Introduction I n view of the very close relation lietwceii gelatin ant1 glue it is evident that a considerable clegree of overlap is possililc where the plasticity of the two inaterials is discussed separately. Piiicr, this paper is to he folloir-ed hy one on the plasticity of glue by Dr. Rogue. I hai-c oniittetl tliecussioii of h!drolytic effects and Iiii~it~ed the matter to Iwiilts ohtainc~ln-ith straight gelatin solutions. Sols and Gels I n this antl another paper icellulosr) I h a w introtlucetl a certain aillourit of matt,er dealing formally with clrrsticitg, hecauw in trcatiiip the iiiechaiiical properties of the colloid gels we encounter h t h plastic ant1 elastic phenonim a . I do riot propose t o traverse at any length the v r w d ground of clefinitions of solids aiid liquids, of elast,icit\-, plasticit>. and 1 k e n discussed w r y ably in a recent paper by Professor Hinghainl. It is in general agreetl that in "perfect elasticity'' the strain (tleformat,ion) is proportional t o the st8ress (Hooke's law). and disappcws iiiinietliatel>- (siiiiiiltaneously) with the removal of the stress. Ringhain points out that t'wo cases are possible on working at' shearing force of constant value ( I . I . So fur-ther cleforination as the $tress continues t o tic applied up to thc point of rupture (perfect elasticity). ( I I . ) S o further tleforination so long as t h c shearing stress does riot esceetl a certain value (yield point i . The suhstance follows Hoolie's laTv 1111to the yield point. and thcii sudtlenlj- 1 ) r c a k do~viiantl shows t,rw plastic flow. He points out further that actual solids never shoTv "perfect elasticity" : these two types are only approsiniately rcalizetl antl Hooke's law is never csactly obeyed even I t very lon strtlsws so that' there is a certain amount of yielding long tiefore the elastic liinit. Practically, under given conditions we can n w a s ~ i r ( a~ i primary c r elastic strain [Ringham's inst,antmeouY elastici.&y]i. c., the instantaneous elastic cleformation which disappears simultaneously with thc siippressiun of the stress (b) the secondary strain or subpermanent tleforinatioii. a reversihle deformation which is a function of time ic) the viscow flow which is irreversible, with time, and produced at a constant rate. lla,rdles' speaks of (c) "viscous or plastic." flon. a s if thesc were equivalent. In view of the definite differentiation of "plastic" from "viscous" flow, this appears unsatisfact,ory, am1 it i s i'u the r q i o i i ( b ) flint the 1jio.d pronotimed
* Paper presented at the 1'l:isticity Symposium. I,uf:i?-ettc C'oll(ye. O p t . 17 1924). '"Communication S o . 2 2 7 from thc Iirscarch 1,:itiorntory of the, Eiistmnn Ihrlak Cornpany. J. Franklin Inst., 194, 99 ( 1 9 2 4 ) . '' cf. E. IY, J . RIardles: T m w . F:iratlny S o ( ... 19. I 18 i 1923 I .
PLASTICITY I S REL;ITIOS TO GEL.ITIS
122.i
p l w t i c eflects qf solids are shotcn. iPseutlo-pIast,ic flon-! Ringliani et :tl). The> iiiipc~rfectionof elasticity, or elastic tleficieiicy, is therefore closely ri?latccl to I)l:?,.,ant1 plastic measiireiiients g i r t ~ - d u a i ) indications I~ of t h c plasj.ici[J- of niaterials, once the liiiiit of elasticit>- is passetl. ?‘his liiiiit is not :i\)solute but depends upon the rate atr which stress is applied. :is well :xs on prcvious loatling of the materia.1. t
,101
I
FIG.2
Fluidity and Plasticity of Gelatin Sols
X good deal of time has been wast,ed in the past i n t h e endeavor l o iiiwktl i,c!atively precise viscosity measurements of gelatin sols. It vas o I ~ s ~ r r e ! l that the “viscosities”, whether measured 11)- capillary pipettes or otlicr iiie.tliads, generally shon-et1 ( a ) great variations depending upon t h e iiiethotl of preparation and pretreatnient (h) showed markecl progressive (or regressive i variations with time. For a while these were cheerfully chronicled as outstanding characteristics of those mysterious colloids-everythiiig not understood being magnificent in colloid chemistry. Thanks largely t o O a k s and Tlavis. Ropiie ant1 others! t h e following fects ma\- he reparc!etl as estahlishd :
S. E. SHEPPARD
1226
