sihility of analogous ineasuremcnts in liquid ammonia but 1 week of washing the conductivity cell was reis restricted because the conductivity due to the quired to achieve 10-9.16 The lowest achicvcd in this transient ions produced by the radiation must be work was 4.5 X In view of the irreversible differentiated from that due to pure S H a and to the increase in Conductivity with y- irradiation, achicvcionic iiiipurities. To do this demands much higher ment of the highest purities would probably not transient ion concentrations than needed in hexane, be profitable in investigations of the present type. It is possible that the major impurity introduced by irradiaand these produce niuch higher recombination rates. Allcn and Hunimel state that the ion-pair concentration is water formed by the reaction of ammonia with tions in their experinients were IOy nil.-' or less, absorbed O2 on the electrodcs and walls or with oxygen while the liquid ainnionia experiments reported here bound in the silicates in the walls. Conducting inipurirequired of the order of 10l2 ion pairs at the ties are relatively unimportant in carefully purified steady state. A t this 1000-fold higher concentration hydrocarbon solvents. Allen and H u i i i i i ~ l ' ~used of transitory ions, the initial half-time of recombination hexane having a specific conductivity of lO-'5 to 10-l~ was clearly niuch less than 1 sec. and very lilicly similar ohm-' cin. - I . to t h e time required for removal of the source. A specific conductivity as low at lo-" ohni-' tin.-' (16) V. r'. Hnisda and C. A. Kraus, J . Am. Chcm. Soc., 71, 15Ci5 has been reported for highly purified liquid a ~ i i n i o n i a ~ ~(1949).
Application of Crystallization Theory to the Behavior of Greases
by J. Panzer 8880
Research and Engineering Company, Linden, New J e r s e y
(Receiued A p d 29, 1.964)
Thcoittical equations derived in the litci,at'urc for nucleation and growth ratcs in crystallizatioii have been iiiodified and coinbincd to obt'ain the cffects of isolated reaction variablcs 011 t h c i.atc of paiticle size change. Undcr the conditiotis used to ilialie greases, the cquations show that the average grease thiclmw particle size is reduced as the average tempciaturc of ivaction is rcduccd, as the thicliener concentration is reduced, aiid as the oil viscosity is dccrcascd. The predicted rcsults agree well with nuinerous cxperinicntal o h s c i ~ ~ t i o i i~ported is in thc literature. The cffects of oil coinposition and surfactants 011 interfacial free energy and the effect of changes in the latter on particle size depend on the suisface energy of the grease thickener and the 111annerin which adsorption on the solid surface takes place. The relationship between particle size, as a function of reaction variables, on grease properties, such as flow behavior and oil separation, will also be discussed.
'I'lic~i~carc i\rsiiy illustratioiis in the grease literature of thc dt'ect of thickciicr particle size aiid shapc on gi'casc properties. Although soiiie recciit work sug-
arid shapc of the priiiiary particles will itifluoiico strongly the nature of the aggregates. I t is also well
idI’P1,lCATION
OF
CRYSTALLIZATlON T H E O R Y
TO THE
BEHAVIOR OF GREASES
known that variation in the reaction conditions during grease preparation will affect the particle shape and sizr distribution and hence affect the properties of the grease. I t was of interest to determine how well the theories of crystallization explain and predict the effects of reaction conditions on the formation of grease thickcncrs. In order to achieve this objective, sonic of the niatheinatical relationships described by currently accepted crystallization theory were nianipulated so that the effect of several reaction variables on particle size could be defined. The predictions resulting from these equations were then compared with experimental observations made on inany greases and sonie colloidal dispersions reported in the literature.
