Barba et al JAPS 114(2) 688-695 (2009)

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InvestigationofPluronic(c)F127-WaterSolutionsPhaseTransitionsbyDSCandDielectricSpectroscopyARTICLEinJOURNALOFAPPLIEDPOLYMERSCIENCEOCTOBER2009ImpactFactor:1.64DOI:10.1002/app.30586

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Investigation of PluronicVC

F127Water Solutions PhaseTransitions by DSC and Dielectric Spectroscopy

Anna Angela Barba,1 Matteo dAmore,1 Mario Grassi,2 Serafina Chirico,3 Gaetano Lamberti,3

Giuseppe Titomanlio3

1Dipartimento di Scienze Farmaceutiche, Universita` degli Studi di Salerno, Via Ponte don Melillo,Fisciano 84084 (SA), Italy2Dipartimento di Ingegneria Chimica, dellAmbiente e delle Materie Prime, Universita` degli Studi di Trieste,Via Valerio 10, 34127 Trieste, Italy3Dipartimento di Ingegneria Chimica e Alimentare, Universita` degli Studi di Salerno, Via Ponte don Melillo,84084 Fisciano (SA), Italy

Received 18 October 2008; accepted 5 April 2009DOI 10.1002/app.30586Published online 8 June 2009 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: The water solutions of the block copoly-mers PEOn-PPOm-PEOn, known as pluronics, show a com-plex thermal behavior, since they are liquid at lowtemperature (5C), and they can give soft gel when heatedat body temperature (37C). These properties are of greatinterest in biomedical applications. To properly designthese applications, a prerequisite is the knowledge of thethermodynamicshow muchand of the kineticshowfastwith which these transformations take place. In thiswork, solutions of F127 (the copolymer for which n 100and m 65) were studied by varying the concentrationand the temperature and analyzing their behavior whenheated under several heating rates. The studies were per-

formed by differential scanning calorimetry (DCS) anddielectric spectroscopy. The investigations carried outunder equilibrium conditions allowed us to determine thethermodynamics of the phase transitions, whereas theinvestigations carried out under varying conditionsallowed us to quantify the kinetics of the phase transitions.Empirical models were also proposed to describe both thethermodynamics and the kinetics observed. VVC 2009 WileyPeriodicals, Inc. J Appl Polym Sci 114: 688695, 2009

Key words: biological applications of polymers; blockcopolymers; dielectric properties; differential scanningcalorimetry (DSC); gelation

INTRODUCTION

Background

The block copolymers PEOn-PPOm-PEOn constitute aclass of biocompatible surfactants known as plur-onics or poloxamers. Their amphiphilic nature isdue to the PEO water-soluble chains and to thehydrophobicity of the PPO segment.

Their water solutions exhibit complex phasebehavior with temperature. Starting from tempera-tures close to 0C, the affinity between water andPEO segments decreases on heating, and the singlechain of polymer in solution (the unimers) can ag-gregate building up micelles, the phenomenon ofmicellization. Further temperature increase can causea close packing of the micelles, building up to a softgel with interesting properties for biomedical appli-cations, the phenomenon is noted as gelation.1,2

The pluronic F127 (PEO100PPO65PEO100), whosesolutions of proper concentration (around 20% w/w)

give a gel at body temperature (37C), is of particu-lar interest in biomedical applications. e.g., its use isunder consideration to cover the stents used in per-cutaneous transluminal angioplasty.1,2 To do this, aliquid solution (at 5C) must be pumped into a cath-eter, and it must gelate only in the proper positionin the cardiac artery. To predict the solidificationbehavior, both the thermodynamics and the kineticsof the micellization and gelation must be known.

State of the art

The complex phase behavior of the pluronic watersolutions gained much attention from researchers inthe past.

Alexandridis et al.3,4 studied the micellization phe-nomena by fluorescent spectroscopy and by DSC,obtaining the micellization temperature as a functionof the solution concentration for several pluronics andsuggesting an entropy-driven micellization process.

