Optimal Chain Architectures for the Molecular Design of Functional Polymer Surfaces

Optimal Chain Architectures for the Molecular Design of FunctionalPolymer Surfaces

Patricia Anne V. O’Rourke-Muisener and Jeffrey T. Koberstein*,†

Department of Chemical Engineering, Polymer Program, Institute of Materials Science, University ofConnecticut, Storrs, Connecticut 06269

Sanat Kumar

Department of Materials Science and Engineering, The Pennsylvania State University,University Park, Pennsylvania 16802

Received November 13, 2001

ABSTRACT: The Scheutjens-Fleer self-consistent mean-field theory is used to calculate the surfacesegregation of various chemical functional moieties located on functional polymers of different architec-tures. Our results demonstrate the importance of the number and location of functional groups and theirsurface preference relative to polymer backbone segments in determining surface segregation. In general,we conclude that adjacency of similar functional groups is the most effective means for enhancing surfacesegregation of functional groups and that having two functional groups of similar character is alwayspreferable to having two functional groups of opposite character, the Pushmi-Pullyu architecture, whereone group prefers the surface while the other is repelled from it. The calculations demonstrate that theoptimal architecture for producing a low-energy release surface is a functional polymer with adjacentlow-energy functional groups located at one chain end. In this situation, both enthalpic and entropicfactors serve to drive chain ends to the surface. In contrast, high-energy adhesive surfaces are best obtainedby placing adjacent high-energy functional groups at the center of the polymer chain. High-energy groupssituated at the middle of the chain locate preferentially in the second lattice layer, from which they canmigrate readily to the surface when it is contacted with any other high surface energy medium.

Introduction

Strategies for polymer surface modification are animportant element in many different technologies in-cluding paints, coatings, adhesives, lubricants, and poly-mer blends. Achieving the desired surface properties isusually dependent upon the ability to locate particularfunctional groups at the surface. When release proper-ties are the goal, for example, a common approach tosurface modification is the inclusion of low-energyfluorocarbon or silicone components that lower the sur-face tension. High-energy functional groups are oftenincorporated into the polymer structure when adhesiveproperties are desired. Early surface tension measure-ments on block and graft copolymers prepared from twomonomers of different surface energy provide clear evi-dence that the distribution of various functional groupsalong the polymer chain has a marked influence on theirsurface properties.1,2 Surface tension is much lower forthe block copolymers where lower-energy repeat unitsare less constrained and freer to adsorb preferentiallyat the air-polymer interface. Chain architecture isexpected to have a similarly potent influence on thesurface properties of functional polymers. An importantgoal of our research, therefore, is to gain a molecular-based understanding of how the distribution and natureof functional groups attached along a polymer chain canbe used to design the surface properties of a functionalpolymer. In this sense, we broadly define a functionalgroup as any chemical unit that imparts a particulardesired property to the surface.

Functional polymers must be considered as hetero-geneous materials, particularly with respect to theirsurface properties, and are therefore susceptible tosurface segregation phenomena. That is, a functionalgroup that has a lower surface energy than its polymerbackbone will segregate to the surface in order todecrease the overall surface energy and free energy ofthe system. The degree of segregation is determined bya balance between the free energy gain associated withthe surface tension reduction and the free energy costof relocating the functional groups to the surface.Surface segregation is a general phenomenon for mis-cible and immiscible multicomponent systems and hasbeen studied for polymer blends,3,4 copolymers,5 polymersolutions,6 and end-functional homopolymers.7

End-functional polymers serve as a convenient modelsystem for understanding the general behavior of func-tional polymer surface properties. Surface tension mea-surements8 on functionally terminated poly(dimethyl-siloxane) indicated that end groups with low surfaceenergy relative to the chain backbone were selectivelyadsorbed at the polymer-air interface. Conversely, endgroups with higher surface energy relative to the chainbackbone were depleted from the surface. X-ray photo-electron spectroscopy measurements9 confirmed thedepletion of higher surface energy end groups from thesurface and showed that the depletion zone was na-nometers in thickness, comparable to the chain dimen-sions.

Neutron reflectometry experiments were performedon three end-functional polystyrenes: a “neutral” controlspecimen prepared by proton termination, a “repulsive”end group system terminated with high surface energycarboxylic acid end groups, and an “attractive” endgroup system containing low surface energy fluorocar-

* To whom correspondence should be addressed.† Present address: Department of Chemical Engineering,

MC4721, Columbia University, 500 West 120th Street, New York,NY 10027.

771Macromolecules 2003, 36, 771-781

10.1021/ma011969q CCC: $25.00 © 2003 American Chemical SocietyPublished on Web 01/04/2003

bon chain ends.7 The fluorinated end groups wereabsorbed at the surface, and the carboxylic acid endgroups were depleted from the surface. For the “neutral”end group system, the sec-butyl initiator fragmentslocated at the opposite chain end segregated preferen-tially to the air interface since they were the lowestsurface energy constituent of the polymer.

Several groups have examined the effects of fluori-nated end groups on the surface composition and prop-erties of different model systems, in particular polysty-rene and poly(ethylene oxide).10-14 Angle-dependentX-ray photoelectron spectroscopy studies of ω-fluorinat-ed polystyrenes demonstrated a surface excess of thelow-energy fluorosilane end groups,15 and contact anglemeasurements revealed that the degree of end groupsurface enrichment decreased with increasing molecularweight.16

Theodorou17,18 applied the mean-field self-consistentlattice theory of Scheutjens and Fleer19 to the case ofcopolymers with arbitrary architecture in order to studythe behavior of a polymer chain with an “attractive” endgroup. It was found that selective adsorption of thelower energy end groups in the topmost lattice layer wasaccompanied by depletion in deeper layers, the latterresult arising from chain connectivity. The tendency ofthe attractive end groups to absorb on the surfacebecame more pronounced with increasing chain length.

