Thermally Induced Phase Separation of a LiquidCrystal in a Polymer under Microgravity:

Comparison with Simulations

J.-M. Jin, K. Parbhakar,* and L. H. Dao*

Laboratoire de Recherche sur les Materiaux Avances, INRS-EÄ nergie et Materiaux,1650 Montee Ste-Julie, Varennes, Quebec, Canada J3X 1S2

Received October 2, 1995X

The influence of cooling rate on the size and uniformity of liquid crystal droplets dispersed in a polymermatrix by a thermally induced phase separation (TIPS) process is investigated under a microgravityenvironment. The experimental results are compared with Monte Carlo simulations. Even though thesimulations are carried out on a two-dimensional lattice, the results are in reasonably good agreementwith the experiments. We find that a fast cooling rate gives smaller droplet sizes andhence amore uniformdistribution as compared to the ones produced under a slow cooling rate. The formation of droplets undera fast cooling rate is similar to the simulated annealing process. For a fast cooling rate the system is unableto attain the global minimum and stays in a higher surface energy state which is associated with smallerdroplets. For a given cooling rate, the effect of quench depth is studied by varying the final temperature.Simulation results show that at a shallow quench depth (high final temperature) a fast cooling rate is noteffective in controlling the droplet morphology due to the high thermal energy possessed by the particles.

I. IntroductionBecauseof theirpotential in industrial applicationssuch

as optical shutters, switches, and displays1-3 there hasbeenagrowing interest inpolymerdispersed liquid crystal(PDLC) materials. A PDLC film consists of a polymerbinder and a large number of liquid crystalmicrodropletsor domainsdispersed in it. A simpleway topreparePDLCmaterials is to exploit phase separationphenomena. Thiscanbeaccomplishedbyavariety ofways: thermal quench(TIPS, thermally induced phase separation), solventevaporation (SIPS, solvent inducedphase separation), andchemical or photochemical polymerization (PIPS, polym-erization induced phase separation).In this studyweanalyze theTIPSprocessanddetermine

the critical parameterswhich control thephase separationand the subsequent growth of the liquid crystal droplets.Under terrestrial conditions, gravitational forces canstrongly influence theparticle sizes and their distributionvia sedimentation and coalescence, thereby making itdifficult to study the importance of the intrinsic param-eters which control the process. Since the electro-opticperformance characteristics of PDLC materials arestrongly dependent on the morphology and the dis-tribution4-6 of liquid crystal droplets, it is essential thatwe understand the role of the characteristic parametersassociatedwith the process. In the case of a TIPS processwebelieve that for a given concentration thequenchdepthand the cooling rate are the two important parameters.The aim of this study is to understand the critical role ofthese two parameters under amicrogravity environmentand compare the experimental results with simulations(Monte Carlo).

Experimentswere carried out at theZARMDropTowerFacility in Bremen Germany, which provides a micro-gravity environment for a duration of 4.74 s.7 Because ofthe fixed microgravity exposure time in the presentexperimental setup it is difficult to separate the effects ofquench depth and cooling rate. Experiments show thata fast cooling rate, which is also associated with a deeperquench depth, yields smaller size droplets as compared toa slowcooling rate,which corresponds to a shallowquenchdepth.However, the simulation results show that up to a

certain quench depth (called the critical quench depth,considered here) the difference between the droplet sizesunder fast and slow cooling rates is negligible. For deeperquenchdepths than the critical one thedifference (asgivenby the correlation function, defined later) between thedroplet sizes becomes apparent. The correlation functionrises rapidly and then saturates.In section II, we describe the experimental details, and

insectionIIIweexplain thesimulationmodel. Theresults,the comparison with simulations, and discussions aregiven in section IV. Finally, the conclusionsarepresentedin section V.

