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Interfacial characterization of mesoscopic particle suspensions by means of radiowave dielectric spectroscopy: a minireview
Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
Interfacial characterization of mesoscopic particle suspensions by means of radiowave dielectric spectroscopy: a minireview A. Bonincontroa,b,∗ , C. Camettia,b b
a Dipartimento di Fisica, Universita’ di Roma "La Sapienza", Rome, Italy Istituto Nazionale per la Fisica della Materia (INFM-CRS SOFT), Unita’ di Roma1, Italy
Received 21 October 2003; accepted 27 February 2004 Available online 17 September 2004 Dedicated to the memory of B. Sesta.
Abstract Heterogeneous systems, in particular aqueous suspensions of colloidal particles, are very complex systems characterized by a variety of dynamic processes, occurring at different length and time scales, that involve, in a very intruing manner, the structural properties of both the dispersed particles and the disperding medium. Over the last three decades, knowledge of the behavior of such systems has taken greatly advantage by dielectric spectroscopy techniques. This is due to the rapid growth of the technology that makes possible, both in the frequency domain and in the time domain, to acquire dielectric spectra in a very huge frequency interval, typically from 10−5 to 109 Hz, or, correspondly, in the time interval from 104 s to 10 ps. In this paper, we will consider several typical colloidal systems, such as aqueous liposome suspensions, ionic and non-ionic micellar solutions, biological cell suspensions. We will describe how dielectric spectroscopy technique can be employed to obtain information concerning the different electrical polarization mechanisms occurring at different time scales and the way to evaluate the structural parameters governing the mesoscopic behavior of these complex systems. © 2004 Elsevier B.V. All rights reserved. Keywords: Mesoscopic particle suspension; Radiowave dielectric spectroscopy
1. Introduction Bianca Sesta introduced us more than 20 years ago to the field of aqueous surfactant solutions and we are very pleased to be asked to write a short review on this subject for this memorial issue. In particular, our contribution concerns the characterization of the electrical interfacial properties of heterogeneous mesoscopic systems by means of frequency domain dielectric spectroscopy technique. Over the last three decades, knowledge of the behavior of colloidal particle suspensions has taken greatly advantage from dielectric spectroscopy measurements since this technique can investigate the relaxation processes in an extremely wide range of characteristic times, ranging from 104 to 10−11 s [1–4]. This peculiarity allows us to investigate both the structural properties ∗
Corresponding author. Fax.: +39 06 4463 158. E-mail address: [email protected] (A. Bonincontro).
0927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2004.02.033
of the colloidal particles and the alteration they induce on the aqueous phase. Moreover, using different frequency ranges, it is generally possible to separate the different contributions causing electrical polarizations in the system. From a macroscopic point of view, the complex dielectric constant ∗ (ω) of a medium is defined through the linear relationship J = iω0 ∗ (ω)E between the volume averaged current density J 1 J = J (r ) dV V
(1)
(2)
V
and the external applied electric field E 1 =− E ∇φ(r ) dV V V
(3)
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A. Bonincontro, C. Cametti / Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
where φ(r ) is the electrical potential at position r , V is a sufficiently large system volume and 0 is the dielectric constant of free space. ω is the angular frequency of the applied field. In general, the dielectric constant ∗ (ω) of a heterogeneous system is expressed by a general relation involving the dielectric constants ∗i (ω) for constituents i and parameters characteristic for their constituent proportions, for instance the volume fractions Φi ( N i=1 Φi = 1) ∗ (ω) = f (∗i (ω), Φi )
(4)
The function f must fulfill adequate analytical conditions and must depend on all the physical interactions occurring among the various components of the system, besides the geometry of the constituents. The functional dependence of the function f is obtained by solving the general equations of electromagnetism, specialized to the system under investigation. In the absence of source densities localized inside the and the electrical displacement system, the electric field E ∗ D = 0 (ω)E satisfy the equations =0 curl(E)
(5)
=0 div(D)
(6)
Eqs. (5) and (6) are valid throughout the bulk of each medium characterized by the appropriate values of the complex dielectric constant ∗ (ω). In the case of heterogeneous medium, whose structure is formed by various interconnected adjacent media, Eqs. (5) and (6) must be completed by analogous surface equations stating the conservation of the tangential component of the electric field (the thermodynamic force, in the context of irreversible processes) and of the normal component of the displacement (the flux) at any interface [5]. In general, the problem of solving Eqs. (5) and (6) is a formidable one and only in a limited number of simple cases, an exact solution can be obtained. Nevertheless, in the most cases of practical interest, approximate solutions have been developed and the heterogeneous system can be appropriately described in the light of effective medium theory. In what follows, we will consider several heterogeneous systems and we will describe how dielectric spectroscopy technique over an appropriate frequency range can be utilized to investigate complex systems in order to obtain information at molecular level about their mesoscale structure.
2. Ionic and non-ionic micelle solutions Aqueous micellar solutions are formed by the selfassembly of surfactant molecules into aggregates, which first appear at the critical micelle concentration (c.m.c.), with minimal contact between the hydrocarbon chains and water. Micellar solutions are often regarded as a two-phase mixture, an approximation that can be very useful in dielectric measurements, where different regions are characterized by different dielectric properties (permittivity and electrical conductivity).