Derivation of Crystallization Equations The formation of grease thickeners by the reaction of two or more coniponents or by precipitation from a hot solution is a crystallization process involving two steps as in all crystallization processes-nucleation and growth. Sucleation involves soine type of conibination of molecules until a critical-sized embryo is foriiied, after which growth takes place by deposition of niolecules froni the supersaturated solution onto the nuclei. Usually, after the initial nuclei are fornied, further nucleation and growth proceed siniultaneously until the supersaturation of the systeni is relieved. The theories of nucleation and growth show that the rates of .both these stcps are proportional to the diffusion rate of the crystallizing niolecules and the degree of their supersaturatioii and are inversely proportional to the surface free energy of the n ~ c l e i . ~For any systeni, it is possible to show7 for different reaction conditions related to the above variables that either nucleation rate or growth rate is predoniinant and, hence, deterniines how the particle size will change. The Reeker-Doring equation for the rate of hoinogeneous nucleation may he expressed as3
where 13 is the interfacial free energy between the enibryo of the nucleus and supersaturated solution, S is the supersaturation ratio (ratio of concentration hi supersaturated system to that at saturation), and ?’ is the teniperature. All other terms in the original equation arc coiisidered as constant and characteristic of any particular systcni under study. Diffusion rate has been coiisidered in the above equation and is cxpressed as a functioii of tcniperature. The rate eyuation for heterogeneous iiuclcatioii is siniilar to eq. 1 and has ai1 additional teriii which considers the iiitcrfacial energy between the heterogeneous nuclei and the
2953
crystallizing material Since this term is characteristic of the particular system, it has been disregarded in this qualitative treatnient. In attempting to express RN as a function of individual variables it is necessary to iiiake soine assumptions about the relationships of s, T, and E to each other. Because all the factors in the BeckerDoring equation which are characteristic of specific crystallizing systems are not known quantitatively, the assumed relationships between S, T, and E are rather primitive. It is known that in most system containing a given quantity of solute and solvent, a reduction in tcniperature mill increase the supersaturation for a finite tiiiie. Therniodynaniics suggests that the relationship between S and T may not be linear, but for the sake of simplifying this qualitative treatnient, it has been speculated that a linear relationship exists which niay be expressed as S 0: 1/T. Therniodynaniics also shows that interfacial free energy is linearly related to teinperature and in a systeiii i n which all other variables are constant, it can be assumed that R 7’ As nientioned above the diffusion rate has been incorporated into eq. 1 as a function of teinperature, using the Seriist diffusion lam. Substitutiiig thcse simple relationships into eq. 1 the following was obtained IjN(T)
o: T-3.’
e-!iOn
T)’
(2)
Holding T and E constant for any systcni, RY may be expressed as a function of supersaturation RNM)
cc g + , - I / ( I n
SI2
(3)
Finally by considering T and S constants, RY as a function of E was obtained
R v c E ,a
]{‘I9e
(4)
A relation for growth rate has been derived by Tausch3and niay he cxprcssed
IZC
TD(S - 1) 111 S l3
cc ---__
1
+ K+ K ’In Y o YO
(5)
D = diffusion rate; Yo o: E / T In S, K and K’are constants charactwistic of any systeni. Unless the values for K and K’ are known, it I S
difficult to use eq. 5 to determine the relative effects of temperature, supersaturation, and interfacial energy on growth rate. Numerical analysis of eq. 5 indicated that changes in the denoniinator caused by changes in the variables are directionally the sanie as those in the nunierator and showed that the denominator changes at a much lower rate than the nunierator. Thus, by disregarding the denominator in eq. 5 siniilar rclationships were obtained, and the equation can be used to determine relative changes in RG. RG was now expressed as
RG
TD(S a
- 1) In
S
E
RG as a function of temperature only niay be obtained by considering again the relationships between T , S, and E . D 0: T by the Sernst diffusion law. Therefore R G ( ~c:) ( T - 1) In T
(7)
Comparison of Theory and Literature Observations In the following discussions each variable is treated individually so that comparisons with observations reported in the literature may be made. A . Ej'ect of Temperature. A graphical reprcsentation of eq. 2 and 7 is shown in l'ig. 1. Before interpreting the curves in Fig. I, one should kecp in mind that the curves in this and in other figures to follow merely represent the reZative effect of a particular variable on crystallization. The actual shaprs of the curves for a specific system would depend on the constants characteristic of the systcni. The important
w
I-
RGas a function of S, only with T , D, and E constant, is
d W
-I>R G ( ~ ) (S
- 1) In
S
(8)
4 W
oi
Finally, RG as a function of E may be obtained b y holding T , D, and S constant.
