NOTES
Sept., 1959 contains no sodium except a t concentrations near the phase boundary. For convenience the water is regarded as water of hydration, although it is recognized that the time and temperature of drying do not necessarily eliminate all absorbed moisture. The ratio x/y (Table I) is calculated from
"'
wt. of Ca in ppt. ~ 3 0 1 0 in ppt.
= wt. of
(mol. wt.P3010) at. wt. Ca
(2)
(mol. wt. P3010) (3) at. wt. Ca
TABLE I NasPsOi concn., mrnoles/l.
Wt. of ppt.,
Wt. of Ca in
g.
PPt.9 g.
0 0.0124 .0236 .0300 .0308 .0216 .0036
.... 0.0029 ,0053 ,0069 .0075 .0053 .0005
.0008
....
0.2
.4 .6 .8 1.0 1.2 1.4 1.6 1.8
....
0
% He0
X/Y
20.3 20.3 20.3 16.2 16.2 16.2
2.57 2.45 2.53 2.57 2.61 1.27
..
..
.. ..
.. ..
yo H20 was determined for 4 samples in each of the water percentage ranges defined by Quimby. The averages of these values were assigned to the samples above. These calculations yield a ratio z/y constant within experimental error, in the range from 0.4 t o 1.2 mmoles/l. of sodium tripolyphosphate. The data for Na5P3010concentrations greater than 1.2 mmoles/l. do not conform t o this ratio, as would be expected, because of the known presence of sodium in the precipitates.2 With x/y = 2.5, the simplest whole number ratio of Ca to P3010is 5:2 and the simplest (empirical) formula with 20% H20is Cas(P3O1o)2.l0H20. Using LaPine atomic models, the only molecule which could be constructed with the simplest ratio was
1529
+
NatCal(Ps010)~ N ~ s P ~ O K ?JftaCa3(P301& J.
+ NaaCaP3010 (6)
The uniformity of the Ca/PaOlo ratio in the range of 0.4 t o 1.2 mmoles/l. of NaaPoOlois contrary to the finding of Quimby and would appear to indicate a uniform chemical composition in this range. However, in Fig. 1, the tripolyphosphate concentration for optimum weight of precipitate approximately corresponds to that reported by Quimby as separating the amorphous precipitates wlth 20-21% water and the crystalline precipitates with 16-17% water. Conclusions A constant ratio of 2.55 for Ca/PaOlo was found for the precipitates formed by the reaction of solutions containing 2 mmoles/l. of CaClzwith solutions containing 0.4 to 1.2 mmoles of sodium tripolyphosphate/liter a t 25". The empirical formula Ca6(P3010):! would satisfy this ratio. DIFFUSION OF ALLYL CHLORIDE I N POLYVINYL ACETATE AT 40' BY AKIRAKISHIMOTO AND KINYAMATSUMOTO Physical Chemistry Laboratory, Department of Fdaheries, University o Kyoto, Maizuru, Japan Received January 16, 1060
It is often reported that integral diffusion coefficients D of systems of organic vapor and polymer (amorphous or primarily amorphous) above their glass transition temperatures increase exponentially with increasing penetrant concentration C. These coefficients at the limit of C = 0 are quantities of great physical interest which are expected to be eventually correlated with polymer-solvent interactions; and they are generally determined by extrapolating the observed exponential relation (which gives a straight line on a log D vs. C plot) graphically down to zero concentration. Recently, Mearesl made accurate measurements of D for the system polyvinyl acetate (PVAc) and allyl chloride at 40" by using the steady-state method and compared his results with those obtained for the same system by Kokes and Long2 who used the transient-state method (measurements of rates of P O0 sorption a_nd desorption). He found that his O'PO values of D not only showed a marked deviation I I(a) 1w (1) ](a) 1 from the exponential concentration dependence -P=O O=P-o-ca-o-J=O o=P-o which the data of Kokes and Long had obeyed, but I I 1 I 0-Ca-0 0-Ca-0 also gave at zero concentration a value which was The transition from the above molecule to the about one-half of that extrapolated from the rechelate (CaP3010)-3could be explained in terms sults of the latter authors. The considerable of simple chelation of both the ring Ca between the difference in the magnitude of fj as well as its con1 and 3 phosphorus and the Ca joining the 1,l- centration dependence found by these investigaphosphorus by additional sodium tripolyphosphate. tors may not be unexpected because the temperature used was not sufficiently above the glass ca~(P3010)~ 3NaJ'a010 5NaaCaPs010 (4) transition point of the polymer (28-30'). At such The presence of sodium in the precipitates near the a temperature the macro-Brownian motion of the phase boundary2.was not examined but could be polymer chains is not yet so rapid and active that explained easily by postulating intermediate re- the time effect as discussed by Crank and Park3 may be involved in transient-state measurements; actions as shown by the equations steady-state measurements are apparently free Ca6(PsOlo)2 Na~PaOlo
4%
+
+
and
NazCa4(PaO10)z 4
+ Na&aPaOlo
(5)
(1) P.Meares, J . PoEymer Sci., Z7,391 (1958). (2) R.J. Kokes and F. A. Long, J . A m . Chsm. SOC.,75,8142 (1953). (3) J. Crank and 0.El. Park, Trane. Faraday Soc., 47,1072 (1951).