Wanka et al.5 obtained the phase diagrams forseveral pluronic water solutions by dynamic lightscattering (DLS), SANS, and polarized microscopy,identifying the micellization and the gelation ther-modynamics (i.e., the equilibrium conditions under

Journal of Applied Polymer Science, Vol. 114, 688695 (2009)VVC 2009 Wiley Periodicals, Inc.

Correspondence to: A. A. Barba ([email protected]).

which micellization and gelation take place). Theyalso performed measurements of surface tension (toget the critical micellization concentration, i.e., theconcentration at which the micellization occurs for agiven temperature) and DSC experiments (to quan-tify and to localize the micellization and the gelationconditions).

Malmsten and Lindman6 carried out C-NMRmeasurements of pluronic water solutions underconditions close to micellization, clarifying the rolethat the PPO and PEO segments play during themicellization phenomenon. They also built the phasediagram of the Pluronic F127, and they investigatedthe effect of several co-solutes on the phase stability.

Song et al.7 suggested the use of dielectric measure-ments and of the Hanai equation to quantify thedegree of volume filling occupied by the micelle. Theyalso estimated the micellization temperature from achange of slope in the graph dielectric constant vs.temperature. Their approach has been followed in thepresent work to get similar information, under equilib-rium as well as under nonequilibrium conditions.

Prudhomme et al.8 used the SANS technique toinvestigate the F127 micellization/gelation. Theyobserved the presence of geometrical entities withdefined size (the micelles), the size of which was inde-pendent from temperature and solution concentra-tion. Thus, they hypothesized that the gelation wasdue to the close packing of the micelle and not to mi-celle growth.

Lau et al.9 investigated the Pluronic F108 micelli-zation/gelation process by rheology and DSC. Theyobserved the large endothermic peak due to micelli-zation and the very small endothermic peak due togelation. Furthermore, the elastic modulus measure-ments during solution heating allowed them to fol-low the gelation process. However, it is worthnoting that the rheological measurements carried outduring heating do not allow the direct evaluation ofthe gelation thermodynamics, since the data weregathered under conditions far from equilibrium.

Li et al.10 studied the gelation of the F127 watersolution by SANS and the Monte Carlo simulationmethod, with the aim of clarifying the role of thesolvent in the process. They confirmed that a frac-tion of the water is bonded with the polymer, andthis fraction plays a significant role in the gelation,increasing the bond strength between the PEO seg-ments in the micelle corona.

Cabana et al.11 analyzed the gelation of F127 watersolutions by rheology, DSC, and FTIR. Theyobserved the increase in viscosity during the heatingcaused by the gelation. They also confirmed the verysmall endothermic gelation peak and explained theminimal enthalpy effect as the transition of the lastunimers that enters the micelle, which are closelypacked to form the gel.

Mortensen and Talmon12 studied water solution ofF127. They confirmed the presence of a hard sphereby direct visual observation of vitrified specimenby cryo-TEM (cryogenic temperature transmissionelectron microscopy), and they quantified the vol-ume fraction occupied by the sphere by SANSmeasurements.

Most of the work was thus done with the aim ofclarifying the fundamentals of the observed phenom-ena. In particular, the thermodynamics of the phe-nomena have been widely investigated, whereas itshould be emphasized that the kinetics of the phe-nomena have been neglected in the studied per-formed. However, for practical applications, it shouldbe known to which extentthe thermodynamicsand with which ratethe kineticsthe phenomenadevelop. Therefore, an overall description of the ther-modynamics and kinetics of micellization and of gela-tion still lacks, and it is highly desirable.

Aim

Aim of this work was to observe and to quantify thethermodynamics and the kinetics of the micellizationand gelation phenomena for F127s water solutions.

MATERIALS AND METHODS

Materials

Pluronic F127 flakes (CAS no. 9003-11-6) were pur-chased from Sigma Aldrich (Milano, Italy). Solutionscontaining 10, 15, 20, and 22% w/w of the polymerwere prepared by adding cold distilled water to theflakes, gently mixing, and allowing the stabilization,keeping them at 4C overnight (cold method).