In the high-frequency region, at frequencies above 500 MHz or more, the dielectric spectra of surfactant selfassembled structures are mainly due to the orientational polarization mechanisms of the aqueous phase and to their modification induced by the interactions with the solute. This approach is particularly useful to investigate the dielectric properties of the interfacial water (hydration water) in aqueous micellar solutions, where the ionic character of the hydrophilic groups of the surfactants induces a strong correlation in the surface organization of the water molecules adjacent to the interface. As an example, we report an investigation on concentrated sodium deoxycholate [NaDOC] solutions at different temperatures in the interval from 10 to 50 ◦ C [6]. This surfactant forms spherical micelles at concentrations above the c.m.c. (about 10 mM, at room temperature). The dielectric data collected at the frequency of 10 GHz were analyzed in terms of a very simple mixture equation, considering a two-phase system (a surfactant domain with volume fraction Φ and a water domain with volume fraction (1 − Φ)), where the aqueous domain is characterized by the overlapping of two contributions, the one associated to the bulk water and the one associated to the interfacial water. Both these two contributions are weighed with their respective volume fractions. Within this simple scheme, the complex dielectric constant (ω) of the whole system is given by
w (1 − q) h q (ω) = (1 − Φ) + 1 + iωτw 1 + iωpτw
+ Φp
(7)
where w , h and τw , τh are the dielectric increments and the relaxation times of the bulk and interfacial water, respectively, p is the permittivity of the dispersed phase and q is the volume fraction of the hydration water. The parameter p = τh /τw takes into account the shift of the relaxation time of the hydration water with respect to the bulk water. Under the hypothesis that the static permittivity of bulk and interfacial water are similar, a non-linear least-squared minimization yields the behvior of q as a function of temperature and concentration. A typical result of this analysis is shown in Fig. 1, where q is plotted as a function of the concentration C of the surfactant at two selected temperatures. The results show, superimposed to a regular increase on the concentration, a marked change (more evident at lower temperature) around 0.2–0.3 M, suggesting, at these concentrations, a reorganization, in a more structured arrangement, of the micellar component. It is worth noting that a similar change also occurs in the reduced viscosity of the solution, in the same concentration range [6]. Moreover, on the basis of a similar analysis, the influence of the ionic strength on the hydration number, i.e., a measurement of the amount of the hydration water, has been investigated [7]. For example, we observed an increase of the hydration number from 30 to 50 as the concentration of the added salt (in this case NaBr) is increased from 0.1 to 0.4 M. This increase is in agreement with the formation of aggre-
A. Bonincontro, C. Cametti / Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
Fig. 1. The fraction q of modified water deduced from dielectric measurements at the frequency of 10 GHz in NaDOC aqueous solutions as a function of concentration C, at two different temperatures (T = 15 and 45 ◦ C)
Also in this case, the influence of the hydration water can be investigated by means of microwave dielectric measurements. In the system under investigation, because of to the high value of the NPEG concentration, the whole water present in the system is affected by the solute and its structure undergoes a long-range molecular order. A typical dielectric spectrum in the temperature range from −20 to 50 ◦ C is shown in Fig. 3, for the two different (hexagonal and lamellar) structures. It must be noted the absence of a discontinuity of the liquid water–ice phase transition at 0 ◦ C. This peculiarity evidentiates that, in this case, the water molecules are completely affected by the solute. Under the above approximation, the dielectric behaviour of the lyotropic mixture can be described by the equation (∗ )1/2 = (1 − Φ)(∗w )1/2 + Φ(∗p )1/2
gations above the primary c.m.c., favoured by the presence of interfacial water, able to promote a steric arrangement of micelles to form superaggregates. Non-ionic surfactants are able to organize, at sufficiently high concentration, a variety of arrangements that span from the hexagonal to the lamellar phase, whose stability depends on the hydrophilic–lipophilic balance and on the hydration processes. Both these two characteristics may be investigated by means of dielectric spectroscopy at appropriate frequencies. For example, in the case of aqueous mixture of pnonylphenol-decaoxyethylene glycol [NPEG] [8], radiowave dielectric measurements evidence a structural transition from a hexagonal mesophase to a direct micelle solution as the temperature increases. This transition is clearly shown in Fig. 2, where the permittivity abruptly changes in value at the temperature of about 30 ◦ C. Also, the activation energy deduced from an Arrhenius plot shows a change from 1.5 to 2.0 kcal/mol close to the above transition.
Fig. 2. The low-frequency permittivity of NPEG–water mixture as a function of temperature. (A) (◦) Hexagonal mesophase; (B) (•) lamellar mesophase.
117
(8)
where ∗p and ∗w are the complex dielectric constant of the dispersed phase and the hydration water, respectively, and Φ the volume fraction of the dispersed phase. If the hydration water has a Debye-type relaxation, Eq. (8) allows the relaxation time to be evaluated. At room temperature, we find a relaxation time of 2–3 × 10−11 s, i.e., three-four times larger than that of bulk water. In the case of non-ionic surfactants, radiowave dielectric investigation can help in the evaluation of the surface charac-
Fig. 3. (A) The high-frequency permittivity of NPEG aqueous solution as a function of temperature in two different phases: () hexagonal mesophase, 49% (w/w) sample; (◦) lamellar mesophase, 69% (w/w) sample. (B) The high-frequency dielectric loss of NPEG aqueous solution as a function of temperature in two different phases: () hexagonal mesophase, 49% (w/w) sample; (◦) lamellar mesophase, 69% (w/w) sample.
