Crystallization of condensation droplets on a liquid surface Olivier Pitois, Bernard François

To cite this version:

Olivier Pitois, Bernard François. Crystallization of condensation droplets on a liquid surface. Colloid and Polymer Science, Springer Verlag, 1999, 277, pp.574-578. ￿hal-01990802￿

HAL Id: hal-01990802 https://hal.archives-ouvertes.fr/hal-01990802 Submitted on 31 Jan 2019

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Colloid Polym Sci 277:574±578 (1999) Ó Springer-Verlag 1999 SHORT COMMUNICATION

O. Pitois Crystallization of condensation droplets B. FrancËois on a liquid surface

Abstract Highly ordered micropo- with time of the mean droplet radius Received: 4 January 1999 Accepted in revised form: 15 February 1999 rous two-dimensional membranes has been found to be described by a have been obtained from polymer power law with an exponent of 1/3, solutions (Widawski et al. (1994) proving that no coalescence pro- Nature 369: 397±399). Recently, a cesses occur. This particular behav- mechanism for the formation of iour is attributed to the precipitation such membranes was proposed, in- of the polymer at the water/solution volving water vapour condensation interface and to the formation of a O. Pitois (&) Laboratoire des Mate riaux et Structures (induced by the rapid evaporation of mechanically resistant polymer layer du Ge nie Civil the volatile solvent) onto the surface encapsulating each droplet. In this U.M.R. 113 (C.N.R.S./L.C.P.C.) of solutions and the formation of way, water droplets behave like solid 2, alle e Kepler ¯oating water droplets. Unfortu- particles, allowing compact sheets to F-77420 Champs-sur-Marne, France e-mail: [email protected] nately, the droplets growth process be formed. The presence of impor- Fax: +33-81-40 43 54 85 was not observed, and consequently tant surface currents is believed to only qualitative information was promote the formation of ``poly- B. FrancËois Laboratoire de Recherche sur reported. In the present paper, re- crystal'' and ``monocrystal'' les Mate riaux PolymeÁ res sults of light-scattering experiments patterns. C.N.R.S./U.P.P.A. with this system are reported. The Centre He lioparc Pau-Pyre ne es formation of water droplets growing Key words Condensation ± Mem- 2, avenue du Pre sident Angot F-64000 Pau at the surface of the solution has brane ± Scattering ± Droplet ± France been observed and the evolution Polymer

Introduction on the surface of the solution [3]. The key element in this process was found to be related to the particular surface The formation of highly ordered microporous polymeric tension properties of this system. Firstly, it was shown membranes has previously been reported [1]. These that the shape of a water droplet ¯oating on the solution membranes consist of one (or possibly several) layer(s) surface is in accordance with the pore shape observed in of spherical micron-sized pores organized in a regular the membranes. In addition, PS-PPP was found to triangular lattice (an example of a membrane surface is precipitate at the solution/water interface, forming a shown in Fig. 1). They are obtained by rapidly evapo- solid polymer layer around each droplet. In this way, rating a thin layer of a solution of CS2 containing coalescence processes are prevented, allowing the drop- poly(p-phenylene)-block-polystyrene (PS-PPP). It was lets to behave like solid particles trapped at a liquid observed that the formation of the ordered structure interface. Then, capillary interactions and above all required the presence of moisture in the surrounding surface currents, contribute to organize the ¯oating atmosphere [1, 2]. Recently, a mechanism for the ``raft'' as packed sheets. In a previous paper [3], we formation of such structures was proposed, assuming reported optical microscopy observations of the solu- the formation of micron-sized water droplets condensed tion surface during the condensation process. Unfortu- 575

