Kinetically driven intra-and interchain association of hydrophobically and hydrophilically modified poly(acrylic acid) in dilute aqueous solutions

Article abstract of DOI:10.1021/ma101659c

Effects of pH, dodecyl, and PEO contents as well as the method of preparing the solution on the formation of the unimolecular micelles (unimer micelle) or aggregates made of poly(acrylic acid)-graftpoly( ethylene oxide)-graft-dodecyl (PAA-g-PEO-g-dodecyl) and PAA-g-dodecyl have been studied by a combination of static and dynamic laser light scattering (SLS and DLS). It revealed that: in most cases, these copolymers tend to form interchain associates; while low pH value, proper high dodecyl content and fast switch rate of solvent quality promote intrachain association. These phenomena of the system being trapped in a metastable state can be mainly attributed to its kinetic pathway: the factors mentioned earlier can enhance the initial intrachain contraction, leading to τ_c (interaction time) < τ_e (entanglement time) for the two interaction intrachain globules. So they behave like tiny "elastic balls" and their further merge/fusion become nearly impossible during their interaction time (τ_c). In this way, the copolymer system is trapped in the metastable, unimer micelle state. The interplay of τ_c and τ_e in the formation of metastable unimer micelles or stable aggregates has been discussed in detail.

Full text of DOI:10.1021/ma101659c

9534 Macromolecules 2010, 43, 9534–9540
DOI: 10.1021/ma101659c
Kinetically Driven Intra- and Interchain Association of
Hydrophobically and Hydrophilically Modified Poly(acrylic acid)
in Dilute Aqueous Solutions
Jinkun Hao,†,‡ Zhiyong Li,†,‡ He Cheng,*,† Chi Wu,§,^ and Charles C. Han*,†
†State Key Laboratory of Polymer Physics and Chemistry, Joint Laboratory of Polymer Science and Materials,
The Beijing National Laboratory for Molecular Sciences, and The Institute of Chemistry, The Chinese Academy
of Sciences, Beijing 100190, P. R. China, ‡Graduate University of the Chinese Academy of Sciences, Beijing,
100049, China, §The Hefei National Laboratory of Physical Science at Microscale and The Department of
Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China, and
^Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Received July 23, 2010; Revised Manuscript Received September 8, 2010
ABSTRACT: Effects of pH, dodecyl, and PEO contents as well as the method of preparing the solution on
the formation of the unimolecular micelles (unimer micelle) or aggregates made of poly(acrylic acid)-graft-
poly(ethylene oxide)-graft-dodecyl (PAA-g-PEO-g-dodecyl) and PAA-g-dodecyl have been studied by a
combination of static and dynamic laser light scattering (SLS and DLS). It revealed that: in most cases, these
copolymers tend to form interchain associates; while low pH value, proper high dodecyl content and fast
switch rate of solvent quality promote intrachain association. These phenomena of the system being trapped
in a metastable state can be mainly attributed to its kinetic pathway: the factors mentioned earlier can enhance
the initial intrachain contraction, leading to τc (interaction time) , τe (entanglement time) for the two
interaction intrachain globules. So they behave like tiny “elastic balls” and their further merge/fusion become
nearly impossible during their interaction time (τc). In this way, the copolymer system is trapped in the
metastable, unimer micelle state. The interplay of τc and τe in the formation of metastable unimer micelles or
stable aggregates has been discussed in detail.
