Polymer Molecular Weight Measurements: Special Cases
5.1 Polyelectrolytes
Because polyelectrolytes dissociate counterions, their solutions have at least three
components: polymer, counterion, and solvent. The polyelectrolyte itself is the least
abundant species (by number of molecules) in a dilute solution. If additional low
molecular weight electrolyte is present, the number of components is greater. Many
procedures associated with standard methods of M measurement assume just two solution
components, polymer and solvent. The extra components in polyelectrolyte systems not
only create complexity, they may render standard methods useless.
Most polyelectrolytes are studied in aqueous media, environments with properties
unfavorable for M measurement. For example, water has a high surface tension and
dielectric constant. The former makes water “attractive” to airborne particulates, which
can be enormously troublesome (e.g., to light scattering and viscometry).
Because of their multiple charges, polyelectrolytes experience potentially strong
electrostatic interactions, especially if low molecular weight electrolyte is not added to
the solution to screen these interactions, and indeed, the distinct behaviors of
polyelectrolytes are often said to manifest the long-range nature of their interactions.
Although long-range interactions certainly influence polyelectrolyte properties, they
don’t have a major impact on M measurement methods, excepting those that exploit a
correlation between M and molecular size (e.g., intrinsic viscosity and diffusion). More
often, the dominant polyelectrolyte difficulty for M measurements is the presence of
counterions and low molecular weight electrolyte.
Although reasons differ, many standard M methods DO APPLY to polyelectrolytes
dissolved dilutely in water alongside a large excess of low molecular weight electrolyte
(i.e., at high salt). Although dependent on method, the threshold for added electrolyte is
often about 0.1 M. The standard M methods most appropriate to polyelectrolytes are
light scattering, GPC, membrane osmometry, sedimentation, and intrinsic viscosity.
Electrophoresis, of course, is a polyelectrolyte-specific method; unlike the other listed
methods, it works best when there is not a large excess of added low molecular weight
electrolyte (conductive heating is thereby minimized). A method that fails completely in
the context of polyelectrolytes is vapor phase osmometry; this method equally counts the
nonvolatile dissociated counterions along with the polymer chains, and since there are
many more counterions than chains, the calculated M is much too small.
The following sections highlight differences between neutral polymer and
polyelectrolytes in the application of specific methods. A good reference is H.
Dautzenberg et al., Polyelectrolytes: Formation, Characterization, and Application,
Hanser, NY, 1994.
5.5.1 Membrane Osmometry and Light Scattering
For reasons that will become clear shortly, these methods will be discussed together.
1
Salt-free solutions. If we dissolve a monodipserse polyelectrolyte sample of molecular
weight M in salt-free water, the osmotic pressure  at concentration c will reflect the
total number of dissolved solutes. Specifically, if the polyelectrolyte has Z ionizable
units, all of which dissociate,

RT
=
1 Z 
c
M
Since Z is large and nearly proportional to M, the right-hand-side is essentially
independent of M. One therefore cannot determine M from osmometry measurements on
a salt-free polyelectrolyte solutions.
The above expression is usually corrected for counterion condensation, which reduces the
number of osmotically active (“free”) counterions as assessed by o, the osmotic
coefficient. The non-osmotically active counterions are considered electrostatically
“bound” to the polyelectrolyte such that their binding energy much exceeds kT.
According to the Manning theory of counterion condensation, o is much lower than
unity and M-independent. We can thus write

RT
=
1 Z  o
c
M
where o captures the nonideality of counterions due to their attraction to the
polyelectrolytes.. Even if counterion condensation is not accepted (the concept is
controversial), the electrostatic interactions of a polyelectrolyte solution make the
counterions highly nonideal, with o much less than unity even without the condensation.
From the fluctuation theory of light scattering, the normalized scattered intensity from a
solution at zero angle is inversely proportional to the osmotic compressibility, the factor
in parenthesis on the right-hand-side of the equation below,
1
R (  0)
 
= RT
 c 
Kc
where the other variables are as defined in the second handout. From the salt-free
polyelectrolyte expression for ,
M
R ( = 0) = Kc
(1 Z)o
Once again, all M dependence is lost if Z is large and proportional to M. Further, the
scattered intensity becomes extremely weak, more comparable to that of a small molecule
than a polymer. Plugging in values for poly(styrene sulfonate) in water, if o=0.2,
dn/dc=0.2 ml/g, and c=1x10-3 g/ml, the calculated value of R is much less than the
scattered intensity of pure water, which scatters less than most organic solvents since
hydrogen bonding suppresses solvent density fluctuations.
