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2414

Macromolecules

1994,27, 2414-2425

Micellization of Poly(ethy1ene oxide)-Poly(propy1ene

oxide)-Poly(ethy1ene oxide) Triblock Copolymers in Aqueous

Solutions: Thermodynamics

of

Copolymer Association

Pasc hal is Alexandrid is? Josef F.Holzwar th f and

T.

lan Hatton'J

Department

of

Chemical Engineering, Massachusetts Institute

of

Technology,

77

Massachusetts Avenue, Cambridge, Massachusetts

02139,

and Fritz-Haber-Institut der

Max-Planck-Gesellschaft,

Faradayweg 4-6, D- 141

95

Berlin-Dahlem, Germany

Received September

27, 1993;

Revised Manuscript Received November

29,1993.

ABSTRACT The critical micellization temperature (cmt) and critical micellization concentration (crnc)

values

of

12 Pluronic poly(ethy1ene oxide)-poly(propy1ene oxide)-poly(ethy1ene oxide) (PED-PPO-PEO)

block copolymers, covering a wide range of molecular weights

(2900-14

600 and PPO/PEO ratios (0.19-1.79),

were determined employing a dye solubilization method. A closed association model was found

to

describe

adequately the copolymer micellization process for the majority of the Pluronics and used to obtain the

standard free energies (AGO), enthalpies

(AH o) ,

nd entropies(AS )f micellization. I t was determined that

the micellization process isentropy-driven and has an endothermic micellization enthalpy. The hydrophobic

part of the Pluronics, PPO, was responsible for the micellization, apparently due to diminishing hydrogen

bonding between water and PPO with increasing temperature. The cmc dependence on temperature and

size of headgroup (PEO) of Pluronics follows a similar trend with lower molecular weight CjEj nonionic

surfactants, the effect

of

temperature being more pronounced with the Pluronics. The PEO -PPO-PEO

block copolymers were compared

to

PPO-PEO-PPO block and PEO-PPO random copolymers, in an attem pt

to

probe the effect

of

molecular architecture in the formation

of

micelles.

No

micelles were observed in

aqueous PPO-PEO-PPO block copolymer solutions with increasing temperature, up

to

the cloud point.

In t roduc t ion

Water-soluble triblock copolymers of poly(ethy1ene

oxide) (PEO) and poly(propy1ene oxide) (PPO), often

deno ted PEO-PPO-PEO or (EO),1(PO),(E0),2, are

commercially available nonionic macromolecular surface

active agents. Variatio n of the molecular characteristics

(P PO /P EO ratio, molecular weight) of th e copolymer

during th e synthesis allows th e production of molecules

with optimum properties th at m eet th e specific require-

ments in different areas.

As

a result, PEO-PPO-PEO

block copolymers are an important class of surfactants

and find widespread in dust rial applications in detergency,

dispersion stabilization , foaming, emulsification, lubrica-

tion, etc.,lI2 along with more specialized applications in ,

e.g., pharmaceutics (drug solubilization and controlled

re lea~e3-~) ,ioprocessing (protecting microorganisms

against mechanical damage'), an d sepa ratio ns (solubili-

zation of organics in aqueous solutions8J'). Comm ercial

names for these surfactants are Poloxamers

(ICI)

nd

Pluronics (BASF).

Tem perature-de pendent micellizationand gel formation

are two of the most characteristic properties of aqueous

PEO-PPO-PEO block copolymer solutions. Owing to th e

marked change in water solubility of the center poly-

(propyleneoxide) block

at

elevated temperatures , the block

copolymers form various aggregates, depending on the

degree of polymerization

( m l , m 2 ,

and n).

A

num ber of

triblock copolymers have been shown to aggregate in th e

form of mice l le~ , l0- ~~ith a core presumably dominated

by PP O and a corona domin ated by hy dr ate dP E0 blocks.16

I t is also known that, a t temperatures close to ambien t,

high-concentration copolymer solutions exhibit a dr ama tic

change in viscosity, revealing a "thermoreversible gela-

tion".l1J3J7J8 Several mechanisms have been proposed

* Author to whom all

correspondence

should be addressed.

+ Massachusetts Institute of Technology.

Fritz-Haber-Institut

der Max-Planck-Gesellschaft.

Abstract publishedinAdvance ACS Abstracts, February 1,1994.

0024-9297/94/2227-2414 04.50/0

as driving forces for this therm al gelation: Rassing and

Attwoodlg related th e gel transition to intrinsic changes

in the m icellar properties and Vadnere e t al.20 discussed

th e gelation in terms of entropic changes involving o cally

ordered water molecules

close

to the hydrophobic units,

whereas Wanka et al. and Wang

and

Johnston'* specu-

lated a t t he possibility of

an

ordered three-dimensional

structured sta te or network. Recently, neutron-scattering

studies showed tha t th e observed change in viscosity is

due to a "hard-sphere crystallization" as the micelle

concentra tion appro aches the c ritical volume fraction of

0.53.15 T he critical micellization concentration (cmc), he

fraction of polymer molecules in micellar form, and the

size and the aggregation number of the micelles, as well

as the tempe rature dependence of these parameters, are

of grea t inter est for aqueous PEO-PPO-PEO block

copolymer micellar solutions. Star ting with the average

aggregation numb er, it ha s been shown by refs

10

and

15,

using stat ic light scatt ering an d fluorescence quenching,

th at th is increases with tem perature; t he absolute values,

nevertheless, vary between different systems and even

between different copolymer batches. Furt herm ore, the

size of the micelles generally increases with increasing

temperature, the extent of the increase varying between

different copolymers; indeed for some sy stems th e micelle

hydrodynamic size remain s constan t while the aggregation

numbe r increases with temperature, probably a result of

dehy drati on of th e PE O headgroups.1°

Perh aps th e parameter of greatest fundamental value

is the critical micellization concentration, th e copolymer

concentration at which micelles start forming.21 As we

show below, an d ashas previously been observed, th e cmc

of aqueous PEO-PPO-PEO block copolymer solutions

decreases with increasing temperature.lOJ2J3 In compari-

son

with conventional, low molecular weight amp hiphiles,

there is some inhere nt complexity in th e micellization of

block copolymers, which depe nds strongly on their com-

position. Th e composition polydispersity could be ap-

preciable even for a copolymer with a narrow d istrib ution

of molecular w eight, and accordingly, no sh arp cm c or cmt

1994 American Chemical Society



Macromolecules,

Vol.

27,No. , 994

(critical micellization em pera ture , th e copolymer solution

tempe rature a t which micelles form) has been observed

for block copolymers. In practice, a certai n cmc range

with some notable uncertainty could be detected. A large

difference is often noted between t he cmc values deter-

mined by different method s because their sensitivity to

the quantity of molecularly dispersed copolymers (un-

imers) present may vary.l0 For common detergents, a

considerable am oun t of cmc da ta have been collected an d

summarized by Mukerjee an d Mysels,22whereas for block

copolymers

so

far only scarce cmc da ta (e.g., refs 23 and

24)

re available in the literature. Furtherm ore, the values

reported in t he litera ture differ substantially; th e lack of

sufficient temperature control, in conjunction with batch -

to-batch variations, may be responsible for the observed

variations.26

Th e need for a systematic stud y of th e cmc and cmt for

the PEO-PPO-PEO block copolymers becomes appa rent

from t he discussion in th e preceding paragrap h, both from

an ap plications point of view (mapping th e micellization/

solubilization regime for a given copolymer) and from

theoretical considerations (determining the origin of

micellization and the effects of hydrophilic PEO and

hydrophobic PPO ). Furthermore, the thermodynamic

param eters of copolymer micellization can be derived from

cmc data at different temperatures, given a copolymer

association m e ~ h a n i s m , ~ ~ * ~ ~roviding furt her insight on

the energetics of the micellization.

In a recen t study th at explored th e potential for using

PEO-PPO-PEO block copolymer micelles in th e treat -

ment of water contaminated with polycyclic aromatic

hydrocarbons, it was shown th at solubilization efficiency

depended strongly on t he molecular struc ture, composi-

tion, and molecular weight of th e copolymer used.g S ome

speculation was made as to the reasons for thi s behavior,

but verification of thes e arguments , which requires either

struc tural experimental characterization or detailed the-

oretical analysis of the association and solubilization

behavior of these polymer system s, is still lacking. In a n

attempt to address this issue, we undertook a detailed

theoretical (using a self-consistent mean-field theory28)

and experimental investigation on th e micellization and

solubilization in the aqueous PEO-PPO-PEO block

copolymer solutions. We report here experimental results

on block copolymer micelle formation and micellization

thermodynamics.

