Measurement of Diffusivity of Organic Liquids through Polymer Membranes A Simple and Inexpensive Laboratory Experiment U. Shanthamurthy Aiial and Tejraj M. Aminabhavi' Karnatak University. Dharwad, India 580 003
A common laboratory experiment to study the interaction of polymer membranes with organic liquids is of great relevance in chemical industries and allied areas in view of the fact that the real tests of measuring the rate of absorption of a liquid by large pieces of polymer samples are highly timeconsuming and often expensive. Thus, characterization of liquid interaction with polymer membranes by using simple laboratory tests using a small sample of polymer membrane is certainlv -~~~ " of ereat value in understanding the actual behavior of a large industrial rubber sample. Theoreticallv. the contact of polvner membranes with organic liquidscan be described by absorption and diffusion ohenomena ( 1 ) . It is essential to know at what rate the liquid biffuses inti the polymer matrix. Often simple laboratory methods such as sorption experiments yield useful information on the transport characteristics of polymer membranes. Here we describe a simple and inexpensive laboratory experiment to study the diffusion of organic liquids through polymer membranes. This experiment can be performed by most undergraduate physical chemistry students. This procedure helps to assess the resistivity of a polymer toward well-known, commonly available organic liquids like benzene, toluene, mesitylene, cblorobenzene, n-hexane, and carbon tetrachloride. Interactions of these liquids with an industrial polymer membrane, namely polyurethane, are being investigated. ~
-
Theory Liquid absorption by polymer membranes is considered to be a diffusion process. The diffusion of liquids and relax-
' Author to whom correspondence should be addressed.
82
Journal of Chemical Education
ation processes in a polymer above its glass transition temperature (T,) are mainly governed by the segmental mobility of the chains, which in turn are considered to be affected by the total free volume and its distribution within the polymer matrix (2). In rubbery polymers well above their T,, the polymer chains adjust so rapidly to the presence of penetrant that they do not cause diffusion anomalies. For such situations the diffusion process is generally described by Fick's theorv and is often controlled by a concentrationindependent diffusivity. One of the easiest and simplest ~rocedurestoestablish the transport mode within apolymer membrane is to analyze the sorption data and thereby estimate the numerical value of the exponent n of eq 1.
MJM. = k t "
(1)
Here, M,is the mass uptake at time t, M , is the equilibrium value, and k is a constant that depends on the structural characteristics of the polymer in addition to its interaction with the solvent. The value of n determines the type of transport mechanism (3.4). A value of n = 0.5 suggests the Fickian mode, whereas for the uon-Fickian diffusion n is unitv. Often. n mav v a n between 0.5 to 1. and this suggests -the Lomalo& diffusion pattern. The solvent transport in a polymer membrane has been described (2) bv Fick's second law of diffusion. which for a constant diffnsrvity D is given as
where c is the concentration of the diffusing material (gI100 gof original sample) in the direction of x coordinate axis and t is diffusion time (s). Equation 2 upon integration gives the percentage fractional mass uptake Q(t) as
where h is membrane thickness. T h e first term of the integrated infinite series can be used to determine the maximum absorption; D of the penetrant within the polymer matrix for values of Q(t) u p to 50% can he calculated from the slope ( 8 ) of the straight line of the plot of Q(t) versus t1I2and hy using
Treatment of Data The sorption data are interpreted in terms of both percent uptake Q(t) and percent increase in thickness h(t) of the membrane versus square root of time, t112.~ h e s plots, e as are given in Figures 1and 2, exhibit linearity during early stages of absorption [up to -50% of either Q(t) or h(t)]. From the slopes of the linear portions of the curves of Q(t) or h(t) versus tlR, diffusivities are calculated using eqs 4 and 6, respectively, and these data, when compared (see Table l ) , I
0
Often attempts have been made to calculate the theoretical sorption curves from eq 3 using D as obtained from eq 4. Another useful approach (5-7) for studying diffusivity is through the dimensional response of the membrane: this approach is based on the of "hygroelasti&ty", where one is confronted with questions such as how much the polymer swells and what is the magnitude of the internal stress that develops in it. Thus, hygroelasticity can be treated by examining the relative dimensional change in relation t o absorption, which may be expressed in a number of ways. Expressing liquid absorption in terms of the relative weight gain yields the definition of "coefficient of hygroe1asticity"p
I
I
Benzene
I
Chlorobenzene
o
Toluene
8
Carbon tetrachloridt
A
Mesitylene
A
n-Hexane
*=- Ahlh,
AWIW,
where Ahlh, and AWIW, are. res~ectivelv. the relative change in thkkness and weight' of &e polymer membrane. The coefficient fi can be determined from the slope of the curve relating thickness change to weight change. For many polymer-solvent systems, p is independent of AWIW, and may he regarded a s a constant throughout the swelling process. Such considerations lead to the following relation for diffusivity: Figure 1. Variations of percent maos uptake 40 of solvem wRh square rwt of time (t'I2). Symbols: 0, benzene; 0, toluene: A, mesitylene; 0 , chlwobenZene; B, w b o n tetrachiaide; A, rrhexane, where 9, is the slope obtained from the initial linear portions o f t h e plot h(t) I-(Ahlh,)1001 versus 1' ".and h, is themaximum thickness: Several experiments on a wide variety of polymer-solvent systems (8) tell us that eqs 4 and 6 give nearly identical results on diffusivities through polymer membranes, and this approach will be demonstrated in this paper.
