Pierre Letellier

Mireille Turmine
email: mireille.turmine@upmc.fr

Solubility of gas in confined systems. Non Extensive Thermodynamics approach

Keywords: bubbles, nano-bubbles, sessile bubbles, thermodynamics, nonextensive thermodynamics, solubility, negative pressure, Henry's law, Laplace's law

The use of the concepts of the nonextensive thermodynamics allows reconsidering the equilibrium of bubble solubilization, and more commonly of gaseous aggregates in supersaturated solutions of gas. The introduced relations are general and include as particular cases the equations usually used to describe these phenomena. These equations are discussed.

Especially, we specified the domain of application of Kelvin's relation which was illustrated by the solubility of gases in fogs and clouds. Various possibilities of thoughts on the behavior of the gaseous aggregates and nano-systems are proposed. Thus, the introduced relations permit to consider the presence of gaseous aggregates in equilibrium with the solution even for undersaturated solution. Non-extensive thermodynamics admits the notion of negative pressure at the inner of confined phases (solid or liquid).

Introduction

The behavior of fluids supersaturated in gases concerns numerous scientific domains such as geologic field with the formation of bubbles in magmas [1,2], in industrial domain with the obtaining of structured materials (foams, micro-cellular materials), in food-processing industries (soda drinks [3]), in water treatment [4], surface cleaning [5] or medicine [6].

These situations are particularly studied for the establishment of the procedures of decompression of the persons working in hyperbaric atmosphere (divers, deep-sea divers) [7][8][9][10][11][12], or for the understanding of the breathe of marine species [13]. Their study is therefore of the highest importance by their benefits. There are many theoretical approaches of this subject [14], but as S. Lubetkin [15] pointed out, rarely the experimental results can confirm their relevance. His judgment on this point is interesting: "This disagreement is on two fronts: (1) first, quantitative, in that theory predicts much higher supersaturations are needed to cause bubble nucleation than are found necessary experimentally (characteristically, a factor of at least 2 orders of magnitude in the supersaturation); (2) second, qualitative, in that theory predicts that it is only the nature of the liquid which dictates the conditions required for gas bubble nucleation. Experimentally, the chemical nature of the gas is found to be important".

Our goal in this paper is to sum up on this subject, but also to consider it in the light of the concepts of non-extensive thermodynamics.

Generally, the modeling of the behavior of supersaturated fluids is conducted by assigning a specific form to the gaseous aggregate (spherical bubble, sessile bubble on a surface, in crevices of a material, etc.). The interfacial energy between the gas in the bubble and the fluid is then introduced, in equilibrium conditions, based on the Laplace's law. However, in natural systems, the gas/environment interfaces are often vague and do not permit to locate precisely the geometric boundaries of gaseous aggregate. Its form is most often imposed by the system itself. As example, let's take the case of a "gas bubble" formed in physiological tissue in the decompression of the diver. Where is located the border between the gaseous aggregate and its environment? What is the value of the interfacial area and the associated energy? How these parameters can be introduced in the relations of classical thermodynamics to describe the behavior of the system and its possible evolution?

In a set of previous works, we tackled this type of situation for condensed phases (solid and liquid) and showed that we could obtain conditions of equilibrium and evolution of the systems from thermodynamics based on non-extensive conventions. In these approaches formalized in 2004 [16], the phases' borders are not specified. The interfaces are supposed to be "fuzzy". We so treated the solubility of the small aggregates [17], their redox potential [18], their melting point [19], their surfactant properties in a solvent [20] or their wettabilities [21]. In these studies, we showed that, for non-extensive phases, the chemical potential, which is an intensive variable in the case of the unlimited phases, loses this property. Its value depends on the quantity of aggregates according to a power law.

In this paper, we will show that the properties of the gaseous aggregates in the presence of solutions supersaturated in gas can also be described by this type of approach. We shall thus propose a new formulation of the "equilibrium of super-saturation" of a gas in a liquid by taking into account the conventions of nonextensive thermodynamics. We shall find the classical descriptions and propose other possibilities of thinking. For example, we shall show that unlike the classical approaches, we can foresee conditions of degassing of fluids in conditions of sub-saturation.

2.

Equilibrium conditions: the gas is confined; the liquid is an unlimited phase

Studied confined system and equilibrium conditions

In the following development, we shall not try to determine the conditions of appearance of the gaseous aggregate, but the conditions for which this one is at thermodynamic equilibrium with its environment.

At temperature T and external pressure P, the system schematized on the figure 1 is constituted by -ni moles of pure gas i in a confined phase supposed to be non-extensive. The "shape" of the aggregate has not to be spherical [22]. It can be forced by its surrounding. To simplify the reasoning, we will suppose that the vapor pressure of the solvent in the confined gaseous phase is low enough to be neglected with regard to the internal pressure of the gas PNE.

-a phase (matrix) susceptible to solubilize the gas. This phase can be a pure liquid, a solution or a solvents mixture [23]. It will be considered as an unlimited phase. Its pressure is equal to the external pressure, P.

-an interface between the gas and the matrix which is supposed to be fuzzy.

PNE PNE

Figure 1 : scheme of the studied system. The gas is the non-extensive phase in contact with the matrix through a fuzzy interface.

The gas i contained in the confined phase is in equilibrium with the solute i dissolved in the matrix with which it is in contact. The equilibrium condition of the system is translated by the equality of the chemical potential of i under its forms gas,

The expressions of the chemical potentials in the two media are expanded

    i P , ) sol ( i i * ) gas ( i a ln RT f ln RT       (2) * ) gas ( i 
is the standard chemical potential of the gas. This quantity does not vary with the temperature.

             i n , T P , ) sol ( i V P i  (3)  i
V is the partial molar volume of the gas in solution.

We define   i f as the value of the gas fugacity. The latter is linked to the pressure of i pure in the nonextensive phase by

    NE P i i P f NE   ( 4
) NE P i
 is the fugacity coefficient of the gas at the pressure of the nonextensive phase.

  i a is the value of the activity of i, in the concentration scale, referred to the behavior of infinite diluted solutions. Let's take the case of gases slightly soluble in liquids, for which values of activity and concentration of i are equal

    i i C a  (5)
The equilibrium condition can be written as,

    i P , ) sol ( i i * ) gas ( i C ln RT f ln RT       (6)
Since, the standard chemical potential of the solute i varies with the pressure of the unlimited liquid phase, we can refer to an arbitrary pressure P°, for example, the pressure of 1 bar. If the value of the partial volume of i is supposed to be independent of the pressure, the expression of the chemical potential of the gas become

  o i P , ) sol ( i P , ) sol ( i P P V o         (7) And then,       i o i * ) gas ( i P , ) sol ( i i C ln RT P P V RT f ln o          (8) With, o i * ) gas ( i P , ) sol ( i Kh ln RT o      (9) o i
Kh is the solubility constant of the system, it is a dimensionless extent. The concentration of the gas i in the solution is linked to the nonextensive pressure of the gas in the confined phase by

    RT P P V i P i o i RT P P V i P i ref o i ref NE o i NE o i NE e C K e C C Kh P P         (10)
Pref and Cref are the pressure and concentration taken as units to express the adopted reference systems. o i K is a dimensioned magnitude. This relation is identical to the one proposed by Krichevsky and Kasarnovsky [24] in 1935.

The problem is now to link this magnitude to the external pressure, P. For that, we used the results of the nonextensive thermodynamics [16].

Solubility of a gas forming a nonextensive phase

The main advance we had realized in 2004, was to show that the pressure in a nonextensive phase is different from the ambient pressure since an energy is associated with the interface, whatever "the shape" of the phase is, even if this one is indistinct. In the general case, we demonstrate that, for a system involving only a single interface with its environment, the difference of pressure between the nonextensive phase PNE and the controllable external pressure, P, can be written as

dV d P P NE     (11)
V is the volume of the confined phase. For condensed systems, it is an extensive extent, i.e., whose value varies proportionally with the system mass.

χ is an « extensity ». It is a nonextensive magnitude characteristic of the fuzzy interface. In the general case, the value of  does not vary proportionally with the mass of the considered system (contrary to the extensive magnitude). The variable  is the intensive magnitude associated to the extensity . Its value can be positive or negative. It depends on the gas nature and the matrix. For condensed phases (solids and liquids), we set down by convention that  is an Euler's function of order m (

0 1   m
) of the number of moles, ni. The value of  increases with the system mass. Since the volume is an extensive extent (Euler's function of order 1 of the mass),  is a homogeneous function of order m of the volume. Eq. 11 becomes,

V m dV d P P NE        (12)
As is shown in our previous works, this relation permits to simply recover the expression of Laplace's law for a spherical system of radius r. the extensity  is identified with the sphere area which is an Euler's function of order 2/3 of the volume and  with the superficial tension.

  V A r r d r d dV dA P P NE       3 2 2 3 4 4 3 2            (13)
The approach we followed for condensed phases must be adapted to gases because these are compressible. As a result the volume of a gaseous aggregate is not any more an extensive magnitude; this can be easily checked for a sphere containing ni moles of gas the internal pressure of which is fixed by Laplace's law.

V r PV RT n PV V P i NE  2     (14)
By taking into account the geometrical characteristics of the spherical bubble,

3 2 3 1 3 4 2 V P V P RT n i           (15)
We see that if the number of moles ni is multiplied by , at constant external pressure P, the volume is not multiplied by .

Thus, for gases, we shall be restricted the original convention of the nonextensive thermodynamics which is that the extensity  is a homogeneous function of order m of the aggregate volume (eq. 12). We shall not try to link the magnitudes ( and V) to the contents of the system from geometrical relations characteristic of particular shapes.

In our previous studies, we showed (especially in reference [21]) that when the nonextensive phase, of volume V, involves several interfaces with its surrounding, the pressure difference is the sum of the contributions of each interface, j,

    j j j j NE V m dV d P P     (16)
The expression of PNE can be introduced in eq. 10

       j j j j RT P P V i P i o i V m e C K P o i NE    (17)
This relation links the solubility of a gas contained in a confined phase at the fixed external pressure. It is "Henry's law" generalized to small gaseous systems in the presence of a matrix susceptible to solubilize the gas.

To continue the discussion more easily, we adopt simplifying conditions.

Simplifying conditions

Let take the simple case where the variations of pressure are weak enough such as

  1    RT P P V o i e
. This approximation is justified by the very low value of the partial molar volume of the gases [25][26][27][28] in the liquids. Besides, the gas is supposed to behave as perfect gas ( 1

 NE P i  ).
In this framework, eq. 17 can be simplified,

   j j j j i o i V m C K P   (18)
This relation, which considers several interfaces, links the concentration of the gas solubilized in the matrix and the external pressure imposed on the system. The solubility of the gas in this condition can be compared its solubility, o i C if the phases would be unlimited,

o i o i C K P      j j j j o i i m PV C C   1 1 R (19)
R is the rate of supersaturation. We can clarify this relation by introducing the fact that the variables of extensities, , are Euler's functions of order m of the volume of the confined phase, by convention. We ascribe to them a shape of "power law", such as

j m j j V    (20)
αj is a constant characteristic of the considered interface and characterized by

j  . This leads to     j m j j j i o i j V m C K P 1   (21)
This relation shows that there is no proportionality between P and Ci in the case where the gas is constituted by the confined phase. The solubility of the gas depends on the volume of the gaseous aggregate according to a power law. The relation between the solubilities is written as

     j m j j j o i i j V m P C C 1 1 1   R (22)
Besides, we notice that according to the sign of the variables of intensity j, which can be positive or negative, the concentration, i C , can be higher or lower to o i

C , what allows envisaging the existence of systems for which there is presence of gaseous aggregates in equilibrium with the gas solubilized for concentrations lower than the saturation.

