighted and weighted figures, respectively. The fitness of weighted figures is slightly better than for non-weighted figures due to the higher efficiency of shipping networks and their high load factors for valued cargoes such as containers. Therefore, this empirical analysis adopted weighted figures as indicators for discussion of the relationship with regional activities. Differences in data sources such as time coverage and measurement unit may lower the relationship as well as the inclusion of landward (hinterland) flows in port tonnage.

[Table 16.1 here] [Table 16.2 here]

Preliminary results

A principal components analysis (PCA) was applied to the 17 port and regional variables (see also Table 16.2), from which Figure 16.1 presents the two first main factors (see also Appendix 16.1 for more detailed results). Overall, the results point to a very significant relationship between traffic specialisation and regional specialisation. As such, regions specialised in primary activities tend to have a higher share of solid bulk, standing apart from other variables (the second quadrant in the figure). An opposite trend is that regions specialised in services (tertiary sector) while being richer and more densely populated concentrate container flows (the fourth quadrant in the figure). This opposition already underlined by Ducruet and Itoh (2015) based on port throughput statistics in a global perspective, confirms that (maritime) traffic is not randomly distributed across space and therefore reflects the dominant character of the place where it is handled, despite the impossibility of distinguishing transit flows (transhipment) from trade flows (hinterland) in total shipping activity, and correcting for possible spatial and functional mismatches between administrative regions and port hinterlands.

In addition, on the first factor, degree centrality is clearly if onlypartly determined by demographic concentration and GRP per capita and high traffic share, which corroborates the aforementioned works on airline networks and cities. Regions specialised in the secondary (industrial) sector are likely to act as hubs in the maritime network, i.e. to be distribution platforms of hub-and-spokes configurations with an average hub function. When considering the second factor alone, negative scores underline some affinity between the tertiary sector, liquid bulk, domestic, and inbound traffic, as service or urban regions are important consumption centres for fuels [START_REF] Graham | Telecommunications and the future of cities: debunking the myths[END_REF]Decker et al., 2000). The remaining variables have less significance along the two first factors. However, results show that passenger and vehicle traffic is closer to the tertiary sector and to population share and population density to a lesser extent for the third factor, while general cargo traffic is closer to the industrial (secondary) sector, and density to GRP for the fourth factor.

[Figure 16.1 here]

Eight coherent groups of port regions were obtained from a non-hierarchical clustering based on the PCA (see Appendix 16.2 3 for an overview). The first cluster (industrial centre) is the largest by the number of port regions and its share in total vessel traffic (36.8 percent). It is also the only cluster with a positive, pronounced specialisation in the industrial sector rather than services. Yet, its traffic profile is only slightly specialised in solid bulk, containers, outbound, international, and degree centrality, but a negative score for hub function. The second cluster (value-added cityhub), with only 10 regions but 18 percent of the sample's traffic, is highly specialised in containers, general cargo, and international outbound traffic, with important degree centrality, traffic share, and hub function. Interestingly, such a profile goes along with the concentration of population, density, but also unemployment and a balanced role of the tertiary and industrial sectors. The third cluster (agri-bulk hub), with only seven regions, still captures 17.4 percent of total traffic as it shares the same profile than the former as a hub concentrating traffic and population, but with a specialisation in primary activities and solid bulk and traffic share, and a lower density. The second and third clusters only have higher degree centrality and hub function both with high traffic share and population share, but a higher unemployment rate than the national average, probably caused by excessive immigration inflows. The fourth cluster (energy centre), with 25 regions, accounts for only 10.3 percent of total traffic. Such regions are smaller in size (traffic, demography) and are mostly domestic import regions for liquid bulk to fuel primary and tertiary activities.

The fifth cluster is a special case with only three regions and less than 1 percent traffic, mostly defined by passengers and vehicles, tertiary activities and to a lesser extent some primary activities as well as containers and international outbound. The sixth cluster (construction centre), with 19 regions, has only a small traffic share (7.5 percent), as these regions handle small traffic volumes of mostly solid bulk and inbound flows, but within a dense and tertiary environment, relatively poorer than average and more peripheral in the network. The combination of solid bulk and tertiary sector may relate to the importance of construction activities. The seventh cluster (metropolitan gateway) is similar to the second by its specialisation in containers, general cargo, density, and degree centrality, but its profile is much more influenced by GDP (a much richer region), tertiary activities, and domestic outbound traffic, with less unemployment, less developed hub functions, and a higher concentration of traffic and lower population within the host countries. Because port regions in this cluster have high degree centrality (or many links) but a limited hub function (or in a relatively secondary position in the maritime network), their negative score for the industry sector and highly positive score for bulky traffic underline needless supply chain advantages. Finally, the last cluster (periphery), with 13 regions, has a very low traffic share (1.1 percent) and specialises in general cargo and the primary sector. The combination of low population density, low GDP, and lower degree centrality and lower hub function suggests a region with logistical and socioeconomic difficulties. In contrast to the second and third clusters, or hub clusters, periphery regions are far away from maritime trunk lines.