II. Experimental Section

(a) Materials. In the formation of PDLC materials by theTIPS process, a mixture of monomeric liquid crystals consistingof 4-cyano-4′-n-alkylbiphenyls and4-cyano-4′-n-alkoxybiphenyls(n ) 1-12 carbon atoms), commercially known as E7 (EMChemical), was used as the dispersing phase. A thermoplasticepoxy was formed by mixing 1 equiv by weight of EPON 828(from Shell Company) with 1 equiv of commercial hardenercapcure 3800 (Henkel Inc.) and 1 equiv of liquid crystal E7. Themixture was sandwiched between two ITO glass plates. Filmthickness (12-30 µm) was controlled by polycarbonate orpolyamide film spacers. The sampleswere cured at 65 °C, abovethenematic-isotropic transition temperature ofE7, to formsolidwhite materials.(b) Methods. Microgravity experiments were carried out at

the ZARM Drop Tower in Bremen Germany. This facilityprovides amicrogravity duration of 4.75 s.7 TheTIPSapparatusconsists of sample cells sandwiched between Peltier platesmounted on heat sinks. The Peltier plates are used in heatingand cooling. Different heating temperatures and cooling rates

* Corresponding authors. Telephone: (514) 929-8143. Fax:(514) 929-8102.

X Abstract published inAdvanceACSAbstracts,March15, 1996.(1) Doane, J. W.; Vaz, N. A.; Wu, B. G.; Zumer, S. Appl. Phys. Lett.

1986, 48, 269.(2) Doane, J.W. InLiquid Crystal: Applications andUses; Bahadur,

B., Ed.; World Scientific Publishers: New Jersey, 1990; Chapter 14.(3) Parbhakar, K.; Dao, L. H.; Tabrizian, M.; Gingras, S.; Campbell,

G. Proceedings ofDropTowerDays 94, July 8, 1994,Bremen,Germany,p 18-25.

(4) Alt, P. M.; Pleshko, P. IEEE Trans. Electron Devices 1974, 21,146.

(5) Montgomery,G.P., Jr.;West, J. L.; Tamura-Lis,W.J.Appl.Phys.1991, 69, 1605.

(6) Fuh, A.; Caporaletti, O. J. Appl. Phys. 1989, 66, 5278. (7) Drop TowersBremen, User manual, version 2-1-2/91.

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(see for example Figure 1, cooling rate ) (Tf - Ti)/4.75) are ob-tained by using Peltier plates of different powers. Fast RTDprobes andhigh-speedacquisition systemsareused to determineand follow the temperature variation. Three sets of experimentswith each set consisting of three identical PDLC cells, in orderto insure the reproducibility of our results, are used for eachdrop.The morphology and microstructure of the PDLC films are

studied by scanning electron microscopy (SEM). Photomicro-graphs giving details of the PDLC film cross sections wererecorded using a Hitachi S-530 SEM unit. A thin conductinglayer of gold alloy was vacuum sputtered onto the section. Thesolubility limit of the liquid crystal in the polymermatrix aswellas the fraction of liquid crystal dispersed as microdroplets isdetermined bydifferential scanning calorimetry (DSC) analysis.Before we present the experimental data, we will describe thesimulation model.

III. Model

A 60 × 60 square lattice with a periodic boundarycondition is used to simulate themixture of liquid crystaland polymer.8,9 Simulations on a 100 × 100 system arealso tested toproduce onlyminormodifications, indicatingthat the presentmodel size is large enough to give reliableresults. The lattice sites are either occupied by liquidcrystal orpolymermolecules. Each liquid crystalmoleculeoccupies one single lattice site, whereas each polymermolecule occupies (m + 1) lattice sites, withm being thenumber of segments (of the same length as the latticeconstant) inonepolymermolecule. The interactionenergybetween the segment ends (each segment has two ends)of the same polymer molecule is assumed to be zero; asa result, the polymer molecules are flexible. In otherwords, a polymer molecule is free to assume any shape,ranging from a straight line to a coil. Moreover, in orderfor the phase separation between liquid crystal andpolymer to take place below the critical point, theinteraction energy (ε) between the liquid crystalmoleculesand thepolymersegmentends is consideredpositive,whileall the other interactions are zero. The movement of thepolymer molecules in the simulation is accomplished bythe reptation techniques,10-12 and no double occupancy ofany lattice sites is allowed. Oneattempted reptationmoveof the polymer molecules is defined as one Monte Carlostep (MCS), the number of which measures the evolutiontime of the system in the simulation process. Anyattemptedreptationmove is further checkedbyastandardMetropolis algorithm13 and accepted only when thefollowing condition is satisfied, i.e., min{exp[-∆E/kT], 1}g ú, where min stands for the minimum of the twoquantities, ∆E ) Ef - Ei is the change in total energy ofthe system due to the move, k is the Boltzmann constant,T is the temperature of the system, and ú is a uniformlydistributed random number between zero and unity.In each simulation themixture of the liquid crystal and