NOTES
1530
Vol. 63
sient-state methods should agree with each other, at least provided the temperature of the system is above its glass transition temperature. This is because the time effect, if any, should disappear at the limit of zero concentration where swelling or deswelling of the polymer accompanied with the sorption or desorption of the vapor is apparently negligible. The present work was undertaken to obtain information which may aid to clarify this point.
1
60.5 &
0
10
5
0
(Q'h(min.Va).
Fig. 1.-Sorption and desorption curves for allyl chloride in polyvinyl acetate at 40". Allyl chloride vapor pressure = 130 mm.; equilibrium concentration Q m = 4.60 X 10-9 g./g.; film thickness = 1.90 X lo-* cm.
o b 0 D* 0
x o
6 b
(PRESENT WORK) LONG)
( KOKES
+
I
I
Experimental The PVAc which we had used in our previous study4 of stress relaxation in swollen polymers also was employed for the present work. Its viscosity-average molecular weight was 3.5 X 10'. The films for the sorption measurements were prepared in exactly the same manner as described previously.' The allyl chloride used as penetrant was dried over calcium sulfate and fractionally distilled. The sorption apparatus and the procedure for its actual uses were similar to those given elsewhere.4 All measurements were made a t 40 f: 0.1'. External pressures of allyl chloride in the sorption tube were kept constant to within fl mm. during each experiment.
Results and Discussion Figure 1 shows typical plots of absorption and desorption runs. Here Q is the amount of allyl chloride absorbed or desorbed per gram of dry PVAc for a time t from the start of either a sorption or desorption run, and Q m is the value of Q a t sorption equilibrium. Both sorption and desorption plots are linear in the region of small value of (t)'/z and concave against the abscissa for large (t)'/z. This indicates that the diffusion process of allyl chloride in PVAc a t 40" is of the Fickian type. The initial slope of the sorption plot is larger than that of the desorption one. It was found that not only these initial slopes themselves but also their difference increased with increasing & m e These facts imply that the diffusion coefficient D of the system PVAc and allyl chloride at 40" is an increasing function of penetrant concentration C in the range studied here. The initial diffusion c_oefficien_tsfor sorption and desorption, denoted by D,and D d , respectively, are defined by the relations (&/& m ).or, = 4(b.)'/E ( t )W ( T )'/EX (1) (&/& m)dasorp = 4( b d ) ' 1 2 (t) ' 1 9 / ( T )'/ax
where X is the thickness of the sample film. Thus Ds and D d are evaluated from the initial slopes of the curves of the type shoyn in Fig. 1. The integral diffusion coefficient D of the system is defined by =I
(1/C) L c D ( C ) dC
(2)
Fig. 2.-Concentration dependences of integral diffusion coefficients 6,b. and b d . where
from such an effect, because they deal with the state of a polymer in which all chain molecules are fully relaxed. Although it is very unlikely, as Meares mentioned, the fact that the molecular weights of the samples used might have been responsible for the difference between the data by the two methods is a subject of further consideration. The most interesting point is the discrepancy found for the values of D a t Eero concentration. As expected by Meares, the D values at zero concentration determined from the steady-state and tran-
I
D(C) is the (mutual) diffusion coefficient of the system as a function of C . -Crank6 has shown that to a good approximation D is given by the arithmetic mean of D,and D d . Thus b = W 2 ) (b. nil (3) The error involved in this approximation is immaterial for the pppose o j the present discussion. Values of D,, Dd and D were computed from all data obtained, and are plotted semi-logarithmically
+
(4) H. Fuiita and A. Kiahimoto. J . Polymer Sci., 28, 547 (1958). (5) J. Crank. "The Mathemcttiaa of Diffusion.'' Clarendon Presr.
oxfdrd, 1966. .