In previous work, we used a similar lattice model tostudy end group partitioning in R,ω-functional poly-mers.20 The theory successfully reproduced experimen-tal surface tension data for several R,ω-functional poly-(dimethylsiloxanes).8 End group segregation was pri-marily controlled by surface energy differences betweenthe chain ends and repeat units; entropic effects werefound to be negligible for most practical cases. Theentropic driving force for end group segregation wasshown to be of the order of 1/2kBT and to lead to a slightsurface excess of nonfunctional chain ends at the sur-face, in agreement with previous theoretical results.18,21

The goal of this paper is to answer a number ofremaining questions regarding the surface propertiesof functional polymers. An extension of Theodorou’sformalism17 is applied to theoretically probe how thelocation, number, and type of functional groups placedalong a polymer chain influence the composition anddistribution of functional groups at a surface. Thedependence of surface properties on the chain lengthand the surface energy difference between functionalgroups and the chain backbone is also examined. Theinformation obtained through this study provides aframework for the molecular design of functional poly-mer surfaces with properties that are optimized for aparticular application.

Theoretical Background

The framework for the calculations is the self-consistent mean-field lattice theory originally developedby Scheutjens and Fleer19 to study adsorption in poly-mer solutions. A similar approach was utilized byHariharan et al.22,23 to study the surface properties ofpolydisperse polymer melts and binary polymer blends,Theodorou17,18 to study the behavior of copolymers ofarbitrary architecture near a hard surface, and our owngroup to investigate the surface properties of R,ω-functional polymers.20

The functional polymer is placed on a cubic latticeconfined within two impenetrable walls that are suf-

ficiently separated to provide a bulklike region in thecenter of the film. The lattice is incompressible witheach lattice site occupied by a single chain segment.Normally the lattice volume is set equal to the volumeof the polymer repeat unit; however, it is more conve-nient in the present case to equate it to the volume ofthe functional group. The number of total chain seg-ments, or normalized chain length, r, is then the totalvolume of the chain divided by the volume of thefunctional group

where Z is the number of repeat units of volume vr, vrefis the reference volume for a lattice site which is setequal to volume of the functional group, and N is thetotal number of functional groups per polymer chain.

Surface segregation is governed by a balance betweenthe resultant surface energy reduction and the requiredchange in chemical potential associated with segrega-tion of the functional group. The magnitude of the lattereffect is related to the bulk interaction parameter, ø,between a functional group and the chain backbone. Weneglect bulk interactions in the calculations but showin the Appendix that bulk interactions simply increasethe degree of surface segregation but do not alter thequalitative nature of surface segregation behavior.

The surface interaction parameter is related to thedifference in adsorption energies of the functional groupand a repeat unit segment

where kB is Boltzmann’s constant, T is temperature, andU s

i is the change in energy associated with moving asegment of type i from the pure bulk to the surface. Thelatter adsorption energy is equal to the surface tension,γi, multiplied by the surface area per lattice site, whichfor a cubic lattice is a ) vref

2/3. The surface interactionparameter is defined so that a positive value indicatesthat a functional group is repelled from the surface(repulsive or high surface energy functional group),while a negative value implies that functional groupsare preferentially absorbed at the surface (attractive orlow surface energy functional group).

The equations utilized in the self-consistent-fieldtreatment are outlined in the Appendix. The parametersneeded for these calculations are the number and loca-tion of the functional groups, the polymer chain length,and surface interaction parameters, øs. The output ofthe calculations is the functional group concentrationfor each lattice layer.

Results and DiscussionBasic Features of End-Functional Polymer Sur-

faces. The characteristic features of all functionalpolymer surfaces that we have studied are qualitativelysimilar and can be conveniently illustrated by reviewingthe surface properties of R-functional polymers. To makethis review more relevant, we first consider the rangeof surface interaction parameter values that might bepractically encountered in real systems. øs values re-ported in the literature range from -1.5 for an endfluorinated polystyrene12 to 0.61 for carboxyl-terminated

r )Zvr + Nvref

vref(1)

øs )Us

1 - Us2

kBT)

(γ1 - γ2)akBT

(2)

772 O’Rourke-Muisener et al. Macromolecules, Vol. 36, No. 3, 2003

PDMS.20 General discussions are therefore confined toa range of reasonably expected øs values defined by -4e øs e 4. To simplify discussion, we adopt the conventionof referring to a functional group as “attractive” whenit has a lower surface tension than that of the polymerbackbone (øs < 0) and it adsorbs preferentially at thesurface and as “repulsive” when it has a higher surfacetension than the chain backbone (øs > 0) and is depletedfrom the surface.

The molecular configurations anticipated from latticemodel calculations for functional and nonfunctionalpolymers at an air-polymer interface are qualitativelyillustrated in Figure 1. The darker cubes represent acubic lattice site occupied by an end group while thelighter cubes are lattice sites occupied by the chainrepeat units. The end groups on the nonfunctionalpolymers (Figure 1b) are distributed randomly through-out the cubic lattice. Attractive end groups on theR-functional polymer (Figure 1a) are enriched at thesurface and depleted in subsequent layers with the endgroup concentration gradually rising to the bulk endgroup concentration. Repulsive end groups (Figure 1c)are depleted in the top lattice layer and enriched indeeper layers with the end group concentration gradu-ally decaying to the bulk value.