2
The M independence and low scattering of salt-free polyelectrolytes solutions can also be
understood by recognizing that weight average molecular weight of all dissolved species
– counting both polyelectrolytes and counterions – is much closer to that of counterion
than to that of polyelectrolyte.
These considerations seem to disallow the two most important methods, osmometry and
light scattering, for M determination of polyelectrolytes.
Also, an unexplained peak is found when intensity for a polyelectrolyte is plotted vs. q,
suggesting that even in a very dilute solution, some type of electrostatic-induced ordering
of polymer chains occurs, further affecting  vs. c from that anticipated in the standard
formula.
Salted solutions. The dim outcome of the salt-free case motivates a consideration of
osmotic pressure and light scattering measurements taken in the presence of a large
excess of added salt.
The added salt can equilibrate between compartments during the membrane osmometry
experiment. Equilibration of a salt-containing solution such that a large charged solute is
unable to pass between the two osmometer compartments defines “Donnan equilibrium”.
With this equilibrium, an electrostatic potential difference spontaneously appears across
the membrane. Derivations of the equations of Donnan equilibrium are not difficult but
tedious, care taken that the chemical potentials of solvent and each salt ion are matched
across the membrane and that charge neutrality is maintained in the two compartments.
In a 1:1 salt with univalent counterions for the polyelectrolyte, under Donnan equilibrium
the expression for  has the form,
 1

 d
= RT 
+ A2d c  ...
c
Mn

where
 2Z 2
A2d = o 2
4Mn c s
where the subscript “d” reminds us that  is to be evaluated at Donnan equilibrium, and
cs is the molarity of the added 1:1 salt.
d
The factor A2 is the Donnan second virial coefficient. This quantity is only an apparent
virial coefficient, since it doesn’t reflect the interactions between polymer molecules but
rather the c-dependence of equilibration across the membrane. The real virial coefficient
A2 would be associated with a second c-dependent term (not shown) within the
parenthesis.
Note that if cs is large (high salt), the Donnan term disappears and the usual equation for
osmotic equilibrium allows determination of Mn from d.
3
The osmotic method has not been much used for polyelectrolytes. However, if sufficient
salt is present, it works in exactly the same manner as for neutral polymers, and indeed,
there are many good choices of membrane material.
The light scattering method is more frequently used for polyelectrolytes, and from the
discussion just given, it shouldn’t be too surprising that, if salt is present in sufficient
concentration, this method too works pretty much as for a neutral polymer.
[There is one subtle difference: in the polyelectrolyte measurement of M, each
polyelectrolyte chain can be considered to be in Donnan equilibrium with its local
environment. Thus, the value of dn/dc should be determined such that each
polyelectrolyte solution has been equilibrated across a polymer-impermeable membrane
with a salt solution of the desired high salt concentration. This condition keeps the salt’s
chemical potential constant in the polyelectrolyte solutions as the polymer concentration
changes. In practice, one must dialyze each polyelectrolyte solution of different c against
a large excess of the salt solution and then determine dn/dc by referencing the polymersalt solution refractive index against the equilibrated salt solution refractive index.
Unfortunately, dialysis tends to dilute the polymer, and so c must be redetermined after
dialysis, mandating a rather tedious set of steps. In practice, diluting the polyelectrolyte
with a salt solution of fixed c causes only a small error (<10%).]
Finally, note that the value of dn/dc reflects the identity of the counterion. Larger
counterions, with their larger polarizability, increase the scattering contrast and make M
accuracy greater.
5.1.2 Intrinsic Viscosity
In salted aqueous solutions, at cs high enough to screen repulsive electrostatic
interactions between different charged chain sections, the intrinsic viscosity methods
works just as for neutral polymers. At low cs, the method works poorly, if at all, as the
electrostatic expansion of the chain due to these interactions strongly depends on c. For
low cs, electrostatic screening is mainly by released counterions, so the level of screening
– and thus the magnitude of the electrostatic interactions – depends on c. The intrinsic
viscosity method can still work, but excess salt must be added to hold electrostatic
interactions constant as the polyelectrolyte is diluted. This compensation of counterions
by added salt becomes quite messy to analyze. Fortunately, when done wrong, the MarkHouwink plot is highly nonlinear, so the error is apparent.