RG(C
1
(9)
I n attempting to combine the over-all effect of the variables in both nucleation and growth steps on the rate of particle size increase, R,, it has been assumed that R , is proportional to the growth rate and inversely proportional to the nucleation rate as in expression 10. The nucleation and growth terms are R P
RG
+ n1,
used additively in the particle size equation since the two crystallization steps are sequential. E'or the purposes of this qualitative discussion it does not matter whcthcr we express R , as in eq. 10 or as
RDa
RG RN -
since both equations give siniilarly shaped curves. The effects of the variables on R,, niay be expressed by the equations
The Joiirnal of Physical Chemistry
RELATIVE TEMPERATURE
Figure 1. Effect of temperature on nucleation and growth rates.
point is that the general habit of the curves, indicating directionally the changes in growth and nucleation rates, would be the sanie for all systenis. I n Fig. 1, as the temperature is increased up to some critical teniperature characteristic of the system, the nucleation rate and growth rate both increase rapidly. Above the critical temperature the growth rate continues to rise but the nucleation rate decrcases. This effect is shown inore clearly in I'ig. 2 where the rate of particlc size increase, R,, is plotted as a function of temperature (eq. 11). Figure 2 shows that the rate of particlc size increase falls to a niininiuni level at sonic: critical teniperature and then rises with increasing temperature. This observation suggests that each grease system has soiiie characteristic critical teinperature at which particle growth rate niay be carcfully controlled to obtain a desired particle size. Consistent with this suggestion is the finding that soiiie soap-thickened greases have transition temperatures at which optiniuni fiber formation occurs.4
APPLICATIONOF CWSTALLIZATIOX THEORY TO
THE
BEHAVIOR OF GREASES
n
0:
RELATIVE TEMPERATURE
Figure 2. Effect of temperature on rate of particle size increase.
For a given grease iiianufacturing procedure it is difficult to say what effect temperature has on particle size unless one knows the critical teniperature for the systein. However, in order to obtain grease thickener particles of suitablc size a t a reasonable rate, the average temperature used in inost greases would probably be above the critical point. The theory predicts that the lower this average temperature (or the greater the cooling rate), the lower the average particle size. This prediction is supported by an equation derived by I’ackter, showing the effect of temperature on particle size, insofar as it affects solubility and super~ a t u r a t i o n . ~A suniniary of the data reported in the literature for several different greases shows agreement with the predictions in every case (see Table I). Particle size observations in most instances were made by electron microscopy after eluting the oil from
Table I : Effect of Cooling Rate on Grease Properties
_____Effect of increase in rate on--.--Grease type
Sodium Lithium Lithium Lithiurn Lithium Arylurea
Particle sire of thickener
Decrease Ilecresse Decrease Decrease; shorter fibers Decrease Decrease ’
Grease viscosity
Oil separation
Ref
Increase
Decrease Decrease
a b
Increase Increase
Increase
C
d
Decrease Decrease
e
f
a I. E. Puddington, jVI,GI Spokesman, 9 (9), 1 (1945); W. Gslllty and I. E . Puddington, Can. J . Res., B22, 90 (1944). “V. V. Sinitsyn, et ul., Kolloidn. Zh., 22, 469 (1960). B. W. Hotten and I). H. Birdsall, J . Colloid Sci., 7, 284 (1952). A. A. Trapeznikov, et al., [ t u . A k a d . >Vazck S S S R , Ser. Piz., 23, 777 (1950). A. .4.Trapeznikov and G . G. Shchegolev, Kolloidn. Zh., 24, 104 (1962). J . J. Chessick and J. B. Christian, NLGI Spokesntun, 26, 172 (1962).
