Dispersity effects in polymer self-assemblies: A matter of hierarchical control

Abstract

Advanced applications of polymeric self-assembled structures require a stringent degree of control over such aspects as functionality location, morphology and size of the resulting assemblies. A loss of control in the polymeric building blocks of these assemblies can have drastic effects upon the final morphology or function of these structures. Gaining precise control over various aspects of the polymers, such as chain lengths and architecture, blocking efficiency and compositional distribution is a challenge and, hence, measuring the intrinsic mass and size dispersity within these areas is an important aspect of such control. It is of great importance that a good handle on how to improve control and accurately measure it is achieved. Additionally dispersity of the final structure can also play a large part in the suitability for a desired application. In this Tutorial Review, we aim to highlight the different aspects of dispersity that are often overlooked and the effect that a lack of control can have on both the polymer and the final assembled structure.

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Cite this: Chem. Soc. Rev., 2017,
46, 4119
Dispersity effects in polymer self-assemblies:
a matter of hierarchical control†
Kay E. B. Doncom,
a
Lewis D. Blackman,
a
Daniel B. Wright,‡
a
Matthew I. Gibson
ab
and Rachel K. O’Reilly *
a
Advanced applications of polymeric self-assembled structures require a stringent degree of control over such
aspects as functionality location, morphology and size of the resulting assemblies. A loss of control in the
polymeric building blocks of these assemblies can have drastic effects upon the final morphology or function
of these structures. Gaining precise control over various aspects of the polymers, such as chain lengths and
architecture, blocking efficiency and compositional distribution is a challenge and, hence, measuring the
intrinsic mass and size dispersity within these areas isanimportantaspectofsuchcontrol.Itisofgreat
importance that a good handle on how to improve control and accurately measure it is achieved.
Additionally dispersity of the final structure can also play a large part in the suitability for a desired application.
In this Tutorial Review, we aim to highlight the different aspects of dispersity that are often overlooked
and the effect that a lack of control can have on both the polymer and the final assembled structure.
Key learning points
1. What do we mean by dispersity within polymers?
2. What methods do we have to reliably measure the dispersity within polymers and their self-assembled structures?
3. How do polymer properties relate to assembly structure and function?
4. Do we always need control on lower hierarchical levels in order to obtain well-defined higher order structures?
5. In what instances are controlled polymers and assemblies required?
Introduction
Amphiphilic block copolymers, like small molecule surfactants,
can form a range of nanostructures in a selective solvent. These
polymeric self-assembled nanostructures are finding more
potential applications and uses as a result of the higher stability
and robustness that the polymers infer on the particles, due to
their low critical aggregation concentrations and the ability to
contain discrete functionalized domains within the assembly.
There are manyfactors that can impact the properties of the self-
assembled structure, some are a result of the self-assembly
process, such as preparation pathway, and some are factors that
are inherent to the polymers of which these nanoparticles
comprise, such as molar mass variation, block ratio variation
and compositional variation. Hence, it is important to consider
these aspects individually and the impact that they can have on
the desired properties of the assembled structure. The size
distribution of self-assembled structures is often reported in
scientificarticles, but there are fewer reports of how dispersity in
polymer composition and functionality can affect the overall
properties of the nanoparticle. In this Tutorial Review, we aim to
highlight the different areas, both in the polymer building
blocks and the assembly route, which can impact the properties
of the final structures. We also discuss whether control on the
polymer scale is always needed to impart control over the
nanoparticles formed and highlight areas where absolute control
over the self-assembled structure, in terms of dispersity and
functionality, are indeed required.
Controlling and determining polymer
dispersity in polymers
Polymer length dispersity
Before considering the effect of dispersity on a self-assembled
system, one must consider the effect of variation within the
a
Department of Chemistry, University of Warwick, Coventry, CV47AL, UK.
E-mail: rachel.oreilly@warwick.ac.uk
b
Warwick Medical School, University of Warwick, Coventry, CV47AL, UK
†Electronic supplementary information (ESI) available: Additional references,
figures regarding how dispersity relates to morphology and table of size depen-
dence on dispersity range. See DOI: 10.1039/c6cs00818f
‡Current Address: Department of Chemistry & Biochemistry, University of
California, La Jolla, San Diego, CA, USA.
Received 15th November 2016
DOI: 10.1039/c6cs00818f
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building blocks of the nanoparticle, i.e. the polymer chains.
Advances in living polymerization techniques such as ionic
polymerization, and more recently reversible deactivation
radical polymerization (RDRP) techniques, which will be the
main focus of this Tutorial Review, have paved the way for the
synthesis of well-defined block copolymers. Although the molar
mass distributions of polymers prepared by these techniquesare
narrow when compared to free-radical processes for instance,
some level of dispersity remains. The most commonly studied
form of dispersity amongst polymer chains is that of their
molar mass; this is assessed by studying both the breadth
and shape of the molar mass distribution. Commonly, size
exclusion chromatography (SEC) is used to reveal this informa-
tion, however care should be taken when considering the absolute
Kay E. B. Doncom
Kay Doncom graduated from the
University of Leeds in 2010 with a
BSc and MChem (1st class). She
then moved to the University of
Warwick to undertake her PhD
under the supervision of Prof.
Rachel O’Reilly. In 2014 she
started a post-doctoral position
at the University of Sheffield,
working for Prof. Steven Armes
on polymerization-induced self-
assembly formulations using bio-
compatible zwitterionic monomers.
After spending some time
travelling Kay returned to the University of Warwick to join the
O’Reilly group as a Research Fellow. Her research interests include
the synthesis of stimuli-responsive polymers by RAFT
polymerization and post-polymerization modifications, the self-
assembly of polymers in solution and the analysis of the
resulting polymeric nanostructures.
Lewis D. Blackman
Lewis Blackman graduated from
the University of Southampton
with a 1st class Master’s degree
in Chemistry in 2012. He is
currently in his final year of his
PhD at the University of Warwick
under the joint supervision of
Prof. Rachel O’Reilly and Prof.
Matthew Gibson. His research
focuses on the solution self-
assembly of responsive polymers,
and the development of new
synthetic routes towards enzyme-
loaded nanoreactors.
Daniel B. Wright
Daniel Wright graduated from his
undergraduate degree from the
University of Brighton in 2011.
He went on to complete his PhD
in 2015, under the supervision of
Prof. Rachel O’Reilly at the
University of Warwick, which
focused on lubricant additives
for automotive engines. He is
currently working in the group of
Prof. Nathan Gianneschi as a
postdoctoral scholar at the
University of California, San
Diego. His current research
topics deal with the design and characterization of enzyme
responsive polymeric self-assemblies towards the development of
active-targeting therapeutics.
Matthew I. Gibson
Professor Matthew I. Gibson holds
a joint appointment between the
Department of Chemistry and
Medical School at the University of
Warwick, UK. Matthew received his
MChem (2003) and PhD (2007,
with Prof Neil Cameron) from the
University of Durham, UK. After a
postdoctoral period under the
direction of Prof Harm-Anton Klok
at EPFL, Switzerland (2007–2009)
Matthew was appointed at Warwick
and has been promoted to Assistant
(2012), Associate (2015) and Full
(2016) Professor. Matthew leads a multi-disciplinary research group
combining chemists, microbiologists and cell biologists with the aim of
addressing global healthcare challenges with polymer/carbohydrate
science. Current research includes the development of polymer
cryoprotectants for storage of donor tissue, new diagnostics and
glycosylated materials for targeting infection. Matthew holds a
European Research Council starter grant (2015) and his work has
been recognized with awards including the 2012 MacroGroup Young
researchers medal, a 2014 RSC emerging technologies prize, 2015
Dextra medal, and 2015 PAT young talent prize.
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values obtained by this analysis technique. The obtained retention
time for a polymer chain moving along the SEC column is related
to the hydrodynamic volume of the chain in solution, assuming
no chemical interaction with the SEC column, as opposed to its
molar mass. Typically, the distribution of retention times is
transformed mathematically into a distribution of molar
masses by use of a series of calibrants of known narrow molar
mass distributions, however one must consider the similarity of
the solution behavior between the sample polymer and the
calibrant standard. More accurate results can be obtained by
use of a multi-detector SEC setup that employs the use of a
multi-angle light scattering (MALS) and/or an intrinsic viscosity
detector in conjunction with a refractive index (RI) or ultraviolet
(UV) detector. For additional information regarding SEC, the
reader is referred to the following text.
