What does boiling temperature measure?

Figure. The boiling temperatures of the n-alkanes

Why do you suppose that curvature is observed as the size of the n- alkane increases?

Modeling boiling temperature An exponential function has previously been used to model the behavior observed for the n-alkanes. Woolf, A. A. “Relations between the boiling points of perfluoro-ethers, perfluoroalkanes and normal alkanes”, J. Fluorine Chem. 1993, 63, Kreglewski, A.; Zwolinski, B. J. “A new relation for physical properties of n-alkanes and n-alkyl compounds”, J. Phys. Chem ,

Is the boiling temperature of an infinite polymer, finite?

Figure. A plot of the  l g H m (T B ) measured at T = T B versus the  l g S m (T B ) also calculated at T = T B of the n-alkanes (C 3 to C 20 ): circles, n-alkylcyclo- pentanes (C 7 to C 21 ): triangles, and n-alkylcyclohexanes (C 8 to C 24 ): squares.

 l g H m (T B ) = m  l g S m (T B ) +C  l g H m (T B )/ T B =  l g S m (T B ) Therefore  l g H m (T B ) = m  l g H m (T B )/ T B +C Solving for T B : T B = m  l g H m (T B )/(  l g H m (T B ) - C) This is an equation of a hyperbola As  l g H m (T B )   ; T B  m

Table 1. The Correlation Equations of Figures 1 and 2 Obtained by Plotting  l g H m (T B ) Versus  l g S m (T B ) n-alkanes  l g H m (T B ) = (  22.6)  l g S m (T B ) – (  350); r 2 = n 1-alkenes  l g H m (T B ) = (  109.7)  l g S m (T B ) – (  951); r 2 = n-alkylbenzenes  l g H m (T B ) = (  37.3)  l g S m (T B ) – (  296); r 2 = n-alkylcyclopentanes  l g H m (T B ) = (  97.4)  l g S m (T B ) – (  926); r 2 = n-alkylcyclohexanes  l g H m (T B ) = (  87.3)  l g S m (T B ) – (  999); r 2 = n-alkanethiols  l g H m (T B ) = (  162.6)  l g S m (T B ) – (  1728); r 2 = T B (  ) ~ 3000 K

If T B approaches 3000 k in a hyperbolic fashion, then a plot of 1/(1 – T B /T B (  ) versus N, the number of repeat units should result in a straight line Recall that:

Melting temperatures of the even n-alkanes versus the number of methylene groups

A plot of 1/[1- T B /T B (  )] versus the number of methylene groups using a value of T = 411 K.

Figure. A plot of 1/[1- T B /T B (  )] versus the number of methylene groups using a value of T B (  ) = 3000 K. squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes

Use of T B (  ) = 3000 K did not result in straight lines as expected. Why wasn’t a straight line obtained as suggested by the plot of  l g H m (T B ) versus  l g S m (T B ) ? Consequently T B (  ) was treated as a variable until the best straight line was obtained by using a non-linear least squares program. This resulted in the following:

Figure A plot of 1/[1-T B (N)/T B (  )] against the number of repeat units, N; , 1-alkenes; , n-alkanes; , n-alkylcyclopentanes; , n-alkylcyclohexanes.

Table 2. The Results Obtained by Treating T B of a Series of Homologous Compounds as Function of the Number of Repeat Units, N, and Allowing T B (  ) to Vary; a Bm, b Bm : Values of a B and b B Obtained by Using the Mean Value of T B (  ) = 1217 K Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkanes methyl-n-alkanes alkenes n-alkylcyclopentanes n-alkylcyclohexanes n-alkylbenzenes amino-n-alkanes chloro-n-alkanes bromo-n-alkanes fluoro-n-alkanes hydroxy-n-alkanes hydroxy-n-alkanes n-alkanals alkanones

Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkane-1-thiols n-dialkyl disulfides n-alkylnitriles n-alkanoic acids methyl n-alkanoates Mean Value of T B (  ) = (1217  246) K The results for T B (  ) are remarkably constant considering the use of data with finite values of N to evaluate T B (N) for N (  ). These results are also in good agreement with the values reported previously for the n- alkanes by Kreglewski and Zwolinski (T B (  ) = 1078 K) and Somayajulu (T B (  ) = 1021 K). Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem , Somayajulu, G. R. Internat. J. Thermophys. 1990, 11,