r
P '
Sept., 1959 against Qm in Fig. 2 . In this graph are included the
NOTES
1531
ponential concentration dependence of
holds
b values obtained by Kokes and Long2 from their over the complete region of low concentrations. transient-state measurements (crosses) and those by Mearesl from his steady-state measurements (squares). It should he noted that the steady-state method yields the integral diffusion coefficient without such i i n app~oximatioainvolvcd in equation 3. It is seen from Fig. 2 that in the concestra t’ion range where comparison can be made, our D values agree satisfactorily with those of Kokes and Long. So far as the behavior in this coizcentration range is concerned, it appears-that the data follow a straight line, L e . , that D increases exponentially with increasing concentration. Thus, as Kokes and Long did, we might extrapolate this straight line down to zero concentration and find a value of 9.5 X 10-10 cm.Z/min. for D ( 0 ) ; as eagly shown from equation 2, the limiting value of D for C = 0 is equal t o D(0). However, as Fig. 2 shows clearly, our data start to deviate downward from the straight line at a value of Qm of about 4.0 X loh2 g./g. and eventually appear to converge to a value 5.4 X 10-lO cm.2/min. a t the limit of zero concentration. Meares’ data from steady-state measurements, though consistently higher than those from our transient-state measurements over the range studied, show a concentration dependence quite similar to ours and can be extrapolated to give a D ( 0 ) value which agrees with that from the present measurements. Thus it is seen that (l), as Meares has expected, both transient-state and steady-state measurements lead t o the same value for D(O), provided the system is above its glass transition temperature, ( 2 ) the exponential concentration dependence of applies only in the region of rather high concentrations and may not be extrapolated to evaluate D(0) unless it does hold down to sufficiently low- concentrations, and (3) the divergence between D values from the steadystate and transient-state methods is not the one due t o the difference in molecular weights of the samples used but must be associated with the difference in molecular mechanisms related to the respective methods. Because the temperature studied is not far above the glass transition point of the pure polymer, the time effect3associated with the retarded segmental reorientation during the process of sorption or desorption is the most plausible reason for the observed divergence of the transient-state data and the steady-state ones. However, it should be emphasized that all the sorption and desorpt,ion curves observed in this study were Fickian within the limits of experimental error. It is apparent that further study needs to be done in order to explore this point. I n connection with the result (2) we shall show in forthcoming papers that plots of the type illustrated in Fig. 2 are of rather general nature for systems of a.morphous polymer and organic solvent above their glass transition temperatures. It will be shown that, with increasing temperature above the glass transition point of the given polymer, the downward curvature of the plot of log D and against Q m becomes less noticeable and eventually the ex-
Part of this investigation was supported by a grant from the Ministry of Education of the Government of Japmi, We are indebted to Professor Hiroshi Fujitn for his guidance in the course of t h i s work.
THE RATE OF DIMERIZATION O F ALLOOCIMENE~ BY
J. ERRKINE HAWKINS
AND
ROBERT E. FUGUITT
Department of Chemistry, Uniuereity of Florida, Uainesville, Florida Recdved January $9,1969
In an earlier publication2 the various reactions taking place when a-pinene is thermally isomerized in the liquid phase have been elucidated. Subsequently, the rates of the simultaneous reactions taking place, namely, the racemization of a-pinene, the conversion to dipentene and the formation of alloocimene, were reported.a I n the first paper it was shown that alloocimene dimerizes and forms an equilibrium mixture containing about 90% dimer when the reaction is carried out at approximately 200”. An excellent summary, including references, of the thermal isomerization of aand @-pinenesis presented by Frost and P e a r ~ o n . ~ The present work was conducted in order to supply additional information concerning the rates of formation of the various products which result when a-pinene is thermally isomerized. By analyzing sampIes of the product when dloocimene was heated for known lengths of time, a t fixed temperatures, i t was possible to calculate the rate of the dimerization of alloocimene. Experimental Purification of Allo8cimene.-Impure alloocimene5 was piirified and had the physical properties described previously.2 The method of heating the samples of alloacimene and analyzing the products was essentially the same as previously reported.2 It was necessary, in some cases, to take into account the rate of heating of the liquid after the tube was placed in the constant temperature bath. This correction was arrived a t by placing 16 g. of alloocimene in a sealed tube with a thermometer enclosed and observing the temperature at various time intervals. Based on this information, the starting time for the reaction was taken as four minutes after the tubes were inserted in the bath. An extra 250 watt heater was turned on during this period in order to counteract the cooling of the oil by the tube. No correction appeared to be necessary for the cooling rate as the temperature dropped so rapidly that no appreciable reaction occurred after removzl from the bath. Since the reaction proved to be second order, the rate const,ant involves a concentration unit. It was therefore necessary to know the density of alloocimene a t the temperaturefl a t which the reaction was measured. To determine this, 35 ml. of alloocimene was placed in a tube of 1 cm. inside diameter and sealed. The levels of the ocimene a t 204.5 and at 25” were marked. After the tube was opened and the (1) Presented at the 131st Meeting of the American Chemical Society, Miami, Florida, April, 1957. (2) R. E. Fuguitt and J. E. Hawkins, J . A m . Chem. Soc., 67, 342 (1945). (3) R. E. Fuguitt and J. E. Hawkins, i b i d . , 69, 319 (1947). (4) A. A. Frost and R. G. Pearaon, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York, N. Y.,1953. pp. 318-325. ( 5 ) Furnished through t h e courtesy of the Naval Store Research Olustee, Florida, and the Naval Stores DiviLaboratory, U.S.D.A., sion, The Glidden Company, Jacksonville, Florida.