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terization of the micellar system and in particular in discriminating between different structures resulting in interactions with aminoacids. It is well known that many aminoacids, such as glycine, show an appreciable influence on the thermodynamic stability of surfactant aggregates. In order to ascertain if glycine directly interacts with the polar head region of micellar aggregates, a typical example is the dielectric behavior of octyl -d-glucopyranoside [OBG] micelles in water and in water–glycine solutions [9]. By taking advantage of the frequency independent behavior of the permittivity of OBG–glycine solutions in the frequency range 107 –108 Hz, it is possible to separate the contributions due to the Maxwell–Wagner effect at lower frequencies and the one due to the solvent phase at higher frequencies. Consequently, we are able to use a simple mixture equation such as, for example, the Polder and Van Santen equation [10] and to evaluate the dielectric properties of the dispersed phase. In particular, the problem we are considering is to distinguish between a direct interaction of OBG and glycine, yielding to the formation of so-called “dressed micelles”, or a modification in the micellar aggregation due to the properties of the mixed solvent (water–glycine solution). The analysis carried out on the basis of an iterative use of the Polder and Van Santen mixture equation, allows us to calculate the permittivity of the micelle polar region. We obtain a value of the permittivity lower than that of a glucose–glycine– water solution at the same concentration ratio that should mimic the composition of the OBG head group region, if glycine interacts with the micellar crown. This finding rules out the presence of glycine in the crown region of the micelles, giving support to the hypothesis that the aggregation properties of the micelles are modulated through the solvent. We want to stress that, in this case, the overall permittivity of the system can be appropriately deconvoluted and the properties of the interfacial region, under reasonable assumptions, evidentiated. Other thermodynamic investigations (such as osmotic pressure, surface tension and so on) would require much heavier approximations and should present a lower capability in evidencing the different contributions of the various components of the system.
tant in a variety of biological phenomena, such as for example cell–cell adhesion or signal transduction. These systems are characterized by the existence of a temperature-dependent transition in which the hydrocarbon chains undergo a reorganization from an ordered crystallinelike state to a disordered fluid-like state. In the case of DPPC, near the room temperature and at high water content, a rippled phase occurs, characterized by a in-plane modulation of the bilayer, in the temperature interval between the pre-transition and the main-transition temperature [11]. This change in the molecular arrangement of the hydrophobic region of the lipid bilayer induced by temperature is manifested by the rapid increase in the dielectric increment as the temperature approaches both the pre-transition and the main-transition temperature. Fig. 4 shows typical dielectric spectra of an aqueous suspension of DPPC liposomes in the radiowave frequency range at different temperatures, from 5 to 50 ◦ C [12]. Once the dielectric spectra have been corrected by the electrode polarization effect (the anomalous increase of the permittivity in the low-frequency tail of the frequency interval investigated in Fig. 4), the resulting dielectric dispersions are well described by a Cole–Cole relaxation function, whose parameters, especially the dielectric increment and the average relaxation time τ, strongly depend on the lipid bilayer structure. As an example, the inset in Fig. 4 shows the dielectric increment as a function of temperature, inbetween the pre-transition and the main-transition temperature and above the main-transition temperature. As can be seen, an abrupt change occurs, exactly at the temperatures at which the system undergoes a structural transition.
3. Aqueous liposome suspensions Liposomes, vesicles whose typical sizes range from 20 nm to several microns in diameter, are closed shells of self-assembled lipid bilayers that encompasse an aqueous core. Aqueous suspensions of phospholipids have been investigated by dielectric relaxation to determine macroscopic properties such as the permittivity of the lipid membrane and to obtain information about the microscopic parameters of the dynamics of the zwitterionic head groups in the polar region of the bilayer. The knowledge of the dielectric properties of the membrane–water interfacial region is particularly impor-
Fig. 4. The permittivity of liposome aqueous suspension as a function of frequency at some selected temperatures from 6 to 46 ◦ C, in 2 ◦ C step (from bottom to top). The spectra show a marked electrode polarization effect in the low-tail of the frequency range investigated. Once corrected for this effect, the data show a dielectric dispersion whose dielectric increment depends markedly on the temperature (see inset, the two vertical arrows mark the interval between the pre-transition and the main-transition temperature of DPPC hydrocarbonic tails).
A. Bonincontro, C. Cametti / Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
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4. Biological cell suspensions In the field of biological systems, a particular relevance assume biological cell suspensions that, from a mesoscopic point of view, behave as a heterogeneous system where interfacial effects are pronounced. A biological cell can be represented as a vesicle that separates an intracellular medium, whose biological structure is very complex, from an extracellular medium that, to a first approximation, can be considered as an electrolyte solution of appropriate ionic strength. The presence of the membrane, whose electrical parameters deeply differ from those of the adjacent media, produces a very strong dielectric dispersion that generally occurs at radiowave frequencies. At these frequencies, the dielectric response of the whole system is practically due only to the membrane region between the extracellular medium and the cytosol. The typical shape of a dielectric spectrum is composed by different dispersions located at different frequency ranges, the lower one being attributed to the electrode polarization effect [13], the intermediate one to the presence of the membrane and, finally, the one at higher frequencies to the bulk properties of the aqueous phase. In this case too, as we have above stated in the other systems we described, the approach based on the effective medium theory describes the macroscopic dielectric behavior of the system in terms of an appropriate mixture equation of the form f (∗eff (ω), ∗m (ω), ∗si (ω), Φi ) = 0
(9)
where ∗eff (ω) and ∗m (ω) are the complex dielectric constant of the effective medium and host medium, respectively, ∗si (ω) is the corresponding quantity of the inclusion media and Φi their volume fractions. Eq. (9) allows the dielectric and conductometric properties of the cell membrane to be evaluated. Particular functional dependences of the mixture equations take into account also the geometrical shape of the biological cell, so that the method is not confined to spherical objects. We have applied this technique to a wide variety of biological cell suspensions, ranging from human erythrocytes to lymphocytes and stabilized normal and tumoral cell lines [14–17]. As an example, we are showing here the permittivity and the electrical conductivity of human erythrocyte cells deduced from radiowave dielectric spectroscopy measurements in the frequency range from 1 kHz to 2 GHz (Fig. 5). The large dielectric dispersion both in the permittivity and in the electrical conductivity results in a membrane permittivity of the order of s = 2.5 and a membrane conductivity of about σs = 5 × 10−5 mho/m. These values account for the hydrophobic region of the membrane double layer and for the ionic and/or polar character of the interface. A comparison between different mixture equations has been discussed recently elsewhere [18] This circumstance favours the observation of possible alterations both in the structural and in the functional aspects
Fig. 5. Radiowave dielectric spectra of an erythrocyte suspension (hematocrit Φ = 0.15, temperature T = 25 ◦ C) as a function of frequency. (A) The permittivity ; (B) the electrical conductivity σ. The interface polarization due to the presence of the cell membrane results in a dielectric and conductometric dispersion located between the electrode polarization effect, in the low-frequency tail, and in the aqueous phase orientational dispersion, in the high-frequency tail. The full lines represent the calculated values of the permittivity and the electrical conductivity σ according to the heterogeneous system effective medium theory. In the inset, the dielectric loss , having substracted the contribution due to the ionic losses, is shown.
