Supplementary Information

Transcription

1 Supplementary Information Computer Simulation of Dendronized Polymers: Organization and Characterization at the Atomistic Level Oscar Bertran, 1,* Baozhong Zhang, 2 A. Dieter Schlüter, 2 Avraham Halperin, 3 Martin Kröger, 2 and Carlos Alemán 4,5,* 1 Departament de Física Aplicada, Escola d Enginyeria d Igualada, Universitat Politècnica de Catalunya, Pça Rei 15, Igualada 08700, Spain 2 Department of Materials, Institute of Polymers, Swiss Federal Institute of Technology, ETH Zurich, HCI J 541, 8093 Zurich, Switzerland 3 Université Grenoble 1 / CNRS, LIPhy UMR 5588, Grenoble, France 4 Departament d Enginyeria Química, E. T. S. d Enginyeria Industrial de Barcelona, Universitat Politècnica de Catalunya, Diagonal 647, Barcelona E-08028, Spain 5 Centre for Research in Nano-Engineering, Universitat Politècnica de Catalunya, Edifici C, C/Pasqual i Vila s/n, Barcelona E-08028, Spain S 1

2 Description of the conformational search and growth procedure Trial initial molecular conformations of PG1-PG7 were grown generation by generation. To this end a multidimensional conformational analysis was performed within a limited space of the following variables: (i) The shape of the backbone (Figure 2a). Five backbone initial conformations, varied between a perfect linear arrangement and a helical shape with both large period (i.e Å) and large radius (i.e. 5.1 Å), were constructed by requiring that the backbone dihedral angles of the N repeat units are identical. (ii) The angle and the dihedral characterizing relative orientation between strands and branching units (Figure 2b). The angle is related with the aperture of the branching unit with respect to its two outgoing strands, initially taking values of 80º or 120º. The dihedral defines the relative orientation between two adjacent branching units (i.e. their benzole rings), the values being initially of 0º and 90º. To provide a simple characterization of the conformations of the DPs, accompanying and enhancing the efficiency of the conformational generation-wise growth process, the arrangement of their complex side groups was quantified using the distribution of absolute orientations and lengths of, and relative angles between, the two terminal strands of their (currently) outermost branching units, sometimes denoted as external 1-generation dendrons, or external dendrons of a g-generation dendron. To be specific, we considered the vectors between the first aromatic carbon of the corresponding branching unit and the center of masses of the tert-butyloxycarbonyl Boc groups (vectors d of length d) and the angle ( ) between the two vectors d for each external dendron. Figure 2c depicts the definition of d and for a repeat unit of PG2. At S 2

3 given generation g of the growth process we thus have 2 g values for both d and contributing to their averages and standard deviations. The conformational search was carried out using the following bottom-up strategy. Initially, 5 (shape of the backbone) 2 ( ) 2 ( ) = 20 start conformations were constructed for PG1, those without steric conflicts being subjected to energy minimization. Conformations able to retain a ``homogeneous and regular, defined as possessing a distribution of angles and backbone dihedral angles with standard deviations below 20%, were used to build the start conformations of PG2. This criterion was imposed for two reasons: (i) we are seeking for DPs which are uniform over the length scale we are able to study, (ii) inhomogeneous conformations tend to be rejected due to steric conflicts in subsequent generations; their rejection thus helps to reduce the computational effort. To build PG2 the angle and the dihedral of the external layer of 1-generation dendrons were varied considering the two pairs of values given above, while the rest of the DP was kept at the regular arrangements found for PG1. Energy minimization of the PG2 structures without steric conflicts led to an interesting observation: many of these attempted conformations were not able to retain a regular and homogeneous structure because of the strong steric repulsions between neighboring side groups. The number of regular conformations after minimization was lower for PG2 than PG1, even though the number of starting structures was by a factor two higher in the former case. Similarly, the pre-equilibrated regular structures of PG2 were used to build the start conformations of PG3 by varying the dihedral angles and of their external dendrons. As expected, the number of start conformations without steric conflicts was relatively small in relation to PG2, and only a small amount of regular and homogeneous structures were obtained after energy minimization. An identical procedure was applied for PG4 and PG6, the number of homogeneous and regular S 3

4 structures obtained after minimization further decreasing with increasing g. It should be mentioned that in few cases minimization of different initial conformations led to a single pre-equilibrated conformation. Some helical conformations of PGg with g < 4 evolved towards the elongated backbone conformation during the conformational search. The structures that preserved regularity and homogeneity after minimization were submitted to 0.3 ns of MD at 298 K in vacuum. Visual inspection of the structures obtained after such short simulation time indicated that the enforced helical conformation of many of them was lost during thermalization. After this, the stability of one of the remaining homogeneous structures of each generation was investigated in vacuum and in chloroform solution. Simulations of 10 ns were run in vacuum for systems with N 75, while NVT-MD simulations of 10 ns were carried out in chloroform solution for systems with N 30. We will refer to these relaxation runs as constituting the ``equilibration phase''. S 4