the polymer is first heated up to a very high temperature(here γ0 ) ε/kT0 ) 0) to ensure uniformmixing. Then thesystem is cooled down at a certain cooling rate to sometemperature Tf below the critical point (which is deter-mined8 to be γc ) ε/kTc ) 1.5) and allowed to evolve to itsthermodynamic equilibrium state. The temperature ofthe system is lowered according to the following: γ ) γft/tc, for t < tc, and γ ) γf, when t g tc. Here γf ) ε/kTf is the

final temperature of the system, t is the simulation time,and tc is the time when the temperature of the systemreaches its final value. Evidently, the value of tc deter-mines the cooling rate, and the smaller tc, the faster thesystem cools.

IV. Results and Discussion

(a) Drop Tower Experiments. Two identical speci-mens with liquid crystal concentration c) 0.50 were firstheated to ∼76 °C and then cooled at two different rates.The cooling was started at 0.25 s before the drop and wascontinued for 1.25 s after the drop. Because of the fixedduration for free fall ()4.75s) in thedrop tower, thequenchdepth and the cooling rate could not be controlledindependently. A faster cooling ratealwaysendedupwithadeeper quenchdepth. Figure 1 shows scanning electronmicroscopypictures of liquid crystalmicrodroplets for twodifferent cooling rates at 10-6 g. We find that the dropletsformedwitha slower cooling rate are larger in size (Figure1a) as compared to the ones producedwith a faster coolingrate (Figure 1b). These figures show that the combinedeffect of a faster cooling rate and a deeper quench depthis to yield smaller droplets. However, as shown below inthesimulation results, thedroplet sizesarehardlyaffectedby the quench depth in the case of a slow cooling rate. Inthe case of a fast cooling rate the droplet sizes areconsiderably affected within a finite range of quenchdepths, showing a saturation tendency for deeper quenchdepths.

(8) Jin, J.-M.; Parbhakar, K.; Dao, L. H. Comput.Mater. Sci. 1995,4, 59.

(9) Jin, J.-M.; Parbhakar, K.; Dao, L. H.MicrogravitysSci. Technol.1995, 8, 106.

(10) Wall, F. T.; Mandel, F. J. Chem. Phys. 1975, 63, 4592.(11) Baumgartner, A. J. Chem. Phys. 1984, 81, 484.(12) Baumgartner, A.; Heermann, D. W. Polymer 1986, 27, 1777.(13) Metropolis, N.; Rosenbluth, A. N.; Rosenbluth, M. N.; Teller, A.

H.; Teller, E. J. Chem. Phys. 1953, 21, 1087.

Figure1. Scanning electronmicroscopypictures forTIPScells(Epon/E7 50:50) at 10-6 g: (a) initial temperature Ti ) 75.96°C, final temperature Tf ) 63.28 °C with a cooling rate of 2.67°C/s (slow cooling); (b)Ti )76.56 °C,Tf )52.16 °Cwitha coolingrate of 5.14 °C/s (fast cooling).

Phase Separation of a Liquid Crystal in a Polymer Langmuir, Vol. 12, No. 8, 1996 2097