DSC measurements

The DSC measurements were performed in a MettlerToledo DSC 822, by heating the samples at 1C/min.The heating rate was selected as a compromisebetween the need for a condition close to the equi-librium (heating rate as low as possible) and a sig-nal/disturbance ratio acceptable (heating rate nottoo low). The signals were recorded and, after aproperly designed baseline subtraction procedure,used to localize the micellization phenomenon.

Dielectric constant measurements

The dielectric constants of the water/pluronic sys-tems were measured in the frequency range 200 MHzto 6 GHz, using the network analyzer Agilent Net-work Analyzer mod. ES 8753, equipped with thecoaxial probe mod. 85070D. The dielectric spectros-copy is a nondestructive analysis, requires short timeto assay the values, and has a good repeatability.

PLURONICVC

F127WATER SOLUTIONS PHASE TRANSITIONS 689

Journal of Applied Polymer Science DOI 10.1002/app

RESULTS AND DISCUSSIONS

Thermodynamics of micellization

The first phenomenon that takes place during pluronicwater solution heating is the so-called micellization,i.e., the aggregation of polymer single-chain unim-ers to form micelles, with a central core built up ofPPO hydrophobic segments and an external coronabuilt up of PEO hydrophilic segments. The micelliza-tion is an endothermic phenomenon; thus it can bedetected by a properly designed DSC test. In thiswork, small quantitiesthe order of 10 to 20 mgofF127 water solutions were inserted in DSC sampleholder, and then they were subjected to the followingthermal history: heating at 1C/min from 0 to 140C,followed by a short staying at 140C and then by acooling to 25C at 10C/min. During the heating, themost important phenomenonthe one that requiresthe maximum amount of energyis of course thewater evaporation, with a peak around 100C; duringthe cooling the polymerwhich at this point is drygives up to the solidification with a related exothermicpeak around 35C. An example of such behavior is inFigure 1, for a F127 solution 20% w/w.

The micellization phenomenon takes place aroundroom temperature, and it is noticeable as a very smallshoulder on the large endothermic peak of waterevaporation. To quantify the micellization, there is theneed for a careful signal manipulation. The waterevaporation peak was thus fitted by a proper function

that plays the rule of the baseline for micellizationpeak analysis. The region of interest and the baselineare emphasized in the inset in Figure 1. After thebaseline fitting, this baseline was subtracted fromDSC signal, giving the evolution of the signal as dueonly to the micellization phenomenon.

In Figure 2, the DSC signals were reported for sev-eral F127 concentrations, after baseline subtraction.The data were reported as positive if endothermic,i.e., the opposite of the data in previous figure, for amatter of convenience. For some concentrations, twosignals were reported to confirm the data reproduci-bility. Peaks are due to the micellization phenom-enon; thus from this graph the micellizationtemperatures were obtained as a function of solutionconcentrations. At higher concentrations, the signalsshow small shoulders at temperatures higher thanthe micellization ones: They can be assigned to thegelation phenomena, which require much less heat.

The molar fraction of F127 (X, which has a molarmass MMF127 12.6 kg/mol) can be calculated fromthe weight/weight concentration C, as follows:

X C

MMF127C

MMF127 1CMMWater

(1)

The molar concentration can then be drawn versusthe micellization temperature (or versus the inverseof absolute micellization temperature). In Figure 3,the data obtained in this work (four data symbols,

Figure 1 DSC signal recorded during the heating/coolingof a solution of F127 (20% w/w). Continuous line: DSCsignal; dashed line: baseline. Temperature program: heat-ing from 0 to 140C at 1C/min, holding at 140C for 10min, then cooling from 140C to 20C at 10C/min. Inset:The zone where micellization and gelation take place, to-gether with the baseline to be subtracted.

Figure 2 DSC signals, after baseline subtraction, for sev-eral F127 solutions. Runs are repeated to verify experimentreproducibility. Continuous and dashed line, C 10%;dotted and dash-dotted line, C 15%; dash-dot-dottedand short dashed line, C 20%; short dotted line, C 22%. The large peaks are due to micellization; the smallshoulders (for higher solution concentrations) are due tothe gelation phenomenon.