In practice, the intrinsic viscosity method is difficult unless cs is greater than ~0.2M.
At the higher cs levels where the method applies, one must make certain that the MarkHouwink coefficients were determined by M standards examined exactly as the test
sample.
4
5.1.3 GPC
With GPC, as with the other methods, performance with polyelectrolytes is best at high
cs. This necessity arises through several new effects:
a. Ion Exclusion
b. Ion Inclusion
c. Ion Exchange
d. Coil Expansion
e. Intermolecular Interactions
- coil overlap
- viscosity
f. Adsorption
- driven by electrostatics
- driven by hydrophobicity
In addition, water differs from organic solvents in several important ways that affect
materials choices for GPC parts. Each effect is more fully described below:
Ion exclusion – polyelectrolytes of size small enough to enter a pore are prevented from
doing so by repulsive electrostatic interactions with like charges on pore walls
Impact on GPC analysis: large
Even small ions may be totally excluded at low salt. All aqueous GPC
packings bear charge, always negative unless otherwise specified.
Trends: overestimation of M, multimodal peaks (extraneous peak at
exclusion limit)
Cure: add salt to about 0.05 to 0.2 M; high salt levels may cause
polyelectrolyte adsorption
Ion Inclusion – Donnan equilibrium between intraparticle pores and interstitial space
creates an electrostatic potential difference (“the Donnan potential”) that drives
polyelectrolytes into the pores. The Donnan equilibrium arises from the inability of the
polyelectrolyte, based on its size, to enter pores freely (KSEC<1) while small ions of
opposite charge do (KSEC=1)
Impact on GPC analysis: large
Occurs with GPC packings with or without charge
Trends: underestimation of molecular weight, broadening of the
distribution
Cure: added salt to about 0.05 to 0.2 M; with salt, ions of the same charge
as the polyelectrolyte will elute as a spurious permeated peak that may
obscure analysis of low molecular weight polyelectrolyte that elutes near
the permeation limit
Ion Exchange – Counterions of the polyelectrolyte are ion exchanged with counterions
of the packing
Impact on GPC analysis: small
Occurs with GPC packings with charge
Trends: spurious peak of permeated polyelectrolyte counterions
5
-
Cure: added salt to about 0.05 to 0.2 M such that the salt has the same
counterion as the polyelectrolyte
Coil Expansion – Polyelectrolyte coil size varies sharply with cs, affecting
polyelectrolyte elution
Impact on GPC analysis: varies
If counterions are a significant component compared to added salt,
electrostatic screening alters across the polyelectrolyte band
Trends: anomalous asymmetric peaks and peak position depends on
injected polyelectrolyte concentration
Cure: added salt to about 0.05 M
Intermolecular Interactions – When polyelectrolytes are not dilute, (i) chains interact as
they enter pores and (ii) the viscosity of the injected band is elevated above solvent. Both
of these problems occur with neutral polymers, but their presence is heightened for
polyelectrolytes
Impact on GPC analysis: sometimes large
Occurs mainly for high molecular weight polyelectrolyte
Trends: underestimation of molecular weight, asymmetric broadening of
the distribution
Cure: reduce injected concentration to well below c*; unfortunately, with
RI detection, the polyelectrolyte may not be detactable. For this reason,
UV and fluorescence detection is popular; both methods work well in
water and typically are more sensitive to RI detection
Adsorption – due to the strength of electrostatics, hydrophobicity, and hydrogen
bonding, polyelectrolytes often irreversibly adsorb to packings. The usual steps to
control adsorption are:
i) introduce additives such as methanol, DMF, or surfactant to suppress
hydrophobic interactions
ii) add cosolutes such as guanidine hydrochloride or urea to weaken hydrogen
bonding interactions
iii) chemically modify the packing surface
iv) sacrificially adsorb polyelectrolyte until adsorption is saturated
v) chemically modify the polyelectrolyte, in the extreme case rendering it
uncharged
Water as solvent - Most polyelectrolyte characterizations are conducted in aqueous
media. This fact has several implications for all molecular weight measurements:
•
Water has low interfacial energy, making it difficult to keep clean; in-line
filters are mandatory to protect the GPC system.
• Many aqueous electrolytes are highly corrosive to stainless steel; never store
a GPC for any period of time with electrolyte present.
