PHYSICAL REVIEW E, VOLUME 63, 061802

Theoretical simulation of holographic polymer-dispersed liquid-crystal filmsvia pattern photopolymerization-induced phase separation

Thein Kyu,* Domasius Nwabunma,† and Hao-Wen Chiu‡

Institute of Polymer Engineering, The University of Akron, Akron, Ohio 44325~Received 13 July 2000; published 15 May 2001!

A theoretical simulation has been performed to elucidate the emergence of nematic domains during patternphotopolymerization-induced phase separation in holographic polymer-dispersed liquid crystals. We consider areference system consisting of a single-component nematic, namely, 4-n-heptyl-48-cyanobiphenyl (TNI

542 °C), and a polymer network made from multifunctional monomers. To mimic pattern photopolymeriza-tion, the reaction rate was varied periodically in space through wave mixing. In the theoretical development,the photopolymerization kinetics was coupled with the time-dependent Ginzburg-Landau modelC equationsby incorporating the local free energy densities pertaining to isotropic liquid-liquid mixing, nematic ordering,and network elasticity. The simulated morphological patterns in the concentration and orientation order pa-rameter fields show discrete layers of liquid-crystal droplets alternating periodically with polymer-network-richlayers. The Fourier transforms of these patterns show sharp diffraction spots arising from the periodic layers.As the layer thickness is reduced, the liquid-crystal molecules are confined in the narrow stripes. The liquid-crystal domains appear uniform along the stripes, which in turn gives rise to sharper diffraction spots in Fourierspace. Of particular interest is that our simulated stratified patterns are in qualitative agreement with reportedexperimental observations.

DOI: 10.1103/PhysRevE.63.061802 PACS number~s!: 61.25.Hq, 61.41.1e, 64.75.1g

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I. INTRODUCTION

It has been well established that thin composite films ctaining liquid crystals~LC’s! and polymers are heterogeneous systems generally prepared via phase separatioduced by thermal quenching, solvent removal, and thermor photochemically initiated polymerization@1,2#. Of thesemethods, polymerization-induced phase separation~PIPS!initiated by UV radiation is a preferred way of producinthese composite films because of the ease of the fabricaprocess, which requires no solvent. Polymer-dispersed liqcrystals~PDLC’s! containing substantial amounts of polymand polymer-stabilized liquid crystals~PSLC’s! containing avery small amount of network polymer are two commtypes of LC/polymer composite. These composites hbeen customarily prepared via PIPS under uniform UV irdiation to obtain uniform distributions of LC droplets incontinuum of cross-linked polymer.

Recently, another type of LC/polymer composite knowas a holographic polymer-dispersed liquid crystal~H-PDLC!composite has been developed@3–8# through patternphotopolymerization-induced phase separation of Lmonomer mixtures by wave mixing, viz., allowing twpropagating UV laser beams to interfere at a certain anThe constructive and destructive interference of these plawaves gives rise to stripe fringes, the periodicity of whi

*Author to whom correspondence should be addressed. Emaidress: tkyu@uakron.edu

†Present address: 3M Company, Science Research CenterCenter, Bldg. 201-1N-34, St. Paul, MN 55144.

‡Present address: Essilor of America, Inc., Optical ThermoplasR&D, St. Petersburg, FL 33709.

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depends on the incident angles. When the spatially molated UV intensity fringes are imprinted on LCphotoreactive-monomer mixtures, photoreaction takes pin periodic striations, thereby creating a H-PDLC film wialternating LC-rich and polymer-rich layers. The refractiindex mismatch between the H-PDLC layers gives risediffraction of light, while the LC directors can be electricalswitched across the film. Thus H-PDLC’s have found potetial applications such as spatial light modulators, agile filtebeam steering, etc.

Most studies on H-PDLC films hitherto reported have fcused on experimental investigations of the effects of momer type, functionality, and LC concentration on morphogy development and electro-optical properties@3–8#. Forefficient fabrication of H-PDLC’s, it is essential to betteunderstand the mechanism underlying the pattern formprocess. Krongauz, Schmelzer, and Yohannan@9# studied thekinetics of anisotropic photopolymerization in a plasticizpolymer without examining any phase separation or msophase ordering. On the other hand, Wang, Yu, and Ta@10# performed a one-dimensional simulation on anisotrophase separation in a PDLC system based on the MCarlo approach. Although the qualitative features of tH-PDLC structure were captured in the simulation, the neatic ordering of the LC directors was not accounted fortheir theoretical formulation.

