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Molecular Approach to Supramolecular Polymer Assembly by Small Angle Neutron Scattering Ana R. Brás,†,* Claas H. Hövelmann,† Wiebke Antonius,† José Teixeira,‡ Aurel Radulescu,§ Jürgen Allgaier,† Wim Pyckhout-Hintzen,†,* Andreas Wischnewski,† and Dieter Richter† †

JCNS-1/ICS-1, Forschungszentrum Jülich, D-52425 Jülich, Germany CEA Saclay, Lab Leon Brillouin, CEA CNRS, F-91191 Gif Sur Yvette, France § Outstation FRM 2, JCNS-1, Forschungszentrum Jülich, D-85747 Garching, Germany ‡

S Supporting Information *

ABSTRACT: We present a small angle neutron scattering (SANS) study of the association of heterocomplementary telechelic polypropylene glycol (PPG) polymers, bearing either diaminotriazine (DAT) or thymine (Thy) stickers as end-groups, both in the melt and in dilute solution. The SANS data are critically examined for the architecture and morphology as well as relative extent of linear assembly in the apolar solvent toluene. A random phase approximation (RPA) approach, adapted for a supramolecularly assembled multiblock copolymer is presented, which allows to extract the interaction parameters between the constituents and the medium. From the proposed approach, which describes very well heterocomplementary hydrogen-bonding telechelic polymers in both diluted toluene solution and in the melt, we conclude that linear association prevails.

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INTRODUCTION Supramolecular polymers have become an increasingly important class of polymers, which in contrast to covalently linked polymers, are able to assemble spontaneously by reversible noncovalent interactions such as metal ligand complexation or hydrogen bonding.1−10 The noncovalent interaction implicates a dynamic equilibrium between bonded and free building blocks. As a consequence of this equilibrium, the average length of the supramolecular polymer chain depends on the monomer concentration and also on the choice of the solvent. Therefore, supramolecular polymers are known to give rise to a rich variety of self-organizing structures on the mesoscale with a multiplicity of macroscopic properties.11−17 These can be realized by changing the relevant parameters to adjust the chain length in situ. The transient nature of the supramolecular association makes these polymers ideal candidates for the development of new materials with, e.g., intrinsic self-healing properties, which has recently gained increased interest from both commercial and academic side.18,19 One of the simplest examples of associating supramolecular systems are telechelic polymers.20 Typical building blocks are oligomers (spacers) having self-complementary binding stickers with hydrogen bonding motifs.21,22 Self-complementary denotes the association of two identical end-groups, whereas in the heterocomplementary case, two different end-groups are binding together (Figure 1). It is also well-known that in many of these systems, microphase segregation between the spacer and the stickers, © 2013 American Chemical Society

may occur, due to the different chemical composition, e.g polar stickers connected to an apolar spacer oligomer.23−44 The compatibility between both is typically very low but can be enhanced by the ability of the stickers to form hydrogen bonds. It is controlled by the Flory−Huggins χ parameter. This microphase segregation phenomenon can manifest itself either as a disordered clustering of the stickers24,26−34 or as an ordered microphase separation as observed for block copolymers.45−47 Here scattering techniques, in particular small angle neutron scattering (SANS), are most ideally suited since they explore both, phase morphology as well as chain structure by using the appropriate blending and contrast matching.48−50 Consequently, for the design of new nanostructured materials based on telechelic supramolecular polymers, it is of utmost importance to gain a well founded and rigorous understanding of the underlying interactions, quantified by χ. Indeed, directed hydrogen bonds have been shown to be particularly effective in facilitating a tuning of binding constants. Also the selective, recognition controlled, association between molecular monomers bearing heterocomplementary stickers with specific hydrogen-bond matching pairs are important for novel material properties.19,25,51−53 Received: August 15, 2013 Revised: October 30, 2013 Published: November 22, 2013 9446

dx.doi.org/10.1021/ma401714r | Macromolecules 2013, 46, 9446−9454

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In addition dihydroxy PPG was received from Sigma-Aldrich having a molecular weight Mn = 2000 g/mol (N = 35). The polymer was modified by etherification to a CH3-terminated PPG, in order to determine independently the second virial coefficient (A2) and the molecular weight of this oligomeric spacer in toluene-d8 solvent (99.9% D, dried over sodium) by SANS. For these experiments, concentrations of PPG in toluene-d8 were chosen to be 1, 2, 4, and 6 mass %. Bifunctional Thy-PPG-Thy and DAT-PPG-DAT were synthesized from Jeffamine D2000 according to literature procedures.22,54 Monofunctional Thy-PPO/PEO and DAT-PPO/PEO were synthesized likewise from Jeffamine M2005. Equimolar mixtures of bifunctional Thy-PPG-Thy and DAT-PPGDAT compounds (Table 1) were prepared by solution blending of stock solutions in dry toluene-d8. The concentrations of these mixtures were chosen between 0.8 and 8.6 mass %.