Th e solubilization of a dye (1,6-diphenyl-1,3,5-hexatriene,

DP H) in copolymer solutions, detected by it s fluorescence

and UV-visible spe ctra, was employed in our investigation

for the determ ination of the solution cmt and cmc values.

Spectroscopic techniques , based eith er on optical absorp-

tion or on emission of light from some "probe" molecule,

are now well established for investigating a wide range of

physical properties of micellar

solution^.^^^^

The fact that

micelles can solubilize elatively large amo unts of sparingly

water-soluble compo unds has been used to determine the

onset of micelle formation,22J1 by m easuring t he concen-

tratio n of a chosen sparing ly soluble substanc e, possessing

a convenient UV-visible absorb ing chromophore, in th e

presence of increasing am ount s of surf acta nt. Below th e

cmc, the concentration of t he solubilizate in solution is

the same as in aqueous solution in the absence of

surfactant. Above thecmc, the total am ount of th e additive

in solution increases sharply as th e tota l micelle concen-

tration increases. Chattop adhyay and London used

fluorescence from DP H to determine the cmc

of

various

surfactants,32 obtaining values t ha t were within

10%

of

th e ones determ ined by other methods. Surface tension

Micellization of PEO-PPO-PEO Triblock Copolymers

2415

Table

1.

Properties

of

the P luronic Copolymers Used in

This

St udy

PPO

polymer

MW

segmwt

POunita

EOunita lotno.

L64

P65

F68

P84

P85

F88

P103

P104

P105

F108

P123

F127

25R4

2900

3 400

8

400

4 200

4 600

11

400

4 950

5900

6 500

14 600

5 750

12 600

3 600

1740 30

2 X 13

1700 29 2 x

18

1680 29 2 X 76

2520 43

2

x 19

2300 40 2

X

26

2280 39 2 X 103

3465 60

2

X

17

3540 61 2

X

27

3250 56

2

x 37

2920 50 2 X 132

4025 69

2

x 19

3780 65

2 x 1 0 0

2500

2

X 2 1

25

WPWN-505A

WPAN-605B

WPON-611B

WPTN-561B

WPAN-628B

WPDN-616B

WPHM-539B

WPAN-603B

WPDI-S22A

WPDN-564B

WPYM-569B

WPON-593B

WPMN-516B

results showed tha t probe m olecules, a t th e levels used

to

determ ine th e cmc by fluorescence

(<10-8

mol mq), did

not noticeably affect th e surfac tant properties, viz., surface

tension, nor the surface tension derived cmc value.33

Edwards et al. eported tha t, in general, th e cmc values

they obta ined from the surface tension data for solutions

of deionized water a nd nonionic su rfac tants showed fairly

close agreement to the cmc values inferred from poly-

arom atic hydrocarbon solubilization data. Similar values

for th e cmc of the PEO-PPO -PEO block copolymers

measured by surface tension and dye solubilization

meth ods have been reported by Schmolka and Raymond.3s

T he following are an example: L64 mc value

at

25

C

s

0.0016 g/dL or 5.6

pM

(measured with dye absorption)

and 4.2pM (measured with surface tension); cmc value a t

40 OC is 0.0033 g/dL or 11.5 pM (measured with dye

absorption) and 13.9pM measured with surfacetension).3s

However, different values for th e cmc of th e PEO-PPO-

PE O block copolymers measured by surface tension and

dye (benzopurpurine) solubilization methods have been

reported byAnderson.36 Itbecomes app aren t though, from

a closer inspection of his da ta, t ha t Anderson misinter-

pret ed th e dye solubilization vs copolymer concentr ation

curve. Such a curve is usually sigmoidal, with th e

first

inflection indicating the m icelle formation and th e second

inflection th e complete solubilization of th e dye. Anderson

based his conclusions on the second inflection; the cmc

value obtained from the first inflection of the dye

solubilization vs copolymer (F68) concentration curve is

actually very close to he cm c value derived from his surface

tension measurements (-2 X lO-S ).

We measured t he cm t and cmc values of 12 Pluronic

PEO-PPO -PEO block copolymers, covering a wide range

of molecular weights

(2900-14 600)

nd PPO /PEO ratios

(0.19-1.79).

A closed association model was found to

describe adequately the copolymer micellization process

for the ma jority of the P luronics. Using such a model, we

obtained the standard free energies (AGO), enthalpies

(A ), nd entropies (ASo)of micellization

and

correlated

them to th e copolymer molecular weight an d composition.

We also compared the PEO-PPO -PEO block copolymers

to PPO-PEO-PPO block and PEO-PPO random copoly-

mers, in an attempt to probe the effect of molecular

a r c h i te c t u r e o n t h e f o r m a t i o n

of

micelles.

Materials and Methods

Cop olym ers. Th e Pluronic PEO-PPO-PEO block copoly-

mers were obtained from BASF Corp., Parsippauy,

NJ,

and used

as

eceived. The se polymers are available in a range of molecu lar

weights and PPO/PEO ratios.1.2*3' Table 1 ists the physical

properties of the polymers studied (data supplied by the

ma nufac turer). T o facilitate ana lysis of the results, a brief

description of the sy stem of nomenclature for the BASF Pluronica



2416

Alexandridis e t

al.

Macromolecules,

Vol.

27, No. 9, 994

follows. Th e notation for the Pluronic triblock copolymersstarts

with the letters L (for liquid), P (for paste), or F (for flakes). The

first two numbers are indicative of the molecular weight of th e

PP O block, and the la st numbe r signifies the w eight fraction of

the PE O block. For example, P103 and P104 have the same

molecular weight of P PO (on the order of 3000) bu t P103 has 30

w t

%

andP10440wt % PEO. TherandomPEO/PPOcopolymer,

UCON 50HB-3520 (50% PEO, 3520 molecular weight), was

purchased from Union Carbide Chem icalsand Plastics Company

Inc., South Charleston, WV; the PPO-PEO-PPO Pluronic-R

block copolym er, 25R4

(40

PEO ), was obtained from BASF

Corp.

Spec t roscop i c Probe .

1,6-Diphenyl-1,3,5-hexatriene

DPH)

was obtained from Molec ular Probe s Inc., Eugene, OR, and used

as

eceived. Th e DPH dye used for the determination of the cm t

and crnc in the pre sent s tudy is a well-known probe of mem brane

interiors. Th e primary application of DPH has been to est imate

mem brane "fluidity", based on fluorescence depolarization

measurements.58 Solvent and temperature effects on the fluo-

rescence of DPH have been studied by Cehelnic et

al.39

T h e

fluorescence of DPH is minimal in water and is substantially

enhance d by association with lipids and other surfactants. Thi s

property has been exploited to determ ine the cmc's of anionic,

uncharged, zwitterionic,and cationic detergents.32 DPH has

also

been use d in probing micelles of tetradecyltrialkylammonium

bromidesa and

didodecyldimethylammonium

romide (DDAB)/

alkane/water micro emulsion^.^^

Sa m ple Prep ara tion . Aqueous copolymer solutions were

prepared by dissolving the polym er in Milli-Q water (18MQ cm)

and diluting

to

the desired concen tration (rang ing from 0.001 %

to

20% w/v). Th e experimenta on the Pluronic solutions were

performed within a few days of th e solution prepa ration. A dye

solubilization technique32was employed to determine the onset

of copolymer micellization (cmc, cmt). Samp le preparation was

similar to th at of Cha ttopadhy ay a nd London:s2 a stock solution

of 0.4 mM DPH in methanol was prepared; 25 pL (measured

with a Ham ilton microsyringe) of the DP H/m ethano l solution

was added to 2.5 mL of copolymer solution,

so

that the final

copolymer solution contained 1% v/v methano l and 0.004 mM

DPH. Th e solutions were left in the dark to equilibrate for at

least 3 h (and no more than 24 h) before the spectroscopic

measurement. A single DPH concentration was used

(0.004

mM),

as

no e ffect of

DPH

concentration on the cmc was observed (for

DP H conce ntration range 0.0025-0.025 mM) by Chatto padhy ay

and Lond0n.3~

Effectof

Methanol. Th e aqueous block copolymer solutions

used for the determination of the crnc and cmt contained

approximately 1% methano l; methano l was used todissolve DP H,

the latter b eing sparingly soluble in water. Methan ol was also

used in the preparation of a solution of high-concentration

polycyclic aromatic hydrocarbons (PAH s), employe d in PAH

solubilization experimen ts from aqueo us solutions by Edwa rds

et a1.a They found tha t methanol was a preferred solvent,

as

their tests showed no effect on surfactan t solubilization; most

highe r alcohols could not

be

utilized since they a ffected the cmc

values significantly.42 Measu red ap pare nt PA H solubilities at

zero surfacta nt concentration in the presence of 1

%

by volume

methanol appear

to

be enhanced by - 0-30% relative toreported

solubilities in pur e water. Th e presence of methanol did n ot

shift the cm c or the slope of the solubilization curve for a solution

of

pyrene andoetylphenol PEO surfa ctant.s Bedo

et al.

studied

the e ffect of m ethanol, etha nol, and isopropyl alcohol on the

micellization of ethoxylated nonylphenols, and the ir datas ugge st

t ha t 1%methanol increased the cmc by approximately

40 ;

isopropyl alcohol ha d a far m ore pronounced effect on the cmc.