1
Additionally, more
advanced techniques employing 2D chromatography, such as
SEC coupled to an affinity column, or liquid chromatography
under critical conditions of absorption, coupled to information
rich detectors such as those discussed above, as well as FT-IR or
NMR spectroscopy, or ESI-ToF and MALDI-ToF MS exist.
2
These
advanced techniques can give information on not only length
but also compositional dispersity, and can even decipher poly-
mer chains of identical length that vary only in their end group.
The calculated molar mass distribution obtained can be
described in terms of different molar mass averages, of which
we shall consider the number average molar mass (M
n
) and the
weight average molar mass (M
w
). These are defined in eqn (1)
and (2), respectively, where N
i
is the number of chains with
mass M
i
. The dispersity (Ð
M
) of the polymer is the ratio of these
two molar mass averages as shown in eqn (3) and is generally
considered a measure of the broadness of a polymer’s molar mass
distribution. However, the standard deviation (S
n
) associated
with a polymer’s M
n
is given in eqn (4).
3
Mn¼PMiNi
PNi
(1)
Mw¼PMi2Ni
PMiNi
(2)

M¼Mw
Mn
(3)
Sn2
Mn2¼

M1(4)
As can be seen by this equation, S
n
is related to both Ð
M
and
M
n
. Therefore, although Ð
M
is often used to describe how well
defined a polymer is, two polymers with identical Ð
M
values
but with differing M
n
values have very different breadths of
their molar mass distributions. For instance, a polymer with
M
n
= 20 kg mol
1
and Ð
M
= 1.08 has a S
n
of 5700 g mol
1
,
whereas a polymer with M
n
= 200 kg mol
1
and Ð
M
= 1.08 has a
S
n
of 57 000 g mol
1
. This means that for the 20 kg mol
1
polymer, 95% of its chains fall between 8.6–31.4 kg mol
1
(2S
n
), whereas for the 200 kg mol
1
polymer with an identical
Ð
M
, 95% of the molar mass distribution falls between
86–314 kg mol
1
. This is something that should be considered
when comparing the dispersity of polymer samples with signifi-
cantly different molar masses. Additionally, this shows that
although the latter polymer is relatively well-defined, with a
Ð
M
value that is reasonable from an RDRP process, 95% of
its molar mass distribution occupies a molar mass range of
228 kg mol
1
. As such, even polymers with Ð
M
values as low as
1.01 cannot be considered well defined in terms of its molar
mass, when compared to an entity with a single molar mass. In
this case, an M
n
= 100 kg mol
1
polymer of Ð
M
= 1.01 occupies a
molar mass range between 80–120 kg mol
1
in 95% of its
chains. Polymer molar mass, and the dispersity thereof, is a
factor that affects numerous polymer properties including the
glass transition temperature (T
g
), processability, viscosity and
strength, resistance and wear.
5
As will be discussed later in
this review, polymer dispersity can also have an effect on the
properties of the self-assembled structures, such as morphol-
ogy and size. As such, there have been a few reports in recent
years that have focused on tuning the Ð
M
and shape of a
polymer’s molar mass distribution, whilst keeping other prop-
erties, such as M
n
, constant. Recently, Fors and coworkers were
able to tune both the breadth and shape of the molar mass
distribution of a series of polymers synthesized by nitroxide-
mediated polymerization (NMP).
4
Here, the authors used different
total addition times of the nitroxide initiator to the polymeriza-
tion, at a constant addition rate, which led to the preparation of
polymers with a controlled Ð
M
. Additionally, by using different
addition rate profiles, the shape of the molar mass distribution
could also be controlled. The authors used an asymmetry factor
(A
s
) to describe the symmetry of the shape of the distribution,
Rachel K. O’Reilly
Rachel K. O’Reilly is a Professor
and an ERC consolidator grant
holder at the University of
Warwick. Her group undertakes
research in the fabrication of
polymer nanostructures using
advances in self-assembly. She
also leads projects in the area of
catalysis, responsive polymers,
nanostructure characterization
and DNA nanomaterials. She
has published over 150 papers
to date and has been awarded 6
highly competitive young scientist
medals, including in 2012 the RSC Hickinbottom medal and
IUPAC-Samsung young polymer scientist award, and in 2013 the
American Chemical Society Mark Young Polymer Scientist award.
In 2016 she was awarded the Gibson-Fawcett Award from the RSC
in recognition of her innovative research in materials science. She
is on the reviewing board of editors for Science and the editorial
advisory board of Polymer Chemistry, Chemical Science, Chemical
Society Reviews, Chemical Communications, Bioconjugate
Chemistry and Polymer International.
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the calculation of which is defined in eqn (5).
4
The values for
Band Aare the deviations of the molar mass of the upper and
lower 10% of the distribution, respectively, from the molar
mass of the peak of the distribution (M
p
) (Fig. 1).
As¼B
A¼MWupper 10% Mp
MWlower 10% Mp

(5)
Polymer block dispersity
By their very nature, block copolymers will show discrepancies
in both the length of each block and their respective end-group
fidelity. This will typically depend on the type of polymerization(s)
employed. For instance, ring opening metathesis polymerization
(ROMP) and ionic polymerizations that are truly ‘‘living’’ in
character generally show better end-group fidelity of the growing
chain between each chain extension than RDRP processes
by virtue of the fact that chain termination does not occur.
However, one must also consider the inherent limitations of
these techniques such as backbiting in ROMP, which can lead
to branching and therefore dispersity in the polymer chain’s
architecture and hydrodynamic volume, or the lack of functional
group compatibility in ionic polymerizations. Additionally, the
block sequence control in living ring opening polymerizations
(ROP) is limited by transesterification reactions and unwanted
initiation from contaminants such as water. Furthermore,
intermolecular chain transfer to polymer in ROP results in
shuffling of the polymer segments, and therefore leads to
dispersity in the monomer or block sequence. This behavior
is subtle as it results in a broadening of the molar mass
distribution but no change in M
n
as the total number of chains
remains constant. RDRP techniques have gained popularity
owing to their tolerance to a wide variety of different chemistries
in the monomer and being less synthetically taxing than ionic
polymerizations. In the case of RDRP, techniques that make use
of the persistent radical effect, such as ATRP and NMP, often
show the most promising efficiency in the subsequent chain
extension of macroinitiators (also referred to as the blocking
efficiency) because of the lack of a requirement for a second
small molecule initiator. However, since termination is still a
contributing factor in these techniques, ‘‘dead’’ chains that will
not chain extend in subsequent polymerizations can still arise.
Keddie has discussed a further complication in synthesizing
block copolymers by reversible addition fragmentation chain
transfer (RAFT) polymerization.
6
Although typically very low
concentrations are employed, the need for an initiator means
that some chains from the polymerization of the first block will
be initiator derived and will bear this functionality at the a-end
group. Therefore, if a specific functional moiety (e.g. targeting
ligand, fluorescent dye, etc.) of the chain transfer agent was
expected to be present on the a-end group, 100% functionaliza-
tion of the chains will not be achieved in the case of RAFT
polymerization. Additionally, some chains undergo termina-
tion so functionality at the o-end group will also be lost in these
cases. Whilst important for homopolymers, both these factors
become even more so when considering the synthesis of
block copolymers. After just a single chain extension of a homo-
polymer (A) to synthesize a diblock copolymer (AB), the polymer
sample will contain a mixture of both dead and living RAFT
CTA-derived AB diblock copolymer chains, both dead and living
initiator-derived AB diblock copolymer chains, both dead and
living initiator-derived B homopolymer chains, and dead initia-
tor- and RAFT CTA-derived A homopolymer chains (see Fig. 2).
6
The contribution of initiator-derived chains can be minimized
by methods developed by Perrier and coworkers.
7
Here, mono-
mers that show high propagation rates, and therefore high
k
p
/(k
t
)
1/2
, such as acrylamides, were employed at high concen-
trations, in aqueous media, in order to increase the overall
Fig. 1 Depiction of the calculation of the asymmetry factor (A
s
)fora
molar mass distribution. Adapted from ref. 4 with permission from the
American Chemical Society, copyright 2016.
Fig. 2 The various polymer species formed during a chain extension by RAFT polymerization. Figure adapted from ref. 6 with permission from the Royal
Society of Chemistry, copyright 2014.
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reaction rate. Crucially, this allowed for very small initiator
equivalents to be used in order to reduce the amount of initiator-
derived chain ends but still allow for reasonable reaction times.
The low degree of termination coupled with the excellent end-
group retention resulting from the low initiator concentration
allowed for the synthesis of multiblock copolymers with low
dispersities by RAFT polymerization in a one-pot process.
