Rodrigo Teles Hermeto
email: teleshermeto@unistra.fr

Antoine Gallais
email: gallais@unistra.fr

Fabrice Theoleyre
email: theoleyre@unistra.fr

Fabrice Théoleyre

Impact of the Initial Preferred Parent Choice in Wireless Industrial Low-Power Networks

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Introduction

The Internet of Things has emerged in the last years as a concept that leads to a wireless Internet that connects a myriad of smart systems, from temperature sensors, HVAC systems, to intrusion detectors [1]. All these objects are expected to be deployed in homes, warehouses, streets, or amusement parks. Industry 4.0 is currently an emerging approach, aiming to re-use the IoT concepts in the automation world. The so-called Industrial Internet of Things (IIoT) relies on wireless technologies that are able to provide a high Quality of Service (QoS) for a plethora of industrial applications such as vehicle automation, smart grid, automotive industry or airport logistics. All those applications share similar network performance requirements regarding lowlatency and high network reliability.

To provide Quality of Service (QoS) for industrial-like wireless networks, the IEEE 802.15.4-2015 standard was published in 2016 [2]. Time-Slotted Channel Hoping (TSCH) is among the Medium Access Control (MAC) schemes defined in this standard, and targets specifically the low-power, deterministic and reliable wireless industrial networks. TSCH relies on a strict schedule of the transmissions such that each application has enough transmission opportunities while avoiding transmission collisions. When a node is not involved in a transmission or reception, it can safely switch its radio interface off to save energy.

To construct an accurate schedule, the network needs to select the best route(s) for each flow, and to allocate enough transmission opportunities to each node along the path to the sink. Estimating the link quality is consequently of prime interest: Selecting a suboptimal preferred parent implies that many packets have to be retransmitted to be correctly received by the next hop. The routing topology is in other words inefficient and the incriminated nodes may quickly run out of energy. Iova et al. [START_REF] Iova | Stability and efficiency of RPL under realistic conditions in Wireless Sensor Networks[END_REF] highlighted the presence of oscillations in RPL, with many parent changes when using a dynamic link quality metric.

In this letter, we propose to focus on the initial parent choice when a node has to join the network. We share here our experimental characterization, which focuses on the convergence phase.

Convergence of RPL when using a default initial metric

Let us consider the topology depicted in Figure 1. In this letter, we propose to focus on the initial parent choice when a node has to join the network. We share here our experimental characterization, which focuses on the convergence phase.

We assume that RPL is used for routing [START_REF] Winter | RPL: IPv6 Routing Protocol for Low-Power and Lossy Networks[END_REF]. Let us consider that RPL uses the ETX metric (i.e. average number of transmissions before receiving an acknowledgment) to select the best routes. RPL relies on an objective function to translate a link metric into a rank, denoting the virtual distance between the node and the border router. To use the best routes, a node selects as preferred parent its lowest ranked neighbor [START_REF] Winter | RPL: IPv6 Routing Protocol for Low-Power and Lossy Networks[END_REF]. The ranks of nodes in its vicinity are derived from the respective estimated quality of the links with these nodes. Unfortunately, measuring the ratio of packet errors requires to exchange first some data packets. Thus, an initial default link quality may be associated with the inactive neighbors. While the 6TiSCH-minimal draft [START_REF] Vilajosana | Minimal 6TiSCH Configuration[END_REF] does not recommend any default ETX value for inactive neighbors, the OpenWSN1 implementation uses a fixed default link cost equal to 4, thus assuming that the ETX toward an inactive neighbor is 4.

Let consider the Figure 1, with a multihop topology of 6 nodes, including the sink. Each node (N) computes its rank based on the rank of its preferred parent (P), and its link quality:

𝑟𝑎𝑛𝑘(𝑁) = 𝑟𝑎𝑛𝑘(𝑃) + MinHopRankIncrease * ETX(N → P)
with MinHopRankIncrease being a constant (by default equal to 256), and (ETX(N→P)) denotes the ETX metric from N to P.

If a default ETX value is used when a link is unprobed. Thus, the node N selects as preferred parent its neighbor with the lowest rank, i.e. the node A. After the association, the link (N,A) is used, and the link quality estimation is refined, with the correct ETX value: its rank is finally updated (1537). Since the node B provides now a lower rank with default ETX value (4*256+260<1537), N changes its preferred parent to B (which will give a lower rank using the default value 1284). We can note that the node N probes iteratively each of its neighbors as preferred parent.

Inversely, N will not select C or D as parent although they provide a better path to the border router. Indeed, their rank with the default value would be 1304 and 1324 respectively. Unfortunately, the rank of B (with its actual ETX) is 1028, strictly inferior to the default rank of the other possible parents. A too large ETX default value for inactive neighbors prevents to select the best parents eventually.

