Tuning polymer thickness: Synthesis and scaling theory of homologous series of dendronized polymers

Article abstract of DOI:10.1021/ja9032132

The thickness of dendronized polymers can be tuned by varying their generation g and the dendron functionality X. Systematic studies of this effect require (i) synthetic ability to produce large samples of high quality polymers with systematic variation o

Full text of DOI:10.1021/ja9032132

Published on Web 07/31/2009
Tuning Polymer Thickness: Synthesis and Scaling Theory of
Homologous Series of Dendronized Polymers
Yifei Guo,† Jacco D. van Beek,‡ Baozhong Zhang,† Martin Colussi,† Peter Walde,†
Afang Zhang,*,† Martin Kro¨ger,† Avraham Halperin,*,§ and A. Dieter Schlu¨ter*,†
Department of Materials, Institute of Polymers, Swiss Federal Institute of Technology, ETH
Zurich, HCI J 541, 8093 Zurich, Switzerland, Department of Chemistry and Applied Biological
Sciences, Swiss Federal Institute of Technology, ETH Zurich, 8093 Zurich, Switzerland, and
Laboratoire de Spectrome´trie Physique (LSP) CNRS UniVersite´ Joseph Fourier, BP 87,
38402 Saint Martin d’Hères cedex, France
Received April 22, 2009; E-mail: afang.zhang@mat.ethz.ch; avraham.halperin@ujf-grenoble.fr;
ads@mat.ethz.ch
Abstract: The thickness of dendronized polymers can be tuned by varying their generation g and the dendron
functionality X. Systematic studies of this effect require (i) synthetic ability to produce large samples of high
quality polymers with systematic variation of g, X and of the backbone polymerization degree N, (ii) a theoretical
model relating the solvent swollen polymer diameter, r, and persistence length, λ, to g and X. This article presents
an optimized synthetic method and a simple theoretical model. Our theory approach, based on the
Boris-Rubinstein model of dendrimers predicts r ∼ n1/4g1/2 and λ ∼ n2 where n ) [(X - 1)g - 1]/(X - 2) is the
number of monomers in a dendron. The average monomer concentration in the branched side chains of a
dendronized polymer increases with g in qualitative contrast to bottle brushes whose side chains are linear.
The stepwise, attach-to, synthesis of X ) 3 dendronized polymers yielded gram amounts of g ) 1-4 polymers
with N ≈ 1000 and N ≈ 7000 as compared to earlier maxima of 0.1 g amounts and of N ≈ 1000. The method
can be modified to dendrons of different X. The conversion fraction at each attach-to step, as quantified by
converting unreacted groups with UV labels, was 99.3% to 99.8%. Atomic force microscopy on mixed polymer
samples allows to distinguish between chains of different g and suggests an apparent height difference of 0.85
nm per generation as well as an increase of persistence length with g. We suggest synthetic directions to allow
confrontation with theory.
polymers1 and regularly branched, dendron side chains leading
to dendronized polymers (Figure 1).2 This paper focuses on the
second family. The main result reported in this article is the
large scale synthesis of a homologous series of long dendronized
polymers whose backbone monomers carry dendrons. To
underline the polymer physics interest in the homologous series
of dendronized polymers we first briefly discuss the theoretical
scaling behavior of their thickness and persistence length with
respect to n. The conformations of the polymers are character-
ized via analysis of their AFM images. This method permits
fast data acquisition and analysis but introduces effects due to
surface interactions and the preparation method.
I. Introduction
Tuning the thickness of a polymer requires chemical modi-
fication of the backbone monomers, repeat units, by introducing
substituents. Among the possible substituents, it is useful to
distinguish between two extreme categories: Small groups such
as phenyl or halide and side chains of different length and
branching. The second category is of special interest because
the number of monomers in the side chain, n, provides an
adjustable tuning parameter of their thickness and persistence
length. In other words, producing a homologous series of
polymers that differ only in n allows studying the variation in
thickness, persistence length and related physical properties as
a function of n. From a chemistry point of view such polymers
are of interest because they are endowed with a large number
of end groups permitting control of solubility as well as further
chemical modification. From a polymer physics perspective they
afford the possibility of studying the scaling behavior with
respect to n in addition to the familiar scaling behavior with
respect to the backbone polymerization degree N. Among the
side chains utilized, it is helpful to distinguish between two
extremes: linear nonbranched chains producing “bottle brush”
(1) For example, see: (a) Tsukahara, Y.; Namba, S. I.; Iwasa, J.; Nakano,
Y.; Kaeriyama, K.; Takahashi, M. Macromolecules 2001, 34, 2624–
2629. (b) Fischer, K.; Schmidt, M. Macromol. Rapid Commun. 2001,
22, 787–791. (c) Shinoda, H.; Miller, P. J.; Matyjaszewski, K.
Macromolecules 2001, 34, 3186–3194. (d) Zhang, M.; Breiner, T.;
Mori, H.; Mu¨ller, A. H. E. Polymer 2003, 44, 1449–1458. (e) Li, C.;
Gunari, N.; Fischer, K.; Janshoff, A.; Schmidt, M. Angew. Chem.,
Int. Ed. 2004, 43, 1101–1104. (f) Bolisetty, S.; Airaud, C.; Xu, Y.;
Mueller, A. H. E.; Harnau, L.; Rosenfeldt, S.; Lindner, P.; Ballauff,
M. Phys. ReV. E 2007, 75, 040803.
(2) (a) Schlu¨ter, A. D.; Rabe, J. P. Angew. Chem., Int. Ed. 2000, 39, 864–
883. (b) Zhang, A.; Shu, L.; Bo, Z. S.; Schlu¨ter, A. D. Macromol.
Chem. Phys. 2003, 204, 328–339. (c) Frauenrath, H. Prog. Polym.
Sci. 2005, 30, 325–384. (d) Schlu¨ter, A. D. Top. Curr. Chem. 2005,
245, 151–191.
† Department of Materials, Swiss Federal Institute of Technology.
‡ Department of Chemistry and Applied Biosciences, Swiss Federal
Institute of Technology.
§ Universite´ Joseph Fourier.
9
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J. AM. CHEM. SOC. 2009, 131, 11841–11854 11841

A R T I C L E S
Guo et al.
Figure 1. Dendronized polymers (b) vs bottle brushes (d). In both
architectures the polymer comprises a semiflexible backbone (c) carrying
side chains. The side chains in the dendronized polymers are repeatedly
branched dendrons (a) while in the bottle brush the side chains are linear.
For simplicity we depict dendrons comprising of monomers jointed by rigid
rod like bonds.
Figure 2. Synthetic Strategies: In the “attach to” route, P units carrying
each two blocked functionalities (a) are polymerized thus forming a g ) 1
dendronized polymer PG1 (b). The resulting polymer is deblocked (c) and
reacted with blocked D units (d) to yield a g ) 2 dendronized polymer
PG2. Higher generations are created by repeating steps (c) and (d). In the
macromonomer route, the P units carry already a dendron of generation g
(g ) 2 in the figure) (f) and their polymerization leads directly to the
dendronized polymer of this generation. Currently the macromonomer route
does not allow to produce long dendronized polymers with g > 2 because
the bulkiness of the P units (f) affects the polymerization reaction.
The combination of theory and synthesis is uncommon and
requires comment. The synthetic method described affords the
possibility of producing polymer samples comprising long
chains of high quality and in gram amounts. It enables physics
type experiments, involving for example scattering techniques,
aiming to study the scaling behavior of dendronized polymers.
This prospect poses questions of optimizing the polymer design
to this end. The simple theoretical model proposed identifies
physically relevant design parameters and their conformational
effects. Combining these results with synthetic chemistry
considerations suggests directions for future synthesis to better
develop the study of the scaling behavior. Importantly, the theory
also identifies distinctive problems associated with the study
of such polymers and suggests a synthetic effort aimed to
confront these questions. This point may be illustrated by
considering the role of free ends. Dendronized polymers differ
qualitatively from linear chains and bottle brushes in the
importance of end effects. In linear chains comprising N
monomers, end effects diminish as 1/N and are thus negligible
for long chains. Their role is more important in bottle brushes
where their importance diminishes as 1/n. In marked distinction,
free ends comprise more than 50% of the monomers in a
dendronized polymer. Since their spatial distribution favors the
exterior envelope of the chain, the free ends may dominate their
solubility even if the “middle” monomers are poorly soluble.
We return to this issue in more detail in sections II and III.
Two examples illustrate this point. The first3 is the increase of
the fluorescence quantum yield of dendronized conjugated
polymers with the generation number. In this case the dendrons
afford the double advantage of solubilizing the backbone and
preventing collisional quenching of its excited states. The second
example concerns DNA adsorption onto oppositely charged,
cationic dendronized polymers.4 The DNA wraps the den-
dronized polymers forming a helix whose pitch decreases as
the generation and the thickness increases.
The dendronized polymers were prepared using two types
of trifunctional building blocks, polymerization (P) and den-
dronization (D) units (Figure 2). Both have two of the three
functional groups blocked by protecting groups that can be
removed or deprotected. The P unit, used for the creation of
the polymer backbone carries a polymerizable methacrylate
functionality. Upon polymerization of P one obtains a polymer,
PG1, with every repeat unit carrying two protected function-
(3) Sato, T.; Jiang, D.-L.; Aida, T. J. Am. Chem. Soc. 1999, 121, 10658–
10659.
