José Santa
email: josesanta@um.es

Manabu Tsukada

Thierry Ernst

Olivier Mehani

Antonio F Gómez-Skarmeta

Antonio F Gomez-Skarmeta

Assessment of VANET multi-hop routing over an experimental platform

Keywords: vehicular communications, VANET, experimental evaluation, ad-hoc networks, multi-hop communications, OLSR

AbstractEvaluation of vehicular ad-hoc networks (VANETs) over real environments is still a remaining issue for most researchers. There are some works which carry out performance tests to evaluate the communication channel according to physical and MAC conditions. Only a few works deal with multi-hop experimentation in this field, and practically none tests multihop protocols. In this paper an integral VANET testbed is evaluated, using 802.11b and a multi-hop network managed by the Optimized Link State Routing protocol (OLSR). Up to four vehicles are used to study the VANET performance over different traffic environments and different metrics are considered to analyse the results in terms of delay, bandwidth, packet loss and distance between nodes. Furthermore, a deeper analysis is carried out to track the routes followed by packets end to end. Since a routing protocol is used, results differ from traditional one-hop and static-route tests, presenting a more realistic study.

INTRODUCTION

Vehicular networks are becoming essential for telematic services inside the Intelligent Transportation Systems (ITS) field. Apart from autonomous solutions, such entertainment and some collision avoidance systems exclusively based on vehicle sensors, for example, distributed and collaborative services extend the driver perception and integrate the vehicle in the traffic environment. Safety services are the most studied ITS solutions in the current literature, where vehicular networks are commonly used to exchange navigation and road-side events with the aim of detecting potential hazards. Nonetheless, comfort, traffic management, and monitoring systems, are also more and more dependent on vehicular networks, and implementations of services such as platooning, vehicle tracking, parking reservation and distributed games are only some examples of this expansion.

There are several communication paradigms involved in vehicular networks, which can be essentially summarised as vehicle to vehicle (V2V), vehicle to infrastructure (V2I), infrastructure to vehicle (I2V), and even infrastructure to infrastructure (I2I). Wireless technologies through 802.11 and cellular networks are the most extended communication links, although their usage depends on concrete applications. Among all possible combinations of communication paradigms and wireless technologies, there is one field specially studied by the ITS community, known as Vehicular Ad-hoc Networks, or VANET. In this case, wireless local area networks, such as 802.11 and DSRC (Dedicated Short Range Communications), are applied into the V2V case using concepts inherited from MANETs (Mobile Adhoc Networks).

Although there are a lot of works related to VANET applications and basic research at physical, MAC and, overall, network layers, there is an important lack of real evaluation analysis. Many VANET solutions and protocols could be considered as non practical designs if they were tested over real scenarios, as it has been proved in MANET [START_REF] Tschudin | Embedding MANETs in the real world[END_REF]. Performance of VANET protocols based on a pure broadcast approach can be more or less expected in simple configurations, even if they are not experimentally tested; but the number of issues concerning the real performance of multi-hop designs is much more tricky. As we detail in next section, the amount of works related with real evaluation of VANET designs is limited, rare if we consider the concrete case of multi-hop transmissions, and practically null in the evaluation of routing protocols. Performing real evaluations in VANET research imply a number of issues, most of them inherited from MANET, and even accentuated. Some of the most important drawbacks of performing VANET experiments are:

• Implementation of routing protocols and/or applications. Most VANET projects end at the simulation stage; hence, almost none of them implement the real

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system.

• Equipment cost. The hardware cost which imply the evaluation of a VANET architecture might not be assumed by all researching groups. If a multi-hop solution is considered, a minimum of three cars equipped with some kind of computer and communication interfaces are necessary.

• Logistic issues in experiments. Not only the necessary equipment is important, but also people to drive cars and control the nodes is essential. When the number of vehicles grow, setting-up experiments is more and more difficult.

• Necessary work to cover a meaningful set of tests.

When nodes are ready, a number of realistic scenarios have to taken into account to get meaningful results, what can be a time-consuming task.

In this paper, a multi-hop VANET is evaluated over real environments, setting-up four cars with the necessary equipment, and involving an interdisciplinary group of people which works on ITS. The goal of the work is becoming a reference point for the VANET community, giving an evaluation of a real multi-hop VANET and IPv6 platform, which uses a standardised ad-hoc routing protocol, as the Optimised Link State Routing (OLSR) protocol is. Testing scenarios have been divided into urban and highway; mobility has been set to static, urban-like speed, and high speed; and a wide range of performance metrics have been used, such as bandwidth, RTT (Round-Trip delay Time), jitter and PDR (Packet Delivery Ratio). Because a low level study has been carried out, it is also possible to count the number of hops and calculate PDR per link in data transmissions. This study is done by a filtering software, which merges information from GPS, dump files and traffic generator traces. Moreover, specific scenarios to test the routing protocol behaviour have been considered. The data traffic considered in tests embraces the requirements of most ITS applications, hence ICMPv6, TCP and UDP transmissions have been analysed.

The structure of the paper has been divided into the following Sections: Section 2 briefly describes previous works related to VANET experimental evaluation; Section 3 gives a small overview of VANET concepts and OLSR; Section 4 presents the experiment set-up, in terms of hardware used, place of tests, considered scenarios, and the software developed to analyse the network traffic; the results gathered in the tests are analysed in Section 5 and, finally, the paper is concluded in Section 6. with this issue, although most of them are still focused on studying the feasibility of 802.11 and DSRC technologies in the vehicular field. In [START_REF] González | Experimental demonstration of the viability of IEEE 802.11b based inter-vehicle communications[END_REF] the applicability of 802.11b in V2V communications is evaluated over urban and highway scenarios, and it is demonstrated that direct line of sight is one of the most important issues in the network performance. The hardware platform considered is similar to the one chosen in the current work, based on an embedded PC which acts as access router for in-vehicle devices. A similar analysis is found in [Jerbi et al., 2007a], where several evaluation metrics are used to quantify the performance of the wireless channel between two vehicles. Also using 802.11b, in [START_REF] Singh | Wireless LAN performance under varied stress conditions in vehicular traffic scenarios[END_REF] authors demonstrate how mobility and environment factors can seriously degrade the network operation. In addition to consider the most common performance metrics in VANET evaluation, the post-processing software described in next sections, implemented to analyse data logs, enable us to trace packets among communication nodes. Using such feature, it is possible to detect link failures and study the routing protocol performance, in terms of number of hops in transmissions.

Communication between a vehicle and a static terminal is also important for some ITS services. This communication pattern can be considered as a subset of I2V and V2I, where vehicles connect with a local end-point installed at the road side. This is the reason why they are called roadside to vehicle and vehicle to road-side communications, RVC and VRC, respectively. VANET evaluation papers, as the current one, usually consider this special case in testing scenarios. In [START_REF] Wewetzer | Experimental evaluation of UMTS and wireless LAN for inter-vehicle communication[END_REF] a communication scenario considering a static terminal and a moving vehicle is studied in detail. Among all metrics considered in this work, the transmission power is the more original one, determining the maximum communication range. The type of data traffic used to test the performance of the communication channel is also of interest. Most VANET designs use UDP packets, due to poor TCP performance over wireless channels. In [START_REF] Hui | Experimental characterization of multi-hop communications in vehicular ad hoc network[END_REF] and [START_REF] Festag | Fleetnet: Bringing car-to-car communication into the real world[END_REF] this issue is studied through different configurations; idea also included in the current paper.

The previous works only consider two terminals in performance tests, what is not too representative in VANET research. In [START_REF] Maltz | Lessons from a fullscale multihop wireless ad hoc network testbed[END_REF] a MANET is evaluated using up to eight vehicles and a wide set of experiments are performed, however, the testing environment is too small to be significant for the vehicular community. Two recent works evaluate a multi-hop VANET over real conditions, using three [Jerbi et al., 2007b] and even six vehicles [START_REF] Jerbi | Characterizing multi-hop communication in vehicular networks[END_REF]. These papers offer a wide study about a real VANET set-up, and the last one includes an interesting analysis describing the impact of the number of hops on the final performance, what is also treated in the current paper. Nonetheless, static routes are used in that work, presenting a non-realistic vehicular network. Our work, by contrast, considers a real and standardised ad-hoc routing protocol to dynamically modify communication paths. The hardware test-bed presented is also suited for future ITS research, with a flexible in-vehicle and inter-vehicle IPv6 network based on mobile routers.

VEHICULAR AD-HOC NETWORKS

The origin of VANET is found in the more general researching subject of ad-hoc networks. However, as it is explained later, vehicular networks present specific conditions which have to be specially studied. OLSR is a well-known proposal of an ad-hoc routing protocol, whose performance in a VANET environment is analysed in this paper.