Port-region specialisation and the maritime network

The share and dominant commodity type of vessel traffic among the clusters are presented in Figure 16.2. Each line corresponds to the sum of (weighted) vessel flows between each cluster and others, while the specialisation of each link (crossing) is highlighted by grayscale based on a coefficient calculated by rows and columns. For instance, 25.1 percent of flows of industrial centres connect value-added city-hubs, and this link is mostly made of containers, whereas 40.8 percent of flows of valueadded city-hubs connect industrial centres, mostly based on liquid bulks. In other words, this figure shows the degree of vessel traffic dependences for each link between regions of each cluster. The specialisation coefficient differs on the same link depending on which cluster is the reference for the total. Unsurprisingly, the two clusters specialised in container traffic connect each other and other clusters mostly through container flows, while container flows do not occur on any pair of other clusters. They also have a high degree centrality (but middle and negative hub function) and density, and tertiary region, or urbanized (less industrialised) profile. Dependence and specialisation linkages can vary depending on the chosen perspective.

All clusters are linked to agri-bulk hubs with varying degrees of dependence but dominantly based on solid bulks, albeit conversely, while agri-bulk hubs depend for 60 percent of their traffic upon industrial centres, again based on solid bulks. The rest of their flows with other clusters are more specialised in other commodities. Thus, there is a spatial division of economic activities among port regions that is well apparent when looking at the nature of maritime flows connecting them. Although this analysis does not take into account the flows between port regions and inland regions through land-based transport, it is already able to capture a noticeable part (if not the backbone) of the value chains for this part of the Pacific Rim area.

[Figure 16.2 here]

Lastly, the analysis proposes a simplification of the graph to highlight the dominant structure of the maritime network (Figure 16.3), based on the "nodal region" methodology proposed by Nystuen and Dacey (1961). Based on weighted vessel traffic in the multigraph (or multiplex graph), only the largest flow (or vessel traffic) link of each region to another region has been kept, with its commodity type and shipping direction, thus making a weighted and directed tree graph while splitting the network into three connected components, or strings of links. The largest component has a line or corridor structure centralised on a few large hubs, such as Gyeongnam (Korea), Kanagawa (Japan), California, Shanghai, Beijing/Tianjin, and Western Australia. All these hubs have a different nature, so one may assume the existence of a polycentric, multifunctional system. Two other smaller components are made of Queensland and New South Wales centralising mainly Japanese regions by means of solid bulk and general cargo flows on the one hand, and of Maharashtra (India) and Selangor (Malaysia), connecting mainly South Asian regions through container and general cargo flows.

The largest component is geographically diverse in terms of port region clusters and nodal commodity flows. It conveys major flows from two distribution or consolidation sources (Gyeongnam and Western Australia) towards one sink, composed of Chinese port regions (Shanghai and Beijing/Tianjin metropolitan gateways) alongside a number of other secondary sources in terms of traffic volume.

Even though this analysis only focuses on the Pacific Rim area, California stands out as the largest traffic region to which multiple commodity flows of various natures converge, mostly containers. California is also the gateway for inland freight movements in North America. While the right-hand side of the figure (south, mainly Australia) is made of bulk chains, the left-hand side (mainly Japan and South Korea) is composed of light industry chains. Although directionality only applies to vessel movements, not trade import or export, it helps in understanding how major production regions of raw materials (e.g. grain, coal, minerals, and ores) are focal nodes for redistribution towards consumption regions and intermediate regions between them.

[Figure 16.3 here]

One very important outcome of this analysis is that the network centrality of port regions is much influenced by the local socio-economic environment (see also Appendix 16.2). For instance, the cluster of agri-bulk hubs is the only case where regions can have low GDP, high degree centrality, and lower population density, due to the specific case of (solid) bulk traffic that employs relatively lower-skilled workforce and less advanced technologies for production and shipment, and also fewer industries or services, with less connectivity function for industries. Most of the time, strong hub functions and high degree centrality (i.e. many maritime links) go along with a higher GDP than the national average. Although this may be in some way counterintuitive due to the limited developmental impact of transhipment hub ports, it still validates a number of ideas about the positive externalities provided by (dynamic) cities to ports (Hall and Jacobs, 2012).

In the maritime network, the so-called industrial centres as well as the agri-bulk hubs are essential for feeding the more urbanised port regions concentrating populations and services along the main trunk line. Important subsystems also appear, such as among Chinese provinces in the northern part of the country (Shanghai, Beijing, Shandong, Liaoning, Zhejiang, Jiangsu), while Guangdong, the factory of the world, is more strongly connected with California, the main gateway to China's largest customer of finished products. International and domestic logistics intermingle due to complex distribution circuits such as coal shipping, notably since China shifted from being the world's main exporter to being its main importer, using coastal shipping internally (Wang and Ducruet, 2014). Still, the largest regional economies are much connected with each other along the trunk line, proving the influence of hierarchy and market size on network configuration. As a complement, most of the secondary linkages are dominantly in proximity, i.e. within specific sub-regions of the Pacific Rim: Yellow Sea (Korea-China), Japan (coastal shipping), China (domestic river transport), East Sea (Korea-Japan-Russia), etc. The role of multifunctional distribution platforms such as Busan (Gyeongnam region), is of course one main explanation, beyond shortsea linkages. Although Hong Kong and Singapore, two dominant East Asian hubs, are excluded from this study due to the absence of districtlevel socio-economic data, such evidence well depicts the emergence of Asian hubs in a context of intensifying trans-Pacific trade (Robinson, 1998).