A value of T B (  ) = (1217  246) K is considerably less than T B (  ) = 3000 K, the value obtained by assuming that  l g H m (T B )   as T B  . Since T B = m  l g H m (T B )/(  l g H m (T B ) - C) from the plot of  l g H m (T B ) vs  l g S m (T B ), solving for  l g H m (T B ) max in this equation results in:  l g H m (T B ) max = C (T B (  ))/(m - T B (  ))  l g H m (T B ) max =  18.5 kJ mol -1 Why do all of the polyethylene series converge to approximately  18.5 kJ mol -1 ? A limiting value kJ mol -1 for  l g H m (T B ) max suggests that this property may also be modeled effectively by a hyperbolic function

A plot of 1/[1-  l g H m (T B )/  l g H m (T B (  )] against the number of repeat units, N For the 1-alkenes (circles) and n-alkylcyclohexanes (squares) using a value of 154 kJ mol -1 for  l g H m (T B ) max..

A plot of  l g H m (T B ) against the number of repeat units, N; points: experimental values; lines: calculated values; circles: n-alkanes; triangles: alkylthiols; squares: alkylcyclopentanes.

Table. Values of the Parameters of a H and b H Generated in Fitting  l g H m (T B ) of Several Homologous Series Using a Value of  l g H m (T B ) max =  18.5 kJ mol -1. a H b H  /kJ. mol -1 data points n-alkanes n-alkylbenzenes n-alkylcyclohexanes n-alkylcyclopentanes n-alk-1-enes n-alkane-1-thiols

Why does  l g H m (T B ) max reach a limit of 154 kJ mol -1 ?

T C = T B + T B /[c + d(N+2)] Ambroses’ Equation where c and d are constants and N refers to the number of methylene groups. Since this equation is an equation of a hyperbola, a plot of Ambrose, D. "NPL Report Chemistry 92" (National Physical Laboratory, Teddington, Middlesex UK, 1978).

Figure. A plot of experimental critical temperatures versus N, the number of methylene groups for (top to bottom) the alkanoic acids (hexagons), 2-alkanones (diamonds), 1-hydroxalkanes (solid circles) 1-alkenes (triangles), and the n-alkanes (circles)

Since Ambrose equation is an equation of a hyperbola, a plot of 1/[1- T B /T B (  )] versus the number of methylene groups should result in a straight line.

Table. Results Obtained for the Constants a C and b C by Treating T C as a Function of the Number of Repeat Units, N, and Allowing T C (  ) to Vary; a Cm, b Cm : Values of a C and b C Obtained by Using the Mean Value of T C = 1217 K Polyethylene data Series T C (  )/K a C b C  /K T C (  )/K a Cm  b Cm  /K points n-alkanes n-alkanals alkanoic acids alkanols alkanones alkanones alkenes methylalkanes

What are the consequences if T B = T C ?

At T C,  l g H m (T B ) = 0 This explains why  l g H m (T B ) fails to continue to increase but infact decreases as the size of the molecule get larger. Any inconsistancies here? What does  l g H m (T B ) measure?

An equation reported by Somayajulu provides a means of describing the possible behavior of  l g H m (T B ) as a function of T B and T C.  l g H m (T B ) = e 1 X + e 2 X 2 + e 3 X 3 +e 4 X 4 where X = (T C -T B )/T C Somayajulu, G. R. “The critical constants of long chain normal paraffins”, Internat. J. Thermophys. 1991, 12,

 l g H m (T B ) against the number of repeat units, N.

If we know how  l g H m (T B ) varies as a function of the number of repeat units, and we know how T B also varies, we can determine how a plot of  l g H m (T B ) versus  l g S m (T B ) should vary.

Figure. Experimental values of  l g H m (T B ) as a function of  l g S m (T B ); n-alkanes: circles, experimental values; solid line, calculated values.

Are their any other consequences if T B = T C ?

If T B = T C, what about P C ? P C = the pressure necessary to keep the material as a liquid at T = T C P B = 1 atm ( kPa) If T C  T B, then shouldn’t P B  1 atm ( kPa) Furthermore, if P C is finite at T C and approaches kPa as the size of the molecule increases, then shouldn’t it also be modeled by a hyperbolic function? Remember for a descending hyperbolic function: X = X min / [1- 1/(mN + b)] as X  X min

In this case: P C = P C min / [1- 1/(mN + b)] as P  kPa (0.101 MPa)

Figure. A plot of the critical pressure versus the number of repeat units for the 1- alkanols (triangles), the n-alkanes (circles), and the 2-methylalkanes (squares).