Fig. 1 Picture of a membrane surface formed from a solution of poly(p-phenylene)-block-polystyrene (Mw = 3000±30 000) in carbon disulphide (0.02 g/cm3) Fig. 2 Light-scattering experiment set-up. The patterns formed on the screen were ®lmed by means of a high-speed charge-coupled device camera 2 3 nately, the surface was made hardly visible with high magni®cation because of rapid surface currents (due to 6 XN XN Á7 ~à ~ 6 7 solvent evaporation and to the gas ¯ow carrying water I h†ˆE h†ÁE h†ˆIa h†Á4N ‡ exp i~q Á~rij 5 ; iˆ1 jˆ1 vapour). Nevertheless, ¯oating micron-sized droplets j6ˆi were distinguished under particular experimental con- ditions, allowing some qualitative information to be 2† gathered about the mechanism of formation of the ~ where Ea h† and Ia h† are the electric ®eld and the structure. In the present paper, we report recent results intensity scattered by one droplet, respectively, and of light-scattering experiments performed with the ~q ˆ ~k ~k is the scattering momentum transfer (where system previously described. In contrast to previous 0 d ~ observations in direct space, we have been able to kd is the wave vector of the scattered light) with observe the condensation process under optimum j~qjˆ2k sin h=2†ˆ 4p=k† sin h=2†. The ®rst term in conditions for preparing well-ordered membranes. In Eq. (2) represents incoherent scattering and the second the next section, we brie¯y present some theoretical accounts for the interference of radiation scattered by aspects of correlated light scattering by a two-dimen- the droplets. Converting the sums to integrals over the sional assembly of droplets. The experiment performed surface coordinates and assuming a constant number and the corresponding results are presented in subse- density of droplets (r) over the surface, the following quent sections. expression is obtained for an isotropic system [5] Z 1 I h†ˆNIa h†Á 1 ‡ 2pr r drg‰ŠÁ r†1 J0 2kr sin h† Scattered light by a two-dimensional assembly 0 of droplets ˆ NIa h†S h† ; 3† Consider N droplets of radius a on a surface and where where J0 is the zero-order Bessel function and S(h) is the the centres of the droplets are located by the position scattering structure factor, which is, with the exception of the leading factor of unity and the number density r, vector ~ri with 1 £ i £ N. Light of wavelength k and ~ the Fourier transform of g(r) ) 1, where g(r) is the pair wave vector k0 is sent normal to the surface (see Fig. 2). The electric ®eld and the intensity scattered can correlation function. be written [4]

XN Experimental ~ ~ ~ ~ E h†ˆ Ea h†Áexp‰i k0 kd†Á~riŠ 1† Experiments were performed under optimum conditions for iˆ1 preparing the membranes. A solution (50 ll) was spread on a 576

glass plate at room temperature. A carrier gas (nitrogen) was for r >2a and I(h) » NIa(h). Then, the intensity of the bubbled through a ¯ask of distilled water at room temperature. central peak decreased strongly and spread on the disk The jet of saturated nitrogen was then sent from a nozzle onto the liquid surface (the average velocity of the gas ¯ow was approx- surface (Fig. 3A). The droplets were no longer arranged imately 20 cm/s). Moisture condensation on the bottom side of the randomly and so coherent scattering appeared. As r glass plate (which could induce parasite scattering during the increased, the droplet arrangement became semi-ordered cooling of the solution due to evaporation of the solvent) was locally. At this stage g(r » 2a) > 1 and so a peak prevented by sending dry gas onto this side. A laser beam (He-Ne, appeared in the structure function S(h), and since the k = 0.6328 lm, beam width » 1 mm) was directed towards the sample, normal to the glass plate (Fig. 2). Scattered light was scattering system constituted by the droplets remained projected on a screen and the patterns so formed were recorded by isotropic, a ring (®rst Debye±Scherrer ring) was ob- means of a charge-coupled device camera. The solution was served on the projection plane (Fig. 3B). The maximum 3 composed of CS2 and PS-PPP (Mw = 30 000±3000, 0.02 g/cm ). in the structure function rises up at Pure solvent was also used for comparison. 4p h 2p q ˆ sin max ˆ : 4† max k 2 2a Results The patterns revealed a drastic di€erence between Four typical patterns, corresponding to four stages of polymer solutions and pure solvent. In the ®rst case, the condensation process, are presented in Fig. 3. About the sharpness of the ®rst ring and the presence of a well- 3 s after the gas ¯ow had been sent, the ®rst pattern to de®ned third ring (see Fig. 3C) prove that the assembly appear on the projection plane was a di€use central peak of droplets is a ``polycrystal'' [6], while only typical (not presented in Fig. 3). At this stage, water droplets liquid-like scattering patterns were produced with pure were randomly arranged on the surface and the surface solvent (the ring was generally badly de®ned, which fraction occupied by the droplets remained small. The accounts for the large polydispersity in the droplet correlation function was well approximated by g(r)=1 radius). In the next stage, the sharp ring obtained with