’
2955
the grease with a suitable solvent. I n soiiie of the older reports the observations depended on light niicroscopy. Viscosity nieasurenients on the greases were made with the A S T N penetrometer which measures the penetration of a weighted cone into a cup of grease. It is believed that this measurement provides an indication of yield stress and viscosity a t low shear rates. I n several reports describing fluid suspensions, viscosity measurements were made with conventional viscometers. Shear breakdown is the extent to which a grease softens, as measured by the penetrometer, after it is sheared in a fixed, arbitrary manner. Oil separation nieasurenients were determined by the amount of oil which passed through a filter or screen after a grease had been subjected to the forces of gravity or additional pressure. The significance of the temperature effect is that as the particle size decreases, the grease viscosity (or consistency) increases, and the oil separation decreases. A iiiore coiiiplete summary of the observed effects of particle size decrease on grease properties, regardless of how reaction variables affect particle size, is shown in Table 11. The few deviations in Table I1 from the general effects suggest that for any grease systeni there may be an optimum particle size on either side of which changes in particle size may have bpposite effects on grease properties. R. Effect of Thickener Concentration. The concentration of the thickener in solution deterinines the degree of supcrsaturation, one of the variables in the crystallization equations. An increase in coiicentration would also increase the diffusion rate, but offsetting this is an increase in viscosity produced by the higher concentration. Because of these effects and because both nucleation and growth rates are related to diffusion rate in the same way, for all practical purposcs we can ignore the effect of the concentratioii on diffusion rate in comparing the two crystalliza,tioii steps and consider only supersaturation a t any given temperature. Therefore, the effect of the colicelitration on the nucleation and growth rates inay be expressed by eq. 3 and 8. These equations are shown graphically in Pig. 3. Although both rates increase as supersaturation increases, the growth rate increases faster initially, but more slowly after soiiie level of supersaturation. The over-all effect of concentration (or supersaturation) on particle size is defined by eq. 12. The curve representing this function is shown by Fig. 4 and indi(4) J . B. Mntthews, J . Inst. Prtrol., 39, 265 ( 1 9 5 3 ) ; 11. M . Suggitt, S L G I S p o k e s m a n , 24, 307 (ISGO). ( 5 ) A. I’nckter, J . Phys. Chem., 6 2 , 1025 (1958).
Volume 68. ,\‘umber
10
Octobcr, 1864
J. PANZER
2956
~
~
Table 11: Effect of Decrease in Particle Size on Grease Properties
______ Effect on-----Grease type
Lilhium Lithium Lithium (decrease Lithium Aluminum Calcium acetaLe Calcium carbonate Calcium carbonate Starch Glase spheres (Several greasos compared)‘ Sodium Arylurea
Viscosity
Shear breakdown
Oil separation
Ref.
a
Increase Decrease Increase
Increase Increase Increase Increase Increase Increase Increase
Increase Increase
Decrease Decrease Increase Decrease
b d e
f g
h
i j k
Decrease Decrease Decrease
m n o
* T. A. Renshaw, Ind. Eng. Chem., 47, a See ref. c, Table I. 834 (1955). The change in particle size for this system involved the lengt>h to diameter ratio ( L I D ) . A. C. Borg and It. H. Leet, Sci. Lubrication (London), 9 (6), 24 (1957); Lubrication Eng., 13, 156 (1957); ibid., 15, 450 (1959). e See ref. b, Table I. A. Rochow, “Physical Methods of Organic Chemistry,” T701, I, Part 3, A. Weissberger, Ed., John Wiley and Sons, J . Panxer, Lubrication Eng., 15, Inc., New York, N. Y., 1954. 453 (1959). H. W. Yiesholtz and I,. H. Cohan, Ind. Eng. Chem., 41, 390 (1949). A. C. Zettlemoyer and G. W. Lower, J . Colloid Sei., 10, 29 (1955). H. R. Kruyt and F. G. van Selms, Rec. trav. chim., 62, 407 (1943). P. S.Williams, Discussions Farad a y Soc., 11, 47 (1951). This study didnot consider differences in thickener type. B. W. Hotten and L). H. Birdsall, Ind. Eng. Chem., 47,447 (1985). I . E. Puddington, footnote a, Table I. See ref. f , Table I.
’
cates that as S increases from unity, R, falls rapidly to a inininiuni and then increases. Von Wciniarn’s rule that an increase in S would reduce the particle size is predicted from the left portion of the curve.
R E L A T I V E SUPERSATURATION
Figure 3. I!M”’ct of supersaturation on nucleation and growth rates.
T h e Journal of Physical Ch,emistrii
R E L A T I V E SUPERSATURATION
Figure 4. Effect of supersaturation on rate of particle size increase.
