Vol. 4, No. 2/February 1987/J. Opt. Soc. Am. B 287
Dynamics associated with laser-induced modification ofsurface tension
Shlomo Efrima
Department of Chemistry, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
Received June 23, 1986; accepted September 15, 1986
Modification of the surface tension of liquids by laser radiation is discussed as a means to investigate the molecularorigin of surface tension and the dynamics of the superfacial processes that lead to and maintain surface tension.Sessile drops are used as a specific example.
1. INTRODUCTION
Surface tension is a macroscopic, thermodynamic surfaceproperty that is important in determining many surface andinterfacial properties and phenomena, such as shape ofdrops, contact angles, wetting, and emulsification.
Surface tension (or surface energy) originates from inter-molecular interactions and depends on molecular structureand properties and on the particular assembly and orienta-tion at the interface. In multicomponent systems, it de-pends on surface adsorption, surface segregation, and thespecific chemical environment at the interface. These, inturn, strongly depend on molecular structure and intermo-lecular interactions.
In principle, the molecular origin of surface tension isunderstood." 2 The surface tension can be calculated fromintermolecular interaction potentials and pair distributionfunctions or, alternatively, from density profiles and directcorrelation functions. Some measure of approximation isinvolved (such as pair potentials), although exact schemescan be outlined. The computations may also involve spacederivatives of some of the quantities, which poses an addi-tional obstacle in the application of such methods. To date,only a small number of calculations have been carried out,mainly involving model systems or using computer simula-tion techniques when more complex interaction potentialsare applied.
From the experimental side, there is a wealth of datapertaining to surface tension and related properties, such ascontact angles, spreading coefficients, critical micellationconcentrations, and their dependence on chemical identityand composition.3-5 Noteworthy is the vast literature deal-ing with emulsions and micelles, which often addresses thequestions of dependence on molecular structure and inter-molecular interactions.6
Nevertheless, there is a much smaller body of direct ex-perimental work relating to the dynamics associated withestablishing the equilibrium surface tension and determin-ing various measurable quantities. These dynamic process-es may involve molecular dynamics and microscopic changescoupled to macroscopic geometrical rearrangements.
In the past, the most common dynamic investigationswere carried out by changing the temperature or the chemi-cal composition.7 In general, nonequilibrium conditions,
such as temperature gradients and differences in concentra-tions, can lead to time dependence. One could mention inthat connection surface-driven phenomena8 or the Maran-goni effect.9 Possibly adsorption-desorption processes canalso lead to time-dependent changes in interfaces.1 0 Timedependence is most often encountered in the context ofmicellar or emulsion stability."
In this paper we discuss the use of laser radiation (or, ingeneral, electromagnetic radiation) as a driving force forchanges in the interface that bring about variations in thesurface tension of liquids, thus permitting the study of thedynamic processes and the structural effects associated withestablishing and maintaining the surface tension of liquids.
In what follows we will not make a distinction betweensurface tension and interfacial tension and will use bothterms to denote either of the two quantities. The term,surface energy, will also be used in the same sense.
The main advantage of using laser radiation to study sur-face tension is that the perturbation driving the system awayfrom equilibrium can be applied in durations that are muchshorter than characteristic times of the rearrangement pro-cesses that follow. Also, one can turn on specific perturba-tions, often localized to the surface or part of it, or distribut-ed throughout the bulk, at will. This temporal and spacialresolution can, in principle, enable one to deconvolute thevarious parallel and consecutive processes affecting the sur-face tension. In addition, the perturbation can be engi-neered so as to affect a well-defined molecular property orstate selectively. Thus facilitating elucidation of the con-nection between molecular structure and surface tension.
