Vincenzo Ciancaglini
email: vincenzo.ciancaglini@inria.fr

Giuseppe Piro
email: g.piro@poliba.it

Riccardo Loti
email: riccardo.loti@inria.fr

Luigi Alfredo Grieco
email: a.grieco@poliba.it

Luigi Liquori
email: luigi.liquori@inria.fr

CCN-TV: a data-centric approach to real-time video services

Keywords: Content-Centric Networking, Multimedia Services, Live Streaming

Content-Centric Networking (CCN) is a promising data-centric architecture, based on in-network caching, name-driven routing, and receiver-initiated sessions, which can greatly enhance the way Internet resources are currently used, making support for a broader set of users with increasing traffic demands possible. The CCN vision is, currently, attracting the attention of many researchers across the world, since it has all the potential to become ready to the market, to be gradually deployed in the Internet of today, and to facilitate a graceful transition from a host-centric networking rationale to a more effective data-centric working behaviour. At the same time, several issues have to be investigated before CCN can be safely deployed at the Internet scale. They include routing, congestion control, caching operations, name-space planning, and application design. With reference to application-related facets, it is worth noticing that the demand for TV services is growing at an exponential rate over time, thus requiring a very careful analysis of their performance in CCN architectures. To this end, in the present contribution we deploy a CCN-TV system, capable of delivering real-time streaming TV services, and we evaluate its performance through a simulation campaign based on real-world topologies.

I. INTRODUCTION

Due to the relevant importance that content sharing applications are going to play in the upcoming future [START_REF]Cisco visual networking index: Forecast and methodology[END_REF], [START_REF] Ahlgren | Content, connectivity, and cloud: ingredients for the network of the future[END_REF], the Content Centric Networking (CCN) rationale [START_REF] Jacobson | Networking named content[END_REF] has been proposed as a possible way to drive the current host-centric Internet paradigm towards a novel content-centric behaviour. It is based on in-network caching operations, receiver initiated data exchange, hierarchical content naming, and native support to security and privacy.

In a CCN, contents are split in chunks which are requested using opposite Interest messages, generated at the client side. Each Interest is then routed until it reaches a node which has, in its own cache, a copy of the requested item. Then, this copy is sent, as a Data message, back along the path the Interest had gone through. Intermediate nodes can cache the Data before forwarding it to the next node (more details on the CCN working behavior is provided in Sec. II).

Since its born, the CCN vision has gained a warm attention from both scientific and industrial communities to discover the bounds of its real potential from different perspectives. Many studies have focused on modeling and designing caching strategies and data-transfer performance such as in [START_REF] Carofiglio | Modeling data transfer in content-centric networking[END_REF]- [START_REF] Rossi | On sizing CCN content stores by exploiting topological information[END_REF]. In that direction, it is now clear that the cache size may have a major impact on the overall performance of a CCN even if finding an optimal caching strategy is still an open problem to address. With respect to congestion control issues, instead, recent studies shown as the classic additive increase multiplicative decrease algorithm, at the foundation of TCP, could be inherited by CCN, provided that some countermeasures are employed to limit unfairness issues that could arise among contents with different popularities [START_REF] Grieco | AIMD and CCN: past and novel acronyms working together in the Future Internet[END_REF], [START_REF] Carofiglio | Joint hop-byhop and receiver-driven interest control protocol for contentcentric networks[END_REF]. Another very relevant topic in CCN research covers routing operations, which are essential to properly drive the dissemination of receiver generated Interest packets. To this end, the adoption of Bloom filters appears a promising solution [START_REF] Tortelli | CCN forwarding engine based on bloom filters[END_REF], [START_REF] You | Dipit: A distributed bloom-filter based pit table for CCN nodes[END_REF] that merits further investigations. Starting from this premise, it is evident that all facets of CCN are going to be afforded in an ebullient panorama of activities that cover both the underlying mechanisms within the protocol architecture and the design of content oriented applications and services. With reference to application-related features, it is worth to notice that the demand for TV services is growing at an exponential rate over the time [START_REF]Cisco visual networking index: Forecast and methodology[END_REF], thus requiring a very careful analysis of their performance in CCN architectures. A preliminary study presented in [START_REF] Li | Time-shifted TV in content centric networks:the case for cooperative in-network caching[END_REF] addresses time shifted applications only, whereas live streaming operations are currently under investigation as testified in the interesting contribution [START_REF] Xu | Live streaming with content centric networking[END_REF].

To complement the research efforts of the community in a so relevant domain, the present manuscript is intended to design a complete CCN-TV system encompassing all the main facets of typical live streaming video services. The proposed CCN-TV has been tested through a solid simulation campaign based on real topologies. To this end, the ccnSim simulator [START_REF] Rossini | Large scale simulation of ccn networks[END_REF] has been properly tailored to our purposes by adding window based flow control, handling of playout delay and real-time data, advanced logging functions, links with bandwidth constraints, and data session bootstrapping. Simulation results shown that in-network caching seems to play a minor role in live streaming video services, mainly because cached data looses its utility after the deadline is expired. On the other hand, the way CCN handles client requests for TV contents helps improving the performance of the system with respect to a plain IP infrastructure.

The rest of the paper is organized as follows: Sec. II illustrates the core concepts of CCN. Sec. III describes the CCN-TV system we propose in this paper, which is then evaluated in Sec. IV. Finally, Sec. V summarizes the main findings of this contribution and draws future research.

II. BASIC BACKGROUND ON CCN

Internet usage has undergone a radical change during the last ten years: content-sharing applications are now dominant whereas the IP architecture still provides a connection-less service among remote hosts [START_REF] Ahlgren | Content, connectivity, and cloud: ingredients for the network of the future[END_REF]. Users ask for contents, looking for what they intend to retrieve from the Internet while the language spoken by the underlying IP infrastructure provides answers on where a packet should be sent. This mismatch is actually overcome by a number of workarounds at different levels of the protocol stack, which, indeed, limit the overall efficiency of the Internet.

The so-called Future Internet represents a family of possible solutions to the aforementioned issues, embracing novel communication models that can better accommodate and fulfill users' requirements related to efficiency, security, support to mobility, and integrated media experience [START_REF] Ahlgren | Content, connectivity, and cloud: ingredients for the network of the future[END_REF].

At the present stage, many valid proposals for the Future Internet exist, such as the Publish Subscribe Internet Routing Paradigm, the 4WARD NetInf project, and the Cache-and-Forward Network Architecture, the Data-Oriented Network Architecture and the CCN approach [START_REF] Jacobson | Networking named content[END_REF], [START_REF] Ahlgren | A survey of information-centric networking[END_REF], having different levels of compatibility with the IP paradigm.