Table 1. Different Concentrations of the Bifunctional 50/50 Mixtures concentration (mass %)

concentration (mol/L)

0.8 2.2 4.4 6.0 8.6

0.003 0.008 0.016 0.023 0.032

Figure 1. (a) DAT-PPG-DAT, (b) Thy-PPG-Thy, and (c) heterocomplementarity interaction between the DAT and Thy end groups, leading to association which is much stronger than the dimerization of components a or b.

Flory−Huggins Interaction Parameters χ. The affinity of the solvent to the particular blocks of the hydrogen-bonded multiblock copolymer and the blocks to each other can be evaluated through Hildebrand solubility parameter estimations. These are mostly empirical estimates and only a limited number of experimental values are available. The better mixture is obtained for vanishing difference in the solubility parameters. The solubility parameters δ of a given material can be estimated by different methods. The most popular ones were developed by Fedors and by Hansen.56,57 Therefore, slightly different values for the same molecule appear in the literature. The results for the systems studied here are shown in Table 2.57−59 From Table 2, the polymeric spacer is readily soluble in toluene and

In this study we focus on the assembly mechanism of model telechelic materials as homoditopic mixtures, bearing heterocomplementary stickers. The macromonomers have a polypropylene glycol (PPG) polymeric part with thymine (Thy) or 2,4-diaminotriazine end-groups as exemplified in Figure 1, parts a and b, respectively.22,54,55 The association between Thy-DAT units (Figure 1c) is more effective due to the existence of three sites where hydrogen bonds are formed compared to weaker self-association between Thy-Thy or DAT-DAT, which involves only two hydrogen bonding sites. The similarity of supramolecular associated blocks with block copolymers in the melt of the same system was already noted in the literature, based on a qualitative X-ray study.22,54 However, here we have successfully transferred a random phase approximation (RPA)45,50 formalism to describe the SANS data of block copolymers to the heterocomplementary systems. A quantitative RPA analysis for multiblock copolymers applied to the homogeneous bulk and solution phase was performed taking into account the distinct interaction parameters between the different components (sticker, spacer and solvent). This allows a molecular description of the formed supramolecular polymers. The wave vector dependence of the scattering intensity of such systems is strongly sensitive to the size and shape and is also able to distinguish between different scenarios of assembly. It will be shown that the present system in dilute solution as well as in the bulk phase is strongly dominated by linear aggregates.

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Table 2. Estimates of the Solubility Parameter Following the Hansen Method57 a δ (J1/2·cm−3/2) PPG Thy DAT toluene chloroform

17.4 27.5 28.0 18.3 19.0

a Note that the reported δPPG is about the average of the experimental ones (15.4−20.3 J1/2·cm−3/2).56

the often used chloroform, despite their different polarity. The endgroup stickers in the mixture, exhibiting large differences in δ with the solvents and oligomeric spacers are clearly far less soluble. As such, the aggregation of Thy and DAT, that hardly differ in the solubility parameter, thereby shielding the H-bonds, is promoted to reduce the unfavorable solvent contact. The thermodynamic interaction parameter χ for a polymer P and a solvent S can be expressed as:

EXPERIMENTAL SECTION

Samples. The precursor amino-functionalized PPG materials, Jeffamine with different molecular weights and functionalization patterns was received as a generous gift from Huntsman International LLC. Jeffamine D2000 is an amine terminated telechelic PPG that was used in the synthesis of the bifunctional macromonomers (Figure 1 a and b). The molecular weight given by Huntsman is Mn = 2200 g/mol (N = 38) where N is the chain number of monomers. Jeffamine M2005 is a monoamine functionalized PPO/PEO copolymer with a PO/EO mol ratio of 29/6 and a molecular weight of 2000 g/mol that was used in the synthesis of monofunctional compounds.