Predicted surface concentration depth profiles forR-functional polymers with chain length r ) 11 arepresented in Figure 2, where φf,i is the volume fractionof functional groups in lattice layer i. Results are shownfor three cases: attractive end groups, “neutral” endgroups (øs ) 0), and repulsive end groups. The concen-tration depth profiles for attractive functional groups(Figure 2a) exhibit two regions of behavior. End groupsare enriched at the surface, but the zone of excess isonly one lattice layer deep. The magnitude of enrich-ment increases as øs becomes more negative. A gradientof functional group depletion begins in the second latticelayer and continues to a depth that corresponds roughlyto the chain length. Maximum depletion is observed inthe second lattice layer, and the degree of depletiondecreases gradually with increasing depth.

The profile for neutral end groups (Figure 2b) isqualitatively similar to that for the attractive end group,although the degree of enrichment and depletion aremuch smaller. When øs ) 0, the enthalpic driving forcefor end group segregation vanishes, but an entropicdriving force favoring end group surface segregationleads to a small surface excess of end groups. Chainbackbone units placed at an interface suffer a loss ofentropy because configurational paths that penetratethe interface are disallowed. In a cubic lattice, apropagating chain has five paths to follow; however, thechain cannot follow the path that is normal to thesurface. The loss of one out of five possible trajectoriescauses a net entropic change of kBln(1/5) or a free energypenalty of about 0.5kBT for chain backbone units tolocate at a surface.18,20,21 End groups do not suffer thisentropy loss and are therefore driven preferentially tothe surface, even in the absence of surface energy effects(i.e., when øs ) 0).

The concentration depth profiles for repulsive endgroups (Figure 2c) also show two regions of behavior:depletion in the first lattice layer and enrichment fordeeper layers with the magnitude of enrichment de-creasing with depth. The magnitude of surface depletionincreases with increasing øs.

Figure 1. Schematic representation of functional polymerchains configured on a cubic lattice. The darker cubes indicatea lattice site occupied by a functional end group, and thelighter cubes are occupied by polymer chain segments. Part aillustrates a chain with a low-energy attractive end group, partb depicts a nonfunctional polymer with neutral end groups,and part c shows the configuration of a polymer with high-energy repulsive end groups.

Macromolecules, Vol. 36, No. 3, 2003 Functional Polymer Surfaces 773

The effects of chain length are illustrated in Figure3. The depth of the initial zone of enrichment ordepletion associated with the direct surface interactionis always confined to the first lattice layer, consistentwith the concept of screening. Interactions betweenlattice sites are screened over distances larger than thescreening length, equal to the statistical segment lengthfor bulk polymers. Because the lattice size is roughlyequivalent to the statistical segment length, screeningis expected for distances greater than one lattice layer.

The depths of the depletion or enrichment gradientsthat follow scale with the chain dimensions, becausechain connectivity dictates that the overall compositionmust equal that of the bulk when integrated over adepth corresponding to the size of an individual chain.

Theodorou18 studied R-functional polymers with anattractive end group for øs values within the range -5e øs e -33. The reported reduced concentration depthprofiles show essentially complete depletion in severallattice layers due to the extremely large øs values usedand therefore differ significantly in appearance from theprofiles presented here for much lower øs values.

Calculated end group surface volume fractions, φf,1,for R-functional polymers are a function of chain lengthand surface interaction parameter, and this dependencecan be conveniently expressed through the followinginterpolation formula20

wherein the chain-length-dependent regression coef-ficients are given in Table 1.

The surface tension can be calculated from the fol-lowing group contribution relationship developed previ-ously for R,ω-functional polymers using φf,1 valuesestimated from (3)

If not known, the surface energies of the functionalgroup, γf, and repeat units, γr, required in (4) may becalculated by group contribution methods.

Figure 2. Functional group volume fraction for R-functionalpolymers with r ) 11 as a function of the lattice layer number,i, for various values of the surface interaction parameter: (a)øs ) -4 (filled circles), -1 (filled squares); (b) 0 (filledtriangles); (c) 1 (open squares), 4 (open circles).

Figure 3. Functional group surface composition-depth pro-files for R-functional polymers with øs ) -4 (bottom) and øs )4 (top) for four different values of r: r ) 5 (filled circles), r )11 (open squares), r ) 25 (filled triangles), and r ) 101 (opencircles).

Table 1. Regression Parameters for InterpolationFormulas

chain length, r a0(r) a1(r) a2(r)

5 0.202 79 -0.048 10 0.001 927 0.146 94 -0.040 50 0.002 29

11 0.095 93 -0.031 57 0.002 3915 0.071 76 -0.026 42 0.002 2925 0.044 73 -0.019 62 0.002 0151 0.023 12 -0.012 85 0.001 55

101 0.012 24 -0.008 51 0.001 15201 0.006 39 -0.005 59 0.000 83

φf,1 ) a0(r) + a1(r)øs + a2(r)øs2 (3)

γ ) γfφf,1 + γr(1 - φf,1) (4)


The influence of the number of functional groups onsurface properties can be evidenced by comparing thebehavior for the two functional polymers with thesimplest chain architectures: R,ω-functional and R-func-tional polymers. The surface concentrations for R,ω-functional and R-functional polymers are compareddirectly in Figure 4 for two different chain lengths. Thefunctional end group surface composition for the R,ω-functional polymer, φf,1

R,ω, and the corresponding R-func-tional polymer, φf,1

R , generally do not differ by a factorof 2 (see also the ratio of surface compositions in Figure5), as would be expected from stoichiometric consider-ations. Deviations from stoichiometric behavior occurbecause entropic and enthalpic effects become coupledfor functional polymers as a result of chain connectivity.That is, surface segregation of end groups requiresreorientation of the chain backbone and a commensu-rate loss in configurational entropy. Deviations fromstoichiometric behavior increase with decrease in mo-lecular weight as configurational constraints becomemore severe. Stoichimetric behavior is found in the limit

of infinite molecular weight where configurational ef-fects vanish and surface segregation behavior reducesto that of an ideal gas mixture.22