The limits of eq. 22 allow recovering the properties of unlimited systems. When the volume of the aggregates becomes big, the phase gas loses its nonextensive properties. For m < 1,

0 1   j m j j j V m   what implies that i C is equal to o i C .
We shall discuss afterward the particular case in which mj = 1.

Solubilities of gases in confined phase

Now, let imagine various cases of applications of these relations and consider the particular case of the systems presenting a single interface with the matrix. The application of eq. 22 to a single interface allows examining the behavior of a gaseous aggregate in solution in equilibrium with the dissolved gas.

1 1 1     m o i i V m P C C  R (23)
In the case of a spherical aggregate, of radius r, this relation allows to get the relation used by numerous authors to express the solubility of bubbles

r P C C o i i  2 1 1   R (24)
However, its experimental check was rarely undertaken. Recently, Ohgaki et al. [29] published a study on the behavior of nano-bubbles of various gases of radius of 50 nm in water at 298 K. For nitrogen, these authors show that they obtain suspensions of stable bubbles during more than two weeks, containing until 600 cm 3 of confined gas (standard condition) by liter of solution. Even if it is thermodynamically "unstable" in the sense where the free energy is maximum, the equilibrium of the system constituted by bubbles in the medium is not quickly destroyed by the fluctuations of the environment. The nitrogen solubility in the solution is 36 times higher than the solubility in unlimited phases. The experimental value of the internal pressure was found equal to 63 bars, while the use of the eq. 24 with a superficial tension equal to 72 10 -3 N m -1 leads to a value of 30 bars, is approximately half of that determined. The value of the internal pressure thus exceeds the calculated one, while it is shown that the superficial tension of the bubble decreases when its curvature increases [30]. The discrepancy between calculated and experimental values can have various origins of which an estimation too much idealized of the shape and the size of bubbles. The micrographies show that the aggregates are not perfect spheres and the opinion of the authors is that the suspension of nano-bubbles is not strictly homogeneous. But if we preserve the hypothesis that Laplace's law applies to these systems, then it is necessary to imagine that all the nano-bubbles, even imperfect, behave as a set of spheres of radius of 50 nm.

It seems more reasonable to envisage that the law of Laplace does not apply to these objects, using the argument that their geometrical border is badly defined.

This remark had already been made by Bowers [31] in 1996. The latter supposed that the interfaces for nano-bubbles were vague, and that there was a domain of transition between the gas and the liquid (blobs). Eq. 12, applied to a single interface, allows expressing the pressure difference between the inside of this type of aggregate and the environment according to its volume by a power law.

1    m NE V m P P  (25)
The gas solubility is then given by

P V m PV m C C m o i i 1 1 1          R (26)
The validity of these relations has to be checked from further studies as those proposed by Ohgaki et al. [29], by determining the gas solubility for various nanobubbles sizes and external pressure, that obviously raises the problem of controlled obtaining of such systems. Anyway, eq. 26 shows that for a given rate of supersaturation, there is a situation of (unstable) equilibrium for which the mass of the gaseous aggregate is perfectly defined, in the conditions imposed by its environment, in particular for its shape which cannot be spherical. It is surprising that, in some analyses, the authors wonder on the stability of bubbles using the argument that their internal pressures are much higher than the surrounding pressure. This pressure difference is the reason for which the system is at equilibrium. So this pressure difference cannot be regarded as the origin of a thermodynamic force therefore disequilibrium. The affinity of such a system is then null.

0      P i P i i i NE     A (27)
The only thermodynamic force at stake involves the chemical potentials.

However, the equilibrium corresponding to a maximum of free energy, these systems should evolve either toward the solubilization of aggregates or toward their increase due to the fluctuations in environmental parameters such as temperature. This does not seem to be the case, suggesting a small change in the Gibbs energy with the radius around the critical radius.

The existence of nanobubbles solutions [32][33][34][35] and stable encapsulated microbubbles [36,37] is one example. Different authors suggest several assumptions to justify this property [13,38]. The molecular dynamics simulation can provide on this subject some precious elements of thinking [39].

The originality of eq. 26 is to allow considering the creation of bubbles in a sub-saturation medium when τ is negative.

We had encountered this kind of situation when analyzing the values of the melting points of nano-systems [19]. The melting point of a particle of the same metal can decrease (τ > 0) when its size decreases, or on the contrary, increase (τ < 0) depending on the environment of non-extensive phase. In the case of particles embedded in a matrix, it increases.

In this case, the possibility of observing the creation of gas clusters in equilibrium with the solution cannot be dismissed even at concentrations below saturation.

As τ can be negative, we can then consider that the pressure in the aggregates is lower than this of the environment, but with the condition

1    m V m P  
, since the term PNE (occurring in a logarithm in the expression of the gas chemical potential) must be positive.

The problem is different if one considers a non-extensive condensed phase. Internal pressures of the aggregates can then be negative. This will be detailed in the discussion.

Eq.26 allows considering different system behaviors depending on the chosen value of m. We showed that with m = 2/3, we formally found the behavior of spherical bubbles. Other values are interesting, such as m = 1. In this case, when the number of moles of the aggregate is multiplied by λ, the extensity variable χ and the volume of non-extensive phase are also multiplied by λ. Then, the solubilization law takes the form

       i o i C K P ( 28
)
This case corresponds for example to a non-extensive phase which is replicated when the amount of gas increases. The discrepancy between the concentration of the supersaturated solution and the concentration at saturation is constant and does not vary with the amount of gas.

An illustration of this behavior is given in the paper of Bowers et al. [40] which shows a "super-Henry's Law" for the solubility of oxygen produced by the catalyzed decomposition of iodine by hydrogen peroxide. In this study, the plot of the concentration of dissolved gas according to the pressure is parallel to the Henry's Law, since it corresponds to the following relation

    o i o i i K K P C    (29)
In the work of Bowers et al. [31,40], this behavior is considered as particular case of the classical nucleation theory (CNT), for which the rate of nucleation is constant.

Discussion

The previous relations form a framework of thoughts which permit to examine some works and to imagine others on the behaviors of bubbles in solution and more generally, on the conditions of solubilization equilibrium of gases in liquids in confined spaces.

Use of Kelvin's relation

In some studies, the solubility in liquids of gases contained in bubbles is discussed from Kelvin's relation, by simply changing the sign before the term relative to the contribution of the interfacial energy. The equilibrium between a liquid and its vapor is treated by the same way. Thus, Defay [START_REF] Defay | Surface tension and adsorption[END_REF] suggested the following relation to express the variations in vapor pressure of a liquid in equilibrium with bubbles, with the conclusion that the smaller is the vapor pressure of the liquid, the stronger is the curvature. This relation was recently used by Castellanos et al. [START_REF] Castellanos | [END_REF] to show the need to consider the decrease of the surface tension of bubbles with their radius for much higher size ranges (of about 4 log units of the radius) than those assumed for the drops.

RT V r P P ln * o i i  2   (30)
In our opinion, eq. 30 is not suitable to describe the behavior of a gas bubble in an unlimited environment. In fact, it is simply shown that vapor pressure in a bubble is invariant with the radius of the bubble, which has been further confirmed by simulation [43].

Consider a liquidgas equilibrium, for which the pressure of the liquid phase is P and that of the gas, Pb. The equilibrium condition is written

P ) liq ( i P ) gas ( i b    (31)
Both terms are expanded

  * ) liq ( i b * ) gas ( i P ln RT     (32)
Which involves that

  constant    RT P ln * ) gas ( i * ) liq ( i b   (33)
The value of vapor pressure in a bubble, put in an unlimited solution at pressure P, is then constant. It does not depend on the curvature radius of the bubble.

We share the skepticism of Seddon et al. [44] about the work of Colaço et al. [45] on the inappropriate use of the Kelvin relation. The latter applies only to limited condensed phases.

This can be merely shown by considering the solubility of a gas (in an unlimited phase) in a liquid aggregate. This is the opposite case to the one discussed above.

Using the same formalism as before, the equilibrium condition concerns the equality of chemical potentials of i in its gas form, P ) gas ( i  and as solute,

NE P ) liq ( i  , NE P ) liq ( i P ) gas ( i    (34)
The expressions are expanded in the framework of the nonextensive thermodynamics

    i ) sol ( i P ) sol ( i P ) sol ( i P ) sol ( i * ) gas ( i C ln RT V m P ln RT NE                (
Considering the fogs as systems where water is in the form of spherical liquid drops, the application of eq.39 provides an under-saturation of the aqueous phase. This property is not verified for many systems where there are sometimes supersaturations. Such behavior cannot be justified by classical thermodynamics. However, in the context of non-extensive thermodynamics we can assume that the natural environment that can be fog or cloud mades of liquid aggregates whose boundaries are ill-defined and for which the intensity variable τ is negative. In this case, it is possible to observe gas supersaturation in the aqueous entities with an amplification of the phenomenon when the aggregate size decreases [46,47].

Conclusion

In this paper, we have shown that the use of non-extensive thermodynamics' concepts allowed formalizing in a very general way, even in complex systems, the equilibrium solubility of gases contained in bubbles, or in gas aggregates, in the presence of supersaturated solutions. Besides introducing new relationships and discussion of the applicability of other (Kelvin), the main contributions of this work were to show -that the application of Laplace's law to the interface gas / solution at nanometric state is unlikely. This interface is probably geometrically ill-defined and can be described as a fuzzy interface.

  chemical potential of the solute, referred to the behavior of infinite diluted solution. This quantity varies with the temperature and the pressure according to the following relation

i P and o i P

 i are respectively the vapor pressures of the liquid in the bubble and in the unlimited gas phase, * V is the bubble volume.

35 )

 35 The relation linking the gas solubility in the confined phase to the pressure of the unlimited phase is the gas solubility in the liquid in unlimited phase, o i C , and in condensed phase is written as  is positive (this is the case of water drops) the gases are less soluble in the condensed liquid phase as the volume of the aggregates decreases. For a spherical aggregate (m=2/3, τ = γ), one obtains

-the possibility of considering the presence of gaseous aggregates in equilibrium with the solution even when the latter is under-saturated.

