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RESEARCH ARTICLE | NOVEMBER 15 1998
Coil–globule transition of poly(methyl methacrylate) by
intrinsic viscosity
Bahattin M. Baysal; Nilhan Kayaman
J. Chem. Phys. 109, 8701–8707 (1998)
https://doi.org/10.1063/1.477536
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17 O
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JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER 19 15 NOVEMBER 1998
17 O
ctober 2023 14:15:42meric chain is considered using both mean-field theories and
other new approaches over a wide range of temperature.5–7
The application of these theoretical equations to the expan-
sion and contraction of a polystyrene chain were given in a
previous article.8
Birshtein and Pryamitsin indicated that the evaluation of
the configurational entropy ~and entropy force! in earlier pa-
pers published on the coil–globule transition were based on
an expression inapplicable to the contraction of the chains
but valid for the case of chain expansion.9 For this reason
these authors carried out a rigorous approach to calculate the
elastic entropy or the corresponding entropy force connected
with chain deformation. For the contracted coil (t,0) they
derived an equation for the expansion factor a as
a32a2C~a2321 !5BN1/2t , ~1!
where N represents the number of Kuhn segments in the
chain, B and C are parameters that do not depend on both
ascribed to the metastable state of the test solutions.11–13
However, chain contractions reported for a polystyrene–
cyclohexane system was only about 75% of the unperturbed
theta state.11–14,8 This small decrease in size does not satisfy
the criteria of a densely packed collapsed globule.
Recently, Chu and co-workers reported a two-stage ki-
netics of single-chain collapse for polystyrene in cyclo-
hexane.15–17 In a study of the time dependence of the hydro-
dynamic radius (RH) of a single polystyrene chain in solu-
tion, the sample was quenched from 35 to 28.0 °C. The un-
perturbed RH value of a single polystyrene molecule is
reduced initially by 29% forming a crumpled globule. Sub-
sequently in a second stage it is further reduced to a compact
globule, indicating a total reduction of about 69% of its
original radius. A theoretical two-stage kinetics of a single-
chain collapse was proposed earlier.18,19 However, the possi-
bility of chain clustering during the second stage of collapse
was taken into consideration by Raos and Allegra.20 Normal-Coil–globule transition of polymethy
Bahattin M. Baysal and Nilhan Kayaman
Department of Chemistry, Marmara Research Center, P.O
and Bogˇazic¸i University, Department of Chemical Enginee
~Received 8 August 1997; accepted 14 August 1998!
The coil–globule transition for poly~methyl methacr
tert-butyl alcohol1water system. Two polymeric sa
3106 and M w54.733106 were used. The contractio
determined by viscometric measurements. The resu
obtained recently for the same system. A smooth and
the u temperature ~41.5 °C!. The temperature depen
curve in ah
3 utuM w
1/2 vs utuM w
1/2 plot, where ah
3 5@h(T
t5(T2u)/T is the reduced temperature. A compar
theory for contracted coil confirmed the coil–globule
Institute of Physics. @S0021-9606~98!52443-9#
I. INTRODUCTION
The transition from random-coil behavior in the theta
state to a globular compact form in the collapsed state of
macromolecular chains has been the subject of extensive
studies. This change in the state of a polymer chain from the
open coil to the globular particle is called the coil–globule
transition, and was first predicted by Stockmayer in 1960.1
Williams et al.2 summarized the contributions made by the
end of 1970s, and Fujita3 presented a review on this subject
at 1992.
Most of the coil-collapse experiments were carried out
for polystyrene solutions at extremely low concentrations.
Various experimental methods such as static and quasielastic
light scattering, small-angle neutron scattering, ultracentri-
fuge and viscosimetric measurements were used for the de-
termination of linear polymer dimensions.
The temperature dependence of the expansion factor a
can be obtained from the classical Flory equation given for
the excluded volume effect.4 The contraction of the poly-8700021-9606/98/109(19)/8701/7/$15.00methacrylate by intrinsic viscosity
ox 21, 41470 Gebze, Turkey
g, 80815 Bebek-Istanbul, Turkey
ate! has been studied in the mixed solvent
ples having molecular weights M w52.55
and expansion of the molecular chains were
were compared with light scattering data
ontinuous contraction was observed below
nce of @h# can be represented by a master
/@h(u)# is a viscosity expansion factor and
on of the observed globular radius with a
nsition for this system. © 1998 American
molecular weight M and temperature T but depend on chain
stiffness; t5(T2u)/u is the reduced temperature, and C is
caused by the third virial coefficient.9 Equation ~1! has a
critical point below which the coil–globule transition be-
comes discontinuous. The critical point appears at C
50.005 487 and BN1/2t520.4135. The value of a at the
critical point is 0.4714.
For chain expansion (t.0) the following Flory type
relation,
a52a35
2
p2
BN1/2t , ~2!
was obtained.9
Two sets of contradictory experimental data for contrac-
tion of polystyrene in cyclohexane were reported in earlier
works10—one giving a very sharp transition and the other
indicating a gradual contraction. Extensive static and dy-
namic light scattering studies carried out by Chu and co-
workers have indicated that the previously observed very
sharp coil–globule transitions in polystyrene solutions can be1 © 1998 American Institute of Physics
17 O
ctober 2023 14:15:42ized rms radii of gyration of a single chain and of the clusters
of several chains were calculated considering two- and three-
body interactions. It was found that the clusters of two to five
polystyrene chains have a smaller radius than a single chain.
Raos and Allegra20 concluded that the much smaller objects
observed in the second stage of collapse, reported as ‘‘com-
pact globules’’ by Chu and co-workers,19 under kinetic con-
ditions are actually macromolecular clusters resulting from
the aggregation of a small number of polymer chains. Con-
sequently the initial collapse stage ~about 25% contraction!
corresponds to the final equilibrium state for polystyrene in
cyclohexane.20
Considering contradictory experimental data and limited
contraction observed for the polystyrene–cyclohexane sys-
tem, we have studied the collapse behavior of poly ~o-
chlorostyrene! and poly ~p-chlorostyrene! under poor solvent
conditions.21 For these polymers we have not observed a
two-stage kinetics. Although a values for these chains ex-
ceed the contraction reported for polystyrene in cyclohexane,
they are still not satisfactory for a single globule formation.
Recently Nakata carried out detailed light scattering ex-
periments using a poly~methyl methacrylate! ~PMMA!
sample with an average molecular weight M w52.383106
and a molecular weight distribution M w /M n.1.20 in the
mixed solvent water1tert-butyl alcohol.22 Since the phase
separation occurred very slowly for this system, the mean
square radius of gyration ^s2& and the second virial coeffi-
cient A2 were determined reliably even far below the phase
separation temperature.
In this article, the coil–globule transition was studied for
poly ~methyl methacrylate! ~PMMA! in a theta solvent ~tert-
butyl alcohol1water! by viscosimetric measurements. The
results were compared with light scattering data obtained re-
cently for the same system by Nakata.22
II. EXPERIMENT
A. Polymers and solvents
Poly~methyl methacrylate! is purchased from Poly-
sciences Inc., Cat. No. 16217. M w52.33106. Two PMMA
samples were prepared by fractional precipitation at 25.0 °C.
1.0 g of PMMA is dissolved in toluene to produce 0.1 wt %
solution in a 5 L round-bottom flask. After dropwise metha-
nol addition, and stirring, the first fraction was precipitated,
equilibrium conditions were maintained overnight and sepa-
rated from the mother solution. This fraction was dissolved
in toluene, precipitated in methanol, and filtered and dried at
40 °C in a vacuum oven overnight. This first fraction ~0.310
g! is designated as PMMA-1. A portion ~0.150 g! of this
fraction is dissolved in toluene to produce 0.027 wt % solu-
tion and fractionated again with a similar procedure. A 0.040
g PMMA is obtained after this second-stage precipitation.
This fraction is called PMMA-2. The characterizations of
these samples are given in Table I.
The tert-butyl alcohol was purified by fractional distilla-
tion. The water was distilled by standard methods twice im-
8702 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998mediately before use. The present study on the coil–globule
transition was performed with a mixed solvent of tert-butylalcohol1water ~97.5% v/v tert-BuOH! by varying the tem-
perature.
