On the thermodynamics of chain architecture in

acrylic block terpolymers

James A. Bergman, Nacu B. Hernandez, Eric W. Cochran, and Jennifer M.

Heinen

Department of Chemical and Biological Engineering, Iowa State University, Ames, IA 50011

E-mail: ecochran@iastate.edu

Abstract

In this article we report the manipulation of block terpolymer morphology through

control of the segment distribution. We consider a model system comprised of

three acrylic monomers: hydrophilic poly(hydroxyethylacrylate) (H), hydrophobic

poly(octylacrylate) (O), and polar poly(methylacrylate) (M). For each of four chemical

compositions, we altered the M segment distribution in four terpolymer architec-

tures with Reversible Addition-Fragmentation chain Transfer (RAFT) polymerization

to yield: two triblock terpolymer architectures, HOM and HMO, and two diblock

terpolymer architectures, HMO and HMO, where the M segments are statistically

distributed in the O or H blocks, respectively. Using a combination of small angle

x-ray scattering and dynamic shear rheology, we illustrate how the M monomer dis-

tribution can be used to manipulate the thermodynamic behavior of terpolymers at

constant chemical composition. These results will be of use to those wishing to partially

decouple the formulation of a block copolymer from its morphology.

To whom correspondence should be addressed

1

Introduction

The self-assembly of block copolymers (BCPs) has received much attention over the past

forty years and the thermodynamic behavior of diblock copolymers is well understood.15

Diblock copolymers are known to self-assemble into a limited number of microstruc-

tures: body-centered cubic packed spheres (Q229), hexagonally packed cylinders (H),

orthorhombic Fddd network (O70), double gyroid (Q230), and lamellae (L). Manipulating

BCP self-assembly may be achieved by changing the composition ( fA), chemistry (Flory

interaction parameter AB and Kuhn lengths bi), and segregation strength ( N/T, where N

is the degree of polymerization and T is the absolute temperature). In a qualitative sense,

the phase behavior of diblock copolymers is universal; that is, the sequencing of phases

with composition and temperature is fixed and only the quantitative locations of the phase

boundaries vary from system to system. In principle, the simplicity of this universal phase

behavior is desirable from an applications design perspective. In practice, however, the

design of an application fixes the chemistry and places constraints on the composition

and segregation strength. This facet of the copolymer parameter space unfortunately

that the simultaneous optimization of chemical composition and retention of the desired

morphology may be unachievable. This is, simplicity comes at the expense of flexibility.

Alternatively, the phase space of triblock terpolymers is known to be far more expansive

due to the number of independent variables that describe the system; the parameter

space now includes an additional two interaction parameters (BC and AC) and an

additional independent volume fraction ( fB).6 The addition of the third C component

increases the number of possible microstructures by at least five-fold, to date over 30

microstructures have been identified.7 Numerous groups have contributed to our collective

understanding of how multicomponent block copolymers behave with the introduction

of additional interfaces. Much of the first work in this was produced by the research

groups of Stadler,811 Abetz,1214 and Matsushita;1517 many reports included countless

juxtapositions of diblock copolymer-like structures. For example, a number decorated

2

phases such as spheres-on-spheres,18 a tetragonal lattice of A and C cylinders in a B

matrix,17 or A and C spheres in a CsCl-like packing.17 Moreover, fascinating new structures

such as the knitting pattern19 and the orthorhombic network phases O70 and O52 were

quite unlike any structure observed in soft matter20,21 (although O70 was later discovered

in diblock copolymers3,5). Star architectures, various blending strategies, and even the

introduction of a fourth component have further supplemented the current palette of

known mesophases. While the possibilities attendant with the ever-increasing complexity

and richness of polymer phase behavior continue to captivate researchers imaginations,

complexity is not necessarily ideal for material design.

This Article presents work in which we begin to explore the role of the C component

as a tool that can be used to simplify the task of block terpolymer design while retaining

the flexibility engendered by the third component. That is, given a fixed chemical com-

position, we seek to establish the design rules associated with the segment distribution

function in a model A/B/C three-color system. This work is conceptually related to

the gradient2227 or taper2831 architectures in A/B copolymer systems. As Fig. 1

illustrates, the monomer sequences embodied by these two copolymer types lie on one

of many paths that span the continuum between a purely statistical A/B copolymer and

a perfectly discrete AB diblock copolymer. Gradients and tapers are typically prepared

using a semi-batch reaction scheme in conjunction with a (pseudo-)living polymerization

chemistry, e.g., nitroxide-mediated radical polymerization,24 atom transfer radical poly-

merization,22 reversible addition-fragmentation chain transfer (RAFT) polymerization,27

or anionic polymerization.28,29 In essence, the width of the chemical A/B interface maps to

the width of the corresponding spatial interfaces, and accordingly the effective segregation

strength of the copolymer effN can be tuned through simple reaction engineering, leav-

ing the overall molecular weight and chemical composition fixed. The extension of this

principle to three-color systems is straightforward; again semi-batch addition techniques

may be used to taper the A/B/C segment distribution, although the number of resultant

3

A B

A B

A B

AB

e

Copolymer architectures

A(a) C B

A(b) BCA(c) B C

(d) CAB

?

