ANALYTICAL CHEMISTRY
684 by the acid hydrolysis method. The results indicate t h a t the described method determines only potential yeast fermentable substances. Critical techniques in the procedure are the draining of each solvent before the addition of the succeeding one in the washing of the grain, the correct concentration of the dispersion hydrochloric acid, and following other details as outlined. The accuracy and reproducibility of the analyses depend on these factors. Under the conditions mentioned, t h e water-soluble carbohydrates are determined separately from the pure starch which is hydrolyzed mildly in order t o exclude dextrins and hydrolyzable materials other than starch. When the method is carefully followed according t o described procedure, fermentation efficiencies very close to 100% are obtained. In the analyses of cereal graine these results are superior t o those obtained by the acid hydrolysis procedure.
ACKNOWLEDGMENT
The authors wish t o express their appreciation t o F. 51. Hildebrandt for his helpful suggestions during the course of this work. LITERATURE CITED (1) Assoc. Offic. Agr. Chemists, "Official and Tentative Methods of Analysis." 6th ed., p. 249, 1945. (2) Ibid.. p. 410. (3) Clendenning, K. A., Can. J . Research, 23B,239-59 (1945). (4) Krocker, Ann., 58, 212-27 (1846). (5) Lane, J. H., and Eynon, Lewis, "Determination of Reducing Sugars by Fehling's Solution with Methylene Blue Indicator,'' London, England, Norman Rodger, 1934. (6) Rask, 0. S.,J . Assoc. Ofic.Agr. Chemists, 30, 37&8 (1947). RECEIVEDSeptember 28, 1949. Presented before the Division of Agricultural and Food Chemistry a t the 116th Meeting of the AYEHICANCHEMICAL SOCIETY, Atlantic City, N. J.
Analysis of Data on Plastics Life Tests W. L. GORE, E. Z. d u Pont de Nemours & Company, Znc., Arlington, A'. J . Analytical methods of treating data are outlined, which are genera11)-applicable where individual tests may be divided into two categories (good and bad) and where miiltiple tests may be run, so that the classifications can be expressed as fractions. .4naI>-sisof data on life of plastics is illustrated.
P
LASTICS generally lose strength and toughness when they are exposed outdoors t o sunlight or are heated for any considerable period of time in the presence of osygen. The variations in resistance to heat and sunlight are large, and modifications in composition or the addition of stabilizers will oftrri result in important changes in the resistanw of a given plast,ir.
Fr equency Before Exposure
20 I O
0
100
200
300
400
500
X Elongotion 3om Frequency After Exposure
20 I O
0
m a 100 200 300 400 %Elongation
two classifications-those that are tough and those that contain a brittle spot somewhere in the test section. I t is apparent that this method of classifying the data is the most reasonable one, because the average e1ong:ttion is likely t o be a figure that does not represent any of the artual material and this average is extremely subject t o rhanre Hurtuations, depending on whether tough or brittle test lengths are chosen. A survey of heat emhrittlenient, and outdoor wcatheriiig embrittlement data for :i nunibtar of plastics has sho\r.n that the exposure tends to gt,nc,r:itr random points of emhrittlemeiit rather than a continuous itntl honiogrIirous decrease in st iengt'h tint1 toughness. With this concept of thc phenonirna of heat and weather degradation of pl:tstic.s, one is faced irith confusion in defining the "failuw" point, Should the f:iilure poilit be defined as the tiin? of exposure that, K i v a single h i t t l e test? an all test>sh i t t l e ? From a iritermediat,e fr:irtioii of brittlc tost functional point of view, the criterion of failure is thc t,inie when t,he first inc.ipit~nt,enlt)ritt,lrnirnt occurs. This csxpoaure time is obviously impracticid of measurement-for ex:t~nplc,it specification of 1% tlc.fective as thc failure point requires about 230 tests without t failure to be OOyGsure that the miterial is less
500
Table I .