Figure 1: Convergence of the preferred parent choice when using a default ETX value

The problem becomes even trickier to handle with temporal variations, very common for this kind of scenario [START_REF] Ding | Link Investigation of IEEE 802.15. 4 Wireless Sensor Networks in Forests[END_REF]. For inactive neighbors, the link metric was evaluated a long time ago and does not reflect the current quality. De facto, these neighbors will never be considered again to serve as preferred parent, except if the current one crashes or its link quality becomes very bad (i.e. ETX > 4).

For higher network densities, a node may limit the number of neighbors to be included in its neighbors table. In such scenarios, the node would exclude periodically from its table bad neighbors or even nodes that have stayed a long time without communicating. Later, they might be added back with the default link cost until they are probed again. With this inclusion/removal, a node may consider again a bad neighbor when a parent changing is required.

Initial Link Quality Estimation with a Reservation Based MAC layer

IEEE 802.15.4-2015-TSCH requires a strict schedule of the transmissions. Each cell is identified by its timeslot and channel offset, and is allocated to a set of transmitters. During a shared cell, several transmitters can transmit using a backoff value to regulate the contention. Typically, all the nodes have to stay awake during a shared cell so that a broadcast packet is received by all the nodes with a single radio transmission. Inversely, dedicated cells are contention free, and are allocated to a set of transmitters and receivers which do not mutually interfere.

When executed on top of the IEEE 802.15.4-2015-TSCH, a node has consequently to reserve an amount of transmissions opportunities (cells) after having selected its preferred parent. Reserving a set of cells in the scheduling matrix allows the node to transmit its data packets in a contention free manner.

However, estimating the link quality for inactive neighbors is particularly challenging. Reserving some contentionfree cells for probing each neighbor would provide a very accurate link quality estimation, but would also waste a large amount of radio resource. Inversely, the probes may be broadcasted [START_REF] Ancillotti | Trickle-L2: Lightweight link quality estimation through Trickle in RPL networks[END_REF], with transmissions being scheduled in the cells dedicated to broadcast (with contention). Unfortunately, the collisions may distort the estimation.

Moreover, changing the preferred parent over a reservation-based MAC layer is very expensive. A node has to reinstall a new set of cells for its new parent. Meanwhile, the data packets use the shared cells, prone to collisions. Thus, routing instabilities negatively impact both the reliability and the overhead.

For this purpose, we used the FIT IoT-Lab 2 testbed of Strasbourg to measure the number of preferred parent changes, and the reliability before the network converges. We used the OpenWSN 1 stack, which implements both Figure 2(a) exhibits this instability during the convergence phase. We measured the number of parent changes and the number of requests generated by the 6P protocol to modify the schedule. They denote the convergence of the stack. We can observe a high frequency of parent changes and 6P requests. The nodes switch their preferred parents even if the link quality estimation has varied slightly. Because at first a node does not know the link quality to an inactive neighbor, it uses the default link cost. Then, nodes will keep changing their preferred parent until they find a neighbor that fulfills the reliability requirement (i.e. ETX < 4). In addition, the instability also affects the Packet Delivery Rate as shown in Figure 2(b). The proportion of lost packets is much higher during the convergence phase, as the nodes 'blindly' select parents using the default link quality value. The packets are even dropped because the node has no transmission opportunity toward its preferred parent. Using a hysteresis function [START_REF] Gnawali | The Minimum Rank with Hysteresis Objective Function[END_REF] would reduce the number of parent changes, but at the price of using very suboptimal parents.

Conclusion

In this paper, we highlighted the impact of the default link quality metric for non-probed links on the routing convergence. Changing several times its preferred parent is particularly expensive in TSCH: new transmission opportunities have to be reserved in the schedule, requiring many control packets. Besides, many data packets may be dropped before the new cells are reserved. Our experiments highlighted the need of estimating accurately the link quality before attaching to a preferred parent. Using initially a default link quality is suboptimal, and leads to several parent changes. A more accurate passive link quality estimation would be very beneficial in this situation.

2 4 -

 4 https://www.iot-lab.info/ TSCH and RPL protocols. We selected 31 nodes to highlight the instability which arises even in small-scale topologies.

