Use Sauerbrey equation explain Δf Vs. analyte concentration

In summary, the Sauerbrey equation describes how the change in resonance frequency of a quartz crystal can be related to an analyte concentration. This equation takes into account the liquid viscosity and shear modulus in a Newtonian liquid. However, it can also be combined with an adsorption isotherm to explain the relationship between frequency change and analyte concentration through surface adsorption.
  • #1
Carmen Wong
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1. Explain, using the Sauerbrey equation, how the change in the resonance frequency of a quartz crystal can be related to an analyte concentration


2. Sauerbrey equation:
upload_2015-5-5_1-38-32.png



3. I knew Quartz crystal microbalance work according to the change of frequency after mass loaded, and when working in a Newtonian liquid the corresponding frequency shift is
upload_2015-5-5_1-42-29.png
(Kanazawa and Gordon, 1985), whichηL is the liquid viscosity; andμ is the shear modulus.
But I cannot understand the relation between the change of frequency and the analyte concentration according to the Sauerbrey equation.

thank you for helping
 
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  • #2
And not through the adsorption isotherm?
 
  • #3
Borek said:
And not through the adsorption isotherm?
Thank you for replying. It could be relate to the surface adsorption, but must explain according to the Sauerbrey equation.
 
  • #4
I haven't said "don't use Sauerbrey equation". I said "combine it with an isotherm".
 
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1. What is the Sauerbrey equation?

The Sauerbrey equation is a mathematical formula that describes the relationship between the change in resonant frequency (Δf) of a quartz crystal microbalance (QCM) sensor and the mass of an analyte deposited on the sensor's surface. It is commonly used in biosensors and other analytical applications.

2. How is the Sauerbrey equation used to measure analyte concentration?

The Sauerbrey equation can be used to calculate the mass of an analyte deposited on a QCM sensor's surface by measuring the change in resonant frequency. By knowing the density and thickness of the deposited analyte, the concentration can be determined using the following formula: C = Δf / (k * A * Δm), where C is the concentration, k is the Sauerbrey constant, A is the sensor's surface area, and Δm is the mass of the deposited analyte.

3. What are the assumptions made by the Sauerbrey equation?

The Sauerbrey equation assumes that the deposited analyte is rigidly attached to the sensor's surface and that its thickness is much less than the wavelength of the acoustic wave. It also assumes that the density and acoustic properties of the analyte are similar to those of the sensor material.

4. Are there any limitations to the Sauerbrey equation?

Yes, the Sauerbrey equation has some limitations. It is only applicable for thin, rigid films that do not undergo any phase transitions or chemical reactions on the sensor surface. It also does not take into account any viscoelastic effects of the analyte, which may affect the accuracy of the results.

5. Can the Sauerbrey equation be used for all types of analytes?

No, the Sauerbrey equation is most accurate for small, rigid molecules. It may not provide accurate results for larger or more complex analytes, such as proteins, which can undergo conformational changes or have varying densities. In these cases, alternative methods, such as the Voigt model, may be more suitable.

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