Although the relevance of the overall relations could not be verified by lack of experimental data, it remains true that the proposed relations are a way of thinking to interpret the behavior of these complex systems, to imagine or to justify other. This is the case of the concept of negative pressure which was presented in different works [48][49][50] and variously commented [51,52]. In non-extensive thermodynamics, nothing opposes to a negative value of the nonextensive pressure for condensed phases, since we consider negative intensities, τ,

The increases in melting temperatures, observed for coated metallic clusters when their size decreases [19], fall within this property.

The concepts of non-extensive thermodynamics apply to a wide scope in confined condensed phases. In the nanometric scale, classical thermodynamics is undoubtedly no more applicable [53,54].

The nano-thermodynamics is probably not extensive.


Julien Bonnet

Gad Suissa

Matthieu Raynal

Laurent Bouteiller

Organogel formation rationalized by Hansen solubility parameters: dos and don'ts

Some organic compounds gelate liquids by forming a network of anisotropic fibres. Hansen solubility parameters can be used to predict the range of liquids that are likely to be gelled by any given gelator. We critically review the various approaches recently proposed in the literature. In particular, we discuss the shape of the gelation domain, the relevance of the Teas plot representation and use of group contribution calculations. We also propose an improved scheme for the solubility tests, and a detailed procedure for 10 the determination of the gelation domain.

Introduction

Organogels are obtained when a limited amount of a low molecular weight gelator (LMWG) is dispersed in a liquid where it self-assembles into elongated fibrillar structures, that form an entangled network. [START_REF]Molecular Gels: Materials with Self-Assembled Fibrillar Networks[END_REF][START_REF] George | [END_REF] These gels are often thermally reversible and show a rich variety of rheological properties going from a purely elastic to a thixotropic or viscoelastic behaviour. [3][4][5][6][7] Such fibrillar structures are highly promising candidates for a wide range of applications 8,9 such as drag reducing agents, 10 biomaterials, 11,12 stimuli-responsive materials, 11,[13][14][15][16][17][18][19] sensors, 14,16- 18,20,21 templating components for organic or inorganic nanostructures, 22,23 liquid crystalline materials, 24,25 optoelectronic materials, [26][27][28][29] host-guest systems, 30 and in the field of catalysis. 31,32 They can even be used to improve the mechanical properties of soft solids. 33 To date, a wide range of LMWGs are known, but most of them have been discovered by serendipity. As a matter of fact, it is still difficult to design a gelator de novo to yield a gel in a specific liquid. In contrast, we now have guiding principles to predict if a previously described LMWG will gelate an untested liquid, based on the known ability of the LMWG to gelate a range of more or less similar liquids. Early attempts to rationalize the gelling power of a LMWG were proposed based on various solubility indicators: dielectric constant, [34][35][36] Reichardt's polarity scale (E T ), 36 Hildebrand solubility parameter, 36,37 Kamlet-Taft parameters, 36,[38][39] Hansen solubility parameters (HSPs), 36,40 dissolution enthalpy and entropy. 41 Each of these attempts was focused on a particular LMWG family, and while the conclusions are of interest, they cannot easily be applied to other LMWGs. In contrast, we recently extended the HSP approach and showed that it is possible to predict the gelling ability of any LMWG based on its behaviour in a limited set of solvents. 42 Since then, several groups have tested our approach with new LMWGs and have confirmed the validity of the concept. [43][44][45][46] However, some concerns have been expressed about the mathematical difficulties involved in the method, 47,48 while several studies have proposed related approaches. [47][48][49][50][51][52][53][54][55][56] Therefore, the objective of the present report is both to better explain our approach to make it more accessible and to critically discuss the recent developments in the field.

General comments on the method

The basic principle For several decades, HSPs have been successfully used in the field of polymer science to select solvents for various applications. [START_REF] Hansen | Hansen Solubility Parameters: A User's Handbook 2 nd Ed[END_REF][START_REF] Hansen | [END_REF] In this approach, molecular interactions are categorized into three groups: dispersive interactions (𝛿 ! ), polar interactions (𝛿 ! ) and hydrogen bonds (𝛿 ! ). In practice, the procedure consists in comparing the HSPs for the solvent (𝛿 ! ! , 𝛿 ! ! , 𝛿 ! ! ) to the HSPs for the polymer (𝛿 ! , 𝛿 ! , 𝛿 ! ). If the distance between the two points in Hansen space (defined as 𝑅 =

4(𝛿 ! -𝛿 ! ! ) ! + (𝛿 ! -𝛿 ! ! ) ! + (𝛿 ! -𝛿 ! ! ) !
) is smaller than an empirical and case specific value R Sol , then the polymer and the solvent have a high probability of being miscible. The values for the HSPs of liquids can be found in the literature, [START_REF] Hansen | Hansen Solubility Parameters: A User's Handbook 2 nd Ed[END_REF][START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF] and the values for the polymer are determined by testing the solubility of the polymer in a range of liquids and plotting the results in a 3D representation, with 𝛿 ! ! , 𝛿 ! ! and 𝛿 ! ! as axes (the Hansen space).

The points for the good solvents tend to cluster in a particular region in space, thus defining a solubility sphere for the polymer, with (𝛿 ! , 𝛿 ! , 𝛿 ! ) as its centre and R Sol as its radius. [START_REF] Hansen | Hansen Solubility Parameters: A User's Handbook 2 nd Ed[END_REF][START_REF] Hansen | [END_REF][START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF] After dissolution of a LMWG in a liquid at an elevated temperature and subsequent cooling, a gel may form rather than a solution or a precipitate, if solute-solvent and solute-solute interactions are suitably balanced. [START_REF] Van Esch | [END_REF][61][62][63] We can therefore guess that in a favourable domain in Hansen space, the liquids are gelated because they do not compete too much with inter-gelator interactions, but still allow dissolution at high temperature. We have actually proved through extensive literature data analysis that there is a strong correlation between HSPs and gel formation. 42 The method consists in plotting the solubility data in Hansen space, where each liquid is represented by a point of coordinates (𝛿 ! ! , 𝛿 ! ! , 𝛿 ! ! ) and labelled according to the group it belongs to: S (solution forming), I (either insoluble or formation of a precipitate after cooling) and G (gel forming). The good solvents (S) tend to cluster in a particular region of space, whereas the gelating liquids (G) tend to cluster in a distinct region of space (or sometimes two regions).

Fig. 1 Solubility data from Jamart--Grégoire et al. 50 for amino acid based LMWG 1a (5g/L), represented in Hansen space. The gelated liquids (G) are represented by blue points; both good solvents (S) and non--solvents (I) are represented by red points. The gelation sphere is green and its centre is light green. The plot is generated with the HSPiP software. [START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF] In order to turn this plot into a predictive tool, a model is needed. By analogy with the polymer solubility sphere, the centre and the radius of a gelation sphere can be determined so that as many G liquids as possible lie inside the sphere, but as many I and S liquids as possible lie outside (see below for the practical determination of the sphere). Fig. 1 shows the result of this approach applied to the data from an amino acid based LMWG recently reported by Jamart-Grégoire et al. 50 When the experimental data is comprehensive, as in this example, the gelation sphere is unambiguously defined and it can then be used to predict if an untested liquid (or liquid mixture 46 ) will be gelated by this particular LMWG, according to whether its HSP coordinates fall inside or outside the gelation sphere. This straightforward approach considerably reduces the number of trials usually involved during the identification of a suitable gelator for a particular application, i.e. in a particular formulation. Moreover, it allows using the extensive solubility data available in the literature to predict if liquids of industrial interest can be gelled by a particular LMWG that was only tested in usual organic solvents.

Of course, as explained in our initial publication, 42 it is also possible to determine a solubility sphere from the same data, but we will not focus on this feature here, as the main purpose of using LMWGs is to obtain gels.

The shape of the gelation domain

It is not clear to us whether the gelation domain should theoretically be a sphere or not. However, most experimental data available show compact and globular gelation domains, [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] and the sphere is the mathematically most simple object that can be used to describe these domains. In a few cases however, a very elongated or even two discontinuous gelation domains have been identified. 42,44 From a theoretical perspective, this is in fact not surprizing because a given gelator may not necessarily form fibres with the same crystalline structure in every tested liquid. 51,64,65 Therefore, the functional groups of the gelator that are exposed at the fibre surface can actually depend on the gelated liquid, 66 which obviously affects the interfacial energy. In such cases, several gelation domains can be expected: one gelation domain for each polymorphic form displayed by the fibres (for an example, see Fig. S1). From a practical standpoint, in these special situations, one can advantageously try to describe the gelation domain with an ellipsoid shape or with a pair of spheres.

The importance of using all three HSPs

Several authors have analysed their gel data in the light of HSPs but have unfortunately considered each parameter (𝛿 ! ! , 𝛿 ! ! , 𝛿 ! ! or

𝛿 ! = (𝛿 ! ! ) ! + (𝛿 ! ! ) ! + (𝛿 ! ! ) !
) independently of the others. 36,40,50,51,55 Even if some correlation with a particular parameter exists, it is obvious that an improved description of the data is possible if all three parameters are used. For example, Jamart-Grégoire et al. noticed a better correlation of the gelation behaviour of an amino acid based LMWG with 𝛿 ! ! than with any other parameter: with only a few exceptions, [START_REF]methylnaphthalene and p-xylene[END_REF] the liquids are gelled by LMWG 1a if and only if they are situated in the range 0.4 < 𝛿 ! ! < 2.9 MPa 1/2 . 50 While this is correct, Fig. 1 shows that the correlation is even better in a three dimensional plot: without a single exception, the liquids are gelled if and only if they are situated in the sphere of centre (𝛿 ! = 18.8, 𝛿 ! = 2.8, 𝛿 ! = 2.1 MPa 1/2 ) and radius R = 3.8 MPa 1/2 . Fig. S2 shows that the other gelator in this study is also perfectly described by a gelation sphere. Interestingly, the slight variation in gelator structure is translated into a slight shift of the gelation sphere, whereas the one-dimensional analysis based on 𝛿 ! ! does not capture this subtle effect. While the use of a single HSP may be sufficient to describe a particular system, it is obvious it cannot be universal. For example, the hydrogen bond forming gelator of Jamart-Grégoire et al. was ruled (in a first approximation) by the hydrogen bonding parameter 𝛿 ! (see above), whereas the behaviour of polar oxadiazole gelators reported by Li et al. was reported to be better correlated to a combination of the hydrogen bond and polar parameters 𝛿 ! = (𝛿 ! ) ! + (𝛿 ! ) ! . 51 Unsurprisingly, both systems can be advantageously rationalized if all three HSPs are used (Figs. 1 andS3).

Even more eloquently, Fan et al. reported the absence of correlation between the gelation ability of a two-component LMWG in water/solvent mixtures and any HSP taken individually. 48,52 While this is apparently correct, Fig. 2 shows that in a three dimensional plot all the gelled liquids are clustered in a region of high 𝛿 ! ! and intermediate 𝛿 ! ! . In this particular example, the determination of a reliable gelation sphere is not feasible because of a lack of data; however, the correlation between gelation and position in Hansen space is obvious.

