Broad frequency range dielectric spectroscopy ofaqueous suspensions of phospholipid vesicles

M�oonica Tirado a,*, Constantino Grosse a,b, Wilfried Schrader c, Udo Kaatze c

a Departamento de F�ıısica, Universidad Nacional de Tucum�aan, Av. Independencia 1800, 4000 San Miguel de Tucum�aan, Argentinab Consejo Nacional de Investigaciones Cient�ııficas y T�eecnicas, Buenos Aires, Argentina

c Drittes Physikalisches Institut, Universit€aat G€oottingen, Gottingen, Germany

Abstract

The dielectric properties of aqueous suspensions of unilamelar phospholipid vesicles were measured over a broad

frequency range extending from 1 kHz to 1 GHz. The low-frequency measurements (1 kHz to 10 MHz) were performed

at Tucum�aan using a HP 4192 A Impedance Analyzer with a variable spacing cell and Short-Open-Load calibration. The

high-frequency spectra (1 MHz to 1 GHz) were obtained at G€oottingen using a HP 8753 A Network Analyzer with a

reflection cut-off measuring cell. The vesicles were prepared using different concentration mixtures of non-ionic and

ionic phospholipids: 1,2 Dimyristoyl-sn-Glycero-3 Phosphocholine and L-a-Phosphatidyl-DL-Glycerol-Dimyristoyl

(Na-Salt). Their mean diameter had the value of 116 nm, obtained by means of multiple extrusions. They were sus-

pended in either tridistilled water or an aqueous NaCl solution. The dielectric spectra were described and interpreted

using existing theoretical models (for the counterion polarization and the membrane charging together with the

Maxwell–Wagner dispersion processes) with the f potential as the only adjustable parameter. � 2002 Elsevier Science

B.V. All rights reserved.

PACS: 77.22.)d; 77.22.Ch; 77.22.Gm; 77.84.Nh

1. Introduction

Phospholipids constitute one of the main com-ponents of biological membranes. When suspendedin water, they form stable structures of doublelayered membranes that under appropriate condi-tions, take the shape of spherical vesicles. Thesestructures are often used in Medicine as micro-capsules for medication transport and in Chemistryas analytical microreactors, for example.

They also constitute the simplest model systemfor biological cells. The similarity can be furtherextended using mixtures of non-ionic and ionicphospholipids. The membrane acquires then a sur-face charge that attracts counterions from the bulkelectrolyte solution leading to the appearance of asurface conductivity.

In this work we investigate the dielectric prop-erties of aqueous suspensions of unilamelar phosp-holipid vesicles at frequencies between 1 kHz and1 GHz. The unilamellar vesicles with a mean di-ameter of 116 nm were prepared using differentconcentrations of non-ionic and ionic phospholi-pids and suspended in either tridistilled water or

Journal of Non-Crystalline Solids 305 (2002) 373–378

www.elsevier.com/locate/jnoncrysol

* Corresponding author. Tel.: +54-381 436 4093x218.

E-mail address: mtirado@herrera.unt.edu.ar (M. Tirado).

0022-3093/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0022-3093 (02 )01132-8

an aqueous NaCl solution. The dielectric spectraobtained were described and interpreted using ex-isting theoretical models with a single adjustableparameter: the f potential.

2. Materials and methods

The vesicles were prepared using mixtures ofnon-ionic and ionic phospholipids: 1,2 Dimyri-stoyl-sn-Glycero-3 Phosphocholine, from AvantiPolar-Lipids Inc., (DMPC) and L-a-Phosphatidyl-DL-Glycerol-Dimyristoyl (Na-Salt), from Sigma-Aldrich, (DMPG), respectively. The relativeconcentrations of DMPC/DMPG were: 8:2, 6:4,4:6, and 2:8.

The phospholipids were dissolved in chloro-form and dried under reduced pressure. The filmwas hydrated in the proportion: 1 ml solvent each2.5 mg of phospholipids, using tridistilled water oran aqueous NaCl solution (0.051 wt%). The mix-tures were submitted to five freeze-thaw processes.This involved freezing the solutions by immersioninto liquid nitrogen, followed by immersion into 35�C water, and a thorough vortexing. The resultingvesicle dispersions were extruded using a stain-less steel extruder with a 47 mm, 50/pk, PolyesterDrain Disc and a 47 mm, 100 nm, PolycarbonateMembrane (both from Poretics Corporation), re-peating the process 20 times at 35 �C and undera pressure of 2 bars. This procedure assures theformation of unilamellar vesicles [1]. Their averageradius, measured using quasi-elastic light scatter-ing, was of 58 nm with a standard deviation of 19nm [2].

