Partial molar volumes and heat capacities of the N-acetyl amide derivatives of the amino acids asparagine, glutamine, tyrosine, and lysine monohydrochloride in aqueous solution at temperatures from T = 288.15 K to T = 328.15 K

Article abstract of DOI:10.1016/j.jct.2006.03.015

The partial molar volumes, V₂^{{ring operator}}, and partial molar heat capacities, C_{p, 2}^{{ring operator}}, at infinite dilution have been determined for the compounds N-acetylasparaginamide, N-acetylglutaminamide, N

Full text of DOI:10.1016/j.jct.2006.03.015

J. Chem. Thermodynamics 38 (2006) 1640–1650
www.elsevier.com/locate/jct
Partial molar volumes and heat capacities of the N-acetyl
amide derivatives of the amino acids asparagine, glutamine,
tyrosine, and lysine monohydrochloride in aqueous solution
at temperatures from T = 288.15 K to T = 328.15 K
a
a
b,
*
Jin L. Liu , Andrew W. Hakin , Gavin R. Hedwig
a
Department of Chemistry and Biochemistry, University of Lethbridge, 4401 University Drive, Lethbridge, Alta., Canada T1K 3M4
b
Institute of Fundamental Sciences – Chemistry, Massey University, Private Bag 11 222, Palmerston North, New Zealand
Received 14 February 2006; received in revised form 20 March 2006; accepted 22 March 2006
Available online 4 April 2006
Abstract
The partial molar volumes, V ꢀ2, and partial molar heat capacities, Cpꢀ;2, at infinite dilution have been determined for the compounds
N-acetylasparaginamide, N-acetylglutaminamide, N-acetyltyrosinamide, and N-acetyllysinamide monohydrochloride in aqueous solu-
tion at T = (288.15, 298.15, 313.15, and 328.15) K. These results, along with the literature data for the compound N-acetylglycinamide,
have been used to calculate the amino acid side-chain contributions to the thermodynamic properties. These side-chain contributions are
compared with those obtained using small peptides as side-chain model compounds.
Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Partial molar volume; Partial molar heat capacity; N-Acetyl amino acid amides; Amino acid side-chain contributions; Group additivity;
Aqueous solution
1. Introduction
identical to that found in proteins. In this regard, these
tripeptides are good model compounds for investigating
side-chain effects in proteins [9,12,13].
The determination of various partial molar properties at
infinite dilution for aqueous solutions of solutes that model
specific structural features of globular proteins has been the
focus of our research for many years [1–11]. The main
objective of our recent work has been to establish reliable
group additivity methods that can be used to calculate
the partial molar heat capacities [8,9] and volumes [9,10]
of completely unfolded, random coil, proteins in aqueous
solution over a wide temperature range. In these additivity
schemes, the amino acid side-chains of proteins are modelled
using tripeptides of sequence glycyl–X–glycine (gly-X-gly),
where X represents one of the 20 naturally occurring amino
acids. For these tripeptides, the side-chain of amino acid X
is flanked by two peptide groups, which is structurally
It is desirable to establish that the group contributions
used in any additivity scheme to evaluate thermodynamic
properties are not model dependent. This can be achieved
for the side-chain group contributions by choosing an
alternative set of compounds that are also realistic models
for the side-chains of proteins. The neutral N-acetyl amino
acid amides, CH3CONH(R)CONH2, which have the side-
chain R adjacent to two peptide groups, are one such set
of compounds. These amino acid derivatives have been
used previously as model systems to determine side-chain
partial molar volumes and compressibilities [14–16], to
establish a side-chain hydrophobicity scale [17], and to
study the interactions between hydrated amino acid side-
chains [18,19].
*
In earlier work [6], it was established that the partial
molar heat capacities and volumes of the hydrophobic
Corresponding author. Tel.: +64 6 356 9099; fax: +64 6 350 5682.
E-mail address: G.Hedwig@massey.ac.nz (G.R. Hedwig).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jct.2006.03.015

J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
1641
alanyl, valyl, leucyl, and isoleucyl side-chains obtained
using the N-acetyl amino acid amides as model compounds
were in general agreement with those based on the tripep-
tides as model compounds. To investigate whether the
same agreement is also found for polar and charged side-
chains, we report herein the partial molar volumes, V ꢀ2,
and heat capacities, Cꢀp;2, at infinite dilution for aqueous
solutions of N-acetylasparaginamide, N-acetylglutamina-
mide, N-acetyltyrosinamide, and N-acetyllysinamide
monohydrochloride at T = (288.15, 298.15, 313.15, and
328.15) K. These results have been used to derive the
side-chain contributions which are compared with those
obtained previously using tripeptides as model compounds.
indicated the amino group was still present in the reaction
mixture. After a further hour, when the acetylation was
judged to be complete, the aqueous reaction mixture was
extracted twice using ethylacetate. The ethylacetate solu-
tion was then evaporated under reduced pressure to give
an oil. Although attempts to obtain a solid product were
unsuccessful, the oil was chromatographically pure as indi-
cated by t.l.c., which gave a single spot with I2 stain and no
spot with ninhydrin using the solvent mixture butanol/ace-
tic acid/water, 4/1/1.
The oily product was dissolved in 10 cm3 of methanol,
about 100 cm3 of a solution of methanol saturated with
anhydrous NH3 was added, and the sealed vessel was
stored at room temperature. After several days, the volatile
solvent was removed to give a white oily-like solid, which
was chromatographically pure as judged by t.l.c. An
attempted recrystallization of the solid from hot ethanol
gave a gel-like solid on cooling.
2. Experimental
The N-acetylglutaminamide (AcglnNH2), which was
purchased from Bachem Feinchemikalien AG, was recrys-
tallized from (methanol + diethylether), m.p. T = (465 to
466) K. Elemental analyses gave the mass fractions: C,
0.452; H, 0.070; N, 0.224; cf. calculated composition for
C7H13O3N3: C, 0.449; H, 0.070; N, 0.225. The N-acetylty-
rosinamide (ActyrNH2), (Bachem), was recrystallized from
(ethanol + diethylether), m.p. T = (497 to 499) K. The ele-
mental mass fractions were: C, 0.597; H, 0.062; N, 0.127;
cf. calculated composition for C11H14O3N2: C, 0.595; H,
0.064; N, 0.126.