Figure. A plot of the critical pressure versus the number of repeat units for the n-alkanoic acids (circles), and 1-alkenes (squares). The data for the alkanoic acids includes a few multiple determinations to give a sense of the scatter in the experimental data.

Summary: All of the homologues series examined related to polyethylene 1. approach a limiting boiling temperature, 1217 K; 2. approach a limiting critical temperature, 1217 K; 3. have vaporization enthalpies that increase initially, and then decrease to 0 kJ mol -1 ; 4. have critical pressures that can be modeled as approaching a limiting pressure of kPa.

All of the homologous series examined so far, in the limit, become polyethylene. Hypothesis: If a homologous series is related related to a different polymer, that series in the limit should also approach the boiling temperature of that polymer. For example, how do the boiling temperatures of the perfluorinated compounds compare to each other?

Boiling temperatures of the perfluoro-n-alkanes and perfluoro-n-alkanoic acids

1/[1-T B /T B (  )] was plotted against the number of CF 2 groups using T B (  ) as a variable

Table. Values of the Parameters of a B and b B Generated in Fitting T B of Several Homologous Perfluorinated Series and Allowing T B (  ) to Vary in 5 K Increments; a Bm, b Bm : Values of a B and b B Using an Average Value of T B (  ) = 915 K T B (  )/K a B b B  /K T B (  )/K a Bm b Bm  /K N n-perfluoroalkanes n-perfluoroalkanoic acids methyl n-perfluoroalkanoates iodo-n-perfluoroalkanes

Figure. A plot of 1/[1-T B /T B (  )] vs the number of CF 2 groups using T B (  ) = 915 K; squares: perfluorocarboxylic acids; circles: perfluoro-n-alkanes.

What about T C of the perfluorinated compounds?

Figure. A plot of experimental critical temperatures versus N, the number of methylene groups for (top to bottom) the alkanoic acids (hexagons), 2-alkanones (diamonds), 1-hydroxalkanes (solid circles) 1-alkenes (triangles), the n-alkanes (circles), and n-perfluoroalkanes (solid squares). The lines were calculated using of T C (  ) = 1217 K for the hydrocarbons and derivatives and T C (  ) = 915 K for the fluorocarbons.

Polyperfluoroethylene Series T C (  )/K a C b C  /KT C (  )/K a Cm b Cm  /K N n-perfluoroalkanes Despite the limited amount of available data, T C of the perfluorinated compounds behave analogously to the corresponding hydrocarbons.

Recall the equation reported by Somayajulu as a means of describing the possible behavior of  l g H m (T B ) as a function of T B and T C.  l g H m (T B ) = e 1 X + e 2 X 2 + e 3 X 3 +e 4 X 4 where X = (T C -T B )/T C Somayajulu, G. R. “The critical constants of long chain normal paraffins”, Internat. J. Thermophys. 1991, 12,

Figure. Values of  l g H m (T B ) as a function of the number of repeat units; n- alkanes: solid line, calculated values; circles, experimental values; n-perfluoro- alkanes: dashed line, calculated values, triangles, experimental values.

Figure. Experimental values of  l g H m (T B ) as a function of  l g S m (T B ); n-alkanes: circles, experimental values; solid line, calculated values; n-perfluoroalkanes: triangles, experimental values; dashed line, calculated values.

What about P C for the perfluorinated compounds? Remember for a descending hyperbolic function: P = P min / [1- 1/(mN + b)] as P  P min or 0.1 MPa

Figure. A plot of the critical pressure versus the number of repeat units for the n- alkanoic acids (circles), 1-alkenes (squares), and perfluoroalkanes (solid diamonds). The data for the alkanoic acids includes a few multiple determinations to give the reader a sense of the scatter in the experimental data.

Summary: both homologous series composed of hydrocarbons related to polyethylene and perfluorinated compounds related to Teflon behave similarly in their properties as the size of the series incresaes.

Figure. Calculated boiling temperatures, T B, versus experimental values; circles: series related to polyethylene using T B (  ) = 1217 K; solid triangles: series related to polytetrafluoroethylene using T B (  ) = 915 K. The equation of the line is given by: T B (calc) = (1.000  0.001)T B (expt) + (0.117  2.23); correlation coefficient r 2 = for 262 observations.

Figure. Calculated critical temperatures, T C, versus experimental values; circles: series related to polyethylene using T C (  ) = 1217 K; solid triangles: series related to polytetrafluoro- ethylene using T C (  ) = 915 K. The equation of the line is given by: T C(calc) = (1.003  0.006)T C (expt) - (2.07  5.22); correlation coefficient r 2 = for 106 observations.