Dynamics of short as compared with long poly(acrylic acid) chains hydrophobically modified with pyrene, as followed by fluorescence techniques

Dynamics of short as compared with long poly(acrylic acid) chains

hydrophobically modified with pyrene, as followed by fluorescence

techniquesw

J. Seixas de Melo,*aTelma Costa,

aAlexandra Francisco,

aAntonio L. Macanita,

b

Sandra Gagocand Isabel S. Goncalves

c

Received 14th September 2006, Accepted 5th January 2007

First published as an Advance Article on the web 2nd February 2007

DOI: 10.1039/b613382g

New low and high molecular weight poly(acrylic acid), PAA, 2000 g mol�1 and 450 000 g mol�1,

respectively, were tagged with pyrene (low and high contents of probe) and its behaviour in

solution was investigated using absorption and fluorescence (steady-state and time-resolved)

techniques. Fluorescence data shows that the degree and level of intramolecular association

strongly depends on the molecular weight. With the short pyrene-labeled PAA chains in aqueous

solution, the excimer-to-monomer fluorescence ratio IE/IM decreases with the increase of pH,

oppositely to the increase in the IE/IM ratio with the increase in pH previously observed with the

long chain PAA. Time-resolved data suggest that excimer formation with the short pyrene-labeled

PAA polymers (ca. 28 acrylic acid monomers per chain) in water is largely due to excitation of

Ground State Dimers, GSD. The increment of pH, and the consequent gradual ionization of the

carboxylic groups in the chain, initially increases the fraction of GSD, possibly due to the

occurrence of special micelle-like chain conformations, inside which the pyrene units are

accommodated. A further increase of the pH above the pKa values, resulting in the full ionization

of carboxylic groups, apparently destabilizes such chain conformations, which leads to a pH effect

on the photophysical properties identical to that of the long chain polymers. In water, the

dynamic data shows the existence of two excimers coexisting with two monomer classes. In

methanol and dioxane (good solvents for the pyrene probe) at room temperature, where one

excimer and two monomers are present, all rate constants could be obtained, as well as the

fractions of ground-state species. It is thus shown that different types of interactions are produced

with small- and long-sized PAA polymers, i.e., the size of the polymer matters.

1. Introduction

The study of polymers modified with aromatic probes has

gained recent and increasing interest because their conforma-

tional and dynamic properties can be followed on a molecular

level (for example, see ref. 1–6 and references therein). In such

studies, fluorescence techniques are probably the most popular

tool, because the experimental techniques available can di-

rectly and indirectly provide information concerning events

occurring in a very short time scale.

Pyrene is one of the most widespread fluorescence probes

for various applications in colloidal and biochemistry do-

mains. Being a hydrophobic probe, pyrene presents low

solubility in water, but when associated to water soluble

polymers its solubility increases. Moreover, pyrene, like some

other popular probes such as carbazole,7 perylene8 and

naphthalene,9 has the additional property of displaying ex-

cimer emission in addition to the fluorescence of the fluor-

ophore itself (monomer emission).10,11 Excimer formation

(which may result from intra- or inter-molecular association)

occurs if the excited fluorophore collides with another non-

excited fluorophore and thus the monomer fluorescence is

quenched by the excimer formation. The light emitted by the

monomer and excimer species occurs in different regions of the

emission spectra, with the latter red-shifted relative to the

former.

In pyrene photophysics, the conventional wisdom considers

that maximum overlap between the two chromophores de-

mands parallel orientation in a sandwich-like conformation at

a maximum distance of ca. 3 A.10–13 However, this does not

seem to be the general rule as others have suggested and

exemplified with intramolecular excimer formation in 1,3-

dipyrenylpropanes.14 It has also been seen that with randomly

labeled polymers with pyrene, the coexistence of two excimers

(parallel and twisted sandwich conformations).15 In the

present study, we will extend this problem to discuss the

a Chemistry Department, University of Coimbra, 3004-535 Coimbra,Portugal. E-mail: [email protected]; Fax: +351 239 827703

bCentro de Quımica Estrutural, Instituto Superior Tecnico (IST),Lisboa, Portugal

cDepartamento de Quımica, Universidade de Aveiro, 3810-193 Aveiro,Portugalw Electronic supplementary information (ESI) available: Scheme S1and Fig. S1–S8. See DOI: 10.1039/b613382g

1370 | Phys. Chem. Chem. Phys., 2007, 9, 1370–1385 This journal is �c the Owner Societies 2007

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

behaviour found in PAA polymers labeled with pyrene,

namely in water (a poor solvent for the probe), which leads

to the presence of two excimers, and in methanol (a good

solvent for the pyrene probe), which leads to the existence of a

single excimer.

One common and important parameter used to probe

colloidal properties is the excimer-to-monomer fluorescence

intensity ratio (IE/IM), which can reflect the higher or lower

probability of excimer formation in a particular circumstance

or environment. Additionally, the ratio of the first and third

vibronic fluorescence intensities (I1/I3) of pyrene strongly

increases with solvent polarity, thus providing information

on the polarity of the local environment of the probe. From

the dependence of the IE/IM ratio, or the I1/I3 ratio (between

the first and third vibronic band of monomer emission

of pyrene16–24), with for example the concentration of surfac-

tant, polymer, etc., it is possible to predict the Critical

Micelle Concentration (CMC) or Critical Aggregation Con-

centration (CAC).

The study and use of polyelectrolytes is a current area

of major importance in colloid science, due to their practical

use in stabilizing colloidal dispersions.25,26 Classic applica-

tion examples are the use of hydrophobically modified

water-soluble polymers in all modern water-based paints

and as rheology modifiers.27 Poly(acrylic acid) (PAA) is a

polyelectrolyte of particular interest in colloidal systems

because it can act as a neutral and anionic polymer, depend-

ing on the medium. In addition to its particular role as a

charged polymer (except at low pH), the aqueous solubility

of this polyelectrolyte can further influence the electrostatic

forces between colloidal particles. By hydrophobically

modifying the polymer with alkyl or aromatic groups (includ-

ing the fluorescent naphthalene or pyrene chromophores),

a balance can be promoted between electrostatic forces

and hydrophobic interactions. The introduction of fluores-

cent probes allows studying the polymer behaviour in

solution at very low concentrations, thus permitting a

conformational study of the isolated polymer. This is

because hydrophobic association in the ground state and

excimer formation in the excited state is reflected in the

steady-state and time-resolved fluorescence properties of the

polymer.

We have previously studied the intramolecular association

of a PAA polymer with a MW = 150 000 g mol�1, randomly

grafted with pyrene and naphthalene units to different degrees

in solution (aqueous and organic solvents) using steady-state

and time-resolved fluorescence.2,28,29 It was shown that, de-

pending on the degree of substitution, solvent and pH, the

PAA can change from a coiled to an expanded conformation.

This work extends these studies made with analogous ran-

domly modified PAA polymers.2,28,29

The polymers subject to the present investigation are of low

[2 kg mol�1 and abbreviated as PAAMe(2)] and high [450 kg

mol�1 and abbreviated as PAAMe(450)] molecular weight.

The Pyrene (Py) content of the labeled PAA polymers corre-

sponds to 52, 53, 77 or 87 PAA monomer units per Py

chromophore and are denoted as PAAMePy(2)52, PAAMe-

Py(450)53, PAAMePy(2)77 and PAAMePy(450)87, respec-

tively, see Scheme 1.

The present study gives particular emphasis to the short-

sized PAA polymers (principle aim of the study) and compar-

ison is made with the long PAAMePy(450) polymers.