The N-acetylasparaginamide (AcasnNH2) was prepared
by acetylation of the corresponding amino acid amide.
Asparaginamide monohydrochloride (2.08 g, 0.0124 mol,
Bachem) was dissolved in 10 cm3 of distilled water at room
temperature. To this solution were added 5 cm3 of aqueous
NaOH (0.0248 mol in 10 cm3 of water) followed by acetic
anhydride (1.40 g, 0.0137 mol, Riedel-de Hae¨n R.G.) and
the remaining NaOH(aq), which were added in three por-
tions. The progress of the reaction was monitored by thin
layer chromatography (t.l.c.) with detection using ninhy-
drin. A precipitate began to separate from the reaction
mixture about 5 min after the final addition of reagents.
The reaction mixture was cooled to T = 273 K for about
2 h after which the white product was removed by filtration
and recrystallized from hot water to give crystalline Aca-
snNH2. yield 1.34 g (62%); m.p. T = 517 K (dec.). Elemen-
tal analyses gave the mass fractions: C, 0.416; H, 0.062; N,
0.244; calculated composition for C6H11O3N3: C, 0.416; H,
0.064; N, 0.243.
The carbobenzoxy protecting group on the lysine side-
chain of the acetylated amide was removed by catalytic
hydrogenation. Batches of the gel-like solid were dissolved
in ethanol and hydrogenated using a Paar low-pressure
shaker-type hydrogenator with 5% Pd/C as a catalyst.
After removal of the catalyst by filtration, the filtrates from
several batch hydrogenations were combined and evapo-
rated to dryness to give an oil. Several attempts to crystal-
lize the N-acetyllysinamide using various solvent
combinations were unsuccessful. The oily product was
dried under vacuum then the amount of aqueous HCl
required to give a solution of the monohydrochloride salt
was added. Following filtration using a 0.22 lm millipore
filter, the solvent was removed by freeze drying to give a
glassy product, which was crystallized, but only with the
aid of ‘‘seeding’’ using a small amount of AclysNH2 Æ HCl
purchased from Bachem. The procedure used was as fol-
lows. The solution formed on dissolving the glassy product
in a minimum volume of warm methanol was stirred in an
ice-salt bath. Ethyl acetate was added until the solution
became cloudy and the seed material was then added.
The addition of ethyl acetate in small portions was contin-
ued over several hours as the product separated from the
mixture. The solid product was removed by filtration,
washed with ethyl acetate and dried under vacuum at
T = 318 K for 24 h. Overall yield 2.8 g (46%); m.p.
T = (417 to 418) K. Analysis by alkalimetric titrimetry
[20,21] gave a relative molar mass of (223.5 1.2), which
is in good agreement with that expected for the anhydrous
compound (Mr = 223.69). Elemental analyses gave the
mass fractions: C, 0.428; H, 0.080; N, 0.188; calculated
composition for C8H18O2N3Cl: C, 0.430; H, 0.081; N,
0.188.
The N-acetyllysinamide monohydrochloride (AclysN-
H2 Æ HCl) was prepared using the following synthetic
procedure. N-e-Carbobenzoxylysine methyl ester monohy-
drochloride (9.02 g, 0.0273 mol, Bachem) was dissolved in
50 cm3 of ice-cold distilled water. Acetic anhydride (2.8 g,
0.0274 mol) and ice-cold aqueous NaOH (0.0545 mol in
10 cm3 of water) were added to the solution in several por-
tions over a 20 min period. The mixture, which became
cloudy, was stirred at T = 273 K and t.l.c. was used to
monitor the progress of the reaction. Extra acetic anhy-
dride (0.006 mol) was added after about 1 h because t.l.c.
All the compounds were dried overnight in a vacuum
oven at T = 318 K before use. The water used to prepare
solutions and as the reference solvent was either obtained
from an Osmonics model Aries High-purity D. I. Loop,
that can produce water with a resistivity of typically
1.8 Æ 105 X Æ m, or was deionised and glass distilled. All

1642
J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
TABLE 1
solutions were prepared by mass and appropriate buoy-
ancy corrections were applied.
Densities, apparent molar volumes, and apparent molar heat capacities of
aqueous solutions of N-acetylasparaginamide at T = (288.15, 298.15,
313.15, and 328.15) K
The experimental measurements for all but two systems
were carried out at the University of Lethbridge. Solution
densities were measured with a Sodev O2D vibrating-tube
densimeter using the procedures outlined in previous work
[22,23]. The reproducibility of an individual density mea-
surement was to within 5 Æ 10ꢁ3 kg Æ mꢁ3. Heat capacity
measurements were carried out using a Picker differential
flow microcalorimeter [24]. The experimental procedures
used were the same as those described previously [22,23].
A heat-leak correction factor [25] for this instrument of
f = (1.011 0.008) [23] was used in the calculation of the
apparent molar heat capacities. Measurements on solutions
of AclysNH2 Æ HCl at T = (288.15 and 313.15) K were
made at Massey University. Solution densities were mea-
sured using an Anton Paar digital density meter (model
DMA 60/602) as outlined previously [1,26]. The reproduc-
ibility of an individual density measurement was to better
than 3 Æ 10ꢁ3 kg Æ mꢁ3. Heat capacity measurements were
carried out using a Picker differential flow microcalorime-
ter. The experimental procedures used were the same as
those described in previous work [1,26] with the exception
that the output from the calorimeter was connected to a
Keithley model 181 nanovoltmeter that was interfaced to
a PC.