Figure 1. Distribution of Elongation of Nylon
Mandrel Tests
Before a n d a f t e r 3 m o n t h s ' outdoor weathering
&cause outdoor and high temperature uses for plastics are important, reliable tests of useful life under various conditions of exposure are required, but a number of difficulties are encountered in making these life tests. hleasurements of properties such w tensile strength and elongation are variable and unreliable. Figure 1 shows the frequency distribution of elongation for an e\truded nylon u-ire sample before exposure and after exposure outdoors for 3 months. Evidently the embrittlement occurred in a spotty fashion; in some of the tests results were couivalent to the orieinal average value for the material. whereas othprs were very low. The samples tested can be divided into
-
-
A{>
Expo-iirc.
/> Fraction Breaking
Change i n Vrartion Breaking
240
0.10
270
0 00 0.10
300 330 360
0.32 0.52
0.08
Blin.
390 420
0.60 0.88 1.00
0.22 0.20 0.28 0.12
+
d
AId
Sjd2
-3 -2 - 10
-0 30 -0.44 - 00. 2 0
+0.90
+1
+0.28
f0.48
f2 24jd
+
e -0.42
.t0.88 1 00. 2 0 f0.28
X3fd2 2 . 7 1
i ( a v e r a g e ) = .YO C(TA/d) = 345 30(-0.12) = 33'2 minutes r ( q = 48 (Standard deviation) = C d Z A j d 2 - (Z4jd)Z = 3 0 d minutes C = time interval between samples (30 minutes) X O = working origin (for purposes of calculation) d = time intervals deviation of exposure time f r o m Xo ~
~
~ _ -_
685
V O L U M E 22, NO. 5, M A Y 1 9 5 0 I II:III I % defective, i(-..i.: i l l ortlrr to bv
and a t le:ist one f:tilure must be found in 53 !IO% sure t,hat the triie per cent defective is gn,:it(*r than 1%. The same difficulty is encountered if the vriti,i.iiiii of failure'is chosen as thr exposure time t h a t causes 10070 (or Y 9 ~ o )failure in test lengt,hs. Therefore, from the t. :I 111 I i i i i t of the practical requircmrn t s of mt~asui~ement , the ~11is1~1~v:iticins must t)e madr :it intcrniedi:ttc~pcrwnt:tgcs of failure :iti~I.il ii(,cwi:iry, the results extixpol:itril to vc~1'ysmall per< ~ ( ~ i i t : t g ;lcwrdirig (~~. to stati?;tic:ilt hc~or~y, the most rc~producihlc l i o i i i t f(ii, ~li~finirig failurr is tlic t i l i l t * of ~ ~ s l ~ o st o~ givch r c ,5070 t : i i l i i i i - i l l t t w tchst I(~iigt1is.
The answers to the first question require an assumption regarding the form of the distribution for degree of embrittlement with time of exposure. The author's data with nylon heat and light degradation do not, discredit the hypothesis t h a t these distributions are in accord:tnce with the law of random errors (the Gaussian or normal dist,ribution),although no theoretical reasoning is known which supports this hypothesis. However, a good enough representation of observed data is obtaiiied to permit practical problenis to be solved, and it is then possible t o calculate the times of exposure that give incipient and complete embrittlenient. Tables of the integrals of the norinal distiihution curve (5)give the fraction of the distribution relative t o the deviation of the measured variable (time of exposure) in standard deviation units. Thus, from such a tablr, approximately 2.2y0 embrittlenierit is expected at 2 s t a n d m 1 deviation units less exposure than that, which givcs 50% embrittlement. Two standard deviations (2 X 18 = 96 minutes) less t,haii 332 minutes are equal to 23ti minutes' exposure and this might be given as an estimate of the safe exposure tiine of nylon a t 200" C. in air before embrittlement to bending will oorur. to the reliability of the average time, 2,and the standard deviation, u, :ire ansa.ered for practical purposes by t h v :Lpplicntion of staiid:ird niethods of estimating errors for statistics c:tli:ulated from riitidom samples of a , normally distribut,rd continuous variatr. [ Epytein a n d Churchman ( 1 ) give thr precise crrors iiivolvcvl. The treatment outlined here 1 r : h t o slightly greater t!stim:$tcs of the cwors than is correct. 1 Thv !)5yoassurance limits f o i . tho calcu1:itrd average :ire given as
-
S
100
( 3 1
=
332
*
2u - = 332 d Y
=
f
t'50
332
*
13 G n i i n u t r ~
\
(3
2
0 ff-
60 . .____._..._. ~
#
40 20
-
X = 332 min.