The thickness of dendronized polymers has a demonstrated
effect on a variety of phenomena associated with such chains.
(4) Go¨ssl, I.; Shu, L. J.; Schlu¨ter, A. D.; Rabe, J. P. J. Am. Chem. Soc.
2002, 124, 6860–6865.
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Tuning Polymer Thickness
A R T I C L E S
Figure 3. AFM images of g ) 4 dendronized polymer (a), “hybrid” dendronized polymers (g ) 2) where the terminal monomers of the dendrons carry
linear chains (n ≈ 200) forming an exterior bottle brush (b),7 and bottle brush polymers with n ) 52 attached to a “simple” polymer backbone (c).8 The
dendronized polymers in (a) and (b) appear as dense “sausages” while the linear side chains in (b) and (c) adsorb onto the surface thus forming a quasi
two-dimensional brush.
alities. The protected functionalities of the polymer were then
deprotected and reacted with D units having, in turn, two of
their reactive functionalities blocked thus creating a second
generation dendronized polymer PG2. The PG2 polymer was
then deprotected and reacted with unit D to create a third
generation dendronized polymer PG3 and upon further iteration
fourth generation PG4. The following points merit attention:
(i) The polymerization degree of the backbone, N, is kept
constant5 throughout the synthesis; (ii) In contrast to earlier work
where the typical N range was N ≈ 200-4006 and the maximum
value reported was N ≈ 1000,6e in the present work N ≈ 1000
and N ≈ 7000 were attained; (iii) Identical D units were utilized
at every step thus leading to true homologous series; (iv) At
each stepwise addition 99.3-99.8% of the deprotected sites were
successfully reacted with D units; (v) The synthetic route
reported is optimized to produce gram amounts of dendronized
polymers. Earlier work allowed to produce 0.1 g amounts6 while
in the present work the maximum attained was 8 g of PG4 with
N ≈ 1000 and 1.5 and 0.7 g of PG3 and PG4 with N ≈ 7000,
respectively. In addition, it is important to note that the stepwise
addition, “attach to” route, allows the production of long PG3
and PG4 polymers whereas the polymerization of dendronized
monomers, the macromonomer route,2b only allows the produc-
tion of short PG3 and PG4.
chains, with different positioning of their free ends, are
discernible. “Polymer thickness” in these two systems assumes
a different form. To rationalize these observed differences it is
helpful to outline the theoretical description of three common
manifestations of polymer thickness, in linear chains, bottle
brushes and dendronized polymers. For simplicity we focus on
polymer thickness as it applies to free chains in solution, when
polymer-surface interactions do not play a role. This will allow
us to qualitatively rationalize the AFM observations noted above.
It also provides a basis for the quantitative interpretation of
experiments concerned with the tunable thickness of dendronized
polymers. Here we note that considerable effort was devoted
to the theoretical description of dendrimers9 and of bottle
brushes.10-14 In contrast, limited effort was devoted thus far to
dendronized polymers.15 Our discussion of this system utilizes
approaches advanced for the study of dendrimers and of bottle
brushes. In particular, we will utilize a Flory type model of
dendronized polymers based on the Boris-Rubinstein16 model
for dendrimers combined with scaling arguments invoked in
the discussion of persistence length of bottle brushes.13 Using
these methods we obtain the scaling behavior of the thickness,
r, and persistence length, λ, of dendronized polymers with
respect to g, the generation of the dendron and to the total
number of monomers in the dendron, n. A simple version of
the Flory model, overlooking the possible role of spacer chains,
reveals three main conclusions: (i) As expected the “thickness”
of dendrimers and of dendronized polymers exhibit slight
differences in scaling behavior because the first are spherical
objects while the second are locally cylindrical. Within the
model we use the equilibrium thickness of dendronized polymers
As we shall discuss, the thickness of dendronized polymers
allows to distinguish between species of different generation
using Atomic Force Microscopy (AFM) (Figure 3). In contrast,
it is clearly more difficult to discriminate between bottle brushes
carrying side chains of different length (Figure 3). This is
because the side chains are adsorbed and the individual side
scales as req ∼ n1/4g1/2 while the dendrimer span scales as req
∼
(5) The dendronization does not affect n but the chromatographic
separations may introduce an n bias.
(7) Zhang, A.; Barner, J.; Go¨ssl, I.; Rabe, J. P.; Schlu¨ter, A. D. Angew.
Chem., Int. Ed. 2004, 43, 5185–5188.
(6) For the step-by-step construction of higher generation dendronized
polymers, see: (a) Shu, L.; Scha¨fer, A.; Schlu¨ter, A. D. Macromolecules
2000, 33, 4321–4328. (b) Grayson, S. M.; Fre´chet, J. M. J. Macro-
molecules 2001, 34, 6542–6544. (c) Zhang, A.; Vetter, S.; Schlu¨ter,
A. D. Macromol. Chem. Phys. 2001, 202, 3301–3315. (d) Shu, L.;
Go¨ssl, I.; Rabe, J. P.; Schlu¨ter, A. D. Macromol. Chem. Phys. 2002,
203, 2540–2550. (e) Yoshida, M.; Fresco, Z. M.; Ohnishi, S.; Fre´chet,
J. M. J. Macromolecules 2005, 38, 334–344. (f) Al-Hellani, R.;
Schlu¨ter, A. D. HelV. Chim. Acta 2006, 89, 2745–2763. (g) Al-Hellani,
R.; Barner, J.; Rabe, J. P.; Schlu¨ter, A. D. Chem.sEur. J. 2006, 12,
6542–6551. (h) Lee, C. C.; Fre´chet, J. M. J. Macromolecules 2006,
39, 476–481. (i) Benhabbour, S. R.; Parrott, M. C.; Gratton, S. E. A.;
Adronov, A. Macromolecules 2007, 40, 5678–5688. For the attachment
of varyingly sized dendrons to non-dendronized backbones, see: (j)
Desai, A.; Atkinson, N.; Rivera, F., Jr.; Devonport, W.; Rees, I.; Branz,
S. E.; Hawker, C. J. J. Polym. Sci., Part A: Polym. Chem. 2000, 38,
1033–1044. (k) Helms, B.; Mynar, J. L.; Hawker, C. J.; Fre´chet,
J. M. J. J. Am. Chem. Soc. 2004, 126, 15020–15021. (l) Liu, Z.-T.;
He, Y.-M.; Li, B.-L.; Liu, J.; Fan, Q.-H. Macromol. Rapid Commun.
2007, 28, 2249–2255.
(8) (a) Sheiko, S. S.; Prokhorova, S. A.; Beers, K. L.; Matyjaszewski,
K.; Potemkin, I. I.; Khokhlov, A. R.; Mo¨ller, M. Macromolecules
2001, 34, 8354–8360. For reviews see: (b) Sheiko, S. S.; Mo¨ller, M.
Chem. ReV. 2001, 101, 4099–4123. (c) Pyun, J.; Kowalewski, T.;
Matyjaszewski, K. Macromol. Rapid Commun. 2003, 24, 1043–1059.
(9) Ballauff, M.; Likos, C. N. Angew. Chem., Int. Ed. 2004, 43, 2998.
(10) Birshtein, T. M.; Borisov, O. V.; Zhulina, E. B.; Khokhlov, A. R.;
Yurasova, T. A. Polym. Sci. USSR 1987, 29, 1293.
(11) Zhulina, E. B.; Vilgis, T. A. Macromolecules 1995, 28, 1008–1015.
(12) Fredrickson, G. H. Macromolecules 1993, 26, 2825–2831.
(13) Potemkin, I. I.; Khokhlov, A. R.; Reineker, P. Eur. Phys. J. E 2001,
4, 93–101.
(14) Panyukov, S.; Zhulina, E. B.; Sheiko, S. S.; Randall, G. C.; Brock, J.;
Rubinstein, M. J. Phys. Chem. B 2009, 113, 3750–3768.
(15) For a discussion of statistical properties of dendronized polymers under
various solvent conditions, based on a lowest order virial expansion,
see: Efthymiopoulos, P.; Vlahos, C.; Kosmas, M. Macromolecules
2009, 42, 1362–1369.
(16) Boris, D.; Rubinstein, M. Macromolecules 1996, 29, 7251–7260.
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A R T I C L E S
Guo et al.
7,12
n1/5g2/5
.
(ii) Bottle brushes and dendronized polymers are
ethylene hydrogen by different atoms or groups for instance,
polyvinyl alcohol, polystyrene and polyvinyl chloride. In the
second group the primary control parameter is the number of
monomers in the side chain, n. The boundary between these
two approaches is not sharp and they are clearly indistinguish-
able when n ) 1. However, for n . 1 the “side chain” approach
leads to qualitatively different features. In the following we
discuss these differences from the point of view of a simple
Flory type theory. Our discussion aims to identify qualita-
tive trends and their origins rather than to present a complete
theoretical picture. We first recall the leading features of simple
linear polymers which serve as reference case for our discussion
of thickness and its consequences.
The theoretical description of large scale polymer behavior
does not incorporate explicitly the detailed molecular structure
of the chains. Rather the molecular structure is absorbed into
two coarse grained parameters. One is the monomer diameter,
a, that accounts for the “thickness” of a linear polymer chain.