Conclusion

The analysis of the socio-economic determinants of port and maritime traffic across the Pacific Rim region is fruitful in many ways. First, it confirms that the intensity, specialisation, and spatial distribution of maritime flows are far from being random or disconnected from the local environment where such flows are handled. Such evidence confirms previous empirical investigation based on worldwide port traffic statistics (Ducruet and Itoh, 2015), despite the fact that land-based (or hinterland) flows are not included per se in vessel movement data. As such, tertiary regions tend to concentrate container flows, and regions specialised in the primary sector concentrate solid bulk traffic. One particularity of the Asia-Pacific area is the higher centrality of industrial regions in the maritime network, due to the export-led profile of many Asian economies for manufacturing, as part of a global horizontal division of supply chains, especially in Northeast Asia, including Taiwan. Another peculiarity is the hub function of certain regions specialised in raw (solid) materials traffic as they distribute natural resources worldwide in a context of growing regional and global demands, especially in Australia. Still, one commonality is that on average, larger and more value-added traffic concentrates at larger, richer, and more urbanised regions, a trend which appears to be more evident when weighting traffic figures to lower the rather artificial importance of bulk traffic, because maritime transport for high valueadded goods achieves efficient vessel schedules and frequencies.

Policy orientations can be addressed based on this research. In line with Hall and Jacobs (2012), our results point to the need to motivate maritime transport actors (and beyond, transport and value chain actors) to cultivate a certain embedding with the local level beyond their logistical needs and short-term network configurations. They should be aware that their activity contributes to and benefits from localised socioeconomic structures. In turn, such actors may wish to further participate in the related territorial debates when it comes to promoting efficient urban and regional planning. It is the role of the local players (the so-called port community and beyond) to open the door to fruitful discussions with the ocean carriers in order to ensure their mid-or long-term development and sustainable position in maritime networks. As already suggested by Ducruet and Itoh (2015), there is a subtle equilibrium at stake between port-region match and mismatch when it comes to the local embedding of commodity flows. Large urban agglomerations and service centres are, at the same time, important markets dictating the origin and destination of major flows and logistical constraints to the fluid transit of such flows due to land use tensions for port operations. In parallel, certain commodities are more embedded than others in the local port-industrial complex, and a strong port-industry relationship may cause either growth or decline alongside price and geopolitical fluctuations at the international level. Lastly, this new identification of the spatial division of port region specialisation within certain maritime circuits can lead to new policies for interregional cooperation to avoid the growth of inequalities in a context of excessive regional and port competition, especially in Asia.

Further research shall address in more depth the linkages between cargo types and economic activities performed by localities based on more disaggregated figures of regional employment, based on six rather than on three categories. But this will require more thorough investigation into the statistical sources available in each country. Another important possible refinement will be to complement the measurement of maritime flows by adding more exhaustive movements to reach a higher representativeness of the yearly total. At present, this study has captured only a very small portion of annual vessel movements, so that it remains hindered by possible seasonality bias and trade fluctuations. One potential remedy would be to offer a more dynamic view on the way regional economies and maritime flows have co-evolved on a middle and longer-term, possibly going back to the early 1980s as long as vessel types and capacities are reported uniformly by the data source.

Expanding the study to other regions of the world such as Europe and Africa (as well as the Atlantic Ocean and the Mediterranean and Black Sea as a whole) would certainly help to verify whether the Pacific Rim trend is emblematic of a more universal one in terms of the ties that bind regional development and maritime transport.

  The mutual specialisation of port regions connected by multiple commodity flows in a maritime network César DUCRUET, CNRS & UMR 7235 EconomiX, Nanterre, France Hidekazu ITOH, Gwansei Gakuin University, Kyoto, Japan Pre-final version of the chapter published in Ducruet C. (Ed.) (2015) Maritime Networks. Spatial Structures and Time Dynamics. Routledge Studies in Transport Analysis, pp. 285-301.

Percentage of actual closed triplets (or triangles) in the maximum possible number of closed triplets (or triangles) for each port and its neighbours.

Port tonnage statistics in metric tons were obtained from various international and national organisations for the year 2009.

This table shows the weighted impact values of each indicator calculated by cluster' centres and components' scores from PCA in each cluster.

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'. In addition, the research was supported by JSPS KAKENHI Grant Number 24730259, Japan.

