N N N NH2 NH2 O N H x N N H O O O O N H x
TOWARDS THE MICROSCOPIC UNDERSTANDING OF
SELF-HEALING MECHANISMS
A. R. Brás1, C. Hövelmann1, W. Antonius1, M. Krutyeva1, A. Radulescu2, J. Allgaier1, W. Pyckhout-Hintzen1, A. Wischnewski1 and D. Richter1
1
Forschungszentrum Jülich, Jülich Centre for Neutron Science JCNS, D52425 Jülich, Germany – e-mail: a.bras@fz-juelich.de; c.hoevelmann@fz-juelich.de; w.antonius@fz-juelich.de; m.krutyeva@fz-w.antonius@fz-juelich.de; j.allgaier@fz-w.antonius@fz-juelich.de; w.pyckhout@fz-w.antonius@fz-juelich.de; a.wischnewski@fz-juelich.de; d.richter@fz-juelich.de
2
Forschungszentrum Jülich, Jülich Centre for Neutron Science JCNS, Outstation at FRM II, D85747 Garching, Germany – e-mail: a.radulescu@fz-juelich.de
Keywords: Supramolecular polymers, hydrogen bonds, neutron scattering, random phase approximation
ABSTRACT
In the present work we report on a Random Phase Approximation (RPA) which can be applied to multiblock copolymers consisting of supramolecular building blocks and hydrogen-bonded compounds including interactions in solution. These systems are model for the self-healing process due to the hydrogen-bonding interaction between the end-groups. This new analysis allowed to quantitatively access the assembly route with varying concentration.
1. INTRODUCTION
Supramolecular polymers are an increasingly important class of polymers, where designed intermolecular interactions allow a specific tailoring of polymer properties. One of the most recent additions to this field are self-healing polymers, which bases on the hydrogen-bonding interaction of groups on parts of the molecules. Small Angle Neutron Scattering (SANS) measurements were performed on systems as a 50/50 mixture [1] in deuterated toluene, using the complementary end-groups Thy and DAT (Fig. 1) and polypropylene glycol as backbone.
Figure 1: Complementarity between DAT and THY, leading to self-assembly. Recently [1], Small Angle X-Ray (SAXS) was performed on the same systems in the bulk. It shows the typical behavior of a block copolymer [1] in a 1-phase region. In solution, the same behavior as in an homogenous phase in the respective diagram is expected. More, even though in literature cyclization is possible to occur upon dilution in the formation of supramolecular polymers, the polymers in this study showed, at our experimental conditions, a much smaller fraction of rings as expected by theory (~50 %) [2]. We cannot distinguish rings from linear aggregations within ~10%. In practice, any imbalance of stoichiometries, monofunctional imperfection or disproportion of the building blocks of which the exact molecular weights differ, shifts the equilibrium to unclosed or linear species.
The intriguing question how to quantitatively access the assembly route is tested by an RPA for a thought multiblock copolymer consisting of simple blocks and hydrogen-bonded compounds including for the first time interactions between the separate components in solution.
2. METHODS
Experiments were performed at the SANS diffractometer KWS2 @FRM2, Munich.
3. RESULTS
The RPA structure factor for a diblock copolymer, considering no interactions between the blocks (χAB=0) is [3]:
1)
In this work we need to consider a ternary system of a block copolymer in solution. In our terminology, this is a third “component” case with the block as components A, B and the solvent as component C. The number of components is determined by the number of different scattering length densities. Block A is connected to block B leading to the general multiblock copolymer(AB)Nagg-1A. In addition we have included
in the multi-component RPA all possible interactions Xij with i,j=A,B,C.
Assuming the complex and solvent as oligomers of the same stiffness as the main blocks, one can express the partial structure factors by a number of monomers noted as nA, nB and nC (polymer, end-groups and solvent, respectively), the volume
fractions (ϕA, ϕB and ϕC), the specific monomeric volumes (vA, vB and vC), the form
factors are PAA(Q), PBB(Q) and PC(Q), the Flory-Huggins interaction parameters are
χAB, χBC and χAC (χAB polymer-endgroups, χBC endgroups-solvent and χAC
polymer-solvent), the different contrasts to the background (ΔρA, ΔρB) and the number of
aggregates(Nagg):SRPA f(Nagg,,,c)
In the related polycondensation theory the Nagg is defined as (Nagg ≈ Sqrt(Kass . ϕp) [4],
Kass being the equilibrium association constant in solution of the system Thy-Thy
/DAT-DAT mixture and assumed as a fit parameter of the model. The RPA approach is strictly valid only in the melt state and assumes Gaussian statistics. Deviations therefore are possible especially at high Q but the main information will be independent from this. As a further approximation the non-bonded end-groups at the beginning and end of the multiblock are neglected.
Figure 2: Sketch of the suggested block copolymer structure of the type (AB)n-1A.
With Nagg one could naively obtain an apparent size of living chain MW. Assuming
Gaussian statistics and monomolecularity as polydispersity in connection with RPA is not manageable, a concentration-dependent overlap or critical concentration can be estimated from published chain dimensions depending on Mw. As the Kass is not
known and depends on the specific purity of the experimental system a range of concentrations was selected between 0 and c*=ϕp=~10% from the chloroform
constant. The used concentration of the mixture of the components A-B were 0.9 to
B A toluene: C [AB]Nagg-1A ) 0 ( S 2 S S S S S S AB BB AA 2 AB BB AA RPA ICSHM2013_________________________________________________________________________________ 379
9% (m/m): Neglecting in a first approximation inter-component interactions, a general model-independent Guinier representation of the low Q data, ln I (Q)= ln I0 (Q)-
1/3Q2Rg2, allows us to qualitatively interpret the data. The range of scattering vectors was restricted to QRg∼2 here, for which the Guinier approximation is valid. At Q=0 the intercept intensity I0 is proportional to MW. Thus for the system Thy-Thy/DAT-DAT
mixture, if association occurs, its expected dependence should be I0 ≈ (ϕp)3/2.