The second parameter, lp, allows for chain rigidification due to
hindered rotation. It gives rise to persistent rodlike segments,
comprising p > 1 monomers and thus having a length of roughly
lp ≈ pa. The diameter a and persistence length lp are correlated
since the potential barrier to rotation increases upon introduction
of bulky side groups. This is evident from empirical observations
and their rationalization by the rotational isomeric state model.17
While a is related to the monomer structure and reflects bond
lengths, angles and the bulkiness of the side groups attached, it
is typically considered as a phenomenological parameter. In
particular a is determined from the specific volume per
persistence length lp. Importantly, a is considered as a mono-
meric property that is weakly affected by the composition and
the sequence of a copolymer chain. This is in contrast, as we
shall discuss later, to the thickness of polymers carrying side
chains which is strongly dependent on the side chain crowding
induced by the polymerization.
realizations of cylindrical brushes comprising side chain ter-
minally attached to a backbone. In both cases the side chain
stretch along the normal to the backbone in order to lower the
monomer concentration and the associated interaction free
energy. The competition between the elastic penalty and the
interaction energy determines req. For bottle brushes it leads to
req ∼ n3/4 while for dendronized polymers it results in req
∼
n1/4g1/2. While both req increase with n, the n dependence of
dendronized polymers req is much weaker because their side
chains are repeatedly branched. This leads to a qualitative
difference in the n dependence of the average monomer volume
fraction, φeq, φeq ∼ n1/2/g of dendronized polymers increases as
g and n grow. In contrast φeq of bottle brushes decreases as φeq
∼ n-1/2. Dendronized polymers thus occupy an intermediate
position between linear chains and bottle brushes because their
much higher density results in lower compressibility and
deformability of the side chain corona. (iii) The persistence
length of both bottle brushes and of dendronized polymers scales
as λ ∼ n2.
We should emphasize that at present it is difficult to confront
the theory with experimental results: (i) The theory, in its
simplest form, applies to g g 4 polymers and a minimal
comparison to scaling results requires a homologous series with
g ) 4,5,6. The applicability range can be extended by introduc-
ing long spacer chains. However, this requires a modification
of the synthetic route. (ii) It is further necessary to characterize
the quality of the different solvents in order to identify the Θ
and good solvent regimes in terms of the corresponding virial
coefficients. As noted earlier, this task is complicated by the
high fraction of free ends in the dendronized polymers. As a
result it is necessary to allow for interactions involving free
ends, “middle” segments and the cross term (iii) to obtain
theoretical estimates of the characteristics of a particular g it is
necessary to obtain the dimensions of the side chain monomer.
In the following, we first discuss polymer thickness from a
theoretical point of view. This discussion proceeds from the
well studied cases of linear chains and bottle brushes to the
poorly explored case of dendronized polymers. We then address
the considerations motivating the choice of synthetic strategy
for producing samples for physical exploration of thickness
effects. Physics type experiments, such as the ones involving
scattering techniques impose requirements in terms of sample
size and polymer dimensions that limit the choice of synthetic
methods. The synthesis used is then described, underlining the
new features required to obtain gram amounts as well as the
careful characterization of the final product and the intermediates.
The effects of a and p on polymer behavior are illustrated
by their role in the Flory type description of semiflexible chains
with p > 1.18 When p is much smaller than the polymerization
degree N, N . p > 1, the chain can be viewed as a coil
comprising N/p persistent segments. This affects three aspects
of the chain behavior as discussed within a Flory type theory
aiming to obtain the chain’s span R. First, the elastic free energy,
Fel/kBT ≈ (R/R0)2 is weakened because the radius of a random
walk of persistent segments is larger R0/a ≈ (N/p)1/2p ) (Np)1/2
> N1/2. Second, two mutually canceling changes occur in the
interaction free energy Fint/kBT ≈ Vc2R3 where c ) φ/a3 is the
monomer concentration within the coil, φ is the corresponding
volume fraction and V is the virial coefficient of binary
monomer-monomer interactions. Viewing the two interacting
persistent segments as cylinders leads, following Onsager theory,
II. Polymer Thickness from Linear Chains to Bottle
Brushes and Dendronized Polymers - A Theoretical
Perspective
2
to a second virial coefficient V ≈ lp aτ ) p2a3τ instead of V ≈
a3τ for a flexible chain of spherical monomers. Here τ )(T -
Θ)/T is the reduced temperature defined in terms of the Θ
temperature. On the other hand, the monomer concentration c
) N/R3 is replaced by the concentration of persistent segments
N/pR3. As a result, the Flory radius of a persistent chain, when
Fel ≈ Fint, is RF ≈ (pτ)1/5N3/5a rather than RF ≈ τ1/5N3/5a. Two
additional effects are of greater importance. One is the appear-
ance of a marginal solvent regime for p > 1. In this regime,
Polymer thickness assumes different character as one moves
from “simple” linear chains to polymers decorated by crowded
side chains. The latter group includes polymers carrying side
chains of different branching schemes. In the following we focus
on the two extreme forms of branching: bottle brushes where
the main chain monomers carry linear, nonbranched chains and
dendronized polymers where the side chains are repeatedly
branched dendrons (Figure 1). In the first group one may tune
the polymer thickness and associated properties by modifying
the backbone monomer structure with small substituents such
as chloride or phenyl groups. This is exemplified by the different
vinyl polymers obtained upon replacing one or more of the
(17) Flory, P. J. Statistical Mechanics of Chain Molecules; John Wiley:
New York, 1969.
(18) Schaefer, D. W.; Joanny, J. F.; Pincus, P. Macromolecules 1980, 13,
1280–1289.
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Tuning Polymer Thickness
A R T I C L E S
occurring roughly at τ g φ g τ/p3, the chains are Gaussian and
the osmotic pressure scales as φ2. In contrast the osmotic
pressure of semidilute polymer solutions in a Θ solvent and in
a good solvent scales respectively as φ3 and φ9/4.15,16 Second,
liquid crystalline order can occur when p . 1.19
As noted above, tuning a and lp is possible by chemically
introducing bulkier substituents into the monomer so as to
increase the potential barriers for rotation around monomer-
monomer bonds. When this approach works, it affords a
powerful and cost-effective method. Its scope is however limited
for the following two reasons: (i) While the general trend is
that bulkier side groups rigidify the linear chain, as illustrated
for example by polystyrene, there are exceptions to the rule
such polyethylene whose persistence length is high in spite of
the absence of bulky substituents;20 (ii) Chemical modification
can strongly affect the solubility of the polymer.
Tuning the thickness and persistence length by introducing
side chains incorporating n monomers is an alternative strategy.
As noted earlier, the boundary between the two is fuzzy for
small n. Yet, for n . 1 the side chain effect on the polymer
thickness and the persistence length changes qualitatively. To
underline this distinction we denote the “side chain” thickness
by r and the corresponding persistence length by λ. While the
effects of r and λ are similar to those of a and lp, as discussed
above, four points merit emphasis: (i) r is no longer a
monomeric quality since it reflects the stretched conformations
of the crowded side chains thus becoming a chain attribute. (ii)
While “normal” monomers are impenetrable, a polymer deco-
rated by side chains can accommodate solvent and solutes within
its diameter r. Furthermore, r in contrast to a will be modified
by compression and the interactions between different chain
segments are not expected to exhibit hard core repulsion at
separations smaller than r. In effect, the “hard thickness” of
simple chains is replaced by “soft thickness” for polymers
carrying side chains. (iii) The variation of r and λ with n for n
. 1 becomes systematic while the effect on the solubility is
weakened thus permitting rational design. (iv) The theoretical
description of r involves the statistical physics of the flexible
side chains rather than the quantum chemistry of the backbone
monomers. Accordingly, the equilibrium thickness req is deter-
mined by minimization of the appropriate free energy.
To illustrate the flavor of the polymer thickness as tuned by
n of the side chains we consider bottle brushes and dendronized
polymers using a Flory type theory. We first discuss the well
established case of bottle brushes and then modify the descrip-
tion to the case of dendronized polymers. In both cases an
important control parameter is the number of backbone mono-
mers m between monomers carrying side chains. For brevity
we limit the discussion to the range 1 e m e p when the spatial
separation between the anchoring sites of side chains, δ, is fixed
and does not vary with the crowding. For m g p it is necessary
to allow for the extension of the chain segments separating the
grafting sites.10 In addition, we restrict our analysis to the limit
of λ much larger than lp of the backbone thus assuring a
cylindrical local symmetry.
ary at r. (ii) The associated monomer concentration profile is
step like with a constant monomer concentration of n/r2δ. The
Flory free energy per side chain is
F
kBT
r2
r02
Vn2
r2δ
≈
+
(1)
where V is the second virial coefficient and r0 ≈ n1/2a is the
span of an ideal side chain. The first term specifies the Gaussian
elastic free energy of a flexible side chain extended beyond r0.