The influence of the surface interaction parameter onconfigurational entropy effects is illustrated in Figure5, which shows the relationship between the entropiccontribution to surface tension and the ratio of surfacefunctional group concentration for R-functional and R,ω-functional polymers. When øs is negative (i.e., attractivefunctional groups), the ratio of the surface concentra-tions of functional groups is less than 2 because theentropic contribution to surface tension is higher for theR,ω-functional polymer. When øs equals zero, the ratioof surface concentrations is exactly two because theentropic contribution to surface tension is the same forboth the R,ω-functional and R-functional polymers.When øs is positive (i.e., repulsive functional groups),the ratio of surface concentrations is much greater thantwo because the entropic contribution to surface tensionis again greater for the R,ω-functional polymer. In thecase where high-energy reactive functional groups (i.e.,repulsive functional groups) are desired at a surface,the effects of entropic constraints may be beneficialbecause they oppose the segregation of repulsive func-tional groups away from the interface and lead to ahigher surface concentration.

Optimizing Functional Polymer Chain Archi-tecture. The functional chain architectures depictedschematically in Figure 6 were studied in order todetermine which architecture provided optimal surfaceproperties for various applications. The architecturesinvestigated include R-terminated and R,ω-terminated

Figure 4. Dependence of functional group surface fractionon øs for two different chain lengths (r ) 101, circles; r ) 11,squares) and two different architectures: an R-functionalpolymer (filled circles or squares) and an R,ω-functionalpolymer (open circles or squares).

Figure 5. Influence of øs on the entropic contribution tosurface tension for R-functional (filled circles) and R,ω-functional polymers (open circles) and the ratio of functionalgroup surface concentrations (triangles) for the two architec-tures.

Figure 6. Functional polymer architectures. Circles representpolymer repeat units with the letter F indicating the positionof a functional group (attractive functional groups are indi-cated by the letter A and repulsive groups are indicated bythe letter R). Functional groups denoted with a bold circle arelocated at the nth or mth repeat unit along the chain.


end-functional polymers, n-functional polymers wherea functional group is located at the nth repeat unit alongthe backbone of the polymer chain, n,c-functional poly-mers with one functional group at the nth repeat unitand a second functional group at the center of the chain,polymers with functional groups located both at thechain ends and at the nth repeat unit along the chainbackbone (R,n-functional and R,n,ω-functional poly-mers), polymers with adjacent functional groups locatedat sequential positions n and m along the chain back-bone (n,m-functional polymers), and “Pushmi-Pullyu”polymers containing an attractive functional group oftype A and a repulsive functional group of type R locatedalong the same chain.

The two-headed llama named Pushmi-Pullyu featuredin the Dr. Dolittle series of children’s novels24 providedthe inspiration for designating the latter architecture.The two-headed llama provides a vivid visual illustra-tion of how conflict and cooperativity affect the surfacesegregation problem. When the llama wants to move, acooperative decision for one head to pull and the otherhead to push is required. Stagnation results when bothheads attempt to push or pull at the same time. Theintrinsic conflict or cooperation embodied in the Pushmi-Pullyu llama reflects the behavior of a functionalpolymer that contains both repulsive and attractivefunctional groups. The question to be addressed iswhether the Pushmi-Pullyu mechanism can be em-ployed to enhance the magnitude of functional groupsurface segregation in functional polymers.

Herein we will adopt the convention that group A isan attractive functional group with surface tensionlower than that of the chain backbone (i.e., øs < 0) andgroup R is a repulsive functional group with surfacetension higher than that of the chain backbone (i.e., øs> 0). The convention is applied by subscripting theposition variable either with the letter A or R dependingupon the type of group resident at that location. Pushmi-Pullyu polymers, for example, are either RA,nR-func-tional Pushmi-Pullyu polymers with a low-energy endgroup and a high-energy functional group located alongthe chain or RR,nA-functional inverse Pushmi-Pullyupolymers with a high-energy end group and a low-energy functional group located along the chain. Whenfunctional polymers contain both repulsive and attrac-tive functional groups, a similar convention is appliedto label volume fractions. For example, φA,1 is thevolume fraction of attractive functional groups in thefirst lattice layer and φA,b is the bulk average volumefraction of attractive groups.

Optimizing Chain Architecture for Release Prop-erties. In applications where release properties areimportant, it is desirable to maximize the surface con-centration of attractive functional groups, thereby mini-mizing the surface tension. The optimization of chainarchitecture for this case is straightforward: one choosesa chain architecture that provides the highest concen-tration of attractive functional groups within the firstlattice layer.

The number and nature of attractive functionalgroups can greatly affect their surface concentration andthus the surface properties of the polymer. Figure 7shows the relative enrichment of attractive functionalend groups as a function of their surface interactionparameter for two chain lengths (r ) 11 or r ) 101) andfour different chain architectures: an R-functionalpolymer with an attractive end group, an RA,nR-

functional Pushmi-Pullyu polymer with one attractiveend group and one repulsive group (øs ) 4) located atthe center of the polymer (i.e., n ) r/2), an R,ω-functionalpolymer with two attractive end groups, and an RA,nR,ωA-functional Pushmi-Pullyu polymer with two attractiveend groups and one repulsive group (øs ) 4) located atthe center of the polymer chain. The relative surfaceenrichment defined as the surface concentration ofattractive functional groups, φA,1, divided by their bulkconcentration, φA,b. For all four architectures, the rela-tive enrichment increases with chain length, eventhough the bulk concentration scales inversely withmolecular weight. When a repulsive functional groupis placed at the center of a chain with one attractivefunctional end group, both the surface concentration andrelative enrichment of the attractive functional groupsincrease, thus validating the Pushmi-Pullyu mechanismfor the RA,nR-functional Pushmi-Pullyu polymer. TheRA,nR,ωA-functional Pushmi-Pullyu architecture is alsoeffective in enhancing the surface segregation of attrac-tive functional groups for the polymers. Both Pushmi-Pullyu architectures bring about an increase in surfacesegregation when compared to the corresponding end-functional control polymers.