To achieve crystallization a t the high rate that is generally practiced in grease inanufacture, the value of S would probably be high enough so that a further increase in S would result in larger particles. Thus, one would predict that the greater the concentration, the larger the ultiniate particle size. Packter’s equation shows a siniilar prediction for systems with a given ~ o l u b i l i t y . ~Two literature reports on sodium greases are in agreement with this prediction (see Table 111).
Table I11 : Effect of Increase in Thickener Concentration on Grease Properties
Grease type
Effect on particle size of thickener
Sodium Sodium
Increase L I D Increase L I D
Kef
a b
B. B. Farrington and D. H. Birdsa 11 a See ref. a, Table I. NLGI Spokesman, 11 ( l ) ,4 (1947).
C. Eflect of Oil Viscosity. The viscosity of the base oil in a grease affects the diffusion rate, but this variable is related in the saine way to both nucleation and growth rate (directly proportional). Therefore, the theoretical equations do not indicate which rate will predominate unless one knows the niagnitude of the constant ternis in the equations (characteristic of the particular system). One may speculate that, because nucleation is the first step in Crystallization, its rate would determine the particle size. An increase in viscosity would decrease the diffusion rate which in turn would decrease the nucleation rate. Although the growth rate also would be decreascd, the fact that the niaterial in solution would not be used up too
APPLICATION OF CRYSTALLIZATION THEORY TO THE E~EHAVIOR
rapidly in nucleation means that particle growth could proceed to some extent. If the reaction time were long enough, one would expect an increase in particle size as the viscosity increases. This prediction is borne out in most cases, as shown in Table IV. The grease system showing the reverse behavior illustrates the difficulty in making a prediction when diffusion affects both rates in the same way.
Table IV: Effect of Increase in Oil Viscosity on Grease Properties
Grease type
Sodium Sodium Lithium Lithium Lithium (thermally dispersed) Lithium Li thiurn-calciu4 Barium Calcium Aluminum Silica Bentone 34
Particle size of thickener
Effect 4 on-------Grease viscosity
Decreases LID Increases LID Increase Increases L I D
Oil separation
Decrease Decrease Decrease Decrease Increase
Decrease Increase Increase
Decrease Decrease Decrease Decrease
Ref.
a b c d e
OF
GREASES
2937
of the particles caused by a viscosity increase would easily account for a decrease in oil separation. D. E$ect of Oil Conaposition and Surlactants. Variation in oil coinposition and the use of surfaceactive additives can affect particle size by changing the interfacial free energy, E , between the particles and the supersaturated solution. Therefore, the relationships expressed in eq. 4 and 9 should apply to these variables. The curves for these two equations are shown in Fig. 5. The relative effect of any change in the energy on nucleation and growth rate depends on the value of E a t which the observations are initiated. For example, if E is below soine critical value (represented by E = 0.5, Fig. 5), a further reduction in E would produce an increase in growth rate and a decrease in nucleation rate and larger particles would be expected to form. If E is initially a t sonie point higher than this critical level, a reduction in E would produce a larger increase in nucleation rate, so that sinaller particles forin. The net effect of nucleation and
f g h i e e e
'
A. Bondi, et al., World Petrol. Congr., a See ref. a, Table I. Proc. Srd, The Hague, VII, 373 (1951). V. V. Sinitsyn, et ul., Zh. Prikl. Khini., 31, 1202 (1958). V. V. Sinitsyn, et al., Kolloidn.'Zh., 22,469 (1960). e B. W. Hotten and A. I,. McClennan, NLGI Spokesman, 24, 268 (1960). G. S. Bright and J. H. Greene, ibid., 26, 294 (1962). J. L. Zakin and G. W. Murray, Jr., ibid., 25, 354 (1962). T. I). Smith, F. Amott, and L. W. McClennan, ibid., 14 (4), 10 (1950). B. B. Farrington and R. I,. Humphreys, Znd. Eng. Chern., 31, 230 (1930).
W
'
RELATIVE INTERFACIAL ENERGY (E)
Figure 5. Effect of interfac*ialfree energy on nucleation and growth rates.
