Structure and dynamics of irregular multiarm star polymers
Melt properties of highly branched star polymers consisting of a 1,2-polybutadiene core and nearly 270 arms of 1,4-polybutadiene with varying sizes have been investigated using small angle X-ray scattering (SAXS) and dynamic rheological measurements in the linear viscoelastic limit. Despite thei...
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Інститут фізики конденсованих систем НАН України
2002
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| Цитувати: | Structure and dynamics of irregular multiarm star polymers / D. Vlassopoulos, T. Pakula, J. Roovers // Condensed Matter Physics. — 2002. — Т. 5, № 1(29). — С. 105-116. — Бібліогр.: 23 назв. — англ. |
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irk-123456789-1205812017-06-13T03:05:21Z Structure and dynamics of irregular multiarm star polymers Vlassopoulos, D. Pakula, T. Roovers, J. Melt properties of highly branched star polymers consisting of a 1,2-polybutadiene core and nearly 270 arms of 1,4-polybutadiene with varying sizes have been investigated using small angle X-ray scattering (SAXS) and dynamic rheological measurements in the linear viscoelastic limit. Despite their difference in internal structure compared to the regular stars with 128 arms and spherical dendritic core, these polymers exhibit the same features: a liquid-like ordering resulting from their specific intramolecular monomer density distribution. This leads to a dual terminal viscoelastic relaxation, consisting of a fast arm relaxation and a slow structural relaxation mechanisms. Both modes conform quantitatively to the generic behaviour of multiarm star polymers, suggesting a universality of the behaviour of highly branched macromolecular objects. Досліджено властивості розчинення сильно розгалужених зіркових полімерів із основою 1,2-полібутадієну і близько 270 гілок 1,4-полібутадієну змінного розміру, використовуючи рентгенівське випромінювання при малих кутах і динамічні реологічні вимірювання у границі лінійної в’язкоеластичності. Нехтуючи різницею внутрішньої структури, порівняно із періодичними зірками із 128 відгалуженнями і сфе- ричною деревоподібною основою, ці полімери мають ту ж рису: рідиноподібне впорядкування, що є результатом специфічного розподілу густини мономерів. Це приводить до кінцевої в’язкоеластичної релаксації, що складається із швидкої релаксації відгалужень і повільної структурної релаксації. Обидві моди кількісно узгоджуються із характерною поведінкою, припускаючи універсальність поведінки сильнорозгалужених макромолекулярних об’єктів. 2002 Article Structure and dynamics of irregular multiarm star polymers / D. Vlassopoulos, T. Pakula, J. Roovers // Condensed Matter Physics. — 2002. — Т. 5, № 1(29). — С. 105-116. — Бібліогр.: 23 назв. — англ. 1607-324X PACS: 61.25.Hq, 83.10.Nn, 81.05.Lg DOI:10.5488/CMP.5.1.105 http://dspace.nbuv.gov.ua/handle/123456789/120581 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Melt properties of highly branched star polymers consisting of a 1,2-polybutadiene
core and nearly 270 arms of 1,4-polybutadiene with varying
sizes have been investigated using small angle X-ray scattering (SAXS)
and dynamic rheological measurements in the linear viscoelastic limit. Despite
their difference in internal structure compared to the regular stars with
128 arms and spherical dendritic core, these polymers exhibit the same
features: a liquid-like ordering resulting from their specific intramolecular
monomer density distribution. This leads to a dual terminal viscoelastic relaxation,
consisting of a fast arm relaxation and a slow structural relaxation
mechanisms. Both modes conform quantitatively to the generic behaviour
of multiarm star polymers, suggesting a universality of the behaviour of
highly branched macromolecular objects. |
| format |
Article |
| author |
Vlassopoulos, D. Pakula, T. Roovers, J. |
| spellingShingle |
Vlassopoulos, D. Pakula, T. Roovers, J. Structure and dynamics of irregular multiarm star polymers Condensed Matter Physics |
| author_facet |
Vlassopoulos, D. Pakula, T. Roovers, J. |
| author_sort |
Vlassopoulos, D. |