In this paper, we undertake a two-dimensional simulatof a H-PDLC via stratified pattern photopolymerizatioinduced phase separation by incorporating the pertinent ptopolymerization kinetics. In the simulation, we emplosome material parameters such as the nematic-isotropicsition temperature of the LC, network functionality, etc., oreference system that has been studied extensively inlaboratory@11–13#. The spatiotemporal evolution of the concentration and orientational order parameters has been c

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THEIN KYU, DOMASIUS NWABUNMA, AND HAO-WEN CHIU PHYSICAL REVIEW E 63 061802

lated by incorporating the local free energies of isotromixing, nematic ordering, and network elasticity into ttime-dependent Ginzburg-Landau equations~TDGL modelC! @14,15# in conjunction with the photopolymerization knetics. It is of particular interest that our simulated resuqualitatively capture the experimental H-PDLC morpholoreported by Bunning and co-workers@3–8#.

II. THEORETICAL MODEL

A. Description of pattern photopolymerizationof LC Õmonomer mixture

Let us consider a binary mixture of nematic LC and mtifunctional monomer that exhibits an upper critical solutitemperature~UCST! phase diagram overlapping with thnematic-isotropic transition of the constituent LC~see Fig.1!. Polymerization is triggered isothermally in the isotropstate by allowing two propagating UV laser beams to intfere at a certain angle~see Fig. 2!. Photopolymerization ofmonomer occurs preferentially in the high intensity regiorelative to that in the low intensity regions. As a consquence, a concentration gradient develops in the mixtuwhich allows LC molecules to diffuse from a high intensito a low intensity region, whereas monomer moleculesfuse in the opposite direction, thereby forming LC-rich laers alternating periodically with polymer-rich layers~Fig. 2!.

FIG. 1. Calculated coexistence and spinodal curves of mixtuof LC/monomer and LC/cross-linked polymer in comparison wthe experimental cloud point phase diagrams of the K21/NOAsystem. The coexistence regions for the LC/network system wlabeled with italic letters to distinguish them from those of tLC/monomer blend.

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In previous papers@11–13#, we have investigatedtheoretically and experimentally the dynamicsphotopolymerization-induced phase separation in mixturea low molar mass nematic LC and a multifunctional monmer subjected to uniform UV irradiation. For pattern photpolymerization one must account for the spatial variationthe reaction rate induced by the periodic UV intensity~Fig.2!.

Consider a H-PDLC film in the form of a square gridlength L. Let N be the number of periodic layers~i.e., in-versely proportional to layer thickness!; then the intensity ofradiationI may be described as

I 5I 0 cos2S xN

Lp D , ~1!

where I 0 is the maximum intensity, whilex is the distancemeasured along the horizontal axis. Since the rate of phpolymerizationda/dt8 is proportional to the square root othe incident intensity, i.e.,da/dt8}I 1/2, one may write

da

dt85k8I 0

1/2cosS xN

Lp D ~12a!, ~2!

wheret is time,a represents fractional conversion of monmer to polymer, andk8 is the apparent reaction constantunits of reciprocal time. I 0 is the intensity of incident ra-diation, which was accounted for through the reaction cstant during the simulation. For a fixedN and L, x is thevariable that determines the regions where the photoreacrate varies periodically. In the simulation, the reaction timt8 and the reaction kinetic coefficientk8 may be renormal-ized in dimensionless units ast5(L/ l 2)t8, k5( l 2/L)k8,whereL is the mutual diffusion coefficient andl is the char-acteristic length scale. WhenN50, Eq.~2! reduces to that ofthe uniform illumination case~see Ref.@13#!.