Figure 2 -

 2 Figure 2 -(a) Number of parent changes/6p commands and (b) the distribution of packet losses during the convergence.

http://www.openwsn.org


Zhiqiang Cao

Françoise Méchin

Jean-Pierre Pascault

HAL is

The acrylonitrile content of the rubbers and the molar mass of the PES additives also have a great influence on their miscibility. During an isothermal cure, phase separation always occurs before vitrification; in rubber it generally occurs before gelation, and in PES it occurs together with gelation. The temperature and viscosity at which phase separation occurs are critical for the final morphology. Reactive additives accelerate the curing process and modify this morphology by inducing a complex matrix-particle interface, and a substructure inside the dispersed particles; these modifications produce the best toughening effects.

Brittle thermosets are best toughened by the introduction of a rubbery or thermoplastic dispersed phase [START_REF]Advances in Chemistry[END_REF][START_REF]Rubber-Toughened Thermosetting Polymers in Structural Adhesives-Developments in Resins and Primers[END_REF][START_REF]Advances in Chemistry[END_REF][START_REF]Toughened plastics I: Science and Engineering[END_REF]. The dispersed phase can be produced by two methods: in situ reaction and adding preformed particles. The first method is used much more because it is easy and it can create specific morphologies. In the first method, the initial mixture of monomer(s) and additive is homogeneous at the isothermal curing temperature, Ti and the dispersed phase is obtained by the phase separation induced by polycondensation of the monomer(s).

The main factors that determine the degree of toughening are the final polymer blend morphology and the adhesion between the two phases. For initially miscible reactive systems, the first factor (including diameters, number, and volume fraction of the dispersed spherical particles) is determined by the competition between the rates of phase separation and polycondensation. Adhesion between the two phases depends on the chemical and physical properties of both the additive and the monomer [START_REF] Williams | Rubber Modified Thermoset Resins[END_REF][START_REF] Montarnal | In Rubber-Toughened Plastics[END_REF][START_REF] Verchère | Toughened plastics I: Science and Engineering[END_REF][START_REF] Rozenberg | [END_REF]. The phase-separation process induced by the reaction and the formation of the morphology are intricate phenomena; for thermosetting systems, their study is focused mainly on rubber-toughened polyepoxy matrices [START_REF]Advances in Chemistry[END_REF][START_REF]Advances in Chemistry[END_REF]. An analysis of the experimental results leads to the following conclusions:

1. The concentration of dispersed particles decreases with Ti 2. The volume fraction of dispersed phase, VD , remains practically constant, goes through a maximum, or decreases with Ti 3. The number-average diameter, , of the spherical particles increases with Ti 4. and VD increase with the initial volume fraction of the additive, фa,0 5. But VD is always greater than фa,0. This fact means that the dispersed phase is not formed only of pure rubber additive, R, but also contains some epoxy-amine copolymer.

It can be about 50 wt%. A second phase separation has been demonstrated to occur inside the dispersed particles. (9) On the other hand, the initial miscibility of the monomer(s) with the additive has a great influence on both the phase separation and the final morphologies. Many experimental results [START_REF] Williams | Rubber Modified Thermoset Resins[END_REF][START_REF] Montarnal | In Rubber-Toughened Plastics[END_REF][START_REF] Verchère | Toughened plastics I: Science and Engineering[END_REF][START_REF] Rozenberg | [END_REF](9)(10) show that phase separation occurs well before gelation time, tgel, or conversion, xgel , and before vitrification (tvit, xvit). The better the initial miscibility, the higher the conversion at the cloud point, xcp, where the phase separation induced by polycondensation occurs at a given value of Ti. Initial miscibility and Ti control the "chemical quench". The viscosity at the cloud point, ηcp, obviously increases with the conversion, xcp. The viscosity, ηcp, can affect the nucleation and growth of the dispersed-phase particles and consequently their average diameter [START_REF] Montarnal | In Rubber-Toughened Plastics[END_REF]11), and sometimes also the shape of the particles, which is not necessarily spherical.

Cyanate ester (CE) resins are the key monomers for a new type of high-performance polymer. They were developed by Hi-Tek Polymers during the 1980s, then Rhône-Poulenc, and now Ciba-Geigy. The polycyclotrimerization of cyanates can take place by simple heating, or it can be catalyzed by transition metal cations together with labile hydrogen compounds, phenols, alcohols, or amines (12).