Mobile Ad-hoc Networks

Mobile Ad-hoc Networks (MANET) are designed to enable wireless communications in dynamic topologies without any infrastructure. In order to adapt to topology changes, MANET nodes exchange control messages to establish the routes used to forward data packets. MANETs have the additional advantage of extending the one-hop communication range, since the packets can be delivered through multiple nodes. MANET routing protocols [START_REF] Chang | Routing protocols for mobile ad-hoc networks: Current development and evaluations[END_REF] can be classified into the proactive ones, where nodes periodically exchange messages to create routes, and the reactive protocols, in which control messages are exchanged on demand when it is necessary to reach a terminal. Generally, proactive protocols have the advantage of starting communication rapidly by making the routing table ahead; however, this makes battery life shorter due to frequent signalling. If the topology is highly dynamic and the data traffic is frequent, a proactive protocol could be more appropriate. Reactive protocols, on the contrary, keeps the battery life longer by reducing signalling messages when there is no data to transmit. Some routing protocols specified by the IETF MANET working group1 are: the proactive Optimized Link State Routing (OLSR) [START_REF] Clausen | Optimized Link State Routing protocol (OLSR)[END_REF] and the Topology Dissemination Based on Reverse-Path Forwarding (TBRPF) [START_REF] Templin | Topology Dissemination Based on Reverse-Path Forwarding (TBRPF)[END_REF]; and the reactive Ad hoc On-Demand Distance Vector Routing (AODV) [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF], the Dynamic Source Routing (DSR) [START_REF] Johnson | The Dynamic Source Routing Protocol (DSR) for Mobile Ad Hoc Networks for IPv4[END_REF] and the Dynamic MANET Ondemand (DYMO) [START_REF] Chakeres | Dynamic MANET On-demand (DYMO) Routing[END_REF].

MANET vs. VANET

Vehicular

Ad-hoc Networks (VANET) [START_REF] Li | Routing in vehicular ad hoc networks: A survey[END_REF] are a particular case of MANET, which are characterised by battery constraints free, high speed and regular distribution and movement. First, vehicles have a better battery than mobile terminals or sensor devices, which is also charged when the engine is on. Second, the speed of vehicles is also higher than common portable terminals, and relative speeds can reach 300 Km/h; hence, the duration of the routing entries is extremely short. Third, the movement and density of the nodes are not random, since vehicles drive on roads, what makes the nodes position somehow predictive. This concept can be used to detect stable structures or clusters to improve the network performance [START_REF] Little | An information propagation scheme for VANETs[END_REF].

Moreover, a GPS device can be assumed in many cases, whose information improves the network performance in some proposals [Maihöfer, 2004, Mauve et al., 2001, Sun et al., 2006]. In the same way, it would be also possible to send packets only to a set of nodes grouped in a geographical area (geocast) [START_REF] Liao | GeoGRID: a geocasting protocol for mobile ad hoc networks based on grid[END_REF].

OLSR

OLSR is the routing protocol used in the experiments performed in the work, as it has been stated. Control overhead of this proactive protocol is quite reduced by multipoint relays (MPRs), which characterise OLSR. Each node selects its MPRs among all one-hop terminals, assuring that all neighbouring nodes at two hops can be reached through a minimum set of them. By using MPRs, the network overhead decreases when node density is high, since only the nodes designated as MPRs forward messages. OLSR nodes detect each other by HELLO messages, which are periodically sent. Topology Control (TC) messages are used to disseminate neighbour information throughout the network. Since OLSR nodes can interconnect different networks, another special message is also periodically disseminated to advertise these in the OLSR network, called Host and Network Association (HNA) message. In VANETs, this information is necessary, for example, to exchange invehicle network addresses. This is the case of the communication platform presented in the paper, where each on-board unit acts as a mobile router (MR) for in-vehicle devices.

OLSR is a well-known protocol in the MANET literature. Since the application of MANET concepts in the particular VANET case is a common procedure, the results given in this paper assess how a common ad-hoc proactive protocol operates under vehicular conditions. Because vehicles are not constrained by battery restrictions, one may think that a proactive protocol tuned for highly dynamic topologies could be suitable in the vehicular domain. Evaluating this idea is a key point in the work; hence, the VANET testbed presented in next section uses the OLSR protocol.

EXPERIMENT SET-UP

A set of common vehicles have been equipped with the necessary hardware to create a VANET using OLSR. Network traffic and positioning information is logged and then processed in order to analyse the VANET performance. The experiment set-up is described in detail in this section, in terms of hardware and software modules developed, network metrics considered and traffic scenarios.

Testbed Platform

Up to four Citröen C3 cars have been used in the trials, mounting the proper hardware to integrate the vehicle in the VANET and log positioning and network traffic information. Figure 1 illustrates the main components of the on-board platform, during one of the field trials. As can be seen, an embedded computer is used as mobile router (MR) in each car. This comprises a Soekris net4521, with a mini-PCI 802.11 Texas Instruments ACX 111 802.11 b/g wireless transceiver and a compact flash hard disk. The wireless interface has been set-up at 11 Mbps, emulating an 802.11b device. The computer is connected, via serial port, with a Trimble AgGPS 323 GPS receiver, whose external antenna is visible in the photo. The wireless card uses another external antenna, fixed on the car's roof too. One of the two ethernet connections of the MR is used to connect it with the in-vehicle wired network, by means of a hub. In the sender and receiver vehicles, a laptop is connected to the in-vehicle network. The sender laptop is a Windows XP-based system, whereas the second one comprises a Linux Debian computer.

A Linux Voyage distribution with kernel 2.6.22 has been installed on MRs, and the olsr.org daemon 0.5.6-rc72 (an implementation of the OLSR protocol) has been configured on each one. The OLSR configuration parameters are listed in Table 1. The transmission period of hello packets has been adjusted to deal with vehicle mobility, through a set of preliminary tests and considering a previous study about tuning OLSR in movility environments [START_REF] Cheng | Tuning OLSR[END_REF]. Since the topology is highly variable, the same has been made with TC Interval and TC ValidityTime periods. It is important to remember that TC messages are useful to exchange topology information between network nodes. MRs do not use more than one interface in the VANET, hence multiple interface declaration (MID) parameters are left with default values. Host and network association (HNA) parameters have been adjusted. Since HNA messages are used to announce other networks accessible through OLSR nodes, increasing the frequency of these notifications makes faster advertising the in-vehicle networks. The last two parameters should have the same value than the topology control ones [START_REF] Clausen | Optimized Link State Routing protocol (OLSR)[END_REF]. As it has been stated, the network prefixes of in-vehicle networks are advertised using HNA messages of OLSR. These networks are listed in the configuration file of OLSR daemon. This mechanism implies a set of security issues, such a denial of service, which should be covered in a real deployment of the system.

Data Gathering and Post-Processing Fusion

An overview of the experimental evaluation process carried out in the work is given in Figure 2. In the tests, up to four vehicles have been used, however, the system is , and log the vehicle position continuously. All these data is analysed in post-process by the AnaVANET software. This is a Java application which traces all the data packets transmitted from the sender node. This way, it is possible to detect packet losses and calculate statistics for each link and end-to-end, and merge all these per-hop information with transport level statistics of the traffic generator. As a result, AnaVANET outputs an XML file with statistics of one-second periods, and a packet trace file with the path followed by each data packet. The first file is uploaded to a Web server, which uses Google Maps functionalities to graphically replay the tests. The Graphic Generator module gives another view of the network performance, using both XML and packet traces to process results and then create several types of figures through the GNU Plot utility.

Analysed Traffic and Performance Metrics

Three different types of data traffic have been considered in the tests carried out over the IPv6 network. These are described in next points, together with the software used to generate the packets:

• UDP. A unidirectional transmission of UDP packets from the sender laptop to the receiver one, has been generated using the IPerf tool4 . The packet length has been fixed to 1450 bytes, to avoid fragmentation with IPv6, and they are sent at a rate of 1 Mbps. Note that the maximum packet length could be fixed at 1452, since the IPv6 and UDP headers imply 40 and 8 bytes, respectively.

• TCP. A TCP connection is established between the sender and receiver laptops, non limiting the maximum bandwidth. The IPerf tool is again used in the traffic generation and the maximum segment size used was 1440, since the IPv6 and TCP headers imply 40 and 20 bytes, respectively.

• ICMPv6. The Windows XP Ping6 utility is used to generate IPv6 ICMP (Internet Control Message Protocol) echo request packets from the sender laptop, and to receive echo reply packets from the remote one.

These three types of traffic have been used to analyse the network performance hop-by-hop and end-to-end, considering the most extended metrics in MANET evaluation [START_REF] Chang | Routing protocols for mobile ad-hoc networks: Current development and evaluations[END_REF]. In the TCP case, the high level information given by IPerf, at a 0.5-second rate, is considered in the process. ICMPv6 and UDP packets are, however, traced across nodes. Since there is no fragmentation for UDP packets, a direct correspondence exists between MAC and IP layer packets in the study. At this level, the packet delivery ratio (PDR), the number of hops and the jitter are calculated. For ICMPv6 data flows, the round-trip delay time (RTT) have been also considered. At the transport level, the IPerf information used is the instantaneous bandwidth.

Experimental Scenarios

A set of scenarios have been considered with the aim of obtaining significant results under different conditions. The main factors which determine these scenarios are:

• Mobility. Static and dynamic scenarios have been considered to test the network operation under controlled and common traffic settings.

• Environment. Two different environments have been considered: a semi-urban one, inside INRIA-Rocquencourt installations, which contains a set of small buildings surrounded by streets, and a highway stretch, the French A-12, near INRIA-Rocquencourt.

• Number of vehicles. Up to four vehicles are considered in the field trials, in order to check the delay increase with the number of hops.