Even though block copolymers may have poor blocking
efficiency, they may not necessarily have a poor length disper-
sity and vice versa. For example, Matyjaszewski and coworkers
investigated the use of activators regenerated by electron transfer
atom transfer radical polymerization (ARGET ATRP) to achieve
polymer distributions with controllable Ð
M
. By varying the
catalyst loadings in the polymerization, the Ð
M
values of a series
of poly(methyl acrylate) and poly(styrene) homopolymers could
be controlled. At very low catalyst amounts (o5 ppm), the
polymers showed relatively high Ð
M
values up to 2.0, however
they still retained their end group functionality and were able to
undergo successful chain extensions to form diblock copolymers
with narrow molar mass distributions.
8
Harrisson and coworkers carried out statistical analyses
on both real and theoretical precision polymers prepared by
different synthetic techniques.
9
Using a monomer (B) that
could not homopolymerize into a growing polymer chain and
targeting a polymer of composition A
10
–B
1
–C
10
, single monomer
addition resulted in only 12.5% of chains actually displaying
this exact composition. Similarly, the addition of a rapidly
polymerizing monomer into a slowly polymerizing mixture
resulted in only 4.6% of chains containing just one unit of
monomer B, at position 11, in the polymer chain. The prob-
ability of finding monomer B in the target position was also
found to increase with increasing DP of B; there is a 95% chance
of finding monomer B at the midpoint (in this case position 16)
if the target composition is A
10
B
11
C
10
compared with just a
17.5% chance for A
10
B
1
C
10
(position 11).
For (multi)block copolymers synthesized by coupling
chemistries employed using the end group, such as click
chemistries, the assessment of the success of the coupling
reaction becomes increasingly complicated as the dispersity
of the two constituent blocks increases. By investigating the
quantitative click conjugation of theoretical molar mass distri-
butions, Barner-Kowollik found that the conjugation of polymers
led to conjugates with a lower Ð
M
than their constituent blocks,
and M
n
values equal to the sum of the M
n
values of their
constituent blocks, regardless of constituent block dispersity.
10
The author showed that when conjugating polymers with narrow
molar mass distributions (Ð
M
o1.10), a clear shift in the entire
distribution could be observed with no significant change in the
overall shape of the distribution. However, when conjugating
polymers with Ð
M
42.0, although the M
n
of the conjugate
equaled the M
n
of the constituent blocks, the peak molar mass
(M
p
) decreased relative to the higher molar mass block. Although
the conjugate appeared to have a lower molar mass than one
of its constituent blocks, on closer inspection of the overall
distribution, fewer lower molar mass species existed in the
conjugate, which allowed M
n
to increase despite the decrease
in M
p
. For constituent blocks with vastly different M
n
and Ð
M
values, the ideal shape of the molar mass distribution for a
quantitatively conjugated block copolymer was found to be
bimodal, when analyzed by SEC (Fig. 3). This was rationalized
by considering that a distribution obtained by using a refractive
index detector of an SEC calculated the number of repeat units at
a certain molar mass, not the number of chains at a certain molar
mass. By calculating the concentration (i.e. number distribution)
and plotting against molar mass in a linear plot, the distributions
of the conjugates were found to be unimodal and of higher molar
mass than their constituent block copolymers.
10
It is important to stress from considering the above examples,
that molar mass values, and molar mass distributions obtained
from SEC, are not always particularly informative for block
copolymers, although commonly employed. Two polymer chains
within a distribution can have an identical molar mass but
can ultimately be very different in terms of their hydrophilic
to hydrophobic ratio, block volume ratio in solution, degree of
functionality and overall block sequence. These challenges can
lead to a loss of control or understanding when considering
block copolymer self-assembly, particularly when close to a phase
boundary, which can lead to ill-defined morphologies in
certain cases.
End group fidelity
Because of the inherent challenges in controlling and under-
standing the dispersity in block copolymers, it is possible to
achieve a pseudo block copolymer by utilizing an end group on
a homopolymer, where the end group resembles a second block
of differing solvophilicity to the homopolymer chain. This can
obviously reduce the dispersity, particularly in the length, of
a system to that contained within the single polymerized
block. Du et al. designed a series of RAFT chain transfer agents,
based on a common, commercially available RAFT CTA, with
differing hydrophobic functionalities on the a- and o-ends.
11
Fig. 3 Expected theoretical distributions obtained from conjugation of
two polymer distributions in a quantitative process. Two constituent
blocks, one with a narrow molar mass distribution (green) and one with
a broad molar mass distribution (red) form a conjugate block with a
bimodal molar mass distribution (blue) when quantitatively conjugated
together. Reproduced from ref. 10 with permission from John Wiley &
Sons Ltd, copyright 2009.
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These RAFT agents were then used to homopolymerize hydro-
philic monomers to form hydrophilic homopolymers with
hydrophobic end groups. It was found that these homopoly-
mers underwent self-assembly in aqueous solution, driven by
the hydrophobicity of the end groups. However, it is important
to consider that when functionalizing a polymer, either by a
post-polymerization method or by introducing the functionality
into the end groups before polymerization, the amount of
functionalization can introduce another level of dispersity
between polymer chains. As mentioned in the previous section,
RAFT chain transfer agents can contain two different function-
alities, but one or both of these can be lost on some chains
during the polymerization. Post-polymerization methods do
not always yield 100% functionalization either, however by
employing highly efficient chemistries, the dispersity in end
group functionality between chains can be reduced.
12
Analysis
techniques, such as NMR spectroscopy, that are often used to
calculate the degree of functionalization always carry a level of
error, as well as showing an average of all the components of
the sample, so it is often difficult to accurately state that every
single chain within the sample contains the desired end block.
Instead, one should use a variety of complementary techniques
dependent upon the end group in question, such as MALDI-
ToF-MS, UV-Vis spectroscopy, including the UV trace obtained
from SEC analysis, elemental analysis, FT-IR spectroscopy and
fluorescence spectroscopy. However, one must also consider that
these techniques often consider averages across the sample and
carry their own associated errors. It is worth considering such
effects when using chain transfer agents or similar that end up
attached to the polymer chain and whether hydrophobic func-
tionality introduced by this method can act as a pseudo block.
Polymer compositional dispersity
Copolymerization is typically employed to tune the properties
of a polymer chain, or of a block within a block copolymer. For
instance, copolymerization of monomers with very different
hydrophilicities can lead to the tuning of the copolymer’s overall
hydrophilicity, or even introduce thermoresponsive properties
in certain solvents. Copolymerization can also be used to intro-
duce functionality (e.g. for targeting, sensing, responsiveness
or catalysis) along a section of a block copolymer. Although
copolymerization is a robust method for achieving such proper-
ties, copolymerization itself introduces another dimension of
dispersity in the location of functionality along the polymer
chain. Compositional dispersity, for instance differences in the
degree of functionality along the length of each polymer chain
(also known as compositional drift) or variation in the degree of
functionality between chains, is a factor that can play a major
role in polymer performance and function. The average compo-
sition of a polymer chain can be obtained relatively easily
using NMR spectroscopy or in some cases elemental analysis,
however determining the dispersity in a polymer’s composition
is challenging since two polymer chains with similar molar
masses within a single sample can possess different functionality
loadings. Considering that polymer chains with different compo-
sitions may not behave similarly in solution, compositional
dispersity may lead to a broadening of the dispersity of a
polymer’s higher order self-assembled structures, be it in terms
of size, volume, shape etc. Additionally, variation in the distribu-
tion and loading of a functional group may then affect other
properties of the self-assembled structure. For example in a
nanoreactor, poorly defined functionality location may impact
the nanoreactors’ catalytic capabilities.
Commonly, reactivity ratios are employed to ascertain the
compositional distribution along a copolymer chain. Note that
this method only applies to RDRP, or other ‘‘controlled’’ poly-
merization techniques and not to free radical polymerizations.
A plot of f
A
vs. F
A
is often fit to a non-linear least squares (NLLS)
method to obtain values for r
A
and r
B
.