690 BARBA ET AL.


closed squares) were reported in comparison withdata taken from literature.5,7 The data compare well,and they were very well described by an Arrhenius-like equation (dashed line):

lnX

X0

DH

R

1

T 1T0

(2)

In eq. (2), the reference value is (T0 292 K 19C,X0 1.59 104, i.e., C0 10%), and the micellizationenthalpy is DH 80.25 kJ/mol, R = 8.314 J/(K mol)being the universal gas constant. Equation (2) is a firstresult of this work: For a given F127 solution, it allowsthe micellization temperature calculation.

The micellization could be viewed as an energy bar-rier-triggered phenomenon. i.e., the micelle formationtakes place as soon as the free enthalpy of the micelleis lower than the unimers one. It is reasonable toassume that the transport phenomena do not play arole in their formation (which takes place on the nano-metric size scale); thus the micellization itself is a veryfast process. Therefore, the (practically immediate)kinetics of the micellization is of no practical interest.

Thermodynamics of gelation

The gelation phenomenon takes place on heating attemperatures higher than the micellization. It con-sists in both micelle growth and aggregation. A softgel was obtained from F127 solutions as soon as the

degree of space filling due to the micelles reachesthe value of 52.3%, which corresponds to the criticaldegree of space filling for simple cubic packing ofspherical particles. As already noted in DSC signalanalysis, the gelation phenomenon is scarcely endo-thermic, thus it is hard to investigate it by calorime-try. Instead, the dielectric behavior (orientation andrelaxation of polar structures under electromagneticfields) of gel is different than the behavior of micellesolution; thus the dielectric spectroscopy (measure-ments of complex permittivity) has been found to beuseful to carry out studies on gelation.7,13

The dielectric constant (the real part of the com-plex permittivity) values of F127 solutions as func-tion of frequency are reported in Figure 4 for twodifferent temperatures, 15 and 30C. The dielectricconstant is a decreasing function of frequency (thehigher the electromagnetic wave frequency, thelower the time allowed to the dipolethe watermoleculeto orientate with the electric field andthen to storage energy) and it also decreases withF127 concentrations (since higher polymer contentmeans less water, which contributes mainly to thedielectric constant of the solutions).

A single value of the dielectric constant, i.e., corre-spondent to a single frequency, is needed for theanalysis of gelation phenomenon. The dependenceof permittivity on frequency of F127 solutions ismonotonic; thus the analysis will give the sameresult whatever frequency value is chosen as the

Figure 3 The micellization concentration (in term ofmolar fraction) versus the temperature (on the top axis)and versus the inverse of temperature (on the bottomaxis). Data from literature are reported for comparison,and the data obtained in this work are linearly fitted, witha very good correlation coefficient. Full squares, this work,by DSC; open circles, Wanka et al., by DSC; open upwardtriangles, Song et al., by dielectric measurements.

Figure 4 Dielectric constant of several F127 solutions asfunction of frequency. Curves parameter is the solution con-centration. Above, the graph at T 15C; below, the graphat T 30C. Continuous line, C 10%, dashed line, C 15%; dotted line, C 20%; dash-dotted line, C 22%.

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fundamental one. Since for technological reasons themost important frequency is 2.45 GHz (the value atwhich most microwave apparatuses work), thisvalue was chosen as the fundamental frequency forthe subsequent analysis.

The dielectric constant measurements were per-formed on F127 solutions stored under controlled lowtemperature (4C) after their conditioning at the testtemperature. Each test was carried out in triplicate,and the measurements were performed after allowingthe sample enough time for stabilizing at the test tem-perature. Furthermore, the measurements wererepeated after 1 h of conditioning to ensure that thethermodynamic equilibrium value has been mea-sured, i.e., to be sure that the gelation process hasreached the maximum extend compatible with theconcentration and the temperature. Nine tempera-tures were investigated (10, 15, 20, 25, 30, 35, 40, 45,and 50C) for four concentrations (10, 15, 20, and22%). The dataaverage of three measurements, after1 h of conditioning at the test temperaturewerereported as permittivity at 2.45 GHz versus tempera-ture, with the concentration as the parameter, in Fig-ure 5. The dielectric constant of distilled water wasreported as a comparison. These data were the basisto get the degree of space filling, i.e., the measurementof the gelation extent. Indeed, the degree of space fill-ing, /, could be calculated on the basis of Hanaisequation, as suggested by Song et al.7:

1 / e0slz e0sphere

e0medium e0spheree0spheree0slz

!13

(3)

In eq. (3), the Hanais equation, / is the degree ofspace filling, which identifies the gelation as it

reaches the value of 52.3% (simple cubic packing ofspherical particles); e0slz is the dielectric constant ofthe F127 solution, as measured by dielectric spec-troscopy; e0medium is the dielectric constant of the me-dium that surrounds the micelles; and e0sphere is thedielectric constant of the pure micelles (the spheres).All the dielectric constants must be evaluated atsame frequency (2.45 GHz, as above reported). Themeasured value is e0slz, the model aids to calculatethe degree of space filling, /. Therefore, eq. (3) musthave e0medium and e0sphere values to be used.

The medium that surrounds the micelles wasmade up the solution itself for temperatures lowerthan the micellization temperature (i.e., around thefirst micelles there is the solution itself until themicellization/gelation takes place). After the maxi-mum packing of the micelles (after the gelation hasreached its maximum extent, which Song et al.7

located at 50C), the medium surrounding themicelles is made up of pure water. For temperaturebetween the micellization one and the maximumpacking one, the medium is made up of a solutionwith decreasing concentration, since unimers leavethe medium to build up or to increase the size ofmicelles. Thus, the medium dielectric constant canbe calculated by eq. (4):

e0medium

T < Tmic e0slz

Tmic T Tpacking an average betweene0slz and e

0water

T > Tpacking e0water

8>>>>>>>>>>>:

(4)

To use eq. (3), the permittivity of the sphere mustbe known. A linear dependence from temperaturecan be postulated,7 i.e.,

e0sphere a bT (5)

From DSC measurements (Fig. 2), the gelationtakes place at 17C for C 22% and at 18C for C 20% (in agreement with the SANS measurementsperformed by Mortensen and Talmon12). Thus, thevalues for parameters a = 58.56 and b = 0.187 havebeen obtained by forcing eq. (3) to give / 52.3%(the gelation) at 20% and 22% for temperatures of18C and 17C, respectively.

Figure 6 summarizes the data and the analysisrequired to get the degree of space filling by apply-ing the Hanai equation (3). Both experimental per-mittivity data for water (full squares) and for F127solution at 20% (closed triangles) were reported,along with the medium permittivity as obtained byeq. (4) (closed diamonds) and sphere permittivity as

Figure 5 Dielectric constant at 2.45 GHz for several F127solutions (and of the water) as a function of temperature.Continuous line and open squares, water; dashed line andopen circles, C 10%; dotted line and open upward trian-gles, C 15%; dash-dotted line and downward triangles,C 20%; dash-dot-dotted line and open diamonds, C 22%.

692 BARBA ET AL.


calculated by eq. (5) (continuous line). All thesedielectric constant values were reported versus thetemperature. A graph similar to Figure 6 wasobtained for each concentration investigated.

Applying the Hanai equation (3) to these data, thedegree of space filling values were obtained as afunction of temperature (in the range of 10 to 50C)and concentration (in the range of 10 to 22%). Thesevalues are reported as symbols in Figure 7. Thesame graph reports, as lines, the predictions of anempirical model that is made up by eq. (6):

/T;C T < TmicC 0T TmicC AC 0AC

1expTTmicCa1a2Ca3

with AC a4C a5 1 exp Ta6

8>>>>>>>:

(6)

In eq. (6), the temperature is in Celsius and theconcentration in w/w. The six parameters in eq. (6)have the values: a1 3.58, a2 79.02, a3 17.385,a4 3.098, a5 0.0357, and a6 = 10.837; and theywere obtained by regression from experimental data(by minimization of sum of square error 0.0764,with Pearsons correlation coefficient of 0.8188).

Equation (6), in which Tmic(C) is given by eq. (2),is another result of this work: For a F127 solution ofconcentration C, at a given temperature T, eq. (6)allows to calculate the degree of space filling /, andif it is not less than 52.3%, it means that in thesecondition the solution is a soft gel.