The second term accounts for its interaction free energy due to
binary interactions of the side chain monomers with a “monomer
cloud” having a concentration of n/r2δ. Here we focus on the
limit of strongly crowded and long side chains in a good solvent
where additional terms, allowing for ternary interactions and
folding back of the ends, are negligible. Minimization with
respect to r yields the equilibrium condition when the elastic
term and the interaction penalty are comparable. This determines
the equilibrium span of the side chains req,
1/4
V
a
a
δ
req
≈
1/4n3/4a
(2)
( )
3
( )
thus specifying the equilibrium monomer volume fraction
1/2
na3
1
a
δ
a3
1/2
φeq
≈
≈
(3)
( V )
( )
r2eqδ n1/2
Upon substitution of req in F (eq 1), one obtains the
equilibrium free energy per unit length
Feq
1/2
1 V
a
δ
≈
3/2n1/2
(4)
( )
3
a( )
δkBT
a
With Feq/δ and req at hand we may estimate the persistence
length owing to the bottle brush using a scaling argument due
to Birshtein et al.10,11,13 For an infinite bottle brush, the only
energy density scale is Feq/δ and the only length scale is req.
Accordingly the free energy per unit length of a uniformly bent
rod with radius of curvature F is
2
Frod
Feq
req
≈
1 +
(5)
( )
[
]
kBT δkBT
F
This form is obtained by expanding Frod in powers of r/F
and retaining the first non vanishing term, assuming that the
bottle brush has no spontaneous curvature thus imposing the
absence of a term linear in r/F. Comparison to the bending free
energy density of a persistent chain, Fbend ≈ kBTλ/F2,21 then
yields
Feq
V a
λ ≈
r2eq
≈
2n2a
(6)
( )
a3
δkBT
δ
The scaling behavior of λ as obtained above is appropriate
to polymers under marginal solvent conditions. In a good solvent
the Flory free energy yields the correct req but overestimates
Feq. Accordingly, λ obtained for such conditions via blob
arguments, allowing for correlation effects neglected in the Flory
approach, exhibits a slightly weaker n dependence. Further
differences occur when the backbone is allowed to stretch so
as to lower the crowding of the side chains. Finally, note that
II.a. Bottle Brushes. The Flory type theory of bottle brushes
introduces two assumptions (i) the linear side chains are
uniformly stretched with their ends straddling the brush bound-
(19) Grosberg, A. U.; Khokhlov, A. R. Statistical Physics of Macromol-
ecules; AIP Series in Polymers and Complex Materials: New York,
1994.
(20) Rubinstein, M.; Colby R. H. Polymer Physics; Oxford University Press:
Cambridge, 2003.
(21) Odijk, T. J. Polym. Sci. Polym. Phys. Ed 1977, 15, 477–483.
9
J. AM. CHEM. SOC. VOL. 131, NO. 33, 2009 11845

A R T I C L E S
Guo et al.
eq 6 describes the polymer rigidity when the side chain
contribution is dominant. Current experiments suggest that n >
30 is necessary to reach this regime.22
nFeq
λ ≈
r2eq
≈
2n2a
(11)
V a
( )
a3
gδkBT
δ
II.b. Dendronized Polymers. We now turn from bottle
brushes, where the side chains are linear, to dendronized
polymers carrying repeatedly branched side chains. For simplic-
ity we first consider the case of dendrons comprising of
monomers attached by rigid freely jointed bonds of length a.
The dendrons are characterized by two chemical design
parameters. One is the functionality of the monomers forming
the junctions, X. The second is the generation of the dendron,
g, which counts the number of monomers in a strand joining
the origin and a free end. In chemistry terms g - 1 is the number
of deblocking steps in the synthesis. The currently experimen-
tally attainable values are X e 6 and g e 5. For the formulation
of theory it is convenient to use g and n ) [(X - 1)g - 1]/(X -
2) instead of g and X. The implementation of the Flory approach
to dendrimers is less obvious in comparison to the bottle brushes.
This is because of the difficulty in characterizing the elastic
free energy of repeatedly branched chains. To this end we follow
Boris and Rubinstein16 and consider the free energy of a linear
strand comprising g monomers joining the origin and a terminal
group and having a Gaussian span of r0 ≈ g1/2a. As before our
analysis concerns a locally cylindrical chain with crowded
dendrons, δ < r0, leading to a Flory free energy per strand of
The free energy 7 considers free ends and “middle” monomers
as identical. We focus on this simplest situation for brevity and
because it does allow to confront computer simulations. In view
of the large number of free ends a more realistic treatment
should distinguish between three different interactions: free
end-free end, middle monomer-middle monomer as well as
middle monomer-free end. These are associated with four
different virial coefficients, Vee, Vem, Vme and Vmm. Upon denoting
the number of free ends by ne the interaction term Vng/r2δ should
then be replaced by [Vee(ne - 1) + Vem(n - ne) + Vme(g - 1) ne
+ Vmm(n - ne)(g - 1)]/r2δ. One may further envision the case
that the middle monomers or the free ends experience Θ or
poor solvent conditions thus requiring the introduction of ternary
interactions terms. Such analysis is beyond the scope of this
paper, especially since the virial coefficients, Vee, Vem, Vme and
Vmm are currently unknown. Importantly, the second virial
coefficient of a dendronized polymer will reflect the overall
interactions between repeat units of the polymer and will not
specify Vee, Vem, Vme and Vmm. On the other hand, a rough estimate
of Vmm and Vee may be obtained from the solution properties of
linear polymers comprising of bifunctional variants of the D
units and P units. We address the synthetic issues involved in
section III.
We should emphasize two additional reservations concerning
our discussion of dendronized polymers. First, while the
shortcomings of the Flory approach are well understood for
linear chains its performance for dendrons received less atten-
tion. Second, for brevity we focused on dendrons whose
junctions are joined by freely jointed rigid bonds thus ignoring
the possible role of flexible spacers.
II.c. Bottle Brushes vs Dendronized Polymers. The number
of free ends per grafting site, ne, as well as the key physical
attributes of dendronized polymers and bottle brushes, as
obtained from the Flory type theory we utilized, are summarized
in Table 1.
r2
r02
Vng
r2δ
Fstrand
≈
+
(7)
kBT
This free energy differs from 1 in two respects. First, r0 ≈
g1/2a replaces r0 ≈ n1/2a and the elastic penalty is thus controlled
by g. Second, while the interaction free energy per monomer
remains Vn/r2δ the interaction free energy per strand becomes
Vgn/r2δ. The equilibrium condition ∂F/∂r ) 0, when the two
terms are comparable, leads to
1/4
V
a
a
δ
req
≈
1/4n1/4g1/2
a
(8)
( )
3
( )
In both systems, req and λ are tunable and reflect the size
and the crowding of the side chains. Yet, the branching of the
dendron side chains makes for smaller req and higher φeq. Thus
req of a dendronized polymer with X g 3 is smaller by a factor
of (g/n)1/2 < 1 where n ) [(X - 1)g - 1]/(X - 2), while their
average monomer volume fraction φeq is larger by a factor of
n/g. Since req scales as ∼n1/4g1/2 while n scales as ∼(X - 1)g,
both req(n) and req(g) curves depend strongly on X (Figure 4).
req(g) of bottle brushes, where n ) g, is steeper than req(g) of
dendronized polymers with X g 3. This is associated with a
qualitative effect on φeq. For bottle brushes φeq decreases with
n ) g while for dendronized polymers it is an increasing
function of g. The different φeq suggest corresponding differ-
ences in penetrability and compressibility. For example, the
and
1/2
na3
r2eqδ
a3
a
δ
1/2n1/2
φeq
≈
≈
(9)
( V )
( )
g
Upon substituting req in Fstrand, eq 7, one obtains the
equilibrium free energy per strand Feq. However, in order to
estimate the persistence length λ we need the equilibrium free
energy per dendron. Since a strand comprises g monomers while
a dendron consists of n monomers, the equilibrium free energy
per dendron is n/g larger. Accordingly the free energy density
specifying λ is
1 V
a
δ
3/2n3/2
nFeq
1/2
attainable maximal g corresponding to φeq ) 1 is gmax
≈
( )
n1/2(a/δ)1/2 arising because the volume occupied by the dendron
is roughly na3 while the maximal available volume is g2a2δ.
There is no corresponding effect for bottle brushes. On the other
hand, within our Flory type analysis, the persistence length λ
of the two polymer families is identical. This is because the
characteristic free energy density we utilize assumes the form
n2kT/δ2r2eq for both systems. Another important difference
concerns the number of free ends, ne. This affects, of course,
the number of reactive groups available for further chemistry.
However, it also plays a role in the theoretical description of
≈
(10)
3
a( )
gδkBT
g
a
leading, using eq 5 as introduced earlier, to
(22) Zhang, B.; Gro¨hn, F.; Pedersen, J. S.; Fischer, K.; Schmidt, M.
Macromolecules 2006, 39, 8440–8450.
(23) The configurations of long dendronized polymers can be deduced from
scattering in the range 1/Rg , q , 1/λ where q is the amplitude of
the scattering vector. In this range the scattered intensity scales as
q-D where D is the fractal dimension of the polymer.18 The L g 10λ
requirement is a lower bound on the necessary q range.