m/(mol Æ kgꢁ1
)
q/(kg Æ mꢁ3
)
V//(cm3 Æ molꢁ1
)
C )
p,//(J Æ Kꢁ1 Æ molꢁ1
T = 288.15 K
124.12 0.07
124.09 0.08
124.13 0.08
124.06 0.09
124.11 0.10
124.06 0.11
124.03 0.12
124.00 0.13
124.24 0.14
124.24 0.16
124.02 0.17
0.07059
0.06513
0.06036
0.05772
0.05278
0.04651
0.04222
0.03929
0.03680
0.03172
0.02910
1002.538
1002.276
1002.043
1001.919
1001.677
1001.375
1001.168
1001.026
1000.896
1000.649
1000.528
308.0 3.4
306.5 3.8
303.7 2.6
302.8 2.7
306.6 4.7
305.7 2.6
309.5 2.9
308.2 3.6
307.6 5.8
310.0 2.0
307.3 3.3
T = 298.15 K
125.50 0.07
125.42 0.08
125.53 0.08
0.07247
0.06667
0.06198
0.06197
0.05666
0.05136
0.04618
0.04348
0.03810
0.03296
0.02807
1000.487
1000.219
999.991
999.994a
999.741
999.495
999.246
999.124
998.865
998.617
998.384
331.0 0.7
332.5 1.5
333.0 3.4
330.9 3.5
333.4 7.0
330.7 1.0
330.2 3.7
330.6 1.4
333.3 1.3
329.6 5.2
333.1 2.1
125.51 0.09
125.43 0.10
125.50 0.11
125.36 0.12
125.45 0.13
125.57 0.15
125.59 0.18
T = 313.15 K
127.39 0.07
127.43 0.07
127.35 0.08
127.42 0.08
127.25 0.09
127.44 0.10
127.26 0.11
127.50 0.11
127.52 0.12
127.18 0.13
127.26 0.16
0.07187
0.07077
0.06612
0.06055
0.05423
0.05166
0.04810
0.04501
0.04273
0.03777
0.03215
995.524
995.471
995.264
995.006
994.726
994.598
994.444
994.291
994.186
993.972
993.709
357.7 3.6
355.6 4.1
356.4 3.7
358.6 2.9
357.7 4.7
353.7 3.2
358.6 1.5
361.1 1.5
355.6 1.4
356.0 4.4
353.5 3.5
3. Results
Densities at T = (288.15, 298.15, 313.15, and 328.15) K
for aqueous solutions of AcXNH2, X = (asn, gln, tyr,
and lys Æ HCl) are given in tables 1 to 4. These data were
used to calculate the apparent molar volumes of the sol-
utes, V/, using the equation
V / ¼ ðM2=qÞ ꢁ ðq ꢁ qꢀ1Þ=ðm ꢂ q ꢂ q1ꢀÞ;
ð1Þ
where M2 is the molar mass of the solute, q and qꢀ1 are,
respectively, the densities of the solution and solvent, and
m is the solution molality. The values of qꢀ1 for water at the
various temperatures used were those reported by Kell [27]
{ðqꢀ1 ¼ 999:101; 997:047; 992:219; and 985:696Þ kg ꢂ mꢁ3 at
T = (288.15, 298.15, 313.15, and 328.15) K, respectively}.
The V/ values, together with their uncertainties estimated
using the procedures outlined earlier [26], are given in
tables 1 to 4. For the dilute solutions used in this work,
the molality dependence of V/ for the neutral solutes can
be represented by the linear equation
T = 328.15 K
128.86 0.07
128.87 0.08
128.89 0.08
128.95 0.09
128.79 0.10
128.90 0.11
128.85 0.12
128.88 0.14
128.81 0.16
0.06958
0.06488
0.06115
0.05694
0.05183
0.04683
0.04280
0.03805
0.03205
a
988.834
988.623
988.455
988.263
988.042
987.812
987.633
987.418
987.150
380.2 5.6
376.5 3.3
377.1 4.1
380.7 7.2
377.2 6.6
379.4 3.0
373.4 1.3
377.4 4.5
378.3 2.5
Calculated using equation (7). See text.
V / ¼ V ꢀ2 þ ðSv ꢂ mÞ;
ð2Þ
statistically significant. The V ꢀ2 results given in table 5 are
actually the mean values of the V/ data and the uncertain-
ties given are the standard deviations. The molality range
accessible for the sparingly soluble ActyrNH2 is too narrow
to obtain reliable results from an analysis of the V/ data
using equation (2). The values of V ꢀ2 for ActyrNH2 given
in table 5 are the means of the V/ data.
where V ꢀ2 is the partial molar volume of the solute at infi-
nite dilution and Sv is the experimental slope. Values of
V ꢀ2 and Sv, and their standard errors obtained from
weighted least-squares analyses of the V/ data, are given
in table 5. In these analyses, the weighting factors used
were the inverse squares of the uncertainties of the appar-
ent molar volumes. For AcasnNH2, the values of Sv ob-
tained from the least-squares analyses were not
For the electrolyte AclysNH2 Æ HCl, the molality depen-
dence of V/ was determined using the equation [28]:

J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
1643
TABLE 2
TABLE 3
Densities, apparent molar volumes, and apparent molar heat capacities of
aqueous solutions of N-acetylglutaminamide at T = (288.15, 298.15,
313.15, and 328.15) K
Densities, apparent molar volumes, and apparent molar heat capacities of
aqueous solutions of N-acetyltyrosinamide at T = (288.15, 298.15,
313.15, and 328.15) K
m/(mol Æ kgꢁ1
)
q/(kg Æ mꢁ3
)
V//(cm3 Æ molꢁ1
)
C
p,//(J Æ Kꢁ1 Æ molꢁ1
)
m/(mol Æ kgꢁ1
)
q/(kg Æ mꢁ3
)
V//(cm3 Æ molꢁ1
)
C )
p,//(J Æ Kꢁ1 Æ molꢁ1
T = 288.15 K
140.24 0.05
140.44 0.05
140.26 0.06
140.26 0.06
140.50 0.07
140.54 0.09
140.41 0.10
140.39 0.12
140.46 0.13
T = 288.15 K
172.03 0.25
172.17 0.26
172.02 0.28
172.12 0.29
171.74 0.32
171.78 0.34
171.76 0.36
172.21 0.37
171.76 0.39
171.74 0.42
171.93 0.43
0.10081
0.09265
0.08453
0.07857
0.06967
0.05943
0.05070
0.04349
0.03981
1003.777
1003.385
1003.029
1002.755
1002.329
1001.856
1001.461
1001.128
1000.955
353.9 1.0
354.1 2.4
356.6 3.8
350.8 2.4
356.4 2.2
355.1 1.8
353.7 2.2
350.3 2.5
353.8 3.0
0.01984
0.01902
0.01790
0.01705
0.01591
0.01495
0.01395
0.01344
0.01302
0.01200
0.01175
1000.096
1000.052
999.999
999.955
999.904
999.855
999.805
999.773
999.758
999.707
999.692
502.6 3.7
503.4 4.8
501.6 1.0
500.4 2.9
501.9 5.8
502.3 5.0
