Order-disorder transition and alignment dynamics of a block copolymer under high magnetic fields by in situ x-ray scattering

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by  Manesh Gopinadhan

Order-disorder transition and alignment dynamics of a block copolymer under high
magnetic fields by in situ x-ray scattering
Manesh Gopinadhan,∗ Pawel(cid:32) W. Majewski,† and Chinedum O. Osuji‡
Department of Chemical and Environmental Engineering, Yale University, New Haven CT 06511
(Dated: July 9, 2012)
Wepresentresultsoftemperatureresolvedscatteringstudiesofaliquidcrystallineblockcopoly-
mer undergoing an order-disorder transition (ODT) in the presence of magnetic fields and time-
resolved measurements during isothermal field annealing at sub-ODT temperatures. In each case,
fieldinteractionsproducedstronglytexturedmesophaseswiththecylindricalmicrodomainsaligned
parallel to the field. We find there is no measurable field-induced shift in the ODT temperature
(T ) which suggests that selective melting does not play a role in mesophase alignment during
ODT
2 isothermal experiments. Our data indicate instead that sub-ODT alignment occurs by slow, large
1 scale grain rotation whereas alignment during cooling from the disordered melt is rapid and driven
0 by the nucleation of weakly ordered but preferentially aligned material. We identify an optimum
2 sub-cooling that maximizes alignment during isothermal field annealing. This is corroborated by
a simple model incorporating the competing effects of an exponentially decreasing mobility and
l
u divergent,increasingmagneticanisotropyoncoolingbelowT . Theabsenceofmeasurablefield-
ODT
J effectsonT isconsistentwithroughestimatesderivedfromtherelativemagnitudesofthefree
ODT

6 energy due to field interaction and the enthalpy of the isotropic-LC transition.

] PACSnumbers: 83.80.Uv,61.30.Vx,64.75.Yz
t
f
o
s Self-assembly on mesoscopic length scales in soft mat- netic nanoparticle inclusions can also provide an elegant
.
t ter gives rise to a fascinating variety of microstructures. means for advancing field directed self-assembly of ly-
a
m Blockcopolymers(BCPs)areparticularlyintriguingdue otropic mesophases as recently demonstrated [14]. De-
tothewiderangeofmorphologiesandfunctionalitiesthat liberateincorporationofliquidcrystallinityinBCPscan
-
d are accessible by appropriate control of chemical compo- therefore be used as a convenient handle to control mi-
n sition, chain architecture and molecular weight. Their crostructureinthesesystemsbymagneticfields. Despite
o utilization in various applications is often predicated on this potential, studies of field driven phase behavior and
c
the ability to control the orientation of their microstruc- alignment dynamics in BCPs have been limited. This
[
ture. External inputs such as shear flow, electric fields is in part due to the need for superconducting magnets

1
and magnetic fields provide utility in this regard, as well and the experimental difficulty associated with conduct-
v
reviewed [1]. Due to the absence of dielectric break- ing studies in the presence of high fields.
6
2 down concerns and their space pervasive nature, mag- In this Letter we report on a series of in situ scatter-
6 netic fields are particularly well suited for this purpose. ing studies of an LC BCP under magnetic fields using
1 They effectively permit arbitrary control over grain tex- a custom designed x-ray instrument coupled to a high
.
7 ture in appropriately field-responsive materials, even in field magnet. Temperature resolved measurements show
0 complex geometries [2]. no discernible field effects on the order-disorder transi-
2
Microstructure alignment by magnetic fields is driven tion(ODT)ofthesystem. Timeresolvedexperimentson
1
: by anisotropy in the system’s magnetic susceptibility, pre-aligned materials show that alignment at sub-ODT
v ∆χ, that gives rise to an orientation dependent field in- temperatures occurs via grain rotation with slow kinet-
i
X teraction energy. Suitably large interactions can domi- ics. The response of the system is critically limited by
r natethermalforcesorotherexternalinputsontimescales the mesophase viscosity such that alignment can only be
a dictatedbytheviscosityofthematerial. Typicalcoil-coil advanced by residence in a small temperature window
BCPs such as poly(styrene-b-methyl methacrylate) sup- near TODT. This residence produces a weakly aligned
port vanishingly small anisotropies with ∆χ O(10−9) in system which thereafter transitions to a strongly aligned
dimensionless volume SI units. This is due to the short stateoncooling,evenintheabsenceofthefield. Wepro-
persistence length or random coil nature of the chains vide simple models which correctly capture the absence
and the similarity of the susceptibilities of the compo- ofmeasurablefield-effectsontheODTandtheexistence
nent species. The presence of rigid anisotropic moi- of an optimum sub-cooling for the maximization of ori-
etiessuchasaromaticmesogensinliquidcrystalline(LC) entation order parameters in isothermal experiments.
