Polymer International Polym Int 49:469±471 (2000)

Effect of polymer architecture on the miscibilityof polymer/clay mixturesChandralekha Singh and Anna C Balazs*Chemical Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261, USA

(Rec

* CoContCont

# 2

Abstract: Using self-consistent ®eld calculations, we investigate the interactions between two closely-

spaced surfaces and the surrounding polymer melt. Short surfactants are terminally anchored to each

of the surfaces. The coated substrates model organically-modi®ed clay crystallites (sheets). Holding

the polymer length ®xed, we systematically vary the architecture of the chains, from linear to ten-

armed stars. We then calculate the free energy of the system as the surfaces are prised apart in the

different polymer melts. Through these calculations, we isolate conditions that drive these chains to

penetrate the gap between the surfaces. The studies provide guidelines for tailoring the miscibility and

morphology of the mixture and thus, fabricating thermodynamically stable polymer/clay composites.

# 2000 Society of Chemical Industry

Keywords: nanocomposites; polymer/clay mixtures; intercalated composites; exfoliated composites

INTRODUCTIONThe blending of polymers and clay under optimal

conditions can yield nanocomposites with a greater

tensile strength, heat resistance and gas permeability

than the pure polymer matrix.1 Furthermore, only

1±10wt% of the clay additive is needed to produce

these improvements. However, most polymers and the

hydrophilic clays are incompatible. In addition, clay

particles are composed of sheets that are stacked

roughly 1nm apart. The narrow spacing between the

inorganic sheets inhibits polymer permeation into the

particles. Thus, fabricating thermodynamically stable

composites where the clay sheets are uniformly

dispersed (or `exfoliated') within the polymer matrix

poses signi®cant synthetic challenges.

To facilitate the ef®cient production of polymer/clay

nanocomposites, we must isolate conditions that

promote the penetration of polymers into the `gallery'

between the closely spaced sheets. Grafting short-

chain surfactants to the clay sheets can increase the

gallery spacing and promote polymer permeation. In

previous studies,2,3 we used self consistent ®eld (SCF)

theory to investigate the effect of varying the properties

of both the surfactants and polymers on the miscibility

of the polymer/clay mixture. In these calculations, we

considered two in®nite, parallel plates immersed in a

`bath' of molten polymer. To model the organically-

modi®ed clays, we introduced terminally-anchored

surfactants onto the plates. These surfaces lie parallel

to each other in the XY plane and we investigated the

effect of increasing the separation between the surfaces

in the Z direction.

eived 15 February 1999; accepted 7 February 2000)

rrespondence to: Anna C Balazs, Chemical Engineering Department,ract/grant sponsor: Army Office of Researchract/grant sponsor: ONR; contract/grant number: N00014-91-J-1363

000 Society of Chemical Industry. Polym Int 0959±8103/2000/$1

As the surface separation is increased, polymer from

the surrounding bath penetrates the gap between these

walls and the calculations yield the corresponding

change in the free energy, DF, of the system. By

systematically increasing the surface separation H, we

obtain pro®les for DF versus H. The pro®les reveal not

only whether the polymer/clay mixture is miscible or

immiscible, but for miscible mixtures the plots also

indicate whether the composite exhibits an inter-

calated structure (where the polymers penetrate the

gallery and enhance the layer spacing) or exfoliated

morphology (where the sheets are dispersed through

out the polymer).

In this paper, we use our SCF calculations to

investigate the effect of polymer architecture on the

miscibility of the polymer/clay mixture. In particular,

we determine if increasing the number of branches for

polymers of ®xed molecular weight promotes or

inhibits miscibility. Establishing the role of architec-

ture is particularly relevant in designing cost-effective

nanocomposites from commercially available poly-

mers.

THE MODELOur self-consistent ®eld model is derived from the

theory developed by Fleer et al. 4 Much has been

written about this theory; here, we provide a brief

synopsis of the method and refer the reader to ref 4 for

more details. In this treatment, the phase behaviour of

polymer systems is modelled by combining Markov

chain statistics with a mean ®eld approximation for the

University of Pittsburgh, PA 15261, USA

7.50 469

Figure 1. The free energy per unit area DF/A as a function of surfaceseparation H for the organically-modified surfaces in the polymer melt. Thelength of the end-grafted organic modifiers, or surfactants, is fixed atNsurf=25 and the grafting density of these short chains is equal to r=0.04.The length of the homopolymers is given by N =100. Here, wwall=0, and w(which characterizes the polymer-surfactant interaction) is also zero. Thecartoons on the right label the different polymer architectures that wereexamined. From top down, the plots are for the following architectures:linear chain, comb, four-armed star, six-armed star and ten-armed star.The arms are all of comparable length. Though all mixtures will producemiscible systems, the top three polymers will yield intercalated composites,while the bottom two polymers will give rise to exfoliated materials.

C Singh, AC Balazs

free energy. Given the probability of ®nding a single

monomer at a particular site and the fact that all the

monomers in a chain are connected, the statistics for

chains of arbitrary length can be obtained through a

series of recursion relations. These recursion relations

involve the potential of mean-force acting at a site r.

This potential, in turn, is determined from the local

distribution of all the components at the point r, as

well as the Flory±Huggins interaction parameters, or wvalues, between the different components. Solving this

series of equations numerically and self-consistently

yields the equilibrium characteristics of the system.