The surface concentration of attractive functionalgroups and the surface composition-depth profile aredependent upon the location of the attractive functionalgroup along the chain backbone. The effect of locationfor a single attractive functional group is illustrated inFigure 8. The surface concentration of functional groupsis highest when the functional group is placed at eitherchain end and lowest when it is located at the chaincenter. Location of attractive functional groups at thechain ends is optimal because both the enthalpic factorsassociated with surface tension reduction and entropicfactors associated with configurational entropy lossesfavor segregation of the chain ends to the surface.

Figure 9 compares the surface concentration of at-tractive functional groups obtained for four architec-

Figure 7. Effect of øs on the relative surface enrichment ofattractive end groups for four different architectures: anR-functional polymer with one attractive end group (filledcircles), an R,ω-functional polymer with two attractive endgroups (open circles), an RA,nR-functional Pushmi-Pullyupolymer with one attractive end group and one repulsivefunctional group (øs ) 4) located at the center (i.e., n ) r/2) ofthe polymer (open squares), and an RA,nR,ωA-functional Pushmi-Pullyu polymer with two attractive end groups and onerepulsive group (øs ) 4) located at the center of the polymerchain (filled squares). The inset illustrates each chain structurewith A representing an attractive group and R representing arepulsive group.


tures: R,n-functional polymer with two attractive func-tional groups, RA,nR-functional Pushmi-Pullyu polymerwith an attractive functional end group and a repulsivefunctional group located at position n, RR,nA-functionalinverse Pushmi-Pullyu polymer with a repulsive func-tional end group and an attractive functional grouplocated at position n, and n-functional polymer with oneattractive functional group located at position n. Theabscissa on the plot denotes the position, n, of thefunctional groups indicated by the bold circles in thefigure inset.

Both the Pushmi-Pullyu and the inverse Pushmi-Pullyu architectures are more effective than the n-functional control when the two opposing functional

groups are separated by more than 3-4 segments alongthe chain. When functional groups of opposing energiesare well separated, the repulsive functional groups pre-fer to locate in the bulk and, in so doing, convey adja-cently connected polymer chain segments away from thesurface. Movement of the repulsive functional groupsand connected chain segments away from the surfacegenerates an additional convective driving force forpolymer chain segments connected to attractive func-tional groups to segregate to the surface. Adjacency ofopposing functional groups is detrimental, because adja-cent repulsive functional groups are carried along whenattractive functional groups adsorb at the surface andcause an elevation in the overall surface energy. TheRA,nR-functional Pushmi-Pullyu architecture is gener-ally more efficient than its inverse RR,nA-functionalcounterpart, because the favored location of low surfacetension attractive functional groups is always at thechain end.

The optimal placement of the repulsive functionalgroup for RA,nR-functional Pushmi-Pullyu polymersdepends on molecular weight, as illustrated in Figure10. There exists a maximum in the relative enrichmentat a specific location of the repulsive functional groupthat differs for each chain length. For all chain lengths,the optimum position of the repulsive functional groupis approximately 3r/4 when the attractive functionalgroup is located at the R-terminus.

The Pushmi-Pullyu and inverse Pushmi-Pullyu ar-chitectures are more efficient at increasing the surfaceconcentration of attractive functional groups than theR-functional architecture; however, when evaluating theeffectiveness of various architectures, it is important toperform any comparisons at equal total number offunctional groups. When this is done, it is clear that theoptimal surface segregation for polymers containing twofunctional groups occurs when both functional groupsare attractive, as shown in Figure 9. Regardless of theposition of the second attractive functional group, thesurface concentration of attractive functional groups forthis architecture always exceeds that of any of thePushmi-Pullyu architectures. A chain architecturewherein both attractive functional groups are adjacentto each other at one end of the polymer chain provides

Figure 8. Surface composition-depth profiles for n-functionalpolymers with one attractive functional group for øs ) -4 andr ) 11. n ) 1 (filled triangles), n ) 3 (filled circles), n ) 5(open circles). The inset illustrates each chain structure withA representing an attractive group.

Figure 9. Surface volume fraction of attractive functionalgroups as a function of the position, n, of a midchain group(denoted by bold circles on the figure inset) for four differentarchitectures with r ) 11: R,n-functional polymer with twoattractive functional groups (open diamonds); RA,nR-functionalPushmi-Pullyu polymer with an attractive functional endgroup and a repulsive functional group at position n (filledsquares); RR,nA-functional inverse Pushmi-Pullyu polymer witha repulsive functional end group and an attractive functionalgroup at position n (open squares); n-functional polymer withone attractive functional group at position n (filled circles).The attractive functional groups have øs ) -1, and therepulsive functional groups have øs ) 4. The inset illustrateseach chain structure with A representing an attractive groupand R representing a repulsive group.

Figure 10. Relative enrichment of attractive functionalgroups as a function of the position, n, of repulsive functionalgroup for RA,nR-functional Pushmi-Pullyu polymers with fivedifferent chain lengths: r ) 11 (filled circles), 18 (open circles),25 (filled squares), 51 (open squares), and 101 (filled triangles).The repulsive groups have øs ) 4, and the attractive groupshave øs ) -1.


for the highest degree of surface segregation and shouldexhibit the best overall release properties for a polymercontaining two functional groups.