B. Description of dynamics of phase separationand pattern formation

The model proposed here is based on coupled timdependent Ginzburg-Landau equations, known as modeC,which consists of conserved concentration and nonconseorientational order parameters@14,15#. Model C has beensuccessfully applied to the elucidation of dynamics of ph

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FIG. 2. Schematic illustration of periodic fringes formed bmixing of two UV waves, showing constructive and destructiinterference. During photopolymerization, monomers diffuseward the bright region where the reaction rate is the highest, avice versa, the LC molecules diffuse into the dark region wherereaction rate is minimum.

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THEORETICAL SIMULATION OF HOLOGRAPHIC . . . PHYSICAL REVIEW E 63 061802

separation and pattern formation in thermal-quench-induphase separation of liquid-crystal polymer solutions@16,17#and LC/linear polymer mixtures@18–22#. Recently, modelChas been coupled with the reaction kinetics to describephotopolymerization-induced phase separation dynamicLC/polymer mixtures subjected to uniform irradiation@13#.

We extend the same methodology to describe the dynics of pattern polymerization-induced phase separationH-PDLC films. In view of the fast nature of photopolymeization, it is reasonable to assume that the conversionmonomer to polymer is almost instantaneous; residual momer, if any, is considered to be miscible with the emergpolymer. Treating the system as pseudo-two-phase, the rtion kinetics of the pattern photopolymerization@Eq. ~3!#may be coupled with the TDGL modelC equations@Eqs.~4!and ~5!# by incorporating the free energies of isotropic miing, nematic ordering, and network elasticity as follow@14,15#:

]wM

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dF

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]t5“•FL“S dG

dwLD G1hw , ~4!

]s~r ,t !

]t52RS dG

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wherewL(r ,t) is the conserved concentration order paraeter~or volume fraction! of the LC at positionr and dimen-sionless timet, whereass(r ,t) is the nonconserved orientational order parameter of the LC at the same locationtime. Note that the orientational order parameters(r ,t) istreated as scalar for simplicity. A general and more compapproach would be to treat it as a tensor form~e.g., see Refs@18# and@19#!. If the monomer and polymer are immisciblit is necessary to solve three coupled equations, i.e., E~3!–~5!; otherwise, only two coupled equations would be aequate, e.g., Eq.~5! with Eq. ~3! or with Eq. ~4!. We choseEqs.~4! and ~5! in the simulation under the assumption ththe monomers and the emerging polymer are miscible. Fthermore, the monomerwM(r ,t) and the emerging polymewP(r ,t) concentrations are related towL(r ,t) via the frac-tional conversiona as follows@13#

wM5~12a!~12wL! or wP5a~12wL!. ~6!

As polymerization is initiated, some of the monomer is coverted to polymer; thus the system is composed of Lmonomer, and polymer. The incompressibility conditigiveswL1wP1wM51. The quantityL in Eq. ~3! is the mu-tual diffusion coefficient having the property of Onsagreciprocity @23#

L5LLLM1LLLP1LMLP

LL1LM1LP, ~7!

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where LL5wLr LDL , LM5wMr MDM , and LP5wPr PDP .DL , DM , andDP are the self-diffusion coefficients of LCmonomer, and polymer, respectively, whiler L , r M , andr Pare their respective segment lengths. Since the self-diffuscoefficient of the polymer is inversely proportional to thsquare of the number of segments (DP}1/r P

2 ), andr 5` fora cross-linked polymer, it follows thatDP50. ThusLP50.

The coefficientR in Eq. ~5! is related to the rotationamobility of the LC molecules, and is taken as constantsimplicity @16#, while the quantitieshw and hs are thermalnoise in the concentration and orientation fields, respectivsatisfying the fluctuation dissipation theorem. Sinces iscoupled tow, it follows that hs is also coupled tohw . Thetotal free energy of the system,G, may be written as@14#

G5Ev@g~wL ,wM ,wP ,s!1kwu¹wLu21ksu¹su2#dv ~8!

whereg(wL ,wM ,wP ,s) is the local free energy density othe system. The termskwu¹wLu2 and ksu¹su2 are nonlocalterms associated with the gradients of the LC concentraand orientational order parameters, respectively.kw and ksare the coefficients of the corresponding interface gradiewhich are taken as constants for simplicity. The local frenergy density of the mixture,g, consists of isotropic mixinggi , nematic orderinggn, and elasticityge free energy densi-ties. The free energy density of isotropic mixing maydescribed in the context of the Flory-Huggins theory@24,25#as extended to a three-component system in what follo@23#:

gi5wL ln wL

r L1

wM ln wM

r M1

wP ln wP

r P

1~xLMwLwM1xLPwLwP1xM PwMwP!. ~9!