2. Experimental

2.1 Materials

The polymers poly(acrylic acid) (PAA) with nominal Mn =

2000 g mol�1 and 450 000 g mol�1 (Aldrich), 1-methylpyrro-

lidone (Riedel de Haen), 1,3-dicyclohexylcarbodiimide

(Aldrich), 1-pyrenylmethylamine hydrochloride (Aldrich),

sodium hydroxide pellets (Aldrich), were obtained from com-

mercial sources and used as received. Triethylamine (Aldrich)

was freshly distilled under reduced pressure.

Dowex 50W-X8, Na-form, 20–50 mesh cation exchange

resin (Fluka) was treated with a solution of 2M HCl overnight

to obtain the H-form. After the treatment, the resin was

washed several times with distilled deionized water.

2.2 Synthesis

The polymers labelled with 1-pyrenylmethylamine were pre-

pared as described in the literature or with minor changes.2,30

2.2.1 PAAMePy(2)77. A mixture of PAA (1.0 g) with

nominal Mn = 2000 g mol�1 and 1-methylpyrrolidone (50

ml) was heated for ca. 2 h up to 60 1C and stirred under inert

atmosphere. A solution of 1-pyrenylmethylamine hydrochlor-

ide (0.096 g, 0.417 mmol) in 1-methylpyrrolidone (5 ml) was

added quickly, followed by freshly distilled triethylamine (65

ml, 0.47 mmol) and a solution of 1,3-dicyclohexylcarbodiimide

(0.095 g, 0.459 mmol) in 1-methylpyrrolidone (5 ml). This

reaction mixture was shielded from light with aluminium foil

and refluxed at 60 1C for 24 h under inert atmosphere.

After cooling, the resulting solution was neutralized with

concentrated aqueous sodium hydroxide, until the modified

polymer had completely precipitated as a yellow solid. The

solid was filtered by suction and washed three times with

1-methylpyrrolidone (20 ml) (previously heated to 60 1C)

and three times with cold methanol (20 ml). The solid was

then dissolved in 4 ml of distilled deionized water and 40 ml of

methanol were added. After storing the mixture overnight in a

Scheme 1

This journal is �c the Owner Societies 2007 Phys. Chem. Chem. Phys., 2007, 9, 1370–1385 | 1371

refrigerator, the resultant precipitate was decanted and dried

under reduced pressure. The remaining mixture was left to

precipitate further and the last procedure repeated once more.

An aqueous solution of the purified polymer was passed

through the cation exchange column to convert it to the acid

form. The solution was then lyophilized and water was further

removed by sublimation.

2.2.2 PAAMePy(2)52. A second sample of PAA with

nominal Mn = 2000 g mol�1 containing a higher amount of

pyrene groups was prepared following the procedure describe

above, starting with PAA (1.0 g), 1-pyrenylmethylamine hy-

drochloride (0.287 g, 1.25 mmol), triethylamine (195 ml,1.41 mmol) and 1,3-dicyclohexylcarbodiimide (0.284 g,

1.377 mmol).

2.2.3 PAAMePy(450)87. This sample was prepared as

described for PAAMePy(2)77 but using PAA with nominal

Mn = 450 kg mol�1. After the washings with 1-methylpyrro-

lidone and methanol, the solid was dissolved in hot water due

to its higher viscosity. Two precipitations were carried out, the

last being in ethanol.

2.2.4 PAAMePy(450)53. This sample was prepared as

described for PAAMePy(2)52 but using PAA with nominal

Mn = 450 kg mol�1. All washings and precipitations were

carried out in ethanol.

The pyrene (Py) labeling content was determined by UV

spectroscopy by comparison with the parent compound

1-pyrenylmethylamine (e = 37 070 M�1 cm�1 at l = 340 nm

in methanol).

It should be noted that, in the case of the short labelled

polymers, the degree of labelling is quite low. In fact, simple

calculations based on the number of AA monomer units

(MW = 72 g mol�1) lead to (2000/72E) 28 AA units in the

PAAMe(2)xx polymers. From the above designation, in which

PAAMePy(2)xx means that there is 1 pyrene unit per xx units

of AA, the mean value of pyrene units per polymer chain m is

0.36 in the case of PAAMePy(2)77, and 0.53 in the case of

PAAMePy(2)52 polymer. Assuming a Poisson distribution of

pyrene units in polymer chains, ca. 70% of the PAAMe-

Py(2)77 chains are unlabeled, 25% chains are single-labeled

and only 4.5% and 0.5% chains possess two and three pyrene

units, respectively. Higher order labelled chains amounts to ca.

0.06%. Therefore, the labelling introduced in the PAA back-

bone of the short-sized polymers essentially amounts to one

and two pyrene units per chain (Table 1).

The solvents used for the polymer solutions were of spectro-

scopic or equivalent grade. Water was twice distilled and

passed through a Millipore apparatus. The measured pH

values were obtained with a Crison micropH 2000 and adjust-

ments of the hydrogen ion concentration of the solutions were

made with dilute HCl and NaOH solutions. The chromophore

concentration of the aqueous PAAMePy solutions ranged

from 1 � 10�5 to 10�6 M. Prior to experiments, solutions

were deoxygenated by bubbling with N2 or Ar gas and

sealed.31 This procedure was utilized for both time-resolved

and steady-state experiments. The polymer concentration in

the different solutions was 0.05 g L�1, which for this molecular

weight is well below the critical value for coil overlap, c*, and

intermolecular chain contacts are therefore improbable in

homogeneous solutions (see also the ESIw).32 In fact, as stated

elsewhere, a concentration of 0.05 g L�1 is still far below the

overlap concentration (c* D 1/[Z], where [Z] stands for the

intrinsic viscosity of the polymer33) of the unlabelled PAA,

which was found to be approximately 10 g L�1 in water at

pH D 3.32

The absorption spectra were recorded on a Shimadzu UV-

2100 spectrophotometer; all spectra were acquired with a

minimum resolution of 0.2 nm. The fluorescence spectra were

recorded with a Horiba-Jobin-Ivon SPEX Fluorog 3-22 spec-

trometer and were corrected for the instrumental response.

The Fluorolog consists in a modular spectrofluorimeter with

double grating excitation (range 200–950 nm, optimized in the

UV and with a blazed angle at 330 nm) and emission (range

200–950 nm, optimized in the visible and with a blazed angle

at 500 nm) monochromators. The bandpass for excitation and

emission is 0–15 nm (values that are continuously adjustable

from computer Datamax/32 software) and the wavelength

accuracy is of �0.5 nm. The excitation source consists in an

ozone-free 45O W Xenon lamp and the emission detector is

Hamamatsu R928 Photomultiplier (200–900 nm range),

cooled with a Products for Research thermoelectric refriger-

ated chamber (model PC177CE005), or a Hamamatsu R5509-

42 (900–1400 nm range), cooled to 193 K in a liquid nitrogen

chamber (Products for Research model PC176TSCE-005-),

and a photodiode as the reference detector.

