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Polydispersity effects in poly(isoprene--styrene--ethylene oxide) triblock terpolymers
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10.1063/1.3140205
/content/aip/journal/jcp/130/23/10.1063/1.3140205
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/23/10.1063/1.3140205

Figures

Image of FIG. 1.
FIG. 1.

Plots summarizing the morphologies identified in ISO triblock terpolymers as a function of composition and either the (a) PS or (b) PEO PDI. All of the materials have comparable PI and PS molecular weights and have compositions that lie on the isopleth (see Tables I and II). The pairs of adjacent solid symbols indicate an OOT upon heating. Here we note that a distinction between and , which share a common symmetry, is somewhat arbitrary based on SAXS data alone and thus not made in Fig. 1 (Ref. 48). We expect that is the likely morphology at higher PEO contents.

Image of FIG. 2.
FIG. 2.

Synchrotron SAXS data acquired at [ for IS(1.06)O(0.05)]. All samples were annealed at for 5 min [at for IS(1.06)O(0.05)] before data were collected. The data for (a) IS(1.06)O(0.05) and (d) IS(1.06)O(0.33) are indexed to a lamellar morphology; the absence of the 002 peak in the IS(1.06)O(0.05) data is consistent with a structure factor extinction for symmetric (Ref. 52). The Bragg peaks for (b) IS(1.06)O(0.26) are indexed to CSG and the diffraction pattern for (c) IS(1.06)O(0.27) is indexed to .

Image of FIG. 3.
FIG. 3.

SAXS data acquired at 120 and for ISO(1.46, 0.20). The sample was annealed for 5 min at each target temperature prior to data collection ( anneal preceded anneal). The Bragg pattern at is indexed to CSG while the peaks at are indexed to a hexagonal mesostructure (here identified as ).

Image of FIG. 4.
FIG. 4.

Synchrotron SAXS data acquired at for two IS(1.06)O blends with overall . The polymers were annealed at for 5 min prior to a 5 min anneal and data collection at . (a) ISO(1.40, 0.30) SAXS data are indexed to CSG and (b) ISO(1.73, 0.30) Bragg peaks are indexed to a hexagonal morphology (here identified as ).

Image of FIG. 5.
FIG. 5.

SAXS data acquired at 120 and for blend ISO(1.27, 0.33). The sample was annealed for 4 min at each target temperature prior to data collection ( anneal preceded anneal). The Bragg pattern at is indexed to , while the peaks at are indexed to CSG.

Image of FIG. 6.
FIG. 6.

SAXS data acquired at 120 and for sample IS(1.16)O(0.25). The sample was annealed for 5 min at and then annealed for 5 min at each target temperature prior to data collection ( anneal preceded anneal). The Bragg pattern at is indexed to while the peaks at are indexed to . The low intensity peak in the data (marked with ◆) corresponds to the 113 reflection from and is consistent with a small fraction of the material being trapped in a metastable mesostructure.

Image of FIG. 7.
FIG. 7.

SAXS data acquired at for samples (a) IS(1.44)O(0.17), (b) IS(1.44)O(0.21), (c) IS(1.44)O(0.22), and (d) IS(1.44)O(0.24). All of the materials were annealed at for 5 min before they were held at for 5 min. The peaks for (a) IS(1.44)O(0.17) and (c) IS(1.44)O(0.22) are indexed to , those for (b) IS(1.44)O(0.21) are indexed to LAM, and those for (d) IS(1.44)O(0.24) are indexed to CSG. The low intensity peak in the IS(1.44)O(0.24) data (marked with a ◆) is consistent with the 113 reflection for ; a small portion of the material has formed that coexists with the CSG network.

Image of FIG. 8.
FIG. 8.

