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Determination of the refractive index increment (dn/dc)of
molecule and macromolecule solutions by surface plasmon resonance
Tathyana Tumolo
a
, Lucio Angnes
b
, Mauricio S. Baptista
a,*
a
Departamento de Bioquı
´mica, Instituto de Quı
´mica, Universidade de Sa˜ o Paulo, Sa˜ o Paulo, Brazil
b
Departamento de Quı
´mica Fundamental, Instituto de Quı
´mica, Universidade de Sa˜ o Paulo, Sa˜ o Paulo, Brazil
Received 16 April 2004
Available online 20 July 2004
Abstract
An automated method for dn/dc determination using a surface plasmon resonance instrument in tandem with a flow injection
gradient system (FIG–SPR) is proposed. dn/dc determinations of small molecule and biomolecule, surfactant, polymer, and biopoly-
mer solutions with precision around 1–2% and good accuracy were performed using the new method. dn/dc measurements were also
carried out manually on a conventional SPR equipment with similar accuracy and precision. The FIG–SPR instrument is inexpen-
sive and could be easily coupled to commercially available SPR and liquid chromatography instruments to obtain several properties
of the solutions, which are based on measurements of refractive index.
2004 Elsevier Inc. All rights reserved.
Keywords: Surface plasmon resonance; Refractive index increment; Flow injection gradient
The change in refractive index of solutions as a func-
tion of solute concentration (dn/dc, also called refractive
index increment) is an essential parameter to several
physical and analytical techniques that are based on op-
tical measurements [1]. For example, it is necessary to
know dn/dc to (i) characterize the sizes, shapes, molecu-
lar weights, and the virial coefficients of polymers,
macromolecules, and surfactant aggregates through
light-scattering methods [2], (ii) calculate solute concen-
tration based on refractive index measurements in any
kind of column chromatography [3], and (iii) obtain
concentration and kinetics of molecules adsorbing on
surfaces through optical methods such as surface plas-
mon resonance (SPR)
1
and ellipsometry [4].
The search for refractometers with high precision
(10
5
–10
6
refractive index units, RIU) and the capabil-
ity of measuring dn/dc led to the developments of the dif-
ferential refractometers (DRs) [5,6]. In fact, most of the
dn/dc values reported in the literature were measured us-
ing DRs, including low-molecular weight compounds [7]
block copolymers [8], agarose [9], poly(thiocarbonate)s
and poly(carbonate)s [10], and surfactants [11]. Other
refractometers, such as the Zeiss interferometer and
the Mach–Zehnder interferometer [6], have also been
used to obtain dn/dc of polymethylmethacrylate
(PMMA) in different solvents [12].
SPR is a surface-sensitive method that measures the
reflectance intensity as a function of incident angle h
0003-2697/$ - see front matter 2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.ab.2004.06.010
*
Corresponding author. Fax: +5511-3815-5579.
E-mail address: baptista@iq.usp.br (M.S. Baptista).
1
Abbreviations used: SPR, surface plasmon resonance; RIU, refractive index unit; DR, differential refractometer; PMMA, polymethylmeth-
acrylate; FIG, flow injection gradient; MC, mixing chamber; BSA, bovine serum albumin; CTAB, cetyltrimethylammonium bromide; HPS, 3-(N-
hexadecyl-N,N-dimethylammonio)propanesulfonate; PEG 4000, poly(ethylene glycol) 4000; PEG 6000, poly(ethylene glycol) 6000; PVP,
polyvinylpirrolidone; SDS, sodium dodecyl sulfate; I/F box, interface box; LOD, limit of detection.
www.elsevier.com/locate/yabio
Analytical Biochemistry 333 (2004) 273–279
ANALYTICAL
BIOCHEMISTRY
of a light beam incident on a thin metal film. It has been
used extensively to evaluate properties of thin films self-
assembled on gold, to study the adsorption of molecules
at surfaces, and to characterize intermolecular interac-
tions in general [13]. The application of SPR to study in-
termolecular interactions in high-throughput screening
assays using combinatorial libraries opened a wide win-
dow for its application in mutation detection, genomics,
proteomics, and drug development [14].