The dielectric properties of the suspensionswere measured at 25� 0:1 �C in a broad frequencyrange extending from 1 kHz to 1 GHz, com-bining the capabilities of two laboratories: Tu-cum�aan, Argentina (TUC) andG€oottingen, Germany(GOE). The low-frequency measurements: 1 kHzto 10 MHz (TUC), were performed with a HP4192 A Impedance Analyzer using a cell withparallel platinum black electrodes, variable spac-ing, and Short-Open-Load calibration [3]. Thehigh-frequency spectra: 1MHz to 1 GHz (GOE),were obtained using a HP 8753 A Network Ana-lyzer with a reflection cut-off measuring cell [4].

These measurements were complemented withdeterminations of the low-frequency conductivity,using an Orion 160 Conductivity Meter with afour electrode cell and of the pH, using a Perp-HecT model 370 meter.

3. Experimental results

Examples of the relative permittivity e0 xð Þ=e0spectra appear in Figs. 1 and 2 that show a gen-erally excellent overlap of the low- and high-fre-quency data around 10 MHz.

The spectra show a strong permittivity in-crease at low frequencies that corresponds toan alpha dispersion at around 1 kHz. The vari-able spacing technique [5] combined with aShort-Open-Load calibration, performed at all themeasurement frequencies using a load impedancevalue close to that of the sample [3,6], assures thatthis increase is not due to an electrode polarizationartifact.

Furthermore, a second dispersion region existsat around 100 kHz. This can be shown by pur-posely neglecting the contribution of the electrodeimpedance and calculating the ‘permittivity’ frommeasurements made at any single cell spacing. Aplot of the derivative of the real part of this ‘per-mittivity’ with respect to the logarithm of the fre-quency [7] is presented in Fig. 3. The straight line

Fig. 1. Relative permittivity of the DMPC/DMPG 6:4 vesicle

suspension: (�) TUC experimental values, (�) GOE experi-

mental values, (––) fitted values.

374 M. Tirado et al. / Journal of Non-Crystalline Solids 305 (2002) 373–378

at low-frequencies corresponds to the electrodepolarization impedance, while the maximum athigh-frequencies clearly shows the presence of adielectric dispersion. The alpha dispersion can notbe seen in Fig. 3 because, at frequencies of theorder of 1 kHz and lower, the contribution ofthe electrode reactance to the total reactance ofthe cell is greater than the contribution of thesample.

4. Theoretical interpretation

In view of the observed characteristic frequencyvalues, the experimental data were interpreted con-sidering a superposition of the alpha (counterionpolarization) dispersion and a combination of thebeta (membrane charging) and delta (Maxwell–Wagner) relaxations. The expression for e0ðxÞ wasfitted to the experimental data using the followinganalytical expression [8–11]:

e0 xð Þ ¼Dea 1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffixsa=S

p� �1þ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffixsa=S

p1þ xsað Þ þ 2xsa=S þ xsað Þ2

þDeabd

1þ xsabd

� �2þ

Debbd

1þ xsbbd

� �2þ e1:

The parameters appearing in the right-hand side ofthis equation are determined by the following ex-pressions [11,12], where v is the volume fractionoccupied by the vesicles, a is their radius, and thelower index ‘e’ corresponds to the electrolyte so-lution.

4.1. Alpha dispersion

Dea ¼ 9vee16

v2a2 Rþ Rð Þ2S2

Rþ 2ð Þ2;

sa ¼ Sa2 Dþ þ Dð Þ

4DþD ;

v ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2re

Dþ þ Dð Þee

s;

R� ¼ 4

vaexp

�� ef

2kT

� 1

�1�

þ 3m�� 6m�ef

vakT;

m� ¼ 2ee3gD�

kTe

� �2

;

R ¼ DþRþ

Dþ þ D þ DR

Dþ þ D ;

Fig. 2. As in Fig. 1 but for DMPC/DMPG 2:8þNaCl vesicle

suspension.