Introduction
and they found that DodMAM content is critical to the association
behavior of these copolymers.20 Many of these studies clearly
The associations of amphiphilic copolymer have attracted
many scientific and industrial interests for several decades.1-8
They have been widely used as rheological modifiers in water-
based paint formulations, stabilizers in emulsions, gelling agents
in food, and dispatchers of active substance in drug or pesticide
formulations9-12 and in enhanced oil recovery.13
indicate that the nature of hydrophilic and hydrophobic segments,
copolymer composition, sequence distribution and spacer between
the hydrophobe and polymer backbone are main architectural
parameters to determine the self-associative properties of the
polymers.24,25 Besides the nature of copolymers, the solution prep-
aration procedure can also influence the association behavior of
polymers. Itakura et al. studied the solvent composition dependence
of the association of poly(N,N-dimethylacrylamide)-graft-poly-
(methylmethacrylate) (PDMA-g-PMMA) in a methanol-water
mixture and found that a quick switch of solvent quality from good
to poor could lead to smaller aggregates while a slow change
procedure results in larger aggregates.21
Most theories about associations are based on equilibrium
thermodynamics. However, it can not explain the formation of
unimer micelle, because smaller particle with larger surface area
and higher free energy should be less stable. This counterintuitive
phenomenon can be resolved from the competition between
intermolecular interaction time and entanglement time.26-28
In order to take advantage of this phenomenon to encapsulate
hydrophobic agrochemical active agents, we designed terpoly-
mers with three distinct functions: (1) a pH-dependent amphi-
philicity function, (2) the complexation function with hydro-
phobic agrochemical active agents, and (3) the ability to mediate
the colloidal stability in aqueous solutions. Each of these func-
tions can be addressed individually by the different components
of a terpolymer. In the present work, the option of a pH-sensitive
poly(acrylic acid) (PAA) backbone with grafted blocks of a
hydrophilic and dispersing PEO component as well as blocks of
The amphiphilic copolymers containing hydrophobic and hydro-
philic segments in aqueous solution can give rise to two distinctly
separated parts: hydrophobic inner core and hydrophilic outer shell.
And the direct driving forces for association include hydrophobic
and electrostatic interaction, metal complexation, and hydrogen
bonding.10,13-18 It is found that the self-association of amphiphilic
copolymer can occur either within a single polymer chain or among
many polymer chains, or both.19,20 For the association of diblock or
triblock amphiphilic copolymer in selective solvent, the micelle is
formed through multichain association, because single chain only
have one or two associative segments. On the contrary, graft poly-
mer has many associative side chains, and it can form micelle with
less chains or even single polymer chain.21,22 Wu et al. reported that
a linear poly(N-isopropylacrylamide) chain grafted with poly(ethyl-
ene oxide) (PNIPAM-g-PEO) in water can form a stable single
chain core-shell nanostructure when the temperature is revealed
higher than 33 ꢀC.23 Yamamoto et al. studied the intra- and inter-
chain association of poly (sodium 2-(acrylamido)-2-methylpropane-
sulfonate-co-dodecylmethacrylamide(P(AMPS-co-DodMAM)),
*Corresponding authors. Telephone: þ86-10-8261-8089. Fax: þ86-
10-6252-1519. E-mail: (C.C.H.) c.c.han@iccas.ac.cn; (H.C.) chenghe@
iccas.ac.cn.
pubs.acs.org/Macromolecules
Published on Web 10/26/2010
r 2010 American Chemical Society

Article
Macromolecules, Vol. 43, No. 22, 2010 9535
Table 1. Characteristics of PAA-g-PEO-g-dodecyl and PAA-g-dodecyl
no. of PEO grafts
in each copolymer
no. of dodecyl graftsb
in each copolymer
M
w of copolymerc/
105 g moL-1
copolymer
wt % PEOa
wt % dodecyl
PAA-D4
4
10
16
26
34
40
12
19
34
10
25
56
146
259
465
697
906
206
365
785
178
518
2.6
2.8
3.0
3.4
3.8
4.2
3.0
3.3
4.1
3.1
3.7
PAA-D10
PAA-D16
PAA-D26
PAA-D34
PAA-D40
PEO7-D12
PEO7-D19
PEO7-D34
PEO13-D10
PEO13-D25
7
7
7
13
13
9.4
9.4
9.4
18.5
18.5
a The content of PEO is defined as the PEO weight percent in PAA-g-PEO precursors. b The dodecyl grafts should be randomly distributed along the
PAA backbone. c The molecular weights are examined by 1H NMR: the sum of molecular weight of PAA segment, PEO and dodecyl segments (the Mw/Mn
after the grafting reaction is approximated to be unchanged).
a hydrophobic and complexing dodecyl component is being
pursued. However, it turned out that not all the three functions
are distinct; the components interact with each other, and make
the system more complicated as a result. Similar to what we have
previously reported that the double hydrophilic PAA-g-PEO
showed a tendency for interchain association in aqueous solution
through hydrogen-bonding,29 the aqueous solution of PAA-g-
PEO-g-dodecyl, in which both hydrogen-bonding and hydro-
phobic interactions lead to the association of terpolymer.