B. Viscosity measurements
A precision capillary viscometer ~Cannon 75 M-710!
was used for the intrinsic viscosity measurements which has
a time resolution of 60.001 s. The viscometer was immersed
in a constant temperature bath controlled to 60.01 °C over a
temperature range 14–70 °C. The efflux times for ;1 ml
chloroform and tert-butyl alcohol1water mixture were 45.05
s ~20.0 °C! and 293.28 s ~41.5 °C!, respectively.
TABLE I. Specification of poly~methyl methacrylate! samples.
Sample @h#a (dL g21) M w (g mol21) M w /M n
PMMA-1 6.12 2.573106 1.35
PMMA-2 10.5 4.733106 1.29
Tacticity and long range tacticity determined from 1H NMR
Triadb Tacticity p~r! or p~m!c
PMMA2 rr 60.2 0.775
mr 33.9
mm 5.9 0.243
100
mrrd 0.55~peak area ratio!
rrr 1.00
aIn chloroform at 20.0 °C.
brr refers to the percent syndiotriads, mr to atactic triads, and mm to isotri-
ads.
cp~r! is the probability of adding a monomer to form a racemic diad, inde-
pendent to the configuration of the previously added monomer units, and
p~m! is the probability of adding a meso unit.
drrr refers to long range tacticity.
B. M. Baysal and N. KayamanFIG. 1. 1H NMR spectrum for poly~methyl methacrylate! in CDCL3.
17 O
ctober 2023 14:15:42C. 1H NMR spectroscopy
For tacticity determination, 1H NMR spectrum of
PMMA in CDCl3 was recorded on a Bruker AC 200 L in-
strument at 200.133 MHz proton frequency, with 3.3 ms
pulses and 0.1 s relaxation delay. It can be seen from Fig. 1
that the three peaks which appear at the highest field were
used to estimate triad tacticities. The bands at 0.85, 1.00, and
1.25 ppm represent the resonance of syndiotactic, atactic,
and isotactic methyl groups. The area under each of these
three peaks corresponds to the amount of each triad present
in the polymer chain. The data are calculated with this
method and included in Table I.23 The b-methylene proton of
PMMA resonances between 1.4 and 2.4 ppm. The major
intensity peak at 1.55 ppm was assigned to the rrr quartet of
the predominantly syndiotactic sample. The peak area ratios
which illustrate long-range syndiotacticity tendency were de-
termined as 1.0/0.55 for syndiotactic tetrads, rrr~1.55 ppm!
mrr~1.80 ppm!, and rmr~1.88 ppm!.24,25
TABLE II. Specific viscosities of poly~methyl methacrylate! ~M w52.55
3106 g/mol in tert-BuOH1water mixture!. C52.5531025 g/mL.
Temp
~°C! 103hsp
ah
3
(hsp /hspu )
a2
(ah3 5a2.43) t M w1/2 a3t M w1/2
70.00 15.257 1.199 1.161 fl fl
65.15 14.922 1.173 1.140 fl fl
59.90 15.382 1.209 1.169 fl fl
55.30 14.564 1.145 1.118 fl fl
50.00 14.290 1.123 1.100
45.10 13.587 1.068 1.055 fl fl
43.00 13.340 1.048 1.040 fl fl
42.05 13.054 1.026 1.021 fl fl
41.50 12.725 1.000 1.000 0 0
41.00 11.644 0.915 0.930 2.537 2.274
40.10 10.486 0.824 0.853 7.11 5.595
37.90 9.161 0.720 0.763 18.27 12.18
35.05 7.290 0.573 0.632 32.73 16.46
34.10 6.680 0.525 0.588 37.55 16.95
32.15 5.552 0.436 0.505 47.45 17.04
30.00 4.526 0.356 0.427 58.36 16.29
28.00 3.411 0.268 0.338 68.51 13.49
25.10 2.547 0.200 0.266 83.23 11.42
22.10 2.256 0.177 0.241 98.46 11.63
21.05 2.032 0.160 0.221 103.79 10.71
20.00 2.081 0.164 0.225 109.12 11.65
19.10 2.019 0.159 0.220 113.68 11.71
18.00 1.943 0.153 0.213 119.26 11.72
17.00 1.872 0.147 0.207 124.34 11.67
16.00 1.770 0.139 0.197 129.41 11.33
21.05a 1.931 0.152 0.212 103.74 10.12
20.00a 2.026 0.159 0.220 109.11 11.29
41.00b 12.385 0.973 0.978 2.54 2.45
40.10b 11.218 0.882 0.902 7.11 6.08
37.90b 9.263 0.728 0.770 18.27 12.34
36.00b 7.815 0.614 0.670 27.91 15.29
20.00b 2.021 0.159 0.220 109.11 11.25
18.00b 1.948 0.153 0.213 119.26 11.72
16.00b 1.849 0.145 0.205 129.41 12.27
a
J. Chem. Phys., Vol. 109, No. 19, 15 November 1998Shock cooling from 55 °C.
bRepeat experiments with a new solution.D. Procedure
The intrinsic viscosities were calculated using the fol-
lowing relation:
@h#5 lim
c!0
~hsp /c !, ~3!
where the specific viscosity hsp5(h2h0)/h0 , with h and
h0 being the polymer solution viscosity and solvent viscos-
ity, respectively, and c is the polymer concentration. At finite
concentrations, in the dilute solution regime
hsp /C5@h#~11kH@h#c !, ~4!
where kH is the Huggins interaction coefficient. In our case,
as (c52.5531025 g/mL) is very near infinite dilution ~i.e.,
kH@h#c!1!, @h#>hsp /c!.
III. RESULTS AND DISCUSSION
The experimental results of specific viscosities in tert-
butyl alcohol1water mixture for two poly~methyl methacry-
late! samples are reported in Tables II and III. Since the
viscosity measurements were carried out at very low concen-
trations (2.5531025 g/mL), we assumed that the measured
values of specific viscosities are identical to intrinsic viscosi-
ties. Nakata recently has found that the second virial coeffi-
cient, A2 , vanishes at 41.5 °C so that this temperature can be
taken as the u temperature for PMMA in a mixed solvent
system.22
It is well established that viscosity measurements per-
formed on solutions at the u conditions can yield information
on the dimension of polymeric chains with the aid of the
following relations:
TABLE III. Specific viscosities of PMMA (M w :4.733106 g/mol) in tert-
BuOH1water mixture!. C52.5431025 g/mL.
Temp
~°C! 103hsp
ah
3
(hsp /hspu )
a2
(ah3 5a2.43) t M w1/2 a3t M w1/2
70.00 17.967 1.332 1.266 fl fl
65.15 18.133 1.344 1.276 fl fl
59.90 17.811 1.320 1.257 fl fl
55.10 17.321 1.284 1.228 fl fl
50.00 16.793 1.244 1.198
45.10 15.819 1.173 1.140 fl fl
43.00 14.681 1.088 1.072 fl fl
42.00 14.163 1.050 1.041 fl fl
41.50 13.490 1.000 1.000 0 0
41.00 12.099 0.897 0.914 3.456 3.021
40.00 10.859 0.805 0.836 10.37 7.931
38.00 9.125 0.676 0.725 24.19 14.93
37.00 8.716 0.646 0.698 31.10 18.14
36.00 8.081 0.599 0.656 38.02 20.19
35.00 6.953 0.515 0.580 44.93 19.82
34.00 6.002 0.445 0.514 51.84 19.08
32.00 4.875 0.361 0.433 65.66 18.69
30.00 3.832 0.284 0.355 79.49 16.46
28.00 2.677 0.199 0.264 93.31 12.66
25.10 2.145 0.159 0.220 113.36 11.71
22.00 1.919 0.142 0.200 134.78 12.06
21.00 1.805 0.134 0.191 141.69 11.98
8703B. M. Baysal and N. Kayaman20.00 1.749 0.130 0.186 148.61 11.92
17 O
ctober 2023 14:15:42@h#5@h#uah
3
, ~5!
