1712
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
M. D. Croucher and M. L. Hair
slows the H2 sorption rate of LaNi5. If this could be prevented, the rate of H2 uptake or release by this material might be increased 100-fold. A model has been proposed specifically for the sorption of hydrogen by LaNi5. Studies on related intermetallic compounds, PrCo5, PrNi5, and ErFe2, indicate surface features similar to that exhibited by LaNi5. The general similarity of the kinetic features of hydrogen sorption by the several rare earth intermetallics which have been studied, for examples, the second-order kinetics observed by Goudy et al.,3 the extremely rapid rate of reaction of C2H4with hydrogenated ErFe2,22etc., suggests that the present model may be of rather general validity.
K. Soga, H. Imamura, and S. Ikeda, Nippon Kagaku Kaishi, g, 1304 (1977). A. G. Moldovan, Ph.D. Thesis, University of Pittsburgh, 1978; A. G. Moldovan, S. G. Sankar, and W. E. Wallace, to be submitted for publication. S. Tanaka, J. D. Clewley, and T. B. Flanagan, J. Catal., 51, 9 (1978). Th. Von Waklkirch and P. Zurcher, Appl. Phys. Lett., 33,669 (1978). T. B. Flanagan in “Hydrides for Energy Storage”, A. F. Andresen and A. J. Maeland, Ed., Pergamon Press, New York, 1978, p 135. Also, private communication from Professor Fianagan to W. E. Wallace. D.M. Gualtieri, K. S.V. L. Narasimhan, and T. Takeshita, J. Appl. Phys., 47, 3432 (1976). A. G. Moldovan, H. K. Smith, and W. E. Wallace, to be submitted for publlcation. V. T. Coon, T. Takeshita, W. E. Wallace, and R. S. Craig, J . Phys. Chem., 80, 1878 (1976). A. Elattar, T. Takeshita, W. E. Wallace, and R. S. Cralg, Sclence, 196, 1903 (1977). A. G.Moldovan, A. Elattar, W. E. Wallace, and R. S. Craig, J. Solhl State Chem., 25, 23 (1978). A. Elattar, W. E. Wallace, and R. S.Craig, “The Rare Earths In Science and Technology”, G. J. McCarthy and J. J. Rhyne, Ed., Plenum Press, New York, 1978, p 63. V. T. Coon, W. E. Wallace, and R. S. Craig, ref 16, p 93. A. Elattar, W. E. Wallace, and R. S.Cralg, Adv. Chem. Ser., in press. S.Tanaka, J. D. Clewley, and T. B. Flanagan, J. Phys. Chem., 81, 1684 (1977). S.Tanaka, J. D.Clewley, and T. B. Flanagan, J. Less-Common Met., 56, 137 (1977). W. E. Wallace, R. S.Craig, and V. U. S. Rao, Adv. Chem. Ser., in press. H. Imamura and W. E. Wallace, unpublished measurements.
Acknowledgment. This work was supported by a grant from the Army Research Office.
References and Notes J. H. N. Van Vucht, F. A. Kuijpers, and H. C. A. M. Bruning, Philips Res. Rep., 25, 133 (1970). 0. Boser. J. Less-Common Met.. 46. 91 (1976). A. Goudy,’ W. E. Wallace, R. S.Craig, and T. ‘Takeshita, Adv. Chem. Ser., No. 167, 312 (1978). K. S w , H. Imamura, and S.Ikeda, J. Phys. Chem., 81, 1762 (1977). H. C. Siegmann, L. Schhpbach, and C. d. Brundle, Phys. Rev. Lett., 40, 972 (1978).