In this study, the effects of pH values, dodecyl content, PEO
content, and solution preparation procedure on the association
behavior of graft copolymers PAA-g-dodecyl and PAA-g-PEO-
g-dodecyl in aqueous solution have been investigated. Although
interchain associations are dominant in most cases, with a high
enough hydrophobicity of polymer chain and a preparation
procedure to achieve fast switch rate of solvent quality, the
formation of unimer micelle can be obtained. The variation of
association behavior with conditions has been explained from
thermodynamic and kinetic point of view.
(1/2.5 in volume), and then 0.5 g of dodecylamine was added. After
30 min, 1.5 g of DMTMM was added, and the reaction lasted for
18 h. Most THF was removed by rotary evaporation. The
remaining solution was dialyzed against water for 4 days and
then freeze-dried. To remove unreacted dodecylamine, the crude
product was dialyzed against ethanol/water (acidic) mixture for
4 days, and then dialyzed against water. The final product was
obtained by freeze-drying. The composition of the copolymer
was examined by 1H NMR. Several samples with different
dodecyl contents were obtained following this procedure. The
details are listed in Table 1. These copolymers were named as
PAA-g-PEO-x-g-dodecyl-y (x and y stand for PEO content and
dodecyl content respectively) or PAA-g-dodecyl-y (y stands for
dodecyl content), and shortened as PEOx-Dy or PAA-Dy,
respectively.33 The weight average molecular weight (Mw) of
PAA segment is 2.5 ꢀ 105 g moL-1 (the degree of polymeriza-
tion: about 3470), and the Mw of these graft polymers range
from 2.6 ꢀ 105 to 4.2 ꢀ 105 g moL-1 as listed in table 1.
Preparation of Polymer Micelle. Micelle solutions were pre-
pared by adding graft copolymer solution in DMF (1 wt %)
dropwise to excessive amount of aqueous NaCl solution (0.025 M)
under stirring. The obtained solutions were then dialyzed against
aqueous NaCl solution for 24 h to remove the small amount of
DMF. A specific part of samples were prepared in a reverse
procedure: an excessive amount of aqueous NaCl solution was
slowly added into stirring copolymer solution in DMF (0.2 wt %),
and then dialyzed against aqueous NaCl solution. The pH of newly
prepared solutions is 4.0, and it can be adjusted to other pH values
if needed. The final polymer concentration in this study is 2.7 ꢀ
10-4 g mL-1 with 0.025 M NaCl.
Experimental Section
Materials. Poly(acrylic acid) (PAA) aqueous solution (weight
fraction 35%, Mw = 2.5 ꢀ 105 g mol-1) from Sigma-Aldrich,
2-chloro-4,6-dimethoxy-1,3,5-triazine ethyl (CDMT) from Beijing
F&F Chemical Co., Ltd., N-methylmorpholine (NMM), dode-
cylamine from Sinopharm Chemical Reagent Co. Ltd., and tetra-
hydrofuran (THF) from Beijing Chemical Works were used as
received. N,N-Dimethylformamide (DMF) from Beijing Chemical
Works was purified by distillation with CaH2 under reduced
pressure. Water used in this study was purified with a milli-Q
system from Millipore. Dialysis bag (regenerated cellulose, cutoff
molecular weight = 1.4 ꢀ 104 g mol-1) from Beijing Jingkehongda
Biotechnology Co., Ltd. was pretreated by successively boiling in
ethanol/water (1:1 v/v), 0.01 M NaHCO3 and 0.001 M 2-[2-(bis-
(carboxymethyl)amino)ethyl(carboxymethyl)amino]acetic acid
(EDTA) aqueous solution.
Synthesis of 4-(4,6-Dimethoxy-1,3,5-triazin-2-yl)-4-methyl-
morpholinium Chloride (DMTMM). First, 8.8 g CDMT was
dissolved in 120 mL of THF, and then 5.5 mL of NMM was
added as droplets. The mixture was kept stirring at room
temperature for 30 min and then filtrated. The resultant pre-
cipitate was washed with THF. The product has been character-
ized by 1H NMR in DMSO-d6 (dimethyl sulfoxide).30-32
Synthesis of PAA-g-PEO-g-dodecyl and PAA-g-dodecyl.