Terpolymer architectures

Figure 1: Schemes for manipulating block polymer self-assembly through the segmentdistribution. (Left) The segment distibution of diblock copolymers can be manipulated inmany ways, for example by using a combination of sequential and gradient copolymeriza-tion techniques. In this way the transition from A to B occurs gradually along the chaincontour. Tuning this transition allows the decoupling of eff from design parameters f andN (Right). In ternary systems, manipulation of the sequence distribution can influence boththe effective domain composition f and the effective interaction strength eff, partiallydecoupling both the chemical composition and molecular weight from thermodynamicallypreferred morphology.

permutations of polymers that can be produced becomes large. Moreover, the trivial case

in the engineering of diblock copolymers through sequence distributionthat is, the statis-

tical A/B copolymeris no longer trivial in the analogous progression of possible A/B/C

sequence distributions. Rather, sequences such as AB/C or A/BC represent intermediates in

the progression from BAC to ABC to ACB.

In this work we employ a model system comprised of three types of acrylic segments:

poly(hydroxyethyl acrylate) (H), a hydrophilic polymer; poly(methyl acrylate) (M), a polar

polymer; and poly(octyl acrylate) (O), a hydrophobic molecule. As we will show, the

interaction parameters for this system satisfy the sequence HO 2HM 2MO. TheH/O system is of technological interest as a source of a new family of amphiphilic materials;

the simplest such material would be the diblock copolymer HO whose phase behavior is

governed by fH and HON. We show that the introduction ofM, with intermediate polarity,

serves to influence the phase morphology and transition temperatures while leaving the

chemical composition and molar mass fixed. The terpolymer architectures depicted in Fig. 1

4

020

40

60

80

100

0 20 40 60 80 1000

20

40

60

80

100

MH

O

O O

n

HO

poly(hydroxyethylacrylate)

O O

n

poly(methylacrylate)

O O

n

7

poly(octylacrylate)

(1) (2) (3) (4)

H OM

H OMH MO

OHM

H O M

H OMHM O

OHM

Figure 2: Composition diagram for H/M/O system investigated in this study. Details forcompositions 1-4 are listed in Table 1.

illustrate a thought experiment in which M (block B) segments progress from right

to left in chain architectures (a) through (d) . Fig. 2 plots the copolymer compositions

that were synthesized for this work on the H/M/O ternary composition diagram. We

hypothesized that for the H/M/O systemat sufficiently small M volume fraction fM

the phase behavior of all architectures should mimic that of classical diblock copolymers.

That is, for the purposes of targeting a particular morphology, it should be possible to

define a mapping of the three parameters and two composition variables to a reduced

diblock-equivalent parameter space that defines an effective domain composition f and

interaction strength eff that serve as a 1st-order predictor for the thermodynamic behavior

of a particular material. For diblock terpolymers, i.e., HMO and HMO, there is clearly a

single interface that partitions the polymers into two-domain morphologies that implies

diblock-copolymer-like phase behavior. On the other hand, the triblock architectures

HMO and HOM will be governed by competing H/M and O/M interfaces where no such

simplifying mappings can necessarily be prescribed.

5

Experimental

Chemicals

Anhydrous ethanol (200 proof), carbon disulfide (99%), hydroxyethyl acrylate (96%), and

ethyl -bromoisobutryate (98%) were purchased from Sigma-Aldrich Chemical Company

and used as received. Potassium hydroxide (85%), tetrahydrofuran (THF), and 1,4-dioxane

were purchased from Fisher Scientific and used as received. Methyl acrylate (99%) and

n-octyl acrylate (96%) were purchased from Sigma-Aldrich and Scientific Polymer Prod-

ucts respectively; both were passed through an SDHR-4 column, purchased from Scientific

Polymer Products, to remove the inhibitors hydroquinone and monomethyl ether hydro-

quinone prior to use. The initiator 2,2-azobisisobutyronitrile (98%) was purchased from

Sigma-Aldrich and was recrystallized in ethanol prior to use.

Reversible Addition-Fragmentation Chain Transfer Agent Synthesis

The reversible addition-fragmentation chain transfer agent (RAFT CTA), ethyl 2-(eth-

oxycarbonothioylthio)-2-methylpropanoate (ETMP) was synthesized using a procedure

adapted from Stenzel et al.32 Potassium hydroxide (0.05 mol) was stirred in ethanol (20

mL) at room temperature until it completely dissolved. Then carbon disulfide (10 mL)

was added over 90 minutes, and the solution was allowed to stir for five hours. Ethyl

-bromoisobutyrate (14.8 mL) was added and the solution was stirred for 12 hours before

the mixture was filtered and the ethanol was removed by evaporation. The resulting

yellow liquid was diluted with diethyl ether and twice passed through a chromatography

column packed with basic aluminum oxide. The diethyl ether was evaporated and 1H

NMR was used to verify the structure of the product. The 1H NMR spectra were collected

on a Varian VXR-300 spectrometer using CDCl3 as solvent at room temperature. 1H NMR

(300 MHz, CDCl3): 1.27 (t, 3H, CH3CH2), 1.39 (t, 3H, CH3CH2), 1.61 (s, 6H, CCH3),

4.17 (m, 2H, CH3CH2), 4.59 (m, 2H, CH3CH2).

6

Table 1: Molecular characteristics of the 19 copolymers considered in the Article. Threediblock copolymers were evaluated to quantify the -parameters of the H/M/O system. 16terpolymers were produced to illustrate the utility of the segment distribution to manipulatethe morphology: each terpolymer represents one of four distinct chemical compositionsand one four segment distribution functions.