To obtain the concentration of molecules adsorbing
over surfaces (C) by the response of an SPR instrument
(Dhwhere his the SPR angle) in the linear regime (small
refractive index variations) [15], it is necessary to know
the instrument calibration constant (X) and the refrac-
tive index increment of the ligand ((dn/dc)
ligand
)[16]:
Cligand ¼Dh
Xðdn=dCÞligand
:ð1Þ
Accurate values of dn/dc were not fundamental in
many SPR applications. The usual data treatments, such
as determining kinetic ‘‘on’’ and ‘‘off’’ rates and estimat-
ing equilibrium constants of simple binding processes,
do not require absolute concentrations. However, actual
ligand concentrations, and thus accurate values of dn/dc,
are needed when studying binding processes with stoi-
chiometries different from 1:1 [17,18]. Accurate dn/dc
values are also extremely important in the combinatorial
library investigations involving the testing of a wide
range of different compounds whose dn/dc values can
vary from 0.1 to 0.3 cm
3
g
1
, thereby directly affecting
the interpretation of the results [7].dn/dc values also en-
able the calculation of bulk refractive index of com-
pounds (n), which is necessary to estimate film
thickness and surface coverage [16,19].
Because the SPR technique measures refractive index
variations that occur up to 300 nm above the dielectric
thin film (usually gold or silver thin films), its signal is
sensitive to the adsorption of molecules at the gold sur-
face (whether functionalized or not) and to the presence
and concentration of molecules in the liquid above the
interface [13,16]. In theory, the dn/dc value of ligands
could be estimated from any equation fitting SPR angle
versus reflection data [16]. However, parameter compen-
sation during the fitting prevents accurate calculation of
all other parameters, and it is usually necessary to ob-
tain the dn/dc value from one of the independent tech-
niques cited above. This severely increases the amount
of time needed to obtain the measurements and also
hinders the more extensive application of SPR to high-
throughput screening techniques. Therefore, it is desir-
able to develop a method in which the dn/dc values of
ligands could be calculated directly using the SPR
instrument. Also, this method should be easily automat-
ed to facilitate its use in high-throughput screening
assays.
dn/dc corresponds to the slope of the dependence of
refractive index (n) of a solution as a function of the sol-
ute concentration (c). The variation of the SPR signal as
a function of solute concentration in the regime of small
refractive index variations directly provides the ratio of
Dn/Dc, where Dnis the difference of refractive indexes re-
lated to a difference in solute concentration (Dc)[1,2].
This is also true for the case in which there is the forma-
tion of a thin film at the interface, below the fluid in
which the dn/dc determination is being performed, so
long as the thickness of this film is small (<50 nm) com-
pared with the decay length of the evanescent field
(300 nm using our instrument) [16]. In fact, to precisely
calculate adsorption and desorption of surfactants in
functionalized gold films, Sigal et al. [20] were able to
successfully calculate dn/dc values of surfactant solu-
tions using SPR.
In this study, we set up an instrument in which the
SPR chip is connected to a flow injection gradient
(FIG) system [21,22]. With the FIG technique, a mixing
chamber (MC) is used as a device to generate reproduc-
ible concentration gradients whose refractive indexes are
monitored continuously in the SPR chip. The obtained
concentration profiles not only can replace the manual
preparation and the measurement of several solutions
with different concentrations of the reactants but also
can speed up the experiments, keeping the high precision
and accuracy of the determinations. The dn/dc determi-
nation of several compounds was performed using clean
gold film with and without an MC. Therefore, we de-
scribe an automated method to obtain the dn/dc of poly-
mers, surfactants, macromolecules, and small molecules
solutions using an SPR instrument.
Materials and methods
Samples
All reagents used were at least of analytical grade. So-
lutions of Alanine (Aldrich), bovine serum albumin
(BSA, Acros Organics), cetyltrimethylammonium bro-
mide (CTAB, Acros Organics), DNA sodium salt type
I from calf thymus (Sigma), guanidine (Sigma), heparin
(Sigma), 3-(N-hexadecyl-N,N-dimethylammonio)pro-
panesulfonate (HPS, Sigma), lactose (J.T. Baker), glu-
cose (Vetec), maltose (Merck), poly(ethylene glycol)
4000 (PEG 4000, Polysciences), poly(ethylene glycol)
6000 (PEG 6000, Fluka), polyvinylpirrolidone (PVP
K90, Acros Organics), sodium chloride (Synth), sodium
dodecyl sulfate (SDS, Merck), spermine (Acros Organ-
ics), sucrose (Synth), tartaric acid (Aldrich), and urea
(Cine
´tica Quı
´mica) were prepared with Milli-Q water.