(b) Simulations. Monte Carlo simulations were donefor c)0.50underazerogravityenvironment. Thenumberof molecules in each polymer segment was fixed; here m) 7 was chosen. There are a total of 225 polymers whichoccupy 1800 (225 × 8) sites, wherease the liquid crystalmolecules occupy the remaining sites of the lattice. As inour earlier work,8 the pair correlation function G(r,t) isintroduced, which is defined as

where the summation is over all the sites of the latticeand n ) 60 × 60 ) 3600 is the total number of sites. Fora given site the occupation variable n is not unique andtakes a value of zero or unity. In the case when the twosites ri and ri + r are occupied by a heteropair, the productof the occupation variables is unity, and otherwise, it iszero. Here r is the distance between two sites and cantake any value allowed by the square lattice. However inthis study we consider only the case for r ) a (the latticeconstant) because small scale fluctuations are dominantin the early stage of the phase separation process. Fromits definition in eq1,wenote thatG(a,t) directlymeasuresthe size of the liquid crystal droplets. The larger valuesofG(a,t) areassociatedwithsmaller liquid crystaldroplets.Figure 2 shows the time dependence of the pair

correlation functionG(a,t) for different cooling rates. Thefinal temperature γf ) ε/kTf ) 10.0, which is considerablylower than the critical temperature (γc ) ε/kTc ) 1.5)8 forthis system. The phase separation takes place in theunstable (spinoidal decomposition) region. Curves A, B,and C correspond respectively to tc ) 0, 0.1× 109, and 1.5× 109 (MCS units). For each curve G(a,t) first decreaseswith simulation time t and attains a constant value. Thisevolution represents the complete process of phaseseparation, i.e. separation of the liquid crystal from thepolymer, growth, and relaxation of the liquid crystaldroplets to equilibrium. The difference among the curveslies in the final value ofG(a,t),whichdecreases from0.334(A) to 0.248 and 0.197 for curves B and C, respectively,indicating that the size of the liquid crystal dropletsincreases with tc (i.e. as the cooling rate is reduced). Thedependence of themorphology of the final state on coolingrate is clearly shown in Figure 3, where parts A, B, and

C correspond respectively to tc ) 0, 0.1 × 109, and 1.5 ×109 (MCS). In fact, the evolution of the mixture of theliquid crystal and the polymer on cooling is similar to thesimulated annealing process.14 When the temperaturedecreases, the system relaxes to its newequilibriumstate(which corresponds to a globalminimum in energy), givenby the low temperature. In our simulationmodel, as wellas in our experimental system, the interaction energy isgiven by the interface between the liquid crystal and thepolymer. Therefore the only way to reduce the energy of

(14) Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P. Science 1983, 220,671.

Figure 2. Variation of pair correlation function G(a,t) withsimulation time t. Curves A, B, and C correspond respectivelyto tc ) 0, 0.1 × 109, and 1.5 × 109 (MCS). The temperature ofthe system is γf ) ε/kTf ) 10.0, and the concentration of theliquid crystal is c ) 0.50.

Figure3. Morphology of the equilibriumstate obtainedunderdifferent cooling rates. Parts A, B, and C are for the cases oftc ) 0, 0.1 × 109 and 1.5 × 109 (MCS), respectively. Here thetemperature and concentration of the liquid crystal are thesame as in Figure 1. The open circles represent the liquidcrystal molecules, and the white background, the polymers.

G(r,t) )1

n∑i)1

n

η(ri,t) η(ri+r,t) (1)

2098 Langmuir, Vol. 12, No. 8, 1996 Jin et al.

the system is by diminishing the interface, i.e., byseparating the liquid crystal fromthepolymerand formingdroplets. Note that, for a given volume of liquid crystal,the final state with larger droplets possesses lowerinterfacial energy than the onewith smaller size droplets.During the process of relaxation to the global minimum,the system must overcome lots of energy barriers due tothe large number of degrees of freedom of the system.Consequently, for a slow cooling process, the system hasplenty of time to relax and overcome the energy barriersto reach its global minimum. On the other hand if thesystem is cooled rapidly, it has a greater chance to betrapped in some localminimum(which is higher in energythan the global minimum). Thus fast cooling results insmaller droplets as compared to slow cooling. This is inagreement with the experimental result as far as tenden-cies are concerned. An exact comparison is difficult atpresent because simulations are two dimensional. Onewouldrequire three-dimensional simulationresults,whichare very time consuming. As mentioned earlier, since inthe present experimental setupweare unable to separatethe quench depth from the cooling rate, it is difficult tosay which is the controlling factor. The net result is thata fast cooling rate combined with a deeper quench depthresults in small-size droplets and a slow cooling rate witha shallow quench depth produces larger droplets. Sinceit is important to know the effect of these parametersseparately,wehaveextendedoursimulations todeterminethe effect of final temperature Tf on droplet sizes for agiven cooling rate.We now examine the influence of final temperature on