Models. Trade and Macroeconomics Division Research Paper No. 35, International Food Policy Research Institute, Washington DC. McCann P., Shefer D. (2004) Location, agglomeration and infrastructure. Papers in Regional Science, 83(1): 177-193. Merk O., Manshanden W.J.J., Dröes M.I. (2013) Inter-regional spillovers of seaports: The case of Northwest Europe. International Journal of Transport Economics, 40(3): 401-417. Neffke F., Henning M., Boschma R. (2011) How do regions diversify over time? Industry relatedness and the development of new growth paths in regions. Economic Geography, 87(3): 237-265. Nystuen J.D., Dacey M.F. (1961) A graph theoretical interpretation of nodal regions. Papers in Regional Science 7(1): 29-42. Pelletier J.F., Alix Y. (2004) Vers une nouvelle approche méthodologique pour analyser le phénomène de la conteneurisation des marchandises au Canada. Proceedings of the 39th GRTC Annual Conference, 1: 326-341. Quintero J.P. (2007) Regional Economic Development: An Economic Base Study and Shift-Share Analysis of Hays County, Texas. Research Report, Texas State University-San Marcos, Dept. of Political Science, Public Administration. Rimmer P.J. (2014) Asian-Pacific Rim Logistics. Global Context and Local Policies. Cheltenham and Northampton: Edward Elgar. Robinson R. (1998) Asian hub/feeder nets: The dynamics of restructuring. Maritime Policy and Management, 25(1): 21-40. Scott A.J., Storper M. (2003) Regions, globalisation, development. Regional Studies, 37(6-7): 579-593. Song L., van Geenhuizen M. (2014) Port infrastructure investment and regional economic growth in China: Panel evidence in port regions and provinces. Transport Policy, 36: 173-183. Tabuchi T., Thisse J.F. (2002) Regional Specialization and Transport Costs. Discussion Paper (London: CEPR). UNCTAD (2008) Review of Maritime Transport. Geneva: United Nations. Wang C., Ducruet C. (2014) Transport corridors and regional balance in China: The case of coal trade and logistics. Journal of Transport Geography, 40: 3-16.


Yiying Zhang

Hui Li

Jianhong Chang

Xinyu Guan

Prof Lingxue Q Tang

Qianrong Fang
email: qrfang@jlu.edu.cn

Valentin Valtchev

Yushan Yan

Shilun Qiu
email: sqiu@jlu.edu.cn

Prof S Fang

Qiu

Prof V Valtchev

Prof Y Yan

3D Thioether-Based Covalent Organic Frameworks for Selective and Efficient Mercury Removal

Keywords: covalent organic framework, mercury removal, selective adsorption, thioether functionalization

published or not. The documents may come

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Introduction

Covalent organic frameworks (COFs) are a type of burgeoning crystalline porous polymers constructed by organic building blocks regularly linked via strong covalent bonds. [1] Their high porosity, large surface areas, excellent chemical/thermal stabilities, and structurally adjustable reticular skeletonsare the basis of different applications, [2] ranging from gas adsorption and separation, [3] catalysis, [4] sensing, [5] optoelectronics, [6] drug delivery, [7] and many others. [8] The introduction of specific functional groups in COF materials allows tailoring their interactions with guest species for the target application. To date, however, most of the applications were focused on the two-dimensional (2D) COFs with layered eclipsed stacking structures.

By contrast, the exploration of three-dimensional (3D) COFs, is still extremely limited. [9] This is mainly due to the related synthetic challenges, [10] structural instability, [11] narrow microporous channels, [12] and complicated structure determination. [13] In spite of these issues, 3D COFs have been considered as a powerful design platform for future applications. [1f] We have recently reported some 3D functionalized COFs by elaborate pre-design, such as 3D ionic COFs for selective ion exchange, [14] 3D Salphen-based COFs as catalytic antioxidants, [15] 3D tetrathiafulvalene-based COFs for tunable electrical conductivity, [16] and so on. [17] It must be noted that the functionalization of 3D COFs still remains largely unexplored.

Thus, the development of new 3D functionalized COF materials is vital to enrich the structural diversity and expand their potential applications. Mercury (Hg) is one of the most harmful heavy metal due to its high toxicity, bioaccumulation, and persistence. [18] Particularly, excessive Hg species in the environment will cause severe damages to human beings and other living organisms.

Most Hg species exist in water in the form of Hg 2+, which can be easily converted to more toxic organic mercury species through biological activities. [19] Consequently, the elimination of the Hg 2+ from the water-body is a long-term global subject and an urgent stupendous challenge. Owing to the diversity of skeleton structure and pore chemical environment, COFs can be designed as functional target materials that are promising for handling environmental issues. Generally, there are two ways to achieve this goal, namely either the bottom-up approach [20] or post-synthetic modification. [21] However, the latter method has nonnegligible shortcomings, which including complicated procedure, [22] structural breaking, [23] and uncontrollable quantity of functional site. [24] On the contrary, the above issues can be effectively avoided through the bottom-up approach that means the direct synthesis of COFs from pre-designed precursors with specific functional groups. At present, only some 2D COFs have been used for Hg 2+ removal. [25] Compared to 2D COFs with one-dimensional (1D) channels, 3D COFs not only feature more opening structures, but also possess numerous accessible, functional sites and higher surface areas, which are highly beneficial in Hg 2+ adsorption. However, there is no related work has been reported yet.