Experimental Procedures Any elastomer available as a rubhery material at room temperature may be used for experimentation. In this investigation,due to the widespread use of polyurethane in industry and engineering (9), we have employed a commercially availshle polyurethane. The base polymer was a Vibrathane B600 (Uniroyal)cured with 4,4'-methylene-bis-o-chloroaniline (MOCA). A sample of uniform thickness (0.250 cm) was used throughout; these were cut into circular pieces of diameter 1.9 cm, weighing approximately 0.8 g. These should be dried in vacuum oven at room temperature before experimentation. The solvents, namely benzene, toluene, mesitylene, chlorobenzene, n-hexane, and carbon tetrachloride, were obtained in their highest purity and were double-distilled to ascertain extreme purity. Caution should be exercised in handling these chemicals. As many of these are highly toxic, the experimentsshould be conducted under hood, with eztrerne core. Sorption experiments were performed by placing the cut polymer membranes in the respective liquids in screw-tight metal-capped test hottles maintained at 25 OC (10.5 "C). At regular time intervals the samples were removed from the test containers, blotted with Kimwipes to remove the surface-adhered excess liquid. These were then weighed (10.05 mg) under closed environments, the thieknesses were measured (10.01 em) at several points by means of a micrometer and then placed hack into the containers.
0
Benzene
Chlorobenzene
Mesitylene
Carbon tetrachloride n-Hexane
35 A
A
Figure 2. Variatimofpercem increase in mickness Wnot ths memocans w m 4. Symbols have ths same meanmg as in Figne 1.
sqme rwt ol time 0'
Volume 67
Number 1 January 1990
83
Table 1.
Penetrant benzene toluene mesilylene ~hl~~obenzene shexane wrbon tebachl~~lde
Solvent Properties and DlWuslvRy Data
Molar volume (cm3/mol)
Exponent
89.41 106.85 139.58 102.24 131.61 97.09
0.563 0.590 0.532 0.605 0.501 0.553
(4 eq 1
DiffusioncDefficlent D x lo' (cm2/5) by wt. gain by hygmelasticily eq 4 eq 6
2.55 2.59 0.86 2.81 1.22 1.15
2.67 1.83 0.98 2.31 1.06 1.29
Tabla 2. 1.0
-
0.8
Penetrant
.
0.6 -
T
2-
0.4
-
-
expCrimPnf c ~ ~ c u l a t e from d
0.2 -
benzene toluene masilylene chlarobenzene Mexane carbon tetra-
Maximum wt. gain M. (%)
Maximum thickness h- (%)
67.19 60.17 40.15 105.52 6.94 105.70
25.01 21.92 13.88 31.02 5.75 21.60
Thermodynarnlc Data and Swelllng Parameters Molswlar weight Solubility parameter Swelllng Volume Interaction between 6. (wl/ coefficient fraction parameter mass-links *P X ~m~)''~ a &.t
9.2 8.9 8.8 9.5 7.3 6.6
0.769 0.698 0.463 0.958 0.106 0.666
0.541 0.565 0.662 0.467 0.896 0.576
0.354 0.405 0.456 0.340 1.416 0.473
596 703 600 890 614 710
rhlnrida
used t o estimate the Flory-Huggins-type polymer-solvent interaction parameter x as Figure 3. ComDarisan of meOretlcal and experimental sorptlon curves for polyurethane-Mexane system at 25 T.