Measured (by SAXS, solid points) and predicted (by SCFT, open points) normalized values for the ISO samples with (a) , 0.33 and (b) . The experimentally measured principal scattering lengths are normalized by dividing them by measured for triblock IS(1.06)O(0.20) (data for ), triblock IS(1.06)O(0.33) (data for ), or blend ISO(1.16, 0.30) (data for ). Here is approximated as 1 for samples IS(1.06)O(0.20) and IS(1.06)O(0.33). The predicted values are normalized by dividing them by either computed for monodisperse ISO triblocks with the same composition or by calculated for blend ISO(1.16, 0.30) . In all cases was computed for the morphology identified using experimental data, even if it was not the mesostructure with the lowest calculated free energy [e.g., the predicted for blend ISO(1.46, 0.20) was computed for the CSG morphology, not ].

Image of FIG. 9.
FIG. 9.

Calculated SCFT free energies (relative to LAM and normalized by ) of competing mesostructural candidates for model systems that approximate the experimental [(a) and (b)] IS(1.16)O, (c) IS(1.31)O, and (d) IS(1.44)O systems. All of the free energy curves were computed at the molecular weights and along the isopleths defined by the number-averaged and values that are listed in Table I. The and morphologies have higher computed free energies for all of the systems and, for clarity, their free energy curves are not provided on the (b) IS(1.16)O, (c) IS(1.31)O, and (d) IS(1.44)O plots. The solid lines are the curves computed for the polydisperse materials, while the dashed lines are calculated for monodisperse systems with the same compositions and molecular weights.

Image of FIG. 10.
FIG. 10.

Differences in computed free energy components (normalized by ) of the and LAM morphologies between the model IS(1.44)O system and its monodisperse counterpart. The values plotted on the ordinate are obtained by (i) subtracting the value of each free energy component calculated for LAM from the value of each component computed for (i.e., ) and (ii) subtracting these component differences for a PS from these component differences for a PS . The solid curves represent the components of the free energies and are labeled using the nomenclature described in Table III. The dashed curve represents the overall Helmholtz free energy. The horizontal lines at ordinate values of −0.01 and −0.02 (marked with ◼) connote the compositions at which SCFT predicts to be the equilibrium mesostructure for the monodisperse and polydisperse systems, respectively.

Image of FIG. 11.
FIG. 11.

Curves representing the relative stability of the LAM mesostructure relative to a homogeneous, disordered state for the polydisperse systems, and their monodisperse analogs. The values plotted on the ordinate were obtained by (i) computing for both the monodisperse and polydisperse systems and (ii) subtracting this difference for the monodisperse system from this difference for the polydisperse system (e.g., ). When the ordinate value is negative, LAM is more stable for the polydisperse material (i.e., higher for the polydisperse systems). When the ordinate value is positive, LAM is more stable for the monodisperse material (i.e., lower for the polydisperse systems).

Image of FIG. 12.
FIG. 12.

Normalized LAM domain periodicities computed using SCFT for the three polydisperse ISO systems. The values are normalized by dividing them by the lattice spacings calculated for the monodisperse analogs to the polydisperse series. Results are only plotted when SCFT predicts LAM to be the equilibrium mesostructure for both the monodisperse and polydisperse systems; the gaps represent compositions at which is predicted to be the equilibrium morphology for the polydisperse and/or monodisperse materials.

Tables

Generic image for table
Table I.

Neat ISO characterization data.

Generic image for table
Table II.

ISO blend characterization data.

Generic image for table
Table III.

Differences in free energy components and relative domain spacings of the morphologies with comparable free energies for the multicomponent ISO blends. All free energies are computed with respect to a reference volume of and are normalized by . In the top half of Table III, all differences are listed as the value for CSG minus the value for LAM. In the bottom half of Table III, all differences are listed as the value for minus the value for CSG.

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/content/aip/journal/jcp/130/23/10.1063/1.3140205
2009-06-17
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Polydispersity effects in poly(isoprene-b-styrene-b-ethylene oxide) triblock terpolymers
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/23/10.1063/1.3140205
10.1063/1.3140205
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