The traps of the Teas plot representation

The full HSP approach with three parameters is thus quite successful but unfortunately requires the use of a software that allows to generate 3D plots. In order to alleviate this graphical representation drawback, several authors proposed to use a 2D representation called Teas plot. 43,47,49,53 The idea is to normalize the HSPs to be able to plot them in a triangular 2D representation with coordinates: While this approach appears to be successful in cases when a limited number of data points are available and while it is undeniably simple to manipulate, one has to realize that the Teas plot formula has no theoretical justification and that the representation can be misleading. Indeed, two points that are close to each other in the 3D Hansen space representation are also close to each other in the Teas plot representation, but the reverse is not true. For instance, diethyl ether (𝛿 ! ! = 14.5, 𝛿 ! ! = 2.9,

𝑓 ! = 𝛿 ! 𝛿 ! + 𝛿 ! + 𝛿 ! 𝑓 ! = 𝛿 ! 𝛿 ! + 𝛿 ! + 𝛿 ! 𝑓 ! = 𝛿 ! 𝛿 ! + 𝛿 ! + 𝛿 !
𝛿 ! ! = 4.6 MPa 1/2 ) and chloroform (𝛿 ! ! = 17.8, 𝛿 ! ! = 3.1, 𝛿 ! ! = 5.7 MPa 1/2 )
are far apart in the 3D plot, which reflects their well known solubility differences, but they are nearly at the same location in the Teas plot (Fig. 3). Consequently, it is not surprizing that in some cases the solubility data correlation visible in a 3D representation is blurred in a Teas plot (Fig. 3). This example clearly contradicts the claim that the gelation can be predicted based on Teas plot representation of HSPs. The gelation sphere and the solubility sphere do not necessarily have the same centre Organogel formation requires a suitably balanced solubility, because the gelator should be soluble at high temperature and should assemble without precipitating at room temperature. Therefore it is reasonable to expect that the gelation domain is situated close to the solubility domain in Hansen space. Several authors went a step further and assumed that the gelation domain and the solubility domain have the same centre. 45,46,49 This leads to a core-shell graphical representation with two concentric spheres, where the solubility domain is in the core and the gelation domain is in the shell. Although this particular repartition of the solubility and gelation data might be observed in some cases, the data presented up to now does not unambiguously prove it because of the scarcity of data points (see Figs. S4 andS5). Moreover, most of the examples described in reference 42 can clearly not be modelled by two concentric spheres, as shown in a particular example in Fig. 4. Therefore this model cannot be generally valid. The centre of the gelation sphere cannot be estimated from group contribution

Several approaches have been developed to calculate the HSP of compounds by a group contribution method. 70,[START_REF] Brandrup | Polymer Handbook[END_REF] These approaches are very useful when the HSPs cannot be measured experimentally. Therefore, it is tempting to calculate the HSPs for a gelator from its chemical structure by a group contribution method. 43,48,49,54 However, one should realize that the value that is obtained may be a good approximation for the centre of the solubility sphere, but has no reason to be related to the centre of the gelation sphere, unless both domains are concentric, which remains to be proved (see above). For example, Fig. 5 shows in Hansen space the gelation data of reference 43 together with the point calculated for the gelator (12-hydroxystearic acid) by a group contribution method. 43 This point is clearly not situated within the gelation domain. Therefore, the absence of correlation (that was noted by the authors) between gelation and the distance to the gelator is not surprizing. Another example, provided in Fig. S6, shows that the point obtained by group contribution is situated in the solubility domain, and not in the gelation domain.

The importance of kinetics

In fact, one should be aware of an important difference when applying the HSP approach (i) to describe the solubility of polymers or (ii) to rationalize the gel formation of LMWGs. Indeed, the (polymer) solubility is an equilibrium property, whereas the gel formation is a kinetically controlled process. 54 For instance, the viscosity of the liquid has been suggested to influence the stability of gels because it affects the diffusion rate of the gelator molecules in the liquid. 47 Moreover, organogels are known to be metastable objects that may evolve toward a more stable precipitate or crystal characterized by a reduced interfacial area between the LMWG and the liquid. Such kinetic effects are definitely not taken into account in the HSP theory and may be responsible for some discrepancies between experiment and the HSP rationalization. Of course in order to minimize such effects, it is of utmost importance to use consistent preparation conditions within each study (i.e. the same concentration and cooling rate). The present HSP approach is quite successful in predicting if a given LMWG should form a gel in a given liquid. It would be highly interesting to be able to extend this yes/no information into a more quantitative prediction of the gel stability. Although no universal criteria is available yet, some interesting trends have been reported between the gel stability and HSPs. Within homologous series of liquids, the gelation temperature (T gel ) below which the gel is stable or the critical gelator concentration (CGC) above which the gel is stable have been correlated to HSPs. 36,43,45,56,[START_REF] Edwards | [END_REF] It remains to be seen if this approach can be extended in order to be able to estimate the T gel or the CGC without prior data on closely related liquids.

HSP in practice

The acquisition of the solubility data Obviously, the robustness of the predictions that can be made based on this HSP approach heavily rests on the comprehensiveness of the solubility data available to determine the gelation sphere. Therefore, the choice of the test liquids is crucial. Ideally a high density of points in the Hansen space is desired, and this is especially true in the initially unknown regions where the behaviour switches from "gel" to "no gel". In order to a comprehensive solubility data set at a reasonable experimental cost, we suggest a two-step procedure. In the first step, about 20 liquids of known HSPs are selected so that they are homogeneously scattered in Hansen space. Table S3 provides such a list of liquids with HSPs in the following range (14.7 < 𝛿 ! ! < 20, 0 < 𝛿 ! ! < 18, 0 < 𝛿 ! ! < 42.3 MPa 1/2 ). Then gel formation is tested in these liquids. A priori any concentration of the gelator and any gel formation procedure can be selected, with the obvious caveat that the predictions based on these tests will only be relevant to the experimental conditions selected. Fig. 6a shows a typical data set obtained for a member of a well-known family of hydroxystearic amide based LMWG (C12). 73 As expected, the gel forming liquids are grouped in a particular region of the Hansen space (low 𝛿 ! ! , 𝛿 ! ! and 𝛿 ! ! ), but because of the relatively large distance between the experimental points, the determination of a gelation sphere (see below) cannot be precise. However, based on this preliminary data set it is now possible to select a second list of liquids focusing in the region in direct contact with the initial group of gel forming liquids. For this second step, it is possible to choose either new liquids or mixtures of the former liquids. To illustrate this, we have selected from the initial gelation data 5 gel forming liquids and 6 non-gel forming liquids and mixed them in various proportions to generate 44 new test liquids, the HSPs of which were calculated as the volume average of the pure liquids (Table S4). Fig. 6b shows the extended gel formation data obtained after the second step. We now have a very precise picture of the gelation domain. The gelated liquids (G) are represented by blue points; both good solvents (S) and non--solvents (I) are represented by red points. The gelation sphere is green. The plot is generated with the HSPiP software. [START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF] The determination of the gelation sphere

The objective is to find the centre and the radius of a sphere, so that as many G liquids as possible lie inside the sphere, but as many S and I liquids as possible lie outside. This can be done straightforwardly with any basic spreadsheet software as exemplified in the Microsoft Excel spreadsheet provided in ESI. First, a table is created containing the HSPs of the test liquids and the results of the gelation test in the form of a column with values of 1 or 0 depending on whether a gel is formed or not. Then arbitrary values for the gelation sphere centre and radius are chosen and the distance between this centre and each test liquid is calculated. A mathematical criterion has to be applied to these distances to quantify in what measure the guessed centre and radius are suitable and to allow their optimization. Several such criteria can be used, but we found the procedure proposed by Gharagheizi et al. 74 to be particularly simple and effective, and we implemented it in the Microsoft Excel spreadsheet provided in ESI. The optimization of the gelation sphere can then be done manually or more conveniently with a minimization routine (the Solver function in the case of Microsoft Excel spreadsheet). This step is technically very simple but requires some critical evaluation, as is the case for any numerical minimization. In particular, the procedure should be repeated several times with distinct initial guesses to check the robustness of the final result.

For instance, if the procedure is applied several times to the limited data of Fig. 6a, one realizes that several gelation spheres are possible and therefore that the uncertainty is high. In contrast, the same procedure applied to the extended data of Fig. 6b, reproducibly yields the same gelation sphere (𝛿 ! = 15.9, 𝛿 ! = 6.2, 𝛿 ! = 0.3 MPa 1/2 , R = 6.8 MPa 1/2 ). Finally, a visualization software is needed to plot the HSPs of the test liquids and the gelation sphere in a 3D plot. [START_REF]We have used Mathematica software[END_REF] Alternatively, one can use a specialized software dedicated to this task (HSPiP). [START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF] This software contains a comprehensive list of HSPs for the test liquids and allows to perform both the numerical determination of the gelation sphere and its 3D visualization.

Conclusion

Based on solubility tests of a LMWG in a set of liquids, it is possible to define one (or more) gelation spheres. If the HSPs of an untested liquid (or of an untested mixture of liquids) fall in the gelation sphere, then this liquid or mixture of liquids is likely to be gelled by the LMWG. Of course, the reliability of the prediction will critically depend on the quality of the solubility data set, that can be significantly improved by a two-step procedure. This straightforward method should become a useful data mining tool, allowing to considerably reduce the number of trials usually involved during the identification of a suitable gelator for a particular application. Although the use of a Teas plot representation or of only one or two HSPs out of the three has been proposed to simplify the analysis, we stress that significant information is lost in the process. Moreover, the calculation of the gelator HSPs by a group contribution method cannot yield the centre of the gelation sphere.

Fig. 2

 2 Fig.2Solubility data from Fan et al.52 for a two--component LMWG, represented in Hansen space. The gelated liquids (G) are represented by blue points; both good solvents (S) and non--solvents (I) are represented by red points. The plot is generated with the HSPiP software.[START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF]

Fig. 3

 3 Fig. 3 Solubility data from Shinkai et al. 68 for cholesterol--based LMWG 2Me, represented in Hansen space (a) and in a Teas plot (b). The gelated liquids (G) are represented by blue points; both good solvents (S) and non--solvents (I) are represented by red points. The centre of the gelation sphere and the projection of the sphere on the Teas plot are in green.

47

 47

Fig. 4

 4 Fig.4 Solubility data from Dastidar et al.69 for cinnamate--based LMWG 3--BrCIN, represented in Hansen space. Blue: gel; magenta: soluble; orange: insoluble.

Fig. 5

 5 Fig. 5 Solubility data from Rogers et al. 43 for 12--hydroxystearic acid LMWG, represented in Hansen space. Blue: gel; magenta: soluble. The black point represents the coordinates calculated by Rogers et al. with a group contribution method for the gelator (12--hydroxystearic acid: 𝛿 ! = 17.59, 𝛿 ! = 2.86, 𝛿 ! = 6.77 MPa 1/2 ). The green point is the centre of the gelation sphere determined by the present method (𝛿 ! = 16.3, 𝛿 ! = 7.3, 𝛿 ! = 0.1 MPa 1/2 , R = 7.5 MPa 1/2 ).