agree quite satisfactorily. The concentration-independentD thus calculated is further used to generate the theoretical curve from eq 3; a typical plot is shown in Figure 3 for nhexane. The ohsemed good agreement between theoretical and exnerimental curves is sue~estiveof the reliahilitv of the m e t h 2 of estimating D frogeither eq 4 or eq 6. F k h e r more, the exponent value n of eq 1, heing close to 0.5 but varying u p to a maximum of 0.6, suggests that the diffusion Drocess deviates sli,qhtly from the expected Fickian value i n d could be classified as anomalous. Several other useful ohsewations are ohtained from Figures 1 and 2. For instance, chlorobenzene shows highest value for both Q(t) and h(t), whereas n-hexane shows the lowest values. exhibitine almost a flat de~endenceof both ). ~ G p r i s i n ~forl ~carbon , tetrachloride Q(f) and h(t)'on It the Q ( 0 is hieher than those of the remainine Denetrants: on the other hand, i t has a smaller h(t) than do benzene, toluene, or chlorobenzene. Further insight into polymer-solvent interactions may be ohtained by the application of the Flory-Rehner model (10.11) to the swelling data. This model assumes the dependence of factors such as (1) molecular weiaht (M,) between cross-links, (2) volume fraction (Qp) of the polymer in its swollen state, and (3) polymer-solvent interaction parameter (x) on the overall morphological behavior of the polymer. In order to compute the M, values, we must obtain the sorption data in terms of swelling coefficient (a)defined as M.-M, 1 a=(7) M, PS where M, is the mass of the swollen polymer (i.e., equilibrium saturation) and M, is the original mass of the polymer membrane; p, is the liquid density. These data are further 84
Journal of Chemical Education
where 6, and 6, represent the solubility parameters of liquid and polymer, 6 is a lattice constant whose value is about 0.34, and Vs is the molar volume of the solvent, the term RT has the usual meaning. For equilibrium swelling of a crosslinked network in a solvent, the M, can be calculated using Flory and Rebner theory:
where Q,, volume fraction of the polymer in the swollen membrane a t equilibrium with solvent, is calculated as
The results of this analysis are given in Table 2. The value of
x indicates the strength of polymer-solvent interaction.
Generally, lower values of x (i.e., well below the assigned value of x = %) indicates that the particular penetrant would be a good solvent for the polymer in the absence of the restraining effects of hard segments of the polymer. In any case. this method vields a somewhat satisfactorv Drocedure to estimate M, vilues, which are found to v&from one Denetrant to the other. From the experimental result of Tables 1and 2 it is ohvious that high M, (106%) and h , (31%) as observed for the polyuretha~e-chlo~oben~ene system resulted in lower values of x (0.340) and higher values of M,(-890) as compared to the remaining liquids. This suggests that, out of all the monocyclic aromatics chosen for this investigation, chlorobenzene is the good solvent. Similarly, carbon tetrachloride behaves ina manner similar to that ofchlorobenzene.On the other hand, n-hexane, being a poor solvent for the polymer, exhibited the smallest values for M , and h. and the highest value for x (1.416).