@h#u5KuM 1/2, ~6!
where @h# and @h#u represents the intrinsic viscosities in or-
dinary and u solvent, respectively, M is the molecular
weight, and Ku is a constant. However, since the hydrody-
namic radius of a polymer chain increases less rapidly than
the statistical radius as the excluded volume increases, the
expansion factors given in Eqs. ~1!, ~2!, and ~5! are not
identical.26 Several theoretical approaches exist in order to
find a relation in between these expansion factors. For prac-
tical purposes, in our calculations we have preferred to use
the following exponential type of relation:27
ah
3 5a2.43. ~7!
Figure 2 shows the temperature dependence of intrinsic
viscosities for these two PMMA samples in tert-butyl
alcohol1water solution at above and below the theta tem-
perature. The contraction of PMMA chains covers a wide
range of intervals. For PMMA-1 a gradual transition was
observed up to 16 °C. At lower temperatures it was not pos-
sible to obtain reproducible results. After performing viscos-
ity measurements at 16 °C, the solution was heated to 55 °C
and shock cooled to 21 °C. The same specific viscosity re-
sults were obtained for these runs at 21.05 and 20.00 °C. The
viscosity measurements were replicated using the same
PMMA-1 solution and the results were given in Table II. It
FIG. 2. Intrinsic viscosity @h# vs temperature for poly~methyl methacrylate!
in tert-butyl alcohol1water mixture. The intrinsic viscosities for: ~s! M w
54.733106; ~d! M w52.553106; ~h! M w52.553106 ‘‘shock cooling ex-
periments;’’ ~,! M w52.553106 ‘‘repeat experiments with a new solu-
tion.’’
8704 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998will be seen that viscosity data are reproducible within the
accuracy of experiments. These viscosity experiments elimi-nate the possibility of adsorption of polymer chains on the
glass wall, or the existence of any aggregation and precipi-
tation. The decrease of the viscosity is therefore related to
the shrinking of the polymer chains.
The ah
3 values of PMMA samples were calculated ac-
cording to Eq. ~5! and plotted against temperature in Fig. 3.
In order to use the observed behavior of ah in Eqs. ~1!
and ~2!, a2 values were calculated using Eq. ~7! and the data
were plotted in Fig. 4 against the temperature. Literature val-
ues of light scattering data22 were also included in Fig. 4. As
it will be seen in Fig. 4, the variations of expansion factor
with temperature based on our viscosity experiment are very
similar to Nakata’s observations.22 Since the contraction fac-
tor (a2) obtained from light scattering data did not show
evidence of aggregation in the collapsed state, we can as-
sume that our viscosity data are consistent with the previ-
ously published results.22 These observations, together with
the results of our shock cooling and repeat experiments
prove that there is not any evidence of aggregation in the
collapsed state.
To evaluate the parameters B and C given in Eq. ~1!,
(a32a)/(12a23) values were plotted against
tN1/2/(12a23) in Fig. 5, for the contraction of PMMA
chains (a,1) below u temperature. The light scattering data
reported by Nakata22 is also depicted in Fig. 5. From the
slopes and intercepts of the linear plots B and C values were
calculated and given in Table IV. The parameters B and C
are related to the second virial coefficient, and the third virial
9
FIG. 3. Plot of the expansion factor, ah3 , vs temperature for poly~methyl
methacrylate! in tert-butyl alcohol1water mixture. The polymers and types
of experiments are identified in Fig. 2.
B. M. Baysal and N. Kayamancoefficient of segment interactions, respectively. It will be
seen from Fig. 5 and Table IV that both the B and C values
17 O
ctober 2023 14:15:42show slight dependence of molecular weight and the method
of measurements for the globularization regime (a,1) of
PMMA.
Parameter B in Eq. ~2! is evaluated by plotting
(a52a3) values against N1/2t in Fig. 6 for the expansion of
PMMA chains (a.1) above the u temperature. The calcu-
lated B values were also included in Table IV. Figures 4 and
6 show that the temperature dependence of the radius expan-
FIG. 4. Comparison of theoretical and experimental values of the expansion
factor a2. Theoretical curves calculated from Eq. ~1! for T,u and Eq. ~2!
for T.u and denoted by broken lines. The polymers and types of experi-
ments are identified in Fig. 2. For comparison, a2 values obtained from Ref.
22 were included and denoted by open diamonds L. For experimental
points, the ordinate denotes a25ah6/2.43 ~see the text!. The crosses indicate
coil–globule transition points.
FIG. 5. A plot of (a32a)/(12a23) vs N1/2t/(12a23) for random coil–
J. Chem. Phys., Vol. 109, No. 19, 15 November 1998globule transition of poly~methyl methacrylate!. The polymers are identified
in Figs. 2 and 4.sion factor determined by light scattering is much more pro-
nounced compared to the viscosity expansion factor. This
observation is also valid for the polystyrene–cyclohexane
system.6,28
The solid and broken lines in Fig. 4 were described by
Eq. ~1! with the values of B and C reported in Table IV for
a,1. B values given in Table IV for a.1 were used in Eq.
~2! to plot the curves at above the theta temperature.
In Fig. 7, universal curves of the scaled expansion factor,
a3utuM w
1/2
, are plotted against scaled reduced temperature,
utuM w
1/2
, to observe the transition to the globule state. The
points represent the experimental data. The light scattering
data are included to compare the results of experimental
methods.22 The curves give the calculation due to Eq. ~1!.
The horizontal lines at the right indicate asymptotic values
a3utuM w
1/25(C/B). The curves approach the asymptotic
limit for utuM w
1/2.90.
The inflection points of the curves in Fig. 4 represent
critical conditions and indicate coil–globule transition
points. a2 values were obtained by considering d2T/da2
50. The evaluated values of a2 were 0.604 and 0.574 for
PMMA-1 and 2, respectively. The reported light scattering
value was 0.511.22 Corresponding utuM w1/2 values were 36.2,
45.5, and 26.7, respectively. The crossover points were also
shown in Fig. 7.
5 3 1/2
TABLE IV. The values of parameters of B and C for PMMA-tert-butyl
alcohol1water system.
M w52.553106 M w54.733106 M w52.383106 ~Ref. 22!
~t,0!
B 0.377 0.295 0.506
C 0.110 0.085 0.044
(C/B) 0.292 0.288 0.087
(C/B)a 9.23 9.15 2.75
(t.0)
B 0.061 0.092 0.569
aReported ratios were obtained multiplying the (C/B) values by (M /N)1/2
values.
8705B. M. Baysal and N. KayamanFIG. 6. A plot of (a 2a ) vs N utu for expansion of poly~methyl meth-
acrylate!. The polymers are identified in Figs. 2 and 4.
17 O
ctober 2023 14:15:42A. The radius of globular PMMA
Nakata in his paper on the coil–globule transition of
PMMA in a mixed solvent22 and in isoamyl acetate,29 has
calculated the volume fraction of PMMA in the polymer
domain. At low temperatures the segment fraction is not di-
lute but concentrated in the polymer domain. In this work we
have calculated the dimensions of PMMA molecules under
various conditions as follows.
~a! Let us consider solid isotropic spheres of amorphous
poly~methyl methacrylate! molecules ~PMMA-1 and
PMMA-2! having molecular weights, M w52.553106 and
4.733106 g mol21, respectively. Using the density of amor-
phous PMMA as 1.191 g cm23, we have calculated the ra-
dius of each single molecule for these two samples. The
calculated values were given in Table V.
~b! The ratio of radius and viscosity expansion factors
were given by the following well-known relations;
as
2
ah
2 5
^Rg
2&
^Rh
2&
^Rh
2&u
^Rg
2&u
. ~8!
Since ^Rg
2&u
1/2/^Rh
2&u
1/251.25,30 as250.331 ~Ref. 22, 20 °C!
and ah
2 50.517 ~Table II, 16 °C!, we can calculate the fol-
lowing ratio at the collapsed state as (Rg /Rh)50.798, which
is in agreement with (3/5)1/250.774 given for a single
globule.6
~c! The viscosity of a suspension of spheres is given as
follows:31
h
h0
5112.5f217.349f221fl , ~9!
where f2 is the volume fraction of spheres and h, h0 are the
FIG. 7. Plot of scaled expansion factor a3utuM W1/2 of intrinsic viscosity as a
function of scaled reduced temperature utuM W1/2 . The closed and the open
circles are for viscosity data of PMMA 1 and PMMA 2, respectively. The
open diamonds denote the dynamic light scattering data obtained from Ref.