The various traffic types (UDP, TCP and ICMPv6) have been applied over each defined scenario. In Figure 3, four common scenarios in VANET evaluation, with up to three vehicles, are illustrated. The first one has been used to check the maximum communication range between two vehicles, with the aim of isolating the creation and loss of one link in the OLSR network. The second scenario considers a typical urban environment, where a building (or a set of them) hides the line of sight between the source and the destination cars (blue and black, respectively). A multihop network is suited in this kind of situations. A new vehicle (number two, in red color) forwards the messages received from the source vehicle to the destination one. In the third scenario the three vehicles move around this blockage area. The last scenario of Figure 3 (number four) uses the same vehicles over a highway environment.

Figure 4 shows the overtaking and four-vehicle scenarios. The fifth scenario considers static tests with four vehicles, where packets are always forwarded by two intermediate cars. A new car (the fourth one, in green) has been included. In the sixth scenario, an overtaking situation is tested, where the receiver car (number one, in black) and car two (in red) are parked, and the sender one (number three, in blue) passes them in the two directions two times. When the distance between the sender and receiver cars is too big, the direct link is lost, and the OLSR protocol setsup a multi-hop path using car two (in red) as a relay node. The sender car, after passing the last car in one direction, usually reaches a position where the communication is lost. The last scenario follows the same idea, but four vehicles are now used, using car four (in green) as another relay node. The parked vehicles are more separated now, to avoid non-desired direct links.

EVALUATION AND ANALYSIS

The VANET experiments described in the previous seven scenarios have been performed considering the UDP, TCP and ICMPv6 traffic types. Results of the experiments have been processed by AnaVANET and then showed with a graphical software. Multitude of plots have been generated and used in this section to analyse the main results of the vast experimental evaluation.

Web-Based Network Analysis

The carried out experiments are available in our public website5 , and they can be replayed to see the momentary performance of the network during the tests. Figure 5 shows a screenshot of the website. All the experiments can be selected and main performance metrics can be monitored at any time. Users can play and stop at any arbitrary point of the test with the control bottons on the left side of the page. The player speed, one step forward and one step backward are also implemented. On the map, the position and movement of the vehicle are depicted with the speed of each vehicle and the distance between them. The transferred data size, bandwidth, packet loss rate, roundtrip delay time and jitter, for each link and end to end are displayed. The user can see the network performance by attending the width of link lines and the colour used to draw them.

Maximum Range Tests

Maximum range tests have been performed with two cars through Scenario 1. The sender starts leaving from the receiver vehicle position (static), and then it comes back, at about 180 meters, to approach again to the initial point. The speed of the sender was maintained under 10 Km/h to smoothly check the loss of connectivity.

Figure 6 shows PDR in the case of the UDP transmission. Packets start to be dropped around 100 meters of distance. The last packet arrives around 120 meters away and, after this point, there are no delivered packets, until the sender vehicle comes back and reaches 100 meters of distance. Since periodical OLSR control messages are lost when the distance is around 120 meters, the path is removed of the routing table and the transmission ends at this point. The jitter in the same test is illustrated in Figure 7. When the sender car leaves the receiver one, at a distance between 75 and 120 meters, the jitter is higher, due to layer-two retransmissions caused by the increase of the distance. When the sender approaches the receiver again, this effect is again visible at distances between 100 and 50 meters. It is noticeable how the communication is lost at a point further away than it comes back. This is due to timeout periods in the reception of control messages give an extra time to maintain the communication link. When the vehicle comes back, some signalling traffic must be also exchanged before the routing table of the sender vehicle is updated.

The TCP performance over the same scenario is showed in Figure 8. As can be seen, only a one-way path has been logged. When the route is lost at 100 meters of distance, the TCP timeout expires and the transport layer link is broken. Finally, Figure 9 shows the RTT values collected in a Ping test over the same scenario, measured end to end. The base line of RTT is about 10 ms, but several peaks appear even under good conditions, due to route updates carried out by OLSR and the movement of the sender vehicle. The communication is again lost at a similar distance to the previous cases, however, it comes back earlier than in the UDP test. This is due to the network overhead is much lower in the Ping test (only one message per second), hence the OLSR signalling messages can be efficiently sent and the communication is reestablished earlier.

Static Tests

Static results using Scenarios 2 and 5 are summarised in Table 2, using three and four vehicles, respectively. The duration of all the tests was 15 minutes. The total distance between the sender and receiver cars was 120 meters (70 plus 50 meters) in Scenario 2, and 155 meters (50 plus 70 plus 35 meters) in Scenario 5. As can be seen, the UDP performance is almost ideal, considering that the emission of packets was fixed at a rate of 1 Mbps. Packet losses are not frequent, and the mean PDR is 99.99%. Small variances of performance are only due to route updates, noticeable in jitter values. In TCP results, the average bandwidth is 1.9 Mbps, what reveals a good performance too. However, frequent variations are evident if the standard deviation (STD) is considered. Since the vehicles are static and the network topology does not present variations, wireless conditions are considered to impact on the TCP performance. By means of the slow start mechanism, TCP dynamically adjusts the transmission rate accord- (ms)

ing to network performance, but this algorithm does not converge properly in wireless networks. Frequent packet losses, mainly due to interferences in the medium, and the presence of eventual route updates imply an unstable network environment for TCP. During all static tests, the wireless channel was chosen among all of them not used in the surroundings at the beginning of the trial, but interferences in the medium could not be avoided at all. Ping tests show the good two-way latency of the network. With three vehicles, the average RTT is 4.96 ms, but this value is exceeded when four vehicles are considered, reaching a mean RTT of 7.25. Hence, the addition of one hop increments the latency by more than 2 ms. The RTT standard deviation is also higher in the last case, due to the new node imply additional control traffic and, overall, new occasional route updates. Moreover, since the route from the source to the destination terminals comprises a linear path across the four MRs, as the number of nodes increases, the probability of finding routing or delay problems along the path is higher.

Dynamic Tests under Urban Conditions

According to Scenario 3, three vehicles have been driven around a set of buildings, with the intention of blocking the direct link between Cars 3 and 1. The speed of the test where set between 15 km/h and 30 km/h. The right and left roads illustrated in Scenario 3 are in reality very narrow, hence some communications problems appear in the corners. The results collected in the UDP test are plotted in Figure 10. The upper plot shows the number of hops used in the paths followed by UDP packets, whereas the lower graphs show the PDR, computed end to end and per link. PDR is calculated per second, while the number of hops is plotted for each packet transmitted from the sender node. When no hops are drawn, the route to the destination vehicle is not available. Zero hops means that the packet was sent by the first MR, but it was not received by any other. Negative values represent those packets which did not arrive to the destination vehicle, but some hops were reached. As can be seen, a direct relation exists between PDR and number of hops. When this last value is equal or lower than zero, the PDR decreases. When the vehicles are in the same street, some direct paths (one-hop) appear; however, when the distance between the sender and the receiver cars is large enough, the two-hop route is used. These different types of paths can be also seen if the perlink PDR is observed. Whereas the direct link (MR3-MR1) gives intermediate PDR values, the PDR between consecutive vehicles is almost identical and near 100% when the two-hop link is used, due to the lower distance between nodes.

Since communication problems appear at corners in some laps, OLSR signalling messages are lost, and the communication is temporary down. An interesting effect is also noticeable at time 250 seconds of the UDP test. Here, several paths with more than two hops are registered. This is due to routing problems of OLSR when the destination node suddenly disappear, what provokes cycles in the network. When the network topology is finally updated in all the nodes, these packets are finally dropped, if the receiver node is out of range, or they reach the destination. These cycles provoke a great eventual jitter, which is also highly variable in the rest of the test, due to stressful conditions.

The bandwidth obtained in the TCP test is showed in Figure 11. The performance of the network is very good in the first fifty seconds, due to the vehicles started the trial parked very near. However, the rest of the test shows a high variability, due to continuous changes in topology and communication problems in corners. When conditions are favourable, TCP tries to normalise the bandwith, but soon a link disappears and the bandwidth falls. Peaks of performance are obtained when the sender and receiver cars are in a direct line of sight. TCP timeouts do not expire because there are no long disconnection periods, hence the transport-level communication is maintained.

The final test (Figure 12) comprises a Ping transmission. As can be seen, several steps appear between two main RTT values: five and seven milliseconds. This match with two-hop and four-hop two-way paths. Several three-hop routes have been collected, due to, sometimes, the ICMP Echo Request packets take a different route than the Echo Reply ones. If the ratio of non delivered packets (negative hop counts in this case) is compared with the one obtained in the UDP test, it is noticeable how it is lower now. Since the data traffic is much more lower in the Ping case (one message per second), signalling traffic is more efficiently propagated, and changes in network topology are earlier known.

Dynamic Tests in Highway

The dynamic tests performed over highway conditions follow Scenario 4. The speed of the cars was around 100 km/h, but the distance between vehicles was variable, due to the rest of traffic on the road. Moreover, communica-tion problems in this test are not only due to buildings, but also to surrounding vehicles.

The PDR obtained in the UDP test is presented in the lower part of Figure 13. As can be seen, when the distance between vehicles increases, the PDR becomes lower. As in the urban scenario, intermediate values between 0 and 100% are not very frequent, due to OLSR remove the routes between nodes when signaling packets are lost. At the beginning, the network performance is good, due to the direct path is chosen, as can be seen in the partial PDR study of the MR3-MR1 link. When vehicles start to separate, the two-hop path is used, as it is showed in the PDR of MR2-MR1 and MR3-MR2 links and the number of hops of chosen paths, showed in the upper graph. High variations of distance provoke route updates and, therefore, packet losses. Around 300 seconds of test, vehicles regroup, but the three-hop path is maintained, due to the time OLSR needs to adapt to the new topology. The high variability of distance around time 350 seconds, makes the network does not stabilise and many packets are lost. A higher period of 0% of PDR is noticeable, however, around 150 seconds of test. In this case, the communication between the sender vehicle and the others is blocked by a near building.

