Nanoparticles: Synthesis, Stabilization, Passivation ... - ACS Publications

Chapter 24

“Frozen” Micelles: Polymer Nanoparticles of Controlled Size by Self-Assembly Downloaded by PURDUE UNIVERSITY on September 14, 2013 | http://pubs.acs.org Publication Date: September 19, 2008 | doi: 10.1021/bk-2008-0996.ch024

R. Nagarajan Molecular Sciences and Engineering Team, Natick Soldier Research, Development and Engineering Center, Kansas Street, Natick MA 01760

Block copolymer micelles generated by spontaneous molecular self-assembly can serve as nanoparticles that are intrinsically passivated as well as stable, and with a controlled dispersion of size. But micelles are not “permanent” nanoparticles, because the equilibrium self-assembly process involves free exchange of block copolymer between the micelle and the surrounding solvent medium. However, micelles that are “frozen” in the kinetic sense can be prepared if one block of the copolymer has a high enough glass transition temperature or large enough hydrophobicity, so as to cause a large activation energy barrier for molecular exchange. In such systems, the nanoparticle preparation method involves the molecular dissolution of the block copolymer in a solvent common to both blocks, followed by the replacement of the common solvent by a selective solvent to cause the freezing of the micelle. In this work, we present a theory for predicting the size and shape of such “frozen” micelles in selective solvents, prepared using mixed solvents. We show that the resulting micellar properties are significantly different compared to those predicted based on the nature of the selective solvent alone, without considering the micelle preparation procedure.

U.S. government work. Published 2008 American Chemical Society.

341

In Nanoparticles: Synthesis, Stabilization, Passivation, and Functionalization; Nagarajan, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

342

Downloaded by PURDUE UNIVERSITY on September 14, 2013 | http://pubs.acs.org Publication Date: September 19, 2008 | doi: 10.1021/bk-2008-0996.ch024

Introduction The preparation of passivated and stable nanoparticles of controlled size and shape is a problem of general interest to nanotechnology. A convenient way to achieve this goal for polymer nanoparticles is by self-assembly of amphiphilic polymers, possessing a block representing the nanomaterial of interest, to form micelles. This block forms the core of the micelle, serving as the desired nanoparticle and its passivation and stabilization are guaranteed by the presence of the other block forming the corona of the micelle. The micelles formed by self-assembly are not permanent nanoparticles in the sense that free exchange of block copolymer molecules occurs between the micelles and the surrounding solvent medium. However, one can use the selfassembly process and create permanent nanoparticles if the core forming polymer block has a high glass transition temperature or is highly solvophobic with respect to the solvent medium in which the particle is to be dispersed. Consider, for example, the synthesis of polystyrene nanoparticles to be dispersed in aqueous medium. We can start with diblock copolymers of polystyrenepolyethyleneoxide (PS-PEO). Three key stages in the self-assembly process are schematically shown in Figure 1.

Figure 1. Process offorming block copolymer micelles. Thick and thin lines represent hydrophobic (PS) and hydrophilic (PEO) blocks. Open circles denote common solvent (THF) andfilled circles denote solvent (water) selective to the hydrophilic block and non-selective to the hydrophobic block.

The block copolymer is first dissolved at the molecular scale in tetrahydrofiiran (THF) which is a common good solvent for both PS and PEO blocks and no self-assembly takes place (Figure 1—left). Then water, which is a good solvent for PEO block and a very poor solvent for PS block, is added to the system, progressively replacing THF. The changing solvent composition induces the formation of block copolymer micelles in the solvent medium with a PS core



343 and a PEO corona (Figure 1-middle). The micelle core consists of PS and the common solvent THF since it is a good solvent for PS; but the selective solvent water is excluded from the core. The corona region consists of PEO blocks and the solvent mixture of THF and water, the same as the surrounding bulk solvent. The self-assembly process involves free molecular exchange, typical of an equilibrium process, since the PS blocks are in a liquid state under these conditions and pose no kinetic barriers to exchange. As THF is progressively removed from the system by solvent substitution, the volumefractionof THF in the micelle core continues to decrease and reaches a critical volume fraction at which the PS block becomes glass. This critical volume fraction of diluent (THF, in this case) is a function of the temperature, molecular weight of the PS block and the molecular volume of the diluent. When the PS blocks become glassy, the micelle is considered frozen. The free exchange of block copolymer molecule is now forbidden. As THF continues to be removed from the system, the number of block copolymer molecules in the micelle (the aggregation number) will remain unaltered, since the block copolymer molecules are forbidden to enter or leave the micelle. The volume fraction of THF in the core continues to decrease and the conformation of the corona block PEO continues to change with changing solvent composition. Finally, when all THF is removed, the micelle is in pure water (Figure 1-right). Indeed, we have great control over such a nanoparticle formation process by our ability to change the solvent composition gradually or abruptly. At any stage in the process, well before the volume fraction of THF in the core reaches the critical value, we can abruptly change the solvent composition by adding a large volume of water to the system causing the micelle to freeze at any bulk solvent volume fraction. Therefore, depending on the volume fraction of THF in the core (or in the bulk solvent) at which the abrupt change in solvent composition is caused, one can obtain a nanoparticle of different size. A theoretical method to predict the size and shape of such frozen micelles currently does not exist in the literature. We develop such a predictive model here by implementing the following steps: • First formulate a theory of micelle formation and solubilization in binary solvent mixtures (THF + water), allowing the common solvent (THF) to be also solubilized in the micelle core. • Second, use the above theory to determine the volume fraction of THF in the core and the aggregation number of the micelle as a function of the volumefractionof THF in the bulk solvent medium. • Third, freeze the micelle at a specific volumefractionof THF in the micelle core, thus freezing the aggregation number of the micelle. For this frozen aggregation number, determine the micelle core radius and the corona thickness when all THF is removed and only water remains as the solvent. The theory developed here follows our previous treatments of micelle formation (/) and solubilization (2) in selective solvents and therefore the construction of


344 various free energy expressions are only briefly described here. We refer the reader to the earlier papers (7-5) for more descriptive information. The model developed here is applicable to all aggregate shapes and indeed calculations have been performed for both spherical and cylindrical micelles. However, only the results for spherical micelles are discussed here because of space limitations and the results for cylindrical micelles will be presented in a different publication.