χ = 0.34 +

vs (δP − δS)2 RT

(1)

where δP and δS are the solubility parameters of the polymer and the solvent which depend on the molecular structure and involve the 9447


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important hydrogen-bonding effect as well. A similar expression is available for the case of two polymers interacting:

χ=

(vAvB) (δA − δB)2 RT

conditions, and the incoherent scattering contribution of the hydrogeneous polymer as well. Latter value was obtained from experiments done on fully hydrogeneous mixtures and taking into account the different concentrations.

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(2)

The estimations of χ in Table 3 were entirely obtained following the above equations. νS, νA, and νB are molecular volumes.

THEORETICAL APPROACH The block copolymer-like structure of the supramolecularly assembled polymers requires the use of the random phase approximation formalism for multicomponent systems. The theoretical background of this technique has been reviewed in detail in the existing literature to which we refer for further reading.50,60−65 The interactions between the components which are accounted for by the Flory−Huggins parameters χ control the microphase separation and can be included. These arise due to the strongly different solubility parameters (vide infra) of the different components in the system. The well-known RPA result for a 2-component AB-diblock copolymer without interactions between the blocks (i.e., χAB = 0) and contrast Δρ2 = (ρA − ρB)2, ρ being the scattering length density, is written in terms of the ideal noninteracting structure factors S0 as follows:50,64−66

Table 3. Empirical Estimations of χ at 298 K χ

PPG

Thy

DAT

toluene

chloroform

PPG Thy DAT toluene

− 3.3 3.3 0.37

3.3 − 0.01 4.0

3.3 0.01 − 4.4

0.37 4.0 4.4 −

0.42 2.7 3.0 0.02

Small Angle Neutron Scattering. SANS experiments were carried out at the SANS diffractometer KWS2@FRM2, Munich, Germany, and at the SANS instrument PAXE G5-4 at LLB, Saclay, France. Absolute scattering intensities were measured over a scattering range from Q = 0.0047 to 0.44 Å−1 using sample-to-detector distances of 2, 4, and 8 m and corresponding collimation lengths and corrected by the standard procedure. The corresponding scattering length densities of the components, defined as ρi =

Σbz vi

2

0 S 0 S 0 − SAB dΣ /Δρ2 = SRPA = 0 AA BB0 0 dΩ SAA + SBB + 2SAB

(3)

(4)

where the scattering vector Q was omitted for clarity. In this work now we consider a ternary system of a multiblock copolymer in solution. Although chemically a 4component system (Figure 2i), it may be reduced to a pseudo 3-component mixture by merging both associating end-groups into a single effective block (Figure 2ii). This is allowed since the DAT and THY units possess very similar scattering length densities and additionally almost identical solubility parameters (Table 2). Thereby the system can be modeled as the general multiblock copolymer (AB)Nagg‑1A with association degree Nagg (Figure 2 (iii). Iffor further simplificationone considers the component C as the “background” component, the scattering can be treated again as for a 2-component case but contrasts now are defined relative to this background.50,67

were calculated to be ρPPG = 3.42 × 109 cm−2, ρDAT = 2.76 × 1010 cm−2, ρThy = 2.05 × 1010 cm−2, ρDAT‑Thy = 2.41 × 1010 cm−2, and ρtoluene‑d8 = 5.67 × 1010 cm−2. νi is the molecular volume of the entity. These values were obtained assuming the following densities: dPPG = 1.036 g/cm3 and dtoluene‑d8 = 0.943 g/cm3, and estimated densities dThy = 1.23 g/cm3 and dDAT = 1.6 g/cm3 for 298 K.56 It is noted that considerable contrast is given between the end-groups and the spacer as well as between end-groups and the deuterated solvent. The fully hydrogeneous ditopic system Thy-PPG-Thy/DAT-PPGDAT in a 1:1 ratio (stoichiometrically) was measured at 298 and 333 K in bulk and in different concentrations in toluene. In addition, also the monofunctionalized Thy-PPO/PEO and DAT-PPO/PEO mixture in the same 1:1 ratio was measured in bulk only at 298 and 333 K. The samples in solution were corrected for incoherent scattering by subtraction of the deuterated toluene, measured at the same