Fig. 3. Derivative of the relative permittivity (calculated at a

fixed 4.5 mm electrode spacing without any correction for

electrode polarization) with respect of the logarithm of the

angular frequency for the DMPC/DMPG 2:8 vesicle suspen-

sion.

M. Tirado et al. / Journal of Non-Crystalline Solids 305 (2002) 373–378 375

S ¼2 Rþ2ð Þ

Rþþ2ð Þ Rþ2ð Þ

1 P Rþ2Rþþ2ð Þ Rþ2ð Þ

;

P ¼ Dþ þ D

2DþD48D�m�

valn cosh

ef4kT

� � �;

where D� are the diffusion coefficients of counte-rions and co-ions, f is the zeta potential, and g isthe viscosity. The electrolyte solution conductivityre and absolute permittivity ee are considered to befrequency independent in view of the frequencyrange used in this work.

4.2. Beta and delta relaxations

Dea;bbd ¼

em ah e2e

2ka þ 2re

� 3eer2

e sa;bbd

h i e2e

2ka re

� 2sa;bbd sc

� �3ee 2k

a þ 2re

� 2sb;abd sa;bbd

� � ;

sa;bbd ¼þ;

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisc þ sl þ shð Þ2 4scsh

qþ sc þ sl þ sh

2;

where k ¼ areR=2 is the surface conductivity, and

sc ¼ema=h

re

; sl ¼ema=h

2k=aþ 2re

;

sh ¼ev1 þ 2ee2k=aþ 2re

;

the lower index ‘m’ corresponds to the membrane,and h is its thickness.

Both dispersion regions could be described withthe above expressions and fitted using a singleadjustable parameter: the f potential. The valuesof the constants used in the calculations are:ee ¼ 78:36e0, em ¼ 6e0, h ¼ 3� 109 m [13], andg ¼ 8:8� 104 Nts=m2. The values of re were de-termined from the measured low-frequency con-ductivities of the suspensions r 0ð Þ by means of [11]

Table 1

Measured, fitted, and calculated values for the five studied vesicle suspensions. Also included are the characteristic parameters cor-

responding to the three dispersion processes, calculated using the equations appearing in the text, and other parameters discussed in the

text

DMPC/DMPG 8:2 6:4 4:6 2:8 2:8þNaCl

Measured values

r 0ð Þ (S/m) 0.00302 0.00389 0.00451 0.00751 0.110

pH 6.84 6.58 7.19 7.31 6.60

Fitted values

f (mV) 60 60 60 60 38

Calculated values

re (S/m) 0.0030 0.0039 0.0045 0.0075 0.11

v 0.018 0.017 0.016 0.011 0.019

va 7.0 8.0 8.6 11 43

k (S) 2.4E-10 2.8E-10 3.0E-10 3.8E-10 5.9E-09

Dispersion parameters

Dea=e0 89 110 120 140 300

sa (ls) 38 41 43 51 1.9

Deabd=e0 0.77 0.89 0.96 1.2 1.2

sabd (ls) 0.77 0.60 0.52 0.32 0.022

Debbd=e0 0.96 0.83 0.76 0.55 0.59

sbbd (ls) 0.13 0.11 0.094 0.062 0.0041

Other parameters

qrDH (103 C/m2) 4.4 5.0 5.3 6.7 15

qrflat (10

3 C/m2) 4.8 5.4 5.9 7.6 16

Dea= e0vð Þ 4900 6600 7800 13 000 16 000

Deabd= e0vð Þ 42 52 62 110 61

Debbd= e0vð Þ 53 49 49 50 31

2k= areð Þ 2.3 2.0 1.9 1.4 1.5

376 M. Tirado et al. / Journal of Non-Crystalline Solids 305 (2002) 373–378

The limiting high-frequency permittivities of thesuspensions were calculated using the Maxwellmixture formula [11]:

e1 ¼ ee 1

�þ 3v

ev1 eeev1 þ 2ee

�;

ev1 ¼ em3ee 2 1 a hð Þ3=a3

h iee emð Þ

3em þ 1 a hð Þ3=a3

h iee emð Þ

8<:

9=;;

where the lower index ‘v’ corresponds to the vesi-cles.