a. the “viscosity“ of gelatin sols below a certain teinpcrature tends to increase steadily n ith time. due t o gelation. b. the “viscosity” of gelatin sols above a certain temperature may f::ll off with time till a fairly constant value is reached, c. at still higher temperatures (aboir i o o (‘.) the “ ~ i s c o s i t ‘j’ falls stta,tlily, due t o hydrolysis, d. with change of pH. the rate of ch,znge nith tiiiic is leait (Coguri at the isoelectric point 4. j - 4.8. The “viscosity” figures here were uwally tlc terniiried from tiiiies of flonat one rate of shear. C‘omparison of such figure- A. Bzegvari (108.I i j ) the flow of colloidal solutions under varying shearing stress is discussed. I n particular the theory is dealt with by the last named. S o mcntion is made of the ~ v o r l iof Bingham. Buckingham antl others in this country. Pzegvsri dewlops a theory of "plastic" flow on the simple assumption of superposition of elastic resistunw on \+coiiR flow, the theoretical viscosity heing supposed independent of the sh JJlth these assumptions he obtains ia) for the Couette (AIaclIirhael. e t c . ) the cxpressicn inre (apparent viscosity) A =elastic constant \v=A(i+q G = velo(rity gradient 7) = thcoretical viscosity
taking
4 =angle of deflcrtion w=velocity of rotation
this becomes 4
or
w =
+q
A w
+=.l+ltw
which gives a function identical ivith Bingham's for simple plastic flow. dimi1ar:y for ( 1 ) ) it capillary, in this case he adds a const.ant to the vrlocit>--gradientt o tali(. ciire of the assumed reduction of diameter of free flow tiy the elastica elements. This gives \v
=
A
__ G +k
f q
hencc.. i f v =volume of flow per unit time p =pressure A
I \-=-
P+k -
A7 +71=
~
+$
P +h
7
giving again a curve of similar tFpc for the flow: pressur(' curvc. Thprp does not appcmr to lie any advancc in this upon Bingham'a primar>. conclusion. :ind furthermore no notice is taken of the failure of this relation at low rates of shear. J. Am. Chem. Sor.. 41, Igj (1919j.
1228
8 . E. SHEPPARD
tained. Between these values, the rotation was found to take intermediate values according t o the temperature. Smith conqictereti this indicated the existence of two distinct f o r m of gelatin, onc. the sol form stable at 3 jo C. and above, the othcr the gel form stable at I;’ ( ‘ . and below. ,It teniperatures between an equilibriuiii lietn een the tn-o forms existed. The esistence of TWO critical temperatures of tliic type, or a t e m p e r n t i i r e rririge instead of a transition temperature for th~i~iiiod~-iiaiiiicall~ tlistirict forriis of a suhstance did not appear prohuhle. ( h k e s ant1 I)avisl froni an investigation of the change of “apparent viccwity” with time a t cliii’erent temperatiires con-
cluded that at a teiiipcrature of 38.03’ c‘. gelatin qol and pel were in equilibrium. that is. that this is a true transition temperature, hut generally masked by phenoniena of retarded transition-analogous t o superqaturation. Comparative invariance of “apparent viscosity” for a 2 percent gelatin at 38’ C. was observed alw in this laboratory hut later work of Loeb? and Bogue3 showed that this teiiiperature is n function of the hydrion concentration. In general the variation is, least at pH = i . j r the isoelectric point, but, as shown by Bopue. other factors influence it, and there is not sufficient evidence for a definite transition temperature. This leaves th-n the former view that the sol or gel transition is continuous as most probable, and it is likely t h a t , as in soaps. the particles oi the sol and the gel are identical. The continuity J. Am. Chem. SOC.,44, 464 (19221. J . C h . Physiol. 4, IO; ( 1 9 2 1 ) . J. -1m. Chem. Soc.. 44. 13-13 (192-1
I’L.15TICITY I S R E L A T I O S TO (rI.L.4TIS
1229
of this change. and the existence of a region in which plusticity is preeminently tlcveloped is then illust,rated in comparing. 11y the saiiie. if arbitrary. mctliod, a wries of so-called meltirzg and s e t t i ~ ypoints at, tliflererit conccntration9 of gelatin. Thr general form of these curves ir; shon-n i n Fig. 4.
Frc:. C;
I
+3
l l e l t i n g Points
G z Setting Points
7‘hc enclosed rcgion is one of imperfect temperature equilihriim~hut also :1 region in which plnsticify is well dcvelopetl. A%lbovc the upper curve, the ~ 0 1 . s c~xaiiiinerlivoultl skiow little plasticitmy:hut hehare as viscoiix liquids, helow the lou-er curve we have elastic gels.
Plasticity of Jellies Gelatin jellies subjectcd to increasing qtresses helon- a certain temperaturc show a high degree of elasticity’. This is illustrated in Figs. 5 and 6 where the elastic resistance to torsion and t o stretch is shown graphically. \\-hen an increasing load is applied fairly rapidl>-, the jelly follows Hoolte’q law practically up to the breaking point. The volimie of jelly reiliains con-
* Cf.
S, E:, Shcppartl ant1 S . ,