• Water is UV transparent, making UV absorbance an attractive detection
strategy that is often more sensitive than RI detection
• It is desirable to pick an electrolyte that is also a buffer, thereby fixing
polyelectrolyte and packing charges
6
5.2 “Complex” Polymers
“Simple polymer” – one that has one broad molecular property distribution
“Complex polymer” – one that has two or more broad molecular property distributions
5.2.1 Characterization of Linear Copolymers
In addition to its M distribution (MWD), a linear copolymer sample is characterized by
its Chemical Composition Distribution (CCD). In the simplest case, in analogy to the
MWD, the CCD might be plotted as the mass fraction of molecules of a given copolymer
composition against copolymer composition.
Unfortunately, such a plot offers only a cloudy picture of copolymer chemistry, as the
CCD might vary with M. We can ignore CCD in determining MWD by ordinary
methods in only two cases: 1. The copolymer’s CCD is very narrow and thus not
impacting on the M measurement or (2) the average composition does not shift with M.
Measurement of M or MWD in the presence of a broad CCD is tractable only for binary
copolymers, so ter- and higher copolymers are ignored in subsequent discussion. Binary
polymers have components generically designated A and B
In addition to the CCD, linear AB copolymers are characterized by a Sequence Length
Distribution (SLD) of the two repeat units, spanning from alternating to block (ABABAB
to AAA….BBB). The SLD can also shift with M and A/B composition.
To characterize a linear binary copolymer completely, we thus need – in theory - to
determine a trivariate distribution of MWD, CCD, and SLD. In practice, there is no
systematic way to achieve this goal. We thus make due with bivariate distributions of the
types shown below. The first shows the coupling between MWD and CCD, and the
second shows the coupling between SLD and CCD; LA and LB are the number average
sequence lengths of A and B, respectively, and XA is the mole fraction of A repeat units.
The second plot illustrates the start of a binary copolymerization at constant reactivity
ratio; the instantaneous composition generally differs from the cumulative distribution for
a batch polymerization unless the reactivity ratio is unity.
[H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, NY, 1999, pp. 7-8]
7
Another distribution arises when polymers have chain branches or other complex
topological features. In a few cases, e.g. graft copolymers with uniform arms of the same
chemistry as backbone, branches can be viewed as “defects” treated as the second
component of a binary linear copolymer. More often, branching is statistical, capable of
forming a spectrum of complex molecular architectures. Depending on the length of
branches, short chain branching (SCB) is distinguished from long chain branching
(LCB). A SCB consist of a few repeat units while a LCB may be comparable to the
main chain backbone in length. Sub-branches form from branches that are themselves
branched.
5.2.2 Characterization of Branched Polymers
A large number of experimentally unavailable parameters is usually needed to
characterize a branched polymer fully. Just as with linear copolymers, substance-specific
methods (spectroscopy) can be helpful, in the branched case, to assess the density of
branch points if this density is high enough to detect and quantify.
Universal branching methods, on the other hand, rely on the alteration of branched coil
size from that of a linear chain of the same M and composition. Universal methods are
used to advantage when the density of branch points is too low to detect by spectroscopic
means but still large enough to modify coil size, i.e, the method predominately apply to
LCB. SCB, on the other, is nearly always determined by spectroscopic methods. This
does not mean that SCB has no effect on coil size; SCB effectively increases stiffness,
raising the coil size with respect to a chain of comparable length without SCB.
Universal Methods for LCB –
An especially important case for LCB measurement is low density polyethylene.
Compared at equal M, a branched polymer is smaller than a linear one of the same chemistry.
The contraction factor g is defined through the square radii of gyration of the two polymer
topologies, using the subscript “b” for branched and “l” for linear,
g =
(Rg 2 )b
(Rg 2 ) l
This value of g depends on solvent conditions, with the subscript”o” attached to all
parameters evaluated at the theta condition. Importantly, for complex branching
architectures, g may also be a 
function of M.
The above formula is most useful when polymers are evaluated by light scattering, which
directly provides the needed radii of gyration. Just as frequently, molecular size is
assessed by a hydrodynamic method such as intrinsic viscosity, so a second contraction
factor is defined.
[ ]b
g  =
[]l
where the prime  indicates a hydrodynamic measurement.
8
To calculate LCB from molecular size measurements, a correlation of g or g with n is
desired, where n is the number of branch points per polymer. This correlation will
obviously depend on the topological description of the branched polymer and may
depend on M. Usually, one does not have a sufficiently detailed topological description
to complete this step with much confidence.