Th e sample preparation for the cmc determination of Chatto-

padhyay and London32 involved dissolving PDH in THF and

adding

1p L

o

2

mL of surfactant solution. The se author s found

t ha t up t o

1-2 %

(v/v) T H F had l i t tle effect on the cmc for several

detergents.

Sp ec tros cop y. Emission fluorescence spec tra of the copoly-

mer/DPH /water samples were obtained with a Shimadzu RF-

5000 recording

spectrofluorophotometer,

using an excitation

waveleng th of 350 nm an d emission wave length range 350-650

nm. Th e emission intensity peak used to observe the DPH

solubilization in th e copolymer micelles was a t 457 nm. UV-vis

0 3

0 2

0 1

0

320 330

340

350

360

370

380

390

400

Wavelength (nm)

0.3

0 2

0.1

10 15 20

25 30 35

40 45 50

Temperature

(OC)

F i g u r e

1.

Effect of temperatu re o n (a, top) UV-vis absorption

spectra and (b, bottom) the absorption intensity at 356 nm for

D PH in a 0.5% w/v solution of Pluronic P104. Th e estimation

of the critical micellization tempera ture from th e da ta is indicated

in b.

absorption spectra of the copolymer/DPH/water samples were

recorded in the 300-500-nm range using a Perkin-Elmer Lam bda

3B UV/vis spectrophotom eter, controlled by the Perkin-Elmer

Computerized Spectroscopy Software (PECSS). Th e main

absorption intens ity peak, charac teristic of DP H, was at 356 nm.

For both fluorescence and absorp tion spectroscopy experimen ts,

the samples were placed in Teflon-stoppered quartz cuvettes.

Tem peratur e control within 0.05 "C was achieved using a Neslab

RTE-110 refrigerated bath/circulator. Th e temperature range

employed was 15-55 OC,

as

measured in the thermostated

photometer referenc e cell. At least 1 was allowed for the sa mple

temp erature e quilibration. After establishing th at emission

fluorescence spectroscopy gave the same results

as

visible

absorption spectroscop y, we used the latte r

to

obtain the data

reported here (the absorption spec trum of a molecule is, in

principle, h e same

as

he fluorescence excitationspectrum,which,

in tur n, is the m irror image of the fluoresce nce emission

spectrum4).

Results

and

Discussion

UV-vis

spectra

of a q u e o u s

Pluronic solutions

with

c o n c e n t r a t i o n s f r o m 0.001

o

20% w/ v con t a i n i ng DPH

w e r e

taken at 5 "C temperature

intervals over

the

r a n g e

15-55 "C.

A t low concen t r a t i ons

and/or low

t e m p e r a t u r e s ,

the Pluronics

d i d n o t

associate

n

aqueous

solut ion,

DPH

was

no t so l ub i l i zed in

a

h y d r o p h o b i c e n v i r o n m e n t ,

and,

as

a r esu l t ,

the

f l uo rescence and UV-vis i n t ens i t i es due to

DPH

w e r e v e r y

low.

A t h i g h e r c o n c e n t r a t i o n s

and/or

t e m p e r a t u r e s , t h e Pluronics fo rm ed m i ce ll es , and

DPH

w a s

solubilized in

t h e hydrophob i c m i ce ll e i n t e r i o r , g iv i ng

a c h a r a c t e r i s ti c s p e c t r u m . Figure la shows h e U V - v is

a b s o r p t i o n s p e c t r a o f

a

t y p i c a l D P H / P l u r o n i c / w a t e r

so l u t i on (P104 ,0 .5

5

w/ v) at d i f f e r e n t t e m p e r a t u r e s

and

Figure l b he absorption n t ens i t y at356nm of

the

previous

s a m p l e ,

asa

f u n c t i o n

of

t e m p e r a t u r e . T h e c m t v a lu e s f o r



Macromolecules,

Vol.

27,

No

, 1994


2417

pyrene and naphth alene solubilization in L64, P104, and

F108.47 Th e agreement between our cm t data (from dye

solubilization experiments) and cmt data from light

scattering intensity

is

not asgood for F68;Zhou a nd ChulO

obtained cmt values of 42.3,

39.0,

and 36.3 OC for 1.25,

2.50, and 5.17 % polymer concentrations, respectively,

compared to our 46 and 40 C for 2.5 and 5.0%,

respectively. F68 is fairly hydrophilic (80%PEO) and

may form premicellar aggregates discernible with light

scattering but with no w ell-defined hydrophobic core to

allow for DP H solubilization.

Critical Micellization Concentration Data. Figure

3 shows the dependence of the intensities at 356 nm

(spectral maximum due to DPH) on Pluronic P104

concentration, at various temperatures.

The critical

micellization co ncentration

was

stimated again from the

first inflection of the intensity vs log concentration

sigmoidal curve; he uncertainty in th e cmc values reported

is less than *15% (the uncertainties in the cmc values

arose similarly to those discussed for cmt). Table 3 lists

the cmc values for various Pluronics as a function of

solution temperature.

Given the num ber of publications dealing with aqueous

solution s of Pluro nics, there are surprising ly few reliable

cmc data for Pluronics. Th e cmc values we obtained are

generally

1

order of magnitude higher than the values

reported by S chmolka and Raym ond36 or F68, P84, P85,

F88, P104, and F108. Prasad et al.@measured the surface

tension of aqueou s Pluronic solutions (L64, F68, P85, and

F88) and detected in several systems two points of

inflection in the surfac e ension vs log conc entratio n plots.

The y interpreted this as due to th e formatio n of so-called

"monomolecular" aggregates in dilu te solution and multi-

molecular aggregates in more concentrated solutions.

Wanka et al.ll found that the surface tension of P104,

P123, and F127 decreased linearly with th e logarithm of

the copolymer concentration according to the Gibbs

isotherm of adsorptio n over several conc entratio n decades.

At

a characteristic concentration, there

was

a break in the

curve; the surface tension kept decreasing with further

increase in con centration, but w ith a smaller slope, until

a second concentration was reached above which the

surface ension remained constant. This transition region

extended approximately1 once ntration decade. Accord-

ing to Wan ka et al., the two breaks in the curves could be

interpreted as being due to the existence of two critical

concentrations; taking other types of mea surements into

account, however, it seemed more conceivable that the

transition region could be related tothe fact th at the block

copolymerswere not well-defined samples but had a broad

molecular weight distribution.ll In addition, any trace

impurities (originating from the manufacturing process)

in th e polymer solutions would have a significant effect

on surface tension measurements. Interestingly enough,

the concentrations at the second inflection point from ref

11(0.3% for F127 and 0.01% for P104, both a t 25 C) and

ref 48 are comparableto the cmc values found in ou r study.

Two breaks can also be observed in a surface tension data

set for P94 pu blished by B ahad ur a nd Pandya,49 who

derived the cmc from the first break. In detailed surface

tension me asurements with th e same copolymers used for

the d ye solubilizationexperiments

(to

avoid inconsistency

due to different polymer batches), we have also observed

the two inflection points in th e surface tension curves.m

Th e ambiguities in the different ways

of

measuring the

cmc in Pluronic solutionspoint to the need todefine clearly

the applications for which the da ta are intended. Th e dye

solubilization method for determining th e cmc is ideal for

E

p

v

C

-

0.35

I

I I I

I ,

I

1

0.3

0.25

0.2

0.15

0.1

0.05

20%

0.1 -

15

10 0.05 -

I

~

10 15

20 25

30 35 40 45 50

Temperature (OC)

Figure 2. Temperature effects on th e absorption intensity of

DPH at

356

nm in aqueous solutions of Pluronic P104

of various

concentrations. The critical micellization temperatures can be

estimated from the first break in th e curves.

