E. Pines, K. 1. Wun, and W. Prins Syracuse University Syracuse, New York 13210
Mechanochemical Energy Conversion
In many Departments of Chemistry, enrollment in undergraduate physical chemistry courses consists of chemistry and biology majors including premedical students and a sprinkling of students from various engineering departments. It is the contention of the present article that, for such an audience, the traditional emphasis on ideal gas cycles in the exposition of the basic laws of thermodynamics is unwarranted and leads to disinterest and to later difficulties with the concepts of chemical potential, solution behavior, and chemical equilibria. One method to alleviate this situation is to move rather quickly from a treatment of thermal engines to that of electrochemical or fuel cells, where chemicals are demaded isothermally to compounds of lower energy content. A disadvantage of this method is that the work obtained is electrical work, which still has to he converted to mechanical work to make the connection with the mechanical work production by thermal engines. By employing macromolecular working substances, both thermal and chemical, cyclic energy conversion engines can he envisaged which both lead to the direct production of mechanicalwork, with the latter, moreover, &owing an early introduction into the concept of chemical potential and solution thermodynamics. Direct mechanochemical energy conversion underlies all biological motility processes, such as muscle contraction, flagella1 motion, protoplasmic streaming, as well as hiological transduction mechanisms, such as occur in sense receptors and nerve impulse initiation and propagation. Indeed, the unravelling of the precise molecular hachinery employed by nature in all of these mechanochemical conversions might he called "the ouestion of the centurv" for the biologic2 sciences. Nature employs macromolecules for these purposes hecause of their tremendous conformational versatility. Depending on the chemical surrounding it, a macromolecule may assume a variety of conformations leading to different shapes of the molecule. Most conspicious of these shapes are the regular helical state of large linear dimen-
'Steinberg, I. Z., Oplatka, A., Katchalsky, A., Nature. 210, 568
(1966); see also Katchalsky, A. and Oplatka, A,, "Mechanoehemistry," (Editors:Lee, E. K. and Capley, A. L.) Intern. Congress of Rheology, ~ i ~ ~ 1965, ~ -part~I, p.~ 73, tand ~wasser. ~ ~ mann, A. (Editor), "Size and Shape changes of polymers,'. per. gamon Press, Oxford, 1960. 2Mssels, K. J., "Introduction to Colloid Chemistrv." WilevInterscience, New York, 1965.
sions and the random-coil state of much smaller average dimensions. In the following we will give a summary of the pertinent thermodynamics of macromolecular systems and a description of a simple inexpensive undergraduate laboratory experiment hased on the mechanochemical energy conversion cycle of Steinberg, Oplatka, and Katchalsky.' The experiment has been tested in this form in the undergraduate laboratory a t Syracuse University and has met with a great deal of positive response from the students. Thermal Cycle with Rubber as Working Substance
The conservation of enerm -. for a auasi-staticallv stretched piece of ruhher (= a collection'of chemical$ crosslinked, randomly coiling macromolecules) reads dU = TdS
+ fdL
(1)
since there is essentially no volume change upon stretching, ~h~~
-
f
( a u ~ a ~-) T~(.~ s / ~ L ) ,
the function F = U
-SdT
+ fdL so that
-
(2)
TS one has d F =
-(~sI~L)= , (afla~),
(3)
consequently
f
=
( ~ U I ~ L+ ) TT ( ~ ~ I ~ T ) L
(4)
Experimentally, many rubbers are found to exhibit the fol'owingforce f
=
(vkT/L,)(A -
= AT
(5)
where u is the number of macromolecular chains between crosslinks, Li is the initial length and A = L/Li. Because of the proportionality between f and T, one deduces from eqn. (4) (au /aL),
=
o
In other words, the energy content of an ideal ruhher does not depend on elongation in the same way that the energy content of an ideal gas does not depend on the volume. Process all the work ex~ iIn an ~ isothermal ~ ~ stretching ~ , pended by the surroundings must therefore he used up to pump heat out of the rubber, thus leading to a lowering of its entropy. Indeed, the theory of ideal rubber elasticity is based o n t h i s consideration a n d has led to a molec;lar