PAA-g-PEO was prepared as reported before (PEO is grafted
to PAA backbone, the Mw of PEO is 2.0 ꢀ 103 g moL-1).29
PAA-g-PEO-g-dodecyl and PAA-g-dodecyl were synthesized
according to the classical reaction of amino with carboxylic
groups in the presence of DMTMM. Typically, the reaction was
carried out according to the procedure as followed. First 2.5 g
of PAA-g-PEO or PAA was dissolved in 140 mL of water/THF
Laser Light Scattering. A commercial LLS spectrometer
(ALV/DLS/SLS-5022F) equipped with a multi-τ digital time
correlator (ALV5000) and a cylindrical 22 mW UNIPHASE
He-Ne laser (λ0 = 632.8 nm) was used. The LLS cell is held in a
thermostat index matching vat filled with purified and dust-free
toluene, with the temperature controlled to within 0.1 ꢀC. The
details of LLS instrumentation and theory can be found
elsewhere.34-36 In static LLS (SLS), the angular dependence
of the excess absolute time-averaged scattered intensity, i.e., the
Rayleigh ratio Rvv(q), of a very dilute dispersion can lead to
the weight-averaged molar mass Mw and the z-averaged root-
2
mean-square radius of gyration ÆRg æz1/2, (or written as ÆRgæ) of
scattering objects by using Zimm plot (according to eq 1) or
Berry plot (eq 2).37,38
ꢀ
ꢁ
Kc
1
1
ꢁ
1 þ q2ÆRg2æ þ 2A2c
ð1Þ
ð2Þ
RvvðqÞ Mw
3
ꢂ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
1=2
1=2
Kc
1
1
ꢁ
1 þ q2ÆRg2æ þ A2Mw1=2
c
RvvðqÞ
Mw
3

9536 Macromolecules, Vol. 43, No. 22, 2010
Hao et al.
where K = 2π2n2(dn/dc)2/(NAλ0 ) and q is the scattering vector
4
(q = (4πn/λo)sin(0/2)) with NA, dn/dc, n, and λ0 being the
Avogadro number, the specific refractive index increment, the
solvent refractive index, and the wavelength of the light in a
vacuum, respectively. In this study, the solution was so dilute
that the extrapolation for c f 0 was not necessary. So we
extrapolated for q f 0 according to eq 1 or 2 omitting the c
term, and got the Mw,app from the intercept. For high molecule
weight structures (above several million g moL-1), eq 2 was used
to analyze the experimental data; otherwise eq 1 was used.
In dynamic LLS (DLS), the intensity-intensity time correla-
tion function g(2)(t,q) in the self-beating mode was measured,
where t is the decay time. G(τ) can be calculated from the
Laplace inversion of the measured g(2)(t,q).39 In this study, the
CONTIN program supplied with the correlator was used. G(τ)
can be inverted to a line-width distribution G(Γ). For a pure
diffusive relaxation, Γ is related to the translational diffusion
coefficient D by (Γ/q2)qf0,Cf0 = D, so that G(Γ) can be
converted to a translational diffusion coefficient distribution
G(D) or further to a hydrodynamic radius distribution f(Rh) via
the Stokes-Einstein equation, Rh = kBT/6πη0D, where kB, T,
and η0 are the Boltzmann constant, the absolute temperature,
and the solvent viscosity, respectively.
Results and Discussion
The association of PAA-g-dodecyl and PAA-g-PEO-g-dodecyl
in aqueous solution has been investigated. Since water is the
poor solvent for dodecyl, in PAA-g-dodecyl aqueous solution, it
is the hydrophobic interaction induces the copolymer association.
As demonstrated by many studies, PAA-PEO or PAA/PEO can
from intermolecular hydrogen-bonding complexes in aqueous
solution.29,40-42 So in PAA-g-PEO-g-dodecyl aqueous solution,
besides the hydrophobic interaction, there also exists hydrogen
bonding between PAA segments and PEO segments, which
together leads to the association of copolymer.