22. The broken lines are for Eq. ~1!. The horizontal lines at the right indicate
the asymptotic limits of Eq. ~1!. The transitions to globule states occur at
C/B52.75 and 9.2 for light scattering and viscosity data, respectively. The
crosses indicate crossover points.
8706 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998viscosities of suspension and pure solvent, respectively. Us-
ing the hsp values given for the lowest temperatures ~16 °Cfor PMMA-1, and 20 °C for PMMA-2! in Tables I and II one
can calculate the volumes (Vl) and the radii of the spheres
using the following relation;32–34
f25
Vl
~M /N ! c2 , ~10!
where Vl is the effective hydrodynamic volume, M is the
molecular weight of the sample, N is the Avogadro number,
and c2 is the concentration of the solution. The calculated
values of radius from hydrodynamic volume are also given
in Table V.
~d! The dimensional quantities of PMMA samples could
also be calculated by using the following relation:
@h#5F
^r2&3/2
M , ~11!
where F is a constant3,23 (2.8531021), ^r2& is the mean-
square end-to-end distance, and M is the molecular weight of
the sample. Calculated ^r2& values were included in Table V.
The calculated radii of PMMA-1 and PMMA-2 samples
from Eqs. ~9! to ~11! were not identical to the amorphous
solid molecules. That means collapsed globules still contain
considerable amounts of solvent molecules. The segment
volume fraction for PMMA-2 is calculated as (116/295)3
51/18. That means only 6.1% of each collapsed globule.
The segment volume fraction in the polymer domain was
calculated by Nakata22 as 17% based on the calculation using
the radius of gyration, ^s2&1/2. Since the viscosity and the
light scattering measurements evaluate different properties of
a polymeric globule, we cannot expect identical segment vol-
ume fraction values in the polymer domain of a collapsed
globule.
The mean square radius of gyration reported by Nakata22
for a PMMA sample having approximately identical molecu-
lar weight (2.383106 g mol21) in the same u-solvent system
at 20 °C is found to be ^s2&50.16310211 cm2. As it is well
known, the following relation holds for ideal polymer chains;
^r2&/^s2&56. ~12!
Using the hydrodynamic radius given in Table IV the calcu-
lated ratio for the collapsed globule of PMMA-1 is as fol-
lows: (30431028)2/1.631021255.8, which is in agreement
with Eq. ~12!.
If we try to calculate the same ratio using the mean-
square end-to-end distance, ^r2&, calculated from Eq. ~11!
we obtain, (86331028)2/1.6310212546.55. We have to di-
vide this figure by the value of characteristic ratio of PMMA
(46.55/7.556.2) in order to obtain a comparable value given
TABLE V. Dimensions of PMMA molecules.
Radius of an
amorphous
solid molecule
Radius calculated from
hydrodynamic volume
Eqs. ~9! and ~10!
^r2&1/2 calculated from
Eq. ~11!
T5u
PMMA-1 95 A° 304 A° ~16 °C! 1648 A° 863 A° ~16 °C!
B. M. Baysal and N. KayamanPMMA-2 116 A° 295 A° ~20 °C! 2067 A° 1046 A° ~20 °C!
in Eq. ~12!. In this calculation, dividing ^r2& by the value of
the characteristic ratio we obtain a value corresponding to a
freely joint chain.
IV. CONCLUSIONS
The coil–globule transition by viscosity measurements
for two PMMA samples in the mixed solvent of water1tert-
butyl alcohol shows similar temperature dependence to that
syndiotriads compared to an atactic free radical PMMA.23
We suspect that considerably higher contractions observed at
low temperatures for PMMA compared to other flexible
polymeric chains is probably due to the existence of a certain
amount of tacticity for this polymer. For this reason, a chain
dimension study using a syndiotactic PMMA sample is un-
der progress in our laboratory.
8707J. Chem. Phys., Vol. 109, No. 19, 15 November 1998 B. M. Baysal and N. Kayaman
17 O
ctober 2023 14:15:42observed by light scattering experiments.22 The measure-
ments were carried out in a wide temperature range below
the u ~41.5 °C! temperature taking advantage of the very
slow phase separation of the dilute solution. A smooth and
continuous contraction was observed down to 16 °C for
PMMA-1 ~20 °C for PMMA-2!. The viscosity expansion
factors ah
3
, were reduced by 86%–87% of their u-state di-
mension, which means that a true collapse experiment was
realized in this system.
The expansion factors obtained below and above the u
temperature were compared with theoretical predictions pro-
posed for a,1 and a.1. A quantitative agreement between
the experimental data and Eq. ~1! ~for a,1! and Eq. ~2! ~for
a.1! is obtained.
The coil–globule transition for this flexible polymer was
identified by the fact that the scaled expansion factor
a3utuM w
1/2 approached to a constant (B/C) with decreasing
temperature as predicted by theoretical calculations.9 The
transition points from coil to globule could not be deter-
mined exactly because of the continuous change of a. How-
ever, the crossover points were calculated.
Small deviations were observed in expansion factors
evaluated by using light scattering and viscosity data ~Figs. 3
and 4!. Two reasons can be offered to explain these minor
discrepancies. First of all, the polydispersity of the PMMA
sample used in light scattering experiments (M w /M n;1.2)
was smaller compared to samples which were used in our
viscosity experiments. Furthermore, a2 values calculated by
using semiempirical Equation ~7!, which has certain approxi-
mations, may cause some deviations.
For the collapsed state of a globule, the following two
quantities are used in Eq. ~12!, ~a! the hydrodynamic radius,
^r2& , which was calculated from our viscosity data using
Eqs. ~9! and ~10!; and ~b! the radius of gyration, ^s2& value
reported for a PMMA sample having about the same molecu-
lar weight. A very good agreement is obtained. On the other
hand, at low temperatures the segment volume fraction is
still not concentrated in the polymer domain, and it is only
6.1% of each collapsed globule.
For the PMMA samples we used in this work, tacticity
determined from 1H NMR ~Table I! indicates the presence ofACKNOWLEDGMENTS
This work was supported by TUBITAK-Turkish Scien-
tific and Technical Research Council and the National Sci-
ence Foundation, ~NSF Grant No. INT-9507751!.
1 W. H. Stockmayer, Macromol. Chem. Phys. 35, 54 ~1960!.
2 C. Williams, F. Brochard, and H. L. Frisch, Annu. Rev. Phys. Chem. 32,
433 ~1981!.
3 H. Fujita, Polymer Solutions ~Elsevier, Amsterdam, 1990!.
4 P. J. Flory, Principles of Polymer Chemistry ~Cornell University Press,
Ithaca, 1953!.
5 I. C. Sanchez, Macromolecules 12, 1980 ~1979!.
6 S. T. Sun, I. Nishio, G. Swislow, and T. Tanaka, J. Chem. Phys. 73, 5971
~1980!.
7 B. Erman and P. J. Flory, Macromolecules 19, 2342 ~1986!.
8 B. M. Baysal and N. Uyanik, Polymer 33, 4798 ~1992!, and references
cited therein.
9 T. M. Birshtein and V. A. Pryamitsin, Macromolecules 24, 1554 ~1991!.
10 A complete presentation of the literature is given in Chap. 4 of Ref. 3.
11 I. H. Park, Q.-W. Wang, and B. Chu, Macromolecules 20, 1965 ~1987!.
12 I. H. Park, L. Fetters, and B. Chu, Macromolecules 21, 1178 ~1988!.
13 B. Chu and Z. Wang, Macromolecules 21, 2283 ~1988!.
14 B. Chu and Z. Wang, Macromolecules 22, 380 ~1989!.
15 J. Q. Yu, Z. L. Wang, and B. Chu, Macromolecules 25, 1618 ~1992!.
16 B. Chu, J. Yu, and Z. Wang, Prog. Colloid Polym. Sci. 91, 142 ~1993!.
17 B. Chu, Q. Ying, and A. Yu. Grosberg, Macromolecules 28, 180 ~1995!.
18 P.-G. de Gennes, J. Phys. ~France! Lett. 46, L-639.3 ~1985!.
19 A. Yu. Grosberg, S. K. Nechaev, and E. I. Shakhnovich, J. Phys. ~France!
49, 2095 ~1988!.