Among them, the CCN vision looks promising since, besides being "data-centric", it can be gracefully integrated with today's IP-based Internet. In a CCN, all content is unambiguously identified by a hierarchical name, allowing users to retrieve information without being aware about the physical location of servers (e.g. IP address). Also, communication is receiver-driven and based on content chunk exchange, name-based routing, and self-certifying packets [START_REF] Jacobson | Networking named content[END_REF].

Nevertheless, the real performance bounds of a CCN and the actual benefits it can bring to the Internet are still not entirely known, mainly because there are many open issues that surround the CCN architecture, such as those related to: (i) routing, (ii) congestion control, (iii) strategy layer design, (iv) name space definition, (v) semantic layer, (vi) accurate models, and (v) fairness among heterogeneous applications and contents having different popularities.

As specified before, CCN communications are driven by the consumer of data and only two types of messages are exchanged (namely Interest and Data). A user may ask for a content by issuing an Interest, which is routed within the CCN towards the nodes in posses of the required information, thus triggering them to reply with Data packets.

The routing operations are performed by the strategy layer only for Interest packets. Data messages, instead, just follow the reverse path to the requesting user, allowing every intermediate node to cache the forwarded content.

CCN adopts a hierarchical structure for names, which leads to a name tree. In particular, it is formed by several components, each one made by a number of arbitrary octets (optionally encrypted), so that every name prefix identifies a sub-tree in the name space. An Interest can specify the full name of the content or its prefix, thus accessing to the entire collection of elements under that prefix.

Finally, since contents are exchanged based on their names, multiple nodes interested in a particular data can share it using multicast suppression techniques over a broadcast medium. Analyzing a CCN node, it is possible to identify three main structures [START_REF] Jacobson | Networking named content[END_REF].

• the Content Store (CS): a cache memory that can implement different replacement policies as Least Recently Used (LRU) and Least Frequently Used (LFU);

• the Forwarding Information Base (FIB): is similar to an IP FIB except for the possibility to have a list of faces1 for each Content Name entry, thus allowing Interest packets to be forwarded towards many potential sources of the required Data;

• the Pending Interest Table (PIT): is a table used to keep track of the Interest packets that have been forwarded upstream towards content sources, combining them with the respective arrival faces, thus allowing the properly delivery of backward Data packets sent in response to Interests. When an Interest packet arrives to a CCN node, the CS is searched to discover whether a data item is already available as an answer to be sent immediately back to the requesting user. Otherwise, the PIT is consulted to find out if others Interest packets, requiring the same content, have been already forwarded towards potential sources of the required data. In this case, the Interest's arrival face is added to the PIT entry. Otherwise, the FIB is examined to search a matching entry, indicating the list of faces the Interest has to be forwarded through. At the end, if there is not any FIB entry, the Interest is discarded.

On the other hand, when a Data packet is received, the PIT table comes into play, which, keeping track of all previously forwarded Interest packets, allows to establish a backward path to the node that requested the data.

III. CCN-TV ARCHITECTURE

Unlike Video-On-Demand, real-time video distribution has to deal with a specific class of problems to ensure the timely delivery of an ordered stream of chunks. Video chunks have to be received in playing order and within a given time interval (the playout delay), before they are actually played, thus "expiring". A chunk not delivered before its expiration will result in degradation of the rendered video, impacting the end user Quality of Experience; the extent of the video degradation may vary depending on the video codec and the type of the lost frame. To solve these challenges, client nodes implement a receiving buffer queue where the chunks are stored in order, that is emptied while the video is being played. Therefore, any chunk not received before its playing instant becomes useless. To reduce the chance of chunk loss several mechanisms can be put in place to retransmit requests for chunks close to expiration. Furthermore, in modern codecs, such as H.264 [START_REF] Wiegand | Overview of the H.264/AVC video coding standard[END_REF], there are different types of video frames, encoded using intraframe or inter-frame techniques, each having a different level of importance. For example, the so called I-frames, derived using intra-frame compression techniques, actually represent a full video image, providing a fundamental reference for subsequent inter-frame encoded images.

With this in mind in CCN-TV we considered a network of nodes requesting different real-time video streams, identified by a channelID, served by one or more broadcast server.

Unlike canonical UDP/TCP-based streaming, in CCN-TV each video chunk, identified by a progressive chunk number, has to be requested individually, via a dedicated Interest.

Although this might look costly at a first sight, CCN's mechanisms ensure that Interests for the same chunk do not propagate twice along the same routing path (unless under specific conditions, as explained in Sec. III-B), and the caching strategy implemented by every node can make sure that Interests for the most popular contents are served before going through the whole routing path. Moreover, the Interest/data exchange allows for a natural flow control mechanism, where each node can request for new chunks just when the old ones have arrived.

Herein we thoroughly describe the design rationale and all the details of the CCN-TV system this paper targets. Specifically, in what follows, we present: the bootstrap phase, the flow control strategy, and the management of retransmitted Interest packets.

A. Channel bootstrap

One challenge we are faced with in a real-time scenario is to bootstrap the channel to be received. Bootstrapping a channel involves the operations of finding a routing path to the nearest channel provider and locating the first valid chunkID of the video stream. Due to video codec requirements, the video stream can be visualized only once the first I-frame has been received. Therefore, a client has to first gather from the server the first chunk (and the corresponding chunkID) of the last generated I-frame. To do so, it sends an Interest packet for the URI: To this Interest, the server responds with a data message in the format [domain]/[channelID]/[chunkID], with chunkID being the first chunk of the last generated I-frame, and the corresponding Frame ID field value. Upon receipt, the node starts asking for subsequent chunks, using the sliding window mechanism detailed in Sec. III-B. The use of a nonce (a uniquely generated identifier) in the Interest URI allows the Interest to propagate to the server without being blocked along the routing path, as every bootstrap Interest for the same channel has a different nonce. It also avoids the retrieval of the data response from the cache of an intermediate node; the risk, in this case, is the retrieval of a bootstrap data message for a given channel from a cache containing an already expired chunk of an I-frame.

