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Calvin D. Ritchie
science forum beginner
Joined: 30 Apr 2006
Posts: 10
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 Posted: Wed May 24, 2006 7:04 pm Post subject:
Re: Chemical Reaction Rate Formula
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Richard Saam wrote:
| Quote: | ref: Aquatic Chemistry, Stumm and Morgan
An interesting variation on the theme
is nucleation and crystal growth
from solution
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These kinds of phenomena are known as "first order phase transitions"
(having a discontinuity in entropy) and have been treated in all kinds
of ways; none very successful SFAIK. Having done more than my fair
share of crystallizations/re-crystallizations, I wouldn't trust any
theoretical treatments that don't include the phase of the moon,
number of clouds in the sky, and a few other things. There's a story
told around the light of the Bunsen burners about old sugar chemists
shaking their beards over the flasks in which they were trying to
crystallize some new sugar. All visiting sugar chemists were also
asked to shake their beards in the hope that they might have a
different set of "seed" crystals.
On the other hand, there has been amazing progress in treating
(Understanding may be a different question; see Weinberg, TQTF Vol 2,
pg 148.) second-order phase transitions and I am just beginning to get
into that. There's a good book available on such many body problems,
free, at www.physics.rutgers.edu/~coleman. Zee, QFT in a Nutshell,
also has a little on such things.
Don Ritchie |
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Richard Saam
science forum Guru Wannabe
Joined: 20 May 2005
Posts: 137
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| Posted: Thu Jun 08, 2006 3:45 am Post subject:
Re: Chemical Reaction Rate Formula
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Calvin D. Ritchie wrote:
| Quote: | Richard Saam wrote:
ref: Aquatic Chemistry, Stumm and Morgan
An interesting variation on the theme
is nucleation and crystal growth
from solution
These kinds of phenomena are known as "first order phase transitions"
(having a discontinuity in entropy) and have been treated in all kinds
of ways; none very successful SFAIK. Having done more than my fair
share of crystallizations/re-crystallizations, I wouldn't trust any
theoretical treatments that don't include the phase of the moon,
number of clouds in the sky, and a few other things. There's a story
told around the light of the Bunsen burners about old sugar chemists
shaking their beards over the flasks in which they were trying to
crystallize some new sugar. All visiting sugar chemists were also
asked to shake their beards in the hope that they might have a
different set of "seed" crystals.
On the other hand, there has been amazing progress in treating
(Understanding may be a different question; see Weinberg, TQTF Vol 2,
pg 148.) second-order phase transitions and I am just beginning to get
into that. There's a good book available on such many body problems,
free, at www.physics.rutgers.edu/~coleman. Zee, QFT in a Nutshell,
also has a little on such things.
Don Ritchie
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Model presented again with proper sign
and addition of Go energy variable.
**************
J = A exp (- delta G / kT)
A is collisions per volume per time
J is successful nucleating collisions per volume per time
delta G = -(4 pi r3 / V) kT ln (a/ao) + 4 pi r2 gamma + Go
V is molecular Volume ( ~ a few Angstrom cubed)
r is nucleated crystal radius
a/ao = saturation ratio
gamma is nucleus surface free energy / area
(on the order of 100 mJ/m2 for inorganic material
*********************
I would agree that
"phase of the moon,
number of clouds in the sky"
may have something to do with it
The energies are extremely low
and any known or unknown Go could influence the nucleation reaction.
I have modeled oil water coalescence phenomena
with ortho kinetic principle after Miron Smoluchowski
to arrive at drop collisions per volume per time (A)
where gamma ranges over many orders of magnitude (.0001 to 73 mJ/m^2)
A approach with probabilistic input
and analysis of probabilistic output
achieves some conformance with experiment or practice.
In final synergy between nucleation theory and practice
Sugar does pour
paper is a controlled white
oil is separated from water and
floc settles in the clarifier, etc.
I have heard anecdotally that NASA is somewhat disappointed in its
crystallization experiments conducted in the orbiting space station
where all the Go's were to be minimized.
Looking at the model,
I cannot resist the thought of applicability to the Big Bang.
Was there an initial gamma "surface tension" that had to be overcome
before the Universe "inflated" spontaneously?
Richard |
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