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11846 J. AM. CHEM. SOC. VOL. 131, NO. 33, 2009

Tuning Polymer Thickness
A R T I C L E S
Table 1. Dendronized Polymers vs Bottle Brushes: Number of Free Ends Per Grafting Site, ne, Equilibrium Span of the Side Chain, req
,
Equilibrium Monomer Volume Fraction, φeq, and Persistence Length λa
ne
req/a
φeq
λ/a
Dendronized polymers
Bottle brushes
(X - 1)g-1
1
(V/a3)1/4(a/δ)1/4n1/4g1/2
(V/a3)1/4(a/δ)1/4n3/4
(a3/V)1/2(a/δ)1/2n1/2/g
(a3/V)1/2(a/δ)1/2n1/2
(V/a3)(a/δ)2n2
(V/a3)(a/δ)2n2
a The expressions correspond to the case of dendrons comprising monomers jointed by rigid bonds of length a ignoring the effect of flexible spacers,
addressed briefly later in the text.
especially for confronting theory with experiment. Some of the
missing points are briefly discussed below, beginning with the
bottle brush results. The Flory approximation as presented earlier
considers flexible side chains in a good solvent. In this regime
this approximation yields the correct req and average φeq but
overestimates Feq. The Flory approximation will yield the correct
scaling forms for the marginal solvent regime of semiflexible
chains with p > 1. In this case req/a is larger by p1/4 while φeq
and Feq are smaller by a factor of p-1/2. These effects cancel in
λ ≈ r2eqFeq/(δkBT) which remains unmodified. In a good solvent
it is necessary to allow for correlations due to self-avoidance
of the chains. This can be done using blob arguments. For
cylindrical brushes of flexible chains the blob picture yields, as
we discussed, an identical req ≈ (a/δ)1/4n3/4 but a lower Feq
≈
(a/δ)5/8n3/8. It leads accordingly to9 λ ≈ (a/δ)17/8n15/8 instead of
λ ≈ (a/δ)2n2 as obtained from the Flory approximation. Note
that within the blob picture the monomer concentration profile
decreases with r as φ ≈ r-2/3 in contrast to the step-like
concentration profile, φ ≈ r0, assumed in the Flory approxima-
tion.10 The results cited above, as in our earlier discussion,
assume a non extendable backbone. A somewhat different
scaling behavior is obtained for m > p, when the extension of
the backbone should be taken into account.10
Our discussion of the dendronized polymers did not allow for
the role of spacer chains between the junctions. A simple discussion
of this effect is possible, along the lines proposed by Boris and
Rubinstein,16 by considering a dendron such that each junction is
attached to its predecessor by a flexible spacer comprising s
monomers of size b. For simplicity there is no distinction between
the junction monomers and spacer monomers and all binary
interactions are characterized by the same virial coefficient V. In
this approach a is replaced by s1/2b thus leading to r0 ≈ (gs)1/2b
instead of r0 ≈ g1/2a. The interaction term Vng/(r2δ) becomes Vs2ng/
(r2δ). Altogether, the introduction of spacers lowers the elastic free
energy by a factor of s-1 while increasing the interaction energy
by a factor of s2. It gives rise to stronger stretching of the side
chains req/b ≈ (V/b3)1/4(b/δ)1/4s3/4n1/4g1/2 and thus to a lower
monomer volume fraction φeq ≈ nsb3/(re2qδ) ) (b3/V)1/2(b/δ)1/2(n/
s)1/2/g. The equilibrium free energy per dendron is also higher Feq/
kBT ≈ (V/b3)1/2(b/δ)1/2s1/2n1/2 leading to a persistence length λ ≈
nFeqre2q/(gδkBT) or λ ≈ (V/b3)(b/δ)2s2n2b. Note that the separation
of a strand into junctions and spacers is somewhat arbitrary and
different virial coefficients may be actually necessary to describe
junction-junction, junction-spacer and spacer-spacer interactions.
The above results for the persistence length assume that λ .
lp and that the chain rigidity is dominated by the side chain
interactions. The precise boundary of this regime is not well
established. Recent experimental results concerning the persis-
tence length of bottle brush polymers with 6gn g 33 did not
follow a power law behavior predicted by any of the bottle brush
models. Rather, they suggested that the effective persistence
length leff behaves as leff ) lp + λ(n) and that this n range
corresponds to a cross over between backbone dominated regime
and the side chain domination regime.22 Experimental study of
the scaling behavior of r and λ requires samples spanning a
Figure 4. (a) Plots of n1/4g1/2 ≈ req/constant of dendronized polymers and
n3/4 ≈ req/constant of bottle brushes vs log10(n) for different junction
functionalities X. For bottle brushes with X ) 2, g ) n while for X > 2, n
) [(X - 1)g - 1]/(X - 2). Increasing the junction functionality X results in
a much wider range of n and req. (b) Plots of n1/2/g ≈ φeq/constant of
dendronized polymers and n-1/2 ≈ φeq/constant of bottle brushes. The
average density of bottle brushes decreases with g ) n while dendronized
polymers exhibit the opposite trend.
the systems. Our highly simplified approach does not distinguish
between end groups and “interior monomers” thus ignoring end
effects. This is reasonable for bottle brushes, where ne/n ) 1/n,
when n is large enough. It is never reasonable in the case of
dendronized polymers where ne/n is of order unity since ne/n g
(X - 2)/(X - 1) g 1/2. Accordingly, a more realistic Flory
free energy should distinguish between monomer-monomer,
end-end and end-monomer interactions. Note that in our
simplified discussion, bottle brushes constitute a special case
of dendronized chains. All the quantities ne, req, φeq, and λ of
dendronized polymers reduce to the bottle brush form when X
) 2 leading, upon invoking L′Hoˆpital’s rule to evaluate n )
[(X - 1)g - 1]/(X - 2), to n ) g.
The simple picture presented above was attained at a price
of overlooking many refinements of possible importance,
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J. AM. CHEM. SOC. VOL. 131, NO. 33, 2009 11847

A R T I C L E S
Guo et al.
wide range of g and n values. Since the currently accessible
range of g is limited to g e 5, this goal can be attained by
variation of the functionality X thus allowing to explore a wide
range of n . 1 between n(X ) 6,g ) 5) ) 781 and n(X ) 3,g
) 5) ) 31. In implementing this approach it is desirable to
minimize the structural differences between junction monomers
of different X.
polymer chain. This immediately raises the issue of structural
fidelity, that is, the conversion fraction per dendronization step.
Though structural fidelity was not normally addressed in a
quantitative manner in the pertinent literature, there is a
precedent that such procedures can in fact be carried out in high
level of conversion.27 It was therefore a natural choice to use
this approach, with all its particular chemistry, in the present
case.
The step-by-step process also raises the question as to whether
the length of the starting polymer (PG1) has an impact on the
structural fidelity especially for the synthesis of high generation
polymers. This is an issue that has not yet been addressed
quantitatively in the literature, but it is useful to note that all
starting polymers used so far for which quantitative experiments
are reported have short chains with Pn e 400, thus much shorter
than the target of the present work. There is the one exception
with Pn ) 1100 and Pw ) 1300.6e,28 Obviously new grounds
had to be explored in regard to how, polymer chains with, for
example, Pn ≈ 7000 and weight average degrees of polymer-
ization Pw ≈ 13 000 behave in consecutive dendronization
reactions. Finally, the aspect of quantity needs to be addressed.
Typically, attach-to experiments are performed on a scale that
allows doing the final steps (PG3 to PG4) with a few tenths of
a milligram material.6 Sometimes the amounts obtained are not
even stated, which may indicate that they are rather small. For
studying polymer thickness effects, milligram quantities are
inadequate. It is thus important to establish a protocol enabling
the synthesis of each member of a homologous series at least
on the gram scale. All these considerations led us to devise the
route in Scheme 1.
The advantages of this strategy are manifold. Monomer MG1
and the two polymers PG1 and PG2 are known from earlier
work which facilitates their characterization.29 Also the depro-
tection chemistry, using neat trifluoroacetic acid, has been
employed numerous times and found to be highly reliable.30
The key building block for dendronization, compound 1
(Scheme 1), is new. However, its synthesis rests upon a
commercially available dendrons, 2a and 2b. Furthermore the
way it bonds to peripheral amines during the dendronization
event, succinidyl active ester amidation, has been quantified in
the few similar cases mentioned above. Under carefully
optimized conditions, coverages of up to 99.8% were repro-
ducibly achieved6d which obviously suggested this building
block for the present purpose. Finally, monomer MG1 can be
polymerized by controlled or, alternatively, free radical poly-
merization. This allowed obtaining starting polymers PG1 with
different chain lengths in the range of several hundred nanometers.
Considering the enormous increase in molar mass during the
homologization which may also be referred to as consecutive
dendronization or thickening, the molar mass of the starting
polymer PG1 had to be carefully chosen. High molar masses
may result in handling and characterization problems. The initial
focus was therefore placed on a “short” PG1 with Pn ≈ 1000
and L ≈ 250 nm. Assuming complete coverage throughout, its
corresponding PG4 had a molar mass of approximately 5.5 ×
III. Synthesis of Homologous Series
III.a. Conceptual Considerations. To systematically explore
the properties of homologous series of dendronized polymers
aiming at unraveling potential thickness effects, its representa-
tives must (i) have sufficiently long backbone chains, (ii) have
high structural fidelity, and (iii) be available in gram quantity.