Figure 2. (i) Sketch of the homoditopic telechelic polymers as 1:1 mixture; (ii) sketch of the suggested block copolymer structure of type (AB)Nagg‑1A including the dispersing component C, and (iii) sketch of the multiplicities implicit in the suggested block copolymer-like structure, including the solvent component C, according to the RPA approach. The similarity of the different stickers in scattering length density, size and estimated χ interaction parameters, allowed joining both into the effective block B. 9448


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We have thus applied a full three-component RPA including all interactions χij with i, j = A, B, C. With the number of monomers denoted as nA, nB, and nC (polymer, compound endgroups and (polymeric) solvent, respectively), the volume fractions ϕA, ϕB and ϕC, specific monomeric volumes νA, νB and νC, form factors PAA(Q), PBB(Q), PAB(Q) and PCC(Q), the interaction parameters χAB, χBC, and χAC (χAB polymer−end groups, χBC end groups−solvent, and χAC polymer−solvent), the different contrasts ΔρA,B = ρA,B − ρC (i.e., relative to the background) and the number of aggregates Nagg, the structure factor is now schematically given as SRPA = f (Nagg , χ , Δρ , ϕ)

0 0 0 + VBBSBB SAA(Q ) = ⎡⎣SAA (1 + VABSAB ) 0 0 0 0 0 − SAB(VABSAA + VBBSAB)⎤⎦/⎡⎣(1 + VAASAA + VABSAB ) 0 0 0 0 (1 + VABSAB + VBBSBB) − (VAASAB + VABSBB) 0 0 + VBBSAB (VABSAA )⎤⎦ 0 0 0 + VAASAA SBB(Q ) = ⎡⎣SBB (1 + VABSAB ) 0 0 0 0 0 − SAB + VAASAB + VABSAB (VABSBB )⎤⎦/⎡⎣(1 + VAASAA ) 0 0 0 0 (1 + VABSAB + VBBSBB) − (VAASAB + VABSBB) 0 0 + VBBSAB (VABSAA )⎤⎦ 0 0 0 + VABSBB SAB(Q ) = ⎡⎣ − SAA (VAASAB ) 0 0 0 + SAB(1 + VAASAA + VABSAB)⎤⎦/ 0 0 0 0 ⎣⎡(1 + VAASAA + VABSAB + VBBSBB )(1 + VABSAB ) 0 0 0 0 − (VAASAB + VABSBB)(VABSAA + VBBSAB)⎤⎦

(5)

(8)

ϕA, ϕB, and ϕC are coupled through the incompressibility condition. Since the process of linearly assembling blocks reminds one of well-known polycondensation theory here also the average number of aggregates Nagg may be linked accordingly to the concentration of monomer, c, with Nagg ≈ (Kassnc)1/2.68,69 The association constant Kassn is defined as Kassn = [Thy-DAT]/[Thy][DAT] in equilibrium. As we will see, it is a fit parameter of the model which is obtained from a simultaneous fitting of different concentrations. The ideal noninteracting structure factors for an incompressible ternary blend in the homogeneous phase are given by:

The full scattering cross section for the pseudo 3-component case is analytically obtained as66 d Σ (Q ) = ΔρA 2 SAA(Q ) + ΔρB 2 SBB(Q ) dΩ + 2ΔρA ΔρB SAB(Q )

For the multiblock copolymer case with Nagg ≥ 2, the total 0 0 SAA and SBB correlation functions are composed of 2 contributions.60,65,68,70 One arises from the intrablock correlations between segments belonging to the same block (AA and BB) and a second contribution is due to interblock correlations from segments lying on different blocks, separated by at least 1 hydrogen-bonded complex compound block (A··· A, and B···B). The S0AB functions are defined in the same way and different between adjacent and nonadjacent blocks. The total RPA structure factor and the associated multiplicities are summarized below and are sketched in Figure 2iii. We make use of 3 functions, commonly retrieved within the context of RPA,66,71 associated with the block structure, in terms of the parameters a and the number of monomers per block n, exploiting the Gaussian nature of the chains in the limit for large n. For short n-blocks, the respective discrete summation of the correlations can be used.