Fig. 3A±D Typical scattering patterns observed during the condensation process, and cor- responding to the following situations. A Small density of droplets, weak order but the droplets are no longer random- ly disposed on the surface, B locally semi-ordered droplets, appearance of a characteristic length in the system, C poly- crystal and D monocrystal 577 the polymer solution split into well-de®ned spots. longer times, we are in a position to con®rm our Possibly, only six spots remained: monocrystallinity is previous optical observations [3]: the solid polymer layer thus obtained over an area equal to that of the incident formed at the solution/water interface inhibits coales- laser beam (Fig. 3D). In the case of pure solvent, a cence processes between droplets. It must be noted that sixfold modulation possibly appeared (more or less the presence of the polymer at the interface does not clearly) in the structure factor, but the spots remained a€ect the droplet growth. In fact, previous experiments di€use. In contrast to polymer solutions, the structure with millimetre-sized water drops, formed in PS-PPP/ was destroyed when the solvent completely evaporated. CS2 solutions by means of a syringe, revealed that the In addition, it was observed that the radius of the ®rst polymer coating could inhibit coalescence between two Debye±Scherrer ring decreased by about a factor of 2.5 drops pressed one against the other (even when the during the condensation process (see Fig. 3B, C). The radius of the contact area was close to the drop radius), corresponding values of qmax are plotted in Fig. 4 as a but do not stop their growing by injection of additional function of time (the time t = 0 refers to the appearance amounts of water. It seems that the weak tensile strength of a well-de®ned ring). It can be seen that the time of the polymer layer allows the increase in the surface evolution for qmax is described by a power law: qmax  of the drop and the creation of new portions of the t)0.35 for times longer than 4 s. solution/water interface. With regard to the variation of a at shorter times, we have to note that in contrast to longer times, r increased in a wide range during the ®rst Discussion stages of condensation. In addition, we expect some From the patterns observed in Fig. 3, it appears that temperature ¯uctuations during this period. We refer to water vapour condenses onto the liquid surface in the the following expression for the variation of a as a shape of micron-sized droplets. The droplet growth is function of the temperature di€erence between the gas then observed through the evolution of the ®rst Debye- and the substrate (DTs = Tvapour ) Tsurface) [11] Scherrer ring. It is deduced from Fig. 4 that the time p à 0:8 1=3 evolution for the mean droplet radius can be described a  U DTs D12t† ; 5† by a power law with an exponent very close to 1/3. This Á where U à ˆ U Á mD2 1=3 is the reduced ¯ow velocity exponent was found theoretically and by experiments, in 12 the case of single noninteracting drops condensing onto (U is the average velocity of the gas), m is the kinematic solid and liquid substrates (heterogeneous condensation) viscosity and D12 is the mutual di€usion coecient of [7±11]. Note also that in the case of an assembly of water in the gas. It is deduced from Eq. (5) that a power interacting droplets (i.e. including coalescence processes) law is obtained when DTs is constant. Analysing our an exponent of unity is predicted [7]. Consequently, the results with respect to Eq. (5), it seems that DTs condensation process in the present system can be decreases at shorter times before reaching a constant described as the growing of noninteracting water value. This behaviour was previously observed during droplets. Insofar as the exponent referring to coales- experiments on solid surfaces [11], and was attributed to cence processes (a  t) has not been identi®ed, even at heat-transfer processes associated with the latent heat of condensation. Our case is somewhat di€erent, in the sense that the low temperature of the liquid surface is induced by the rapid evaporation of the solvent, which is related to the ``free'' liquid surface of the solution. Obviously, as the ``free'' liquid area is reduced during the ®rst stage of the condensation process, the rate of evaporation is strongly decreased; so, we expect the temperature of the solution surface to increase until an almost constant value for r is attained. The evolution of the temperature of the liquid surface seems to us hardly predictable, considering the complex heat-transfer pro- cesses inside the liquid ®lm, but our results seem to indicate that the temperature remains at a constant value during the following stages of condensation. Scattering patterns observed during the membrane formation are similar to those obtained with monolayers of solid particles [12±14]. The evolution of the patterns reveals the formation of compact sheets of droplets, promoted by the increase in r and by the presence of Fig. 4 Plot of qmax =2p/2a (maximum in the structure function) as a function of time surface currents. Besides, capillary forces contribute to 578 locally arrange the droplets in a stable hexagonal the evolution with time of the mean droplet radius is geometry so that well-ordered areas are formed. The described by a power law with an exponent of 1/3. This observation of ``polycrystal'' patterns is in accordance value is predicted in the case of single noninteracting with previous results obtained through optical micros- drops growing by heterogeneous condensation, and so copy experiments [3]; however in the present case, the our result proves that the growing droplets do not experimental conditions allowed the growth of larger coalesce during the condensation process. This is in good ``crystallites'' at the expense of smaller ones, and so accordance with the fact that the pore radius found in the monocrystals were obtained over large areas (»1mm2). resulting membrane structure is highly monodisperse. As It seems to us that the presence of a gas ¯ow of relatively previously proposed [3], we attribute this spectacular high velocity (U > 10 cm/s) promotes the formation of result to the precipitation of the polymer at the water/ large ordered areas. The present experimental method solution interface and to the formation of a polymer therefore seems to be of great interest for the study of layer encapsulating each droplet and inhibiting coales- this system under optimum conditions of preparation. cence processes. Moreover, the establishment of the ®nal structure has been found to result from droplet aggre- Conclusion gation processes, promoted by important surface cur- rents induced by the rapid evaporation of the solvent. A We performed light-scattering experiments with a system ``polycrystal'' is generally formed during the evolution of composed of PS-PPP in CS2 solution. During the the droplet array. Finally, a hexagonal structure is experiment, a ¯ow of nitrogen saturated with water obtained through the growth of ``crystallites''. The vapour was sent towards the liquid surface. The scattered present experimental method appears to be an interesting light patterns have revealed that water vapour condenses tool for studying the in¯uence of the system parameters in the shape of micron-sized droplets ¯oating on the (¯ow parameters, polymer concentration, etc.) on the solution surface. In addition, it has been observed that membrane structure, and in particular on the pore size.