| title |
Structure and dynamics of irregular multiarm star polymers |
| title_short |
Structure and dynamics of irregular multiarm star polymers |
| title_full |
Structure and dynamics of irregular multiarm star polymers |
| title_fullStr |
Structure and dynamics of irregular multiarm star polymers |
| title_full_unstemmed |
Structure and dynamics of irregular multiarm star polymers |
| title_sort |
structure and dynamics of irregular multiarm star polymers |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2002 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120581 |
| citation_txt |
Structure and dynamics of irregular
multiarm star polymers / D. Vlassopoulos, T. Pakula, J. Roovers // Condensed Matter Physics. — 2002. — Т. 5, № 1(29). — С. 105-116. — Бібліогр.: 23 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT vlassopoulosd structureanddynamicsofirregularmultiarmstarpolymers AT pakulat structureanddynamicsofirregularmultiarmstarpolymers AT rooversj structureanddynamicsofirregularmultiarmstarpolymers |
| first_indexed |
2025-07-08T18:10:12Z |
| last_indexed |
2025-07-08T18:10:12Z |
| _version_ |
1837103279774892032 |
| fulltext |
Condensed Matter Physics, 2002, Vol. 5, No. 1(29), pp. 105–116
Structure and dynamics of irregular
multiarm star polymers
D.Vlassopoulos 1 , T.Pakula 2 , J.Roovers 3
1 Foundation for Research and Technology-Hellas (FO.R.T.H.)
Institute of Electronic Structure and Laser,
71110 Heraklion, Crete, Greece
2 Max-Planck Institute for Polymer Research,
Postfach 3148, 55021 Mainz, Germany
3 National Research Council,
Institute for Chemical Process and Environmental Technology, Ottawa,
Ontario K1A0R6, Canada
Received October 1, 2001
Melt properties of highly branched star polymers consisting of a 1,2-po-
lybutadiene core and nearly 270 arms of 1,4-polybutadiene with varying
sizes have been investigated using small angle X-ray scattering (SAXS)
and dynamic rheological measurements in the linear viscoelastic limit. De-
spite their difference in internal structure compared to the regular stars with
128 arms and spherical dendritic core, these polymers exhibit the same
features: a liquid-like ordering resulting from their specific intramolecular
monomer density distribution. This leads to a dual terminal viscoelastic re-
laxation, consisting of a fast arm relaxation and a slow structural relaxation
mechanisms. Both modes conform quantitatively to the generic behaviour
of multiarm star polymers, suggesting a universality of the behaviour of
highly branched macromolecular objects.
Key words: star polymers, structure, rheology, linear viscoelasticity,
relxation processes, dynamics
PACS: 61.25.Hq, 83.10.Nn, 81.05.Lg
1. Introduction
Star polymers with a high number of arms (functionality) and a spherical core,
thereafter called “regular” multiarm stars (see figure 1) are a class of architecturally
complex soft materials with properties that can be regarded as intermediate between
those characteristic for polymers (the individual arms) and those characteristic for
colloids (with a compact spherical shape) [1–4]. This can be rationalized by consid-
ering, that, on the one hand the polymers (a contiguous sequence of N covalently
bonded monomers) are characterized by weak interactions at monomeric scales, of
c© D.Vlassopoulos, T.Pakula, J.Roovers 105
D.Vlassopoulos, T.Pakula, J.Roovers
chart 1
Figure 1. Schemes of molecular structures of regular (left) and irregular (right)
multiarm star polymers.
O(kBT ) or less, and by a relevant correlation length ξc of O(nm) independent of N .
Consequently, very high concentrations are needed in order to reach short range or-
dering, if attainable at all. On the other hand, colloidal dispersions of solid particles
with the radius R0 in a host fluid, exhibit a size-dependent dynamic behaviour with
correlation length of O(R0), with their long-range ordering occurring at relatively
low number densities [2]. As a result of this, multiarm star polymers exhibit a very
rich behaviour combining both polymeric and colloidal properties, whose relative
importance can be tuned at the molecular level by variation of arm size and arm
number.