B. Flow control

From the moment a node receives the bootstrap data message, it can initiate the sliding window mechanism to request the subsequent chunks in an optimal way. Each node has a windows of size W to store W pending chunk. We define pending chunk a chunk whose Interest has been sent by the node, and the window containing the pending chunks a Pending Window. Together with the chunkID, we store in the pending window other information, such as the timestamp of the first request and the timestamp of the last retransmission. Whenever a new data message is received, the algorithm described in Fig. 2 runs over the Pending Window, to perform the following operations:

1) Purge the Pending Window from all the chunks who are expired, i.e., who have already been played, to free new space in the sliding window. 2) Retransmit all chunks that have not been received for a given timeout (onward denoted as windowTimeout. 3) Transmit, for each slot that got freed by the received or expired chunks, the Interest for a new one. end for 23: end procedure Furthermore, the same operations are performed if a node doesn't receive any data for at least windowTimeout seconds, in which case, all the Interests for non-expired chunks in the Pending Window are retransmitted, together with new chunks if new slots have been freed due to expired chunks. Fig. 2 details the implemented algorithm; for the purpose of brevity and readability, the variable names have been contracted: PW is the Pending Window, W is the aforementioned system parameter, indicating how many Interests should a node have ongoing, WinT is the window timeout, after which Interests in the Pending Window are resent, Int is a new Interest message, CID is a chunkID in the pending window, lastTx is the transmission time of the most recent Interest for a given chunkID, LC is the chunkID of the most recent requested chunk and NNC is the number of new chunks to request, after the pending window has been purged.

To provide a further insight, we reported in Fig. 3 an example of the conceived sliding window algorithm, in which we have set the value of W to be equal to 3.

C. Interest routing

As described in Sec. II, CCN nodes along the routing path of an Interest will stop the propagation of said Interest, if they have previously routed another Interest for the same resource, and the correspondent data has note been sent back yet; instead, they will simply update their Pending Interest This mechanism ensures flow control and limits the propagation of duplicate Interests, in case several nodes in the same network are watching the same channel.

However, to make the Interest retransmission mechanism effective, a retransmitted Interest needs to propagate all the way up to the server, or to the first node with the desired chunk in cache. Therefore, retransmitted Interests carry the Status field set to Retransmission to mark if the Interest is a retransmission or not, and each node along the routing path propagates the Interests marked as retransmitted, thus skipping the usual CCN mechanism, unless the correspondent chunk is found in the cache.

Publisher ID

Optional.

Signature Optional (for increased content authentication).

Stale Time

Set to the frame time of the frame the chunk belongs to. Frame ID ID of the frame the chunk belongs to.

Data

The request video chunk binary data.

D. CCN-TV messages

As detailed above, additional functionalities required by the system for real-time video streaming are implemented on top of existing CCN data and Interest messages via new fields carrying the required additional information.

However, should the situation require the system to conform to classical CCN messages, all additional fields can be easily replaced by additional fields in the content name.

Tab. I shows how we made use of the classical CCN message fields, together with the new fields and their use.

In particular, CCN-TV Interests carry an additional Status fields marking if the Interest is a bootstrap Interest (Section III-A), a normal one or a retransmission (Section III-C).

Concerning CCN data message, we extended the messages with an additional field, i.e., Frame ID, containing the ID of the frame to which the embedded chunk belongs to.

IV. SIMULATION RESULTS

In this section, we will evaluate performances of the proposed CCN-TV architecture. To this end, we implemented it within ccnSim, i.e., an open source and scalable chunklevel simulator of CCN [START_REF] Rossini | Large scale simulation of ccn networks[END_REF] built on top of the Omnet++ framework [20], dedicated to the evaluation of Video On Demand systems on top of CCN. By itself, ccnSim models a complete video distribution systems, with a high degree of fidelity concerning catalogs, requests and repositories distribution, and network topologies. Since, however, it did not support the real-time constraints required by our evaluations, it has been modified and improved in the following ways:

• we added support for links with bounded capacity and packets with a well defined size, which was missing in ccnSim, to be able and estimate the CCN behavior under some bandwidth constraints;

• due to the datarate channels, we a transmission for each face of each node, in order to properly manage the packet transmission;

• we added the support for synthetic video traces, so to be able to transmit and receive chunk of real videos, and consequently being able to reconstruct the received video and evaluate its PSNR;

• due to possible expiration of Interests, we implemented a cleanup mechanism for each node's PIT, to avoid having in long term stale entries due to expired chunks;

• we improved and enriched the logging system, so to be able to record each node's received chunks and reconstruct the received video;

• we added more controls server-side, to send a data only for those chunks who have already been generated. Furthermore, the following mechanisms, beyond the provided ones, have been implemented in the simulator:

• the sliding window mechanism described above, and all the related data structures;

• the Interest forceful propagation in case of retransmission;

• constant data reception, until a channel is changed. The extended ccnSim simualtor is available at [21].

The aim of our study is to evaluate how the behavior of the CCN-TV system is influenced by (i) the amount of the network bandwidth dedicated to real-time streaming services, (ii) the windowTimeout adopted by the sliding window mechanism, (iii) the playout delay, and (iv) the cache decision policy.

We focus the attention on the GEANT network, which interconnects the European research and education institutions and it is composed by 22 routers [START_REF]Geant project website[END_REF]. Every node of the network is considered to be a direct CCN node, i.e. no TCP or UDP encapsulation is implemented. We assume the presence of only one small video streaming provider that offers 5 parallel real-time transmissions to remote clients. It is connected to one of the nodes forming the GEANT topology. In every simulation round, each video content is mapped to a video stream compressed using H.264 [START_REF] Wiegand | Overview of the H.264/AVC video coding standard[END_REF] at a average coding rate randomly chosen in the range [250,2000] kbps. Clients, i.e., CCN nodes that download video contents from the server, are connected to remaining nodes (1 client per node). In order to catch the behavior of people watching TV, we modeled two groups of users: faithful and zapping. Faithful users are attached to one video channel for the whole simulation. Zapping users, instead, change frequently the channel among those offered by the server according to a Poisson process with parameter λ = 0.0666. Further, the channel selection process has been modeled considering that contents popularities follow a Zipf distribution. According to [START_REF] Rossi | Caching performance of content centric networks under multi-path routing (and more)[END_REF], the most of works presented in literature set the parameter α of the Zipf distribution in the range [0.6, 2.5]. In line with these common settings, we set α = 1. Once a client decides to watch a specific channel, it performs the bootstrap process described in the previous section and then starts sending Interest packets following the designed sliding window mechanism.

In our tests, we adopted the optimal routing strategy, already available within the ccnSim framework. According to it, Interest packets are routed towards the video server along the shortest path. On the other hand, three caching strategies have been considered in our study: no-cache, LRU, and FIFO [START_REF] Rossi | Caching performance of content centric networks under multi-path routing (and more)[END_REF]. When well known LRU or FIFO policies are adopted, we set the size of the cache to 100 chunks. The no-cache policy is intended to evaluate the performance of the CCN without using any caching mechanism.