Fluorescence decays were measured using a home-built

Time-Correlated Single Photon Counting apparatus as de-

scribed elsewhere,31,34 except that as excitation source, a

Horiba-JI-IBH NanoLED, lexc = 339 nm, was used. Besides

the excitation source, the apparatus consists of a Jobin-Ivon

H20 monochromator, a Philips XP2020Q photomultiplier,

Table 1 Mean value of pyrene units per polymer chain m, theoreticala fractions of unlabelled N0, single-labelled N1, double-labelled N2, andmulti-labelled (n 4 2) chains, and fraction of single-labelled chains relative to all labelled chains b (intrinsically isolated pyrene units)

PAAMePy(2)77 PAAMePy(2)52 PAAMePy(450)87 PAAMePy(450)53

m 0.36 0.53 72 118N0 0.70 0.59 0 0N1 0.25 0.31 0 0N2 0.045 0.084 0 0N42 0.005 0.016 1 1b 0.83 0.76 0 0

a Calculated assuming a Poisson distribution Ni = mi exp (�m)/i ! where Ni is the fraction of chains containing i pyrene units and m stands for

mean number of pyrene units per chain.


and a Canberra instruments time-to-amplitude converter

(2145), Multichannel Analyser (AccuSpec) and START

and STOP discriminators (2126). Alternate measurements

(500 counts per cycle), controlled by Decays software

(Biodinamica-Portugal), of the pulse profile at 339 nm and

the sample emission (375, 480 and 520 nm) were performed

until 5–10 � 103 counts at the maximum were reached. The

fluorescence decays were analysed using the modulating func-

tions method of G. Striker.35,36 A more detailed description of

the equipment with drawings of the different components as

well as decays of typical aromatic hydrocarbons (including

pyrene) can be found in detail in ref. 31.

Temperature control (for steady-state and time-resolved

fluorescence) was achieved using a home-built system based

on cooled nitrogen and electric heating, which is automatically

controlled by the difference between the input temperature

value and the sample real temperature, determined with a

PT100 thermometer.

3. Results

3.1 pH effect in the absorption spectra

From the variation of the absorption spectra (see Fig. S1 in the

ESIw) of the PAAMePy polymers with the pH, two parameters

can be extracted (see Fig. 1): the wavelength maxima (lmax)

and the PA parameter (defined as the peak-to-valley absor-

bance ratio in the first vibronic S2 ’ S0 transition).2 With all

polymers, a blue-shift of the lmax with increasing pH is

observed (see inset plots in Fig. 1). On the other hand, the

pH dependence of the PA is opposite in the cases of short-

and long-sized polymers (Fig. 1). It is also worth noting that

in the case of the PAAMePy(2) polymers (left panels in Fig. 1),

the PA values decrease with increasing pH, whereas with the

PAAMePy(450) polymers (right panels in Fig. 1), PA increases

with pH. Both the dependence of the PA and lmax with the pH

were fitted to a sigmoidal Boltzmann-like equation of the

formula:

PA; lmax ¼ A0 þA1 � A0

1þ epH�pKa

dpH

ð1Þ

The plot of the PA and lmax dependencies with pH (Fig. 1),

shows a clear inflexion from which the pKa could be estimated.

The obtained results are shown in Table 2.

3.2 Steady-state fluorescence in water

The fluorescence excitation spectra (Fig. 2) collected in the

monomer and excimer emission regions are different, and pH

dependent. This leads to differences in the PM and PE values,

which are the analogous to the PA value in the fluorescence

excitation spectra when collected at the monomer (PM) or

excimer (PE) emission wavelengths. A difference in the PM and

Fig. 1 Dependence of the PA ratio and wavelength maxima, lmax (shown as inset), with pH for the PAAMePy(2)52, PAAMePy(2)77,

PAAMePy(450)53 and PAAMePy(450)87 polymers.

Table 2 Values of pKa for the different polymers obtained by fittingthe data in Fig 1 [PA and wavelength absorption maxima (lmax) vs.pH] with eqn 1. The results are presented with the standard deviationresulting from five independent measurements

Polymer pKa (from PA) pKa (from lmax)

PAAMePy(2)52 6.67 � 0.13 5.92 � 0.18PAAMePy(2)77 5.23 � 0.14 5.67 � 0.19PAAMePy(450)53 5.8 � 0.05 4.82 � 0.54PAAMePy(450)87 5.71 � 0.09 4.65 � 0.43


PE values indicates the presence of Ground State Dimers

(GSD) and PM � PE = 0 indicates the opposite, i.e., absence

of GSD.2,37

For the PAAMePy(2) polymers, it can be observed that the

variation of the PM � PE difference is clearly pH dependent

and changes dramatically when the pKa is reached. However,

with the long chain PAAMePy(450) polymers it seems reason-

able to consider that there is practically no change of the PM �PE difference with the pH (see right hand panels in Fig. 2).

Another interesting feature, observed in comparing the

fluorescence steady-state data of the PAAMePy(2) and PAA-

MePy(450) polymers, is the opposite trend of the IE/IM ratio

with pH for the long and short chain-length polymers (Fig. 3).

In the case of the long PAA chain polymers [PAAMePy(450)],

the IE/IM ratio decreases from relatively high values (0.6 and

2.0) at pH ca. 3.5 to much lower values (ca. 0.1) in the alkaline

region. In the case of the PAAMePy(2) polymers, however,

there is first an increase of the IE/IM ratio with pH, up to

Fig. 2 Fluorescence excitation spectra for the studied polymers obtained at acidic (first column) and alkaline (second column) pH values with

lem = 520 nm (full line) and lem = 375 nm (dashed line) at T = 293 K. The third column reports the PM � PE difference. In the case of

the PAAMePy(2) polymers, the lines showed for the PM � PE vs. pH variation result from an adjustment obtained with eqn (1).


values close to the pKa value, and only above this pH region

the IE/IM ratio slightly decreases.

Fig. 4 shows plots of the ln(IE/IM) vs. 1/T, the so-called

Stevens–Ban plots,29,38 for a short PAAMePy(2)52 and long

size PAAMePy(450)53 polymer at two pH values each. These

plots have two limiting regions: the High Temperature Limit

(HTL) and the Low Temperature Limit (LTL) regions, where

excimer formation is, respectively, reversible or non-reversible

(see inset in Fig. 4).29 With the present systems, the transition

temperature between the HTL (reversible) and LTL (non-

reversible) regimes, which depends on the polymer and pH

considered, is found at values below 17 1C (Fig. 4). Although

the interpretation of these plots is not as straightforward as it

is with simple Birks’ kinetics11 (two excimers, ground-state

dimers and isolated monomers are present, see below), this

seems to indicate that at room temperature (20 1C) the system

is found in the HTL regime.

3.3 Time-resolved fluorescence in water

Fig. 5 shows fluorescent decay profiles of PAAMePy(2)52 in

water at pH = 4.62, measured at the monomer (375 nm) and

excimer (480 and 520 nm) emission wavelengths. The figure also

shows tri-exponential (A) and tetra-exponential (B) fits from

Fig. 3 Fluorescence spectra (two left hand panels) and excimer-to-monomer (IE/IM) ratio (right hand panels) obtained at different pH values (and

with different excitation wavelengths) for the (A) PAAMePy(2)77, (B) PAAMePy(2)52, (C) PAAMePy(450)87 and (D) PAAMePy(450)53

polymers. The lines in the IE/IM vs. pH dependences for C and D are guidelines for the eye.


global (simultaneous) analysis of the three decays; the indivi-

dual analysis of the decays can be found in the Fig. S5 of the

ESIw. The sum of three exponentials does not properly fit the

decays, as can be attested by the poor quality of the weighted

residues and the Auto-Correlation (A.C.) functions. This is

particularly evident in the decays at 480 and 520 nm (Fig. 5).

For these decays there are two important features: first,

the longest decay time (220 ns) is present only at the mono-

mer emission wavelength (375 nm). In fact, the preexponential

coefficients of this component, either at 480 nm (0.008) or

520 nm (�0.024), show negligible values that have no physical

meaning, which is an artefact resulting from the global

analysis procedure. This is more clearly observed with the

independent analysis of the 480 nm and 520 nm decays

shown in Fig. S5 of the ESIw, which shows good triple-

exponential fits without the 220 ns component.

