Is There Life Beyond Micelles? - American Chemical Society

Chapter 2

Is There Life Beyond Micelles? Mechanisms of Latex Particle Nucleation

Downloaded by UNIV OF ARIZONA on August 6, 2012 | http://pubs.acs.org Publication Date: June 3, 1992 | doi: 10.1021/bk-1992-0492.ch002

F. K. Hansen Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo 3, Norway

The theory for particle nucleation in emulsion polymerization has been generally described by the Smith-Ewart/Roe and HUFT (Hansen, Ugelstad, Fitch & Tsai) theories. The HUFT theory recognizes 3 different loci for particle nucleation; homogeneous, micellar and droplet nucleation. More recently several new investigations have been published, considerably inpoving the amount and quality of experimental data; in addition, the stability of new particles above the CMC has been questioned. Some of the results seem to confirm the theory at its present stage, while other data call for novel theoretical considerations. From the HUFT theory, it can be calculated that micelles have a high probability for nucleation. However, the view of the micelles as dynamic species, and the dynamic interaction between micelles, monomer and oligomer chains could give better understan ding of the physical processes involved. This view might result in a more flexible and general theory. In this paper the state-of-the-art of particle formation theory will be reviewed and the new ideas will be discussed.

The theories for particle nucleation in emulsion polymerization up to 1980 have been extensively described by this author earlier (1) and will not be repeated here. In this paper I will give a personal view of the present state-of-the-art of particle nucleation, especially on the basis of the H U F T theory, and including later work. In this background the main historic data and arguments must be repeated The part of nucle ation theory that concerns nucleation in monomer droplets will not be treated in this article. At the end of the paper I will discuss some propositions that may bring further understanding to the field and act as a basis for further experimental and theoretical ventures.

0097-6156/92/0492-0012$06.00/0 © 1992 American Chemical Society In Polymer Latexes; Daniels, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

2. HANSEN

Is There Life Beyond Micelles?

13


The Smith-Ewart theory The attempt to quantitatively understand the latex particle nucleation phenomenon starts with the Smith-Ewart theory (2) based on Harkins' micellar theory. The fundamental assumption of this theory is that free radicals generated by initiator in the aqueous phase are absorbed in surfactant micelles at a rate proportional to the surface area of the micelle. The rate of absorption is either assumed constant (upper limit) or decreasing with time because of competition with new particles (lower limit). Nucleation stops when all surfactant has been consumed by adsorption onto the new particles. The particle number is not proportional to the number of micelles (or total surfactant area) because particles grow at a constant rate during the nucleation period, thereby decreasing the number of micelles at a higher rate than that of pure nucleation. The Smith-Ewart expression is usually presented as: N-k(p /u)0.4(a S)0.6 i

s

(1)

where pj is the rate of radical generation, u = dv/dt is the (constant) rate of particle volume growth, a$ the specific area of the surfactant, and S the surfactant concen tration. The constant k is 0.53 for the upper limit, and 0.37 for the lower limit. This theory has been extensively discussed by many workers, and it seemed (and still seems) to fit well for monomers of low water solubility (e.g., styrene) (3). The theory was developed with the early emulsion polymerization systems in mind (e.g., in the artificial rubber industry) where such monomers were often utilized, together with surfactants (e.g., soaps) of low critical micelle concentration (CMC). Before long it became apparent, however, that the Smith-Ewart theory has several drawbacks. The most important objections are: a) b) c) d)

Particles are formed even i f no micelles are present. Estimated particle numbers are double that found by experiment. More water soluble monomers do not fit the theory. A maximum rate in interval I is predicted, but never observed.

