Single-Molecule Single Crystals of lsotadic Polystyrene
HAISHAN BU,' ERQIANG CHEN,' SHENGYONG XU,* KEXIN GUO,' and BERNHARD WUNDERLICH3
' Department of Materials Science,
Fudan University, Shanghai, 200433, People's Republic of China; 'Beijing
Laboratory of Electron Microscopy, Academia Sinica, Beijing 100080, People's Republic of China; 3Department of
Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600 and Chemistry Division,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6197
SYNOPSIS
Single-moleculesingle crystals were grown from amorphous droplets of fractionated isotactic
polystyrene. The crystals were analyzed by electron microscopy and electron diffraction.
The molecular mass distribution could be matched with a statistical analysis of singlemolecule particles (amorphous and crystals). Proof was brought that single molecules of
isotactic polystyrene do not reach equilibrium dimensions on crystallization, rather assume
the lamellar morphology with chain-folded macroconformation, also known from crystallization of polymolecular crystals. 0 1994 John Wiley & Sons, Inc.'
Keywords: polystyrene single molecule crystal molecular mass distribution
INTRODUCTION
In a first article we showed that it is possible to grow
single-molecule single crystals from flexible linear
macromolecules.' Poly ( oxyethylene ) was the first
such polymer analyzed. The method involved separation of the molecules in the surface of a Langmuir
balance, followed by crystallization. Analysis of the
large body of information about crystalline macromolecules suggested some time ago that it is of importance to study the fate of a single molecule in a
single crystal.' The best way of doing this, is to analyze single-molecule single crystals and, ultimately,
connect the properties of these to poly-molecule
single crystals.
We are presenting new research on isotactic
polystyrene of known molecular mass, and can show
that amorphous droplets of single molecules can
crystallize, but do not reach equilibrium dimensions
at the crystallization temperature. The main tools
for this research are electron microscopy, electron
diffraction, molecular mass fractionation, and statistical size analysis of the observed particles. Scanning tunneling microscopy (STM) was carried out
on the same samples and was reported earlier.3 It
suggested, next to the morphology, also seen by the
electron microscopy, that the fold surface is regular,
with fold sectors being arranged parallel to (110).
EXPERIMENTAL
Materials
Isotactic polystyrene (i-ps) was purchased from
Scientific Polymer Products, Inc., its isotacticity was
above 90% and the molecular mass was estimated
by the manufacturer to be 4 X lo5by gel permeation
chromatography (GPC ) .
Reagent-grade benzene was used with normal
safety precaution after distillation. Similar quality
o-dimethylphthalate and cyclohexanol were not
further purified. Reagent-grade tetrahydrofuran was
also distilled after it was dried with NaOH. Water
was deionized and the glass apparatus was cleaned
with concentrated K2Mn207/HzS04solution and
thoroughly rinsed with the deionized water.
Fractionation
* This article is a US Government work and, as such, is in the
public domain in the United States of America. US Government
contract No.DE-AC05-840R-21400.
Journal of Polymer Science: Part B Polymer Physics, Vol. 32,1351-1357 (1994)
CCC 0887-6266/94/081351-07
0 1994 John Wiley & Sons, Inc.
The fractionation was carried out using a semipreparative Rigaku LC-3A gel permeation chromatograph. The i-ps was added into a mixed solvent of
1351
1362
BU ET AL.
o-dimethylphthalate and cyclohexanol ( 1: 1by volume), the mixture was slowly heated to 423.2 K
within 0.5 h under a nitrogen atmosphere and held
at this temperature for 3 h, then heated to 453.2 K
and refluxed for 1.5 h, eventually a clear solution
was obtained. The solution was cooled to 333.2 K
and added to a proper amount of tetrahydrofuran,
then heated and refluxed for 0.25 h to make a solution of about 0.1 wt %, used in the fractionation
with a solution injection volume of 0.5 mL. The
eluent solvent was tetrahydrofuran, and the flowrate was 1.0 mL/min a t a total pressure of 2 MPa.
The initial i-ps has a wide molecular-mass distribution. Five fractions of the given molecular mass
distribution were collected between the onset and
the end of the elution peak. The procedure was repeated, in order to collect a sufficient amount of ips in each fraction. Molecular mass and molecular
mass distributions of starting material and fractions
were examined using the same instrumentation. The
results are displayed in Table I.