References

1. Widawski G, Rawiso M, FrancËois B 6. Woolhouse GR, Chaudhari P (1974) 11. Beysens D, Steyer A, Guenoun P, (1994) Nature 369: 397±399 Philos Mag 31: 161±172 Fritter D, Knobler CM (1991) Phase 2. FrancËois B, Pitois O, FrancËois J (1995) 7. Kuz VA (1994) Phys Rev E 49: 1246± Transitions 31: 219±246 Adv Mater 7: 1041±1044 1250 12. Krieger IM, O'Neill F (1968) J Am 3. Pitois O, FrancËois B Eur Physical J B 8. Beysens D, Knobler CM (1986) Phys Chem Soc 90: 3114 (to appear in 1999) Rev Lett 57: 1343 13. Goodwin JW, Ottewill RH, Parent- 4. Hart RW, Farell RA (1969) J Opt Soc 9. Fritter D, Roux D, Beysens D, Kno- lich A (1980) J Phys Chem 84: 1580± Am 59: 766±774 bler CM (1988) J Stat Phys 52: 1447 1586 5. Lock JA, Chiu C-L (1994) Appl Opt 10. Knobler CM, Beysens D (1988) Euro- 14. Van Winkle DH, Murray CA (1986) 33: 4663±4671 phys Lett 6: 707 Phys Rev A 34: 562±573