0 '
60
120
'
I80 180
'
MINUTES Fipurr 2.
'0 0300 3 240 '
360
'
420
EXPOSURE
Itesiilts o f \Iaticl~~el Test o f SJl o l l
U-ticrc~.\' is the number of iritlrpriitl(~iitt w t s n i : t i l t b ;tftc.r c,:ich tisposure period. When a sufficient nniouiit, of testing has l i ( ~ t ~doire n with a givrn t?-pe of plastic, so th:it the v:tluca of t h c a st,:iiidard deviation c ~ is r , possible, t o 411iplii'y t h r test is known with soin(' c ~ o r i f i d ~ ~ n it piwetlure by niaking only o i i twt ~ :it iucah an c'xposure time tli:it a n intcwiiedi:Lt(, fraction i l t ~ f w t i v cis~ obt:tinetl, preferably i r i thtb range br.t,\vecti 0.20 :iiitl 0.80. Thi> may be ~ccompli.;lirtlby ni:iking tests :it i~xp(i*iirci i i t i ~ i ~ \ ~ :of i l s tt1)oiit rvc'ry t\vo st:iii~I:trd tlt,vi:itioris. With the, t t 2 . t 0 1 iiyloii r e c w d d i i i T:il)lo I , the, (sspopurc p(3riiJil.s(wulil hi, i r i ( ~ i c . : i i c * t l from 30 minutes to 90 or 100 iiiiriutrs. (.llxiut 3 tcait. \voul(l h i v e been iwluircvl :it 100minute iriterval.: :is ciirnpu~~c~tl t o t l i e s 1-4 1vhii.h \vere, rii:tilcl :it 30n i i n u t i ~tcs.;t iiitc.i,v:ils.) The ust' of this ,siniplilii~ilt1.l.t pi~uc:edui~c~ :tgtin involveh t , h c s assumptioii of iio~~~iiality uf i I i . < t ritmtiori :tiid the use of :t table of intcypls of tlic. iioriiml ei'i'or fuiirtiori. If J', synibolizes the fr:ictinii I,rc.akiiiy :iftcsr a t i i i i r of i ~ x p o s u i ~X,, e :tnd the st:tritlartl tleviat,ion iwiy I)(, :wsunicd to I I I * r(1ii:iI t o a given value, u , the value t o corrcspon(1irig to f, ni:iy tic! tlrterniiwd from the normal int.rgral tnblr whtsrr. t,, is the nuinher of standard deviation units by which X,, thc t ~ x p o s utii~n w , diffcw from X,t h e csposure tinic. giving 50% of t h c tevts hreakiiig. 2 is t h m found from X = - uto
x,
x
The error of can be estimated by calculating the 95% assur:irire limits by the formula
This estimation is cwrrect oiily when the test is m:td(~at thr period a n d beconies somewhat larger at other
fjOyoruposure
ANALYTICAL CHEMISTRY
686 exposure periods. I t is believed to be practical for this use, however. If the test is made at an exposure period which gives close to 50% defective tests, the to term is very small and therefore the value used for u, the standard deviation, is of little importance in estimating X. APPLICATION OF ANALYSIS
The analytical methods of treating data outlined here are generally applicable R here the degradation can be measured by a classification of individual tests into two categories (good and bad) and where it is possible to run multiple tests so t h a t the classifications can be expressed as a fraction. Fewer than 20 or 25 trials to a n evaluation usually give results too unreliable to be of much use, and 50 t o 100 trials are desirable. Tensile strength, elongation, and bending brittleness data have been analyzed by the foregoing schemes. Exposures have been made outdoors and uiider ultraviolet from carbon arc lamps, a t elevated temperatures in air and under oxygen pressure, and a t very high temperatures in the absence of oxygen where pyrolysis was the Cause of degradation. The advantages of the use of an intermediate degree of degradation a s the