The bandwidth results of the TCP test are showed in Figure 14. The vehicles are grouped at the beginning of the tests and the bandwidth is around 5 Mbps. However, when Car 3 enters the highway and the distance with the other two cars increases, the bandwidth dramatically falls. As can be seen during the whole test, there is again a direct relation between the distance of vehicles and the final performance. Taking into account the maximum range and static tests, it is easy to identify in the graph the moments in which a three-hop path is used. Bandwidths around 2 Mbps represent these cases, whereas results between 4 and 5 Mbps belong to direct paths.

Finally, Figures 15-16 show the results collected during the Ping test. As can be seen, the RTT increases when the vehicles are far enough to use a four-hop two-way route. At this moment, the RTT passes from around three milliseconds to reach the five milliseconds. It is advisable again, how intermediate RTT values are not frequent, being the number of hops the main factor which determines the result. When the distance among vehicles grows and communication starts to be difficult, the links between MRs break, due to losses of OLSR signalling messages.

Overtaking Tests

The overtaking tests using three and four vehicles have been carried out according to Scenarios 6 and 7. Two and three cars, respectively, were parked at a straight avenue, to simulate they are driving at the same speed, and the sender vehicle overtakes them several times in both directions (see Figure 4).

The results of the UDP test with three vehicles are depicted in Figure 17. The distances are calculated taking into account the moving vehicle (Car 3) as the reference. It can be seen that two-hop routes appear when the sender vehicle is around the non receiver one. However, during periods of route updates, packets are not delivered. Since the parked vehicles are in an open area and they have a direct line of sight, there are no practically packet losses in the MR1-MR2 link. It is advisable how the number of correctly delivered packets is greater between peaks of distance, but shifted to the left. This is due to the time required by OLSR to adapt to the new topology. Therefore, the best results are obtained when the routes are maintained for a long time. This is the case when the sender car comes back after "overtaking" the other two, since the appropriate route was established when the sender vehicle passed them. Figure 17 also reflects that a high jitter is maintained during all the test, due to high dynamism of the network. At the beginning, jitter starts to increase when the sender vehicle goes away of its initial position and, during the rest of the test, it is highly variable due to route updates.

The bandwidth results of the TCP test are plotted in Figure 18. As in the previous TCP tests, the two characteristic values around 5 and 2 Mbps are again visible when one-hop and two-hop routes are established, respectively. As can be seen, the direct path is used when the distance between the sender and receiver cars is lower. The distance curves are now a bit different, because the sender vehicle comes back earlier after passing both cars, in order to maintain the TCP session.

Two ping tests with three and four vehicles were made following the same overtaking pattern. Figure 19 shows the results of the first one. RTT fluctuations between three and five milliseconds, depend wether the two or four-hop two-way paths are chosen. Some three-hop paths have been collected, due to the different path taken by some Echo Request and Echo Reply messages. As can be seen, the behaviour of the network is more regular than in the UDP case, and packet losses are mostly due to peaks of distance. This is explained again by the low data traffic, which allows OLSR control messages to be efficiently transmitted. This way, route updates due to topology changes are made faster. In the four-vehicle test of Figure 20, the paths are more varied. However, one-way paths of three hops are not frequent. OLSR bet on maintaining two-hop paths when communication is possible, hence Car 2 is bypassed when it is "overtaken" the first time. In the second passing of this car, some two-way paths of six hops are collected, however. More packet losses have been collected than in the previous Ping test, because the parked vehicles were further separated to avoid direct paths among them.

The work presented in this paper offers a complete testbed for VANET evaluation, suited to carry out performance trials over the IPv6 basis, but, overall, it gives an original evaluation of an ad-hoc routing protocol in the vehicle domain. The platform enables the researcher to analyse the network performance at low level. Several logs collected from individual mobile routers are post-processed to calculate several performance metrics at link, network and transport level. This way, typical statistics are obtained, such as the packet delivery ratio, round-trip delay time, jitter and bandwidth; but also new performance metrics are offered, such as the number of hops used to deliver a packet, or the per-link PDR, for example.

Up to four vehicles have been set-up to perform multitude of tests in the surroundings of INRIA Ronquencourt. These cover both urban and highway environments, and take into account static and dynamic conditions. Main results of all these field trials have been analysed in the paper. The results show the great performance difference which can be found if a routing protocol is used in VANET evaluation, in comparison to previous experimental analysis available in the literature based on static routes. Although it has been tuned to dynamic conditions, the OLSR protocol shows limitations to efficiently update routing tables under stressful conditions. This effect is more noticeable when the volume of data traffic is high, due to network overload. The maximum communication range between vehicles also presents a different pattern, if we compare the results with the ones obtained in static route configurations. Now, the communication is not possible when some control messages are lost and OLSR timeouts expire. Hence, obtaining medium/low PDR results is less frequent than in static route tests, due to, when a great part of messages start to be lost the routes become directly unavailable.

The TCP operation over real VANET deployments should be specially taken into account, because the lack of routing information for a while can lead to transportlevel disconnection. In all the tests, the line of sight between vehicles has been a key factor to maintain communication links. Moreover, the number of hops has been identified as another key performance factor. An incremental delay between two and three milliseconds per hop has been detected when direct paths between nodes are not used. These cases can be found when the distance between sender and receiver vehicles increase significantly, or when near buildings block the direct communication. However, it is expected that this increment in delay follows a quasiexponential increase when more vehicles are in the communication range, due to interferences. Moreover, according to the experiences with four nodes, it has been checked that OLSR prefers smaller paths when communication is possible. This has been checked when an overtake scenario has been emulated, with a vehicle passing three cars in an open area.

In the future, the data recorded during the set of tests will be further exploited, considering, for instance, the impact of driving speed in the final performance and the increase in signaling traffic when OLSR parameters are tuned for the vehicular environment, as it has been explained. A more VANET-oriented protocol developed at INRIA will be also evaluated through new field trials, using the presented test-bed. This is located inside the geographic-based routing proposals, which are demonstrating to be the correct direction in vehicular network research. New wireless devices compliant with current 801.11p specifications have also been acquired in order to perform a new set of trials which can be compared with the results obtained in this work. The different traffic priorities available in 802.11p will be evaluated for propagating signaling and data traffic among nodes. At the University of Murcia, ongoing cellular network evaluations will be soon complemented with WiMAX trials in the vehicular frame, thanks to a current project to deploy a WiMAX infrastructure in the Campus of Espinardo.

Figure 1 :

 1 Figure 1: Equipment used in tests.

Figure 2 :

 2 Figure 2: System overview and data processing units.

Figure 3 :

 3 Figure 3: Maximum range and three-vehicles tests.

Figure 4 :

 4 Figure 4: Overtaking and four-vehicles tests.

Figure 5 :

 5 Figure 5: Screenshot of the Report Website.

Figure 6 :

 6 Figure 6: UDP range test with 2 cars (dist./PDR).

Figure 8 :

 8 Figure 8: TCP range test with 2 cars (dist./band.).

Figure 9 :Figure 11 :

 911 Figure 9: Ping range test with 2 cars (dist./RTT).

Figure 12 :

 12 Figure 12: Ping urban test with 3 dynamic cars (hops/RTT).

Figure 13 :Figure 14 :

 1314 Figure 13: UDP highway test with 3 cars.

Figure 15 :

 15 Figure 15: Ping highway test with 3 dynamic cars (RTT/dist.).

Figure 16 :

 16 Figure 16: Ping highway test with 3 dynamic cars (hops/dist.).

Figure 20 :

 20 Figure 17: UDP overtaking test with 3 cars.

Table 1

 1

	: OLSR configuration parameters
	Parameter	Value (s) Default (s)
	Hello Interval	0.5	2.0
	Hello Validity Time	6.0	6.0
	TC Interval	3.0	5.0
	TC Validity Time	9.0	15.0
	MID Interval	5.0	5.0
	MID Validity Time	15.0	15.0
	HNA Interval	3.0	5.0
	HNA Validity Time	9.0	15.0
	prepared to consider any number of vehicles. The sender
	laptop is in charge of generating data traffic, and both the
	sender and the receiver save a high level log, according to
	the application used to generate network traffic. All MRs
	save information about forwarded data packets, by means
	of the tcpdump software 3

Table 2 :

 2 Network performance in static tests

	Test Metric	Min.	Ave.	Max. STD
	UDP PDR	98.84	99.99	100	0.11
	3 v.	(%)
		Band.	545.20 1001.59	1020.8 34.15
		(Kbps)
		Jitter	0.14	0.57	5.57	0.78
		(ms)
	TCP Band.	327.68 1915.95 2282.24 359.1
	3 v.	(Kbps)
	Ping RTT	4.00	4.96	23	1.38
	3 v.	(ms)
	Ping RTT	6.00	7.25	19	1.49
	4 v.