The main problem of utilizing such techniques is the typi-cal short lifetimes of most radiation-induced changes (exci-tations, for instance). Therefore the question of time scalesof the various processes associated with surface-tensionchanges by radiation is fundamental in this context. It isdiscussed in Section 3, where we also dwell on several mecha-nisms for coupling radiation and surface tension. In Section2 we discuss the dependence of the contact angle on changesof the surface tension. Explicitly, we focus the analysis onsessile drops and their dimensions. The conditions underwhich measurable changes will be detected will be derived.Then we also discuss the important issue of contact anglehysteresis on which laser-induced surface-tension changescan help to shed some light.
288 J. Opt. Soc. Am. B/Vol. 4, No. 2/February 1987
2. CONTACT ANGLES AND DIMENSIONS OFSESSILE DROPS
A convenient general system to study the effect of changes inthe interfacial energies is the solid-liquid-gas junction.More specifically, we focus our discussion on sessile dropsand their geometrical dimensions, as an illustrative exampleand a convenient system to investigate. However, we firstdiscuss contact angles in the three-phase junction, indepen-dent of any specific system.
A. Contact AnglesThe contact angle is determined by the surface tensions andis given by Young's equation 12 :
instance, excited state less polar than ground state) theperturbation can bring about a wetting transition.
These points are further demonstrated in terms of thecontact angle itself, in Fig. 2. For 6 = -0.1 one has a transi-tion to total wetting below 00 _ 37°. The larger changes inthe contact angles are at small angles, but, even at largecontact angles, the effect is still substantial (at 140° there isstill a 30 effect).
B. Large Sessile DropsConsider now a large sessile drop, such that its top hasflattened out (Fig. 3a).
The height of the drop h, neglecting the edge effects, isgiven approximately by4
cos 0 = (sg - Ysi)/,yg, (1)
where yjj is the interfacial tension between the phases i andj; i, j = s, g, 1; s indicates a solid, g, a gas, and 1, a liquid.
The interfacial tension for the solid-liquid interface isgiven approximately by13
Ysl = Ysg + Yl g Yd
Ysg -yS1-Y1g =-/2pGh 2 , (8)
where pl is the density of the liquid (or the differences in
(2)
where yigd is the contribution of the London forces to thesurface energy of the gas-i-phase interface. Such a separa-tion of the forces is convenient and is still a major approachadopted by chemists, even though the interdependence ofthe various contributions is significant.
We assume that we will carry out a perturbation such thatwill affect yd to a much lesser degree than the other contri-butions to the surface energy. (For instance, consider suchan electronic excitation of the molecules as that which willbring about a large change of molecular dipole.) We furtherassume that the surface-tension perturbation occurs only inmolecules in the liquid phase and that its magnitude is (normalized to ylg). Other cases can be considered; howev-er, it is feasible to set up an experiment that agrees with thestipulations outlined above.
Under these assumptions we obtain
YIg = 71g0(1 + ), (3)
Ysl Ysg0 + Yjg0(1 + 3) - sg = s + &YIg 0 s (4)
,Ysg =sg (5)
where the zeros denote unperturbed quantities.The contact angle will change from Oo to 0, according to
Cos 0 - Cos 00 =(1 + COS Oo)6/(l + ).
U3aU
-1
-1
cos' 1
Fig. 1. Cosine of perturbed contact angle (0) versus cosine of initialcontact angle (0o), for 6 = ±0.1, according to Eq. (6). 6 is themagnitude of the surface-tension perturbation in units of the liq-uid-gas surface tension. a, 6 = 0; b, 6 = -0.1; c, 6 = 0.1.
b
bA
(6)
Figure 1 shows the (linear) dependence of cos 0 on cos ofor fixed values of 6(+0.1). These values for are probablyat the high limit of changes of surface tension that are easilyaccessible. They were chosen to emphasize the trends.
The important point to note in Fig. 1 is that relativelylarge effects are expected for small contact angles (close towetting), whereas for large contact angles there is a relativeinsensitivity to changes in the surface tension.
For small 6 we have, to a good approximation,
A Cos 0 Cos 0 - Cos 00 =-(1 + Cos 00)6. (7)
Thus A cos 0 is linear in with the largest slope (of 2) close tothe wetting transition.