Sample Architecture fH fO fM Mn, kDa PDI Morphology q?, nm1 (d, nm)

HO H O 0.5 0.5 10.1 1.09

HM H M 0.5 0.5 20.5 1.23

MO M O 0.5 0.5 19.3 1.14

HOM-1 H OM (a) 0.68 0.16 0.16 17.0 1.09 L 0.271 (23.2)

HOM-2 H O M (b) 0.54 0.30 0.16 23.7 1.53 H 0.292 (21.5)

HOM-3 H O M (c) 0.34 0.50 0.16 16.6 1.22 Q230 0.257 (24.4)

HOM-4 H O M (d) 0.15 0.69 0.16 11.3 1.16 DIS 0.471 (13.3)

HMO-1 H OM (a) 0.68 0.16 0.16 22.0 1.47 H 0.263 (23.9)HMO-2 H OM (b) 0.54 0.30 0.16 20.9 1.20 Q230 0.261 (24.1)HMO-3 H OM (c) 0.34 0.50 0.16 17.1 1.22 H 0.270 (23.3)HMO-4 H OM (d) 0.15 0.69 0.16 11.1 1.22 DIS 0.463 (13.6)

HMO-1 H MO (a) 0.68 0.16 0.16 14.5 1.15 H 0.261 (24.1)

HMO-2 H M O (b) 0.54 0.30 0.16 13.7 1.14 H 0.256 (24.5)

HMO-3 H M O (c) 0.34 0.50 0.16 15.4 1.16 Q230 0.240 (26.2)

HMO-4 HM O (d) 0.15 0.69 0.16 11.3 1.17 H 0.345 (18.2)

HMO-1 OHM (a) 0.68 0.16 0.16 15.4 1.10 H 0.220 (28.6)HMO-2 OHM (b) 0.54 0.30 0.16 14.6 1.12 H 0.217 (29.0)HMO-3 OHM (c) 0.34 0.50 0.16 12.7 1.20 Q230 0.204 (30.8)HMO-4 OHM (d) 0.15 0.69 0.16 10.8 1.24 H 0.319 (19.7)

Terpolymer Polymerizations

Diblock and triblock terpolymers of hydroxyethyl acrylate (H), methyl acrylate (M), and

octyl acrylate (O), were prepared by RAFT polymerization with sequential monomer

addition using ETMP as the CTA. The molecular characteristics of the nineteen polymers

synthesized are tabulated in Table 1. Preliminary kinetic studies of these polymerizations

showed that H must be polymerized first, either as a homopolymer block or as a copolymer

block with M; reaction times for complete conversion for each monomer were: 75 min

for H, 90 min for M, and 120 min for O. Kinetic data of monomer conversion (ln[M][M]0)

7

20 40 60 80

3

2

1

0

M

H

O

kH = .063min1

kO = .021min1

kM = .033min1

t, h

ln[M

] /[M] 0

Figure 3: Homopolymer conversion versus time for O (filled squares), H (filled triangles),and M (open circles) polymerization.

versus time (min) for the homopolymerization of each monomer are shown in Fig. 3. Least

squares regression of the conversion data to a 1st-order kinetic model yields apparent rate

constants for each monomer: kH=0.063 min-1, kM=0.033 min-1, and kO=0.021 min-1.

The synthesis of an exemplar triblock terpolymer polymerization of HMO-2, is as

follows. H (5.44 mL, 5.50 g, 46 mmol) and the chain transfer agent ETMP (0.21 g, 0.84 mmol)

were dissolved in 20 mL of dioxane in a round-bottom flask with a magnetic stir bar. The

initiator 2,2-azobisisobutyronitrile (AIBN, 0.013 g, 0.084 mmol) was added at a 1:10 molar

ratio relative to ETMP. The round-bottom flask was sealed with a rubber septum, and

the solution was purged with argon for 10 minutes at 25 C prior to heating to 65 C.

The polymerization was allowed to proceed for 2.5 h, then an aliquot was removed for

subsequent measurements of conversion and molecular weight. This monomer:CTA ratio

was chosen to produce an H block with 54 H repeat units and an Mn,H=6.5 kDa at 98%

conversion. M (1.53 mL, 1.45 g, 17 mmol) was purged with argon, and introduced to the

round-bottom flask via syringe pump. This monomer:CTA ratio was chosen to produce

an M block with 20 M repeat units and an Mn,HM = 8.2 kDa at 98% conversion. After

three hours a small aliquot was removed, and argon-purged O (3.13 mL, 2.74 g, 15 mmol)

was fed to the round-bottom flask via syringe pump slowly, at a rate of 0.021 mL/min,

8

to prevent phase separation of the H. The O was allowed to react for two hours after the

feeding was complete. This monomer:CTA ratio was chosen to produce an O block with

17 O repeat units and an Mn,HMO = 11.3 kDa at 98% conversion. Complete monomer

conversion for each block was verified gravimetrically, and polymer molecular weight

was determined by size exclusion chromatography (SEC). Copolymerized blocks were

synthesized by initially adding M to the reaction vessel, and then slowly adding H or O.