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derivation of eqn. (5): upon stretching, each chain in the network loses a certain number of its iso-energetic random coil conformational states. If the stretching is done quickly, not enough time is available for isothermal removal of heat. The rubber will, therefore, be temporarily somewhat warmer than its surrounding. This can be measured with a thermocouple. It should be mentioned, however, that in many rubbers a high degree of stretching causes crystallization, and that the heat of crystallization is many times larger than the rubber-elastic heating effect we are presently considering. In addition, there will be a small amount of heating due to frictional losses during the stretching process. Using now a rubber-elastic material as a working substance in a cyclic, thermal engine operating between two heat reservoirs, the analogy with an ideal gas cycle is evident (see Fieure l). Strokes (1) . . and (3) . . are adiabatic. strokes (2) an; (4) are isothermal. The efficiency of the thermal cycle is defined as usual
where Qll is the amount of heat removed from the high temperature reservoir (TI1). Figure 2 shows a realization of this type of cycle. The rubber spokes of the wheel contract upon heating so that the center of gravity of the wheel is displaced to the left. As a result the wheel will rotate counterclockwise. The flow of heat from the electric heater to the surroundings has to be set properly in order to ensure continuous rotation of the wheel.
LiBr) the triple helix is no longer stable, but is denatured into the random-coil state where the molecular dimensions are much smaller. As a result the whole tape contracts. Upon removal of the salt or lowering its concentration (e.g., to 2.5 M LiBr), the collagen renatures to the oriented triple helix form because the introduction of crosslinks has prevented the complete disappearance of the oriented crystalline regions. Consequently, the tape lengthens again. Since we are dealing with an open system in which we do not only exchange heat with the surroundings but also chemicals, the conservation of energy will now require dU
=
TdS
+ f d L + p,dN* + p , d N ,
(7)
where dN, is the amount of salt entering the collagen tape and dN, the amount of water; p, and p, are the chemical potentials of these two components. Figure 3 shows the cyclic operation between a reservoir of high chemical potential and one of low chemical potential. Only the p, N, plane is shown for simplicity; a similar diagram exists for the p, - N , couple. In the isothermal cycle we now consider the free energy per stroke rather than the energy as in Figure 1. Strokes ( I ) and (3) are isochoric, strokes (2) and (4) isopotential. The engine derives its power from the isothermal transport of salt and water from high to low chemical potential, just as the thermal engine derives its power from the transport of entropy from high to low temperature. The efficiency of the mechanical work generation is sensibly defined as
Isothermal, Chemical Cycle with Collagen a s Working Substance Isothermal, chemical cycles are well known in electrochemistry to yield more work (electrical) from the degradation of chemicals (oxidation) than is obtainable from thermal cycles, where the same chemicals are simply burned in order to create the high temperature reservoir. A direct coupling between the degradation of chemical free energy and the production of mechanical work can, however, only be achieved by employing a macromolecular working substance. Steinberg, Oplatka, and Katchalsky1 have pointed out that reconstituted, cross-linked collagen tape can be used for this purpose. Such tape contains crystalline collagen fibers in triple helix conformation, oriented in the direction of the fiber and tape axis. Upon exposure to a concentrated salt solution (e.g., 5 M
+
'4 A& = o = -TIAS 0
=f
f d
bicycle wheel
rubberbands
support Figure 2. Thermally rotating wheel employing rubber as working substance. (Drawing tram Reference ( Z ) . )
+r
f d ~
4 ~+ ( T * - 7 ' ) ~ s
AS = kv(fi2+2/h-3) Figure 1. Thermal cycle with rubber as working substance.