Second, the 104 ns decay is present only at the excimer

emission wavelengths (480 and 520 nm); the tri-exponential

individual fit of the 375 nm decay is acceptable with

values that are approximately identical to those obtained

with the tetra-exponential global fit excluding the 104 ns

component.

The implications of these observations are: first, the longest

decay time t0 (220 ns) must be assigned to monomers

that cannot form an excimer, i.e., unquenched ‘‘isolated’’

pyrene units.2 These monomers are pyrene units in single-

labelled chains (intrinsically isolated), and/or pyrene units in

multi-labelled chains but in a position or conformation that

prevents them from forming an excimer. Second, the shortest

time t3 (ca. 7 ns) appears as a rise-time at 480 and 520 nm,

being thus assigned to pyrene monomers that form excimers

(MAGRE2). Third, the two middle decay times (t1 = 53 ns and

t2 = 104 ns) indicate the emission of two conformationally

different excimers (see the Discussion section). Fourth, the

sum of the preexponential coefficients at both 480 and 520 nm

differs from zero, indicating the presence of pre-formed

dimers. Finally, the preexponential coefficient of t2 (E104 ns)

at 375 nm is negligible, thus indicating an irreversible

excimer, while that of t2 (E53 ns) is large, indicating a

reversible excimer.

3.4 Absorption and steady-state fluorescence in good solvents

(dioxane and methanol)

The absorption spectra of the PAAMePy polymers of low and

high MW in good solvents such as dioxane and methanol are

presented in Fig. 6. In contrast with the behaviour found in

water (Fig. 1), the absorption spectra in dioxane (and metha-

nol) do not present significant differences for the different

polymers. Moreover, the steady-state fluorescence spectra

obtained with different excitation wavelengths shows little

variation (Fig. 6) when compared with the behaviour found

in water (Fig. 3). The exception is when excitation is made at

Fig. 4 Plots of ln (IE/IM) vs. 1/T obtained at different pH values for

the PAAMePy(2)52 and PAAMePy(450)53 polymers. The inset is a

generic parabolic-type curve showing the HTL and LTL regions; the

difference (d) between the curve defining the normal regime and the

line defining the HTL regime at the crossing point, T* (transition

temperature between the two regimes), are clearly identified.

Fig. 5 Global analysis of the fluorescence decays of PAAMePy(2)52

in water (pH = 4.62, T = 293 K), at three emission wavelengths

obtained with fits to three (A) and four (B) exponentials. The instru-

ment profile curve, weighted residuals and Auto-Correlation (A.C.)

functions are also shown. The negative preexponential values of the

longest times in the global analysis result are artifacts resulting from

this kind of analysis, i.e., the components do not exist, as seen in the

individual analysis (Fig. S5 in the ESIw). A clear poor adjust of the

experimental decay with the fitted three-exponential function can be

observed, particularly in the weighted residuals and A.C. functions;

see text for further details.


the red-edge of the absorption (350 nm), denoting that GSD

are still present in these solvents. Moreover, and once more in

contrast with the behaviour found in water, the excitation

spectra in methanol (or dioxane) collected at excimer and

monomer emission are not much different from each other, see

Fig. 6. From these overall observations, one can conclude that,

in methanol (or dioxane), excimer formation through a static

route (direct excitation of ground-state dimers) is strongly

diminished, and the dynamic mechanism is the major route for

excimer formation. The exact amount of this fraction of

ground-state dimers or mole fractions (a and b in Scheme 2

below) can be evaluated from the time-resolved data treat-

ment,2 discussed in the forthcoming section.

3.5 Time-resolved fluorescence in good solvents (dioxane and

methanol)

Fig. 7 shows the decay profiles for PAAMePy(450)87 obtained

in methanol and their fittings with global (at 375 nm and

520 nm) analysis. The results (triple and double-exponential

decays) indicate the presence of only three species: the isolated

monomer (t0 = 209 ns), the MAGRE2 monomer and one

excimer, i.e., one less species than in water. The two shortest

decay times (t1 and t2) are attributed to the kinetically-coupled

MAGRE and respective excimer, and the longest component

(t0) is assigned to free monomers (not able to form excimer).2

The independent analysis of these decays can be found in

Fig. S6 in the ESIw.

Finally, we observe that the preexponential coefficient of the

rise-time at 520 nm is substantially more negative in the good

solvents (for the hydrophobic probe) dioxane and methanol

than in water for both the short [PAAMePy(2)] and long

[PAAMePy(450)] polymers, which is consistent with fewer

ground-state dimers and a major contribution from the dy-

namic route of excimer formation. Summarizing, the fluores-

cence decays in methanol and dioxane follow sums of

exponential laws described by eqn (2) and (3).2

IMðtÞ ¼ I375 nmðtÞ ¼ A10e�t=t0 þ A11e

�t=t1 þ A12e�t=t2 ð2Þ

IEðtÞ ¼ I520 nmðtÞ ¼ A21e�1=t1 þ A22e

�1=t2 ð3Þ

4. Discussion

4.1 Absorption and steady-state fluorescence data in water

The S2 ’ S0 absorption wavelength maxima, lmax, of the

long-sized PAA pyrene-labeled polymers at pH 4 (343.9 and

343.4 nm) are 1.5 nm blue-shifted with respect to the short-

sized polymers maxima (345.4 and 344.9), Fig. 1 and S1w. Thisdifference suggests that factors other than the presence of GSD

are present. The blue-shift likely suggests that, at pH 4, the

pyrene labels are exposed to a more polarizable environment

in the case of the long-sized polymers (the absorption spectra

of pyrene is known to respond essentially to solvent polariz-

ability). Increasing the pH results in a blue-shift of the

absorption maximum of all polymers (Fig. 1 and Fig. S1w),compatible with a decrease in the environment polarizability,

i.e., exposure to water. The differences between short- and

long-sized polymers practically vanish at high pH values (48),

where lmax = 342.3� 0.1 nm for the four polymers, indicating

a similar solvent polarizability in all cases. The degree of

pyrene labeling has a comparatively smaller effect on lmax

(0.5 nm red-shift for the more labeled polymers), as expected if

the presence of GSD has minor influence on lmax.

Fig. 6 Absorption (left hand panel), fluorescence emission (middle hand panel and obtained with three excitation wavelengths) and fluorescence

excitation (right hand panel obtained collecting the emission at the monomer and excimer bands) spectra for PAAMePy(2)52 (top panels) and

PAAMePy(450)53 (bottom panels) in methanol at T = 293K.

Scheme 2


For the PAAMePy(2) polymers, the apparent pKa values

(see Table 2 and potentiometric titrations, Fig. S2 in the ESIw)varies from 5.23 to 6.67, whereas for the PAAMePy(450)

polymers the range is 4.65–7.08 (Table 2 ). The pKa for acrylic

acid is, at 25 1C, equal to 4.25 (4–4.5)39 and for PAA is ca.

4.740 (strongly dependent on the dissociation degree, see the

ESIw for further information). From the apparent pKa values

obtained from the PA and lmax dependencies with pH (Fig. 1),

it seems clear that the introduction of the pyrene probe

increases the apparent pKa of the modified PAA polymer.