Size Exclusion Chromatography

Polymer molecular weight and polydispersity were determined by size exclusion chro-

matography (SEC). The instrumentation consisted of a Waters In-Line Degasser AF, a

Waters 515 HPLC Pump, a Waters 717Plus auto-sampler, a DAWN HELEOS II MALLS

detector, and an Optilab T-rEX RI detector set at 658 nm wavelength. Samples were made

by dissolving 1015 mg of polymer in 1 mL of HPLC-grade tetrahydrofuran (THF), and

then filtering the solutions using low protein binding Durapore 0.22 m filters. Samples

were passed through four PLgel 5 m, 7.5 mm ID SEC columns purchased from Varian

Inc., in the following order: 50 mm guard column, 300 mm 100 A column, 300 mm 500 A

column, and 300 mm 10,000 A column. THF was used as the eluent at a flow rate of

1 mL/minute. Data were collected and analyzed using Astra 5.3.4 software by Wyatt

Technology. The derivative of refractive index with respect to composition was approxi-

mated as dn/dc = 0.082 mL/g for all polymers; this value was reported for a polymer of

poly(methyl methacrylate/butyl methacrylate) (60/40 mole) at 63 kDa and was chosen for

the purpose of determining polydispersity.33 Representative SEC traces for composition 3

appear in Fig. 4.

9

16 18 20 22 24

HMHMO

OHM

Elution Volume (Time), mL (min)

HHMHMO

H M O

MOHMO

H OM

HO

HHOM

H O M

RISignal,a.u.

Figure 4: SEC chromatographs for composition 3 of each architecture.

Small Angle X-ray Scattering (SAXS)

Diamond Light Source. Standard differential scanning calorimeter (DSC) aluminum

pans and lids (part numbers 900786.901 and 900779.901 respectively) were purchased from

TA Instruments of New Castle, DE. Muscovite mica of V-1 quality, in 50 mm by 75 mm

sheets that were 0.15 0.21 mm thick (part number 71855-01) were purchased from Electron

Microscope Sciences of Hatfield, PA. Centered, 3 mm holes were punched into the DSC

pans and lids and 5 mm discs were punched out of the mica sheets. A small amount of the

material of interest was sandwiched between two mica discs. The mica-sample-mica was

then put into a DSC pan and lid. The DSC pan and lid were sealed using a TA Instruments

Tzero pan press.

Samples were then examined (under contract) by Dr. Claire Pizzey of the Diamond

Light Source, Ltd., in Didcot, Oxfordshire, OX11 0DE, United Kingdom, at beamline I22.

SAXS data for the samples were collected at ambient temperature using 12.4 keV xrays and

a Pilatus 2M area detector. The momentum transfer (q) calibration was performed using a

silver behenate standard, which was also used to determine the beam center position. 120

frames of one second exposure each were acquired per sample, to allow for subsequent

10

data evaluation to assess radiation damage. Data reduction was performed in a standard

manner using software developed at Diamond.

Advanced Photon Source. SAXS experiments were conducted at beamline 12-BM-B

at the Advanced Photon Source, Argonne National Laboratory. Tzero differential scan-

ning calorimeter (DSC) low-mass pans and hermetic lids (part numbers 901670.901 and

901684.901 respectively) were purchased from TA Instruments of New Castle, DE. A small

amount of the material of interest was put into a DSC pan and lid and sealed using a TA

Instruments Tzero pan press. SAXS data for the samples were collected at various temper-

atures ranging from ambient to 250 C on beamline 12-BM-B at the Advanced Photon

Source using 11.0 keV x-rays and a MarCCD165 (Rayonix, LLC) detector over a q range

of 0.007 to 0.44 A1. A Linkam THMS600 heating and freezing stage (Linkam Scientific

Instruments Ltd.) was used to control sample temperature. The momentum transfer

(q) calibration was performed using a silver behenate standard, which was also used to

determine the beam center position. Data were acquired with single, continuous exposures

with exposure times ranging from 5 seconds to 20 seconds. Data reduction was performed

in a standard manner using Fit2D software developed by Dr. Andy Hammersley.34

All data were normalized to the transmitted beam intensity. Data were plotted in excel.

The primary scattering and reflection scattering peaks were identified using software

developed by Dr. Eric Cochran.

Rheology

Flory-Huggins interaction parameters () for HO, HM, and MO diblock polymers were de-

termined rheologically (Table 2). A TA instruments ARES-LS1 strain controlled rheometer

with a convection oven was used under nitrogen gas flow to prevent polymer degradation.

The HM polymer was pressed into 25 mm diameter discs with 1 mm thickness with a

Carver press at 80 C prior to being tested. The HO and MO polymers were measured

11

Table 2: Summary of diblock copolymers used for a first approximation of Flory-Hugginsinteraction parameters () between each monomer pair (H-O, H-M, and O-M), where isestimated at room temperature (293 K) using Equation 1 and degrees of polymerization(N) is determined is a reference volume of 149 A3 per molecule.

Polymer Mn, kDa N TODT, K ij @ 293 K

H O 10.1 116 401 0.13H M 20.5 230 392 0.06M O 19.3 232 449 0.07

without pressing due to their low glass transition temperature. The polymer samples were

subjected to a 10 C per minute temperature ramp at a constant strain of 3% and with

a frequency of 3.14 radians per second. A plot of the dynamic elastic modulus (G(Pa))

versus temperature ( C) was produced and is shown in Fig. 5. This plot was then used to

estimate the onset temperature of the order to disorder transition (TODT), and interaction

parameters were estimated at 20 C using Equation Eq. (1), and a methyl acrylate reference

volume of 149 A3.