Both the Figure 7 and eq. (6) rightly show that thegelation process is not allowed for concentrations of

10% and 15% for all the temperatures investigated.Otherwise, for higher concentrations, namely 20%and 22%, the gelation takes place, respectively, at22C and 18C, accordingly with rheological meas-urements, as reported by Grassi et al.14 It is worthnoting that rheological measurements in temperaturesweep are performed under nonequilibrium condi-tions (involving a heating rate), thus not allowingdiscernment thermodynamic from kinetic aspects.However the gelation temperatures obtained bydielectric spectroscopy nicely match with rheologicalmeasurements, as reported by Lau et al.9 and Grassiet al.14

Kinetics of gelation

It is worth noting that eqs. (2) and (6) are models ofa certain practical interest, since they allow us topredict the micellization and the gelation phenom-ena for F127 solutions as functions of concentrationand of temperature. They were tuned and thus theycan predict only equilibrium situations, i.e., theywere useful in descriptions of the thermodynamicsfor these systems. Very often, the real process inwhich the F127 solutions were used involves anheating step (to build up the soft gel) or a coolingstep (to liquefy the gel), during which the systemexperiences situation far from equilibrium. It has

Figure 7 The equilibrium degree of space filling as func-tion of temperature for F127 solutions at different concen-trations. The value of 52.3% (the horizontal line) identifiesthe gelation point. Symbols are experimental data; linesare model predictions. Open squares and dash-dotted line,C 10%; open upward triangles and dotted line, C 15%; open circles and dashed line, C 20%; open down-ward triangles and continuous line, C 22%.

Figure 6 The different dielectric constant values used inHanai analysis. The solution here is at 20% w/w of F127.Full squares, water; dashed line, water data linear fit; fullupward triangles, solution; dotted line, solution data linearfit; continuous line, sphere; continuous line and full dia-monds; medium.

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already been noted that the kinetics of micellizationdo not have a practical interest because once themicelles have been produced, the time delay in thesoft gel production can be fully ascribed to the gela-tion process. Thus, whereas the kinetics of micelliza-tion could be assumed to be too fast to be observedand thus is not useful to investigate, it is of great im-portance to quantify the kinetics of gelation.

To investigate the kinetics of gelation, the dielec-tric measurements were performed during con-trolled heating runs, recording the permittivity at2.45 GHz and the temperature evolution with time.The heating was accomplished by a water thermalbath, and thus only a limited range of temperaturesand of heating rates can be explored. The measure-ments were carried out only on F127 solutions withC 20%, and the results of two tests are reported inFigure 8. The temperature evolution can be read onthe left axis, whereas the permittivity evolution canbe read on the right axis. During the two tests, thesamples experiences practically the same thermalhistory, and since the permittivity measured is prac-tically the same, the reproducibility of the data wasassessed (only one example was reported, but theexperiments were carried out in triplicate for eachtest, giving similar results).

The thermal history experienced by the sampleduring an heating run obtained simply inserting thesample itself in a thermostatic bath can be describedby solving the lumped energy balance, obtaining:

Tt T1 T0 T1 exp ts

(7)

In eq. (7), the parameters are: the initial tempera-ture, T0; the asymptotic value, T1 (the bath tempera-ture); and the time constant, s. The heating rate isnot constant during this kind of test; however, tosimplify the forthcoming analysis, a single parameterable to describe how fast the sample was heatedduring a test is highly desirable. Differentiating eq.(7) it is straightforward to obtain the heating rate_T T T1=s, thus the heating rate is related tothe ratio T1/s, which can be taken as the single pa-rameter needed for the subsequent analysis.