5

 5 The next step: rationalization of the gel stability (CGC and T gel )

Fig. 6

 6 Fig. 6 Solubility data for hydroxystearic amide based LMWG C12, represented in Hansen space. The solubility was tested in the first step in 21 liquids (a) and in the second step in 44 additional liquid mixtures (b).The gelated liquids (G) are represented by blue points; both good solvents (S) and non--solvents (I) are represented by red points. The gelation sphere is green. The plot is generated with the HSPiP software.[START_REF] Abbott | Hansen Solubility Parameters in Practice software, eBook, datasets[END_REF]

Acknowledgments

Prof. Steven Abbott is gratefully acknowledged for sharing his insight and providing us with the HSPiP software. Financial support from Total company is also acknowledged.

Notes and references

a Sorbonne Université, UPMC Univ Paris 06, UMR 8232, IPCM, Chimie des Polymères, F-75005 Paris, France, b CNRS, UMR 8232, IPCM, Chimie des Polymères, F-75005 Paris, France † Electronic Supplementary Information (ESI) available: Additional solubility data; excel file for the determination of the gelation sphere. See DOI: 10.1039/b000000x


Cécile Fonteneau

Sandrine Pensec

Laurent Bouteiller

Versatile synthesis of

come

Introduction

The dynamic character of reversible non covalent interactions in supramolecular polymers is responsible for the appearance of new properties as compared to those of usual covalent polymers. For example, they can display thermoreversible polymer-like properties (such as viscoelasticity), 1 or form self healing materials. 2,3 To obtain such materials, the synthesis of polymers bearing hydrogen bonding stickers is a highly successful approach. [START_REF] Binder | Hydrogen Bonded Polymers[END_REF][START_REF] Herbst | [END_REF] The introduction of the hydrogen bonding unit can be made by several ways: 6 postpolymerization functionalization, [7][8][9] the use of functionalized monomers, [10][11][12][13] or functionalized initiators or transfer agents. 14,15 In this context, it is of particular interest to use controlled polymerization strategies to introduce the hydrogen bonding units at precise positions. Numerous techniques have been used such as NMP, 16 ROP, 17 ROMP, 18,19 RAFT 14,20,21 and ATRP. 15,[22][23][24] Various architectures have been obtained: macrocyclics, 9,25 star-shaped, 14,17,26 reversibly crosslinked, [27][28][29] block copolymers 18,19,30 . However most of these edifices bear at least two stickers per chain, that are designed to form dimers or small clusters which is particularly of interest to obtain thermoplastic elastomers 31 . In contrast, the introduction of a single hydrogen bonding sticker in the middle of the chain, that can form large size aggregates, has been rarely reported. 32,33 It is however very interesting to form comb-shaped supramolecular polymers to combine the nanostructuration due to the stickers without inducing macroscopic gelation. 34,35 We have previously reported the synthesis of a comb-shaped supramolecular polymer where the backbone is dynamic. 36,37 The bisurea synthon formed a ditopic sticker connecting a large number of polyisobutene side chains without cross-linking them. This polymer displays interesting properties in solution and in bulk especially regarding its adhesion on low energy surfaces like poly(dimethylsiloxane). 38 To further investigate the properties of this type of polymers, we have now developed a modular method for tuning the polymer structure. We report here the synthesis by atom transfer radical polymerization of precisely defined polyacrylates bearing a Hbonding ditopic sticker in the middle of the chain, where it is possible to tune the self-association strength, the molar mass and the monomer structure. Self-assembly of these functionalized polymers is characterized by FTIR and SANS in solution.

Experimental Section

Materials

The following reactants were used without purification: 2chloropropionylchloride (98%), hydrazine hydrate (64%), triphosgene (98%), CuCl (99.99%), Cu(0) (<75µm, 99%), CuCl 2 , and HCl 4M in dioxane from Aldrich; 2-aminobutanol (Alfa Aesar, 99%), di-tertbutyl dicarbonate (Fluka, 99%), triethylamine (99%) and palladium on carbon from ABCR, 2,4-dimethyl-5nitroaniline (Apolloscientific), diisopropylethylamine (Acros, 98%), DMF (Normapur). n-butylacrylate (Acros, 99%), 2ethylhexylacrylate (Aldrich, 99%), 3,5,5-trimethylhexylacrylate (Aldrich, 99%), and pentamethyldiethylenetriamine (PMDETA) (Acros, 99%) were distilled prior to use. All the anhydrous solvents were used from a solvent purification system (MBraun SPS).

Characterization methods

NMR spectroscopy. 1 H and 13 C NMR spectra were recorded on a Bruker AC200 (200MHz) and AC300 (300MHz) using CDCl 3 and (CD 3 ) 2 SO. Size exclusion chromatography (SEC). The molar masses (M n , M w ) and the molar mass distribution (Đ = M w /M n ) were determined by size exclusion chromatography in THF at a flow rate of 1 mL/min with two different set-ups. Relative molar masses (M n,SEC (RI) ) were determined using a Waters HPLC 515 pump, a Viscotek VE 5200 automatic injector, two columns thermostated at 40°C (PSS SDV, linear M, 8 mm x 300 mm, bead diameter: 5 µm, separation range: 400-10 6 Da), a Viscotek 3580 differential refractive index and a Waters UV 484 detectors. Calculations were made using the Omnisec software. The calibration curve was based on polystyrene standards from Polymer Laboratories. The polystyrene calibration in THF is appropriate for linear poly(n-butylacrylate) samples 39 . Absolute molar masses (M n,SEC (triple) ) were determined using a Viscotek Detector Array Model TDA 302 equipped with a two angles light scattering detector (LALS: θ = 7°, RALS: θ = 90°; laser: λ = 670 nm), a refractive index detector (λ = 670 nm), a viscosimetric detector and three Polymer Laboratories Mixed C columns thermostated at 40°C. MALDI-TOF spectroscopy. MALDI-TOF-MS was performed using a Autoflex III Smartbeam (Bruker) using the flexControl V3 software. The data were treated with the flexAnalysis V3 software. The Maldi mass spectra represent averages over 256 consecutive laser shots. The polymer solutions (5g.L -1 ) were prepared in THF. The matrix, 1,8-dihydroxy-9[10H]anthracenone (dithranol), was also dissolved in THF (25 g.L -1 ). A 10 µL portion of the polymer solution was mixed with 20 µL of the matrix solution. A sodium iodide solution (10 µL of a solution at 20 g.L -1 in THF) was finally added to favour ionization by sodium attachment. A 1µL portion of the final solution was deposited onto the sample target. Standards (polystyrenes of known structure, from Polymer Standards Service) were used to calibrate the mass scale. Fourier transformed infrared spectroscopy. Infrared spectra were recorded on a Nicolet iS10 spectrometer in KBr cells.

Small Angle Neutron Scattering (SANS). SANS measurements were made at the LLB (Saclay, France) on the PACE instrument, at two distance-wavelength combinations to cover the 4.1 10 -3 to 0.23 Å -1 q-range, where the scattering vector q is defined as usual, assuming elastic scattering, as q = (4π/λ)sin(θ/2), where θ is the angle between incident and scattered beam. Data were corrected for the empty cell signal and the solute and solvent incoherent background. A light water standard was used to normalize the scattered intensities to cm -1 units.

Synthesis of 1

2-aminobutanol (168 mmol, 14.93 g) was dissolved in 300 mL of anhydrous dichloromethane in a round-bottom flask under argon. Triethylamine (168 mmol, 16.99 g) was added with a syringe. The solution was cooled to 0°C in an ice bath. Then di-tertbutyl dicarbonate (168 mmol, 36.84 g) was added slowly. The solution was allowed to reach room temperature and stirred overnight. Then dichloromethane was evaporated under reduced pressure and the product was dissolved in diethyl ether. This solution was washed with 75 mL of HCl 1M and then three times with 75 mL of distilled water. The organic layer was collected and dried with MgSO 4 . The solvent was removed under reduced pressure. The resulting product is a yellow oil (27.24 g, 86%).

Synthesis of 2

1 (144 mmol, 27.24 g) was dissolved in 200 ml of anhydrous THF in a round-bottom flask under argon. Triethylamine (144 mmol, 14.57 g) was added with a syringe. The solution was cooled to 0°C in an ice bath. Then a solution of 2chloropropionylchloride (144 mmol, 18.28 g) in 50 mL of anhydrous THF was added dropwise in one hour in the cooled flask. The solution was allowed to reach room temperature and stirred overnight. The mixture was filtered and the solvent | 3 removed under reduced pressure. This product was dissolved in diethyl ether and washed 3 times with distilled water. The organic layer was collected and dried with MgSO 4 . The solvent was removed under reduced pressure. The resulting product is a yellow oil (31 g, 77%).

Synthesis of 3

2 (111 mmol, 31 g) is placed in a round-bottom flask with an ice bath under argon. HCl 4M in dioxane (333 mmol, 88 mL), is added with a syringe. The solution was allowed to reach room temperature and stirred overnight. Then dioxane was evaporated under reduced pressure. The crude product was purified by recrystallization in a mixture (toluene/cyclohexane: 70/30). The product is a white powder (16.5 g, 69 %).

Synthesis of 4

In a round-bottom flask, 2,4-dimethyl-5-nitroaniline (69 mmol, 11.46 g), palladium on carbon (9 mmol, 0.96 g) and ethanol (400 mL) were stirred. Then hydrazine hydrate (1.02 mol, 50 mL) was added. The mixture was heated under reflux during 5 days, filtered on celite and then ethanol was removed under reduced pressure. The product was dissolved in 400 mL of ethyl acetate and washed three times with distilled water. The organic layer was collected and dried with MgSO 4 . The solvent was removed under reduced pressure. The resulting product is a white-grey powder (5.4 g, 60 %).

Synthesis of 5

Diisopropylethylamine (17 mmol, 3 mL) and 4 (8.4 mmol, 1.14 g) were dissolved in 15 mL of anhydrous dichloromethane under argon and added with a syringe-pump (3.5 mL/h) to a roundbottom flask containing triphosgene (5.6 mmol, 1.67 g) dissolved in 30 mL of anhydrous dichloromethane under argon. After one hour stirring at room temperature, a solution of 3 (18 mmol, 3.7 g) in 20 mL of anhydrous dichloromethane and diisopropylethylamine (35 mmol, 6 mL) were added to the mixture. The reaction was followed by infrared spectroscopy until the disappearance of the NCO band at 2270 cm -1 . When the reaction was over, the solvent was removed under reduced pressure. The crude product was purified by two recrystallizations in acetonitrile. A white solid is obtained (2.6 g, 58 %).

General procedure for the ATRP of n-butylacrylate initiated by 5

Copper chloride (0.913 mmol, 90 mg), PMDETA (0.913 mmol, 158 mg), 5 (0.913 mmol, 0.5 g), DMF (1.1 mL) and nbutylacrylate (77 mmol, 10 mL) were introduced in a Schlenk flask sealed with a rubber septum. This mixture was degassed by three freeze/pump/thaw cycles. The schlenk was placed in an oil bath at 80°C. Samples were withdrawn periodically from the reaction to determine conversion by NMR and molar mass by SEC. After completion of the reaction, the flask was opened to air and ethyl acetate was added. This solution was washed with brine until the organic layer was copper free (yellow solution). The organic layer was collected and dried with MgSO 4 . The solvent was removed under reduced pressure.