The window size W has been set to 10, ensuring that faces of the server are almost fully loaded in all considered scenarios. Also, the transmission queue length associated to each face, Q, has been set, in order to be larger than

Q = 2 * L c * P D (1)
where L c and P D represent link capacity and maximum propagation delay in the considered network topology. All simulation parameters have been summarized in Tab. II.

A. Interest generation process

As a first step, we investigate the impact that the sliding window mechanism has on the amount of sent Interest packets, which is shown in Fig. 4. From these plots it is evident that the highest windowTimeout, the lowest the total number of Interest messages sent by end users. When the windowTimeout increases, the probability that a given client does not receive any chunks within such a time interval decreases and, as a consequence, also the number of retransmitted Interest packets decreases as well. As a further confirm of this result, Fig. 5 shows that the percentage of duplicated Interest packets increases when the windowTimeout decreases due to a high number of chunks that are unable to reach the client within the expected timeliness.

As expected, playout delay has a minor impact on the number of generated Interest messages, which, as is known from the theory on sliding window mechanisms [START_REF] Kurose | Computer Networking: A Top-Down Approach[END_REF], can be only influenced by window size (W ) and windowTimeout.

Also, caching operations do not have any significant impact on the number of generated Interest messages. The main reason being that chucks stored in cache memories lose their effectiveness after their deadline is expired.

On the other hand, the link capacity greatly influence the Interest transmission rate. From Fig. 4 emerges, in fact, that the number of Interest lowers when the capacity of links decreases. This is because a limited bandwidth reduces the quota of received chunks, thus preventing a rapid advancement of the sliding window. In other terms, this result proves, once again, the effectiveness of the sliding window mechanism in CCN.

B. QoS and QoE

The first important parameter that describes how CCN-TV settings affect the quality of service offered to end users is the chunk loss ratio, which represents the percentage of chunks that have not been received in time (i.e., before the expiration of the playout delay) by clients.

From Fig. 6, showing the chunk loss ratio measured in all considered network scenarios, we note that playout delay plays a fundamental role. When the playout delay increases, in fact, the client could receive a Data packet within a longer time interval, thus reducing the amount of chunks discarded because out of delay. On the other hand, a slight increment of the chunk loss ratio can be registered by increasing the windowTimeout. If the client retransmits an Interest packet after long time, there is the risk that the Data packet will be reached by the destination after the expiration of the playout delay. In addition, we note that a reduction of the link capacities leads to a higher number of lost chunks, due to increased latencies induced by network congestion.

It is very important to remark that the presence of the cache can guarantee only a small reduction of the chunk loss ratio. With our study, we found that, in the presence of real-time flows, the cache does not represent an important CCN feature. On the other hand, we noticed that the PIT plays a more relevant role. In fact, in presence of live video streaming services, clients that are connected to a channel request the same chunks simultaneously. In this case, a CCN router has to handle multiple Interest messages that, even though sent by different users, are related to the same content. According to the CCN paradigm, such a node will store all of these requests into the PIT, waiting for the corresponding Data packet. As soon as the packet is received, the router will forward it to all users that have requested the chunk in the past. According to these considerations, the use of the cache will not produce a relevant gain of network performances. Indeed, the PIT helps reducing the burden at the server side by avoiding that many Interest packets for the same chunk are routed to the server.

To conclude our study, we have computed Peak Signal to Noise Ratio (PSNR), which is nowadays one of the most diffused metrics for evaluating user satisfaction, together with interactivity level, in real time video applications [START_REF] Piro | Two-level Downlink Scheduling for Real-Time Multimedia Services in LTE Networks[END_REF]. Results shown in Fig. 7 are in line with those reported for chunk loss ratio (the PNSR is higher in the same case in which the chunk loss ratio is lower). Again, link capacity greatly influences the quality of the TV service provided to users. According to [START_REF] Ohm | Multimedia Communication Technology[END_REF], the obtained PSNR values can be translated to a Mean Opinion Score (MOS) not less than 4, corresponding to satisfactory quality for almost all users.

V. CONCLUSIONS AND FUTURE RESEARCH

In this work, the effectiveness of TV services in a CCN has been investigated. To this end, the ccnSim simulator has been modified to add several relevant features such as window-based flow control, handling of playout delay and real-time data, advanced logging mechanisms, and data session bootstrapping. Preliminary results reported herein clearly show that the most relevant CCN feature to TV services is the management of Interest packets through the PIT data structure. In fact, such a mechanism limits the number of requests for the same chunk at the server side for multiple clients watching the same TV channel, thus decreasing the link and the computational load at the server. Further research will explore: wider scenarios with many users and available channels, advanced optimization techniques for TV services in CCN (including routing and congestion control), and the adoption of scalable video coding. Moreover, a more deeply investigation on the relevance of the cache and the PIT in live TV services will be also conducted.

  [domain]/[channelID], with the Status field set to BOOTSTRAP and the Nonce field set by the client, as in in Sec. III-D. An Interest with Status = BOOTSTRAP would travel unblocked until it reaches the first good stream repository (i.e. a node who can provide a continuous real-time flow of chunks, not just cached ones).

  INT: bbc.co.uk/3 Status: BOOTSTRAP Nonce: #easd2 INT: bbc.co.uk/3 Propagate? True Check cache? False FrameID: 23 DATA: bbc.co.uk/3/234 FrameID: 23 DATA: bbc.co.uk/3/234 INT: bbc.co.uk/3/235 INT: bbc.co.uk/3/236 RX Start ...

Figure 1 .

 1 Figure 1. Bootstrap handshake

1 : 9 :

 19 procedure SENDINTERESTS(P W, W, W inT, N ow, LC) for all CID in P W do 10: if lastT x(CID) < N ow -W inT then ← Wsize(P W ) 17: for i ← 1, N N C do 18: send(Int(LC)) 19: lastT x(LC) ← N ow 20: add LC to P W 21: LC ← LC + 1 22:

Figure 2 .

 2 Figure 2. Sliding window algorithm

Figure 3 .

 3 Figure 3. Sliding window example

Figure 4 .

 4 Figure 4. Total number of Interest packets sent by clients with playout delay of (a) 10s and (b) 15s.

Figure 5 .

 5 Figure 5. Percentage of duplicated Interest packets sent by clients with playout delay of (a) 10s and (b) 15s.

Figure 6 .

 6 Figure 6. Chunk loss ratio with playout delay of (a) 10s and (b) 15s.

Figure 7 .