SDS, HPS, sodium chloride, CTAB, and urea solutions
were stirred for 5 min, heparin for 1 h, and PEG 4000
and 6000 for 3 h. PVP was dried in an oven for 3 days
274 T. Tumolo et al. / Analytical Biochemistry 333 (2004) 273–279
prior to weighting, and its aqueous solution was left
mixing for 2 days. BSA solution was warmed at 32 C
for better solubilization and was left mixing for 10 min.
To determine dn/dc without the MC, solutions were
prepared with different concentrations (in g cm
3
) as fol-
lows: BSA (0.005, 0.010, 0.015, 0.020, 0.025, 0.030,
0.035, 0.040, 0.045, 0.050), CTAB (0.006, 0.009, 0.012,
0.015, 0.018, 0.021, 0.024, 0.027), heparin (0.005,
0.010, 0.015, 0.020, 0.025, 0.030, 0.035, 0.040, 0.045),
HPS (0.00391, 0.00587, 0.00783, 0.00979, 0.01175,
0.01566, 0.01762, 0.01958), PEG 4000 (0.0040, 0.0081,
0.0121, 0.0161, 0.0201, 0.0242, 0.0282, 0.0322, 0.0363,
0.0403), SDS (0.0053, 0.0064, 0.0073, 0.0079, 0.0087,
0.0116, 0.0131, 0.0145), and sucrose (0.0104, 0.0207,
0.0415, 0.0518, 0.0622, 0.0726, 0.0830, 0.1037).
To determine the dn/dc with the MC, the concentra-
tions (in g cm
3
) of the stock solutions used were as fol-
lows: alanine (0.1354), BSA (0.0100), CTAB (0.01795),
DNA (0.00329), glucose (0.0117), guanidine (0.01785),
heparin (0.0206), HPS (0.0085), lactose (0.0111), malt-
ose (0.0097), PEG 4000 (0.0504), PEG 6000 (0.0405),
PVP (0.0448), SDS (0.0183), spermine (0.0043), sucrose
(0.0718), tartaric acid (0.0119), and urea (0.1201).
In the case of surfactant solutions, the value of con-
centration used in the dn/dc determination was ex-
pressed as the total surfactant concentration minus the
critical micelle concentration (cmc) because we aimed
to determine the dn/dc value of micellized surfactant so-
lutions (11). This correction was performed both when
using the MC and when not using the MC.
Instrumentation
Refractive index values were obtained with a minia-
ture integrated SPR sensing system (Spreeta sensor,
Texas Instruments) that uses a near infrared light-emit-
ting diode (840 nm) to excite surface plasmon in a 50-nm
thickness gold film (Fig. 1). This sensor is interfaced
with an 8-bit interface box (I/F box). The data acquisi-
tion and instrument control was performed by a Pen-
tium 2 microcomputer. The flow cell was constituted
by a Teflon piece fixed over the SPR device. Between
these two parts was positioned a Teflon spacer defining
the volume of the flow cell (25 ll). The small internal
volume of this laminar SPR cell and its geometrical
characteristics favor the rapid washout of the analytes
when they are not adsorbed on the gold surface.
The solutions were propelled by a peristaltic pump
(Tris model, Isco) using a flow rate of 2.7 cm
3
min
1
.
Limit of detection (LOD) was calculated as the minimal
refractive index change that can be detected over three
times the noise standard deviation. With our device, in
performing 100 averages, which gives sample acquisition
rates of 1.9 Hz, a noise standard deviation of 2.9 ·10
6
RIU was obtained, giving an LOD of 8.7 ·10
6
RIU.
The values of these parameters expected for the Spreeta
sensor itself (100 averages) are 0.3 ·10
6
and 1 ·10
6
RIU for noise standard deviation and LOD, respectively
[23]. These values are equivalent to those of the best
classical methods available [5,6].
dn/dc determinations were carried out in two different
ways: (i) under steady-state conditions in which each
stock solution with known concentration was injected
in triplicate and the refractive indexes were measured in-
dependently and (ii) using FIG line with a homemade
MC with an internal volume of 1.50 cm
3
and magnetic
stirrer. The value of h
SPR
(angle of minimum reflectance)
was obtained by fitting the SPR curve with the polyno-
mial method. All analyses were performed in a thermos-
tatized room (23 ± 1 C).
Before the analysis was begun, the gold surface of the
sensor was cleaned with isopropyl alcohol and Kodak
lens-cleaning paper, rinsed with Milli-Q water, and cal-
ibrated in air (n= 1) and water (n= 1.333). To clean up
the sensor surface after each analysis, a 50-mM SDS so-
lution was injected into the cell, followed by an excess of
water sufficient to obtain the value of nmeasured previ-
ously for pure water.