13,14
These reactivity
ratio values yield theoretical information on the compositional
distribution throughout the copolymer. For instance, if both r
A
and r
B
are close to zero, neither monomer preferentially reacts
with itself and so an alternating copolymer structure is pre-
dicted. If r
A
and r
B
are close to one, the monomers show no
preference for either monomer and so a random distribution of
the monomers throughout the chains is obtained. As the values
increase to greater than one, the monomers preferentially react
with themselves so homopolymerization dominates, although
if single incidents of cross-propagation occur, a block-like
structure is obtained. In the extreme case where both r
A
and
r
B
c1, copolymerization does not occur, leading exclusively to
homopolymerization. In the case where the reactivity ratios are
very different from one another (e.g. if r
A
c1cr
B
), compositional
drift is likely to occur. This is where, for an RDRP process, in the
initial stages of the reaction, both A- and B-terminal growing
chains preferentially react with monomer A. As the reaction
proceeds, the concentration of monomer A rapidly decreases,
where the concentration of monomer B remains roughly constant,
making the chances of monomer B addition higher, which
outweighs the preference for monomer A addition. This change
in monomer preference leads to asymmetrically functionalized
gradient copolymers. Note that such methods yield point
estimates for r
A
and r
B
but a 95% joint confidence interval
should also be obtained in order to determine the uncertainty
associated with these values, and therefore the uncertainty in
the monomer distribution along the chain.
15
Copolymerization in ring opening polymerizations that
proceed via an ‘‘activated monomer’’ mechanism is further
complicated by virtue of the fact that the actual reactive
monomer species are the activated versions of the cyclic
monomers and not the cyclic monomers themselves. Therefore,
measurement of the reactivity ratios is challenging as the
relative concentrations of the active monomers does not always
match the feed ratios and as such careful consideration of the
relative equilibria must be employed.
The use of reactivity ratios to predict the overall composition
along a chain can be very powerful because the various polymer
compositions produced cannot be distinguished by standard
techniques such as SEC or NMR spectroscopy of the prepared
polymers. As such, understanding the architecture of the polymer
distribution, which is necessary for understanding the polymer’s
solution behavior, can only be achieved using specialized
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techniques such as reactivity ratio determination
15
and those
discussed further below.
13
C NMR spectroscopy was a technique employed by Kaur
and Brar to observe this compositional distribution throughout
a polymer chain synthesized by ATRP.
16
Firstly, they calculated
the reactivity ratios between methyl methacrylate (M) and
n-butyl acrylate (B), which showed different reactivity ratios
(r
M
= 2.17, r
B
= 0.42) implying a moderate gradient copolymer
would form. In order to experimentally measure this pheno-
menon, the authors compared the
13
C NMR spectra across a
range of monomer feeds at different conversions during the
copolymerizations and compared the relative integrals of
the dyads consisting of MB, MM and BB compositions, and
both M-centered (MMM, BMM, and BMB) and B-centered (BBB,
MBB, and MBM) triads. The results showed that BB dyads
increased as a function of conversion, whereas MM dyads
decreased in relative intensity. The same corresponding trends
were also observed for BBB and MMM triads. The results were
in good agreement with the compositional drift predicted from
the reactivity ratios.
Both compositional and molar mass dispersity can have
drastic implications on the solvent interaction parameter and the
packing parameter, respectively, and therefore the self-assembly
behavior of block copolymers. As such, when considering
dispersity in block copolymers, not only the molar mass
dispersity but also dispersity in the composition, end groups,
block order and blocking efficiency must be considered when
designing these polymers for use in self-assembly.
Self-assembly
It is necessary at this point to give a brief overview of the aspects
that affect the self-assembly of polymers in aqueous solution. For
more detailed literature please refer to the relevant section in the
ESI.†When amphiphilic block copolymers are dispersed into a
selective solvent (or solvent mixture) the polymers spontaneously
self-assemble in dilute solution into a range of structures on the
nanoscale, similar to those adopted by surfactant molecules in
solution, with the most commonly formed structures being
spherical micelles.
17
The vast range of nanostructure morphol-
ogies formed at equilibrium is governed by the minimization of
free energy between the two blocks in solution (polymer–polymer
interaction parameter, w
AB
) and between each block and the
surrounding solvent (polymer–solvent interaction parameters,
w
AS
and w
BS
).
18
This is typically dictated by the relative volume
fractions ( f), the solvophobicity, and the degree of polymeriza-
tion of each block, and is strongly related to the packing
parameter by which surfactant micelles abide.
The packing parameter of surfactant molecules as investi-
gated by Israelachvili, Mitchell and Ninham
19
is a simple
concept that allows the relationship between surfactant mole-
cular structure (such as head group area, a
0
, hydrophobic tail
length, l
c
and volume of the hydrophobic segment, v) and the
resulting particle morphology to be understood using a critical
packing parameter, p, where p=v/a
0
l
c
(Fig. 4). Altering
these parameters leads to the molecule adopting a different
interfacial curvature and therefore a different morphology.
Amphiphilic block copolymers can be considered mimics of
these small molecule surfactants where the hydrophobic block
is a mimic of the surfactant tail and the hydrophilic block is a
mimic of the polar head group.
20
Spherical micelles, with high
curvature, are formed when pr1
3, cylinders between 1
3opr1
2
and when 1
2opr1, vesicles are formed (Fig. 4). It should be
noted that this situation applies to structures at equilibrium,
which is true in the majority of cases for surfactants. However,
block copolymers can also adopt structures that are kinetically
trapped, out-of-equilibrium structures that cannot be predicted
in this way and relate instead to the self-assembly process. For
instance, the use of a cosolvent that is a common solvent for
both blocks to aid the transition into the selective solvent is
more likely to result in morphologies closer to their equilibrium
structures than direct dissolution in the selective solvent. In
practice, pis extremely difficult to calculate and therefore only
occasionally used. Instead the hydrophilic and hydrophobic
mass fractions, which relate to the volume fractions, are more
commonly considered parameters.
21
One must also consider the
relative volume changes that occur when considering different
monomers, e.g. monomers containing branched side chains,
such as 2-ethylhexyl methacrylate, occupy more volume than
their linear counterparts of the same mass.
By controlling the volume fraction of each block through
polymerization methods, specific morphologies can be targeted.
Altering the hydrophilicity of one block will also cause a shift in
both the volumefraction of the block and in the polymer–solvent
interaction parameter. This control over both hydrophilic and
Fig. 4 The different morphologies obtained by targeting different packing
parameters, p.
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hydrophobic domains and overall polymer architecture allows
access to a rich range of nanostructure phases in solution.
However, dispersity within the block copolymers close to a
phase boundary could result in a hydrophobic/hydrophilic
distribution that exists on either side of the phase boundary,
which in turn will result in a mixture of morphologies at
equilibrium. Possible implications of this include obtaining a
mixed morphology phase, as will be exemplified later in the
review. It is important to stress that the morphology predicted
by the packing parameter is the morphology adopted at
thermodynamic equilibrium. If the polymers cannot reach
thermodynamic equilibrium then intermediate morphologies
may be formed, with the ultimate morphology predicted by p
never being reached. However, a discussion of such cases is
beyond the scope of this review.
Size distribution within self-assembled structures
After self-assembly to form polymeric nanostructures several
analysis techniques can be utilized in order to study their
properties. These include both scattering and microscopic
analyses, of which some will be discussed herein. For further
information regarding more advanced techniques such as
small angle X-ray and neutron scattering (SAXS and SANS)
and a broader overview of microscopy techniques, the reader
is referred to the following text.
22
One such property is the size
and the size distribution of the particles in solution. A common
method to analyze this is to use dynamic light scattering (DLS).
Light scattering techniques analyze a large number of particles
and therefore give excellent statistics. For a more in depth
discussion on light scattering techniques the reader is referred
to the following texts.
22,23
In order to obtain the diffusion
coefficient and therefore information on the size of the parti-
cles in solution one must first obtain the electric field and
intensity autocorrelation functions, g
1
(q,t) and g
2
(q,t). The
intensity autocorrelation function, g
2
(q,t), can be expressed in
terms of the decay in scattered intensity as in eqn (6).
g2ðq;tÞ¼ IðtÞIðtþtÞ
hi
IðtÞ
hi
2(6)
where I(t) and I(t+t) are the scattered light intensity at time t
and t+t, respectively. The intensity autocorrelation function
can also be expressed in terms of the electric field correlation
function, g
1
(q,t) (eqn (7)).
g
2
(q,t)=1+f[g
1
(q,t)]
2
(7)
For a sample with a single population, all of identical size and
shape (i.e. with no dispersity), g
1
(q,t) can be fit as a single
exponential decay which exhibits a single relaxation time, t.
However, this is never true for polymer samples and therefore
g
1
(q,t) must be represented as a distribution of relaxation times
and a cumulant analysis is routinely applied.
24
Cumulant
analysis fits a 3rd order fit to the semi-logarithmic plot of the
correlation data. The first cumulant gives the average decay
rate and therefore Z-average mean particle size and the 2nd
cumulant gives information on the variance in the sample, or
overall size dispersity.
Assuming a Gaussian distribution of particle sizes, this
dispersity can be expressed, as a dispersity (Ð), in terms of
the standard deviation of the distribution and the mean size of
the sample, see eqn (8).

