The phrase "apparently to illustrate" is correct and usable in written English.
It can be used when indicating that something seems to serve the purpose of illustrating a point or concept, though the certainty of that purpose is not confirmed.
Example: "The author included several anecdotes, apparently to illustrate the main theme of the book."
Alternatives: "seemingly to demonstrate" or "reportedly to clarify".
Scott Compton was apparently trying to illustrate how the idea of what America stands for is greater than material objects like the flag that represent it.
Little is known of Heraclitus' life; most of what has been handed down consists of stories apparently invented to illustrate his character as inferred from his writings (Diogenes Laertius 9.1 17).
"We just went to the Queens Botanical Gardens because there was a pumpkin patch and a fall petting zoo," adds Ortiz, apparently attempting to illustrate that his group sometimes appears in other boroughs.
In Analyze Philidor used apparently fictitious games to illustrate his principles for conducting a strategic, rather than tactical, battle.
By way of illustrating all this, one Lib Dem MP was sensibly photographed at the conference in a Farage mask, holding the obligatory pint and fag, apparently so as to illustrate how feeble the party's latest enemy is.
Two mechanisms have been proposed to illustrate the apparently beneficial effects of the ankle support and foot orthoses on standing stability.
This paper presents a system dynamics computer simulation model to illustrate unintended consequences of apparently rational allocations to curative and preventive services.
While this apparently implies loss of generality for our results, actually, it allows us to illustrate vividly the impact of size and magnetic field on the emission features of AQDPs.
In her well-known textbook, Kirkwood 18 used an apparently hypothetical example of staffing planning in the face of merging two obstetrical departments to illustrate the Poisson distribution.