293 K = 10.5TODT

N(293 K)(1)

Master curves for the investigated terpolymers were produced on the same Rheometrics

ARES LS1 strain controlled rheometer. The terpolymers were measured under air, with

isothermal frequency sweeps ranging from 0.1 to 100 radians per second using a maximal

strain amplitude of max=12. Frequency sweeps were taken every 20 C from 35 C to

175 C, and shifted according to the time-temperature superposition principle to construct

mast curves; all master curves use a reference temperature of Tre f = 55 C.

12

40 60 80 100 120 140 160 180

1.5

2

2.5

3

3.5

4

HO

MO

HM

128 C

120 C

178 C

Temperature, C

logG

/Pa

Figure 5: Isochronal temperature sweep of the dynamic modulus at = 1 rad s1 foreach diblock copolymer. ODT onset temperatures were used for the approximation of .

Results

Interaction Parameters for the H/M/O System. Order-disorder transition (ODT) char-

acterization of the diblock copolymer HO, HM, and MO were assessed with isochronal

temperature scans of the dynamic shear modulus as shown in Fig. 5. The ODT temperature

TODT can be identified as the temperature at which the slope of the dynamic modulus

drastically decreases. The identified TODTs are listed in Table 2, and were used in the

calculation of for H/O, H/M, and M/O. As the polymers are symmetric (ie all block

volume fractions equal 0.5), the accepted N for estimating at the ODT is 10.5.35 From

these experiments, we see the interaction between H and M is very similar in magnitude

as the interaction between O and M. Additionally, the interaction between H and O

is approximately twice as large as the interaction between M and either monomer, i.e.

HO 2HM 2MO. The calculated interaction parameters are presented in Table 2.

Synthetic Details. The four terpolymer architectures (a)(d) were synthesized at four

compositions (1)(4) as enumerated in Table 1 and illustrated in Fig. 2. All 16 terpolymers

were designed such that the total molecular volume was 11, 800 mL/mol, thus keeping

13

N the same for all polymers. The diblock architectures, HMO and HMO, have compositions

that span a wide range of block volume fractions. The block development and polymer

growth was followed by gravimetric conversion and SEC; representative SEC results for

the four architectures at composition (3) are shown in Fig. 4. The molecular weight (Mn)

data as determined by SEC indicate the polymers possess Mn ranging from 11 kDa to

24 kDa. The main reason for variations in the molecular weight is incomplete activation

of the RAFT chain transfer agent; as a lower percentage of the RAFT agent is activated

the molecular weight is expected to increase proportionally. This proportional increase is

expected for each monomer block, therefore the polymers with high molecular weights

still possess the volume fraction compositions reflected in Table 1. The effectiveness

of the RAFT system used to produce the terpolymer architectures is illustrated in the

realization of low polydispersity indices (PDIs, tabulated in Table 1). With the exception

of outliers HOM-2 and HMO-1, PDIs fall within the range [1.09, 1.24], as expected in

xanthate-mediated RAFT polymerizations.32

Kinetics for the homopolymerization of each monomer were studied to ensure that

statistical copolymers could easily be produced. As the data in Fig. 3 indicate, the monomer

consumption rate is consistent with the pseudo-first order expression d[M]/dt = kapp[M].Apparent rate constants for homopolymerizations are shown as the slope of ln [M]/[M]0

versus time in Fig. 3. From this we see that kH=0.063 min1, kM=0.033 min1, and

kO=0.021 min1. The rate constants are on the same order of magnitude, indicating

that statistical copolymers can be produced from batch copolymerization.

Structural Characterization. The self-assembly of the polymers was characterized

with small-angle x-ray scattering (SAXS) and rheology. Table 1 displays the microstructures

observed in the four architectures across the four compositions. A large number of

hexagonally packed column (H) structures were observed across the compositions, with 9

of the 16 materials indicating this structure. Fig. 6 outlines all sixteen SAXS traces; each

14

OHM

34H MO

3 4 H OM

H OM

q

34

logIn

tens

ity,

a.u.

q

OHM

H M O

H OM

H O M

9

49

34

3 4

6

8

2022

24263032 72

3

0.2 0.4 0.6 0.8 1

OHM

6

8

72

H M O

3 4H OM

6 H O M

68

20222426

3032

2022

2426

30

32

8

2022242630

32

q, nm1

logIn

tens

ity,a.u.

0.2 0.4 0.6 0.8 1

q

4

7OHM

4

7

HM O

H O M

H OM

q, nm1

Figure 6: SAXS for all materials at room temperature. The azimuthally integrated scatter-ing intensities for each of the four polymers of a specific composition are shown in eachwindow: upper-left (1), upper-right (2), bottom-left (3), and bottom-right (4). Primary scat-tering peaks and reflections are indicated with black arrows and numbers that correspondto q/q ratios. Locations of q and domain spacings (d) are reported in Table 1.

panel shows each of the four architectures at a single composition. Peak reflections are

indicated with a black arrow and number indicating the q/q location of the peak.

SAXS for composition (1) is in the top left panel of Fig. 6. PolymersHMO-1, HMO-1, andHMO-1 all have scattering reflections q/q = 1,

3 and

4. Polymer HOM-1 shows only a

primary peak with no higher-order reflections. At composition (2), in the top right panel

of Fig. 6, the spectra of HOM-2, HMO-2, and HMO-2 all contain clearly distinguishable

peaks at q/q = 1,

3,

4. Additionally, HOM-2 and HMO-2 show scattering at q/q =

9.