Another point to be noted in Fig. 1 is that for < 0 (for
perturbed angle e
Fig. 2. Perturbed contact angle versus contact angle. a, B = 0; b, b= -0.01; c, 6 = 0.01; d, 6 = -0.1; e, 6 = 0.1.
Shlomo Efrima
Vol. 4, No. 2/February 1987/J. Opt. Soc. Am. B 289
a
U /
\. ,
C
I j' I / \I It / I 7I7
Fig. 3. Schematic representation of a, large sessile drop; b, smallsessile drop, small contact angle; c, small sessile drop, large contactangle.
densities if phase g is also a liquid) and G is the gravitationalacceleration.
Alternatively, Eq. (8) can be rewritten as
cos 0 = 1 - 'I2pjGh 2/yg. (9)
Thus the dependence on the contact angle and the connec-tion to Subsection 2.A is emphasized. The second term onthe right-hand side of Eq. (9) is the average gravitationalpotential energy of the drop, normalized to the gas-liquidinterfacial energy.
Using Eqs. (3)-(5) and (8) and (9), one obtains for small a
Ah/ho = 6/('/2pjGh0/Iylg0 ) = 61(1 - cos 0). (10)
Thus we expect larger sensitivities for small contact an-gles. In fact, at 00 = 300 the relative change in the height ofthe drop is -7.56, whereas at larger contact angles it de-creases asymptotically to the value of /26. In either case,when 6 is several percent, the effect is substantial and stillmeasurable even for smaller 6.
C. Small Sessile DropsThe precise shape of sessile drops has been thoroughly inves-tigated in the past and was shown to be a rather complexfunction of the surface tensions and the density. 4"15 Anellipsoid of revolution is a good representation of the actualshape.
For the case of small drops, we consider here an approxi-mate derivation. We assume that the sessile drop is a spher-ical cap (small contact angle), as shown in Fig. 3b. For smalldrops, gravity has a smaller role, and the shape is nearspherical. The case of large contact angles is, within thisapproximation, a capless sphere; it is shown in Fig. 3c. Inthis model the polar angle p is equal to the contact angle,which substantially simplifies the analysis.
The volume of the drop is given by
V = 1rR 3 [2 + cos -(cos2 so-3)], (11)
where R is the radius of curvature of the drop in its sphericalpart.
The height above the flat solid surface h is given by
h = R(1 - cos ).
The radius of the circle of contact with the solid r is
r = R sin y.
(12)
(13)
We assume now that the volume of the drop V does notchange in the experiment, so we have R as a function of thepolar angle yo or the contact angle :
R = $(3V/7r)/[2 + cos 0(cos2 0 -3)11/'.
Using Eq. (6) and Eqs. (12)-(14), we fihally obtain
Figure 4 shows AR/RI and JA/hi [in units of 6(1 + 6)] as afunction of the unperturbed contact angle. Note the largevariations for small contact angles [at 300 Ah/hj 4.96/(1 +6) while IAR/RI 9.16/(1 + 6)]. Nevertheless even at largecontact angles, there is a substantial effect [at 1200 IAh/h _0.26/(1 + 6)] for proper values of 6. Note that, as was foundfor the large drop discussed in Subsection 2.B, the geometri-cal change in the small drop is considerable for 6 of the orderof a few percent. A drop of -0.1-cm linear dimensions willhave its height changed by several micrometers when 6 is 1%.Such changes should be easily measurable. Unless 6 is ex-ceptionally large (10% or so), measurements at contact an-gles larger than 1200 are much more difficult, if feasible atall. Ar/r follows a similar pattern of behavior as Ah/h, withsomewhat higher sensitivity.
3
,,,2us
"-2 \
Fig. 4. Log of relative change in height lh/hl and radius lAR/RI ofa small sessile drop as a function of initial contact angle. Values arenormalized to the perturbation 6/(1 + 6).