Values of PA = 3 for pyrene-labeled polymers are generally

considered to indicate the absence of GSD.2,41 As can be

observed from Fig. 1 (and Fig. S1 in the ESIw), the values of

PA are much lower than 3 for all polymers, indicating the

presence of GSD over the whole pH studied range. The values

of PA are lowest for the long-sized polymers (1.65 and 1.85

against 2.2 and 2.48 for the short-sized polymers) at pH 4, and

increase upon increasing pH, whereas with the short chains, a

decrease with increasing pH is observed (Fig. 1 and Fig. S1 in

the ESIw). At pH 4 ca. 9, the PA values of short- and long-

sized polymers become closer to each other (1.90 and 2.25 vs.

1.90 and 1.95).

Deprotonation of the carboxylic acids of the PAA chain is

known to induce a change from a coiled to an extended

conformation (due to electrostatic repulsions), leading to less

excimer formation (essentially due to the existence of fewer

GSD).2,29,32 With PAAMePy(450) polymers, this is reflected

by a complete overlap of the absorption spectra of the low and

high labelled polymers at alkaline pH values (figure not

shown). This shows that at alkaline pH values the absorption

spectra mainly reflects the contribution of the pyrene chromo-

phore, whereas at acidic pH values, pyrene dimers absorb and

thus the displayed absorption spectra is the sum of the two

(monomer and dimer). However, these differences seen in the

absorption, at different pH values, are also revealing the

nature of the adopted polymer conformation.

With the small PAAMePy(2) polymers, the opposite situa-

tion is observed, i.e., increasing pH results in more GSD

contribution. At low pH values, the matching of the absorp-

tion spectra indicates a lower level of GSD as compared to the

PAAMePy(450). This is consistent with the theoretical Poisson

distribution for the PAAMePy(2) polymers, indicating that

25–30% of the chains are labelled with a single pyrene, only

5–8% with two pyrenes and less than 1% with 3 or more

pyrene units (Table 1). The increase on the fraction of GSD at

high pH values, not being due to intermolecular association

(see the Experimental section and the ESIw for further details),can only result from a change in the polymer conformation,

which leads the pyrene units in double-labelled chains to be

located at van der Waals distances. Apparently, such confor-

mations are possible, without increasing the carboxylate–

carboxylate electrostatic repulsion, only with very short chain

lengths. A possible explanation is that the small 28 acrylic acid

units can be accommodated in conformations where the

carboxylate groups are exposed to water and kept apart from

each other, thus creating a kind of ‘‘hydrophobic’’ core where

the (essentially two) pyrenes are located. Such micellar-like

conformations do not seem favourable in the case of long

polymer chains.

A more recent study on the formation of interpolyelectro-

lyte complexes formed by the mixing of polystyrene-

block-poly(N-ethyl-4-vinylpyridinium bromide) (PS-b-PEVP)

micelles and poly(methacrylic acid) (PMAA) showed the

existence of self-assembled stable water-soluble colloid nano-

particles (micelle-like structures) in which the polystyrene

units form a core with an intermediate water-insoluble layer

of polyions and an outer layer made of charged fragments of

the excess polyelectrolyte (PMAA).42 Although a straightfor-

ward comparison with the structure here proposed is not

possible, since our system is less complex, it gives support to

the proposed ‘‘micelle-like’’ structure of the low MW PAA-

MePy polymers.

The pH dependence of the IE/IM ratio, obtained with three

different excitation wavelengths, shows that excitation at

longer wavelengths always results in a higher IE/IM ratio

(Fig. 3). This is again compatible with the preferential light

absorption of GSD at longer wavelengths, as was previously

observed for analogous PAA polymers.2 The abnormal

IE/IM vs. pH trend of the short chain polymers [PAAMePy(2)]

is again consistent with the adoption of the above proposed

‘‘micelle-like’’ conformation by these polymers at inter-

mediate pH values. These ‘‘micelle-like’’ structures appear to

persist until the apparent pKa of the short sized polymers

is reached. Indeed, the inflection observed at pH = 5.1–5.2

(IE/IM vs. pH in Fig. 3) for the low MW polymers more

likely resembles a critical micelle concentration. After this

pH value is reached, the IE/IM curves denote a decrease

that seems to indicate that ‘‘micelle-like’’ structures are falling

apart. Moreover, if we compare the values of the IE/IMat alkaline pH values, i.e., at the plateau level, for the

corresponding identically labelled polymers, i.e., PAAMe-

Py(2)52 with PAAMePy(450)53 and PAAMePy(2)77

with PAAMePy(450)87, we note that this ratio takes identical

values. This suggests that, at these pH values, the two types

of polymers [PAAMePy(2) and PAAMePy(450)] have

reached an identical and expanded conformation. It is worth

nothing that for lower pH values the IE/IM ratio for the

Fig. 7 Global analysis of the fluorescence decays for the PAAMe-

Py(450)87 polymers in methanol at T = 293 K with excitation at

339 nm and emission at 375 and 520 nm. The instrument profile curve

is also shown. For a better judgment of the quality of the fits shown as

insets are the weighted residuals and the A.C. functions.


PAAMePy(2) polymers is very low (in contrast with the

situation observed with the PAAMePy(450) polymers),

see Fig. 3. This suggests that in this situation the polymers

are in a constrained geometry where little interaction between

the pyrene units is allowed.

The excitation spectra, collected in the monomer and ex-

cimer regions, and the variation of the PM � PE difference

with pH in Fig. 2 provide similar indications. With the

PAAMePy(2) polymers there is an increase of the PM � PE

difference with pH, while this difference decreases in the case

of the PAAMePy(450) polymers. With the PAAMePy(2)

polymers, the increase of PM � PE with pH can only result

from the adoption of special chain conformations, such as the

proposed ‘‘micelle-like’’ conformation.

In summary, all the above data (absorption and steady-state

fluorescence) are consistent with the contribution of GSD,

strong in water and smaller in dioxane or methanol. In water,

the contribution of GSD increases with the pH for the

PAAMePy(2) polymers, which seems due to the possible

adoption of ‘‘micelle-like’’ conformations of short chains,

and decreases for the PAAMePy(450) polymers, due to the

expansion of the chain.

4.2 Time-resolved fluorescence in water

Fig. 8 shows the decay time and preexponential coefficient

dependence with pH for the studied polymers. Although the

behaviour is obviously different for each polymer, from Fig. 8

it can be observed that, in general, the longest decay time (t0)is found with values above 200 ns and slightly decreases with

increasing pH. The three other decay times, t1, t2 and t3,display values varying respectively from 90–130 ns, 40–65 ns

and 5–10 ns. The t2 decay time is found with values similar to

those obtained for pyrene’s intermolecular excimer: 65 ns in

cyclohexane.11 With aromatic molecules the parallel sandwich-

type geometry is usually considered as the adopted excimer

conformation.12,13 However, by comparison of the decay times

for intramolecular excimer formation with 1,3-(1,10-dipyre-

nyl)propane [1Py(3)1Py, which displayed a triple exponential

decay] and 1,3-(2,20-dipyrenyl)propane [2Py(3)2Py, which was

fitted with a double exponential decay] systems, Zachariasse et

al.14 showed that the triple-exponential decays of 1Py(3)1Py

resulted from the presence of two excimers. The shortest-lived

excimer (the more stable excimer) displays a twisted sandwich

geometry with its lifetime identical to the lifetime of the pyrene

Fig. 8 Fluorescence decay times (ti) and preexponential factors (aij) at 375 nm (a1j) and 520 nm (a2j) as a function of pH for the four studied

polymers. (A) PAAMePy(2)77, (B) PAAMePy(2)52, (C) PAAMePy(450)87 and (D) PAAMePy(450)53 polymers.


intermolecular excimer (ca. 60 ns),11 while the longer lived (ca.