Like epoxy systems, CE systems can be toughened with (1) engineering thermoplastics (13)[START_REF] Arnold | Proceedings of the 37th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF][START_REF] Yang | Proceedings of the 35th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF][START_REF] Yang | Proceedings of the 36th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF][START_REF] Shimp | Society for the Advancement of Material and Process Engineering[END_REF][START_REF] Srinivasan | High Perform[END_REF], including polysulfones or poly(ether sulfone)s, polyimides, and polyesters or polyarylates, and (2) rubbers, including butadiene-acrylonitrile copolymers (13), polysiloxanes [START_REF] Arnold | Proceedings of the 37th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF], and preformed particles [START_REF] Yang | Proceedings of the 35th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF][START_REF] Yang | Proceedings of the 36th International SAMPE Symposium; Society for the Advancement of Material and Process Engineering[END_REF]. We can conclude that the different concepts, rubber-or thermoplastic-modified thermosets, work as well with CE as with epoxy. But unlike epoxy, only a few results in the literature give relations between the initial miscibility of monomer and additive, the curing conditions, and the morphologies and properties. This chapter examines the influence of rubber and thermoplastic additives (nature and end groups) on polymerization kinetics and, mainly, on the evolution of phase diagrams. Work on morphologies and properties is examined elsewhere (19).

Experimental Methods

Monomers. Preparation of the Blends. The CE blends, which contain 15 wt% additive, were prepared by manual stirring at room temperature for rubber additives, and with dichloromethane as a solvent for PES additives.

Polymerization Reaction. The differential scanning calorimetry (DSC) pan, containing 10-15 mg of sample, was sealed under air. It was then placed in the oven at 180 °C, and the reaction allowed to proceed. In order to measure the temperature at the cloud point, Tcp, during polymerization, about 2 g of sample in a test tube was isothermally polymerized in situ inside the light-transmission device (21).

Cure of Plates.

In an oven, ~240 g of blend in a 6-mm-thick mold was precured at 180, 150, or 120 °C for a time necessary to arrest the phase separation, and then it was postcured with the same cycle at higher temperatures until completion of the polycondensation of CE monomer without any degradation. The evolution of the real temperature of the plate was followed by use of a thermocouple.

Chart 1. Chemical structures and characteristics of dicyanate monomers, elastomer additives, and PES additives

Analytical Techniques. The cloud point of the blends was determined with a light-transmission device (21). Once the blend was cloudy, the test tube was taken out and chilled in ice, so that the time and conversion at the cloud point, tcp and xcp could be obtained. The Tg value and conversion were measured by DSC (Mettler TA3000 microcalorimeter) (22). The gel time, tgel, of rubber-cyanate blends was determined as the time at which insolubles appeared in tetrahydrofuran (THF). That of PEScyanate was determined by dynamic mechanical analysis (Rheometrics RDA700). We observed the fracture surfaces using a scanning electron microscope (SEM, JEOL 840A) after coating them with a gold sputterer. Transmission electron micrographs (TEMs) were obtained by using a JEOL 1200 device for ultramicrotomed samples. Using a procedure previously described (23), we calculated the following parameters: number-average diameter: = ∑ ∑ volume fraction of the dispersed phase:

N C-O- C -O-C H CH 3 N N C-O- C -O-C CH 3 CH 3 N HOOCCH 2 CH 2 CH 2 CH 2 COOH C CH 3 CN (R) C CH 3 CN CN CH 3 CH 3 C (R) CN CH 3 C CH 3 R'NCOCH 2 CH 2 CH 2 CH 2 CONR' C 4 H 9 C 4 H 9 CN CH 3 C (R) CN CH 3 C R = CH=CH 2 (CH 2 -CH=CH-CH 2 ) a (CH 2 -CH) b (CH 2 -CH) c CN NH C 4 H 9 HN C 4 H 9 R NHC 4 H 9 CH 2 R' = R' SO 2 O n
= ( /4) ∑
where AT is the total area of the micrograph region under analysis.

Tensile and compressive tests were performed at room temperature with a tensile testing machine (DY25, Adamel-Lhomargy). For the tensile tests, strain measurements were performed with an extensometer (EX-10) at a strain rate of 3.3 x 10 -4 s -1 , using ISO-60 standard specimens. Samples of dimension 20 x 12 x 6 mm were deformed in a compression cage between polished steel plates. The nominal strain was determined by averaging the results from two linear variable differential transformer (LVDT) transducers. The strain rate used was 8.3 x 10 -4 s -1 .

Fracture toughness was studied with opening mode I tests and in a plane strain rate. The samples were loaded to failure using a crosshead speed of 1 mm/min (5.2 x 10 -4 s -1 ), at room temperature. Values for the critical stress intensity factor, Klc , were calculated by using the following formula:

= √ (1)
where σc is the critical fracture stress, a is the crack length, and w is the specimen width. The correction factor is given by:

= 1.
Once Klc was determined, the fracture energy, GIc, was calculated with Young's modulus and the Poisson coefficient, which were determined experimentally for every formulation following usual procedures.