Pluronics of various concentrations were obtained from

the first inflection of the absorption inte nsity a t 356 nm

vs temperature plot.

Critical Micellization Temperature Data. Figure 2

shows the depend ence of th e intensities at 356 nm (spectral

maximum due to DPH) on temperature, for various

concentrations of a typical Pluronic (P104) aqueous

solution. Th e critical micellization temp erature values

were obtained from th e first inflection of the intensity vs

temperature sigmoidal curve (or alternatively from the

first appearance of a well-defined peak in the sample

spectrum) tha t indicated the formation of a hydrophobic

domain. This domain appea rs to be the result of aggre-

gation of many Plu ronic molecules to form a micelle, rather

tha n the coiling of a single molecule. Dye solubiliza tion

experimentswith random PE O/ PP O copolymers of similar

PE Ol PP O composition and block PPO-PEO-PPO co-

polymers of comparable PEO and PPO segment sizes

showed no increase in the absorption intensity due to the

DPH, indicating that the existence of hydrophobic (PPO )

patches in a single molecule are not sufficient for solu-

bilizatio n of DPH. Th e second inflectio n of the intensity

vs temperature sigmoidal curve was indicative of the

complete solubilization of D PH in the block copolymer

micelles. Th e use of DP H solubilization o determine cmt

proved to be a reliable and reproducible method; the

uncertainty in the cmt values reported here is less than

*l

C the uncertainties in the cmt values arose mainly

from the use of lines tangen t to part s of the intensity vs

temperature curve for deriving the temperature corre-

sponding

to

the cm t). There was some difficulty involved

in the cmt determination only for L64,

as

the samples

becam e turbi d in th e vicin ity of m icelle formation.10

Th e cmt values obtained for various Pluronics are listed

in Table

2

as a function of copolymer concentration,

expressed n both percent w/vand m M concentrationunits.

To the best of our knowledge, this is the first compre-

hensive compilation of cmt data for aqueous Pluronic

solutions and th e only one available for F123, P103, P104,

P105,

F108,

P84, nd

P65;

uch a data set should

prove

to be useful for the num erous applications of Pluronics

th at depend on their micelle forming abilities. Th e few

cmt values available in the literature agree well with our

data: 15 C cmt for 10%F127 solution reporte d in ref 45,

compared to our 16

"C;

25

C

cmt for 5% P85 solution

reported in ref 1 3 compa red to our 25 C; 5 C mt for

6 % L64 solution reported in ref 46 compared

to

our 26

OC.

Furthermore, the cmt values obtained from the DPH

solubilization method compa re very well to th e onset

of



2418 Alexandridis et al. Macromolecules, Vol. 27, No. 9,

1994

Table 2. Critical Micellization Temperatures for Pluronic Copolymer Aqueous Solutions

as

a Function of Copolymer

Concentration

L64 P65 F68 P84 P85 F88

concn,%w/v mM CMT mM CMT mM CMT mM CMT mM CMT mM CMT

-

-

-

0.024

46.5 0.022 46.5

-

0.119

39.5 0.109 40 0.044 52.5

- 0.238 37 0.217

37.5 0.088 48.5

0.01

0.025 0.086 44.5

0.147 49

.05 0.172 42

0.1 0.345 39.5 0.294 46

0.862 36.5 0.735 42

-

0.595 33.5 0.543 33.7 0.219 45

0.25

0.595 52.5 1.19 31 1.09 32 0.439 41

.5 1.72 34 1.47 39

1.0

3.45 31.5 2.94 36 1.19 50 2.38 28.5 2.17 29.5 0.877 38

2.5 8.62 28.5 7.35 31.5 2.98 46 5.95 25.5 5.43 27 2.19 34

5.0 17.2 26.5 14.7 28.5 5.95 40 11.9 23 10.9 25 4.39 30.5

23.8 19 8.77 26

-

-

13.2 21.5

10 34.5 23.5 29.4 25.5 11.9 33

15 17.9 27

-

- 0.059 42.5 0.054 43

-

-

-

P103 P104 P105 FlO8 P123 F127

concn,%w/v

mM CMT mM CMT mM CMT mM CMT mM CMT mM CMT

~~

0.01 0.02 29.5 0.017 33.5 0.015

0.025

0.05

0.1

0.25

0.5

1.0

2.5

5.0

10

15

0.05 27.5 0.042

0.101

26 0.085

0.202 24.5 0.169

0.505 22.5 0.424

1.01

21 0.847

2.02 19.5 1.69

4.24

8.47

-

-

-

-

31 0.038

29.5 0.077

27.5 0.154

25.5 0.385

23.5 0.769

21.5 1.54

19.5 3.85

18

-

-

-3 .5 -2.5 - 1 5 -0.5 0.5 1.5

log

c

“i /v

Figure 3. Effect of concentration, with temperature as

param-

eter, on the absorption intensity of DPH at 356 nm in aqueous

solutions

of

Pluronic P104. The critical micellization concen-

trations can be estimated from the first break in the curves.

determining the range of solubilization enhancement of

otherwise sparingly soluble organics in the presence of

Pluronic copolymers, provided t he molecules to be solu-

bilized are of comparable hydrophobicity an d size to DP H.

In fact, the p artition coefficient for DP H in th e copolymer

micelles can be estim ated from th e same set of d ata used

to obtain th e cmc values. Th e molar solubilization ratio

(MSR), defined as the number of moles of organic

compound solubilized per mole of surfactant added to

solution, is a measure of th e effectiveness of a particular

surfactant in solubilizing a given solubilizate.26 The

increase in solubilizate concentration per u nit increase in

micellar surfactant concentration is equivalent to the MSR.

In th e presence of excess hydropho bic organic compo und,

the MSR may be obtained from th e slope of th e curve th at

results when the solubilizate concentration is plotted

against surfactant concentration.% T he effect of copoly-

mer PPO/PEO composition, molecular weight, solution

concentration and temperature on th e molar solubilization

ratio of D PH in aque ous block copolymer solutions will

be presented in detail el~ewhere.~O

-

0.017 26

32

30 0.017 40.5 0.043 24 0.02 35.5

28.5 0.034 38 0.087 22.5 0.04 33

27 0.068 36 0.174 21 0.079 31

25 0.171 33.5 0.435 19 0.198 28

23.5 0.342 31.5 0.87 17.5 0.397 26.5

21.7 0.685 29.5 1.74 16 0.794 24

19.5 1.71 27 4.35 14 1.98 21.5

3.42 24.5 8.70 12.5 3.97 19.5

6.85 21

-

-

-

-

-

- -

- -

crnc and cmt Values

as

a Function of Pluronic

Structure and Molecular Weight.

Th e cmc and cmt

values listed in Tables

2

and

3

are discussed in this sectio n

in terms of the number of propylene oxide (PO) and

ethylene oxide (EO)units in th e Pluronic block copolymer

molecules. This enables estimation of the effect of the

polymer stru cture and molecular weight on m icellization

behavior.

PPO Effect. Th e cmc values for Pluronics P65, P84,

and P123, which have th e same hydrophilic (PE O) segment

and varying hydrophobic (PPO) segment, are plotted

semilogarithmically in Figure 4a

as

a function of the

number of P O units in th e Pluronic molecule, for different

solution temperatu res (25,35, and 45 OC . Th e log(cmc)

values for the Pluronics solutions (at a given solution

temperatu re) decreased in

a

roughly linear fashion

R 2

>

0.99)

as

a function of PO units, indicating tha t polymers

with a larger hydrophobic (PO ) doma in form micelles at

lower concentra tions. Higher tempera tures resulted in

lower cmc values, with t he slope of t he log(cmc) vs PO

number curve increasing with temperature. Th e cmt

values for the Pluronics solutions (at a given copolymer

concentration) decreased as a function of PO units, as

shown in Figure 4b, indicating th at polymers with a larger

hydrophobic doma in form micelles at lower temperatures.