140–150 ns), less stable excimer has the parallel sandwich

conformation14 and, also important, no distributions of decay

times were observed in these systems even when picosecond

resolution was used.43 For 2Py(3)2Py, where only one excimer

(less stable and parallel sandwich-like) was present, the ex-

cimer lifetime was found to be 150 ns.14 From these results it

was clear that two pyrenes linked through the position 1 can

form two spectroscopically different excimers, whereas label-

ling in the position 2 allows only the parallel sandwich

conformation. However, this depends on the chain connecting

the two interacting pyrenes and the environment where it is

found. Specifically, when the chain is sufficiently flexible for

allowing relaxation to the most stable (short-lived) excimer,

only the stable excimer is observed. These studies were further

confirmed by Yamamoto and co-workers, who have found

that the partial-overlap excimer (twisted sandwich geometry)

was ca. 1 kcal mol�1 more stable than that of the full-overlap

(sandwich-like) excimer due to the contribution of the ring

repulsive force to the excimer conformation.44

With the present polymers, the random grafting of the

pyrene units is done by way of position 1 of the probe. It does

not seem thus unreasonable to observe, under conditions

where the relaxation to the most stable excimer is hindered,

the simultaneous presence of two excimers.

As can be seen in Fig. 5 and 8 with the PAAMePy polymers,

the decay time values associated with the two excimers are

similar to those found for intramolecular excimer formation in

1Py(3)1Py.14,43,45,46 It is thus very likely that we are in the

presence of two excimers: the first involves an asymmetric

configuration between the two interacting pyrenes (decay time

40–65 ns depending on the degree of labelling, pH and solvent)

and the second with a symmetric sandwich-like structure

involving the two pyrenes, with a longer-lived lifetime (in

our case varying from 90–130 ns).

Finally, it is also important to consider the dependence of

the preexponential factors with pH (Fig. 8). In general these

do not seem to depend on the PAA chain polymer (or degree

of labelling) considered.

The A10 preexponential coefficient assigned to the presence

of a certain fraction of conformationally isolated monomers

and directly related to the b factor in Scheme 2 displays, at pH

3.5, large values of ca. 0.88 and 0.78 for the short-sized

polymers [PAAMePy(2)77 and PAAMePy(2)52, respectively].

These values are similar to the theoretical mole fractions of

single-labelled chains relative to all labelled chains, i.e., in-

trinsically isolated monomers (Table 1). The A10 values for the

long-sized PAAMePy(450) polymers at pH 3.5 are substan-

tially smaller (ca. 0.3), but larger than the negligible theoretical

fraction of single-labelled chains in the long size polymers

(Table 1) and abruptly increase to values of 0.8–0.9 at alkaline

pH values. The increase of the A10 values with increasing the

pH is compatible with a pronounced expansion of the long

polymer chains upon deprotonation of the carboxylic groups.

As can be observed in Fig. 8, for the two PAAMePy(450)

polymers, there is a reciprocal behaviour of the A10 vs. A11 and

A12 preexponential factors. Although some scatter exists, it is

clear that there is an increment of A10 with the pH and a

concomitant decrease of the A12 and A11 preexponentials. This

shows that as the pH increases more ‘‘free’’ pyrene is present,

and thus a decrease in the excimer formation yield is experi-

enced. From Fig. 8 it is seen that the A23 factor (520 nm

emission wavelength) increases with the pH, which reveals the

gradual vanishing of the dynamic contribution for excimer

formation.

With the PAAMePy(2) polymers, the A12 and A11 preexpo-

nential factors basically do not show significant variations

with the pH. The only preexponential seeming to change with

the pH is A23 (associated with the rising component). This

preexponential is related with the degree of dynamic vs. static

excimer formation.2 Its increase with pH seems to indicate the

decrease of the dynamic contribution along with the increase

in the pH. The increase in the A23 preexponential factor with

pH also shows that the increase in excimer formation (ob-

served in Fig. 3) is mainly due to an increase in the GSD

contribution, as also indicated by the pH dependence of the

PM � PE and IE/IM data.

4.3 Determination of rate constants and fractions of ground-

state species in good solvents

The kinetic scheme shown below (Scheme 2) summarizes the

behaviour of the PAAMePy polymers in good solvents. In the

scheme, ka and kd are the rate constants of excimer formation

and dissociation, respectively, and a(1 � b), (1 � a)(1 � b) andb are the fractions of light that are absorbed, respectively by

the monomers that give rise to excimer (MB or MAGRE), the

GSD (E) and the isolated monomers (MA).

From Scheme 2, the excited-state concentration time depen-

dence of each species (MA, MB and E) is given by:

½M�A�ðtÞ ¼ a0e

�l0t ð4Þ

½M�B�ðtÞ ¼ a11e

�l1t þ a12e�l2t ð5Þ

½E��ðtÞ ¼ a21e�l1t þ a22e

�l2t ð6Þ

Since at the monomer emission region both types of mono-

mers contribute, the time dependence of monomer fluores-

cence can be described by eqn (2) and (3), respectively, where

l1 and l2 are the reciprocals of the decay times t1 and t2 andare given by:

l2;1 ¼ kX þ kY �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðkX � kYÞ2 þ 4kakd

q� �=2 ð7Þ

where kX = ka + 1/tM, kY = kd+1/tE and t0 is the decay time

of the uncoupled monomer, equal to tM. From the kinetic

scheme, it can be seen that there are six unknowns: ka, kd, kM,

kE, a and b, to be evaluated from six equations: l2, l1, l0, A10,

A and B; see Appendix 1 for the relation between all the rate

constants and the a and b values with the experimental data

li and aij.

By using the appropriate kinetic equations derived from

Scheme 22 and with the data obtained from the fluorescence

decays (decay times and preexponential coefficients), see Fig.

7, all the rate constants and the a and b factors could be

determined for the situations found in good solvents (dioxane

and methanol). The equations and formalism relating the rate

constants to the decay times and preexponential factors can be


found in detail in ref. 2, but are here presented with a new

formalism (see Appendix 1), which simplifies the equations.

The rate constants obtained with this procedure are summar-

ized in Table 3.

4.3.1 Ground-state fractions of isolated monomers (b) and

GSD [a(1 � b)]. Let us first analyze the ground-state fractions

of the three species (isolated monomers, MAGRE monomers

and GSD). In dioxane and methanol, the fraction of isolated

monomers b is large in the PAAMePy(2) short size polymers

with values (0.5–0.7) slightly smaller than the theoretical

values of intrinsically isolated monomers (0.7–0.8; Table 1).

With the PAAMePy(450) polymers, b has lower values (o0.3).

The fraction of GSD, a(1 � b), is low and similar with the

PAAMePy(2) and PAAMePy(450), increasing by a factor of

ca. 1.5 with the degree of labeling.

4.3.2 Rate constant of excimer formation. The rate con-

stant for excimer formation is, with the short-sized PAAMe-

Py(2) polymers, independent from the pyrene-labeling degree,

in both dioxane and methanol. This, at first glance unexpected,

result is again a consequence of the very short chain length and

low pyrene-labeling degree of the PAAMePy(2) polymers. In

fact, inspection of Table 1 shows that increasing the pyrene-

labeling degree from PAAMePy(2)77 to PAAMePy(2)52 es-

sentially results in increasing the number of double-labeled

chains N2, and has negligible effect on the mean number of

pyrene units per chain (the fraction of multi-labeled chains

N 4 2 increases from 0.005 to 0.016, but stays very low). The

dynamic route is thus not affected, but the static one is (which

is accounted for in the IE/IM values), due to the increase of the

double-labeled chain fraction. On the other hand, with the

long-sized polymers, the value of ka clearly increases with

increasing the labeling degree, from PAAMePy(450)87 to

PAAMePy(450)53, as expected from the corresponding in-

crease in the number of pyrene units per chain.

