20-Bio-B10 Biomechanical Device Design & Human Factors · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 04-Bio-B10 Analytical Biochemistry. Three hours, closed book, any non-communicating calculator. Six questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All six are solved here, because this set is a study resource rather than an examination script. Every question is essay/descriptive (technique principle, interpretation of an instrument trace or image) rather than numerical, except Question 2(d), which asks for a short exponential-growth calculation from PCR cycle theory.
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The sharp tip sits at the free end of a flexible cantilever, positioned just above (or, in contact mode, gently touching) the sample surface. A laser is focused onto the back of the cantilever and reflects onto a position-sensitive, segmented photodetector; as the tip encounters surface topography, the cantilever bends, which deflects the reflected beam and shifts where it lands on the detector segments. This deflection signal is fed into a feedback loop that drives a piezoelectric x–y–z scanner, which raises or lowers the sample (or tip) to restore the cantilever to its setpoint deflection as the tip is scanned line by line across the sample — the vertical (z) motion the scanner must apply at each x,y point is what is recorded as the topographic height image.
[Figure not reproduced: AFM topographic image from Question 4(b). See the official exam paper or the cited reference text.]
In a standard AFM topographic (height) image rendered in greyscale, brightness encodes z-height: lighter regions correspond to features that are physically higher (the tip has to be raised further by the feedback loop to stay on-setpoint), and darker regions correspond to features that are lower (recessed, or the floor between raised features). The image supplied shows a regular, close-packed lattice of dark, roughly circular depressions set into a lighter, continuous matrix — the pattern expected of a top-down scan of a periodic (crystalline) array of membrane-embedded protein subunits: the light ridges are the raised protein/lipid surface, and the dark spots are lower-lying pores, channels, or the gaps between adjacent protein subunits.
Van der Waals forces are weak, short-range, non-covalent attractive interactions that arise from instantaneous, fluctuating dipoles: at any instant, the electron cloud around an atom or molecule is not perfectly symmetric, and this transient dipole induces a complementary dipole in a neighbouring atom, producing a net, always-attractive dipole–induced-dipole force between them (the London dispersion component; permanent-dipole and induced-dipole terms can also contribute). The attractive potential falls off very steeply with distance (proportional to 1/r6), so van der Waals forces are significant only over sub-nanometre to few-nanometre separations — exactly the tip-to-sample distance regime an AFM tip operates in, which is why they dominate the long-range part of the tip–sample interaction before the tip makes hard contact.
At large tip–sample separation the net force is essentially zero. As the tip approaches, weak van der Waals attraction switches on and strengthens (the curve dips below the zero line), reaching a maximum attractive force at a characteristic separation — the bottom of the attractive "well" on the graph. If the tip is brought even closer, the electron clouds of the outermost tip and sample atoms begin to overlap; Pauli exclusion and direct electrostatic core–core repulsion then dominate, producing a very steep, strongly repulsive force that rises almost vertically as separation decreases further — this is the sharp upward branch on the left of the graph. The point where the curve crosses zero net force, between the attractive well and the steep repulsive rise, is the equilibrium "contact" separation. This single curve is what defines AFM's different imaging modes: contact mode operates on the steep repulsive branch (tip in mechanical contact with the surface), while non-contact/tapping mode operates in, or oscillates through, the attractive regime, sensing the gentler van der Waals attraction without the tip fully contacting (and potentially damaging) the sample.