Shlomo Efrima
290 J. Opt. Soc. Am. B/Vol. 4, No. 2/February 1987
D. Advancing and Receding Contact AnglesIt is well known that, in practice, the thermodynamic con-tact angle is seldom obtained, but, instead, a history-depen-dent angle is usually measured. Specifically, two differentcontact angles are observed, the advancing angle 6a and thereceding angle 0 ,. The thermodynamic contact angle 0 hasan intermediate value
0 < 07 < 0,a (18)
Thus a region of equilibrium exists, not a well-defined singlecontact angle. This region often extends over several dozendegrees, and it is therefore important to discuss its implica-tion on the problem at hand.
There are several explanations for the contact-angle hys-teresis, most of which are reviewed by Chappuis.1 6 Theyinvolve surface heterogeneity, surface roughness, modifica-tion of the solid surface after contact with the liquid, or anycombination of these. The last-named cause is really illdefined and of a complex nature. Modification of the solidsurface can be brought about by surface structural changes,by alteration of absorbed layers, by varying the nature andthe quantity of impurities at the surface, etc. Thus a moreprofound understanding of the hysteresis is clearly needed.
Using laser radiation to bring about rapid changes of thesurface tension of a specific phase in a prescribed mannermay provide a unique way to investigate this phenomenon.In cases of large differences between the advancing and thereceding angles, one could establish working conditions nearone of these angles with proper consideration of the natureof the laser-induced perturbation. Equation (7) shows thatincreases in the liquid surface tension bring about increasesin the contact angle. For such perturbations, therefore, it ispreferable to investigate the neighborhood of tOa. For a la-ser-induced perturbation that results in a lower surface ten-sion, it would be advantageous to probe angles near 0,.
In addition, it is not clear at present to what extent hyster-esis is affected by such changes in surface tension. Mea-surement of advancing and receding contact angles usuallyinvolves changes of predominantly mechanical parametersof the system (such as when one is withdrawing or immersinga slab). It would be of interest to see whether the same typeof hysteresis is associated with in situ surface energychanges. An additional feature occurs because the actualshape of sessile drops is not spherical; changes can involvemodification of the height without affecting the liquid-solidarea of contact.
Finally, when 0ta - 0r is small, and when the changes in the
contact angle induced by the radiation are relatively large(usually at small contact angles, 0 < 80°; see Fig. 2), then theadvancing-receding problem is not important in these ex-periments.
3. LASER-INDUCED CHANGES IN SURFACETENSIONS
In the previous section we assumed that one could bringabout changes in the surface tension in the liquid-gas andliquid-solid interfaces and analyzed the consequences ofsuch modifications. It was shown that a change of about 1%would give an easily detected variation of height, radius, orcontact angle of a sessile drop. In this section we discuss
some possible mechanisms by which such changes can beinduced by laser radiation.
At first, we discuss the basic requirement on the durationof the laser-induced changes in the surface tension, so thatthe mechanical, macroscopic relaxation of the system (asessile drop, for instance) has time to occur. We have inmind a pulsed-mode operation of the laser, which permitslarge enough perturbations, and a good time resolution. Ameasure of the mechanical relaxation time is obtained by theduration of a free fall over a distance of -0.01 cm (10% of a 1-mm-high sessile drop); it is -5 msec. This would be thecharacteristic time for mechanical rearrangement for thecase when the contact angle is decreased by the perturba-tion. When the laser-induced perturbations result in anincrease of the contact angle, the reshaping of the dropwould occur over a period of time, probably of the sameorder of magnitude as in the previous case. We base thisconjecture on the similar magnitude of the forces acting inthese two directions. It would be of interest to measurethese relaxation times, thus obtaining further insight intothe superfacial processes. In particular, a connection toMarangoni or surface-driven phenomena is apparent.