However, if one does, a large number of such correlations are available, as derived by
theorists under various assumptions. For example, a Zimm-Stockmeyer relationship can
be used for a randomly branched molecule with trifunctional branch points,
 n 1/ 2 4n 1/ 2
go (n) = 1 +   
9 

 7 

After correction for PDI, which introduces the Mw as an additional parameter, this
correlation works well for LCB polyethylene.

The figure below shows go(n) derived under several simple assumptions.
go(n) vs. n for (1,3) trifunctional and (2) tetrafunctional branch points. (1,2) is for
monodisperse bridged segments and (3) is for polydisperse segments.
[Schröder et al., Polymer Characterization, Hanser, 1988, p 255.]
As n grows, the size of a branched molecule of constant M becomes smaller, explaining
the monotonic decrease of these curves.
Alternatively, when both light scattering and hydrodynamic data are available in a good
solvent at the same M for branched polymers of a range of M , one can determine the
exponent e of the scaling relationship
g  (n) ~ g(n)e
which offers insight in topology independent of the choice of a specific functional
relationship for g(n). Detailed hydrodynamic models find that different values of e
manifest different branch structures. For example, with star polymers e0.50, while with
comb polymers e1.5.
With this brief background, one can begin to understand how to do M measurements on
branched polymers. One must use an absolute method (light scattering, osmometry) as
9
opposed to a relative method (viscometry, GPC), as the latter reflect molecular size more
directly than M. However, by combining absolute and relative measurement methods on
a branched sample of monodisperse M, one can learn about branching.
The previous paragraph gives reasons, in the case of branched polymers, for employing a
GPC with not just the usual refractive index detector but also with a light scattering and/or
viscosity detectors. Using the GPC-generated fractions of narrow molecular size variance,
one can get absolute values for the MWD by combining data from the refractive index and
light scattering detector data (relative c value for each fraction by refractive index and M
value by light scattering), and further, one can also get information about branching from the
light scattering detector data (using radius of gyration derived for each fraction by light
scattering and model assumptions about branching architecture) or from both light scattering
and viscosity detector data (using radius of gyration and intrinsic viscosities for each
fraction).
At present, there is no general method that uncovers the full distribution of branching
parameters for an arbitrarily branched polymer sample. On a rigorous basis, one can only
determine the average number of branch points in a polymer molecule of a particular M.
In addition to MWD, the branch indexing  as a function of M is the usually reported
outcome of a GPC analysis using light scattering and viscosity detectors.
 =
nw
Mw
5.5.3 Characterization of M or MWD for Linear Copolymers
Conventional MeasurementsAs noted above, the CCD does not disturb the application of absolute M methods for a
linear copolymer if the CCD is independent of M.
Specifically, colligative property measurements can be performed unchanged from those
for a homopolymer. For light scattering, the correct value of dn/dc is the weight average
of the two component values of dn/dc, and it may be easier to calculate dn/dc in this
manner than to make an actual measurement on the copolymer, especially for sequenced
or block copolymers (in the unlikely scenario that the interaction between repeat units did
affect optical frequency polarizabilities, then a dn/dc measurement for the copolymer
would be mandatory). The biggest problem with absolute M measurements is to find an
appropriate solvent, especially for sequenced or block copolymers with constituents of
highly different chemistry. These systems tend to form micelles that are difficult to
dissociate with dilution.
Relative methods will generally not provide a route to M, as the coil size of a copolymer
is strongly affected by composition.
If the copolymer CCD is a function of M, then we are forced to consider the sort of CCDMWD analysis plotted on the bottom left corner of page 7 (the SLD is always evaluated
10
by chemistry-specific spectroscopic methods).
CCD-MWD analyses are not
straightforward, and different practitioners advocate different approaches. In general, an
orthogonal or two-dimensional analysis is required, one for composition and one for M.
The crude analysis avoids this strategy at the cost of rigor.
Crude CCD-MWD Analysis The crude analysis is based on adding a composition-specific detector to the detector
sequence at the end of a GPC column. In concept, the column fractionates polymers by
M, and the relative amount and M of each fraction are determined by refractive index and
light scattering/viscosity detectors before eluting past the added detector (normally
UV/Vis or IR) that ascertains the copolymer composition. Composition and M for each
fraction are then possibly known.
The problem here is that GPC separates by molecular size and not M. Molecular size is
affected by both M and composition, so M is not really known for each fraction as
supposed in the previous paragraph. Anyway, absolute M is hard to measure by on-line
light scattering in this case, since the measured scattered intensity depends on
composition as well as M.