STATE OF THE ARTBecause of the drawbacks described above, literature in experimental evaluation of VANET architectures is limited, although these works are of key importance for the ITS community. Up to now, there are several works dealing

http://www.ietf.org/html.charters/manet-charter.html

http://www.olsr.org/

http://www.tcpdump.org/

http://dast.nlanr.net/Projects/Iperf/

http://fylvestre.inria.fr/∼tsukada/experiments/vanet-jose/

CONCLUSIONS

ACKNOWLEDGMENTS

The Authors would like to thank the Ministerio de Ciencia e Innovación for sponsoring these research activities under the grant TIN2008-06441-C02-02. This work has been partially carried out inside the Intelligent Systems group of the University of Murcia, awarded as an excellence researching group in frames of the Spanish Plan de Ciencia y Tecnología de la Región de Murcia (04552/GERM/06).


T William Bentley
email: t.w.bentley@swansea.ac.uk

Keywords: nucleophilicity scales, Swain-Scott equation, nucleophiles, benzhydrylium cations, quinone methides nucleophilicity scales, Swain-Scott equation, nucleophiles, benzhydrylium cations, quinone methides

Nucleophilicity parameters for strong nucleophiles in dimethyl sulfoxide. A direct alternative to the s(E + N) equation

T.

INTRODUCTION

The general equation (1) has recently been proposed to correlate logarithms of rate constants (log k) at 20 ˚C for a huge range of reactions of electrophiles (electrophilicity E) and nucleophiles (nucleophilicity N); in Eqn (1), s N is referred to as a 'nucleophilespecific' parameter and s E as an 'electrophile-specific' parameter. [1,2] It is then assumed that s E = 1 for many reactions, so 'deriving' Eqn (2) which had already been used in plots of log k vs. E to evaluate values of s N (from slopes) and N (from the intercept on the abscissa) for over 100 nucleophiles. [3,4] Originally [1][2][3][4] the symbol s was chosen for Eqn (2), but it is not the same as the s (or s E ) parameter in the well established Swain-Scott equation (3). [5] Consequently s N is more appropriate than s for Eqn (2). Equation (4) fits many cationanion recombinations, [6] and the absence of an response parameter is consistent with the assumption [1,2] that s E = 1. In Eqns (3) and (4), n or N + quantify nucleophilicity, and k 0 refers to a reference reaction, so relative rates are correlated. (1)

log k = s N (E + N) (2) log k/k 0 = sn (3) log k/k 0 = N + (4)
The question 'How constant are Ritchie's constant selectivity relationships' was the title of a recent paper, [7] concluding that s E is constant if anomalous data for water are excluded. Recognising this problem earlier, Ritchie proposed [6] that the reference nucleophile (rate constant k 0 ) be hydroxide, instead of water which was chosen in earlier work [8] in line with Eqn (3). There are various N + scales, [6] and ideally the reference electrophile should be specified when N + correlations are reported.

Published work [3,4] on N scales uses values of E for a 'basis set' of 23 reference electrophiles; the electrophilicities of seven benzhydrylium cations, ranging in values of E from 0 to 6 were defined by rate constants for reactions with 2-methylpent-1-ene, [3] and values of E down to -10 (along with N values for 38 nucleophiles) were then obtained by a multi-parameter extrapolation procedure (MPC1, Scheme 1). [3] Plots of log k vs. E for individual nucleophiles then gave new values of N. This complex procedure (upper half of Scheme 1) leads to a floating scale when s N ≠ 1, referring to dichloromethane (DCM) as solvent at 20 ˚C: (i) which deviates from a fixed scale by 5 orders of magnitude; (ii) in which none of the >200 parameters are defined by directly-determined experimental data. [9] Reference [3] and MPC2 is based on References [11, 12]; there are 6 MPC3 correlations (3a, 3b etc) in References [13 -18] An alternative design was reported recently; [9] two benzhydrylium cations were chosen to define N′ and N′′ directly from experimental data (Eqns ( 5) and ( 6)), and the two fixed scales were linked by the formula N′ -N′′ = 6.6. To avoid complications from solvent effects, [10] only kinetic data in DCM were evaluated. [9] log k = N′ for decay of 1n, at 20 ˚C (5) log k = N′′ for decay of 1a, at 20 ˚C (6) To further extend the N scale to reactions of carbanions and other nucleophiles in dimethyl sulfoxide (DMSO), six cations (1a -1f) and seven quinone methides (QM, 1g -1m) were chosen [11,12] as reference electrophiles (the codes 1a -1m in Scheme 2 are the same as in the key paper [11] ). Kinetic data for reactions of these electrophiles with key nucleophiles (Scheme 3) underwent another correlation (MPC2, Scheme 1), further

extrapolating the E scale from -10 to -18. [11] The derived N values were then the input for MPC3a, MPC3b etc, characterising E values for other electrophiles from E = -8 to -23. [13- 18] Finally, log k vs. E plots gave additional values of N for stronger nucleophiles. [19][20][21][22][23][24][25] Using Eqn (2) the slope defines s N and intercept on the abscissa defines N, so residual errors are incorporated into the parameters, and when s N ≠ 1 the N scale 'floats'

(the reference point is variable and hypothetical). Consequently, it is virtually impossible to define the parameters, and revision of one input rate constant in MPC1 would affect hundreds of other parameters. This procedure is indirect (N values are obtained from the E scale) and requires long extrapolations, exacerbating errors inherent in a simple model.

A much simpler alternative design, avoiding a floating scale and requiring much shorter extrapolations, will now be presented using the same published kinetic data. [7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] The results will complete the alternative design, [9] will lead to a N′′′ scale in DMSO (fixed 6 not floating), and will show (contrary to recent claims [1,2,7] ) that the electrophile parameter (s E ) varies significantly. Selection of the mid-range electrophile (1a) as reference for a unified N′′ scale (linked to N′′′ and N′) will also be discussed.

RESULTS

N′ (Eqn ( 5)) refers to the reactions of the relatively reactive dianisyl cation (1n, Scheme

2), for which E = 0, giving N′ values for very weak nucleophiles (e.g. arenes). [9] The less reactive dimethylaminobenzhydrylium cation (1a) gives N′′ (Eqn ( 6)) for more reactive nucleophiles (e.g. enamines). [9] N′′′ for even more reactive nucleophiles including carbanions will now be evaluated from cation (1f) using Eqn (7) and from additional Swain-Scott type correlations (Eqn ( 8)) for the auxiliary reference QM (1m). to Eqn (2); [11] [11,[13][14][15][16][17][18] The data including QMs (1g -1m) were processed [11] by MPC2, assuming the same E values of cations (1a -1f) from previous work [11] in DCM; 21 adjustable parameters (E values of 7 quinone methides (QM, 1g -1m) and s N and N values for 7 enolates, 2a -2g, Scheme 3) were obtained from 70 data points, [11] (additional rate constants for MeCHNO 2 -reacting with 1k. 1l and 1m were included in MPC2 [11] ).

In contrast, values of N′′′ (Eqn (7)) can be obtained directly from experimental data; [11,12] considering Eqn (8) when N′′′ = 0, log k = E′′′ + c = 0, so no adjustable parameters are required at this stage. Values of N′′′ and N (Eqn (2)) show that N -N′′′ increases as N increases (Table 1), as expected for a floating N scale. [9] Values of N′′′ for 27 additional nucleophiles (Scheme 4) were also calculated (Table 2) from data published later, [7,[19][20][21][22][23] giving a total of 34 values of N′′′ from Eqn (7) in Tables 1 and2. Correlations using Eqn (8, Tables 3 and4) require 24 2 and5)

The data in Table 3 were obtained using Microsoft Excel, and show slopes, intercept, correlation coefficients (r) and number of data points (n). The slopes show that s E is very close to unity, but the data vary from extensive (n = 19) for 1e, for which the correlation is very good, to less convincing for 1a and 1b because n ≤ 5 (also, despite their small number the range of nucleophiles is diverse (Table 3 footnotes d and f)).

Correlations using Eqn (8) for QMs (1g -1m) reacting with carbanions (Table 4) include rate constants for 1l and 1m covering less than 2.5 log units; the data show 'scatter' when the additional nucleophiles are included; the distribution of data points also increases uncertainties in the values of intercepts (E′′′ + c), because extrapolations are required from typical values of N′′′ (> 3.0) to N′′′ = 0. Another indication of the reliability of the correlations is the standard errorsthe worst is small (0.27 for 1l). In contrast to the data in Table 3, the results show a substantial increase in s E (selectivity) as E′′′ (reactivity) decreases. 3), it is predicted that log k calc = 2.22 (log k obs = 2.02 [21] ) for reaction of 1d with the ylid Ph 3 PCHCO 2 Et; however, reaction of the ylid with 1h is predicted to be slower than observed (log k calc = -1.04, log k obs = 0.03 [21] ).

Eqn (9), based on the first entry for 1m in Table 4, was then applied to estimate N′′′ values for 10 more reactive nucleophiles by extrapolation (Table 5). Provisional data for 3 other nucleophiles are estimated from correlations for other QMs (1h. 1j and 1k).

N′′′ = (log k (for 1m) -8.0)/1.43 (9)
Having obtained values of N′′′ for 34 nucleophiles from the same reference nucleophiles and electrophiles as LLM (Schemes 2 and 3), [11] correlations using Eqn (8) were carried out for 19 other electrophiles (Table 6); these all involve Michael additions to structurally-similar substrates (10 -18), Scheme 5. Correlations for 5 additional QMs (Scheme 6) reacting with key carbanions (Scheme 3) are shown in Table 7.