Another characteristic time of interest is that of the trans-fer of the pressure changes due to the change in surfacetension and to the subsequent shape relaxation. This wouldoccur essentially in the speed of sound. Thus, for a drop of0.1-cm linear dimension, the typical time would be severalmicroseconds.
An additional process to be expected following the directstimulation by the laser light is adsorption on and desorp-tion from the various interfaces involved. The characteris-tic time for such essentially diffusional processes is a strongfunction of the bulk concentration and the change in surfaceconcentration associated with the light-induced molecularperturbations. For concentrations of surfactants in therange of 10-4-10-5 M, it could take -0.01-1 sec for a consid-erable concentration distribution relaxation to take place.However, the most significant changes occur right near thesurface, over distances of 1-10 nm. Diffusion over suchdistances takes only -10-1000 nsec. These diffusional pro-cesses are not so interesting, as they are generally well un-derstood. However, they should be considered in our con-text as far as they affect the observed quantities and theirtime dependence.
One can summarize the time hierarchy of the various pro-cesses in the following manner: laser activation (10 psec-10nsec) < surface concentration relaxation (0.01-1 sec) <pressure relaxation (1-10 4sec) < shape relaxation (1-100msec) < bulk-concentration relaxation (larger than 0.01sec). The slow bulk-concentration distribution relaxation isnot expected to affect either the surface tension or the shapeof the sessile drop to any large extent. Thus there is a cleartime-scale separation of the various processes. Further-more, the shape relaxation is probably fast enough to permitrepeated experiments at a reasonable repetition rate. Thisis a convenient feature from the experimental point of view.
Let us now consider a few of the ways by which laserradiation can, in principle, induce such molecular changes,which in turn will lead to surface-tension changes:
(1) Heat generation by rotational, vibrational, or elec-
Shlomo Efrima
Vol. 4, No. 2/February 1987/J. Opt. Soc. Am. B 291
tronic excitations and relaxations or by activating exother-mic reactions.
(2) Induction of photochemical changes in molecules byUV or visible light.
(3) Creation of electronically excited molecules andcomplexes.
Surface tension normally decreases with temperature at arate of the order of 0.1 erg/(cm 0C) (0.2%/ 0 C) for liquids.In the case of solutions, the surface-tension changes are alsodue to the dependence of the surface adsorption (surfaceexcess) on the temperature. Heating is an unselective wayof changing the surface tension, and it does not easily permita direct analysis in terms of molecular structure and interac-tions. In addition, heating involves volume changes, of theorder of 0.1%/0 C for typical liquids (for water at 200 C it is-0.02%/°C). Thus changes in the shape of the drop result-ing from density variations can be a significant contributionwhen compared with the change due to the surface tensionitself. Heating is therefore an undesirable way to affect thesurface tension, and in fact one must strive to minimize it.Fortunately, in typical cases the temperature change will bemuch too small to have any appreciable effect. Neverthe-less, one should have the heating in mind when consideringany specific system (for instance, high-intensity IR lasersmay be detrimental in this respect).
Photochemical reactions can be used to induce changes inmolecular structure and, consequently, in the surface ten-sion. The advantage of this technique is that the modifiedmolecular species can often be easily monitored during thecontact angle, or shape, measurement, and it can be isolatedand characterized at its termination. Also, the modificationis long lived and can allow the investigation of extremelyslow geometric rearrangements of the system. The molecu-lar modifications can, in this case, be well defined and char-acterized. As a general example, consider a molecule of theform RCCI = CICR', where R and R' can be chosen so thatthe molecule will be a good surfactant and absorb at theproper wavelength. One could start from one isomer, the cisisomer, for instance, and induce a transition to the trans-isomer by laser excitation. These two forms may have alarge difference in their dipolar character, which should af-fect the surface tension. The disadvantage of using photo-chemical reactions is that they are usually nonreversible.That is, once the light is turned off, the system does notrevert to its initial state. Thus a repetitive experiment onthe same specimen is excluded. If the quantum yields forthe reaction are small or the laser intensity is low, a gradualchange toward the limit of complete reaction is expectedwhen the experiment is performed repetitively on the samespecimen.