These conditions fundamentally affect the kind of chemistry to
be used for their synthesis as will become evident from the
following considerations. With regard to scattering experiments
it is useful to distinguish between two situations: Polymers
whose contour length L is comparable to the persistence length
λ and those with L . λ. Polymers with L ≈ λ . req are expected
to behave as bendable rods while long polymers with L . λ
will behave as coils of L/λ segments of length λ each. In practice
L/λ g 10 is necessary for scattering experiments aiming at this
last regime.21 Current results suggest that λ of PG4 is in the
range 10 - 50 nm.24 Accordingly, the L ≈ 10λ criterion requires
polymers of length of several hundred nanometers up to a
micrometer. This condition rules out the use of the by far most
often used synthesis method, the so-called macromonomer route
(Figure 2),2b in which macromonomers already carrying the
dendrons of final size are polymerized. Even with the recent
improvement of the number average degrees of polymerization,
Pn, in the polymerization of macromonomers under supercriticial
carbon dioxide high pressure conditions,25 L > 500 nm and L >
40 nm are presently unrealistic for g ) 3 and g ) 4 polymers,
respectively. The attach-to route was therefore the only option
for g ) 4 polymers with L ≈ 10λ. It suggested itself strongly
also for g ) 3 polymers inasmuch as flask-type chemistry under
ambient conditions was preferable to synthesis under high
pressure.26 In this method the dendronized polymers are obtained
in a step-by-step process in which generation after generation
is added to an already existing starting polymer (Figure 2);
thousands of reactions have to be performed with each individual
(24) A theoretical study predicts persistence lengths λ of third and fourth
generation dendronized polymers to be 50 and 120 nm, respectively,
and lead to the “Janus chain” model for dendronized polymers: (a)
¨
Ding, Y.; Ottinger, H. C.; Schlu¨ter, A. D.; Kro¨ger, M. J. Chem. Phys.
2007, 127, 094904. Kro¨ger, M.; Peleg, O.; Ding, Y.; Rabin, Y. Soft
Matter 2008, 4, 18–28. Ding, Y.; Kro¨ger, M. Macromolecules 2009,
42, 576–579. For λ of dendronized polymers up to generation three
determined by SANS, see: (b) Stocker, W.; Schu¨rmann, B. L.; Rabe,
J. P.; Fo¨rster, S.; Lindner, P.; Neubert, I.; Schlu¨ter, A. D. AdV. Mater.
1998, 10, 793–797. (c) Fo¨rster, S.; Neubert, I.; Schlu¨ter, A. D.; Lindner,
P. Macromolecules 1999, 32, 4043–4049. A comprehensive LS and
SANS study on homologous series of dendronized polymers is
presently being performed: (d) Sigel, R.; Guo, Y.; Zhang, A.; Schlu¨ter,
A. D.; Schurtenberger, P. In preparation. For λ of dendronized
polymers up to the fifth generation determined by MALLS, see: (e)
Percec, V.; Ahn, C.-H.; Cho, W. D.; Jamieson, A. M.; Kim, J.; Leman,
T.; Schmidt, M.; Gerle, M.; Mo¨ller, M.; Prokhorova, S. A.; Sheiko,
S. S.; Cheng, S. Z. D.; Zhang, A.; Ungar, G.; Yeardley, D. J. P. J. Am.
Chem. Soc. 1998, 120, 8619–8631. (f) Ouali, N.; Me`ry, S.; Skoulios,
A.; Noirez, L. Macromolecules 2000, 33, 6185–6193. See also ref
6e.
(27) For studies in which structural defects were quantified by either UV-
and fluorescence spectroscopic or NMR-spectroscopic analysis, see
refs 6d, f and 6g.
(28) Reference 6e does not provide information on the quantity in which
these polymers were synthesized.
(25) Costa, L. I.; Kasemi, E.; Storti, G.; Morbidelli, M.; Walde, P.; Schlu¨ter,
A. D. Macromol. Rapid Commun. 2008, 29, 1609–1613.
(26) In certain special cases mixed strategies may be feasible alternatives
as well.
(29) Canilho, N.; Kasemi, E.; Mezzenga, R.; Schlu¨ter, A. D. J. Am. Chem.
Soc. 2006, 128, 13998–13999.
(30) For example, see Shu, L.; Schlu¨ter, A. D.; Ecker, C.; Severin, N.;
Rabe, J. P. Angew. Chem., Int. Ed. 2001, 40, 4666–4669.
9
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Tuning Polymer Thickness
A R T I C L E S
Scheme 1. Attach-to Route to a Strictly Homologous Series of First through Fourth Generation Dendronized Polymers PG1-PG4 and
Structures of Compounds 2a and 2b, Mg2, and 3a and 3ba
a Boc stands for tert-butyloxycarbonyl, a common protecting group for amine functional groups. Dendron 1 serves as the key building block to
increase g.
106. With our experience such a PG4 was expected to be soluble
in organic solvents at room temperature and still exhibit
sufficiently resolved NMR spectra. It was therefore considered
a “safe” series. A longer and potentially more interesting series
starting from a PG1 with L > 1 µm was also planned. This of
course involved the risk of lower solubility and complicated
structural analysis especially for higher generation polymers.
In order to synthesize these two PG1’s of different length both
reversible addition-fragmentation chain transfer polymerization
(RAFT)31 and free radical polymerization (FRP) of MG1
suggested themselves.
methods comprised gel permeation chromatography (GPC), 13
C
NMR spectroscopy, and atomic force microscopy (AFM)
apparent height measurements. To be on the safe side all the
samples were also checked by a quantitatiVe method based on
UV absorption. In it the unreacted terminal amines of the
dendronized polymers were converted into UV labels with high
extinction coefficient by reacting them with an excess of Sanger
reagent (see Supporting Information).6d Finally, the NMR
spectra of the second generation polymers obtained by the
attach-to route were compared to those obtained by the
macromonomer route starting from MG2 (Scheme 1). This latter
polymer is referred to as PG2M.
III.b. Synthesis and Structure Analysis. FRP of MG1 has
already been reported.29 It was typically carried out on a 500
mg scale and yielded extremely high molar mass products. For
the present work this scale was considered too low and
polymerizations were done with up to 8 g of monomer per batch.
Whereas PG1 obtained from smaller scale experiments showed
monomodal distributions with a polydispersity index PDI )
3-4, the present scale gave products with number average molar
The main characterization effort involved methods providing
qualitatiVe insights concerning the growth processes. These
(31) (a) Chiefari, J.; Chong, Y. K.; Ercole, F.; Krstina, J.; Jeffery, J.; Le,
T. P. T.; Mayadunne, R. T. A.; Meijs, G. F.; Moad, C. L.; Moad, G.;
Rizzardo, E.; Thang, S. H Macromolecules 1998, 31, 5559–5562. For
a review, see: (b) Barner-Kowollik, C.; Davis, T. P.; Heuts, J. P. A.;
Stenzel, M. H.; Vana, P.; Whittaker, M. J. Polym. Sci. Polym. Chem.
Ed. 2003, 41, 365–375. For an application to dendronized polymers,
see: (c) Zhang, A.; Wei, L.; Schlu¨ter, A. D. Macromol. Rapid Commun.
2004, 25, 798–803.
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A R T I C L E S
Guo et al.
Figure 5. GPC elution curves based on refractive index (left) and Light Scattering (LS) detection at 15° scattering angle (right) of the homologous series
(a) PG11000-PG41000 and (b) PG17000-PG47000. All elution curves of one set belong to one and the same homologous series. All measurements were done
in DMF (1% LiBr) at 45 °C.
masses in the range of Mn < 1 × 106 and a rather broad PDI ≈
6.5. Fractionating precipitation of the 5.8 g of raw PG129
obtained yielded two fractions with Mn ≈ 6.2 × 106 (1.6 g)
and Mn ≈ 3.6 × 106 (1.5 g); the remaining broadly distributed
material amounted to 2.7 g. The second fraction, whose elution
curve is shown in Figure 5 contained chains with Pn ≈ 6800
(PDI ) 1.9) and was used as starting material for the high molar
mass series, hereafter referred to as PG17000. The shorter chain
PG1 was obtained using the RAFT reagent 3b (Scheme 1),
which was synthesized from the corresponding carboxylic acid
3a32 by standard esterification. The polymerization was done
in 20-30 mL solvent. Though the procedures required a couple
of days, the materials obtained had a very fine, foam-like
morphology. Samples that easily flew upon friction induced
electrostatic charging were considered of sufficient quality. If
the mixtures happened to partially melt during the process, the
products were sticky and freeze-drying was repeated. Depro-
tections were typically done on the 2 g scale in neat trifluoro-
acetic acid. The reactions were quenched with MeOH by which
the acid was converted into the more volatile corresponding
methylester. A second portion of MeOH was always added to
remove the last traces of residual trifluoroacetic acid as the
corresponding ester during freeze-drying (see Experimental).
The completion of deprotection was confirmed prior to the next
step by rigorously applied NMR spectroscopy showing the
disappearance of the tert.-butyl signal at δ ) 1.38 ppm.
The synthesis conditions and results for PG11000 and PG17000
are compiled in Table 2. For the shorter series, the yields of
isolated products were essentially constant and above 80% for
each step, whereas for the longer series they decreased from
80% for PG27000 to 70% for the two higher homologues. These
numbers refer to freeze-dried, ready to use samples and are
considered optimized. The yields observed can neither be
correlated with the achieved degree of coverage nor do they
give insight into whether or not inadvertent fractionation has
taken place during chromatographic purification. High molar
mass chains may adhere preferentially to the column support
material. The possibility that insufficient coverage affects the
yields was addressed by determining the degrees of coverage
by the published method,6d using the same reference compound.