The value of ka is solvent-dependent for both short- and

long-sized polymers, increasing from dioxane to methanol,

which follows the dependence with the reciprocal of the

solvent viscosity (0.55 cP for methanol and 1.44 cP for dioxane

at T = 293 K47). Moreover, the values of ka are in the 1–4 �107 s�1 range, consistent with the values found for intramole-

cular excimer formation with 1,n-di(1,10-dipyrenyl)alkanes

(n = 12–16) in solvents of similar viscosity.48 With a parent

model compound with 16 atoms covalently linked to two

terminal pyrene by way of identical amide groups, the values

of the rate constants obtained using the Birks formalism

(modified with the presence of GSD) and assuming a t0 =

230 ns, were: ka = 4.2� 107 s�1 and kd = 0.26� 107 s�1, tE =

55 ns and a = 0.3 (see the ESIw for further details). A direct

comparison of these values with the intermolecular rate con-

stant (diffusion-controlled) is not possible due the strong

contribution of the chain to the activation energy and its effect

on excimer-forming conformations (Hirayama’s rule49).

Nevertheless, the intramolecular ka should be approximately

proportional to the mean number of pyrene units per chain m

(in the case of the long polymers), under the assumption that

the root-mean-square end-to-end distance of the polymer is

not affected by labelling (constant polymer volume).50 In fact,

the ratio of the ka values of PAAMePy(450)53 and PAAMe-

Py(450)87 (0.15/0.009 = 1.67), Table 3, is similar to the ratio

of the respective m values (118/72 = 1.64), Table 1.

Last but not least, is the observation that the ka values are

significantly smaller with the PAAMePy(450) polymers, which

suggests a reduced mobility of the longer chains.

4.3.3 Rate constant of excimer dissociation. The values

found for the dissociation rate constant kd (1 � 3 � 107 s�1)

are not much different from those obtained for the reciprocal

excimer lifetime kE (1.4 � 1.8 � 107 s�1). In the absence of

GSD and isolated monomers, the equality kd = kE would

signify that the PAAMePy polymers are, at room temperature,

in the transition from the LTL to the HTL regions.29 This

conclusion is in agreement with the IE/IM temperature depen-

dence in water (Fig. 4), within the limitations resulting from

the presence of GSD and isolated monomers and the differ-

ence in solvent.

4.3.4 Lifetimes of monomer and excimer. The monomer

lifetime values t0 (=1/k0) 222–290 ns are found within the

expected range for a pyrene chromophore substituted in

position 1. As an example, for 1-ethylpyrene in n-hexadecane

the lifetime value t0 (degassed with the use of freeze-pump-

thaw cycles in vacuum sealed cuvette) is 237 ns51 and has

Table 3 Rate constants of excimer formation, ka, dissociation, kd, and decay, kE, and fractions of isolated monomers, b, MAGRE monomers[(1 � a)(1 � b)] and ground-state dimers [a(1 � b)] for PAAMePy polymers in dioxane and methanol at T = 293 K

Polymer (solvent) ka/ns�1 kd/ns

�1 kE/ns�1 tE/ns

�1 t0/ns�1 a b a(1 � b) (1 � a)(1 � b)

PAAMePy(2)77Dioxane 0.017 0.029 0.018 57 240 0.11 0.61 0.04 0.35Methanol 0.027 0.017 0.015 66 291 0.23 0.66 0.08 0.26PAAMePy(2)52Dioxane 0.022 0.029 0.015 66 223 0.13 0.55 0.06 0.39Methanol 0.031 0.010 0.014 70 270 0.30 0.62 0.11 0.27PAAMePy(450)87Dioxane 0.009 0.019 0.016 61 234 0.07 0.19 0.06 0.75Methanol 0.019 0.017 0.016 61 290 0.14 0.31 0.10 0.60PAAMePy(450)53Dioxane 0.014 0.018 0.017 57 234 0.11 0.01 0.11 0.88Methanol 0.025 0.016 0.018 56 228 0.16 0.14 0.14 0.72


244 ns46 or 284 ns43 values in n-heptane. Note that for

2-ethylpyrene the lifetime has a much longer value, t0 = 367 ns14

in methylcyclohexane at 25 1C.

The value for kE could be considered constant with an

average value of 1.4 � 1.8 � 107 ns�1 (tE D 55–70 ns). This

recovered excimer lifetime value is in agreement with those

obtained for other pyrene-labeled polymers such as the analo-

gous PAAMePy2, among others,41,52 in water (in this last case

making use of the ‘‘blob model’’ alternative method) and again

with the value obtained for the most stable excimer in pyrene

(asymmetric sandwich), which is found to be ca. 60 ns.11,14,43

For simple (not absolute) comparison purposes, the more stable

excimer in 1,3-di(1-pyrenyl)propane (in n-heptane) displays a

tE = 76 ns45 and the 1Py(22)1Py, i.e., with 22 carbon atoms

between the two pyrenyl units displays a tE = 52 ns.45

In summary, the foregoing results indicate that pyrene

excimer formation in the PAAMePy polymers in good sol-

vents is correctly described by conventional kinetics, where the

number of exponential terms is equal to the number of species

that are kinetically involved. Therefore, this method of ana-

lysis seems preferable to alternative methods, which do not

provide results containing the same amount of direct physical

insight (rate constants and fractions of ground-state species).

This was also suggested by Siu and Duhamel, who studied

excimer formation kinetics using two models (the ‘‘blob

model’’ and the ‘‘differential’’ method ’’sums of exponen-

tials’’), and concluded that the procedure of using sums of

exponentials is more general than the ‘‘blob model’’.15

4.4 Formalism for determination of rate constants and

fractions of ground-state species in water

As previously mentioned, the fluorescence decays of the PAA-

MePy polymers are tetra-exponential in water, indicating more

complex kinetics than in dioxane or methanol. The additional

decay term was tentatively assigned to a second excimer, on the

basis of three observations. First, the decay time is similar to the

lifetime of the less stable excimer of 1Py(3)1Py. Second, this

fourth exponential term is not observed in good solvents, where

there are less conformational restrictions to the polymer chain.

Third, the preexponential coefficients of the additional decay

term depends on the emission wavelength, within the wave-

length range where the monomer emission is negligible

(lem 4 480 nm), indicating the presence of more than one

emitting species in the excimer emission region.

The simplest mechanism accounting for the presence of two

excimers is shown in Scheme 3, where MA and MB have the

same meaning as in Scheme 2 and E1 and E2 represent the

asymmetric and symmetric sandwich-like excimers.

The differential equations ruling the time-dependent

concentration of the four excited species are, according to

Scheme 3, given by:

d

dt

M�A

M�B

E�1E�2

2664

3775 ¼

�k0 0 0 00 �kX kd1 kd20 ka1 �kY 00 ka2 0 �kZ

2664

3775�

M�A

M�B

E�1E�2

2664

3775 ð8Þ

where M*A, M

*B, E

*1 and E*

2 are the concentrations of MA, MB,

E1 and E2 in the excited state and

kX ¼ k0 þ ka1 þ ka2 ð9Þ

kY ¼ kE1þ kd1 ð10Þ

kZ ¼ kE2þ kd2 ð11Þ

After matrix factorization, one arrives to a 3 � 3 matrix of rate

constants [ki,j] which could then be evaluated from eqn (12).53

ki;j ¼�kX kd1 kd2ka1 �kY 0ka2 0 �kZ

24

35 ¼ ½Aij � � ½�li;j � � ½Ai;j ��1 ð12Þ

The data that are provided by the fluorescence decays are not

sufficient for solving eqn (11). Although there are only six

unknown rate constants (k0 is equal to the reciprocal longest

decay time t0), the preexponential coefficients matrix [Aij] must

be evaluated from the experimental preexponential coefficients

and five additional unknowns: the three fractions of ground-

state species (a, b and g), plus the two spectral overlapping

factors at the two excimer emission wavelengths. A study

aiming to solve eqn (12) and thus to obtain all the rate

constant values and fractions of ground-state species (a, band g) in Scheme 3 (for all the four polymers) is currently

under progress using a procedure and methodology analogous

to the one used in ref. 53.