 7 Figure 7. PSNR of the Y components of received videos with playout delay of (a) 10s and (b) 15s.

  Table adding the face from where this newcomer Interest was originated, so to reroute the data back recursively along the path the Interest has gone through.

	CLIENT		SERVER
	Interest [chunkID=1, status=normal]
	Data [chunkID=1]
	Timeout
		Interest [chunkID=2, status=retransmit]
		Interest [chunkID=3, status=retransmit]
		Interest [chunkID=4, status=retransmit]
			Data [chunkID=2]
	Timeout	Lost!	Data [chunkID=3]
		Lost!
	Interest [chunkID=4, status=retransmit]	Interest [chunkID=4, status=retransmit]
	Interest [chunkID=5, status=normal]	Interest [chunkID=5, status=normal]
	Interest [chunkID=6, status=normal]	Interest [chunkID=6, status=normal]

Interest [chunkID=2, status=normal] Interest [chunkID=3, status=normal] Interest [chunkID=4, status=normal] Interest [chunkID=2, status=normal] Interest [chunkID=3, status=normal] Interest [chunkID=4, status=normal] Interest [chunkID=2, status=retransmit] Interest [chunkID=3, status=retransmit] Interest [chunkID=4, status=retransmit]

In CCN it is used the term "face" instead of the "interface" because packets are also exchanged between application process, besides being forwarded only over real network interfaces.


Isabelle Bergonzi

Lionel Mercury

Infrared-Thermodynamics Conversion as a Function of Temperature: Towards Confined Water

An experimental method has been developed to calculate the thermodynamic properties of water from its vibrational properties, relevant to study (in near future) the properties of adsorbed or confined water. The infrared absorption of the intra-molecular OH stretching mode of liquid water has been measured over a wide range of temperature (from -10°C to 90°C). The corresponding large band has been decomposed into three Gaussian components standing for three different water connectivities (percolation model) that feature the liquid state as a function of temperature: network, intermediate, multimer, water. Measurements evidenced that the components are differently shifted with temperature, giving a quantitative insights into the internal energy change of liquid. A vibrational partition function has been used to calculate the corresponding thermodynamic properties, neglecting all energy components except the present intra-molecular vibrational mode. Interestingly, the vibrational free enthalpy thus computed differs of the total free enthalpy only by a multiplicative constant all along the thermal range.

INTRODUCTION

Liquid water presents a remarkable ability to fill in any cavity or channel, even of nanometric dimensions (confinement), and to stay as thin films onto almost any solid surfaces (adsorption). The term confinement relates to the influence of the close solids on the sandwiched liquid, while adsorption is a confinement between solid and air. Interestingly, confinement and adsorption are states that allow liquid water to stay inside a pore network under arid or semi-arid conditions, affording a minimum water content in soils, with the thin films hydraulically connecting capillary clusters confined in wedges, crevices or small channels. This minimum water content directly impacts the soil wettability, its ability to host drought-tolerant species, and to maintain residual microbial activity and mobility. In terms of weathering, these water types are intimately contacting the host solid and also stay immobile for long period of time, making them a probably important (and overlooked) actor in the global mass balance. Confined and adsorbed waters have properties that deviate from the bulk water (e.g., [START_REF] Derjaguin | Surface forces[END_REF][START_REF] Handa | Effect of restricted geometries on the structure and thermodynamic properties of ice[END_REF][START_REF] Teixeira | Water in confined geometries[END_REF][START_REF] Dore | Structural studies of water in confined geometry by neutron diffraction[END_REF][START_REF] Christenson | Confinement effects on freezing and melting[END_REF][START_REF] Johari | Water's size-dependent freezing to cubic ice[END_REF][START_REF] Tombari | Thermodynamic functions of water and ice confined to 2 nm radius pores[END_REF]), which give them specific driving forces in terms of transport, weathering, and biological habitats. Confined water is found in saturated and nonsaturated media, actually whenever liquid is occluded in host spaces smaller than 0.1 µm (e.g., [START_REF] Shelton | Collective molecular rotation in water and other simple liquids[END_REF][START_REF] Putnis | The effect of pore size on cementation in porous rocks[END_REF][START_REF] Rijniers | Experimental evidence of crydtallization pressure inside porous media[END_REF][START_REF] Musat | Finite size effects on hydrogen bonds in confined water[END_REF][START_REF] Caër | A trapped water network in nanoporous material : the role of interfaces[END_REF]). Adsorbed water is encountered in non-saturated media, as thin films of nanometer to hundreds of nanometers thickness (e.g., [START_REF] Derjaguin | Surface forces[END_REF][START_REF] Pashley | Surface forces in adsorbed multilayers of water on quartz[END_REF]). Despite this large versatility in natural settings, the properties of these water types and the characteristic thresholds describing their evolution with sizes/thicknesses are not well apprehended in the natural sciences community. Meanwhile, their characteristic properties are essentially measured at very high confinement around the nanometer, and their thermodynamic behaviour in the 5-100 nm range is poorly known. Infrared (IR) spectroscopy have been used to probe the water liquid state with solutes addition [START_REF] Masuda | Structural change of water whith solutes and temperature up to 100°C in aqueous solutions as revealed by Attenuated Total Refelctance Infrared Spectroscopy[END_REF], when adsorbed on surfaces [START_REF] Musat | Finite size effects on hydrogen bonds in confined water[END_REF][START_REF] Richard | Diffuse reflectance infrared Fourier transform spectroscopy as a tool to characterize water in adsorption/ confinement situations[END_REF] or filling restricted spaces [START_REF] Musat | Finite size effects on hydrogen bonds in confined water[END_REF][START_REF] Caër | A trapped water network in nanoporous material : the role of interfaces[END_REF], at the solid-water or liquid-air interfaces [START_REF] Mercury | Infrared imaging of bulk water and water-solid interface under stable and metastable conditions[END_REF]. These studies demonstrated the sensitivity of the IR signal to record slight changes of the properties of liquid, even for small amount of matter. This sensitivity indicates that vibrational energy changes correctly probe energetic changes with environment. Among all the IR absorption modes, the intra-molecular OH-stretching band revealed to be the most significant, showing shifts both in terms of global shape, intensity and location of the main peak. However, there is not a direct conversion of these IR shifts into macroscopic thermodynamic properties to date. Some studies proposed a statistical deconvolution of the IR and Raman spectra to obtain thermodynamic values of diluted solutions of HOD molecules in D 2 O (or H 2 O), but this approach cannot describe the IR spectra of normal water [START_REF] Yu | Fluctuation theory of hydrogen bonding applied to vibration spectra of HOD molecules in liquid water. I. Raman spectra[END_REF][START_REF] Yu | Fluctuation theory of hydrogen bonding applied to vibration spectra of HOD molecules in liquid water. II. Infrared spectra: contour shape, integrated intensity, temperature dependence[END_REF][START_REF] Yu | Thermodynamic functions of liquid water calculated from the temperature evolution of the vibration spectrum contour[END_REF]. It is why infrared spectroscopic measurements have been targeted to record the change in the vibrational properties of water trapped into artificial rectangular channels having depths varying from 100 to 5 nm (1D nano-channels). However, this paper lets aside the confinement topic to deal with a required prior step: devising a calculation method for the IR-thermodynamics conversion based on a partition function, and calibrating it on a well-known thermodynamic change, here the thermodynamic behavior of liquid water from -10°C to 90°C.