¼standard deviation
mean Zaverage diameter

2
(8)
For a perfectly uniform sample Ðwould be 0.0. A sample with
low dispersity would have a value of 0.0–0.1, a moderately
disperse sample would have a value between 0.1–0.4 and a
broad sample has a value 40.4. Since this dispersity is con-
nected to the mean size of the particles, the same dispersity
value will actually have a different range, in terms of distribu-
tion width, depending upon the size of particle analyzed. For a
particle with a D
h
of 10 nm and a low Ðof 0.1, the overall size
range of the sample (assuming a Gaussian distribution and
therefore 2 standard deviation covers 95% of sizes) will be
6.32 nm, meaning the particles range in size from 3.68 nm to
16.32 nm (see Fig. 5 and Table S1 in ESI†). Increasing the
particle size to 250 nm but keeping the dispersity value of
0.1 gives a range of particle sizes from 92 nm to 408 nm. In both
cases this is a size variation of 63% of the mean size, but in
practical terms the wider size distribution for the larger particle
could have implications when considering applications (vide
infra). Therefore it is clear that simply stating that a sample is
‘‘relatively well-defined’’ gives little practical information on
the distribution of particle sizes in the sample.
It should be noted that one drawback to DLS analysis is that
the hydrodynamic diameter obtained for the particle is that of a
hard sphere that moves at the same speed in solution as the
particle in question. For this reason, sizes obtained by DLS may
not be representative for non-spherical morphologies. Quite often
benchtop DLS instruments only measure at one or two angles.
This can lead to large errors in the particle size obtained,
particularly when multiple populations are present in the
sample.
25
There are more sophisticated instruments that are
able to measure at a range of angles and these give advanced
Fig. 5 Graph showing the size variation with polydispersity index of particles
with different average sizes. The dotted line represents the Z-average
hydrodynamic diameter and the solid lines show the range of sizes
obtained at two standard deviation at a given polydispersity index.
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information, such as better analysis of multi-modal particle
size distributions and can also give information on the inter-
action between the particles. However, even sophisticated
instruments cannot distinguish between particles with little
difference in size, instead giving an average particle size or
sizes. Practically, a difference of 3 times the diameter is needed
to be able to distinguish two different populations. For example,
in one study three monomodal samples of polystyrene beads of
220 nm, 330 nm and 410 nm were mixed and it was observed
that DLS analysis gave a broad intensity distribution, weighted
towards the larger particles, rather than separating the different
populations.
26
This demonstrates how dispersity observed in
DLS is not always a result of a continuum of sizes, but can also
be caused by discrete populations of a similar size. Therefore it is
important to use a range of complementary techniques to fully
characterize any sample.
Static light scattering (SLS) uses the same principles as DLS
but uses the mean value of the scattered light rather than the
fluctuations over a given time period.
22,23
Experiments are
often performed over a range of angles (y) and at multiple
concentrations (c). The Zimm equation (eqn (9)) can then be
used to obtain information about the molar mass (M
w
) and the
radius of gyration (R
g
) of the scatterers. Here, A
2
is the second
virial coefficient, cis the sample concentration and Kand R
y
are
defined in the ESI.†
Kc
Ry
¼q2Rg2
3Mw
þ1
Mw
þ2A2c(9)
Although Zimm analysis is the most commonly used method
for the solution analysis of polymers in some instances it
can be insufficient, for example if the influence of the virial
coefficient is too pronounced (exhibited by an upturn in the
Zimm plot) then a correction needs to be applied to the Zimm
analysis. This correction is typically given in the form of a Berry
plot where a simple linearization of data can be observed
and further extrapolated. Large particles in solution can also
produce distortions to a linear Zimm or Berry plot, typically as a
consequence of long range particle–particle interference and
aggregation. In such cases, a Guinier plot can be used, where a
linear plot of I(0)/I(q)vs. q
2
is produced. Nevertheless, these
plots are all within the range of qR
g
o1. When the particles to
be analyzed are too large to fulfil this criteria, or when reason-
able extrapolations are not obtained from the aforementioned
plots, particle and structure factors must be used. An explana-
tion of such data interpretation is beyond the scope of this
review and will not be expanded upon.
Combining DLS and SLS allows for information about size
and molar mass to be obtained simultaneously. If the molar
mass of the polymer is known then the molar mass of the self-
assembled particle can be used to give an aggregation number,
N
agg
, defined as the number of polymer chains per particle.
This is important in determining differences between similar
particles, for example, two particles may have a similar size
when measured in solution but widely different aggregation
numbers. This dispersity could result in differences in functional
behavior, as the aggregation number relates to the density of
chains and therefore the two particles will have different core
densities, and a different number of chains making up the
corona, which if used for a functional application such as
targeting in nanomedicine, could be crucial parameters.
Combining the hydrodynamic size information, R
H
, from
DLS and the R
g
from SLS can give information on the morphol-
ogy of the particles. R
g
/R
H
values are representative of different
density of morphologies. R
g
/R
H
value of 0.775 suggests a homo-
geneous sphere, i.e. a spherical micelle whereas a R
g
/R
H
value of
1 is indicative of a hollow sphere and therefore suggests a
vesicular morphology. Values of R
g
/R
H
41 account for extended
structures in solution, for example a flexible polymer chain has
an R
g
/R
H
of between 1.5–1.7 whereas a rigid rod has R
g
/R
H
42.
27
This parameter can also allow for comparison between two
similarly sized particles and can give information on the internal
structure of each particle.
Complementary techniques to such solution based scatter-
ing methods are in the form of microscopy. One of the most
widespread methods used to visualize particles is transmission
electron microscopy (TEM). Most commonly this is done in the
dry state; although cryogenic TEM (cryo-TEM) is becoming
more widely used it is still prohibitive for many research groups
due to lack of access to the specialized equipment, the high
expense and a lack of technical expertise. In dry state TEM
particles are dried to a substrate, commonly on a grid containing
a carbon based film support or, more recently, atomically thin
graphene oxide,
28
and depending on the phase contrast between
the sample and the support, a high atomic number stain
(e.g. uranyl acetate, phosphotungstic acid etc.) that selectively
binds to either the sample or to the grid may be applied. Very
recently, Lieberwirth and coworkers have also described the use
of low vapor pressure trehalose solutions, which are typically used
fortheanalysisofbiologicalsamples,aswellasionicliquidsas
embedding free-standing solvents for ambient temperature TEM
analysis of polymer nanoparticles in solution.
29
Microscopy techniques, such as TEM, are useful in visualizing
the morphology of the particles and by performing tomography
can give information about the 3D shape of the particle and some
information on internal structure. It is worth keeping in mind
that the particles observed in dry state TEM are no longer
hydrated and this could affect the morphology and size observed.
Additionally, using high trehalose concentrations necessary for
ambient temperature liquid phase TEM analysis also alters the
solutionenvironmentofthepolymer nanoparticles, which may
affect its solution behavior. There has been progress in the use of
liquid cell TEM to analyze particles directly in solution without the
need for cryogenic temperatures, however this relatively new field
has yet to be used widely by the scientific community.
30
To obtain the average particle size after TEM analysis it is
common to utilize some imaging software, the most commonly
used being ImageJ, and to measure individual particles. Some
software packages allow for automatic particle size measuring
but one should be aware of some of the limitations of this
technique. In order for automatic particle sizing to be employed,
the particles must satisfy several criteria. They must be spherical,
isolated and have a high contrast compared to the background.
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If these criteria apply then automatic software can be a useful
tool for measuring the size of a large number of particles.
A threshold value must be set to allow the software to distinguish
what ‘‘brightness’’ equates to a particle and what ‘‘brightness’’
equates to background. Setting the threshold too low or too high
can result in the loss of small or large particles, giving an inaccurate
representation of the sizes of the particles in the solution. There are
also semi-automatic methods whereby one can select a large
number of particles and then manually remove any aggregates or
other objects not of interest from the measurements. These auto-
matic methods are useful in generating size measurements from a
large number of particles, important when comparing to light
scattering methods that look at 410
9
particlesinagivenmeasure-
ment. However, the particles must still have a good contrast
with the background grid and even automated particle counting
analyses do not produce anywhere near the statistical relevance of
averaging techniques such as light scattering. This highlights a key
difference as light scattering techniques give intensity-weighted
distributions and microscopy yields a number-weighted distribu-
tion. The majority of publications report the average size obtained
by TEM S
n
. As stated previously, this range of S
n
only accounts
for 68% of the size distribution, hence this should be kept in mind
when analyzing particle sizes.