505.4 1.5
509.0 3.9
504.9 4.5
504.2 2.1
508.1 5.3
T = 298.15 K
141.78 0.04
141.77 0.04
141.82 0.04
141.81 0.05
142.00 0.05
141.89 0.06
141.98 0.07
141.95 0.09
141.86 0.11
0.14551
0.13295
0.12174
0.10547
0.09722
0.08263
0.06765
0.05783
0.04537
1003.563
1003.013
1002.512
1001.793
1001.409
1000.771
1000.096
999.659
382.4 1.9
381.1 2.1
379.5 4.3
382.8 2.5
382.3 4.1
379.9 3.4
378.0 3.5
383.7 4.3
377.9 1.4
T = 298.15 K
173.48 0.25
173.25 0.26
173.07 0.28
173.15 0.30
173.28 0.32
173.18 0.34
173.32 0.34
173.46 0.36
173.50 0.39
173.18 0.42
0.02018
0.01905
0.01809
0.01700
0.01592
0.01497
0.01493
0.01383
0.01300
0.01196
998.035
997.984
997.940
997.885
997.830
997.785
997.781
997.725
997.684
997.637
511.5 2.4
519.4 7.6
516.9 2.7
999.104
517.0 5.7
515.6 2.4
517.7 2.0
517.0 4.9
T = 313.15 K
143.66 0.05
143.61 0.06
143.63 0.06
143.66 0.07
143.81 0.08
143.87 0.09
143.87 0.11
0.10020
0.08959
0.08191
0.07398
0.06371
0.05555
0.04565
0.03917
996.596
996.143
995.809
995.463
995.007
994.650
994.219
993.936a
409.0 1.9
408.6 2.9
408.9 3.8
410.7 3.0
410.7 4.2
410.8 4.5
409.1 3.5
407.2 3.6
T = 313.15 K
176.47 0.27
176.19 0.29
176.21 0.30
176.23 0.32
176.07 0.34
176.37 0.36
176.34 0.39
176.10 0.43
0.01892
0.01787
0.01693
0.01596
0.01501
0.01401
0.01299
0.01197
993.101
993.057
993.013
992.967
992.925
992.874
992.827
992.782
542.6 5.2
543.5 3.2
541.4 2.7
546.3 2.5
545.3 3.7
543.0 5.7
543.8 4.2
542.3 2.5
T = 328.15 K
145.23 0.05
145.25 0.06
145.39 0.06
145.27 0.07
145.34 0.08
145.41 0.09
145.48 0.11
145.51 0.14
0.10559
0.09030
0.08069
0.07189
0.06260
0.05585
0.04577
0.03787
a
990.212
989.565
989.147
988.783
988.383
988.092
987.659
987.321
429.9 4.9
430.4 3.1
432.4 3.1
431.6 3.0
431.2 4.7
430.0 6.5
430.2 4.9
T = 328.15 K
178.90 0.27
178.45 0.29
178.77 0.30
178.40 0.32
178.24 0.35
178.54 0.37
178.21 0.40
178.57 0.43
0.01890
0.01796
0.01694
0.01590
0.01490
0.01394
0.01295
0.01201
986.548
986.514
986.462
986.421
986.378
986.330
986.289
986.242
555.1 3.8
555.6 4.3
552.0 4.6
554.4 3.3
556.4 4.6
549.9 3.0
552.2 5.8
553.5 5.4
Calculated using equation (7). See text.
À
Á
V / ¼ V 2ꢀ þ Av ꢂ m1=2 þ ðBv ꢂ mÞ;
where Av is the theoretical slope as given by the Debye–
ð3Þ
procedure, with the weights taken as the inverse squares
of the uncertainties in the V ꢀ2 values. The quantity
(T ꢁ 308.15) was taken as the independent variable because
308.15 K is the mid-point of the temperature range used.
The polynomial coefficients of equation (4) along with their
errors obtained from the least-squares analyses are given in
table 6. The value of the coefficient c for ActyrNH2 was not
statistically significant so a linear function was used in the
least-squares analysis. The curves shown in figure 1 for
these solutes are those calculated using equation (4) and
the polynomial coefficients given in table 6.
Huckel limiting law, and B is an adjustable parameter.
¨
v
The values used for Av were taken from the compilation
of Archer and Wang [29]. The V ꢀ2 and Bv results, together
with their standard errors obtained from the weighted
least-squares analyses of the V/ data using equation (3),
are given in table 5.
The temperature dependence of V ꢀ2 for each of the N-
acetyl amino acid amides is displayed in figure 1. The
equation
2
V ꢀ2 ¼ a þ b ꢂ ðT ꢁ 308:15Þ þ c ꢂ ðT ꢁ 308:15Þ
ð4Þ
Apparent molar volumes for aqueous solutions of the
solute ActyrNH2 for temperatures in the range
T = (278.15 to 318.15) K have been reported by Kikuchi
was fitted to the V ꢀ2 data for each of the solutes AcXNH2,
X = asn, gln, and tyr, using a weighted least squares

1644
J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
TABLE 4
For the solute AclysNH2 Æ HCl, equation (4) and a linear
function in (T ꢁ 308.15) both give a poor representation of
the V ꢀ2 data, as is shown in figure 1. The solid line repre-
sents a linear fit and the dotted curve is that calculated
using equation (4). The coefficients for each fit are given
in table 6. Although the uncertainty calculated for the coef-
ficient c negates the validity of the quadratic function, the
results have been included in table 6 because the overall
fit, as judged by the value of correlation coefficient, is
essentially the same as that for the linear function. The
scatter of the V ꢀ2 results for AclysNH2 Æ HCl may have been
a consequence of the batches of solid material used. Den-
sity measurements at T = (298.15 and 328.15) K were made
on solutions prepared using the same batch of solid, while
solutions for measurements at T = (288.15 and 313.15) K
were prepared using recovered material. Although analyses
suggested that the two batches of solid used were the same,
within the experimental uncertainties, perhaps there were
indeed some subtle differences between the solid samples.
While it would be desirable to have a better set of V ꢀ2ðTÞ
data for this compound, given the experimental difficulties
in obtaining solid samples from oils, the V ꢀ2ðT Þ results
obtained were deemed to be adequate for the current
purposes.