The volume fractions of vesicles v were deter-mined from the weights and densities of the com-ponents of the suspensions: DMPC, DMPG, andwater (or NaCl solution). The fraction of freeDMPG molecules in the electrolyte solution wascalculated from the change of its conductivityvalue: re minus the conductivity of tridistilledwater (or NaCl solution).

All the calculations were performed taking intoaccount the size distribution of the vesicles. Thesuspensions were considered as being made ofvesicles having nine different sizes with radii andnumber fractions determined by the experimen-tally obtained histogram.

The measured, fitted, and calculated parametersappear in Table 1. Examples of the fitted curves areshown in Figs. 1 and 2, together with the experi-mental data. The characteristic frequency of the adispersion is much lower than usual for particles ofthis size, because of the very small co-ion mobility(D ¼ 1� 1011 m2/s) [14]. This behavior was notobserved for the DMPC/DMPG 2:8+NaCl system,since the mobilities of Cl (2� 109 m2/s) and Naþ

(1� 109 m2/s) are comparable.

5. Conclusion

The dielectric properties of suspensions of uni-lamellar vesicles made with different proportions

of DMPC and DMPG were investigated in abroad frequency range.

There is no single theoretical model for thiskind of systems that embraces the whole range offrequencies considered in this study. Therefore,numerical calculations are needed to provide aquantitative interpretation. However, the repre-sentation used in this work: a superposition of thealpha dispersion and a combination of the betaand delta relaxations, is able to provide a reason-able fit to the experimental data using a singleadjustable parameter: the f potential.

The value obtained for this parameter is of theorder of 60 mV for vesicles suspended in tridis-tilled water and decreases to 38 mV for vesiclesin NaCl solution. Qualitatively this change is ex-pected in view of the increased conductivity of thislast suspending medium. The fit of the theoreticalvalues to the experimental data was not sufficientto determine meaningful variations of the f po-tential values for different DMPC/DMPG weightfractions. While an increase of the f potential withthe fraction of the ionic component could be ex-pected, this increment appears to be compensatedfor by the increase of the conductivity re, which isdue to the increasing concentration of free DMPGmolecules and their corresponding counterions inthe suspending medium.

No analytical expression exists for the surfacecharge qr of suspended particles as a function of thef potential, in the general case. Nevertheless, forlow values of f, the Debye-H€uuckel approximation:

qrDH ¼ eef 1ð þ vaÞ=a

can be used while, for large values of va, thesurface charge coincides with the solution corre-sponding to a flat interface:

qrflat ¼

2vkT eee

sinhef2kT

� �:

Surface charge values calculated using these lim-iting expressions appear in Table 1. They are quite

re ¼r 0ð Þ

1þ 3vDþ

Dþ þ DRþ 1

Rþ þ 2þ D

Dþ þ DR 1

R þ 2 3PSDþD

2 Dþ þ Dð Þ2Rþ Rð Þ2

Rþ 2ð Þ Rþ þ 2ð Þ R þ 2ð Þ

" # :

M. Tirado et al. / Journal of Non-Crystalline Solids 305 (2002) 373–378 377

close to one another and both show an increase ofqr with increasing fraction of the ionic componentDMPG.

The alpha dispersion amplitude per unit volumefraction Dea=v increases with the DMPG fraction,as expected, in view of the corresponding increaseof the electrolyte solution conductivity re that leadsto an increment of the product va. The charac-teristic time of this dispersion remains approxi-mately constant (constant values of the particleradius and ion diffusion coefficients) with a slightincrease that is only due to the inclusion of theparameter S in the definition of sa [15].

An individual interpretation of the beta anddelta relaxation parameters is not possible sincetheir relaxation times are so close of one another.Nevertheless, it can be seen that the relaxationamplitude per unit volume fraction Deabd=v in-creases with the DMPG fraction, despite the cor-responding increase of the surface conductivity.This happens because the equivalent particle con-ductivity relative to the conductivity of the elec-trolyte solution 2k= areð Þ decreases, diminishingthe shielding of the membrane. Both relaxationtimes sabd and sbbd decrease with the DMPG fractiondue to the corresponding increase of the electrolytesolution conductivity.

Acknowledgements

The authors gratefully acknowledge the finan-cial support provided by the Ministry of Science,

Culture & Sport of the State of Israel, the Tel-AvivUniversity, and the organizers of the DS 2001International Conference.

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