PEO Effect.

The cmc and cmt values for groups of

Pluron ics with t he sam e hydrophobic segment and varying

hydrophilic segment, e.g., with

30 L64, 65, 68), 0 P84,

P85,

F88),

nd

60

(P104, P104, F108) PO units, plotted

as a functio n of

EO

units (plot not shown), show a small

increase in the cmc and cmt with increasing number of

EO

units. This would indicate tha t the micelle formation

becomes more difficult th e more hydrophilic he molecules,

although the effect of PEO on the cmc and cmt is less

pronounced than that of PPO, intimating that PPO is a

primary factor in the micellization process.

Molecular Weight Effect.

The cmc and cm t values

for copolymers of con stant PPO /PE O ratio but varying

molecular weight decrease with increasing number of EO

units (at a given copolymer solution temperature and

concentration for th e cmc an d cm t, respectively).

It

can



Macromolecules,

Vol. 27,

No. 9,

994

Micellization of PEO-PPO-PEO Trib lock Copolymers

2419

Table 3. Criticai M icelliaation Concentrations for P luronic Copolymer Aqueous Solutions as a Function of Solution

Temperature

L64 P65 F68 P84 P85 F88

temp,OC

% w/v

mM

% w/v

mM

%

w/v

mM

% w/v

mM

% w/v

mM

% w/v

m M

-

- - - - -

-

- -

2.6 6.190 4 8.695 -

20

25

30 1.5 5.172 4 11.76 0.6 1.428 0.9 1.956 -

35 0.4 1.379 1 2.941 -

0.15

0.357 0.2 0.434 1.7 1.491

40 0.1 0.344 0.35 1.029 7 8.333 0.04 0.095 0.05 0.108 0.6 0.526

45 0.02 0.069 0.1 0.294 3 3.571 0.013 0.031 0.014 0.030 0.24 0.210

50

-

0.04 0.117 0.9 1.071

- -

0.09 0.079

55 0.3 0.357

-

0.04 0.035

-

- - -

P103 P104 P105 F108 P123 F127

temp,OC

% w/v

mM

% w/v

mM

% w/v

mM

% w/v

mM

% w/v

mM

% w/v

mM

20 0.7 1.414

2 3.389 2.2

0.18

0.313 4 3.174

25 0.07 0.141 0.3 0.508 0.3

30 0.01 0.020 0.04 0.067 0.025

0.002 0.004 0.008 0.013 0.005

- 0.002 0.003 0.001

35

40

45

50

55

- - -

- -

-

- -

-

100

I I I I

I

J

1

0.01

1o4

1OB

P123

I

I I I

20 30 40 50 60

70

80

Number of PO units, N,

K

0 I I I I

45

40

35

30

25

20

-

l

P123

10 1

I I I I I I

20 30 40 50

60

70 80

Number of PO units, N,,

Figure

4.

(a, top) Critical micellization concentrations and

(b,

bottom) critical micellization temperatures of Pluronic copoly-

mers, having the same number of EO units, as a function of the

number of PO units.

thus be concluded that, for given PPO/PEO ratio, Plu-

ronics of higher molecular weight form micelles more

readily, e.g., a t lower concen trations an d temperatu res.

Parts a and b of Figure 5 show the cmc and cm t values,

respectively, for various Pluronics

as

a function of the

number

of

EO un its, for groups

of

copolymers w ith 40%

(L64, P84, P104), 50% (P65, P85, P105), and 8 0% (F68,

F88,F108) PE O content a nd a t various copolymer solution

tempe ratures (in Figure 5a) and concentrations (in Figure

5b). Th e cmt values were influenced more by molecular

weight the lower the relative EO content and the lower

th e copolymer concentration ,as isevidenced by th e steeper

3.384

-

0.461 4.5

0.038 0.8

0.007 0.15

0.001 0.04

0.008

-

-

10

g 1

C

m

0.1

8

9

0.01

5

0.001

3.082 0.03 0.052 0.7 0.565

0.547 0.005 0.009 0.1 0.079

0.103 0.001 0.002 0.025 0.019

0.027

-

0.008 0.006

0.005 -

-

-

I I ,

\

0 30 'C

'

35'C

A 45 'C

80%

PEO

40 PEO P)

8

I I

0 50 100 150

200

250 300

Number

of EO

uni ts, NE,

'

0.1

60 I

, 5096PEO

5

\

0 50 100 150 200 250 300

Number of

EO

units, NE,

Figure

5.

(a, top) Critical micellization concentrations for

Pluronic copolymers at various solution temperatures and (b,

bottom) critical micellization emperatures at various copolymer

concentrations, as a function of the number of EO units, for

copolymers of 40, 50,and 80%

EO

content.

slopes for th e curves for these conditions. A linear fit

was

found to describe adequately the cmc and c mt dependence

on the number of EO units for copolymers of constant

relative PEO content and varying molecular weight (R2

0.98 for F igure 5 a, while R2 0.94 for

40%

PEO nd

R2

> 0.99 for 50 and 80% P EO in Figure 5b).

Comparison of Pluronic cmc and cmt Values to

Those

of CjEj Nonionic Surfactants.

It is interesting

to com pare th e micellization of Plu ronic block copolymers

to tha t

of

CiEj

0

ethylen e glycol-i alkyl ethers ) low

molecular weight nonionic surfactants, which has been



2420 Alexandridis et al.

Macromolecules, Vol. 27, No. 9, 1994

more widelystudied.51*62

In

the latter systems, it was found

that he cmc decreased and t ha t the micellar size increased

strongly, both with increasing temper ature. Thu s, in these

respects, the analogy between Pluronics and CiEj seems

valid. However, th e pronounced sensitivity of the cmc

to

temperature, or of th e cmt t o concentration,as ound here

for many Pluronics, is not evident with th e n-alkyl poly-

(ethylene glycol) ethers, CiEj,53

The decrease of the

hydrophilicity of the PE O blocks with increasing tem-

perature has comparatively little effect on the cmc for

CiEj: for Cl2E8 the cmc is reported

as

9.7

X

10-5

M

at 15

"C and 5.8 X 103M at 40 "C (-40% decrease in the cmc

for 25 "C increase n te m ~e ra tu re )? ~n the case of P luronic

copolymer solutions, a 10 "C decrease in temperature

results in changes of t he cmc by more tha n an o rder of

magnitude (see Figure 5a). Also, the numb er of EO un its

has little effect, at least for sho rt EO headgroups: the cmc

is

given as 6.5

X 10-5 M

for C12E5 and 7.2

X

1 0 3

M

for

C1&.63 For longer EO cha ins (C16Ej,j = 17,32,44,63) ,

log(cmc) increased linearly

as

a function of EO weight

fraction, the cmc varying by up t o an order of magn itude

over the EO range studied, the slope being steeper at higher

temperature^.^^ Although the increase in th e cmc with

increasing EO may app ear significan t for the C1&j,

j =

17,32 ,44,63 , surfactant series, the change in the cmc per

EO unit in thiscase is less pronounced th an t he cmc change

between an d C12E8.

In the case of Pluronics, the

change in cmc per EO unit w as found to be even smaller,

indicating th at th e influence of PEO on cmc diminishes

as he size of th e surfa ctant increases.

This

an be observed

in Figure 5a where, for the sa me change of cm c, it takes

50 EO unit s for Pluronics of high molecular weight (80 %

EO group) but only 10 EO units for th e lower molecular

weight Pluronics. T he main determ inant of the cmc for

CiEl was found to be the le ngth of t he alky l (hydropho bic)

cham . T he loga rithm of cmc for th e CiE8,

=

10-15, series

decreased linearly with increasing carbon number in the

alkyl chain (cmc varied by approximately 2.5 orders of

magnitude over the carbon number range studied).52For

the Pluronics, an increasing hydrophobicity of the PO

block with increasing temperatu re, in combination with

the size polydispersity of the PO blocks, has been advanced

as

the reason for the strong tem perature dependence of

the C ~ C , ~ ~

Thermodynamicsof Block Copolymer Micelle

For-

mation. It is well establishe d th at block copolymers of

the A-B or A-B-A type form micelles in selectiv e solvents

which are therm odynam ically good solvents for one block

and precipitants for the other block. In general, micel-

lizat ion of block copoly mers,

as

n the case of conven tional

detergents, obeys the closed association model, which

assumes an equilibrium between molecularly dispersed

copolymer (unimer) an d multimolecular aggregates (mi-

celles).a955 Th ere are two main approach es

to

the ther-

modynamicanalysisofth e micellization

process:

the phase

separation model, in which th e m icelles are considered

to

form a separate phase at the cmc, and the mass-action

model tha t considers micelles an d unassociated monomers

in association-dissociation equilibrium.26 In both ap-

proaches, he stan dard free-energy change for the transfer

of

1

mol

of

amphiphile from solution to the micellar phase

(free energy of micellization),

AGO,

in the absence of

electrostatic interactions (nonionic surfactants)

is

given

by2627

AGO

=

RT n(X,,)

(1)

where

R

is the

gas

law constant,

T

is the absolute

tem perat ure, and Xcm, is the critica l micellization con-

0'0036

0035

1

/ 4

0.0031

0003

I I I

I

-17 -15 -13

- 1

1

-9 -7

In

C

(mole

fraction)

Figure 6. Reciprocal

T t

vs copolymer concentration plots for

various Pluronics, used

for

the determination of the micelliition

enthalpy in terms

of

the closed association model.

centration in mole fraction units.