mesophases[3–8]andextendedchainsinsemi-crystalline The polymer studied is poly(ethylene oxide-b-
polymers [9, 10] as well as surfactants [11–13] gives rise methacrylate), PEO-PMA/LC in which the methacry-
to ∆χ O(10−6) which is sufficient to drive alignment at late block is side functionalized using a cyanobiphenyl
readily accessible field strengths of a few tesla. Mag- mesogen (Polymersource Inc.), Fig. 1a. The num-
2
FIG.1. a: ChemicalstructureofLCBCP.b: Schematicshow-
ing homogeneous anchoring of mesogens at IMDS. Mesogens
andPEOcylindersalignparalleltothefieldasshownbyasso-
ciated2DSAXSandWAXS(inset). c: Temperatureresolved
SAXS at zero-field. The blue trace marks T
ODT
ber average molecular weight M is 10.4 kg/mol with
n
PEO weight fraction f =0.23 and polydispersity in-
PEO
dex ≈ 1.1. The system forms hexagonally packed cylin-
ders of PEO in the PMA/LC matrix, with a d-spacing,
d =9.6 nm . Samples were prepared by solvent cast-
CYL
ingfrom5wt.%dimethylformamidesolutionstoprovide FIG. 2. Inverse peak intensity as a function of 1/T for BCP
onheating(a)andcooling(b),andforsmecticLCscattering
3 mm diameter discs of 1-2mm thickness. Small angle
on cooling (c). d: T and T as a function of B2.
x-ray scattering (SAXS) measurements were conducted ODT SmA−N
using a custom SAXS bench (Rigaku) integrated with a
6 T cryogen-free magnet (American Magnetics Inc.). the experimental uncertainty of roughly ±0.5 ◦C associ-
Thepolymerphasebehavioristypicalofweaklysegre- atedwiththeexperimentalapparatus. Inallcasesexcept
gated LC BCPs. DSC (not shown) and zero-field SAXS the zero-field measurement, the samples displayed align-
measurements, Fig. 1c, show that the ODT at ≈ 72 ◦C ment of the hexagonally packed cylinders parallel to the
is effectively coincident with the nematic-isotropic tran- field direction. There was pronounced narrowing of the
sition around 69 ◦C. The BCP microphase separation azimuthal intensity distribution (not shown) of the pri-
is driven by the change in block interaction that occurs mary scattering peak for field strengths above 2 T, with
on formation of the nematic mesophase, as observed in a saturation of the peak width (FWHM) of roughly 7-8
analogous LC BCPs [15]. A second transition from ne- and 4-5 degrees for the microdomain and smectic layer
matictosmecticAoccursnear63◦C.Thecyanobiphenyl reflections at q=0.7 and 1.8 nm−1 respectively.
mesogens exhibit a homogeneous anchoring condition at The role of the field on the isotropic-nematic transi-
the inter-material dividing surface (IMDS) between the tion T and thus the ODT can be considered through
NI
PEO and PMA blocks. This implies that the orienta- construction of a Clausius-Clapeyron relation incorpo-
tion of the cylindrical microdomains will be parallel to rating the field interaction energy at constant pressure
that of the mesogens themselves pand the periodicity of [16]. Thenormalizedchangeintransitiontemperatureis
the smectic layers, d =3.5 nm, is orthogonal to that given by Eq. 1 where the susceptibility of the nematic
LC
of the cylindrical microdomains as in Fig. 1b. Fig. 2 state can be closely related to that of the isotropic state
showsplotsoftheinverseintensityofthescatteringpeaks and the molecular anisotropy as χ = χ +(2/3)∆χ ,
N I m
from the smectic layers and cylindrical microdomains as thefieldinteractionenergydifferenceis(χ −χ )B2/2µ
N I 0
functions of inverse temperature. Samples were initially and∆H istheenthalpyassociatedwiththetransition.
NI
heated to ≈ 85 ◦C, well above T and then cooled
ODT
at 0.1 ◦C/min to room temperature under different field
∆χ B2
strengths, stopping every 1 ◦C for 600 s for data col- ∆T/T = m (1)
NI 3µ ∆H
lection. The data were fitted using a standard logistic 0 NI
function to determine T and T , Fig. 2d. The For the present system, using representative values of
ODT N−SmA
results show clearly that there is no discernible influence ∆H =1 J/g (from DSC), ∆χ =10−6 and density ρ=1
NI m
of the field on the phase transition temperatures beyond g/cm3, a field strength of 6 T would impose a very small
3
shift of ∆T ≈ 4 mK, which is far below the resolution of c
(i)
the measurements. Such mK-scale shifts are consistent
with prior work on electric [17] and magnetic field stud-
ies[16]onsmallmoleculeLCs. Intriguingly, Segalmanet (ii) 50oC
al. observed a large 30 K shift in the ODT of a weakly
segregatedrod-coilblockcopolymerunderapplicationof
a7Tfield[18]. Itislikelythatthesmallentropychanges (iii)
associated with ODTs in rod-like systems results in this
exceptionally large field effect by comparison with the
present side-chain LC BCP and small molecule systems
basedonanalogouscyanobiphenylmesogens. Conversely
Samulski et al. examined a system based on a bent-core
FIG. 3. a: Azimuthal intensity at selected times (hrs).