Intercepts refer to N′′′ = 0, and errors for neutral substrates (Tables 6 and7) are relatively large because long extrapolations from N′′′ ~ 5 are often required. Calculated values agree better than expected from the errors in individual parameters: e.g. for Michael addition of 9 to 10, Z = OMe, the two entries (Table 6) for Eqn (8) predict log k = 6.03 and 6.09, in agreement with the Eqn (2) prediction of 6.14; the experimental value is only 5.26, [24] and as noted earlier [22,24] Michael acceptors react more slowly than expected from parameters based on cations and QMs (e.g. see Table 6, footnotes h and j).

Nucleophilicity parameters for amines (Table 2) can be used to predict rate constants for Michael additions (kinetic data for amines were not included in the 6). Predicted rate constants by either Eqn (2) or Eqn (8) for reactions of amines with 12, Z = H agree satisfactorily with experimental values. [14] However, primary and secondary amines react with 16 about 100-fold faster than predicted, perhaps because of transition state stabilisation by H-bridges. [16] O 8)) for over 300 rate constants in DMSO at 20 ˚C show good correlations for benzhydrylium ions (Table 3) and QMs (Tables 4 and7), but are less satisfactory for Michael additions (Table 6). As for other cations, [6,8] the parameter s E is approximately constant (s E =1.00, Table 3), but s E varies between 1.0 and 1.5 for QMs (Tables 4 and7). Nucleophilic attack on activated 9-methylenefluorenes is known to give slopes > 1 in plots vs. N + , [26] and the tri-p-anisylmethyl cation has a lower response to changes in N + than less reactive cations (crystal violet or malachite green). [27] In general s E ≠ 1.00, [28] so Eqn ( 4) is a special case, and a selectivity parameter should be incorporated into the Ritchie Eqn (4). [26,27,29,30] Consequently, it is not appropriate to 'derive' Eqn (2) by setting s E =1.00 in Eqn (1), [1,2] and to then apply Eqn

O H C + X X X X _ 19a, Y = 3-F, X = Bu t , E = -15.03 19b, Y = 3,5-F, X = Bu t , E = -14.50 19c, Y = 4-NO 2 , X =
(1) to other electrophiles. [11,12] Despite the questionable derivation, Eqn (2) is a useful way to predict structural effects on reactivity using the E scale of electrophilicity and the substituent effect parameter (s N ), assuming that the 'electrophile specific' parameter s E = 1.00. [1][2][3][4]7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] The alternative assumption that s N = 1.00 leads to a variation on the Swain-Scott equation (Eqn ( 8)) and gives more reliable values for nucleophilicity parameters. [9,10] The two approaches are different ways to locate a point in 3D space, and s E and s N are interdependent parameters. [9,10] N′′′ correlates satisfactorily with pK a for 27 nucleophiles in DMSO (Figure 1). enolates (2a, 2b, 2c and 2g) fit a parallel line (such family behaviour is typical [35] ). The remaining eight nucleophiles (all nitro-stabilised) are close to the two correlation lines, but show distinct curvature possibly due to the failure of pK a to model the kinetic phenomena of desolvation. [35] The value of  = 0.35 ± 0.04 (Figure 1) for reactions of 1f with nucleophiles, is the same within errors or slightly lower than the value of = 0.40 [33] for reactions of n-butyl chloride reacting with benzyl phenylsulfonyl carbanions. Both  and s E show the effect of varying the nucleophile for a fixed electrophile, so an S N 2 reaction is responding more than a cation-anion recombination. A correlation of N + (Eqn (4)) with n (Eqn (3)) in water has a slope of 2.0 [36] or 2.1. [37] So, in contrast to the results in DMSO, cation-anion recombinations (N + ) in water are twice as sensitive as S N 2 reactions (n) to variations in nucleophilicity.

For nucleophilic additions to the QM (1l) in DMSO,  = 0.58 [22] (or ~ s E x 0.35 = 0.50), again illustrating that s E > 1 for QMs (1, 19). QM (20) may be treated as a strongly resonance-stabilised carbocation; [36] for nucleophilic additions to 20 in water, an N + correlation has slope (s E ) of only 0.92, [36] fitting the trend that more reactive QMs have lower values of s E (Tables 3 and7).

CF 3 F 3 C O + CF 3 F 3 C O 20 _
When N′′′ is defined directly by Eqn (7), values of N = N -N′′′ for the key carbanions (Table 1) vary by 3.1 log units, whereas the total range of values of N′′′ is only 3.2; the additional nucleophiles in Table 2 also show substantial variations in N (Table 2). When the extrapolated data for more reactive carbanions is included, values of N range from 10.5 (Table 1) or 10.8 (Table 2) to 18.9 (Table 5). The floating N scale varies from 12.15 (Table 2) to 28.95 (Table 5), and all of the correlations (MPC2, 2, 3a 3b, 3c etc, Scheme 1) are needed. For the same range of nucleophiles, the fixed N′′′ scale varies only from 1.35 (Table 2) to 10.1 (Table 5). The above calculations indicate that during the complex sequences of processing of the kinetic data (Scheme 1), the N scale floats by 8 orders of magnitude away from the initial reference point (1n). It was mentioned over a decade ago that N is a floating scale, [38] but the large extent of floating has only recently been highlighted. [9] Theoretically, it should be possible to correct from the floating N scale to a fixed scale s N N. However, this requires a high level of confidence in a long extrapolation of complex substituent effects, [39,40] and neglect of solvent effects. In practice, s N N does not give a satisfactory trend with pK a for arylacetonitriles (Table 8), and, these carbanions also deviate from a plot of N vs. pK a . [23] in contrast to N′′′ (Figure 1).

Constant selectivity plots and electrophilicity parameters

The chosen methodology [9,10] (Case 1: fix E, vary N, extrapolate to estimate E) is designed to lead to a reliable scale of nucleophilicity, with most of the errors incorporated into the extrapolated values of E′′′ + c. In contrast, published procedures (Case 2: fix N, vary E, extrapolate to obtain N [3,7,[19][20][21][22][23][24][25] ) lead to less reliable values of N, which include most of the errors. Both cases are based on the assumptions that log k depends on parameters for electrophilicity and nucleophilicity. Consequently, published values of E should be closely related to the extrapolated values of E′′′ + c, as observed (Figure 2).

The slopes of the correlation lines for reactions of the key carbanions with benzhydrylium ions (Table 3) and QMs (Table 4) are both 1.00 within calculated errors (Figure 2), but there is a separation between the two lines corresponding to 0.5 units on the x-axis. These results, coupled with the variations in s E for QMs (Table 4), are unexpected. Therefore the constant selectivity plots, which are the foundations of Eqn (2), [41] were reinvestigated. The constant selectivity plots for QMs [12] are based on data for only 4 QMs (1j -1m), and slopes (based on limited data) vary from 0.81 for 2a to 12 for 2c and 2d, relative to log k for 2f as the model nucleophile for an E scale. These results were shown [12] in a graph omitting numerical values of the slopes, and the interpretation was made that the correlation lines are 'parallel'. [12] -10 3) and quinone methides (1g -1m, Table 4); the slopes of the correlation lines are 0.996 ± 0.050 (n = 6,excluding 1a, r = 0.996) and 0.984 ± 0.034 (n = 6, r = 0.997) respectively; data from Tables 6 and7 are plotted for comparison (not fitted to correlation lines)

Combining two sources of experimental data [11,12] leads directly (without 'optimisation') to an E scale spanning 7 orders of magnitude in which QMs are for the first time included on the same selectivity plots as benzhydrylium ions. The 'E scale' (Figure 3) is defined by log k for 2b, the only nucleophile for which kinetic data for all cations and QMs (1a -1m) are available.

The slopes of correlation lines vary from 0.96 to 1.13 (Figure 3), are dominated by QMs, and cations show deviations (e.g. for 2g). Despite the idea that QMs are activated [11,12,36] there is not a seamless connection between these reference electrophiles (see also Figure 2). MPC2 [11] is able to adjust E to enforce a fit to Eqn (2), but this procedure does not give confidence in extrapolations needed to obtain N. ˚C; slopes (errors: ± 0.02, r = 0.999) refer only to QMs; data from References [11,12] Sufficient data are available to permit the calculation of s N and N for 4 key nucleophiles (2a -2d) from standard plots [3,7,[19][20][21][22][23][24][25] of log k vs. E for benzhydrylium ions; values of N require a long extrapolation, and are significantly different (Table 9) from those obtained by MPC2 which includes data for QMs. Because of a leverage effect, s N is determined mainly by QMs, not benzhydrylium cations, and the differences in slopes (Figure 3 and s N , Table 9) show that s N is not exactly 'nucleophile specific'. Also, unlike Eqn (8) which utilises a different equation to calculate parameters, the differences in Table 9 are due solely to the exclusion of QMs from the data processing to fit Eqn (2).

Towards a unified N′′ scale of nucleophilicity

As expected from N + correlations, [6,8] slopes (Table 3) are close to unity for reactions of cations (1a -1f) with nucleophiles, and this allows connections to be made between the N′, N′′ and N′′′ scales (Eqns (5 -7)). Data for five nucleophiles (Table 3, footnote f) are available in DMSO for both 1a and 1f, giving N′′ -N′′′ = 2.2 ± 0.2 in DMSO. However, the scope of a unified scale for addition of nucleophiles to cations in DMSO is limited by the relatively high nucleophilicity of DMSO (N = 9.75 in acetonitrile [25] ), so by this measure DMSO is more nucleophilic than water or typical alcohols, but less nucleophilic than amines (Table 2). Therefore, changes of solvent and consideration of solvent effects on rates is also required.