Densities, apparent molar volumes, and apparent molar heat capacities of
aqueous solutions of N-acetyllysinamide monohydrochloride at
T = (288.15, 298.15, 313.15, and 328.15) K
m/(mol Æ kgꢁ1
)
q/(kg Æ mꢁ3
)
V//(cm3 Æ molꢁ1
)
C )
p,//(J Æ Kꢁ1 Æ molꢁ1
T = 288.15 K
172.37 0.03
172.36 0.03
172.33 0.04
172.31 0.04
172.23 0.05
172.29 0.06
172.25 0.07
172.23 0.08
172.26 0.11
172.27 0.13
0.09720
0.08886
0.08089
0.07273
0.06411
0.05396
0.04378
0.03720
0.02858
0.02301
1004.018a
1003.603
1003.207
1002.800
1002.371
1001.855
1001.341
1001.007
1000.567
1000.282
343.1 2.6
340.4 2.6
341.3 3.0
342.0 3.4
343.1 3.3
339.8 4.1
339.8 4.8
339.9 5.4
336.3 4.9
333.4 8.3
T = 298.15 K
174.09 0.06
174.09 0.06
174.11 0.07
174.05 0.08
174.02 0.09
174.06 0.11
174.01 0.14
174.01 0.18
0.08995
0.08347
0.07363
0.06514
0.05411
0.04507
0.03712
0.02795
1001.472b
1001.158
1000.678
1000.268
999.729
999.283
998.893
998.439
379.0 0.6
378.8 2.2
379.0 2.5
378.6 2.3
379.1 4.0
379.4 2.8
377.9 4.8
377.8 3.2
T = 313.15 K
175.68 0.04
175.64 0.05
175.61 0.05
175.57 0.05
0.07802
0.06804
0.06361
0.05752
0.05469
0.05213
0.04583
0.03705
0.03035
0.02397
995.990a
995.516
995.306
995.015
994.878c
994.754
994.449
994.027
993.703
993.394
406.1 2.9
408.0 3.1
405.8 3.7
The partial molar expansibility of a solute at infinite
dilution, Eꢀ2 ¼ ðoV 2ꢀ=oTÞp, can be obtained by differentia-
tion of equation (4) with respect to temperature at constant
pressure to give
404.0 3.9
175.60 0.06
175.63 0.07
175.55 0.08
175.51 0.10
175.45 0.13
Eꢀ2 ¼ b þ 2c ꢂ ðT ꢁ 308:15Þ:
ð5Þ
409.4 3.8
406.4 5.4
411.1 4.6
404.5 5.5
It follows from equation (5) that the quantity {b ꢁ 20c} is
equivalent to Eꢀ2 at T = 298.15 K. Values of Eꢀ2 for the four
acetyl amino acid amides are given in table 6. Two results
are shown for AclysNH2 Æ HCl, one calculated using the
linear coefficients for equation (4) and the other obtained
using the quadratic coefficients. The difference between
these two values illustrates that high quality V ꢀ2ðTÞ data
are required if reliable E2ꢀ results are to be obtained from
a minimal data set.
The apparent molar heat capacities, Cp,/, of the N-acetyl
amino acid amides in aqueous solution were calculated
from the experimental massic heat capacities, cp, using
the equation
T = 328.15 K
177.49 0.06
177.50 0.06
177.42 0.07
177.40 0.08
177.47 0.10
177.32 0.12
177.30 0.14
177.34 0.19
0.08770
0.08088
0.07041
0.06308
0.05273
0.04352
0.03581
0.02685
a
989.846b
989.527
989.042
988.699
988.207
987.778
987.412
986.984
433.2 2.5
432.4 2.1
431.9 2.5
431.9 3.2
429.2 1.5
428.9 1.9
428.0 3.7
429.0 1.5
The uncertainty in q is 3 Æ 10ꢁ3 kg Æ mꢁ3
The uncertainty in q is 5 Æ 10ꢁ3 kg Æ mꢁ3
Calculated using equation (7). See text.
.
.
b
c
Cp;/ ¼ ðM2 ꢂ cpÞ þ ðcp ꢁ cꢀpÞ=m;
ð6Þ
et al. [14]. These V/ data were analysed in the usual manner
using linear least-squares but the uncertainties reported for
the experimental slopes, Sv, are significantly larger than the
absolute values of Sv [14]. For the purposes of comparison
with the V ꢀ2 results obtained in this work, average values of
the V/ data reported by Kikuchi et al. [14] are displayed in
figure 1. Although there is good agreement between the two
results at T = 288.15 K, at the remaining temperatures our
where cꢀp is the massic heat capacity of pure water, and the
remaining symbols are defined as for equation (1). The cꢀp val-
ues used in the calculations are those given by Stimson [30]
{cꢀp ¼ ð4:1855; 4:1793; 4:1783; and 4:1821Þ J ꢂ Kꢁ1 ꢂ gꢁ1 at
T = (288.15, 298.15, 313.15, and 328.15) K, respectively}.
The Cp,/ results and their estimated uncertainties, deter-
mined as described in previous work [26], are given in tables
1 to 4. In a few cases, massic heat capacity measurements
were made on solutions for which the density was not mea-
sured. For these solutions, the densities, which are needed
to convert the heat capacities per unit volume into massic
V ꢀ2 values are significantly smaller (by ca. 0.6 cm3 Æ molꢁ1
)
than those reported by Kikuchi et al. However, the temper-
ature dependence of V ꢀ2 for ActyrNH2 is linear for both sets
of V ꢀ2ðT Þ results.