mesogen with non-trivial transition enthalpies but iden- b: Peak intensities at φ=90◦ and 180◦ and exponential fits
tified a large 4 K shift in TNI and TSmC−N at 1 T. This (lines). c: 2D SAXS and grain reorientation schematics at
was attributed to the presence of partially ordered clus- t=0 (25 ◦C), t=250 (50 ◦C) and t=900 min (25 ◦C).
ters which couple to the field in this novel class of cyb-
otactic materials [19]. Pronounced field-induced changes
intransitiontemperaturescangiverisetoselectivemelt- ing the experiment. This supports the finding from the
ing whereby domains which are not in the energy mini- temperature-resolved study that selective melting is not
mizing orientation are destabilized, and thus shrink, or relevant as such melting would have resulted in a tran-
“melt”, and are gradually replaced by aligned material sient overall intensity reduction. We thus conclude that
that grows from the disordered melt [20–23]. This acts alignment proceeds by grain rotation as shown schemat-
as an effective mechanism for mesophase alignment. In ically in Fig. 3c.
the present case, given the imperceptible field effects, we Exponential fits of the time traces reveal characteris-
can conclude that while selective melting may occur, it tic times of roughly 400 and 200 minutes for the equato-
does so only over a mK-scale window which cannot be rial rise and meridional decrease of scattering intensity.
easily leveraged in practice as a viable means of struc- Consistent with this, at short times there is an initially
ture control. Correspondingly, this mechanism has little faster loss of intensity from the 90◦ peak than the cor-
consequence in the current experiments. responding gain of intensity at the 180◦ direction. Cor-
The alignment kinetics were probed using isothermal respondingly, at long times, the 180◦ peak continues to
field annealing to monitor microstructure re-orientation gain in intensity while loss at 90◦ has plateaued. These
at sub-ODT temperatures. A sample was initially well data clearly indicate that there is an intermediate state
alignedbyslowlycoolingtoroomtemperatureacrossthe via which the system transitions from horizontal to ver-
ODTat0.1◦C/minatthehighestfieldstrength,6T.The tically aligned cylinders. This is confirmed by the 2D
field was ramped to 0 T and the sample was physically diffractograms in which 4-fold symmetric chevron like
rotated by 90 degrees around the axis defined by the x- patterns are clearly observed, as shown in inset (ii). To
ray beam (x-axis, Fig. 1b) such that in lab-space, the collectthisdata,thesamplewascooledto50◦Cafter250
cylindrical microdomains now lay perpendicular to the minutes at 67 ◦C. This results in increased segregation
field direction, i.e. long axes along the y-axis. The field strength between the blocks and an improvement in the
was ramped up to 6 T and the system quickly heated to abilitytoresolveindividualscatteringpeakswhichcould
67 ◦C, just below T . Time resolved measurements be smeared out at higher temperature. Such a display
ODT
followed the reorientation of the cylinders from the ini- of 4-fold symmetric scattering is not unexpected. It is
tial horizontal alignment to the final preferred vertical consistentwithwhatisobservedexperimentally[24]and
alignment, parallel to the field and z-axis. The scatter- insimulation[25]duringthereorientationoflamellarmi-
ing intensity from the hexagonally packed cylinders thus crodomanis under tensile deformation and is clearly the
progressivelyshiftedfromconcentrationalongthemerid- result of the n=2 degeneracy with which the system can
ionallineorz-axis(φ=90◦ and270◦ azimuthally)tocon- rotate to re-align with the field - i.e. microdomains can
centration along the equatorial line or y-axis (φ=180◦ rotate to the right or the the left, with equal probabil-
and360◦ azimuthally)andvice versa forthesmecticlay- ity. This appears to be the first observation, however, of
ers. The intensity variation of the cylinder microdomain the expected 4-fold symmetric chevron-like state from in
scattering as a function of φ and time are shown in Fig. situ experiments in field alignment of block copolymers.
3,with2DSAXSdiffractogramsatpertinenttimepoints. Prior work by B¨oker et al. [22, 26] observed an apparent
Comparison of the initial and final time points (Fig. 3b) isotropic intermediate state during electric field induced
indicates that the combined peak intensity is conserved. re-alignment, but it is entirely possible that this was the
Likewise, the total scattered intensity integrated across result of peak broadening that blurred the identification
all azimuthal angles at q=0.7 nm −1 is invariant dur- ofthesefeaturesintheweaksegregationregimeinwhich
4
theexperimentwasconducted. Thefactthatthesystem a b
here needed to be cooled to 50 ◦C in order to unambigu-
ously observe the 4-fold intermediate state underscores
this point.