Preparation of Single Molecules
Two fractions (F-3and F-4) were chosen as samples
for this study. The tetrahydrofuran was removed
from the fractions until a concentration of 0.1 wt %
was reached, benzene was then added to the fractions
to achieve a concentration of 1 X
wt %. The
dilute solution was used to prepare single molecules
Table I. Fractionation by Semipreparative GPC and
Results of Amorphous Single Molecule Particle
Analysis
M, x 10-~
Fractions
GPC of initial
sample
GPC of F-1
GPC of F-2
GPC of F-3
Particle Analysis
of F-3
GPC of F-4
Particle Analysis
of F-4
GPC of F-5
GPC of F-6
(daltons)
dw
Vi
Vt
22.9
437.2
265.0
133.7
6.17
1.08
1.13
1.25
28.2
28.0
28.2
29.2
43.5
31.5
33.6
35.8
127
76.4
1.55
1.19
30.4
36.3
67
38.8
14.6
1.59
1.17
1.29
31.8
33.4
36.5
39.3
M,,: Number-average molecular mass, dw: polydispersity.
Vi:Elution volume corresponding to the onset of the GPC
curve, in cm3.
V,:Elution volume corresponding to the end of the GPC curve,
in cm3.
using a Langmuir film balance. Before use, the solution was heated to 333.2 K for 20 min to dissolve
any crystals that might form when the solution is
kept for a long time.
The solution was then spread on a water surface.
After the benzene had evaporated, isolated singlemolecule particles formed. Next, the surface was
compressed properly to concentrate the particles,
but avoiding aggregation. The particles were then
transferred to copper grids for electron microscopy.
The copper grids were covered with collodion film,
reinforced with evaporated carbon. A detailed description of preparation of these particles of single
molecules was given in the previous paper.' The
"biospread method" was also attempted to prepare
single molecules. A needle was inserted into the water at an angle of 45", then a drop of the dilute solution was placed on the needle, it slipped down the
needle and spread quickly on the water surface. The
needle was gently moved right and left, to enable
the single molecules to separate uniformly. The particles were transferred to copper grids by touching
the grids to the water surface.
The coated copper grids were put in a thermostat
under a nitrogen atmosphere to crystallize the i-ps
molecules at 448.2 k 0.1 K.2
Observation by Electron Microscopy and Electron
Diffraction
The copper grids were observed either with a Hitachi
H-500H transmission electron microscope (TEM) ,
Philips EM-420 TEM, or Opton EM-902 TEM, and
images of the particles were recorded. The operation
voltage was 100 kV. The size of the particles was
digitized with a computer using a scanner for electron micrographs. The cross-sections of the particles
could be obtained by image analysis, based on the
principle of mathematical morphology and were
converted to particle diameters.
Copper grids with particles were shadowed with
heavy metal ( P t / P d , 40/60) at an angle of about
12'. The shadow-length of particles was recorded
and measured to estimate the thickness of the particles.
Selected-area electron diffraction was carried out
with the Philips EM-420 for the larger crystals which
may contain several tens of molecules and for simultaneous analysis of large numbers of singlemolecule crystals. Microbeam electron diffraction
was performed on isolated single-molecule crystals.
For the latter, the electron beam was concentrated
to a spot with a diameter of 30-40 nm, to cover no
more than a single-molecule crystal. Reflections of
SINGLE MOLECULE CRYSTALS OF POLYSTYRENE
copper were used as internal calibration standard.
By evaporating copper onto the i-ps particles, the
reflections of copper would be obtained together with
the i-ps reflections.
1353
zu
.
.
I
Number of
Particles
100
RESULTS AND DISCUSSION
Amorphous Single Molecules of i-ps
50
It was reported that the concentration, C*, of the
approximate molecular mass used in this research
a t which the molecules begin to overlap for atactic
polystyrene (a-ps) in benzene is about 1 X 10-1
wt %.4 In solution, i-ps molecules will have a similar
conformation to a-ps molecules, thus the C* of i-ps
in benzene should be the same order of magnitude.
A 1X
wt % solution of i-ps in benzene was,
thus, used to prepare the single molecules in our
experiment to stay well below C*. Figure 1shows a
collection of amorphous single molecules of fraction
F-3 prepared on the Langmuir film balance. Most
of the particles have an irregular, close to spherical
shape. Some particles are much bigger and some
particles are so far from a circular cross-section that
they may be considered to be an aggregate of several
molecules.
