J. Phys. Chem. 1980, 84,577-582
577
Calorimetric Investigation of Hydrolyzed Copolymers OX Maleic Anhydride with Butyl and Lower Alkyl Vinyl Ethers' Paul J. Martin, Lester R. Morss, and Ulrlch
P. Strauss"
Department of Chemistry, Rutgers, The State University of New Jersey, New Brunswick, New Jersey 08903 (Received August 6, 1979) Publ/cat/oncosts assisted by the National Institutes of Health
The differential enthalpy of deprotonation, aH/a a,of maleic acid copolymers of methyl, ethyl, propyl, and butyl vinyl ethers was determined in 0.2 M tetramethylammoniumchloride (TMACl) and in 0.2 M LiCl by titration calorimetry. In TMAC1, the aH/a cy curves for the copolymers show sharp breaks at half-neutralization, consistent with pronounced electrostriction of water by doubly deprotonated dicarboxylate groups. The aH/a a curve for the butyl copolymer shows an anomaly in the region where it is known to undergo a conformational transition from compact to random coil structure. The corresponding entropy curves, derived with the help of supplementary free-energy data obtained by potentiometric titrations, as well as the heat capacity curves, show similar anomalies. Differences between the effects of TMA' and Li' were observed only in the second ionization region. The enthalpy and entropy changes accompanying the conformational transition at zero charge show a marked temperature dependence, characterized by a positive value of the corresponding heat capacity change. The nature of the hydrophobic effect in this conformational transitions is examined in the light of the experimental results.
Introduction I t has been shown that the alternating copolymers of maleic acid and alkyl vinyl ethers are useful as macromolecular model compounds for elucidating phenomena important in the control of the conformational behavior of biopolymer^.^-^ By systematically varying the size of the alkyl group one can obtain insight into the nature of the hydrophobic effect and its role in the conformational transitions exhibited by many of these copolymers. By varyirng the nature of the counterion, one can observe specificities and learn how these relate to and modify the effects of hydrophobic and other intermolecular interactions. We are currently engaged in an investigation of these copolymers using a variety of experimental methods. In this paper we report the results of calorimetric determinations of the enthalpy of deprotonation for the methyl, ethyl, propyl, and butyl copolymers carried out in 0.2 M tetramethylammonium chloride (TMAC1) and in 0.2 M LiCl. Supplementary free-energy measurements were also made. It will be shown that the enthalpy, free energy, entropy, and heat capacity results give valuable information cloncerriing polyacid ionization, the conformational transition, and the role of water in these processes. Experimental Section Materials. The methyl copolymer was GAF sample Gantrez-An no. 139, which was purified by successive precipitations with tetrahydrofuran as the solvent and ethyl ether as the nonsolvent. The ethyl (sample A-VII), propyl. (sample Pr-I), and butyl (sample B-IV) copolymers were synthesized and purified by n previously described metho~d.~~~ All acids, bases, and electrolytes were reagent grade. Water was distilled, deionized, boiled to remove COz, and tested for purity by conductivity measurements. Preparation of Solutions. The same stock solutions were used for the potentiometric titrations and the calorimetric titrations. The titrant was standardized 2.055 M HC1. Each polyacid stock solution was prepared by combining copolymer, chloride salt, base having the same cation as the chloride, and water to give a solution which was 1.5 X 1W2monomolar in polyacid, 0.2 M in salt, and 0022-3654/80/2084-0577$0 1.OO/O
at a formal concentration of 2.0 x M for TMAOH or M for LiOH. The copolymer was hydrolyzed 2.5 x by agitation under nitrogen. Every polyacid stock solution prepared in this manner had a pH of about 8. Blank solutions were 0.2 M in simple chloride salt. Potentiometric Titrations. Potentiometric titrations were carried out under nitrogen with a Radiometer PHM64 research pH meter equipped with a Radiometer G202B glass electrode and a Radiometer K401 calomel electrode. The titrant was delivered by a 0.25-mL Gilmont micrometer buret into a titration vessel containing 20 mL of polyacid solution thermostated at 25.0 f 0.1 "C. At each point, the degree of deprotonation, CY, is given by (Y