It

is assumed here that

the concentration of free surfactant in the presence of

micelles is constant and equal to the cmc value, in the case

of the phase separation model, or that the micelle

aggregation number is large for the mass-action model.

Applying the Gibbs-Helmholtz equation and assuming

the aggregation number tobe independent of tempe rature

in the case of t he mass-action model, we can express the

standard enthalpy of micellization,

AH ,

s26l27

AHo

= -RT 2[d ln(Xcm,)/dTl, =

R[d

ln(Xmc)/~(1/ l')],

(2)

Finally, the s tan dar d entropy of m icellization per mole of

surfactant,

AS",

can be obtained from

AS

=

(AH

- AG ) /T (3)

It

has been shown for block copolymer micelli~ation1~*5'j?57

tha t, within experimental error,

d

l n ( X m c ) / W T )= ln(X)/dW'cmt) (4)

where X is the concentration expressed

as

mole fraction

and Tcmts the critical micellization tempera ture; thus, eq

2 becomes

AH = R[d ln(X)/d(l/Tmt)lP (5)

l/Tcmt s In(-

Plot:

Mode of Copolymer Aesoci-

ation.

In accordance with eq 5 , the inverse cmt values

were plotted

as

a function of th e logarith m of copolymer

concentr ation (m ole-fraction units) for a n umbe r of

Pluronics, as shown in Figure 6. We chose

to

use this

representation (cmt for

a

given concentration) in stead of

eq 2 (cmc for a given temperatu re)

as

t

more closely reflec ts

our experimental procedures, where the temperatu re of a

sample

of

given polymer concentration

was

varied.

The

cmt d ata, plotted in this m anner, are generally described

well by

a

straight line. Exceptions

to

the linear

fit

are

F68, F88, and F108, for which the elopesappear

to

increase

at high concentrations (>5 7 w/v). These three polymers

are all hydroph ilic and of high molecular weight; it may

be tha t for them the simple assumptions of the thermo-

dynamic analysis do not hold well at high polymer

concentrations. Th e hydrated PE O chains of the micelle

coronaswill overlap and entangle with increasingpolymer

concentration, up to t he formation of a gel-like structure

(F108 of

20

w/v forms a gel at room tkmperature).

One of th e assump tions involved in deriving eqs 1-5 is

that

the micelle aggregation number is independent of



Macromolecules,

Vol.

27,No.

9,

994

Table

4.

Standard

Free

Energies (A@), Enthalpies A P ) ,

and Entropies (ASD)

of

Micellization of Various Pluronic

Copolymers at Their Critical

Micellization

Temperature

for

1

Solutions

AH',

AGO, As ,

polymer

MW

PPO/PEO kJ/mol kJ/mol kJ/(molK)

L64

P65

F68

P84

P85

F88

P103

P104

P105

F108

P123

F127

2 900

3 400

8 400

4 200

4 600

11 400

4 950

5 900

6 500

14 600

5 750

12 600

1.155

0.766

0.190

1.149

0.764

0,190

1.791

1.146

0.763

0.190

1.788

0.326

230

182

215

211

229

169

339

296

331

266

329

253

-24.5 0.835

-25.3 0.671

-28.8 0.756

-25.2 0.784

-26.5 0.842

-28.5

0.638

-24.8 1.244

-25.4

1.092

-25.6 1.212

-28.4 0.975

-24.9

1.223

-27.5 0.944

temp erature. Although th ere a re some studies (e.g., ref

10

for

F68,

ref

15

for

P85,

ref

54

for

L64,

and ref

58

for

F127

indicating an increase in th e aggregation nu mber

with temperature, eq

5,

based on a closed associationmodel,

correlated the cm t data in a satisfactory way. Conse-

quently, we did not attem pt to fit a stepwise association

model to our data set,

as

that would have required an

additional degree of freedom with no enhanc eme nt in th e

fit of the data. Reddy et

al.12

examined the mode of

association of a purified L64 sample in aqueous solutions

by measuring t he light scattering intensity as a function

of temperatu re

and

concentration. Th e association a t

34.5

and 40 Cwas described by a coo perativeassociation model

which assume d aggregate grow th by stepwise add ition of

unimers. Deviation of th e expe rime ntal curves from th e

computed curves

was

observed a t high conc entrations and

attrib uted to solution nonideality.12 It should be noted,

though, tha t the dat a set used for the analysis of ref

12

was

relatively limited. A concentration-independe nt diffusion

coefficient an d m icelle weight-average molecular weight

have been explained by a closed association model for

hexa(oxyethy1ene glycol) monoether rn i~ el le s? ~he use

of a closed association model in t h e case of th e copolymer

we studied ap pears well justified based on th e good fit of

the data to eq

5;

we conse quen tly employed such asmodel

for estimating AHo and ASo of th e micellization process.

AG

A P , and

A s 0

as a

Funct ion o f P lu ron ic

S t r u c t u r e and Mo lecula r Weight. The standard en-

thalpy of micellization,

AHo

was calculated from the

inverse slope of the linear fit to the 1/TCmts ln(mo1e

fraction) data, in accordance with eq 5. AH values,

together with AGO and

ASo

(calculated from eq

1

and

3,

respectively, a t th e critical micellization tempe rature for

1% copolymer solutions), are listed in T able 4 for various

Pluronics. It is emphasized that these d ata are for a

constan t cmc, and not co nstant tem perature (for any given

concentration, there is a unique cmt; conversely, for any

given temperature , there is a unique cmc). Th e values for

the tabulated

AH",

AGO,

and

ASorange between

169

and

339

kJ/mol,

-24.5

and

-28.8

kJ/mol, and

0.638

and

1.244

kJ/( mo lK ), respectively.

The

higher values of

A H o

AGO,

and

AS"

were observed for

P103

and

L64

(relatively

hydrophobic copolymers), while the lower values were

observed for the relatively hydrophilic copolymers F68

and

F88.

Th e standard en thalpy of micelliiation,A H o s positive,

indicating th at the transfer

of

unimers from solution

to

the micelle is an enthalpically unfavorable endothermic

process. The free energy,

AGO,

is negative, since ther-

Micellization of

PEO-PPO-PEO

Triblo ck Copolymers

2421

1

10

- -

-40 -

h 0.01%

I

-50

2000 4000 6000

8000

10000 12000 14000 16000

Pluronic Molecular Weight

0

t

f P 6 5

~

.

2000

4000 6000 8000

10000

12000

14000 16000

Pluronic Molecular

Weight

Figure

7.

Effect of Pluronic

molecular w eight

on the free energies

of micellization for various polymer concentrations expressedas

(a,top) AGO (kJ/molTand

(b,

ottom)

AG0/(Nrn+

Npo (kJ/mol

of monomer unit).

mo dyn am icdy stable micelles are formed spontaneously.