By means of the image-analysis system, the particle-diameter distribution was calculated, measuring about 1500 particles. The accuracy of the results,
shown in Figure 2, is about +5%. The particle diameter distribution was transformed to a cumulative
weight fraction distribution based on the empirical
equation:
10
'0
50
20
30
40
Diameter (nm)
Figure 2. Particle diameter distribution of 600 molecules of i-ps as in Fig. 1.
D
0.133M0.38
=
(1)
where M is the molecular mass and D is the particle
diameter. The result is shown in Figure 3 for the
fraction F-3. The number-average molecular mass
and polydispersity index dw were also estimated and
are listed in Table I. It can be seen that the results
measured by TEM are in reasonable agreement with
those obtained by gel permeation chromatography.
Furthermore, the highest molecular mass in fraction
F-3, corresponding to the onset of the GPC peak
(estimated to be 4.8 X lo6) should lead to the formation of a (hemispherical) particle with a diameter
of 46 nm. Particles with a diameter larger than 46
nm can, thus, not be considered to be single molecules and were omitted in the image analysis. The
largest particles considered in the image analysis
had a diameter of 43.2 nm. For fraction F-4, the
highest molecular mass was 2.7 X lo6,corresponding
1.0
" " I , ,
..
. =
, ,
, , I . ,
I .
,
. I - ,
,
-. ,
, , I . .
.
0.8 0
:
I(M)
0.6 -
0.4 0.2~
0.0
200
nm
Figure 1. Amorphous single molecules of i-ps. (Fraction
F-3).
"
I '
' '
' "
'
' ' I
' ' ' '
I
'
'
.
'
"
'
' '
I
'
' '
Figure 3. Molecular mass distribution of fraction F-3.
Open squares from particle distribution; filled squares from
the GPC.
1354
BU ET AL.
to a particle diameter of 37 nm and the largest particle diameter considered in the image analysis was
35.5 nm.
Single-Molecule Single Crystals of i-ps
The amorphous single molecules of fraction F-3 were
crystallized to produce single-molecule single crystals. Figure 4 shows the single-molecule single crystals crystallized at 448.2 f 0.1 K for 3 h. Clearly,
most of the particles have now polygonal shapes instead of being irregular spheres. The particles become more transparent to the electrons, indicating
a thinner structure offering less mass for the electron
beam. The uniformity of the contrast suggests a lamellar morphology. When the samples were crystallized for longer times, the regularity in crystal
shape increased. These facts, together with the electron diffraction results, described below, indicate
that the particles are crystals, even single crystals.
Furthermore, the crystalline c-axis prefers to orient
in a direction normal to the substrate.
Assuming the molecules form a small equilibrium
crystal, their dimensions can be calculated, assuming
minimum surface free energy is reached (Wulff construction, see ref. 2, Sec. 3.1 and 7.1.2):
where y e is the ( 001 ) surface free energy, reported
to be 31 m J / ~ m ' ;y,
~ the side-surface free energy,
usually assumed to be about of ye; and V is the
total crystal volume. Using the weight average mo-
p
100 nm
Figure 4. Single-moleculesingle crystals of i-ps fraction
F-3 crystallized at 448.2 K for 3 h. The magnification bar
indicates 100 nm.
lecular masses by GPC of Table I and the x-ray density of crystalline polystyrene (1.13 mg/m3),' one
can compute L, for fractions F-3 and F-4 to be 36.6
and 30.4 nm, respectively. The corresponding lateral
dimensions (assumed to give a quadratic cross-section) are 7.9 and 6.4 nm, respectively.
The thickness of the single-molecule single crystals was measured between 10 and 20 nm with an
average of 14 nm, far below the equilibrium value.
Even single-molecule droplets of polystyrene can
thus not reach equilibrium on crystallization, but
form metastable lamellae with a much reduced fold
length. Instead of a rod-like morphology, the crystals
are lamellar. Assuming classical theory of crystallization can be applied to the crystallization of a
single molecule, the free enthalpy of formation of a
primary homogeneous nucleus is (ref. 2, Sec. 5.1.1):
AG
=
+
4LANo.5y 2NA2y, - NA2LAg
(3)
where Ag represents the bulk free enthalpy of fusion;
L is the dimension of the nucleus in the chain direction; N is the number of (folded) chain segments
(stems) in the nucleus with a cross-section A2; y
and y e represent lateral and end surface free energies, respectively. The critical nucleus dimensions
are calculated by differentiation of AG with respect
to L and N and setting the derivatives equal to zero
and substituting Ag by AhATIT,,,:
L*
=
4yeT,/(AhAT)
N*
=
~ ~ Y ~ T ; / ( A ~ A T A ) ~( 5 )
(4)
where T , is the equilibrium melting temperature;
Ah, the heat of fusion per cm3; and AT, the supercooling.
