During the 18th Century, it seems like every philosopher had an interest in science, and every scientist had an interest in philosophy. When did there become a sharp division in the two?

This is a simple question and the answer to it could fill a small library. But I can at least write down some thoughts that may give you an impression what we’re talking about.

Obviously, a lot depends on what counts as science. For example, in Germany, and partially in France and Italy too, some humanities are still called ‘science’, just like ‘political science’ in the anglophone world. Even if we stick to natural science for the sake of simplicity, things are a bit complicated at times – do medicine and engineering and applied maths count as ‘science’? Medicine, for example, has been around since before writing was invented, largely through trial and error, and has always worked independently from philosophy. Then you have these strange fields like alchemy, which is at best a pseudoscience, but which has had some indirect but noticeable impact on both modern philosophy and modern science. But let’s ignore these fringe cases and stick to physics, biology, and chemistry.

What makes an academic discipline – beyond organizational necessities, i.e. that you need to belong to a certain department or faculty? Speaking very broadly, each discipline has

1.) its own type(s) of objects of inquiry,

2.) its own methodology,

3.) and its own epistemic principles that help you distinguish between relevant and irrelevant data, between valid and invalid proofs, and that tells you where to look for answers to your questions.

So even if you find someone like Descartes who writes both philosophical books (the Meditations) and scientific ones (such as Les Météores), we can still see that both are very different in method and objects and aims and goals. This could still be possible today and occasionally you still have people who provide important innovations to both philosophy and science (like Ernst Mayr or Roger Penrose or Amartya Sen), it is mostly due to the increasing complexity of scientific questions that you need to dedicate your full time to one discipline only. But let's look at the three points mentioned above.

Speaking very broadly, in early modern times, physics has been successfully defined as the science of motion. Arguably this notion starts with Galileo, who has refused to include occult powers and substantial forms in his explanations; and Bacon and Descartes have provided the appropriate philosophical theory that physical questions need physical answers, not metaphysical ones. Herein it is important to note that motion had been reduced to change of place relative to other bodies – antiquity did still include qualitative transformations, growth, decay, and coming into being as types of motion. For a while, the science of motion (occasionally also called kinematics or phoronomia) was seen as separate from the science of forces, namely dynamics, and the science of moving bodies under forces, usually called mechanics. They get united first with Newton, who ties the inquiry into forces to their expression in motion; and with D’Alembert, who shows that the quarrel about the reality of forces is just a quarrel about words and that we can treat dynamics and mechanics as a statical and closed system.

To this day, physical method oscillates between a deductive, mathematical (algebraic) approach and an empirical, observational one (top-down vs. bottom-up). During the 17th and 18th century, both methods are often used arbitrarily and together with other tools, such as thought experiments, metaphysical deliberations, geometrical methods, etc. While early physicists such as Tycho Brahe or Galileo were more inclined towards observation and its mathematical interpretation, a more mathematically inclined physics is on the rise in people like the Bernoullis, Euler, or Lambert. In the late 18th century, Lagrange writes his Analytical Mechanics, which is the first proper physical theory expressed solely in mathematical (algebraic) terms. From then on, physics tries to get rid of the confusing conceptual and metaphysical baggage inherited from philosophy for the sake of the certainty gained through mathematical deduction.

The objects of biology are more clearly defined early on. While ‘natural history’ as the observational study of nature has existed since antiquity, in the debate between Leibniz and G. E. Stahl the notion of ‘organism’ is coined, in direct opposition to the physical term ‘mechanism.’ Especially Leibniz and the early Leibnizians such as Blumenbach or Haller make it clear that the science of organisms requires both different methods and principles than physics, and they reinvigorate old Aristotelian notions of self-regulating, teleologically directed systems that are dealing with self-subsistence in form of autopoiesis (‘creation of oneself’) and procreation. So biology has always been more inclined towards observation and conceives classification as one of its core tasks (famously illustrated by Linné, the inventor of the modern taxonomy). While earlier philosophers were interested in the nature of living beings and inquiring into the nature of the presumed union of the body and soul or the theory of embodied cognition, even the early biologists were interested in understanding the functions and inner workings of organisms conceived as internally and externally regulated systems.

However, biology also falls apart into many different and independent disciplines, such as anatomy, natural geography, cellular theory, ethology (study of behavior), biochemistry, pre-Darwinian theories of evolution, etc. It takes until Darwin before all these fields can be tied together, because evolutionary theory allows us to use the findings of one discipline to explain those of another (such as anatomy can be explained by behavior and evolutionary pressure). Then Mendel helps to tie evolutionary theory together with genetics. But before Darwin, the method of biological research and explanation is driven by assuming purposiveness, which is firmly rejected in physics and hence biology has easily established its own independence from physics.

I don’t know much about the history of chemistry, but here Lavoisier is the major figure, as he introduced the modern elementary system and modern methods of inquiring into the relations between elements. His predecessors in the fields of alchemy were fringe figures that were not really part of the philosophical mainstream.

Philosophy now comes to its own self-conscious separation from the sciences with Kant. In his groundbreaking and era defining philosophy, empirical observation has been successfully excluded from philosophy with much better and much clearer arguments than ever before. The objects of philosophy have been marked by being synthetical judgments a priori, or, if you will, limited to the analysis of concepts, the examination of principles and postulates, and the inquiry into the conditions and limits of (different types of) knowledge. With Kant, philosophy conceives of itself as the ‘Leitwissenschaft’, leading science or guiding science, i.e. the meta-theoretical inquiry that strives to provide the principles and conceptual (‘metaphysical’) foundations of all sciences. Here, with Kant, the method, objects, and principles of philosophy are sharply distinguished from all knowledge that requires empirical observation or that just has to be individuated in intuition, as Kant would say.

Edit: I don't have any particular sources in mind and I don't know any singular volume on the interrelated history of philosophy and the sciences. The histories of physics by Ernst Mach and Pierre Duhem are insightful in this regard; Max Jammer has written good books on the history of notions such as force, mass, and space that deal with this issue; good books on early biology are written in French by François Duchesneau (La physiologie des Lumières. Empirisme, modèles et théories; and Genèse de la théorie cellulaire) or in English by John Zammito (The Gestation of German Biology: Philosophy and Physiology from Stahl to Schelling); I also recommend Helmut Pultes book on early physical methodology to anyone willing to read in German (Axiomatik und Empirie. Eine wissenschaftstheoriegeschichtliche Untersuchung zur mathematischen Naturphilosophie von Newton bis Neumann).