Application of Corresponding States Theory to the Steric Stabilization of Nonaqueous Dispersions Melvln D. Croucher” and Michael L. Halr Xerox Research Centre of Canada, 2480 Dunwin Drive, Mississauga, Ontario L5L 1J9, Canada (Received December f 1 , 1978) Publicatlon costs assisted by Xerox Research Centre of Canada
The incipient flocculation behavior of sterically stabilized nonaqueous dispersions is discussed in terms of the corresponding states theories of polymer solutions. This has been achieved by incorporating a temperatureand pressure-dependent x parameter into the theory of steric stabilization. It is found that the free energy of interpenetration (AGIM) of such dispersions consists of (i) a combinatorial contribution (AGI’(comb)), (ii) a contact energy dissimilarity contribution (AGIM(contactenergy)),and (iii) a free volume dissimilarity contribution (AGIM(freevolume)). The AGIM(comb)term always acts to stabilize the particles against flocculation while the AGI’(contact energy) and AGIM(freevolume) terms act to flocculate the latices. In principle, flocculation at the LCFT is usually brought about by the AGIM(contactenergy) term while flocculation at the UCFT is dominated by the AGIM(freevolume) term. The theory is able to predict both the temperature and pressure dependence of incipient flocculation and has been applied to some recently reported experimental results.
Introduction The “protection” of colloidal particles against flocculation with nonionic macromolecules is known as steric stabilization.’ It has been found to be an especially useful method of stabilizing particles in a dispersion media of low dielectric constant where electrostatic stabilization appears to be relatively ineffective. Investigations of the repulsive forces between stable particle^,^" stability in polymer melts?5 and incipient flocculation behavior have been reported for such dispersions. Incipient flocculation has been the most extensively reported measurement1 and this can be induced by changing the solvent quality of the dispersion medium relative to that of the stabilizing polymer. It has been established that it is a reversible phenomenon1 and redispersion occurs if the solvency of the disperse medium 0022-3654/79/2083-1712$01 .OO/O
is improved with respect to that of the stabilizing polymeric moiety. Using thermodynamic arguments, Napper has distinguished‘ three types of steric stabilization in the vicinity of the critical flocculation temperature. They are (i) enthalpic stabilization which is characterized by flocculation on heating, (ii) entropic stabilization which is characterized by flocculation on cooling, and (iii) combined enthalpic-entropic stabilization where in principle the dispersion cannot be flocculated at any accessible temperature. It has been shown6 that poly(acrylonitrile) (PAN) latices stabilized by poly(isobuty1ene) (PIB) in 2-methylbutane flocculate on heating to the 0 point associated with the lower critical solution temperature (LCST) of the PIB-methylbutane solution. This corresponds to an enthalpically stabilized system, whereas Q 1979 American Chemical Society
Steric Stabilization of Nonaqueous Dispersions
poly(viny1 acetate) latices stabilized by poly(l2-hydroxystearic acid) in n-heptane flocculate on cooling to the 0 temperature associated with the upper critical solution temperature (UCST) of the poly(12-hydroxystearic acid) plus n-heptane s ~ l u t i o n . This ~ corresponds to an entropically stabilized system. Recently it has been reported8 that PAN lattices stabilized by poly(a-methylstyrene) in n-butyl chloride flocculate on both heating and cooling. The upper and lower critical flocculation temperatures were found to correlate qualitatively with the independently determined 8 points associated with the LCST and UCST of the poly(a-methylstyrene) plus n-butyl chloride system, respectively. In principle, it was shown,8 by using a temperature-dependent excluded volume integral, that all sterically stabilized nonaqueous dispersions should flocculate both on heating and on cooling, i.e., they should show both enthalpic and entropic stabilization, provided that a large enough temperature range can be scanned. The flocculation behavior observed on heating and on cooling is analogous to the behavior observed in polymer solutions, which show liquid-liquid type phase separationg on heating and on cooling. The phase boundary observed on cooling is known as the UCST while that observed on heating is paradoxically called the LCST. The limiting critical solution temperature for an infinite molecular weight polymer is known as the 0 temperaturelo at which point polymer-polymer interactions are zero. In principle every polymer-solvent system has two 0 points? although it is not always possible to observe these experimentally. From the corresponding states (also known as free volume) theories of polymer solutionsll it has been established that phase separation at the UCST can be ascribed to the contact energy dissimilarity between the polymer and solvent, while phase separation at the LCST is dominated by the free volume dissimilarity between polymer and solvent. The correlation between the upper and lower critical flocculation temperatures and the 0 points associated with the LCST and UCST, respectively, suggests that the phenomenon causing phase separation in polymer solutions are also operative in bringing about flocculation in nonaqueous sterically stabilized dispersions. The purpose of this paper is to extend the theory for the free energy of interaction of anchored, sterically stabilized particles to include the effect of the free volume dissimilarity between the stabilizing polymer and the dispersion medium. This is achieved by utilizing the results of corresponding states theory,12J3which allows the effect of both temperature and pressure on the incipient flocculation behavior to be predicted.
