CONTRACTILE POLYMERS VIOLATE THE SECOND LAW OF THERMODYNAMICS

Macroscopic contractile polymers designed by Dan Urry contract and
lift a weight as one adds protons (H+) to the system (the force of
contraction increases as the pH of the system decreases):

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11025, fig. 16A

Then (the polymer is contracted) one can remove the same amount of
protons, the pH of the system would increase, the force of contraction
would decrease and the work one would spend to stretch the polymer and
restore its initial (stretched) state would be less than the work
gained previously. The net work gained from contraction and subsequent
stretching is positive. So far the second law seems to be violated
but:

The above balance does not take into account the work involved in
adding protons to the system and removing them subsequently. Note that
one GAINS work as one transfers H+, isothermally and reversibly, to
the polymer-containing system from a reservoir at higher H+
concentration, but then LOSES work as one moves the same amount of H+
back to the reservoir. The behaviour of Urry's polymers - they absorb H
+ as they stretch and release H+ as they contract - is such that the
net work gained from adding protons to the system and removing them
subsequently is positive again:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11020: "In short,
stretching causes an uptake of protons."

"Stretching causes an uptake of protons" implies that, as one
initially adds protons to the systems in order to increase the
contraction force, the H+ concentration difference between the
reservoir and the system is relatively GREAT - accordingly, one gains
A LOT of work. "Stretching causes an uptake of protons" also implies
that, as one subsequently moves the protons back to the reservoir, the
polymer is contracted and the H+ concentration difference between the
reservoir and the system is SMALLER - accordingly, one loses LESS
work.

The net work extracted from the cycle is positive - the second law of
thermodynamics is violated.

Pentcho Valev

On Feb 18, 1:15*pm, Pentcho Valev wrote:
Macroscopic contractile polymers designed by Dan Urry contract and
lift a weight as one adds protons (H+) to the system (the force of
contraction increases as the pH of the system decreases):

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11025, fig. 16A

Then (the polymer is contracted) one can remove the same amount of
protons, the pH of the system would increase, the force of contraction
would decrease and the work one would spend to stretch the polymer and
restore its initial (stretched) state would be less than the work
gained previously. The net work gained from contraction and subsequent
stretching is positive. So far the second law seems to be violated
but:

The above balance does not take into account the work involved in
adding protons to the system and removing them subsequently. Note that
one GAINS work as one transfers H+, isothermally and reversibly, to
the polymer-containing system from a reservoir at higher H+
concentration, but then LOSES work as one moves the same amount of H+
back to the reservoir. The behaviour of Urry's polymers - they absorb H
+ as they stretch and release H+ as they contract - is such that the
net work gained from adding protons to the system and removing them
subsequently is positive again:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11020: "In short,
stretching causes an uptake of protons."

"Stretching causes an uptake of protons" implies that, as one
initially adds protons to the systems in order to increase the
contraction force, the H+ concentration difference between the
reservoir and the system is relatively GREAT - accordingly, one gains
A LOT of work. "Stretching causes an uptake of protons" also implies
that, as one subsequently moves the protons back to the reservoir, the
polymer is contracted and the H+ concentration difference between the
reservoir and the system is SMALLER - accordingly, one loses LESS
work.

The net work extracted from the cycle is positive - the second law of
thermodynamics is violated.

Pentcho Valev



Idiot

The crucial fact that allows Urry's polymers to violate the second law
is that they ABSORB protons on stretching. This is somewhat
paradoxical: one expects the pKa of carboxyl groups to decrease as the
distance between them increases and accordingly the polymer to RELEASE
protons on stretching:

https://data.epo.org/publication-ser...9&iepatch=.pdf
Dan Urry (pp. 14-15): "When the pH is lowered (that is, on raising the
chemical potential, mu, of the protons present) at the isothermal
condition of 37°C, these matrices can exert forces, f, sufficient to
lift weights that are a thousand times their dry weight. This is
chemomechanical transduction, also called mechanochemical coupling.
The mechanism by which this occurs is called a hydration-mediated
apolar-polar repulsion free energy and is characterized by the
equation 0(dmu/df)_n; that is, the change in chemical potential with
respect to force at constant matrix composition is a negative
quantity. Such matrices take up protons on stretching, i.e.,
stretching exposes more hydrophobic groups to water which makes the
COO- moieties energetically less favored. This is quite distinct from
the charge-charge repulsion mechanism for mechanochemical coupling of
the type where (dmu/df)_n0 and where stretching of such matrices
causes the release of protons."