Thetimescaleforreorientationisunderstandablylarge
as rotational motion is severely hindered by the polymer
viscosity. In general, alignment of soft mesophases by
externalfieldsisadvancedonpassageacrosstheODTas
this is presumed to maximize the coupling of the field to
thesystem[1]. Thisiscertainlyobservedempirically,but
theunderlyingphysicsisasubtlecombinationofthermo-
dynamic and kinetic contributions. The system’s mobil-
c d
ity is high near T , but the thermodynamic driving
ODT
forceforalignmentislinkedtotherelevantorderparam-
eter, ∆χ in the present case, which increases from zero
onlyonpassage(cooling)throughtheODT.Wecancon-
struct a simple model describing the alignment kinetics
as a function of temperature. We represent ∆χ(T) for
the first order N-I transition in the conventional Haller
approach [27] as ∆χ(T) = ∆χ (1−T/T )m where
0 NI
∆χ is the limiting value of the order parameter, T
0 NI
is the nematic-isotropic transition temperature and m is
a fitting parameter capturing the steepness of the diver-
gence and assumes a value of 0.22 in the Maier-Saupe
mean-field approximation [28]. The characteristic time
FIG. 4. a,b: (cid:104)P (cid:105) dependence on annealing temperature
2
for alignment τ is given by the balance of viscosity η(T) at time t = 0.1τ ; m = 0.22, (2µ η /∆χ B2) = 1,
T˜=0.05 0 0 0
against the field interaction energy F(∆χ(T)). Using a ∆χ = 1, E/k T = 1.5. c: Azimuthal intensity variation
0 B NI
simple Arrhenius model, η = η0exp(E/kBT) where E forsamplesannealedatdifferenttemperatures. d: FWHMof
represents the energetic barrier to flow, and F ∼ ∆χ as azimuthal intensity. Line is a guide to the eye.
discussedpreviously. Thusweexpectτ asshowninEq.2
and that the orientational order parameter which cap-
tures the degree of alignment evolves exponentially ac- dominates in this system. The BCP has a very limited
cordingtothistimescaleas(cid:104)P (cid:105)∼1−exp(−t/τ)[26,29]. ability to respond to the field due to severe kinetic limi-
2
Any contributions from the influence of the field on the tations starting only 6-8 ◦C below T . This suggests
ODT
orderparameter∆χaresmallasdiscussedaboveandcan that the strong alignment observed in samples that were
be reasonably neglected. slowly cooled to 25 ◦C originates only due to the resi-
dence of the system within this small temperature range
(cid:18) (cid:19) and not due to the continuous action of the field down
2µ η exp(E/k T)
τ ∼ 0 0 B (2) to the final temperature. This is confirmed by samples
∆χ B2 (1−T/T )m
0 NI which were zero-field quenched at ≈ 10 ◦C/min after an
Itisclearthatforagivenannealingtime,therewillbe isothermal anneal for 1 hour at 5 T at 69 ◦C. As shown
an optimum temperature range over which (cid:104)P (cid:105) is max- in Fig. 5, the system is only weakly ordered and aligned
2
imized, as shown in Fig. 4a,b in terms of normalized at69◦C,butcoolingtoroomtemperatureintheabsence
temperature T˜ = 1−(T/T ). This qualitative behav- of the field produces a sharply aligned system with simi-
NI
ior is remarkably well captured experimentally. Samples lar intensities and azimuthal FWHM as obtained during
were quenched from the disordered state to various tem- continuous cooling ramps of 0.1 ◦C/min (Fig. 1b). The
peratures below T and isothermally annealed at 6 T weak alignment produced during the isothermal anneal
ODT
for 1 hour. The azimuthal variation of scattered inten- isthussufficienttobiasortemplatethealignmentofthe
sityfromtheBCPmicrodomainsisshowninFig. 4cwith system as it undergoes additional ordering on cooling,
the temperature dependence of the FWHM of Gaussian even in the absence of the field. We speculate that the
fits (Fig. 4d) where smaller FWHM are correlated with intervening N −SmA transition may underpin this ori-
higher (cid:104)P (cid:105). FWHM is used here as an internally consis- entation refinement, but further studies are required to
2
tent measure of the degree of alignment in preference to properly address this interesting feature.
estimations of (cid:104)P (cid:105) from the scattering data due to the In summary, we have provided new results concerning
2
sensitivity of this calculation to background subtraction. the real-time response of LC BCPs under high magnetic
From Fig. 4d it is apparent that viscosity strongly fields. Our work shows that in these systems, there is no
5
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