Theory of Steric Stabilization The current theories of steric stabilization fall into three main classes which may be classified as entropy, solvency, or entropy plus solvency the0ries.l The entropy plus solvency theories14-17assume that the total free energy of interaction (AG) can be written as the sum of a mixing (AGM) or osmotic term, an elastic (AGE) or volume restriction term, and a van der Waals term (VA),thus AG = AGM + AGE + VA (1) The mixing term results from excluded volume effects and the elastic term results from a loss of configurational entropy of the stabilizing chains as the two particles approach one another. Dolan and Edwards have recently observed17 that these two terms should not be treated independently since they are interdependent. However, as a first approximation eq 1should be adequate, since the
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
1713
evidence from incipient flocculation experiments for dilute dispersions suggests that the elastic contribution is of minor importance18 and therefore the AGE term can be ignored. Napper has also arguedl that van der Waals forces are very weak between polymer particles and play little part in the incipient flocculation of such latices; therefore, the interaction is dominated by the mixing term. Two regimes of close approach of the particles have been defined by Smitham et al.16 They are the interpenetration domain which is defined by L 5 d < 2L, and the interpenetration plus compression domain in which d < L, where L is the thickness of the stabilizing barrier and d is the distance of separation of the stabilizing chains. For dilute dispersions where the interparticle distance is large, interpenetration will be caused by Brownian collisions, therefore, we neglect compression of the chains since this would only seem to be important for concentrated dispersions. The problem of the interpenetration of two polymer chains in solution has been treated by Flory and Krigbaum.lg The adaption of this theory to the case of sterically stabilized particles has been carried out by Smitham, Evans, and Napper.16 The resulting expression for the free energy of interpenetration (AGIM) of two sterically stabilized particles is given by
aGIM= 2~akT(u,2/VJ(l/z- x)a2i2S
(2)
where a is the number of polymer chains each containing i segments in a volume element normal to the unit surface area of the particle. The radius of each particle is a, U S is the volume of a segment of the steric stabilizer, and V, the molar volume of the dispersion medium. The x parameter represents the interaction between the steric stabilizer and the dispersion medium, and the S parameter in eq 2 describes the distance dependence of the free energy of interpenetration, which is a function of the segment density distribution function of the stabilizing chains. For a high molecular weight steric stabilizer a Gaussian distribution function has been usedl8 to evaluate S, while for a low molecular weight stabilizer a constant segment density distribution function has been utilized16 which gives the simple expression
s = 2(
2) 2
1-
(3)
where do is the minimum distance of separation of the chains which must lie between L 5 do 5 2L. Numerous other distribution functions have been reported in the 1iterat~re.l~~~~
Interpretation of the Thermodynamic Interaction Parameters Qualitative Discussion. Recent theoriessJ1 concerned with the thermodynamics of polymer solutions recognize three contributions to the mixing process: (i) The combinatorial or configurational entropy contribution to the free energy. This enumerates the number of ways of arranging the different kinds of molecules together in forming a solution and turns out to be a function of the number of molecules in the system. In the dilute solution theory of Flory and Krigbaumlg and in the theory of steric stabilization, eq 2, it is represented by the factor (ii) An interactional or contact energy dissimilarity term is associated with an energetic weakness of the solvent-polymer (1-2) contacts relative to the solventsolvent (1-1) and polymer-polymer (2-2) contacts on forming the solution. The interchange energy associated
1714
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
M. D. Croucher and M. L. Hair
volume-dependent degrees of freedom of the molecule. N is Avagadro's number. (ii)Extension to Mixtures. When two components, both of which are assumed to obey the law of corresponding states, are mixed, the differences in intersegmental potential and in the sizes of the segments of the two chains are characterized by the parameter~'~ 6 and p , respectively
In a mixture of homologues, e.g., poly(isobuty1ene) in an alkane, then 6 = p = 0, but there could still be differences in chain lengths and in chain flexibility between the components. These differences are characterized through a structural parameter, A, which is defined13 by TEMPER ATU R E
*U
8,
x
Flgure 1. Schematic diagram of the parameter as a function of temperature. The contact energy dissimilarity and the free volume dissimilarity contributions to are also shown.