Induction of changes in molecular properties by carryingout molecular excitations is another way by which laserradiation can be employed to perturb the surface tension.Obviously, rotational, vibrational, and most electronic exci-tations are not useful in this context because of the shortlifetimes of such excitations. However, triplets often live anexceptionally long time, and it is feasible to utilize excitationto a triplet state for the designated purpose. This can be amolecular excitation or a transition that involves an excimeror a charge-transfer complex. The latter, by its very nature,
ensures a large change in the dipolar nature. McGlynn etal.'7 as well as Nagakura'8 have discussed charge-transfertriplets in great detail.
Many intramolecular transitions are also known to involvelarge changes in polarity.' 9 A n -,7r* transition could be agood candidate in that respect. In such cases there is gener-ally also a high-phosphorescence quantum yield (for in-stance, for the azines7). Dyes with r - lr* transitionsusually have low quantum yields for phosphorescence.However, some acridine dyes may be suitable for the pur-pose of the study suggested here. It is known that profla-vine (3,6-aminoacridine) has hardly any regular fluorescencebut has mostly delayed fluorescence with typical lifetimes of70 msec and a phosphorescence radiative lifetime of 3.4 secat room temperature.2 0 Other acridines are known to giveintense triplet-triplet absorptions, implying a high concen-tration of triplets. 2 ' Such dyes are especially interesting, asthey are usually soluble in water and have a high absorption.They can be derivatized to yield surfactants, if one attachesto them some hydrocarbon, hydrophobic parts. With suchmolecules, high concentrations of triplets can be achieved(Zanker 2 l reports up to 90% conversion), resulting in a largeexpected change in the surface tension.
Incidentally the acridinelike molecules are sensitive tophotoreductions, and the surface tension can also bechanged by this method.
6. SUMMARY
We have shown that laser radiation can be used to investi-gate the connection between molecular properties and thestructure of the interface and macroscopic properties such assurface tension. The radiation drives well-defined molecu-lar modifications that are then followed by monitoring geo-metrical parameters of the system. The results of suchexperiments involve changes in surface tension associatedwith well-defined changes in molecular parameters. Thesedifferentials could perhaps be more susceptible to theoreti-cal modeling and calculations, as some contributions maycancel out.
We have seen that such experiments are feasible and havesuggested the main outlines of a prototype system, consist-ing of a sessile drop of an aqueous solution of a light-absorb-ing surfactant (perhaps from the acridine family). Onewould prefer a composition that is characterized by a smallcontact angle.
Perturbing the surface tension by laser radiation has someunique advantages over more conventional ways of studyingsurface tension. The perturbation is of an intrinsic proper-ty of the system in a molecularly well-defined mode andoccurs over a very short time scale. There is a large degree ofversatility. For instance, one could modify only one of theinterfaces and then monitor the complex relaxation towardequilibrium. As an illustration, consider exciting only mole-cules in the liquid-solid interface by using an internal-reflection technique, which penetrates only about 1 gm intothe liquid from the solid side. We have also indicated therole of laser-induced surface-tension modifications when in-vestigating the classical problem of contact-angle hysteresis.The sessile drop was considered in this paper, but otherconfigurations could be studied as well. A reviewer of this
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292 J. Opt. Soc. Am. B/Vol. 4, No. 2/February 1987
paper suggested the experimental setup used by Bohr.22
We believe that the general field of understanding macro-scopic properites of surfaces, in terms of its molecular pa-rameters, warrants the attention of the research community.The study of surface tension by using laser radiation asproposed here is a step in that direction.
ACKNOWLEDGMENTS
The author thanks C. B. Harris for the stimulation and forhis hospitality and P. Alivisatos and A. Haymet for helpfuldiscussions.
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