Figure 1. pH dependence of characteristic relaxation time distributions
and corresponding apparent molecular weight of associates: (a) PAA-g-
PEO-7-g-dodecyl-12; (b) PAA-g-PEO-13-g-dodecyl-10; (c) PAA-g-
PEO-13-g-dodecyl-25 aqueous solutions at 20 ꢀC. Cpolymer = 2.7 ꢀ
10-4 g mL-1, CNaCl = 0.025 M.
1. The Effects of pH on the Association of PAA-g-dodecyl
and PAA-g-PEO-g-dodecyl in Dilute Aqueous Solution. At
pH 4.0, the degree of neutralization, R, of the carboxylic acid
groups of PAA segment is about 0.1-0.15, i.e. most of them
are protonated; at pH 10.0, they are almost fully ionized
(R≈1.0); and at pH 7.0, R is 0.2-0.9, the carboxylic acid
groups are partially ionized depending on modifications of
PAA chain and the exact conditions.37,43 Figure 1 shows the
pH dependence of characteristic relaxation time distribu-
tions and apparent molecular weight of (a) PAA-g-PEO-7-g-
dodecyl-12, (b) PAA-g-PEO-13-g-dodecyl-10, and (c) PAA-
g-PEO-13-g-dodecyl-25 in aqueous solutions (note: the
Mw,app in all figures are referring to the apparent weight
average molecular weight of associates). Within the studied
pH range, there are two groups of relaxation modes, and the
corresponding apparent weight average molecular weight
(Mw,app) obtained from SLS is in the range of 6.2 ꢀ 106 to
2.7 ꢀ 107 g moL-1. Furthermore, as shown in figure 2, the
plots of the average characteristic relaxation rate (Γ) of fast
mode and slow mode of PAA-g-PEO-13-g-dodecyl-25 vs q2
under different pH conditions are straight lines and the
extrapolation at qf0 passes through the origin. It clearly
reveals the diffusive character of the two modes (they are
diffusive for the other samples too, which is not shown here).
Each slope leads to a ÆDæ0, and further to a ÆRhæ. The ÆRhæ (in
the following part of this paper, Rh is used for simplicity) of
fast modes are in the range 10-30 nm, while the Rh for slow
modes are in the range 100-300 nm. The above DLS and
SLS data indicate that the interchain association is dominant
in these PAA-g-PEO-g-dodecyl aqueous solutions within
all studied pH ranges. And there are about 20-100 single
polymer chains in each associate. At pH 4.0, the Rh of
Figure 2. Scattering vector (q) dependence of average characteristic
relaxation rate (Γ) of fast and slow relaxation modes for PAA-g-PEO-
13-g-dodecyl-25 aqueous solutions with pH 4.0 and 7.0, 20 ꢀC, Cpolymer
=
2.7 ꢀ 10-4 g mL-1, and CNaCl = 0.025 M.
associates are around 100 nm; but at pH 7.0 and 10.0, the
Rh increase to 200-300 nm. That is because the R of PAA
segments as well as its hydrophilicity increases with pH. So,
at pH 4.0, the associates are more compact than those at
higher pH.44
Figure 3 shows the plots of KC/Rvv(q) (a) and [KC/Rvv(q)]1/2
(b) versus q2 for PAA-g-PEO-g-dodecyl aqueous solution with
different compositions under pH 4.0 together with the linear
fitting of the plots (see eqs 1 and 2), where the slopes of the fitted

Article
Macromolecules, Vol. 43, No. 22, 2010 9537
Figure 3. Angular dependence of (a) KC/Rvv(q) and (b) [KC/Rvv(q)]1/2
of PAA-g-PEO-g-dodecyl aqueous solution under pH 4.0, 20 ꢀC,
Cpolymer = 2.7 ꢀ 10-4 g mL-1, CNaCl = 0.025 M.