x
with this quasi-chemical mixing process is related to the x parameter. It is this contribution which is responsible for phase separation occurring a t the UCST. (iii) The third contribution to the solution process arises from volume changes that occur during mixing. This is a consequence of the free volume dissimilarity between the dense polymer and the highly expanded solvent. This contribution is able to account for the LCST phenomena in polymer solutions. This effect also contributes to the value of the x parameter. The total noncombinatorial contribution to the free energy mixing function and, therefore, the x parameter is the sum of contributions (ii) and (iii), viz. x = X(contact energy) + X(free volume) (4) The two contributions are shown schematically in Figure 1 as a function of temperature. The interactional contribution is found to decrease with increasing temperature while the free volume term increases with increasing temperature. The total x is then found to be a parabolic function of temperature. Since x is a free energy parameter it is related to its enthalpic ( K ) and entropic ($) componentslO through 1 /2
-
x = K-ic/
(5)
where both K and $ are also composed of contact energy and free volume dissimilarity contributions. These contributions to the thermodynamic functions will also be of importance in the stabilization of nonaqueous dispersions and they are discussed in a more quantitative manner below. Quantitative Discussion. (i) Parameters f o r Pure Components. In corresponding states theories the pure ccmponents ar_echaracterized by the reduced temperature (T), volume (V), and pressure = T/T* = P/P* = V/V* (6) V is the molar volume. The starred quantities are reduction parameters which are defined12 in terms of basic molecular parameters: T* = qe*/ck P* = qe*/ra3 V* = Nra3 (7) e* and a are the intermolecular energy and distance parameters of the pair interaction potential. The parameters r, q, and c can be considered as effective numbers of segments per molecule. Only c can be ascribed an absolute significance with 3c being the number of external or
The contact energy dissimilarity term enters the theory through the v2 ~ a r a m e t e r which ' ~ ~ ~ is ~ given as v 2 = 62/4 18p2 (10)
+
Numerous other semiempirical expressions for v2 are also available in the l i t e r a t ~ r e . ~ ~ ! ~ ~ The free volume dissimilarity between the components is introduced through the T parameter13 which is written as
Values of T for polymer-solvent systems are of the order of 0.4 and the occurrence of the LCST is associated with large values of this parameter. Equation 11indicates that such phase behavior can occur not only because of a difference in molecular chain lengths between the components, as with homologues, but also because of a difference in the strengths of the intermolecular potential around the segments of molecules of different species. In nonpolar polymer solutions it has been found that the LCST invariably arises from effects in X rather than from effects in 6. In applying corresponding states theory to the thermodynamics of steric stabilization, we have not used eq 10 and 11to calculate v2 and T ~respectively. , Instead, we have treated them as parameters that must satisfy the incipient flocculation results. (iii) Thermodynamic Interaction Parameters. An expression for the concentration independent x parameter has been derived,13by utilizing the Prigogine-Patterson corresponding states theory, which is of the form
contact free volume energy where U1 is the molar configurational energy, Cp,l is the molar configurational heat capacity, and a1and p1 are the thermal expansion coefficient and isothermal compressibility of the solvent at a pressure P , respectively. Also
= = -P1* 1 (13) pz* Under conditions of atmospheric pressure, P = 0, and eq 12 simplifies to give
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
Steric Stabilization of Nonaqueous Dispersions
Expressions have also been derived25for K and $, viz. + TCpJ T dC,i/dT v2 T~ (15) K = 2R RT and
(-ui
In the expression for x, eq 14, the u2 term is usually found to dominate a t the UCST. Consequently, it would be expected that flocculation a t the LCFT would also be dominated by this term. Conversely, the ? term is the cause of the phase separation at the LCST and would be expected to dominate the flocculation process at the UCFT. It is now the usual practice in predicting the interaction parameters to use a model for the configurational properties of the liquid and this approach is adopted here. (iu) T h e Flory Model. This allows the re_du_cedand reduction parameters to be calculated. The P, V, and T parameters are linked by an equation of state of the formz1 in13
1
from which can be obtained for any temperature and pressure. The dependence of Ul and Vl is of the van der Waals type, thus -u1
= P,*V1*V1-l
and (21)
The reduction parameters required for application of the theory can be calculated from equation of state quantities by using the prescription of Flory21or by utilizing values reported in the literature.