20 G. Raos and G. Allegra, Macromolecules 29, 8565 ~1996!.
21 E. E. Hamurcu, L. Akcelrud, B. M. Baysal, and F. E. Karasz, Polymer 39,
3850 ~1998!.
22 M. Nakata, Phys. Rev. E 51, 5770 ~1995!.
23 J. M. G. Cowie, Polymers: Chemistry & Physics of Modern Materials
~Chapman & Hall, Glaskow, 1991!, Chap. 10.
24 J. R. Fried, Polymer Science and Technology ~Prentice–Hall, Englewood
Cliffs, NJ, 1995!, Chap. 2.
25 B. B. Sauer and Y. H. Kim, Macromolecules 30, 3323 ~1997!.
26 M. Kurata and W. H. Stockmayer, Fortschr. Hochpolym.-Forsch. 3, 196
~1963!.
27 H. Yamakawa, Modern Theory of Polymer Solutions ~Harper and Row,
New York, 1991!, Chap. 3.
28 N. Uyanik and B. M. Baysal ~unpublished!.
29 M. Nakata and T. Nakagawa, Phys. Rev. E 56, 3338 ~1997!.
30 J. G. Kirkwood and J. Riseman, J. Chem. Phys. 16, 565 ~1948!.
31 V. Vand, J. Phys. Colloid Chem. 52, 277 ~1948!.
32 B. M. Baysal and F. Yilmaz, Polym. Int. 27, 339 ~1992!.
33 J. C. Selser, Macromolecules 18, 585 ~1985!.
34 J. Li, S. Harville, and J. W. Mays, Macromolecules 30, 466 ~1997!.
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Citation
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RESEARCH ARTICLE | NOVEMBER 15 1998
Coil–globule transition of poly(methyl methacrylate) by
intrinsic viscosity
Bahattin M. Baysal; Nilhan Kayaman
J. Chem. Phys. 109, 8701–8707 (1998)
https://doi.org/10.1063/1.477536
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JOURNAL OF CHEMICAL PHYSICS VOLUME 109, NUMBER 19 15 NOVEMBER 1998
17 O
ctober 2023 14:15:42meric chain is considered using both mean-field theories and
other new approaches over a wide range of temperature.5–7
The application of these theoretical equations to the expan-
sion and contraction of a polystyrene chain were given in a
previous article.8
Birshtein and Pryamitsin indicated that the evaluation of
the configurational entropy ~and entropy force! in earlier pa-
pers published on the coil–globule transition were based on
an expression inapplicable to the contraction of the chains
but valid for the case of chain expansion.9 For this reason
these authors carried out a rigorous approach to calculate the
elastic entropy or the corresponding entropy force connected
with chain deformation. For the contracted coil (t,0) they
derived an equation for the expansion factor a as
a32a2C~a2321 !5BN1/2t , ~1!
where N represents the number of Kuhn segments in the
chain, B and C are parameters that do not depend on both
ascribed to the metastable state of the test solutions.11–13
However, chain contractions reported for a polystyrene–
cyclohexane system was only about 75% of the unperturbed
theta state.11–14,8 This small decrease in size does not satisfy
the criteria of a densely packed collapsed globule.
Recently, Chu and co-workers reported a two-stage ki-
netics of single-chain collapse for polystyrene in cyclo-
hexane.15–17 In a study of the time dependence of the hydro-
dynamic radius (RH) of a single polystyrene chain in solu-
tion, the sample was quenched from 35 to 28.0 °C. The un-
perturbed RH value of a single polystyrene molecule is
reduced initially by 29% forming a crumpled globule. Sub-
sequently in a second stage it is further reduced to a compact
globule, indicating a total reduction of about 69% of its
original radius. A theoretical two-stage kinetics of a single-
chain collapse was proposed earlier.18,19 However, the possi-
bility of chain clustering during the second stage of collapse
was taken into consideration by Raos and Allegra.20 Normal-Coil–globule transition of polymethy
Bahattin M. Baysal and Nilhan Kayaman
Department of Chemistry, Marmara Research Center, P.O
and Bogˇazic¸i University, Department of Chemical Enginee
~Received 8 August 1997; accepted 14 August 1998!
The coil–globule transition for poly~methyl methacr
tert-butyl alcohol1water system. Two polymeric sa
3106 and M w54.733106 were used. The contractio
determined by viscometric measurements. The resu
obtained recently for the same system. A smooth and
the u temperature ~41.5 °C!. The temperature depen
curve in ah
3 utuM w
1/2 vs utuM w
1/2 plot, where ah
3 5@h(T
t5(T2u)/T is the reduced temperature. A compar
theory for contracted coil confirmed the coil–globule
Institute of Physics. @S0021-9606~98!52443-9#
I. INTRODUCTION
The transition from random-coil behavior in the theta
state to a globular compact form in the collapsed state of
macromolecular chains has been the subject of extensive
studies. This change in the state of a polymer chain from the
open coil to the globular particle is called the coil–globule
transition, and was first predicted by Stockmayer in 1960.1
Williams et al.2 summarized the contributions made by the
end of 1970s, and Fujita3 presented a review on this subject
at 1992.
Most of the coil-collapse experiments were carried out
for polystyrene solutions at extremely low concentrations.
Various experimental methods such as static and quasielastic
light scattering, small-angle neutron scattering, ultracentri-
fuge and viscosimetric measurements were used for the de-
termination of linear polymer dimensions.
The temperature dependence of the expansion factor a
can be obtained from the classical Flory equation given for
the excluded volume effect.4 The contraction of the poly-8700021-9606/98/109(19)/8701/7/$15.00methacrylate by intrinsic viscosity
ox 21, 41470 Gebze, Turkey
g, 80815 Bebek-Istanbul, Turkey
ate! has been studied in the mixed solvent
ples having molecular weights M w52.55
and expansion of the molecular chains were
were compared with light scattering data
ontinuous contraction was observed below
nce of @h# can be represented by a master
/@h(u)# is a viscosity expansion factor and
on of the observed globular radius with a
nsition for this system. © 1998 American
molecular weight M and temperature T but depend on chain
stiffness; t5(T2u)/u is the reduced temperature, and C is
caused by the third virial coefficient.9 Equation ~1! has a
critical point below which the coil–globule transition be-
comes discontinuous. The critical point appears at C
50.005 487 and BN1/2t520.4135. The value of a at the
critical point is 0.4714.
For chain expansion (t.0) the following Flory type
relation,
a52a35
2
p2
BN1/2t , ~2!
was obtained.9
Two sets of contradictory experimental data for contrac-
tion of polystyrene in cyclohexane were reported in earlier
works10—one giving a very sharp transition and the other
indicating a gradual contraction. Extensive static and dy-
namic light scattering studies carried out by Chu and co-
workers have indicated that the previously observed very
sharp coil–globule transitions in polystyrene solutions can be1 © 1998 American Institute of Physics
17 O
ctober 2023 14:15:42ized rms radii of gyration of a single chain and of the clusters
of several chains were calculated considering two- and three-
body interactions. It was found that the clusters of two to five
polystyrene chains have a smaller radius than a single chain.
Raos and Allegra20 concluded that the much smaller objects
observed in the second stage of collapse, reported as ‘‘com-
pact globules’’ by Chu and co-workers,19 under kinetic con-
ditions are actually macromolecular clusters resulting from
the aggregation of a small number of polymer chains. Con-
sequently the initial collapse stage ~about 25% contraction!
corresponds to the final equilibrium state for polystyrene in
cyclohexane.20
Considering contradictory experimental data and limited
contraction observed for the polystyrene–cyclohexane sys-
tem, we have studied the collapse behavior of poly ~o-
chlorostyrene! and poly ~p-chlorostyrene! under poor solvent
conditions.21 For these polymers we have not observed a
two-stage kinetics. Although a values for these chains ex-
ceed the contraction reported for polystyrene in cyclohexane,
they are still not satisfactory for a single globule formation.