0 (Q ) = nA ϕA vAPAA(Q ) SAA 0 (Q ) = nBϕBvBPBB(Q ) SBB 0 (Q ) = SAB

nA nBϕA ϕBvAvB PAB(Q )

0 (Q ) = nCϕCvCPCC(Q ) SCC 0 0 (Q ) = SBC (Q ) = 0 SAC

(6)

The respective volume fractions of A and B are defined as ϕA = (NaggnA)ϕP/(NaggnA + (Nagg − 1)nB) and ϕB = ((Nagg − 1) nB)ϕP/(NaggnA + (Nagg − 1)nB), where ϕp is the volume fraction of polymer in the solution. ϕC is then determined as 1 − ϕp. Taking into account interactions, the excluded volume factors Vij(Q), i, j = A, B, C are found to be:

G(a , n) = F(a , n) =

1 0 SCC (Q )

+

χAB v0

−

χAC v0

−

(an)2 1 − exp( −an) an (10)

All are written in terms of the dimensionless parameter a=(Qlst)2/6 reflecting the random-walk statistics of the building blocks, with statistical segment length lst, such that Rg2 = an, where n is the to be specified “block length”. The following correlation functions in this manuscript are strictly valid for a (AB)Nagg‑1−A system; i.e., we disregard differences between odd and even number of aggregates in view of the fact that for large aggregation number the difference between odd and even supramolecular-bonded chains vanishes.68 Further, both tips of the resulting assembly are neglected. Because of the comparable size of the compound B-block with the step length of the polymer, also no distinction between the rigidity of both blocks was made. Rather easy corrections could account for the

χBC v0

2(exp( −an) + an − 1)

E(a , n) = exp( −an)

χ 1 VAA(Q ) = 0 − 2 AC v0 SCC(Q ) χ 1 VBB(Q ) = 0 − 2 BC v0 SCC(Q ) VAB(Q ) =

(9)

(7)

The reference volume, ν0, was considered the same as νA. Then the partial structure factors for the fully interacting mixture are given in terms of the bare structure factors and excluded volume matrix by:66 9449


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stiffness but we do not expect the presented results to be influenced due to the short length scales involved with block B. With these simplifications we end up with the following form factors where the multiplicities are now a detailed function of the number of aggregation: Nagg − 1

PAA = Nagg G(nA ) +

∑

(2Nagg − 2i)F 2(nA )Ei(nB)

i=1

× E(i − 1)(nA ) PBB = (Nagg − 1)G(nB) Nagg − 2

+

∑

(2(Nagg − 1) − 2i)F 2(nB)Ei(nA )

i=1

Figure 3. SANS data of the pure hydrogeneous mixture 1:1 of nominally bifunctional oligomers (squares) and monofunctionals (circles) in the melt at T = 298 K (filled symbols) and T = 333 K (open symbols), respectively after correction for incoherent background. The black solid lines are calculations with the RPA equation at 298 K. The arrow indicates the decrease in the peak height at higher temperature due to the overall decrease of χ.N with T.

× E(i − 1)(nB) Nagg − 1

PAB =

∑

(2Nagg − 2i)F(nA )F(nB)(E(nA ) × E(nB))(i − 1)

i=1

(11)

The relevant contrast factors are ΔρA 2

length densities, the number of aggregated blocks and the χparameters.45,61,64,68 The Q-dependence of the scattering in the high Q region is found close to Q‑2 in the log−log plot (not shown), which is an evident signature of a disordered, Gaussian conformation of the blocks.45,48 Therefore, microphase separation in the strong segregation limit that would lead to denser, compact, and ordered spherical entities can be excluded. From the correlation peak the statistical segment length, lst of (6.4 ± 0.2) Å could be determined which is close to the expected size for PPG. No difference was observed in both modified polymers. This indicates that in the melt one should not expect large changes in the size and statistics of the flexible spacer due to the end-groups. The χ parameter between both blocks in both samples is about 3, which fits exactly to the calculated value given in Table 4. This corroborates the former

2 ⎛b b ⎞ = (ρA − ρC )2 = ⎜ A − C ⎟ vc ⎠ ⎝ vA

2 ⎛b b ⎞ ΔρB2 = (ρB − ρC )2 = ⎜ B − C ⎟ vc ⎠ ⎝ vB

(12)