Often it is difficult to utilize this software when imaging
polymer self-assemblies. Polymeric nanoparticles are often low
contrast due to their hydrocarbon nature and drying effects
often bring them into contact on the TEM grid. The use of a
stain to increase the contrast can cause problems within the
automatic software if the background staining is not even across
the grid or if there are artefacts caused by the stain. Other potential
problems for using the automatic software is the presence of
multiple morphologies, or non-spherical morphologies. In most
automatic image analysis software, the size of the particle is
calculated either by taking the area of the particle, or by taking
the average of the maximum and minimum particle dimensions.
For spherical particles, either of these methods will be suitable,
but for non-spherical particles, this may not lead to accurate
results. Worms for example are often highly anisotropic in length.
In these instances manual particle counting must be performed.
This is more time consuming and has the potential to be more
subjective. The researcher must be disciplined to ensure that
they measure all particles within a given area and not be tempted
to ‘‘cherry-pick’’ the particles that most suit their hypothesis. It is
also important that a significant number of particles are
counted, and the number required to obtain good statistics will
vary according to the distribution of sizes observed. Ideally,
enough particles will be counted that a Gaussian distribution
can be fitted to the histogram of sizes, with the outermost
populations reaching full width at a quarter maximum peak
height. Therefore using microscopy methods in conjunction
with light scattering methods gives the best possible analysis.
Does polymer mass dispersity affect morphology?
As has been described in a previous section, whilst great care is
often taken to gain control over the polymerization conditions
and therefore produce a well-defined polymer in the hope that
this will give a well-defined self-assembled structure, some
dispersity in the system will remain. It can be thought of that
dispersity within a block copolymer affects not only the length
distribution but also the relative volume fractions of the
different blocks within the copolymer. For example, a diblock
copolymer where one block has a greater length dispersity than
the other will mean that the length of the block with the
broader molar mass distribution varies more throughout the
sample than the block with the narrower molar mass distribu-
tion and so chains with an overall higher molar mass effectively
have a lower volume fraction of the latter block. In an amphi-
philic block copolymer this will result in the solvophilic/
solvophobic volume fractions varying throughout the sample.
Since the volume fraction is related to the packing parameter,
different polymers within the same sample will prefer to adopt
different interfacial curvatures and hence the final morphology
adopted may not be that predicted by the average solvophilic
volume fraction (Fig. S1A, ESI†). This is particularly true if the
block ratio of the copolymer sits close to a phase boundary.
Additionally, a longer solvophobic block will result in an
increase in the interaction parameter between the core block
and the surrounding solvent, providing another driving force
for potential morphological variety.
This inhomogeneity resulting from polymer block dispersity
has been demonstrated to occur in bulk self-assembly. For
instance, Hillmyer and Lynd found that for a high interaction
parameter polymer, poly(ethylene-co-propylene)-block-poly(lactide),
increasing the dispersity of the block copolymer from 1.16 to
1.34 whilst keeping the M
n
constant at ca. 15 kg mol
1
, resulted
in an increase in the domain spacing of the lamellar phase of the
bulk self-assembly.
31
For lower molar mass (weakly segregating,
low interaction parameter) block copolymers, they found that
entirely different morphologies, namely lamellar, cylinder and
gyroid phases, could be obtained using block copolymers that
only varied in their molar mass dispersity.
31
This same phenomenon also occurs in solution self-
assembly. Eisenberg and coworkers looked at the effect of the
dispersity of the corona block in a poly(styrene-b-acrylic acid)
(PS-b-PAA) diblock copolymer upon the final morphology
achieved when assembled in water.
32,33
Dispersity was artifi-
cially broadened by mixing polymers with very low dispersity
(Ð
M
o1.05) and identical PS block lengths but different PAA
chain lengths in order to create a range of polymers with the
same overall average chain length but Ð
M
ranging from 1.1
to 2.2.
32
At low Ð
M
, large ill-defined vesicles with a broad size
range were formed. Increasing the dispersity of the system
resulted in smaller vesicles with a narrower size range, and
the appearance of spheres. This decrease in vesicle size with
increasing dispersity was a result of segregation between chains
of different lengths (Fig. S1B, ESI†). In a highly disperse sample
the inherent variation in polymer length led to there being
fewer chains with the average length and instead a greater
number of longer and shorter chains, near the extremes of the
size distribution. The short chains preferentially segregated
on the inside wall of the vesicles, whilst the longer chains
tended to favor the outside wall, where they are less confined.
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Hence, this led to more repulsion on the outer surface of the
vesicles and therefore a higher curvature and smaller vesicles.
Equally, shorter chains in the center of the vesicle allowed for a
higher curvature to be adopted. Excessive repulsion between
longer chains eventually lead to spheres forming (Fig. S1B,
ESI†). The phenomenon of asymmetry in polymer vesicles
has been used by Meier and coworkers to afford directionality
to the assembly of a transmembrane protein into a polymer-
some membrane formed from an ABC triblock copolymer with
intentionally different chain lengths of the corona-forming A
and C blocks.
34
The effect of dispersity within the hydrophobic block has
also been demonstrated.
35
Mahanthappa and coworkers
synthesized a triblock copolymer of poly(ethylene oxide-b-1,4-
butadiene-b-ethylene oxide), PEO–PB–PEO. The PEO blocks had
Ð
M
r1.25 whereas the 1,4-butadiene block had a higher Ð
M
of
1.75. The average chemical composition was expected to give
vesicles as the predominant morphology. Since the dispersity of
the 1,4-butadiene block was greater, polymers that had an
overall longer block length would have therefore had a higher
weight fraction of PB, w
B
, a lower weight fraction of PEO, w
O
,
and hence preferred to adopt a different interfacial curvature
compared to shorter chains that had a higher w
O
. This was
demonstrated in a sample with an average w
O
of 24%, a weight
fraction of PEO where vesicles would be expected to form.
Instead cryo-TEM images revealed the presence of spheres,
worms and vesicles. The authors converted the w
O
value into
a volume degree of polymerization (N
v,tot
) and, by comparing
this to a known morphology diagram for PEO–PB copolymers
with a low dispersity, were able to mark the composition cut off
that corresponds to each morphology regime. This demon-
strated that although the sample had a large portion of chains
that preferred to adopt a vesicular morphology, there were also
significant fractions that preferred to form worms and spheres.
Samples that contained higher w
O
resulted in quite different
behavior. At w
O
of 42 and 58% the expected morphology was
spherical micelles, and whilst all chemical compositions of the
polymers within the distribution fall within the spherical
micelle phase, the differing chain lengths caused by the dis-
persity favor different sized spherical micelles. Rather than a
range of micelle sizes, elongated micelles with tapered ends,
similar to an American football shape, were observed by cryo-
TEM. This was rationalized by different length hydrophobic
chains relocating within the micelle to satisfy their preferred
curvature, similar to the chain segregation in vesicles described
earlier (see Fig. 6).
These experimental findings are also backed up by theore-
tical simulations. Yang and coworkers investigated the effect of
dispersity in the polymer chain on the morphology adopted
in solution.
36
Self-consistent field theory (SCFT) was used to
artificially induce dispersity within a polymer by mixing two
AB diblock copolymers of differing chain lengths. When inves-
tigating the effect of dispersity within the hydrophilic block the
overall average block length was kept constant at 27 but the
hydrophilic block length varied, creating samples with Ð
M
ranging from 1.00 to 2.56. For simplicity’s sake, the hydrophobic
block had no length dispersity (Ð
M
= 1.00) in the simulations.
For the sample with both blocks of Ð
M
= 1.00, the polymers
adopted a vesicular morphology in solution. But as the dispersity
increased, and the hydrophilic block length increased, the
assemblies transitioned from vesicles to a mixture of vesicles,
worms and spheres and finally to spheres and large compound
micelles (LCM). The segregation of the different hydrophilic
block lengths was further investigated and, as in Eisenberg’s
work, it was found that the segregation of the longer blocks on
the outside of the vesicles and the shorter hydrophilic chains
on the inside of the vesicles caused an increase in curvature
and therefore induced the morphology change. A similar
morphological trend was observed when the dispersity in the
hydrophobic block was varied from 1.0 to 1.97, keeping the
hydrophilic block with no length dispersity. However, at very short
hydrophobic block lengths (DP
B
o6) the diblock copolymer
acted as a hydrophilic copolymer, being found equally distri-
buted throughout solution.
These simulations used two distinct polymer chain lengths
to artificially create the dispersity, which is not particularly
representative of a disperse polymer sample. However Jiang
et al. also used SCFT in a similar manner but where dispersity
was characterized by a continuous molar mass distribution.