Results and Discussion

Initial Miscibility of the Blends. In Figure 1, we have plotted the cloud-point curves obtained with the following substances:

1. two rubbers with the same percentage of acrylonitrile (AN):

• a nonfunctional rubber, nonfunctional butadiene-acrylonitrile (NFBN)

• a carboxy-terminated rubber, CTBN The NFBN rubber is less miscible than the CTBN rubber. An amino-terminated rubber, ATBN8, with the same amount of AN , 18 wt%, is quite miscible with DPEDC or DGEBA , showing that chain ends of reactive liquid oligomers can have a strong effect on their miscibility (20). Finally, by decreasing the percentage of AN , the miscibility window decreases drastically (21). For example, ATBN31, with only 10 wt% AN , is quite immiscible with DPEDC and DGEBA at temperatures lower than 100 °C.

PES is miscible with DGEBA or DPEDC at room temperature, and PES-DGEBA blends have a lower critical solubility temperature (LCST) behavior (Figure 2). But because of CE reactions at temperatures greater than 100 °C, the comparison between CE and DGEBA is not possible. Polymerization. To plot the evolution of the phase diagram, it is necessary to have a good knowledge of the reaction rates and conversions at different isothermal curing temperatures. These kinetic parameters were determined in a previous study (22), using Ti = 180 °C for systems based on DPEDC, and Ti = 200 °C for those based on DCBA (which is less reactive). Our experiments revealed that in the first part of the curing process, that is, as long as it remained kinetically controlled, the unreactive additives (with respect to the cyanate functions, i.e., NFBN, CTBN, and PES4100P) did not modify the overall kinetics compared with the neat monomer. Systems based on DCBA could be modeled (24) by the following equation:

/0 /1 = 2 3 (1 4 & # 2 & 4 1 4 & (3)
second order second order autocatalyzed Equation 3 is often used in the literature to account for the kinetic behavior of several common dicyanate monomers (25,26). The autocatalytic character of cyanate polycyclotrimerization is now quite well established; we noticed that it was especially enhanced in samples with a large surface directly exposed to air (24,27,28). The kinetics of DPEDC blends were more difficult to describe because they were perturbed by several residual impurities in the monomer. Together with adventitious air moisture, the latter increased gel conversion with respect to the theoretical value (0.5).

In contrast to these unreactive modifiers, the additives that were likely to react with cyanates (ATBN via its secondary amine function, and PES5003P via its phenol function) were shown to appreciably accelerate their cure, even in its very first steps. Phenols (12) usually react with cyanates to yield iminocarbonates; the latter are generally proposed as intermediates in the polycyclotrimerization mechanism:

In our group (29), experiments run with model monofunctional phenols confirmed these possible first steps. The same kind of studies (29) were carried out with a monofunctional aromatic amine and suggested that in ATBN , the following reactions could presumably be involved:

These reactions could explain the reaction activation observed for the blends of DPEDC with PES5003P and ATBN, especially as the latter also contains excess free diamine. Considering the 10% residual Unilink 4200 in ATBN, we determined the reaction rate associated with a 1.74% Unilink 4200-DPEDC blend, which simulates the concentration of the excess free Unilink 4200 in a 15-wt% ATBN8-DPEDC blend. The results are not presented here, but in the presence of Unilink 4200, DPEDC reacted faster, in the same range of reactivity as ATBN-Unilink (22).

All the rubber or thermoplastic-modified cyanates studied were initially miscible at the curing temperature, Ti. At a certain conversion, phase separation occurred as the molar mass of the cyanate oligomers increased and more polar cyanate functional groups were transformed into less-polar cyanurate rings. The phase-separation phenomena could be observed simply by the fact that the solution became cloudy (cloud point). We measured the conversions at which the isothermally cured blends became cloudy (xcp) and the gel conversions (xgel); the xgel values were practically the same for neat systems and blends, considering experimental error. For all the blends, phase separation occurred well before gelation. Therefore, we conclude that in these cases phase separation did not disturb the polymerization kinetics or the network buildup.

For PES4100P and PES5003P, the conversions at the cloud point were respectively 0.44 and 0.40 for Ti = 180 °C. Once again, we conclude that phase separation is unlikely to influence the polycyclotrimerization kinetics.

Finally, we noticed that in the last stages of the reaction, in contrast to the neat systems for which vitrification limited the conversion to about 0.9 at Ti = 180 °C, the conversion of all the rubber-modified systems easily reached 0.95 or more, a result indicating that the vitrification effect was delayed and suggesting that part of the rubber dissolved in the matrix and decreased its Tg(t). The same conclusion could be drawn from the glass-transition temperatures of the final networks (Tg∞), which are displayed in Table III. Such an effect was not observed for the Unilink 4200-DPEDC mixture (without rubber).