1 H NMR (200 MHz, DMSO) δ (ppm): 0.89 (t, (CH 3 -CH 2 ) n ), 1.3 (m, (CH 3 -CH 2 ) n ), 1.51 (m, (CH 3 -CH 2 -CH 2 ) n ), 1.77 (br, (CH 2 -CH- COO) n ), 2.06 (s, 6H, Ph-CH 3 ), 2.

Results and discussion

In order to be able to reach high molar masses, a functionalized initiator strategy was selected.

| 4

Synthesis of the xylyl bisurea ATRP initiator

A symmetrical xylyl bisurea bearing a halogen at each extremity was synthesized to initiate ATRP polymerization of acrylates (Figure 1). First an ammonium functionalized initiator was obtained in three steps. The purpose was to introduce a halogen atom activated by an ester function by reacting an amino alcohol with 2-chloropropionylchloride. The amino alcohol chosen (2aminobutanol) allows to introduce an ethyl branch next to the urea groups, which is expected to promote solubility without putting too much steric hindrance. 52 To avoid the reaction of the amino group with the acid chloride, the amino group was first protected with diboc. After coupling, the amino function of 2 was deprotected with an anhydrous HCl solution in dioxane, thus avoiding hydrolysis of the ester function. The ammonium 3 was purified by recrystallization to give a white powder with an overall yield of 46% for the three steps. In a fourth step, the xylyl bisurea 5 was obtained by reacting the ammonium with a diisocyanate. 1,3-dimethyl-4,6-diisocyanatobenzene was prepared in situ by reacting the corresponding aromatic diamine 4 with triphosgene and then the ammonium 3 was added to give the targeted bisurea. The crude product was purified by recrystallizations to give a white solid 5 with a good yield (58%). NMR and HRMS analysis confirmed the structure and the purity of the product.

Polymerization of n-butylacrylate by ATRP with the xylyl bisurea initiator

The initiation efficiency of xylyl bisurea 5 was first tested in the ATRP polymerization of n-butylacrylate (BA) in DMF at 80°C using the CuCl (or CuBr)/PMDETA system as catalyst. This catalytic system is well known to afford a good control acrylate polymerization. 40,41 All the polymerizations were carried out with a ratio [CuX]/[PMDETA] of 1/1 to have a good control of the polymerization and a reasonable reaction time. The ratio [initiator]/[CuX] was adjusted for each synthesis to have a reasonable reaction time whatever the amount of BA. Finally the [BA]/[initiator] ratio was fixed by the expected molar mass of the polymer. To avoid irreversible termination, the targeted final conversion was 70%. 10%w of DMF was added to improve the solubility of the urea initiator. The latter was not completely dissolved at room temperature but at 80°C a homogeneous solution was observed. Table 1 as well as Figure 2 presents the polymerization results. With a low monomer to initiator ratio [M]/[I] = 86 (CF151), polymerization resulted in a good control. The conversion reached 65% after 5h15, the molar mass increased linearly with monomer conversion and the dispersity index remained below 1.3 (Figure 2

left). Moreover ln([M 0 ]/[M]

) increased linearly with time indicating that the concentration of the propagating species remained constant during the polymerization. As expected, the chromatograms show a displacement of the peak toward higher molar masses with increasing conversion. For high molar masses (Figure 2 right), the evolution of the molar mass versus conversion is qualitatively correct but shows a deviation of the experimental value from the theoretical one at high conversion. This is also visible in Table 1: for high molar masses, a discrepancy between theoretical and experimental molar masses measured by size exclusion chromatography with a refractive index detector is observed. In order to obtain the absolute molar masses, the same polymers were analysed by size exclusion chromatography with a triple detection (refractive index, dynamic light scattering and viscosimetry). Results indicate that the experimental molar masses are in fact very close to the theoretical values. This suggests that our polymers are branched. Indeed, poly(n-butylacrylate) (PnBA) is well known to be a branched polymer, [42][43][44] and this explains why the hydrodynamic volume of the polymers is lower than expected.

The chemical structure of the polymer was determined by means of proton and carbon nuclear magnetic resonance ( 1 H NMR and 13 C NMR). The characteristic NH (7.5 and 6.3 ppm) and aromatic peaks (8 and 7.6 ppm) of the sticker were observed by 1 H NMR (see ESI † ). The carbonyls (156 ppm) and aromatic carbons (136 to 123 ppm) were also visible on 13 C NMR spectra. The structure of this polymer was confirmed by MALDI-TOF mass spectrometry analysis. The MALDI mass spectrum (Figure 3) reveals a main distribution of peaks separated by 128 Da (BA repeat unit). The experimental values of the peaks in this main distribution are in good agreement with the theoretical values for the expected structure, with chlorine at each end. A second distribution in much smaller proportion is also present and separated from the first one by 35 units. It corresponds to the loss of a chlorine atom replaced by a hydrogen atom. This loss of halogen is well known to occur in ATRP when the conversion is high. 45,46 Finally a very small third population is observed at low molar masses. It is separated from the main population by 37 units but it could not be attributed. When high molar masses were targeted (Table 1), a good control was possible only up to 60000 g/mol (CF89, Figure 2 right). For a targeted molar mass of 110000 g/mol in these conditions (CF92), the reaction was very slow (3-4 days) and the control was not as good as for the other polymerizations. Especially a bimodal peak with a large dispersity index (1.7) was observed by SEC (Figure 4). To solve this problem, ARGET (activator regenerated electron transfer) ATRP 47,48 was used with Cu(0) as reducing agent and with a ratio of [initiator]/[Cu(0)]/[CuCl 2 ]/[PMDETA]: 1/0.5/0.25/0.25. The reaction was carried out at 80°C and was followed by SEC and NMR. The reaction was faster than with conventional ATRP (17 h instead of 4 days) and the resulting polymer is well controlled with a dispersity of 1.3 (Figure 4).

Polymerization of other acrylate monomers with the xylyl bisurea initiator

To obtain a range of polyacrylates with a xylyl bisurea sticker but with different structures and polarities, we have chosen 2ethylhexylacrylate and 3,5,5-trimethylhexylacrylate as monomers. The polymerizations were carried out under the same conditions as with BA (80°C, xylyl bisurea 5, CuCl/PMDETA as catalytic system). As shown in Table 1 and ESI † , polymerizations resulted in both cases in a good control.

Polymerization of n-butylacrylate with various urea initiators

These results have validated the method using xylyl bisurea as initiator for ATRP polymerizations. We have previously shown that for small molecules it is possible to tune the self-association strength of urea stickers by changing the number of urea functions and the spacer between these functions. For example, bisureas with a tolyl spacer self-assemble less strongly than bisureas with a xylyl spacer. 49 In order to consider this parameter in our system, we have prepared initiators with a different number of urea functions (2 or 3) and with different spacers (xylyl, tolyl and MDI) (Figure 5). Tolyl bisurea (6), MDI bisurea (7) and trisurea (8) initiators (Figure 5) were prepared by the same approach as the xylyl bisurea initiator. Note that for tolyl and MDI initiators, terminal halogens are either chlorine or bromine or a mixture of both, with no consequence on the control of the polymerization (see ESI † ). Tolyl and MDI bisurea initiators were obtained by reacting the ammonium 3' (see ESI † ) with the corresponding commercially available diisocyanates. The tolyl bisurea was purified by precipitation in cyclohexane with a yield of 56%. The MDI bisurea was purified by column chromatography with a yield of 33%. The diisocyanate required for the synthesis of trisurea (8) was prepared by partial hydrolysis of TDI. 50 A recrystallization in methanol afforded a pure initiator with a yield of 50%. The control of the polymerizations was slightly better with the MDI and tolyl bisurea initiators which are soluble at room temperature (dispersity index below 1.2) than for xylyl bisurea and trisurea initiators soluble only at 80°C. However in all cases the control of the polymerization is good (Table 2). For example, the kinetic monitoring of the polymerization of BA initiated by the tolyl bisurea initiator (Figure 6) shows a linear increase of the ln([M] 0 /[M]) versus time and of molar mass versus conversion.

Characterization of the supramolecular assemblies in solution

Infrared spectroscopy

The self-assembly of bis or trisurea functionalized polyacrylates was investigated by FTIR spectroscopy in solution. Figure 7 shows the FTIR spectra of a xylyl bisurea PnBA (M n = 8500 g/mol) at different concentrations in toluene. The spectrum reveals three main bands: the inter-urea hydrogenbonded N-H vibration band (3350-3250 cm -1 ), 51 the free N-H vibration band at 3450 cm -1 and an intermediate band at 3410 cm - 1 . Because of its weak frequency shift, the latter is attributed to the N-H vibration band for (intermolecular or intramolecular) association of urea with the ester function of BA. 52 The proportion of inter-urea hydrogen-bonded N-H groups (3300 cm -1 ) decreases with decreasing the concentration. At the same time, the contribution of the N-H band at 3410 cm -1 attributed to association between urea and ester functions increases. That means that when the solution is diluted, urea-urea interactions are broken in favour of urea-ester interactions. This suggests that the urea-ester hydrogen bonds are predominantly intramolecular. Therefore, the spectra show that intermolecular association is negligible below 1 mM. This relatively weak self-association is due to the steric bulk of the polymer chains and to the competing hydrogen bonds of the ester groups, because the low molar mass analogue bearing the same sticker is fully assembled at 1 mM in toluene. 49 Importantly, above 10 mM, intermolecular association becomes preponderant. q (Å-1)

Trisurea PnBA Xylyl bisurea PnBA Tolyl bisurea PnBA MDI bisurea PnBA q-1 q-2

The comparison of the spectra of PnBAs bearing various urea stickers (Figure 8) reveals that at 1 mM in toluene the proportion of inter-urea hydrogen bonds is low for all bisurea stickers. For all bisurea polyacrylates, the main band is the N-H vibration band for intramolecular association of urea with the ester function of BA. This means that bisurea polyacrylates are very weakly associated. In contrast, for trisurea a large proportion of inter-urea hydrogen bonds are present suggesting that the assembly is much stronger than for the other stickers. The influence of the nature of the polymer on the assembly was studied by FTIR for a given sticker (xylyl bisurea) (Figure 9). In fact, the spectra are very similar for all the polyacrylates tested.

In particular, the concentration of inter-urea hydrogen bonds (3300 cm -1 ) is the same. However the concentration of intramolecular hydrogen bonds between urea and ester functions (3410 cm -1 ) is slightly larger in the case of poly(3,5,5trimethylhexylacrylate) and poly(2-ethylhexylacrylate) compared to PnBA. This weak effect may be due to the slightly lower polarity induced by longer alkyl sidechains. # Small Angle Neutron Scattering SANS measurements were used to derive information about the structure of the assemblies. The measurements were performed in deuterated toluene at low concentrations (0.8 mM / 6 g.L -1 ) to ensure that no interaction between scattering objects is present in the q range considered. Figure 10 shows the scattered intensities of the PnBAs bearing various urea stickers. At high q values, a q -2 dependence is found for all polymers. This is a characteristic for Gaussian chains. At low q values, three different behaviours are observed depending on the urea sticker.