The above formulation can be reworked in principle for cyclic configurations as well, taking into account the closure relations, or even for the presence of different architectural components with the same labeling scheme. The description for this general 3-component system of copolymer and nonspecific interacting (polymeric) solvent can be again reduced to the much simpler 2-component case. And the background component can be removed by letting ϕp → 1 and letting ρc → 0 simultaneously.65 With this, the classical scattering for a homogeneous disordered melt state of a multiblock copolymer with or without interaction is retrieved. This would be the case for the pure protonated mixture, given that the contrast between the assumed blocks is high enough. On the other hand, by means of nc the length of the Ccomponent can be easily varied from a solvent molecule up to polymeric size.65 The suggested approach will be tested by means of the appropriate model system in the melt before it is applied to the solution. The individual blocks are taken monodisperse and no attempt was made to include a polydisperse treatment of the resulting multiblocks.

Table 4. Fit Parameters Using the New Generalized RPA at T = 298 K T = 298 K

Nagg

lst [Å]

χAB

RPA bifunctional mixture RPA monofunctional mixture

∼19 2

6.4 ± 0.2 6.4 ± 0.2

3.0 ± 0.1 3.0 ± 0.1

made estimation using the empirical Hansen method.57 The data, measured at T = 333 K for both the bifunctional and monofunctional systems are included in Figure 3 for illustrative purpose only. Since the peak intensity is correlated to χ(T) N(T), the overall dependence on temperature of the product of χN (besides small effects of density variation with temperature) is observed. Whereas the peak position is largely unchanged within this 30 degrees range, the peak height decreases with increasing temperature as in block copolymeric systems. In the case of the monofunctional system, the correlation peak even “dissolves” and a total homogeneous solution results. The disordered nature of the mixture was found also in a recent investigation of the bulk system by SAXS.22,54 From this we can safely conclude that the presented polymer RPA model delivers a good description of both the characteristic length scale (peak position) and number of supramolecularly assembling units (peak height). We emphasize that the scattering length densities were fixed to the theoretical

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RESULTS AND DISCUSSION Disordered Multiblock Copolymer Melts. The equimolar mixture of Thy-PPG-Thy/DAT-PPG-DAT serves as an ideal system to (a) confirm the disordered nature of the pseudo block copolymer22,54 and (b) examine the limits of the suggested approach in this work. Figure 3 summarizes these results. Despite a relatively high background and the small but nonzero contrast of the stickers with the spacers, a clear correlation hole peak is observed for both monofunctionally and bifunctionally modified PPG spacers in 50/50 mixtures. The height of the correlation peak is given by the number of correlated segments, the scattering 9450


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values and only the interaction parameters between the blocks, Nagg and lst needed to be optimized. We stress that in the literature on the identical system a qualitative inspection solely based on SAXS curves on an arbitrary intensity scale was attempted,22,54 which did not allow the extraction of the detailed information presented in this study. Dilute Solution Structure. After efficiently testing the proposed RPA model in the bulk state, we are now ready to study the supramolecular assembly of DAT- and Thy-oligomers in solution. In dilute solution the same behavior as in a homogeneous phase is expected.63,72,73 Figure 4 illustrates the obtained SANS scattering profiles I(Q), versus scattering vector Q, for the 1:1 bifunctional

Figure 5. Kratky plot representation of the coherent scattering intensities for the stoichiometric mixture 1:1 bifunctional at the three lowest concentrations. Black solid lines show the prediction for a linear and ring polymer consisting of 2 macromonomers, respectively at 1%. The dashed line corresponds to the prediction of an admixture with 20% rings, which can be dismissed.

like a ring, star or micelle. Instead, a more or less plateauing of the data is found. Figure 5 also demonstrates the simulated form factor of a ring polymer at 1% composed of a cyclic polymer with molecular weight corresponding to two spacers.75−78 At this particular concentration the calculated probability of ring formation is maximal. It is obvious by comparing the Qdependence in the intermediate region, which is highly sensitive to the architecture, that our data do not evidence any signature of such ring-like structures.50,79 The dashed line in Figure 5 illustrates that cyclic contributions higher than 20% can be excluded. We conjecture that the combination of small dimerization constants together with the otherwise larger double ring are determining factors for the lack of this intermediate state. It can be emphasized that ring formation was only indirectly observed for self-associating systems with much higher association constants in dilute concentrations.75−78 In the case of the present system, the Thy-DAT complementary association is much stronger than either the Thy-Thy or DATDAT self-association52,54 but the probability of cyclic structures formation with at least 2 macromonomers is considerably reduced. Figure 6 shows the result from the simultaneous fit with the RPA approach to the scattering data in the dilute range of the selected concentrations. Whereas each concentration could have been fitted separately, we opted for a simultaneous description of all concentrations to avoid oversensitivity to the concentration of the samples. The constant of association is concentration independent and Flory−Huggins parameters should vary only over a much wider concentration range.56,57 As before, the parameters of the model were only lst, Kassn,Tol, χAB and χBC. The monomeric statistical segment length, lst, now becomes an effective one, being derived in solution state but is predominantly determined by the flexible block. Only small changes due to the different chemical composition of the spacer and complex block are expected. The χAC parameter i.e. the PPG-toluene interaction was fixed to the ideal value which we obtained from a separate determination of the second virial coefficient (A2) on a nonassociating CH3-terminated PPG in