Cation-anion recombinations are the reverse of S N 1 reactions, and solvent effects are likely to be significant, particularly for protic solvents. [9,42] Considering only data for aprotic solvents, 22 values of N′′ -N′′′ are available in DCM, giving N′′ -N′′′ = 2.4 ± 0.4, a slightly greater ratio than in DMSO. Reactions of the ylid Ph 3 PCHCO 2 Et, [43] are faster in DCM than in DMSO, and the kinetic effect is larger for 1a, N′′(14-fold) than 1f, N′′′(5fold); reaction of PPh 3 with 1a is also faster (4-fold) in DCM than in DMSO. [44] Carbanion 3, Z = NO 2 reacts about 10-fold faster in acetonitrile than DMSO, so presumably reactions in DCM will also faster. [20] In contrast, other reactions are favoured by solvents with a higher donor number (e.g. ethyl diazoacetate reacting with 1a [45] ); also reactions of amines are faster in DMSO than in acetonitrile (e.g. only 1.4 fold for piperidine and 1f, but 22-fold for CF 3 CH 2 NH 2 and 1a), [7,18] so presumably reactions in DCM will be slower than in DMSO. It appears that corrections for solvent effects in aprotic media will be relatively small, but not insignificant. No other generalisations will be attempted at this stage, because it is not easy to predict even whether rates will increase or decrease. If as a first approximation solvent effects are ignored (as proposed earlier [3] ), connections (Scheme 7) can be made from N′′ to N′′′ and to N′ [9] (= N, when the N scale is correctly attached to the fixed reference point 1n in DCM).

A unified, scale (N′′) is suggested, based on the less reactive electrophile (1a) in DCM at 20 ˚C as the fixed reference. [9] The N′′ scale spans over 22 orders of magnitude from 12.3 for 8, Z = H (N′′′ = 10.1, Table 5) to -10.1 for m-xylene (N′ = -3.5 [9] ), so 1a is located centrally; [46] the corresponding N values are 28.9 [23] and -3.54 [3] with N′ or N′′ in dichloromethane [9] In general, it is not necessary to use a floating scale such as Eqn (2) to design a reactivity scale spanning 20 orders of magnitude. Three reference substrates (e.g. 1a, 1f, substrates and to halides for more reactive substrates. [47] Second order rate constants have the advantage that they can be obtained from pseudo-first order rate constants, and reactivities can be controlled by varying the concentrations of nucleophiles.

Simple additivity rules [48] for estimating orders of magnitude of rates of reactions of electrophiles with nucleophiles can be devised using Scheme 7: e.g. Eqn (10), based on the N′′′ scale and the established E scale. [3,11] Values of (N′′′ + 9) for 7 and 8 are 2 -4 orders of magnitude larger than s N N (Table 8), the hypothetical values of log k when E = 0.

log k ~ E + N′′′ + 9 (10)

CONCLUSIONS

Up to 8 multi-parameter correlations, [3,11,[13][14][15][16][17][18] 3 of which are consecutive (Scheme 1), are required to extend the E scale of electrophilicity from a well defined region between E = 6 and E = 0, all the way back to E = -23.8. [17] Subsequent calculations of N for strong nucleophiles give values which deviate from a fixed scale (N′′′, Eqn 3) and quinone methides (Tables 4 and7), but precision is lower for Michael additions (Table 6). N′′′ also gives a satisfactory Brønsted plot (Figure 1).

Future work based on Eqns (6 -8), with greater emphasis on s E , [27][28][29] should reveal solvent effects on electrophilicity for strong electron pair donor solvents such as water and alcohols. Currently, [3,11] s E = 1.00 is assumed incorrectly ( b Calculated from Eqn (7) and kinetic data referenced for each nucleophile.

c N = N -N′′′.

d Reference [7].

e Reference [21].

f Reference [25].

g Reference [20].

h Reference [19].

i Reference [22]. e The rate constant for reaction with 2g was assumed to be 69.9 M -1 s -1 (not 699, shown in Table 2 [12] ), in accordance with the constant selectivity plot (Figure 2 of Reference [12]).

F
f After deletion of the data points for (EtO) c N = N -N′′′.

d Reference [23].

e Reference [24].

f Reference [19].

g Reference [22]. given in Scheme 2, but the kinetic data were obtained [18] years after MPC1; [11] values of

F

E

  s E s N (E + N)

Scheme 1 .

 1 Scheme 1. An outline of the data processing by multi-parameter correlations (MPC) and

Scheme 2 .

 2 Scheme 2. Codes and electrophilicities for the 6 benzhydryl cations (1a -1f,) and 7

10 From

 10 the equation for 1d (Table

Scheme 5 .

 5 Scheme 5. Additional electrophiles for correlations shown in Table6

YScheme 6 .

 6 Scheme 6. Additional quinone methide (QM) electrophiles for correlations shown in

Figure 1 .

 1 Figure 1. Brønsted plot (N′′′ at 20 ˚C vs. pK a at 25 ˚C ) for 27 carbanions in DMSO. N′′′

Figure 2 .

 2 Figure 2. Plots of E (Scheme 2) vs. E′′′ + c for benzhydrylium cations (1a-1f, Table3)

Figure 3 .

 3 Figure 3. Log k for reactions of 2a, 2c and 2g vs. corresponding data for 2b, reacting

Scheme 7 .

 7 Scheme 7. Interconversion factors (increments of log k) for N′′′ in DMSO (this work)

20 1n)

 20 are sufficient; e.g. a unified data set for bridgehead reactivity spanning 10 23 in first order rate constants was established for tosylates, linked to triflates for less reactive

( 8 )

 8 ) by up to 8 log units (see values of N -N′′′ in Tables 1. 2 and 5), an extent of floating amounting to half of the whole range of N values in DMSO. In contrast, the N′′′ scale based on directly-defined values (Eqn (8)), can be extended by a much shorter extrapolation (Eqn (9)). Good N′′′ correlations using Eqn (8) are observed for cations

b

  Based on Eqn(9) and kinetic data in references shown for each nucleophile, except for the 3 values in parentheses which are estimated from correlations for quinone methides (1h, 1j and 1k).

Table 7 ;

 7 values of E from Reference[18]

	DISCUSSION
	Comparisons of s
	F o
	r
	P
	e e r
	R e v i e w
	12

E with  and of N′′′ with N N′′′ correlations (Eqn (

Table 4

 4

	), and solvent

Table 1 .

 1 Comparisons of N and N′′′ for seven key carbanion nucleophiles in DMSO at 20

	˚Ca
	Nucleophile b	N c	N′′′ d N e
	2a	13.91 3.41 10.50
	2b	16.27 4.78 11.49
	-CH(COMe) 2 (2c)	17.64 5.52 12.12
	2d	18.82 6.08 12.74
	-CH(CN) 2 (2e)	19.36 6.25 13.11
	2f	19.62 6.38 13.24
	-CH(CO 2 Et) 2 (2g)	20.22 6.61 13.61

a Kinetic data from References

[11,12]

.

b See Scheme 3.

c From Eqn (2) and Reference

[11]

.

d From Eqn

(7)

, this work.

e N = N -N′′′.

Table 2 .

 2 Comparisons of N and N′′′ (Eqn (7)) for additional nucleophiles in DMSO at 20

	˚C
	Nucleophile	N a	N′′′ b N c
	CF 3 CH 2 NH 2	d	12.15 1.35 10.80
	ylid Ph 3 PCHCO 2 Et e	12.21 1.40 10.81
	H 2 NCH 2 CO 2 Et d	14.30 2.89 11.41
	EtCH(NH 2 )CH 2 OH f	14.39 2.92 11.47
	PhCH 2 NH 2	f	15.28 3.40 11.88
	MeCH(OH)CH 2 NH 2	f	15.47 3.52 11.95
	Pr n NH 2	d		15.70 3.59 12.11
	NH 2 CH 2 CH 2 OH f	16.07 3.67 12.40
	(HOCH 2 CH 2 ) 2 NH f	15.51 3.79 11.72
	3, Z = NO 2	g	14.49 3.83 10.66
	morpholine d	16.96 4.66 12.30
	4, Z = 4-NO 2	h	16.29 4.71 11.58
	3, Z = CN g	16.28 4.83 11.45
	piperidine d	17.19 5.05 12.14
	4, Z = 4-CN h	16.96 5.21 11.75
	3, Z = CF 3	g	17.33 5.37 11.96
	(EtO) 2 P(O)CH -CN e	18.57 5.56 13.01
	(EtO) 2 P(O)CHC(O -)OEt e 19.23 5.76 13.47

a From Eqn (2) and kinetic data referenced for each nucleophile.

TABLE 3 .

 3 Correlations (Eqn (8)) of second order rate constants for reactions of benzhydrylium ions (1a-1f) with carbanions and amines in DMSO at 20 ˚C with N′′′ a The nucleophiles are 2a, 2b, 2c, (3, Z = NO 2 ), and ylid Ph 3 PCHCO 2 Et. CF 3 CH 2 NH 2 , H 2 NCH 2 CO 2 Et, and ylid Ph 3 PCHCO 2 Et.