EXPERIMENTAL SECTION

IR measurements were recorded in the 400-4000 cm -1 spectral region with a Fourier Transform Infra-Red (FTIR) micro-spectrometer (Nicolet Continuµm, Thermo scientific), equipped with a XT-KBr beam splitter and a liquid nitrogen cooled Mercury Cadmium Telluride (MCT) detector (250 µm). The microscope operates in confocal mode, using a 15x infinity corrected Schwarzchild objective and a matching 15x condenser. To avoid saturating the IR absorption signal due to the enormous amount of water molecules per liquid volume, a thin film cell of varying thickness, down to micrometer, has been developed. This cell is composed of two steel parts compressing two BaF 2 windows (13 mm x 2 mm), sealed with a fluorocarbon O-ring. A liquid water drop is sandwiched between the two windows and the steel parts are tightened to form a bulk water film roughly 1 µm thick. The thermal change is controlled by a heating-cooling stage (THMS-600, Linkam) with windows transparent to IR light. Briefly, the fluid cell is put on a silver block at controlled temperature (±0.1°C), and the acquisition starts after 5 minutes, which is the time needed to afford thermal homogeneity between the two steel parts. Each spectrum is recorded with a resolution of 4 cm -1 with 200 scans per spectrum and no mathematical correction. The infrared absorption coefficient is defined by: ⁄

where I 0 is the transmitted intensity of the empty cell and I the transmitted intensity of the cell filled with water. Spectra are recorded from -10°C to 90°C.

EXPERIMENTAL RESULTS AND DISCUSSION

IR absorption band

The infrared spectrum of liquid water consists of four main bands, spreading from a few wavenumbers and 3800 cm -1 [START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF]. The dominating feature of the IR water spectrum is the band located at 3400 cm -1 which corresponds to the stretching motion of the covalent OH bonds. The HOH bending band (1650 cm -1 ) follows in the decreasing frequency order, then the libration band (675 cm -1 ), and finally the "connectivity" band (200 cm -1 ). The two former bands correspond to intra-molecular modes, either sensitive to the H-bonds environment (stretching) or not sensitive (bending). The two latter reflect inter-molecular modes. The libration mode, through small amplitude oscillations of the whole molecule, provides a mechanism of rupture and rearrangement of the hydrogen bonds at a sub-picosecond rate.

The connectivity band arises from the longitudinal motion of the H-atom along the H-bond axis (H-bond stretching) and therefore characterizes the level of H-bonding between neighboring water molecules.

OH stretching band

The OH stretching band centred at about 3400 cm -1 is a sensitive probe of the H-bond: the wavenumber increases with the distance between O atoms of two molecules linked by H-bond (e.g., [START_REF] Bratos | Relation between the OH-stretching frequency and the OO distance in time-resolved infrared spectroscopy of hydeogen bonding[END_REF]). The absorption corresponds to intramolecular motions of the water molecules crossed by the IR beam, which depend on the molecular environment. As a result, this is a molecular signal averaged over macroscopic amount of matter. The width of the band echoes the energetic distribution of H-bonds along the beam pathway and then is an image of the molecular disorder, what justifies the intense study of this band (e.g., [START_REF] Nucci | Temperature dependence of hydrogen bonding and freezing behavior of water in reverse micelles[END_REF][START_REF] Crupi | Raman spectroscopy: probing dynamics of water molecules confined in nanopous silica glasses[END_REF][START_REF] Maréchal | The Hydrogen Bond and the Water Molecule[END_REF]). The present measurements from -10°C (supercooled water) to 90°C (Fig. 1) are in agreement with previous studies [START_REF] Maréchal | Infrared spectra of water. I. Effect of temperature and of H/D isotopic dilution[END_REF][START_REF] Libnau | Spectra of water in the near-and mid-infrared region[END_REF][START_REF] Czranik-Matusewicz | Temperature-dependent water structural transitions examined by near-IR and mid-IR spectra analyzed by multivariate curve resolution and two-dimensional correlation spectroscopy[END_REF]: Upon heating, the main peak moves to higher wavenumbers (blue-shifted, from 3380.6 cm -1 at -10°C up to 3436.5 cm -1 at 90°C), while the intensity diminishes and the shape visually changes losing the lower wavenumbers and enriched on the higher ones. This shift is classically interpreted by the direct effect of heating that disrupts water intermolecular network and then promotes disorder (e.g., [START_REF] Nucci | Temperature dependence of hydrogen bonding and freezing behavior of water in reverse micelles[END_REF][START_REF] Crupi | Raman spectroscopy: probing dynamics of water molecules confined in nanopous silica glasses[END_REF]). This interpretation applies as well to account for the shape change under heating. The decreasing absorbance is readily accounted for, outlining that the resonance condition required for coupling the OH stretching motion is obtained at low temperature [START_REF] Green | Spectroscopic evidence for spatial correlations of hydrogen bonds in liquid water[END_REF]. These visual observations cannot be turn easily into quantitative calculations because liquid water is a continuum of molecular configurations, each having its own behavior and influence on the change of the total energy. And the modeling of the whole band in terms of discrete molecular energies cannot be performed. The common strategy is to decompose the OH-stretching band into Gaussian components, each standing for a certain type of water that features the liquid at a given time. Decomposition into two (e.g., [START_REF] Libnau | Structure of liquid water determined from infrared temperature profiling and evolutionary curve resolution[END_REF]), three (e.g, [START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF]) and four components (e.g., [START_REF] Masuda | Structural change of water whith solutes and temperature up to 100°C in aqueous solutions as revealed by Attenuated Total Refelctance Infrared Spectroscopy[END_REF]) have been performed, most often related to the purposely existing water clusters. Actually, the vibrational mode causing the stretching motion of the intra-molecular OH bond is sensitive to the strength of H-bonding between molecules. The oscillator strength of a water molecule decrease when its local coordination increases and the corresponding OH frequency is downshifted. The notion of water cluster, and its relation to water structure, is problematic since it is well known that the relaxation time of water is around the picosecond, several order of magnitude quicker than the recording time of the IR absorption. It is why this classic approach has been recently reformulated in terms of the percolation model [START_REF] Stanley | Interpretation of the unusual behavior of H 2 0 and D 2 0 at low temperatures: Tests of a percolation model[END_REF], each Gaussian component featuring an averaged coordination numbers, probabilistically ranging from 0 to 4 [START_REF] Caër | A trapped water network in nanoporous material : the role of interfaces[END_REF][START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF]. The best and most relevant decomposition is done through three Gaussian components (inset in Fig. 1), ascribed to three different types of water molecules. The low-frequency Gaussian is associated to the fully coordinated water molecules, called Network Water (NW) also known as ice-like water since the Gaussian peak is close to the ice's (3250 cm -1 , [START_REF] Maréchal | The Hydrogen Bond and the Water Molecule[END_REF]). The high-frequency Gaussian is ascribed to the molecules with a low coordination number, called Multimer Water (MW) and close to the IR characteristics of vapour molecules. The Gaussian lying in-between has a coordination number close to two, is called Intermediate Water (MW) and refers to the incompletely coordinated liquid molecules. At the scale of one molecule, it is clear that each molecule experiences the three coordination states over the experimental time (minute). The final band represents how the molecular network promotes the different types of coordination related to the energy available in the system.