induced by different physico-chemical agents such as, for example, ionizing radiation, ionic environment of the extracellular medium, action exerted by drugs, besides other biological or chemical agents. All these effects have been shown by means of dielectric spectroscopy measurements and they represent a particular exciting example of the effectiveness of this method. In particular, we want to stress how this approach can be useful in the investigation of the structural alteration of erythrocyte cells induced by anthracyclinic antibiotics (adriamycin, daunorubicin, 4 -epiadriamycin) [19] that substantially modify the molecular architecture of the plasma membrane by their incorporation within the lipid bilayer. Although dielectric technique probes the whole system and consequently only an average response is obtained, the dielectric model on one side and the experimental accuracy on the other side are sufficient to extract information on the particular polarization mechanism we are looking at. Biological cell suspensions are an appropriate example of this feature, since dielectric behavior of the cell membrane can be isolated from contiguous dispersions due to different mechanisms.
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References [1] K. Asami, Characterization of heterogeneous systems by dielectric spectroscopy, Prog. Polym. Sci. 27 (2002) 1617–1659. [2] Y. Feldman, T. Skodvin, J. Sjoblom, Dielectric spectroscopy on emulsion and related colloidal system: a review, in: J. Sjoblom (Ed.), Encyclopedia Handbook of Emulsion Technology, Marcel Dekker, New York, 2000. [3] R. Pethig, Dielectric and Electronic Properties of Biological Materials, Wiley, New York, 1979. [4] K.R. Foster, H.P. Schwan, Dielectric properties of tissues and biological materials: a critical review, Crit. Rev. Biomed. Eng. 17 (1989) 25–104. [5] M. Clausse, Dielectric properties of emulsions and related systems, in: P. Becher (Ed.), Encyclopedia of Emulsion Technology: Basic Theory, Marcel Dekker, New York, 1993. [6] B. Sesta, C. La Mesa, A. Bonincontro, C. Cametti, A. Di Biasio, Molecular aggregation of sodium deoxycholate in water and water–urea mixtures: a multistep process, Ber. Bunsen-Ges. Phys. Chem. 85 (1981) 798–803. [7] B. Sesta, C. La Mesa, A. Bonincontro, C. Cametti, A. Di Biasio, Micellization processes in concentrated sodium deoxycholate solutions: effects of different counterions, Ber. Bunsen-Ges. Phys. Chem. 86 (1982) 664–670. [8] C. La Mesa, B. Sesta, A. Bonincontro, C. Cametti, Hydration properties of lyotropic mesophases in para-nonylphenol decaoxyethylene glycol– water mixtures, J. Colloid Interface Sci. 125 (1988) 634–640. [9] A. Bonincontro, G. Briganti, A. D’Aprano, C. La Mesa, B. Sesta, Dielectric behavior of octyl-beta-d-glucopyranoside micelles in water and in water–glycine solutions, Langmuir 12 (1996) 3206–3210. [10] D. Polder, J.H. Van Santen, The effective permeability of mixtures of solids, Physica 12 (1946) 257–271.