Since residual monomers and the emerging polymers aresumed to be miscible, it is reasonable to regardxM P as zeroor negligibly small relative to the other interaction parameters. Therefore, we takexLM5xLP5x. Since for a cross-linked polymerr P5`, andr L5r M51 for LC and monomermolecules, Eq.~9! reduces to

gi5wL ln wL1wM ln wM1x~wLwM1wLwP!. ~10!

The isotropic interaction parameterx is taken to be an in-verse function of temperatureT of the form x5A1(xc2A)Tc /T, whereTc and xc are critical values with refer-ence to the starting LC/monomer system~see Fig. 1!, whileA is an adjustable parameter to account for the broadnesthe coexistence curve. In the context of Maier-Saupe the@26,27#, the nematic ordering free energy densitygn may beexpressed as

gn51

r L~2wL ln z1 1

2 nwL2S2!, ~11!

where z and s are, respectively, the normalized partitiofunction and the nematic order parameter defined by thetegrals@21#

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THEIN KYU, DOMASIUS NWABUNMA, AND HAO-WEN CHIU PHYSICAL REVIEW E 63 061802

z5E0

1

expFnwLs

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s53

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wherex5cosu, while u is the angle between the nematic Ldirector and the reference axis. The nematic interactionrametern is related to the nematic-isotropic transition temperatureTNI asn54.541(TNI /T) @27#. For a flexible cross-linked polymer chain obeying ideal Gaussian chain statisthe elastic free energyge may be described as@28#

ge52ae

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2/3~wP1/32wP!1

be

r cwP ln wP , ~14!

whereae andbe are network model parameters andr c is thesegment length between cross-linked points. The Flory afnetwork model@30# was employed in the calculation assuming the network functionalityf 53. The parameterF0 in Eq.~14! represents the reference volume fraction of the polymnetwork, which is taken as the volume fraction at the onof cross-linking, i.e.,F05wP @29#. Taking the variationalderivatives ofG with respect towL ands according to Eq.~8!and inserting them into Eqs.~4! and ~5! gives

]wL

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]wL1

]gn

]wL1

]ge

]wL2kw¹2wLD G1hw , ~15!

]s

]t52RS ]gn

]s2ks¹

2sD1hs , ~16!

where the partial derivatives appearing on the right hasides of Eqs.~15! and ~16! may be obtained@13,21# fromEqs.~10!, ~11!, and~14!.

C. Numerical simulation procedure

To simulate the spatiotemporal growth of PIPSH-PDLC, Eqs.~15! and~16! were solved numerically usingfinite difference method on a 1283128 square grid based ospecified initial and boundary conditions. For spatial stepcentral difference discretization scheme was used, whiforward difference discretization was utilized for temposteps. Both the grid size and the time step were chosenficiently small to ensure that changes in them exerted littleno effect on the calculated results. The periodic boundconditions used were similar to those of previously reporwork @16,21#. In the simulations, photopolymerization wainitiated in the isotropic region of the starting LC/monomphase diagram~see Fig. 1!. The initial LC volume fractionswL(r ,0) at each grid point were calculated by triggering radom thermal noise that satisfied the fluctuation-dissipatheorem. Using knownwL(r ,0), the initial s(r ,0) was ob-tained through the self-consistent solution of Eqs.~14! and~15!. The values ofL, R, kL , andks used in this work arewithin the range employed by others@16,20#. Fourier trans-formation was also undertaken on the emerging patternthe concentration and order parameter fields.