J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
1645
TABLE 5
Partial molar volumes and heat capacities at infinite dilution, and the Sv and Sc values for some N-acetyl amino acid amides in aqueous solution at
T = (288.15, 298.15, 313.15, and 328.15) K
T/K
V ꢀ2=ðcm3 ꢂ molꢁ1
Þ
Sv/(cm3 Æ kg Æ molꢁ2
)
Cpꢀ;2=ðJ ꢂ Kꢁ1 ꢂ molꢁ1
Þ
Sc/(J Æ kg Æ Kꢁ1 Æ molꢁ2
)
AcasnNH2
288.15
298.15
313.15
328.15
124.10 0.08
125.47 0.08
127.37 0.11
128.87 0.05
306.9 2.2
331.7 1.4
356.8 2.3
377.8 2.2
AcglnNH2
288.15
298.15
313.15
328.15
140.62 0.16
142.09 0.08
144.05 0.12
145.60 0.08
ꢁ3.3 1.9
ꢁ2.2 0.7
ꢁ4.4 1.5
ꢁ3.6 1.0
353.9 2.2
376.6 1.3
409.4 1.3
430.8 0.9
40 13
ActyrNH2
288.15
298.15
313.15
328.15
171.93 0.19
173.29 0.15
176.25 0.14
178.51 0.24
504.0 2.7
516.4 2.5
543.5 1.6
553.6 2.2
AclysNH2 Æ HCl
288.15
298.15
313.15
328.15
a
171.94 0.04
173.74 0.03
175.18 0.04
176.93 0.06
ꢁ1.1 0.5a
ꢁ2.2 0.5a
ꢁ1.4 0.7a
ꢁ2.0 0.8a
333.4 1.9
374.3 0.4
403.9 2.7
421.7 1.0
ꢁ55 5b
ꢁ98 58b
ꢁ18 17b
Bv values, see equation (3).
b
Bc values, see equation (9).
heat capacities, were calculated using a power series in molal-
ity of the form
5. For the data at T = 288.15 K, the value for Bc was not
statistically different from zero so the value of Cꢀp;2 given
in table 5 is the mean value of the Cp,/ data.
q ¼ qꢀ1 þ ða1 ꢂ mÞ þ ða2 ꢂ m2Þ;
ð7Þ
The temperature dependence of Cꢀp;2 for each N-acetyl
amino acid amide is shown in figure 2. Since simple second
order polynomials do notꢀadequately account for the tem-
perature dependence of Cp;2 for peptide model compounds
[5,8], no attempts have been made to fit the partial molar
heat capacities to suitable functions of temperature. The
solid lines in figure 2 have been drawn to illustrate that
the Cꢀp;2 data lie on smooth curves.
where a1 and a2 are parameters obtained by least-squares
fitting to the density data for all the other solutions used.
The Cp,/ data for each of the neutral N-acetyl amino
acid amides were analysed by a weighted least-squares
method using the equation
Cp;/ ¼ Cꢀp;2 þ ðSc ꢂ mÞ;
ð8Þ
where Cꢀp;2 is the partial molar heat capacity of the solute at
infinite dilution and Sc is the experimental slope. The
weighting factors used in the analyses were the inverse
squares of the uncertainties in the apparent molar heat
capacities. Only one system studied gave a value of Sc that
wꢀas statistically different from zero. In all other cases, the
Cp;2 results reported in table 5 are the mean values of the
Cp,/ data and the uncertainties given are the standard
deviations.
4. Discussion
The primary objective in this work is to derive, from the
V ꢀ2 and Cꢀp;2 data for the acetyl amino acid amides, the par-
tial molar volumes and heat capacities of the amino acid
side-chains. For the neutral side-chains of the amino acids
asn, gln, and tyr, the side-chain partial molar, Vꢀ(R), is
given by
The Cp,/ data for AclysNH2 Æ HCl were analysed by
weighted least-squares using the equation [28]
V ꢀðRÞ ¼ V ꢀ2ðAcXNH2Þ ꢁ V 2ꢀðAcglyNH2Þ;
ð10Þ
À
Á
Cp;/ ¼ Cpꢀ;2 þ Ac ꢂ m1=2 þ ðBc ꢂ mÞ;
where Ac is the theoretical slope as given by the Debye–
ð9Þ
where R represents the side-chain of amino acid X and
V ꢀ2ðYÞ is the partial molar volume at infinite dilution for
solute Y. Each value of Vꢀ(R) calculated using equation
(10) is not the absolute value of the side-chain volume
but is instead the contribution to the volume upon replac-
ing a methylene hydrogen atom of AcXNH2 by the side-
chain R. These Vꢀ(R) values for the various amino acid
side-chains are the quantities that are used in our group
Huckel limiting law, B is an adjustable parameter and
¨
c
the remaining symbols are as defined for equation (8).
The values used for Ac were those given by Archer and
Wang [29]. The Cꢀp;2 and Bc values, and their uncertainties
obtained from the least-squares analyses, are given in table

1646
J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
V ꢀðlysHþÞ ¼ V ꢀ2ðAclysNH2 ꢂ HClÞ ꢁ V ꢀ2ðHClÞ ꢁ
129
128
127
126
125
124
AcasnNH2
AcglnNH2
ActyrNH2
V ꢀ2ðAcglyNH2Þ þ V ꢀ2ðHþÞ;
ð11Þ
where V ꢀ2ðHþÞ is the partial molar volume of the proton at
infinite dilution, and the remaining terms are the partial
molar volumes of solutes given in parentheses. In recent
work [31], single ion partial molar volumes at infinite dilu-
tion over the temperature range T = (288.15 to 328.15) K
were derived using an extrathermodynamic assumption
based on tetraphenylphosphonium tetraphenylborate
V
146
145
144
143
142
141
140
400
V
)
AcasnNH2
1
-
380
360
340
320
300
l
o
m
.
1
-
179
178
177
176
175
174
173
172
K
(
.
/J
2
,
o
V
)
AcglnNH2
420
400
380
360
340
1
-
l
o
m
.
1
-
.
177
176
175
174
173
172
K
AclysNH2 HCl
.
(
/
J
2
,
o
V
)
550
540
530
520
510
500
ActyrNH2
1
-
l
o
10
20
30
40
50
60
m
.
1
-
T/K - 273.15
K
.
(
/
J
2
,
FIGURE 1. Temperature dependences of the partial molar volumes at
infinite dilution for the N-acetyl amino acid amides: d, this work; h, from
[14].
o
420
400
380
360
340
.
)
AclysNH2 HCl
1
-
l
o
additivity scheme [9,10], along with the contribution of the
backbone glycyl group of a protein, to give the partial mo-
lar volumes of unfolded polypeptides and proteins. The
values of the partial molar volumes for AcglyNH2 used
in the calculations were taken from previous work [6].
The Vꢀ(R) results for the three neutral side-chains, along
with their uncertainties estimated using propagation of er-
rors methods, are given in table 7.
m
.
1
-
K
(
.