In recent years, we have focused on the systematic study of the ordering and
dynamics of regular multiarm star polymers, both in solution and in the melt. These
polymers were synthesized anionically using chlorosilane chemistry and are nearly
monodisperse [5]. Owing to their topology, they exhibit a specific monomer density
distribution. This justifies considering these macromolecules as particles [6] with
a core-corona morphology and two characteristic length scales: a small, ξ c, which
represents the size of a self-avoiding segment (interaction blob) and is of polymeric
nature, and a large, R0, which represents typically the overall radius of the star and
is of colloidal nature [1].
Molecularly dispersed in a good solvent, such regular stars exhibit liquid-like or-
der above their overlap concentration c∗, as demonstrated by SANS experiments [7].
The reason for their liquid-like structure formation is, in this case, the enhanced os-
motic pressure that outbalances the elastic energy of the entropically stretched arms
[10]. This type of weak order persists in the melt state as well [9,10], however, as a
consequence of excluded volume effects on the macromolecular scale because of the
intramolecular monomer density reaching the values of the bulk material [11]. The
dynamics in non-dilute solutions revealed the presence of cooperative diffusion (poly-
106
Irregular multiarm star polymers
Table 1. Molecular characteristics of irregular star polymers (Mw/Mn < 1.1).
Sample f Ma (g/mol) Tg (◦C)
LS2 267 4460 –93
LS3 278 9300 –92
LS4 267 18300 –91
LS5 269 29300 –92
LS6 263 42300 –92
meric) and self diffusion and structural relaxation (colloidal) modes [4,12], whereas
unusual thermal gelation behaviour was detected as a result of the strong excluded
volume interactions [13]. In the melt state, the dynamics was characterized by a
two-step terminal viscoelastic relaxation, consisting of a fast mode related to arm
relaxation (independent of functionality f , but strongly dependent on arm molecu-
lar weight, Ma) and of a slow mode attributed to structural relaxation (cooperative
rearrangements of stars, strongly dependent on both f and Ma) [9,10,14].
In this paper, we extend the above work by addressing the effects of internal
structural changes of multiarm stars to their structure and dynamic properties in
the melt. In particular, we consider multiarm stars with very high functionality
(f ≈ 270), which, however, have been prepared by anionic means different from the
case of regular stars and, as a consequence, have a non-spherical core region. We
find that this microstructural difference does not affect their order and rheological
characteristics, and, based on these results we suggest that the studied systems
belong to the same universality class of highly branched polymers.
2. Experimental
2.1. Materials
The synthesis of multiarm star polymers with 1,4-polybutadiene arms and a very
high functionality (about 270) has been described in detail elsewhere [15]. Briefly,
a short 1,2-polybutadiene backbone chain was hydrosilylated with HSi(CH3)Cl2
yielding two coupling sites per monomer unit; the latter were substituted with
1,4-polybutadiene by adding of poly(butadienyl)lithium. Because the yield of the
hydrosilylation reaction of the polymer did not exceed 80%, the architecture of the
resulting highly branched polymer was such that on average four out of five monomer
segments were substituted with a total of eight arms. The reason for naming these
stars “irregular” stems from the fact that their arms are not grafted to a truly
spherical dendritic core, as in the case of the regular multiarm stars with function-
alities of 64 and 128 [5]. Despite this difference, the irregular stars still possess a
nearly spherical shape, as revealed by SANS measurements in dilute solution and
their comparison to respective data from regular stars [16], but there is certain-
ly a small difference in internal structure (see figure 1). The important molecular
characteristics of the irregular stars used in this work are listed in table 1.
107
D.Vlassopoulos, T.Pakula, J.Roovers
2.2. Small angle X-ray scattering (SAXS)
SAXS measurements were conducted using a rotating anode (Rigaku 18 kW)
X-ray beam with a pinhole collimation and a two-dimensional detector (Siemens)
with 512 × 512 pixels. A double graphite monochromator for the Cu Kα radiation
(λ = 0.154 nm) was used. The beam diameter was about 0.5 mm and the distance
of the sample to the detector was 1.3 m. Measurements were performed at room
temperature for samples of about 1mm thickness. The recorded scattered intensity
distributions were integrated over the azimuthal angle and are presented as functions
of the scattering vector (s = 2 sin θ/λ, where θ is the scattering angle).