5. Conclusions

The photophysical behavior of the four poly(acrylic acid)

polymers with long and short chain-size, randomly labeled

with pyrene chromophores, depend on factors known to

influence the photophysics of the polymers: the fraction of

isolated pyrene monomers (b) and the degree of pre-associated

pyrene dimers (a). Additionally, we have found that the size of

the polymer backbone greatly influences the photophysics of

the polymers. This was particularly true for the short-sized

chain polymers, where a number of peculiar effects were

observed. Moreover, these effects were found to be dependent

on the degree of labeling and on the hydrogen ion concentra-

tion of the medium.

The associative behaviour appears to be predominant with

the small-sized PAAMePy(2) polymers at intermediate pH

values, in spite of the electrostatic repulsion resulting from

partial ionization of the carboxylic groups, whereas with the

long-sized PAAMePy(450) polymers there is predominance of

the associative behaviour at low pH and repulsive electrostatic

repulsions predominance at high pH. Apparently, the small

size of the PAAMePy(2) polymer chains allows the adoption

at intermediate pH values of micellar-like conformations that

promote the occurrence of GSD. At higher pH values, theScheme 3


higher electrostatic repulsion expands the polymer chain, as

happens with the long PAAMePy(450) polymers.

From the time-resolved data obtained in dioxane and

methanol (good solvents for the pyrene probe), a kinetic

treatment, previously described, allowed all the rate constants

for excimer formation and deactivation in these polymers to be

obtained. In water, the fluorescence decays have showed the

need of an additional exponential. This was tentatively as-

signed to an additional (less stable and longer lived) excimer

when compared with the situation found in dioxane (or

methanol), where only a single excimer (more stable) was

found. The kinetic proof for this assignment requires the

coupling of time-resolved and steady-state data in order to

unequivocally solve eqn (11) and test the outcome (rate

constants and fractions of ground-state monomers and exci-

mers) against the independent absorption and fluorescence

data (PA, PE � PM and IE/IM) and the corresponding results

obtained in dioxane and methanol.

Appendix

Under the transient approach (instantaneous formation of the

excited species), the differential equations ruling the time

dependence concentration of the three excited species are,

according to Scheme 2, given by2,53:

d

dt

M�B

E�

M�A

24

35 ¼

�kX kd 0ka �kg 00 0 �k0

24

35 �

M�B

E�

M�A

24

35 ðA:1Þ

where M*A, M

*B and E* are the concentrations of MA, MB and

E in the excited state and

kX ¼ ka þ k0 ðA:2Þ

kY ¼ kd þ kE ðA:3Þ

The integration of eqn (A.1) leads to

M�B

E�

M�A

24

35 ¼

a11 a12 0a21 a22 00 0 �a0

24

35 � e�l1t

e�l2t

e�l0t

24

35 ðA:4Þ

where the eigenvalues li are the reciprocal decay times of the

shorter (l2 = 1/t2), the longer (l1 = 1/t1) and of the isolated

species (l0 = 1/t0) and are related to the rate constants in

Scheme 2 by the characteristic equation:54

l� kX kd 0ka l� kY 00 0 l� k0

�� ¼ 0 ðA:5Þ

the solutions of which are given by eqn (A.6) = (eqn 6) and

eqn (A.7).

2l2;1 ¼ ðkX þ kYÞ � ½ðkX � kYÞ þ 4kakd�1=2 ðA:6Þ

l0 ¼1

t0¼ k0 ðA:7Þ

The sum and product of the lambda values (l1 and l2)resulting from eqn (A.6) are, respectively, given by

kX þ kY ¼ l1 þ l2 ðA:8Þ

and

l1 � l2 ¼ kXkY � kakd ðA:9Þ

The preexponential factors aij are the linear combinations of the

eigenvector basis set that obey the following initial conditions:

X3j¼1

aij ¼ 1ði ¼ 1Þ ðA:10Þ

X2j¼1

aij ¼ 1� a� bþ abði ¼ 1Þ ðA:11Þ

X2j¼1

aij ¼ a 1� bð Þði ¼ 2Þ ðA:12Þ

Simple manipulation of eqn (A.1) and (A.4), together with eqn

(A.8) and (A.9) and considering the initial conditions given by

eqn (A.10)–(A.12), leads to the following relations for the

preexponential amplitudes (aij):

a10 ¼ b

a11 ¼ ð1� bÞ ð1� aÞðX � l2Þ � akdl1 � l2

ðA:13Þ

a12 ¼ ð1� bÞ ð1� aÞðl1 � XÞ þ akdl1 � l2

ðA:14Þ

a21 ¼ �ð1� bÞ ð1� aÞka � aðX � l1Þl1 � l2 ðA:15Þ

a22 ¼ ð1� bÞ ð1� aÞka þ aðX � l2Þl1 � l2

ðA:16Þ

Since b= a10 and kM = l0, we are left with four unknowns (ka,

kd, kE and a), to be evaluated from l2, l1, A and B (eqn (A.17)

and (A.18)).

A ¼ a12

a11¼ X � l1 � zkd

l2 � X þ zkdðA:17Þ

B ¼ a22

a21¼ � ka � zðl2 � XÞ

ka þ zðX � l1ÞðA:18Þ

where:

z ¼ a1� a

ðA:19Þ

Rearrangement of eqn (A.17) leads to:

kX ¼Al2 þ l1Aþ 1

þ zkd ðA:18aÞ

and from eqn (A.8):

kY ¼Al1 þ l2Aþ 1

� zkd ðA:19aÞ

Further manipulation yields:

ka ¼Al2 þ l1Aþ 1

þ zkd � k0 ðA:20Þ


and:

kd ¼Al1 þ l2Aþ 1

� kE

� �1

1þ zðA:21Þ

and from eqn (A.18):

ka ¼Bl1 þ l2Þ1þ B

� k0

� �z

1þ zðA:22Þ

From eqn (A.9) and after simple algebraic manipulations, one

obtains the following relation:

kakE

k0þ kd þ kE ¼

l1l2k0

ðA:23Þ

If we now define:

RA ¼Al2 þ l1Aþ 1

� k0 ðA:24Þ

R0A ¼

Al1 þ l2Aþ 1

ðA:25Þ

RB ¼Al1 þ l2Aþ 1

� k0 ðA:26Þ

and after rearrangement, one finally obtains:

ka ¼l1l2k0� R

0A � k0

kEk0� R

0A�kEþk0R0A

ðA:27Þ

kd ¼ðR0A � kE þ k0ÞðR

0B � kaÞ

R0B

ðA:28Þ

a ¼ ka � RA

ka � RA � kdðA:29Þ

Acknowledgements

Financial support from the Portuguese Science Foundation

(POCI/QUI/55672/2004) and FEDER is acknowledged. TC ac-

knowledges the FCT for a Ph.D. grant (SFRH/BD/17852/2004).

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