944
INDUSTRIAL AND ENGINEERING CHEMISTRY
recovery of 99% could be reached, but' the over-all return \wuld be decreased. As an additional point, factors of safety should not be includea in these calculations. Thus in the same example more than the calculated amount of lean oil would not be used just to be safe. Of fundamental importance in ytudies of ihis t y p . i-, the fac-t t h a t only t,he costs of additional units of the plant variables are rrquired in determining the operating conditions that give maximum plant profit. I n Figure 1 the slopes of the cost curvw and not their total values determine tht: minimum cost, poiiit. III Equation 1 the term A is the cost, per unit of the increiiicntal amount da and is not a n averaged total cost. The ne fixed overhead costs of a plant, such as supervision, depreciation, taxes, etc., are substantially constant, and change indepcndently of small changes in the plant operating conditions. Hon-wrr important these fixed costa may be to total plant profit, thyy do not affect' the operation that' gives maximum plant profit. 'l'ht. reflux to a distillation colunin is not, changrd bccaiiw :i vi(,(,
'
Vol. 39, No. 8
president's salary is increased. Then any elaborate and arbiten) of proration of such fixed costs among subplants or products, however "fair" or "reasonable" it may be and however valuable to management as a "true picture," gives values t h a t are of no use to an engineer in determining the optimum process conditions. Thus in determining the optimum amount of steam for a process, the cost of the steam Should not be increased beCause the total steam production has decreased and the relatively constant boiler house overhead is diqtributed among fewer pounds of steam. .Ivalue obtained in this F a y has no connection with the actual dollars involved in changing the amount of steam. 111grneral for the methods of this art'icle any divisions of single c u t s that are necessarily arbitrary are also necessarily valuelcss. 'The rest calculations are for the single basis of maximum plant profits, and, as a result, the trrnis used do not need 60 have a h i B, C , . . E ) can have only iinr trary values. Each cost term (-4, numerical value a t the optimum operation, howciver 1111in Ynd rlifficdt t o iletprmine this value may tie.
Economical Use of Titanium Dioxide in Enamels 1 .G. 1KIISTRONC; i z u 1 . H. M A D S 0 5 E . I . clri P o r i t d e \ernorcrs d;- Compccni. Inr., Kilmington, V e l . T h e opacity of a coating conLaining rutile titiuiiuni d i oxide depends o n the concentration of that compound in the binder and its spreading rate. Various relations hetween hiding, or opacity, and pigment concentration can be obtained because various spreading rates of titanium dioxide can be employed at any pigment concentratioti. The most significant relations are obtained when all roat-
ing- are applied ds the? ~ o u l dhe in actual u4e. 15ahing enamels applied at a ronstant dry film thickness s h o w maximum hiding a t a pigment tolume of 25%. This hiding, how-eier, ran be duplicated with 2>3070 less titanium dioxide per unit surface area by lowering the pigment Folume to 16qo and increasing the dry film thirkness bt ahou t 10%.
P
cter. The results that xere obtained and several constants of tlie enamels are shown in Table I. The titanium dioxide ranged froni 1 to 8 pounds per gallon, the pigment volumes from 7.9 to 46.5T0, and the consistencies from 54 to 82 Krebs units. Five doctor blade clearances were used with each enamel. .lctual spreading rates were determined by striping and ashing definite areas of film, considering the ash to be titanium dioxide, and relating this to the quantity of \vet paint through the amount of titanium dioxide per gallon of paint indicated by the formulation. T o expand the data, contrast ratios a t spreading rates other than those actually used were determined by interpolation on curves of contrast ratio, or log (10 X contrast ratioj, plotted against spreading rate of enamel. (Since contrast ratios are less than 1 their logarithms would be negative if they were not multiplied by some factor such as 10.) Since these relations were approximately linear, the interpolations should have been fairly accurate. Thus numerous relations between contrast ratio, pigment volume, and spreading rate of enamel are available from these data. Spreading rate of enamel was readily converted to the morc uwful quantity, spreading rate of titanium dioxide, since the titanium dioxide per gallon n-asknonn for all enamels.
