Proper, reliable and repeatable calibration of any measurement device meant to probe a material’s response and provide trustworthy results worthy of holding up to the vigorous standard on which the field of experimental physics was built is – and must always be – the first step before collecting new data. In this spirit, the following section will outline – in detail – the calibration procedure of the force-sensing glass micropipettes used to examine the stress and strain relation of BLC fibers.
The calibration method was a blend of two techniques: the first, a prior art used by Kreiset al.
during their investigation of the adhesive behavior of algae under different lighting conditions [53]
and a second, specific to the extensional rheometry setup used in the experiments described here forth.
2.4.1 Prior Art
Kreiset al.wrote Matlab code for calibrating the spring constant of the micropipettes using an added mass method. By fixing the micropipette above the objective of an inverted microscope and forming an increasingly large water droplet at the opening of its tip by pressing water through the length of the pipette via a syringe, the mass of the droplet versus the deflection of the pipette could be used to calculate the spring constant. Figure 2.18 graphically outlines the procedure which was carried out in the following order:
1. Place a micropipette in a holder so that it is positioned over the objective of an inverted microscope such that the flexible cantilever end of the pipette can deflect vertically, in the direction of gravity.
2. Attach one end of a hose to the 1mm open end of the pipette while attaching the other end of the hose to a syringe filled with water.
3. Using a mirror positioned at 45 degrees to the optical axis placed over the objective, obtain an image of the pipette from its side so that – via a digital camera attached to the imaging port of the microscope – the pipette’s deflection could be observed by image recording software.
4. Ensuring that the tip of the force-sensing segment (cantilever) of the pipette is clearly imaged by the camera, depress the plunger of the syringe until a small water droplet forms at the pipette’s opening.
5. Begin recording video.
6. Slowly press the plunger of the syringe in order to form an increasingly larger droplet.
7. Stop recording video.
8. Remove the droplet from the pipette by either retracting the plunger of the syringe or by carefully using an absorbent laboratory cleaning wipe.
9. Repeat the procedure at least five times in order to obtain reliable statistics.
10. Use the custom Matlab software to calculate the spring constant of the pipette.
This procedure proved reliable and robust. Corrections were made for non-spherical droplet geometry. One setback was that the pipettes was tremendously fragile and the procedure included many smalls steps – such as mounting and dismounting the pipette from the holder and the syringe hose – which often lead to breakage. Moreover, the extensional rheology experiments required that tip of the pipette be melted closed after calibration to keep the liquid crystal material from flowing back into the pipette. Although a pipette calibrated using the droplet method can have its tip melted together post-calibration, this extra step was often risky and lead to pipette damage or breakage.
Figure 2.18:A 45◦tilted mirror between an inverted objective and horizontal light source allows the vertical displacement of the pipette due to the added mass of a water droplet to be measured. The known change in mass and pipette deflection are then plotted and a linear fit is applied. The slope of this fit is the sprint constant. Red indicates the initial position while blue indicates the final position. The graph is shown as Matlab formatted output.
The water droplet method was also slow to perform and doing multiple trials to get a mean spring constant proved tedious. Due to these shortcomings, a new calibration technique was developed and is discussed in the following section.
2.4.2 Optimized Technique
This new technique allowed freshly-made pipettes to be calibrated against an already reliably-calibrated reference pipette. This reference pipette – denoted pipre f – with a spring constantkre f
was initially calibrated by the water droplet method – outlined inSection 2.4.1above – with great care to ensure the consistency of all pipettes calibrated against it in the future. The referencing method discussed in this section took advantage of the extensional rheometer itself and its easily-controllable positional stages. The reference pipette was inserted into the pipette holder attached to the multi-axis, joy-stick controlled side of the rheometer while a new and uncalibrated pipette (pipnew)was placed in the opposing holder fixed to the linear piezo stage. The idea was to press the tips of the pipettes together and calculate the spring constant of the new pipette(knew)by observing their relative deflections. The process could be automated and repeated many times to collect strong statistics in a matter of seconds.
Becausekre f was known, it sufficed to measure the initial velocity ofpipnewbefore contact with pipre f (Vinit) and the velocity of pipnew after the point of contact with pipre f (Vf inal). By tracking the displacement of just pipnewover a range covering pre-and post contact with pipre f, code could be written to detect the pre-contact slope (Vinit) and post-contact slope (Vf inal). Since the deflection ofpipre f did not need to be measured, the rotational axis of the stage was used to rotate pipre f 45 degrees (out of the focal plane) so thatpipnew(both pipettes having a diameter of typically 20µm) could more positively and repeatedly engagepipre f. Calculation ofknewwas done following that
Since the speed of the pipettes after impact can be considered as their speed relative to the speed before impact,Equation 2.16can be written as
knew(Vinew−Vfnew) =kre f Vire f−Vfre f
(2.17) and since the reference pipette is stationary while the new pipette approaches it at a constant velocity,Vire f =0 andVinew =Vi. During contact, both pipettes move at the same speed meaning that
Vfnew =Vfre f =Vf (2.18)
so thatEquation 2.17becomes
knew(Vi−Vf) =kre fVf (2.19)
or, since only the spring constant of the new pipette –knew– is desired, knew=kre f Vf
Vi−Vf
(2.20)
Since only the relative change of the velocity ofpipnewis needed before and after impact with pipre f, the magnification of the objective and pixel-to-micron ratio are not needed, removing another possible source of user error. Imaging of the deflection of the reference pipette is also not needed which means only a thin slice of the viewing area – just enough record the deflection ofpipnew– is required. This greatly reduces data accumulation and processing time.Figure 2.19 graphically outlines the following procedure.
1. Align both pipettes in the same focal plane and their contact points nearly in contact with one another.
2. Rotate pipre f 45 degrees about its axis using the rotational axis of the joystick.
3. Using the command line program, give a speed and displacement and number of cycles und run.
4. Run Matlab (or C++) code to repeatedly calculate the spring constant ofknewand extract a mean value.
The same reference pipette was used to calibrate all other pipettes. The reference pipette itself was calibrated using the water droplet method using a mean spring constant from 10 trials.
Calibration using the reference method was done on each new pipette 10 times and a mean spring constant calculated. The reference method could be repeated as many times as is desired in quick succession. The fitting of the slopesViandVf were done with Matlab code which detected each slope and applied a linear fit. The entire process was automated and took less than one minute to finish. Once the calibration was finished, only the reference pipette needed to be removed from the rheometer; the newly calibrated pipette could stay inside and new rheological measurements could immediately follow. This helped ensure that the new pipette remained safe due to minimal handling.
Figure 2.19:The referencing method for pipette calibration takes place inside the rheometer. In the image of the pipettes, red indicates their initial position (before contact) and blue their final position (after contact). In the deflection versus time plot, the red slope indicates the velocity before impact (Vi) and the blue slope the velocity after impact (Vf).