37
Increasing the dispersity, from 1.0 to 2.0, caused a decrease in
the vesicles sizes owing to the segregation of the short and
longer polymer chains into the inner and outer walls of the
vesicles, respectively, eventually leading to spherical micelles at
high dispersity of 3.4. Similar observations were made whether
the hydrophilic or hydrophobic block was the more disperse.
Whilst these previous examples suggest that dispersity
within the polymer can affect the morphology that the self-
assembled structure adopts in solution, there are also many
reports that find that well-defined self-assembled structures
can be produced from ill-defined block copolymers. Recently
Sawamoto and coworkers synthesized statistical copolymers of
poly(ethylene glycol methyl ether methacrylate) (PEGMA) and
dodecyl methacrylate (DMA) with hydrophobic content between
20 mol% and 50 mol%, varying block lengths and low Ð
M
between 1.2–1.4.
38
These copolymers self-assembled in water
and the overall size of the particles were determined by the
hydrophobic content of the polymer. The size and molar mass
of the particles was independent of polymer molar mass at a
Fig. 6 Schematic demonstrating how the polymers with different lengths
of hydrophobic block migrate within the nanostructure to satisfy
their preferred interfacial curvature, hence forming elongated micelles.
Reprinted with permission from ref. 35. Copyright 2012 American
Chemical Society.
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given DMA mol%, as assessed by SEC in the selective aqueous
solvent. This allowed easy tuning of the aggregation number of
these polymers in water, as the N
agg
was inversely proportional
to the DP. The control over aggregation number could be
especially useful when considering functionalization of specific
domains within polymeric nanoparticles. Polymers with much
broader Ð
M
(2.3–2.4) when analyzed as unimers in DMF were also
found to display such self-assembly behavior. These ill-defined
polymers self-assembled into particles with low Ð
M
(1.2–1.3)
when analyzed by aqueous SEC. The smaller chains within the
distribution assembled into multi-chain aggregates, whilst the
longer chains intramolecularly assembled into single chain
nanoparticles of similar sizes to the corresponding chains with
narrow molar mass distributions (see Fig. 7).
Therefore, whether dispersity within a polymer necessarily
results in dispersity within the self-assembled structure is not
as clear. Also a narrow size distribution, Ð, does not indicate
that all particles are the same. Indeed, as shown in the example
above, particles of similar sizes assembled from the same polymer
can have different properties, such as aggregation number, leading
to differences in such factors as core density or repulsion between
corona chains. It is also worth noting that dispersity within a
structure is not solely confined to size distributions. Distribution
within a polymer in terms of functionality location will therefore
translate into the structure and may affect such properties of
compartmentalization. When targeting specific applications, such
as nanoreactors with functionalized cores, such differences can
affect the efficiency of the particle.
Why does distribution within self-assembled particles matter?
Size. As previously mentioned, dispersity within the length of
the polymer chain can have a large impact on the morphology
adopted, the variation in morphologies achieved and therefore
the suitability of those nanoparticles to specific functions. One
function that is of great interest is the use of functionalized
or loaded nanoparticles as targeted drug delivery agents.
A thorough review of drug delivery methods is beyond the
scope of this tutorial review and for more in-depth reading,
the reader is directed to the relevant section of the ESI†for a
variety of texts. The purpose of this section is to highlight the
potential areas in which dispersity within the system may alter
the nanoparticles’ applicability and behavior.
One way of targeting, by encouraging accumulation of drugs
in tumor vasculature, is by use of the enhanced permeability
and retention (EPR) effect. The theory behind the EPR effect lies
in tumor architecture. Blood vessels in tumors are dilated and
more permeable than in normal tissue and the endothelial cells
in tumors are poorly aligned and have larger gaps between
them. In addition, tumor cells often have poor lymphatic
drainage systems. These defects allow for macromolecules
and nanoparticles in the blood plasma to pass into tumors,
with the poor lymphatic drainage causing the macromolecules
to accumulate in tumor tissues, an effect known as passive
targetting.
39
On this basis, it is possible to accumulate polymer
prodrugs, or drug loaded nanoparticles, at the tumor site.
Conversely, low molar mass drugs do not show the same
accumulation effect because they rapidly diffuse back into the
circulating blood and are cleared by the kidneys (see Fig. 8).
However, solely utilizing the EPR effect to target tumor tissues
has been shown to be inefficient. Chan and coworkers recently
conducted a review of literature on nanoparticle-based target-
ing from the last 10 years and found that, on average, less than
1% of the nanoparticle dose was actually delivered to a solid
tumor.
40
Polymeric-based drugs also offer other advantages,
such as immune system avoidance, prolonged half-life of drugs
in blood plasma and suppressed antigenicity.
Polymeric nanoparticles take these advantages one step
further. They can encapsulate hydrophilic and hydrophobic
drugs and, by incorporation of stimuli-responsive blocks, can
release their payloads in a controlled fashion. They have
extended blood circulation times as a result of their size, being
too large for rapid renal clearance (glomerular filtration).
41
Fig. 7 Graph depicting the constant M
w
of the assembled particles in
water, formed from statistical copolymers of poly(ethyleneglycol methyl
ether methacrylate) (PEGMA) and dodecyl methacrylate (DMA) as the DP of
the overall polymer increases. In DMF the polymers do not assemble,
therefore M
w
increased with DP. Adapted with permission from ref. 38.
Copyright 2016 American Chemical Society.
Fig. 8 Depiction of a low molecular weight drug entering the tumor
tissues but rapidly diffusing out again once the concentration of drug in
the blood plasma decreases and the diffusion of a larger M
w
drug into the
tumor tissue and its accumulation there as a result of its size limiting
diffusion back into the bloodstream. Reproduced from ref. 39 with
permission from Elsevier, copyright 2006.
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For use in such applications, it is important to consider the
factors that dispersity within the nanoparticle may have. We
have previously discussed how a low Ðby light scattering
methods can still equate to a quite considerable range of sizes
in the sample. This size range may be problematic as it leads
to different circulation times and clearance pathways for
differently sized nanoparticles.
42
Different tumor types have
different sized cut offs for nanoparticle accumulation, as a result
of their different blood vessels nanoparticles that are larger
than 200 nm generally do not accumulate in tumor tissues.
43
Therefore when considering this type of passive targeting it is
important that the entire size range of the morphologies in the
system are able to be accumulated within the tumor tissue,
otherwise the system will have low efficiency as the larger
particles cannot diffuse into the tissues. The clearance pathways
of the particle should also be considered. For example, particles
smaller than 5 nm (o40 kDa) are rapidly filtered by the kidneys
whereas particles larger than 8 nm are not.
44
Abroaddistribu-
tion of sizes could cause a significant amount of the delivery
sample to fall either side of these cut-offs, with great implica-
tions related to the targeted dose of drug.
Additionally, when considering the size difference one
should also think about the variation in volume within the
range of nanoparticles. A particle with a D
h
= 100 nm with a Ðof
0.1 will range from 36–164 nm. This equates to a volume range
of 2.44 10
4
nm
3
to 2.31 10
6
nm
3
, with the particles at the
larger end of the spectrum having a volume over 94 times
greater than that of the smallest particles in solution. This
could affect the efficiency of drug encapsulation and causes
difficulties in deducing the exact concentration of drug being
delivered to the target site, which could have potential safety
implications. It will also drastically alter the nanoparticle’s
diffusion behavior and may result in increased or decreased
circulation times or alternativecelluptakemechanismsbecoming
dominant, which could affect the targeting selectivity or specificity
of the nanoparticle.
Surface properties. Utilizing the EPR effect is an example of
passive targeting. Nanoparticles can also be modified to pos-
sess active targeting capabilities. These particles are usually
surface functionalized with specific ligands, such as antibodies
or glycan moieties. This can allow for binding to specific cells
and therefore accumulation in specific areas of the body.
Another surface property that can affect function is charge, for
instance a net positive surface charge can enhance the uptake of
nanoparticles into cells.
45
Different ways that surface functionali-
zation can be achieved is by incorporation of the ligand into the
hydrophilic section of the amphiphilic polymer or by end group
modification, either prior to or post-polymerization. We have
already discussed how end group fidelity is typically lower than
100% when employing RDRP synthetic techniques and how addi-
tion of the functionality after formation of the polymer cannot
guarantee that every chain will contain the desired chemistry.
However, once again it is important to recognize how these
factors can be affected by dispersity within the nanoparticle, in
a previous example, Sawamoto and coworkers demonstrated
that amphiphilic copolymers formed aggregates of the same
size but differing aggregation number based on the size of the
polymer.