Results and discussion
dn/dc determination without the mixing chamber
The plots of nas a function of cfor sucrose and mic-
ellized HPS are shown in Fig. 2. An excellent linearity of
both curves (r> 0.999) can be observed, in agreement
with the assumption that at these low concentration con-
ditions, there is a linear relationship between nand c. The
slope of this curve is the value of dn/dc (in cm
3
g
1
).
Table 1 shows the dn/dc values for several compounds
obtained by SPR and those found in the literature. Stan-
dard deviations of approximately 1–2% in dn/dc were ob-
tained for this series of compounds, attesting to the good
precision of the method. A comparison of the dn/dc val-
ues obtained by SPR with those found in the literature
shows differences smaller than 10%, indicating that the
accuracy of these measurements is also good. The main
causes of divergences among the values obtained by
SPR and those found in the literature are likely to be
Fig. 1. Schematic diagram of the FIG–SPR instrument: A, water; B,
sample; C, peristaltic pump; D, steady-state line; E, FIG line; F,
mixing chamber; G, magnetic stirrer; H, SPR sensor; I, interface box;
J, waste; and L, computer.
T. Tumolo et al. / Analytical Biochemistry 333 (2004) 273–279 275
the different experimental conditions such as differences
in wavelength, temperature, and reagent purity.
dn/dc determination with the mixing chamber
To calculate dn/dc values with this method, it is neces-
sary to generate curves of refractive index as a function
of solute concentration. This can be done by using a cal-
ibrated MC such as in the conventional flow gradient
technique [21,22]. In the MC, a rapid dilution of the
stock solutions occurs and a gradient of solute concen-
trations is generated. Initially, a curve of refractive index
as a function of time is obtained after injecting a specific
solution into the MC. The concentration as a function of
time profile of the injected compound is obtained by cal-
ibrating the system with sucrose. Both the refractive in-
dex versus time curve and the concentration versus
time curve were used to plot the refractive index versus
concentration curve, allowing the dn/dc calculation.
The refractive index versus time curves of sucrose,
urea, and SDS are shown in Figs. 3A, 4A, and 5A, re-
spectively. Note that after the injection of stock solutions
into the MC, an increase in the value of the refractive in-
dex can be observed. For sucrose and urea, there is a con-
tinuous increase. For SDS, there is a small bump at
approximately 10 s after injection that is likely due to sur-
factant adsorption on gold and self-aggregation. Refrac-
tive index reaches a constant value at approximately
200 s after the injection. The increase in solute concentra-
tion in the SPR flow cell reflects an increase in the refrac-
tive index, and the flat region indicates that the solute
concentration in the MC is equal to the solute concentra-
tion in the stock solution. Water or buffer was injected
into the MC 600 s after the injection, and a dilution pro-
file with the respective decrease in the refractive index
was observed. In the case of SDS, there is a more evident
bump in the dilution gradient. The concentration onset
of this bump is approximately 7 mM, which is the value
of the cmc of SDS [27]. We are investigating whether
or not these refractive index changes from linearity can
be used to study surfactant–polymer interactions and ad-
sorption processes in general.
By using a molecule whose relationship between re-
fractive index and concentration is well established,
one can transform the refractive index versus time curve
into a concentration versus time curve, that is, to cali-
brate the MC. Sucrose was chosen as standard because
its dn/dc is well known, it is easy to prepare solutions
with accurate concentrations, and it does not adsorb
on the gold film. Fig. 3B shows the concentration versus
time curve of sucrose, indicating that its concentration
increases, attains a constant value, and then decreases,
as mentioned previously. The numeric values of these
sucrose concentrations are dependent on both the con-
centration of the injected stock solution and the instru-
ment characteristics. To obtain a parameter that is
independent of the concentration of the stock solution,
the dilution factor (DF), which is the concentration at
specific times after injection divided by the concentra-
tion of stock solution, was calculated by Eq. (2) (Fig.
3C). Note that after the stock solution is injected, DF in-
creases from 0 to 1, showing that the concentration in-
creases and reaches the same concentration as the
stock solution (DF =1) (Fig. 3C). Previously, we have es-
tablished that injecting the stock solution in the MC al-
ready filled with water for 200 s is enough to obtain the
Fig. 2. Refractive index as a function of sucrose concentration (A) and
HPS concentration minus cmc (cmc
HPS
=1 ·10
4
M) (B) using the
steady-state line.