Figure 5. Hydrophobic dodecyl content dependence of hydrodynamic
radius distributions and the apparent molecular weight of associates in
(a) PAA-g-dodecyl and (b) PAA-g-PEO-7-g-dodecyl aqueous solutions
at 20 ꢀC, Cpolymer =2.7 ꢀ 10-4 g mL-1, CNaCl = 0.025 M.
hydrophobic dodecyl content on the association of (a) PAA-
g-dodecyl and (b) PAA-g-PEO-7-g-dodecyl in aqueous solu-
tions at pH 4.0. For PAA-g-dodecyl, when the dodecyl
contents (fDod) are in the range 10-34 wt %, there is only
one single fast mode and the Mw,app is similar to a single
chain. So the hydrophobe associations of polymer-bound
dodecyl group occur within single polymer chain, leading to
the formation of unimer micelle. The Rh of unimer micelles
decreases with the increase of fDod, i.e. the micelles become
smaller and more collapsed. When the fDod increases to 40 wt %,
thereisstillonlyonesinglemode, butMw,app is 1.6 ꢀ 106 gmoL-1
(see Figure 3b), which means each micelle contains about
four single chains.
In PAA-g-PEO-7-g-dodecyl aqueous solution, there are
both hydrophobic and hydrogen-bonding interactions. At
low fDod, two diffusion modes are found, and the corre-
sponding Mw,app is 6.5 ꢀ 106 g moL-1, which means large
aggregates are formed. As fDod increases to 19 wt %, only a
single fast mode exists, and the Mw,app is the same as a single
chain, so intrachain association is dominant. A further
increase of fDod leads to the formation of large aggregates
again. These results indicate that proper high hydrophobe
content is favorable for intrachain association. Additionally,
comparing Figure 5a with Figure 5b, the hydrogen-bonding
association of PAA-PEO segment tend to form interchain
aggregates which will be discussed in detail later.
3. Effects of PEO Content on the Association of Graft
Polymer in Aqueous Solution. Figure 6 shows the effects of
PEO content on the association of PAA-g-PEO-g-dodecyl in
aqueous solution. In Figure 6a, the fDod is fixed at around
11 wt %. When the PEO content (fPEO) is 0%, i.e., for PAA-g-
dodecyl, there is only one single fast mode. Combined with
the Mw,app, the dominance of intrachain association can be
obtained. With the increase of fPEO to 7 wt %, two modes
emerge and interchain association is dominant. The further
increase of fPEO to 13 wt % induces no further change. In
figure 6b, the fDod is higher and fixed at around 22 wt %.
When fPEO is 0 and 7 wt %, intrachain association is
preferred. While at fPEO =13 wt %, interchain association
is dominant. These results indicate that the PEO chain in
graft polymer tends to induce interchain association. While,
as described in part 2, proper high dodecyl content is favor-
able for intrachain association. The competition of these
two factors resulted in the formation of unimer micelle at
Figure 4. pH dependence of hydrodynamic radius distributions and the
apparent molecular weight (Mw,app) of associates in (a) PAA-g-dodecyl-26
and (b) PAA-g-PEO-7-g-dodecyl-19 aqueous solutions at 20 ꢀC,
Cpolymer = 2.7 ꢀ 10-4 g mL-1, CNaCl = 0.025 M.
lines give the apparent value of Rg and the intercept represents
the apparent molar weight of the associates. For high molec-
ule weight structures (above several million g mol-1), the SLS
experimental data was analyzed as in Figure 3a, otherwise as in
Figure 3b.
Figure 4 shows that the association behaviors of PAA-g-
dodecyl-26 and PAA-g-PEO-7-g-dodecyl-19 aqueous solu-
tions are quite different from that mentioned above. At pH 4.0,
there is only a single fast mode, with Rh around 10 nm.
And Mw,app values of associates are about 3.5 ꢀ 105 g moL-1,
which are almost the same as that of a single polymer chain.
These results indicate that intrachain association is domi-
nant under these conditions, leading to the formation of
unimer micelles. With pH increase, a slow mode emerges,
which means large aggregate is formed. However, the rela-
tive amplitude of fast mode is larger than that in Figure 1,
which indicates that even at higher pH, these two polymers
have a strong tendency to form unimer micelle or smaller
aggregates.
2. Effects of Dodecyl Content on the Association of Graft
Polymers in Aqueous Solution. Figure 5 shows the effect of

9538 Macromolecules, Vol. 43, No. 22, 2010
Hao et al.
