HYDRODYNAMIC PROPERTIES OF STAR-LIKE AND HYPERBRANCHED POLYMERS
IN DILUTE SOLUTIONS
Tarabukina E.B., Filippov A.P., Tarasova E.V., Shpyrkov A.A., and Amirova A.I.
Institute of Macromolecular Compounds of Russian Academy of Sciences
Bolshoi Pr., 31, 199004, Saint-Petersburg, Russia
SAA@imc.macro.ru
The conformational and hydrodynamic properties of branched polymers were studied by light scattering, sedimentation, diffusion,
and viscometry. Star and hyperbranched macromolecules in solutions are characterized by the compact structure and the density of
polymer substance in molecular coil is higher than the values typical for linear polymers. The hydrodynamic behavior of investigated
polymers differs from those of linear molecules. In particularly, the hydrodynamic invariant for branched polymers is much smaller
than its values for linear chains and theoretical value for rigid spheres.
The goal of this paper is to investigate the features in properties of star and hyperbranched polymers in dilute
solutions and to study the influence of macromolecular architecture and chemical structure of repeating units
on hydrodynamic characteristics of polymer molecules.
Modern synthesis methods have allowed for the preparation of a great variety of polymers with complex
structure such as star polymers, hyperbranched polymers, and dendrimers. Macromolecules of these
polymers are built up of linear chain segments, but they represent new topological classes which differ
basically from linear chains. Consequently, it may be expected that polymers with complex architecture must
have unusual physical chemical properties. In particularly, conformation and hydrodynamic behavior of
individual branched macromolecules is differing strongly from those of linear chains.
In order to solve these questions we have used the methods of molecular optics and hydrodynamics. They are
the static and dynamic light scattering, the flow birefringence, the sedimentation-diffusion analysis, and
viscometry. We have determined the values of weight-average Mw and hydrodynamic MSD molecular masses,
the mean-square gyration radii Rg and mean hydrodynamic radii Rh of macromolecules, and their frictional
coefficients f.
Experiments were performed on samples and fractions of polymers which differ by molecular architecture
and chemical structure of repeating units. There are the star-shape systems (polyacrylates, polystyrenes,
polyisoprenes, and their star-like diblock copolymers) and the hyperbranched structures (polycarbosilanes,
polyaminoacids, and polyesters).
The hydrodynamic characteristics of star and hyperbranched polymers significantly differ from those for
linear polymers with similar chemical structure of repeating units and the same molecular weight M. The
intrinsic viscosity [] (rotational friction coefficient) and translation frictional coefficient f of star polymers
is smaller than the [] and f values of linear analogs. As it follows from theoretical predictions, the [ ] and f
do not depend on M and are determined by the number of the star arms [1, 2]. The difference in the [] and f
values became larger for hyperbranched polymers. Usually we observe the following experimental laws:
[]lin  []star  []hb and flin  fstar  fhb (the indexes lin, star, and hb designate the linear, star, and
hyperbranched polymers, consequently). For investigated branched polymers, the changes in molecular
weight dependences of hydrodynamic parameters take place. For example, the values of exponents a = 0.27
and b = 0.47 in Mark-Kuhn-Howink equations for hyperbranched polymethylallylcarbosilane (PCS) [3] is
smaller than the corresponding characteristics for linear polymers in a good solvent and larger than those for
dendrimers.
The features of hydrodynamic behavior of star and hyperbranched polymers are determined by form and size
of their macromolecules. The low values of [] and f for polymer complex structure suggest a rather high
density of polymer substance in the volume occupied by macromolecules in solution, that is, indicative of
their compact structure. For example, the hydrodynamic radius of PCS macromolecules is not higher than 4
nm at M = 75000 and their shape differs slightly from spherical (the asymmetry factors is p  1.4).
These experimental facts correspond to the data obtained by other authors [4] and theoretical predictions [2].
However, the analysis of character of hydrodynamic interaction in solutions of branched polymers leads to
unusual results. An important characteristic of the solution of macromolecules is provided by the so-called
hydrodynamic invariant [5]
A0  0 (
D0 2 / 3  [ ]S0 R 
) 

T
100(1  v  ) 
1/ 3
(1)
where D0 is the diffusion constant, S0 is the sedimentation constant, 0 is the solvent viscosity, v is the
specific partial volume, k is Bolzman constant, R is the universal gas constant, T is the absolute temperature,
10
A010 , erg/grad/mol
1/3
long linear
non-draining chain
3
rigid
sphere
2
1
1
3
1000
2
4
M
10000
100000
Figure 1. Dependences of A0 on polymer molecular weight M for hyperbranched polycarbosilanes (1) and
polyaminoacids (2), star polyacrylates (3) and polystyrenes (4).
Ф = [] M (6Rg2)-3/2 is Flory parameter, and P = f (6Rg2)-1/2/0 is hydrodynamic parameter. For linear
macromolecules, A0 is invariable over a wide molecular weight range and depends on character of
hydrodynamic interaction. In the case of long flexible-chain polymers, the mean experimental value of A0 is
3.210-10 erg/grad/mol1/3, while for rigid-chain macromolecules, A0 = 3.810-10 erg/grad/mol1/3 [5]. These
estimations are well consistent with the theoretical predictions. Figure 1 shows the hydrodynamic invariant
A0 as a function of M for investigated star and hyperbranched polymers. For star polymers and
polycarbosilanes, no systematic change in A0 is observed. The hydrodynamic invariant for hyperbranched
polyaminoacids is decreased with molecular weight increasing. It is very important that the A0 values for all
investigated polymers are smaller than values for linear macromolecules. In the case of PCS, the averaged
value of A0 is much smaller than that theoretically predicted for non-draining spheres (A0 = 2.8810-10
erg/grad/mol1/3), which is equal to minimum possible theoretical value. It is needed to note that the small
value of hydrodynamic invariant (A0  2.510-10 erg/grad/mol1/3) has been obtained for dendrimers [6]. The
reason for such pronounced difference remains unclear. In order to explain this experimental fact the
molecular model of statistical and hydrodynamic properties of branched polymers must be made more
precise. In conclusion it is pertinent to emphasize that the change in the A0 values is accompanied by the
change of Flory Φ and hydrodynamic P parameters. For example, the Φ values for polycarbosilanes are
increased from 2.51023 mol-1 (the most accurate result from experimental data of long flexible linear chains
[7]) at M = 3000 – 10000 to 71023 mol-1 at M  80000 (the theoretical value of Φ for rigid non-draining
spherical particle is 9.231023 mol-1).
Acknowledgements
The authors are grateful to the Russian Foundation for Basic Researches for a financial support (project No
08-03-99952).
References
[1] Zimm B.H., Stockmayer W.H. J. Chem. Phys. 17, 1301 (1949).
[2] Freire J.J. Adv. Polym. Sci. 143,
35 (1999).
[3] Tarabukina E.B., Shpyrkov A.A., Potapova D.V., Filippov A.P., Shumilkina N.A.,
Muzafarov A.M. Polymer Scince, Ser. A. 48, 974 (2006).
[4] Burchard W. Adv. Polym. Sci. 143, 113
(1999).
[5] Tsvetkov V.N. Rigid-Chain Polymers. New York, Plenum, 1989.
[6] Pavlov G.M.,
Korneeva E.V., Nepogod’ev S.A., Jumel K., Harding S.S. Polymer Scince, Ser. A. 40, 1282 (1998).
[7]
Miyaki Y., Einaga Y., Fujita H., Fukuda M. Macromolecules. 13, 588 (1980).