Pentcho Valev wrote:

Macroscopic contractile polymers designed by Dan Urry contract and
lift a weight as one adds protons (H+) to the system (the force of
contraction increases as the pH of the system decreases):

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11025, fig. 16A

Then (the polymer is contracted) one can remove the same amount of
protons, the pH of the system would increase, the force of contraction
would decrease and the work one would spend to stretch the polymer and
restore its initial (stretched) state would be less than the work
gained previously. The net work gained from contraction and subsequent
stretching is positive. So far the second law seems to be violated
but:

The above balance does not take into account the work involved in
adding protons to the system and removing them subsequently. Note that
one GAINS work as one transfers H+, isothermally and reversibly, to
the polymer-containing system from a reservoir at higher H+
concentration, but then LOSES work as one moves the same amount of H+
back to the reservoir. The behaviour of Urry's polymers - they absorb H
+ as they stretch and release H+ as they contract - is such that the
net work gained from adding protons to the system and removing them
subsequently is positive again:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007-11028, Dan W. Urry,
Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers, p. 11020: "In short,
stretching causes an uptake of protons."

"Stretching causes an uptake of protons" implies that, as one
initially adds protons to the systems in order to increase the
contraction force, the H+ concentration difference between the
reservoir and the system is relatively GREAT - accordingly, one gains
A LOT of work. "Stretching causes an uptake of protons" also implies
that, as one subsequently moves the protons back to the reservoir, the
polymer is contracted and the H+ concentration difference between the
reservoir and the system is SMALLER - accordingly, one loses LESS
work.

The net work extracted from the cycle is positive - the second law of
thermodynamics is violated.

Pentcho Valev

Carnot dealt with two reversible heat engines which DID NOT INTERACT.
In 1850 Clausius used NON-INTERACTING heat engines again:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "If we
now suppose that there are two substances of which the one can produce
more work than the other by the transfer of a given amount of heat,
or, what comes to the same thing, needs to transfer less heat from A
to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process."

Below I will try to show that, by replacing NON-INTERACTION with
INTERACTION, one reaches the conclusion that the second law of
thermodynamics is false.

NON-INTERACTION means that the work-producing force generated by the
first engine, F1, is independent of the displacement, X2, in the
second engine, and vice versa. Under isothermal conditions, if the
system is closed (only energy can be exchanged with the environment),
F1 can be presented as a function of X1 and X2 and the independency
condition can be expressed as the partial derivative (dF1/dX2)_X1
being equal to zero ("partial" because X1 is kept constant):

F1 = F1(X1, X2); F2 = F2(X1, X2)

(dF1/dX2)_X1 = (dF2/dX1)_X2 = 0

It can be shown that, if the two reversible heat engines DO INTERACT,
the equation:

(dF1/dX2)_X1 = (dF2/dX1)_X2

is a consequence of the second law of thermodynamics (Kelvin's
version). Accordingly, if the partial derivatives (dF1/dX2)_X1 and
(dF2/dX1)_X2 are somehow shown not to be equal, then heat CAN,
cyclically and isothermally, be converted into work, in violation to
the second law of thermodynamics.

Consider, for instance, INTERACTING "chemical springs". There are two
types of macroscopic contractile polymers, further called Urry's (U)
and Katchalsky's (K), which on acidification (decreasing the pH of the
system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028, Dan W. Urry,
"Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers"

There is a crucial difference between U and K. Polymers designed by
Urry (U) ABSORB protons on stretching (as their length, Lu,
increases):

https://data.epo.org/publication-ser...9&iepatch=.pdf
Dan Urry (pp. 14-15): "When the pH is lowered (that is, on raising the
chemical potential, mu, of the protons present) at the isothermal
condition of 37°C, these matrices can exert forces, f, sufficient to
lift weights that are a thousand times their dry weight. This is
chemomechanical transduction, also called mechanochemical coupling.
The mechanism by which this occurs is called a hydration-mediated
apolar-polar repulsion free energy and is characterized by the
equation 0(dmu/df)_n; that is, the change in chemical potential with
respect to force at constant matrix composition is a negative
quantity. Such matrices take up protons on stretching, i.e.,
stretching exposes more hydrophobic groups to water which makes the
COO- moieties energetically less favored. This is quite distinct from
the charge-charge repulsion mechanism for mechanochemical coupling of
the type where (dmu/df)_n0 and where stretching of such matrices
causes the release of protons."