The MDI and tolyl bisurea PnBAs both show a low scattering intensity that reaches a plateau value. The data can be fitted with the form factor for a Gaussian chain (see ESI † ). The weight average molar mass extracted from the fit is equal to the molar mass of the polymer, which means that no intermolecular assembly occurs in these conditions. This result unequivocally confirms our previous interpretation of the FTIR spectra: the 3410 cm -1 band is necessarily due to intramolecular hydrogen bonding (to ester groups) because it is the main band in these conditions (Figure 7). The xylyl bisurea PnBA has a very similar behaviour as the other bisurea PnBAs, except that the plateau is slightly higher, corresponding to a molar mass 50% larger than the individual polymer chains (see ESI † ). Moreover, at very low q, the onset of a scattered intensity increase is visible and is probably associated with the presence of a minority second population in solution. Both features indicate that at this concentration, the xylyl bisurea PnBA has begun to assemble but that no large structures are formed. Finally, in the case of the trisurea PnBA, the scattered intensity is characterized at low angles by a q -1 dependence covering more than one decade. This scattering feature is typical of long and rigid fibrillar scatterers. The fact that the q -1 dependence is maintained down to the lowest experimental q values means that cylindrical objects with a rigid core longer than 200 Å, i.e. at least 40 stacked trisureas, are present. A more quantitative description of this curve by a suitable form factor will be the focus of a future study, but the significant fraction of intramolecular hydrogen bonding visible on Figure 7 indicates that the long and rigid objects dominating the SANS scattering curve are probably in equilibrium with a significant fraction of lower size aggregates; i.e. the assemblies are probably very polydispersed in length.

Overall, the SANS and FTIR results are in very good agreement. The trisurea PnBA is the most strongly associated of these polymers with self-assembly occurring at concentrations above 1 mM. The bisureas PnBA are able to self assemble at concentrations of 10 mM with the xylyl bisurea sticker being more efficient than the MDI and tolyl bisurea stickers.

Conclusion

We report the synthesis of well controlled polyacrylates bearing urea moieties in the middle of the chain. Through a functionalized initiator strategy, ATRP polymerization yields a wide range of polyacrylates of various molar masses (3 to 100 kg.mol -1 ), of various nature (ethylhexyl, trimethylhexyl and butyl acrylates) and of various strength of association, depending on the sticker (MDI bisurea ~ tolyl bisurea < xylyl bisurea << trisurea). The control of these polymerizations via ATRP resulted in polymers with a narrow polydispersity and a predictable molar

| 9
mass. The properties of these polymers in solutions reveal a large influence of the urea sticker on the association. In particular, the polymers with a trisurea sticker in the middle of the chain seem of particular interest due to their ability to form long and rigid objects. We are currently investigating the bulk properties of these polymers.

Fig. 1 :

 1 Fig. 1: Synthesis of the xylyl bisurea initiator 5.

1 H

 1 NMR (200 MHz, DMSO) δ (ppm): 0.83 (t, 3H, CH 3 -CH 2 ), 1.14-1.50 (m, 9H+2H, C(CH 3 ) 3 + CH 2 -CH 3 ), 1.61 (d, 3H, CH-CH 3 ), 3.53-3.6 (m, 1H, CH-CH 2 ), 3.88-4.1 (m, 2H, O-CH 2 ), 4.57-4.68 (m, 1H, CH-CH 3 ), 6.78 (d, 1H, NH). 13 C NMR (50 MHz, DMSO) δ(ppm): 10.54 (CH 3 -CH 2 ), 22.25 (CH 3 -CH), 24.13 (CH 3 -CH 2 ), 28.81 (C(CH 3 ) 3 ), 39.3 (CH-Cl), 51.07 (CH-NH), 67.47 (CH 2 -OCO), 78.25 (C(CH 3 ) 3 ), 156.50 (NH-CO), 170.32 (CO-O).

1 H

 1 NMR (200 MHz, DMSO) δ (ppm): 0.93 (t, 3H, CH 3 -CH 2 ), 1.50-1.6 (m, 3H+2H, CH-CH 3 + CH 3 -CH 2 ), 3.37 (m, 1H, CH-NH 3 + ), 4.14-4.28 (m, 2H, O-CH 2 ), 4.72-4.79 (m, 1H, CH-Cl), 8.4 (d, 3H, NH 3 + ). 13 C NMR (50 MHz, DMSO) δ(ppm): 7.4 (CH 3 -CH 2 ), 21.39 (CH 3 -CH), 22.61 (CH 3 -CH 2 ), 51.13 (CH-Cl), 53.05 (CH-NH 3 + ), 64.7 (CH 2 -OCO), 169.93 (CO-O).

1 H

 1 NMR (200 MHz, DMSO) δ (ppm): 1.9 (s, 6H, CH 3 -Ph), 4.3 (s, 4H, NH 2 -Ph), 6.0 (s, 1H, H-Ph), 6.5 (s, 1H, H-Ph). 13 C NMR (50 MHz, DMSO) δ(ppm): 16.8 (CH 3 -Ph), 101.06 (Ph-H), 109.94 (Ph-CH 3 ), 132.04 (Ph-H), 144.84 (Ph-NH 2 ).

  2 (br, (CH 2 -CH-COO)n), 3.99 (br, (CH 2 -O) n ), 6.28 (d, 2H, CH-NH-CO), 6.85 (s, 1H, Ph-H), 7.51 (s, 2H, CO-NH-Ph), 7.99 (s, 1H, Ph-H). 13 C NMR (75 MHz, DMSO) δ(ppm): 10.9 (CH 3 -CH 2 ), 13.77 ((CH 3 -CH 2 ) n ), 18.16 (Ph-CH 3 ), 19.69 ((CH 3 -CH 2 ) n ), 25.8 (CH 3 -CH 2 ), 31.35 ((CH 3 -CH 2 -CH 2 ) n ), 32.5 ((CH 2 -CH-COO)n), 42.44 ((CH 2 -CH-COO) n ), 50.85 (CH-COO), 55.1 (CH 3 -CH), 56.6 (CH-NH), 65 ((CH 2 -O) n ), 66.72 (CH 2 -O), 119.48 (Ph-H), 125.8 (Ph-CH 3 ), 132.49 (Ph-H), 136.31 (Ph-NH), 156.57 (NH-CO-NH), 169.76 (CO-O), 175.31 ((CO-O) n ).

Fig. 2 :

 2 Fig. 2: Kinetic data for the ATRP of n--butylacrylate initiated by 5 in 10% DMF at 80°C. Left (CF151): [BA]/[5]/[CuCl]/[PMDETA] = 86/1/1/1. Right (CF89): [BA]/[5]/[CuBr]/[PMDETA] = 824/1/3/3. a) Evolution of monomer conversion (ln([M]0/[M])) versus time; b) Evolution of molar mass and polydispersity versus conversion (the line represents the theoretical molar mass); c) Size exclusion chromatograms versus monomer conversion.

Fig. 3 :

 3 Fig. 3: MALDI TOF mass spectrum of a PnBA initiated by 5 (CF151, Mn,SEC (RI) = 8500 g/mol).

Fig. 4 :

 4 Fig. 4: Size exclusion chromatograms of the PnBAs obtained by ATRP (CF92) or ARGET ATRP (CF99), [BA]/[5] = 1000/1.

Fig. 5 :

 5 Fig. 5: Structures of a) tolyl bisurea b) MDI bisurea and c) trisurea initiators.

a 1 )

 1 Calculated by 1 H NMR b Theoretical Mn at final conversion = ([M]0/[I]0) * conversion * MW(M) + MW(I) c Evaluated by SEC in THF using polystyrene standards Xylyl bis--urea PnBA Tri--urea PnBA Tolyl bis--urea PnBA MDI bis--urea PnBA

Fig. 6 :

 6 Fig. 6: Kinetic data for the ATRP of BA initiated by tolyl bisurea initiator 6 in 10% DMF at 80°C with [BA]/[6]/CuBr/PMDETA: 86/1/1/1.

Fig. 7 :

 7 Fig. 7: Infrared spectra of xylyl bisurea PnBA (CF151) at various concentrations in toluene.

Fig. 8 :

 8 Fig.8: Infrared spectrum of polyacrylates bearing various urea stickers at 1 mM in toluene (Mn ca 8000 g/mol).

Fig. 9 :

 9 Fig. 9: Infrared spectra of various xylyl bisurea polyacrylates (Mn ca 8000 g/mol) in toluene at 4 mM.

Fig. 10 :

 10 Fig.10: SANS intensity (I) versus scattering vector (q) for solutions of PnBA (Mn ca 8000 g/mol) bearing various urea stickers in d8--toluene at 0.8 mM (the straight lines represent the fit according to a Gaussian model).

  1 H NMR (200 MHz, DMSO) δ (ppm): 0.90 (t, 6H, CH 3 -CH 2 ), 1.30-1.6 (m, 6H+4H, CH-CH 3 + CH 3 -CH 2 ), 2.08 (s, 6H, CH 3 -Ph), 3.8 (m, 2H, CH-NH), 4.1 (m, 4H, CH 2 -O), 4.72 (m, 2H, CH-Cl), 6.32 (m, 2H, CH-NH-CO ), 6.86 (s, 1H, H-Ph), 7.54 (s, 2H, CO-NH-Ph), 8.00 (s, 1H, H-Ph).

	13 C NMR (50 MHz, DMSO) δ(ppm): 10.54 ( CH 3 -CH 2 ), 17.39
	(CH 3 -Ph), 21.63 (CH 3 -CH), 24.77 (CH 3 -CH 2 ), 49.55 (CH-Cl),
	53.50 (CH-NH), 67.21 (CH 2 -OCO), 116.24 (Ph-H); 122.56 (Ph-
	CH 3 ), 132.05 (Ph-H), 136.27 (Ph-NH), 155.51 (NH-CO-NH),
	169.74 (CO-O).
	HRMS m/z [MNa + ]
	C 24 H 36 O 6 N 4 Cl 2 calculated 569.19055 measured 569.19041

Table 1 :

 1 Characteristics of the xylyl bisurea polyacrylates synthetized by ATRP at 80°C in 10% DMF

Table 2 :

 2 Characteristics of the PnBAs with various stickers

Acknowledgments

Support from the French Agence Nationale de la Recherche is acknowledged (project ANR-10-BLAN-0801 Supradhesion). We thank François Boué (LLB, Saclay) for assistance with SANS experiments. Ludovic Dubreucq is thanked for MALDI-TOF analyses. Chirine Ben Osman and Vincent Lemaire are gratefully acknowledged for their help in this work.