Figure 4. Coherent scattering intensities for the 1:1 bifunctional mixture at different concentrations at room temperature. The 6 and 9% samples grossly overlap and clearly show an onset to semidilute behavior.

mixtures in deuterated toluene at 298 K with different concentrations between 0 and 10%. The intensities at low Q grow nonlinearly with the concentration which is a clear proof of an assembly process. This association can be analyzed by means of the equilibrium constant Kassn,Tol. Kassn,Tol strongly depends on the number and strength of H-bonds in the aggregate but does not depend on the concentration.4,19 The inspection of Figure 4 clearly shows that while the quasiplateau at low Q increases for concentrations 6%. We interpret this as a clear indication for chain interactions and a crossover to entangled chains in semidilute solution. The Q-vector probes then only blobs and measures the characteristic mesh size. Therefore, all evaluations were restricted to the systems with concentrations below 6.0%. Concurrently, dilute concentrations should comprise ideal conditions for the occurrence of cyclic structures in which chain ends of identical small chains are closer than those of neighboring ones.65−78 Their proof is complicated by the dynamic equilibrium between the open and closed state, of which the SANS experiments see a snapshot. A sensitive modelindependent verification of the intrinsically more compact cyclic conformation is the Kratky representation or second moment of the scattered intensity.50,79 Figure 5 shows the respective coherent scattering curves in such representation for the 3 lowest and dilute concentrations which all lack the otherwise distinct peak characteristic for a compact structure 9451


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system (K assn,Tol ≈ 2.2 × 10 4 M −1 ). 54 The classical determination of association constants Kassn,Tol by NMR titration is based on a change in the chemical environment of the binding hydrogen upon complexation.81−85 Therefore, the observed value strongly reflects the local environment of the hydrogen bond but does not give any direct information about the aggregation type between different macromonomers in a supramolecular system. Furthermore, it does not give any insight in the real effective aggregation number and distribution function of the chain length. While in a perfect and ideal system the association between the end-groups should directly translate to aggregation of macromonomers, imperfect endgroup functionalization and especially stoichiometric imbalances in the ratio between the different homoditopic macromonomers act as chain stoppers and can dramatically reduce the aggregate size. Therefore, this will inevitably result in lower Kassn,Tol values compared to those determined from NMR titration methods. Neutron scattering methods, on the other hand, directly observe the average structure of the supramolecular polymer. Any association determined by these methods will therefore reflect the real supramolecular system. Unfortunately, the factor between the association constants as determined by NMR on the one hand or derived from the size of the aggregates on the other hand, cannot be easily obtained quantitatively. The underlying study here provides for the first time an independent determination of a structural Kassn,SANS. Small angle X-ray (SAXS) and dilute solution light scattering are less sensitive respectively insensitive due to smaller respectively negligible contrast with the solvent toluene. This observation puts a high constraint on the chemical purity of such supramolecular systems, used for self-assembly and in particular self-healing applications. Also, in the recent study by Cortese et al.,54 the role of the solvent was discussed in terms of viscosities measurements. The enhancement of the latter in toluene was ascribed to small aggregates of constant size consisting of six macromonomers, held together by π−π interactions. In the same concentration range as the present study, the viscosity data were not able to distinguish between a linear aggregation mechanism, cyclic/linear combinations or a colloidal model. With the underlying work this situation is clarified and the preference of mainly linear chains is corroborated. The underlying manuscript shows the growth of an open, diffuse species with random walk characteristics with Nagg up to 5, which can be sufficiently well modeled by basic polymer concepts.