Self-assembly in Binary Solvent Mixture The size distribution of block copolymer micelles in a binary solvent mixture, with the common solvent solubilized in the micelle core, is given by

X

= = g

X f aJ exp-

kT

0) A

Hg

=

— - n f — Hi g

'

L

N

A

T

= X

T

e x

x

P0c w w) T

Here, X is the mole fraction of the micelle with an aggregation number g and containing j molecules of the common solvent (solubilizate) in the micelle core, X i is the mole fraction of the non-aggregated block copolymer molecule (unimer), a is the activity of the common solvent (THF) that is also solubilized, H° is the standard chemical potential of the micelle defined as that of an isolated micelle in the solvent mixture, |x° is the standard chemical potential of the unimer, also defined as that of an isolated unimer in the solvent mixture, and \i is the standard chemical potential of the common solvent THF defined as that of a pure solvent. The variables X and X denote the mole fractions of THF and water in the bulk solvent medium and XTW is the interaction parameter between THF and water. To calculate the size distribution of micelles, one requires an expression for the standard free energy change on aggregation, Au°. Since this depends on the shape and size of aggregates, the geometrical variables describing the aggregates have to be defined as well. g

T

T

T

w

Geometrical Relations for Aggregates The symbols A and B represent the core and corona blocks. We use the variable R to denote the hydrophobic core dimension (radius for sphere or cylinder), D for the corona thickness, and a for the surface area of the aggregate


345 core per constituent block copolymer molecule. The numbers of molecules g and j , the micelle core volume V , and the corona volume V all refer to the total quantities in the case of spherical aggregates and quantities per unit length in the case of cylindrical aggregates. The volumefractionof the solubilizate molecules in the core is denoted by r|. The concentrations of segments are assumed to be uniform in the core as well as in the corona, with (p standing for the volume fraction of the A segments in the core (cp = 1 - r|), and (p for the volume fraction of the B segments in the corona. The geometrical relations describing spherical and cylindrical block copolymer aggregates are summarized in Table 1. If any three structural variables are specified all the remaining geometrical variables can be calculated through the relations given in Table 1. For convenience, R, D and r| (or cp ) are chosen as the independent variables. c

s

A


A

B

A

Table 1. Geometrical Relations for Aggregates

V

g N v +j v

c

A

V

Cylinder

Sphere

Property =

A

3

4TCR /3

T

TCR 3

2

V [(l+D/R) -1]

V [(1+D/R) -1]

c

s

c

g

V (cp /v )

V

a

3 v /(Rcp )

2v /(R(p )

c

A

A

A

A

( (V /Vs)

1-

a

= a

1

(

(

+ a

(

(

a g g A s ( - P BB) ^PAA A AB B P B P^ A

(7)

Here, aagg is calculated recognizing that A interacts with the mixed solvent S (mixture of T and W) and the B block at the interface. a is estimated from the interaction parameter x^. A B

Change in state of dilution of block B


348 The chain expansion parameter a and the segment volume fraction ip i within the unimer in its standard state are calculated using the Flory theory for swollen isolated polymers (

p

o

05

o

«

co

*

o

Scaled Aggregalon Number Aggregation Number


©'-*


356 Acknowledgements Work supported by In-House Laboratory Independent Research (ILIR) Program, Natick Soldier Research, Development & Engineering Center.


References 1. Nagarajan, R.; Ganesh, K. J. Chem. Phys. 1989, 90, 5843. 2. Nagarajan, R.; Ganesh, K. Macromolecules 1989, 22, 4312. 3. Nagarajan, R. In Solvents and Self-Organization of Polymers, Webber, S.E., Munk, P., Tuzar, Z. Eds,; NATO ASI Series E: Applied Sciences, Vol 327, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; p.121. 4. Nagarajan, R. Colloids Surf. B. Biointerfaces 1999, 16, 55. 5. Nagarajan, R. Polym. Adv. Technol. 2001, 12, 23. 6. Flory, P.J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1962. 7. Semenov, A.N. Soviet Phys. JETP 1985, 61, 733. 8. de Gennes, P.G. Scaling Concepts in Polymer Physics;Cornell University Press: Ithaca, New York, 1979. 9. Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D.H. Surface Tension and Adsorption;Wiley: New York, 1966. 10. Siow, K.S.; Patterson, D. J. Phys. Chem. 1973, 77, 356. 11. Stockmayer, W.H. J. Polym. Sci. 1955, 15, 595. 12. Jacobsen, H.; Stockmayer, W.H. J. Chem. Phys. 1950, 18, 1600. 13. CRC Handbook of Chemistry and Physics;CRC Press Inc.: Boca Raton, FL, 1980. 60th Edition. 14. Barton, A.F.M. Handbook of Solubility Parameters and Other Cohesion Parameters;CRC Press: Boca Raton, FL, 1983. 15. Chow, T.S. Macromolecules 1980, 13, 362.


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