2.3. Dynamic rheology
Small amplitude oscillatory shear measurements were carried out over a wide
temperature range (from about – 100 ◦C to 150 ◦C) using a Rheometric Scientif-
ic mechanical spectrometer (ARES 2KFRTN1). Parallel plates with 8 and 6 mm
diameter and 1 mm gap were used, under dry nitrogen atmosphere. The mate-
rial/measurement stability and the linear viscoelastic regime were confirmed via
dynamic time sweep and dynamic strain sweep tests at different frequencies and
temperatures. Frequency dependencies of G′ and G′′ measured within the frequency
range 0.01−100 rad/s at various temperatures were used to construct master curves
providing G′ and G′′ data over a very broad range of frequencies. Only shifts along
the frequency scale have been performed. This procedure provided a temperature
dependence of shift factors (log aT vs. T ). The relaxation times corresponding to
the transition to the Newtonian flow range at low frequencies and to the glassy
range at high frequencies at the reference temperature have been determined as
τ(Tref) = 1/ωc, where ωc is the frequency at which the G′ and G′′ dependencies
cross each other. Relaxation times at other temperatures are then derived using
τ(T ) = τ(Tref) + log aT .
3. Results and discussion
Figure 2 depicts the SAXS intensity distributions for the samples investigated.
It is noted that the presence of carbosilane units in the 1,2-polybutadiene based
core of the LS samples provides the necessary electron density contrast for SAXS
measurements. It is evident that all three samples measured, namely LS2, LS3 and
LS4, exhibit the identifying signature of liquid-like order, i.e., a weak broad primary
peak in the scattered intensity (at a value of the scattering wave vector qpeak), ac-
companied by a weaker and broader secondary peak at a distance roughly
√
3 qpeak.
Note that the primary peak position moves to lower values of the scattering wave
vector and the peak looses intensity as the arm molecular weight is increased; even-
tually, for the samples LS5 and LS6, the primary peak position could not be detect-
ed by SAXS. From the peak intensity position, the distances between the nearest
neighbouring star centers were calculated by considering that the formed liquid-like
structure is controlled by two-body correlations. In that case, these distances are
108
Irregular multiarm star polymers
0.1
100
3.6 3.8 4.0 4.2 4.4 4.6
1.0
1.1
1.2
1.3
In
te
n
si
ty
[
a
.u
.]
s[nm-1]
lo
g(
d/
nm
)
log(M
a
)
Figure 2. SAXS intensity distribution from measurements with the LS2 (△),
LS3 (•) and LS4 (�) irregular multiarm star melt samples, indicating the weak
liquid-like ordering. Arrows show the position of the primary peak speak which
corresponds to the characteristic length scale of the ordered structure. Inset: The
dependence of the characteristic distance between neighbouring star “centers”,
d = 1.23/speak, on the arm molecular weigh for LS (△) and regular multiarm
stars with f = 128 arms (�) from [10]. The dotted line denotes the slope of 1/3
(see text).
-12 -10 -8 -6 -4 -2 0 2
2
4
6
8
structural
arm
Rouse
segmental
lo
g
(G
' /
P
a)
,
lo
g
G
''
log (ω / rad/s)
Figure 3. Dynamic frequency sweeps of stars LS2 (squares), LS3 (circles) and LS4
(up triangles) with reference temperature Tref = 176 K. Open symbols refer to
G′′ and closed symbols refer to G′. Arrows indicate (from right to left) segmental,
Rouse-like, arm and slow structural relaxation modes.