Taking these issues into account, herein, we report 3D functionalized COFs (JUC-570 and JUC-571, JUC = Jilin University China), constructed from thioether functional units, 3,3'',5,5''-tetraisopropyl-2',5'-bis((methylthio)methyl)-

[1,1':4',1''-terphenyl]-4,4''-diamine (TBTD) or 2',5'-bis((methylthio)methyl)-

[1,1':4',1''-terphenyl]-4,4''-dicarbaldehyde (BTD) by bottom-up approach. More importantly, JUC-570 was fully incorporated with isopropyl groups, which can effectively improve the chemical stability and avoid the pore shrinkage. Both COFs demonstrate high uptakes (972 mg g -1 for JUC-570 and 970 mg g -1 for JUC-571 at pH = 5), fast adsorption kinetics (distribution coefficient Kd value of 2.29 × 10 7 mL g -1 for JUC-570 and 2.07 × 10 7 mL g -1 for JUC-571), and excellent selectivity for Hg 2+ ion. In particular, JUC-570 decorated with alkyl groups displays high Hg 2+

adsorption capacity (619 mg g -1 ), and can be recycled at least four times at pH = 1.

To the best of our knowledge, this study represents the first case of 3D thioether-based COFs by the bottom-up approach and their use for the removal of toxic heavy metal ion (Hg 2+ ).

Results and Discussion

Structural Design

Our strategy is based on the flexible thioether groups with small size, which likely possess the compatibility with the synthesis conditions of 3D COFs, and isopropyl groups around imine bonds in the framework that can increase the chemical stability of the material. As shown in Scheme 1, the tetrakis(4-formylphenyl)silane (TFS, Scheme 1a) and tetrakis(4-aminophenyl)methane (TAM, Scheme 1b) were designed as tetrahedral knots, and TBTD with isopropyl groups (Scheme 1c) or BTD without isopropyl groups (Scheme 1d) were chosen as two kinds of linear linkers. The condensation of TFS and TBTD or TAM and BTD resulted in JUC-570 (Scheme 1e)

and JUC-571 (Scheme 1f). Linking C2 and Td symmetrical building units results in 3D networks with the dia topology (Scheme 1g). [26] Owing to the tetrahedral centers separated by long linear linkers, the resulting structures tend to be interpenetrated networks. [27]

Synthesis and Characterization

3D thioether-based COFs were synthesized from TFS and TBTD or TAM and BTD under solvothermal reaction conditions in a mixture of 1,4-dioxane and mesitylene or a pure 1,4-dioxane in the presence of 6 M acetic acid followed by heating at 120 °C for 3 days. Multiple characterizations were subsequently employed for their detailed structural definition. The morphology of both COFs was examined by scanning electron microscopy (SEM) (Figure S1) and transmission electron microscopy (TEM) (Figure S2), which revealed homogeneous ball shape for JUC-570 and rice shape for JUC-571, respectively. Peaks around 1643 cm -1 for JUC-570 and 1624 cm -1 for JUC-571 in Fourier transform infrared (FT-IR) spectra indicated the formation of C=N bond. The concomitant disappearance of the N-H stretching vibration of TBTD (3490~3407 cm -1 ) and TAM (3395~3174 cm -1 ), as well as the C=O stretching vibration of TFS (1706 cm -1 ) and BTD (1696 cm -1 ) gave a piece of direct evidence for the formation of imine linkages (Figures S3 andS4). Solid-state 13 C cross-polarization/magic-angle-spinning (CP/MAS) NMR spectroscopy further verified the presence of imine bonds by the peak at 162 ppm for JUC-570 or 159 ppm for JUC-571 (Figures S5 andS6). Thermogravimetric analysis (TGA) revealed that both COFs were stable up to about 350 °C under N 2 atmosphere (Figures S7 andS8).

The crystallinity and unit cell parameters of 3D thioether-based COFs were determined by powder X-ray diffraction (PXRD) measurements and coupled with the structural simulation using Materials Studio software package (Figure 1). [28] After the PXRD pattern in which peaks at 4. 38, 6.19, 6.92, and 9.30° for JUC-570 correspond to the ( 110), ( 200), ( 210), and (300) Bragg peaks of the space group P-4 (No. 81).