While such SCF calculations do not necessarily yield

quantitative predictions, the results indicate how to

tailor the system to modify the stability and morphol-

ogy of the mixture.

The calculations are carried out on a cubic lattice.

The ends of the surfactants are grafted to the z =1 and

z =N surfaces, which represent the two sheets. The

surfactant length is ®xed at Nsurf=25 and the grafting

density of these tethered chains is ®xed at r=0.04.

(The inverse of the grafting density yields the area per

anchored chain.) The length of the polymers is held at

N =100 and these chains are assumed to be mono-

disperse. The interaction parameter between the

polymers and surface or between the surfactants and

surface is given by wwall=0, representing a rather inert

substrate. The interaction between the polymers and

surfactants is characterized by w.

To consider different architectures, we vary the

number of branches in the polymer for ®xed N. Thus,

as the number of branches increases, the length of the

uniform branches decreases. (The length of each

branch or arm equals N/m, where m is the number of

branches.) We consider the following polymer archi-

tectures: linear chain, three-armed comb, four-, six-

and ten-armed stars.

Figure 2. The free energy per unit area DF/A as a function of surfaceseparation H. The parameters are the same as above, but now w has beenincreased to 0.01. The cartoon on the right again identifies the variouspolymer architectures. While the linear polymer now yields an immisciblemixture, the ten-armed star gives rise to an intercalated composite.

RESULTS AND DISCUSSIONTo investigate the role of chain architecture on the

miscibility of the polymer/clay mixture, we vary the

separation between the parallel sheets and calculate

the change in the free energy DF as the different

polymers penetrate the gap between the surfaces. In

these calculations, the reference state (corresponding

to DF =0) is taken to be the state where the tethered

surfactants form a melt that completely saturates the

space between the two walls. (Recall that our SCF

calculations are based on an incompressible model. In

the reference state for the organically-modi®ed clays,

we consider the system to be composed of the two

surfaces and the tethered surfactants; there are no void

or solvent sites in the system. Thus, the grafted chains

form a melt between the con®ning walls. In the actual

system, there may be vacuum or some free volume in

between the grafted chains.) Our aim is to isolate

conditions where DF is reduced relative to the

reference state, ie DF < 0.

Figure 1 shows the free energy per unit area DF/A as

470

a function of the surface separation H for the various

polymer architectures and w=0. Because all the free

energies are negative, the polymers will form a miscible

mixture with the sheets. The plots nonetheless reveal

that changes in architecture can affect the morphology

of the mixture. Speci®cally, in the case of the linear

polymer, the plot shows a distinct local minimum. The

local minimum indicates that there is an optimal

separation between the sheets and that the mixture will

form an intercalated composite.2,3,5 However, the

curve for the ten-armed star has a global minimum at

large (essentially in®nite) surface separations. This

type of plot indicates that the mixture forms an

exfoliated composite.2,3,5 Overall, the ®gure reveals

Polym Int 49:469±471 (2000)

Polymer/clay mixture miscibility

that for ®xed N, an increase in the number of branches

decreases the free energy of interaction.

In Figure 2, we plot the results for w=0.01, where

the polymer±surfactant interaction is energetically

unfavourable. The other parameters are the same as

in Fig. 1. Now, the free energy in the case of a linear

chain is positive for all separations, implying that the

polymer/clay mixture is immiscible. Again, as the

number of branches is increased, the free energy of the

system decreases. For the ten-armed star, we indeed

see a local, negative minimum, which points to an

intercalated structure. Thus by changing the chain

architecture, the mixture can be altered from a phase-

separated system to a thermodynamically stable,

intercalated composite.

The enhanced miscibility between the organically-

modi®ed clay and the polymers with higher number of

branches is primarily due to the compactness of the

macromolecules. The radius of gyration of the poly-

mers decreases as the number of branches increases,

and the polymer can more easily interact with and

interpenetrate the short, grafted layer. We note that in

our previous studies,2,3 we observed that long linear

polymers do not readily penetrate the layer of short

surfactants. Increasing the number of branches at ®xed

N decreases the disparity in the lengths of the

surfactants and a polymeric arm, thus promoting

better intermixing between the species.

Polym Int 49:469±471 (2000)

CONCLUSIONSWe performed numerical SCF calculations to investi-

gate the effect of polymer architecture on the

miscibility of polymer/clay mixtures. We ®nd that

increasing the extent of branching at ®xed molecular

weight yields more miscible structures. Our results

provide guidelines for enhancing the intermixing

between the clay sheets and the polymer matrix.

ACKNOWLEDGEMENTSThe authors thank Dr E Zhulina for helpful discus-

sions. ACB gratefully acknowledges the ®nancial

support of the Army Of®ce of Research, and Onr

through grant N00014-91-J-1363.

REFERENCES1 Krishnamoorti R, Vaia RA and Giannelis EP, Chem Mater 8:1728

(1996).

2 Balazs AC, Singh C and Zhulina E, Macromolecules 31:8370

(1998).

3 Balazs AC, Singh C, Zhulina E and Lyatskaya Y, Acc Chem Res,

32:661 (1999).

4 Fleer G, Cohen-Stuart MA, Scheutjens JMHM, Cosgrove T and

Vincent B, Polymers at Interfaces, Chapman and Hall, London

(1993).

5 Vaia RA and Giannelis EP, Macromolecules 30:7990 (1997).

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