Figure 6. Scattering intensities vs scattering vector for the stoichiometric mixture at different concentrations in toluene-d8 at 298 K. The solid lines show the fit to the data with the RPA approximation. Approximate Nagg numbers that result from the Kassn,Tol of the simultaneous fit are also shown next to the corresponding concentration. The nonlinear increase with √ϕ is evident.

toluene-d8. The SANS scattering profiles for the CH3terminated PPG were measured well in the dilute regime and a Zimm fit as well as simultaneous fit of the form factor in the full Q-range were performed. The fit to the data yielded A2∼ 0.0026 ± 0.0007 cm3·mol·g−2, i.e., corresponding to χAC ∼ 0.34 ± 0.09 with A2 = (1/2 − χ)1/(Vρ2) .This is in full accordance with literature values.58,80 Further, its Mw is ∼1700 g/mol, lower than the given value of 2000 g/mol and the radius of gyration Rg is compatible with a statistical segment length of 6.7 Å. The refined obtained parameter values are presented in Table 5. As can be seen, the obtained interaction parameters compare well to the estimated ones and clearly show the similarity with block copolymers as suggested earlier.22,54 The incompatibility between the blocks itself is somewhat larger than the empirical estimation. Although very high, they do not lead to the formation of ordered microscaled aggregation and evidence a disordered state. We point out at this stage that variations in χ cannot be compensated by a different Kassn,Tol constant. The statistical segment length is larger than in the melts and absorbs the different rigidities of the blocks. As the fraction of pseudo B-blocks is more or less constant in the concentration range, the larger value may be partly due to the simplifications of the used RPA approach as well. The Nagg numbers shown in Figure 6 result from the fitted Kassn,Tol parameter with the RPA approach and grow roughly with √ϕ. The value of this microscopic structural association constant, Kassn,Tol, resulting from the simultaneous RPA model fit to the SANS data now represents the average global structure of the assembly in solution. The value is slightly lower than obtained by a classical NMR titration in toluene on a similar Thy-DAT containing system with different spacers (Kassn,Tol,NMR ≈ 2.6 × 103 M−1).52 However it is significantly lower than in a recently temperature-dependent NMR−viscosity study on the identical

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CONCLUSIONS

We have investigated by means of SANS the assembly mechanism of model telechelic polymers as homoditopic mixtures, bearing heterocomplementary stickers. It was shown that the chain growth is characterized by random walk statistics with Nagg up to 5. The obtained average Nagg for the heterocomplementary polymers at room temperature increases with ∼ √c, proving a linear association. The scattering data were critically examined by using an RPA model approach, which is usually applied to pure polymer systems. It revealed a

Table 5. Best Parameters Obtained by a Simultaneous Fit to the Scattering Data at 298 Ka RPA a

Kassn,Tol [M−1]

χAC

χAB

χBC

lst [Å]

1400 ± 200

0.34 ± 0.18

6.4 ± 0.8

4.0 ± 0.7

8.99 ± 0.05

χAC was determined separately and fixed at this point of evaluation. 9452


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very reasonably description of the SANS data of the associating polymers, despite the H-bonding groups. More, it underlined the importance of chemical interaction details between the components. It was shown that a linear conformation of these mixtures is present. Ring-association or micellar aggregates are absent or can be neglected in very good approximation. To the best of our knowledge this is the first attempt for a molecular description of heterocomplementary supramolecular polymers using an RPA approximation similar to multiblock copolymers.

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ASSOCIATED CONTENT

S Supporting Information *

Synthesis of thymine-substituted Jeffamine compounds (1, 1a), synthesis of diaminotriazine substituted Jeffamine compounds (2, 2a), GPC analysis of Jeffamine precursors, 1H NMR spectra of synthesized compounds, analysis of remaining Jeffamine impurities by 1H NMR, and a SAXS analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: (A.R.B.) [email protected]. *E-mail: (W.P.-H.) [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge EU for funding through the ITN214627 (DYNACOP). A.R.B., C.H. and W.A. acknowledge DFG-SPP1568 for financial support. We thank Prof. L. Leibler, Dr. Corinne Soulie, ́ and Dr. Jessalyn Cortese for the introduction to the topic and valuable comments prior to this publication.

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