Application of the Theory It has recently been reported8 that poly(acrylonitri1e) latex particles sterically stabilized by poly(&-methylstyrene) in n-butyl chloride flocculate on heating and on cooling. The upper and lower critical flocculation temperatures were found to correlate qualitatively with the 8 temperatures associated with the LCST and UCST of the free polymer-solvent system (see Table I1 of ref 8). From Flory-Huggins theory the critical value of x for phase separation is givenlo by (22) where r is the ratio of the molar volumes or molar volume reduction parameters of the steric stabilizer to the dispersion medium. Since the stabilizer behaves as if it were of infinite molecular weight, r1i2 0 and the critical value of x is 1 / 2 which, from eq 12, gives AGIM = 0. Equation 2, therefore, predicts a sharp transition on passing through the 8 point. If electrostatic forces are absent then this predicts a sharp transition from stability to instability near the 0 point. It should be noted that eq 22 does not indicate
-
255
1
295
335 TEMPERATURE / K
375
415
Figure 2. The free energy of interpenetration (AGY)is shown plotted as a function of temperature for three values of separation ( d o )of the particles.
whether the critical flocculation temperature is an upper or lower CFT, only that flocculation occurs if x exceeds the critical value of 1/2. Combining eq 2 and 12 allows one to predict the free energy of interpenetration, AGIM, as a function of temperature and pressure. Substituting eq 18-21 into eq 14 with P = 0 gives, at the point of incipient flocculation, that
1
4 knowledge of ?Ilat both the LCFT and the UCFT allows
where13
x,(P,T)= Y2(1+ r-1/z)2
N
(18)
The Cp,l under pressure is given by
p1P PV12 &IT - 1 + PV*2
UCFT
LCFT
I
1715
V1 to be calculated from eq 17 when P = 0. Values for u2 and r2 can therefore be calculated from the simultaneous equations resulting from eq 23. The value of the LCFT for the PAN lattices stabilized by poly(&-methylstyrene) in n-butyl chloride was found to be 254 K while the value for the UCFT was 403 K.8 Using a value for T1* of 5065 K26with c = 1.2724gives 10u2 = 0.109 and T~ = 0.108. The relevant expression for the free energy of interpenetration of a low molecular weight stabilizer, expressed in terms of the weight of anchored polymer, can be obtained from eq 2 and 3:
AGP= 4 4 ; )
(1/2-x)
( -"E) 1
u ~ T
(24)
where w is the weight of the stabilizing moiety per unit surface area and uz is the partial specific volume. Vl is the molar volume of the disperse medium and do the distance of separation of the particles. The x parameter may be calculated as a function of temperature from eq 14 by using eq 18-20. When x(T) is combined with eq 24 the temperature dependence of AGIM can be calculated as a function of the distance of separation of the particles. AGIM(T)for the PAN latices for three do values is shown in Figure 2 by using u = 5 X g cm-2, u2 = 0.89 cm3 g-l, V1 = 104.5 cm3 mol-l, a = 100 nm, and L = 12 nm.27 As would be expected, the parabolic nature of x(T) shown in Figure 1 is reflected in the interpenetrational free energy of close approach of a pair of particles as a function of temperature. Between the LCFT and the UCFT the dilute dispersion is indefinitely stable, i.e., AGIM > 0, but at temperatures in excess of the UCFT and lower than the LCFT the dispersion is flocculated, AGIM < 0. Maximum stability for the PAN latices stabilized by poly(&methylstyrene) in n-butyl chloride would be expected to occur at -340 K where AGIMattains its maximum value. This is in good agreement with the value of -325 K obtained previously8 by using the macroscopic approxi-
1716
M. D.Croucher and M. L. Hair
The Journal of Physlcal Chemhtfy, Vol. 83, No. 13, 1979 LCFT 12,
254
UCFT I
295
335 TEMPERATURE /
375
403
K
Figure 3. The combinatorlal, contact energy dissimilarlty, and free volume dissimilarity contrlbutions to the free energy of interpenetration of a pair of s!erlcaily stabilized colloidal partlcles is shown plotted as a function of temperature between the LCFT and the UCFT.