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III. RESULTS AND DISCUSSION

A. Phase diagrams of LCÕmonomer and LCÕcross-linkedpolymer network

Figure 1 shows the calculated binodal and spinodal curof the LC/monomer and the LC/cross-linked polymer sytems in comparison with the experimental cloud point phdiagram of a reference system. For detailed calculationsexperimental procedures, interested readers are referreour previous paper@31#. Here, we shall briefly discuss theffect of cross linking on the phase diagram based onbinodal curve that separates the stable~one-phase! from theunstable~two-phase! regions. As evident in Fig. 1, the LCmonomer coexistence curve is a UCST type overlappwith the nematic-isotropic transition of the constituent LThe LC/monomer phase diagram is similar in shape to tof the LC/linear polymer mixture@27,32#, except that thecritical point of the starting LC/monomer system is located(wL50.5) due to the comparable size of the constituent mecules.

Photopolymerization was carried out on a typical mixtu(wL50.75) in the isotropic region of the starting LCmonomer as indicated by3 in Fig. 1. As polymerizationadvances, the binodal curve moves upward asymmetrictoward the higher LC content side. When it crosses the retion temperature~point 3!, the system becomes unstable aundergoes phase separation. The process of phase sepais influenced by the network elasticity; hence for the Lcross-linked polymer the coexistence curve makes an upwturn asymptotically near the pure LC axis. There appearbe no identifiable critical point in the binodal curve of thLC/cross-linked polymer system. Bauer, Briber, and H@29# made a similar observation in the case of blendslinear polymer/cross-linked network. Since the polymer nwork can no longer dissolve in the pure LC, the equilibriuphases are pure LC solvent and swollen network~or gel!. Itshould be noted that in calculating the LC/cross-linked pomer phase diagram the LC ordering free energy is notfected by the polymer topology@31#.

B. Dynamics of uniform photopolymerization-inducedphase separation

Prior to examining the stripe pattern formation durinPIPS, it is instructive to examine the PIPS dynamics arisfrom uniform UV irradiation. Numerical simulation was conducted on a LC/monomer mixture with the following condtions: N50, L5128, wL50.75, T530 °C, I 051, and k51024. The polymerization temperature corresponds toisotropic state of the LC/monomer mixture~see Fig. 1!. Fig-ure 3 exhibits the dimensionless time sequence of~a! theemergence of LC domains and~b! the corresponding Fourietransform scattering images during the course of phase sration. Note that the gray level of the images was normalizfor the sake of clarity. The initial morphological pictures arepresentative of random thermal fluctuations. With elapstime, interconnected structures emerge in the concentrafield. The pattern in the orientation field lags behind, asmolecules have to segregate out before nematic ordering

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THEORETICAL SIMULATION OF HOLOGRAPHIC . . . PHYSICAL REVIEW E 63 061802

take place. The interconnected structures grow in timethen break down into droplets. With continued elapsed timthe domains increase in size, but the network formatseemingly prevents further coalescence. At late stages, hever, the two order parameter fields appear to merge tosame spatial topology.

As shown in Fig. 3~b!, the initial scattering patterns arvery diffuse and weak. It is seen that the initial scatterpatterns in the orientation order parameter field lag behthose of the concentration field. As time elapses, the scaing patterns intensify and transform to halos, while collaing to smaller diameters. The appearance of sharp scattehalos implies the development of domain periodiciwhereas the collapse of the halos to smaller diametersbe attributed to the domain growth. Later both fields evoto the same scattering halo, which is consistent with thesults of Fig. 3~a!.

C. Dynamics of stratified pattern formation via periodicphotopolymerization-induced phase separation

Next, we examine the emergence of stratified patternmation. The simulation was performed on a LC/monommixture of the same composition under the same conditias that in Fig. 3, except thatN54 and L5128. Figure 4shows snapshots of~a! spatiotemporal evolution of morphologies~first two columns! and~b! the corresponding Fourier transform patterns~last two columns! for both the con-centration and orientation order parameters. With

FIG. 3. Spatiotemporal evolution of simulated morphology aFourier transform patterns of a standard PDLC formed during uform UV irradiation. Simulation was performed usingwL50.75,T530 °C, andk51024. The indicated time steps are in dimensioless units.