Band decomposition

The experimental bands were fitted with the software Igor and its Multipeak fitting 2.0 package. Brubach et al [START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF] suggested that the three Gaussian components were linked to the five species described by the percolation model [START_REF] Stanley | Interpretation of the unusual behavior of H 2 0 and D 2 0 at low temperatures: Tests of a percolation model[END_REF]. This model calculates the variation of the coordination number of one water molecules with its immediate neighbors, with temperature. The number of intact H-bonds per molecule is given by the following probability: ⁄ (2) with n HB the number of established H-bonds and z=4 the maximum number of hydrogen atoms bonded to one oxygen atom (by covalent or intermolecular bond). Molecules are thus divided into five species, by the possible number of intact H-bonds they form with their neighbors, from 0 to 4. The fraction f j of water molecule establishing j bonds is given by the relation:

(3) with j ranging from 0 to 4. The fraction of species j is a function of the temperature T via the temperature dependence of p B written . Brubach et al. [START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF] proposed to ascribe NW to species j=4 and j=3, IW to species j=2 and MW to species j=1 and j=0. The interesting point of such interpretation is the implicit use of the ergodic principle to describe the thermodynamic features of liquid water: the IR signal averaged over time echoes the averaged energetic states making up this liquid. Practically, fits were constrained to make the full width at half maximum of the calculated Gaussian component to match the fraction of water molecules "types" calculated by equation (3) with temperature (Fig. 2). Over -10°C to 90°C, NW fraction dominates up to 40°C, from which temperature IW starts predominating. Interestingly, IW is the fraction that varies the less over the thermal range, while the two others are anti-correlated in the expected way: NW decreases with temperature while the MW increases, in agreement with the chaotropic trend afforded by heating individual molecules that tend toward a vapour-like network organization. This variation is in good agreement with the shape evolution of the OH band with temperature: decreasing absorbance at low wavenumbers echoes the diminution of NW molecular fraction while increasing absorbance at high wavenumbers is naturally linked to the increasing MW molecular fraction. Gaussian maximum are shifted toward lower frequencies with temperature (Fig. 2): NW main peak moves from 3315 cm -1 at -10°C to 3219 cm -1 at 90°c, IW peak is displaced from 3455 cm -1 at -10°C to 3384 cm -1 at 90°C and MW peak slides from 3583 cm -1 at -10°C to 3528 cm -1 at 90°C. This IR downshifting evidences that the characteristic H-bond lengths of each water "types" decreases, what means that the energy to maintain the corresponding network organization must increase due to the additional thermal energy in the system. Otherwise, to keep its connectivity level, each water "types" uses more energy.

As a consequence, the OH-stretching band highlights that the IR shift is a direct measure of the internal energy change of the probed liquid. Summing up the three contributions, should result in deducing the whole thermodynamic change from a given reference state. In all that follows, the reference state is the pure liquid at 25°C and 0.1 MPa.

Figure 2: Location of the main peak of the Gaussian components with temperature. The inset shows the evolution of the molecular fraction of the three water populations: NW, IW, MW (see text and eq. ( 3)).

Thermodynamic treatment

The conversion of the IR absorption band into thermodynamic terms requires a description of the way the characteristics of each energetic state combine into the macroscopic value of the thermodynamic property. The relevant tool is the partition function, here that proposed by Vand and Senior [START_REF] Vand | Structure and partition Function of liquid water. III. Development of the partition function for a band model of water[END_REF]. It is based on the Némethy and Scheraga model [START_REF] Némethy | Structure of water and hydrophobic bonding in proteins. I. A model for the thermodynamic properties of liquid water[END_REF], which is a continuum model based on the concept of "flickering clusters". The H-bonds formation in liquid water is described as a cooperative process, i.e. H-bonds are established or broken simultaneously depending on the local energy fluctuations. Short-lived regions of highly H-bonded clusters thus take place surrounded by non H-bonded molecules. As a consequence, the model features liquid with two main structures, clusters and non H-bonded molecules. The water clusters can be monomer (one bond), dimer (two bonds), trimer (three bonds), or tetramers (four bonds). Despite this "water structure" background, the partition function is built through five species distinguished by their coordination number (four water clusters and the non H-bonded molecules) and an energy level is ascribed to each species, in an analytical approach completely compatible with the percolation model. The molecules distribution between the energy levels is determined by the corresponding Boltzmann factors, where E i is the energy of a given energy level and k is the Boltzmann constant, and by the degrees of freedom allowed for the motion of each species. The corresponding partition function Z writes as follows [START_REF] Némethy | Structure of water and hydrophobic bonding in proteins. I. A model for the thermodynamic properties of liquid water[END_REF]:

∑ [ ] ∏ [ ] (4)
where g is a combinatorial factor written , is the number of molecules of each species, N 0 is the Avogadro's number, x i are mole fractions of each species in the bulk liquid, E i are the energies of each species and f i are the weighting factors describing the vibrational, rotational and translational freedom allowed to each species, ascribed from IR and Raman experimental data. The present approach by IR-shift relative to a reference enables to neglect the modes that are not sensitive to the varying parameter (temperature or confinement, or any other). The intra-molecular IR changes are entirely featured by the OH-stretching band, since the bending mode has a negligible thermal coefficient (-0.1cm -1 .K -1 ; [START_REF] Eisenberg | The structure and properties of water[END_REF]). The intermolecular modes (60 cm -1 to 1000 cm -1 ; libration and connectivity bands) include as well the cooperativity between vibration and rotation modes, and both change with temperature (e.g., [START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF]). Nemethy and Scheraga [START_REF] Némethy | Structure of water and hydrophobic bonding in proteins. I. A model for the thermodynamic properties of liquid water[END_REF] hypothesized that these intermolecular bands that appear in ice, express the contribution of the clustered water. With their partition function, and experimental values for the IR bands, they were able to accurately re-calculate the entropy, free energy and internal energy of liquid water but failed with the specific heat of water. Based on experimental measurements [START_REF] Buijs | NearInfrared studies of the structure of water. I. Pure water[END_REF][START_REF] Buijs | Assignment of the near-infrared bands of water and ionic solutions[END_REF], Vand and Senior [START_REF] Vand | Structure and partition Function of liquid water. III. Development of the partition function for a band model of water[END_REF] alternatively proposed to describe the partition function with three species, each having a certain distribution around a mean effective length ̅ of H-bond in liquid water. As a consequence, the energy of molecules in an energy band (mean effective length ̅ ) will have a similar regular distribution about a mean value E i . Vand and Senior [START_REF] Vand | Structure and partition Function of liquid water. III. Development of the partition function for a band model of water[END_REF] selected arbitrarily a Gaussian distribution to describe the distribution of the three energy bands, and the partition function becomes:

∑ { ( ) ̅ } (5)
where ⁄ , E i is the energy of the ith species, is the power law expression for the weighting factor f i that integrate thermal variation, Δ is the bandwidth of the energy distribution and B is a constant. At first sight, the partition function with three energy bands fits well the decomposition into three Gaussian components done from the OH-stretching band. Using the Gaussian changes as a function of temperature, the Vand and Senior function offers a simple pathway to transform IR shifts into macroscopic water energy changes. In liquid water, the bending and OH-stretching bands are intra-molecular modes and only the latter moves with the temperature. In the meantime, there are frustrated (with respect to vapor) rotational motions (librations, around 675 cm -1 ) due to the networking that changes the inter-molecular vibrational mode of H-atoms. A second inter-molecular mode is featured by the hindered translational (or connectivity) band (around 200 cm -1 ), which correspond to the longitudinal motion of the H-atom along the H-bond axis (H-bond stretching) and therefore characterizes the level of H bonding between neighboring water molecules. Among these four bands, only two exhibit pronounced substructures that significantly evolve with temperature (and probably confinement) (e.g, [START_REF] Caër | A trapped water network in nanoporous material : the role of interfaces[END_REF][START_REF] Brubach | Signatures of the hydrogen bonding in the infrared bands of water[END_REF]): the OH-stretching band and the connectivity bands. These substructures characterize the changing levels of H bonding in the molecular network that are directly related to the thermodynamic properties. As a consequence, the coming interpretation is weakened by the sole consideration of the stretching band, while (at least) the connectivity band contributes to the internal energy.

The IR-thermodynamics conversion corresponds to transform the total mean energies value in equation ( 5) [START_REF] Vand | Structure and partition Function of liquid water. III. Development of the partition function for a band model of water[END_REF] into the three vibrational mean energies given by the peak of the three Gaussian components, resulting in the "vibrational" thermodynamic functions of liquid water as a function of temperature (Fig. 3A). Consistently, the vibrational Gibbs free energy is smaller than the total Gibbs free energy ignoring the contribution of the inter-molecular modes. This first absolute calculation can be easily normalized at 25°C, and only the relative change to this reference is calculated (Fig. 3B), removing all the modes that are not sensitive to thermal change. Here again, ΔG vib has a larger slope than total ΔG, outlining that the intra-molecular vibrational mode is compensated by another energetic contribution of opposite trend with temperature. Consistently, rotational and/or translational motions tend to increase with increasing temperature due to the decreasing of the coordination number of water molecules that favors non Hbond molecules. Assuming that the frustrated rotation (libration) does not change with temperature, and that any other rotation and/or translation modes impact the total energy, we may propose that a simple subtraction lead to predict the change of the inter-molecular connectivity mode. At this stage, obviously, an experimental control of such statement must be done.

For the time being, the multiplicative constant C that enables to retrieve the total ΔG (i.e. ;) all along the thermal range demonstrates that the thermodynamic changes under temperature, are as linear as the intramolecular OH-stretching mode. Thus, the decomposition of the OH stretching band into three Gaussian components, coupled with the Vand and Senior partition function, allows us to obtain a thermodynamic description, though incomplete, of water. Technically, it is interesting to outline the compatibility between the percolation model and the A B original Nemethy and Scheraga approach. The probabilistic H-bonds networking can be assumed in the same continuum framework as that afforded by the flickering water-structured clusters.

CONCLUSION

The IR-to-bulk thermodynamics conversion has been explored following the OH-stretching band behaviour with temperature. The method, based on the percolation model and using mechanistic partition function, appears reliable and gives the correct trend. However, it fails to become strictly quantitative, most probably by overlooking the other significant contribution, mainly the connectivity band. These effects need now to be evaluated with temperature, to decipher the missing link between G vib and G total .

These results give confidence about the ability of the FTIR spectroscopy to probe the thermodynamic properties of liquid water under given conditions. Thus, the protocols to record IR absorption under confinement have been developed as well as the design of the artificial channels with varying depth (1D nano-confinement).

Figure 1 :

 1 Figure 1: OH stretching band of liquid water as a function of the temperature. Inset displays the 3 Gaussian components decomposition classically performed (see text).

Figure 3 .

 3 Figure 3. A. Evolution of the total and vibrational free enthalpies (or Gibbs free energies) as a function of temperature. Dotted line is only guide for eyes. B. Evolution of vibrational and total free enthalpies relative to 25°C. The solid line (calculated Gibbs free energy) is perfectly fitted by the vibrational Gibbs free energy (open circles) multiplied by the constant C (C = 0.241546, see text).

ACKNOWLEDGMENTS

This work has received support from the French Agency for Research (Agence Nationale de la Recherche, ANR) through the grant CONGE BLAN-61001 and ANR-10-LABX-100-01.