Meanwhile, peaks at 4. 41, 6.25, 7.01, 8.87, 12.62, 17.86, and 18.96° for JUC-571 belong to the (110), ( 200), ( 210), ( 300), ( 400), (440), and (600) Bragg peaks of space group P-4 (No. 81). These results were in good agreement with the experimentally observed patterns, indicating by their negligible difference (Rwp = 2.90 % and Rp = 2.08 % for JUC-570; Rwp = 2.59 % and Rp = 1.44 % for JUC-571). It should be noted that a similar structure with 10-fold interpenetrated dia net (LZU-79) has been proved by a single crystal XRD analysis, and the PXRD patterns of JUC-570 and JUC-571 were well consistent with that of LZU-79 (Figures S9 andS10). [29] On the basis of the above results, JUC-570 and JUC-571 were proposed to have the expected 10-fold interpenetrated dia topology, and the overall frameworks had 1D rectangular channels (Figure 2). The formation of highly interpenetrated structures is an expected consequence of the relatively long linear linkers employed. .The interpenetration of the linkers provides the low energy state necessary for the structural stability and generate huge diamond cavities. [17c] The nitrogen (N 2 ) adsorption-desorption isotherms were conducted at 77 K to evaluate the porosity of 3D thioether-based COFs (Figure 3). Both materials showed a sharp uptake at a low pressure of P/P 0 < 0.05, which fits the typical type I sorption model. The inclination of isotherms in the 0.8-1.0 P/P 0 range and small hysteresis can be attributed to the presence of textural mesopores, which is a consequence of the agglomeration of COF crystals. [7b] The Brunauer-Emmett-Teller (BET) equation was carried out in the 0.05 < P/P 0 < 0.30 range, indicating BET specific surface area of 1227 m 2 g -1 for JUC-570. Pore size distributions calculated by nonlocal density functional theory (NLDFT) showed micropores with a dominant size of 1.09 nm for JUC-570 (Figure 3a inset and Figure S11), which is in good agreement with that predicted from its crystal structure (1.17 nm for JUC-570). Obviously, under the support of isopropyl groups, JUC-570 effectively avoids the common breathing effect phenomenon in 3D COFs. [30] By contrast, JUC-571 suffered from pore shrinkage after the solvent guests removal owing to the lack of isopropyl groups, which leads to lower BET specific surface area (254 m 2 g -1 ) and pore size (0.98 nm, Figure 3b inset and Figure S12). [31] The chemical stabilities of 3D thioether-based COFs were also studied by exposure to different environments. As shown in Figure 4, JUC-570 still exhibited intense PXRD patterns after treated with 2 M HCl, 2 M HNO 3, 15 M NaOH, boiling water, and common organic solvents for one week (Figure 4a and Figure S13), which indicates that its crystalline structure is well retained under these conditions. However, JUC-571 was not stable using diluted acid and base as 0.1 M HCl, 0.1 M HNO 3 , 1 M NaOH, and boiling water for 24 h, revealed by the PXRD analysis before and after the treatment (Figure 4b and Figure S14). Notably, the difference in chemical stability between two COFs can be attributed to the presence of isopropyl groups in the framework of JUC-571, which can effectively protect the hydrolytically susceptible backbones. [30,32]

Mercury Sorption Studies

Influence of pH

Giving the high porosity, excellent stability, abundant and accessible thioether arms of 3D thioether-based COFs, we conducted a sequence of systematic adsorption experiments to examine their adsorption ability of Hg 2+ (Figure 5). The pH plays a key role in the adsorption process and affects the capture capacity of the adsorbents. [33] Therefore, we first explored the effect of different pH values on the Hg 2+ removal of 3D COFs. Because insoluble Hg(OH) 2 can be formed at pH > 6, we explored the pH range of 1-6 for JUC-570. The pH range was limited between 2 and 6 for JUC-571 due to its unstable structure at pH = 1. I was found out that the optimal pH value for Hg 2+ adsorption on 3D thioether-based COFs is 5 (Figure 5a). Both COFs showed reduced Hg 2+ capture capacity at other pH values, since the adsorption process is related to the nature of Hg 2+ species formed at different pH values. At lower pH, the protonation effect on the surface of adsorbent, which produces electrostatic impediment repulsion with Hg 2+ and superfluous H + , offers sorption competition with Hg 2+ , and thus prohibits further adsorption. [34] At higher pH conditions, however, Hg 2+ begins to undergo hydrolysis, reducing the adsorption amount of Hg 2+ . [35] Accordingly, a pH = 5 was considered as an optimum condition for subsequent experiments. It is worth noting that even at very low pH (pH = 1), the Hg 2+ adsorption capacity of JUC-570 is still as high as 619 mg g -1 .