HMO-2 displays a scattering pattern similar in character to those that we observe in many

15

of the composition (3) materials, for which scattering data are summarized in the lower-left

panel of Fig. 6. HMO-2, HOM-3, HMO-3, and HMO-3 all feature broad primary peaks

with shoulders, indicative of two adjacent overlapping peaks. Higher-order reflections

are also evident, although distinct Bragg peaks are unresolvable as significant overlap

causes them to appear as one broad peak spread over a 0.2 nm1 region of q-space.In these areas we have indicated where the Bragg reflections associated with an Ia3d

space group symmetry should appear with the black arrows and the associated q/q ratios.

Scattering for HMO-3 indicates q/q = 1,

3,

4. Composition (4) SAXS data appear in the

lower-right panel of Fig. 6. HOM-4 and HMO-4 scatter with broad low-intensity primary

peaks at higher q 0.5 nm1 with no higher-order scattering. HMO-4 and HMO-4 showq/q = 1,

4,

7.

Master curves assembled with dynamic shear rheology for all terpolymers are presented

in Fig. 7. Each panel presents all four architectures at one composition, with composition

(1) in the top left, composition (2) in the top right, composition (3) in the bottom left, and

composition (4) in the bottom right. The classical Rouse-like response for a homogeneous

polymeric liquid is given by the scaling relationship G 2 in the low frequency regime; it

has been long recognized that in block copolymers, composition fluctuations in disordered

melts and the structure of ordered melts give rise to a morphology-dependent scaling

exponent a such that G a.36 In Fig. 7, tangent lines have been added to the graphs to

help visualize the slope a of log G with respect to logaT in the low frequency (terminal

response) regime. Half of the materials indicate a terminal response with a slope of a =

13. In composition (1), HMO-1, HMO-1, and HMO-1 (at low temperature) have a slope of

a = 1/3, while for HOM-1 a = 1/2. At T = 115 C, time-temperature superposition of

HOM-1 begins to fail (gray-shaded circles in Fig. 7), with the liquid-like terminal response

of a = 2 evident at T = 125 C (filled circles, Fig. 7). In composition (2), HOM-2, HMO-2,

and HMO-2 present a slope of a =13. The elastic modulus of HMO-2 appears to approach

a plateau as the frequency is decreased, with a 1/3, although the low torque signal

16

12

132

13

7

1

2

3

4

5

logG

/Pa

H OM

H OMH MO

OHM

5

13

13

4

H O M

H OMH M O

OHM

6 4 2 0 2 40

1

2

3

4

5

log aT

logG

/Pa

H O M

H OM

H M O

OHM

5

2

2

6 4 2 0 2 4

log aT

H O M

H OMHM O

OHM

Figure 7: Master curve data for all materials investigated, reported as elastic modulus(Pa) versus freqency (aT) at a reference temperature of Tref= 55 C. Each window has allfour polymers of a specific composition: upper-left (1), upper-right (2), bottom-left (3), andbottom-right (4). The slopes of the terminal responses for selected materials are indicatedwith tangents.

precluded efforts to sample the lowest frequencies at elevated temperature, corresponding

to logaT < 4.5. The master curves for composition (3) polymers give terminal regimeresponses with slopes approaching zero. The independence of modulus with respect to

frequency is a solid like response and is especially pronounced in the curve for HOM-3. In

composition (4), architectures HOM-4 and HMO-4 show a = 2 throughout the temperature

range, while HMO-4 and HMO-4 exhibit a solid-like response at low temperature through

T = 135 C, at which point time-temperature superposition fails, and the slope of the

terminal response steepens and approaches a = 2.

17

(1) (2) (3) (4)

(a)

H OM H O M H O M H O M

Disordered

(b)

H OM H OM H OM H OM

Disordered

(c)

H MO H M O H M O HM O

(d)

OHM OHM OHM OHM

Figure 8: Montage that illustrates the phase behavior of the H/O/M system as a functionof composition and segment distribution.

Discussion

Combining the SAXS and rheological data allows us to make morphological assignments

to the self-assemblies observed in these materials as summarized in Fig. 8. The locations

of the peak reflections with respect to the primary peak q, informs us of symmetry and

possible morphology.37 Similarly, the slope a of log G in the terminal response of a material

indicates the degree of interconnections between domains and possible morphology and

can be used to supplement SAXS data in the determination of the morphology. Work by

Kossuth et al. put forth an association between the slope of log G with respect to aT at

low frequencies.36 Specifically, the slope in the terminal regieme for a disordered phase is

a = 2; a = 1/2 for L phase ; for H, a = 1/3; and for the highly interconnected Q230 phase

(and other three dimensional structures), the slope approaches the solid-like response,

18

a 0.In the studied materials, commonly observed SAXS reflections q/q = 1,

3,

4 corre-

spond to columns on a hexagonally packed lattice (H); the presence of these reflections

were used to assign morphology. Additionally, q/q =

9, observed in HOM-2, HMO-2,

and HMO-2, and q/q =

7, observed in HMO-4 and HMO-4 are associated with H. Rheol-

ogy was used to support the morphology assignment and of the 9 materials identified with

H morphology (Table 1), 7 materials showed a slope of a = 1/3 in the terminal response.