109
D.Vlassopoulos, T.Pakula, J.Roovers
150 200 250 300 350 400
-10
-8
-6
-4
-2
0
2
4
6
8
T
ref
=190K
lo
g
a
T
T [K]
Figure 4. Temperature dependence of the frequency shift factors for Tref = 190 K
and various stars: Closed symbols refer to regular multiarm stars with 64 and 128
arms, and open symbols refer to the five irregular multiarm stars, namely LS2,
LS3, LS4, LS5 and LS6.
given by d ≈ 1.23/speak with speak = qpeak/2π, which for LS2, LS3 and LS4 amounts
to 10.4, 15.4 and 19.8 nm, respectively. The inset in figure 2 shows the dependence of
d on the arm molecular weight. In this plot, respective SAXS data from regular stars
with f = 128 are also included for comparison. The dotted line through the data
has a slope of 0.33, representative of d ∼ M
1/3
a , typical for a cubic arrangement.
Although one could argue that the present SAXS data slightly deviate from this
relationship, the information available is not sufficient to support such a statement.
More data with a large variety of (yet unavailable) stars would be needed to tackle
this interesting point, which, if indeed true, may relate to the internal structural
differences between regular and irregular multiarm stars.
Typical results of the dynamic response of the LS stars melts, determined by
means of the rheological measurements, are shown in figure 3, which depicts the
frequency dependence of the storage and loss moduli, G′ and G′′, respectively. In
order to obtain the complete information on the material’s response, from the high-
frequency glass region to the low-frequency liquid region, measurements at different
temperatures were combined into master curves in figure 3, by shifting all data
along the frequency axis, according to the time-temperature superposition principle.
Interestingly, all star 1,4-polybutadienes studied irrespectively of functionality and
regularity (including the LS samples of this work) are found to exhibit the same
thermorheologically simple behaviour, as indicated in figure 4, which shows the
temperature dependence of the frequency shift factor αT . The well known WLF
expression logαT = −c1(T − Tref)/(c2 + T − Tref) [17] represents all data well with
110
Irregular multiarm star polymers
10-11 10-9 10-7 10-5 10-3 10-1 101 103
101
102
103
104
105
106
107
108
109
G
',
G
''
[P
a
]
ω [rad/s]
Figure 5. Comparison of the frequency spectra of LS2 with Tref = 176 K with
the theory of Milner and McLeish (solid curve for G′ and dotted curve for G′′)
for the arm relaxation process.
Tref = 190 K and fitted values c1 ≈ 12 and c2 ≈ 50 K, suggesting a universality in
behaviour.
Starting from the higher frequencies of the master curves in figure 3, we note the
glass transition region (extending up to the crossover frequency ωs), the Rouse-like
transition regime (ωe), the rubbery plateau (ωR) and the terminal region. Note that
the plateau modulus G0
N has the same value for the three LS samples in figure 3,
as expected, and, moreover, it is nearly identical with that of the regular multiarm
star polymers with 64 and 128 arms (as well as lower functionality entangled star
polymers), yielding a value of the entanglement molecular weight M e = ρRT/G0
N of
about 1850 g/mol, in accord with literature values for 1,4-polybutadiene [17]. Thus,
the partial stretching of the arms in the near-core region due to high functionality
and the differences in internal structure do not seem to affect Me appreciably, within
the resolution of the experimental techniques used.
The terminal region is characterized by the two-step decay [18], in sharp contrast
to the single terminal relaxation processes of the low functionality stars, linear ho-
mopolymers or colloidal hard spheres, but in agreement with the regular multiarm
stars. The faster one of the two relaxations in the terminal region (ωR) is due to the
star arm relaxation, as already established for regular stars of varying functionality
[10, 11]. In addition, this relaxation mode can be well described by the recent theory
of Milner and McLeish for the arm relaxation, using the concept of dynamic dilution
with the appropriate scaling of entanglement length, and incorporating the effects
of higher Rouse modes on arm retraction [19]. This theory, developed in the frame-
work of the tube model, has been able to quantitatively capture the arm relaxation
of stars of different chemistry and functionality [14]. Its success with the irregular
stars is demonstrated in figure 5. Note that this theory uses as parameters only the
111
D.Vlassopoulos, T.Pakula, J.Roovers
entanglement molecular weight Me, the respective plateau modulus G0
N , and the
(Rouse) relaxation time of an entanglement segment τe, which are determined from
the data. The complex viscoelastic modulus G∗(ω) is obtained from the expression:
G∗(ω) = (x+ 1)G0
N
1
∫
0
ds(1− s)x
[
iωτ(s)
1 + iωτ(s)
]
,
where s is the relaxed fraction of the arm. The total arm relaxation time
τ(s) =
(
e−Ueff (s)
τearly(s)
+
1
τactivated(s)
)−1
incorporates an early fast diffusion of the free end of the arm (τearly) and an activated
arm retraction (τactivated), and depends on τe and on the number of entanglements
per arm; the latter is reduced by the dynamic dilution effect as Me(s) = Me/(1−s)x,
with x = 4/3 [20]. From the results in figure 5, the assignment of the faster terminal
process to arm relaxation is confirmed.
