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1 t = 1 t a + 1 t b size 12{ { {1} over {t} } = { {1} over {t rSub { size 8{a} } } } + { {1} over {t rSub { size 8{b} } } } } {}

For reference, the exact lineshape function (assuming two equivalent groups being exchanged) is given by the Bloch Equation, [link] , where g is the intensity at frequency v , and where K is a normalization constant

g ( v ) = Kt ( v a + v b ) 2 [ 0 . 5 ( v a + v b ) v ] 2 + 2 t 2 ( v a v ) 2 ( v b v ) 2 size 12{g \( v \) = { { ital "Kt" \( v rSub { size 8{a} } +v rSub { size 8{b} } \) rSup { size 8{2} } } over { \[ 0 "." 5 \( v rSub { size 8{a} } +v rSub { size 8{b} } \) -v \] rSup { size 8{2} } +4p rSup { size 8{2} } t rSup { size 8{2} } \( v rSub { size 8{a} } -v \) rSup { size 8{2} } \( v rSub { size 8{b} } -v \) rSup { size 8{2} } } } } {}

Low temperatures to coalescence temperature

At low temperature (slow exchange), the spectrum has two peaks and Δ v >>t. As a result, [link] reduces to [link] , where T 2a’ is the spin-spin relaxation time. The linewidth of the peak for species a is defined by [link] .

g ( v ) a = g ( v ) b = KT 2a 1 + T 2a 2 ( v a v ) 2 size 12{g \( v \) rSub { size 8{a} } =g \( v \) rSub { size 8{b} } = { { ital "KT" rSub { size 8{2a} } } over {1+T rSub { size 8{2a} rSup { size 8{2} } } \( v rSub { size 8{a} } -v \) rSup { size 8{2} } } } } {}
( Δv a ) 1 / 2 = 1 π ( 1 T 2a + 1 t a ) size 12{ \( Dv rSub { size 8{a} } \) rSub { size 8{1/2} } = { {1} over {p} } \( { {1} over {T rSub { size 8{2a} } } } + { {1} over {t rSub { size 8{a} } } } \) } {}

Because the spin-spin relaxation time is difficult to determine, especially in inhomogeneous environments, rate constants at higher temperatures but before coalescence are preferable and more reliable.

The rate constant k can then be determined by comparing the linewidth of a peak with no exchange (low temp) with the linewidth of the peak with little exchange using [link] , where subscript e refers to the peak in the slightly higher temperature spectrum and subscript 0 refers to the peak in the no exchange spectrum.

k = π 2 [ ( Δv e ) 1 / 2 ( Δv 0 ) 1 / 2 ] size 12{k= { {p} over { sqrt {2} } } \[ \( Dv rSub { size 8{e} } \) rSub { size 8{1/2} } - \( Dv rSub { size 8{0} } \) rSub { size 8{1/2} } \] } {}

Additionally, k can be determined from the difference in frequency (chemical shift) using [link] , where Δ v 0 is the chemical shift difference in Hz at the no exchange temperature and Δ v e is the chemical shift difference at the exchange temperature.

k = π 2 ( Δv 0 2 Δv e 2 ) size 12{k= { {p} over { sqrt {2} } } \( Dv rSub { size 8{0} rSup { size 8{2} } } -Dv rSub { size 8{e} rSup { size 8{2} } } \) } {}

The intensity ratio method, [link] , can be used to determine the rate constant for spectra whose peaks have begun to merge, where r is the ratio between the maximum intensity and the minimum intensity, of the merging peaks, I max /I min

k = π 2 ( r + ( r 2 r ) 1 / 2 ) 1 / 2 size 12{k= { {p} over { sqrt {2} } } \( r+ \( r rSup { size 8{2} } -r \) rSup { size 8{1/2} } \) rSup { size 8{-1/2} } } {}

As mentioned earlier, the coalescence temperature, T c is the temperature at which the two peaks corresponding to the interchanging groups merge into one broad peak and [link] may be used to calculate the rate at coalescence.

k = πΔv 0 2 size 12{k= { {pDv rSub { size 8{0} } } over { sqrt {2} } } } {}

Higher temperatures

Beyond the coalescence temperature, interchange is so rapid (k>>t) that the spectrometer registers the two groups as equivalent and as one peak. At temperatures greater than that of coalescence, the lineshape equation reduces to [link] .

g ( v ) = KT 2 [ 1 + πT 2 ( v a + v b 2v ) 2 ] size 12{g \( v \) = { { ital "KT" rSub { size 8{2} } } over { \[ 1+pT rSub { size 8{2} } \( v rSub { size 8{a} } +v rSub { size 8{b} } -2v \) rSup { size 8{2} } \] } } } {}

As mentioned earlier, determination of T 2 is very time consuming and often unreliable due to inhomogeneity of the sample and of the magnetic field. The following approximation ( [link] ) applies to spectra whose signal has not completely fallen (in their coalescence).

k = 0 . Δv 2 ( Δv e ) 1 / 2 ( Δv 0 ) 1 / 2 size 12{k= { {0 "." 5pDv rSup { size 8{2} } } over { \( Dv rSub { size 8{e} } \) rSub { size 8{1/2} } - \( Dv rSub { size 8{0} } \) rSub { size 8{1/2} } } } } {}

Now that the rate constants have been extracted from the spectra, energetic parameters may now be calculated. For a rough measure of the activation parameters, only the spectra at no exchange and coalescence are needed. The coalescence temperature is determined from the NMR experiment, and the rate of exchange at coalescence is given by [link] . The activation parameters can then be determined from the Eyring equation ( [link] ), where k B is the Boltzmann constant, and where ΔH - TΔS = ΔG .

ln ( k T ) = ΔH RT ΔS R + ln ( k B h ) size 12{"ln" \( { {k} over {T} } \) = { {DH rSup { size 8{³} } } over { ital "RT"} } - { {DS rSup { size 8{³} } } over {R} } +"ln" \( { {k rSub { size 8{B} } } over {h} } \) } {}

For more accurate calculations of the energetics, the rates at different temperatures need to be obtained. A plot of ln(k/T) versus 1/T (where T is the temperature at which the spectrum was taken) will yield ΔH , ΔS , and ΔG . For a pictorial representation of these concepts, see [link] .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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how to find Rutherford scattering parameters angles
saksham Reply
advantages of NAA
Sai Reply
how I can reaction of mercury?
Sham Reply

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Source:  OpenStax, Physical methods in chemistry and nano science. OpenStax CNX. May 05, 2015 Download for free at http://legacy.cnx.org/content/col10699/1.21
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