Self-consistent-field theory for interacting polymeric assemblies.II. Steric stabilization of colloidal particlesJiunn-Ren Roana)Doi Project, Japan Chemical Innovation Institute, Nagoya University, Research & Education Center 1-4F,Nagoya 464-8601, Japan and Department of Physics, National Chung-Hsing University,250 Kuo Kuang Road, Taichung, TaiwanToshihiro KawakatsuDepartment of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japanand Department of Physics, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan共Received 29 August 2001; accepted 31 January 2002兲The self-consistent-field 共SCF兲 theory developed in Part I 关J. Chem. Phys. 116, 7283 共2002兲,preceding paper兴 is employed to compute the interaction between particles coated by end-graftedhomopolymers in good solvent, where the particles and the homopolymers have comparable sizes.The result shows that, contrary to the prediction of the conventional theory for colloidal stabilizationand previous SCF studies, the interaction is attractive, repulsive, and attractive at large,intermediate, and small distances, respectively, for densely grafted particles, while it is purelyattractive for sparsely grafted particles. The attractive interaction is a consequence of two importantfactors that were ignored in previous studies: 共i兲 the sphere–sphere geometry of the system and 共ii兲the segment density associated with individual particle being deformed anisotropically, with respectto the particle, under the perturbation of other particles. We argue that the conventional wisdom thatend-grafted homopolymers in good solvent always impart stability indeed is correct only in a kineticsense and that our result will become more observable in systems composed of nanoparticles.Limitations of our prediction and considerations that must be carefully taken into account whengeneralizing our result to micron-sized particles and star polymers are discussed. © 2002American Institute of Physics. 关DOI: 10.1063/1.1463425兴I. INTRODUCTIONInteractions between polymer-coated colloidal particleshave been an important issue for both industrial applicationsand scientific investigations.1–4These interactions form oneof the bases of steric stabilization of colloidal dispersionswidely used in industry. Scientifically, the nature of theseinteractions constitutes an intriguing and challenging prob-lem because they can be purely repulsive or repulsive atsome distances and attractive at other distances, dependingdelicately on many factors such as whether the polymers aregrafted or adsorbed, whether the suspending medium con-tains polymers, and whether bridging effect is significant,etc. Complicated as it appears, there is nevertheless a simplerule: End-grafted homopolymers in good solvent always im-part repulsion. This simple rule is based on numerous experi-mental observation and theoretical studies. Therefore, end-grafted homopolymers have long been widely regarded asone of the best stabilizers.1–3Although in many applicationsdiblock copolymers in selective solvents, instead of ho-mopolymers in good solvents, are used when good stabilizersare needed, the working principle is the same rule becausethe soluble block is like an end-grafted homopolymer whenthe insoluble block of a diblock copolymer is anchored.Since in the experimental and theoretical studies uponwhich the simple rule is established, the particles being sta-bilized were, or were regarded as, much bigger in size thanthe polymers, recent progress in nanotechnology makes itsenseful and important to ask what will happen when theparticles and the polymers have comparable sizes. For ex-ample, dendrimers, which have received increasing attentionin recent years partly because of their potential medicinalapplications,5are nanoparticles with dense grafting sites—afour-generation poly共thioether兲 dendrimer, a typical den-drimer, has radius ⬇2 nm and has 324 binding sites on itssurface.6Some crucial questions for the proposed applica-tions of dendrimers in biomedicine are, What is the mini-mum number of chains per dendrimer needed to achieve sta-bilization? How do DNA molecules and dendrimersinteract?7Another example is the nanoparticles used in con-trolled drug delivery.8Their diameters are usually about 20–200 nm. Polymeric coats are often used to prevent capture bymacrophages or quick clearance through liver uptake.9Willthe coat accidentally induce aggregation, causing embolismof capillaries? How short can the polymers be so that thecoated carrier remains small enough to cross the blood-brainbarrier while the coat provides the carrier with sufficientprotection?10Because of their small sizes, nanoparticles mayrequire new mechanisms and considerations when polymersare used as steric stabilizers. To achieve better preparation,processing, and application of nanoparticles, it is therefore,important to understand the working principles of stabiliza-tion of nanoparticle dispersions.a兲Author to whom correspondence should be addressed. Electronic mail:[email protected] OF CHEMICAL PHYSICS VOLUME 116, NUMBER 16 22 APRIL 200272950021-9606/2002/116(16)/7295/16/$19.00 © 2002 American Institute of PhysicsDownloaded 14 Jun 2003 to 198.11.27.13. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jspIn previous theoretical studies of steric stabilization theparticles were assumed to be so big that either they can beregarded as flat planes1–4or the Derjaguin approximation isapplicable.11These assumptions are apparently inadequatefor nanoparticles. On the other hand, for particles that aremuch smaller than the stabilizers, Witten and Pincus haveconsidered their stabilization by end-graftedhomopolymers.12Their scaling argument, however, is validonly when the polymer is very long. Therefore, the regime inbetween, i.e., systems composed of nanoparticles and poly-mers that have comparable sizes, have been entirely left out.The SCF theory developed in Part I is suitable for studyingthis regime because it explicitly takes into account the finitesizes of the particles by the bispherical coordinate system.Since the formulation and numerical techniques for solvingthe bispherical SCF equations developed in Part I have beenshown quantitatively correct, we shall proceed in this part toapply it to calculating the interaction between polymer-coated nanoparticles. It turns out that, contrary to the predic-tion of the
View Full Document
Unlocking...