= [(MOH) - (OH-)] - [(HCl) - (H+)]/mp
(1)
where (MOH) and (HC1) are the numbers of moles of base and acid added, respectively, per liter of solution being titrated. The quantities (OH-) and (H+)are the molarities of free species determined from the pH as described prev i o ~ s l ywhile ~ ~ ~m ~ ~ the copolymer concentration in P is monomoles per liter, determined by titrating an aliquot of the polyacid solution to the end point with base. The inflection point in TMACl solutions was sharpened by adding LiC1. Defined in this way, (Y ranges from 0 to 2, with deprotonation complete at (Y = 2. Titration Calorimetry. The titration calorimeter was constructed by Mr. C. Brown in the Rutgers University Chemistry Department machine shop. The device is illustrated in Figure l. The cylindrical brass casing unbolts in the middle for easy access to the interior. The titrant is delivered through a 0.8-mm teflon tube from a 0.25-mL Gilmont micrometer syringe driven by a 2-rpm Ilurst synchronous motor. The titrant delivery tube is encased in flexible steel wire shielding, which is thermally connected to the bath jacket. The 20-mL glass reaction cell is seated on a Cambion 801-3960-01ceramic model Peltier cooler. In the cell are the titrant inlet tube, a teflon paddle, a TRW Inc. 250-52 heating resistor, and two temperature probes containing two Fenwal GA51P8 lOO-k52 thermistors each. The stirring paddle is driven at 120 rpm by a Hurst PCDA synchronous motor. The thermistor network acts as one leg of a Wheatstone bridge. The bridge siginal is 0 1980 Amerlcan Chemlcal Society
570
The Journal of Physical Chemistry, Vol. 84, No.
6, 1980
Martin, Morss, and Strauss
i
i
7
,1
L-,
3 c
c 5
1 5
I O
2 0
a Figure 2. Differential enthalpy of deprotonation, aHla a,as a function of degree of deprotonation, a , for the copolymers in 0.2 M TMACI at butyl. 25.0 'C: 0,methyl; A,ethyl; 0, propyl;
*,
does not hold true for this calorimeter. However, a correction can be applied for lack of adiabatic conditions by using Newton's law of cooling:8 do, dt
d0, dt
-= -
Flgure 1. Titration calorimeter: A, stirring motor; B, buret motor; C, digital microburet; D, OFHC copper block to maintain titrant reservoir at bath jacket temperature; E, metal-sheathed titrant delivery tube; F, titrant entrance tube; G, stirring pulley; H, driving belt; I, stirring shift; J, spring-loaded reactor cell support; K, teflon stopper; L, 250-ohm heating resistor; M, thermistors; N, 20-mL glass reaction cell; 0, teflon stirring paddle; P, copper thermal connector; Q, Peltier cooler; R, OFHC copper block as heat sink for Peltier cooler; S,plug and jack assembly for electrical connection of Peltier cooler; T, upper brass calorimeter case; U, lower brass calorimeter case.
amplified by a Keithley 155 microvoltmeter and recorded with a Fisher Recordall dual pen recorder. The second pen of the recorder is used to monitor the bath jacket temperature through a separate Wheatstone bridge. The calorimeter bath jacket consists of a water-filled 25-gal plastic container in a 55-gal metal drum, with fiberglass insulation packed between them. The lid is made of wood. The copper cooling coil is wrapped around the 500-W resistance heating coil to minimize thermal gradientsS6The cooling water is supplied by a Haake Model FK refrigerating-circulating bath. The temperature of the bath jacket is maintained within iO.001 "C with a Miller Energy Corp. Totco Model 1053A temperature controller equipped with a Totco Model 805509 nickel resistance thermometer. The heat capacity of the reaction system is determined both before and after the chemical reaction, and the average is employed in subsequent calculations. Before the thermometric titration is started, the temperature of the polyacid solution is adjusted to that of the bath jacket and maintained there by fixing the Peltier cooler current to offset stirring heat. After about 10 min, the clutch mechanism of the buret-driving motor is tripped and the titrant injected at the rate of 0.02 mL/min. The resultant variation of cell temperature with time is traced by the Fisher strip chart recorder. The maximum that the reaction solution differs in temperature from the bath jacket during a run is 0.05 "C. A tangent taken a t a point in the thermogram would have a slope proportional to the differential heat of reaction, provided the reaction was quick, thermal equilibrium rapid, and the calorimeter a d i a b a t i ~ The . ~ last condition