[11] G. Cevc, D. Marsh, Phospholipid Bilayers: Physical Principles and Models, John Wiley, 1987. [12] A. Raudino, F. Castelli, G. Briganti, C. Cametti, Anomalous dielectric behaviour of undulated lipid membranes. Theoretical model and dielectric spectroscopy measurements of the ripple phase of phosphatidylcholine, J. Chem. Phys. 115 (2001) 8238–8250. [13] H.P. Schwan, S. Takashima, Electrical conduction and dielectric behavior in biological systems, Encyclopedia of Applied Physics, VCH Pub. Inc., 1993. [14] F. Bordi, C. Cametti, R. Misasi, R.G. De Persio, Zimatore Electrical characterization of the human erytrocyte membrane. effect of different alkali metal ions, Eur. Biophys. J. 26 (1997) 215–225. [15] C. Ballario, A. Bonincontro, C. Cametti, A. Rosi, L. Sportelli, Membrane conductivity changes in erytrocytes and white ghosts following gamma irradiation, Int. J. Radiat. Biol. 51 (1987) 934–943. [16] A. Bonincontro, C. Cametti, R.E. Hausman, P.L. Indovina, M.T. Santini, Changes in myoblast membrane electrical properties during cell– cell adhesion and fusion in vitro, Biochim. Biophys. Acta 903 (1987) 89–95. [17] F. Bordi, C. Cametti, A. Di Biasio, Determination of cell passive electrical properties using frequency-domain dielectric spectroscopy technique: a new approach, Biochim. Biophys. Acta 1028 (1990) 201– 204. [18] F. Bordi, C. Cametti, T. Gili, Dielectric spectroscopy of erytrocyte cell suspensions. A comparison between Looyenga and Maxwell–Wagner– Hanai effective medium theory formulations, J. Non-Cryst. Solids 305 (2002) 278–284. [19] G. Arancia, F. Bordi, A. Calcabrini, C. Cametti, M.A. Diociaiuti, Molinari Influence of anthracyclinic antibiotics on membrane of human erythrocytes: a combined radiowave electrical conductivity and electron microscopy study, Bioelectrochem. Bioenerg. 34 (1994) 45–51.
Interfacial characterization of mesoscopic particle suspensions by means of radiowave dielectric spectroscopy: a minireview A. Bonincontroa,b,∗ , C. Camettia,b b
a Dipartimento di Fisica, Universita’ di Roma "La Sapienza", Rome, Italy Istituto Nazionale per la Fisica della Materia (INFM-CRS SOFT), Unita’ di Roma1, Italy
Received 21 October 2003; accepted 27 February 2004 Available online 17 September 2004 Dedicated to the memory of B. Sesta.
Abstract Heterogeneous systems, in particular aqueous suspensions of colloidal particles, are very complex systems characterized by a variety of dynamic processes, occurring at different length and time scales, that involve, in a very intruing manner, the structural properties of both the dispersed particles and the disperding medium. Over the last three decades, knowledge of the behavior of such systems has taken greatly advantage by dielectric spectroscopy techniques. This is due to the rapid growth of the technology that makes possible, both in the frequency domain and in the time domain, to acquire dielectric spectra in a very huge frequency interval, typically from 10−5 to 109 Hz, or, correspondly, in the time interval from 104 s to 10 ps. In this paper, we will consider several typical colloidal systems, such as aqueous liposome suspensions, ionic and non-ionic micellar solutions, biological cell suspensions. We will describe how dielectric spectroscopy technique can be employed to obtain information concerning the different electrical polarization mechanisms occurring at different time scales and the way to evaluate the structural parameters governing the mesoscopic behavior of these complex systems. © 2004 Elsevier B.V. All rights reserved. Keywords: Mesoscopic particle suspension; Radiowave dielectric spectroscopy
1. Introduction Bianca Sesta introduced us more than 20 years ago to the field of aqueous surfactant solutions and we are very pleased to be asked to write a short review on this subject for this memorial issue. In particular, our contribution concerns the characterization of the electrical interfacial properties of heterogeneous mesoscopic systems by means of frequency domain dielectric spectroscopy technique. Over the last three decades, knowledge of the behavior of colloidal particle suspensions has taken greatly advantage from dielectric spectroscopy measurements since this technique can investigate the relaxation processes in an extremely wide range of characteristic times, ranging from 104 to 10−11 s [1–4]. This peculiarity allows us to investigate both the structural properties ∗
Corresponding author. Fax.: +39 06 4463 158. E-mail address: [email protected] (A. Bonincontro).
0927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2004.02.033
of the colloidal particles and the alteration they induce on the aqueous phase. Moreover, using different frequency ranges, it is generally possible to separate the different contributions causing electrical polarizations in the system. From a macroscopic point of view, the complex dielectric constant ∗ (ω) of a medium is defined through the linear relationship J = iω0 ∗ (ω)E between the volume averaged current density J 1 J = J (r ) dV V
(1)
(2)
V
and the external applied electric field E 1 =− E ∇φ(r ) dV V V
(3)
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A. Bonincontro, C. Cametti / Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
where φ(r ) is the electrical potential at position r , V is a sufficiently large system volume and 0 is the dielectric constant of free space. ω is the angular frequency of the applied field. In general, the dielectric constant ∗ (ω) of a heterogeneous system is expressed by a general relation involving the dielectric constants ∗i (ω) for constituents i and parameters characteristic for their constituent proportions, for instance the volume fractions Φi ( N i=1 Φi = 1) ∗ (ω) = f (∗i (ω), Φi )
(4)
The function f must fulfill adequate analytical conditions and must depend on all the physical interactions occurring among the various components of the system, besides the geometry of the constituents. The functional dependence of the function f is obtained by solving the general equations of electromagnetism, specialized to the system under investigation. In the absence of source densities localized inside the and the electrical displacement system, the electric field E ∗ D = 0 (ω)E satisfy the equations =0 curl(E)
(5)
=0 div(D)
(6)
Eqs. (5) and (6) are valid throughout the bulk of each medium characterized by the appropriate values of the complex dielectric constant ∗ (ω). In the case of heterogeneous medium, whose structure is formed by various interconnected adjacent media, Eqs. (5) and (6) must be completed by analogous surface equations stating the conservation of the tangential component of the electric field (the thermodynamic force, in the context of irreversible processes) and of the normal component of the displacement (the flux) at any interface [5]. In general, the problem of solving Eqs. (5) and (6) is a formidable one and only in a limited number of simple cases, an exact solution can be obtained. Nevertheless, in the most cases of practical interest, approximate solutions have been developed and the heterogeneous system can be appropriately described in the light of effective medium theory. In what follows, we will consider several heterogeneous systems and we will describe how dielectric spectroscopy technique over an appropriate frequency range can be utilized to investigate complex systems in order to obtain information at molecular level about their mesoscale structure.
