Macromol. Theory Simul. 3,91-93 (1994) 91

a 0

1.0 .- 1

Fig. 1. Schematic dia- gram showing a homo- u

2 polymer surfactant C at L

an A-B homopolymer al

coordinate is indicated by , 0 the dimensionless ratio x /b , where b could be the Kuhn length 0

interface. The distance - 5

Homopolymer surfactant for immiscible homopolymer blends

A B

Jaan Noolandi

Xerox Research Centre of Canada, 2660 Speakman Drive, Mississauga, Ontario, Canada L5K 2L1

(Received: April 15, 1993)

SUMMARY It is commonly believed that block copolymers are the only type of polymeric surfactants

available for incompatible homopolymers ’). We explore the conditions for which a homopoly- mer will also lower the surface tension between two incompatible homopolymers by lowering the enthalpic contribution to the interfacial free energy, noting that the resulting three-component interface will not necessarily have the same mechanical strength as a block copolymer-homopoly- mer interface.

Fig. 1 shows a three-component homopolymer interface, in which a small amount of homopolymer C has been added to an immiscible blend of homopolymers A and B. A simple criterion in terms of surface tensions for the minority component C accumulating at the A-B interface is2)

which reduces, in terms of the corresponding chi-parameters, to

for high-molecular-weight homopolymers, assuming that other chain parameters are roughly the same.

In order to study this phenomenon in more detail, we turn to the molecular “soup” picture of Paul and Barlow3), used to develop a binary interaction model for the miscibility of copolymers in blends, in which the heat of mixing is of the van Laar type

0 1994, Hiithig & Wepf Verlag, Base1 CCC 1022-1344/94/$03.00

92 J. Noolandi

AH,,,/V= c B , * @ i ’ @ j (3) i>j

where Vis the total volume of the mixture, V = c Vi, Qi is the volume fraction,

and the binary interaction energy B, is related to the chi-parameters by i

B,/(RT) = (4)

Fi being the molar volume of component i. If the homopolymers A and B are, for the purposes of the following argument,

considered to be joined at one end and the resulting A and B blocks of the copolymer are supposed to be equal in size and very large, then the effective interaction parameter for a third homopolymer C to mix with A and B is

in terms of the interactions between the various monomer units. For our problem of three immiscible homopolymers, all three interaction parameters are positive, and according to Sanchez4) there is a “miscibility window” if

XAB > [kAC)’12 + kBC)’/212 (6)

which is the same criterion as given by Eq. (2). Eq. (6) assumes that the molar volumes of all three components are approximately the same.

In order to estimate the amount of hompolymer surfactant at the interface, as well as the reduction in the surface tension, we simplify the analysis further. Referring to Fig. 1, the heat of mixing of the A-C-B interface, relative to the A-B interface, is

where the last term represents the loss of the A-B heat of mixing in the space now occupied by the C homopolymer. Approximating the volume fraction of C homopoly- mer at the middle of the interface by @,-(O) and representing the average volume fractions of A and B in the interfacial region by 112 ’I, the heat of mixing of the three- component interface becomes

where A x = xAB/2 - xAc - xBC, which agrees with Eq. (5). The condition A x > 0 is the same as that given by Eq. (6), provided that xAc is not very different from xBC. The amount of entropy loss of the surfactant in the interfacial region limits the accumulation in this region, which can be calculated as previously6)

aC(0) = @%. exp(AxZc/2) (9)

Homopolymer surfactant for immiscible homopolymer blends 93

where 2, is the degree of polymerization of homopolymer C, @% is the overall volume fraction of C, and AX is assumed to be positive. The corresponding reduction in surface tension from the A-B interface A y = yACB - yAB is given by7)

if A x 2 5 1, d being the width of the interface. Eq. (10) simply expresses the physical result that the surfactant accumulates a t the interface in order to lower the enthalpic contribution to the free energy, and this enthalpic gain is partly offset by the entropic loss of having the surfactant localized within the interfacial region. In other words, the mechanism for reduction of surface tension of the A-C-B interface from the A-B interface is the replacement of strong A-B interactions by weaker A-C and B-C inter- actions, and the amount of homopolymer surfactant accumulating between A and B is limited by the entropy loss of C. As is seen from Eq. (9), higher-molecular-weight homopolymers will be more effective as surfactants, because of lower solubilization in the bulk homopolymers A and B, and because of the lower entropy loss a t the interface, allowing for more accumulation in this region. Although the surface tension of the A- C-B interface is reduced compared to the A-B interface, the small interpenetration of the surfactant into the bulk homopolymer phases does not improve or possibly even maintain the strength of the A-B interface. However a judicious mixture of both block copolymer and homopolymer surfactants may be sufficient to address the interfacial strength issue.

’) I. Piirma, “Polymeric Surfactants’: Marcel Dekker, New York 1992 2, C. Yeung, R. C . Desai, J. Noolandi, to be published; P. G. de Gennes, Rev. Mod. Phys. 57,

827 (1985) 3, D. R. Paul, J. W. Barlow, Polymer 25, 487 (1984) 4, I . C. Sanchez, Annu. Rev. Mateer. Sci. 13, 387 (1983) ’) J. Noolandi, K. M. Hong, Macromolecules 16, 1443 (1983) 6, J. Noolandi, Makromol. Chem., Rapid Commun. 12, 517 (1991) 7, J. Noolandi, K. M. Hong, Macromolecules 17, 1531 (1984)