ItESElUT pigment shortages have made it highly desirable t o use the pigment that is available as efficiently as possible. X pigment can be used with more or less efficiency because its
opacity is not a constant, but a variable depending considerably on the concentration of the pigment in the binder that is used witli it to form a coherent film. This phenomenon has been pointed out, by various authors, such as Sawyer (31, Tightbody and DawS O I I ( I ) , and ~ I c M u l l e nand Ritchie (2). References to other puhlications on this subject are available in the bibliographies compiled b y these authors. Hoxever, altliougli various authors Iiavr pointed out the relation of the hiding poiver of a pigment to its concentrat,ion in the binder, they .have treated the subject rather generally and often stressed other features, such as the effect, of the nature of the binder on hiding or the differences between wet-film hiding and dry-film hiding. The intent of this paper is to show specifically how the phenomenon of change iii hiding power with change in pigment concentration is related to the efficient use of rutile titanium dioxide in white enamels. SOURCE O F DATA
Data were obtained by Lightbody and D~t\vson( 1 ) o n tlie hiding of white baking enamels made by incorporating increasing amounts of rutile titanium dioxidc into a urea-alkyl vehicle o! &OFo nonvolatile matter by weight. Their method of tlc~tc-i~rnining hiding was described in detail in the original paper. Hriefly, it i oil b1ac.k and consisted of using doctor blades to lay d o ~ films white hiding power charts and determining contrast ratios froni measurements made on the dried films with a Hunter rrflectorn-
FUNDAMENTAL RE LATION S r .
I 115. relacioiis of contrast ratio, pigment volume, and spreading t ) t ' titanium dioxide obtained from these data are shoivn diagraniniatically in Figure l. Here contrast ratio is plotted against pigment volume with a family of curves showing various sprcsadi n K rxtra titanium dioxide, expressed as pounds per 1000 i x i t b
6
~
f
August 1947
INDUSTRIAL AND ENGINEERING CHEMISTRY
AS PIGMEST T.LBI,E I. TESTSO S EKMIELSK I T H RUTILET I T . k s ~ r & \ rDIOXIDE
L
V.,liicle, 4 0 7 solids by weight; binder, 40% urea resin/60% alkyd resin b y v e i g h t ; t h i n n ~ r . mixture of toluol, sylol, a n d butanol) Spreading Hiding, R a t e , Sq. Consistency. !Blade Pigment liG, Contrast Ft./Gal. of Krebs Clearance Lb. Gal. Vol. in . Enamel Ratio Cnits Inch %lids. % i Enamel 990.5 0.783 1 0 7.9 54 0.004 0.824 653,8 0.006 0 896 418.9 0.008 349.7 0.919 0.010 278.1 0 931 0.012 2 0
16 1
7
0.004 0.006 0.008 0.010 0 012
944.8 586.2 407.6 314.0 260.1
0.844 0.913 0.951 0.968 0. S i 8
.5.0
21.5
39
0.004 0.006 0.008 0.010 0 012
894.9 578.0 383.8 314.2 268.4
0. S i 5 0.938 0.968 0.977 0 982
4 0
27 2
61
0.004 q.006 0.008 0.010 0.012
836.8 526.3 365.8 288.9 246.4
.i
1)
32.6
R ”,
768.6 485.6 $55.9 -87.3 232.5
n
II
37.7
riS
0.004 0.006 0.008 0.010 0 012 0.004 0.006 0.008 0.010 0 012
0 i 896 0.950 0.9i2 0.983 0.985 0.903 0.950 0.975 0.982 0,989
733.1 483.7 342.6 277.5 229.2
0.906 0.953 0.976 0.985 0,989
7 0
42 2
0.004 0.006 0.008
0.012
706.2 453.1 3 3 i .6 274.4 220.7
0.910 0.954 0.976 0.985 0 990
0,004 0.006 0.008 0.010 0 012
709.6 448.6 32i.3 265.6 210,4
-I‘
.
0.010 46.5
Y O
92
+juare feet of hiding chart.