Moreover, the maximum conversion of the 15-wt% PES5003P-DPEDC blend was lower than that of the 15-wt% PES4100P-DPEDC blend. This difference was attributed to the possible reactions between additive chain ends and cyanate monomer: the mass fraction of PES5003P dissolved in the matrix after phase separation may be higher than that of PES4100P; thus the vitrification of the former occurs earlier. Figure 3 shows that the evolution of xcp with the additive fraction is weak, and xcp is always lower than the gel conversion of the cyanates, about 0.6. For a polymer blend with two components, the free energy of mixing per unit volume of blend can be expressed by the Flory-Huggins equation. Elsewhere (30), we estimate the Flory-Huggins interaction parameter χ by fitting the experimental points. For a given fraction of additive, the Τ versus x phase diagrams would be more useful for practical applications and for better control of the phase-separation process. In these phase diagrams, it is possible to plot the three transformations together: phase separation, Tcp versus xcp; gelation, xgel = 0.6; and vitrification, Tg versus x. A 15-wt% NFBN-DPEDC blend at Ti = 180 °C, and a 15-wt% NFBN-DCBA blend at 200 °C were isothermally polymerized until a certain conversion, then cooled until the blends became cloudy.

(Cooling was achieved by simply stopping the heating of the oven in the light-transmission device. The cooling rate depends on the temperature of the oven.) In this way, Tcp and the corresponding xcp were obtained. Figure 4 shows that the increase in Tcp seems to be linear with respect to x (in the range of Ti studied, because in fact it is an ascending concave curve), which agrees with the UCST-type initial phase diagrams of the blends. On the other hand, at the same Tcp, the xcp of NFBN-DCBA is always higher than that of NFBN-DPEDC, which means that DCBA is a better solvent for NFBN than DPEDC.

Furthermore, the evolution of Tg for the continuous phase of the blends can be plotted in the same figure for both the 15-wt% NFBN-DPEDC and 15-wt% NFBN-DCBA blends (Figure 4). It appears that at a given x, Tcp is always higher than Tg. In other words, during an isothermal cure, phase separation occurs before vitrification of the blends. Figure 4 also shows that xcp is always lower than xgel for Τ < 220 °C.

To study the influence of rubber reactivity on phase separation, we also measured the phase diagrams of the blends with rubbers ATBN8 and CTBN. As in the 15-wt% NFBN blend, for the blends with ATBN8 and CTBN, the overall T versus conversion phase diagrams, including phase separation (Tcp, xcp) , gelation (xgel ≈ 0.6), and vitrification (Tg, x) can be plotted (Figure 5). At one isothermal curing temperature, Ti, it appears that xcp is in the order ATBN8 > CTBN > NFBN. This result is consistent with the order of the initial miscibilities of the rubbers with DPEDC. To isolate these different effects, we did the same experiments with 15-wt% ATBN rubber by replacing small amounts of ATBN8 with ATBN31, which contains only 10% AN (compared with 18% AN in the former) and seems to be immiscible with DPEDC. Figure 6 shows that the AN content of ATBN had a drastic effect on the miscibility of ATBN with DPEDC. Similarly, Chen et al. (20) found that the miscibility of CTBN with DGEBA decreased with the decrease in the AN content of the rubber. Figure 7 shows that in contrast to rubber-DPEDC blends, Tcp decreases almost linearly as x increases (once again in the range of Ti studied, because in fact it is a descending concave curve). This result confirms that the PES-CE blends show LCST behaviors. Moreover, the Tcp versus x curve of the 15% PES4100P-DPEDC blend is to the left of that of the 15% PES5003P-DPEDC blend. These results indicate that PES4100P is more miscible with DPEDC than PES5003P, which is consistent with the fact that PES4100P has a smaller molar mass. In addition, the evolution of Tg of the continuous phase of the blends can be plotted in Figure 7 with the Tcp versus x phase diagram. Once again, phase separation occurs before the vitrification of the blends. For a sample cured at 90 °C, phase separation is expected in the same range as gelation (xcp ≈ xgel), and in fact no phase separation is observed. Pellan and Bloch (31) also reported that this blend was always clear when precured at 90 °C, even when this precuring up to gelation was followed by a postcuring at 200 °C. We think that this observation results from high viscosity during polymerization and gelation of the system. Morphologies and Properties. The phase diagrams of temperature versus conversion (or vs. time) are useful for controlling the curing of a blend. We said in the introduction that the morphologies are mainly controlled by the temperature, Tcp, or the viscosity, ηcp, at which phase separation occurs. Generally, when Tcp decreases or ηcp (or xcp) increases, the dispersed particles become smaller. In Figure 8 we show a series of micrographs obtained by scanning electron microscopy of the fracture surfaces of different samples. Samples are blends of DPEDC and different additives. They were precured at Ti = 180 °C to control phase separation and gelation, then postcured at high temperature (260 °C) in order to reach full conversion (x ≈ 1). As we saw in the phase diagrams, the conversion (xcp) or viscosity (ηcp) at the cloud point depends on the additive used (Table III).