2. Ionic and non-ionic micelle solutions Aqueous micellar solutions are formed by the selfassembly of surfactant molecules into aggregates, which first appear at the critical micelle concentration (c.m.c.), with minimal contact between the hydrocarbon chains and water. Micellar solutions are often regarded as a two-phase mixture, an approximation that can be very useful in dielectric measurements, where different regions are characterized by different dielectric properties (permittivity and electrical conductivity).
In the high-frequency region, at frequencies above 500 MHz or more, the dielectric spectra of surfactant selfassembled structures are mainly due to the orientational polarization mechanisms of the aqueous phase and to their modification induced by the interactions with the solute. This approach is particularly useful to investigate the dielectric properties of the interfacial water (hydration water) in aqueous micellar solutions, where the ionic character of the hydrophilic groups of the surfactants induces a strong correlation in the surface organization of the water molecules adjacent to the interface. As an example, we report an investigation on concentrated sodium deoxycholate [NaDOC] solutions at different temperatures in the interval from 10 to 50 ◦ C [6]. This surfactant forms spherical micelles at concentrations above the c.m.c. (about 10 mM, at room temperature). The dielectric data collected at the frequency of 10 GHz were analyzed in terms of a very simple mixture equation, considering a two-phase system (a surfactant domain with volume fraction Φ and a water domain with volume fraction (1 − Φ)), where the aqueous domain is characterized by the overlapping of two contributions, the one associated to the bulk water and the one associated to the interfacial water. Both these two contributions are weighed with their respective volume fractions. Within this simple scheme, the complex dielectric constant (ω) of the whole system is given by
w (1 − q) h q (ω) = (1 − Φ) + 1 + iωτw 1 + iωpτw
+ Φp
(7)
where w , h and τw , τh are the dielectric increments and the relaxation times of the bulk and interfacial water, respectively, p is the permittivity of the dispersed phase and q is the volume fraction of the hydration water. The parameter p = τh /τw takes into account the shift of the relaxation time of the hydration water with respect to the bulk water. Under the hypothesis that the static permittivity of bulk and interfacial water are similar, a non-linear least-squared minimization yields the behvior of q as a function of temperature and concentration. A typical result of this analysis is shown in Fig. 1, where q is plotted as a function of the concentration C of the surfactant at two selected temperatures. The results show, superimposed to a regular increase on the concentration, a marked change (more evident at lower temperature) around 0.2–0.3 M, suggesting, at these concentrations, a reorganization, in a more structured arrangement, of the micellar component. It is worth noting that a similar change also occurs in the reduced viscosity of the solution, in the same concentration range [6]. Moreover, on the basis of a similar analysis, the influence of the ionic strength on the hydration number, i.e., a measurement of the amount of the hydration water, has been investigated [7]. For example, we observed an increase of the hydration number from 30 to 50 as the concentration of the added salt (in this case NaBr) is increased from 0.1 to 0.4 M. This increase is in agreement with the formation of aggre-
A. Bonincontro, C. Cametti / Colloids and Surfaces A: Physicochem. Eng. Aspects 246 (2004) 115–120
Fig. 1. The fraction q of modified water deduced from dielectric measurements at the frequency of 10 GHz in NaDOC aqueous solutions as a function of concentration C, at two different temperatures (T = 15 and 45 ◦ C)
Also in this case, the influence of the hydration water can be investigated by means of microwave dielectric measurements. In the system under investigation, because of to the high value of the NPEG concentration, the whole water present in the system is affected by the solute and its structure undergoes a long-range molecular order. A typical dielectric spectrum in the temperature range from −20 to 50 ◦ C is shown in Fig. 3, for the two different (hexagonal and lamellar) structures. It must be noted the absence of a discontinuity of the liquid water–ice phase transition at 0 ◦ C. This peculiarity evidentiates that, in this case, the water molecules are completely affected by the solute. Under the above approximation, the dielectric behaviour of the lyotropic mixture can be described by the equation (∗ )1/2 = (1 − Φ)(∗w )1/2 + Φ(∗p )1/2
gations above the primary c.m.c., favoured by the presence of interfacial water, able to promote a steric arrangement of micelles to form superaggregates. Non-ionic surfactants are able to organize, at sufficiently high concentration, a variety of arrangements that span from the hexagonal to the lamellar phase, whose stability depends on the hydrophilic–lipophilic balance and on the hydration processes. Both these two characteristics may be investigated by means of dielectric spectroscopy at appropriate frequencies. For example, in the case of aqueous mixture of pnonylphenol-decaoxyethylene glycol [NPEG] [8], radiowave dielectric measurements evidence a structural transition from a hexagonal mesophase to a direct micelle solution as the temperature increases. This transition is clearly shown in Fig. 2, where the permittivity abruptly changes in value at the temperature of about 30 ◦ C. Also, the activation energy deduced from an Arrhenius plot shows a change from 1.5 to 2.0 kcal/mol close to the above transition.
Fig. 2. The low-frequency permittivity of NPEG–water mixture as a function of temperature. (A) (◦) Hexagonal mesophase; (B) (•) lamellar mesophase.