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progression of time, LC droplets emerge~e.g., see 103 timesteps!. By virtue of the stratified pattern polymerization, i.ethe periodic spatial modulation of the reaction and hencephase separation, the LC droplets formed are confineddiscrete layers alternating periodically with polymer-riclayers~dark regions!. It should be pointed out that only thLC molecule and monomer are permitted to diffuse in tsimulation as the emerging polymer chains are chemicfixed due to network formation. The LC domains grothrough coalescence within the confined layers. These silated patterns are in good accord with the experimenH-PDLC morphologies reported by Bunning and co-worke@5–8#.

Regarding a rough estimation of the droplet size, it dpends on the choice of the length scale, the charactertime, and the mutual diffusion coefficient. If one utilizes aaverage diffusivity of 1026 cm2/s ~for the monomer and alow molecular weight LC!, a characteristic time of 1026 s,and assuming that the photopolymerization time is very fasay 1 s, the estimated characteristic size would be oforder of 33 nm. Hence, the calculated picture frame (13128) would be approximately 4.2mm2. This in turn givesan average droplet size of about 330 nm. These estimlength scales are within the range reported by Bunninget al.@5–8#.

As shown in Fig. 4~b!, the corresponding Fourier transform patterns are very diffuse and weak initially. Scatterirings emerge as droplets form. As the droplet domains gthe diameter of the scattering rings gets smaller. Sub

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FIG. 4. Spatiotemporal evolution of simulated morphology aFourier transform patterns of a H-PDLC formed during pattern ptopolymerization. Simulation was performed with the following prameters: wL50.75, T530 °C, k51024, N54, and L5128 indimensionless units.

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THEIN KYU, DOMASIUS NWABUNMA, AND HAO-WEN CHIU PHYSICAL REVIEW E 63 061802

quently, diffraction spots emerge by overlapping with texisting scattering halo. The diffraction spots may becribed to the development of periodic layers in the conctration field, whereas the weak surrounding scattering hmay be attributed to scattering arising from the interpartiinterference of the droplets within the layers. To improvediffraction performance of a H-PDLC, the scattering rinshould be suppressed or eliminated completely. In otwords, the droplet morphology within the layers musteliminated, which may be achieved by narrowing the laysuch that the LC molecules can grow only along the strip

Figure 5 shows the simulated patterns forN54, 8, and 16and their effects on the emerging H-PDLC morphologies athe corresponding Fourier transform images. The simulaparameters are the same as in Fig. 4 except that the clated patterns are fort5105 steps. As the number of periodilayers N increases, the layer thickness is reduced accoingly. When the number of layersN516, the layer thicknessis so restricted that the LC droplets grow preferentially alothe narrow stripes. It is also apparent that the scatteringresulting from the interparticle interference of the LC drolets disappears.

Figure 6~a! shows the comparison of a one-dimensionscan of the concentration field as a function of the numbelayers. At N54, the LC concentration profile is broad anappears heterogeneous due to the presence of the LCmains within the layer. With eight layers, the LC distributiois somewhat improved. AtN516, the LC concentration istruly uniform. As shown in Fig. 6~b!, the diffracted intensitypeaks~or structure factor in dimensionless units peaks! of theN516 case are well resolved as compared to the othercases, suggesting an improvement in the diffraction eciency. In addition, the growth dynamics of the domacould be affected by the thickness effect.

In Fig. 7 are shown the temporal growth curves for twL50.75 blend for variousN values in comparison with thafor uniform illumination (N50). In the N50 case, phase

FIG. 5. Effect of thickness of periodic layers on simulated mphological and Fourier transform patterns. The simulation pareters are the same as in Fig. 4, except that here the dimensiotime stepst5105.

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FIG. 6. One-dimensional scans of the concentration profilesthe vertical scan of the diffracted intensity of the correspondFourier transform patterns in Fig. 5. Note that the zeroth orFourier peak was masked in order to discern the higher orsmaller peaks. Both the concentration and structure factor ardimensionless units.

FIG. 7. Comparison of the temporal growth dynamic curvesvariousN values~inversely proportional to the layer thickness!.N50 represents the case of uniform illumination.