the liquid crystal droplet sizes. The final temperatureparameter is given by γf ()ε/kTf); a smaller value of γfcorresponds to a shallow quench depth. Figure 4 showsa plot of ∆G(a) ) G0(a) - G1(a) as a function of γf. HereG0(a) is the final value of G(a,t) under fast cooling (tc )0) andG1(a) is for slow cooling (tc ) 1.5× 109 MCS). Eachdata point represents an average over five equivalentcomputer runs under the same conditions but withdifferent sets of random numbers. The error bars are

indicatedbyshortvertical linesattached to thedatapoints.From Figure 4 we note that ∆G(a) remains zero for γf )ε/kTf up to 4; i.e., there is virtually no difference betweenthe effects of fast and slow cooling rates on droplet sizesfor a shallow quench depth. As γf increases (lower Tf),∆G(a) first increases rapidly and then approaches somesaturation value of∼0.18. We also note thatG1(a) variesonly from0.18 to 0.20 (the variation iswithin an error barof 0.02) as γf increases from 4 to 15. Thus under the slowcooling rate the size of the liquid crystal is practicallyindependent of the quench depth. The fast cooling G0(a)increases with γf when the latter exceeds 4, as observedbefore.8 This is an important result, indicating that anycontrol of liquid crystal droplets, in the TIPS process, bycooling rate would be effective for deeper quenches, i.e. γfg 4. Physically one can explain this behavior as follows:for a shallow depth the particle or droplet energies aresufficiently high to overcome interfacial energy barriers,so one does not observe any difference between the effectsof fast and slow cooling rates on droplet sizes. In eachcase a globalminimum is achievedand the systemrelaxestoglobal equilibrium. As the final temperature is lowered,a certainproportionof theparticlesareunable to overcomethebarriers; i.e., energybarriersareactivatedwhichcreatelocal equilibrium positions in the system, and the fastcoolingrate can takeadvantageof these local equilibriums.A further reduction in the final temperature activatesmore barriers till saturation is achieved (i.e. all energybarriers have been activated or no particle has sufficientenergy to cross the smallest energy barrier) and hence∆G(a) is saturated.

V. ConclusionsWe have studied the effect of cooling rate on droplet

sizes in the TIPS process both experimentally and insimulation under microgravity environments. We findthat in both cases a faster cooling rate yields smallerdroplets and improves the uniformity of their dispersionin the polymer binder. In the present experimental setupwe are unable to study the importance of quench depthand the cooling rate separately. However the simulationresults indicate that surface interaction energy plays amajor role in setting up surface barriers which hindersthe growth. For shallow quench depths the dropletspossess sufficient energy to overcome the barriers andweare unable to distinguish between the droplet sizes underfast and slow cooling rates. For deeper quenches, beforesaturation, the surface energy barriers are activated andestablish local equilibriumstateswithhigher energy thantheglobalminimumfor the system. Thusadeeperquenchis essential for the fast cooling rate to be effective. As faras final droplet sizes are concerned, we find a reasonablygoodagreement between simulation and experiments.Anexact comparison is difficult because of the two-dimen-sional nature of the simulation lattice.

Acknowledgment. This work was supported by theNatural Science and Engineering Research Council(NSERC) of Canada and the Canadian Space Agency(CSA). We are grateful to Dr. M. Tabrizian and Mr. S.Gingras for participating in the drop tower experiments.We would also like to thank Mr. G. Campbell of CSA forhis interest in this work. One of the authors (J.M.J.)gratefully acknowledges a postdoctoral fellowship fromINRS.

LA950823F

Figure 4. Dependence of ∆G(a) on γf. Here ∆G(a) ) G0(a) -G1(a), withG0(a) andG1(a) being the final value ofG(a,t) of fast(tc ) 0) and slow (tc ) 1.5 × 109 MCS) cooling, respectively.Each data point represents an average over five equivalentcomputer runs under the same conditions but with differentsets of random numbers. The short vertical lines attached tothe data points are the error bars.

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