With the values of y e = 31 mJ/m2,5 T,,, = 516.2
K, and Ah = 108.5 MJ/m3,6 L* can be calculated
to be 8.7 nm a t the crystallization temperature of
448.2 K. On the basis of fluctuation theory, the
thickness of the crystal grown from the nucleus
should be somewhat larger than L*, and an increase
is also possible from annealing a t the crystallization
temperature. Taking account of the errors in the
measurement of shadow-length, L* is closer to the
measured values of 14 nm than the equilibrium
length L,. The larger experimental thickness, as well
as a wider distribution than assumed by the classical
theory is most likely an indication of annealing subsequent to growth. The molecular mass of the critical
nucleus, M * can be estimated from:
M*
=
N*L*Mo/Lo
(6)
SINGLE MOLECULE CRYSTALS OF POLYSTYRENE
Figure 5. Particle diameter distribution of 600 molecules of i-ps as in Fig. 4.
where M , is the molecular mass of a repeating unit
(104 Da) and Lo is the length of a repeating unit
along the crystalline c -axis, (0.22 nm) .7 Assuming,
again, y = ~ ~ / M*
5 , can be estimated to be 2.3
X lo4.For fraction F-3, the lowest molecular mass,
corresponding to the tail end of GPC curve, is 2.2
X lo5,much larger than M*, and thus one single
molecule with the lowest molecular mass should be
able to crystallize by homogenous nucleation, followed by growth. The zero-entropy-production
melting temperature of the ultimately formed crystal
can be estimated to be 495 K, thus, the crystals are
metastable a t the crystallization temperature (see
ref. 2, Chap. 9 ) .
The particle diameter distribution was obtained
by image analysis from Figure 4, and is shown in
Figure 5 and was transformed to the molecular-mass
distribution shown in Figure 6, assuming the thickness of the crystals is 14 nm and their density is
1355
1.11 mg / m3. The number-average molecular mass
can also be obtained to be 1.5 X lo6 with a polydispersity index of 1.35, in reasonable agreement with
the results from GPC (see Table I, sample F-3).
Most of the analyzed particles must thus have been
of single molecule size. The better agreement with
GPC than in Figure 3 is attributed to the more regular shape of the crystals when compared to the assumed to be hemispherical amorphous particles.
The largest molecular mass, corresponding to the
onset of GPC curve, is 4.8 X lo6 for fraction F-3.
This molecule would form a particle with a diameter
of about 28 nm, thus a particle larger than that cannot be considered to be a single molecule. The largest
particles considered in the image analysis was
25.4 nm.
Morphology
An i-ps crystal grown from dilute solution has usually regular, hexagonal appearance. The morphology
of the single-molecule single crystals grown in this
research were, however, sometimes of quite different
morphology. When single-molecule single crystals
were grown at 448.2 K for a short time (e.g. 3 h )
polygonal crystals, as shown in Figure 4, resulted.
Even close to circular shapes were seen. Single-molecule single crystals grown at the same temperature,
but for a longer time (e.g. 8 h ) showed much more
regular-shaped crystals, as shown in Figure 7. By
close observation, typical morphologies as displayed
in Figure 8 could be seen. The left row in Figure 8
collects crystals which are close to the conventional
1.o
.
0.4
t
.
m
O
5
8O
0.0
' '
'
'
'
'
'
I
' ' ' '
I '
'
'
'
I
.
' '
'
I '
' ' '
' ' '
50 nm
Figure 6. Molecular mass distribution of fraction F-3.
Open squares, from particle distribution; filled squares,
from the GPC curve ( dw is the polydispersity).
Figure 7. Regular-shapedsingle-molecule single crystals of i-ps crystallized at 448.2 K for 8 h. The magnification bar indicates 100 nm.
1356
BU ET AL.
ylene can be seen when the crystals float in solution,
or are deposited on glycerol. Otherwise flat lamellae
are observed due to the collapse of crystals on a substrate. The here presented tent-like single-molecule
single crystals are so small, that they can avoid the
collapse. It may be assumed that the tent-like singlemolecule single crystals of i-ps have the same origin
as the polyethylene crystals grown from solution.
Crystal Structure
20
nm
Figure 8. Typical morphology of single-moleculesingle
crystals of i-ps. The magnificationbar indicates 20 nm.
hexagonal shape, the others contain modifications.