+ k(B, - Ob)
where t is time, Ba and Om are the true adiabiatic and measured reaction cell temperatures, respectively, Bh is the bath jacket temperature, and k is the thermal leakage constant. The thermal leakage constant is measured by bringing the cell to constant temperature, injecting a pulse of electrical heat, and observing the exponential decay of the temperature over at least two half-lives. A plot of the natural logarithm of temperature vs. time yields a slope of k. Sunner and Wadsog outline a second method of calculating k, using slopes before and after an electrical heat calibration. The same result for k was obtained by using either of these techniques. The thermal leakage constant for this calorimeter is 0.0339 f 0.001 m i d , and is demonstrably independent of Peltier cooler operation. In practice, tangents are constructed to the thermogram at known values of a. These slopes are corrected for heat leakage by using eq 2. The corrected tangent slope is transformed into a differential heat of reaction by use of the average cell heat capacity and the titrant delivery rate. The heat of dilution is determined by a separate blank and subtracted from the differential heat of reaction. Errors due to change in reaction cell heat capacity or temperature differences between titrant and titrandlo were found to be negligible. A correction is applied, however, for incomplete reaction of titrant with polyacid at low pH. For example, at a pH of 3.5 only about 90% of the protons in a d'ifferential increment of acid binds to the polyacid. Therefore, it is necessary to divide the differential heat of reaction corrected for dilution by 0.9 to get the true differential heat of protonation per mole of protons bound at pH 3.5. The progress of reaction variable, a,has been defined so that the differential heat of deprotonation per monomole of polyacid, aH/a a,is given by the negative of the differential heat of protonation per mole of protons bound. The enthalpy of neutralizing tris(hydroxymethy1)amine (THAM) with HC1 was measured twice with the titration calorimeter to test the experimental method. The resulting values of 11.33 i 0.12 and 11.30 f 0.27 kcal/mol at 25 "C and 0.07 ionic strength compare well with Ojelund and Wadso'sll result of 11.35 f 0.003 kcal/mol.
The Journal of Physical Chemistry, Vol. 84, No. 6, 1980 579
Calorimetry of Maleic Acid Copolymers
r--
,
1
2-1 0; I
00
0 5
I O
1 5
00
2 0
a Flgure 1. Differential enthalpy of deprotonation, aH/aa, as a function of degree of deprotonation, a, for the copolymers in 0.2 M L i l at 25.0 OC. The symbols are the same as in Figure 2 but shaded.
05
I O
1 5
2 0
a
Figure 5. Differential entropy of deprotonation, aS/a a, as a furtction of degree of deprotonation, a , for the copolymers in 0.2 M LiCl at 25.0 OC. The symbols are the same as in Figure 2 but shaded.
J 0
v
-20-
a \ 3
-
%
-25t
%? c 1 ,
0 0
0 5
1 0
1 5
2 0
a
0 0
a 5
,
1 0
1 5
I
2 0
3.
Flgure 4. Differential entropy of deprotonation, aS/a a, as a function of degree of deprotonation, a, for the copolymers in 0.2 M TMACl at 25.0 OC. The symbols are the same as in Figure 2.
Figure 0. Differential unitary entropy of deprotonation, aS,/a a,as a function of degree of deprotonation, a, for the copolymers in 0.2 M TMACl at 25.0 OC. The symbols are the same as in Figure 2.
Results
bound protons along the backbone at a particular value of a. The estimation of this contribution requires the introduction of a statistical model. If one ignores the possible effects of interactions between dicarboxylate groups on the entropy,15it can be s h o ~ n ~ that 3 ~ Jthe ~ cratic contribution to the differential deprotonation entropy may be given, for a poly-diprotic acid, by the expression aS,/a a =
Figures 2 and 3 show the differential deprotonation enthalpy, a H / a a, as a function of a at 25 "C for the copolymers in 0.2 M TMAC112and 0.2 M LiC1, respectively. The experimental uncertainty in each value is about &lo0 cal/monomol. Calculation of the differential deprotonation entropy, aS/aa, as a function of a requires a knowledge of the corresponding free energy. The value of aG/