The effect of adjacency on the surface segregation ofattractive functional groups is examined more thor-oughly in Table 2. Surface segregation predictions arecompared for four different chain architectures: an R,ω-functional polymer with two attractive functional endgroups, A-P-A; a polymer with two adjacent attractivefunctional groups at one chain end, A2-P; a polymerwith two adjacent attractive functional groups at onechain end and a third attractive functional group at theother end, A2-P-A; and a polymer with three adjacentattractive functional groups at one chain end, A3-P. Forall chain architectures considered in Table 2, the chainlength, r, is set to 25, and the attractive functionalgroups are characterized by a value of øs ) -2. The tablereports the relative enrichment of each individualfunctional group, defined by the concentration of eachfunctional group in the first lattice layer divided by thebulk concentration of all functional groups, as well asthe overall enrichment.

The A3-P chain design exhibits the highest degreeof surface partitioning for attractive functional groups.A comparison of the A2-P and A-P-A architecturesreveals that functional group adjacency enhances thesegregation of attractive functional groups due to chainconnectivity effects. That is, the A2-P chain architectureis more effective at bringing attractive functional groupsto the surface because it is more probable for an adjacentgroup to reside at the surface when the end group isalready absorbed there. In fact, the data in Table 2 showthat the surface composition of the second functionalgroup is almost identical to that of the first group. Thisresult suggests that the conditional probability for thesecond functional group to locate in the first lattice layerif the adjacent chain end is also located there is close tounity. In the case of the A3-P polymer, the surfaceconcentrations of all three attractive functional groupsare nearly identical, illustrating the extreme effective-ness of adjacency in driving surface segregation.

The functional group concentrations in the first layerare nearly equivalent for the A2-P and A2-P-A archi-tectures. The addition of the second functional endgroup in the A2-P-A architecture is not effective dueto the effects of configurational constraints discussedearlier for R,ω-functional polymers; only a minimalincrease in the surface volume fraction is observed.

The data represented in Table 2 clearly show thatfunctional group adjacency is the most effective archi-tectural variant for promoting surface enrichment ofattractive functional groups. For a fixed number ofattractive functional groups, the optimal chain archi-tecture for creating release surfaces is a polymer withall of the functional groups located adjacent to eachother at the chain end.

Optimizing Chain Architecture for AdhesiveProperties. It is not immediately obvious how tooptimize chain architecture for applications requiringan adhesive or reactive surface, because the functionalgroups required to create these types of surfaces nor-mally have higher surface energies than the polymerbackbone and therefore are naturally depleted from thesurface. In this case, the criteria for optimization dependon how the surface will be utilized. In practice, anadhesive or reactive surface will be placed against someother substrate. Upon contact with a substrate, thevalue of øs changes instantaneously, and the functionalpolymer interface reorganizes in an attempt to reach anew equilibrium with the substrate.

In previous experiments,25,26 we have shown that thesurface of functional polymers can reorganize in thisfashion even in the glassy state. The importance ofreorganization is that functional groups below thesurface can still be active in terms of performance.Although repulsive functional groups are repelled fromthe first lattice layer, groups located in the second layerand perhaps even deeper can reorganize to relocate tothe newly formed interface with the contacting sub-strate. Our preliminary results demonstrate that mo-lecular motion over length scales equivalent to only oneor two lattice layers is sufficient to bring about analmost complete reconstruction of the interface.

The fact that surfaces can reorganize provides thebasis for a practical metric that can be applied to opti-mize polymer architecture for adhesive and reactivesurfaces. Adhesive/reactive surface character can beoptimized by maximizing the concentration of repulsivefunctional groups in the second lattice layer under theassumption that the polymer will reorganize when incontact with the substrate of interest. Since the con-centration of repulsive groups in the first lattice layeris very low, we neglect this factor and use the concen-tration of repulsive groups in the second lattice layerherein to judge the efficacies of functional polymerarchitectures in fabricating adhesive and reactive poly-mer surfaces.

The influence of functional group location on thesurface structure of n-functional polymers with repul-sive functional groups is illustrated in Figure 11. The

Table 2. Comparison of Overall Surface Enrichment andEnrichment of Each Attractive Functional Group for

Adjacent End-Functional Polymer Architecturesa

relative enrichment

architecture overall 1st group 2nd group 3rd group

A-P 2.60 2.60A-P-A 2.19 1.095 1.095A2-P 3.73 1.89 1.84A2-P-A 3.78 1.12 1.10 0.56A3-P 4.43 1.50 1.52 1.41a The chain length, r, is 25, and the attractive functional groups,

A, have a øs of -2.

Figure 11. Volume fraction of repulsive functional groupswith øs ) 4 as a function of the lattice layer number i for threedifferent locations of the functional group along a n-functionalpolymer of length, r ) 11. n ) 1 (open triangles); n ) 3 (filledsquares); n ) 6 (open circles).


repulsive case is similar to the attractive case discussedpreviously in that two regions of behavior exist; how-ever, the general trends are reversed. The functionalgroup fraction in the first lattice layer is depleted fromthat in the bulk. For a given chain length, the depletionincreases with øs. Following this depletion, there is anenhancement of repulsive functional groups in subse-quent layers so as to conserve the total number of func-tional groups in the interfacial layer. The width of theinterfacial layer scales with the chain length, and thesurface interaction is confined to the first lattice layer.More complicated architectures with repulsive func-tional groups follow the same basic trends that areexhibited by the simpler end-functional polymers.