This was ruled out because the coverage was virtually quantita-
tive in all cases (see below).
at 60 °C with AIBN as initiator and gave a PG1 with M
≈
n
0.5 × 106 and PDI ) 1.4 in a yield of 83%. This sample had
Pn ≈ 1000 by GPC and was used as starting material for the
low molar mass series, hereafter referred to as PG11000. Its GPC
elution curve is also contained in Figure 5. All dendronizations
were performed in DMF with an excess of the active ester
dendron 1, which was obtained from the corresponding acid
26a on a 200 g scale by standard chemistry. It was critical to
add compound 1 in portions and to lower the temperature before
each addition from 20 to -5 °C. All synthetic operations are
detailed in the Experimental (see SI). Most of the data from
combustion analysis are within the expected range showing that
the polymers do not act as a “sponge” for solvents or impurities
(see Supporting Information, Table S1, for the PG7000 series).
The way the freeze-drying and deprotection procedures were
carried out turned out to be especially important for maximizing
the coverage. Before each synthetic step both the protected and
deprotected polymers were freeze-dried from dioxane and water,
respectively, observing an initial concentration of 2 g of polymer
(32) Lai, J. T.; Filla, D.; Shea, R. Macromolecules 2002, 35, 6754–6756.
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Tuning Polymer Thickness
A R T I C L E S
Table 2. Synthesis Conditions and Results for PG1000 and PG7000
universal calibration results. However, it does not prohibit the
correct determination of Mw, provided that concentration losses
can be avoided. The latter becomes apparent in the peak area
of the RI-detector normalized by the injection concentration
which is shown in Figure 5.
PG1a
PG2b
PG3c
PG4d
Short series
Long series
Yield(%)
Pn
PDI
83
85
85
82
e
1000
1.4
45
950
1.5
66
1000
1.6
75
1300
1.7
73
Tg (°C)
Next, NMR spectroscopy was used to investigate coverage.
First it was shown for the PG17000 series that the intensity of
the backbone signals decreases relative to the signals of the
dendritic shell, when the generation increases. In order to avoid
insurmountable problems with extreme line widths we utilize
Yield(%)
97
80
70
70
e
Pn
6800
1.9
50
6700
1.6
66
6400
1.8
71
6300
1.7
72
PDI
Tg (°C)
a Pn ) 7000: fractionated from PG1 (Mn ) 8.8 × 104, PDI ) 6.5);
Pn ) 1000: [MG1]/[7]/[AIBN] ) 1200/1/0.5 in dry DMF at 60 °C for
24 h. b [de-PG1]/[1] ) 1/10 in dry DMF at -5 °C for 5 d. c [de-PG2]/
[1] ) 1/20 in dry DMF at -5 °C for 10 d. d [d] [de-PG3]/[1] ) 1/40 in
dry DMF at -5 °C for 20 d. e [e] Based on GPC in DMF (1% LiBr) at
45 °C using LS detection.
1
13C NMR spectroscopy in the solid state rather than H NMR
spectroscopy in solution. This was done despite the fact that
all samples, contrary to our initial expectations, dissolved
reasonably quickly and completely (by visual inspection) in
common organic solvents like chloroform, dichloromethane,
THF and DMF at room temperature. Figure 6 compares the
relevant spectra which were normalized to dendron signals and
shows that the intensities of the backbone signals (marked by
arrows) decrease continuously. These spectra were also used
to extract information about the local order of the dendrons in
the four different polymers. Since the line widths of all dendritic
carbons were basically the same (3-5 ppm) the local order is
likely to be the same for all polymers.
The glass transition temperatures Tg are in the expected range
which is well below that of parent PMMA (Tg ) 105 °C). They
are obviously not dominated by the main chain but rather by
the dendrons.33 The Tg’s were compared within the N ) 1000
and N ) 7000 series. In addition, for PG2 and PG3 they were
also compared with PG2M and PG3M.34 Whereas both PG21000
and PG27000 have the transition at the same temperature, Tg )
66 °C, PG2M has Tg ) 67 °C. The third generation polymers
PG31000 and PG37000 have slightly differing values of Tg ) 75
and 71 °C, respectively, while the corresponding PG3M has Tg
) 73 °C. PG41000 and PG47000 have again virtually identical
transitions with Tg ) 75 and 71 °C, respectively. The fact that
the Tg’s of these two PG4’s do not occur at higher temperatures
than that of the PG3’s has precedents.33 Large structural defects
are intuitively expected to result in larger differences of Tg.
The GPC elution curves for the PG17000-PG47000 series are
shown in Figure 5. Note that for the long series the available
PMMA standard did not cover the entire calibration range giving
rise to uncertainty regarding the Pn values. The molar masses
are based on refractive index and single angle light scattering
detection (15°). For both series the elution volumes decrease
with increasing side chain generation. This is qualitatively
expected, because the chain stiffness increases with the dendron
generation leading to a larger hydrodynamic volume. At the
same time the molar mass for a given degree of polymerization
increases dramatically, as reflected in the strongly increasing
peak area for the light scattering signal. The elution curves for
the shorter series are strictly monomodal.6e It is well-known
although not understood in detail that an anomalous elution
behavior might be observed for particularly large polymer
structures with complex chain topologies, such that the longest
chains are retarded and coelute with much shorter ones.35,36 Such
an effect is visible in the elugrams of the PG7000 series causing
peculiar and strongly varying shapes of the elution curves. This
effect depends on the injection concentration, the adsorption
tendency onto the column material and other subtle factors.
Anomalous elution falsifies the determination of PDI and the
Second, the polymers PG27000 and PG2M which had been
prepared by the attach-to and macromonomer routes, respec-
tively, were directly compared by 1H and 13C NMR spectroscopy
(Figure 7). Both pairs of spectra are almost superimposable.
This suggests high coverage. It should be noted though that the
PG1M and PG17000 polymers may differ in their backbone
stereochemistry because of the different steric requirements of
the dendritic substituents MG1 and MG2. MG1 determines the
backbone stereochemistry in PG27000 and MG2 the one of
PG2M.37 By inspection of the region between δ ) 0.8-1.2 ppm
in spectra a and b (Figure 7), it can be concluded that both
polymers are mainly atactic with PG27000 having a somewhat
higher syndiotactic content.38 The respective NMR spectra were
therefore not expected to be superimposable in every detail.
Further, the chain thickening process was visualized by atomic
force microscopy (AFM). Equal parts of dilute chloroform
solutions of the four polymers PG11000-PG41000 were combined
and the resulting solution spin-coated onto mica. The dry
samples were imaged in tapping mode (Figure 8a). All chains,
even in larger scale images showing hundreds of them, could
unambiguously be classed into four categories assigned as
PG1-PG4. Having imaged the four kinds of chains under
identical conditions allowed to determine their apparent heights
using an automated method recently developed by one of the
authors (M.K.).39 This method identifies chains which are not
involved in aggregates or contain other nonanalyzable parts and
determines the height profile along the contour. A typical height
profile for an individual PG41000 chain is shown in Figure 8b,
whose inset indicates how the center-line was obtained. All
height profiles fluctuate. This may be due to several reasons
such as the occurrence of kinetically trapped, frozen-in con-
formations, secondary structure formation (e.g., helices), and
structural defects stemming from synthesis. The average ap-
parent height was determined from the height profile of each
(33) For the glass transition temperatures of closely related polymers made
by the macromonomer route, see:Zhang, A.; Okrasa, L.; Pakula, T.;
Schlu¨ter, A. D. J. Am. Chem. Soc. 2004, 126, 6658–6666.
(34) Kasemi, E.; Schlu¨ter, A. D. unpublished.
(35) This material showed an anomalous elution behavior resulting in a
multimodel elution curve. This may in part be caused by high molar
mass chains eluting at unusually high retention times because of
interaction with the support.
(36) (a) Wintermantel, M.; Antonietti, M. J; Schmidt, J. Appl. Polym. Sci.,
Polym. Symp. 1993, 52, 91. (b) Gerle, M.; Fischer, K.; Mu¨ller, A. H. E.;
Schmidt, M.; Sheiko, S. S.; Prokhorova, S.; Mo¨ller, M. Macromol-
ecules 1999, 32, 2629.
(37) For a recent related case, see Zhang, A.; Rodriguez-Ropero, F.; Zanuy,
D.; Alema´n, C.; Meijer, E. W.; Schlu¨ter, A. D. Chem.sEur. J. 2008,
14, 6924–6934.
(38) Hatada, K.; Kitayama, T.; Ute, K. Prog. Polym. Sci. 1988, 13, 189–
276.
(39) http://www.complexfluids.ethz.ch/polymerAFM.
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A R T I C L E S
Guo et al.
Figure 6. CPMAS 13C NMR spectra of PG17000-PG47000. Note that the signals marked with arrows belong to the backbone. Their intensity decreases
systematically with increasing generation which is especially clear for the signal at approximately δ ) 45 ppm. Color code: black, PG1; blue, PG2; green,
PG3; red, PG4.