In HMO-3 the slope was slightly less than 13, which may have been caused by the onset

of crosslinking due to extended exposure to T > 150 C temperatures. HOM-1, HOM-4,

and HMO-4 gave no indication of higher order reflection peaks in SAXS. The broad, low

intensity peak of HOM-4 and HMO-4 is characteristic of the correlation-hole scattering

observed in disordered block copolymer melts, and slopes for HOM-4 and HMO-4 in the

terminal response is the liquid-like a = 2, indicating that these materials are disordered.

The q peak in the SAXS of HOM-1 is sharp enough to indicate microphase separation; the

rheological data indicate that a = 1/2 in terminal response. These observations strongly

support that HOM-1 is ordered, and tentatively suggest that the L phase is the structure.

Four materialsHMO-2, HOM-3, HMO-3, and HMO-3appear to form the cubic Q230

(double gyroid) phase. In SAXS experiments, these materials presented a broad primary

peak with a shoulder that indexes well to q/q =

6,

8, corresponding to Miller indicies

of 211/220. The secondary peak is consistently broad, spanning the region occupied by

q/q =

20 (024),

22 (224),

24 (233),

26 (134),

30 (125),

32 (044). The melt rheology

of these materials shows a solid-like response in the low-frequency regime, which in block

copolymer melts is consistent with a three-dimensional structure such as Q230.

In the asymmetric composition (1), with a low composition of O ( fO = 0.16) the mor-

phology appears to be L, a structure not associated with diblocks containing a monomer

block with a large majority ( fH = 0.68). Given that d for HOM-1 is comparable to the other

architectures, suggesting the degree of chain extension is similar between HOM and HMO

19

or HMO, we propose there are distinct H, O, and M domains, and the L stacking goes

H-O-M-M-O-H. Increasing O to fO = 0.30 at composition (2) gives H, we propose this is a

core-shell structure with discrete domains of M as columns surrounded by O, in a matrix

of H. This structure would minimize the O and M contacts and the chain conformation

constraints on O and H. Increasing the O content in composition (3) to fO = 0.50 gives

Q230. Finally, increasing fO to 0.69 in composition (4) produces a disordered phase, where

all conformational constraints are minimized.

In architecture HMO at low composition (1) of O, the triblock self-assembles as H.

Again, comparing the d with that of the diblocks, the chain extension is similar, suggesting

there are discrete H, M, O domains, thus it is proposed this is another core-shell H, with

O making columns, surrounded by M, in a matrix of H. In composition (2), HMO is also

H, again proposed to be a core-shell H. The H structure at low compositions of O, allows

the architecture HMO to minimize the O contacts and the conformation constraints on H.

Upon increasing fO = 0.50 (composition (3)), a cubic Q230 is observed. This is similar phase

behavior observed in HOM-3, where a core-shell gyroid structure of H is surrounded

by M, in a matrix of O. This, again minimizes O contacts while balancing the need to

minimize the conformation constraints for both O and H. At high composition (4) of O an

inverse H structure is observed, here the O makes the matrix. A drop in d suggest chain

extension has decreased, indicating the H and M domains are intermixing, so we propose

the columns consist of a mix of H and M. The intermixing of H and M helps to minimize

the conformational constraints, while the H structure helps to minimize the O contacts

and the conformation constraints on O.

Turning to the diblock architectures, we expect a correlation with the diblock universal

phase diagram, where the domain volume fraction can be estimated as fHM fH + fMand fOM fO + fM. Considering architecture HMO, at low O composition, the O/Mdomain fraction is fixed to fOM = 0.32. Here an H structure is observed where the O/M

block make columns in a matrix of H. This phase behavior minimizes the confirmation

20

constraints on the majority H block and is consistent with what would be expected in

traditional diblock polymers.2 In composition (2), with fOM = 0.46, the morphology

shifts to Q230. In the asymmetric HMO-3 ( fOM=0.66) the progression to an O-matrix H is

observed. A disordered state is produced when fOM = 0.85 in HMO-4. The phase behavior

of architecture HMO is consistent with what would be expected from diblock polymers in

the weak segregation regime across the compositions studied here. To better understand

how the phase behavior of this architecture could be predicted, current efforts are focused

on capturing the observed phenomena computationally.

The first two compositions (1, 2) in architecture HMO produce H with columns of O

in a matrix of H/M. The fHM in these compositions are 0.84 and 0.70 respectively. That

HMO self-assembles as H at fHM=0.84, suggest the H envelope is quite large, possibly

asymmetric. Further increasing the composition of O, HMO-3 assembles as the cubic Q230,

similar to the two triblock architectures. Here minimizing both the conformation constrains

for the H/M domain and the O domain produces a traditional double gyroid structure.

The block fractions are symmetric with fHM=0.50, this behavior suggests the material falls

in the weak segregation regime and the phase diagram may be asymmetric compared

to the universal diblock phase diagram. In composition 4, fHM=0.31 and the material

presents an inverse H structure, with columns of H/M in a matrix of O; this behavior is

similar to that observed in material HMO-3 and would be expected in traditional diblock

polymers. Further understanding of the possible asymmetry in the phase diagram and the

breadth of the H envelope is being sought computationally.

Fig. 9 presents a unified view of these results by mapping the terpolymers onto a

transformed phase coordinate system described by a single effective volume fraction,

f and interaction strength effN. Such a mapping is possible in architectures where

the self-assembly is dominated by a single interface. This is clearly the case for diblock

terpolymers HMO and HMO, where phase separation occurs only between the pure block

and the copolymerized block. For HMO, f = fH and for HMO, f = fH + fM. The

21

0 0.2 0.4 0.6 0.8 1

10.5

15

30

Q 230

H-matrixH

L?