38
Considering the case where the corona-forming
blocks or end groups of the assembling polymer contain the
targeting moiety or surface charge, such a variation in N
agg
can
lead to a difference in surface functionalization of the nano-
particle. A particle comprising of fewer chains will have a lower
density of targeting groups than a more densely packed particle
of similar size. For example, consider the hypothetical situation
where the end group of a corona-forming block is utilized as a
means of introducing a targeting ligand on the surface of a
particle, assuming 100% end group functionality and that the
corona chains are well hydrated such that the end groups are
presented on the particle’s outer-most surface at the corona–
solvent interface. In this situation, a core–shell spherical
micelle with R
H
= 100 nm and N
agg
= 50 has approximately
410
4
ligands per nm
2
. It follows that a spherical micelle
with an identical size but twice the molar mass contains twice
the ligand density on its surface. In contrast, dispersity in the
radii of the particles follows a squared relationship in affecting
the ligand density. For instance, a micelle with an identical N
agg
of 50 only has to decrease its radius by a factor of O2, to an R
H
of 71 nm, in order to double its ligand density on its surface.
If considering mixed morphologies present in the block
copolymer self-assembly, the situation gets more complicated;
for instance vesicles typically show N
agg
values in the thousands
so a vesicle of the same size as the aforementioned core–shell
micelle will display a ligand density orders of magnitude
higher. Therefore in these hypothetical examples it is clear that
the surface ligand density is an interplay between the particles’
morphology, size and molar mass and so dispersity in any of
these factors can lead to drastic deviations from the mean ligand
density. Practically, this could have implications in multivalent
binding interactions and diffusion/uptake pathways of the particle
mixture.
Additionally, the same variation in surface density in parti-
cles with well-controlled N
agg
could also be a result of poor end
group modification, whereby the nanoparticle will then be
comprised of a mixture of polymeric chains, those that bear
the desired tag and those that do not. This may have implica-
tions in binding strength and efficiency and therefore affect the
delivery of the therapeutic. Fakhari et al. investigated the
optimum ligand density for binding to carcinomic human
basal epithelial cells and for uptake.
47
A cyclic peptide, cLABL,
was used as the targeting ligand and poly(DL-lactic-co-glycolic
acid) used as the polymeric core of the nanoparticles, stabilized
by Pluronic
s
block copolymers. By using a mixture of differ-
ently functionalized Pluronic
s
stabilizers (either modified with
the ligand or non-modified), nanoparticles with varying surface
densities of the peptide could be synthesized. It was found that
an intermediate ligand surface density (50 : 50 or 25 : 75 ratio
of modified to non-modified Pluronic
s
) maximized cellular
uptake, with lower uptake values being seen for low or very high
levels of surface functionalization. This demonstrates that
for each system there will be an optimum level of nanoparticle
functionalization for cellular binding and therefore changes
in surface functionalization, either through differences in
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aggregation number between particles or through inefficient
end group modification, can affect the desired properties of
the nanoparticle.
Effect of morphology. As has been previously discussed,
the morphology adopted by the polymers in solution can be
affected by the dispersity inherent to the polymer. In drug
delivery applications the shape of the nanoparticle has been
shown to affect cellular uptake, biodistribution, clearance from
the body and, when functionalized with targeting sites, binding
efficiency.
46
In order for particles to accumulate inor be uptaken
by the cells, they must first come into contact with the endo-
thelial cells of the blood vessel wall. Non-spherical nano-
particles have been shown to undergo more lateral drift within
a linear laminar flow thereby increasing the likelihood of inter-
action and accumulation at the wall edges, whereas spherical
nanoparticles tend to flow more towards the center of the vessel
(see Fig. 9).
46
Additionally, theoretical studies have shown that
elongated shapes bind more strongly and can withstand higher
linear sheer flow forces than spherical nanoparticles under the
same physiological conditions.
48
Nanoparticles are cleared from
circulation in the body by macrophages of the mononuclear
phagocyte system (MPS). Particles with a higher aspect ratio of
length to width bind more efficiently to cells, including macro-
phages, but are internalized less than spherical nanoparticles.
This means that elongated particles undergo less phagocytosis
than spherical nanoparticles and therefore more elongated
particles could have higher circulation times within the body,
leading to better accumulation in cells.
49
Hence, gaining con-
trol over the morphology achieved, through polymerization
control or self-assembly control, is important to ensure well-
defined structures are produced that will display the same
application. As was touched on briefly in the previous section
for surface ligand density, the morphology of a nanoparticle
can affect the overall solution behavior. This highlights the
importance of having a single nanoparticle phase that is
specific for the desired application. Since an increase in poly-
mer dispersity or forming out-of-equilibrium structures can in
some cases form a mixture of morphologies, particularly when
close to a phase boundary, careful design of the polymer and
the assembly process should be employed to ensure a well-
defined particle morphology is obtained.
Core properties. Aggregation number, N
agg
, will also have an
effect upon the core of the self-assembled particles. A higher
aggregation number within the same size particle will increase
the core density of a micelle. This may have implications when
considering applications whereby the core of the micelle is
utilized. One such application is in the use of micelles as core–
shell nanoreactors, where the hydrophobic core contains a
catalytic moiety that allows organic reactions to be carried
out within the core of the micelle, in an aqueous external
environment whilst protecting the core from catalyst degrada-
tion or protecting the reactants or products from the reactive
solvent. A variation in aggregation number across a sample
will cause a variation in the number of catalytic moieties
per nanoreactor, therefore potentially affecting the catalytic
efficiency. Another consideration is whether the density of
the hydrophobic chains would affect diffusion of the hydro-
phobic reagents into the core of the nanoreactor. One can
consider that high N
agg
micelles, which have larger core radii
will be able to accommodate more substrates, in addition to
creating a more hydrophobic local environment, which will
drive the sequestration of substrates into the core.
Where chemical functionality is located within the particle
can also have an effect upon the function of the particle. The
location of functionality will be mainly determined by the
polymerization technique, reactivity of the monomers and
chain architecture. Compositional control within the polymer
structure will play a large part in determining location control
in the self-assembled nanoparticle. Block copolymerization
techniques allow for a clear divide between hydrophilic/hydro-
phobic segments of the polymer and can also clearly divide
between functional/non-functional or different functionalities.
Often the functional chemical group is introduced to the
hydrophobic fraction of an amphiphilic block copolymer by
copolymerization with a non-functional hydrophobic mono-
mer. Variations within the copolymerization will mean that
there is a compositional drift across the polymer chain, as
discussed previously. This will therefore translate into a drift in
the composition of the cores of the self-assembled structures.
Note that this will be weighted towards the monomer feed
ratios employed. It is also only possible to predict statistically
where the functionality will reside (e.g. having an increased
chance of being located at a chain end).
Compositional drift within the core block could lead to
enough of a copolymer gradient that effectively the majority
of the functional monomer is located towards one end of
the block, resulting in a functional density either nearer the
core–corona interface or the center of the hydrophobic core.
This could result in phase segregation within the core, or even
lead to unpredicted morphologies. Conversely, discrepancies in
the amount of functionality within the hydrophobic block
between chains may not affect the average micelle core func-
tionality as each particle will consist of a randomized popula-
tion of polymer chains. This demonstrates an example whereby
Fig. 9 Effect of nanoparticle morphology on the margination towards the
outside walls of the blood vessel. Reproduced from ref. 46 with permission
from Future Medicine Ltd, copyright 2013.
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a lack of control at one hierarchical level does not necessarily
contribute to a loss of control at a higher level.
Conclusions
It is crucial to consider the different factors that can affect
dispersity within a self-assembled system. By controlling
various aspects in the polymer chains, e.g. functionality, block
ratio, interaction parameter, molar mass and chain architec-
ture, it is possible to predict and control the properties of the
self-assembly and therefore the solution behavior. Considera-
tion of dispersity in other aspects of the polymeric building
blocks, such as length, blocking efficiency and compositional
distribution has also been discussed as well as the dispersity
within the self-assembled systems, such as morphology ranges,
final sizes and density of surface functionalization. Such con-
siderations are important when considering such polymeric
assemblies for advanced applications, such as in drug delivery or as
nanoreactors. Examples have been given where a lack of control at
the polymer level leads to poorly-defined self-assemblies and
solution behaviors, as well as times where block copolymer disper-
sity does not correlate to dispersity in polymer self-assemblies. We
hope this tutorial review sheds light on the factors that influence
block copolymer solution self-assembly and behavior and enables
readers to consider how polymer design can be used to fine-tune
particle properties for specific applications.
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