Planning of Student Assignments This experiment is somewhat time-consuming as it requires careful preparation by the student for a sequence of experimental operations. We find that four to five continuous laboratory sessions of 4 hours each are required for a pair of students 6 carry out duplicate determinations of D using both the experimental techniques. The entire experiment can be completed in three days. We require the students to start from scratch-cutting the membrane to appropriate - size, purifying and characterizing solvents, etc. One of the virtues of this experiment is that i t provides different experimental and mathematical approaches to the same physical values. Effective educational use of the method and economy of the time can be achieved by assigning different pairs of students to different experiments. For example, one pair of students can be assigned to one type of liquid-polymer pair and evaluate D from both eqs 4 and 6. The second, third, fourth, fifth, and sixth pairs of students can be assigned the same determinations but using different liquids for the same polymer. Another variation suggested is the determination of the same quantities over a ranee of temperatures. I t is desirable t h a t t h e values of diffusiiities be obtained for a t least three temperatures. Such studies lead to the evaluation of ~rrhenius-typeactivation parameters involved in the transport processes. The three most convenient recommended temperatures for rubbery polymers are 25,40, and 55 "C. We find that followine such a nrocedure nroduces a healthy and stimulating interchange bf ideas ambng various groups of students. At the end of the work. a session mav he Leldduring which results from various groups are presented and compared. Thus, students will be exposed to "realand will develop skills necessary to bridge world" from basic science to the solution of technological problems. Afurther analvsis of the data in terms of suitihle theoretical models, nameiy Flory-Rehner theory, leads to a better understanding of the polyrner-solvent interactions and gives an insight into swelling mechanism. ~
~~
~~
~~~~~~
lmpllcations and Conclusions The study of transport of organic liquids through polvmers is important for a variety of engineering applicaiio"s. Contrary to gases, which diffuse through polymeric materials with little interaction, the transpwt of liquids causes polymers to swell; the extent of swelling depends upon thermal condition, chemical nature, and deeree of cross-linkine of the polymer in addition to the molar&ass of the and of the liquid molecule. I t is obvious that eq 6 suggests a new way of measuring D. This method is advantageous over the weight-gain technique in that the evaporation losses, if any, do not affect the final results. However, such evaporation losses are critical in the weight-gain method and affect the final results. The agreement of diffusivity values as ohtained by two entirely different methods is quite remarkable. I t is therefore concluded that the dimensional chanee technique provides a very convenient method for measuring the diffusivity of a solvent throueh a polvmer memhrane. Furthermoreithis technique is apilicabie to many polymerliquid systems whose p values are independent of the absorbed penetrant; also, the experiments can be performed with great precision and do not require any sophisticated instrumentation.
-
Acknowledgment We thank the University Grants Commission, New Delhi. for the award of teacher fellownhir, to USA under the Faculty Improvement Program. Literature Cited 1. Jmt, W.Diffurion in Salids,Liquidsund Gares;Aeademie: New York, 1952. 2. Crank, J. The Molhsmaficsaf Diffusion, 2nd ed.: Oxford University: ond don. 1975. 3. Peppsu,N.A.;Urdhal,K.G.Eur.Polym.J. 1988,24,13. 4. 8mith.M. J.:Peppaa,N.A.Polymer1985.26.569. 5. Cahn, D.: Marom, G. Polym. Ens Sci. 1978,18,IW1. 6. Cohn. D.; Msrom, G.Polymer 1979. W.501. 7. Cohn, D.; Merom, 0.Palym. En#.Sci. 1982,22,8A. 8. Aithal. U.S. PhDTheais, Kamatak University, 1989. 9. Sanders,J. H.: F-h, K. C. Polyurethanes Chemistry and Technology, PLI, Chem.; Krioger: New York. 1978. 10. Flow, P.J. ??inciplssofPolymor Chemlalry: Cornell University: Ithaea, NY, 1953. 11. Flow P. J.; Rehner, J., Jr. J. Chom.Phys.1943.11.521.
Call for Papers-Semon National Undergraduate Research Symposium The 12th Annual Semon Lecture and National Undergraduate Research Symposium will be held at Kent State University an Monday, April 2, 1990. This event is named in honor of Waldo Semon, who was the pioneer at the BF Goodrich Company of Akron, OH, in the development of PVC and, after retirement, senredas a Research Professor at Kent State University. A major focus of this event, which is co-sponsored by Kent State University and Goodrich, will be the SemonNationalUndergraduateResearch Symposium. Students at colleges and universities anywhere in the United States are invited to submit a paper describing their undergraduate research work. This should be limited to 10 double-spaced, typed pages with any number of figures, tables, and references. Six finalists will be invited to present short seminars describing their work at the symposium. The student presenting the best paper will receive a $2,000 prize, with $200 going to each of the five remaining speakers. Limited travel funds will also be available. Interested students should write for further details to: Paul Sampson, Chair, Semon Lecture Committee, Department of Chemistry, Kent State University, Kent, OH 44242, or call (216) 672-2032. The deadline for receipt of papers is March 1,1990.
Volume 67
Number 1
January 1990
85