Thus, it is clear tha t

a

negative entropy contribution mu st

be th e driving force for micellization of th e block copoly-

mers. Th e tradiational view of micelle formationw has

been based on th e study of the solubility of hydrocarbons

inwater and w hat has cometobeknown

s

he hydrophobic

effect.61 T he presence of hydrocar bon molecules in water

causes a significant decrease in th e water entropy , sug-

gesting that it induces an increase in the degree of

structuring of the water molecules, owing to cavity

formation. When hydrocarbo n residues aggregate in

aqueous solution t o form a m icelle, the hydrogen-bonding

structure in the water is, to a large extent, restored and

the water entropy increases; this overcomes the loss of

entropy due to th e localization of t he hydrocarbon chains

in the micelles. T he entrop y contribution usually dom-

inates the micellization process in aqueous surfactant

solutions, with the enthalpy playing a minor role. In the

Pluro nic copolymers, he unfavorable enthalpy component

is significant but is, nevertheless, overcome by an even

stronger entropy effect. In contrast to the entropy-driven

micellization in water, th e micellization of copolymers in

nonpolar solvents originates from entha lpy interactions

between t he copolymer segm ents and th e solvent.24

Free energies of micellization per mole of polymer in

solution, AGO, calculated at the critical micellization

temperatures for the various copolymers at different

solution concentrationsare

shown s

a function of Pluron ic

molecular weight in Figure 7a. Although th e data ex hibit

some scatter, presum ably because of th e widely varying

composition ratios of th e polymers used in th is study, they

do indicate the tendency for higher molecular weight

copolymers to have more negative fre e energies of micel-

lization, indicating a g reater propen sity

to

form micelles




with increasing polymer chain length. This is despite the

fact th at t he larger polymers are generally more hydro-

philic, as they are composed predominantly of ethylene

oxide groups.

The data shown in Figure 7a collapse into a single smooth

curve, indepe ndent of copolymer composition ratio PP O/

PEO, when normalized with respect to the total number

of monomer units in the polymer,

NEO

+ NPO,s shown

in Figure 7b. It can be seenclearly ha t the lower molecular

weight, more hydrophobic P luronics correspond

to

more

negative

AGO

per monomer unit values. These dat a were

correlate d as a fun ction of molecular weight M W and

concentration, C, by th e em pirical equation

Macromolecules,

Vol.

27,

No .

9, 1994

where A 1 and A 2 are concentration-dependent constants

given by

A, = 1263-360.5 log(C ) (7)

and

A ,

=

-1985 + 566.3 lOg(C)

(8)

respectively. T he fit is good E2 0.9971, and the

predictio ns of th e correlat ion for AG /(NEo + Npo) (kJ/

monomer unit) differ at most by 2.5% from the experi-

mentally determined values. Since this correlation holds

for PEO -PPO -PE O copolymers covering a wide range of

molecular weights and P PO /PE O compositions, t can be

used for predicting

AGO

for copolymers th at have not yet

been studied experimentally. Once

AGO

is known, the

criticalmicellization concentrations and temperatures can

also be estimated.

Th e normalization of th e dat a in thi s fashion enables

the composition ratio effects to be decoupled from the

effects of overall molecular weight and copolymer con-

centration on the m icellization process. Th e reason for

th e success of th is norm alization is unclear. It may reflect

the importance of the ether oxygens, common to both

monomer types in the polymer, in determining the

polymer-polymer and pol ym em lve nt interactions. These

interactions can have both enthalpic and entropic con-

tributions, as is discussed later. Th e unfavorable entropic

effects associated with t he localization of t he polym ers

within the micelles would then be reflected in th e molecular

weight dependency,as he a bsolute value of t he fre e energy

per monomer becomes smaller with increasing polymer

molecular weight.

It

must be emphasized again, however,

that the curves presented here are at constant concen-

tration and that the temperature, which is the cmt, is

different for each polymer datum point.

To further probe the origii of micelle formation in

Pluro nic copolymer solution s, th e depend ence of the

thermodynamic parameters AHo and

AGO

on

the PPO/

PEO composition ratio was examined. Figure 8a shows

tha t the normalized AHo (express ed in kJ/m ol of average

monomer unit) approaches zero as the PPO/PEO ratio

goes to zero. It can thus be inferred tha t the m icellization

process is dominated by the PPO (hydrophobic) part of

the copolymer. A similar trend was observed by Arm strong

e t a l . 6 2 based on DSC ntha lpy ch anges of

IC1

Poloxamer

solutions and by Williams et

a1.M

using the increment in

appa rent molar volume on "thermal transition" of Poly-

Science PE O-P PO copolymers

asa

function of PPO /PEO .

Th e fact tha t the normalized

AHo

values are approximately

the same for different Pluronics of a consta nt PP O/ PE O

ratio would indicate th at t he micellization enthalpy

per

5 1 I

k

I

.g 14

I I I

I

0 0.5 1 1 5

2

Polymer Composition Ratio, PPO/PEO

O

60PO

unit

40 POunits

30 PO

units

i

0.5 I

1

0 0.5

1

1.5 2

Polymer Composition Ratio, PPO/PEO

Figure

8. Effect

of

polymer composition ratio,

PPO/PEO, on

(a, top) AH /( , + Npo

and

(b,bottom) AG0l(Nm+ NPO .

monom er unit is inde pen den t of molecular weight. In

contrast to th e trend of decreasing AGO with increasing

Pluronic molecular weight, there is no de f ii t e dependence

of AHo on molecular weight over the rang e covered in this

study. The AHo data presented in Table 4 reveal two

main groups of copolymers, th e relatively hydropho bic

P103, P104, P105, and P123 with

AH

n th e 300-350 kJ /

mol range an d th e relatively hydrophilic L64, P65, P84,

and P85 with

AHo

in the 180-230 kJ/m ol range, while AHo

for the other four copolymers ranges from 170

to

270 kJ/

mol. Th e dependence of the normalized AHo on the

copolymer composition is far more instructive and is

presented in Figure 8a.

A

plot of

AGO

of micellization

(expressed in k J/mol of average monomer unit) as a

function of P PO /PE O (F igure 8b) again shows the AGO/

unit values approaching zero as the P PO /P EO ratio goes

to zero. T he un it free energy, however, decreases (becomes

more negative) with a decrease in molecular weight for

Pluronics with a constant PP O/P EO ratio.

Th e compilation of

AGO,

AH , and

ASo

dat a for a wide

range of Plu ronic block copolymers presente d in this paper

is,

to

th e best of o ur knowledge, the most com plete in the

literature. In

a previous investigation, Reddy

et

d l2

estimated the AGO of micellization a t

-20

kJ/mol and the

AHo of micellization at

200

J/mo l for a solu tion of purified

L64, tilizing ln(cmc) vs l/ T da ta (only hree data points,

though). Th e same gr0upl7 reported the AH o of micel-

lization at

-316f

0 kJ/m ol for a solution of purified

F127

(from Mcon centration) vs 1/T,t data). These values are

close to our estim ates of AGO =

-24.5

kJ/mol and AHo

=

230

kJ/mol for

L64

and AHo =

253

for

F127

(the

copolymers we used were not purified).

A€P from Differential Scanning Calorimetry. An-

other m ethod for obtaining estimates of the free enthalpy

of micellization,AHo s differential scanning calorimetry

(DSC).

DSC

measurem ents for aqueous Pluro nic solutions



Macromolecules, Vol. 27, No. 9,

1994

show broad endothermic peaks, typical for a first-order

phase transition, at concentration-dependent character-

istic temperatures.11p62 The peaks have rather high

enthalpy values (almost 3 orders of m agnitude larger than

typical enthalpy values for phase transitions in lyotropic

liquid crystalall and are rather broad, extending more than

20 "C. Th e atter can be due to he fact

that

the copolymers

are not p ure com pounds but show a broad molecular weight

distribution; it is well-known

also

that melting peaks

become broad in the presen ce of im purities.ll It should

be pointed out here tha t the enthalpy change measured

by the peak area in DSC is not the standard enthalpy

change but depends upon the real

states

of the chains

before and after micellization. Th e standard st ate en-

thalpy change is defined for transfer of

1

mol of chains

from the ideally dilute solution to t he solvated micellar

state. In th e ideally dilute solution, copolymer segments

interact only with solvent, whereas in real solutions

segmentsalso interact with each other, and th is may cause

discrepancies between micellization enthalpies obtained

from DSC and th e ones derived from an analysis similar

to ours.61

It

has also been reported by H ieme nzs tha t

AHovalues calculated by a micellization thermo dynam ics

model generally show poor agreement with those deter-

mined calorimetrically, at least for ionic surfactants.

studied with DSC), Wanka et d.11observed no

propor-

EO portion of th e molecules, but they noted t ha t there

groups,

o afirst

appro~mation.

romthistheyconcluded

th at th e transition is probably due to the dehydration or

ofthe~ o ~ ~ ~ ~ ~ ~ I I

imilar

rends w ere observed

in our

o

data. It appears, though, from our data set


2423

of PE O, is still a ma tter of some controversy. In princip le,

models in the literature are based on either th e solute-

~ o l v e n t ~ ~ ~ ~r th e solu te-so lute interaction^.^^ Kjelander

and Florin67 attempted to reproduce t he negative entropy

and enthalpy of water-PEO mixing and the phase diagram

of the PEO-water system assuming a zone with increased

struc turin g of water to exist around the PEO chain. The

phase separation that takes place at high temperatures

was attr ibu ted t o a breakdown of th e zones of enha nced

water structure. Th e chain length dependence was mainly

determined from the combinatorial entropy of t he chains.