Recently Nakata carried out detailed light scattering ex-
periments using a poly~methyl methacrylate! ~PMMA!
sample with an average molecular weight M w52.383106
and a molecular weight distribution M w /M n.1.20 in the
mixed solvent water1tert-butyl alcohol.22 Since the phase
separation occurred very slowly for this system, the mean
square radius of gyration ^s2& and the second virial coeffi-
cient A2 were determined reliably even far below the phase
separation temperature.
In this article, the coil–globule transition was studied for
poly ~methyl methacrylate! ~PMMA! in a theta solvent ~tert-
butyl alcohol1water! by viscosimetric measurements. The
results were compared with light scattering data obtained re-
cently for the same system by Nakata.22
II. EXPERIMENT
A. Polymers and solvents
Poly~methyl methacrylate! is purchased from Poly-
sciences Inc., Cat. No. 16217. M w52.33106. Two PMMA
samples were prepared by fractional precipitation at 25.0 °C.
1.0 g of PMMA is dissolved in toluene to produce 0.1 wt %
solution in a 5 L round-bottom flask. After dropwise metha-
nol addition, and stirring, the first fraction was precipitated,
equilibrium conditions were maintained overnight and sepa-
rated from the mother solution. This fraction was dissolved
in toluene, precipitated in methanol, and filtered and dried at
40 °C in a vacuum oven overnight. This first fraction ~0.310
g! is designated as PMMA-1. A portion ~0.150 g! of this
fraction is dissolved in toluene to produce 0.027 wt % solu-
tion and fractionated again with a similar procedure. A 0.040
g PMMA is obtained after this second-stage precipitation.
This fraction is called PMMA-2. The characterizations of
these samples are given in Table I.
The tert-butyl alcohol was purified by fractional distilla-
tion. The water was distilled by standard methods twice im-
8702 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998mediately before use. The present study on the coil–globule
transition was performed with a mixed solvent of tert-butylalcohol1water ~97.5% v/v tert-BuOH! by varying the tem-
perature.
B. Viscosity measurements
A precision capillary viscometer ~Cannon 75 M-710!
was used for the intrinsic viscosity measurements which has
a time resolution of 60.001 s. The viscometer was immersed
in a constant temperature bath controlled to 60.01 °C over a
temperature range 14–70 °C. The efflux times for ;1 ml
chloroform and tert-butyl alcohol1water mixture were 45.05
s ~20.0 °C! and 293.28 s ~41.5 °C!, respectively.
TABLE I. Specification of poly~methyl methacrylate! samples.
Sample @h#a (dL g21) M w (g mol21) M w /M n
PMMA-1 6.12 2.573106 1.35
PMMA-2 10.5 4.733106 1.29
Tacticity and long range tacticity determined from 1H NMR
Triadb Tacticity p~r! or p~m!c
PMMA2 rr 60.2 0.775
mr 33.9
mm 5.9 0.243
100
mrrd 0.55~peak area ratio!
rrr 1.00
aIn chloroform at 20.0 °C.
brr refers to the percent syndiotriads, mr to atactic triads, and mm to isotri-
ads.
cp~r! is the probability of adding a monomer to form a racemic diad, inde-
pendent to the configuration of the previously added monomer units, and
p~m! is the probability of adding a meso unit.
drrr refers to long range tacticity.
B. M. Baysal and N. KayamanFIG. 1. 1H NMR spectrum for poly~methyl methacrylate! in CDCL3.
17 O
ctober 2023 14:15:42C. 1H NMR spectroscopy
For tacticity determination, 1H NMR spectrum of
PMMA in CDCl3 was recorded on a Bruker AC 200 L in-
strument at 200.133 MHz proton frequency, with 3.3 ms
pulses and 0.1 s relaxation delay. It can be seen from Fig. 1
that the three peaks which appear at the highest field were
used to estimate triad tacticities. The bands at 0.85, 1.00, and
1.25 ppm represent the resonance of syndiotactic, atactic,
and isotactic methyl groups. The area under each of these
three peaks corresponds to the amount of each triad present
in the polymer chain. The data are calculated with this
method and included in Table I.23 The b-methylene proton of
PMMA resonances between 1.4 and 2.4 ppm. The major
intensity peak at 1.55 ppm was assigned to the rrr quartet of
the predominantly syndiotactic sample. The peak area ratios
which illustrate long-range syndiotacticity tendency were de-
termined as 1.0/0.55 for syndiotactic tetrads, rrr~1.55 ppm!
mrr~1.80 ppm!, and rmr~1.88 ppm!.24,25
TABLE II. Specific viscosities of poly~methyl methacrylate! ~M w52.55
3106 g/mol in tert-BuOH1water mixture!. C52.5531025 g/mL.
Temp
~°C! 103hsp
ah
3
(hsp /hspu )
a2
(ah3 5a2.43) t M w1/2 a3t M w1/2
70.00 15.257 1.199 1.161 fl fl
65.15 14.922 1.173 1.140 fl fl
59.90 15.382 1.209 1.169 fl fl
55.30 14.564 1.145 1.118 fl fl
50.00 14.290 1.123 1.100
45.10 13.587 1.068 1.055 fl fl
43.00 13.340 1.048 1.040 fl fl
42.05 13.054 1.026 1.021 fl fl
41.50 12.725 1.000 1.000 0 0
41.00 11.644 0.915 0.930 2.537 2.274
40.10 10.486 0.824 0.853 7.11 5.595
37.90 9.161 0.720 0.763 18.27 12.18
35.05 7.290 0.573 0.632 32.73 16.46
34.10 6.680 0.525 0.588 37.55 16.95
32.15 5.552 0.436 0.505 47.45 17.04
30.00 4.526 0.356 0.427 58.36 16.29
28.00 3.411 0.268 0.338 68.51 13.49
25.10 2.547 0.200 0.266 83.23 11.42
22.10 2.256 0.177 0.241 98.46 11.63
21.05 2.032 0.160 0.221 103.79 10.71
20.00 2.081 0.164 0.225 109.12 11.65
19.10 2.019 0.159 0.220 113.68 11.71
18.00 1.943 0.153 0.213 119.26 11.72
17.00 1.872 0.147 0.207 124.34 11.67
16.00 1.770 0.139 0.197 129.41 11.33
21.05a 1.931 0.152 0.212 103.74 10.12
20.00a 2.026 0.159 0.220 109.11 11.29
41.00b 12.385 0.973 0.978 2.54 2.45
40.10b 11.218 0.882 0.902 7.11 6.08
37.90b 9.263 0.728 0.770 18.27 12.34
36.00b 7.815 0.614 0.670 27.91 15.29
20.00b 2.021 0.159 0.220 109.11 11.25
18.00b 1.948 0.153 0.213 119.26 11.72
16.00b 1.849 0.145 0.205 129.41 12.27
a
J. Chem. Phys., Vol. 109, No. 19, 15 November 1998Shock cooling from 55 °C.
bRepeat experiments with a new solution.D. Procedure
The intrinsic viscosities were calculated using the fol-
lowing relation:
@h#5 lim
c!0
~hsp /c !, ~3!
where the specific viscosity hsp5(h2h0)/h0 , with h and
h0 being the polymer solution viscosity and solvent viscos-
ity, respectively, and c is the polymer concentration. At finite
concentrations, in the dilute solution regime
hsp /C5@h#~11kH@h#c !, ~4!
where kH is the Huggins interaction coefficient. In our case,
as (c52.5531025 g/mL) is very near infinite dilution ~i.e.,
kH@h#c!1!, @h#>hsp /c!.
III. RESULTS AND DISCUSSION
The experimental results of specific viscosities in tert-
butyl alcohol1water mixture for two poly~methyl methacry-
late! samples are reported in Tables II and III. Since the
viscosity measurements were carried out at very low concen-
trations (2.5531025 g/mL), we assumed that the measured
values of specific viscosities are identical to intrinsic viscosi-
ties. Nakata recently has found that the second virial coeffi-
cient, A2 , vanishes at 41.5 °C so that this temperature can be
taken as the u temperature for PMMA in a mixed solvent
system.22
It is well established that viscosity measurements per-
formed on solutions at the u conditions can yield information
on the dimension of polymeric chains with the aid of the
following relations:
TABLE III. Specific viscosities of PMMA (M w :4.733106 g/mol) in tert-
BuOH1water mixture!. C52.5431025 g/mL.