Table III shows the following: With NFBN, xcp ≈ 0.30 and the particles are spherical and large ( ≈ 7 μm). With ATBN, on the other hand, xcp ≈ 0.47 and the particles are smaller ( ≈ 1.7 μm), but they also have like a branch substructure. In this case, we expect to see not only an effect of the viscosity but certainly also of the reaction between the rubber and cyanate functions before network formation.

Furthermore, with PES5003P, xcp ≈ 0.40 and the particles are also smaller than with NFBN. We also see an effect of the viscosity and of the reactive chain ends of the thermoplastic. But because Ti is 180 °C, which is lower than the Tg of the thermoplastic, one important effect is certainly also the vitrification of the dispersed particles when phase separation occurs. The consequence is that only with thermoplastic additives is an evolution of the morphology observed between precuring and postcuring processes.

With the help of these phase diagrams, it is now possible to define different precuring and postcuring schedules. The effects of the curing process on the final morphologies are presented elsewhere (19).

The introduction of any additive improves the toughness of the material; in particular, KIc of ATBN8-DPEDC is more than twice that of neat DPEDC . In contrast, different additives result in different losses in Young's modulus, from 17% to 50%, and different losses in the final material glass-transition temperature compared with neat DPEDC (Table III). The fact that Tg is lower for ATBN8-or PES5003Pbased materials than for those obtained with NFBN obviously indicates that with the latter, the continuous phase contains smaller amounts of additive because of poorer miscibility. However, the residual fraction of PES in the final matrix [(фa)m∞] calculated from Fox's equation for the PES5003P-DPEDC blend is above the maximum theoretical value. Thus, we believe that the decrease in Tg for the PES5003P-DPEDC blend results not only from the presence of residual additive but also from the modification of the poly(cyanurate) network because of a possible reaction between PES5003P and DPEDC.

In fact, the system with 15-wt% ATBN8 has the best-balanced properties of all the modified systems in this study: This sample shows an excellent improvement of the toughness without too large of a loss in Tg and in the modulus, while the system based on NFBN has worse mechanical properties.

Conclusions

Rubbers and PESs are initially miscible with cyanate ester monomers. Phase separation occurs during the reaction. By plotting the phase diagrams (temperature vs. conversion), it is possible to compare the effects of chain ends and AN content in butadiene-acrylonitrile random copolymers and the effect of molar mass in PES . The cyanate ester monomer based on bisphenol A is a better solvent than DPEDC, and both dicyanates are better solvents than DGEBA.

With the use of phase diagrams, we are also able to control the temperature and the viscosity at which phase separation occurs. The final morphologies of the three systems based on the same dicyanate monomer and modified with NFBN, ATBN, and PES are quite different and have different interfaces. When the additive can react with the monomer before network formation, a two-level structure is observed: a primary structure (dispersed particles), and a substructure inside the dispersed particles. The complex morphology obtained in this case gives the best toughening effect.

2 .

 2 two different reactive monomers: • a CE, DPEDC • bisphenol A diglycidyl ether, DGEBA (DER 332 from Dow)All the blends have an upper critical solubility temperature (UCST) behavior. It is evident that the CE monomer is a better solvent of rubbers than the epoxy prepolymer.

Figure 1 .

 1 Figure 1. Initial cloud-point curves for rubber-DGEBA (DER 332) (---) and rubber-DPEDC (Arocy L10) (--), with NFBN rubber (a) and CTBN rubber (b). R is rubber, and φa is mass fraction

Figure 2 .

 2 Figure 2. Initial cloud-point curves for PES-DGEBA (DER 332). Key: +, PES4100P; and , PES5003P.

  Diagrams. The increase in the molar mass of the cyanate ester with conversion obviously modifies the phase diagram of blends. The evolution of phase diagrams of nonfunctional rubber was first studied. At Ti = 180 °C for NFBN-DPEDC and at Ti = 200 °C for NFBN-DCBA (isothermal polymerization), the conversions, xcp, where blends with different fractions of additive became cloudy, were measured.

Figure 3 .