The effects of oil viscosity on grease properties are also worth noting in Table IV. The effect of oil viscosity on grease viscosity varies. If there were no particle size change and the base oil viscosity increased, we would expect an increase in grease viscosity. This is borne out with silica and bentonite greases. Thercfore, the decrease in grease viscosity (as oil viscosity increases) observed with the other greases indicates that particle size has a substantial effect. Probably an increase in particle size causes a decrease in grease viscosity inore than offsetting the increase contributed by the oil itself. Wherever oil separation was studied, it was found to decrease as oil viscosity increased. It is difficult to say, from the data available, the extent to which particle size affects oil separation, but the decrease in mobility
RE LATl VE INTERFACIAL ENERGY
Figure 6. Effect of interfacial free energy on rate of particle size increase.
Volume 68,.l'irmber 10 October, r.Ya4
growth on the rate of particle size increase is expressed by eq. 13 and is plotted in Fig. 6. Further complicating the picture is how a change in coinpositiori actually affects E. One would expect that the more polar the oil (or with the use of surfactants), the greater the reduction of E. However, the polar materials niay adsorb on the crystal surface and limit further growth by sterically hindering deposition of new molecules, thus reducing the average particle size. If the adsorption occurs preferentially on one crystal face, the particle shape may be altered. Also depending on which part of the crystal the polar niaterial adsorbs, it may decrease or increase E . Because of all these possibilities, it is difficult to predict how a change in oil composition will affect particle size. Still the theory may be useful in one respect. After carrying out a few experiments on a given systeni and observing the actual effects of changes in oil composition, some estimates can be made regarding the ineehanisin of the action of polar materials in the oil. An understanding of the mechanism niay suggest how to control grease properties by the selection of oils or surfactants. The suinmary of literature studies in Table V shows different effects of base oil viscosity index, VI, on particle size (the higher the VI, the less polar the oil) further illustrating the difficulty in making predictions. However, there is no doubt, froin the work done on greases and on other systeiiis, that oil composition does affect particle size. It is interesting to note that in all cases where oil separation was studied, an increase in ’ST1 increased scparation. Unfortunately, it is not yet known to what extent the interactions between the particles and oil alone (irrespective of particle size) are responsible for this effect.
Conclusion Relationships have been derived froin crystallization theory to show the effect of several reaction conditions on the part)icle size of grease thickeners. Agreement with experimental data reported in the literature is excellent. Therefore, the theoretical treatment can be useful in indicating directiorially
T h e ,JozLrnal of Physical Chemistry
Table V :
Effect of Oil Composition on Grease Properties ,___ Effect on-----I
Oil Grease type
variation
Particle size of thickener
Increase VI Decrease Increase VI Increase VI Increase Increase VI Increase VI Increase 6’1
Sodium Lithium Lithium Lithium-calcium Carbon black suspension (Unidentified)
Oil separation
Ref.
a Increase b c
Increase d Increase e Increase .f
Unspecified effect,s Sodium Lithium Carbon black Li thium-calciu rn
9 h, i j k
Affects oil Yeparation Affects oil separation
See ref. a, footnote a, Table I. See ref. b, Table I. See S. J. M. ,4uld, H. M. Davies, and E. G. Ellis, ref. c, Table I. W o r l d Petrol. Congr., Proc., Srd, T h e Hague, VII, 355 (1951). e M. van der Waarden, J . Colloid Sci., 5 , 317 (1950). S. F. Calhoun, S L G I Spokesman, 22,7O (1958). Sce ref. b, Table IV. See ref. c, Table IV. V. V. Sinitsyn, et al., K h i m i T’ekhnol. Topliv. i Masel., 3 ( l l ) ,51 (1958). F. H. Garner, et al., J . Inst. Petrol., 38, 974 (1952). See ref. 9, Table I\’.
’
’
what changes should be inadc in a grease to achieve a desirable particle size distribution or shape. It would be of interest to dctcriiiine the relative effects of the several reaction variables on particle size for a single system. Qualitative evaluation of the cyuations suggests that the factors affecting interfacial free energy would far outweigh variation in temperature or supersaturation. Before the theory can be used to make quantitative predictions, inorc must be learned about thr factors which are characteristic of each system. Also, quaiititative deterniinations of how surfactants aff cct the interfacial free energy need to be made. IGnally, in order to apply particle size information to the yuantitative predictions of grease properties it is neccssary to establish first the physical iriteractioris among the grease components themselves.