Table 1
dn/dc values obtained by SPR (flow gradient) and those found in the
literature
Sample dn/dc (cm
3
/g)
a
±d
b
by SPR
dn/dc (cm
3
/g)
in literature
Difference
(%)
CTAB 0.151 ± 0.007 0.150
c
0.6
Heparin 0.122 ± 0.003 0.129
d
5.4
HPS 0.162 ± 0.003 0.162
e
0.0
PEG 4000 0.128 ± 0.002 0.134
f
3.0
SDS 0.100 ± 0.003 0.108
g
8.0
Sucrose 0.147 ± 0.001 0.144
h
2.1
a
Water, k=840nm, T=23C.
b
Standard deviations obtained with three independent measure-
ments.
c
Water, k=632.8nm [24].
d
Dalteparin sodium, a low-molecular weight heparin, in buffer
(pH 7), k= 690 nm, T=25C[25].
e
k=632.8nm, T=25C[11].
f
Water, k=589nm, T=25C[1].
g
Buffer PBS [20].
h
Water, k=589.3nm, T=20C[26].
276 T. Tumolo et al. / Analytical Biochemistry 333 (2004) 273–279
same nvalue as by injecting the stock solution directly
into the SPR cell:
DF ðtÞ¼ CðtÞ
Cstock
;ð2Þ
where DF(t) is the dilution factor, C(t) is the solute con-
centration monitored as a function of time, and C
stock
is
the concentration of the stock solution.
Provided that the speed of the peristaltic pump and
the volume of the MC are unchanged, this temporal
Fig. 5. Refractive index (A) and SDS concentration (B) as a function of time after injecting a 0.01826-g/ml SDS stock solution. (C) Refractive index
as a function of SDS concentration minus cmc (cmc
SDS
=7 mM), obtained in the FIG line.
Fig. 4. Refractive index (A) and urea concentration (B) as a function of time after injecting a 0.1202-g/ml urea stock solution. (C) Refractive index as
a function of urea concentration, obtained in the FIG line.
Fig. 3. Refractive index (A), sucrose concentration (B), and dilution factor (C) as a function of time after injecting a 0.07184-g/ml sucrose stock
solution, obtained in the FIG line.
T. Tumolo et al. / Analytical Biochemistry 333 (2004) 273–279 277
DF profile will be the same for all compounds injected.
The concentrations at specific times after injection in
the MC for any molecule can be easily obtained simply
by multiplying the concentration of the stock solution
by DF, as is shown for urea and SDS in Figs. 4B and
5B, respectively. Consequently, the refractive index ver-
sus time curves can be converted into refractive index
versus concentration curves (Figs. 4C and 5C), with
the dn/dc values being the slopes of these curves. The in-
creasing concentration portion of the curve was chosen
for these calculations, although the decreasing portions
also work well. Therefore, it is possible to calculate dn/
dc without the cumbersome work of manually preparing
a series of solutions with different concentrations.
Note that in the case of urea, the refractive index ver-
sus concentration curve (Fig. 4C) is linear in all concen-
tration ranges, facilitating the dn/dc determination. This
is due to the fact that urea does not have the tendency to
adsorb on the gold thin film. However, in the case of
SDS, the curve was not linear at low concentrations
(Fig. 5C). This effect was observed for all molecules that
have the tendency to adsorb on the interface (surfactants
and polymers). To calculate dn/dc values in these cases,
we first obtained the derivative graph of the refractive
index versus concentration curve, observed in which
concentration range the derivative is linear, and then
obtained the dn/dc considering this range. Because the
self-assembled film of surfactants or biopolymers is
extremely thin (<20 nm) and the stock solution concen-
trations are well above the surface adsorption concen-
tration limit, the SPR response is linear as a function
of solute concentration. For determining dn/dc values
of solutions containing analyte concentrations smaller
than, or at the same magnitude of, the concentrations
in which adsorption takes place or when thick multilay-
ers are formed on the gold sensor, it will probably be
necessary to modify the gold surface with specific mole-
cules to avoid analyte adsorption.
The dn/dc values of an extended list of substances
were obtained and are shown in Table 2. Note that the
values vary nearly 100% among the compounds tested
(e.g., compare spermine and guanidine with SDS and
tartaric acid), demonstrating the necessity of obtaining
accurate dn/dc values to exploit SPR data correctly.