/J
2
,
o
10
20
30
40
50
60
T/K - 273.15
The partial molar volume for the protonated lycyl side-
chain, Vꢀ(lysH+), was calculated using the equation
FIGURE 2. Temperature dependences of the partial molar heat capac-
ities at infinite dilution for the N-acetyl amino acid amides.
TABLE 6
Coefficients of equation (4), and the partial molar expansibilities at infinite dilution and T = 298.15 K for some N-acetyl amino acid amides in aqueous
solution
Solute
a/(cm3 Æ molꢁ1
)
b/(cm3 Æ molꢁ1 Æ Kꢁ1
)
104 Æ c/(cm3 Æ molꢁ1 Æ Kꢁ2
)
Eꢀ2=ðcm3 ꢂ molꢁ1 ꢂ Kꢁ1
Þ
AcasnNH2
AcglnNH2
ActyrNH2
AclysNH2 Æ HCl
126.76 0.04
143.43 0.02
175.23 0.13
174.59 0.14
174.67 0.24
0.1196 0.001
0.1250 0.0008
0.172 0.010
0.116 0.013
0.113 0.018
ꢁ6.88 1.1
ꢁ8.17 0.7
0.1333 0.0024
0.1413 0.0016
0.172 0.010
0.116 0.013
0.126 0.033
ꢁ6.5 14a
a
See text.

J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
1647
TABLE 7
)
37
1
Side-chain contributions to V 2ꢀ and Cpꢀ;2 derived using N-acetyl amino acid
-
l
o
m
amides as model compounds
.
36
35
34
33
3
Side-chain (R) T/K
Vꢀ(R)/(cm3 Æ molꢁ1
288.15 34.07 0.08
298.15 34.45 0.08
)
CꢀpðRÞ=ðJ ꢂ Kꢁ1 ꢂ molꢁ1
Þ
166.6 2.7
168.8 1.5
165.8 2.4
170.2 2.7
m
c
(
/
)
Asn
n
s
a
(
o
313.15 35.01 0.11
328.15 35.34 0.05
X Data
)
Gln
288.15 50.59 0.16
298.15 51.07 0.08
313.15 51.69 0.12
328.15 52.07 0.08
213.6 2.7
213.7 1.4
218.4 1.5
223.2 1.8
1
-
l
o
52
51
50
49
m
.
3
m
c
(
/
)
n
l
Tyr
288.15 81.90 0.19
298.15 82.27 0.15
313.15 83.89 0.14
328.15 84.98 0.24
363.7 3.1
353.5 2.6
352.5 1.8
346.0 2.7
g
(
o
)
86
85
84
83
82
81
1
-
LysH+
288.15 60.33 0.22
298.15 60.37 0.19
313.15 59.74 0.20
328.15 60.17 0.30
267.7 3.9
276.0 7.1
263.4 7.6
263.7 3.6
l
o
m
.
3
m
c
(
/
)
r
y
t
(
o
(TPTB) as the reference electrolyte [31,32]. The values of
V ꢀ2ðHþÞ used in equation (11) were those derived using this
reference electrolyte method [31]. The values of V ꢀ2ðHClÞ at
the temperatures used in this work were those calculated
using a polynomial in temperature that was derived [31]
from an analysis of the most reliable V ꢀ2ðTÞ data for HCl
taken from the literature. The Vꢀ(lysH+) results calculated
using equation (11), along with their estimated uncertain-
ties, are given in table 7.
)
X Data
1
-
62
61
60
59
l
o
m
.
3
m
c
(
/
)
+
H
s
y
l
(
o
10
20
30
40
50
60
70
The Vꢀ(R) results given in table 7 are compared in figure
3 with those calculated using V ꢀ2 data for tripeptides of
sequence gly-X-gly and expressions analogous to equations
(10) and (11). The solid curves given in the figure represent
the side-chain volumes calculated from solution density
data determined using a scanning densimetric method
(d.s.d.) [10,33]. Although the d.s.d. method has the advan-
tage of being able to determine, in a single scan, the appar-
ent molar volume of a solute over a wide temperature
range, it does lead to higher uncertainties than for densities
determined isothermally. For the tyrosyl side-chain, the
Vꢀ(tyr) values obtained using acetylated amino acid amides
as model compounds are in excellent agreement with those
based on the gly-X-gly tripeptides. Similarly, for the pro-
tonated lycyl side-chain there is also good agreement
between the results obtained in this work and those based
on tripeptide data obtained using the d.s.d. method. This
agreement suggests that maybe the peptide-based
Vꢀ(lysH+) result at T = 298.15 K obtained using density
data determined isothermally [11] is unreliable.
T/K - 273.15
FIGURE 3. Partial molar volumes of the side-chains as a function of
temperature: d, this work; h, V ꢀ2 data for the gly-X-gly tripeptides from
[2,4,11]; ——, V ꢀ2 data for the gly-X-gly tripeptides from [9,10], d.s.d.
method.
The partial molar volumes at infinite dilution over the
temperature range T = (278.15 to 318.15) K have been
determined for aqueous solutions of both N-acetylserina-
mide (AcserNH2) and N-acetylthreoninamide (ActhrNH2)
[15]. It is useful, therefore, to compare the volumes of the
hydrophilic seryl and threonyl side-chains obtained using
these data with those calculated using tripeptides as model
compounds. This comparison is given in figure 4. Although
the two sets of Vꢀ(thr) results are concordant, it would
appear that the temperature dependence of Vꢀ(ser) for
the peptide-based model compounds differs from that
obtained for the acetyl amide model compounds. However,
to assess whether or not this apparent difference between
the two temperature dependences is significant, error bars
for the Vꢀ(ser) values are required. Unfortunately, these
cannot be estimated as the uncertainities for the V ꢀ2 values
of AcserNH2 and ActhrNH2 were not reported by Mizugu-
chi et al. [15].
The comparison given in figure 3 of the Vꢀ(asn) and
Vꢀ(gln) values obtained using the two sets of model com-
pounds indicates that there are indeed small differences
between the two sets of results. However, given the general
limitations of group additivity methods [34–36], such small
differences are of no real significance. The results presented
for Vꢀ(gln) also suggest that the peptide-based result
obtained isothermally [4] maybe of lower reliability.
The general conclusion that can be drawn from the vol-
umetric results presented in figures 3 and 4 is that for polar
and charged side-chains, the volumes based on the neutral

1648
J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
19.0
18.5
18.0
17.5
17.0
16.5
16.0
The uncertainties given, however, do not include any con-
tribution from the CꢀpðHÞ term.