	Cation b	s E	E′′′ + c	r n
	(lil) 2 CH + (1f) 1.00 c	0.0 c
	(jul) 2 CH + (1e) 0.96±0.02 0.62±0.08 0.999 7
		0.98±0.01 0.51±0.03 0.999 19
	(ind) 2 CH + (1d) 0.95±0.03 1.13±0.13 0.999 4
	1.00±0.02 0.84±0.10 0.997 15 o r (thq) 2 CH + (1c) 0.89±0.05 1.88±0.24 0.997 4
	0.99±0.04 1.32±0.19 0.992 11 P (pyr) 2 CH + (1b) 0.91±0.06 2.33±0.29 0.998 3
	1.10±0.07 1.46±0.28 0.994 5 d e (dma) 2 CH + (1a) 0.97 e 2.45 e 2 e r 1.10±0.05 1.87±0.16 0.996 5 f
	R a The first entry for each electrophile refers to kinetic data for reactions of key carbanions e in Scheme 3 from References [11,12]; the second entry includes mostly amines (from v w e i References [7, 25]) and additional carbanion nucleophiles.
				27

b Structures are given in Scheme 2. c By definition. d e Errors not known because n = 2. f The nucleophiles are 2a, 2b,

TABLE 4 .

 4 Correlations (Eqn (8)) of second order rate constants for reactions of quinone methides (1g-1m) with carbanions in DMSO at 20 ˚C with N′′′ a

	Quinone b	s E	E′′′ + c	r	n
	1g	1.00 c	1.08±0.05		3
	1h	1.25±0.02 -2.94±0.13 0.999 7
		1.23±0.08 -2.76±0.46 0.982 11 d
	1i	1.25±0.02 -3.82±0.11 0.999 7
		1.22±0.08 -3.74±0.42 0.978 14
	1j	1.43±0.01 -6.56±0.07 0.999 7
		1.34±0.10 -6.03±0.57 0.969 14
	1k	1.41±0.01 -6.68±0.05 0.999 7
		1.33±0.10 -6.17±0.61 0.965 14
	1l e	1.42±0.03 -7.52±0.20 0.999 6
		1.20±0.15 -6.22±0.87 0.916 15
		1.28±0.12 -6.76±0.72 0.955 13 f
	1m	1.43±0.07 -8.00±0.44 0.995 6
		1.34±0.14 -7.40±0.84 0.949 12
		1.45±0.06 -8.13±0.36 0.993 10 f
	a First entry for each electrophile refers to kinetic data for reactions of the key carbanions
	in Scheme 3 from References [11,12]; a second entry includes additional carbanion
	nucleophiles (

Table 2 )

 2 , usually covering a relatively small range of values of N′′′. Excluding the data point for ylid Ph 3 PCHCO 2 Et.

b Structures are given in Scheme 2. c Assumed s E = 1.00.

d

Table 5 .

 5 Values of N and N′′′ (Eqn (9)) for additional nucleophiles in DMSO at 20 ˚C

	Nucleophile	N a	N′′′ b N c
	8, Z = NO 2	d	19.61 6.2 13.4
	7, Z = NO 2	d	19.67 (6.5) 13.2
	9 e		19.92 (6.5) 13.4
	6a f		20.71 6.7 14.0
	6c f 6b f	20.61 6.9 13.7 r F o 21.54 7.2 14.3
	5, Z = 4-CN g 5, Z = 4-CF 3 g 7, Z = CN d 5, Z = 3-Cl g	22.6 7.5 15.1 P 24.3 7.9 16.4 e 25.11 8.3 16.8 e r 8.4
	8, Z = CN d 7, Z = CF 3 d 8, Z = H d	25.35 8.7 16.7 R e 27.28 8.9 18.4 v w e i 28.95 10.1 18.9
				29

2 P(O)CH -CN and (EtO) 2 P(O)CHC(O -)OEt. a From Eqn (2) and kinetic data in references shown for each nucleophile.

TABLE 6 .

 6 Correlations (Eqn (8)) of second order rate constants for reactions of neutral electrophiles(10-18) with carbanions in DMSO at 20 ˚C with N′′′ a Assuming s E = 1.0 gives more plausible results than Eqn (8) for nucleophiles 7, 8, Z = NO 2 and 9. g 5, Z = NO 2 is predicted to react 20-fold faster than observed. h This equation also fits data for 8, Z = NO 2 . Z = NO 2 is calculated to react 13-fold faster than observed. The additional nucleophiles are 5, Z = 3-Cl, 4-CF 3 and 4-CN.

	Electrophile b	s E	E′′′ + c	r	n b
	10, Z=H c		1.00 d	0.4		3
	10, Z=OMe c 1.38±0.05 -2.88±0.34 0.999 3
			1.18±0.14 -1.64±0.88 0.987 4
	10, Z=NMe 2	c 1.32±0.02 -4.23±0.14 0.999 3
			1.31±0.01 -4.17±0.08 0.999 4
	11 e		o 1.10±0.11 -3.76±0.62 0.986 5
			r 1.16±0.10 -4.21±0.59 0.978 8
	0.97±0.08 -3.19±0.51 0.962 15 P e 1.03±0.10 -2.54±0.56 0.987 5 e 1.07±0.12 -2.89±0.73 0.962 8 e 0.92±0.08 -2.11±0.55 0.955 14 r 12, Z=OMe e 1.0 d 12, Z=NMe 2 -0.8 3 (0.64±0.11 1.13±0.66 0.955 5) R 1.0 f,g -0.8 8 e 12, Z=H e 1.0 d,h -0.1 3 v i 13, X = O i 1.09±0.16 -3.05±0.96 0.959 6 e 1.22±0.09 -3.97±0.54 0.976 11 w 0.89±0.09 -2.06±0.57 0.944 14
	14, Z=NMe 2	i 0.98±0.15 -1.67±0.88 0.957 6
			1.18±0.16 -2.95±0.94 0.948 8
			0.82±0.11 -0.93±0.71 0.908 13
	14, Z=OMe i 1.00±0.07 -0.20±0.38 0.989 7
			0.99±0.07 -0.20±0.42 0.983 8
			0.84±0.18 0.47±1.04 0.857 10 j
	13, X = S i		0.90±0.14 -0.70±0.82 0.957 6
	15 i		0.99±0.09 -0.49±0.48 0.985 6
						30

a Italic entries refer to the same data set of nucleophiles (Tables

2 and 5

), as that used to obtain values of E from the MPC3 optimisations fitting Eqn (2); kinetic data are from the references shown for each electrophile; if an earlier entry is shown, it refers to kinetic data for reactions of the key carbanions (Scheme 3); a later entry refers to the incorporation into Eqn (8) of subsequently-published data from References

[22-24]

. b Structures are given in Scheme 5; values of E are in the References shown below. c Reference

[13]

. d Assumed.

e Reference

[14]

. f i Reference

[15]

. j 5, k Reference

[16]

. l m Reference

[17]

. n Only two key nucleophiles (Scheme 3); additional kinetic data from Reference

[23]

.

TABLE 7 .

 7 Correlations (Eqn (8)) of second order rate constants for reactions of additional quinone methide (QM) electrophiles(19) with key carbanions (Scheme 3) in DMSO at 20 ˚C with N′′′

	QM a	s E	E′′′ + c	r	n
	19a	1.50±0.07 -6.49±0.42	0.997 5
	19b	1.51±0.09 -6.15±0.54	0.995 5
	19c	1.45±0.08 -5.66±0.47	0.994 6
	19d	1.20±0.05 -2.42±0.24	0.998 5
	19e	1.36±0.04 -6.55±0.23	0.999 4 b

a The quinone methide electrophiles (19, Scheme 6) are structural variations on those

Table 8 .

 8 are in Scheme 6 Comparisons of s N N and N′ with pK a values for arylacetonitriles in DMSO Refers to the conjugate acid; data at 25 ˚C from References[31,32]. From Eqn (2), s N N = hypothetical log k estimated for electrophile 1n (E = 0.0) in DMSO at 20 ˚C; data from Reference[23].

	Carbanion a	pK a	b	s N N c	N′′′ d
	7, Z = NO 2	12.3	13.38	6.5
	7, Z = CN	16.0	13.56	8.3
	7, Z = CF 3	18.1	13.64	8.9
	8, Z = H	23.0	16.79	10.1
		F o
		r
			P
			e e r
					R e v i e w
					33

b Data includes carbanion 6b. a Structures are in Scheme 4. b c

Table 9 .

 9 Comparisons of s N and N (Eqn 2) calculated from log k vs. E plots (first entry) with values from the multi-parameter correlation (second entry) a The nucleophiles are key carbanions (Scheme 3) and the number of data points for the log k vs. E plots is also shown. nucleophilicity scale (N′′′) is defined for 34 strong nucleophiles (e.g. carbanions and amines) and is linked to two previously-defined nucleophilicity scales (N′ and N′′) including 96 nucleophiles. The unified N′′ scale spans 10 22 in rate constant, whereas the floating N scale spans 32 orders of magnitude.

	Nucleophile b	s N	N
	2a (6)	0.806±0.033 0.856	14.24 13.91
	2b (6)	0.787±0.036 0.767	16.12 16.27
	2c (5)	0.755±0.026 0.729	17.30 17.64
	2d (4)	0.623±0.027 0.688	19.81 18.82

a Kinetic data and parameters from the multi-parameter correlation (MPC2) are from Reference

[11]

. b A

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