Adsorption Isotherms

To evaluate the Hg 2+ adsorption capacity of 3D thioether-based COFs, Hg 2+ solutions with the initial concentrations in the range of 25 ~ 1000 mg L -1 were employed. After the experiment, the COF material was separated and the Hg concentration in the solution analyzed by ICP. As illustrated in Figure 5b, the adsorption capacity of both COFs increased significantly with the increase of the Hg 2+ ion concentration driven by the concentration gradient force. The experimental maximum Hg 2+ adsorption capacity of JUC-570 and JUC-571 was calculated to be 972 mg g -1 and 970 mg g -1 , respectively, which ranks as one of the top values in most typical benchmark adsorbents, such as porous carbon (518 mg g -1 ), [36] TAPB-BMTTPA-COF (734 mg g -1 ), [25b] Bio-MOF (900 mg g -1 ), [37] and PAF-1-SH (1014 mg g -1 ). [38] Both equilibrium adsorption isotherms were well-fitted with the Langmuir model that yields a correlation coefficient of 0.998 for JUC-570 (Figure S15) and 0.996 for JUC-571 (Figure S16). We reasoned that the outstanding capacity of JUC-570 stems from the synergistic effect of tremendous affinity between sulfur sites and Hg 2+ together with high density and accessibility of thioether groups in inherent opening 3D channels. In addition, their PXRD patterns revealed that both materials remained crystalline and structurally intact after adsorbing Hg 2+ (Figures S17 andS18).

Adsorption Kinetics

To further reveal adsorption process, the adsorption kinetics of Hg 2+ uptake was investigated in a system with 100.0 mL of 10.0 mg L -1 Hg 2+ and 5.0 mg of 3D thioether-based COFs by measuring the Hg 2+ concentration at different time. As shown in Figure 5c, JUC-570 can attain 99% of the adsorption capacity at equilibrium within 20 min. from The fast adsorption kinetics of JUC-570 can be attributed to flexible short thioether chains, which is beneficial to expose sulfur sites and endows the channel of COFs maximum space. [22b] In comparison, the adsorption process of JUC-571 is relatively slow. This may be due to the breathing effect of JUC-571, and related slow rate of pore opening in the water. Both Hg 2+ adsorption data of 3D thioether-based COFs were well fitted with pseudo-second-order kinetic model, and the correlation coefficient as high as 0.9999 for JUC-570 and 0.9996 for JUC-571

(Figures S19 andS20). Distribution coefficient (Kd) represents an important index to evaluate the sorbent affinity to a metal ion, [25b] was calculated by the equation:

K d = (1)
Where V is the volume of the treated solution (mL), m is the mass of adsorbent (g), C 0

and C e are the initial and equilibrium concentration of Hg 2+ , respectively.

Impressively, the Kd values of 3D thioether-based COFs were calculated to equal 2.29 × 10 7 mL g -1 for JUC-570 and 2.07 × 10 7 mL g -1 for JUC-571, which can compare to most typical benchmark adsorbents for Hg 2+ capture, including commercial resins (5.1 × 10 5 mL g -1 ), [39] TAPB-BMTTPA-COF (7.82 × 10 5 mL g -1 ), [25b] Thiol-HKUST-1 (4.73 × 10 5 mL g -1 ), [40] and PAF-1-SH (5.76 × 10 7 mL g -1 ). [38]

Selectivity

Selectivity tests were performed in a mixed solution containing Hg 2+ , Cu 2+ , Ca 2+ , Mg 2+ , Fe 2+ , Zn 2+ , Ni 2+ and K + for each concentration of 10.0 mg L -1 at pH = 5. As described in Figure 5d, both 3D thioether-based COFs could effectively remove Hg 2+

and exhibited negligible capture capability for various nontoxic competitive ions.

Therefore, the interference study indicated that 3D thioether-based COFs can remove Hg 2+ from aqueous solutions selectively and effectively. The high selectivity is due to a strong affinity between sulfur and mercury since the equilibrium constant between the sulfur atom and mercury is significantly higher than between the sulfur other metals. [41]

Cycle Performance

Cycle performance of the adsorbent is a critical index for cutting down the cost of the adsorption process in a practical application. 3D thioether-based COFs can be regenerated by treating with 1,2-ethanedithiol and used for cycle tests. As shown in Figure 5e, due to the high chemical stability, JUC-570 exhibited a similar Hg 2+ removal efficiency after four successive experiments at pH = 5. However, under the same conditions, JUC-571 showed a gradually decreasing Hg 2 + removal efficiency upon cycling test. It is worth mentioning that, even under the condition of pH = 1, JUC-570 can still retain 94% removal efficiency after four cycles (Figure 5f). In addition, the crystallinity of reused 3D thioether-based COFs were negligible declined by PXRD analysis (Figure S21 and Figure S22). These results demonstrated that JUC-570 is robust enough, which make it a promising candidate in practical water remediation.

Adsorption Mechanism

To shed light on the adsorption mechanism staying behind the outstanding performance of 3D thioether-based COFs in mercury capture, we utilized 13

Conclusion

In conclusion, we rationally designed and synthesized two 3D thioether-based COFs JUC-570 and JUC-571, with 10-fold interpenetrated dia topology by the bottom-up approach. By introducing isopropyl groups around imine bonds, JUC-570 showed much higher chemical stability and BET specific surface area (1227 m 2 g -1 ). Owing to the thioether functional groups in their frameworks, both COFs had high uptakes (972 mg g -1 for JUC-570 and 970 mg g -1 for JUC-571 at pH = 5), high adsorption kinetics

(2.29 × 10 7 mL g -1 for JUC-570 and 2.07 × 10 7 mL g -1 for JUC-571), and outstanding selectivity for Hg + ion. More important, JUC-570 displayed a high Hg + adsorption capacity (619 mg g -1 ), and can be recycled at least four times underhighly aciiidic condions (pH = 1) due to its excellent stability. This study not only established an efficient route to prepare stable 3D functionalized COFs, but also explored their application in the field of toxic metal decontamination.