To address the problems, the crude CCD-MWD analysis postulates that the copolymer
calibration curve, relating elution volume to M, can be constructed from the calibration
curves of the two homopolymer constituents,
log Mc,i = WA,i logM A,i  WB,i logM B,i
In essence, the molecular size of the copolymer is asserted to be the sum of the molecular
sizes of the two corresponding homopolymers of the same number of repeat units as
found for the constituents in the copolymer.
A second difficulty is the determination of relative amount for each fraction. If RI or
similar method is used to find c, the signal for each fraction depends as well on the
instantaneous composition. Thus, the composition detector signal must be used to correct
for the sensitivity difference in the c signal.
This crude analysis has been argued to work reasonably well [for example, see G. Meira
and J. Vega, “Characterization of Copolymers by Size Exclusion Chromatography” in
Handbook of Size Exclusion Chromatography and Related Techniques, 2nd., C.-S. Wu,
ed., Elsevier, 2004, p 139]; others argue that it doesn’t work at all well. It certainly isn’t
rigorous. In general, the A and B repeat units will interact in solution, making the factors
affecting coil size more complicated than supposed.
The crude analysis does not require use of viscosity and light scattering detectors.
Indeed, as noted, their application in the case of copolymers is problematic – the signal
detected is not easily corrected for the unknown polymer compositions. For example,
what is the value of dn/dc from which to get the M? Each fraction has its own particular
dn/dc value that is not known ahead of time.
11
Orthogonal (or Multidimensional) Analysis of Copolymers References: D. Berek, “Two-Dimensional Liquid Chromatography of Synthetic
Macromolecules” in Handbook of Size Exclusion Chromatography and Related
Techniques, 2nd., C.-S. Wu, ed., Elsevier, 2004, p 501; S. Balke, “Orthogonal
Chromatography and Related Advances in Liquid Chromatography” in Detection and
Data Analysis in Size Exclusion Chromatography, T. Provder, ed., ACS Symp. Ser. 353,
ACS, 1987, 59; and H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, 1999,
examples throughout book.
Problems uncovered in the previous section suggest need for a more rigorous, twodimensional analysis of copolymers, an analysis in which polymers are fractionated and
analyzed by composition alone in a first step and then these fractions separated by M in a
second step. If the two dimensions of analysis – composition and M - are strictly separate
and independent, the analysis is orthogonal. More likely, the second analysis (M by
GPC, for example) is somewhat composition-dependent and so not fully orthogonal but
still satisfactory.
Liquid Chromatography at the Critical Condition (LCCC) was discussed earlier in the
course. It provides elution of copolymers independent of M by establishing a balance of
entropy against enthalpy. For a statistical copolymer, critical conditions will vary only
slightly with copolymer composition, so essentially a composition fractionation occurs at
the nominal critical condition. Thus, a two-step sequence of LCCC and then GPC should
provide the full CCD-MWD bivariate distribution.
LCCC is not the only front-end method that can achieve the multidimensional purpose
described. A chromatographic separation by composition is more easily achieved when a
chromatographic mobile phase is continuously or discontinuously changed (gradient
elution vs. isocratic elution.) For example, one can fully adsorb or crystallize a polymer
on a column and then ramp a displacer selective for one component, thereby eluting the
polymer sample by composition differences, not M differences. Compared to LCCC,
close control over conditions is not nearly so important. This is a traditional form of
chromatography for small molecules and biopolymers called “displacement
chromatography”, so equipment is readily available (pumps that ramp concentration very
precisely, for example). Also, the approach takes advantage of the irreversible character
of polymer adsorption, in which polymer either adsorbs or desorbs dependent on
solvent/surface conditions, with no M dependence to adsorption/desorption.
An LCCC/GPC analysis of a mixture of three well-defined styrene/methyl methacrylate
block copolymers is shown on the next page. The x-axis is block copolymer molecular
weight and the y-axis is elution volume in the LCCC experiment, which has not been
transformed into composition but could be. The three components were, written in terms
of PS:PMMA molecular weights (g/mol), (1) 93,000:89,000, (2) 55,000:133,000, and (3)
9,800:10,700. The first two components were not well separated in the LCCC portion of
the analysis. (color figure reproduced poorly)
12
[3rd ref. of previous page, pages 208-212.]
13