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(8)
where ∗p and ∗w are the complex dielectric constant of the dispersed phase and the hydration water, respectively, and Φ the volume fraction of the dispersed phase. If the hydration water has a Debye-type relaxation, Eq. (8) allows the relaxation time to be evaluated. At room temperature, we find a relaxation time of 2–3 × 10−11 s, i.e., three-four times larger than that of bulk water. In the case of non-ionic surfactants, radiowave dielectric investigation can help in the evaluation of the surface charac-
Fig. 3. (A) The high-frequency permittivity of NPEG aqueous solution as a function of temperature in two different phases: () hexagonal mesophase, 49% (w/w) sample; (◦) lamellar mesophase, 69% (w/w) sample. (B) The high-frequency dielectric loss of NPEG aqueous solution as a function of temperature in two different phases: () hexagonal mesophase, 49% (w/w) sample; (◦) lamellar mesophase, 69% (w/w) sample.
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terization of the micellar system and in particular in discriminating between different structures resulting in interactions with aminoacids. It is well known that many aminoacids, such as glycine, show an appreciable influence on the thermodynamic stability of surfactant aggregates. In order to ascertain if glycine directly interacts with the polar head region of micellar aggregates, a typical example is the dielectric behavior of octyl -d-glucopyranoside [OBG] micelles in water and in water–glycine solutions [9]. By taking advantage of the frequency independent behavior of the permittivity of OBG–glycine solutions in the frequency range 107 –108 Hz, it is possible to separate the contributions due to the Maxwell–Wagner effect at lower frequencies and the one due to the solvent phase at higher frequencies. Consequently, we are able to use a simple mixture equation such as, for example, the Polder and Van Santen equation [10] and to evaluate the dielectric properties of the dispersed phase. In particular, the problem we are considering is to distinguish between a direct interaction of OBG and glycine, yielding to the formation of so-called “dressed micelles”, or a modification in the micellar aggregation due to the properties of the mixed solvent (water–glycine solution). The analysis carried out on the basis of an iterative use of the Polder and Van Santen mixture equation, allows us to calculate the permittivity of the micelle polar region. We obtain a value of the permittivity lower than that of a glucose–glycine– water solution at the same concentration ratio that should mimic the composition of the OBG head group region, if glycine interacts with the micellar crown. This finding rules out the presence of glycine in the crown region of the micelles, giving support to the hypothesis that the aggregation properties of the micelles are modulated through the solvent. We want to stress that, in this case, the overall permittivity of the system can be appropriately deconvoluted and the properties of the interfacial region, under reasonable assumptions, evidentiated. Other thermodynamic investigations (such as osmotic pressure, surface tension and so on) would require much heavier approximations and should present a lower capability in evidencing the different contributions of the various components of the system.
tant in a variety of biological phenomena, such as for example cell–cell adhesion or signal transduction. These systems are characterized by the existence of a temperature-dependent transition in which the hydrocarbon chains undergo a reorganization from an ordered crystallinelike state to a disordered fluid-like state. In the case of DPPC, near the room temperature and at high water content, a rippled phase occurs, characterized by a in-plane modulation of the bilayer, in the temperature interval between the pre-transition and the main-transition temperature [11]. This change in the molecular arrangement of the hydrophobic region of the lipid bilayer induced by temperature is manifested by the rapid increase in the dielectric increment as the temperature approaches both the pre-transition and the main-transition temperature. Fig. 4 shows typical dielectric spectra of an aqueous suspension of DPPC liposomes in the radiowave frequency range at different temperatures, from 5 to 50 ◦ C [12]. Once the dielectric spectra have been corrected by the electrode polarization effect (the anomalous increase of the permittivity in the low-frequency tail of the frequency interval investigated in Fig. 4), the resulting dielectric dispersions are well described by a Cole–Cole relaxation function, whose parameters, especially the dielectric increment and the average relaxation time τ, strongly depend on the lipid bilayer structure. As an example, the inset in Fig. 4 shows the dielectric increment as a function of temperature, inbetween the pre-transition and the main-transition temperature and above the main-transition temperature. As can be seen, an abrupt change occurs, exactly at the temperatures at which the system undergoes a structural transition.
3. Aqueous liposome suspensions Liposomes, vesicles whose typical sizes range from 20 nm to several microns in diameter, are closed shells of self-assembled lipid bilayers that encompasse an aqueous core. Aqueous suspensions of phospholipids have been investigated by dielectric relaxation to determine macroscopic properties such as the permittivity of the lipid membrane and to obtain information about the microscopic parameters of the dynamics of the zwitterionic head groups in the polar region of the bilayer. The knowledge of the dielectric properties of the membrane–water interfacial region is particularly impor-
Fig. 4. The permittivity of liposome aqueous suspension as a function of frequency at some selected temperatures from 6 to 46 ◦ C, in 2 ◦ C step (from bottom to top). The spectra show a marked electrode polarization effect in the low-tail of the frequency range investigated. Once corrected for this effect, the data show a dielectric dispersion whose dielectric increment depends markedly on the temperature (see inset, the two vertical arrows mark the interval between the pre-transition and the main-transition temperature of DPPC hydrocarbonic tails).