mation for x(T) in AGIM(T). Equations 14 and 24 also show that the free energy of interpenetration can be written as the sum of three contributions: (i) a combinatorial free energy of interpenetration, AGIM(comb),(ii) a contact energy dissimilarity contribution, AGIM(contactenergy), and (iii) a free volume dissimilarity contribution, AGIM(freevolume). Thus
+
+
AGI~(T,P)= AGIM(comb) AGIM(contactenergy) AGIM(freevolume) (25) Figure 3 shows the various contributions to AGIM plotted as a function of temperature for a do value of 12 nm. The AGIM(comb)term has a positive value which increases linearly with temperature. Since this term is positive it always acts to stabilize the particles, the higher the temperature the more stable the particles. If the contact energy and free volume dissimilarity contributions to AGIM are zero then in principle the latices would not flocculate at any accessible temperature. Both the AGIM(contact energy) and AGIM(freevolume) terms give negative contributions to AGIM and therefore act to flocculate the latices. When the sum of AGIM(contact energy) and AGIM(freevolume) outweighs AGIM(comb)then AGIM < 0, and the dispersion will flocculate. The AGIM(contactenergy) term shown in Figure 3 can be seen to have an almost constant value as a function of temperature. This arises because the decrease in the contact energy contribution to x (for this particular system) is almost exactly balanced in the interpenetrational free energy by the increase in the temperature, Le., X(contact energy)T N constant. In general, however, it is expected that AGIM(contactenergy) will become more negative with decreasing temperature. dAGIM(contact energy)/dT will thus have a positive value and become the major factor in causing AGIMto be negative at the LCFT, Le., lAGIM(contactenergy)( > (AGIM(freevo1ume)l. The free volume dissimilarity contribution to AGIMshown in Figure 3 is a steadily decreasing function, becoming more negative as the temperature increases. dAGIM(freevolume)/dT should therefore be a negative quantity which ensures that AGIM becomes negative a t the UCFT, Le., lAGIM(freevo1ume)I > lAGrM(contactenergy)l. For the PAN latices stabilized by poly(&-methylstyrene)in n-butyl chloride it was found that AGIM(contact energy) AGIM(freevolume) at the LCFT, both terms contributing almost equally to the flocculation process. However, at the UCFT AGIM(freevolume) is the dominant term, as expected. Addition of the three contributions to A G I ~
I
I
I
25
50
75
1
100
1
125
I
150
I 5
P R E S S U R E / bars
Figure 4. The theoretical ( P , T ) phase boundaries corresponding to the LCFT and the UCFT of the PAN latices stabilized by poiy(amethylstyrene) in n-butyl chloride.