754 / Journal of Chemical Education
Figure 3. Isothermal, chemical cycle with collagen as working sub-
stance.
which c a n in principle reach 100%. T h i s is analogous t o t h e performance of a n electrochemical cell in which chemicals a r e degraded. I n t h e collagen cycle t h e degradation of t h e chemicals is however one of dilution n o t one of rearrangement of chemical bonds i n t o compounds of lower energy content. I n operating between two levels of s a l t concentration, dp, will b e given by
where a's are activities, C's, concentrations, a n d y's, activit y coefficients. If y" were to equal yl, t h e t o t a l A@, would h e a p u r e entropy of dilution effect. A schematic of t h e rotary engine based o n t h i s principle' is shown in Figure 4. T h e rotary action reaches a steady s t a t e in which t h e t o t a l torque equals zero
ffdL
= mgnL
Figure 5. Schematic of the four stroke laboratory experiment on collagen contraction and work performance.
Figure 4. Schematic of the Steinberg. Oplatka. and Katchaisky ( 1 ) rotary engine employing collagen as working substance.
T h e m a s s balance s e t s t h e radii on t h e pulley
Here 1, a n d 2, represent t h e length p e r g r a m collagen t a p e in the crystalline a n d amorphous state, respectively. If t h e pulley rotates v t i m e s for a full cycle of t h e collagen t a p e , the work performed will h e W = 2arvMg. Since ml, = 2rRlv we have for t h e work p e r u n i t m a s s of t h e t a p e
Undergraduate Laboratory Experiment A 20-30 em length of dry reconstituted collagen tape (courtesy Dr. R. L. Kronenthal, Research Division, Ethicon Inc., Somerville, N.J. 08876) is treated as follows. A buffer solution is prepared by mixing 100 ml of 0.2 M K H ~ P O I and 50 ml of 0.2 M NaOH. A few extra drops of NaOH are added to adjust to a final p H of 8.5; 2 ml of 37% formaldehyde is added to the above solution so that the final concentration is about 0.5% in formaldehyde. The fiber is soaked in such a hath for 24 hr. Subsequently, the crosslinked fiber is soaked in roughly 5 to 6 M LiBr solution for 15 min. The salt is removed by washing in a water bath for 10 min. The last two steps are repeated 6 times. The crosslinked fiber is stored in the LiBr hath to keep the fiber in its contracted state when not in use. To one end a w&ght is tied with a Nylon line and to the other end a glass rod is similarly attached. Figure 5 shows schematically how one measures the work performed by such a length of
Figure 6. Amount of work performed by the collagen tape as a function of the load; AL is the change in length incurred upon exchanging a 2.56 M LiBrfor a 5.16 M LiBr surrounding solution.
crosslinked collagen tape in a set of graduated cylinders. The cylinders correspond to the strokes given in Figure 3, except that stroke (4) takes place in an unloaded condition. The cyclic integral $ fdL is to a very good approximation equal to f(L2 - La) because the slopes of the isoeharic strokes (1) and (3)-corresponding to Young's modulus of the native and denatured collagen, respectively-are both steep. Depending on the load, the amount of work performed will go through a maximum, as shown in Figure 6. Arbitrarily selecting a load o f f = 44 g (50 g weight corrected for buoyancy) we find Lz = 33.0 cm and Lg = 24.5 cmupon using 2.56 M and 5.13 M LiBr, respectively. The contraction takes place in 15 sec. These particular concentrations are not unique. They were selected because under the load employed, the 2.56 M concentration did not yet denature the collagen appreeiahly whereas double this concentration led to essentially complete denaturation. Since the dry collagen content per em wet tape in our case is= = 7 x g/cm, the power generated per gram dry collagen under these conditions is 3.7 X lo6 = 0.14 W / g r collagen 15 X 7 X 10.' X 24 (13) In order to determine the difference in salt and water content of the tape in the concentrated LiBr hath and the dilute LiBr bath (see eqn. (7)) the following procedure is adopted. The tape is removed from one of the baths, its load taken off and the tape then carefully wiped with tissue paper, to remove externally adhering salt solution. The tape is subsequently weighed in a closed weighing bottle. This procedure is repeated until the weight is about constant by the third time. This provides the weight of the saltcontaining tape, Ms. After reattaching the dried-off load, the tape is suspended in a known volume of deionized water and its salt
P
=
f ( L > - L.1) -
~ZL,
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755
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