Other nietliods of plotting these ihree variables could bc used if deiireci. Similar relations \rould t,yist with othpr binders, hut they would differ slightly because , , i differences in ,such properties as the color and the pigmentiispersive poirern of the binder. Using only pigment volume and -preading rate of titanium dioxide to determine hiding assumes that the thinners w e d will have a negligible effect on the results, but this is not an unreasonable’assumption, since there is no apparent reason why the hiding of dry films should be affected by practicable variations in the thinners used for application purposes. On actual test Lightbody anti DaTrson ( 1 l found that a ( . h a n g in t h r typtr of thinner and a change in the evaporatioii r:+te of one type of thinner had no effect on dry-film hiding. .\s an illuitratioii o f t h r significance of thrse relations, suppose (
945
that a paint with a pigment volume oi 1ic‘; \verr applied so t h a t the spreading rate of the titanium dioxide was 5 pounds per 1000 square feet. This ivould give a contrast ratio of ahout 0.950. If it Ivere desired t o increase this hiding by increasing the titanium dioside to 7 pounds per 1000 square feet, it could be done by applying more of the same paint, since the contrast ratio would rise to about 0.973, as indicated for 7 pounds of titanium dioxide per 1000 square feet a t a pigment volume of 17%. On the other hand, i t might, be undesirable to increase the amount of wet paint applied, and a n attempt would be made t o obtain 7 pounds of titanium dioxide per 1000 square feet of surface by putting more pigment into the paint. If this necessitated an increase in pigment volume t o 257& no change in hiding would be obtained. If t h e new pigment volume were lorrer than 25%, some increase would be obtained. If it were over 25C,, a decrease in hiding would be obtained. This illustration serves t,o demonstrate that a knowledge of the fundamental hiding relations indicates certain possibilities bul, does not provide a conclusive answer to the question, “What is the best pigment volume t o use in a n-hitc tiriamc,l made with rutile titanium dioxidc?” HIDING A T VARIOUS PIGMENT VOLUMES
Various curves showing hiding against pignient volume, or the equivalent, have appeared in the literature. These have bren helpful to the formulator brrause they have shown t h a t hiding tends t o pass tlirough a maximum, and that consequently thrre is no advantage in excwding a certain pigment volume. The best pigment . . ., i.ulume I O use, however, has never been obvious. part1.v becauw the curves that have appeared h a w heen dissimilar in marly respects. This is to be espected since hiding is not fixed by pigment volume hut varicas n i t h the spreading rate id the pigment a160 (Figure 1 I . Expressed in othcr ~ o r d s .various curves of hiding against pigment volume can be obtained, because the quantity of paint applied a t any given pigment volume can be varied. The variety of rurves obtainable (‘an be demonstrated by varying the application conditions for tht rnaniels previously described. If these eri;rniels arc’ applied t t ~ hiding power charts so that the amount of titaniuni tlio\-ide per 0.912 0.958 0.979 0.985 0.992
0THINNER
0B I N D E R
=
RUTILE TtO?
,950
Q
5
‘900
tr
2
,850
F
.0W 5
1 0
19
2.0
15
PERCENT PIGMENT VOLUME
30
35
40
45
5
IN SOLIDS
Figure 1. Fundamental Hiding Relations of Rutile Titanium Dioxide i n a Lrea-.ilkyd Vehicle
7.9
16.1 21.5 27.2 32.6 31.7 42.2 PERCENT PIGMENT VOLUME I N SOLIDS
46.5
Figure 2. Application of a Series of Enamels at Constant Spreading Rate of Titanium Dioxide
INDUSTRIAL AND ENGINEERING CHEMISTRY
946
Vol. 39, No. 8
Again there is 5onw quehtion as to ~vhet11(.1. this system of application is represe1it:t:ive oi :I practical application of these enamels, particularl> sirire the cxnanirl.: :it'(. of unequal conaistonr>., increasing fi,om 31 t o 82 Krebs units as pignieiil volume incrcasw (Table 11. If they are applied 30 that a constant (113. film thickness is obtained, i\.itll this thicknow ~elccrrtlso that again the 27.2', pigment volume paint remains unchanged, the film< will bc of the compositions ehown in Figure 5 , antl the hidings will be those shown b,y curve C in Figure 3. This curve reaches a peak a t about 2 j r ; pigment volumts antl shows a much more distirirf drop in hiding above this pigment volume thail does curve R, which was obtained a t a eoii~taiit wet-film thickncw. HIDIIVG AFTER .ZlODIFYING THINNER COZITEN'I'
The three cui'ves discussed were obtained wit11 )
a particular wries of paints by specifying certaiti