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THEORETICAL SIMULATION OF HOLOGRAPHIC . . . PHYSICAL REVIEW E 63 061802

separation is first noticed in the concentration field; thnematic ordering takes place within the domains. A subchange in curvature~or an inflection! in the vicinity of 1000time steps in the growth curve was discerned. This inflecthas been attributed to the consequence of competitiontween the phase separation and the nematic ordering@13,21#.A similar trend was observed for differentN values, exceptthat the growth process was expedited with decreasing lthickness or increasingN. This observation is not surprisinin view of the fact that, as the layer thickness is reduced,growth occurs preferentially along the layer due to the inaity to grow in the lateral direction. It is reasonable to infthat the reduction in layer thickness expedites the coacence process.

Furthermore, it is of interest to investigate the effectinitial LC concentrations~wL50.75, 0.5, and 0.25! on stripepattern formation as depicted in Fig. 8. During photopomerization, LC molecules diffuse to dark~low intensity! re-gions, whereas reactive monomers diffuse to the bright~highintensity! regions. As can be seen at 2500 time stepswL50.75, some LC~white color! domains are seeminglpresent between the successive layers. With elapsedthese LC domains are merged with those within the LC-r

FIG. 8. Spatiotemporal growth of the LC domains within temerging stripes driven by the pattern polymerization-induphase separation for three different LC concentrations. The simtion parameters are the same as in Fig. 4, but emphasis is placshorter dimensionless time steps up to 104 to discern the early stagof preferential coalescence along the stripes.

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layers. The LC domains grow through coalescence prefetially along the stripes, showing elongated~or intercon-nected! domains due to confinement by the layer. A similobservation can be made in the case of 50% LC concention ~middle column!, except that the emergence of the Lstripes is seemingly faster. The faster domain growth wincreasing monomer concentration may be attributed tofaster photopolymerization of the monomer. In the casevery low LC concentration (wL50.25), the coalescence process has been greatly expedited due to the fast photopmerization reaction, and well-aligned LC stripes are exhited.

As shown in Fig. 9~a!, the 75% LC at 105 steps has well-aligned stripes in both the concentration and orientatioorder parameter fields. It should be emphasized that thestripes in the 25% and 50% LC compositions are more uform throughout than those of the 75% LC based H-PDfilms. The diffraction spots remain virtually the same@Fig.9~b!# for the three compositions. Hence, lowering the Lconcentration did not sacrifice the diffraction performancethe H-PDLC. The finding that the LC stripes in the 25% Lare well defined and essentially indistinguishable from thof the 50% and 75% LC content composites suggestsH-PDLC’s may be fabricated with lesser amounts of LC, atherefore the cost of materials may be reduced considera

IV. CONCLUSIONS

We have demonstrated stripe pattern formation in a hographic polymer-dispersed liquid crystal~H-PDLC! via an-isotropic pattern photopolymerization-induced phase seption. The simulated LC droplets are confined in discrelayers alternating periodically with polymer-network-ric

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FIG. 9. Effect of LC concentration on the simulated morphogies and the structure factor~diffraction peaks in dimensionlesunits! of the Fourier transform patterns of the H-PDLC. Note ththe zeroth order Fourier peak was masked in order to discernhigher order, smaller peaks. The simulation parameters are theas in Fig. 8, except for dimensionless time stepst5105.

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THEIN KYU, DOMASIUS NWABUNMA, AND HAO-WEN CHIU PHYSICAL REVIEW E 63 061802

layers. The Fourier transform patterns reveal scattering rinitially, and then show diffraction spots as the periodic laers are formed. As the number of periodic layers is increathe layer thickness is reduced. The LC droplets grow throcoalescing preferentially along the narrow stripes, whichturn gives rise to sharper diffraction spots in the Fourspace. Reducing the LC concentration to 50% or 25% mathe LC directors more uniform throughout the stripes relatto those of 75% LC based H-PDLC films without sacrificin

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the sharpness of diffraction spots. This observation suggthat H-PDLC’s may be fabricated with lesser amounts ofwithout sacrificing the diffraction performance.

ACKNOWLEDGMENT

Support of this work by the NSF-STC Center for Advanced Liquid Crystal Optical Materials~ALCOM! viaGrant No. 89-20147 is gratefully acknowledged.

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