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4. Biological cell suspensions In the field of biological systems, a particular relevance assume biological cell suspensions that, from a mesoscopic point of view, behave as a heterogeneous system where interfacial effects are pronounced. A biological cell can be represented as a vesicle that separates an intracellular medium, whose biological structure is very complex, from an extracellular medium that, to a first approximation, can be considered as an electrolyte solution of appropriate ionic strength. The presence of the membrane, whose electrical parameters deeply differ from those of the adjacent media, produces a very strong dielectric dispersion that generally occurs at radiowave frequencies. At these frequencies, the dielectric response of the whole system is practically due only to the membrane region between the extracellular medium and the cytosol. The typical shape of a dielectric spectrum is composed by different dispersions located at different frequency ranges, the lower one being attributed to the electrode polarization effect [13], the intermediate one to the presence of the membrane and, finally, the one at higher frequencies to the bulk properties of the aqueous phase. In this case too, as we have above stated in the other systems we described, the approach based on the effective medium theory describes the macroscopic dielectric behavior of the system in terms of an appropriate mixture equation of the form f (∗eff (ω), ∗m (ω), ∗si (ω), Φi ) = 0
(9)
where ∗eff (ω) and ∗m (ω) are the complex dielectric constant of the effective medium and host medium, respectively, ∗si (ω) is the corresponding quantity of the inclusion media and Φi their volume fractions. Eq. (9) allows the dielectric and conductometric properties of the cell membrane to be evaluated. Particular functional dependences of the mixture equations take into account also the geometrical shape of the biological cell, so that the method is not confined to spherical objects. We have applied this technique to a wide variety of biological cell suspensions, ranging from human erythrocytes to lymphocytes and stabilized normal and tumoral cell lines [14–17]. As an example, we are showing here the permittivity and the electrical conductivity of human erythrocyte cells deduced from radiowave dielectric spectroscopy measurements in the frequency range from 1 kHz to 2 GHz (Fig. 5). The large dielectric dispersion both in the permittivity and in the electrical conductivity results in a membrane permittivity of the order of s = 2.5 and a membrane conductivity of about σs = 5 × 10−5 mho/m. These values account for the hydrophobic region of the membrane double layer and for the ionic and/or polar character of the interface. A comparison between different mixture equations has been discussed recently elsewhere [18] This circumstance favours the observation of possible alterations both in the structural and in the functional aspects
Fig. 5. Radiowave dielectric spectra of an erythrocyte suspension (hematocrit Φ = 0.15, temperature T = 25 ◦ C) as a function of frequency. (A) The permittivity ; (B) the electrical conductivity σ. The interface polarization due to the presence of the cell membrane results in a dielectric and conductometric dispersion located between the electrode polarization effect, in the low-frequency tail, and in the aqueous phase orientational dispersion, in the high-frequency tail. The full lines represent the calculated values of the permittivity and the electrical conductivity σ according to the heterogeneous system effective medium theory. In the inset, the dielectric loss , having substracted the contribution due to the ionic losses, is shown.
induced by different physico-chemical agents such as, for example, ionizing radiation, ionic environment of the extracellular medium, action exerted by drugs, besides other biological or chemical agents. All these effects have been shown by means of dielectric spectroscopy measurements and they represent a particular exciting example of the effectiveness of this method. In particular, we want to stress how this approach can be useful in the investigation of the structural alteration of erythrocyte cells induced by anthracyclinic antibiotics (adriamycin, daunorubicin, 4 -epiadriamycin) [19] that substantially modify the molecular architecture of the plasma membrane by their incorporation within the lipid bilayer. Although dielectric technique probes the whole system and consequently only an average response is obtained, the dielectric model on one side and the experimental accuracy on the other side are sufficient to extract information on the particular polarization mechanism we are looking at. Biological cell suspensions are an appropriate example of this feature, since dielectric behavior of the cell membrane can be isolated from contiguous dispersions due to different mechanisms.
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References [1] K. Asami, Characterization of heterogeneous systems by dielectric spectroscopy, Prog. Polym. Sci. 27 (2002) 1617–1659. [2] Y. Feldman, T. Skodvin, J. Sjoblom, Dielectric spectroscopy on emulsion and related colloidal system: a review, in: J. Sjoblom (Ed.), Encyclopedia Handbook of Emulsion Technology, Marcel Dekker, New York, 2000. [3] R. Pethig, Dielectric and Electronic Properties of Biological Materials, Wiley, New York, 1979. [4] K.R. Foster, H.P. Schwan, Dielectric properties of tissues and biological materials: a critical review, Crit. Rev. Biomed. Eng. 17 (1989) 25–104. [5] M. Clausse, Dielectric properties of emulsions and related systems, in: P. Becher (Ed.), Encyclopedia of Emulsion Technology: Basic Theory, Marcel Dekker, New York, 1993. [6] B. Sesta, C. La Mesa, A. Bonincontro, C. Cametti, A. Di Biasio, Molecular aggregation of sodium deoxycholate in water and water–urea mixtures: a multistep process, Ber. Bunsen-Ges. Phys. Chem. 85 (1981) 798–803. [7] B. Sesta, C. La Mesa, A. Bonincontro, C. Cametti, A. Di Biasio, Micellization processes in concentrated sodium deoxycholate solutions: effects of different counterions, Ber. Bunsen-Ges. Phys. Chem. 86 (1982) 664–670. [8] C. La Mesa, B. Sesta, A. Bonincontro, C. Cametti, Hydration properties of lyotropic mesophases in para-nonylphenol decaoxyethylene glycol– water mixtures, J. Colloid Interface Sci. 125 (1988) 634–640. [9] A. Bonincontro, G. Briganti, A. D’Aprano, C. La Mesa, B. Sesta, Dielectric behavior of octyl-beta-d-glucopyranoside micelles in water and in water–glycine solutions, Langmuir 12 (1996) 3206–3210. [10] D. Polder, J.H. Van Santen, The effective permeability of mixtures of solids, Physica 12 (1946) 257–271.
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