Figure 7. Intensity-intensity time correlation function [g(2)(t,q) - A]/A
of PAA-g-PEO-7-g -dodecyl-19 in aqueous solutions prepared in two
different procedures: adding a solution of copolymer in DMF into
water or adding water into copolymer-DMF solution, the inset is the
corresponding Rh distribution, pH 4.0, Cpolymer =2.7 ꢀ 10-4 g mL-1
CNaCl = 0.025 M, 20 ꢀC.
,
Figure 6. PEO content dependence of hydrodynamic radius distributions
and apparent molecular weight of associates in PAA-g-PEO-g-dodecyl
aqueous solutions at 20 ꢀC, with dodecyl contents: (a) ∼11 wt % and
(b) ∼22 wt %, pH 4.0, Cpolymer = 2.7 ꢀ 10-4 g mL-1, CNaCl = 0.025 M.
concentration inside aggregates, and am, Nm, and Dm are the
length, number, and diffusion coefficient of the monomer,
respectively. When τc , τe, two collided globules have no
time to stick together and they behave like two tiny non-
adhesive “elastic ball”. The concept of τc and τe is refined to
understand the formation of unimer micelle in this complex
system, although none of our polymer system goes through
phase separation. In order to obtain a stable globular phase,
it is necessary to decrease τc and increase τe. Equation 3
shows that, for a given polymer solution under a fixed set of
experimental conditions, l0, am, Nm, and Dm are constants,
one can only increase ÆDæ and jp to ensure τc , τe in order to
obtain a stable globular phase. It has been reported that long
polymer chain, diluted solution, proper hydrophobicity,
and fast microphase separation are favorable for achieving
τc , τe experimentally.24,26-28
In this study, the polymer aqueous solutions were pre-
pared by adding a small amount of polymer-DMF concen-
trated solution into a large amount of water. When the
polymer contacts selective solvent (water), it contracts in-
tramolecularly into a globule immediately. Then these initial
globules collide with each other. They can either adhere
together or bounce and separate, depending on the relation-
ship between τc and τe. Our results show that under most
conditions, interchain associations are dominant; Intrachain
associations only dominate at low pH values (pH 4.0) and
proper high dodecyl content. Under these conditions (with
high hydrophobicity), the initial graft polymer contraction
will lead to denser globules. And the smaller initial globular
size results in a higher ÆDæ, which leads to smaller τc. Mean-
while, the polymer concentration inside each globule (jp)
increases which makes larger τe, i.e., the more collapsed
chains are more difficult to relax. Therefore, τc , τe can be
achieved, leading to the formation of unimer micelle.
5. The Effects of Solution Preparation Procedure on the
Association of Graft Polymer. Figure 7 shows the intensity-
intensity time correlation function of PAA-g-PEO-7-g-
dodecyl-19 in aqueous solutions prepared in two different
procedures: adding a solution of copolymer in DMF drop-
wise into large amount of water or reverse as described in the
Experimental Section. In the former case, the time correla-
tion function only has one single relaxation mode, and the cor-
responding Rh is around 10 nm. As stated in part 2 of this section,
intrachain association is dominant under this specific condition.
The latter is prepared by adding large amount of water drop-
wise into copolymer solution in DMF (2.0 ꢀ 10-3 g mL-1). It
should be stated that at a higher initial concentration of
polymer solution in DMF, such as (1.0 ꢀ 10-2 g mL-1),
comparably low PEO content (0, 7 wt %) and relatively high
dodecyl content (19 wt %). The increase of PEO content or
decrease of dodecyl content will promote interchain association.
4. Physical Explanation of the Association Behavior from
Thermodynamic and Kinetic Point of View. As mentioned in
parts 1-3 in this section, in most cases, slow mode coexists
with fast mode, and the interchain associations dominate
and the amplitude of slow mode is more than 95%
(z-average). Thermodynamically, interchain associations
are more stable because they possess larger size and smaller
surface area, which lead to minor surface energy and Gibbs
free energy. On the contrary, intrachain associations are in a
higher Gibbs free energy metastable state (in a local potential
well). Usually, the thermo-fluctuations can overcome the
potential energy barrier between the metastable potential
well and the thermodynamic stable, lower surface energy
state, so the interchain associations can become dominant.