The Roe theory Objection (a) is considered by Roe (4), where the Smith-Ewart expression is redeveloped on a homogeneous nucleation assumption. Roe's argument is also that in a mixture of nonionic and anionic micelles, the final particle number is not directly related to the N U M B E R of micelles. Homogeneous nucleation replaces micellar absorption by the argument that the water-soluble free radicals cannot absorb into the hydrophobic interior of a micelle, but will start particle growth in the aqueous phase. The growing radicals will then adsorb surfactant and thus become new stable particles. In the Roe theory Smith and Ewart's parameters and derivations are replaced with exact copies based on homogeneous grounds. For instance the C M C is replaced by a critical stabilization concentration ("CSC"). The volume growth, etc. are assumed the same. B y no surprise, Roe ended up with the Smith-Ewart expression (1), proving that agreement with this expression does not have to imply micellar nucleation. It does however, imply a rather abrupt stop in nucleation at the "CSC". Roe does not make

In Polymer Latexes; Daniels, E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

14

POLYMER LATEXES

any estimates about the magnitude and reason for this "CSC", but he proposes to use "some sort of adsorption isotherm" below the C M C . The Roe theory also does not consider the other arguments.


The Fitch-Tsai theory Because argument (a) is quite obvious, there seems to be general agreement that a homogeneous mechanism must be active below the C M C , but the exact physical model and mathematical treatment have been the subject of discussions. The Fitch and Tsai derivation was the first serious attempt to produce a quantitative model for homogeneous nucleation (5-7). It is based on the Priest idea (8) of propagation in the water phase and self-nucleation when the chains reach a critical degree of polymer ization (c.do.p.), jcr. The assumption of self-nucleation by means of a c.do.p. is different from ordinary nucleation theory where it is the critical (supersaturation) concentration that comes into play. The Fitch theory considers that the final particle number is determined by competition between oligomer precipitation and absorption in already formed particles, dN/dt-pi-pA

(2)

where pj is the rate of radical generation (corrected for aqueous phase termination) and PA is the rate of radical absorption. This rate is derived from geometrical considerations about the average length, L , the radicals can travel before selfnucleation. If the radical collides with an existing particle before it can travel this distance, it will not produce a new particle, PA is expressed by p

A

- *PiLNr

2

(3)

p

where rp is the particle radius. This type of absorption model is called the "collision theory" because it does not consider any concentration gradient outside the particle surface and thereby treats the radicals as points that collide with the particles. The absorption rate is then determined by pure geometric factors, and is proportional to the particle surface A = Nrp2. Fitch and Tsai could express the distance L by means of the c.do.p., jcr, through Einstein's relationship and the particle radius as a function of time by means of non-steady-state kinetics. They ended up with an analytical, although somewhat complicated, expression for the particle formation rate: p

2

2

dN/dt = p t f H * N)V3 {[ 3 v k p M W ( 4 k t ^ p ^ ) ] ln[cosh(p k )V t]} /3]L (4) A

i

tw

This theory was tested on methyl methacrylate systems and called for a very low, but in itself not unreasonable, initiator efficiency. However, the "collision theory" for absorption (Nrp2) has been criticized on more formal physical grounds. Fitch also found later from seed experiments that the absorption rate was proportional to Nr ("diffusion theory", see below) (7). Proportionality with N r , is not physically 2

p


2. HANSEN

15


impossible, however, but requires special conditions (see below). Another important observation of Fitch and coworkers was that at submicellar surfactant concentrations, the particle number did not increase monotonically with time, but rather went through a maximum. This phenomenon, which is called limited coagulation (limited because the coagulation stops when the surface charge and potential has reached a level where the particles are stable) is believed to be the common mechanism for establishing the final particle number in low surfactant and surfactant free systems. At that time, no quantitative theory for this had been presented.