O-matrixH

HMO

HOM

HOM

HMO

DIS

12

3

4

1

2

3

4

1

23

4

1

2

3

4

f

eN

Figure 9: Phase diagram of the HOM, HMO, HMO, and HMO architectures as describedby the f /effN phase coordinates which map the terpolymers to a diblock copolymerequivalent point in phase space. Symbols are enumerated according to their chemicalcomposition (Table 1) and connected by a curve to tie together polymers of the samearchitecture. While the appropriate definition of f is straightforward for diblock terpolymers(solid symbols, solid lines), it may be elusive for triblock copolymers (transparent symbols,dotted lines). The shaded envelope represents the self-consistent mean-field theoreticbinodal line for diblock copolymers.

effective interaction parameter can be estimated by Eq. (2), which results from equating

the disordered state free energy of the diblock equivalent system, Fdis/kBT = f (1 f )eff,equal to that of the real system, Fdis/kBT = fH fMHM + fH fOHO + fO fMOM.

eff =fH fMHM + fH fOHO + fO fMOM

f (1 f ) (2)

The phase diagram, Fig. 9, produced for our diblock terpolymers using this parameter-

ization shows good qualitative agreement between the expectations of classical diblock

copolymers in the intermediate segregation regime2 and what is observed. A broad region

of H-matrix columns is seen over a span of f from 0.68 (HMO-1) to 0.84 (HMO-1). In H

deficient polymers, a region of O-matrix columns contains HMO-3 ( f =0.34); this column

phase presumably persist to the ODT as the very weakly segregated HMO-4 ( f =0.31)

is included. The disordered HMO-4 illustrates that these systems have ODT boundaries

22

qualitatively similar to traditional diblocks. We find that Q230 forms in two symmetric

compositions, HMO-2 ( f =0.54) and HMO-3 ( f = 0.50), rather than the lamellar phase,

which indicates a strong asymmetry in the phase diagram.

Parameterization of the triblock architectures to approximate diblock architectures

proves more difficult. Considering first HOM, it stands to reason that the relatively strong

H/O interface should dominate the phase separation in this sequence, at least given

that the M concentration is small in the materials considered in the present Article. This

suggests that the mapping f = fH provide behavior consistent when compared with the

diblock terpolymer mappings as plotted in Fig. 9. Evidently this consistency exists, with the

exception of HOM-1, which appears to be a lamellar material. Whether the inconsistency

of HOM-1 with the diblock terpolymers is due to the proximity of the composition to the

lamellar window (which we did not observe elsewhere in the investigated compositions)

or a mis-assignment due to an absence of more conclusive scattering data is unclear. HMO,

on the other hand, features two energetically balanced interfaces. This distinction suggests

that only for trivial concentrations of one of the components should this sequence be

mappable in any sense to a diblock-equivalent parameter space. However, in the HMO

materials considered herein, the phase behavior of HMO mirrors that of HMO, suggesting

possible potential for a simplification of the HMO phase space to a diblock system with

f = fH + fM. However, there is no a priori rationale for this mapping and the similarities

in the HMO/HMO materials is coincidental, in the sense that the underlying energetic

aspects leading to these morphologies are substantially different. A larger sampling of

the stable morphologies with changing composition will fill in the extent to which this

observation is coincidental; work in forthcoming papers explores the phase space of these

triblock terpolymers at additional compositions to help further develop any diblock

system simplifications.

23

Conclusion

This work explores the phase behavior of hydroxyethyl acrylate (H), octyl acrylate (O),

and methyl acrylate (M) terpolymers in four different architectures. ODT temperatures

of the symmetric diblock copolymers between the monomers were measured and used

to estimate three binary interaction parameters, yielding HO 2MO 2HM. Diblockterpolymer architectures HMO and HMO, and triblock architectures, HOM and HMO,

were synthesized with RAFT at four different compositions and the phase behavior of the

16 materials was characterized with synchrotron SAXS and dynamic shear rheology.

The diblock terpolymer architectures in every case produced different morphologies

at identical chemical composition. The partial phase diagram assembled by mapping

these terpolymers to a diblock-equivalent parameter space had the familiar topology of

classical diblock copolymers, with a strong asymmetric skew to H-lean compositions. Ar-

guments based on the energetic contribution of the two interfaces in the triblock copolymer

sequence HOM suggested a similar mapping, that is, essentially neglecting the contribu-

tion of the O/M interface. This approximation proved to be consistent for all but HOM-1.

The HMO sequence, however, has no meaningful diblock-equivalent mapping although

its phase behavior is nearly identical to that of the diblock copolymer sequence HMO.

Collectively, these results illustrate the utility of the segment distribution in the selection

of morphology in block copolymer formulation, and present a simple unifying framework

to aid the process of rational design.

Acknowledgement

JMH and JAB are grateful for support from the Department of Energy, Office of Basic

Energy Sciences, Early Career Research Program (DE-SC0003927). EWC acknowledges

financial support from NSF-DMR-0847515. Use of the Advanced Photon Source, an Office

of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science

24

by Argonne National Laboratory, was supported by the U.S. DOE under Contract No.

DE-AC02-06CH11357.

Supporting Information Available

Full characterization data for all new compounds. This material is available free of charge

via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry

Table of Contents Figure

28