)
The partial molar heat capacities at the various tempþer-
atures for the protonated lysine side-chain, CꢀpðlysH Þ,
were estimated using the equation
1
-
l
o
m
.
3
m
c
(
/
CꢀpðlysHþÞ ¼ Cpꢀ;2ðAclysNH2 ꢂ HClÞ ꢁ Cꢀp;2ðHClÞ ꢁ
)
r
e
s
(
Cꢀp;2ðAcglyNH2Þ þ Cpꢀ;2ðHþÞ þ CꢀpðHÞ;
ð13Þ
o
where Cꢀp;2ðHþÞ is the partial molar heat capacity at infinite
dilution for the proton, and the remaining symbols are de-
fined as for equation (12). The values for Cꢀp;2ðHþÞ, which
were derived using an extra thermodynamic assumption
based on TPTB, were taken from previous work [31]. Val-
ues of Cꢀp;2ðHClÞ at the temperatures used in this work were
calculated ꢀusing an expression for the temperature depen-
dence of Cp;2ðHClÞ, reported by Tremaine et al. [38], which
gives a good representation of the literature data over the
temperatureþrange T = (283.15 to 373.15) K [31]. The values
for CꢀpðlysH Þ, and their estimated uncertainties, are given
in table 7.
34.5
34.0
33.5
33.0
)
1
-
l
o
m
.
3
m
c
(
/
)
r
h
t
(
o
0
10
20
30
40
50
T/K - 273.15
The Cꢀp;2ðRÞ results given in table 7 are compared in fig-
ure 5 with those obtained in previous studies using the gly-
X-gly peptides as model compounds. The solid curves
given in the figure represent the side-chain heat capacities
calculated from heat capacity data determined using differ-
ential scanning calorimetry (d.s.c.) [8,37]. For the proton-
ated lysyl side-chain, values of CꢀpðlysHþÞ at all
temperatures in the range T = (288.15 to 328.15) K were
obtained by the addition to the quantities fCꢀpðlysHþÞꢁ
Cꢀ ðHþÞg reported previously [8], a value for Cꢀp;2ðHþÞ of
ꢁp6;23.5 5 J Æ Kꢁ1 Æ molꢁ1, which is an average of the four
values determined previously [31] at T = (288.15, 298.15,
313.15, and 328.15) K.
FIGURE 4. Partial molar volumes of the seryl and threonyl side-chains
as a function of temperature: d, V ꢀ2 data for AcserNH2 and ActhrNH2
from [15]; ——, V ꢀ2 data for the gly-X-gly tripeptides from [10], d.s.d.
method.
N-acetyl amino acid amides as model compounds are in
good agreement with those obtained using the gly-X-gly
model compounds. This result, which is consistent with
previous findings for nonpolar side-chains [6,34], confirms
that the group values used in our additivity scheme [9]
are indeed model independent.
The partial molar heat capacities of the side-chains of
the amino acids asn, gln, and tyr, CꢀpðRÞ, can be estimated
using an equation analogous to that for volumes
As shown in figure 5, the CpꢀðglnÞ values obtained using
the acetyl amino acid amides as model compounds are in
excellent agreement with the peptide-based results that
were obtained by d.s.c. It would appear, however, that
the peptide-based result at T = 298.15 K obtained from
heat capacity data determined isothermally [4], as outlined
above for the side-chain volume, maybe of lower reliability.
On the other hand, for the asn side-chain there is excellent
agreement between the two CꢀpðasnÞ values at T = 298.15 K
determined using acetyl amides and tripeptides as model
compounds. However, the CpꢀðasnÞ results obtained in this
study are about 10 J Æ Kꢁ1 Æ molꢁ1 (ca. 6%) smaller than
those obtained using d.s.c. data for the tripeptides. Despite
the small inconsistencies amongst the CꢀpðasnÞ and CpꢀðglnÞ
results shown in figure 5, it is apparent that using either the
acetyl amide or tripeptide model systems gives essentially
the same CꢀpðRÞ values for these two side-chains.
CꢀpðRÞ ¼ Cꢀp;2ðAcXNH2Þ ꢁ Cꢀp;2ðAcglyNH2Þ þ CꢀpðHÞ;
ð12Þ
where Cꢀp;2ðYÞ represents the partial molar heat capacity
at infinite dilution for solute Y, and CꢀpðHÞ is the heat
capacity of the hydrogen atom of the methylene moiety
for AcglyNH2. It should be noted that equation (12) gives
the absolute value of the partial molar heat capacity of
side-chain R, in contrast to equation (10) for the partial
molar volume which gives a relative value. In previous pa-
pers [6,8], absolute values were determined for side-chain
heat capacities so that comparisons could be made with
the literature results obtained using alternative model com-
pounds. For consistency, the same approach is adopted in
this work. The values chosen for CꢀpðHÞ were those calcu-
lated using a polynomial in temperature reported previ-
ously [37]. The values of the partial molar heat capacities
for AcglyNH2 used in the calculations were also taken
from previous work [6]. The CꢀpðRÞ results for the three
neutral side-chains, along with their uncertainties estimated
using propagation of errors methods, are given in table 7.
For T = (298.15, 313.15, and 328.15) K, the CꢀpðtyrÞ val-
ues determined in this study are about (7 to
13) J Æ Kꢁ1 Æ molꢁ1 (ca. 4%) larger than the peptide-based
results. These small differences are consistent with those
observed previously for the hydrophobic valyl and leucyl
side-chains [6]. However, as shown in figure 5, the

J.L. Liu et al. / J. Chem. Thermodynamics 38 (2006) 1640–1650
1649
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Despite some inconsistencies amongst the CꢀpðRÞ results
that have arisen as a result of this study, in general, there is
reasonable agreement between the CꢀpðRÞ results obtained
using the two sets of side-chain model compounds. This
general agreement confirms, as noted above for the vol-
umes, that the group heat capacities currently used in our
additivity scheme [8,9] are model independent.
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We thank a summer student, Marc Slingerland, for his
assistance with some of the experimental measurements.
A.W.H. gratefully acknowledges the receipt of an operat-
ing grant from the Natural Sciences and Engineering
Council of Canada (NSERC).
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JCT 06/33