But under some specific conditions, such as a proper hydro-
phobic modification of polymer backbone and a certain pH
range, the potential energy well is too deep to be overcome by
thermo-fluctuations; the intrachain globules cannot “escape”
from the metastable wall. So the copolymer system is trapped
in the metastable, unimer state. We will describe this point in
kinetic detail as follows.
Li et al.45 showed that in the association process of
copolymer, the faster intrachain contraction can results in
smaller mesoglobules. The stability of such formed meso-
globular phase mainly depends on the coarsening dynamics.
Many studies demonstrated that in the phase separation
process of a polymer solution, the collision would not be
effective as long as the collision (or contact) time (τc) is
relatively smaller than the time needed to establish a perma-
nent chain entanglement (τe) between two approaching
globules.46-49
Quantitatively, Tanaka50,51 showed that τc and τe can be
roughly characterized as
am2Nm3jp
Dm
3=2
2
l0
l0
< τc <
and τe∼
ð3Þ
Ævæ
ÆDæ
where l0 is the interaction range, Ævæ and ÆDæ are the mean
thermal velocity and translational diffusion coefficient of
the aggregates, respectively, jp is the average polymer

Article
Macromolecules, Vol. 43, No. 22, 2010 9539
Figure 8. Schematic of competition between intrachain and interchain association in PAA-g-PEO-g-dodecyl aqueous solution with different dodecyl
contents or under different conditions.
adding water into the copolymer solution in DMF results in
precipitation. But a reduced initial copolymer concentration
(2.0 ꢀ 10-3 g mL-1) can result in a clear solution. If the copoly-
mer aqueous solution is prepared in this procedure, as shown in
figure 7, a slow mode at around 200 nm emerges, with Mw,app of
associates about 6.7 ꢀ 106 g moL-1, which indicates that
interchain association is dominant. Similar phenomenon has
also been reported by Li et al.45 and Itakura et al.,21 their results
showed that the aggregates obtained from a quick switch of
solvent quality from good to poor are much smaller than that in
a slow switching process. In the former case (adding polymer
DMF solution into water), solvent quality is quickly switched
from good to poor for dodecyl segments. When copolymer
contacts large amount of water, it experiences immediately
intense intrachain contraction, which increases ÆDæ and jp
simultaneously. Therefore, it is easier to attain τc , τe, and
resulting in unimer micelle dominance. In the latter case, water
is added dropwise into polymer solution in DMF, the solvent
quality decreased gradually. The initial intrachain contraction
is small, ÆDæ and jp only increases little, while the initial
polymer concentration is still high. All of these enhance the
chance for polymer chains to associate with each other and
form large aggregates.
All the discussion above can be schematically summarized
in Figure 8. During the association of amphiphilic graft
polymer in dilute solution, a competition between intrachain
and inerchain association is involved. In most cases, inter-
chain association is dominant, but under some specific
conditions (low pH, proper high dodecyl content, fast switch
of solvent quality), intrachain association is favored and lead
to the formation of unimer micelle. This phenomenon can be
explained by the competition of interaction time and entan-
glement time: those specific conditions can promote the
initial intrachain contraction, leading to τc , τe, thus prohib-
iting the resultant unimer micelles to interpenetrate with each
other to form interchain associations.
into water) promote intrachain association. These phenomena
can be explained by the competition between intermolecular
interaction time and entanglement time: the factors mentioned
above can enhance the initial intrachain contraction, which
increases relaxation time (τe) and reduces interaction time
(τc) of the approaching “globules”, and leading to τc , τe. The
interaction between these two intrachain globules behaves like
tiny “elastic balls” and their further merge/fusion become nearly
impossible during their interaction time (τc); thus, they can stay in
the metastable state and intrachain association become dominant
in the solution.
Acknowledgment. The financial support from the National
Natural Scientific Foundation of China Projects 50930003 and
20934005, NSF Young Scientists Fund (20804052), and the
Hong Kong Special Administration Region Earmarked Projects
CUHK4039/08P, 2160361, and CUHK4042/09P, 2160396, is
gratefully acknowledged.
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