Experimental Section

Synthesis of JUC-570: A Pyrex tube (volume: ca. 20.0 ml with a body length of 18.0 cm) was charged with TBTD ( 21.76 mg, 0.04 mmol) and TFS ( 8.96 mg, 0.02 mmol) in a mixed solution of dioxane (0.5 mL), mesitylene (0.5 mL), and acetic acid (0.2 mL, 6 M). The tube was flash-frozen at 77 K (LN 2 bath), evacuated to an internal pressure of 0.15 mmHg, and flame sealed. Upon sealing, the length of the tube was reduced to ca. 13 cm. Upon warming to room temperature, the tube was heated at 120 °C for 3 days to afford a yellow precipitate, which was isolated by filtration and washed with acetone (3  5.0 ml) and yield of 75% for JUC-570.

Synthesis of JUC-571:

In a manner similar to the preparation of JUC-570, a Pyrex tube (volume: ca. 20.0 mL with a body length of 18.0 cm) was charged with BTD (16.24 mg, 0.04 mmol) and TAM (7.6 mg, 0.02 mmol) in a mixed solution of dioxane (1.0 mL) and acetic acid (0.2 mL, 6 M). The tube was flash-frozen at 77 K (LN 2 bath), evacuated to an internal pressure of 0.15 mmHg, and flame sealed. Upon sealing, the length of the tube was reduced to ca. 13 cm. The reaction mixture was heated at 120 °C for 3 days to afford a yellow precipitate which was isolated by filtration and washed with acetone (3  5.0 ml) and yield of 82% for JUC-571.

  geometrical energy minimization, both COFs were set up based on a 10-fold interpenetrated dia net. Subsequently their unit cell parameters were acquired (a = b = 30.2406 Å, c = 7.0039 Å and α= β = γ = 90° for JUC-570; a = b = 28.8381 Å, c = 7.1132 Å and α= β = γ = 90° for JUC-571). Besides, the Pawley refinement yielded a

  C CP/MAS NMR to figure out the interaction between Hg 2+ and frameworks. The signals at 14.5 ppm and 36.2 ppm for JUC-570 (Figure S23, purple curve) and at 15.3 ppm and 35.7 ppm for JUC-571 (Figure S24, green curve) were ascribed to the methyl carbon and methylene carbon adjacent to the S atoms. Upon the capture of Hg 2+ , the carbon signals were shifted to 18.4 ppm and 39.3 ppm for JUC-570 (Figure S23, pink curve) as well as 19.4 ppm and 38.9 ppm for JUC-571 (Figure S24, pink curve), respectively. At the same time, the imine-bond carbons and other signals were almost unchanged. These results pointed out that the flexible thioether groups interact with Hg 2+ in both 3D thioether-based COFs. In contrast, the imine bonds played a limited role in the Hg 2+ capture.

Figures

  Figures and captions:

Figure 1 .

 1 Figure 1. Experimental and refined PXRD patterns of JUC-570 (a) and JUC-571 (b).

Figure 2 .

 2 Figure 2. Extended structures of JUC-570 (a) and JUC-571 decorated with isopropyl

Figure 3 .

 3 Figure 3. N 2 adsorption-desorption isotherms for JUC-570 (a) and JUC-571 (b) at 77

Figure 4 .

 4 Figure 4. PXRD patterns of JUC-570 (a) and JUC-571 (b) after the treatment in

  Annalitically calculated for C 73 H 64 N 4 S 4 : C: 77.90; H: 5.73; N: 4.98; S: 11.39. Found: C: 77.95; H: 5.76; N: 4.89; S: 11.32.

Acknowledgements

This work was supported by National Natural Science Foundation of China (21621001, 21390394, and 21673094), 111 project (BP0719036 and B17020), and the program for JLU Science and Technology Innovative Research Team, and the Computing Center of Jilin Province for supercomputer time. V.V., S.Q. and Q.F. acknowledge funding from the French-Sino International Laboratory (LIA) Zeolites.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Conflict of Interest

The authors declare no conflict of interest.

ToC:

Two 3D thioether-based COFs, JUC-570 and JUC-571, were for the first time prepared by the bottom-up approach, and used for mercury (Hg 2+ ) removal from aqueous solution. In particular, JUC-570 is periodically decorated with isopropyl groups around imine bonds, which displays higher chemical stability, BET specific surface area and Hg 2+ removal performance.

Keywords: covalent organic framework, mercury removal, thioether functionalization Yiying Zhang, Hui Li, Jianhong Chang, Xinyu Guan, Lingxue Tang, Qianrong Fang*, Valentin Valtchev, Yushan Yan, and