5 Influence of the solvent on the molecular models for DPs To investigate the effect of the solvent on the backbone structure and the organization of dendrons, all homogeneous and regular structures derived from the conformational search process applied for systems with N 75 (see Methods section) were transferred to small oligomers. These structures were used as starting configurations for our MD simulations in chloroform solution and, by analogy with solvent-free simulations, energy criteria were applied in the selection of the model for the DPs with smaller g. Consideration of explicit solvent molecules results in systems involving a large number of particles. In view of computational limitations, we had to limit the size of the investigated oligomers to N= 30 (PG1 PG4) and N= 24 (PG6). Configurations obtained for PG1 PG6 in chloroform solution after a 10 ns production run are depicted in Figure S2. As it can be seen, the conformational characteristics of the MBs in PG1 PG4 are similar to those obtained in vacuum. An elongated conformation was obtained in all cases. Inspection of the DPs indicates the existence of important finite N, or equally, end cap effects. The dendrons located at the two DP ends tend to use the available space within the hemispherical end caps to align in the direction of the MB. This effect is getting increasingly pronounced with growing g and/or decreasing N. To avoid undesirable end effects in the analysis of quantities characterizing a representative part of a long DP, average values of d and were calculated by considering the terminal dendrons of the 12 central DP repeat units only (Table 1 of the paper). The mean lengths of their terminal strands, obtained for the four DPs, are very similar to those obtained in vacuum, indicating that they retain the elongated shape in chloroform solution. Also the average values follow the tendencies discussed in previous sections, suggesting a transition towards a higher internal packing of the dendrons when g increases from 3 to 4. Furthermore, as expected, standard S 5

6 deviations of the averaged values evidence that the local order of the terminal strands increases with g. Inspection of the configurations obtained for PG6 reveals that the size of the oligomer (N= 24) is too small to allow drawing conclusions for long PG6, as the organization of the dendrons inside DPs is dominated by end cap effects. Consequently, the resulting DP extension determined by the maximum distance between its atoms is more than twice the value one would roughly expect for an infinitely long DP (PG6 in Figure 8). Furthermore, the backbone is too short to discern the signature of a helical shape of the kind found for longer PG6 (N=75) in vacuum. Nevertheless we are going to discuss results obtained for these systems as they help to provide some qualitative insight. S 6

7 Fractal geometry of the molecular models for PG1 PG6 considering all atoms Box-counting results obtained considering all the atoms of each conformation (including backbone and side group atoms) are displayed in Figure S3a. The fractal dimension increases with g, changing from for PG1 to for PG6. As expected, the pre-exponential factor M 0 in M(l) = M 0 (l/å) -, which provides a rough estimate of the polymer volume, M 0 V g (rough since 3), also increases with g. Inspection of these pre-exponential factors shows that the growing of the relative volume decreases for increasing g. Thus, the relative volume increment, calculated as V g 1 Vg / V, where V g g refers to the pre-exponential factors obtained for PGg, is 1.68 (g=1), 1.45 (g=2), 1.29 (g=3) and 1.30= V V / V, when g changes from 4-to-6, respectively. Within the poor solvent scaling representing a homogeneous cylinder, one expects V g /n α ( 2 g 1) g g and thus Vg 1 Vg / Vg 2 /(2 1), in rough agreement with the measured values up to g=4. Finally, self-similarity analyses (Figure S3b) corroborate that the conformations proposed for PG1 PG6 present fractal dimensionality over a wide range of length scales, as reminiscent of the variation of S M (l)/s M (l max ) against l/l max that remains close to 1 in all cases. S 7

8 Electronic Supplementary Material (ESI) for RSC Advances (a) (c) (b) Figure S1. Electrostatic parameters obtained for the DPs: (a) backbone region; (b) dendron units; and (c) ending groups. S8

9 Figure S2. Atomistic conformations for PG1-PG6 in chloroform solution at the end of the 10 ns MD run. The backbone is represented using a purple coarse track. S 9

10 (a) Log M(l) PG6 PG4 PG3 PG2 PG1 M(l)= l (R 2 = 0.998) M(l)= l (R 2 = 0.998) M(l)= l (R 2 = 0.998) M(l)= l (R 2 = 0.998) M(l)= l (R 2 = 0.999) Log 10 (l / Å) (b) S M (l)/s M (l max ) PG6 PG4 PG 3 PG2 PG l / l max Figure S3. (a) Plot of log 10 M(l) vs. log 10 (l/ Å) for the fractal object defined by all atoms contained in the molecular models proposed for PG1 PG6. Equations adjusted to derive the fractal dimension,, and the corresponding regression coefficient (R 2 ) are displayed. (b) Changing trend of S M (l)/s M (l) max with l/l max. S 10

11 D (Å 2 /ps) PG1 PG3 PG2 PG Time (ps) Figure S4. Plot of the diffusion coefficient of the chloroform molecules (Eqn 10) into PG1-PG4 against the simulation time. S 11