In Figure 9, data of dielectric constant versus tem-perature, obtained from the same test 2 mentionedabove, were reported in the same kind of graph ofFigure 6, with the aim of performing the Hanai anal-ysis. The dielectric constants of the water and of themicelle were supposed to be independent of theheating rate. Thus, the application of Hanai equation(3) allowed us to get the evolution of the degree ofspace filling (i.e., / as function of the time). Sincethe thermal history is known, the data can be trans-lated to a function of temperature. In this way, thedegree of space filling during two heating runs arereported in Figure 10 as opened symbols. The opensquares were obtained during a low heating rate run(T1/s 0.397C/s) and the opened triangles duringfaster heating runs (T1/s 2.059C/s). In the samegraph, the equilibrium data for the 20% solutionwere reported as full symbols, along with the pre-diction of eq. (6) (the continuous line). It is worthnoting that the degree of space filling during a heat-ing run is lower than the value obtained at same

Figure 8 Temperature (on the left axis) and permittivity(on the right axis) evolutions with time during two heatingruns (tests no. 2 and 3), for a 20% w/w water solution ofF127. Full squares and continuous line, temperature fortest 2; full upward triangles and dashed line, temperaturefor test 3; open circles, dielectric constant test 2; opendownward triangles, dielectric constant test 3.

Figure 9 The data for Hanai analysis during heating of a20% w/w water solution of F127 (test no. 2). Full squares,water; dashed line, water data linear fit; open circles, solu-tion; dotted line, solution data linear fit; continuous line,sphere; dash-dotted line; medium.

694 BARBA ET AL.


temperature but under equilibrium conditions. Itmeans that the gelation phenomenon requires sometime to take place. Having in mind a biomedicalapplication that could require the injection into abody, a 20% solution of F127, which under thermalequilibrium gives a gel at 18C, can be kept in liquidphase also at higher temperature (e.g., during theinjection, if the heating rate is high enough). The laststep, to obtain a fulleven if empiricalmodel formicellization and gelation, is to write a mathematicaltool able to predict the kinetics of gelation. A poten-tial model is the following:

/Tt;C /eqT;Cf Tt

with f Tt 1 exp Ttb1T1=sb2

" #(8)

In eq. (8), the equilibrium value for the degree ofspace filling, / eq, was obtained by eq. (6), and thefunction f(T(t)) was built in analogy to the Avramiequation, commonly used to describe the nucleationand growth kinetics of crystalline solids. The twoparameters of the model, b1 and b2, must be esti-mated by comparison with experimental data. Equa-tion (8) best-fitting values are reported in Figure 10as dashed and dotted lines, and from the tuningprocedure the values b1 19 and b2 0.17 wereobtained.

In conclusion, eqs. (2), (6), and (8) allow descrip-tion of the thermodynamics of micellization and ge-lation and the kinetics of gelation for water solutionsof F127.

CONCLUSIONS

In this work, the thermal behavior of Pluronic F127water solutions was investigated by calorimetry anddielectric spectroscopy. The micellization phenom-enon was observed by DSC analysis, successfullycompared with literature data, and its thermodynam-ics was properly quantified. The gelation phenomena,scarcely noticeable during calorimetric tests, wereinvestigated by dielectric spectroscopy, both underequilibrium and nonequilibrium conditions. The equi-librium data allowed the quantification of the thermo-dynamics of gelation, whereas the nonequilibriumdata were used to quantify the kinetics of gelation. Allthe data observed were also described on the basis ofempirical models.

The knowledge of thermodynamics and kinetics ofphase change for these systems constitutes a power-ful tool for designing and for managing biomedicalapplications of the pluronic water solutions. Indeed,by using the models proposed in this work, one canpredict how fastand to what extenta solution ofF127, initially cold and liquid, can give the gel whensubjected to heating (the heating being due to thecontact with the body).

Furthermore, the methods adopted in this workcould be used to study the behavior of differentpluronic water solutions or of more complex systems(e.g., solutions of F127 carrying a drug or differentmolecules).

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14. Grassi, G.; Crevatin, A.; Farra, R.; Guarnieri, G.; Pascotto, A.;Rehimers, B.; Lapasin, R.; Grassi, M. J Colloid Interface Sci2006, 301, 282.

Figure 10 The nonequilibrium degree of space filling for a20% w/w water solution of F127, compared with the equilib-rium data. Horizontal dash-line identifies the 52.3% value.

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Barba et al JAPS 114(2) 688-695 (2009)