Temp
~°C! 103hsp
ah
3
(hsp /hspu )
a2
(ah3 5a2.43) t M w1/2 a3t M w1/2
70.00 17.967 1.332 1.266 fl fl
65.15 18.133 1.344 1.276 fl fl
59.90 17.811 1.320 1.257 fl fl
55.10 17.321 1.284 1.228 fl fl
50.00 16.793 1.244 1.198
45.10 15.819 1.173 1.140 fl fl
43.00 14.681 1.088 1.072 fl fl
42.00 14.163 1.050 1.041 fl fl
41.50 13.490 1.000 1.000 0 0
41.00 12.099 0.897 0.914 3.456 3.021
40.00 10.859 0.805 0.836 10.37 7.931
38.00 9.125 0.676 0.725 24.19 14.93
37.00 8.716 0.646 0.698 31.10 18.14
36.00 8.081 0.599 0.656 38.02 20.19
35.00 6.953 0.515 0.580 44.93 19.82
34.00 6.002 0.445 0.514 51.84 19.08
32.00 4.875 0.361 0.433 65.66 18.69
30.00 3.832 0.284 0.355 79.49 16.46
28.00 2.677 0.199 0.264 93.31 12.66
25.10 2.145 0.159 0.220 113.36 11.71
22.00 1.919 0.142 0.200 134.78 12.06
21.00 1.805 0.134 0.191 141.69 11.98
8703B. M. Baysal and N. Kayaman20.00 1.749 0.130 0.186 148.61 11.92
17 O
ctober 2023 14:15:42@h#5@h#uah
3
, ~5!
@h#u5KuM 1/2, ~6!
where @h# and @h#u represents the intrinsic viscosities in or-
dinary and u solvent, respectively, M is the molecular
weight, and Ku is a constant. However, since the hydrody-
namic radius of a polymer chain increases less rapidly than
the statistical radius as the excluded volume increases, the
expansion factors given in Eqs. ~1!, ~2!, and ~5! are not
identical.26 Several theoretical approaches exist in order to
find a relation in between these expansion factors. For prac-
tical purposes, in our calculations we have preferred to use
the following exponential type of relation:27
ah
3 5a2.43. ~7!
Figure 2 shows the temperature dependence of intrinsic
viscosities for these two PMMA samples in tert-butyl
alcohol1water solution at above and below the theta tem-
perature. The contraction of PMMA chains covers a wide
range of intervals. For PMMA-1 a gradual transition was
observed up to 16 °C. At lower temperatures it was not pos-
sible to obtain reproducible results. After performing viscos-
ity measurements at 16 °C, the solution was heated to 55 °C
and shock cooled to 21 °C. The same specific viscosity re-
sults were obtained for these runs at 21.05 and 20.00 °C. The
viscosity measurements were replicated using the same
PMMA-1 solution and the results were given in Table II. It
FIG. 2. Intrinsic viscosity @h# vs temperature for poly~methyl methacrylate!
in tert-butyl alcohol1water mixture. The intrinsic viscosities for: ~s! M w
54.733106; ~d! M w52.553106; ~h! M w52.553106 ‘‘shock cooling ex-
periments;’’ ~,! M w52.553106 ‘‘repeat experiments with a new solu-
tion.’’
8704 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998will be seen that viscosity data are reproducible within the
accuracy of experiments. These viscosity experiments elimi-nate the possibility of adsorption of polymer chains on the
glass wall, or the existence of any aggregation and precipi-
tation. The decrease of the viscosity is therefore related to
the shrinking of the polymer chains.
The ah
3 values of PMMA samples were calculated ac-
cording to Eq. ~5! and plotted against temperature in Fig. 3.
In order to use the observed behavior of ah in Eqs. ~1!
and ~2!, a2 values were calculated using Eq. ~7! and the data
were plotted in Fig. 4 against the temperature. Literature val-
ues of light scattering data22 were also included in Fig. 4. As
it will be seen in Fig. 4, the variations of expansion factor
with temperature based on our viscosity experiment are very
similar to Nakata’s observations.22 Since the contraction fac-
tor (a2) obtained from light scattering data did not show
evidence of aggregation in the collapsed state, we can as-
sume that our viscosity data are consistent with the previ-
ously published results.22 These observations, together with
the results of our shock cooling and repeat experiments
prove that there is not any evidence of aggregation in the
collapsed state.
To evaluate the parameters B and C given in Eq. ~1!,
(a32a)/(12a23) values were plotted against
tN1/2/(12a23) in Fig. 5, for the contraction of PMMA
chains (a,1) below u temperature. The light scattering data
reported by Nakata22 is also depicted in Fig. 5. From the
slopes and intercepts of the linear plots B and C values were
calculated and given in Table IV. The parameters B and C
are related to the second virial coefficient, and the third virial
9
FIG. 3. Plot of the expansion factor, ah3 , vs temperature for poly~methyl
methacrylate! in tert-butyl alcohol1water mixture. The polymers and types
of experiments are identified in Fig. 2.
B. M. Baysal and N. Kayamancoefficient of segment interactions, respectively. It will be
seen from Fig. 5 and Table IV that both the B and C values
17 O
ctober 2023 14:15:42show slight dependence of molecular weight and the method
of measurements for the globularization regime (a,1) of
PMMA.
Parameter B in Eq. ~2! is evaluated by plotting
(a52a3) values against N1/2t in Fig. 6 for the expansion of
PMMA chains (a.1) above the u temperature. The calcu-
lated B values were also included in Table IV. Figures 4 and
6 show that the temperature dependence of the radius expan-
FIG. 4. Comparison of theoretical and experimental values of the expansion
factor a2. Theoretical curves calculated from Eq. ~1! for T,u and Eq. ~2!
for T.u and denoted by broken lines. The polymers and types of experi-
ments are identified in Fig. 2. For comparison, a2 values obtained from Ref.
22 were included and denoted by open diamonds L. For experimental
points, the ordinate denotes a25ah6/2.43 ~see the text!. The crosses indicate
coil–globule transition points.
FIG. 5. A plot of (a32a)/(12a23) vs N1/2t/(12a23) for random coil–
J. Chem. Phys., Vol. 109, No. 19, 15 November 1998globule transition of poly~methyl methacrylate!. The polymers are identified
in Figs. 2 and 4.sion factor determined by light scattering is much more pro-
nounced compared to the viscosity expansion factor. This
observation is also valid for the polystyrene–cyclohexane
system.6,28
The solid and broken lines in Fig. 4 were described by
Eq. ~1! with the values of B and C reported in Table IV for
a,1. B values given in Table IV for a.1 were used in Eq.
~2! to plot the curves at above the theta temperature.
In Fig. 7, universal curves of the scaled expansion factor,
a3utuM w
1/2
, are plotted against scaled reduced temperature,
utuM w
1/2
, to observe the transition to the globule state. The
points represent the experimental data. The light scattering
data are included to compare the results of experimental
methods.22 The curves give the calculation due to Eq. ~1!.
The horizontal lines at the right indicate asymptotic values
a3utuM w
1/25(C/B). The curves approach the asymptotic
limit for utuM w
1/2.90.
The inflection points of the curves in Fig. 4 represent
critical conditions and indicate coil–globule transition
points. a2 values were obtained by considering d2T/da2
50. The evaluated values of a2 were 0.604 and 0.574 for
PMMA-1 and 2, respectively. The reported light scattering
value was 0.511.22 Corresponding utuM w1/2 values were 36.2,
45.5, and 26.7, respectively. The crossover points were also
shown in Fig. 7.
5 3 1/2
TABLE IV. The values of parameters of B and C for PMMA-tert-butyl
alcohol1water system.
M w52.553106 M w54.733106 M w52.383106 ~Ref. 22!
~t,0!
B 0.377 0.295 0.506
C 0.110 0.085 0.044
(C/B) 0.292 0.288 0.087
(C/B)a 9.23 9.15 2.75
(t.0)
B 0.061 0.092 0.569
aReported ratios were obtained multiplying the (C/B) values by (M /N)1/2
values.