The optimal position for a single repulsive functionalgroup on a polymer chain is at the center of the polymerchain, for which the repulsive functional group concen-tration is highest in the second layer. The strategy forcreating optimal adhesive interfaces is thus exactlyopposite that for creating release surfaces. Optimaladhesive surfaces are obtained by maximizing configu-rational constraints that act upon repulsive functionalgroups. The center-functional architecture, which wewill refer to as a c-functional polymer, is most effectivebecause that segment is more constrained from movingaway from the interface.

Figure 12 compares the concentration of repulsivefunctional groups in the second lattice layer obtainedfor four architectures: a n,c-functional polymer with onerepulsive functional group located at position n alongthe polymer backbone and a second repulsive functionalgroup at the center of the polymer; an RA,nR-functionalPushmi-Pullyu architecture with a repulsive functionalgroup located at position n and an attractive functionalend group; an RR,nA-functional inverse Pushmi-Pullyupolymer with an attractive functional group at positionn and a repulsive functional end group; a n-functionalpolymer control with one repulsive functional end grouplocated at position n.

The Pushmi-Pullyu architectures are only more ef-fective than the n-functional control when the opposingfunctional groups are adjacent on the chain or are nearneighbors. In this case, the tendency for the neighboringattractive functional group to locate in the first latticelayer helps to carry the repulsive group to the secondlattice layer. The inverse Pushmi-Pullyu architectureis more efficient in creating adhesive surfaces than thePushmi-Pullyu architecture, just the opposite of whatwas found for release surfaces. If two functional groupsare to be placed along the polymer chain, however, themost efficient architecture is the n,c-functional polymerwith two repulsive groups. Adjacency of functionalgroups is the most effective means to optimize surfacesegregation for adhesive applications, similar to whatwas found for the case of optimizing release surfaces.In contrast, however, the optimal functional polymerarchitecture for creating adhesive surfaces is a func-tional polymer with adjacent repulsive functional groupslocated at the center of the polymer chain.

Summary

The effects of chain architecture on the surfaceproperties and structure of functional polymers areinvestigated through self-consistent lattice model cal-culations. Functional group concentration depth profilesshow similar qualitative behavior for all of the archi-tectures studied. In the case of functional groups withsurface tensions lower than the chain backbone, thedepth profile exhibits functional group enrichment onlyfor the first lattice layer. The second lattice showsmaximum depletion of functional groups while theconcentration in deeper layers gradually recovers to thebulk value over a distance that is roughly equivalentto the chain dimensions. Functional groups with surfacetensions greater than that of the chain backbone aredepleted from the first lattice layer and are in excessin the second lattice layer. The excess decays in deeperlayers until the bulk concentration is recovered at adepth equivalent to the size of the polymer chain.

The lattice calculations are employed to explore theeffectiveness of a variety of functional polymer archi-tectures to produce surfaces with either release oradhesive properties. The optimal architecture for releaseapplications is a functional polymer with several lowsurface energy functional groups located at one chainend. The optimal structure for an adhesive surface isobtained when high surface energy reactive functionalgroups are placed adjacently at the center of the polymerchain. Optimal architectures arise in functional poly-mers as a result of configurational constraints that areassociated with the coupling of entropic and enthalpiccontributions to the free energy.

Acknowledgment. This material is based uponwork supported by, or in part by, the U.S. ArmyResearch Office under Contract/Grant DAAD19-001-0104 and the National Science Foundation PolymerProgram under Grant DMR-98-09687.

Appendix

The self-consistent lattice model determines the re-duced free segment probabilities for the functionalgroup, pf,i, and the repeat unit segments, pr,i, in eachlayer, i. The reduced free segment probability is definedas the probability that a particular segment in aconformation c locates in layer i with respect to the

Figure 12. Volume fraction of repulsive functional groupswithin the second lattice as a function of the position, n, of amidchain group (denoted by bold circles on the figure inset)for four different architectures: an nR,cR-functional polymerwith two repulsive functional groups (open diamonds); RA,nR-functional Pushmi-Pullyu polymer with an attractive func-tional end group and a repulsive functional group at positionn (filled squares); RR,nA-functional inverse Pushmi-Pullyupolymer with a repulsive functional end group and an attrac-tive functional group at position n (open squares); an n-functional polymer with one repulsive functional group (filledcircles). The attractive functional groups have øs ) -1, andthe repulsive functional groups have øs ) 4.


unconstrained bulk. The free segment probability for thefunctional group in the first layer is given by17

where φj,i is the volume fraction of component j in layeri, λ0 ) 2/3 is the probability that segments are connectedwithin the same layer and λ1 ) 1/6 is the probability thatsegments are connected to a layer lying either above orbelow that layer i. For layers 2 through M - 1, the freesegment probability is

The free segment probability for the center layer is

The volume fraction of repeat units and functional groupin each layer are

Two end segment probabilities must be considered forasymmetric chain architectures. p+(i,s) is the probabilitythat end segments of a subchain of s segments will liein layer i taken in the positive direction, from the leftchain end to the right. p-(i,s) is the end segmentprobability for an s-segment subchain in the negativedirection, taken from the right chain end to the left. p+-(i,s) and p-(i,s) are calculated from

where pt(s)i is the free segment probability for a type ssegment in layer i.

A total segment balance yields the relation

Using the incompressibility constraint and eq A6, thetotal segment balance becomes

This set of M simultaneous equations is solved with the

IMSL subroutine, DNEQNF, starting with an initialguess for the free segment probability of the repeat unit(pri ) 1.2, 1.1, 1, 1, 1, ...). Segment densities in everylayer are then calculated using (A-6) and (A-7).

For calculations with a finite bulk interaction param-eter, ø, a zero-order continuation scheme in ø wasimplemented to solve for the free segment probabilities.Calculations for a given chain length and øs were startedwith the bulk interaction parameter set to zero and thenproceeded to progressively increasing values of ø usingthe solution obtained in each case as an initial guessfor the next one. A step size of ∆ø ) 0.1 proved adequatefor computations up to high values of ø.