Figure 7. NMR spectral comparison of polymers PG2 synthesized according the macromonomer route, PG2M and attach-to route, PG27000:
1H NMR
spectra of PG2M (a) and PG27000(b); 13C NMR spectra of PG2M (c) and PG27000 (d). The 13C NMR spectra were recorded at the highest possible concentration
and accumulating 20000 pulses. Solvent signals (DMF-d7, CDCl3) are marked (*). The signal in the 13C NMR spectrum of PG27000 at δ ) 67 ppm stems
from residual dioxane, the solvent used for freeze-drying.
polymer. The resulting average values of a statistically signifi-
cant ensemble of chains of different generations were then again
averaged. The plot of the resulting apparent height values against
generation is depicted in Figure 8c. The chain heights increase
by approximately 8.5 Å per generation, assuming the interaction
between tip and polymer is identical for all generations. Because
the side chain dendrons all have the same repeat units and the
same terminal units this assumption is reasonable. However,
for the low generation polymers, the polymer-substrate interac-
tions are expected to differ and may result in different cross-
sectional shapes. The linear correlation in Figure 8c may thus
be accidental. The chain height increase was also measured for
the long series PG17000-PG47000 and found to be identical. A
representative AFM image can be found in the Supporting
Information. Similarly, a “persistence length” of the adsorbed
chain has been directly obtained from the tangent-tangent
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Tuning Polymer Thickness
A R T I C L E S
Figure 8. (a) AFM height image of a mixture of PG11000-PG41000 spin-coated from chloroform onto mica showing mainly individual entities. Representative
chains of each generation are marked. For data collection and analysis larger images (1.5 µm x 1.5 µm) were used. (b) Determination of an apparent height
profile of a PG41000 chain using a tool that recognizes chains and their closed envelopes, thus ignores the background, and allows studying height profiles
of single chains, like the one shown, in detail (see ref 39). The inset is a zoom into the contour plot of a region of a dendronized polymer. Lines generally
follow equidistant heights. The green lines, however, are perpendicular to the center-line and are calculated by searching for spatially nearest neighbors on
same contour lines, separated by at least one-third of the size of the whole polymeric object. The “center-line” connects adjacent middle points of the green
lines. Its coordinates allow extracting heights along the centerline. (c) Apparent heights of PG11000-PG41000 versus generation. The straight dotted line is
a least-squares linear fit. Since the AFM measurements were carried out in the air, on dry samples, the thickness of the chains is expected to correspond to
the collapsed state of the side chains when r2δ ≈ Vmonomern leading in the case of X ) 3 to r ≈ (Vmonomer/δ)1/2(2g - 1)1/2(solid line). For the range considered
this expression is close to the observed linear dependence though deviations are expected at higher generations. (d) “AFM persistence length” of the adsorbed
chains versus generation. Solid line is using eq 11.
correlation of the center-line at separations larger than the length
scale of the local undulations. This quantity is shown in Figure
8d. The stiffness clearly increases with number of generations,
as predicted by eq 11. Yet, this agreement should be considered
with caution and may be accidental because eq 11 describes
the behavior of free chains in good solvent while the AFM data
corresponds to adsorbed chains in a dry state. It turns out that
the center-lines of the adsorbed dendronized polymers do not
exhibit wormlike chain statistics, which we attribute to the effect
of the adsorption process.
As noted above, the structural fidelity of both series was also
investigated using a UV labeling technique. For details and the
impact of the nature of the reference compound, see Supporting
Information. For a discussion of the limits of the method, the
reader is referred to the original paper.6d The following results
were obtained for PG21000-PG41000: 99.8, 99.8, and 99.7%,
respectively, and for PG27000-PG47000: 99.8, 99.7, and 99.3%,
respectively. While the coverage decreases with increasing
generation and increasing chain length, it is nevertheless virtually
quantitative.
(the prefix de indicates deprotected), a starting material inde-
pendently prepared form the above series. With the same
procedure as described above the yield for PG2 was only about
65%. To improve this low yield we divided the starting polymer
into 2 g batches which were combined after parallel dendroni-
zation. The combined yield of this procedure could be raised
to 90% and the largest amount of PG21200 which was prepared
this way was 12 g. This splitting and combining technique was
repeated for the remaining two generations to provide these
materials in yields of approximately 80%. The combined
samples of PG31200 and PG41200 amounted to 8 g in both cases.
IV. Discussion
Comparison between theory and synthesis reveals two issues.
One concerns the applicability range of the theory. The second
concerns the solvent quality of the dendronized polymers. The
simple theory represented applies to dendrons whose strands
exhibit Gaussian elasticity. In turn this imposes constraints on
the polymers considered. In the absence of spacer chains the
theory begins to apply roughly at g ) 4. Accordingly the
minimal series allowing to probe the scaling behavior predicted
We explored the synthesis of larger quantities of the N ≈
1000 series. Our initial starting point involved 6 g of de-PG11200
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A R T I C L E S
Guo et al.
By choosing X ) C(O)NHCH3 a homopolymer is obtained
comprising the interior units of the dendrons and for X )
C(O)NHCH2CH2NHBoc the chains obtained consist of repeat
units corresponding each to a dendritic free end. The solubility
and swelling behavior of such polymers will allow specifying
the necessary parameters. With these parameters at hand one
may reformulate the theory so as to capture the swelling regime
of the side chains. A similar approach was explored by Hawker
et al. who synthesized linear analogs of dendrimers.43 The lower
solubility of the linear chains was attributed to their high
propensity to crystallization.
Figure 9. Linear homopolymer comprising either free dendron ends and
interior dendron units or just interior dendron units depending on choice of
X (left). Possible realizations (right).
V. Summary and Outlook
should incorporate g ) 4-6. When the dendronization mono-
mers incorporate long spacer chains the scaling regime is wider
beginning at g ) 1. This last architecture also affords the
advantage of postponing the closed packing limit to higher g
values. Preliminary results suggest g ) 5-6 can be attained
with current “spacer less” chemistry.40 One should note that
synthetic schemes involving long spacer chains have been
reported thus suggesting that homologous series with g ) 1-5
are feasible.41 Monomers with X ) 4 were also reported.42
A second, more insidious problem concerns solvent quality.
Our theoretical analysis focused on the case when free ends
and interior monomer in the dendron experienced identical good
solvent conditions and identical monomer monomer interactions.
This assumption was invoked to allow for a brief discussion of
molecular design parameters and their roles. The generalization
of this picture is straightforward. It incurs however the price of
introducing additional interaction parameters characterizing the
solvent quality experienced by free ends and the interior
monomers as well as their mutual interactions. Since the fraction
of free ends is larger than 50%, their role is never negligible
and confrontation of theory with experiment requires charac-
terization of the individual interaction parameters. In turn this
requires a synthetic effort to create linear homopolymers
comprising of monomers similar to the free ends or to the
interior units and Figure 9 offers concrete suggestions.
The synthetic method announced affords two advantages (i)
gram scale yields, (ii) dendronized polymers with extremely
monodisperse dendrons even in the case where 56 000 den-
dronization reactions are performed per macromolecule as in
the case of converting PG37000 to PG47000. In addition, this
method appears to be a generally applicable dendronization tool
for chains carrying amine groups. This approach allows tuning
the thickness of short as well as long polymers.
The combination of the theory and the synthesis results
suggests that the scaling behavior of dendronized polymers can
be explored in the foreseeable future. It requires however further
synthetic effort to create dendronized polymers in the scaling
regime and linear homopolymers designed to characterize the
different interaction parameters involving free ends and interior
monomers.
Acknowledgment. This work was supported by ETH research
grants TH-1608-1 and TH-0908-2 as well as by EU-NSF contract
NMP3-CT-2005-016375 and FP6-2004-NMP-TI-4 STRP 033339
of the European Community. The authors thank Dr. R. Sigel,
University Fribourg, for helpful comments and are indebted to Profs.
A. Vasella, M. Textor, and N. Spencer (all ETH) for generously
providing access to their equipment. The authors cordially thank
Prof. Manfred Schmidt for constructive discussions.
Supporting Information Available: All synthetic procedures
and analytical data. Determination of coverage. AFM image of
coprepared samples of PG17000-PG47000. This material is
available free of charge via the Internet at http://pubs.acs.org.
(40) Zhang, B.; Kro¨ger, M.; Halperin, A.; Schlu¨ter, A. D. In preparation.
(41) For dendronized polymers with varied spacer lengths, see: Li, W.;
Zhang, A.; Schlu¨ter, A. D. Chem. Commun. 2008, 552, 3–5525. Li,
W.; Zhang, A.; Feldman, K.; Walde, P.; Schlu¨ter, A. D. Macromol-
ecules 2008, 41, 3659–3667.
JA9032132
(42) Buchowicz, M. N.; Holerca, V.; Percec, V. Macromolecules 2001,
34, 3842–3848. Bao, Z.; Amundson, K. R.; Lovinger, A. J. Macro-
molecules 1998, 31, 8647–8649.
(43) Hawker, C. J.; Malmström, E. E.; Frank, C. W.; Kampf, J. P. J. Am.
Chem. Soc. 1997, 119, 9903–9904.
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11854 J. AM. CHEM. SOC. VOL. 131, NO. 33, 2009