aoulication conditions. Another series of mint 5 made with similar materials would be expected r o Figure 4. Hiding of Rutile Titanium Dioxide in a give similar rcsults oil application at the sttrnl' KGea-Alkyd Vehicle spreading rate of titanium dioxide or the sanw dry-film rhirkness, but various results could , t i i s obr:iirid on application at any givcn u-et-film thickness, beeausc: square foot remains constant at some arbitrarily selected valuc~. the hiding of any paint ~vtiuldh r influenced by the quantity of the films will be of the compositions shox-n in Figure 2. The thiilner that it contained. wet-film thickness and the dry-film thickness decrease with inIn the series under diacussioii, thc! thinner in the vehicle \v:i.. creasing pigment volume. The amount, of hinder used \r.ith the ht:ict conjtant a t 60Yc by weight wgarclless of the pigmentation. constant quantity of titanium dioxide changes as required by the If this series were modified by adding or subtracting thinner $ 1 ) changing pigment volume. The hidings obtained under these that the tntal solids in each paint \r.erc 50°; by weight, and thvii conditions are shown by curve .4 in Figure 3. Sinrc this curve these paints were applied a t a constant \vet-film thickness, tht. represents a constant spreading rate of titanium dioxide, it is films ~vouldbe of the compositioris indicated in Figure 6. Thcj really one of the family of curves shown in Figure 1 . It denionat'eas hrlon the dashed lines incliratc~the compositions ht4ow strates once again how the hiding obtainable with a given aniouiit mc~dification.There is no significaticci in the selection of SOc; of titanium dioxide is greatly enhanced by the prcsence ot' grcatcr total solids by weight, sinco under these conditions the paint> quantitirs of binder, even when that binder is decrease considerably i n consistency a3 pigment voluine increases. and practically colorless. If thcxse enanirls wrre t o be applicd in It has been used merely to illustrate how the selection of certaiii practice, howrvcr, they would obviously not hi, applied at such cwitlitioris can cause difference. i i i the hiding power-pigment unequal wet-film t h i c k n e w s volume relations. The probable hidings of these modified paintIf they are applirtf at a constant \vet-filni thicknebs t l i c b films were obtained from the data on hand hy calculating the spreading will he as shoivn iii Figure 4. The aniount of titanium dioxide and ratc of t h r titanium dioxide a t rach pigment volume and using the dry-film thirkness increase r i t h increasing pigment volume. tlie hiding actually ohtained at this spreading rate and pigment To facilitate cornpa1,ison of' the results with those obtained by thc volumc:. The results are shown aa curve 11 in Figure 3. This previous system of application the n-et-film thickness \vas selectid i ~ i r v cis quite different from curve B . which \vas also obtained at so that the enanirl at 27.2';; pigmtwt volume remaiiied una mnstant wet-film thickness. It has a more distinct peak a n t i changed. The hidings obtained after application a t this constant r , c d i e s this peak at a loner pignieiit volumc. wet-film thickness are shown by curve B in Figure 3. This C U ~ T T ( ;EXER.II, Cosc~.usrors. These four curves illustrate thr is quite differvnt from the previous one simply bocausc more or vai,it,ty of curves of hiding against pigment volume that can bc less of rach paint has been applied t o the surfacc, rscc'pt in t l i c b oht iiincd iircaus(~,at any givcn pigment volume, the spreading case of tlie enaniel at 27,2Yc pigment volumca. L
.
0THINNER BINDER
e--
7.9
Figure .I.
~~
16.1
21.5
27.2
32.6
37.7
42.2
465
PERCENT PIGMENT VOLUME IN SOLIDS
-4pplication of a Series of Enamels at Constant Wet-Film Thickness
PflRCENT PIGMENT VOLUME I N SOLIDS
Figure 5 .
Application of a Series of Enamels at Constant Dry-Film Thickness
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1947
:3--
-
-___
80
.-_------_. -
-
c i 2 w
-
-
L
2
-
-
G
-
-
._
CL
~
L?
0’
;’
947
point of properties other than hiding. -425% pigment volume is a pigment-to-binder ratio of about 1.18/1.00 by weight, and a 16% pigment, volume is a pigment-to-binder ratio of about 0.6811 by weight. Use of the lower ratio would save about 10% of the titanium dioxide required a t a n 0.8/1 ratio and about 2 5 5 of the titanium dioxide required a t a 1/1 ratio by m i g h t . There is a possibility of effecting greater savings by using pigment volumes even lower than 16%, but the great increase in film thickness required to obtain adequate hiding at lower pigment volumes would probably introduce various undeairahle features.
U
.9a 1.9
27.2 326 37.7 42.2 PERCENT PIGMENT VOLUME I N SOLIDS 16.1
21.5
465
.96
Figure 6. Application of Constant Wet-Film Thickness after Adjusting Thinner Content so Each Enamel Contains 50% Solids by Weight
0 5.94
I-
2
rate of the titanium dioxide, which determines the hiding at that pigment volume, can be varied b,v changing the quantity of thinnrr o r the wet-film thicknpss.