Figure 6 represents the dependence of the arm relaxation time under isofrictional
conditions (normalized to the segmental time) τa/τs on the arm degree of polymer-
ization, Na (a), or alternatively on the number of entanglements, Ma/Me (b), for
a variety of star polymers with functionality ranging from 4 to 270, regular and
irregular. The universal validity of this type of plot for all systems is noteworthy.
It is also important to point out that these experimental results are in excellent
agreement with simulation results [10, 11]).
The slow relaxation process (ωc) in figure 3 relates to the topological hetero-
geneity of the LS stars, yielding to distinct spatial correlations, as demonstrated
in figure 2. Here, despite the non-spherical core, the very high arm number leads
probably to a large monomer density around the star centers of mass and eventually
results in the observed liquid-like order on the macromolecular scale. This type of
structure is related to the excluded volume interaction between compact but de-
formable macromolecular elements in a dense system. Evidence from experiments
and simulations with regular multiarm stars (with f = 128) [9,10,11,14] indicates
that the slow process can be attributed to translational cooperative rearrangements
of stars (on macromolecular scale) within the ordered state. These rearrangements
are of the same character as these suggested for the cooperative rearrangements in
low molecular liquids [21]. Note that because of the presence of the slow relaxation,
the zero shear viscosity η0 of multiarm stars is not independent of the functionality
f , as in the case of low-f stars [22].
Recently, a mean-field scaling theory was proposed to account for the slow mode.
It considers an activated process involving a partial disentanglement of the interpen-
etrating stars followed by a displacement of a star in a neighbouring ‘cell’, a distance
of its size apart, a process controlled by the free energy of the corona elastic deforma-
tion (arm stretching). The net result of this analysis suggests the following scaling
112
Irregular multiarm star polymers
1.8 2.0 2.2 2.4 2.6 2.8 3.0
5
6
7
8
9
10
11
lo
g
( τ
a/ τ
s)
logN
a
(a)
0 5 10 15 20 25 30
5
6
7
8
9
10
11
lo
g(
τ a/
τ s)
M
a
/M
e
(b)
Figure 6. Isofrictional arm relaxation times (τa/τs) against the arm degree of
polymerization (Na), (a), or the number of entanglements (Ma/Me), (b), for
the irregular star LS samples (◦); for comparison respective data from regular
polybutadiene stars with f=128 (▽), f=64 (�), f=32 (♦), f=18 (△) and f = 4
(⋆) are also shown.
113
D.Vlassopoulos, T.Pakula, J.Roovers
1E7 1E8 1E9 1E10 1E11
6
8
10
12
lo
g(
τ sl
ow
/τ
0)
f2.5(N
a
/N
e
)5
Figure 7. Normalized slow relaxation time (to the segmental time) τslow/τs
against f 2.5(Na/Ne)
5 for irregular multiarm stars (f = 270) LS (◦); for com-
parison, respective data from regular multiarm stars with functionality f = 64
(♦) and f = 128 (�), are also shown. The dotted line serves as a guide to the
eye.