The Hansen and Ugelstad theory The treatment by Hansen and Ugelstad (9-12) was partly based on the Fitch theory as concerns the oligomer propagation and precipitation. The basic idea is threefold: (1) The aqueous phase kinetics is fully developed to take into consideration propagation, termination and absorption of oligomeric radicals. (2) The absorption (capture) of radicals in particles is a reversible diffusion process that is dependent on oligomer solubility, reaction rate in particles (propagation, termination) and surface potential. (3) The new particles - "primary particles" - are not stable unless they are fully covered by emulsifier, and will undergo limited coagulation. (1) The radical kinetics in the aqueous phase are represented by one rate expression for each radical type. For initiator radicals: dRi/dt = pi - k p i R i M - ktwiRiRw - RikapiNp

(5)

w

For oligomer radicals of d.o.p. =j : dRj/dt = k p R j _ i M - k p i R j M - ktwiRjRw - RjkapjN w

w

p

(6)

The rate of nucleation is given by: dN/dt - k p R

j c M

M

(7)

w

which is the propagation rate of the chain with do.p. 1 less the critical. These equations have been elaborated further to include many details (1) but are in principle simple. They may be solved either numerically or by a steady state assumption to different degrees of accuracy. A relatively simple solution for the nucleation rate can be obtained under certain conditions, dN/dt = pi(l + ktwRw/kpMw + < V N / k p M ) l - J < * w


(8)

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POLYMER LATEXES

with the total oligomer radical concentration in the aqueous phase given by


R

2

w

1

- f [ ( < V N ) + 4 p k t ] / 2 . N}/2k i

w

a

tw

(9)

(2) The constants l%j are the 2nd order rate constants of absorption (capture) in the particles and are represented in Equation (8) and (9) by an average value, . The use of an average value is necessary in order to obtain Equation (9), but is physically not very correct. Use of these equations with reasonable values for the constants, also tends to generate far too few particles, especially compared to "stable almost C M C " conditions. The reason for this is that the absorption rate as expressed by the "diffusion theory" is too high. The Hansen and Ugelstad work therefore also included a more detailed reevaluation of the absorption rate constants. By considering the particle geometry and concentration gradients both outside and inside the particles, a new expression for the absorption rate constant was developed Thus kaj could be expressed as kaj-torpIVjFj

(10)

where the factor F, the "efficiency factor" represents the lumped effect of both reversible diffusion and electrostatic repulsion. This factor is given by the expression 1/F = ( I V a D p ) / ( X coth X -1) + W where

X»r (k/Dp) V

(11)

2

(12)

p

and

k = kpMp + nk p/v t

where

(13)

p

n - 0 or 1

(The other constants are given in the symbol list.) The physical and mathematical significance of the F-expression is easier understood by observing the limiting cases (i)

F-l/W

(ii)

F-ar (kDp)l/2/D

(iii)

F-ttpSk/SDj,

p

=>

w

=>

ka - 47cD rp/W' w

= 4*rp2(kD )l/2 p

ka = avpk

(14) (15) (16)

Case (i) corresponds to irreversible diffusion, and it is this that is called the "diffusion theory". In this case there may be some effect of electrostatic repulsion, represented by W (£1). In case (ii) the rate is controlled by diffusion and reaction inside the particles (very low diffusion constant Dp), while in case (iii) there is a dynamic equilibrium distribution of radicals between the particles and the aqueous phase. Both case (ii) and (iii) will lead to much lower values of ka than case (i). One


2. HANSEN

17


important consequence of this expression is the significance of k, which is the total rate constant (1st order) for reaction of a radical inside a particle by propagation or termination. The expression also includes the termination rate through the second term where n is the number of radicals already in the particle. If k - 0 then also F - 0 and there will be no net radical absorption. This expression does not include the consequences of a (static) equilibrium distribution of radicals between the two phases, but in most nucleation cases, this will be negligible. If there is a very dense surface layer involved, the diffusion equations may be modified according to an alternative equation. Also i f radicals are merely adsorbed, the equations will be different. In Figure 1 is shown some calculations of F in the cases n=0 and n l , and it is seen that most cases where F « l corresponds to case (iii) (slope 2 in log F vs. log r ) . In the case where n=l and r

Is There Life Beyond Micelles? - American Chemical Society

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