In contrast, Katchalsky's polymers (K) RELEASE protons on stretching
(as their length, Lk, increases):

http://www.ncbi.nlm.nih.gov/pmc/arti...00645-0017.pdf
POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. KATCHALSKY, pp.
13-15: "Let the polymolecule be a negatively charged polyacid in a
stretched state and have a length L. Now let us add to the molecule a
mineral acid to provide hydrogen ions to combine with the ionized
carboxylate groups and transform them into undissociated carboxylic
groups according to the reaction RCOO- + H+ = RCOOH. By means of this
reaction, the electrostatic repulsion which kept the macromolecule in
a highly stretched state vanishes and instead the Brownian motion and
intramolecular attraction cause a coiling up of the polymeric chains.
Upon coiling, the polymolecule contracts and lifts the attached weight
through a distance deltaL. On lifting the weight, mechanical work
f*deltaL was performed... (...) FIGURE 4: Polyacid gel in sodium
hydroxide solution: expanded. Polyacid gel in acid solution:
contracted; weight is lifted."

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, IF THE
SECOND LAW IS TRUE, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper referred to above. As K is being stretched (Lk increases), it
releases protons, the pH decreases and, accordingly, Fu must increase.
Therefore, (dFu/dLk)_Lu is positive. In contrast, as U is being
stretched (Lu increases), it absorbs protons, the pH increases and Fk
must decrease. Therefore, (dFk/dLu)_Lk is negative. One partial
derivative is positive, the other negative: this proves that the
second law of thermodynamics is false.

Pentcho Valev

On Feb 19, 10:33*am, Pentcho Valev wrote:
Carnot dealt with two reversible heat engines which DID NOT INTERACT.
In 1850 Clausius used NON-INTERACTING heat engines again:

http://www.mdpi.org/lin/clausius/clausius.htm
"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "If we
now suppose that there are two substances of which the one can produce
more work than the other by the transfer of a given amount of heat,
or, what comes to the same thing, needs to transfer less heat from A
to B to produce a given quantity of work, we may use these two
substances alternately by producing work with one of them in the above
process."

Below I will try to show that, by replacing NON-INTERACTION with
INTERACTION, one reaches the conclusion that the second law of
thermodynamics is false.

NON-INTERACTION means that the work-producing force generated by the
first engine, F1, is independent of the displacement, X2, in the
second engine, and vice versa. Under isothermal conditions, if the
system is closed (only energy can be exchanged with the environment),
F1 can be presented as a function of X1 and X2 and the independency
condition can be expressed as the partial derivative (dF1/dX2)_X1
being equal to zero ("partial" because X1 is kept constant):

F1 = F1(X1, X2); F2 = F2(X1, X2)

(dF1/dX2)_X1 = (dF2/dX1)_X2 = 0

It can be shown that, if the two reversible heat engines DO INTERACT,
the equation:

(dF1/dX2)_X1 = (dF2/dX1)_X2

is a consequence of the second law of thermodynamics (Kelvin's
version). Accordingly, if the partial derivatives (dF1/dX2)_X1 and
(dF2/dX1)_X2 are somehow shown not to be equal, then heat CAN,
cyclically and isothermally, be converted into work, in violation to
the second law of thermodynamics.

Consider, for instance, INTERACTING "chemical springs". There are two
types of macroscopic contractile polymers, further called Urry's (U)
and Katchalsky's (K), which on acidification (decreasing the pH of the
system) contract and can lift a weight:

http://pubs.acs.org/doi/abs/10.1021/jp972167t
J. Phys. Chem. B, 1997, 101 (51), pp 11007 - 11028, Dan W. Urry,
"Physical Chemistry of Biological Free Energy Transduction As
Demonstrated by Elastic Protein-Based Polymers"

There is a crucial difference between U and K. Polymers designed by
Urry (U) ABSORB protons on stretching (as their length, Lu,
increases):

https://data.epo.org/publication-ser...=EP0830509%20E....
Dan Urry (pp. 14-15): "When the pH is lowered (that is, on raising the
chemical potential, mu, of the protons present) at the isothermal
condition of 37°C, these matrices can exert forces, f, sufficient to
lift weights that are a thousand times their dry weight. This is
chemomechanical transduction, also called mechanochemical coupling.
The mechanism by which this occurs is called a hydration-mediated
apolar-polar repulsion free energy and is characterized by the
equation 0(dmu/df)_n; that is, the change in chemical potential with
respect to force at constant matrix composition is a negative
quantity. Such matrices take up protons on stretching, i.e.,
stretching exposes more hydrophobic groups to water which makes the
COO- moieties energetically less favored. This is quite distinct from
the charge-charge repulsion mechanism for mechanochemical coupling of
the type where (dmu/df)_n0 and where stretching of such matrices
causes the release of protons."