relation for the structural time τslow [14]:
τslow
τs
∼ α−1/3f 11/9N26/9
a N−1
e exp
[
X1
α
f 5/3
N
1/3
a
+X2α
2 N
11/3
a
N3
e f
4/3
]
,
where α = (a2υ−2/3) and a is the monomer size, and X1 and X2 are unspecified
numerical constants. The main outcome is the strong dependence of the structural
relaxation on both functionality and arm molecular weight, in qualitative agreement
with the experimental findings from the stars for which the slow process could be
detected (f = 64 and 128), as well as with the simulations for stars up to 64 arms
[10, 11]. For these systems, the extracted slow times were found to scale approxi-
mately with arm functionality and molecular weight as τ slow/τs ∼ f 2.5N5
a . Actually,
figure 7 depicts τslow/τs against f
2.5(Na/Ne)
5 for both regular (f = 64, 128) and the
irregular multiarm star polymers; it is apparent that the behaviour of the stars is
rather universal with respect to their structural relaxation as well. The qualitative
agreement of the theoretical prediction (strong f and Na dependence) with the data
is satisfactory, and was obtained using typical values for the numerical constants
X1 = 0.0040 and X2 = 0.0075.
Simulations of comb shaped macromolecules in dense systems, reported elsewhere
[23], indicate that the dynamics of such polymers having comparable lengths of the
backbone and of the side chains are similar to the behaviour of stars because in
both cases the slowest relaxation is controlled by the translational motion of the
114
Irregular multiarm star polymers
compact macromolecules. This can be considered as confirmed by the experimental
results presented here. The simulation has further shown that a cross-over to the
mechanism controlled by the orientation relaxation takes place when the length of
the backbone starts to considerably exceed the length of side chains (arms). Such
a behaviour has also been experimentally observed but for polymers with a large
persistence length and the arms much shorter than the backbone length [23].
4. Conclusions
The investigation of melts of irregular highly branched star 1,4-polybutadienes
with about 270 arms revealed striking similarities to their regular counterparts of
functionality up to 128. Despite their difference in internal structure, these polymers
exhibit liquid-like ordering resulting from their heterogeneous monomer density dis-
tribution and the related macromolecular excluded volume effects. In addition, their
low-frequency dynamics is characterized by a dual viscoelastic relaxation, consisting
of a fast arm relaxation and slow structural relaxation processes. It is concluded
that the behaviour of such highly branched macromolecular objects is independent
of the details of the core structure as long as the global shape of the compact objects
does not deviate considerably from a spherical one.
5. Acknowledgements
The assistance of M.Kapnistos is gratefully acknowledged. Partial support has
been received by the E.U. (grant HPRN-CT-2000-00017).
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Структура і динаміка нерегулярних
багатоланцюгових зіркових полімерів
Д.Влассопулос 1 , Т.Пакула 2 , Дж.Руверс 3
1 Фонд досліджень та технології – Геллас
Інститут вивчення електронної структури та лазерів,
71110 Геракліон, Кріт, Греція
2 Інститут ім. Макса Планка з дослідження полімерів,
55021 Майнц, Німеччина
3 Національна рада з наукових досліджень,
Інститут хімічних процесів та природозберігаючих технологій,
Оттава, Онтаріо K1A0R6, Канада
Отримано 1 жовтня 2001 р.
Досліджено властивості розчинення сильно розгалужених зіркових
полімерів із основою 1,2-полібутадієну і близько 270 гілок 1,4-полі-
бутадієну змінного розміру, використовуючи рентгенівське випромі-
нювання при малих кутах і динамічні реологічні вимірювання у грани-
ці лінійної в’язкоеластичності. Нехтуючи різницею внутрішньої струк-
тури, порівняно із періодичними зірками із 128 відгалуженнями і сфе-
ричною деревоподібною основою, ці полімери мають ту ж рису: ріди-
ноподібне впорядкування, що є результатом специфічного розподі-
лу густини мономерів. Це приводить до кінцевої в’язкоеластичної ре-
лаксації, що складається із швидкої релаксації відгалужень і повіль-
ної структурної релаксації. Обидві моди кількісно узгоджуються із ха-
рактерною поведінкою, припускаючи універсальність поведінки си-
льнорозгалужених макромолекулярних об’єктів.
Ключові слова: зіркові полімери, структура, реологія, лінійна
в’язкоеластичність, релаксаційні процеси, динаміка
PACS: 61.25.Hq, 83.10.Nn, 81.05.Lg
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