Similarly, the chain radius of gyration Rg obtained by the same approach should
depend on ϕp as Rg ≈ (ϕp)1/4. The Gaussian statistics assumption seems to be kept
upright through the Q-2 dependence found even at the lowest dilution. In figure 3 the results from this first analysis are shown, respectively:
Figure 3: The forward scattering intensity I0 and Rg follow closely the predictions of a
linear association in a multiblock-like chain, proven from the different slopes vs. ϕp.
It is evidenced that the above proportionalities are observed only for ϕp<6.0%. It
indicates that, contrarily to the previous estimations for Chloroform (Kass=890 mol-1)
[1], c* is reached at a lower concentration. Hence we are led to the conclusion that in toluene the Kass is higher. As a consequence the full Random Phase Approximation
model described before for these supramolecular associating polymers was only applied to the systems with concentrations below ϕp<6.0%. The only parameters
were the Kass,χAB and χBC. Concerning χAC, i.e. the interaction between PPG-toluene,
the estimated value is in accordance to what was found in literature [5] and therefore was kept constant. All values are presented in Table 1. A simultaneous fit to the data was done in order to obtain the most accurate estimate of Kass and also since the
interaction parameters should not vary in the different concentrations, too. The respective obtained parameters for all systems are summarized in the table below:
1E-3 0.01 0.1 1 1 10 100 I0 [cm-1 ] I0 = 1.5 Rg=0.25 Rg[Å] p [%] 0.01 0.1 1 10
Figure 4: Coherent scattering intensities for the stoichiometric mixture at different concentrations below c* in toluene at room temperature. The solid lines show a fit to the data with the RPA approximation.
The obtained interaction parameters compare very well to the estimated ones and clearly show that the similarity with block copolymers like suggested [1] is appropriate. The fit to the data is shown in figure 4 as solid lines. The high interactions reflect the different solubilities of the specific components and may well form a basis for the occurrence of a considerable nanostructuring into micelle-like or more compact aggregates by phase-separation or stacking mechanisms at concentrations exceeding highly the investigated concentration range below c*.
Table 1: Empirical estimations of χ obtained from solubility parameters following the Hansen method [5] compared to the data parameters from the simultaneous fit to the
data using the new RPA.
Kass χAC χAB ΧBC
Estimation --- 0.34 1.7-4.8 3.8 (Thy)- 4.1 (DAT)
RPA fit 1400200 0.34 6.380.06 4.00.01 4. CONCLUSIONS
It can be seen that the used RPA approach very reasonably describes the SANS data. Except for small discrepancies at high Q which can be explained by the finite size of the blocks, the model is superior over the often-used too simple Guinier approach. The intramolecular interaction parameters are of the order or much larger than for typical flexible polymers. Moreover, from the power-law for both zero-Q-scattering and Rg it could be confirmed that a linear conformation of these mixtures is present, and ring-association and collapsed or in se aggregation are absent or can be neglected in very good approximation.
ACKNOWLEDGEMENTS
Prof. Leibler for introducing these polymers to the FZJ group and DFG-SPP1568 for financial support. 1E-3 0.01 0.1 1 1E-3 0.01 0.1 1 10 I [ cm -1 ] Q [Å-1] ICSHM2013_________________________________________________________________________________ 381
REFERENCES
[1] J. Cortese, C. Soulie-Ziakovic, M. Cloitre, S. Tence-Girault, L. Leibler, Order-Disorder Transition in Supramolecular Polymers, Journal of the American Chemical Society 133 (2011) 19672-19675; J. Cortese, C. Soulié-Ziakovic, S. Tencé-Girault, L. Leibler, Suppression of Mesoscopic Order by Complementary Interactions in Supramolecular Polymers, Journal of the American Chemical Society 134 (2012) 3671-3674.
[2] L. Rique-Lurbet, M. Schappacher, A. Deffieux, A New Strategy for the Synthesis of Cyclic Polystyrenes: Principle and Application, Macromolecules 27 (1994) 6318-6324; H. Jacobson, W. J. Stockmayer, Intramolecular Reaction in Polycondensations. I. The Theory of Linear Systems, Journal of Chemical Physics 18 (1950) 1600-1606.
[3] http://www.ncnr.nist.gov/staff/hammouda/the_SANS_toolbox.pdf
[4] L. Bouteiller, Assembly via Hydrogen Bonds of Low Molar Mass Compounds into Supramolecular Polymers, Advances in Polymer Science (2007) 207, 79-112.
[5] D.W. Van Krevelen, Properties of Polymers, 3rd ed., Elsevier: Amsterdam, New York, 1990; J.E. Mark; Polymer data handbook, Oxford University Press, 1999; S.W. Kuo, H.T. Tsai, Complementary Multiple Hydrogen-Bonding Interactions Increase the Glass Transition Temperatures to PMMA Copolymer Mixtures, Macromolecules, 2009, 42, 4701-4711.