The morphology of all crystals has the common feature of the characteristic angle of 120". It is interesting to note that the single-moleculesingle crystals
did not nucleate heterogeneously on the carbon film
surface, but rather homogeneously. Only in the latter
case could they lie flat on the substrate, as observed.
Surface nucleation of polymers on substrates like
salts and graphite are well known.' In most of these
cases the crystals nucleate heterogeneously and grow
with the molecular chains in the plane of the substrate (i.e. the lamellae grow end-on). Only after
reaching much larger size than the here grown crystals do they sometimes topple and lie flat on the
substrate.
Tent-like crystals can also be recognized, revealing distinct sectors and sector boundaries, as shown
in Figure 8. As is well known, the tent-like morphology and sectorization of polyethylene crystals
grown from solution indicate the different ordering
of the fold structure within each sector of the specific
crystal growth face.' Tent-like crystals of polyeth-
It was reported by Natta et al. that i-ps crystal has
a trigonal unit cell with lattice dimensions of a = b
= 2.19 nm, c = 0.665 nm,7 and the hkO electron
diffraction from an i-ps single crystal has hexagonal
~yrnmetry.~
Figure 9 shows a typical hexagonal selected-area electron diffraction pattern from a large
i-ps crystal which may contain several tens of molecules with lamellar morphology, and the c-axis
normal to the substrate and parallel to the incident
electron beam.
Microbeam electron diffraction patterns from
single-molecule single crystals are shown in Figure
10. Usually the c -axis of these single-moleculesingle
crystals are not exactly a t right angles to the substrate, and since the microbeam electron diffraction
is rather sensitive to the orientation of the crystal,
the electron diffraction patterns do not have full
hexagonal symmetry, as shown in Figure 10a. Furthermore, because of the large beam current used,
reflections disappeared after 60-90 s of irradiation,
so it is not easy to obtain complete diffraction patterns, as shown in Figure 10b and c. The latter two
figures show however that the single-molecule crystals are single crystals and, furthermore, that they
are of trigonal crystal structure.
Figure 9. Selected-area electron diffraction pattern
from a large i-ps single crystal (multimolecule).
SINGLE MOLECULE CRYSTALS OF POLYSTYRENE
(a)
1357
(c)
(b)
Figure 10. Micro-beam electron diffraction patterns from one single-molecule single
crystals. ( a ) Misaligned crystal. ( b ) Crystal with the c-axis parallel to the electron beam
direction. (c) Crystal with the c-axis normal to the electron beam direction (the rings in
b and c are due to reflections of copper, used as an internal calibration standard).
The experimental work described was supported by the
National Science Foundation of China and the Chinese
National Basic Research Project-Macromolecular Condensed State. The U S . contribution was funded by the
Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and
the Division of Materials Sciences, Office of Basic Energy
Sciences, U S . Department of Energy, under Contract DEAC05-840R21400 with Martin Marietta Energy Systems, Inc.
REFERENCES AND NOTES
H.S.Bu, Y. W. Pang, D. D. Song, T. Y. Yu, T. M.
Voll, G. Czornyj, and B. Wunderlich, J . Polym. Sci.,
Polym. Phys. Ed., 29, 139 (1992).
2. B. Wunderlich, Macromolecular Physics, Vols 1-3,
Academic Press, New York, 1973, 1976, 1980.
3. H.S.Bu, E. Chen, J. Yao, S. Xu, and Y. Kuang, Polym.
Eng. Sci., 32,1209 (1992).
1.
4. J. Kumaki, Macromolecules, 19,2258 ( 1986).
5. N. Overbergh, H. Berghmans, and H . Reynaers, J.
Polym. Sci., Polym. Phys. Ed., 14,1177 (1976).
6. ATHAS Data Bank, see for example, Thermal Annlysis. Academic Press, Boston, 1990; or request most
recent copy from B. Wunderlich, Department of
Chemistry, University of Tennessee, Knoxville, T N
37996-1600.
7. G. Natta and P. Corrandini, Macromol. Chem., 16,
77 (1955).
8. D. C. Bassett, Principles of Polymer Morphology,
Cambridge University Press, Cambridge, 1981.
9. Masaki Tsuji, Saroj K. Roy, and R. St. John Manley,
Polymer, 25, 1573 (1984); J . Polym. Sci., Polym.
Phys., Ed., 23, 1127 (1985).
Received March 15, 1993
Revised June 25, 1993
Accepted June 29, 1993