 3 Figure 3. Experimental phase diagram showing conversion (x) versus the mass fraction of rubber (фa). The rubber is NFBN. Key: ,DPEDC, Ti = 180 °C; and , DCBA, Ti = 200°C

Figure 4 .

 4 Figure 4. Experimental phase diagram showing temperature versus conversion. Key: , DPEDC-NFBN (15 wt%); , DCBA-NFBN (15 wt%); a, phase separation; b, gelation (x ≈ 0.6); and c, vitrification (Tg) versus x.

Figure 5 .

 5 Figure 5. Experimental phase diagram showing temperature versus conversion for rubber (15 wt%)-DPEDC blends. Key: , NFBN; +, CTBN; , ATBN8. Curves (a), (b), and (c) are defined as in Figure 4.

Figure 6 .

 6 Figure 6. Experimental phase diagram showing temperature versus conversion for rubber (15 wt%)-DPEDC blends. Key: , ATBN8; and , ATBN8-ATBN31 (5 wt% in the rubber blend). Regions (a), (b), and (c) are defined as in Figure 4.

Figure 7 .

 7 Figure 7. Experimental phase diagram showing temperature versus conversion for PES (15 wt%)-DPEDC blends. Key: , PES5003P; and , PES4100P.

Figure 8 .

 8 Figure 8. SEM images of the fully cured materials. Part a: 15 wt% NFBN-DPEDC. Part b: 15 wt% ATBN8-DPEDC. Part c: 15 wt% PES5003P-DPEDC.

Determination and Use of Phase Diagrams for Rubber-or Thermoplastic-Modified Poly(cyanurate) Networks ZhiQiang Cao, Françoise Méchin, and Jean-Pierre Pascault*

	Laboratoire des Matériaux Macromoléculaires, UMR CNRS 5627,
	Institut National des Sciences Appliquées de Lyon, Bât. 403
	20, Avenue A. Einstein, 69621 Villeurbanne Cedex, France
	Blends of two cyanate ester monomers [4,4'-dicyanato-1,1-diphenylethane (DPEDC) or 4,4'-dicyanato-
	2,2-diphenylpropane (DCBA)] with several initially miscible reinforcing additives were studied as a
	function of cyanate conversion. The phase diagrams (temperature vs. conversion for the different

transitions: phase separation, gelation, and vitrification) provide a good overview of the systems and allow easy comparisons. DCBA is a better solvent than DPEDC. Rubber systems based on butadieneacrylonitrile have an upper critical solubility temperature (UCST) behavior, whereas poly (ether sulfone)s (PESs) induce a lower critical solubility temperature (LCST) behavior.

Table I . Characteristics of the Elastomer Additives

 I From size-exclusion chromatography measurements (polystyrene standards).

	Characteristic	NFBN	CTBN	ATBN	Unilink 4200
	Functionality	0	1.8 (COOH)	1.9 (NHR')	2.0 (NHC4H9)
	% AN ) **** (g/mol) ⁄ ) ***** ) **** Tg (°C)	17.2 3600 2.1 a -67	18.0 3600 1.9 a -60	18.0 3600 + 10% excess Unilink 4200 2.8 (polymer peak) a -47	0 310 1.0 -b
	NOTE: Chemical structures are shown in Chart I.
	b Not measured

a

Table II . Characteristics of the PES Additives

 II

	Reference	, -**** a	, . ***** , -⁄	Tg (°C) b
	PES4100P	15,200	2.7	216
	PES5003P	21,900	2.1	222

NOTE: The chemical structure of PES is shown in Chart I. a From size-exclusion chromatography measurements in dimethylformamide at 80 °C. b From DSC measurements.

Table III . Phase-Separation Process, Morphologies, and Properties for Neat or Modified Poly(cyanurate) Networks

 III

	Reactive system	xcp	xgel	ηcp, Pa.s	, µm	Tg∞, °C KIc, MPa√5	GIc, J/m 2	E, a GPa	σy, b MPa
	Neat DPEDC	-c	0.63	-	-	268	0.71	148	3.00	138
	1.74 wt% Unilink-DPEDC	-	-	-	-	263	0.82	250	2.40	136
	15 wt% NFBN-DPEDC	0.32	0.61	0.015	7.2 ± 0.5	260	0.87	470	1.43	68
	15 wt% ATBN8-DPEDC	0.47	0.61	0.2	1.8 ± 0.2	248	1.40	840	2.00	100
	15 wt% PES5003P-DPEDC	0.40	0.59	1.0	1.1 ± 0.2	246	1.06	390	2.55	128
	NOTE: Blends were procured at 180°C for 2 h and postcured at 260°C.

a E, Young's modulus. b σy, yield stress. c Not measured.