gives the parabolic dependence of temperature shown in Figure 2. The effect of pressure on the incipient flocculation behavior of nonaqueous dispersions is a subject which has been ignored experimentally, but which could prove useful in testing the theories of steric stabilization. A thermodynamic analysis of the pressure dependence in the vicinity of a critical point13 gives (dT/dP), = -(a x/aPh/(a x/aT),
(26)
In the case of the LCST, and consequently the UCFT, application of pressure will decrease the free volume difference between the components. This will increase the affinity of the steric stabilizer for the dispersion medium. ) ~(a will be positive quantities Both -(a x / ~ Pand and thus (dT/dP), should be a positive quantity at the UCFT. At the UCST, and therefore the LCFT, (ax/aVp will be a negative quantity (see Figure 1) but -(a x/aP)~ could be of either sign. (dT/dP), may therefore be either positive or negative. In the expression for the interpenetrational free energy of mixing, eq 24, the effect of pressure is seen in the interaction parameter x,eq 12, and through the S function given by eq 3. The PAN latices were stabilized using a low molecular weight poly(&-methylstyrene)and the effect of pressure on the polymer coil dimensions is counteracted by the temperature dependence of the coil dimensions. We therefore feel justified in ignoring the effect of pressure on the S function, and need only consider the effect of pressure on x. In eq 13, a represents the difference in pressure reduction parameters between the components. The Pz* value for poly(wmethy1styrene) is not available, but it is obviously larger than that of polystyrene (547 J ~ m - and ~ ) we estimate it to be about 600 J ~ r n - ~As . the P1*value for n-butyl chloride is 601 J cm9 we have taken ?r = 0 in eq 13. Utilizing eq 12 and eq 17-21, we calculated the x parameter as a function of pressure a t various temperatures. A plot of x against P, the pressure at which x just exceeded predicts the critical flocculation pressure for a particular temperature. The projection on the (P,T) plane of the critical lines corresponding to the UCFT and LCFT for the PAN latices stabilized by
x/anp
Experimental Investigations
on Light Scattering
poly(a-methylstyrene) in n-butyl chloride is shown in Figure 4. It can be seen that both critical flocculation (P,T) curves are linear over the pressure range calculated. The value of (dT/dP), at the UCFT is a positive quantity, as expected, and is of the order of 0.4 deg bar-' while (dT/dP), at the LCFT is small and negative and of the order of -0.05 deg bar-l. The large value of (dT/dP), a t the UCFT is to be expected since the solvent is readily compressible at such elevated temperatures which makes the steric stabilizer more compatible with the dispersion medium thereby pushing the UCFT to a higher temperature. At the LCFT the solvent is relatively incompressible and this is reflected in the smaller value of (dT/dP),. Figure 4 also indicates that as the pressure is raised the PAN dispersion stabilized by poly( a-methylstyrene) in n-butyl chloride is stable over a greatly increased temperature range.
References and Notes (1) D. H. Napper, J. Colloid Interface Sci., 58, 390 (1977). (2) A. Homola and A. A. Robertson, J . CoNoid Interface Scl., 54, 286 (1976). (3) R. J. Cairns, R. H. Ottewiil, D. W. J. Osmond, and I. Wagstaff, J . Colloid Interface Scl.. 54. 45 11976). (4) J. B. Smltham and D. H. Napper, J . Chem. Soc., Faraday Trans. 7, 72, 2425 (1976). (5) J. B. Smltham and D. H. Napper, J . ColloldInterface Sci., 54, 467 (1976). (6) R. Evans and D. H. Napper, J. ColloHInterfaceSci., 52, 260 (1975). (7) D. H. Napper, Trans. Faraday SOC.,64, 1701 (1968).