In contrast, Katchalsky's polymers (K) RELEASE protons on stretching
(as their length, Lk, increases):

http://www.ncbi.nlm.nih.gov/pmc/arti.../biophysj00645...
POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. KATCHALSKY, pp.
13-15: "Let the polymolecule be a negatively charged polyacid in a
stretched state and have a length L. Now let us add to the molecule a
mineral acid to provide hydrogen ions to combine with the ionized
carboxylate groups and transform them into undissociated carboxylic
groups according to the reaction RCOO- + H+ = RCOOH. By means of this
reaction, the electrostatic repulsion which kept the macromolecule in
a highly stretched state vanishes and instead the Brownian motion and
intramolecular attraction cause a coiling up of the polymeric chains.
Upon coiling, the polymolecule contracts and lifts the attached weight
through a distance deltaL. On lifting the weight, mechanical work
f*deltaL was performed... (...) FIGURE 4: Polyacid gel in sodium
hydroxide solution: expanded. Polyacid gel in acid solution:
contracted; weight is lifted."

Let us assume that two macroscopic polymers, one of each type (U and
K) are suspended in the same system. At constant temperature, IF THE
SECOND LAW IS TRUE, we must have

(dFu / dLk)_Lu = (dFk / dLu)_Lk

where Fu0 and Fk0 are work-producing forces of contraction. The
values of the partial derivatives (dFu/dLk)_Lu and (dFk/dLu)_Lk can be
assessed from experimental results reported on p. 11020 in Urry's
paper referred to above. As K is being stretched (Lk increases), it
releases protons, the pH decreases and, accordingly, Fu must increase.
Therefore, (dFu/dLk)_Lu is positive. In contrast, as U is being
stretched (Lu increases), it absorbs protons, the pH increases and Fk
must decrease. Therefore, (dFk/dLu)_Lk is negative. One partial
derivative is positive, the other negative: this proves that the
second law of thermodynamics is false.

Pentcho Valev



Idiot

When an initially stretched rubber band contracts (isothermally) and lifts a weight, it does work (for us) at the expense of heat absorbed from the surroundings, just like an initially compressed gas which expands (isothermally). How the work-producing force of contraction stems from thermal motion is nicely explained he

http://scifun.chem.wisc.edu/homeexpts/rubberband.html
"This occurs because as a material is heated, its molecules move about more energetically. In materials made up of small, compact molecules, e.g., the liquid in a thermometer, as the molecules move about more, they push their neighboring molecules away. Rubber, on the other hand, contains very large, threadlike molecules. When rubber is heated, the sections of the molecules move about more vigorously. In order for one part of the molecule to move more vigorously as it is heated, it must pull its neighboring parts closer.. To visualize this, think of a molecule of the stretched rubber band as a piece of string laid out straight on a table. Heating the stretched rubber band causes segments of the molecules to move more vigorously, which can be represented by wiggling the middle of the string back and forth. As the middle of the string moves, the ends of the string get closer together. In a similar fashion, the molecules of rubber become shorter as the rubber is heated, causing the stretched rubber band to contract."

Yet, despite the analogy between the contraction force (in rubber-like materials) and the gas pressure, there is an essential difference. Under isothermal conditions, we can only restore the initial (compressed) state of the gas system by doing work against the unaltered work-producing force, that is, by spending back the work we have just gained. Clearly, in this case, net work gained at the end of the operations expansion/compression has nowhere to come from.

In contrast, the restoration of the initial (stretched) state of contractile materials could involve some preliminary loosening of the work-producing contraction force so that more weight is lifted during contraction than dropped during stretching (the net work extracted from the operations contraction/stretching is positive). The following example shows that the work-producing force of contraction can be increased by adding hydrogen ions to the system and subsequently decreased by removing the hydrogen ions:

http://www.ncbi.nlm.nih.gov/pmc/arti...00645-0017.pdf
POLYELECTROLYTES AND THEIR BIOLOGICAL INTERACTIONS, A. KATCHALSKY, pp. 13-15: "Let the polymolecule be a negatively charged polyacid in a stretched state and have a length L. Now let us add to the molecule a mineral acid to provide hydrogen ions to combine with the ionized carboxylate groups and transform them into undissociated carboxylic groups according to the reaction RCOO- + H+ = RCOOH. By means of this reaction, the electrostatic repulsion which kept the macromolecule in a highly stretched state vanishes and instead the Brownian motion and intramolecular attraction cause a coiling up of the polymeric chains. Upon coiling, the polymolecule contracts and lifts the attached weight through a distance deltaL. On lifting the weight, mechanical work f*deltaL was performed... (...) FIGURE 4: Polyacid gel in sodium hydroxide solution: expanded. Polyacid gel in acid solution: contracted; weight is lifted."

Although the net work extracted from the operations contraction/stretching can be made positive (by means of hydrogen ions), there is still no proof that the second law of thermodynamics is violated since the work involved in the operations adding_hyrogen_ions/removing_hydrogen_ions is still not evaluated. Yet scientists free from the strangling hold of the dogma would see that the violation is by no means improbable.

Pentcho Valev