The effects of including these bulk interactions on thedegree of surface segregation for attractive functionalgroups are examined in Figure 13. As øbulk increases,the degree of surface segregation increases linearly forboth R-functional and R,ω-functional polymer. Thequalitative nature of surface segregation, however, isnot altered when bulk interactions are included in thecalculation.

References and Notes

(1) Rastogi, A. K.; St. Pierre, L. E. J. Colloid Interface Sci. 1969,31, 168; J. Colloid Interface Sci. 1971, 35, 16.

(2) Wu, S. Polymer Interfaces and Adhesion, 1st ed.; MarcelDekker: New York, 1982.

(3) Pan, D. H.; Prest, W. M. J. J. Appl. Phys. 1985, 58, 2861.(4) Bhatia, Q. S.; Pan, D. H.; Koberstein, J. T. Macromolecules

1988, 21, 2166.(5) Schmitt, R. L.; Gardella, J. A., Jr.; Magill, J. H.; Salvati, L.,

Jr. Macromolecules 1985, 18, 2675.(6) Gaines, G. L., Jr. J. Chem. Phys. 1969, 73, 3143.(7) Elman, J. F.; Johs, B. D.; Long, T. E.; Koberstein, J. T.

Macromolecules 1994, 27, 5341.(8) Jalbert, C.; Yilgor, I.; Gallagher, P.; Krukonis, V.; Koberstein,

J. Macromolecules 1993, 26, 3069.(9) Jalbert, C.; Balaji, R.; Bhatia, Q.; Salvati, L.; Yilgor, I.;

Koberstein, J. Macromolecules 1994, 27, 2409.(10) Hunt, M. O. J.; Belu, A. M.; Linton, R. W.; DeSimone, J. M.

Macromolecules 1993, 26, 4854.(11) Affrossman, S.; Hartshorne, M.; Kiff, T.; Pethrick, R. A.;

Richards, R. W. Macromolecules 1994, 27, 1588.(12) Hopkinson, I.; Kiff, F. T.; Richards, R. W.; Bucknall, D. G.;

Clough, A. S. Polymer 1997, 38, 87.(13) Schaub, T. F.; Kellogg, G. J.; Mayes, A. M.; Kulasekere, R.;

Anker, J. F.; Kaiser, H. Macromolecules 1996, 29, 3982.

pf,1 ) pr,1 exp[(øs + λ1ø) + 2ø(λ0φf,1 + λ1φf,2 - Nr )](A-1)

pf,i ) pr,i exp[2ø(λ1φf,i-1 + λ0φf,i + λ1φf,i+1 - Nr )]

1 < i < M (A-2)

pf,M ) pr,M exp[2ø(λ1φf,M-1 + (λ0 + λ1)φf,M - Nr )] (A-3)

φf,ipf,i )1

r∑s)1

r

δf(t(s))p+(i,s) p-(i,r-s+1) 1 e i e M

(A-4)

(1 - φf,i)pr,i )1

r∑s)1

r

δr(t(s))p+(i,s) p-(i,r-s+1)

1 e i e M (A-5)

p+(i,s) ) ∑j

λj-i pt(s)ip+(j,s-1) 2 e s e r (A-6)

p-(i,s) ) ∑j

λj-i pt(s)ip-(j,s-1) 2 e s e r (A-7)

φa,ipa,i + (1 - φa,i)pb,i )1

r∑s)1

r

p+(i,s) p-(i,r-s+1)

1 < i < M (A-8)

1 -1

pa,ir∑s)1

r

p+(i,s) p-(i,s) -1

pb,ir∑s)1

r

p+(i,s) p-(i,s) ) 0

(A-9)

Figure 13. Volume fraction of attractive functional groupswith øs ) -2 in the first lattice layer vs the bulk interactionparameter, øbulk, for two different chain architectures: R-func-tional (filled circles) and R,ω-functional polymers (open squares).


(14) Su, Z.; Wu, D.; Hsu, S. L.; McCarthy, T. J. Macromolecules1997, 30, 840.

(15) O’Rourke Muisener, P. A. V.; Yuan, C.; Jalbert, C.; Baetzold,J.; Mason, R.; Wong, D.; Kim, Y. J.; Elman, J. F.; Koberstein,J. T.; Gunesin, B. Macromolecules, submitted for publication.

(16) Mason, R.; Jalbert, C.; O’Rourke Muisener, P. A. V.; Kober-stein, J. T. Adv. Colloids Interface Sci., in press.

(17) Theodorou, D. N. Macromolecules 1988, 21, 1411.(18) Theodorou, D. N. Macromolecules 1988, 21, 1422.(19) Scheutjens, J. M. M. H.; Fleer, G. J. J. Phys. Chem. 1979,

83, 1619.(20) Jalbert, C.; Koberstein, J. T. ; Hariharan, A.; Kumar, S. K.

Macromolecules 1997, 30, 4481.

(21) Kumar, S. K.; Vacatello, M.; Yoon, D. Macromolecules 1990,23, 2189.

(22) Hariharan, A. H.; Kumar, S. K.; Russell, T. P. Macromolecules1990, 23, 3584.

(23) Hariharan, A. H.; Kumar, S. K.; Russell, T. P. Macromolecules1991, 24, 4909.

(24) Lofting, H. Doctor Dolittle’s Circus; Lippincott: Philadelphia,1952.

(25) Koberstein, J. T. MRS Bull. 1996, 21, 16.(26) Jalbert, C. Ph.D. Dissertation, University of Connecticut,

1993.

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Optimal Chain Architectures for the Molecular Design of Functional Polymer Surfaces