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
1717
(8) M. D. Croucher and M. L. Hair, Macromolecules, 11, 874 (1978). (9) D. Patterson, Macromolecules, 2, 672 (1969). (10) P. J. Flory, "Principles of Poiymer Chemlstry", Corneli Universlty Press, Ithaca, N.Y., 1953. (11) D. Patterson, Rubber Chem. Techno/.,40, 1 (1967). (12) D. Patterson and G. Delmas, Discuss. Faraday Soc., 49,98 (1970). (13) D. Patterson and 0.Deimas, Trans. Faraday Soc., 85, 708 (1969). (14) D. J. Meier, J. Phys. Chem., 71, 1861 (1967). (15) F. Th. Hesselink, A. Vrij, and J. Th. G. Overbeek, J . Phys. Chem., 75. 2094 119711. (16) J. B. Smithim, d. Evans, and D. H. Napper, J . Chem. SOC.,Faraday Trans. 1 , 71, 285 (1975). (17) A. K. Dolan and S. F. Edwards, Proc. R. SOC.London, Ser. A , 343, 427 (1975). (18) R. Evans, J. B. Smitham, and D. H. Napper, ColloM Polym. Sci., 255, 161 (1977). (19) P. J. Flory and W. R. Krigbaum, J . Chem. Phys., 18, 1086 (1950). (20) F. Th. Hessellnk, J . Polym. Sci., C61, 439 (1977). (21) P. J. Flory, Discuss. Faraday Soc., 49,7 (1970). , ~equivalent (22) It is of interest to note that the v2 term of Patterson et a ~ . is to X I 2 / P ' , in the Flory theory" where X,2 Is an enthalpic lnteractlon parameter. (23) J. M. G. Cowie and I. J. McEwen, J . Chem. Soc., Faraday Trans. 1, 72, 1675 (1976). (24)J. Blros, L. Zeman, and D. Patterson, h&cromolecules, 4,30 (1971). (25)D. Patterson, J . Polym. Sci., C16, 3379 (1968). (26) In order to obtain a quantitative fit between corresponding states theory and critical solution temperature data, the value of T ' , has to be selected using a semiempirical method. Cowie and M ~ E w e n ~ ~ have given that T*,/K = -17491 74.774TC- 61.085X 10-3T,2 where T, is the solvent critical temperature. For n-butyl chloride they quote T ' , = 5065 K. (27)We have taken L to be constant over the temperature range between the two CFT. In practice L Is temperature dependent which will enhance the parabolic shape of the AGy( T ) curve. (28) P. J. Flory and H. Hocker, Trans. Faraday Soc., 87, 2258 (1971).
+
Experimental Investigations on Light Scattering, 9. Light Scattering of Flow Orlented Nonspherical Particles H. Doppke and W. Heller" Department of Chemlstry, Wayne State Un/vers/ty,Detrolt, Mlchlgan 48202 (Received November 9, 7978)
A brief description of the technique of flow light scattering measurements is followed by a discussion of the results obtained on practically monodisperse systems of nonspherical (rodlike) P-FeOOH crystals of colloidal size. Observations were made at constant 0 = 90° varying systematically the equatorial angle w' and the shear rate. The results, in conjunction with the separately determined axial ratio of the crystals, were used in order to obtain numerical values for the crystal length and width. The analytical potential of the flow light scattering method for the dimensional characterization of monodisperse and heterodisperse nonspherical particles and for the detection and measurements of reversible and irreversible dimensional changes of these particles or their aggregates is outlined. The flow light scattering method is compared with that of flow birefringence.
I. Introduction The determination of the dimensions of rodlike or platelike bodies by means of light scattering is usually carried out by investigating their solutions or dispersions at rest. The light scattering effect thus obtained is that averaged over all possible orientations of the scatterers with respect to the incident beam. On using the theories available for the scattering of randomly oriented prolate or oblate spheroids,' important information on size and shape of the scattering bodies can then be obtained, especially by means of Zimm plotsa2 Random orientation of nonspherical bodies reduces considerably characteristic differences between the scattering of spheres, prolate and oblate spheroids. Consequently, a major improvement in the analytical potential of light scattering measurements is possible on 0022-3654/79/2083-1717$01.00/0
orienting spheroids, thus introducing as additional variables the direction of observation relative to the direction of the orienting vector and the magnitude of the orienting torque. There are essentially three possibilities for preferential orientation: orientation in a magnetic field, in an electric field, or by flow. The first one, which is by far the simplest and therefore most attractive possibility, is unfortunately limited to those not very numerous cases where the magnetic anisotropy of the scatterers is reasonably largeas Orientation in an electric field can be applied to a much larger number of systems and interesting results have been obtained by this method! The electric anisotropy required in order to produce a reasonably large torque is, however, often too small to produce more than a very modest degree of orientation. In contradistinction, orientation by flow 0 1979 Amerlcan Chemical Soclety