As observed in the continuous injection method, the
results obtained with FIG–SPR are also in agreement
with the dn/dc values found in the literature. Differences
smaller than 5% are usually observed when compared
with values found in the literature. These differences
are ascribed to the different experimental conditions re-
lated to temperature, wavelength, and reagent purity.
Note that in the cases of heparin and HPS, whose con-
ditions are similar to ours, the difference in dn/dc is
smaller. Compared with the continuous injection meth-
od (Table 1), the automated FIG technique presented
similar accuracy and precision and had the advantage
of being less time-consuming. It is important to mention
that uncertainty in the estimate of solute concentration
is always a limitation in the measurements of dn/dc by
SPR or by any other method.
Some advantages can be envisioned when comparing
this SPR device with conventional refractive index de-
tectors. These include the ease with which it can be
cleaned and its low cost. The price of the whole instru-
ment is approximately US $3000, and each SPR chip
costs only US $30.
Conclusions
The development of the method for dn/dc determina-
tion with the concentration gradient eliminated the stage
of preparing several samples with different concentrations.
Table 2
dn/dc values obtained by SPR (flow gradient) and those found in the
literature
Sample dn/dc (cm
3
/g)
a
±d
b
by SPR
dn/dc (cm
3
/g) in
literature
Difference
c
(%)
Alanine 0.192 ± 0.001 —
d
—
BSA 0.190 ± 0.002 0.183
e
3.8
CTAB 0.143 ± 0.010 0.150
f
4.6
DNA 0.183 ± 0.006 0.180
g
1.6
Spermine 0.221 ± 0.005 —
d
—
Glucose 0.145 ± 0.005 0.142
h
2.1
Guanidine 0.220 ± 0.001 —
d
—
Heparin 0.130 ± 0.008 0.129
i
0.8
HPS 0.164 ± 0.003 0.162
j
1.2
Lactose 0.153 ± 0.003 0.150
k
2.0
Maltose 0.152 ± 0.003 0.146
l
4.1
PEG 4000 0.128 ± 0.002 0.134
m
4.5
PEG 6000 0.131 ± 0.001 0.134
n
2.2
PVP 0.166 ± 0.005 0.175
o
5.1
SDS 0.110 ± 0.007 0.108
p
2.6
Tartaric acid 0.127 ± 0.002 0.120
q
5.8
Urea 0.143 ± 0.001 0.143
r
0.0
a
Water, k=840nm, T=23C.
b
Standard deviations obtained with three independent measure-
ments.
c
Percentage difference between dn/dc values obtained by SPR and
those obtained in the literature.
d
dn/dc not available.
e
Water, k=589.3nm, T=25C[1].
f
Water, k=632.8nm [24].
g
0.2M NaCl, k=436nm, T=25C[1].
h
Water, k=589.3nm, T=20C[26].
i
Dalteparin sodium, a low-molecular weight heparin, in buffer
(pH 7), k= 690 nm, T=25C[25].
j
k= 632.8 nm, T=25C[11].
k
Water, k=589.3nm, T=20C[26].
l
Water, k=589.3nm, T=20C[26].
m
Water, k=589.3nm, T=25C[1].
n
Water, k=589.3nm, T=20C[1].
o
Water, k=578nm, T=25C[1].
p
Buffer PBS [20].
q
Water, k=589.3nm, T=20C[26].
r
Water, k=589.3nm, T=20C[26].
278 T. Tumolo et al. / Analytical Biochemistry 333 (2004) 273–279
Using only one stock solution, it is possible to obtain
hundreds of refractive index versus concentration data
points, allowing the precise and accurate calculation of
dn/dc values. The MC is a simple and inexpensive appa-
ratus, constructed in our laboratory, that could be in-
cluded in commercially available SPR instruments.
The FIG–SPR technique could be used in any kind of
polymer chromatography methodology, replacing more
expensive refractometers, to obtain refractive index and
dn/dc online. Also, when compared with other SPR
methods, the FIG–SPR technique may be advantageous
in characterizing intermolecular interactions of biomol-
ecules, which is our current focus of investigation.
Acknowledgments
We thank FAPESP, CNPq, and PRP-USP for finan-
cial support and thank D. Briotto for technical assis-
tance. We also thank M.J. Politi and E. Barbieri for
helpful discussions. Tathyana Tumolo is a graduate stu-
dent supported by a FAPESP fellowship.
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