Notes and references


Ilaria Giannicchi

Benjamin Jouvelet

Benjamin Isare

Mathieu Linares

Antonella Dalla Cort

Laurent Bouteiller

Orthohalogen substituents dramatically enhance hydrogen bonding of aromatic ureas in solution

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

The phenylurea moiety is a ubiquitous synthon in supramolecular chemistry. Here we report that the introduction of chlorine or bromine atoms in the ortho positions to the urea unit is a simple and very efficient way to improve its intermolecular hydrogen bond (HB) donor character. This effect was demonstrated in solution both in the context of bis-ureas self-association and of mono-ureas hydrogen bonding to strong HB acceptors.

Developing supramolecular synthons with an improved efficiency and selectivity is an important endeavour in the context of the current increasing complexity of self-assembled systems. 1 A well-known strategy to enhance the HB donor ability of receptors is to introduce electron withdrawing substituents, but a careful design is required to avoid establishing competing intramolecular interactions. Here, we focused our attention on the phenylurea moiety, that is an ubiquitous synthon in supramolecular chemistry. Its direct synthetic accessibility and its HB donor ability have been exploited in the fields of anion complexation, 2 organocatalysis 3 and foldamer conformational control. 4 Moreover, the self-complementarity of the phenylurea synthon is a reliable design motif for crystal engineering, 5 organogelators, 6 liquid crystals, 7 supramolecular polymers, 8 nanostructured polymers, 9 self-assembled capsules 10 and monolayers. 11 The effect of various electron withdrawing substituents on urea assembly is well-known, 12 but the case of halogen atoms in ortho position of the phenylurea moiety has rarely been investigated, probably because such substitution was shown to favour intramolecular HBs. The intramolecular HB to an ortho chlorine atom totally suppresses intermolecular HB for a trisubstituted urea. 13 However, in the case of fluorine, an interesting conformational effect has been described: the presence of a single fluorine atom in ortho position enforces a coplanar conformation of the aromatic and urea moieties, whereas the presence of two fluorine atoms in 2,6 positions is responsible for the clear loss of coplanarity. This is attributed to the electrostatic repulsion between the oxygen and both fluorine atoms, which therefore forbids the formation of a weak N-H … F intramolecular HB. 14 Although the strength of intermolecular HB cannot be deduced from the crystalline structures reported, it is noteworthy that the bisfluorinated urea forms the usual bifurcated intermolecular HB, whereas the monofluorinated analogue does not. This conformational effect is particularly relevant in the context of self-association, because the phenylurea moiety usually displays a strong conformational change on self-assembly to avoid steric clash between the aromatic groups and to allow some π-stacking interaction. 15,16 We therefore reasoned that the presence of two halogen atoms in ortho position to the urea group could have a favourable influence on intermolecular hydrogen bonding, due to a better conformational preorganization of the monomer. In this communication, we report that indeed the presence of halogen atoms in the ortho positions to the urea considerably improves intermolecular hydrogen bonding and that, surprisingly, in the case of chlorine and bromine, this effect is accompanied by the formation of an intramolecular HB.

N N N N X H H O H H O X X bF 3 : bCl 3 : bBr 3 : bH 3 : bMe 3 : X = F Cl Br H CH 3 α β Scheme 1
We consider the 2,4,6-trihalogenated bis-ureas represented in Scheme 1 together with the unsubstituted and trimethylated bis-ureas as references. At low concentration (2x10 -5 mol/L) in chloroform, FTIR spectra show that all these compounds are monomeric and that an intramolecular interaction between the N-H α (Scheme 1) and the halogens in ortho position is present in the case of the chlorinated bCl 3 and brominated bBr 3 bis-ureas (see ESI †). Ab initio calculations on model mono-ureas support these results and highlight the significant influence of the substituents on the dihedral angle (φ) between the urea and aromatic groups (see ESI †). In the absence of substituent (bH 3 ) the most stable conformation is coplanar (φ = 0). With fluorine (bF 3 ) or methyl (bMe 3 ) substituents, the most stable conformations correspond to a dihedral angle of 60 and 120°, separated by a small barrier (1 kcal/mol) at φ = 90°. With chlorine (bCl 3 ) or bromine (bBr 3 ) substituents, the energy surface is completely flat from φ = 60 to 120°.

At higher concentration (10 -2 mol/L), FTIR shows that intermolecular HBs are formed (Fig. 1). In fact, at this concentration, the free N-H vibration band (3420-3450 cm -1 ) 8 is small in the case of bH 3 and bMe 3 and is barely detectable in the case of bF 3 , bCl 3 and bBr 3 , which qualitatively hints at the positive effect of the halogens on the strength of intermolecular association. The structure of the assemblies was examined by Small Angle Neutron Scattering (SANS). All compounds yield very similar scattering profiles in deuterated chloroform (Fig. 2): the low angle region shows a q -1 dependence over more than a decade, which is characteristic for long and rigid fibrillar objects. In principle, the specific dimensions of the scattering objects can be deduced from a fit to a form factor calculated according to a suitable geometrical model. In the present case the use of a form factor for infinitely long rigid filaments (with a circular cross-section and a uniform scattering length density profile) 17 yields an excellent fit over the whole q range (Fig. 2). The values deduced from the fits are summarized in Table S3. According to these results, all five bis-ureas form very similar assemblies, ‡ with a relatively low linear density (n L ≈ 0.25Å - 1 ), which corresponds to the presence of a single bis-urea in the cross-section. 17 Fig. 2 SANS intensity (I) versus scattering vector (q) for bis-urea solutions in CDCl3 at 15 g/L (ca 0.03 mol/L) and 22°C. The plain curves are fits according to a model for long rigid filaments with a circular crosssection (characteristic dimensions in Table S3).

The fact that all five bis-ureas self-assemble into long filaments with the same structure makes the comparison of their association strength particularly relevant. Therefore, their stability to dilution was probed by Isothermal Titration Calorimetry (ITC). Fig. S5 shows the heat effect produced when a drop of a solution containing a self-assembled bis-urea is diluted into chloroform. The endothermic signal results from the breaking of hydrogen bonds consequent to the dilution. Qualitatively, it is possible to see that the halogenated bis-ureas are more strongly self-associated than bH 3 and bMe 3 because in their case the concentration of the experiment had to be reduced to induce full dissociation. To quantify this effect, the experiments were reproduced with optimized initial concentrations and injection volumes, and the heat signal was integrated and plotted versus the concentration in the calorimetric cell (Fig. 3). From these curves, it is possible to determine graphically the critical concentration (c*) 18 below which the assemblies dissociate into monomers: the stability of the assemblies increases very strongly from the reference bis-ureas bH 3 (c* = 1.6mM) and bMe 3 (c* = 0.6mM) to the halogenated bis-ureas bF 3 (c* = 0.1mM), bBr 3 (c* = 0.056mM) and bCl 3 (c* = 0.041mM). Moreover, the exact shape of the titration curves can be accounted for by a simple mass action law model describing the evolution of the concentration of monomers (M) and filaments (F n ) of any degree of polymerisation (n). 19 The values deduced from the fit for the association constants and the enthalpy of association are reported in Table S4. These results show that the replacement in the ortho positions of methyl groups with chlorine or bromine atoms stabilizes the assemblies by more than one order of magnitude. This huge effect may potentially be due to several factors: -the electron withdrawing effect of the halogen atom which should enhance the HB donor character of N-H α , as confirmed by ab initio calculations on model mono-ureas (see ESI †); -the polarization of the aromatic ring by the halogen atom which could increase π-stacking interactions; -the repulsion between oxygen and halogen atoms which may induce a conformational effect.

The fact that the stability of the assemblies does not reflect the electronegativity scale among the halogen atoms means that at least a couple of different effects are involved.

To probe the generality of this halogen effect, we synthesized structurally simpler mono-ureas (Fig. 4) and

| 1

 1 Chem. Commun. 2014, 50, 611 Orthohalogen substituents dramatically enhance hydrogen bonding of aromatic ureas in solution Ilaria Giannicchi, c Benjamin Jouvelet, ab Benjamin Isare, ab Mathieu Linares, d Antonella Dalla Cort c and Laurent Bouteiller* a,b

Fig. 1

 1 Fig.1FTIR spectra for bis-ureas at 10 -2 mol/L in chloroform (20°C).

Fig. 3

 3 Fig.3ITC enthalpograms for bis-urea solutions in chloroform injected into chloroform versus total bis-urea concentration in the cell (T = 20°C).

| 3 probed their association with strong hydrogen bond acceptors such as dimethylsulfoxide (DMSO) and triphenylphosphine oxide (TPPO). Sufficiently dilute solutions of the mono-ureas were prepared to ensure that no self-association would interfere with hetero-association. FTIR spectra of these solutions (Fig. S3) confirm that at 5mM in chloroform, monoureas are not associated. Moreover, the characteristic shift in the N-H stretching vibration band going from mMe 2 -NH to mCl 2 -NH (and from mMe 2 -NMe to mCl 2 -NMe) reveals the presence of intramolecular HB between N-H α and chlorine atoms, as in the case of bis-ureas. The free N-H band intensity was also monitored while a HB acceptor was added. Figs. 4 and S4 clearly show that mCl 2 -NH is a better HB acceptor than mMe 2 -NH. This experiment rules out the enhancement of π-stacking interactions as the main factor.

Moreover, Figs. 4 and S4 also show that mMe 2 -NMe and mCl 2 -NMe are HB donors of similar magnitude. Therefore, the increase of intermolecular association by chlorine substitution is only effective if N-H β is present on the urea. We suggest that this is due to a conformational effect: the repulsion between the oxygen and chlorine atoms favourably orientates the N-H groups for hydrogen bonding. However, in the case of N-H α , the intramolecular HB annihilates this effect, which explains why the chlorine substitution is favourable only in the presence of N-H β . In conclusion, we have shown by FTIR and ab initio calculations that an intramolecular HB is formed when phenylureas are functionalized by chlorine or bromine atoms in ortho positions. Remarkably, the involvement of the aromatic N-H group in an intramolecular HB does not weaken the intermolecular hydrogen bond capacity of the urea group. On the contrary, the association constant of aromatic bis-ureas (measured by ITC) is improved by one order of magnitude when chlorine atoms replace methyl groups or even more when they replace hydrogen atoms in the ortho positions to the urea unit. This effect was demonstrated both in the context of bis-ureas self-association and of mono-ureas hydrogen bonding to strong HB acceptors. We suggest that this halogen effect is due at least in part to conformational constraints resulting from the repulsion between the oxygen and halogen atoms that favourably orientates the N-H groups for hydrogen bonding.

I.G. acknowledges financial support from the Università La Sapienza, COST Action "Supramolecular Chemistry in Water" and Egide. M.L. thanks SERC (Swedish e-Science Research Center) for funding and SNIC for providing computer resources. We thank François Boué (LLB, Saclay) for assistance with SANS experiments. † Electronic Supplementary Information (ESI) available: Additional data and experimental procedures. See DOI: 10.1039/b000000x/ ‡ The vertical shift between the curves results from the significant differences in specific contrast among the bis-ureas (see Table S3).

Notes and references