8705B. M. Baysal and N. KayamanFIG. 6. A plot of (a 2a ) vs N utu for expansion of poly~methyl meth-
acrylate!. The polymers are identified in Figs. 2 and 4.
17 O
ctober 2023 14:15:42A. The radius of globular PMMA
Nakata in his paper on the coil–globule transition of
PMMA in a mixed solvent22 and in isoamyl acetate,29 has
calculated the volume fraction of PMMA in the polymer
domain. At low temperatures the segment fraction is not di-
lute but concentrated in the polymer domain. In this work we
have calculated the dimensions of PMMA molecules under
various conditions as follows.
~a! Let us consider solid isotropic spheres of amorphous
poly~methyl methacrylate! molecules ~PMMA-1 and
PMMA-2! having molecular weights, M w52.553106 and
4.733106 g mol21, respectively. Using the density of amor-
phous PMMA as 1.191 g cm23, we have calculated the ra-
dius of each single molecule for these two samples. The
calculated values were given in Table V.
~b! The ratio of radius and viscosity expansion factors
were given by the following well-known relations;
as
2
ah
2 5
^Rg
2&
^Rh
2&
^Rh
2&u
^Rg
2&u
. ~8!
Since ^Rg
2&u
1/2/^Rh
2&u
1/251.25,30 as250.331 ~Ref. 22, 20 °C!
and ah
2 50.517 ~Table II, 16 °C!, we can calculate the fol-
lowing ratio at the collapsed state as (Rg /Rh)50.798, which
is in agreement with (3/5)1/250.774 given for a single
globule.6
~c! The viscosity of a suspension of spheres is given as
follows:31
h
h0
5112.5f217.349f221fl , ~9!
where f2 is the volume fraction of spheres and h, h0 are the
FIG. 7. Plot of scaled expansion factor a3utuM W1/2 of intrinsic viscosity as a
function of scaled reduced temperature utuM W1/2 . The closed and the open
circles are for viscosity data of PMMA 1 and PMMA 2, respectively. The
open diamonds denote the dynamic light scattering data obtained from Ref.
22. The broken lines are for Eq. ~1!. The horizontal lines at the right indicate
the asymptotic limits of Eq. ~1!. The transitions to globule states occur at
C/B52.75 and 9.2 for light scattering and viscosity data, respectively. The
crosses indicate crossover points.
8706 J. Chem. Phys., Vol. 109, No. 19, 15 November 1998viscosities of suspension and pure solvent, respectively. Us-
ing the hsp values given for the lowest temperatures ~16 °Cfor PMMA-1, and 20 °C for PMMA-2! in Tables I and II one
can calculate the volumes (Vl) and the radii of the spheres
using the following relation;32–34
f25
Vl
~M /N ! c2 , ~10!
where Vl is the effective hydrodynamic volume, M is the
molecular weight of the sample, N is the Avogadro number,
and c2 is the concentration of the solution. The calculated
values of radius from hydrodynamic volume are also given
in Table V.
~d! The dimensional quantities of PMMA samples could
also be calculated by using the following relation:
@h#5F
^r2&3/2
M , ~11!
where F is a constant3,23 (2.8531021), ^r2& is the mean-
square end-to-end distance, and M is the molecular weight of
the sample. Calculated ^r2& values were included in Table V.
The calculated radii of PMMA-1 and PMMA-2 samples
from Eqs. ~9! to ~11! were not identical to the amorphous
solid molecules. That means collapsed globules still contain
considerable amounts of solvent molecules. The segment
volume fraction for PMMA-2 is calculated as (116/295)3
51/18. That means only 6.1% of each collapsed globule.
The segment volume fraction in the polymer domain was
calculated by Nakata22 as 17% based on the calculation using
the radius of gyration, ^s2&1/2. Since the viscosity and the
light scattering measurements evaluate different properties of
a polymeric globule, we cannot expect identical segment vol-
ume fraction values in the polymer domain of a collapsed
globule.
The mean square radius of gyration reported by Nakata22
for a PMMA sample having approximately identical molecu-
lar weight (2.383106 g mol21) in the same u-solvent system
at 20 °C is found to be ^s2&50.16310211 cm2. As it is well
known, the following relation holds for ideal polymer chains;
^r2&/^s2&56. ~12!
Using the hydrodynamic radius given in Table IV the calcu-
lated ratio for the collapsed globule of PMMA-1 is as fol-
lows: (30431028)2/1.631021255.8, which is in agreement
with Eq. ~12!.
If we try to calculate the same ratio using the mean-
square end-to-end distance, ^r2&, calculated from Eq. ~11!
we obtain, (86331028)2/1.6310212546.55. We have to di-
vide this figure by the value of characteristic ratio of PMMA
(46.55/7.556.2) in order to obtain a comparable value given
TABLE V. Dimensions of PMMA molecules.
Radius of an
amorphous
solid molecule
Radius calculated from
hydrodynamic volume
Eqs. ~9! and ~10!
^r2&1/2 calculated from
Eq. ~11!
T5u
PMMA-1 95 A° 304 A° ~16 °C! 1648 A° 863 A° ~16 °C!
B. M. Baysal and N. KayamanPMMA-2 116 A° 295 A° ~20 °C! 2067 A° 1046 A° ~20 °C!
in Eq. ~12!. In this calculation, dividing ^r2& by the value of
the characteristic ratio we obtain a value corresponding to a
freely joint chain.
IV. CONCLUSIONS
The coil–globule transition by viscosity measurements
for two PMMA samples in the mixed solvent of water1tert-
butyl alcohol shows similar temperature dependence to that
syndiotriads compared to an atactic free radical PMMA.23
We suspect that considerably higher contractions observed at
low temperatures for PMMA compared to other flexible
polymeric chains is probably due to the existence of a certain
amount of tacticity for this polymer. For this reason, a chain
dimension study using a syndiotactic PMMA sample is un-
der progress in our laboratory.
8707J. Chem. Phys., Vol. 109, No. 19, 15 November 1998 B. M. Baysal and N. Kayaman
17 O
ctober 2023 14:15:42observed by light scattering experiments.22 The measure-
ments were carried out in a wide temperature range below
the u ~41.5 °C! temperature taking advantage of the very
slow phase separation of the dilute solution. A smooth and
continuous contraction was observed down to 16 °C for
PMMA-1 ~20 °C for PMMA-2!. The viscosity expansion
factors ah
3
, were reduced by 86%–87% of their u-state di-
mension, which means that a true collapse experiment was
realized in this system.
The expansion factors obtained below and above the u
temperature were compared with theoretical predictions pro-
posed for a,1 and a.1. A quantitative agreement between
the experimental data and Eq. ~1! ~for a,1! and Eq. ~2! ~for
a.1! is obtained.
The coil–globule transition for this flexible polymer was
identified by the fact that the scaled expansion factor
a3utuM w
1/2 approached to a constant (B/C) with decreasing
temperature as predicted by theoretical calculations.9 The
transition points from coil to globule could not be deter-
mined exactly because of the continuous change of a. How-
ever, the crossover points were calculated.
Small deviations were observed in expansion factors
evaluated by using light scattering and viscosity data ~Figs. 3
and 4!. Two reasons can be offered to explain these minor
discrepancies. First of all, the polydispersity of the PMMA
sample used in light scattering experiments (M w /M n;1.2)
was smaller compared to samples which were used in our
viscosity experiments. Furthermore, a2 values calculated by
using semiempirical Equation ~7!, which has certain approxi-
mations, may cause some deviations.
For the collapsed state of a globule, the following two
quantities are used in Eq. ~12!, ~a! the hydrodynamic radius,
^r2& , which was calculated from our viscosity data using
Eqs. ~9! and ~10!; and ~b! the radius of gyration, ^s2& value
reported for a PMMA sample having about the same molecu-
lar weight. A very good agreement is obtained. On the other
hand, at low temperatures the segment volume fraction is
still not concentrated in the polymer domain, and it is only
6.1% of each collapsed globule.
For the PMMA samples we used in this work, tacticity
determined from 1H NMR ~Table I! indicates the presence ofACKNOWLEDGMENTS
This work was supported by TUBITAK-Turkish Scien-
tific and Technical Research Council and the National Sci-
ence Foundation, ~NSF Grant No. INT-9507751!.
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