Th e water solubility of P EO could be explained in terms

of a good struc tural

fit

between the water and th e polymer.

While PPO

also

has negative entropy and enthalpy of

mixing with water, they are less negative tha n those for

PEO-water. Kjelander andFlorine7 laim tha t, when PP O

is

introduced into water, it

also

develops a hydration shell

with an enhanced structur e of water, but since th e methyl

groups of PP O con stitute a steric hinderance, th e water

structure is weak and leads

to

phase separation. It should

be noted here tha t, while PPO is practically insoluble in

water at room temperature, it can be soluble at low

tem perat ures (e.g., up t o -7 "C for PP O with degree of

polymerization

=

20, reported in ref 67).

A

weak point

to

the above theory, according to Karl-

solutions that is incompatible with an ordered water

titative

agreement)

the

phase using

the P EO chain may exist in two forms due to the rotations

around

the c-c

and bonds*

From

quantum me-

chanical calcu lations, corroborated by 13CNMR chemical

shift measurements, the conformation of the OCCO

From a very l imited se t of data ( ~ 1 2 3 , 1 2 7 ,nd p i04

StrOm,6' is the highly d h r d e r e d stateof PE O in aqueous

tionality between the enthalpy values and the size of the

was proportionality between these values and the PO

hydration shell- Karl&omsg predic ted (with semiqu an-

Flory-Hugginstheow and assumingthateachsegmentof

Of

th at there is a weak effect of EO on m O s For Pluronics

segment

W a s

divided into two classes, one being Polar,

with the Same size hydrophobic (PPO) segment and

varying size hydrophilic (PEO) segment, i.e., p103, p lo d,

having a low e n e r a and a low statistical weight, and one

being less Polar, or having

a

higher energy and

p105, and F108,

m o

ecreased by -15%

as

the number

of

EO

segments

increased from 17 to 132.

on

he

contrary, for pluronics with the same size hydrophilic

(PEO) segment

and varying size hydrophobic

(PPO)

segm ent, iSe., ~ 6 5 , 8 4 ,nd ~ 1 2 3 ,

O

ncremed by

to 70. The PP O effect

was

more significant and, together

with the data

of

~i~~~~8, leads

to

the conc~usion hat

ronics.

a higher statis tical weight.14 A t low temperatures, the

former class of sta tes domina tes and the solu te-solvent

interaction is favorable, whereas at higher temperature,

the la tter class of states becomes increasingly populated ,

rendering the solute-solvent interaction less favorable.

temperature-dependent

and

Eo-Po

interactions,

to

predict th e micellization behavior of PEO -

both PO a nd EO blocks repel each other progressively ess

with increasing temperatu re until, a t some temperature,

discussion of the mechanisms of the temperature depen-

dence, and clouding in particular, is presented by carison

et

d . 7 0

Th e self-consistent mean-field lattice models used for

predicting PEO-PPO-PEO block copolymer solution

behavior by Hurter et d . 2 6 and Linse et d.71 also

-

00% as the number of PO segments increased from 30

Malmsten and Lin dm al4used asimilar model, assuming

PP O is mainly responsible for the micellization of plu-

PPO-PEO block C oP o be r solutions- They found that

Differential scanning calorimetry was also used by

Beezer et a l a B e on PEO-P PO-P EO block copolymer so h-

the effec tive PO-PO attra ction domin ates Over the EO-

EO repulsion and micelles form,

A

more comprehensive

tions. Th e observed "phase transitions" were in the 100-

300 kJ/mol range a nd were initially thought to result from

changes in the polymer solvation as the temperature

changed. Th e authors claimeds6 hat, a t the concentration

used ( 5 g/L), only monomeric species were present in

solution. In a more recent paper from the same POUP,

Armstrong et a l e e 2 concluded tha t the observed enthalpy

change is indicative ofan ggregation pr m es , accompanied

by desolvation and change in conforma tion of the h ydro-

phobe* Although direct comparison between the d o -

be made

as

the copolymers used were not the same, our

incorporated Karlstrom's ideas a nd accounted for con-

formational distributions in PE O and PP O, thus &-wng

the investigationof temperature effects on th e aggregation

behavior of these copolymers. Th e model predictions of

increasing PPO) agree well with the trends observed

rimetry AH

cannot

data strongly suggest th at the micellization process is the

major contribution to the calorimetrically observed en-

thalpy change.

Molecular Mechanism of the Temperature Effect

on

PEO-PPO-PEO Aqueous Solutions. Th e "molecu-

lar-level"mechanism behind the tem perature dependence

of

PEO-PP O-PEO micellization,and particularlythe effect

Of refs 62

and

66

and Our

refs

28

and 71 (e.g., decrease of the cmc and cmt with

thus supporting the po~ar-nonpolar

model

as an

explanation oft he

temperatureffect on

the

solution behavior of P EO and PPO.

Conclusions

The critical micellization temperature and critical

micellization concentration values of

1 2

Pluronic poly-




Macromolecules,

Vol.

27,

No. 9,

994

(ethyle ne oxide)-poly(propy1ene oxide)-poly (ethylene ox-

ide) (PEO -PPO -PEO ) block copolymers, covering a wide

range of molecular weights (2900-14

600)

and PPO/PEO

ratios (0.19-1-79], have been dete rm ined em ploying a dye

solubilization method. In general, it is evident th at

copolymers with a larger hydrophobic (PPO) domain

formed micelles at lower concentrations or, for a given

copolymer concentration, have lower cmt's. For copolymer

groups with the same PP O/ PE O ratio, Pluronics of higher

molecular w eight form micelles more read ily, e.g., at lower

concentrations and temperatures. Th e hydrophilic group

appears t o play a smaller role in t he m icellization process.

A closed association model was found to describe

adequately the copolymer micellization process for th e

majority of th e Pluronics and was used t o obtain stand ard

free energies (AGO), enthalpies

(AH"),

and entropies

(AS )

of micellization for thes e Pluronics. Th e stan dard en-

thal py of micellization, AH ,was found to be positive for

all Pluronics tested, indicating th at th e ransfer

of

unimers

from solution to th e micelle is an enthalpically unfavorable

endothermic process. A negative entropy contribution

must, therefore,

be

the driving force for th e m icellization

for th e block copolymers.

The comprehensive compilation of cmt and cmc data

for aqueous Pluronic solutions presented here is expected

to be a value in th e num erous applications of P luronics

th at depend on their micelle forming abilities. Th e utility

of these results is enhanced by the finding th at th e free

energies of micellization per monom er un it, AG /(NEo +

Npo),

correlate d well with molecular weight and solution

concen tration over th e wide range of polymer composition

ratios investigated and can be used for th e estimation of

the micellizationparam eters of other polymers in this class.

The basis for this correlation is

as

yet unclear, but it

probably reflects a decoupling of the importance of the

ether oxygens in determining th e polymer-solvent and

polymer-polymer interactions and th e entropic penalties

associated with confining the polymer chain within the

micelles.

Acknowledgment.

This work was supported by the

U S . Departm ent of Energy under Gran t No. DE-FGOS-

92ER14262 and t he Em ission Reduction Research C enter

(ER RC) , Newark, NJ. Subsistence supp ort by the Fritz-

Hab er-In stitu t is gratefully acknowledged. We acknowl-

edge Vassiliki Athanassiou, Shinya Fuk uda, a nd Naoko

Munakata, who participated in this research program

under the M IT U ndergraduate Research Opportunities

Program (UROP), for their valuable assistance in con-

ducting the cmt and cmc measurements. We also tha nk

BASF Corp., Specialty Products, Parsippany, NJ, for

providing us with surfactants free of charge.

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Macromolecules, Vol.

27,

No.

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