(a) An electrophoresis channel etched into a glass plate has...

(a) An electrophoresis channel etched into a glass plate has a rectangular $12 \times 50 \mu \mathrm{m}$ cross section. How long $(\mathrm{mm})$ is the sample zone for a 100 -pL sample? (b) If sample travels $24 \mathrm{~mm}$ in $8 \mathrm{~s}$ to reach the detector, what is the standard deviation in bandwidth contributed by the finite length of the injection zone? (Hint: See Equation 22-32.) (c) If the diffusion coefficient of a solute is $1.0 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}$, what is the diffusional contribution (standard deviation) to band broadening? (d) What is the expected total bandwidth at the baseline $(w=4 \sigma) ?$

(a) An electrophoresis channel etched into a glass plate has a rectangular $12 \times 50 \mu \mathrm{m}$ cross section. How long $(\mathrm{mm})$ is the sample zone for a 100 -pL sample?
(b) If sample travels $24 \mathrm{~mm}$ in $8 \mathrm{~s}$ to reach the detector, what is the standard deviation in bandwidth contributed by the finite length of the injection zone? (Hint: See Equation 22-32.)
(c) If the diffusion coefficient of a solute is $1.0 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}$, what is the diffusional contribution (standard deviation) to band broadening?
(d) What is the expected total bandwidth at the baseline $(w=4 \sigma) ?$

Key Concepts

Diffusive Broadening

Diffusive broadening refers to the natural spreading of the analyte band due to molecular diffusion during migration. The diffusion coefficient of the solute, coupled with the time it takes for the sample to travel to the detector, determines the extent of this broadening. It is an essential concept because it sets a limit on the resolution achievable in electrophoretic separations.

Finite Injection Zone Broadening

This concept deals with the broadening (or dispersion) of the sample peak that arises solely from the finite length of the injection zone. The initial distribution of the sample is not a point but a finite plug, and as it migrates through the channel, this initial spread contributes directly to the overall observed peak width at the detector.

Combined Band Broadening and Baseline Width

This concept involves the combination of multiple independent contributions to the overall peak width, typically assuming that variances add for independent processes. Both the finite injection zone and diffusion contribute to the observed standard deviation, and the total bandwidth (for example, defined as four times the standard deviation for a Gaussian profile) is used to assess the resolution and performance of the separation method.

Electrophoresis Channel Geometry

This concept involves understanding the physical dimensions of a microchannel used in electrophoresis. The geometry of the channel, such as its cross?sectional area and length, plays a critical role in determining the behavior of sample plugs, affecting parameters like the residence time, separation efficiency, and resolution.

Sample Injection and Volume-to-Length Conversion

This concept covers the method of relating the injected sample volume to the resulting physical length of the sample plug within the channel. By dividing the sample volume by the cross-sectional area of the channel, one can determine the sample zone's length. This conversion is fundamental in assessing how much sample is present over a given distance in the separation channel.

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