%
Ey
I-
f, .90 u
.88 PRACTICAL CDNSIDERATIONS
’The most significant curve of hiding against pigment volume is the one that is obtained when each product is thinned and applied as it would be when put into practical use. I n the case of airdrying, brushing, architectural enamels, it is probable that rnamels of different pigment volume would be applied a t about equal consistency and a constant wet-film thickness. All enamels ivould have to be thinned to about the same consistency to obtain briishing properties, and all would tend to go on a t itbout the same wet-film thickness, because sagging would br ~ncounteredat too thick an application, and hard brushing wvuld bc cncounterrd a t too thin an application. Hiding curves obtained under these r:onditions using titanium dioside and a hinder suitable for an architect,ural enamel are not available a t this time, but the data on hand give some practical informatiori on baking enamels because the application conditions are somr-. \ \ h a t different,. Raking enamels are usually applied by spraying to specified dry-film thickness ; hence the hiding relations a t various dry-film thicknesses are important. Film thickness is probably not so closely related to consistency as in brushing enamels because baking enamels are usually quick setting, and quite a range in film thickness can be obtained at any usable consistency bv varying the spraying technique. The relation of hiding to pigment volume for urea-alkyd haking enamels applied at one arbitrarily selected dry-film thickness has already been shown. Results calculated for various specific dry-film thicknesses-namely, 1.00, 1.25, and 1.50 milsare shown in Figure 7 . These indicate that masimuin hiding is obtained when the roncentration of titanium dioside in the film is about 2 5 5 by volumtx. They also indicate that, sirice the curves begin to tlattcri at ahout 16% pigment volume, almost as much hiding is abtained a t a given dry-film thickness when the film contains 16T0 titanium dioxide as when it contains 25% by volumc. .ICtual trial on a specific job would be required to establish whether this difference in hiding would be of practical significance. On the other hand the hiding obtainable at 2570 pigment . volume and a thickness of 1.0 mil could be completely duplicated by using a r6Y0 pigment volume and a film thickness of about 1.1 mils. The latter method employs 25 to 30% less rutile titanium dioxide per unit surface area, even though the same hiding is obtained. Since the increase in film thickness required would be only lOc7,, it could probably be tolerated from the stand-
0
5
10
15
20
25
30
35
40
45
50
PERCENT PIGMENT VOLUME IN SOLIDS Figure 7. Hiding of Rutile Titanium Dioxide in a UreaAlkyd Vehicle at Several Dry-Film Thicknesses
CONCLUSIONS
1. The hiding of a coating made with rutile titanium dioxide
and any given binder is determined primarily by the pigment volume concentration in the binder and the spreading rate of the titanium dioxide. 2. Various relations bet,xeen the hiding of such a coating and t,he pigment volume concentration in the binder can be obtained because a variety of spreading rates of titanium dioside can be employed at, any given pigment volume. 3. Significant relations between the hiding of a coating and the pigment concentration in the binder can be obtained by employing spreading rates of pigment t h a t are typical of those that would be used in practical application. 4. When baking enamels made with rutile titanium dioxide a t various concentrations in a urea-alkyd binder are applied a t a constant dry-film thickness, maximum hiding is obtained at a pigment concentration in the film of 25% by volume. 5 . I n such enamels the hiding obtainable with a given amount of pigment used a t a concentration of 25% by volume in the film can be duplicated with 25 t o 307, less rutile titanium dioxide by lowering the pigment volume t o 16y0 and increasing the dryfilm thickness by about 10%. 6. These hiding relations and a n estimate of the pigment volumes actually being used indicate that, in the field of rutile titanium dioxide white baking enamels, i t may be possible to reduce the consumption of rutile titanium dioxide by 10 t o 25y0 and still produce results equivalent to those being obt,ained today. LITERATURE CITED
(1) Lightbody, A . a n d Dawson, D. H . , IND. EN:. CHEY.,34, 1462-6 (1942).
McMullen, E. W.,and Ritchie, E. J., in Matiello’s “Protective and Decorative Coatings,” Vol. I V , pp. 141-72 (1944). (3) Sawyer, R. H., IND.ENG.CHEM.,ANAL.ED.,6, 113 (1934).
(2)
PRESENTED before the Division of P a i n t , T‘arnish, a n d Plastics Chemistry a t the 110th Meeting of t h e A M E R I C A XCAEXICAL SOCIETY, Chicago, I11
.
